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(IND-HINT-2
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(IND-HINT-2+
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(P-O-2-G-FN-N)
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 (1 1 (:REWRITE |(equal x (/ y))|))
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 (2 2 (:LINEAR EXPT-<-1-TWO))
 (2 2 (:LINEAR EXPT-<-1-ONE))
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(|(ash 0 n)|
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 (10 1 (:REWRITE DEFAULT-TIMES-2))
 (10 1 (:REWRITE DEFAULT-FLOOR-2))
 (10 1 (:REWRITE DEFAULT-DIVIDE))
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 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
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 (1 1 (:REWRITE DEFAULT-ASH-1))
 (1 1 (:REWRITE |(- (- x))|))
 (1 1 (:REWRITE |(* 0 x)|))
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(|(ash x 0)|
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 (2 2 (:REWRITE DEFAULT-TIMES-1))
 (1 1 (:REWRITE REDUCE-INTEGERP-+))
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(NATP-ASH
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 (30 30 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (30 30 (:TYPE-PRESCRIPTION INTEGERP-/-EXPT-1))
 (24 24 (:REWRITE THE-FLOOR-BELOW))
 (22 4 (:REWRITE DEFAULT-FLOOR-2))
 (22 4 (:REWRITE DEFAULT-FLOOR-1))
 (20 2 (:REWRITE |(floor (* x (/ y)) z) rewriting-goal-literal|))
 (19 19 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (19 19 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (19 19 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (19 19 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (19 19 (:REWRITE INTEGERP-<-CONSTANT))
 (19 19 (:REWRITE CONSTANT-<-INTEGERP))
 (19 19 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (19 19 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (19 19 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (19 19 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (19 19 (:REWRITE |(< c (- x))|))
 (19 19 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (19 19 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (19 19 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (19 19 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (19 19 (:REWRITE |(< (/ x) (/ y))|))
 (19 19 (:REWRITE |(< (- x) c)|))
 (19 19 (:REWRITE |(< (- x) (- y))|))
 (18 2 (:REWRITE ACL2-NUMBERP-X))
 (12 12 (:REWRITE DEFAULT-EXPT-2))
 (12 12 (:REWRITE DEFAULT-EXPT-1))
 (12 12 (:REWRITE |(expt 1/c n)|))
 (12 12 (:REWRITE |(expt (- x) n)|))
 (11 11 (:TYPE-PRESCRIPTION FLOOR-ZERO . 3))
 (11 11 (:TYPE-PRESCRIPTION FLOOR-ZERO . 2))
 (11 11 (:TYPE-PRESCRIPTION FLOOR-ZERO . 1))
 (11 11 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 3))
 (11 11 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 2))
 (11 11 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 1))
 (11 11 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 3))
 (11 11 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 2))
 (11 11 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 1))
 (11 11 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 3))
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 (11 11 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 2))
 (11 11 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 1))
 (11 11 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (10 10 (:REWRITE |(- (- x))|))
 (8 8 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (8 8 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (8 8 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (8 8 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (8 2 (:REWRITE RATIONALP-X))
 (4 4 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (4 4 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (4 4 (:REWRITE ODD-EXPT-THM))
 (4 4 (:REWRITE FLOOR-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (4 4 (:REWRITE |(floor x (- y))| . 2))
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 (4 4 (:REWRITE |(< 0 (* x y))|))
 (4 4 (:REWRITE |(- (* c x))|))
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 (4 4 (:LINEAR EXPT-LINEAR-LOWER-<))
 (4 4 (:LINEAR EXPT->=-1-TWO))
 (4 4 (:LINEAR EXPT->=-1-ONE))
 (4 4 (:LINEAR EXPT->-1-TWO))
 (4 4 (:LINEAR EXPT->-1-ONE))
 (4 4 (:LINEAR EXPT-<=-1-TWO))
 (4 4 (:LINEAR EXPT-<=-1-ONE))
 (4 4 (:LINEAR EXPT-<-1-TWO))
 (4 4 (:LINEAR EXPT-<-1-ONE))
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 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (3 3 (:REWRITE |(< (/ x) 0)|))
 (3 3 (:REWRITE |(< (* x y) 0)|))
 (2 2 (:REWRITE REDUCE-RATIONALP-+))
 (2 2 (:REWRITE REDUCE-RATIONALP-*))
 (2 2 (:REWRITE RATIONALP-MINUS-X))
 (2 2 (:REWRITE |(floor x (* y (/ z))) not rewriting-goal-literal|))
 (2 2 (:REWRITE |(floor (* x (/ y)) z) not rewriting-goal-literal|))
 (2 2 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (2 2 (:META META-RATIONALP-CORRECT))
 (1 1 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 )
(|(< (ash x n) x) --- linear|
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 (293 2 (:REWRITE FLOOR-X-Y-=-1 . 2))
 (291 2 (:REWRITE FLOOR-ZERO . 4))
 (263 43 (:REWRITE DEFAULT-TIMES-2))
 (238 2 (:REWRITE CANCEL-FLOOR-+))
 (196 196 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (196 196 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (196 196 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (196 196 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (188 43 (:REWRITE DEFAULT-TIMES-1))
 (154 2 (:REWRITE FLOOR-=-X/Y . 3))
 (148 2 (:REWRITE FLOOR-=-X/Y . 2))
 (106 2 (:REWRITE DEFAULT-FLOOR-RATIO))
 (93 2 (:REWRITE |(* (- x) y)|))
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 (65 11 (:REWRITE DEFAULT-LESS-THAN-1))
 (62 2 (:REWRITE |(integerp (- x))|))
 (50 5 (:REWRITE DEFAULT-DIVIDE))
 (46 2 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (44 2 (:REWRITE FLOOR-X-Y-=--1 . 2))
 (36 3 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (35 5 (:REWRITE |(/ (expt x n))|))
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 (31 1 (:REWRITE |(floor x 1)|))
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 (15 15 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (15 15 (:TYPE-PRESCRIPTION INTEGERP-/-EXPT-1))
 (12 12 (:REWRITE THE-FLOOR-BELOW))
 (12 12 (:REWRITE DEFAULT-EXPT-2))
 (12 12 (:REWRITE DEFAULT-EXPT-1))
 (12 12 (:REWRITE |(expt 1/c n)|))
 (12 12 (:REWRITE |(expt (- x) n)|))
 (11 11 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (11 11 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (11 11 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (11 2 (:REWRITE DEFAULT-FLOOR-2))
 (11 2 (:REWRITE DEFAULT-FLOOR-1))
 (10 10 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (10 10 (:REWRITE INTEGERP-<-CONSTANT))
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 (10 10 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
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 (10 10 (:REWRITE |(< c (- x))|))
 (10 10 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (10 10 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
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 (10 10 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (10 10 (:REWRITE |(< (/ x) (/ y))|))
 (10 10 (:REWRITE |(< (- x) c)|))
 (10 10 (:REWRITE |(< (- x) (- y))|))
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 (10 1 (:REWRITE |(floor (* x (/ y)) z) rewriting-goal-literal|))
 (9 9 (:REWRITE REDUCE-INTEGERP-+))
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 (8 8 (:TYPE-PRESCRIPTION FLOOR-ZERO . 2))
 (8 8 (:TYPE-PRESCRIPTION FLOOR-ZERO . 1))
 (8 8 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 3))
 (8 8 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 2))
 (8 8 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 1))
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 (8 8 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 2))
 (8 8 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 1))
 (8 8 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 3))
 (8 8 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 3))
 (8 8 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 2))
 (8 8 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 1))
 (6 6 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (5 5 (:REWRITE |(- (- x))|))
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 (4 4 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (4 4 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (4 4 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
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 (2 2 (:REWRITE FLOOR-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (2 2 (:REWRITE |(floor x (- y))| . 2))
 (2 2 (:REWRITE |(floor x (- y))| . 1))
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 (2 2 (:REWRITE |(floor (- x) y)| . 1))
 (2 2 (:REWRITE |(< 0 (* x y))|))
 (2 2 (:REWRITE |(- (* c x))|))
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 (2 2 (:LINEAR EXPT-X->-X))
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 (2 2 (:LINEAR EXPT-LINEAR-UPPER-<))
 (2 2 (:LINEAR EXPT-LINEAR-LOWER-<))
 (2 2 (:LINEAR EXPT->=-1-TWO))
 (2 2 (:LINEAR EXPT->-1-TWO))
 (2 2 (:LINEAR EXPT-<=-1-TWO))
 (2 2 (:LINEAR EXPT-<=-1-ONE))
 (2 2 (:LINEAR EXPT-<-1-TWO))
 (2 2 (:LINEAR EXPT-<-1-ONE))
 (1 1 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (1 1 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (1 1 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (1 1 (:REWRITE DEFAULT-ASH-2))
 (1 1 (:REWRITE DEFAULT-ASH-1))
 (1 1 (:REWRITE |(floor x (* y (/ z))) not rewriting-goal-literal|))
 (1 1 (:REWRITE |(floor (* x (/ y)) z) not rewriting-goal-literal|))
 (1 1 (:REWRITE |(<= (/ x) y) with (< x 0)|))
 (1 1 (:REWRITE |(<= (/ x) y) with (< 0 x)|))
 (1 1 (:REWRITE |(< x (/ y)) with (< y 0)|))
 (1 1 (:REWRITE |(< 0 (/ x))|))
 (1 1 (:REWRITE |(< (/ x) 0)|))
 (1 1 (:REWRITE |(< (* x y) 0)|))
 )
(|(< x (ash x n)) --- linear|
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 (39 1 (:REWRITE DEFAULT-FLOOR-RATIO))
 (23 5 (:REWRITE DEFAULT-LESS-THAN-2))
 (21 21 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (21 21 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (21 21 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (21 21 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
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 (10 1 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (10 1 (:REWRITE DEFAULT-FLOOR-2))
 (7 7 (:REWRITE DEFAULT-TIMES-1))
 (5 5 (:REWRITE THE-FLOOR-BELOW))
 (5 5 (:REWRITE THE-FLOOR-ABOVE))
 (5 5 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (5 5 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (5 5 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (5 5 (:REWRITE DEFAULT-LESS-THAN-1))
 (4 4 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (4 4 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (4 4 (:REWRITE INTEGERP-<-CONSTANT))
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 (4 4 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
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 (4 4 (:REWRITE |(< (/ x) (/ y))|))
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 (3 3 (:REWRITE |(expt 1/c n)|))
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 (1 1 (:REWRITE |(< x (/ y)) with (< y 0)|))
 )
(|(< (ash x n) y)|
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 (2156 64 (:REWRITE PREFER-POSITIVE-EXPONENTS-SCATTER-EXPONENTS-<-2))
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 (2122 310 (:TYPE-PRESCRIPTION FLOOR-ZERO . 1))
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 (664 223 (:REWRITE DEFAULT-TIMES-1))
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 (513 17 (:REWRITE |(* (- x) y)|))
 (508 56 (:REWRITE NORMALIZE-FACTORS-SCATTER-EXPONENTS))
 (501 6 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
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 (488 58 (:REWRITE PREFER-POSITIVE-EXPONENTS-SCATTER-EXPONENTS-<))
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 (410 17 (:REWRITE FLOOR-ZERO . 2))
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 (131 131 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
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 (120 19 (:LINEAR EXPT-X->-X))
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 )
(|(ash (ash x n) (- n))|
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(|(equal (ash (mod x c) nn) 0)|
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 (22 7 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (18 18 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
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 (7 7 (:REWRITE DEFAULT-MOD-1))
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 (1 1 (:REWRITE |(equal (/ x) (/ y))|))
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 (1 1 (:REWRITE |(equal (- x) (- y))|))
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(|(ash (ash x n1) n2)|
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 (1 1 (:REWRITE |(floor (floor x y) z)| . 4))
 (1 1 (:REWRITE |(floor (floor x y) z)| . 3))
 (1 1 (:REWRITE |(floor (floor x y) z)| . 2))
 )
(BREAK-LOGAND-APART
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 )
(BREAK-LOGAND-APART-N
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 )
(|(< (logand x y) (expt 2 n))|
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 (7 7 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (7 7 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (7 7 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (7 7 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (7 7 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (7 7 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (7 7 (:REWRITE INTEGERP-<-CONSTANT))
 (7 7 (:REWRITE DEFAULT-LESS-THAN-2))
 (7 7 (:REWRITE DEFAULT-LESS-THAN-1))
 (7 7 (:REWRITE CONSTANT-<-INTEGERP))
 (7 7 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
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 (7 7 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (7 7 (:REWRITE |(< (/ x) (/ y))|))
 (7 7 (:REWRITE |(< (- x) c)|))
 (7 7 (:REWRITE |(< (- x) (- y))|))
 (4 4 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (4 4 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (4 4 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (3 3 (:REWRITE |(< (/ x) 0)|))
 (3 3 (:REWRITE |(< (* x y) 0)|))
 (2 2 (:REWRITE LOGAND-CONSTANT-MASK))
 (2 2 (:REWRITE DEFAULT-LOGAND-2))
 (2 2 (:REWRITE DEFAULT-LOGAND-1))
 (2 2 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (2 2 (:LINEAR EXPT-LINEAR-UPPER-<))
 (2 2 (:LINEAR EXPT-LINEAR-LOWER-<))
 (2 2 (:LINEAR EXPT->=-1-TWO))
 (2 2 (:LINEAR EXPT->-1-TWO))
 (2 2 (:LINEAR EXPT-<=-1-TWO))
 (2 2 (:LINEAR EXPT-<=-1-ONE))
 (2 2 (:LINEAR EXPT-<-1-TWO))
 (2 2 (:LINEAR EXPT-<-1-ONE))
 (1 1 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 )
(|(logand x (lognot x))|
 (3235 6 (:LINEAR LINEAR-FLOOR-BOUNDS-1))
 (2816 11 (:LINEAR LOGAND-BOUNDS-POS . 1))
 (2771 64 (:REWRITE THE-FLOOR-ABOVE))
 (2638 11 (:LINEAR LOGAND-BOUNDS-NEG . 2))
 (2638 11 (:LINEAR LOGAND-BOUNDS-NEG . 1))
 (1608 9 (:REWRITE |(+ y x)|))
 (1434 1434 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (1434 1434 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (1434 1434 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (1434 1434 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (990 32 (:REWRITE DEFAULT-PLUS-2))
 (968 32 (:REWRITE DEFAULT-PLUS-1))
 (944 17 (:REWRITE NORMALIZE-ADDENDS))
 (550 62 (:TYPE-PRESCRIPTION FLOOR-ZERO . 2))
 (550 62 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 1))
 (550 62 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 1))
 (550 62 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 1))
 (550 62 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 1))
 (460 11 (:LINEAR LOGAND-BOUNDS-POS . 2))
 (337 337 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (337 337 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (337 337 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (318 6 (:REWRITE CANCEL-FLOOR-+))
 (310 62 (:TYPE-PRESCRIPTION FLOOR-ZERO . 4))
 (310 62 (:TYPE-PRESCRIPTION FLOOR-ZERO . 3))
 (310 62 (:TYPE-PRESCRIPTION FLOOR-ZERO . 1))
 (310 62 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 3))
 (310 62 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 2))
 (310 62 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 3))
 (310 62 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 2))
 (310 62 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 3))
 (310 62 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 2))
 (310 62 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 3))
 (310 62 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 2))
 (306 3 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (306 3 (:DEFINITION FIX))
 (274 6 (:REWRITE FLOOR-ZERO . 3))
 (206 168 (:REWRITE DEFAULT-TIMES-2))
 (204 6 (:REWRITE FLOOR-X-Y-=--1 . 2))
 (199 61 (:REWRITE INTEGERP-MINUS-X))
 (198 49 (:REWRITE |(* y x)|))
 (186 61 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (170 168 (:REWRITE DEFAULT-TIMES-1))
 (142 6 (:REWRITE FLOOR-ZERO . 5))
 (142 6 (:REWRITE FLOOR-ZERO . 4))
 (138 12 (:REWRITE DEFAULT-FLOOR-RATIO))
 (132 6 (:REWRITE FLOOR-=-X/Y . 3))
 (132 6 (:REWRITE FLOOR-=-X/Y . 2))
 (126 6 (:REWRITE FLOOR-X-Y-=-1 . 2))
 (120 12 (:REWRITE |(floor x 2)| . 2))
 (104 104 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (102 12 (:REWRITE |(* (- x) y)|))
 (98 61 (:REWRITE DEFAULT-LESS-THAN-1))
 (94 94 (:TYPE-PRESCRIPTION |(< (logand x y) 0)| . 2))
 (94 94 (:TYPE-PRESCRIPTION |(< (logand x y) 0)| . 1))
 (83 58 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (83 58 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (78 3 (:LINEAR LINEAR-FLOOR-BOUNDS-3))
 (66 3 (:LINEAR LINEAR-FLOOR-BOUNDS-2))
 (64 64 (:REWRITE THE-FLOOR-BELOW))
 (62 58 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (61 61 (:REWRITE DEFAULT-LESS-THAN-2))
 (60 12 (:REWRITE DEFAULT-MINUS))
 (58 58 (:REWRITE SIMPLIFY-SUMS-<))
 (58 58 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (58 58 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (58 58 (:REWRITE INTEGERP-<-CONSTANT))
 (58 58 (:REWRITE CONSTANT-<-INTEGERP))
 (58 58 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (58 58 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (58 58 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (58 58 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (58 58 (:REWRITE |(< c (- x))|))
 (58 58 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (58 58 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (58 58 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (58 58 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (58 58 (:REWRITE |(< (/ x) (/ y))|))
 (58 58 (:REWRITE |(< (- x) c)|))
 (58 58 (:REWRITE |(< (- x) (- y))|))
 (55 55 (:REWRITE REDUCE-INTEGERP-+))
 (55 55 (:META META-INTEGERP-CORRECT))
 (54 12 (:REWRITE |(- (* c x))|))
 (53 53 (:REWRITE |(< (* x y) 0)|))
 (50 50 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (50 50 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (50 50 (:REWRITE |(< (/ x) 0)|))
 (34 34 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (30 6 (:REWRITE FLOOR-ZERO . 2))
 (30 6 (:REWRITE FLOOR-X-Y-=-1 . 3))
 (30 6 (:REWRITE FLOOR-X-Y-=--1 . 3))
 (30 6 (:REWRITE FLOOR-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (30 6 (:REWRITE |(floor (* x (/ y)) z) not rewriting-goal-literal|))
 (22 7 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (22 7 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (22 6 (:REWRITE FLOOR-CANCEL-*-CONST))
 (15 3 (:REWRITE |(+ 0 x)|))
 (14 14 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (14 12 (:REWRITE DEFAULT-FLOOR-1))
 (12 12 (:REWRITE DEFAULT-FLOOR-2))
 (11 11 (:TYPE-PRESCRIPTION ABS))
 (7 7 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (7 7 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (7 7 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (7 7 (:REWRITE LOGAND-CONSTANT-MASK))
 (7 7 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (7 7 (:REWRITE |(equal c (/ x))|))
 (7 7 (:REWRITE |(equal c (- x))|))
 (7 7 (:REWRITE |(equal (/ x) c)|))
 (7 7 (:REWRITE |(equal (/ x) (/ y))|))
 (7 7 (:REWRITE |(equal (- x) c)|))
 (7 7 (:REWRITE |(equal (- x) (- y))|))
 (7 7 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (6 6 (:REWRITE FLOOR-CANCEL-*-REWRITING-GOAL-LITERAL))
 (6 6 (:REWRITE |(floor x (- y))| . 2))
 (6 6 (:REWRITE |(floor x (- y))| . 1))
 (6 6 (:REWRITE |(floor x (* y (/ z))) rewriting-goal-literal|))
 (6 6 (:REWRITE |(floor x (* y (/ z))) not rewriting-goal-literal|))
 (6 6 (:REWRITE |(floor (- x) y)| . 2))
 (6 6 (:REWRITE |(floor (- x) y)| . 1))
 (6 6 (:REWRITE |(floor (* x (/ y)) z) rewriting-goal-literal|))
 (6 3 (:REWRITE BUBBLE-DOWN-+-MATCH-1))
 (5 5 (:REWRITE ZIP-OPEN))
 (4 4 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (4 4 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (4 4 (:REWRITE |(< 0 (/ x))|))
 (4 4 (:REWRITE |(< 0 (* x y))|))
 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (3 3 (:REWRITE |(+ x (- x))|))
 (2 2 (:REWRITE |(integerp (* 1/2 (logand x y)))| . 4))
 (2 2 (:REWRITE |(integerp (* 1/2 (logand x y)))| . 3))
 (2 2 (:REWRITE |(integerp (* 1/2 (logand x y)))| . 2))
 )
(|(logand x (lognot x) y)|
 (32 32 (:TYPE-PRESCRIPTION |(< (logand x y) 0)| . 2))
 (32 32 (:TYPE-PRESCRIPTION |(< (logand x y) 0)| . 1))
 (14 14 (:REWRITE REDUCE-INTEGERP-+))
 (14 14 (:REWRITE INTEGERP-MINUS-X))
 (14 14 (:META META-INTEGERP-CORRECT))
 (8 8 (:REWRITE LOGAND-CONSTANT-MASK))
 (8 2 (:LINEAR LOGAND-BOUNDS-POS . 2))
 (8 2 (:LINEAR LOGAND-BOUNDS-POS . 1))
 (8 2 (:LINEAR LOGAND-BOUNDS-NEG . 2))
 (8 2 (:LINEAR LOGAND-BOUNDS-NEG . 1))
 (1 1 (:REWRITE |(logand c d x)|))
 )
(CROCK-1+
 (28 28 (:TYPE-PRESCRIPTION NATP-ASH))
 )
(CROCK-1-
 (28 28 (:TYPE-PRESCRIPTION NATP-ASH))
 )
(|(ash (logand x y) 1)|
 (106 2 (:LINEAR LOGAND-BOUNDS-POS . 2))
 (106 2 (:LINEAR LOGAND-BOUNDS-POS . 1))
 (104 2 (:LINEAR LOGAND-BOUNDS-NEG . 2))
 (104 2 (:LINEAR LOGAND-BOUNDS-NEG . 1))
 (92 5 (:REWRITE DEFAULT-FLOOR-RATIO))
 (48 20 (:REWRITE DEFAULT-TIMES-1))
 (47 47 (:TYPE-PRESCRIPTION |(< (logand x y) 0)| . 2))
 (47 47 (:TYPE-PRESCRIPTION |(< (logand x y) 0)| . 1))
 (40 20 (:REWRITE DEFAULT-TIMES-2))
 (37 3 (:REWRITE |(* (if a b c) x)|))
 (32 8 (:REWRITE |(< (ash x n) y)|))
 (24 8 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (24 8 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (24 8 (:REWRITE DEFAULT-LESS-THAN-1))
 (17 5 (:REWRITE DEFAULT-FLOOR-1))
 (16 16 (:REWRITE REDUCE-INTEGERP-+))
 (16 16 (:REWRITE INTEGERP-MINUS-X))
 (16 16 (:META META-INTEGERP-CORRECT))
 (9 9 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (8 8 (:REWRITE THE-FLOOR-BELOW))
 (8 8 (:REWRITE THE-FLOOR-ABOVE))
 (8 8 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (8 8 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (8 8 (:REWRITE SIMPLIFY-SUMS-<))
 (8 8 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (8 8 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (8 8 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (8 8 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (8 8 (:REWRITE INTEGERP-<-CONSTANT))
 (8 8 (:REWRITE DEFAULT-LESS-THAN-2))
 (8 8 (:REWRITE CONSTANT-<-INTEGERP))
 (8 8 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (8 8 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (8 8 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (8 8 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (8 8 (:REWRITE |(< c (- x))|))
 (8 8 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (8 8 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (8 8 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (8 8 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (8 8 (:REWRITE |(< (/ x) 0)|))
 (8 8 (:REWRITE |(< (/ x) (/ y))|))
 (8 8 (:REWRITE |(< (- x) c)|))
 (8 8 (:REWRITE |(< (- x) (- y))|))
 (8 8 (:REWRITE |(< (* x y) 0)|))
 (6 6 (:REWRITE LOGAND-CONSTANT-MASK))
 (5 5 (:REWRITE DEFAULT-FLOOR-2))
 (5 5 (:REWRITE DEFAULT-ASH-2))
 (4 4 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (1 1 (:REWRITE |(logand (* 2 x) (* 2 y))| . 5))
 (1 1 (:REWRITE |(logand (* 2 x) (* 2 y))| . 4))
 (1 1 (:REWRITE |(logand (* 2 x) (* 2 y))| . 3))
 )
(|(ash (logand x y) -1)|
 (432 432 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (432 432 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (432 432 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (354 10 (:LINEAR LOGAND-BOUNDS-POS . 2))
 (354 10 (:LINEAR LOGAND-BOUNDS-POS . 1))
 (344 10 (:LINEAR LOGAND-BOUNDS-NEG . 2))
 (344 10 (:LINEAR LOGAND-BOUNDS-NEG . 1))
 (277 277 (:TYPE-PRESCRIPTION |(< (logand x y) 0)| . 2))
 (277 277 (:TYPE-PRESCRIPTION |(< (logand x y) 0)| . 1))
 (204 9 (:REWRITE DEFAULT-FLOOR-RATIO))
 (159 75 (:REWRITE DEFAULT-TIMES-2))
 (115 75 (:REWRITE DEFAULT-TIMES-1))
 (101 29 (:REWRITE DEFAULT-PLUS-2))
 (98 10 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (98 10 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (87 29 (:REWRITE DEFAULT-PLUS-1))
 (64 9 (:REWRITE |(* y x)|))
 (56 40 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (56 40 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (56 40 (:REWRITE DEFAULT-LESS-THAN-1))
 (49 49 (:REWRITE REDUCE-INTEGERP-+))
 (49 49 (:REWRITE INTEGERP-MINUS-X))
 (49 49 (:META META-INTEGERP-CORRECT))
 (47 47 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (40 40 (:REWRITE THE-FLOOR-BELOW))
 (40 40 (:REWRITE THE-FLOOR-ABOVE))
 (40 40 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (40 40 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (40 40 (:REWRITE SIMPLIFY-SUMS-<))
 (40 40 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (40 40 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (40 40 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (40 40 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (40 40 (:REWRITE INTEGERP-<-CONSTANT))
 (40 40 (:REWRITE DEFAULT-LESS-THAN-2))
 (40 40 (:REWRITE CONSTANT-<-INTEGERP))
 (40 40 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (40 40 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (40 40 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (40 40 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (40 40 (:REWRITE |(< c (- x))|))
 (40 40 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (40 40 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (40 40 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (40 40 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (40 40 (:REWRITE |(< (/ x) 0)|))
 (40 40 (:REWRITE |(< (/ x) (/ y))|))
 (40 40 (:REWRITE |(< (- x) c)|))
 (40 40 (:REWRITE |(< (- x) (- y))|))
 (40 40 (:REWRITE |(< (* x y) 0)|))
 (37 9 (:REWRITE DEFAULT-FLOOR-1))
 (37 3 (:REWRITE |(* (if a b c) x)|))
 (32 8 (:REWRITE |(< (ash x n) y)|))
 (22 22 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (20 20 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (18 2 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (16 10 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (15 15 (:REWRITE LOGAND-CONSTANT-MASK))
 (10 10 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (10 10 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (10 10 (:REWRITE |(equal c (/ x))|))
 (10 10 (:REWRITE |(equal c (- x))|))
 (10 10 (:REWRITE |(equal (/ x) c)|))
 (10 10 (:REWRITE |(equal (/ x) (/ y))|))
 (10 10 (:REWRITE |(equal (- x) c)|))
 (10 10 (:REWRITE |(equal (- x) (- y))|))
 (9 9 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (9 9 (:REWRITE DEFAULT-FLOOR-2))
 (7 7 (:REWRITE |(floor x 2)| . 2))
 (6 6 (:TYPE-PRESCRIPTION ABS))
 (5 5 (:REWRITE DEFAULT-ASH-2))
 (5 5 (:REWRITE |(integerp (* 1/2 (logand x y)))| . 4))
 (5 5 (:REWRITE |(integerp (* 1/2 (logand x y)))| . 3))
 (5 5 (:REWRITE |(integerp (* 1/2 (logand x y)))| . 2))
 (5 5 (:REWRITE |(equal (+ (- c) x) y)|))
 (5 5 (:REWRITE |(equal (* x y) 0)|))
 )
(IND-HINT
 (22 18 (:REWRITE DEFAULT-PLUS-1))
 (20 20 (:REWRITE THE-FLOOR-BELOW))
 (20 20 (:REWRITE THE-FLOOR-ABOVE))
 (20 20 (:REWRITE DEFAULT-LESS-THAN-2))
 (20 20 (:REWRITE DEFAULT-LESS-THAN-1))
 (18 18 (:REWRITE DEFAULT-PLUS-2))
 (16 16 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (16 16 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (16 16 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (16 16 (:REWRITE |(< (/ x) (/ y))|))
 (15 15 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (15 15 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (15 15 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (15 15 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (15 15 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (15 15 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (15 15 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (15 15 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (13 13 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (13 13 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (13 13 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (13 13 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (13 13 (:REWRITE INTEGERP-<-CONSTANT))
 (13 13 (:REWRITE CONSTANT-<-INTEGERP))
 (10 10 (:REWRITE DEFAULT-MINUS))
 (9 9 (:REWRITE |(< (/ x) 0)|))
 (9 9 (:REWRITE |(< (* x y) 0)|))
 (8 8 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (8 8 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (4 4 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (4 4 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (4 4 (:REWRITE |(< 0 (/ x))|))
 (4 4 (:REWRITE |(< 0 (* x y))|))
 (4 4 (:REWRITE |(< (+ c/d x) y)|))
 (4 4 (:REWRITE |(< (+ (- c) x) y)|))
 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (2 2 (:REWRITE ZIP-OPEN))
 (1 1 (:REWRITE REDUCE-INTEGERP-+))
 (1 1 (:REWRITE INTEGERP-MINUS-X))
 (1 1 (:REWRITE |(< y (+ (- c) x))|))
 (1 1 (:REWRITE |(< x (+ c/d y))|))
 (1 1 (:META META-INTEGERP-CORRECT))
 )
(|(ash (logand x y) n)|
 (6024 64 (:REWRITE |(< (ash x n) y)|))
 (2208 14 (:LINEAR LOGAND-BOUNDS-POS . 2))
 (2208 14 (:LINEAR LOGAND-BOUNDS-POS . 1))
 (2194 14 (:LINEAR LOGAND-BOUNDS-NEG . 2))
 (2194 14 (:LINEAR LOGAND-BOUNDS-NEG . 1))
 (1191 1191 (:TYPE-PRESCRIPTION |(< (logand x y) 0)| . 1))
 (1024 32 (:REWRITE DEFAULT-FLOOR-RATIO))
 (640 40 (:TYPE-PRESCRIPTION FLOOR-ZERO . 4))
 (520 40 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 1))
 (520 40 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 1))
 (400 400 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (400 400 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (400 400 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (400 400 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (400 400 (:TYPE-PRESCRIPTION INTEGERP-/-EXPT-2))
 (400 400 (:TYPE-PRESCRIPTION INTEGERP-/-EXPT-1))
 (320 32 (:REWRITE DEFAULT-TIMES-2))
 (320 32 (:REWRITE DEFAULT-FLOOR-2))
 (320 32 (:REWRITE DEFAULT-DIVIDE))
 (288 32 (:REWRITE |(/ (expt x n))|))
 (280 40 (:TYPE-PRESCRIPTION FLOOR-ZERO . 3))
 (280 40 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 3))
 (280 40 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 2))
 (280 40 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 3))
 (280 40 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 2))
 (262 118 (:REWRITE DEFAULT-LESS-THAN-1))
 (260 116 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (180 118 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (164 116 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (136 136 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (136 136 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (136 136 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (136 136 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (136 136 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (136 136 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (136 136 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (136 136 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (136 136 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (133 13 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (133 13 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (129 13 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (126 126 (:REWRITE DEFAULT-PLUS-2))
 (126 126 (:REWRITE DEFAULT-PLUS-1))
 (122 122 (:REWRITE REDUCE-INTEGERP-+))
 (122 122 (:REWRITE INTEGERP-MINUS-X))
 (122 122 (:META META-INTEGERP-CORRECT))
 (118 118 (:REWRITE THE-FLOOR-BELOW))
 (118 118 (:REWRITE THE-FLOOR-ABOVE))
 (118 118 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (118 118 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (118 118 (:REWRITE DEFAULT-LESS-THAN-2))
 (116 116 (:REWRITE SIMPLIFY-SUMS-<))
 (116 116 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (116 116 (:REWRITE INTEGERP-<-CONSTANT))
 (116 116 (:REWRITE CONSTANT-<-INTEGERP))
 (116 116 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (116 116 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (116 116 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (116 116 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (116 116 (:REWRITE |(< c (- x))|))
 (116 116 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (116 116 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (116 116 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (116 116 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (116 116 (:REWRITE |(< (/ x) (/ y))|))
 (116 116 (:REWRITE |(< (- x) c)|))
 (116 116 (:REWRITE |(< (- x) (- y))|))
 (108 108 (:REWRITE DEFAULT-ASH-2))
 (102 102 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (102 102 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (102 102 (:REWRITE |(< (/ x) 0)|))
 (102 102 (:REWRITE |(< (* x y) 0)|))
 (96 16 (:REWRITE |(- (+ x y))|))
 (95 95 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (95 95 (:REWRITE NORMALIZE-ADDENDS))
 (65 65 (:REWRITE LOGAND-CONSTANT-MASK))
 (64 64 (:REWRITE DEFAULT-EXPT-2))
 (64 64 (:REWRITE DEFAULT-EXPT-1))
 (64 64 (:REWRITE |(expt 1/c n)|))
 (64 64 (:REWRITE |(expt (- x) n)|))
 (48 48 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (48 48 (:REWRITE DEFAULT-MINUS))
 (32 32 (:REWRITE DEFAULT-TIMES-1))
 (32 32 (:REWRITE DEFAULT-FLOOR-1))
 (32 32 (:REWRITE |(floor 0 y)|))
 (32 32 (:REWRITE |(* 0 x)|))
 (14 14 (:REWRITE |(< 0 (* x y))|))
 (13 13 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (13 13 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (13 13 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (13 13 (:REWRITE |(equal c (/ x))|))
 (13 13 (:REWRITE |(equal c (- x))|))
 (13 13 (:REWRITE |(equal (/ x) c)|))
 (13 13 (:REWRITE |(equal (/ x) (/ y))|))
 (13 13 (:REWRITE |(equal (- x) c)|))
 (13 13 (:REWRITE |(equal (- x) (- y))|))
 (12 12 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (12 12 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (12 12 (:REWRITE |(< 0 (/ x))|))
 (5 5 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (2 2 (:REWRITE |(< x (+ c/d y))|))
 (1 1 (:REWRITE ZIP-OPEN))
 )
(|(mod (logand x y) c)|
 (3420 20 (:REWRITE CANCEL-MOD-+))
 (2756 20 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (2018 20 (:REWRITE MOD-ZERO . 3))
 (1673 150 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (1649 150 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (1649 150 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (1520 1520 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (1520 1520 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (1520 1520 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (1520 1520 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (1520 1520 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (1520 1520 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (1520 1520 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (1495 20 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (1388 20 (:REWRITE MOD-X-Y-=-X . 3))
 (1235 20 (:REWRITE MOD-X-Y-=-X . 4))
 (1080 20 (:REWRITE DEFAULT-MOD-RATIO))
 (1080 18 (:REWRITE |(< (logand x y) 0)|))
 (1005 116 (:REWRITE DEFAULT-TIMES-2))
 (980 20 (:REWRITE |(integerp (- x))|))
 (962 150 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (948 20 (:REWRITE MOD-ZERO . 4))
 (935 935 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (935 935 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (935 935 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (800 20 (:REWRITE |(* (- x) y)|))
 (760 20 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (760 20 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (759 759 (:TYPE-PRESCRIPTION INTEGERP-/-EXPT-2))
 (759 759 (:TYPE-PRESCRIPTION INTEGERP-/-EXPT-1))
 (722 722 (:TYPE-PRESCRIPTION |(< (logand x y) 0)| . 1))
 (713 713 (:TYPE-PRESCRIPTION |(< (logand x y) 0)| . 2))
 (650 65 (:REWRITE DEFAULT-DIVIDE))
 (610 6 (:LINEAR MOD-BOUNDS-3))
 (580 20 (:REWRITE MOD-X-Y-=-X . 2))
 (559 116 (:REWRITE DEFAULT-TIMES-1))
 (540 20 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (540 20 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (527 31 (:REWRITE |(* y x)|))
 (482 56 (:LINEAR LOGAND-BOUNDS-NEG . 2))
 (482 56 (:LINEAR LOGAND-BOUNDS-NEG . 1))
 (410 82 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A-EXPT))
 (390 65 (:REWRITE |(/ (expt x n))|))
 (385 85 (:REWRITE DEFAULT-MINUS))
 (366 11 (:REWRITE DEFAULT-LOGAND-2))
 (366 11 (:REWRITE DEFAULT-LOGAND-1))
 (360 20 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (360 20 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (360 20 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (349 106 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (349 106 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (341 20 (:REWRITE MOD-CANCEL-*-CONST))
 (316 12 (:LINEAR MOD-BOUNDS-2))
 (313 106 (:REWRITE SIMPLIFY-SUMS-<))
 (313 106 (:REWRITE DEFAULT-LESS-THAN-2))
 (200 20 (:REWRITE DEFAULT-MOD-2))
 (150 150 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (150 150 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (150 150 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (150 150 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (142 106 (:REWRITE DEFAULT-LESS-THAN-1))
 (124 124 (:REWRITE THE-FLOOR-BELOW))
 (124 124 (:REWRITE THE-FLOOR-ABOVE))
 (106 106 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (106 106 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (106 106 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (106 106 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (106 106 (:REWRITE INTEGERP-<-CONSTANT))
 (106 106 (:REWRITE CONSTANT-<-INTEGERP))
 (106 106 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (106 106 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (106 106 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (106 106 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (106 106 (:REWRITE |(< c (- x))|))
 (106 106 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (106 106 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (106 106 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (106 106 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (106 106 (:REWRITE |(< (/ x) (/ y))|))
 (106 106 (:REWRITE |(< (- x) c)|))
 (106 106 (:REWRITE |(< (- x) (- y))|))
 (88 88 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B-EXPT))
 (88 88 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B-EXPT))
 (88 88 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B-EXPT))
 (88 88 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B-EXPT))
 (82 82 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A-EXPT))
 (82 82 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A-EXPT))
 (82 82 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A-EXPT))
 (73 73 (:REWRITE DEFAULT-EXPT-2))
 (73 73 (:REWRITE DEFAULT-EXPT-1))
 (73 73 (:REWRITE |(expt 1/c n)|))
 (73 73 (:REWRITE |(expt (- x) n)|))
 (70 70 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (65 65 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (65 5 (:LINEAR EXPT->=-1-ONE))
 (65 5 (:LINEAR EXPT-<=-1-TWO))
 (63 5 (:LINEAR EXPT->-1-ONE))
 (63 5 (:LINEAR EXPT-<-1-TWO))
 (60 60 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (60 60 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (60 60 (:REWRITE |(< (/ x) 0)|))
 (60 60 (:REWRITE |(< (* x y) 0)|))
 (60 20 (:REWRITE DEFAULT-MOD-1))
 (55 19 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (55 19 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (55 19 (:REWRITE ODD-EXPT-THM))
 (55 5 (:LINEAR EXPT-X->=-X))
 (55 5 (:LINEAR EXPT-X->-X))
 (48 48 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (48 48 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (48 48 (:REWRITE REDUCE-INTEGERP-+))
 (48 48 (:REWRITE INTEGERP-MINUS-X))
 (48 48 (:META META-INTEGERP-CORRECT))
 (23 23 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (23 23 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (23 23 (:REWRITE |(< 0 (/ x))|))
 (23 23 (:REWRITE |(< 0 (* x y))|))
 (20 20 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (20 20 (:REWRITE |(mod x (- y))| . 3))
 (20 20 (:REWRITE |(mod x (- y))| . 2))
 (20 20 (:REWRITE |(mod x (- y))| . 1))
 (20 20 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (20 20 (:REWRITE |(mod (- x) y)| . 3))
 (20 20 (:REWRITE |(mod (- x) y)| . 2))
 (20 20 (:REWRITE |(mod (- x) y)| . 1))
 (20 20 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (20 20 (:REWRITE |(- (* c x))|))
 (19 19 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (19 19 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (19 19 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (19 19 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (19 19 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (19 19 (:REWRITE |(equal c (/ x))|))
 (19 19 (:REWRITE |(equal c (- x))|))
 (19 19 (:REWRITE |(equal (/ x) c)|))
 (19 19 (:REWRITE |(equal (/ x) (/ y))|))
 (19 19 (:REWRITE |(equal (- x) c)|))
 (19 19 (:REWRITE |(equal (- x) (- y))|))
 (18 18 (:REWRITE |(< (logand x y) (expt 2 n))|))
 (11 11 (:REWRITE LOGAND-CONSTANT-MASK))
 (10 10 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (10 10 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (10 10 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (10 10 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (5 5 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (5 5 (:LINEAR EXPT-LINEAR-UPPER-<))
 (5 5 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (5 5 (:LINEAR EXPT-LINEAR-LOWER-<))
 (5 5 (:LINEAR EXPT->=-1-TWO))
 (5 5 (:LINEAR EXPT->-1-TWO))
 (5 5 (:LINEAR EXPT-<=-1-ONE))
 (5 5 (:LINEAR EXPT-<-1-ONE))
 (4 4 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 )
(|(logand x (logior y z))|
 (114154 224 (:LINEAR LINEAR-FLOOR-BOUNDS-1))
 (106398 165 (:LINEAR LOGIOR-BOUNDS-POS . 2))
 (106398 165 (:LINEAR LOGIOR-BOUNDS-POS . 1))
 (102148 165 (:LINEAR LOGIOR-BOUNDS-NEG . 2))
 (101118 5393 (:REWRITE THE-FLOOR-ABOVE))
 (90298 622 (:LINEAR LOGAND-BOUNDS-POS . 1))
 (86581 165 (:LINEAR LOGIOR-BOUNDS-NEG . 1))
 (84960 622 (:LINEAR LOGAND-BOUNDS-NEG . 2))
 (84960 622 (:LINEAR LOGAND-BOUNDS-NEG . 1))
 (79199 79199 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (79199 79199 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (79199 79199 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (79199 79199 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (76189 390 (:REWRITE |(< (logand x y) 0)|))
 (56280 315 (:REWRITE |(+ y x)|))
 (35102 1673 (:REWRITE DEFAULT-PLUS-2))
 (34433 1673 (:REWRITE DEFAULT-PLUS-1))
 (34038 622 (:LINEAR LOGAND-BOUNDS-POS . 2))
 (33307 862 (:REWRITE NORMALIZE-ADDENDS))
 (31727 3631 (:TYPE-PRESCRIPTION FLOOR-ZERO . 2))
 (31727 3631 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 1))
 (31727 3631 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 1))
 (31727 3631 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 1))
 (31727 3631 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 1))
 (21353 4731 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (18155 3631 (:TYPE-PRESCRIPTION FLOOR-ZERO . 4))
 (18155 3631 (:TYPE-PRESCRIPTION FLOOR-ZERO . 3))
 (18155 3631 (:TYPE-PRESCRIPTION FLOOR-ZERO . 1))
 (18155 3631 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 3))
 (18155 3631 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 2))
 (18155 3631 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 3))
 (18155 3631 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 2))
 (18155 3631 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 3))
 (18155 3631 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 2))
 (18155 3631 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 3))
 (18155 3631 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 2))
 (17992 17992 (:TYPE-PRESCRIPTION |(< (logand x y) 0)| . 2))
 (17992 17992 (:TYPE-PRESCRIPTION |(< (logand x y) 0)| . 1))
 (15833 15833 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (15833 15833 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (15833 15833 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (11766 222 (:REWRITE CANCEL-FLOOR-+))
 (11043 4455 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (10774 256 (:REWRITE |(< (+ c/d x) y)|))
 (10710 105 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (10710 105 (:DEFINITION FIX))
 (10607 222 (:REWRITE FLOOR-ZERO . 3))
 (9218 9154 (:TYPE-PRESCRIPTION |(< 0 (logior x y))| . 1))
 (9218 9154 (:TYPE-PRESCRIPTION |(< (logior x y) 0)| . 2))
 (9218 9154 (:TYPE-PRESCRIPTION |(< (logior x y) 0)| . 1))
 (7847 5717 (:REWRITE DEFAULT-TIMES-2))
 (7416 222 (:REWRITE FLOOR-X-Y-=--1 . 2))
 (6990 1884 (:REWRITE INTEGERP-MINUS-X))
 (6981 5717 (:REWRITE DEFAULT-TIMES-1))
 (6839 4312 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (6596 4312 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (6569 4874 (:REWRITE DEFAULT-LESS-THAN-1))
 (6182 4874 (:REWRITE DEFAULT-LESS-THAN-2))
 (5492 222 (:REWRITE FLOOR-ZERO . 5))
 (5492 222 (:REWRITE FLOOR-ZERO . 4))
 (5393 5393 (:REWRITE THE-FLOOR-BELOW))
 (5389 159 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (5389 159 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (5323 159 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (4872 222 (:REWRITE FLOOR-X-Y-=-1 . 2))
 (4800 222 (:REWRITE FLOOR-=-X/Y . 3))
 (4800 222 (:REWRITE FLOOR-=-X/Y . 2))
 (4610 4455 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (4312 4312 (:REWRITE SIMPLIFY-SUMS-<))
 (4312 4312 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (4312 4312 (:REWRITE INTEGERP-<-CONSTANT))
 (4312 4312 (:REWRITE CONSTANT-<-INTEGERP))
 (4312 4312 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (4312 4312 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (4312 4312 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (4312 4312 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (4312 4312 (:REWRITE |(< c (- x))|))
 (4312 4312 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (4312 4312 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (4312 4312 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (4312 4312 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (4312 4312 (:REWRITE |(< (/ x) (/ y))|))
 (4312 4312 (:REWRITE |(< (- x) c)|))
 (4312 4312 (:REWRITE |(< (- x) (- y))|))
 (4232 4232 (:REWRITE |(< (* x y) 0)|))
 (3774 444 (:REWRITE |(* (- x) y)|))
 (3721 3721 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (3721 3721 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (3721 3721 (:REWRITE |(< (/ x) 0)|))
 (3143 112 (:LINEAR LINEAR-FLOOR-BOUNDS-3))
 (3091 3091 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (2989 289 (:REWRITE |(floor x 2)| . 2))
 (2604 112 (:LINEAR LINEAR-FLOOR-BOUNDS-2))
 (2496 24 (:REWRITE |(< (logior x y) 0)|))
 (2452 2452 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (2220 444 (:REWRITE DEFAULT-MINUS))
 (1998 444 (:REWRITE |(- (* c x))|))
 (1800 30 (:REWRITE |(< x (+ c/d y))|))
 (1662 1662 (:REWRITE REDUCE-INTEGERP-+))
 (1662 1662 (:META META-INTEGERP-CORRECT))
 (1368 143 (:REWRITE |(* x (+ y z))|))
 (1110 222 (:REWRITE FLOOR-ZERO . 2))
 (1110 222 (:REWRITE FLOOR-X-Y-=-1 . 3))
 (1110 222 (:REWRITE FLOOR-X-Y-=--1 . 3))
 (1062 222 (:REWRITE FLOOR-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (1062 222 (:REWRITE |(floor (* x (/ y)) z) not rewriting-goal-literal|))
 (981 150 (:REWRITE RATIONALP-X))
 (842 222 (:REWRITE FLOOR-CANCEL-*-CONST))
 (816 104 (:REWRITE ACL2-NUMBERP-X))
 (757 757 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (724 248 (:REWRITE |(+ 0 x)|))
 (684 143 (:REWRITE |(+ c (+ d x))|))
 (595 595 (:TYPE-PRESCRIPTION ABS))
 (461 461 (:REWRITE LOGAND-CONSTANT-MASK))
 (410 410 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (344 344 (:REWRITE |(< 0 (* x y))|))
 (297 297 (:REWRITE DEFAULT-FLOOR-2))
 (293 293 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (293 293 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (293 293 (:REWRITE |(< 0 (/ x))|))
 (270 222 (:REWRITE FLOOR-CANCEL-*-REWRITING-GOAL-LITERAL))
 (270 222 (:REWRITE |(floor (* x (/ y)) z) rewriting-goal-literal|))
 (252 7 (:REWRITE FLOOR-NEGATIVE . 4))
 (222 222 (:REWRITE |(floor x (- y))| . 2))
 (222 222 (:REWRITE |(floor x (- y))| . 1))
 (222 222 (:REWRITE |(floor x (* y (/ z))) rewriting-goal-literal|))
 (222 222 (:REWRITE |(floor x (* y (/ z))) not rewriting-goal-literal|))
 (222 222 (:REWRITE |(floor (- x) y)| . 2))
 (222 222 (:REWRITE |(floor (- x) y)| . 1))
 (216 6 (:REWRITE FLOOR-NONNEGATIVE . 3))
 (210 105 (:REWRITE BUBBLE-DOWN-+-MATCH-1))
 (168 159 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (159 159 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (159 159 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (159 159 (:REWRITE |(equal c (/ x))|))
 (159 159 (:REWRITE |(equal c (- x))|))
 (159 159 (:REWRITE |(equal (/ x) c)|))
 (159 159 (:REWRITE |(equal (/ x) (/ y))|))
 (159 159 (:REWRITE |(equal (- x) c)|))
 (159 159 (:REWRITE |(equal (- x) (- y))|))
 (150 150 (:REWRITE RATIONALP-MINUS-X))
 (142 142 (:REWRITE REDUCE-RATIONALP-+))
 (142 142 (:META META-RATIONALP-CORRECT))
 (105 105 (:REWRITE |(+ x (- x))|))
 (53 53 (:REWRITE ZIP-OPEN))
 (21 21 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (12 6 (:REWRITE |(logand (floor x 2) (floor y 2))| . 3))
 (12 6 (:REWRITE |(logand (floor x 2) (floor y 2))| . 2))
 (10 4 (:REWRITE |(logand (floor x 2) (floor y 2))| . 7))
 (10 4 (:REWRITE |(logand (floor x 2) (floor y 2))| . 4))
 (9 9 (:REWRITE |(equal (+ (- c) x) y)|))
 (8 8 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (7 7 (:REWRITE FLOOR-NEGATIVE . 3))
 (7 7 (:REWRITE FLOOR-NEGATIVE . 2))
 (7 7 (:REWRITE FLOOR-NEGATIVE . 1))
 (6 6 (:REWRITE FLOOR-NONNEGATIVE . 2))
 (6 6 (:REWRITE FLOOR-NONNEGATIVE . 1))
 (4 4 (:REWRITE |(equal (* x y) 0)|))
 )
(|(logand (logior x y) z)|
 (1020 6 (:LINEAR LOGIOR-BOUNDS-POS . 2))
 (1020 6 (:LINEAR LOGIOR-BOUNDS-POS . 1))
 (1004 16 (:REWRITE |(< (logand x y) 0)|))
 (618 6 (:LINEAR LOGIOR-BOUNDS-NEG . 2))
 (542 6 (:LINEAR LOGIOR-BOUNDS-NEG . 1))
 (404 20 (:LINEAR LOGAND-BOUNDS-POS . 2))
 (404 20 (:LINEAR LOGAND-BOUNDS-POS . 1))
 (392 20 (:LINEAR LOGAND-BOUNDS-NEG . 2))
 (392 20 (:LINEAR LOGAND-BOUNDS-NEG . 1))
 (273 273 (:TYPE-PRESCRIPTION |(< (logand x y) 0)| . 2))
 (273 273 (:TYPE-PRESCRIPTION |(< (logand x y) 0)| . 1))
 (100 100 (:REWRITE THE-FLOOR-BELOW))
 (100 100 (:REWRITE THE-FLOOR-ABOVE))
 (100 84 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (100 84 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
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 )
(|(logand c (ash (mod x d) e)) = (ash (mod x d) e)|
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 (1975 1975 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (1975 1975 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (1975 1975 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (1975 1975 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (1975 1975 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
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 (1 1 (:REWRITE |(+ 0 x)|))
 )
(CROCK-4
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 (29 29 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (29 29 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (29 29 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (29 29 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
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 (11 2 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
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 (2 2 (:REWRITE THE-FLOOR-ABOVE))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (2 2 (:REWRITE SIMPLIFY-SUMS-EQUAL))
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 (2 2 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
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 (1 1 (:REWRITE DEFAULT-ASH-1))
 )
(|(logand c (ash (mod x d) e)) = 0|
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 (655 655 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
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 (334 334 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (334 334 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (334 334 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (334 334 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (334 334 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (334 334 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
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 (1 1 (:LINEAR EXPT->=-1-TWO))
 (1 1 (:LINEAR EXPT->-1-TWO))
 (1 1 (:LINEAR EXPT-<=-1-ONE))
 (1 1 (:LINEAR EXPT-<-1-ONE))
 )
(CROCK-1+
 (28 28 (:TYPE-PRESCRIPTION NATP-ASH))
 )
(CROCK-1-
 (28 28 (:TYPE-PRESCRIPTION NATP-ASH))
 )
(|(ash (logior x y) 1)|
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 (149 8 (:REWRITE DEFAULT-FLOOR-RATIO))
 (130 130 (:TYPE-PRESCRIPTION |(< 0 (logior x y))| . 1))
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 (130 130 (:TYPE-PRESCRIPTION |(< (logior x y) 0)| . 1))
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 (70 5 (:REWRITE |(* (if a b c) x)|))
 (66 62 (:REWRITE DEFAULT-LESS-THAN-2))
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 (36 36 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
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 (36 36 (:REWRITE CONSTANT-<-INTEGERP))
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 (23 3 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (22 22 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (10 10 (:REWRITE |(< 0 (* x y))|))
 (8 8 (:TYPE-PRESCRIPTION NATP))
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 (6 6 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
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 (6 6 (:REWRITE |(< 0 (/ x))|))
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 (3 3 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
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 (3 3 (:REWRITE |(equal c (/ x))|))
 (3 3 (:REWRITE |(equal c (- x))|))
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 (3 3 (:REWRITE |(equal (/ x) (/ y))|))
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 (1 1 (:REWRITE |(logior (* 2 x) (* 2 y))| . 5))
 (1 1 (:REWRITE |(logior (* 2 x) (* 2 y))| . 4))
 (1 1 (:REWRITE |(logior (* 2 x) (* 2 y))| . 3))
 )
(|(ash (logior x y) -1)|
 (1704 60 (:REWRITE |(< (+ c/d x) y)|))
 (1380 204 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (1352 28 (:LINEAR |(< (logior x y) (expt 2 n))|))
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 (523 523 (:TYPE-PRESCRIPTION |(< (logior x y) 0)| . 1))
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 (336 12 (:REWRITE |(< x (+ c/d y))|))
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 (240 240 (:REWRITE THE-FLOOR-ABOVE))
 (200 200 (:REWRITE DEFAULT-PLUS-1))
 (168 168 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (168 168 (:REWRITE |(< (* x y) 0)|))
 (152 132 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (152 132 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (144 36 (:REWRITE |(+ c (+ d x))|))
 (140 140 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (132 132 (:REWRITE SIMPLIFY-SUMS-<))
 (132 132 (:REWRITE REMOVE-STRICT-INEQUALITIES))
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 (132 132 (:REWRITE CONSTANT-<-INTEGERP))
 (132 132 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
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 (132 132 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
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 (132 132 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
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 (132 132 (:REWRITE |(< (- x) (- y))|))
 (128 128 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
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 (106 13 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (106 13 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (97 13 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (95 15 (:REWRITE |(* y x)|))
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 (78 78 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (78 78 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (78 78 (:REWRITE |(< (/ x) 0)|))
 (76 76 (:REWRITE REDUCE-INTEGERP-+))
 (76 76 (:REWRITE INTEGERP-MINUS-X))
 (76 76 (:META META-INTEGERP-CORRECT))
 (70 5 (:REWRITE |(* (if a b c) x)|))
 (47 12 (:REWRITE DEFAULT-FLOOR-1))
 (38 38 (:TYPE-PRESCRIPTION ABS))
 (36 36 (:REWRITE |(< 0 (* x y))|))
 (36 36 (:REWRITE |(+ 0 x)|))
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 (30 30 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (28 28 (:TYPE-PRESCRIPTION NATP))
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 (18 18 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (18 18 (:REWRITE |(< 0 (/ x))|))
 (15 13 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (13 13 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
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 (13 13 (:REWRITE |(equal (/ x) c)|))
 (13 13 (:REWRITE |(equal (/ x) (/ y))|))
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 (5 5 (:REWRITE DEFAULT-ASH-2))
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 )
(IND-HINT
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 (20 20 (:REWRITE THE-FLOOR-BELOW))
 (20 20 (:REWRITE THE-FLOOR-ABOVE))
 (20 20 (:REWRITE DEFAULT-LESS-THAN-2))
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 (16 16 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (16 16 (:REWRITE |(< (/ x) (/ y))|))
 (15 15 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (15 15 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (15 15 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
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 (15 15 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (15 15 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (15 15 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (15 15 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (13 13 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (13 13 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (13 13 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (13 13 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (13 13 (:REWRITE INTEGERP-<-CONSTANT))
 (13 13 (:REWRITE CONSTANT-<-INTEGERP))
 (10 10 (:REWRITE DEFAULT-MINUS))
 (9 9 (:REWRITE |(< (/ x) 0)|))
 (9 9 (:REWRITE |(< (* x y) 0)|))
 (8 8 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (8 8 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (4 4 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (4 4 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (4 4 (:REWRITE |(< 0 (/ x))|))
 (4 4 (:REWRITE |(< 0 (* x y))|))
 (4 4 (:REWRITE |(< (+ c/d x) y)|))
 (4 4 (:REWRITE |(< (+ (- c) x) y)|))
 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (2 2 (:REWRITE ZIP-OPEN))
 (1 1 (:REWRITE REDUCE-INTEGERP-+))
 (1 1 (:REWRITE INTEGERP-MINUS-X))
 (1 1 (:REWRITE |(< y (+ (- c) x))|))
 (1 1 (:REWRITE |(< x (+ c/d y))|))
 (1 1 (:META META-INTEGERP-CORRECT))
 )
(|(ash (logior x y) n)|
 (6024 64 (:REWRITE |(< (ash x n) y)|))
 (2432 18 (:LINEAR |(< (logior x y) (expt 2 n))|))
 (2332 18 (:LINEAR LOGIOR-BOUNDS-POS . 2))
 (2332 18 (:LINEAR LOGIOR-BOUNDS-POS . 1))
 (2332 18 (:DEFINITION NATP))
 (2256 18 (:LINEAR LOGIOR-BOUNDS-NEG . 2))
 (1386 1386 (:TYPE-PRESCRIPTION |(< 0 (logior x y))| . 1))
 (1386 1386 (:TYPE-PRESCRIPTION |(< (logior x y) 0)| . 2))
 (1386 1386 (:TYPE-PRESCRIPTION |(< (logior x y) 0)| . 1))
 (1024 32 (:REWRITE DEFAULT-FLOOR-RATIO))
 (770 18 (:LINEAR LOGIOR-BOUNDS-NEG . 1))
 (640 40 (:TYPE-PRESCRIPTION FLOOR-ZERO . 4))
 (520 40 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 1))
 (520 40 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 1))
 (400 400 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (400 400 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (400 400 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (400 400 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (400 400 (:TYPE-PRESCRIPTION INTEGERP-/-EXPT-2))
 (400 400 (:TYPE-PRESCRIPTION INTEGERP-/-EXPT-1))
 (325 149 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (320 32 (:REWRITE DEFAULT-TIMES-2))
 (320 32 (:REWRITE DEFAULT-FLOOR-2))
 (320 32 (:REWRITE DEFAULT-DIVIDE))
 (295 151 (:REWRITE DEFAULT-LESS-THAN-1))
 (288 32 (:REWRITE |(/ (expt x n))|))
 (280 40 (:TYPE-PRESCRIPTION FLOOR-ZERO . 3))
 (280 40 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 3))
 (280 40 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 2))
 (280 40 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 3))
 (280 40 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 2))
 (229 149 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (213 151 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (183 151 (:REWRITE DEFAULT-LESS-THAN-2))
 (168 12 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (168 12 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (168 12 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (151 151 (:REWRITE THE-FLOOR-BELOW))
 (151 151 (:REWRITE THE-FLOOR-ABOVE))
 (151 151 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (151 151 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (149 149 (:REWRITE SIMPLIFY-SUMS-<))
 (149 149 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (149 149 (:REWRITE INTEGERP-<-CONSTANT))
 (149 149 (:REWRITE CONSTANT-<-INTEGERP))
 (149 149 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (149 149 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (149 149 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (149 149 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (149 149 (:REWRITE |(< c (- x))|))
 (149 149 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (149 149 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (149 149 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (149 149 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (149 149 (:REWRITE |(< (/ x) (/ y))|))
 (149 149 (:REWRITE |(< (- x) c)|))
 (149 149 (:REWRITE |(< (- x) (- y))|))
 (136 136 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (136 136 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (136 136 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (136 136 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (136 136 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (136 136 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (136 136 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (136 136 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (136 136 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (134 134 (:REWRITE DEFAULT-PLUS-2))
 (134 134 (:REWRITE DEFAULT-PLUS-1))
 (124 124 (:REWRITE DEFAULT-ASH-2))
 (118 118 (:REWRITE REDUCE-INTEGERP-+))
 (118 118 (:REWRITE INTEGERP-MINUS-X))
 (118 118 (:META META-INTEGERP-CORRECT))
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 (117 117 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (117 117 (:REWRITE |(< (/ x) 0)|))
 (117 117 (:REWRITE |(< (* x y) 0)|))
 (103 103 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (103 103 (:REWRITE NORMALIZE-ADDENDS))
 (96 16 (:REWRITE |(- (+ x y))|))
 (77 77 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (64 64 (:REWRITE DEFAULT-EXPT-2))
 (64 64 (:REWRITE DEFAULT-EXPT-1))
 (64 64 (:REWRITE |(expt 1/c n)|))
 (64 64 (:REWRITE |(expt (- x) n)|))
 (48 48 (:REWRITE DEFAULT-MINUS))
 (32 32 (:REWRITE DEFAULT-TIMES-1))
 (32 32 (:REWRITE DEFAULT-FLOOR-1))
 (32 32 (:REWRITE |(floor 0 y)|))
 (32 32 (:REWRITE |(< 0 (* x y))|))
 (32 32 (:REWRITE |(* 0 x)|))
 (30 30 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (30 30 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (30 30 (:REWRITE |(< 0 (/ x))|))
 (18 18 (:TYPE-PRESCRIPTION NATP))
 (12 12 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (12 12 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (12 12 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (12 12 (:REWRITE |(equal c (/ x))|))
 (12 12 (:REWRITE |(equal c (- x))|))
 (12 12 (:REWRITE |(equal (/ x) c)|))
 (12 12 (:REWRITE |(equal (/ x) (/ y))|))
 (12 12 (:REWRITE |(equal (- x) c)|))
 (12 12 (:REWRITE |(equal (- x) (- y))|))
 (2 2 (:REWRITE |(< x (+ c/d y))|))
 (1 1 (:REWRITE ZIP-OPEN))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 )
(|(mod (logior x y) c)|
 (6042 56 (:LINEAR LOGIOR-BOUNDS-NEG . 1))
 (4100 24 (:REWRITE CANCEL-MOD-+))
 (3395 24 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (2715 24 (:REWRITE MOD-X-Y-=-X . 4))
 (2427 24 (:REWRITE MOD-ZERO . 3))
 (2055 175 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (2031 175 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (2031 175 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (1876 1876 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (1876 1876 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (1876 1876 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (1876 1876 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (1876 1876 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (1876 1876 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (1876 1876 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (1774 24 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (1644 24 (:REWRITE MOD-X-Y-=-X . 3))
 (1629 9 (:REWRITE |(< 0 (logior x y))|))
 (1278 24 (:REWRITE DEFAULT-MOD-RATIO))
 (1236 136 (:REWRITE DEFAULT-TIMES-2))
 (1182 24 (:REWRITE |(integerp (- x))|))
 (1172 24 (:REWRITE MOD-ZERO . 4))
 (1137 175 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (1113 1113 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (1113 1113 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (1113 1113 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (1080 18 (:REWRITE |(< (logior x y) 0)|))
 (942 24 (:REWRITE |(* (- x) y)|))
 (937 937 (:TYPE-PRESCRIPTION INTEGERP-/-EXPT-2))
 (937 937 (:TYPE-PRESCRIPTION INTEGERP-/-EXPT-1))
 (916 24 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (916 24 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (810 81 (:REWRITE DEFAULT-DIVIDE))
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 (700 24 (:REWRITE MOD-X-Y-=-X . 2))
 (658 658 (:TYPE-PRESCRIPTION |(< 0 (logior x y))| . 1))
 (658 658 (:TYPE-PRESCRIPTION |(< (logior x y) 0)| . 2))
 (658 658 (:TYPE-PRESCRIPTION |(< (logior x y) 0)| . 1))
 (650 24 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (650 24 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (620 136 (:REWRITE DEFAULT-TIMES-1))
 (575 181 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (575 181 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (558 31 (:REWRITE |(* y x)|))
 (530 181 (:REWRITE DEFAULT-LESS-THAN-2))
 (492 82 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A-EXPT))
 (486 81 (:REWRITE |(/ (expt x n))|))
 (482 56 (:LINEAR LOGIOR-BOUNDS-NEG . 2))
 (467 105 (:REWRITE DEFAULT-MINUS))
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 (414 24 (:REWRITE MOD-CANCEL-*-CONST))
 (402 64 (:LINEAR |(< (logior x y) (expt 2 n))|))
 (374 24 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (374 24 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (374 24 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
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 (243 9 (:REWRITE |(equal (logior x y) 0)|))
 (240 24 (:REWRITE DEFAULT-MOD-2))
 (226 181 (:REWRITE DEFAULT-LESS-THAN-1))
 (208 208 (:REWRITE THE-FLOOR-BELOW))
 (208 208 (:REWRITE THE-FLOOR-ABOVE))
 (194 2 (:REWRITE MOD-POSITIVE . 3))
 (181 181 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (181 181 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (181 181 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
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 (181 181 (:REWRITE |(< (- x) (- y))|))
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 (108 108 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
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 (108 108 (:REWRITE |(< (* x y) 0)|))
 (108 8 (:LINEAR EXPT-X->=-X))
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 (89 89 (:REWRITE DEFAULT-EXPT-1))
 (89 89 (:REWRITE |(expt 1/c n)|))
 (89 89 (:REWRITE |(expt (- x) n)|))
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 (84 24 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (84 24 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (82 82 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A-EXPT))
 (82 82 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A-EXPT))
 (82 82 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A-EXPT))
 (81 81 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (74 24 (:REWRITE DEFAULT-MOD-1))
 (68 23 (:REWRITE ODD-EXPT-THM))
 (63 63 (:TYPE-PRESCRIPTION NATP))
 (60 60 (:REWRITE REDUCE-INTEGERP-+))
 (60 60 (:REWRITE INTEGERP-MINUS-X))
 (60 60 (:META META-INTEGERP-CORRECT))
 (48 48 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (48 48 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (42 42 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (42 42 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (42 42 (:REWRITE |(< 0 (/ x))|))
 (42 42 (:REWRITE |(< 0 (* x y))|))
 (32 32 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (32 32 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (32 32 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (32 32 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (32 32 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (32 32 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (32 32 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (32 32 (:REWRITE |(equal c (/ x))|))
 (32 32 (:REWRITE |(equal c (- x))|))
 (32 32 (:REWRITE |(equal (/ x) c)|))
 (32 32 (:REWRITE |(equal (/ x) (/ y))|))
 (32 32 (:REWRITE |(equal (- x) c)|))
 (32 32 (:REWRITE |(equal (- x) (- y))|))
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 (24 24 (:REWRITE |(- (* c x))|))
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 (16 16 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
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 (8 8 (:LINEAR EXPT-LINEAR-UPPER-<))
 (8 8 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (8 8 (:LINEAR EXPT-LINEAR-LOWER-<))
 (8 8 (:LINEAR EXPT->=-1-TWO))
 (8 8 (:LINEAR EXPT->-1-TWO))
 (8 8 (:LINEAR EXPT-<=-1-ONE))
 (8 8 (:LINEAR EXPT-<-1-ONE))
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 (2 2 (:REWRITE MOD-POSITIVE . 1))
 )
(BREAK-LOGXOR-APART
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 (513 513 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (513 513 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
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 (144 144 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (144 144 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (144 144 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (144 144 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (109 105 (:REWRITE DEFAULT-TIMES-1))
 (106 58 (:REWRITE DEFAULT-PLUS-1))
 (92 58 (:REWRITE DEFAULT-PLUS-2))
 (78 6 (:REWRITE DEFAULT-FLOOR-RATIO))
 (70 70 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (43 43 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (43 43 (:REWRITE NORMALIZE-ADDENDS))
 (40 40 (:REWRITE REDUCE-INTEGERP-+))
 (40 40 (:REWRITE INTEGERP-MINUS-X))
 (40 40 (:META META-INTEGERP-CORRECT))
 (36 8 (:REWRITE |(* y x)|))
 (22 2 (:REWRITE DEFAULT-MOD-RATIO))
 (20 20 (:REWRITE THE-FLOOR-BELOW))
 (20 20 (:REWRITE THE-FLOOR-ABOVE))
 (20 20 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (20 20 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (20 20 (:REWRITE SIMPLIFY-SUMS-<))
 (20 20 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (20 20 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (20 20 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (20 20 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (20 20 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (20 20 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (20 20 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (20 20 (:REWRITE INTEGERP-<-CONSTANT))
 (20 20 (:REWRITE DEFAULT-LESS-THAN-2))
 (20 20 (:REWRITE DEFAULT-LESS-THAN-1))
 (20 20 (:REWRITE CONSTANT-<-INTEGERP))
 (20 20 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (20 20 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (20 20 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (20 20 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (20 20 (:REWRITE |(< c (- x))|))
 (20 20 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (20 20 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (20 20 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (20 20 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (20 20 (:REWRITE |(< (/ x) 0)|))
 (20 20 (:REWRITE |(< (/ x) (/ y))|))
 (20 20 (:REWRITE |(< (- x) c)|))
 (20 20 (:REWRITE |(< (- x) (- y))|))
 (20 20 (:REWRITE |(< (* x y) 0)|))
 (19 6 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (19 6 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (19 6 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (10 6 (:REWRITE DEFAULT-FLOOR-1))
 (6 6 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (6 6 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (6 6 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (6 6 (:REWRITE DEFAULT-FLOOR-2))
 (6 6 (:REWRITE |(floor x 2)| . 2))
 (6 6 (:REWRITE |(equal c (/ x))|))
 (6 6 (:REWRITE |(equal c (- x))|))
 (6 6 (:REWRITE |(equal (/ x) c)|))
 (6 6 (:REWRITE |(equal (/ x) (/ y))|))
 (6 6 (:REWRITE |(equal (- x) c)|))
 (6 6 (:REWRITE |(equal (- x) (- y))|))
 (5 5 (:REWRITE |(equal (+ (- c) x) y)|))
 (4 4 (:REWRITE |(integerp (* 1/2 (logxor x y)))| . 5))
 (4 4 (:REWRITE |(integerp (* 1/2 (logxor x y)))| . 4))
 (4 4 (:REWRITE |(integerp (* 1/2 (logxor x y)))| . 3))
 (4 4 (:REWRITE |(integerp (* 1/2 (logxor x y)))| . 2))
 (2 2 (:REWRITE FOLD-CONSTS-IN-+))
 (2 2 (:REWRITE DEFAULT-MOD-2))
 (2 2 (:REWRITE DEFAULT-MOD-1))
 (2 2 (:REWRITE |(mod x 2)| . 2))
 )
(LOGXOR-GREATER-OR-EQUAL-TO-ZERO
 (812 812 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (812 812 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (812 812 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (812 812 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (408 408 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (408 408 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (408 408 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (166 14 (:TYPE-PRESCRIPTION FLOOR-ZERO . 2))
 (118 14 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 1))
 (118 14 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 1))
 (118 14 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 1))
 (110 10 (:REWRITE DEFAULT-FLOOR-RATIO))
 (97 50 (:REWRITE DEFAULT-LESS-THAN-1))
 (80 80 (:REWRITE DEFAULT-TIMES-2))
 (80 80 (:REWRITE DEFAULT-TIMES-1))
 (70 14 (:TYPE-PRESCRIPTION FLOOR-ZERO . 4))
 (70 14 (:TYPE-PRESCRIPTION FLOOR-ZERO . 3))
 (70 14 (:TYPE-PRESCRIPTION FLOOR-ZERO . 1))
 (70 14 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 3))
 (70 14 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 2))
 (70 14 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 3))
 (70 14 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 2))
 (70 14 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 3))
 (70 14 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 3))
 (70 14 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 2))
 (66 41 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (66 41 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (64 64 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (50 50 (:REWRITE THE-FLOOR-BELOW))
 (50 50 (:REWRITE THE-FLOOR-ABOVE))
 (50 50 (:REWRITE DEFAULT-LESS-THAN-2))
 (49 43 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (49 43 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (43 43 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (43 43 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (43 43 (:REWRITE INTEGERP-<-CONSTANT))
 (43 43 (:REWRITE CONSTANT-<-INTEGERP))
 (43 43 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (43 43 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (43 43 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (43 43 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (43 43 (:REWRITE |(< c (- x))|))
 (43 43 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (43 43 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (43 43 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (43 43 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
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 (43 43 (:REWRITE |(< (/ x) (/ y))|))
 (43 43 (:REWRITE |(< (- x) c)|))
 (43 43 (:REWRITE |(< (- x) (- y))|))
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 (41 41 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
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 (40 10 (:REWRITE |(* y x)|))
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 (20 20 (:REWRITE NORMALIZE-ADDENDS))
 (20 20 (:REWRITE DEFAULT-PLUS-1))
 (16 16 (:REWRITE ZP-OPEN))
 (12 12 (:TYPE-PRESCRIPTION ABS))
 (10 10 (:REWRITE DEFAULT-FLOOR-2))
 (10 10 (:REWRITE DEFAULT-FLOOR-1))
 (10 10 (:REWRITE |(floor x 2)| . 2))
 (10 2 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 1))
 (6 6 (:REWRITE |(< (+ c/d x) y)|))
 (6 6 (:REWRITE |(< (+ (- c) x) y)|))
 (6 6 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (4 4 (:REWRITE |(integerp (* 1/2 (logxor x y)))| . 5))
 (4 4 (:REWRITE |(integerp (* 1/2 (logxor x y)))| . 4))
 (4 4 (:REWRITE |(integerp (* 1/2 (logxor x y)))| . 3))
 (4 4 (:REWRITE |(integerp (* 1/2 (logxor x y)))| . 2))
 )
(|(< (logxor x y) (expt 2 n)) --- linear|
 (3398 3398 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (3398 3398 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (3398 3398 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
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 (2544 2544 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
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 (1106 1106 (:REWRITE THE-FLOOR-ABOVE))
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 (1081 1079 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
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 (902 794 (:REWRITE REMOVE-STRICT-INEQUALITIES))
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 (861 28 (:LINEAR EXPT-X->-X))
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 (794 794 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (794 794 (:REWRITE |(< (/ x) (/ y))|))
 (794 794 (:REWRITE |(< (- x) c)|))
 (794 794 (:REWRITE |(< (- x) (- y))|))
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 (532 532 (:REWRITE DEFAULT-EXPT-1))
 (532 532 (:REWRITE |(expt 1/c n)|))
 (532 532 (:REWRITE |(expt (- x) n)|))
 (490 98 (:TYPE-PRESCRIPTION FLOOR-ZERO . 4))
 (490 98 (:TYPE-PRESCRIPTION FLOOR-ZERO . 3))
 (490 98 (:TYPE-PRESCRIPTION FLOOR-ZERO . 1))
 (490 98 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 3))
 (490 98 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 2))
 (490 98 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 3))
 (490 98 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 2))
 (490 98 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 3))
 (490 98 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 3))
 (490 98 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 2))
 (407 28 (:LINEAR EXPT-<=-1-TWO))
 (366 34 (:REWRITE DEFAULT-FLOOR-RATIO))
 (224 224 (:REWRITE |(< 0 (* x y))|))
 (172 172 (:REWRITE |(<= (/ x) y) with (< x 0)|))
 (172 172 (:REWRITE |(<= (/ x) y) with (< 0 x)|))
 (172 172 (:REWRITE |(< x (/ y)) with (< y 0)|))
 (150 150 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (140 140 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (113 113 (:REWRITE |(< x (+ c/d y))|))
 (108 12 (:REWRITE ACL2-NUMBERP-X))
 (98 2 (:REWRITE EXPT-EXCEEDS-ANOTHER-BY-MORE-THAN-Y))
 (79 28 (:LINEAR EXPT-<-1-TWO))
 (77 77 (:REWRITE |(< (+ (- c) x) y)|))
 (67 67 (:REWRITE REDUCE-INTEGERP-+))
 (67 67 (:REWRITE INTEGERP-MINUS-X))
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 (60 12 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (60 12 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (60 12 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (60 12 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (56 56 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (56 56 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (56 56 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (56 56 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
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 (43 43 (:REWRITE DEFAULT-LOGIOR-2))
 (43 43 (:REWRITE DEFAULT-LOGIOR-1))
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 (40 40 (:REWRITE |(< (* x y) 0)|))
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 (36 36 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
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 (28 28 (:LINEAR EXPT-LINEAR-LOWER-<))
 (28 28 (:LINEAR EXPT->=-1-TWO))
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 (12 12 (:REWRITE REDUCE-RATIONALP-*))
 (12 12 (:REWRITE RATIONALP-MINUS-X))
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 (10 2 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 1))
 (6 6 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
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 (4 4 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
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 (4 4 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
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 (4 4 (:REWRITE |(mod x 2)| . 2))
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 (2 2 (:REWRITE |(equal (+ (- c) x) y)|))
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 )
(|(< (logxor x y) c)|
 (82 82 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (82 82 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
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 (82 82 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (82 82 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (82 82 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (82 82 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (31 1 (:LINEAR EXPT->=-1-ONE))
 (31 1 (:LINEAR EXPT-<=-1-TWO))
 (30 1 (:LINEAR EXPT->-1-ONE))
 (30 1 (:LINEAR EXPT-<-1-TWO))
 (26 1 (:LINEAR EXPT-X->=-X))
 (26 1 (:LINEAR EXPT-X->-X))
 (6 6 (:REWRITE THE-FLOOR-BELOW))
 (6 6 (:REWRITE THE-FLOOR-ABOVE))
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 (6 6 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
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(CROCK-1-
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(IND-HINT
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(|(ash (lognot x) (- n))|
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