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(HEURISTICX)
(FEATURECOUNT)
(COUNTFEATURES)
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(SOLVEPOLYGREATER0
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 (4 4 (:REWRITE >=ALL-MEMBER-HYPS))
 (4 4 (:REWRITE >-ALL-IS-GREATER-THAN-MEMBERS-HYPS))
 (3 1 (:REWRITE BODY-IMPLIES-POLYLESS-P))
 (3 1 (:REWRITE BODY-IMPLIES-POLYGREATER-P))
 )
(NORMALIZED-VARIABLEBOUND-P-SOLVEPOLYGREATER0
 (968 317 (:TYPE-PRESCRIPTION IMPLIES-NOT-INEQ-OP))
 (524 524 (:TYPE-PRESCRIPTION BODY-IMPLIES-EQ-OP-P))
 (498 186 (:TYPE-PRESCRIPTION IMPLIES-NOT-OP-P))
 (28 4 (:DEFINITION REMOVE-EQUAL))
 (20 20 (:TYPE-PRESCRIPTION GET-POLY-VARIABLES))
 (16 4 (:REWRITE SUBSET-P-UPPER-BOUND-BACKCHAINING))
 (16 4 (:REWRITE SUBSET-NOT-CONSP))
 (8 8 (:REWRITE DEFAULT-CDR))
 (8 8 (:REWRITE DEFAULT-CAR))
 (6 6 (:REWRITE DEFAULT-<-2))
 (6 6 (:REWRITE DEFAULT-<-1))
 (6 6 (:REWRITE >=ALL-MEMBER-HYPS))
 (6 6 (:REWRITE >-ALL-IS-GREATER-THAN-MEMBERS-HYPS))
 (5 5 (:REWRITE ENV-P-WHEN-NOT-CONSP))
 (4 4 (:TYPE-PRESCRIPTION SET-UPPER-BOUND-CTX_UNFIX_CHECK))
 (4 4 (:REWRITE SET-UPPER-BOUND-CTX_UNFIX_CHECK_REDUCTION_3))
 (4 4 (:REWRITE SET-UPPER-BOUND-CTX_REDUCTION))
 )
(BOUND-VARID-SOLVEPOLYGREATER0
 (99 9 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINEQUALITY-P))
 (96 29 (:TYPE-PRESCRIPTION BODY-IMPLIES-POLYLESS-P))
 (96 29 (:TYPE-PRESCRIPTION BODY-IMPLIES-POLYGREATER-P))
 (88 88 (:TYPE-PRESCRIPTION FIX-RELATION))
 (41 41 (:TYPE-PRESCRIPTION IMPLIES-NOT-LT-OP))
 (41 41 (:TYPE-PRESCRIPTION BODY-IMPLIES-LT-OP-P))
 (32 32 (:TYPE-PRESCRIPTION IMPLIES-NOT-GT-OP))
 (32 32 (:TYPE-PRESCRIPTION BODY-IMPLIES-GT-OP-P))
 (28 7 (:TYPE-PRESCRIPTION IMPLIES-NOT-INEQ-OP))
 (18 6 (:REWRITE RELATION-P-FIX-RELATION))
 (16 8 (:TYPE-PRESCRIPTION IMPLIES-VARIABLERELATION-P))
 (16 8 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINTERVAL-P))
 (14 14 (:TYPE-PRESCRIPTION BODY-IMPLIES-EQ-OP-P))
 (14 6 (:TYPE-PRESCRIPTION IMPLIES-NOT-OP-P))
 (6 6 (:REWRITE DEFAULT-<-2))
 (6 6 (:REWRITE DEFAULT-<-1))
 (6 6 (:REWRITE >=ALL-MEMBER-HYPS))
 (6 6 (:REWRITE >-ALL-IS-GREATER-THAN-MEMBERS-HYPS))
 (4 1 (:REWRITE MEMBERP-SET-UPPER-BOUND-BACKCHAINING))
 (4 1 (:REWRITE LIST::MEMBERP-OF-CDR-CHEAP))
 (4 1 (:REWRITE MEMBERP-MEMBER-UPPER-BOUND-BACKCHAINING-SUBSET))
 (4 1 (:REWRITE MEMBERP-MEMBER-UPPER-BOUND-BACKCHAINING-DIFFERENCE))
 (4 1 (:REWRITE LIST::MEMBERP-FROM-MEMBERP-OF-CDR-CHEAP))
 (2 2 (:TYPE-PRESCRIPTION MEMBERP-UPPER-BOUND-CTX_UNFIX_CHECK))
 (2 2 (:REWRITE MEMBERP-UPPER-BOUND-CTX_UNFIX_CHECK_REDUCTION_3))
 (2 2 (:REWRITE MEMBERP-UPPER-BOUND-CTX_REDUCTION))
 (2 1 (:REWRITE LIST::MEMBERP-OF-NON-CONSP-CHEAP))
 (1 1 (:TYPE-PRESCRIPTION SET-UPPER-BOUND-CTX_UNFIX_CHECK))
 (1 1 (:REWRITE SET-UPPER-BOUND-CTX_UNFIX_CHECK_REDUCTION_3))
 (1 1 (:REWRITE SET-UPPER-BOUND-CTX_REDUCTION))
 (1 1 (:REWRITE BAG::NON-MEMBERP-FROM-MEMBERP-OF-OTHER-CHEAP))
 (1 1 (:REWRITE BAG::MEMBERP-OF-REMOVE-BAG-MEANS-MEMBERP))
 (1 1 (:REWRITE BAG::MEMBERP-OF-REMOVE-ALL))
 (1 1 (:REWRITE BAG::MEMBERP-OF-REMOVE-1))
 (1 1 (:REWRITE GENSYM::MEMBERP-GENSYM-N-FORWARD-2))
 (1 1 (:REWRITE GENSYM::MEMBERP-GENSYM-LIST-FORWARD-2))
 (1 1 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINTNESS))
 (1 1 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINT-OF-CONS-TWO))
 (1 1 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINT-OF-CONS-ONE))
 (1 1 (:REWRITE LIST::MEMBERP-DISJOINT-NON-MEMBERP))
 )
(MEMBERP-UPPER-BOUND-BOUND-VARID-SOLVEPOLYGREATER0
 (146 146 (:TYPE-PRESCRIPTION FIX-RELATION))
 (99 9 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINEQUALITY-P))
 (96 29 (:TYPE-PRESCRIPTION BODY-IMPLIES-POLYLESS-P))
 (96 29 (:TYPE-PRESCRIPTION BODY-IMPLIES-POLYGREATER-P))
 (41 41 (:TYPE-PRESCRIPTION IMPLIES-NOT-LT-OP))
 (41 41 (:TYPE-PRESCRIPTION BODY-IMPLIES-LT-OP-P))
 (36 12 (:REWRITE RELATION-P-FIX-RELATION))
 (32 32 (:TYPE-PRESCRIPTION IMPLIES-NOT-GT-OP))
 (32 32 (:TYPE-PRESCRIPTION BODY-IMPLIES-GT-OP-P))
 (28 7 (:TYPE-PRESCRIPTION IMPLIES-NOT-INEQ-OP))
 (16 8 (:TYPE-PRESCRIPTION IMPLIES-VARIABLERELATION-P))
 (16 8 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINTERVAL-P))
 (14 14 (:TYPE-PRESCRIPTION BODY-IMPLIES-EQ-OP-P))
 (14 6 (:TYPE-PRESCRIPTION IMPLIES-NOT-OP-P))
 (12 12 (:REWRITE DEFAULT-<-2))
 (12 12 (:REWRITE DEFAULT-<-1))
 (12 12 (:REWRITE >=ALL-MEMBER-HYPS))
 (12 12 (:REWRITE >-ALL-IS-GREATER-THAN-MEMBERS-HYPS))
 (9 9 (:REWRITE MEMBERP-UPPER-BOUND-PRED-CHAINING))
 )
(BOUND-VARID-SOLVEPOLYGREATER0-REWRITE
 (276 77 (:TYPE-PRESCRIPTION BODY-IMPLIES-POLYLESS-P))
 (276 77 (:TYPE-PRESCRIPTION BODY-IMPLIES-POLYGREATER-P))
 (143 13 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINEQUALITY-P))
 (139 139 (:TYPE-PRESCRIPTION IMPLIES-NOT-LT-OP))
 (139 139 (:TYPE-PRESCRIPTION BODY-IMPLIES-LT-OP-P))
 (116 29 (:TYPE-PRESCRIPTION IMPLIES-NOT-INEQ-OP))
 (104 104 (:TYPE-PRESCRIPTION IMPLIES-NOT-GT-OP))
 (104 104 (:TYPE-PRESCRIPTION BODY-IMPLIES-GT-OP-P))
 (66 66 (:TYPE-PRESCRIPTION BODY-IMPLIES-EQ-OP-P))
 (66 26 (:TYPE-PRESCRIPTION IMPLIES-NOT-OP-P))
 (12 6 (:TYPE-PRESCRIPTION IMPLIES-VARIABLERELATION-P))
 (12 6 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINTERVAL-P))
 (8 2 (:REWRITE >-ALL-UPPER-BOUND-BACKCHAINING))
 (2 2 (:TYPE-PRESCRIPTION SET-UPPER-BOUND-CTX_UNFIX_CHECK))
 (2 2 (:REWRITE SET-UPPER-BOUND-CTX_UNFIX_CHECK_REDUCTION_3))
 (2 2 (:REWRITE SET-UPPER-BOUND-CTX_REDUCTION))
 )
(BOUNDING-VARIABLES-SOLVEPOLYGREATER0
 (725 725 (:TYPE-PRESCRIPTION FIX-RELATION))
 (424 106 (:REWRITE >-ALL-UPPER-BOUND-BACKCHAINING))
 (404 74 (:DEFINITION REMOVE-EQUAL))
 (166 166 (:REWRITE DEFAULT-CAR))
 (147 84 (:REWRITE DEFAULT-<-1))
 (144 6 (:REWRITE REMOVE-EQUAL-COMMUTES))
 (134 84 (:REWRITE DEFAULT-<-2))
 (120 10 (:REWRITE >-ALL-GREATER-THAN-REMOVE-EQUAL))
 (118 118 (:REWRITE DEFAULT-CDR))
 (110 110 (:TYPE-PRESCRIPTION SET-UPPER-BOUND-CTX_UNFIX_CHECK))
 (110 110 (:REWRITE SET-UPPER-BOUND-CTX_UNFIX_CHECK_REDUCTION_3))
 (110 110 (:REWRITE SET-UPPER-BOUND-CTX_REDUCTION))
 (108 36 (:REWRITE RELATION-P-FIX-RELATION))
 (99 9 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINEQUALITY-P))
 (98 98 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (96 29 (:TYPE-PRESCRIPTION BODY-IMPLIES-POLYLESS-P))
 (96 29 (:TYPE-PRESCRIPTION BODY-IMPLIES-POLYGREATER-P))
 (70 70 (:REWRITE >=ALL-MEMBER-HYPS))
 (62 2 (:REWRITE >-ALL-IS-GREATER-THAN-MEMBERS))
 (42 6 (:REWRITE LIST::EQUAL-CAR-DIFFERENTIAL))
 (41 41 (:TYPE-PRESCRIPTION IMPLIES-NOT-LT-OP))
 (41 41 (:TYPE-PRESCRIPTION BODY-IMPLIES-LT-OP-P))
 (36 36 (:LINEAR >=ALL-REMOVE-EQUAL-IMPLICATION))
 (36 36 (:LINEAR >=ALL-MEMBER))
 (32 32 (:TYPE-PRESCRIPTION IMPLIES-NOT-GT-OP))
 (32 32 (:TYPE-PRESCRIPTION BODY-IMPLIES-GT-OP-P))
 (30 6 (:REWRITE LIST::MEMBERP-OF-CDR-CHEAP))
 (30 6 (:REWRITE LIST::MEMBERP-FROM-MEMBERP-OF-CDR-CHEAP))
 (28 10 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINTERVAL-P))
 (28 7 (:TYPE-PRESCRIPTION IMPLIES-NOT-INEQ-OP))
 (24 6 (:REWRITE MEMBERP-MEMBER-UPPER-BOUND-BACKCHAINING-SUBSET))
 (24 6 (:REWRITE MEMBERP-MEMBER-UPPER-BOUND-BACKCHAINING-DIFFERENCE))
 (18 1 (:REWRITE OPEN-BOUNDING-VARIABLES))
 (16 8 (:TYPE-PRESCRIPTION IMPLIES-VARIABLERELATION-P))
 (16 4 (:REWRITE MEMBERP-SET-UPPER-BOUND-BACKCHAINING))
 (14 14 (:TYPE-PRESCRIPTION BODY-IMPLIES-EQ-OP-P))
 (14 6 (:TYPE-PRESCRIPTION IMPLIES-NOT-OP-P))
 (12 12 (:TYPE-PRESCRIPTION MEMBERP-UPPER-BOUND-CTX_UNFIX_CHECK))
 (12 12 (:REWRITE MEMBERP-UPPER-BOUND-CTX_UNFIX_CHECK_REDUCTION_3))
 (12 12 (:REWRITE MEMBERP-UPPER-BOUND-CTX_REDUCTION))
 (10 10 (:REWRITE LEADING-VARIABLE-IS-LESS-THAN-VARID-IF-IN-POLY-VARIABLES))
 (8 4 (:REWRITE LIST::MEMBERP-OF-NON-CONSP-CHEAP))
 (6 6 (:REWRITE VARID-LISTP-REMOVE-EQUAL))
 (6 6 (:REWRITE BAG::MEMBERP-OF-REMOVE-BAG-MEANS-MEMBERP))
 (6 6 (:REWRITE BAG::MEMBERP-OF-REMOVE-ALL))
 (6 6 (:REWRITE BAG::MEMBERP-OF-REMOVE-1))
 (6 6 (:REWRITE LIST::CARS-MATCH-FROM-FIRSTN-FACT-2))
 (6 6 (:REWRITE LIST::CARS-MATCH-FROM-FIRSTN-FACT))
 (4 4 (:REWRITE BAG::NON-MEMBERP-FROM-MEMBERP-OF-OTHER-CHEAP))
 (4 4 (:REWRITE GENSYM::MEMBERP-GENSYM-N-FORWARD-2))
 (4 4 (:REWRITE GENSYM::MEMBERP-GENSYM-LIST-FORWARD-2))
 (4 4 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINTNESS))
 (4 4 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINT-OF-CONS-TWO))
 (4 4 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINT-OF-CONS-ONE))
 (4 4 (:REWRITE LIST::MEMBERP-DISJOINT-NON-MEMBERP))
 (4 2 (:REWRITE BAG::MEMBERP-CAR-WHEN-DISJOINT-CHEAP))
 (3 1 (:REWRITE BODY-IMPLIES-VARIABLEINTERVAL-P))
 (2 2 (:REWRITE VARID-LISTP-WHEN-NOT-CONSP))
 (1 1 (:REWRITE T-IMPLIES-VARID-LISTP-BOUNDING-VARIABLES))
 )
(SET-UPPER-BOUND-VARIABLES-SOLVEPOLYGREATER0
 (237 237 (:TYPE-PRESCRIPTION FIX-RELATION))
 (99 9 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINEQUALITY-P))
 (96 29 (:TYPE-PRESCRIPTION BODY-IMPLIES-POLYLESS-P))
 (96 29 (:TYPE-PRESCRIPTION BODY-IMPLIES-POLYGREATER-P))
 (60 24 (:REWRITE SUBSET-P-UPPER-BOUND-BACKCHAINING))
 (60 24 (:REWRITE SUBSET-NOT-CONSP))
 (48 16 (:REWRITE RELATION-P-FIX-RELATION))
 (41 41 (:TYPE-PRESCRIPTION IMPLIES-NOT-LT-OP))
 (41 41 (:TYPE-PRESCRIPTION BODY-IMPLIES-LT-OP-P))
 (32 32 (:TYPE-PRESCRIPTION IMPLIES-NOT-GT-OP))
 (32 32 (:TYPE-PRESCRIPTION BODY-IMPLIES-GT-OP-P))
 (28 10 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINTERVAL-P))
 (28 7 (:TYPE-PRESCRIPTION IMPLIES-NOT-INEQ-OP))
 (28 4 (:DEFINITION REMOVE-EQUAL))
 (22 12 (:REWRITE DEFAULT-<-1))
 (20 20 (:REWRITE ADVISER::SUBSET-P-BY-MULTIPLICITY))
 (20 20 (:REWRITE SUBSET-P-BY-MULTIPLICITY))
 (19 2 (:REWRITE OPEN-BOUNDING-VARIABLES))
 (16 8 (:TYPE-PRESCRIPTION IMPLIES-VARIABLERELATION-P))
 (14 14 (:TYPE-PRESCRIPTION BODY-IMPLIES-EQ-OP-P))
 (14 6 (:TYPE-PRESCRIPTION IMPLIES-NOT-OP-P))
 (12 12 (:TYPE-PRESCRIPTION SET-UPPER-BOUND-CTX_UNFIX_CHECK))
 (12 12 (:REWRITE SET-UPPER-BOUND-CTX_UNFIX_CHECK_REDUCTION_3))
 (12 12 (:REWRITE DEFAULT-<-2))
 (12 12 (:REWRITE >=ALL-MEMBER-HYPS))
 (12 12 (:REWRITE >-ALL-IS-GREATER-THAN-MEMBERS-HYPS))
 (8 8 (:REWRITE DEFAULT-CDR))
 (8 8 (:REWRITE DEFAULT-CAR))
 (7 7 (:REWRITE SET-UPPER-BOUND-PRED-CHAINING))
 (3 1 (:REWRITE BODY-IMPLIES-VARIABLEINTERVAL-P))
 )
(SOLVE-MUL--1
 (50 21 (:REWRITE DEFAULT-TIMES-2))
 (40 16 (:REWRITE DEFAULT-MINUS))
 (36 2 (:DEFINITION GET-BINDING))
 (28 2 (:REWRITE WF-BINDING-FIX-WF-BINDING))
 (26 7 (:REWRITE DEFAULT-PLUS-2))
 (23 21 (:REWRITE DEFAULT-TIMES-1))
 (22 7 (:REWRITE DEFAULT-PLUS-1))
 (16 8 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (10 4 (:REWRITE POLY-EVAL-CONST-POLY))
 (9 4 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (9 4 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (8 8 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (8 8 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (8 8 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (8 8 (:TYPE-PRESCRIPTION BINDING-P))
 (8 8 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (8 4 (:TYPE-PRESCRIPTION BODY-IMPLIES-WF-BINDING-P))
 (8 2 (:REWRITE WF-BINDING-P-OF-CAR-WHEN-ENV-P))
 (7 7 (:REWRITE EVAL-POLY-CONST-DIFFERENCE))
 (6 6 (:TYPE-PRESCRIPTION NOT-CONSTP))
 (6 5 (:REWRITE |(equal (- x) (- y))|))
 (6 4 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (6 2 (:REWRITE BODY-IMPLIES-WF-BINDING-P))
 (5 5 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (5 5 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (5 5 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (5 5 (:REWRITE NORMALIZE-ADDENDS))
 (5 5 (:REWRITE DEFAULT-DIVIDE))
 (5 5 (:REWRITE |(equal c (/ x))|))
 (5 5 (:REWRITE |(equal c (- x))|))
 (5 5 (:REWRITE |(equal (/ x) c)|))
 (5 5 (:REWRITE |(equal (/ x) (/ y))|))
 (4 4 (:TYPE-PRESCRIPTION WF-BINDING-P))
 (4 4 (:TYPE-PRESCRIPTION ENV-P))
 (4 4 (:REWRITE-QUOTED-CONSTANT RFIX-UNDER-RATIONAL-EQUIV))
 (4 4 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (4 4 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (4 4 (:REWRITE |(- (* c x))|))
 (4 2 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (4 1 (:REWRITE RATIONALP-X))
 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (2 2 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (2 2 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (2 2 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (2 2 (:REWRITE-QUOTED-CONSTANT PAIR-LIST-FIX-UNDER-PAIR-LIST-EQUIV))
 (2 2 (:REWRITE VARID-FIX-VARID))
 (2 2 (:REWRITE ENV-P-WHEN-NOT-CONSP))
 (2 2 (:REWRITE DEFAULT-CDR))
 (2 2 (:REWRITE DEFAULT-CAR))
 (1 1 (:REWRITE REDUCE-RATIONALP-+))
 (1 1 (:REWRITE REDUCE-RATIONALP-*))
 (1 1 (:REWRITE REDUCE-INTEGERP-+))
 (1 1 (:REWRITE RATIONALP-MINUS-X))
 (1 1 (:REWRITE INTEGERP-MINUS-X))
 (1 1 (:META META-RATIONALP-CORRECT))
 (1 1 (:META META-INTEGERP-CORRECT))
 )
(SOLVEPOLYGREATER0-CONTRACT
 (1568 497 (:TYPE-PRESCRIPTION IMPLIES-NOT-INEQ-OP))
 (794 794 (:TYPE-PRESCRIPTION BODY-IMPLIES-EQ-OP-P))
 (722 266 (:TYPE-PRESCRIPTION IMPLIES-NOT-OP-P))
 (315 315 (:TYPE-PRESCRIPTION FIX-RELATION))
 (173 10 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (144 18 (:REWRITE ACL2-NUMBERP-X))
 (144 8 (:DEFINITION GET-BINDING))
 (112 8 (:REWRITE WF-BINDING-FIX-WF-BINDING))
 (95 17 (:REWRITE RATIONALP-X))
 (72 8 (:REWRITE RFIX-IDENTITY))
 (62 37 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (61 37 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (55 42 (:REWRITE DEFAULT-LESS-THAN-1))
 (54 42 (:REWRITE DEFAULT-LESS-THAN-2))
 (53 37 (:REWRITE SIMPLIFY-SUMS-<))
 (47 10 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (42 42 (:REWRITE THE-FLOOR-BELOW))
 (42 42 (:REWRITE THE-FLOOR-ABOVE))
 (41 41 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (41 41 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (41 41 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (41 41 (:REWRITE INTEGERP-<-CONSTANT))
 (41 41 (:REWRITE CONSTANT-<-INTEGERP))
 (41 41 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (41 41 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (41 41 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (41 41 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (41 41 (:REWRITE |(< c (- x))|))
 (41 41 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (41 41 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (41 41 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (41 41 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (41 41 (:REWRITE |(< (/ x) (/ y))|))
 (41 41 (:REWRITE |(< (- x) c)|))
 (41 41 (:REWRITE |(< (- x) (- y))|))
 (40 24 (:REWRITE POLY-EVAL-CONST-POLY))
 (32 32 (:TYPE-PRESCRIPTION RFIX))
 (32 32 (:TYPE-PRESCRIPTION BINDING-P))
 (32 16 (:TYPE-PRESCRIPTION BODY-IMPLIES-WF-BINDING-P))
 (32 8 (:REWRITE WF-BINDING-P-OF-CAR-WHEN-ENV-P))
 (29 29 (:REWRITE >=ALL-MEMBER-HYPS))
 (29 29 (:REWRITE >-ALL-IS-GREATER-THAN-MEMBERS-HYPS))
 (25 9 (:REWRITE RELATION-P-FIX-RELATION))
 (24 24 (:REWRITE EVAL-POLY-CONST-DIFFERENCE))
 (24 8 (:REWRITE BODY-IMPLIES-WF-BINDING-P))
 (17 17 (:REWRITE REDUCE-RATIONALP-+))
 (17 17 (:REWRITE REDUCE-RATIONALP-*))
 (17 17 (:REWRITE REDUCE-INTEGERP-+))
 (17 17 (:REWRITE RATIONALP-MINUS-X))
 (17 17 (:REWRITE INTEGERP-MINUS-X))
 (17 17 (:REWRITE |(< (/ x) 0)|))
 (17 17 (:REWRITE |(< (* x y) 0)|))
 (17 17 (:META META-RATIONALP-CORRECT))
 (17 17 (:META META-INTEGERP-CORRECT))
 (17 11 (:REWRITE EVAL-INEQ-POLYINTERVALP))
 (16 16 (:TYPE-PRESCRIPTION WF-BINDING-P))
 (16 16 (:TYPE-PRESCRIPTION ENV-P))
 (16 16 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (16 16 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (16 16 (:REWRITE |(< 0 (/ x))|))
 (16 16 (:REWRITE |(< 0 (* x y))|))
 (13 13 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (13 13 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (11 10 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (10 10 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (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))|))
 (8 8 (:REWRITE VARID-FIX-VARID))
 (8 8 (:REWRITE ENV-P-WHEN-NOT-CONSP))
 (8 8 (:REWRITE DEFAULT-CDR))
 (8 8 (:REWRITE DEFAULT-CAR))
 )
(SOLVEPOLYLESS0)
(RELATION-P-POLY-P-ENV-P-IMPLIES-VARIABLEINEQUALITY-P-SOLVEPOLYLESS0
 (1076 158 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINEQUALITY-P))
 (456 184 (:TYPE-PRESCRIPTION IMPLIES-NOT-OP-P))
 (168 28 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLERELATION-P))
 (163 3 (:REWRITE BODY-IMPLIES-VARIABLEINEQUALITY-P))
 (53 1 (:REWRITE VARIABLEGREATER-FROM-VARIABLEINEQUALITY))
 (46 7 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (40 8 (:REWRITE ACL2-NUMBERP-X))
 (37 1 (:REWRITE VARIABLELESS-FROM-VARIABLEINEQUALITY))
 (16 4 (:REWRITE RATIONALP-X))
 (16 1 (:REWRITE BODY-IMPLIES-VARIABLELESS-P))
 (16 1 (:REWRITE BODY-IMPLIES-VARIABLEGREATER-P))
 (14 7 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (9 8 (:REWRITE |(equal (- x) (- y))|))
 (9 7 (:REWRITE DEFAULT-LESS-THAN-2))
 (8 8 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (8 8 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (8 8 (:REWRITE |(equal c (/ x))|))
 (8 8 (:REWRITE |(equal c (- x))|))
 (8 8 (:REWRITE |(equal (/ x) c)|))
 (8 8 (:REWRITE |(equal (/ x) (/ y))|))
 (8 7 (:REWRITE DEFAULT-LESS-THAN-1))
 (8 4 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (7 7 (:REWRITE THE-FLOOR-BELOW))
 (7 7 (:REWRITE THE-FLOOR-ABOVE))
 (7 7 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (7 7 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (6 6 (:REWRITE-QUOTED-CONSTANT RFIX-UNDER-RATIONAL-EQUIV))
 (6 4 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (6 4 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (5 5 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (5 5 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (5 5 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (5 5 (:REWRITE ENV-P-WHEN-NOT-CONSP))
 (5 5 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (5 5 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (5 5 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (5 5 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (5 5 (:REWRITE |(< c (- x))|))
 (5 5 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (5 5 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (5 5 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (5 5 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (5 5 (:REWRITE |(< (/ x) (/ y))|))
 (5 5 (:REWRITE |(< (- x) (- y))|))
 (5 3 (:REWRITE DEFAULT-MINUS))
 (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 SIMPLIFY-SUMS-<))
 (4 4 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (4 4 (:REWRITE REDUCE-RATIONALP-+))
 (4 4 (:REWRITE REDUCE-RATIONALP-*))
 (4 4 (:REWRITE REDUCE-INTEGERP-+))
 (4 4 (:REWRITE RATIONALP-MINUS-X))
 (4 4 (:REWRITE INTEGERP-MINUS-X))
 (4 4 (:REWRITE INTEGERP-<-CONSTANT))
 (4 4 (:REWRITE CONSTANT-<-INTEGERP))
 (4 4 (:REWRITE >=ALL-MEMBER-HYPS))
 (4 4 (:REWRITE >-ALL-IS-GREATER-THAN-MEMBERS-HYPS))
 (4 4 (:REWRITE |(< 0 (/ x))|))
 (4 4 (:REWRITE |(< 0 (* x y))|))
 (4 4 (:META META-RATIONALP-CORRECT))
 (4 4 (:META META-INTEGERP-CORRECT))
 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (3 1 (:REWRITE BODY-IMPLIES-POLYLESS-P))
 (3 1 (:REWRITE BODY-IMPLIES-POLYGREATER-P))
 (2 1 (:REWRITE DEFAULT-TIMES-2))
 (1 1 (:REWRITE DEFAULT-TIMES-1))
 (1 1 (:REWRITE |(< (/ x) 0)|))
 (1 1 (:REWRITE |(< (* x y) 0)|))
 (1 1 (:REWRITE |(* (- x) y)|))
 )
(SOLVEPOLYLESS0)
(T-T-T-IMPLIES-VARIABLEINEQUALITY-P-SOLVEPOLYLESS0
 (944 136 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINEQUALITY-P))
 (344 136 (:TYPE-PRESCRIPTION IMPLIES-NOT-OP-P))
 (163 3 (:REWRITE BODY-IMPLIES-VARIABLEINEQUALITY-P))
 (157 157 (:TYPE-PRESCRIPTION FIX-RELATION))
 (136 20 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLERELATION-P))
 (120 9 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (96 12 (:REWRITE ACL2-NUMBERP-X))
 (53 1 (:REWRITE VARIABLEGREATER-FROM-VARIABLEINEQUALITY))
 (42 6 (:REWRITE RATIONALP-X))
 (37 1 (:REWRITE VARIABLELESS-FROM-VARIABLEINEQUALITY))
 (36 9 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (18 6 (:REWRITE RELATION-P-FIX-RELATION))
 (16 1 (:REWRITE BODY-IMPLIES-VARIABLELESS-P))
 (16 1 (:REWRITE BODY-IMPLIES-VARIABLEGREATER-P))
 (11 10 (:REWRITE |(equal (- x) (- y))|))
 (10 10 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (10 10 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (10 10 (:REWRITE |(equal c (/ x))|))
 (10 10 (:REWRITE |(equal c (- x))|))
 (10 10 (:REWRITE |(equal (/ x) c)|))
 (10 10 (:REWRITE |(equal (/ x) (/ y))|))
 (9 9 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (9 9 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (9 7 (:REWRITE DEFAULT-LESS-THAN-2))
 (8 7 (:REWRITE DEFAULT-LESS-THAN-1))
 (8 4 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (7 7 (:REWRITE THE-FLOOR-BELOW))
 (7 7 (:REWRITE THE-FLOOR-ABOVE))
 (6 6 (:REWRITE-QUOTED-CONSTANT RFIX-UNDER-RATIONAL-EQUIV))
 (6 6 (:REWRITE REDUCE-RATIONALP-+))
 (6 6 (:REWRITE REDUCE-RATIONALP-*))
 (6 6 (:REWRITE REDUCE-INTEGERP-+))
 (6 6 (:REWRITE RATIONALP-MINUS-X))
 (6 6 (:REWRITE INTEGERP-MINUS-X))
 (6 6 (:META META-RATIONALP-CORRECT))
 (6 6 (:META META-INTEGERP-CORRECT))
 (6 4 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (6 4 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (5 5 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (5 5 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (5 5 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (5 5 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (5 5 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (5 5 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (5 5 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (5 5 (:REWRITE |(< c (- x))|))
 (5 5 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (5 5 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (5 5 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (5 5 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (5 5 (:REWRITE |(< (/ x) (/ y))|))
 (5 5 (:REWRITE |(< (- x) (- y))|))
 (5 3 (:REWRITE DEFAULT-MINUS))
 (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 SIMPLIFY-SUMS-<))
 (4 4 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (4 4 (:REWRITE INTEGERP-<-CONSTANT))
 (4 4 (:REWRITE CONSTANT-<-INTEGERP))
 (4 4 (:REWRITE >=ALL-MEMBER-HYPS))
 (4 4 (:REWRITE >-ALL-IS-GREATER-THAN-MEMBERS-HYPS))
 (4 4 (:REWRITE |(< 0 (/ x))|))
 (4 4 (:REWRITE |(< 0 (* x y))|))
 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (3 1 (:REWRITE BODY-IMPLIES-POLYLESS-P))
 (3 1 (:REWRITE BODY-IMPLIES-POLYGREATER-P))
 (2 1 (:REWRITE DEFAULT-TIMES-2))
 (1 1 (:REWRITE DEFAULT-TIMES-1))
 (1 1 (:REWRITE |(< (/ x) 0)|))
 (1 1 (:REWRITE |(< (* x y) 0)|))
 (1 1 (:REWRITE |(* (- x) y)|))
 )
(BOUNDING-VARIABLES-SOLVEPOLYLESS0
 (270 75 (:TYPE-PRESCRIPTION BODY-IMPLIES-POLYLESS-P))
 (270 75 (:TYPE-PRESCRIPTION BODY-IMPLIES-POLYGREATER-P))
 (135 135 (:TYPE-PRESCRIPTION IMPLIES-NOT-LT-OP))
 (135 135 (:TYPE-PRESCRIPTION BODY-IMPLIES-LT-OP-P))
 (132 12 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINEQUALITY-P))
 (108 27 (:TYPE-PRESCRIPTION IMPLIES-NOT-INEQ-OP))
 (108 12 (:REWRITE ACL2-NUMBERP-X))
 (102 102 (:TYPE-PRESCRIPTION IMPLIES-NOT-GT-OP))
 (102 102 (:TYPE-PRESCRIPTION BODY-IMPLIES-GT-OP-P))
 (60 60 (:TYPE-PRESCRIPTION BODY-IMPLIES-EQ-OP-P))
 (60 24 (:TYPE-PRESCRIPTION IMPLIES-NOT-OP-P))
 (48 12 (:REWRITE RATIONALP-X))
 (16 8 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINTERVAL-P))
 (16 4 (:REWRITE >-ALL-UPPER-BOUND-BACKCHAINING))
 (12 12 (:REWRITE THE-FLOOR-BELOW))
 (12 12 (:REWRITE THE-FLOOR-ABOVE))
 (12 12 (:REWRITE REDUCE-RATIONALP-+))
 (12 12 (:REWRITE REDUCE-RATIONALP-*))
 (12 12 (:REWRITE REDUCE-INTEGERP-+))
 (12 12 (:REWRITE RATIONALP-MINUS-X))
 (12 12 (:REWRITE INTEGERP-MINUS-X))
 (12 12 (:META META-RATIONALP-CORRECT))
 (12 12 (:META META-INTEGERP-CORRECT))
 (12 6 (:TYPE-PRESCRIPTION IMPLIES-VARIABLERELATION-P))
 (8 1 (:REWRITE OPEN-BOUNDING-VARIABLES))
 (6 6 (:REWRITE SIMPLIFY-SUMS-<))
 (6 6 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (6 6 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (6 6 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (6 6 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (6 6 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (6 6 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (6 6 (:REWRITE INTEGERP-<-CONSTANT))
 (6 6 (:REWRITE CONSTANT-<-INTEGERP))
 (6 6 (:REWRITE >-ALL-IS-GREATER-THAN-MEMBERS-HYPS))
 (6 6 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (6 6 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (6 6 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (6 6 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (6 6 (:REWRITE |(< c (- x))|))
 (6 6 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (6 6 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (6 6 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (6 6 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (6 6 (:REWRITE |(< (/ x) (/ y))|))
 (6 6 (:REWRITE |(< (- x) c)|))
 (6 6 (:REWRITE |(< (- x) (- y))|))
 (6 2 (:DEFINITION REMOVE-EQUAL))
 (4 4 (:TYPE-PRESCRIPTION SET-UPPER-BOUND-CTX_UNFIX_CHECK))
 (4 4 (:REWRITE SET-UPPER-BOUND-CTX_UNFIX_CHECK_REDUCTION_3))
 (4 4 (:REWRITE SET-UPPER-BOUND-CTX_REDUCTION))
 (4 4 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (3 3 (:REWRITE >=ALL-MEMBER-HYPS))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (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 DEFAULT-CDR))
 (2 2 (:REWRITE |(< 0 (/ x))|))
 (2 2 (:REWRITE |(< 0 (* x y))|))
 (2 2 (:REWRITE |(< (/ x) 0)|))
 (2 2 (:REWRITE |(< (* x y) 0)|))
 (2 2 (:LINEAR >=ALL-REMOVE-EQUAL-IMPLICATION))
 (2 2 (:LINEAR >=ALL-MEMBER))
 (1 1 (:REWRITE-QUOTED-CONSTANT RFIX-UNDER-RATIONAL-EQUIV))
 (1 1 (:REWRITE BODY-IMPLIES-VARIABLEINTERVAL-P))
 )
(BOUND-VARID-SOLVEPOLYLESS0
 (173 173 (:TYPE-PRESCRIPTION FIX-RELATION))
 (116 7 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (99 9 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINEQUALITY-P))
 (96 29 (:TYPE-PRESCRIPTION BODY-IMPLIES-POLYLESS-P))
 (96 29 (:TYPE-PRESCRIPTION BODY-IMPLIES-POLYGREATER-P))
 (96 12 (:REWRITE ACL2-NUMBERP-X))
 (42 6 (:REWRITE RATIONALP-X))
 (41 41 (:TYPE-PRESCRIPTION IMPLIES-NOT-LT-OP))
 (41 41 (:TYPE-PRESCRIPTION BODY-IMPLIES-LT-OP-P))
 (32 32 (:TYPE-PRESCRIPTION IMPLIES-NOT-GT-OP))
 (32 32 (:TYPE-PRESCRIPTION BODY-IMPLIES-GT-OP-P))
 (32 7 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (28 7 (:TYPE-PRESCRIPTION IMPLIES-NOT-INEQ-OP))
 (18 6 (:REWRITE RELATION-P-FIX-RELATION))
 (16 8 (:TYPE-PRESCRIPTION IMPLIES-VARIABLERELATION-P))
 (16 8 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINTERVAL-P))
 (14 14 (:TYPE-PRESCRIPTION BODY-IMPLIES-EQ-OP-P))
 (14 6 (:TYPE-PRESCRIPTION IMPLIES-NOT-OP-P))
 (10 9 (:REWRITE DEFAULT-LESS-THAN-1))
 (9 9 (:REWRITE THE-FLOOR-BELOW))
 (9 9 (:REWRITE THE-FLOOR-ABOVE))
 (9 9 (:REWRITE DEFAULT-LESS-THAN-2))
 (9 8 (:REWRITE |(equal (- x) (- y))|))
 (8 8 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (8 8 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (8 8 (:REWRITE |(equal c (/ x))|))
 (8 8 (:REWRITE |(equal c (- x))|))
 (8 8 (:REWRITE |(equal (/ x) c)|))
 (8 8 (:REWRITE |(equal (/ x) (/ y))|))
 (7 7 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (7 7 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (7 7 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (7 7 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (7 7 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (7 7 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (7 7 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (7 7 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (7 7 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (7 7 (:REWRITE |(< c (- x))|))
 (7 7 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (7 7 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (7 7 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (7 7 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (7 7 (:REWRITE |(< (/ x) (/ y))|))
 (7 7 (:REWRITE |(< (- x) (- y))|))
 (6 6 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (6 6 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (6 6 (:REWRITE SIMPLIFY-SUMS-<))
 (6 6 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (6 6 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (6 6 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (6 6 (:REWRITE REDUCE-RATIONALP-+))
 (6 6 (:REWRITE REDUCE-RATIONALP-*))
 (6 6 (:REWRITE REDUCE-INTEGERP-+))
 (6 6 (:REWRITE RATIONALP-MINUS-X))
 (6 6 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (6 6 (:REWRITE INTEGERP-MINUS-X))
 (6 6 (:REWRITE INTEGERP-<-CONSTANT))
 (6 6 (:REWRITE CONSTANT-<-INTEGERP))
 (6 6 (:REWRITE >=ALL-MEMBER-HYPS))
 (6 6 (:REWRITE >-ALL-IS-GREATER-THAN-MEMBERS-HYPS))
 (6 6 (:REWRITE |(< 0 (/ x))|))
 (6 6 (:REWRITE |(< 0 (* x y))|))
 (6 6 (:META META-RATIONALP-CORRECT))
 (6 6 (:META META-INTEGERP-CORRECT))
 (5 3 (:REWRITE DEFAULT-MINUS))
 (4 1 (:REWRITE MEMBERP-SET-UPPER-BOUND-BACKCHAINING))
 (4 1 (:REWRITE LIST::MEMBERP-OF-CDR-CHEAP))
 (4 1 (:REWRITE MEMBERP-MEMBER-UPPER-BOUND-BACKCHAINING-SUBSET))
 (4 1 (:REWRITE MEMBERP-MEMBER-UPPER-BOUND-BACKCHAINING-DIFFERENCE))
 (4 1 (:REWRITE LIST::MEMBERP-FROM-MEMBERP-OF-CDR-CHEAP))
 (2 2 (:TYPE-PRESCRIPTION MEMBERP-UPPER-BOUND-CTX_UNFIX_CHECK))
 (2 2 (:REWRITE-QUOTED-CONSTANT RFIX-UNDER-RATIONAL-EQUIV))
 (2 2 (:REWRITE MEMBERP-UPPER-BOUND-CTX_UNFIX_CHECK_REDUCTION_3))
 (2 2 (:REWRITE MEMBERP-UPPER-BOUND-CTX_REDUCTION))
 (2 1 (:REWRITE LIST::MEMBERP-OF-NON-CONSP-CHEAP))
 (2 1 (:REWRITE DEFAULT-TIMES-2))
 (1 1 (:TYPE-PRESCRIPTION SET-UPPER-BOUND-CTX_UNFIX_CHECK))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (1 1 (:REWRITE SET-UPPER-BOUND-CTX_UNFIX_CHECK_REDUCTION_3))
 (1 1 (:REWRITE SET-UPPER-BOUND-CTX_REDUCTION))
 (1 1 (:REWRITE BAG::NON-MEMBERP-FROM-MEMBERP-OF-OTHER-CHEAP))
 (1 1 (:REWRITE BAG::MEMBERP-OF-REMOVE-BAG-MEANS-MEMBERP))
 (1 1 (:REWRITE BAG::MEMBERP-OF-REMOVE-ALL))
 (1 1 (:REWRITE BAG::MEMBERP-OF-REMOVE-1))
 (1 1 (:REWRITE GENSYM::MEMBERP-GENSYM-N-FORWARD-2))
 (1 1 (:REWRITE GENSYM::MEMBERP-GENSYM-LIST-FORWARD-2))
 (1 1 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINTNESS))
 (1 1 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINT-OF-CONS-TWO))
 (1 1 (:REWRITE BAG::MEMBERP-FALSE-FROM-DISJOINT-OF-CONS-ONE))
 (1 1 (:REWRITE LIST::MEMBERP-DISJOINT-NON-MEMBERP))
 (1 1 (:REWRITE DEFAULT-TIMES-1))
 (1 1 (:REWRITE |(< (/ x) 0)|))
 (1 1 (:REWRITE |(< (* x y) 0)|))
 (1 1 (:REWRITE |(* (- x) y)|))
 )
(MEMBERP-UPPER-BOUND-BOUND-VARID-SOLVEPOLYLESS0
 (303 303 (:TYPE-PRESCRIPTION FIX-RELATION))
 (282 19 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (247 39 (:REWRITE ACL2-NUMBERP-X))
 (104 17 (:REWRITE RATIONALP-X))
 (99 9 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINEQUALITY-P))
 (96 29 (:TYPE-PRESCRIPTION BODY-IMPLIES-POLYLESS-P))
 (96 29 (:TYPE-PRESCRIPTION BODY-IMPLIES-POLYGREATER-P))
 (74 19 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (41 41 (:TYPE-PRESCRIPTION IMPLIES-NOT-LT-OP))
 (41 41 (:TYPE-PRESCRIPTION BODY-IMPLIES-LT-OP-P))
 (36 12 (:REWRITE RELATION-P-FIX-RELATION))
 (32 32 (:TYPE-PRESCRIPTION IMPLIES-NOT-GT-OP))
 (32 32 (:TYPE-PRESCRIPTION BODY-IMPLIES-GT-OP-P))
 (28 7 (:TYPE-PRESCRIPTION IMPLIES-NOT-INEQ-OP))
 (24 19 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (23 21 (:REWRITE |(equal (- x) (- y))|))
 (21 21 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (21 21 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (21 21 (:REWRITE |(equal c (/ x))|))
 (21 21 (:REWRITE |(equal c (- x))|))
 (21 21 (:REWRITE |(equal (/ x) c)|))
 (21 21 (:REWRITE |(equal (/ x) (/ y))|))
 (20 18 (:REWRITE DEFAULT-LESS-THAN-1))
 (19 19 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (18 18 (:REWRITE THE-FLOOR-BELOW))
 (18 18 (:REWRITE THE-FLOOR-ABOVE))
 (18 18 (:REWRITE DEFAULT-LESS-THAN-2))
 (17 17 (:REWRITE REDUCE-RATIONALP-+))
 (17 17 (:REWRITE REDUCE-RATIONALP-*))
 (17 17 (:REWRITE REDUCE-INTEGERP-+))
 (17 17 (:REWRITE RATIONALP-MINUS-X))
 (17 17 (:REWRITE INTEGERP-MINUS-X))
 (17 17 (:META META-RATIONALP-CORRECT))
 (17 17 (:META META-INTEGERP-CORRECT))
 (16 8 (:TYPE-PRESCRIPTION IMPLIES-VARIABLERELATION-P))
 (16 8 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINTERVAL-P))
 (14 14 (:TYPE-PRESCRIPTION BODY-IMPLIES-EQ-OP-P))
 (14 14 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (14 14 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (14 14 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (14 14 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (14 14 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (14 14 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (14 14 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (14 14 (:REWRITE |(< c (- x))|))
 (14 14 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (14 14 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (14 14 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (14 14 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (14 14 (:REWRITE |(< (/ x) (/ y))|))
 (14 14 (:REWRITE |(< (- x) (- y))|))
 (14 6 (:TYPE-PRESCRIPTION IMPLIES-NOT-OP-P))
 (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 SIMPLIFY-SUMS-<))
 (12 12 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (12 12 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (12 12 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (12 12 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (12 12 (:REWRITE INTEGERP-<-CONSTANT))
 (12 12 (:REWRITE CONSTANT-<-INTEGERP))
 (12 12 (:REWRITE >=ALL-MEMBER-HYPS))
 (12 12 (:REWRITE >-ALL-IS-GREATER-THAN-MEMBERS-HYPS))
 (12 12 (:REWRITE |(< 0 (/ x))|))
 (12 12 (:REWRITE |(< 0 (* x y))|))
 (10 6 (:REWRITE DEFAULT-MINUS))
 (9 9 (:REWRITE MEMBERP-UPPER-BOUND-PRED-CHAINING))
 (4 4 (:REWRITE-QUOTED-CONSTANT RFIX-UNDER-RATIONAL-EQUIV))
 (4 2 (:REWRITE DEFAULT-TIMES-2))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (2 2 (:REWRITE DEFAULT-TIMES-1))
 (2 2 (:REWRITE |(< (/ x) 0)|))
 (2 2 (:REWRITE |(< (* x y) 0)|))
 (2 2 (:REWRITE |(* (- x) y)|))
 )
(BOUND-VARID-SOLVEPOLYLESS0-REWRITE
 (276 77 (:TYPE-PRESCRIPTION BODY-IMPLIES-POLYLESS-P))
 (276 77 (:TYPE-PRESCRIPTION BODY-IMPLIES-POLYGREATER-P))
 (143 13 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINEQUALITY-P))
 (139 139 (:TYPE-PRESCRIPTION IMPLIES-NOT-LT-OP))
 (139 139 (:TYPE-PRESCRIPTION BODY-IMPLIES-LT-OP-P))
 (116 29 (:TYPE-PRESCRIPTION IMPLIES-NOT-INEQ-OP))
 (104 104 (:TYPE-PRESCRIPTION IMPLIES-NOT-GT-OP))
 (104 104 (:TYPE-PRESCRIPTION BODY-IMPLIES-GT-OP-P))
 (66 66 (:TYPE-PRESCRIPTION BODY-IMPLIES-EQ-OP-P))
 (66 26 (:TYPE-PRESCRIPTION IMPLIES-NOT-OP-P))
 (12 6 (:TYPE-PRESCRIPTION IMPLIES-VARIABLERELATION-P))
 (12 6 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINTERVAL-P))
 (8 2 (:REWRITE >-ALL-UPPER-BOUND-BACKCHAINING))
 (2 2 (:TYPE-PRESCRIPTION SET-UPPER-BOUND-CTX_UNFIX_CHECK))
 (2 2 (:REWRITE SET-UPPER-BOUND-CTX_UNFIX_CHECK_REDUCTION_3))
 (2 2 (:REWRITE SET-UPPER-BOUND-CTX_REDUCTION))
 (1 1 (:REWRITE THE-FLOOR-BELOW))
 (1 1 (:REWRITE THE-FLOOR-ABOVE))
 (1 1 (:REWRITE SIMPLIFY-SUMS-<))
 (1 1 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (1 1 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (1 1 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (1 1 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (1 1 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (1 1 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (1 1 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (1 1 (:REWRITE INTEGERP-<-CONSTANT))
 (1 1 (:REWRITE DEFAULT-LESS-THAN-2))
 (1 1 (:REWRITE DEFAULT-LESS-THAN-1))
 (1 1 (:REWRITE CONSTANT-<-INTEGERP))
 (1 1 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (1 1 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (1 1 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (1 1 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (1 1 (:REWRITE |(< c (- x))|))
 (1 1 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (1 1 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (1 1 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (1 1 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (1 1 (:REWRITE |(< (/ x) (/ y))|))
 (1 1 (:REWRITE |(< (- x) c)|))
 (1 1 (:REWRITE |(< (- x) (- y))|))
 )
(SET-UPPER-BOUND-VARIABLES-SOLVEPOLYLESS0
 (429 429 (:TYPE-PRESCRIPTION FIX-RELATION))
 (368 29 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (311 47 (:REWRITE ACL2-NUMBERP-X))
 (132 21 (:REWRITE RATIONALP-X))
 (120 4 (:DEFINITION REMOVE-EQUAL))
 (104 29 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (99 9 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINEQUALITY-P))
 (96 29 (:TYPE-PRESCRIPTION BODY-IMPLIES-POLYLESS-P))
 (96 29 (:TYPE-PRESCRIPTION BODY-IMPLIES-POLYGREATER-P))
 (60 24 (:REWRITE SUBSET-P-UPPER-BOUND-BACKCHAINING))
 (60 24 (:REWRITE SUBSET-NOT-CONSP))
 (48 16 (:REWRITE RELATION-P-FIX-RELATION))
 (41 41 (:TYPE-PRESCRIPTION IMPLIES-NOT-LT-OP))
 (41 41 (:TYPE-PRESCRIPTION BODY-IMPLIES-LT-OP-P))
 (35 33 (:REWRITE |(equal (- x) (- y))|))
 (34 29 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (33 33 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
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(BOUND-VARID-RESTRICTINEQUALITY
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(UPPER-BOUND-BOUND-VARID-LIST-RESTRICTINEQUALITY
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(UPPER-BOUND-BOUNDING-VARIABLES-RESTRICTINEQUALITY
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(CHOOSEBESTCOMPLEMENT-VARIABLELESS-VARIABLEINTERVAL)
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(CHOOSEBESTCOMPLEMENT-VARIABLELESS-VARIABLEINTERVAL
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(ANDTRUE-VARIABLELESS-VARIABLELESS)
(AND-AND-ENV-P-IMPLIES-VARIABLEBOUND-P-VARIABLEBOUND-LISTP-ANDTRUE-VARIABLELESS-VARIABLELESS
 (364 124 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEGREATER-P))
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(ANDTRUE-VARIABLELESS-VARIABLELESS
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(AND-AND-ENV-P-IMPLIES-NORMALIZED-VARIABLEBOUND-P-NORMALIZED-VARIABLEBOUND-LISTP-ANDTRUE-VARIABLELESS-VARIABLELESS
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(BOUND-VARID-LIST-ANDTRUE-VARIABLELESS-VARIABLELESS
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(UPPER-BOUND-ALL-BOUND-LIST-VARIABLESANDTRUE-VARIABLELESS-VARIABLELESS
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(BOUND-VARID-ANDTRUE-VARIABLELESS-VARIABLELESS
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(UPPER-BOUND-BOUND-VARID-LIST-ANDTRUE-VARIABLELESS-VARIABLELESS
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(UPPER-BOUND-BOUNDING-VARIABLES-ANDTRUE-VARIABLELESS-VARIABLELESS
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(ANDTRUE-VARIABLELESS-VARIABLELESS-INV2
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(CHOOSEBESTCOMPLEMENT-VARIABLEGREATER-VARIABLEINTERVAL)
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(CHOOSEBESTCOMPLEMENT-VARIABLEGREATER-VARIABLEINTERVAL
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(CHOOSEBESTCOMPLEMENT-VARIABLEINEQUALITY-VARIABLEINTERVAL
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(VARIABLEINEQUALITY-P-VARIABLEINTERVAL-P-IMPLIES-VARIABLEINEQUALITY-P-CHOOSEBESTCOMPLEMENT-VARIABLEINEQUALITY-VARIABLEINTERVAL
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(ANDTRUE-VARIABLEGREATER-VARIABLELESS)
(AND-AND-ENV-P-IMPLIES-VARIABLEBOUND-P-VARIABLEBOUND-LISTP-ANDTRUE-VARIABLEGREATER-VARIABLELESS
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(BOUND-VARID-LIST-ANDTRUE-VARIABLEGREATER-VARIABLELESS
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(UPPER-BOUND-BOUND-VARID-LIST-ANDTRUE-VARIABLEGREATER-VARIABLELESS
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(ANDTRUE-VARIABLEGREATER-VARIABLEGREATER)
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 (5 1 (:REWRITE SET-EQUIV-QUANT-APPEND-COMMUTES))
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 (2 1 (:REWRITE LIST::APPEND-OF-NON-CONSP-2))
 (1 1 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (1 1 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (1 1 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1 1 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
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 (1 1 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE DEFAULT-CAR))
 (1 1 (:REWRITE |(equal c (/ x))|))
 (1 1 (:REWRITE |(equal c (- x))|))
 (1 1 (:REWRITE |(equal (/ x) c)|))
 (1 1 (:REWRITE |(equal (/ x) (/ y))|))
 (1 1 (:REWRITE |(equal (- x) c)|))
 (1 1 (:REWRITE |(equal (- x) (- y))|))
 )
(UPPER-BOUND-ALL-BOUND-LIST-VARIABLESANDTRUE-VARIABLEGREATER-VARIABLEGREATER
 (789 322 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLELESS-P))
 (722 276 (:TYPE-PRESCRIPTION IMPLIES-NOT-INEQ-OP))
 (595 595 (:TYPE-PRESCRIPTION BODY-IMPLIES-EQ-OP-P))
 (556 192 (:TYPE-PRESCRIPTION IMPLIES-NOT-OP-P))
 (392 227 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINTERVAL-P))
 (348 178 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEEQUALITY-P))
 (242 242 (:TYPE-PRESCRIPTION IMPLIES-NOT-GT-OP))
 (206 4 (:REWRITE VARIABLEGREATER-FROM-VARIABLEINEQUALITY))
 (142 2 (:REWRITE BODY-IMPLIES-VARIABLEINEQUALITY-P))
 (85 5 (:DEFINITION ALL-BOUND-LIST-VARIABLES))
 (58 13 (:REWRITE OPEN-BOUNDING-VARIABLES))
 (55 5 (:DEFINITION ALL-BOUND-VARIABLES))
 (45 41 (:TYPE-PRESCRIPTION LIST::APPEND-CONSP-TYPE-TWO))
 (45 41 (:TYPE-PRESCRIPTION LIST::APPEND-CONSP-TYPE-ONE))
 (29 4 (:REWRITE SUBSET-NOT-CONSP))
 (22 4 (:REWRITE BODY-IMPLIES-VARIABLEGREATER-P))
 (20 2 (:REWRITE VARIABLELESS-FROM-VARIABLEINEQUALITY))
 (20 2 (:REWRITE BODY-IMPLIES-VARIABLELESS-P))
 (18 9 (:REWRITE LIST::APPEND-OF-NON-CONSP-ONE))
 (15 5 (:REWRITE BODY-IMPLIES-VARIABLEINTERVAL-P))
 (15 5 (:REWRITE LIST::APPEND-OF-CONS))
 (14 4 (:REWRITE SET-UPPER-BOUND-PRED-CHAINING))
 (14 2 (:REWRITE SET-UPPER-BOUND-APPEND))
 (8 4 (:REWRITE LIST::APPEND-OF-NON-CONSP-2))
 (7 7 (:REWRITE SET-UPPER-BOUND-CTX_UNFIX_CHECK_REDUCTION_3))
 (7 7 (:REWRITE SET-UPPER-BOUND-CTX_REDUCTION))
 (6 2 (:REWRITE IMPLIES-VARIABLEINEQUALITY-P))
 (6 2 (:REWRITE BODY-IMPLIES-POLYLESS-P))
 (6 2 (:REWRITE BODY-IMPLIES-POLYGREATER-P))
 (6 1 (:REWRITE LIST::CONSP-APPEND))
 (5 5 (:REWRITE DEFAULT-CDR))
 (5 5 (:REWRITE DEFAULT-CAR))
 (1 1 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (1 1 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (1 1 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1 1 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (1 1 (:REWRITE ENV-P-WHEN-NOT-CONSP))
 (1 1 (:REWRITE |(equal c (/ x))|))
 (1 1 (:REWRITE |(equal c (- x))|))
 (1 1 (:REWRITE |(equal (/ x) c)|))
 (1 1 (:REWRITE |(equal (/ x) (/ y))|))
 (1 1 (:REWRITE |(equal (- x) c)|))
 (1 1 (:REWRITE |(equal (- x) (- y))|))
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(BOUND-VARID-ANDTRUE-VARIABLEGREATER-VARIABLEGREATER
 (805 326 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLELESS-P))
 (722 276 (:TYPE-PRESCRIPTION IMPLIES-NOT-INEQ-OP))
 (595 595 (:TYPE-PRESCRIPTION BODY-IMPLIES-EQ-OP-P))
 (556 192 (:TYPE-PRESCRIPTION IMPLIES-NOT-OP-P))
 (378 221 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINTERVAL-P))
 (356 182 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEEQUALITY-P))
 (242 242 (:TYPE-PRESCRIPTION IMPLIES-NOT-GT-OP))
 (206 4 (:REWRITE VARIABLEGREATER-FROM-VARIABLEINEQUALITY))
 (142 2 (:REWRITE BODY-IMPLIES-VARIABLEINEQUALITY-P))
 (22 4 (:REWRITE BODY-IMPLIES-VARIABLEGREATER-P))
 (20 2 (:REWRITE VARIABLELESS-FROM-VARIABLEINEQUALITY))
 (20 2 (:REWRITE BODY-IMPLIES-VARIABLELESS-P))
 (6 2 (:REWRITE IMPLIES-VARIABLEINEQUALITY-P))
 (6 2 (:REWRITE BODY-IMPLIES-POLYLESS-P))
 (6 2 (:REWRITE BODY-IMPLIES-POLYGREATER-P))
 (1 1 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (1 1 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (1 1 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1 1 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (1 1 (:REWRITE ENV-P-WHEN-NOT-CONSP))
 (1 1 (:REWRITE |(equal c (/ x))|))
 (1 1 (:REWRITE |(equal c (- x))|))
 (1 1 (:REWRITE |(equal (/ x) c)|))
 (1 1 (:REWRITE |(equal (/ x) (/ y))|))
 (1 1 (:REWRITE |(equal (- x) c)|))
 (1 1 (:REWRITE |(equal (- x) (- y))|))
 )
(UPPER-BOUND-BOUND-VARID-LIST-ANDTRUE-VARIABLEGREATER-VARIABLEGREATER
 (789 322 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLELESS-P))
 (722 276 (:TYPE-PRESCRIPTION IMPLIES-NOT-INEQ-OP))
 (595 595 (:TYPE-PRESCRIPTION BODY-IMPLIES-EQ-OP-P))
 (556 192 (:TYPE-PRESCRIPTION IMPLIES-NOT-OP-P))
 (372 217 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINTERVAL-P))
 (348 178 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEEQUALITY-P))
 (242 242 (:TYPE-PRESCRIPTION IMPLIES-NOT-GT-OP))
 (206 4 (:REWRITE VARIABLEGREATER-FROM-VARIABLEINEQUALITY))
 (142 2 (:REWRITE BODY-IMPLIES-VARIABLEINEQUALITY-P))
 (45 41 (:TYPE-PRESCRIPTION LIST::APPEND-CONSP-TYPE-TWO))
 (45 41 (:TYPE-PRESCRIPTION LIST::APPEND-CONSP-TYPE-ONE))
 (29 4 (:REWRITE SUBSET-NOT-CONSP))
 (22 4 (:REWRITE BODY-IMPLIES-VARIABLEGREATER-P))
 (20 2 (:REWRITE VARIABLELESS-FROM-VARIABLEINEQUALITY))
 (20 2 (:REWRITE BODY-IMPLIES-VARIABLELESS-P))
 (15 5 (:DEFINITION BOUND-VARID-LIST))
 (14 4 (:REWRITE SET-UPPER-BOUND-PRED-CHAINING))
 (14 2 (:REWRITE SET-UPPER-BOUND-APPEND))
 (8 8 (:REWRITE OPEN-BOUNDING-VARIABLES))
 (8 4 (:REWRITE LIST::APPEND-OF-NON-CONSP-ONE))
 (8 4 (:REWRITE LIST::APPEND-OF-NON-CONSP-2))
 (7 7 (:REWRITE SET-UPPER-BOUND-CTX_UNFIX_CHECK_REDUCTION_3))
 (7 7 (:REWRITE SET-UPPER-BOUND-CTX_REDUCTION))
 (6 2 (:REWRITE IMPLIES-VARIABLEINEQUALITY-P))
 (6 2 (:REWRITE BODY-IMPLIES-POLYLESS-P))
 (6 2 (:REWRITE BODY-IMPLIES-POLYGREATER-P))
 (6 1 (:REWRITE LIST::CONSP-APPEND))
 (5 5 (:REWRITE DEFAULT-CDR))
 (5 5 (:REWRITE DEFAULT-CAR))
 (1 1 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (1 1 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (1 1 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1 1 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (1 1 (:REWRITE ENV-P-WHEN-NOT-CONSP))
 (1 1 (:REWRITE |(equal c (/ x))|))
 (1 1 (:REWRITE |(equal c (- x))|))
 (1 1 (:REWRITE |(equal (/ x) c)|))
 (1 1 (:REWRITE |(equal (/ x) (/ y))|))
 (1 1 (:REWRITE |(equal (- x) c)|))
 (1 1 (:REWRITE |(equal (- x) (- y))|))
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(UPPER-BOUND-BOUNDING-VARIABLES-ANDTRUE-VARIABLEGREATER-VARIABLEGREATER
 (813 328 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLELESS-P))
 (722 276 (:TYPE-PRESCRIPTION IMPLIES-NOT-INEQ-OP))
 (595 595 (:TYPE-PRESCRIPTION BODY-IMPLIES-EQ-OP-P))
 (556 192 (:TYPE-PRESCRIPTION IMPLIES-NOT-OP-P))
 (382 223 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINTERVAL-P))
 (360 184 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEEQUALITY-P))
 (242 242 (:TYPE-PRESCRIPTION IMPLIES-NOT-GT-OP))
 (206 4 (:REWRITE VARIABLEGREATER-FROM-VARIABLEINEQUALITY))
 (142 2 (:REWRITE BODY-IMPLIES-VARIABLEINEQUALITY-P))
 (45 41 (:TYPE-PRESCRIPTION LIST::APPEND-CONSP-TYPE-TWO))
 (45 41 (:TYPE-PRESCRIPTION LIST::APPEND-CONSP-TYPE-ONE))
 (29 4 (:REWRITE SUBSET-NOT-CONSP))
 (22 4 (:REWRITE BODY-IMPLIES-VARIABLEGREATER-P))
 (20 2 (:REWRITE VARIABLELESS-FROM-VARIABLEINEQUALITY))
 (20 2 (:REWRITE BODY-IMPLIES-VARIABLELESS-P))
 (14 4 (:REWRITE SET-UPPER-BOUND-PRED-CHAINING))
 (14 2 (:REWRITE SET-UPPER-BOUND-APPEND))
 (13 13 (:REWRITE OPEN-BOUNDING-VARIABLES))
 (8 4 (:REWRITE LIST::APPEND-OF-NON-CONSP-ONE))
 (8 4 (:REWRITE LIST::APPEND-OF-NON-CONSP-2))
 (7 7 (:REWRITE SET-UPPER-BOUND-CTX_UNFIX_CHECK_REDUCTION_3))
 (7 7 (:REWRITE SET-UPPER-BOUND-CTX_REDUCTION))
 (6 2 (:REWRITE IMPLIES-VARIABLEINEQUALITY-P))
 (6 2 (:REWRITE BODY-IMPLIES-POLYLESS-P))
 (6 2 (:REWRITE BODY-IMPLIES-POLYGREATER-P))
 (6 1 (:REWRITE LIST::CONSP-APPEND))
 (1 1 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (1 1 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (1 1 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1 1 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (1 1 (:REWRITE ENV-P-WHEN-NOT-CONSP))
 (1 1 (:REWRITE |(equal c (/ x))|))
 (1 1 (:REWRITE |(equal c (- x))|))
 (1 1 (:REWRITE |(equal (/ x) c)|))
 (1 1 (:REWRITE |(equal (/ x) (/ y))|))
 (1 1 (:REWRITE |(equal (- x) c)|))
 (1 1 (:REWRITE |(equal (- x) (- y))|))
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(ANDTRUE-VARIABLEGREATER-VARIABLEGREATER-INV1
 (1100 420 (:TYPE-PRESCRIPTION IMPLIES-NOT-INEQ-OP))
 (895 362 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLELESS-P))
 (889 889 (:TYPE-PRESCRIPTION BODY-IMPLIES-EQ-OP-P))
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 (416 212 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEEQUALITY-P))
 (314 314 (:TYPE-PRESCRIPTION IMPLIES-NOT-GT-OP))
 (206 4 (:REWRITE VARIABLEGREATER-FROM-VARIABLEINEQUALITY))
 (142 2 (:REWRITE BODY-IMPLIES-VARIABLEINEQUALITY-P))
 (126 14 (:DEFINITION GET-BINDING))
 (94 14 (:REWRITE RFIX-IDENTITY))
 (70 14 (:REWRITE WF-BINDING-FIX-WF-BINDING))
 (42 14 (:REWRITE SIMPLIFY-SUMS-<))
 (42 14 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (42 14 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (42 14 (:REWRITE POLY-EVAL-CONST-POLY))
 (40 10 (:REWRITE RATIONALP-X))
 (28 28 (:TYPE-PRESCRIPTION NOT-CONSTP))
 (28 14 (:TYPE-PRESCRIPTION BODY-IMPLIES-WF-BINDING-P))
 (28 14 (:REWRITE DEFAULT-LESS-THAN-2))
 (28 14 (:REWRITE DEFAULT-LESS-THAN-1))
 (22 4 (:REWRITE BODY-IMPLIES-VARIABLEGREATER-P))
 (20 2 (:REWRITE VARIABLELESS-FROM-VARIABLEINEQUALITY))
 (20 2 (:REWRITE BODY-IMPLIES-VARIABLELESS-P))
 (18 18 (:REWRITE DEFAULT-CDR))
 (18 18 (:REWRITE DEFAULT-CAR))
 (14 14 (:TYPE-PRESCRIPTION WF-BINDING-P))
 (14 14 (:TYPE-PRESCRIPTION BINDING-P))
 (14 14 (:REWRITE WF-BINDING-P-OF-CAR-WHEN-ENV-P))
 (14 14 (:REWRITE VARID-FIX-VARID))
 (14 14 (:REWRITE VARIABLELESS-P-IMPLIES-LT-OP-P-RELATION-OP))
 (14 14 (:REWRITE THE-FLOOR-BELOW))
 (14 14 (:REWRITE THE-FLOOR-ABOVE))
 (14 14 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (14 14 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (14 14 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (14 14 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (14 14 (:REWRITE INTEGERP-<-CONSTANT))
 (14 14 (:REWRITE EVAL-POLY-CONST-DIFFERENCE))
 (14 14 (:REWRITE CONSTANT-<-INTEGERP))
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 (14 14 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
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 (10 10 (:REWRITE REDUCE-INTEGERP-+))
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 (7 4 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (6 2 (:REWRITE IMPLIES-VARIABLEINEQUALITY-P))
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 (4 4 (:REWRITE SIMPLIFY-SUMS-EQUAL))
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 (4 4 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (4 4 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (4 4 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (4 4 (:REWRITE |(equal c (/ x))|))
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 (4 4 (:REWRITE |(equal (/ x) (/ y))|))
 (4 4 (:REWRITE |(equal (- x) c)|))
 (4 4 (:REWRITE |(equal (- x) (- y))|))
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(ANDTRUE-VARIABLEGREATER-VARIABLEGREATER-INV2
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 (1752 1752 (:TYPE-PRESCRIPTION BODY-IMPLIES-EQ-OP-P))
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 (903 517 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINTERVAL-P))
 (824 16 (:REWRITE VARIABLEGREATER-FROM-VARIABLEINEQUALITY))
 (644 326 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEEQUALITY-P))
 (568 8 (:REWRITE BODY-IMPLIES-VARIABLEINEQUALITY-P))
 (558 42 (:DEFINITION GET-BINDING))
 (530 530 (:TYPE-PRESCRIPTION IMPLIES-NOT-GT-OP))
 (390 42 (:REWRITE WF-BINDING-FIX-WF-BINDING))
 (314 42 (:REWRITE RFIX-IDENTITY))
 (136 34 (:REWRITE RATIONALP-X))
 (132 44 (:REWRITE SIMPLIFY-SUMS-<))
 (132 44 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (128 44 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (124 62 (:TYPE-PRESCRIPTION BODY-IMPLIES-WF-BINDING-P))
 (110 42 (:REWRITE POLY-EVAL-CONST-POLY))
 (102 102 (:TYPE-PRESCRIPTION BINDING-P))
 (102 42 (:REWRITE WF-BINDING-P-OF-CAR-WHEN-ENV-P))
 (88 44 (:REWRITE DEFAULT-LESS-THAN-2))
 (88 44 (:REWRITE DEFAULT-LESS-THAN-1))
 (88 16 (:REWRITE BODY-IMPLIES-VARIABLEGREATER-P))
 (80 8 (:REWRITE VARIABLELESS-FROM-VARIABLEINEQUALITY))
 (80 8 (:REWRITE BODY-IMPLIES-VARIABLELESS-P))
 (68 68 (:TYPE-PRESCRIPTION NOT-CONSTP))
 (62 62 (:TYPE-PRESCRIPTION WF-BINDING-P))
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 (50 50 (:REWRITE DEFAULT-CDR))
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 (44 44 (:REWRITE THE-FLOOR-BELOW))
 (44 44 (:REWRITE THE-FLOOR-ABOVE))
 (44 44 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (44 44 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (44 44 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (44 44 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (44 44 (:REWRITE INTEGERP-<-CONSTANT))
 (44 44 (:REWRITE CONSTANT-<-INTEGERP))
 (44 44 (:REWRITE >-ALL-IS-GREATER-THAN-MEMBERS-HYPS))
 (44 44 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
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 (24 8 (:REWRITE BODY-IMPLIES-POLYGREATER-P))
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(ANDTRUE-VARIABLEINEQUALITY-VARIABLELESS
 (14 4 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLELESS-P))
 (6 4 (:TYPE-PRESCRIPTION BODY-IMPLIES-POLYLESS-P))
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(AND-AND-ENV-P-IMPLIES-VARIABLEBOUND-P-VARIABLEBOUND-LISTP-ANDTRUE-VARIABLEINEQUALITY-VARIABLELESS
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 (601 601 (:TYPE-PRESCRIPTION IMPLIES-NOT-LT-OP))
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 (477 477 (:TYPE-PRESCRIPTION BODY-IMPLIES-EQ-OP-P))
 (435 245 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINTERVAL-P))
 (416 10 (:REWRITE BODY-IMPLIES-VARIABLEINEQUALITY-P))
 (400 225 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEEQUALITY-P))
 (340 2 (:REWRITE BODY-IMPLIES-VARIABLERELATION-P))
 (268 1 (:DEFINITION VARIABLEBOUND-LISTP))
 (138 4 (:REWRITE VARIABLEGREATER-FROM-VARIABLEINEQUALITY))
 (135 3 (:REWRITE BODY-IMPLIES-LT-OP-P))
 (105 3 (:DEFINITION LT-OP-P))
 (102 3 (:REWRITE VARIABLELESS-P-IMPLIES-LT-OP-P-RELATION-OP))
 (93 12 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (90 18 (:REWRITE ACL2-NUMBERP-X))
 (89 11 (:REWRITE BODY-IMPLIES-VARIABLELESS-P))
 (40 4 (:REWRITE BODY-IMPLIES-VARIABLEGREATER-P))
 (36 9 (:REWRITE RATIONALP-X))
 (24 10 (:REWRITE IMPLIES-VARIABLEINEQUALITY-P))
 (24 7 (:REWRITE BODY-IMPLIES-POLYLESS-P))
 (22 2 (:REWRITE NORMALIZED-VARIABLEBOUND-LISTP-IMPLIES-VARIABLEBOUND-LISTP))
 (21 12 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (16 2 (:DEFINITION NORMALIZED-VARIABLEBOUND-LISTP))
 (12 12 (:REWRITE SIMPLIFY-SUMS-EQUAL))
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(ANDTRUE-VARIABLEINEQUALITY-VARIABLELESS
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 (37 21 (:TYPE-PRESCRIPTION BODY-IMPLIES-POLYLESS-P))
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 (4 1 (:TYPE-PRESCRIPTION IMPLIES-NOT-INEQ-OP))
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 (1 1 (:TYPE-PRESCRIPTION IMPLIES-NOT-LT-OP))
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(AND-AND-ENV-P-IMPLIES-NORMALIZED-VARIABLEBOUND-P-NORMALIZED-VARIABLEBOUND-LISTP-ANDTRUE-VARIABLEINEQUALITY-VARIABLELESS
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 (595 338 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINTERVAL-P))
 (521 287 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEEQUALITY-P))
 (507 177 (:TYPE-PRESCRIPTION IMPLIES-NOT-OP-P))
 (485 9 (:REWRITE VARIABLELESS-FROM-VARIABLEINEQUALITY))
 (484 484 (:TYPE-PRESCRIPTION BODY-IMPLIES-EQ-OP-P))
 (186 4 (:REWRITE BODY-IMPLIES-VARIABLEINEQUALITY-P))
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 (94 13 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
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 (56 2 (:REWRITE VARIABLEGREATER-FROM-VARIABLEINEQUALITY))
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(BOUND-VARID-LIST-ANDTRUE-VARIABLEINEQUALITY-VARIABLELESS
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 (311 1 (:REWRITE VARIABLEBOUND-LISTP-IMPLIES-VARID-LISTP-ALL-BOUND-LIST-VARIABLES))
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 (2 2 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (2 2 (:REWRITE |(< (/ x) (/ y))|))
 (2 2 (:REWRITE |(< (- x) c)|))
 (2 2 (:REWRITE |(< (- x) (- y))|))
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 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (1 1 (:REWRITE |(< 0 (/ x))|))
 (1 1 (:REWRITE |(< 0 (* x y))|))
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(UPPER-BOUND-ALL-BOUND-LIST-VARIABLESANDTRUE-VARIABLEINEQUALITY-VARIABLELESS
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 (847 461 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEEQUALITY-P))
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 (105 95 (:TYPE-PRESCRIPTION LIST::APPEND-CONSP-TYPE-TWO))
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(BOUND-VARID-ANDTRUE-VARIABLEINEQUALITY-VARIABLELESS
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 (861 468 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEEQUALITY-P))
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 (491 10 (:REWRITE BODY-IMPLIES-VARIABLEINEQUALITY-P))
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 (96 14 (:REWRITE BODY-IMPLIES-VARIABLELESS-P))
 (90 2 (:REWRITE BODY-IMPLIES-LT-OP-P))
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(UPPER-BOUND-BOUND-VARID-LIST-ANDTRUE-VARIABLEINEQUALITY-VARIABLELESS
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 (135 3 (:REWRITE BODY-IMPLIES-LT-OP-P))
 (128 7 (:REWRITE VARIABLEGREATER-FROM-VARIABLEINEQUALITY))
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 (106 16 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (105 95 (:TYPE-PRESCRIPTION LIST::APPEND-CONSP-TYPE-TWO))
 (105 95 (:TYPE-PRESCRIPTION LIST::APPEND-CONSP-TYPE-ONE))
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 (101 21 (:REWRITE ACL2-NUMBERP-X))
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 (40 10 (:REWRITE RATIONALP-X))
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(UPPER-BOUND-BOUNDING-VARIABLES-ANDTRUE-VARIABLEINEQUALITY-VARIABLELESS
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 (865 470 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEEQUALITY-P))
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 (491 10 (:REWRITE BODY-IMPLIES-VARIABLEINEQUALITY-P))
 (135 3 (:REWRITE BODY-IMPLIES-LT-OP-P))
 (128 7 (:REWRITE VARIABLEGREATER-FROM-VARIABLEINEQUALITY))
 (112 16 (:REWRITE BODY-IMPLIES-VARIABLELESS-P))
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 (105 95 (:TYPE-PRESCRIPTION LIST::APPEND-CONSP-TYPE-TWO))
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(ANDTRUE-VARIABLEINEQUALITY-VARIABLELESS-INV1
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 (249 47 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
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(ANDTRUE-VARIABLEINEQUALITY-VARIABLEGREATER
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(AND-AND-ENV-P-IMPLIES-VARIABLEBOUND-P-VARIABLEBOUND-LISTP-ANDTRUE-VARIABLEINEQUALITY-VARIABLEGREATER
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(AND-AND-ENV-P-IMPLIES-NORMALIZED-VARIABLEBOUND-P-NORMALIZED-VARIABLEBOUND-LISTP-ANDTRUE-VARIABLEINEQUALITY-VARIABLEGREATER
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 )
(BOUND-VARID-ANDTRUE-VARIABLEINEQUALITY-VARIABLEGREATER
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 (90 2 (:REWRITE BODY-IMPLIES-LT-OP-P))
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(UPPER-BOUND-BOUND-VARID-LIST-ANDTRUE-VARIABLEINEQUALITY-VARIABLEGREATER
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(UPPER-BOUND-BOUNDING-VARIABLES-ANDTRUE-VARIABLEINEQUALITY-VARIABLEGREATER
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(ANDTRUE-VARIABLEINEQUALITY-VARIABLEGREATER-INV1
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(ANDTRUE-VARIABLEINEQUALITY-VARIABLEGREATER-INV2
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(ANDTRUE-VARIABLEINTERVAL-VARIABLELESS
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(AND-AND-ENV-P-IMPLIES-VARIABLEBOUND-P-VARIABLEBOUND-LISTP-ANDTRUE-VARIABLEINTERVAL-VARIABLELESS
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(ANDTRUE-VARIABLEINTERVAL-VARIABLELESS
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 (1 1 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (1 1 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (1 1 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
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 (1 1 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
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 (1 1 (:REWRITE |(equal (/ x) (/ y))|))
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(UPPER-BOUND-ALL-BOUND-LIST-VARIABLESANDTRUE-VARIABLEINTERVAL-VARIABLELESS
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(BOUND-VARID-ANDTRUE-VARIABLEINTERVAL-VARIABLELESS
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(UPPER-BOUND-BOUND-VARID-LIST-ANDTRUE-VARIABLEINTERVAL-VARIABLELESS
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(UPPER-BOUND-BOUNDING-VARIABLES-ANDTRUE-VARIABLEINTERVAL-VARIABLELESS
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(ANDTRUE-VARIABLEINTERVAL-VARIABLELESS-INV2
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(ANDTRUE-VARIABLEINTERVAL-VARIABLEGREATER)
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 (6 2 (:REWRITE BODY-IMPLIES-VARIABLEINTERVAL-P))
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(UPPER-BOUND-ALL-BOUND-LIST-VARIABLESANDTRUE-VARIABLEINTERVAL-VARIABLEGREATER
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(BOUND-VARID-ANDTRUE-VARIABLEINTERVAL-VARIABLEGREATER
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 (11 2 (:REWRITE BODY-IMPLIES-VARIABLEGREATER-P))
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 (10 1 (:REWRITE BODY-IMPLIES-VARIABLELESS-P))
 (3 1 (:REWRITE IMPLIES-VARIABLEINEQUALITY-P))
 (3 1 (:REWRITE BODY-IMPLIES-VARIABLEINTERVAL-P))
 (3 1 (:REWRITE BODY-IMPLIES-POLYLESS-P))
 (3 1 (:REWRITE BODY-IMPLIES-POLYGREATER-P))
 (1 1 (:REWRITE SIMPLIFY-SUMS-EQUAL))
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 (1 1 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
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 (1 1 (:REWRITE |(equal (/ x) (/ y))|))
 (1 1 (:REWRITE |(equal (- x) c)|))
 (1 1 (:REWRITE |(equal (- x) (- y))|))
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(UPPER-BOUND-BOUND-VARID-LIST-ANDTRUE-VARIABLEINTERVAL-VARIABLEGREATER
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(UPPER-BOUND-BOUNDING-VARIABLES-ANDTRUE-VARIABLEINTERVAL-VARIABLEGREATER
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(ANDTRUE-VARIABLEINTERVAL-VARIABLEGREATER-INV1
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(ANDTRUE-VARIABLEINTERVAL-VARIABLEGREATER-INV2
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(ANDTRUE-VARIABLEINTERVAL-VARIABLEINEQUALITY
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(AND-AND-ENV-P-IMPLIES-VARIABLEBOUND-P-VARIABLEBOUND-LISTP-ANDTRUE-VARIABLEINTERVAL-VARIABLEINEQUALITY
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(ANDTRUE-VARIABLEINTERVAL-VARIABLEINEQUALITY
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(UPPER-BOUND-ALL-BOUND-LIST-VARIABLESANDTRUE-VARIABLEINTERVAL-VARIABLEINEQUALITY
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(BOUND-VARID-ANDTRUE-VARIABLEINTERVAL-VARIABLEINEQUALITY
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(UPPER-BOUND-BOUND-VARID-LIST-ANDTRUE-VARIABLEINTERVAL-VARIABLEINEQUALITY
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(UPPER-BOUND-BOUNDING-VARIABLES-ANDTRUE-VARIABLEINTERVAL-VARIABLEINEQUALITY
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(ANDTRUE-VARIABLEINTERVAL-VARIABLEINEQUALITY-INV2
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(ANDTRUE-VARIABLEGREATER-VARIABLEINEQUALITY
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(AND-AND-ENV-P-IMPLIES-VARIABLEBOUND-P-VARIABLEBOUND-LISTP-ANDTRUE-VARIABLEGREATER-VARIABLEINEQUALITY
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 (477 477 (:TYPE-PRESCRIPTION BODY-IMPLIES-EQ-OP-P))
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 (435 245 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINTERVAL-P))
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(ANDTRUE-VARIABLEGREATER-VARIABLEINEQUALITY
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(AND-AND-ENV-P-IMPLIES-NORMALIZED-VARIABLEBOUND-P-NORMALIZED-VARIABLEBOUND-LISTP-ANDTRUE-VARIABLEGREATER-VARIABLEINEQUALITY
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(BOUND-VARID-LIST-ANDTRUE-VARIABLEGREATER-VARIABLEINEQUALITY
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(UPPER-BOUND-ALL-BOUND-LIST-VARIABLESANDTRUE-VARIABLEGREATER-VARIABLEINEQUALITY
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(BOUND-VARID-ANDTRUE-VARIABLEGREATER-VARIABLEINEQUALITY
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 )
(UPPER-BOUND-BOUND-VARID-LIST-ANDTRUE-VARIABLEGREATER-VARIABLEINEQUALITY
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 (887 518 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINTERVAL-P))
 (850 463 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEEQUALITY-P))
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 (491 10 (:REWRITE BODY-IMPLIES-VARIABLEINEQUALITY-P))
 (392 10 (:REWRITE VARIABLEGREATER-FROM-VARIABLEINEQUALITY))
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 (109 13 (:REWRITE BODY-IMPLIES-VARIABLELESS-P))
 (106 16 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (105 95 (:TYPE-PRESCRIPTION LIST::APPEND-CONSP-TYPE-TWO))
 (105 95 (:TYPE-PRESCRIPTION LIST::APPEND-CONSP-TYPE-ONE))
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(UPPER-BOUND-BOUNDING-VARIABLES-ANDTRUE-VARIABLEGREATER-VARIABLEINEQUALITY
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(ANDTRUE-VARIABLEGREATER-VARIABLEINEQUALITY-INV1
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(ANDTRUE-VARIABLEGREATER-VARIABLEINEQUALITY-INV2
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(ANDTRUE-VARIABLELESS-VARIABLEINEQUALITY
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(AND-AND-ENV-P-IMPLIES-VARIABLEBOUND-P-VARIABLEBOUND-LISTP-ANDTRUE-VARIABLELESS-VARIABLEINEQUALITY
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 (601 601 (:TYPE-PRESCRIPTION IMPLIES-NOT-LT-OP))
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 (477 477 (:TYPE-PRESCRIPTION BODY-IMPLIES-EQ-OP-P))
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 (40 4 (:REWRITE BODY-IMPLIES-VARIABLEGREATER-P))
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 (24 7 (:REWRITE BODY-IMPLIES-POLYLESS-P))
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(AND-AND-ENV-P-IMPLIES-NORMALIZED-VARIABLEBOUND-P-NORMALIZED-VARIABLEBOUND-LISTP-ANDTRUE-VARIABLELESS-VARIABLEINEQUALITY
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 (1 1 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE DEFAULT-CAR))
 )
(BOUND-VARID-LIST-ANDTRUE-VARIABLELESS-VARIABLEINEQUALITY
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 (973 335 (:TYPE-PRESCRIPTION IMPLIES-NOT-OP-P))
 (969 969 (:TYPE-PRESCRIPTION BODY-IMPLIES-EQ-OP-P))
 (901 525 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINTERVAL-P))
 (858 467 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEEQUALITY-P))
 (717 15 (:REWRITE VARIABLELESS-FROM-VARIABLEINEQUALITY))
 (606 13 (:REWRITE BODY-IMPLIES-VARIABLEINEQUALITY-P))
 (412 1 (:DEFINITION >-ALL))
 (319 2 (:REWRITE VARID-FIX-VARID))
 (317 1 (:REWRITE VARID-P-OF-CAR-WHEN-VARID-LISTP))
 (311 1 (:REWRITE VARIABLEBOUND-LISTP-IMPLIES-VARID-LISTP-ALL-BOUND-LIST-VARIABLES))
 (297 1 (:DEFINITION VARIABLEBOUND-LISTP))
 (228 1 (:REWRITE BODY-IMPLIES-VARIABLEBOUND-P))
 (170 1 (:REWRITE BODY-IMPLIES-VARIABLERELATION-P))
 (169 8 (:REWRITE VARIABLEGREATER-FROM-VARIABLEINEQUALITY))
 (106 15 (:REWRITE BODY-IMPLIES-VARIABLELESS-P))
 (90 2 (:REWRITE BODY-IMPLIES-LT-OP-P))
 (79 3 (:REWRITE DEFAULT-LESS-THAN-1))
 (78 14 (:REWRITE ACL2-NUMBERP-X))
 (71 8 (:REWRITE BODY-IMPLIES-VARIABLEGREATER-P))
 (70 2 (:DEFINITION LT-OP-P))
 (68 2 (:REWRITE VARIABLELESS-P-IMPLIES-LT-OP-P-RELATION-OP))
 (65 11 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (60 3 (:DEFINITION ALL-BOUND-LIST-VARIABLES))
 (33 3 (:DEFINITION ALL-BOUND-VARIABLES))
 (32 8 (:REWRITE RATIONALP-X))
 (30 3 (:REWRITE OPEN-BOUNDING-VARIABLES))
 (29 9 (:REWRITE BODY-IMPLIES-POLYLESS-P))
 (22 2 (:REWRITE NORMALIZED-VARIABLEBOUND-LISTP-IMPLIES-VARIABLEBOUND-LISTP))
 (21 7 (:REWRITE BODY-IMPLIES-POLYGREATER-P))
 (18 3 (:REWRITE SET-EQUIV-QUANT-APPEND-CONS-COMMUTES-1))
 (17 11 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (16 2 (:DEFINITION NORMALIZED-VARIABLEBOUND-LISTP))
 (15 3 (:REWRITE SET-EQUIV-QUANT-APPEND-COMMUTES))
 (12 4 (:REWRITE BODY-IMPLIES-VARIABLEINTERVAL-P))
 (11 11 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (11 11 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (11 11 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (11 11 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (11 11 (:REWRITE |(equal c (/ x))|))
 (11 11 (:REWRITE |(equal c (- x))|))
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 (11 11 (:REWRITE |(equal (/ x) (/ y))|))
 (11 11 (:REWRITE |(equal (- x) c)|))
 (11 11 (:REWRITE |(equal (- x) (- y))|))
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 (8 8 (:REWRITE REDUCE-RATIONALP-*))
 (8 8 (:REWRITE REDUCE-INTEGERP-+))
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 (8 8 (:REWRITE DEFAULT-CAR))
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 (6 3 (:REWRITE LIST::APPEND-OF-NON-CONSP-2))
 (3 3 (:REWRITE THE-FLOOR-BELOW))
 (3 3 (:REWRITE THE-FLOOR-ABOVE))
 (3 3 (:REWRITE ENV-P-WHEN-NOT-CONSP))
 (3 3 (:REWRITE DEFAULT-LESS-THAN-2))
 (3 1 (:REWRITE IMPLIES-VARIABLERELATION-P))
 (3 1 (:REWRITE BODY-IMPLIES-VARIABLEEQUALITY-P))
 (3 1 (:DEFINITION REMOVE-EQUAL))
 (2 2 (:TYPE-PRESCRIPTION VARID-LISTP))
 (2 2 (:TYPE-PRESCRIPTION SET-UPPER-BOUND-CTX_UNFIX_CHECK))
 (2 2 (:REWRITE SIMPLIFY-SUMS-<))
 (2 2 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (2 2 (:REWRITE SET-UPPER-BOUND-CTX_UNFIX_CHECK_REDUCTION_3))
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 (2 2 (:REWRITE REMOVE-WEAK-INEQUALITIES))
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 (2 2 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (2 2 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (2 2 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (2 2 (:REWRITE INTEGERP-<-CONSTANT))
 (2 2 (:REWRITE CONSTANT-<-INTEGERP))
 (2 2 (:REWRITE >=ALL-MEMBER-HYPS))
 (2 2 (:REWRITE >-ALL-IS-GREATER-THAN-MEMBERS-HYPS))
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 (2 2 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (2 2 (:REWRITE |(< c (- x))|))
 (2 2 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (2 2 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (2 2 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (2 2 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (2 2 (:REWRITE |(< (/ x) (/ y))|))
 (2 2 (:REWRITE |(< (- x) c)|))
 (2 2 (:REWRITE |(< (- x) (- y))|))
 (1 1 (:REWRITE VARID-LISTP-WHEN-NOT-CONSP))
 (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 |(< 0 (/ x))|))
 (1 1 (:REWRITE |(< 0 (* x y))|))
 )
(UPPER-BOUND-ALL-BOUND-LIST-VARIABLESANDTRUE-VARIABLELESS-VARIABLEINEQUALITY
 (1037 441 (:TYPE-PRESCRIPTION IMPLIES-NOT-INEQ-OP))
 (973 335 (:TYPE-PRESCRIPTION IMPLIES-NOT-OP-P))
 (969 969 (:TYPE-PRESCRIPTION BODY-IMPLIES-EQ-OP-P))
 (935 542 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINTERVAL-P))
 (850 463 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEEQUALITY-P))
 (807 16 (:REWRITE VARIABLELESS-FROM-VARIABLEINEQUALITY))
 (491 10 (:REWRITE BODY-IMPLIES-VARIABLEINEQUALITY-P))
 (204 12 (:DEFINITION ALL-BOUND-LIST-VARIABLES))
 (147 30 (:REWRITE OPEN-BOUNDING-VARIABLES))
 (135 3 (:REWRITE BODY-IMPLIES-LT-OP-P))
 (132 12 (:DEFINITION ALL-BOUND-VARIABLES))
 (128 7 (:REWRITE VARIABLEGREATER-FROM-VARIABLEINEQUALITY))
 (112 16 (:REWRITE BODY-IMPLIES-VARIABLELESS-P))
 (106 16 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (105 95 (:TYPE-PRESCRIPTION LIST::APPEND-CONSP-TYPE-TWO))
 (105 95 (:TYPE-PRESCRIPTION LIST::APPEND-CONSP-TYPE-ONE))
 (105 3 (:DEFINITION LT-OP-P))
 (102 3 (:REWRITE VARIABLELESS-P-IMPLIES-LT-OP-P-RELATION-OP))
 (101 21 (:REWRITE ACL2-NUMBERP-X))
 (61 7 (:REWRITE BODY-IMPLIES-VARIABLEGREATER-P))
 (58 8 (:REWRITE SUBSET-NOT-CONSP))
 (42 21 (:REWRITE LIST::APPEND-OF-NON-CONSP-ONE))
 (40 10 (:REWRITE RATIONALP-X))
 (39 13 (:REWRITE BODY-IMPLIES-VARIABLEINTERVAL-P))
 (36 12 (:REWRITE LIST::APPEND-OF-CONS))
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 (29 9 (:REWRITE SET-UPPER-BOUND-PRED-CHAINING))
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 (16 16 (:REWRITE |(equal c (/ x))|))
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 (16 16 (:REWRITE |(equal (/ x) (/ y))|))
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 (10 10 (:META META-RATIONALP-CORRECT))
 (10 10 (:META META-INTEGERP-CORRECT))
 (3 3 (:REWRITE ENV-P-WHEN-NOT-CONSP))
 )
(BOUND-VARID-ANDTRUE-VARIABLELESS-VARIABLEINEQUALITY
 (1037 441 (:TYPE-PRESCRIPTION IMPLIES-NOT-INEQ-OP))
 (973 335 (:TYPE-PRESCRIPTION IMPLIES-NOT-OP-P))
 (969 969 (:TYPE-PRESCRIPTION BODY-IMPLIES-EQ-OP-P))
 (897 523 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINTERVAL-P))
 (864 470 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEEQUALITY-P))
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 (491 10 (:REWRITE BODY-IMPLIES-VARIABLEINEQUALITY-P))
 (128 7 (:REWRITE VARIABLEGREATER-FROM-VARIABLEINEQUALITY))
 (96 14 (:REWRITE BODY-IMPLIES-VARIABLELESS-P))
 (90 2 (:REWRITE BODY-IMPLIES-LT-OP-P))
 (75 12 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (71 15 (:REWRITE ACL2-NUMBERP-X))
 (70 2 (:DEFINITION LT-OP-P))
 (68 2 (:REWRITE VARIABLELESS-P-IMPLIES-LT-OP-P-RELATION-OP))
 (61 7 (:REWRITE BODY-IMPLIES-VARIABLEGREATER-P))
 (28 7 (:REWRITE RATIONALP-X))
 (26 8 (:REWRITE BODY-IMPLIES-POLYLESS-P))
 (19 12 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (18 6 (:REWRITE BODY-IMPLIES-POLYGREATER-P))
 (13 12 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (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))|))
 (7 7 (:REWRITE REDUCE-RATIONALP-+))
 (7 7 (:REWRITE REDUCE-RATIONALP-*))
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 (7 7 (:REWRITE RATIONALP-MINUS-X))
 (7 7 (:REWRITE INTEGERP-MINUS-X))
 (7 7 (:META META-RATIONALP-CORRECT))
 (7 7 (:META META-INTEGERP-CORRECT))
 (3 3 (:REWRITE ENV-P-WHEN-NOT-CONSP))
 )
(UPPER-BOUND-BOUND-VARID-LIST-ANDTRUE-VARIABLELESS-VARIABLEINEQUALITY
 (1037 441 (:TYPE-PRESCRIPTION IMPLIES-NOT-INEQ-OP))
 (973 335 (:TYPE-PRESCRIPTION IMPLIES-NOT-OP-P))
 (969 969 (:TYPE-PRESCRIPTION BODY-IMPLIES-EQ-OP-P))
 (887 518 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINTERVAL-P))
 (850 463 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEEQUALITY-P))
 (807 16 (:REWRITE VARIABLELESS-FROM-VARIABLEINEQUALITY))
 (491 10 (:REWRITE BODY-IMPLIES-VARIABLEINEQUALITY-P))
 (135 3 (:REWRITE BODY-IMPLIES-LT-OP-P))
 (128 7 (:REWRITE VARIABLEGREATER-FROM-VARIABLEINEQUALITY))
 (112 16 (:REWRITE BODY-IMPLIES-VARIABLELESS-P))
 (106 16 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (105 95 (:TYPE-PRESCRIPTION LIST::APPEND-CONSP-TYPE-TWO))
 (105 95 (:TYPE-PRESCRIPTION LIST::APPEND-CONSP-TYPE-ONE))
 (105 3 (:DEFINITION LT-OP-P))
 (102 3 (:REWRITE VARIABLELESS-P-IMPLIES-LT-OP-P-RELATION-OP))
 (101 21 (:REWRITE ACL2-NUMBERP-X))
 (61 7 (:REWRITE BODY-IMPLIES-VARIABLEGREATER-P))
 (58 8 (:REWRITE SUBSET-NOT-CONSP))
 (40 10 (:REWRITE RATIONALP-X))
 (36 12 (:DEFINITION BOUND-VARID-LIST))
 (30 9 (:REWRITE BODY-IMPLIES-POLYLESS-P))
 (29 9 (:REWRITE SET-UPPER-BOUND-PRED-CHAINING))
 (28 4 (:REWRITE SET-UPPER-BOUND-APPEND))
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 (26 16 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
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 (18 9 (:REWRITE LIST::APPEND-OF-NON-CONSP-2))
 (18 6 (:REWRITE BODY-IMPLIES-POLYGREATER-P))
 (17 16 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (16 16 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (16 16 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (16 16 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (16 16 (:REWRITE |(equal c (/ x))|))
 (16 16 (:REWRITE |(equal c (- x))|))
 (16 16 (:REWRITE |(equal (/ x) c)|))
 (16 16 (:REWRITE |(equal (/ x) (/ y))|))
 (16 16 (:REWRITE |(equal (- x) c)|))
 (16 16 (:REWRITE |(equal (- x) (- y))|))
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 (10 10 (:REWRITE REDUCE-RATIONALP-+))
 (10 10 (:REWRITE REDUCE-RATIONALP-*))
 (10 10 (:REWRITE REDUCE-INTEGERP-+))
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 (10 10 (:META META-INTEGERP-CORRECT))
 (3 3 (:REWRITE ENV-P-WHEN-NOT-CONSP))
 (3 1 (:REWRITE BODY-IMPLIES-VARIABLEINTERVAL-P))
 )
(UPPER-BOUND-BOUNDING-VARIABLES-ANDTRUE-VARIABLELESS-VARIABLEINEQUALITY
 (1037 441 (:TYPE-PRESCRIPTION IMPLIES-NOT-INEQ-OP))
 (973 335 (:TYPE-PRESCRIPTION IMPLIES-NOT-OP-P))
 (969 969 (:TYPE-PRESCRIPTION BODY-IMPLIES-EQ-OP-P))
 (917 533 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINTERVAL-P))
 (868 472 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEEQUALITY-P))
 (807 16 (:REWRITE VARIABLELESS-FROM-VARIABLEINEQUALITY))
 (491 10 (:REWRITE BODY-IMPLIES-VARIABLEINEQUALITY-P))
 (135 3 (:REWRITE BODY-IMPLIES-LT-OP-P))
 (128 7 (:REWRITE VARIABLEGREATER-FROM-VARIABLEINEQUALITY))
 (112 16 (:REWRITE BODY-IMPLIES-VARIABLELESS-P))
 (106 16 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (105 95 (:TYPE-PRESCRIPTION LIST::APPEND-CONSP-TYPE-TWO))
 (105 95 (:TYPE-PRESCRIPTION LIST::APPEND-CONSP-TYPE-ONE))
 (105 3 (:DEFINITION LT-OP-P))
 (102 3 (:REWRITE VARIABLELESS-P-IMPLIES-LT-OP-P-RELATION-OP))
 (101 21 (:REWRITE ACL2-NUMBERP-X))
 (66 30 (:REWRITE OPEN-BOUNDING-VARIABLES))
 (61 7 (:REWRITE BODY-IMPLIES-VARIABLEGREATER-P))
 (58 8 (:REWRITE SUBSET-NOT-CONSP))
 (40 10 (:REWRITE RATIONALP-X))
 (30 9 (:REWRITE BODY-IMPLIES-POLYLESS-P))
 (29 9 (:REWRITE SET-UPPER-BOUND-PRED-CHAINING))
 (28 4 (:REWRITE SET-UPPER-BOUND-APPEND))
 (26 16 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
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 (18 9 (:REWRITE LIST::APPEND-OF-NON-CONSP-2))
 (18 6 (:REWRITE BODY-IMPLIES-POLYGREATER-P))
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 (16 16 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (16 16 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (16 16 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (16 16 (:REWRITE |(equal c (/ x))|))
 (16 16 (:REWRITE |(equal c (- x))|))
 (16 16 (:REWRITE |(equal (/ x) c)|))
 (16 16 (:REWRITE |(equal (/ x) (/ y))|))
 (16 16 (:REWRITE |(equal (- x) c)|))
 (16 16 (:REWRITE |(equal (- x) (- y))|))
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 (10 10 (:REWRITE REDUCE-RATIONALP-+))
 (10 10 (:REWRITE REDUCE-RATIONALP-*))
 (10 10 (:REWRITE REDUCE-INTEGERP-+))
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 (10 10 (:REWRITE INTEGERP-MINUS-X))
 (10 10 (:META META-RATIONALP-CORRECT))
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(ANDTRUE-VARIABLELESS-VARIABLEINEQUALITY-INV1
 (2911 981 (:TYPE-PRESCRIPTION IMPLIES-NOT-OP-P))
 (2909 2909 (:TYPE-PRESCRIPTION BODY-IMPLIES-EQ-OP-P))
 (1904 1146 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINTERVAL-P))
 (1690 924 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEEQUALITY-P))
 (838 20 (:REWRITE BODY-IMPLIES-VARIABLEINEQUALITY-P))
 (485 31 (:REWRITE BODY-IMPLIES-VARIABLELESS-P))
 (408 16 (:REWRITE VARIABLEGREATER-FROM-VARIABLEINEQUALITY))
 (407 70 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (360 72 (:REWRITE ACL2-NUMBERP-X))
 (332 6 (:REWRITE VARIABLEGREATER-P-IMPLIES-GT-OP-P-RELATION-OP))
 (324 36 (:DEFINITION GET-BINDING))
 (258 26 (:REWRITE BODY-IMPLIES-POLYLESS-P))
 (222 16 (:REWRITE BODY-IMPLIES-VARIABLEGREATER-P))
 (208 52 (:REWRITE RATIONALP-X))
 (190 14 (:REWRITE BODY-IMPLIES-LT-OP-P))
 (180 36 (:REWRITE WF-BINDING-FIX-WF-BINDING))
 (126 12 (:REWRITE BODY-IMPLIES-POLYGREATER-P))
 (119 70 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (108 36 (:REWRITE POLY-EVAL-CONST-POLY))
 (96 96 (:TYPE-PRESCRIPTION BINDING-P))
 (94 6 (:REWRITE BODY-IMPLIES-GT-OP-P))
 (86 34 (:REWRITE SIMPLIFY-SUMS-<))
 (86 34 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (86 34 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (74 70 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (72 72 (:TYPE-PRESCRIPTION NOT-CONSTP))
 (70 70 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (70 70 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (70 70 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (70 70 (:REWRITE |(equal c (/ x))|))
 (70 70 (:REWRITE |(equal c (- x))|))
 (70 70 (:REWRITE |(equal (/ x) c)|))
 (70 70 (:REWRITE |(equal (/ x) (/ y))|))
 (70 70 (:REWRITE |(equal (- x) c)|))
 (70 70 (:REWRITE |(equal (- x) (- y))|))
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 (60 34 (:REWRITE DEFAULT-LESS-THAN-1))
 (52 52 (:REWRITE REDUCE-RATIONALP-+))
 (52 52 (:REWRITE REDUCE-RATIONALP-*))
 (52 52 (:REWRITE REDUCE-INTEGERP-+))
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 (52 52 (:META META-RATIONALP-CORRECT))
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 (36 36 (:REWRITE WF-BINDING-P-OF-CAR-WHEN-ENV-P))
 (36 36 (:REWRITE VARID-FIX-VARID))
 (36 36 (:REWRITE EVAL-POLY-CONST-DIFFERENCE))
 (36 12 (:DEFINITION CONJOINRESULTS))
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 (34 34 (:REWRITE THE-FLOOR-ABOVE))
 (34 34 (:REWRITE REMOVE-STRICT-INEQUALITIES))
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 (34 34 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (34 34 (:REWRITE INTEGERP-<-CONSTANT))
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 (34 34 (:REWRITE >-ALL-IS-GREATER-THAN-MEMBERS-HYPS))
 (34 34 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (34 34 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
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 (34 34 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (34 34 (:REWRITE |(< (/ x) (/ y))|))
 (34 34 (:REWRITE |(< (- x) c)|))
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 (31 23 (:REWRITE EVAL-INEQ-POLYINTERVALP))
 (26 26 (:REWRITE REMOVE-WEAK-INEQUALITIES))
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 (5 5 (:REWRITE ENV-P-WHEN-NOT-CONSP))
 (4 4 (:REWRITE ANDTRUE-VARIABLELESS-VARIABLELESS-INV2))
 (4 4 (:REWRITE ANDTRUE-VARIABLEGREATER-VARIABLELESS-INV2))
 )
(ANDTRUE-VARIABLELESS-VARIABLEINEQUALITY-INV2
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 (1404 108 (:DEFINITION GET-BINDING))
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 (968 42 (:REWRITE VARIABLEGREATER-FROM-VARIABLEINEQUALITY))
 (884 78 (:REWRITE BODY-IMPLIES-VARIABLELESS-P))
 (508 508 (:TYPE-PRESCRIPTION BINDING-P))
 (490 93 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
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 (4 2 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
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 (3 3 (:REWRITE >-ALL-IS-GREATER-THAN-MEMBERS-HYPS))
 (3 1 (:REWRITE IMPLIES-VARIABLERELATION-P))
 (3 1 (:REWRITE BODY-IMPLIES-VARIABLEINTERVAL-P))
 (3 1 (:REWRITE BODY-IMPLIES-VARIABLEEQUALITY-P))
 (3 1 (:REWRITE BODY-IMPLIES-POLYLESS-P))
 (3 1 (:REWRITE BODY-IMPLIES-POLYGREATER-P))
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 (1 1 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (1 1 (:REWRITE |(equal (+ (- c) x) y)|))
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 (1 1 (:REWRITE |(< (+ c/d x) y)|))
 (1 1 (:REWRITE |(< (+ (- c) x) y)|))
 (1 1 (:REWRITE |(< (* x y) 0)|))
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(RESTRICTDISEQUALITY
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 (28 15 (:REWRITE DEFAULT-PLUS-2))
 (28 15 (:REWRITE DEFAULT-PLUS-1))
 (9 6 (:REWRITE DEFAULT-LESS-THAN-1))
 (6 6 (:REWRITE THE-FLOOR-BELOW))
 (6 6 (:REWRITE THE-FLOOR-ABOVE))
 (6 2 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (6 2 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (6 2 (:REWRITE POLY-EVAL-CONST-POLY))
 (4 2 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (3 3 (:REWRITE EVAL-POLY-CONST-DIFFERENCE))
 (3 2 (:REWRITE |(equal (- x) c)|))
 (3 2 (:REWRITE |(equal (- x) (- y))|))
 (3 2 (:REWRITE |(< (- x) c)|))
 (3 2 (:REWRITE |(< (- x) (- y))|))
 (3 1 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (3 1 (:REWRITE SIMPLIFY-SUMS-<))
 (2 2 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (2 2 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (2 2 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (2 2 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (2 2 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (2 2 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (2 2 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (2 2 (:REWRITE INTEGERP-<-CONSTANT))
 (2 2 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (2 2 (:REWRITE ENV-P-WHEN-NOT-CONSP))
 (2 2 (:REWRITE CONSTANT-<-INTEGERP))
 (2 2 (:REWRITE |(equal c (/ x))|))
 (2 2 (:REWRITE |(equal c (- x))|))
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 (2 2 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (2 2 (:REWRITE |(< (/ x) (/ y))|))
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 (1 1 (:REWRITE-QUOTED-CONSTANT RFIX-UNDER-RATIONAL-EQUIV))
 (1 1 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (1 1 (:REWRITE >=ALL-MEMBER-HYPS))
 (1 1 (:REWRITE >-ALL-IS-GREATER-THAN-MEMBERS-HYPS))
 (1 1 (:REWRITE |(equal (+ (- c) x) y)|))
 (1 1 (:REWRITE |(< (/ x) 0)|))
 (1 1 (:REWRITE |(< (+ c/d x) y)|))
 (1 1 (:REWRITE |(< (+ (- c) x) y)|))
 (1 1 (:REWRITE |(< (* x y) 0)|))
 )
(POLY-P-POLY-P-RELATION-P-ENV-P-IMPLIES-NORMALIZED-VARIABLEBOUND-LISTP-RESTRICTDISEQUALITY
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 (579 55 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINEQUALITY-P))
 (382 106 (:TYPE-PRESCRIPTION IMPLIES-NOT-INEQ-OP))
 (342 342 (:TYPE-PRESCRIPTION IMPLIES-NOT-LT-OP))
 (340 2 (:REWRITE BODY-IMPLIES-VARIABLERELATION-P))
 (276 94 (:TYPE-PRESCRIPTION IMPLIES-NOT-OP-P))
 (257 257 (:TYPE-PRESCRIPTION BODY-IMPLIES-EQ-OP-P))
 (233 233 (:TYPE-PRESCRIPTION IMPLIES-NOT-GT-OP))
 (230 6 (:REWRITE BODY-IMPLIES-VARIABLEINEQUALITY-P))
 (228 1 (:REWRITE BODY-IMPLIES-VARIABLEBOUND-P))
 (216 1 (:REWRITE NORMALIZED-VARIABLEINTERVAL-FROM-VARIABLERELATION-P))
 (178 12 (:REWRITE DEFAULT-LESS-THAN-2))
 (174 1 (:DEFINITION >-ALL))
 (141 11 (:REWRITE DEFAULT-LESS-THAN-1))
 (108 6 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLERELATION-P))
 (82 2 (:REWRITE VARIABLEGREATER-FROM-VARIABLEINEQUALITY))
 (56 2 (:REWRITE VARIABLELESS-FROM-VARIABLEINEQUALITY))
 (54 6 (:REWRITE ACL2-NUMBERP-X))
 (30 10 (:REWRITE POLY-EVAL-CONST-POLY))
 (26 12 (:REWRITE DEFAULT-PLUS-2))
 (24 6 (:REWRITE RATIONALP-X))
 (22 12 (:REWRITE DEFAULT-PLUS-1))
 (20 2 (:REWRITE BODY-IMPLIES-VARIABLELESS-P))
 (20 2 (:REWRITE BODY-IMPLIES-VARIABLEGREATER-P))
 (15 7 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (14 6 (:REWRITE IMPLIES-VARIABLEINEQUALITY-P))
 (12 12 (:REWRITE THE-FLOOR-BELOW))
 (12 12 (:REWRITE THE-FLOOR-ABOVE))
 (12 6 (:REWRITE SIMPLIFY-SUMS-<))
 (12 4 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (11 11 (:REWRITE EVAL-POLY-CONST-DIFFERENCE))
 (10 7 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (10 7 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (10 1 (:REWRITE OPEN-BOUNDING-VARIABLES))
 (9 3 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (8 7 (:REWRITE |(< (- x) c)|))
 (8 7 (:REWRITE |(< (- x) (- y))|))
 (8 2 (:REWRITE >-ALL-UPPER-BOUND-BACKCHAINING))
 (7 7 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (7 7 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (7 7 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (7 7 (:REWRITE INTEGERP-<-CONSTANT))
 (7 7 (:REWRITE CONSTANT-<-INTEGERP))
 (7 7 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (7 7 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
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 (7 7 (:REWRITE |(< (/ x) c) 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))|))
 (6 6 (:REWRITE REDUCE-RATIONALP-+))
 (6 6 (:REWRITE REDUCE-RATIONALP-*))
 (6 6 (:REWRITE REDUCE-INTEGERP-+))
 (6 6 (:REWRITE RATIONALP-MINUS-X))
 (6 6 (:REWRITE INTEGERP-MINUS-X))
 (6 6 (:REWRITE DEFAULT-CAR))
 (6 6 (:REWRITE >=ALL-MEMBER-HYPS))
 (6 6 (:REWRITE >-ALL-IS-GREATER-THAN-MEMBERS-HYPS))
 (6 6 (:META META-RATIONALP-CORRECT))
 (6 6 (:META META-INTEGERP-CORRECT))
 (6 2 (:REWRITE VARID-FIX-VARID))
 (6 2 (:REWRITE IMPLIES-VARIABLERELATION-P))
 (6 2 (:REWRITE BODY-IMPLIES-VARIABLEINTERVAL-P))
 (6 2 (:REWRITE BODY-IMPLIES-VARIABLEEQUALITY-P))
 (6 2 (:REWRITE BODY-IMPLIES-POLYLESS-P))
 (6 2 (:REWRITE BODY-IMPLIES-POLYGREATER-P))
 (5 5 (:REWRITE DEFAULT-CDR))
 (5 4 (:REWRITE |(equal (- x) c)|))
 (5 4 (:REWRITE |(equal (- x) (- y))|))
 (4 4 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (4 4 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (4 4 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (4 4 (:REWRITE ENV-P-WHEN-NOT-CONSP))
 (4 4 (:REWRITE |(equal c (/ x))|))
 (4 4 (:REWRITE |(equal c (- x))|))
 (4 4 (:REWRITE |(equal (/ x) c)|))
 (4 4 (:REWRITE |(equal (/ x) (/ y))|))
 (4 2 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (3 3 (:REWRITE-QUOTED-CONSTANT RFIX-UNDER-RATIONAL-EQUIV))
 (3 1 (:REWRITE VARID-P-OF-CAR-WHEN-VARID-LISTP))
 (3 1 (:DEFINITION REMOVE-EQUAL))
 (2 2 (:TYPE-PRESCRIPTION SET-UPPER-BOUND-CTX_UNFIX_CHECK))
 (2 2 (:REWRITE SET-UPPER-BOUND-CTX_UNFIX_CHECK_REDUCTION_3))
 (2 2 (:REWRITE SET-UPPER-BOUND-CTX_REDUCTION))
 (2 2 (:REWRITE |(< (/ x) 0)|))
 (2 2 (:REWRITE |(< (* x y) 0)|))
 (2 2 (:REWRITE |(+ c (+ d x))|))
 (2 1 (:REWRITE DEFAULT-MINUS))
 (1 1 (:REWRITE T-IMPLIES-VARID-P-BOUND-VARID))
 (1 1 (:REWRITE T-IMPLIES-VARID-LISTP-BOUNDING-VARIABLES))
 (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 NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (1 1 (:REWRITE |(equal (+ (- c) x) y)|))
 (1 1 (:REWRITE |(< 0 (/ x))|))
 (1 1 (:REWRITE |(< 0 (* x y))|))
 (1 1 (:REWRITE |(< (+ c/d x) y)|))
 (1 1 (:REWRITE |(< (+ (- c) x) y)|))
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(EVAL-INEQ-CONJOINRESULTS
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 (182 62 (:REWRITE EVAL-INEQ-POLYINTERVALP))
 (120 120 (:TYPE-PRESCRIPTION POLYRELATION-P))
 (120 120 (:TYPE-PRESCRIPTION POLYINTERVAL-P))
 (28 28 (:REWRITE DEFAULT-CAR))
 (17 17 (:REWRITE DEFAULT-CDR))
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(CONJOINRESULTS-RESTRICTDISEQUALITY
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 (84 45 (:REWRITE DEFAULT-PLUS-1))
 (57 12 (:REWRITE DEFAULT-LESS-THAN-2))
 (21 12 (:REWRITE DEFAULT-LESS-THAN-1))
 (18 6 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (18 6 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (18 6 (:REWRITE POLY-EVAL-CONST-POLY))
 (18 6 (:REWRITE EVAL-INEQ-POLYRELATIONP))
 (18 6 (:REWRITE EVAL-INEQ-POLYINTERVALP))
 (12 12 (:TYPE-PRESCRIPTION POLYRELATION-P))
 (12 12 (:TYPE-PRESCRIPTION POLYINTERVAL-P))
 (12 12 (:REWRITE THE-FLOOR-BELOW))
 (12 12 (:REWRITE THE-FLOOR-ABOVE))
 (12 6 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (9 9 (:REWRITE EVAL-POLY-CONST-DIFFERENCE))
 (9 6 (:REWRITE |(equal (- x) c)|))
 (9 6 (:REWRITE |(equal (- x) (- y))|))
 (9 6 (:REWRITE |(< (- x) c)|))
 (9 6 (:REWRITE |(< (- x) (- y))|))
 (9 3 (:REWRITE SIMPLIFY-SUMS-EQUAL))
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 (6 6 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (6 6 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (6 6 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
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 (6 6 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
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 (6 6 (:REWRITE INTEGERP-<-CONSTANT))
 (6 6 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (6 6 (:REWRITE CONSTANT-<-INTEGERP))
 (6 6 (:REWRITE |(equal c (/ x))|))
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 (4 4 (:REWRITE DEFAULT-CDR))
 (4 4 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE-QUOTED-CONSTANT RFIX-UNDER-RATIONAL-EQUIV))
 (3 3 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
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 (3 3 (:REWRITE |(equal (+ (- c) x) y)|))
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 (3 3 (:REWRITE |(< (+ c/d x) y)|))
 (3 3 (:REWRITE |(< (+ (- c) x) y)|))
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(RESTRICTDISEQUALITY-INV2
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 (336 96 (:TYPE-PRESCRIPTION BODY-IMPLIES-POLYGREATER-P))
 (231 21 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINEQUALITY-P))
 (222 103 (:REWRITE DEFAULT-PLUS-2))
 (204 51 (:TYPE-PRESCRIPTION IMPLIES-NOT-INEQ-OP))
 (198 103 (:REWRITE DEFAULT-PLUS-1))
 (183 183 (:TYPE-PRESCRIPTION IMPLIES-NOT-LT-OP))
 (183 183 (:TYPE-PRESCRIPTION BODY-IMPLIES-LT-OP-P))
 (133 16 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (132 132 (:TYPE-PRESCRIPTION BODY-IMPLIES-EQ-OP-P))
 (132 48 (:TYPE-PRESCRIPTION IMPLIES-NOT-OP-P))
 (128 44 (:REWRITE POLY-EVAL-CONST-POLY))
 (126 126 (:TYPE-PRESCRIPTION IMPLIES-NOT-GT-OP))
 (126 126 (:TYPE-PRESCRIPTION BODY-IMPLIES-GT-OP-P))
 (108 108 (:TYPE-PRESCRIPTION FIX-RELATION))
 (99 44 (:REWRITE DEFAULT-LESS-THAN-2))
 (96 12 (:REWRITE ACL2-NUMBERP-X))
 (82 44 (:REWRITE DEFAULT-LESS-THAN-1))
 (60 27 (:REWRITE DEFAULT-MINUS))
 (44 44 (:REWRITE THE-FLOOR-BELOW))
 (44 44 (:REWRITE THE-FLOOR-ABOVE))
 (42 6 (:REWRITE RATIONALP-X))
 (40 36 (:REWRITE |(< (- x) c)|))
 (40 36 (:REWRITE |(< (- x) (- y))|))
 (39 36 (:REWRITE |(< c (- x))|))
 (39 1 (:REWRITE |(<= (/ x) y) with (< x 0)|))
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 (39 1 (:REWRITE |(< x (/ y)) with (< y 0)|))
 (39 1 (:REWRITE |(< x (/ y)) with (< 0 y)|))
 (36 36 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
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 (19 15 (:REWRITE SIMPLIFY-SUMS-EQUAL))
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 (16 16 (:REWRITE |(equal c (- x))|))
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 (7 7 (:REWRITE |(< y (+ (- c) x))|))
 (7 7 (:REWRITE |(< x (+ c/d y))|))
 (7 6 (:REWRITE |(< 0 (/ x))|))
 (6 6 (:REWRITE REDUCE-RATIONALP-+))
 (6 6 (:REWRITE REDUCE-RATIONALP-*))
 (6 6 (:REWRITE REDUCE-INTEGERP-+))
 (6 6 (:REWRITE RATIONALP-MINUS-X))
 (6 6 (:REWRITE INTEGERP-MINUS-X))
 (6 6 (:REWRITE |(< 0 (* x y))|))
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 (6 6 (:REWRITE |(< (+ c/d x) y)|))
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 (4 4 (:REWRITE DEFAULT-CAR))
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 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (3 1 (:REWRITE EVAL-INEQ-POLYRELATIONP))
 (3 1 (:REWRITE EVAL-INEQ-POLYINTERVALP))
 (3 1 (:REWRITE |(equal x (/ y))|))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (2 2 (:REWRITE FOLD-CONSTS-IN-+))
 (2 1 (:REWRITE DEFAULT-DIVIDE))
 (2 1 (:REWRITE |(not (equal x (/ y)))|))
 (1 1 (:TYPE-PRESCRIPTION EVAL-INEQ))
 (1 1 (:REWRITE |(equal (+ (- c) x) y)|))
 )
(RESTRICTDISEQUALITY-INV2-EXCLUSIVE
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 (162 75 (:REWRITE DEFAULT-PLUS-2))
 (146 75 (:REWRITE DEFAULT-PLUS-1))
 (130 26 (:REWRITE ACL2-NUMBERP-X))
 (119 41 (:REWRITE POLY-EVAL-CONST-POLY))
 (118 34 (:TYPE-PRESCRIPTION BODY-IMPLIES-POLYLESS-P))
 (118 34 (:TYPE-PRESCRIPTION BODY-IMPLIES-POLYGREATER-P))
 (88 8 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINEQUALITY-P))
 (84 46 (:REWRITE DEFAULT-LESS-THAN-1))
 (82 46 (:REWRITE DEFAULT-LESS-THAN-2))
 (78 2 (:REWRITE |(<= (/ x) y) with (< x 0)|))
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 (78 2 (:REWRITE |(< x (/ y)) with (< y 0)|))
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 (65 65 (:TYPE-PRESCRIPTION BODY-IMPLIES-LT-OP-P))
 (52 13 (:REWRITE RATIONALP-X))
 (50 50 (:TYPE-PRESCRIPTION BODY-IMPLIES-EQ-OP-P))
 (50 18 (:TYPE-PRESCRIPTION IMPLIES-NOT-OP-P))
 (46 46 (:REWRITE THE-FLOOR-BELOW))
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 (36 34 (:REWRITE |(equal (/ x) (/ y))|))
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(RESTRICTDISEQUALITY-INV1-INCLUSIVE
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(RESTRICTEQUALITY)
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(ANDTRUE-VARIABLEEQUALITY-VARIABLELESS)
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(UPPER-BOUND-BOUNDING-VARIABLES-ANDTRUE-VARIABLEEQUALITY-VARIABLEGREATER
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 (2 2 (:REWRITE |(< (- x) (- y))|))
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 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (1 1 (:REWRITE |(< 0 (/ x))|))
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 )
(UPPER-BOUND-ALL-BOUND-LIST-VARIABLESANDTRUE-VARIABLEEQUALITY-VARIABLEINEQUALITY
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 (876 538 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINTERVAL-P))
 (498 10 (:REWRITE VARIABLELESS-FROM-VARIABLEINEQUALITY))
 (278 7 (:REWRITE BODY-IMPLIES-VARIABLEINEQUALITY-P))
 (204 12 (:DEFINITION ALL-BOUND-LIST-VARIABLES))
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 (135 3 (:REWRITE BODY-IMPLIES-LT-OP-P))
 (132 12 (:DEFINITION ALL-BOUND-VARIABLES))
 (106 16 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (105 95 (:TYPE-PRESCRIPTION LIST::APPEND-CONSP-TYPE-TWO))
 (105 95 (:TYPE-PRESCRIPTION LIST::APPEND-CONSP-TYPE-ONE))
 (105 3 (:DEFINITION LT-OP-P))
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 (101 21 (:REWRITE ACL2-NUMBERP-X))
 (83 4 (:REWRITE VARIABLEGREATER-FROM-VARIABLEINEQUALITY))
 (79 10 (:REWRITE BODY-IMPLIES-VARIABLELESS-P))
 (58 8 (:REWRITE SUBSET-NOT-CONSP))
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(BOUND-VARID-ANDTRUE-VARIABLEEQUALITY-VARIABLEINEQUALITY
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 (838 519 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINTERVAL-P))
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 (63 8 (:REWRITE BODY-IMPLIES-VARIABLELESS-P))
 (31 4 (:REWRITE BODY-IMPLIES-VARIABLEGREATER-P))
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 (19 12 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
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(UPPER-BOUND-BOUND-VARID-LIST-ANDTRUE-VARIABLEEQUALITY-VARIABLEINEQUALITY
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 (135 3 (:REWRITE BODY-IMPLIES-LT-OP-P))
 (106 16 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (105 95 (:TYPE-PRESCRIPTION LIST::APPEND-CONSP-TYPE-TWO))
 (105 95 (:TYPE-PRESCRIPTION LIST::APPEND-CONSP-TYPE-ONE))
 (105 3 (:DEFINITION LT-OP-P))
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 (101 21 (:REWRITE ACL2-NUMBERP-X))
 (83 4 (:REWRITE VARIABLEGREATER-FROM-VARIABLEINEQUALITY))
 (79 10 (:REWRITE BODY-IMPLIES-VARIABLELESS-P))
 (58 8 (:REWRITE SUBSET-NOT-CONSP))
 (40 10 (:REWRITE RATIONALP-X))
 (36 12 (:DEFINITION BOUND-VARID-LIST))
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 (16 16 (:REWRITE |(equal c (/ x))|))
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 (3 1 (:REWRITE BODY-IMPLIES-VARIABLEINTERVAL-P))
 )
(UPPER-BOUND-BOUNDING-VARIABLES-ANDTRUE-VARIABLEEQUALITY-VARIABLEINEQUALITY
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 (858 529 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINTERVAL-P))
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 (278 7 (:REWRITE BODY-IMPLIES-VARIABLEINEQUALITY-P))
 (135 3 (:REWRITE BODY-IMPLIES-LT-OP-P))
 (106 16 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (105 95 (:TYPE-PRESCRIPTION LIST::APPEND-CONSP-TYPE-TWO))
 (105 95 (:TYPE-PRESCRIPTION LIST::APPEND-CONSP-TYPE-ONE))
 (105 3 (:DEFINITION LT-OP-P))
 (102 3 (:REWRITE VARIABLELESS-P-IMPLIES-LT-OP-P-RELATION-OP))
 (101 21 (:REWRITE ACL2-NUMBERP-X))
 (83 4 (:REWRITE VARIABLEGREATER-FROM-VARIABLEINEQUALITY))
 (79 10 (:REWRITE BODY-IMPLIES-VARIABLELESS-P))
 (66 30 (:REWRITE OPEN-BOUNDING-VARIABLES))
 (58 8 (:REWRITE SUBSET-NOT-CONSP))
 (40 10 (:REWRITE RATIONALP-X))
 (31 4 (:REWRITE BODY-IMPLIES-VARIABLEGREATER-P))
 (29 9 (:REWRITE SET-UPPER-BOUND-PRED-CHAINING))
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(ANDTRUE-VARIABLEEQUALITY-VARIABLEINEQUALITY-INV1
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 (1038 670 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINTERVAL-P))
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 (166 3 (:REWRITE VARIABLEGREATER-P-IMPLIES-GT-OP-P-RELATION-OP))
 (144 16 (:DEFINITION GET-BINDING))
 (123 11 (:REWRITE BODY-IMPLIES-POLYLESS-P))
 (104 26 (:REWRITE RATIONALP-X))
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 (91 6 (:REWRITE BODY-IMPLIES-VARIABLEGREATER-P))
 (80 16 (:REWRITE WF-BINDING-FIX-WF-BINDING))
 (62 36 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (60 20 (:REWRITE POLY-EVAL-CONST-POLY))
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 (47 3 (:REWRITE BODY-IMPLIES-GT-OP-P))
 (44 44 (:TYPE-PRESCRIPTION BINDING-P))
 (42 36 (:REWRITE SIMPLIFY-SUMS-EQUAL))
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 (36 36 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (36 36 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
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(ANDTRUE-VARIABLEEQUALITY-VARIABLEINEQUALITY-INV2
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 (204 204 (:TYPE-PRESCRIPTION BINDING-P))
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 (166 3 (:REWRITE VARIABLEGREATER-P-IMPLIES-GT-OP-P-RELATION-OP))
 (164 60 (:REWRITE POLY-EVAL-CONST-POLY))
 (159 23 (:REWRITE BODY-IMPLIES-POLYLESS-P))
 (143 13 (:REWRITE BODY-IMPLIES-VARIABLEGREATER-P))
 (114 48 (:REWRITE WF-BINDING-P-OF-CAR-WHEN-ENV-P))
 (107 57 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
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 (98 10 (:REWRITE BODY-IMPLIES-LT-OP-P))
 (83 57 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (72 9 (:REWRITE BODY-IMPLIES-POLYGREATER-P))
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 (18 18 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (18 18 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (18 18 (:REWRITE INTEGERP-<-CONSTANT))
 (18 18 (:REWRITE CONSTANT-<-INTEGERP))
 (18 18 (:REWRITE >-ALL-IS-GREATER-THAN-MEMBERS-HYPS))
 (18 18 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (18 18 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (18 18 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (18 18 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (18 18 (:REWRITE |(< c (- x))|))
 (18 18 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (18 18 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (18 18 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (18 18 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (18 18 (:REWRITE |(< (/ x) (/ y))|))
 (18 18 (:REWRITE |(< (- x) c)|))
 (18 18 (:REWRITE |(< (- x) (- y))|))
 (16 16 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (16 16 (:REWRITE >=ALL-MEMBER-HYPS))
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 (12 4 (:REWRITE BODY-IMPLIES-VARIABLEEQUALITY-P))
 (6 6 (:REWRITE BODY-IMPLIES-LT-OP-P))
 )
(ANDTRUE-VARIABLEEQUALITY-VARIABLEEQUALITY)
(AND-AND-ENV-P-IMPLIES-VARIABLEBOUND-P-VARIABLEBOUND-LISTP-ANDTRUE-VARIABLEEQUALITY-VARIABLEEQUALITY
 (84399 12315 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINEQUALITY-P))
 (38805 15451 (:TYPE-PRESCRIPTION IMPLIES-NOT-OP-P))
 (9811 160 (:REWRITE BODY-IMPLIES-VARIABLEINEQUALITY-P))
 (7876 33 (:REWRITE VARIABLEINEQUALITY-P-IMPLIES-INEQ-OP-P-RELATION-OP))
 (4080 24 (:REWRITE BODY-IMPLIES-VARIABLERELATION-P))
 (3408 648 (:REWRITE ACL2-NUMBERP-X))
 (3353 123 (:REWRITE BODY-IMPLIES-VARIABLEGREATER-P))
 (3216 12 (:DEFINITION VARIABLEBOUND-LISTP))
 (3024 132 (:REWRITE SUBSET-P-UPPER-BOUND-BACKCHAINING))
 (2899 79 (:REWRITE BODY-IMPLIES-POLYGREATER-P))
 (2633 328 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (2568 123 (:REWRITE VARIABLEGREATER-FROM-VARIABLEINEQUALITY))
 (1868 112 (:REWRITE BODY-IMPLIES-VARIABLELESS-P))
 (1782 72 (:DEFINITION REMOVE-EQUAL))
 (1750 112 (:REWRITE VARIABLELESS-FROM-VARIABLEINEQUALITY))
 (1666 14 (:DEFINITION >-ALL))
 (1650 33 (:REWRITE VARIABLEGREATER-P-IMPLIES-GT-OP-P-RELATION-OP))
 (1572 44 (:REWRITE SET-UPPER-BOUND-GET-POLY-VARIABLES-SUB))
 (1469 68 (:REWRITE BODY-IMPLIES-POLYLESS-P))
 (1403 353 (:REWRITE RATIONALP-X))
 (1144 22 (:REWRITE VARIABLELESS-P-IMPLIES-LT-OP-P-RELATION-OP))
 (816 12 (:REWRITE ZP-OPEN))
 (792 88 (:REWRITE ABSTRACT-GET-POLY-VARIABLES-RELATION-BOUNDING-POLY))
 (770 22 (:DEFINITION GT-OP-P))
 (616 176 (:REWRITE OPEN-BOUNDING-VARIABLES))
 (616 88 (:REWRITE SET-UPPER-BOUND-APPEND))
 (484 44 (:REWRITE SET-UPPER-BOUND-PRED-CHAINING))
 (432 432 (:REWRITE REDUCE-INTEGERP-+))
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 (432 432 (:META META-INTEGERP-CORRECT))
 (426 6 (:REWRITE BAG::ZP-NFIX))
 (414 6 (:REWRITE BAG::NOT-ZP-NFIX-REDUCTION))
 (411 303 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (410 160 (:REWRITE IMPLIES-VARIABLEINEQUALITY-P))
 (385 11 (:DEFINITION LT-OP-P))
 (375 181 (:REWRITE DEFAULT-PLUS-2))
 (353 353 (:REWRITE REDUCE-RATIONALP-+))
 (353 353 (:REWRITE REDUCE-RATIONALP-*))
 (353 353 (:REWRITE RATIONALP-MINUS-X))
 (353 353 (:META META-RATIONALP-CORRECT))
 (353 328 (:REWRITE |(equal (- x) c)|))
 (353 328 (:REWRITE |(equal (- x) (- y))|))
 (337 181 (:REWRITE DEFAULT-PLUS-1))
 (336 336 (:TYPE-PRESCRIPTION SET-UPPER-BOUND-CTX_UNFIX_CHECK))
 (328 328 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (328 328 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (328 328 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (328 328 (:REWRITE |(equal c (/ x))|))
 (328 328 (:REWRITE |(equal c (- x))|))
 (328 328 (:REWRITE |(equal (/ x) c)|))
 (328 328 (:REWRITE |(equal (/ x) (/ y))|))
 (304 304 (:REWRITE THE-FLOOR-BELOW))
 (304 304 (:REWRITE THE-FLOOR-ABOVE))
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 (292 292 (:REWRITE SET-UPPER-BOUND-CTX_REDUCTION))
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 (236 236 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
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 (236 236 (:REWRITE INTEGERP-<-CONSTANT))
 (236 236 (:REWRITE CONSTANT-<-INTEGERP))
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 (236 236 (:REWRITE |(< (- x) (- y))|))
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 (180 180 (:REWRITE DEFAULT-CDR))
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 (171 123 (:REWRITE BODY-IMPLIES-VARIABLEINTERVAL-P))
 (160 32 (:REWRITE SET-EQUIV-QUANT-APPEND-COMMUTES))
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 (140 14 (:REWRITE VARID-P-OF-CAR-WHEN-VARID-LISTP))
 (130 130 (:REWRITE |(< (/ x) 0)|))
 (130 130 (:REWRITE |(< (* x y) 0)|))
 (112 28 (:REWRITE >-ALL-UPPER-BOUND-BACKCHAINING))
 (88 88 (:REWRITE ADVISER::SUBSET-P-BY-MULTIPLICITY))
 (88 88 (:REWRITE SUBSET-P-BY-MULTIPLICITY))
 (87 87 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (87 87 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (75 75 (:REWRITE |(< 0 (/ x))|))
 (75 75 (:REWRITE |(< 0 (* x y))|))
 (73 73 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (73 73 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (72 72 (:LINEAR >=ALL-REMOVE-EQUAL-IMPLICATION))
 (72 72 (:LINEAR >=ALL-MEMBER))
 (72 24 (:REWRITE IMPLIES-VARIABLERELATION-P))
 (70 70 (:TYPE-PRESCRIPTION REMOVE-EQUAL))
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 (50 25 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
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 (33 11 (:REWRITE LT-OP-P-T-T-IMPLIES-VARIABLELESS-P-VARIABLERELATION))
 (28 28 (:TYPE-PRESCRIPTION VARID-LISTP))
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 (25 25 (:REWRITE |(equal (+ (- c) x) y)|))
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 (11 11 (:REWRITE LEADING-VARIABLE-IS-LESS-THAN-VARID-IF-IN-POLY-VARIABLES))
 )
(ANDTRUE-VARIABLEEQUALITY-VARIABLEEQUALITY
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 (2680 850 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLELESS-P))
 (2680 850 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEGREATER-P))
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 (696 472 (:TYPE-PRESCRIPTION IMPLIES-NOT-OP-P))
 (284 182 (:TYPE-PRESCRIPTION BODY-IMPLIES-VARIABLEINTERVAL-P))
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 (108 12 (:REWRITE ACL2-NUMBERP-X))
 (48 12 (:REWRITE RATIONALP-X))
 (46 46 (:REWRITE THE-FLOOR-BELOW))
 (46 46 (:REWRITE THE-FLOOR-ABOVE))
 (32 32 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (32 32 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (32 32 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (32 32 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (32 32 (:REWRITE INTEGERP-<-CONSTANT))
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(AND-AND-ENV-P-IMPLIES-NORMALIZED-VARIABLEBOUND-P-NORMALIZED-VARIABLEBOUND-LISTP-ANDTRUE-VARIABLEEQUALITY-VARIABLEEQUALITY
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 (56947 495 (:REWRITE BODY-IMPLIES-POLYGREATER-P))
 (44064 9272 (:REWRITE ACL2-NUMBERP-X))
 (42962 5017 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (41024 2112 (:REWRITE SUBSET-P-UPPER-BOUND-BACKCHAINING))
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 (22506 1221 (:REWRITE VARIABLEGREATER-FROM-VARIABLEINEQUALITY))
 (21648 754 (:DEFINITION REMOVE-EQUAL))
 (20394 495 (:REWRITE VARIABLEGREATER-P-IMPLIES-GT-OP-P-RELATION-OP))
 (17792 704 (:REWRITE SET-UPPER-BOUND-GET-POLY-VARIABLES-SUB))
 (17419 4357 (:REWRITE RATIONALP-X))
 (16170 462 (:DEFINITION GT-OP-P))
 (11880 990 (:REWRITE VARIABLELESS-FROM-VARIABLEINEQUALITY))
 (9856 1408 (:REWRITE SET-UPPER-BOUND-APPEND))
 (9768 264 (:REWRITE VARIABLELESS-P-IMPLIES-LT-OP-P-RELATION-OP))
 (8085 231 (:DEFINITION LT-OP-P))
 (7744 704 (:REWRITE SET-UPPER-BOUND-PRED-CHAINING))
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 (5632 1408 (:REWRITE ABSTRACT-GET-POLY-VARIABLES-RELATION-BOUNDING-POLY))
 (5042 5017 (:REWRITE |(equal (- x) c)|))
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 (5017 5017 (:REWRITE |(equal c (- x))|))
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 (302 302 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
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 (257 257 (:REWRITE >-ALL-IS-GREATER-THAN-MEMBERS-HYPS))
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 (97 97 (:REWRITE |(< 0 (* x y))|))
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 (72 72 (:LINEAR >=ALL-MEMBER))
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 (25 25 (:REWRITE |(equal (+ (- c) x) y)|))
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 )
(BOUND-VARID-LIST-ANDTRUE-VARIABLEEQUALITY-VARIABLEEQUALITY
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 (46059 11517 (:REWRITE RATIONALP-X))
 (43114 5015 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (32832 4356 (:DEFINITION REMOVE-EQUAL))
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 (26953 276 (:REWRITE BODY-IMPLIES-POLYLESS-P))
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 (16170 462 (:DEFINITION GT-OP-P))
 (12216 1002 (:REWRITE VARIABLELESS-FROM-VARIABLEINEQUALITY))
 (11753 11753 (:REWRITE THE-FLOOR-BELOW))
 (11753 11753 (:REWRITE THE-FLOOR-ABOVE))
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(UPPER-BOUND-ALL-BOUND-LIST-VARIABLESANDTRUE-VARIABLEEQUALITY-VARIABLEEQUALITY
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(BOUND-VARID-ANDTRUE-VARIABLEEQUALITY-VARIABLEEQUALITY
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(UPPER-BOUND-BOUND-VARID-LIST-ANDTRUE-VARIABLEEQUALITY-VARIABLEEQUALITY
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(UPPER-BOUND-BOUNDING-VARIABLES-ANDTRUE-VARIABLEEQUALITY-VARIABLEEQUALITY
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(BOUND-VARID-LIST-ANDTRUE-VARIABLERELATION-VARIABLEBOUND
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(UPPER-BOUND-ALL-BOUND-LIST-VARIABLESANDTRUE-VARIABLERELATION-VARIABLEBOUND
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(BOUND-VARID-ANDTRUE-VARIABLERELATION-VARIABLEBOUND
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(UPPER-BOUND-BOUND-VARID-LIST-ANDTRUE-VARIABLERELATION-VARIABLEBOUND
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(UPPER-BOUND-BOUNDING-VARIABLES-ANDTRUE-VARIABLERELATION-VARIABLEBOUND
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(UPPER-BOUND-BOUNDING-VARIABLES-ANDTRUE-VARIABLEBOUND-VARIABLEBOUND
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(ANDTRUE-VARIABLEBOUND-VARIABLEBOUND-INV1
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(ANDTRUE-VARIABLEBOUND-VARIABLEBOUND-INV2
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