(CNF::Q)
(CNF::LEGAL)
(CNF::REDUCE-ONE-STEP)
(CNF::PROOF-STEP-P)
(CNF::EQUIV-P)
(CNF::TRANSFORM-TO-VALLEY)
(CNF::CHUCH-ROSSER-PROPERTY)
(CNF::PROOF-IRREDUCIBLE)
(CNF::NORMALIZING)
(CNF::NORMALIZING-NOT-CONSP-PROOF-IRREDUCIBLE)
(CNF::NORMALIZING-CONSP-PROOF-IRREDUCIBLE
 (11 1 (:DEFINITION CNF::EQUIV-P))
 (5 4 (:REWRITE DEFAULT-CAR))
 (5 1 (:DEFINITION CNF::PROOF-STEP-P))
 (4 4 (:REWRITE CNF::NORMALIZING-NOT-CONSP-PROOF-IRREDUCIBLE))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 1 (:DEFINITION LAST))
 (2 2 (:TYPE-PRESCRIPTION R-STEP-P))
 (1 1 (:TYPE-PRESCRIPTION LAST))
 )
(CNF::INDUCT-EQUIV-P)
(CNF::EQUIV-P-INDUCT)
(CNF::FIRST-ELEMENT-OF-EQUIVALENCE
 (3 3 (:REWRITE CNF::NORMALIZING-NOT-CONSP-PROOF-IRREDUCIBLE))
 (2 2 (:REWRITE DEFAULT-CAR))
 )
(CNF::LAST-ELT-OF-EQUIVALENCE
 (45 40 (:REWRITE DEFAULT-CAR))
 (20 20 (:REWRITE CNF::NORMALIZING-NOT-CONSP-PROOF-IRREDUCIBLE))
 (17 17 (:REWRITE CNF::FIRST-ELEMENT-OF-EQUIVALENCE))
 (17 17 (:REWRITE DEFAULT-CDR))
 (5 5 (:TYPE-PRESCRIPTION LAST))
 )
(CNF::EQUIV-P-IS-IN-P-F-C
 (12 12 (:REWRITE CNF::NORMALIZING-NOT-CONSP-PROOF-IRREDUCIBLE))
 (11 11 (:REWRITE DEFAULT-CAR))
 (8 8 (:REWRITE CNF::FIRST-ELEMENT-OF-EQUIVALENCE))
 (3 3 (:REWRITE DEFAULT-CDR))
 )
(CNF::PROOF-APPEND
 (221 168 (:REWRITE DEFAULT-CAR))
 (111 99 (:REWRITE DEFAULT-CDR))
 (102 102 (:REWRITE CNF::NORMALIZING-NOT-CONSP-PROOF-IRREDUCIBLE))
 (74 74 (:REWRITE CNF::FIRST-ELEMENT-OF-EQUIVALENCE))
 (68 34 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (34 34 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (34 34 (:TYPE-PRESCRIPTION BINARY-APPEND))
 (17 17 (:TYPE-PRESCRIPTION LAST))
 )
(CNF::EQUIV-P-REFLEXIVE)
(CNF::EQUIV-P-SYMMETRIC
 (88 86 (:REWRITE DEFAULT-CAR))
 (60 12 (:DEFINITION BINARY-APPEND))
 (49 49 (:REWRITE CNF::FIRST-ELEMENT-OF-EQUIVALENCE))
 (47 47 (:REWRITE DEFAULT-CDR))
 (39 39 (:REWRITE CNF::NORMALIZING-NOT-CONSP-PROOF-IRREDUCIBLE))
 (6 2 (:DEFINITION LAST))
 (2 2 (:TYPE-PRESCRIPTION LAST))
 )
(CNF::EQUIV-P-TRANSITIVE
 (21 20 (:REWRITE DEFAULT-CAR))
 (18 18 (:REWRITE CNF::NORMALIZING-NOT-CONSP-PROOF-IRREDUCIBLE))
 (12 12 (:REWRITE CNF::FIRST-ELEMENT-OF-EQUIVALENCE))
 (9 9 (:REWRITE DEFAULT-CDR))
 (3 1 (:DEFINITION LAST))
 (3 1 (:DEFINITION BINARY-APPEND))
 (1 1 (:TYPE-PRESCRIPTION LAST))
 )
(CNF::EQUIV-P-CONTAINS-REDUCTION
 (3 3 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE CNF::NORMALIZING-NOT-CONSP-PROOF-IRREDUCIBLE))
 (1 1 (:REWRITE DEFAULT-CDR))
 )
(CNF::EQV)
(CNF::EQV-CONTAINS-REDUCTION)
(CNF::EQV-REFLEXIVE)
(CNF::EQV-SYMMETRIC)
(CNF::EQV-TRANSITIVE)
(CNF::EQUIV-P-THE-LEAST-EQUIVALENCE-CONTAINING-REDUCTION
 (117 117 (:REWRITE DEFAULT-CAR))
 (53 53 (:REWRITE CNF::FIRST-ELEMENT-OF-EQUIVALENCE))
 (45 45 (:REWRITE CNF::NORMALIZING-NOT-CONSP-PROOF-IRREDUCIBLE))
 (14 14 (:REWRITE DEFAULT-CDR))
 )
(CNF::REDUCIBLE-STEPS-UP
 (35 35 (:REWRITE CNF::NORMALIZING-NOT-CONSP-PROOF-IRREDUCIBLE))
 (20 20 (:REWRITE CNF::FIRST-ELEMENT-OF-EQUIVALENCE))
 (7 7 (:TYPE-PRESCRIPTION LAST))
 )
(CNF::TWO-IREDUCIBLE-CONNECTED-BY-A-VALLEY-ARE-EQUAL
 (123 12 (:REWRITE STEPS-UP-STEPS-VALLEY))
 (76 69 (:REWRITE DEFAULT-CAR))
 (64 64 (:REWRITE DEFAULT-CDR))
 (23 23 (:REWRITE CNF::NORMALIZING-NOT-CONSP-PROOF-IRREDUCIBLE))
 (8 8 (:REWRITE CNF::FIRST-ELEMENT-OF-EQUIVALENCE))
 (7 7 (:TYPE-PRESCRIPTION LAST))
 (3 1 (:REWRITE DEFS-R-STEP-P-INCLUDES-WEAK-R-STEP-P))
 )
(CNF::IF-CR--TWO-IREDUCIBLE-CONNECTED-ARE-EQUAL
 (5 2 (:REWRITE DEFAULT-CAR))
 (3 3 (:TYPE-PRESCRIPTION LAST))
 (3 1 (:DEFINITION LAST))
 (2 2 (:REWRITE CNF::NORMALIZING-NOT-CONSP-PROOF-IRREDUCIBLE))
 (2 2 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE CNF::REDUCIBLE-STEPS-UP))
 )
(CNF::NORMAL-FORM)
(CNF::IRREDUCIBLE-NORMAL-FORM
 (6 2 (:DEFINITION LAST))
 (4 4 (:REWRITE DEFAULT-CDR))
 (4 2 (:REWRITE DEFAULT-CAR))
 (2 2 (:TYPE-PRESCRIPTION LAST))
 (2 2 (:REWRITE CNF::LAST-ELT-OF-EQUIVALENCE))
 )
(CNF::EQUIVALENT-PROOF-N-F
 (12 4 (:REWRITE CNF::REDUCIBLE-STEPS-UP))
 (8 6 (:REWRITE DEFAULT-CAR))
 (6 6 (:REWRITE DEFAULT-CDR))
 (6 2 (:DEFINITION LAST))
 (6 1 (:DEFINITION STEPS-UP))
 (6 1 (:DEFINITION CNF::PROOF-STEP-P))
 (5 5 (:TYPE-PRESCRIPTION STEPS-UP))
 (3 3 (:REWRITE CNF::NORMALIZING-NOT-CONSP-PROOF-IRREDUCIBLE))
 (2 2 (:TYPE-PRESCRIPTION R-STEP-P))
 (2 2 (:TYPE-PRESCRIPTION LAST))
 (2 2 (:REWRITE CNF::LAST-ELT-OF-EQUIVALENCE))
 (2 2 (:REWRITE CNF::FIRST-ELEMENT-OF-EQUIVALENCE))
 )
(CNF::PROOF-IRREDUCIBLE-ATOM-NORMAL-FORM)
(CNF::PROOF-IRREDUCIBLE-CONSP-NORMAL-FORM
 (6 2 (:DEFINITION LAST))
 (4 4 (:REWRITE DEFAULT-CDR))
 (4 2 (:REWRITE DEFAULT-CAR))
 (2 2 (:TYPE-PRESCRIPTION LAST))
 (2 2 (:REWRITE CNF::LAST-ELT-OF-EQUIVALENCE))
 (1 1 (:REWRITE CNF::PROOF-IRREDUCIBLE-ATOM-NORMAL-FORM))
 )
(CNF::R-EQUIV)
(CNF::MAKE-PROOF-BETWEEN-NORMAL-FORMS
 (37 23 (:TYPE-PRESCRIPTION BINARY-APPEND))
 )
(CNF::CONSP-INVERSE-PROOF
 (23 5 (:DEFINITION BINARY-APPEND))
 (10 10 (:REWRITE CNF::FIRST-ELEMENT-OF-EQUIVALENCE))
 (10 10 (:REWRITE DEFAULT-CAR))
 (9 9 (:REWRITE DEFAULT-CDR))
 )
(CNF::LAST-ELT-APPEND
 (282 141 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (141 141 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (54 24 (:REWRITE DEFAULT-CDR))
 (35 13 (:REWRITE DEFAULT-CAR))
 )
(CNF::LAST-ELT-INVERSE-PROOF
 (318 159 (:TYPE-PRESCRIPTION LAST))
 (280 280 (:TYPE-PRESCRIPTION INVERSE-PROOF))
 (187 17 (:DEFINITION BINARY-APPEND))
 (142 52 (:REWRITE DEFAULT-CDR))
 (137 56 (:REWRITE DEFAULT-CAR))
 (56 56 (:REWRITE CNF::CONSP-INVERSE-PROOF))
 (32 16 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (20 20 (:REWRITE CNF::FIRST-ELEMENT-OF-EQUIVALENCE))
 (16 16 (:TYPE-PRESCRIPTION BINARY-APPEND))
 (6 2 (:REWRITE DEFS-R-STEP-P-INCLUDES-WEAK-R-STEP-P))
 (4 4 (:TYPE-PRESCRIPTION R-STEP-P))
 )
(CNF::FIRST-ELEMENT-OF-PROOF-IRREDUCIBLE
 (1 1 (:REWRITE CNF::PROOF-IRREDUCIBLE-ATOM-NORMAL-FORM))
 (1 1 (:REWRITE CNF::FIRST-ELEMENT-OF-EQUIVALENCE))
 (1 1 (:REWRITE DEFAULT-CAR))
 )
(CNF::MAKE-PROOF-BETWEEN-NORMAL-FORMS-INDEED
 (119 29 (:REWRITE CNF::REDUCIBLE-STEPS-UP))
 (55 42 (:REWRITE DEFAULT-CAR))
 (39 24 (:REWRITE DEFAULT-CDR))
 (39 15 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (36 4 (:DEFINITION BINARY-APPEND))
 (21 15 (:TYPE-PRESCRIPTION BINARY-APPEND))
 (18 3 (:DEFINITION STEPS-UP))
 (16 16 (:TYPE-PRESCRIPTION STEPS-UP))
 (15 15 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (11 2 (:DEFINITION LAST))
 (8 1 (:REWRITE STEPS-UP-INVERSE-PROOF))
 (6 1 (:DEFINITION STEPS-DOWN))
 (4 4 (:TYPE-PRESCRIPTION STEPS-DOWN))
 (1 1 (:TYPE-PRESCRIPTION LAST))
 )
(CNF::R-EQUIV-COMPLETE
 (6 6 (:REWRITE CNF::PROOF-IRREDUCIBLE-ATOM-NORMAL-FORM))
 (5 2 (:REWRITE DEFAULT-CAR))
 (3 3 (:TYPE-PRESCRIPTION LAST))
 (3 1 (:DEFINITION LAST))
 (2 2 (:REWRITE DEFAULT-CDR))
 )
(CNF::MAKE-PROOF-COMMON-N-F
 (5 5 (:TYPE-PRESCRIPTION BINARY-APPEND))
 )
(CNF::R-EQUIV-SOUND
 (68 4 (:DEFINITION INVERSE-PROOF))
 (59 37 (:REWRITE DEFAULT-CAR))
 (50 15 (:REWRITE CNF::REDUCIBLE-STEPS-UP))
 (47 5 (:DEFINITION BINARY-APPEND))
 (41 20 (:REWRITE DEFAULT-CDR))
 (21 21 (:REWRITE CNF::NORMALIZING-NOT-CONSP-PROOF-IRREDUCIBLE))
 (12 4 (:DEFINITION INVERSE-R-STEP))
 (11 3 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (6 6 (:REWRITE CNF::FIRST-ELEMENT-OF-EQUIVALENCE))
 (3 3 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (3 3 (:TYPE-PRESCRIPTION BINARY-APPEND))
 (3 1 (:DEFINITION LAST))
 (1 1 (:TYPE-PRESCRIPTION LAST))
 )
