(FIX-SUBSTITUTION)
(FIX-TERM)
(THE-TOP-TERM-ANTI-UNIFY-VARIABLE-P)
(THE-TOP-TERM-MG-INSTANCE-VARIABLE-P-1)
(THE-TOP-TERM-MG-INSTANCE-VARIABLE-P-2)
(SUBSTITUTION-P-ALISTP-FORWARD-CHAINING
 (51 51 (:REWRITE DEFAULT-CAR))
 (36 9 (:REWRITE O-P-O-INFP-CAR))
 (20 20 (:REWRITE DEFAULT-CDR))
 (9 9 (:REWRITE O-P-DEF-O-FINP-1))
 (8 8 (:REWRITE SYSTEM-P-TERM-P-AUX-ARGUMENTS))
 )
(EXT-TERM-S-P)
(EXT-TERM-P)
(EXT-SUBSTITUTION-S-P)
(EXT-SUBSTITUTION-P)
(APP<=
 (1 1 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE DEFAULT-CAR))
 )
(S<=
 (4 4 (:REWRITE DEFAULT-CDR))
 (4 4 (:REWRITE DEFAULT-CAR))
 )
(MATCH<=
 (4 4 (:REWRITE DEFAULT-CDR))
 (4 4 (:REWRITE DEFAULT-CAR))
 )
(MATCH<=-EXT-SUBSTITUTION-S-P
 (37 4 (:DEFINITION TERM-S-P-AUX))
 (20 4 (:DEFINITION LEN))
 (14 14 (:REWRITE DEFAULT-CDR))
 (8 8 (:REWRITE DEFAULT-CAR))
 (8 4 (:REWRITE DEFAULT-+-2))
 (4 4 (:TYPE-PRESCRIPTION LEN))
 (4 4 (:REWRITE DEFAULT-+-1))
 (4 1 (:REWRITE O-P-O-INFP-CAR))
 (2 2 (:TYPE-PRESCRIPTION O-P))
 (1 1 (:REWRITE SYSTEM-S-P-TERM-P-AUX-ARGUMENTS))
 (1 1 (:REWRITE O-P-DEF-O-FINP-1))
 )
(APP<=-SUBSTITUTION-S-P
 (66 3 (:DEFINITION SUBSTITUTION-S-P))
 (60 3 (:DEFINITION APPLY-SUBST))
 (57 6 (:DEFINITION TERM-S-P-AUX))
 (45 33 (:REWRITE DEFAULT-CDR))
 (42 30 (:REWRITE DEFAULT-CAR))
 (42 3 (:DEFINITION VAL))
 (36 9 (:REWRITE O-P-O-INFP-CAR))
 (30 6 (:DEFINITION LEN))
 (18 18 (:TYPE-PRESCRIPTION O-P))
 (12 6 (:REWRITE DEFAULT-+-2))
 (9 9 (:REWRITE O-P-DEF-O-FINP-1))
 (6 6 (:TYPE-PRESCRIPTION LEN))
 (6 6 (:REWRITE DEFAULT-+-1))
 (3 3 (:REWRITE THE-TOP-TERM-MG-INSTANCE-VARIABLE-P-2))
 (3 3 (:REWRITE THE-TOP-TERM-MG-INSTANCE-VARIABLE-P-1))
 (3 3 (:REWRITE THE-TOP-TERM-ANTI-UNIFY-VARIABLE-P))
 (3 3 (:REWRITE SYSTEM-S-P-TERM-P-AUX-ARGUMENTS))
 )
(APP<=-S<=-RELATIONSHIP-1
 (48 1 (:REWRITE RENAMING-IMPLIES-RENAMED))
 (46 1 (:DEFINITION RENAMING))
 (40 2 (:DEFINITION APPLY-SUBST))
 (29 13 (:REWRITE DEFAULT-CDR))
 (28 2 (:DEFINITION VAL))
 (24 6 (:REWRITE O-P-O-INFP-CAR))
 (20 12 (:REWRITE DEFAULT-CAR))
 (19 1 (:DEFINITION SETP))
 (15 1 (:DEFINITION VARIABLE-SUBSTITUTION))
 (8 1 (:DEFINITION CO-DOMAIN))
 (7 1 (:DEFINITION MEMBER-EQUAL))
 (6 6 (:REWRITE O-P-DEF-O-FINP-1))
 (6 1 (:REWRITE VARIABLE-MINIMUM-SUBSUMPTION))
 (5 5 (:TYPE-PRESCRIPTION VARIABLE-SUBSTITUTION))
 (5 5 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (4 4 (:TYPE-PRESCRIPTION SETP))
 (4 4 (:TYPE-PRESCRIPTION CO-DOMAIN))
 (4 4 (:REWRITE THE-TOP-TERM-MG-INSTANCE-VARIABLE-P-2))
 (4 4 (:REWRITE THE-TOP-TERM-MG-INSTANCE-VARIABLE-P-1))
 (4 4 (:REWRITE THE-TOP-TERM-ANTI-UNIFY-VARIABLE-P))
 (3 3 (:TYPE-PRESCRIPTION VARIABLE-P))
 (1 1 (:TYPE-PRESCRIPTION RENAMING))
 )
(APP<=-S<=-RELATIONSHIP-2
 (36 6 (:REWRITE VARIABLE-MINIMUM-SUBSUMPTION))
 (21 1 (:DEFINITION APPLY-SUBST))
 (14 1 (:DEFINITION VAL))
 (12 12 (:TYPE-PRESCRIPTION VARIABLE-P))
 (8 4 (:REWRITE DEFAULT-CAR))
 (8 2 (:REWRITE O-P-O-INFP-CAR))
 (7 7 (:REWRITE THE-TOP-TERM-MG-INSTANCE-VARIABLE-P-2))
 (7 7 (:REWRITE THE-TOP-TERM-MG-INSTANCE-VARIABLE-P-1))
 (7 7 (:REWRITE THE-TOP-TERM-ANTI-UNIFY-VARIABLE-P))
 (7 3 (:REWRITE DEFAULT-CDR))
 (4 4 (:TYPE-PRESCRIPTION O-P))
 (2 2 (:REWRITE O-P-DEF-O-FINP-1))
 (1 1 (:REWRITE APP<=-S<=-RELATIONSHIP-1))
 )
(S<=-REFLEXIVITY)
(S<=-TRANSITIVITY
 (18 3 (:REWRITE VARIABLE-MINIMUM-SUBSUMPTION))
 (6 6 (:TYPE-PRESCRIPTION VARIABLE-P))
 (3 3 (:REWRITE THE-TOP-TERM-MG-INSTANCE-VARIABLE-P-2))
 (3 3 (:REWRITE THE-TOP-TERM-MG-INSTANCE-VARIABLE-P-1))
 (3 3 (:REWRITE THE-TOP-TERM-ANTI-UNIFY-VARIABLE-P))
 (3 3 (:REWRITE APP<=-S<=-RELATIONSHIP-1))
 )
(S<)
(MEASURE-S<)
(MEASURE-S<-ORDINALP
 (7 3 (:REWRITE O-P-DEF-O-FINP-1))
 (2 2 (:TYPE-PRESCRIPTION MAKE-ORD))
 (2 2 (:REWRITE MAKE-ORD-EQUAL-4))
 (1 1 (:TYPE-PRESCRIPTION SUBSUMPTION-MEASURE))
 )
(S<-WELL-FOUNDED
 (36 6 (:REWRITE VARIABLE-MINIMUM-SUBSUMPTION))
 (23 2 (:REWRITE O-FIRST-EXPT-<))
 (18 2 (:REWRITE O-FIRST-COEFF-<))
 (12 12 (:TYPE-PRESCRIPTION VARIABLE-P))
 (10 10 (:TYPE-PRESCRIPTION SUBSUMPTION-MEASURE))
 (7 7 (:TYPE-PRESCRIPTION O-FINP))
 (7 3 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (6 6 (:REWRITE THE-TOP-TERM-MG-INSTANCE-VARIABLE-P-2))
 (6 6 (:REWRITE THE-TOP-TERM-MG-INSTANCE-VARIABLE-P-1))
 (6 6 (:REWRITE THE-TOP-TERM-ANTI-UNIFY-VARIABLE-P))
 (5 5 (:TYPE-PRESCRIPTION MAKE-ORD))
 (5 2 (:REWRITE O-FIRST-COEFF-DEF-O-FINP))
 (5 2 (:REWRITE O-FINP-<))
 (5 2 (:REWRITE AC-<))
 (4 1 (:REWRITE O-INFP-O-FINP-O<=))
 (3 3 (:REWRITE MAKE-ORD-EQUAL-4))
 (3 1 (:REWRITE O<=-O-FINP-DEF))
 (3 1 (:REWRITE O-FIRST-EXPT-O-INFP))
 (2 2 (:REWRITE |a < b & b < c  =>  a < c|))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2 1 (:REWRITE DEFAULT-<-2))
 (2 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE S<=-TRANSITIVITY))
 (1 1 (:REWRITE APP<=-S<=-RELATIONSHIP-1))
 )
(GLB-S<=
 (4 4 (:REWRITE DEFAULT-CDR))
 (4 4 (:REWRITE DEFAULT-CAR))
 )
(GLB-S<=-LOWER-BOUND-1
 (10 10 (:TYPE-PRESCRIPTION GLB-S<=))
 (4 4 (:REWRITE THE-TOP-TERM-MG-INSTANCE-VARIABLE-P-2))
 (4 4 (:REWRITE THE-TOP-TERM-MG-INSTANCE-VARIABLE-P-1))
 (4 4 (:REWRITE THE-TOP-TERM-ANTI-UNIFY-VARIABLE-P))
 )
(GLB-S<=-LOWER-BOUND-2
 (10 10 (:TYPE-PRESCRIPTION GLB-S<=))
 (4 4 (:REWRITE THE-TOP-TERM-MG-INSTANCE-VARIABLE-P-2))
 (4 4 (:REWRITE THE-TOP-TERM-MG-INSTANCE-VARIABLE-P-1))
 (4 4 (:REWRITE THE-TOP-TERM-ANTI-UNIFY-VARIABLE-P))
 )
(GLB-S<=-IS-GREATER-THAN-ANY-LOWER-BOUND
 (22 22 (:TYPE-PRESCRIPTION GLB-S<=))
 (19 19 (:REWRITE THE-TOP-TERM-MG-INSTANCE-VARIABLE-P-2))
 (19 19 (:REWRITE THE-TOP-TERM-MG-INSTANCE-VARIABLE-P-1))
 (12 4 (:REWRITE S<=-TRANSITIVITY))
 (4 4 (:REWRITE APP<=-S<=-RELATIONSHIP-1))
 )
(GLB-S<=-CLOSURE-PROPERTY
 (40 8 (:DEFINITION LEN))
 (27 27 (:TYPE-PRESCRIPTION GLB-S<=))
 (24 24 (:REWRITE DEFAULT-CDR))
 (16 8 (:REWRITE DEFAULT-+-2))
 (8 8 (:TYPE-PRESCRIPTION LEN))
 (8 8 (:REWRITE DEFAULT-CAR))
 (8 8 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE THE-TOP-TERM-MG-INSTANCE-VARIABLE-P-2))
 (2 2 (:REWRITE THE-TOP-TERM-MG-INSTANCE-VARIABLE-P-1))
 (2 2 (:REWRITE THE-TOP-TERM-ANTI-UNIFY-VARIABLE-P))
 )
(LUB-S<=
 (4 4 (:REWRITE DEFAULT-CDR))
 (4 4 (:REWRITE DEFAULT-CAR))
 )
(LUB-S<=-UPPER-BOUND-1
 (7 7 (:REWRITE THE-TOP-TERM-MG-INSTANCE-VARIABLE-P-2))
 (5 5 (:REWRITE THE-TOP-TERM-ANTI-UNIFY-VARIABLE-P))
 (5 5 (:REWRITE IF-SUBSUME-COMMON-THERM-MG-INSTANCE))
 )
(LUB-S<=-UPPER-BOUND-2
 (5 5 (:REWRITE THE-TOP-TERM-MG-INSTANCE-VARIABLE-P-1))
 (5 5 (:REWRITE THE-TOP-TERM-ANTI-UNIFY-VARIABLE-P))
 (5 5 (:REWRITE IF-SUBSUME-COMMON-THERM-MG-INSTANCE))
 )
(LUB-S<=-LESS-THAN-ANY-UPPER-BOUND
 (11 11 (:REWRITE THE-TOP-TERM-MG-INSTANCE-VARIABLE-P-2))
 (11 11 (:REWRITE THE-TOP-TERM-MG-INSTANCE-VARIABLE-P-1))
 (11 11 (:REWRITE THE-TOP-TERM-ANTI-UNIFY-VARIABLE-P))
 (2 2 (:REWRITE S<=-TRANSITIVITY))
 (2 2 (:REWRITE APP<=-S<=-RELATIONSHIP-1))
 )
(LUB-S<=-CLOSURE-PROPERTY
 (54 6 (:DEFINITION TERM-S-P-AUX))
 (30 6 (:DEFINITION LEN))
 (18 18 (:REWRITE DEFAULT-CDR))
 (12 6 (:REWRITE DEFAULT-+-2))
 (6 6 (:TYPE-PRESCRIPTION LEN))
 (6 6 (:REWRITE DEFAULT-CAR))
 (6 6 (:REWRITE DEFAULT-+-1))
 (5 5 (:REWRITE IF-SUBSUME-COMMON-THERM-MG-INSTANCE))
 (2 2 (:REWRITE THE-TOP-TERM-MG-INSTANCE-VARIABLE-P-2))
 (2 2 (:REWRITE THE-TOP-TERM-MG-INSTANCE-VARIABLE-P-1))
 (2 2 (:REWRITE THE-TOP-TERM-ANTI-UNIFY-VARIABLE-P))
 )
