0.07/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.13	% Command    : do_cvc5 %s %d
0.13/0.34	% Computer   : n012.cluster.edu
0.13/0.34	% Model      : x86_64 x86_64
0.13/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.34	% Memory     : 8042.1875MB
0.13/0.34	% OS         : Linux 3.10.0-693.el7.x86_64
0.20/0.34	% CPULimit   : 1200
0.20/0.34	% WCLimit    : 120
0.20/0.34	% DateTime   : Tue Jul 13 11:21:01 EDT 2021
0.20/0.34	% CPUTime    : 
0.20/0.49	%----THF division
0.20/0.50	------- cvc5-thf casc 28 : /export/starexec/sandbox2/benchmark/theBenchmark.p at 120...
0.20/0.50	--- Run --ho-elim --full-saturate-quant at 10...
2.14/2.37	% SZS status Theorem for theBenchmark
2.24/2.41	% SZS output start Proof for theBenchmark
2.24/2.41	(proof
2.24/2.41	(let ((_let_1 (= finite90785608at_nat (lambda ((A5 set_nat_nat_nat)) (collec617280953at_nat (lambda ((X6 set_nat_nat_nat)) (and (finite2045569477at_nat X6) ((ord_le940807492at_nat X6) A5)))))))) (let ((_let_2 (forall ((A3 (-> nat nat)) (P2 (-> (-> nat nat) Bool))) (= ((member_nat_nat A3) (collect_nat_nat P2)) (P2 A3))))) (let ((_let_3 (= finite_Fpow_nat (lambda ((A5 set_nat)) (collect_set_nat (lambda ((X6 set_nat)) (and (finite_finite_nat X6) ((ord_less_eq_set_nat X6) A5)))))))) (let ((_let_4 (= finite_Fpow_nat_nat (lambda ((A5 set_nat_nat)) (collect_set_nat_nat (lambda ((X6 set_nat_nat)) (and ((ord_le1415039317at_nat X6) A5) (finite570312790at_nat X6)))))))) (let ((_let_5 (not (finite570312790at_nat (collect_nat_nat (lambda ((P (-> nat nat))) ((number1551313001itions P) n))))))) (let ((_let_6 (= finite_finite_nat (lambda ((N4 set_nat)) (exists ((M2 nat)) (forall ((X nat)) (=> ((member_nat X) N4) ((ord_less_nat X) M2)))))))) (let ((_let_7 (forall ((A set_nat_nat) (B set_nat_nat)) (=> ((ord_le1415039317at_nat A) B) (=> (finite570312790at_nat B) (finite570312790at_nat A)))))) (let ((_let_8 (ord_le1415039317at_nat (collect_nat_nat (lambda ((P (-> nat nat))) ((number1551313001itions P) n)))))) (let ((_let_9 (_let_8 (collect_nat_nat (lambda ((F (-> nat nat))) (and (forall ((I nat)) (=> ((ord_less_eq_nat ((plus_plus_nat n) one_one_nat)) I) (= (F I) zero_zero_nat))) (forall ((I nat)) ((ord_less_eq_nat (F I)) n)))))))) (let ((_let_10 (forall ((P3 (-> nat nat)) (N nat) (I2 nat)) (=> ((number1551313001itions P3) N) ((ord_less_eq_nat (P3 I2)) N))))) (let ((_let_11 (finite570312790at_nat (collect_nat_nat (lambda ((F (-> nat nat))) (and (forall ((I nat)) (=> ((ord_less_eq_nat ((plus_plus_nat n) one_one_nat)) I) (= (F I) zero_zero_nat))) (forall ((I nat)) ((ord_less_eq_nat (F I)) n)))))))) (let ((_let_12 (ord_less_eq_nat one_one_nat))) (let ((_let_13 (forall ((P2 (-> (-> nat nat) Bool)) (Q (-> (-> nat nat) Bool))) (= ((ord_le1415039317at_nat (collect_nat_nat P2)) (collect_nat_nat Q)) (forall ((X (-> nat nat))) (=> (P2 X) (Q X))))))) (let ((_let_14 (= ord_less_eq_set_nat (lambda ((A5 set_nat) (B2 set_nat)) ((ord_less_eq_nat_o (lambda ((X nat)) ((member_nat X) A5))) (lambda ((X nat)) ((member_nat X) B2))))))) (let ((_let_15 (ord_less_eq_nat zero_zero_nat))) (let ((_let_16 (= ord_less_eq_nat (lambda ((B4 nat) (A2 nat)) (or (= A2 B4) ((ord_less_nat B4) A2)))))) (let ((_let_17 (= finite1633036872at_nat (lambda ((A5 set_nat_nat_nat2)) (collec309745849at_nat (lambda ((X6 set_nat_nat_nat2)) (and (finite1440337093at_nat X6) ((ord_le633272388at_nat X6) A5)))))))) (let ((_let_18 (= finite252967095at_nat (lambda ((A5 set_nat_nat_nat_nat3)) (collec1702444712at_nat (lambda ((X6 set_nat_nat_nat_nat3)) (and ((ord_le2040082867at_nat X6) A5) (finite1064868788at_nat X6)))))))) (let ((_let_19 (forall ((P2 (-> (-> nat nat) Bool)) (Q (-> (-> nat nat) Bool))) (=> (forall ((X2 (-> nat nat))) (= (P2 X2) (Q X2))) (= (collect_nat_nat P2) (collect_nat_nat Q)))))) (let ((_let_20 (= ord_le1415039317at_nat (lambda ((B4 set_nat_nat) (A2 set_nat_nat)) (or (= A2 B4) ((ord_less_set_nat_nat B4) A2)))))) (let ((_let_21 (forall ((P2 (-> (-> (-> nat nat) nat) Bool)) (Q (-> (-> (-> nat nat) nat) Bool))) (=> (forall ((X2 (-> (-> nat nat) nat))) (= (P2 X2) (Q X2))) (= (collect_nat_nat_nat P2) (collect_nat_nat_nat Q)))))) (let ((_let_22 (ho_547 k_546 k_309))) (let ((_let_23 (ho_199 k_548 _let_22))) (let ((_let_24 (ho_547 k_546 k_373))) (let ((_let_25 (ho_199 k_548 _let_24))) (let ((_let_26 (= _let_24 _let_22))) (let ((_let_27 (not _let_23))) (let ((_let_28 (not (finite570312790at_nat (collect_nat_nat ll_135))))) (let ((_let_29 (EQ_RESOLVE (ASSUME |:args| (_let_5)) (TRANS (PREPROCESS |:args| ((= _let_5 _let_28))) (PREPROCESS |:args| ((= _let_28 _let_27))))))) (let ((_let_30 (ho_547 k_546 k_374))) (let ((_let_31 (ho_199 k_548 _let_30))) (let ((_let_32 (not _let_31))) (let ((_let_33 (ho_199 (ho_251 k_252 _let_24) _let_30))) (let ((_let_34 (not _let_33))) (let ((_let_35 (= _let_30 _let_24))) (let ((_let_36 (not _let_35))) (let ((_let_37 (and _let_36 _let_34))) (let ((_let_38 (or _let_37 _let_32 _let_25))) (let ((_let_39 (forall ((A set_nat_nat) (B set_nat_nat)) (or (and (not (= A B)) (not (ho_199 (ho_251 k_252 A) B))) (not (ho_199 k_548 B)) (ho_199 k_548 A))))) (let ((_let_40 (EQ_RESOLVE (ASSUME |:args| (_let_20)) (MACRO_SR_EQ_INTRO |:args| (_let_20 7 12))))) (let ((_let_41 (ASSUME |:args| (_let_18)))) (let ((_let_42 (ASSUME |:args| (_let_17)))) (let ((_let_43 (EQ_RESOLVE (ASSUME |:args| (_let_16)) (MACRO_SR_EQ_INTRO |:args| (_let_16 7 12))))) (let ((_let_44 (ASSUME |:args| (_let_14)))) (let ((_let_45 (EQ_RESOLVE (ASSUME |:args| (_let_6)) (MACRO_SR_EQ_INTRO |:args| (_let_6 7 12))))) (let ((_let_46 (EQ_RESOLVE (ASSUME |:args| (_let_4)) (MACRO_SR_EQ_INTRO _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 |:args| (_let_4 7 12))))) (let ((_let_47 (EQ_RESOLVE (ASSUME |:args| (_let_3)) (MACRO_SR_EQ_INTRO _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 |:args| (_let_3 7 12))))) (let ((_let_48 (ASSUME |:args| (_let_1)))) (let ((_let_49 (EQ_RESOLVE (ASSUME |:args| (_let_7)) (TRANS (MACRO_SR_EQ_INTRO |:args| (_let_7 7 12)) (MACRO_SR_EQ_INTRO _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 |:args| ((forall ((A set_nat_nat) (B set_nat_nat)) (or (not ((ord_le1415039317at_nat A) B)) (not (finite570312790at_nat B)) (finite570312790at_nat A))) 7 12)) (PREPROCESS |:args| ((= (forall ((A set_nat_nat) (B set_nat_nat)) (or (and (not (= A B)) (not ((ord_less_set_nat_nat A) B))) (not (finite570312790at_nat B)) (finite570312790at_nat A))) _let_39))))))) (let ((_let_50 (not _let_37))) (let ((_let_51 (ho_202 k_374 skv_610))) (let ((_let_52 (ho_202 k_309 skv_610))) (let ((_let_53 (= _let_52 _let_51))) (let ((_let_54 (forall ((BOUND_VARIABLE_25604 |u_(-> nat nat)|)) (= (ho_202 k_309 BOUND_VARIABLE_25604) (ho_202 k_374 BOUND_VARIABLE_25604))))) (let ((_let_55 (= _let_30 _let_22))) (let ((_let_56 (not _let_54))) (let ((_let_57 (or _let_56 _let_55))) (let ((_let_58 (ho_202 k_468 skv_609))) (let ((_let_59 (ho_202 k_373 skv_609))) (let ((_let_60 (= _let_59 _let_58))) (let ((_let_61 (forall ((BOUND_VARIABLE_25604 |u_(-> nat nat)|)) (= (ho_202 k_373 BOUND_VARIABLE_25604) (ho_202 k_468 BOUND_VARIABLE_25604))))) (let ((_let_62 (ho_547 k_546 k_468))) (let ((_let_63 (= _let_62 _let_24))) (let ((_let_64 (not _let_61))) (let ((_let_65 (or _let_64 _let_63))) (let ((_let_66 (ho_199 k_548 _let_62))) (let ((_let_67 (or _let_35 _let_33))) (let ((_let_68 (forall ((BOUND_VARIABLE_26683 |u_(-> _u_(-> nat nat)_ Bool)|) (BOUND_VARIABLE_26681 |u_(-> _u_(-> nat nat)_ Bool)|)) (let ((_let_1 (ho_547 k_546 BOUND_VARIABLE_26681))) (let ((_let_2 (ho_547 k_546 BOUND_VARIABLE_26683))) (= (or (= _let_1 _let_2) (ho_199 (ho_251 k_252 _let_2) _let_1)) (forall ((BOUND_VARIABLE_26680 |u_(-> nat nat)|)) (or (not (ho_202 BOUND_VARIABLE_26683 BOUND_VARIABLE_26680)) (ho_202 BOUND_VARIABLE_26681 BOUND_VARIABLE_26680))))))))) (let ((_let_69 (forall ((BOUND_VARIABLE_26680 |u_(-> nat nat)|)) (or (not (ho_202 k_373 BOUND_VARIABLE_26680)) (ho_202 k_374 BOUND_VARIABLE_26680))))) (let ((_let_70 (= _let_67 _let_69))) (let ((_let_71 (ho_202 k_373 skv_610))) (let ((_let_72 (not _let_71))) (let ((_let_73 (or _let_72 _let_51))) (let ((_let_74 (ho_191 (ho_308 k_307 skv_610) n))) (let ((_let_75 (= _let_52 _let_74))) (let ((_let_76 (ho_198 k_197 skv_610))) (let ((_let_77 (ho_199 _let_76 _let_30))) (let ((_let_78 (= _let_77 _let_51))) (let ((_let_79 (= _let_71 _let_74))) (let ((_let_80 (ho_199 _let_76 _let_24))) (let ((_let_81 (= _let_80 _let_71))) (let ((_let_82 (CNF_OR_NEG |:args| (_let_67 0)))) (let ((_let_83 (EQ_RESOLVE (ASSUME |:args| (_let_13)) (TRANS (MACRO_SR_EQ_INTRO |:args| (_let_13 7 12)) (MACRO_SR_EQ_INTRO _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 |:args| ((forall ((P2 (-> (-> nat nat) Bool)) (Q (-> (-> nat nat) Bool))) (= ((ord_le1415039317at_nat (collect_nat_nat P2)) (collect_nat_nat Q)) (forall ((X (-> nat nat))) (or (not (P2 X)) (Q X))))) 7 12)) (PREPROCESS |:args| ((= (forall ((P2 (-> (-> nat nat) Bool)) (Q (-> (-> nat nat) Bool))) (let ((_let_1 (collect_nat_nat Q))) (let ((_let_2 (collect_nat_nat P2))) (= (or (= _let_2 _let_1) ((ord_less_set_nat_nat _let_2) _let_1)) (forall ((X (-> nat nat))) (or (not (P2 X)) (Q X))))))) _let_68))))))) (let ((_let_84 (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_83 |:args| (k_373 k_374)) |:args| (_let_68))))) (let ((_let_85 (REORDERING (CNF_EQUIV_POS1 |:args| (_let_70)) |:args| ((or _let_69 (not _let_67) (not _let_70)))))) (let ((_let_86 (_let_69))) (let ((_let_87 (skv_610))) (let ((_let_88 (ASSUME |:args| _let_86))) (let ((_let_89 (not _let_73))) (let ((_let_90 (not _let_52))) (let ((_let_91 (_let_53))) (let ((_let_92 (forall ((BOUND_VARIABLE_22879 |u_(-> nat nat)|)) (= (ho_202 k_309 BOUND_VARIABLE_22879) (ho_191 (ho_308 k_307 BOUND_VARIABLE_22879) n))))) (let ((_let_93 (forall ((u |u_(-> set_nat_nat _u_(-> _u_(-> nat nat)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> nat nat)_ Bool)|) (e |u_(-> _u_(-> _u_(-> nat nat)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> nat nat)_ Bool)|) (i set_nat_nat)) (not (forall ((v |u_(-> set_nat_nat _u_(-> _u_(-> nat nat)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> nat nat)_ Bool)|)) (not (forall ((ii set_nat_nat)) (= (ho_452 v ii) (ite (= i ii) e (ho_452 u ii)))))))))) (let ((_let_94 (forall ((x |u_(-> set_nat_nat _u_(-> _u_(-> nat nat)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> nat nat)_ Bool)|) (y |u_(-> set_nat_nat _u_(-> _u_(-> nat nat)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> nat nat)_ Bool)|)) (or (not (forall ((z set_nat_nat)) (= (ho_452 x z) (ho_452 y z)))) (= x y))))) (let ((_let_95 (forall ((u |u_(-> _u_(-> _u_(-> nat nat)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> nat nat)_ Bool)|) (e |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> nat nat)_ Bool)|) (i |u_(-> _u_(-> nat nat)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> nat nat)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> nat nat)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> nat nat)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (= (ho_453 v ii) (ite (= i ii) e (ho_453 u ii)))))))))) (let ((_let_96 (forall ((x |u_(-> _u_(-> _u_(-> nat nat)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> nat nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> nat nat)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> nat nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> nat nat)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (= (ho_453 x z) (ho_453 y z)))) (= x y))))) (let ((_let_97 (forall ((u |u_(-> _u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ Bool)_ _u_(-> nat nat)_ set_nat_nat _u_(-> nat nat)_ Bool)|) (e |u_(-> _u_(-> nat nat)_ set_nat_nat _u_(-> nat nat)_ Bool)|) (i |u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ Bool)_ _u_(-> nat nat)_ set_nat_nat _u_(-> nat nat)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ Bool)|)) (= (ho_293 v ii) (ite (= i ii) e (ho_293 u ii)))))))))) (let ((_let_98 (forall ((x |u_(-> _u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ Bool)_ _u_(-> nat nat)_ set_nat_nat _u_(-> nat nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ Bool)_ _u_(-> nat nat)_ set_nat_nat _u_(-> nat nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ Bool)|)) (= (ho_293 x z) (ho_293 y z)))) (= x y))))) (let ((_let_99 (forall ((u |u_(-> set_nat_nat_nat set_nat_nat_nat Bool)|) (e |u_(-> set_nat_nat_nat Bool)|) (i set_nat_nat_nat)) (not (forall ((v |u_(-> set_nat_nat_nat set_nat_nat_nat Bool)|)) (not (forall ((ii set_nat_nat_nat)) (= (ho_448 v ii) (ite (= i ii) e (ho_448 u ii)))))))))) (let ((_let_100 (forall ((x |u_(-> set_nat_nat_nat set_nat_nat_nat Bool)|) (y |u_(-> set_nat_nat_nat set_nat_nat_nat Bool)|)) (or (not (forall ((z set_nat_nat_nat)) (= (ho_448 x z) (ho_448 y z)))) (= x y))))) (let ((_let_101 (forall ((u |u_(-> _u_(-> nat _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat)_ nat Bool)|) (e |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat Bool)|) (i |u_(-> nat _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> nat _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat)_ nat Bool)|)) (not (forall ((ii |u_(-> nat _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (= (ho_445 v ii) (ite (= i ii) e (ho_445 u ii)))))))))) (let ((_let_102 (forall ((x |u_(-> _u_(-> nat _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat)_ nat Bool)|) (y |u_(-> _u_(-> nat _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat)_ nat Bool)|)) (or (not (forall ((z |u_(-> nat _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (= (ho_445 x z) (ho_445 y z)))) (= x y))))) (let ((_let_103 (forall ((u |u_(-> _u_(-> _u_(-> nat nat)_ Bool)_ set_nat_nat _u_(-> nat nat)_ Bool)|) (e |u_(-> set_nat_nat _u_(-> nat nat)_ Bool)|) (i |u_(-> _u_(-> nat nat)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> nat nat)_ Bool)_ set_nat_nat _u_(-> nat nat)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> nat nat)_ Bool)|)) (= (ho_509 v ii) (ite (= i ii) e (ho_509 u ii)))))))))) (let ((_let_104 (forall ((x |u_(-> _u_(-> _u_(-> nat nat)_ Bool)_ set_nat_nat _u_(-> nat nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> nat nat)_ Bool)_ set_nat_nat _u_(-> nat nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> nat nat)_ Bool)|)) (= (ho_509 x z) (ho_509 y z)))) (= x y))))) (let ((_let_105 (forall ((u |u_(-> nat _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (e |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (i nat)) (not (forall ((v |u_(-> nat _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (not (forall ((ii nat)) (= (ho_442 v ii) (ite (= i ii) e (ho_442 u ii)))))))))) (let ((_let_106 (forall ((x |u_(-> nat _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (y |u_(-> nat _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (or (not (forall ((z nat)) (= (ho_442 x z) (ho_442 y z)))) (= x y))))) (let ((_let_107 (forall ((u |u_(-> set_na1064332610at_nat Bool)|) (e Bool) (i set_na1064332610at_nat)) (not (forall ((v |u_(-> set_na1064332610at_nat Bool)|)) (not (forall ((ii set_na1064332610at_nat)) (= (ho_584 v ii) (ite (= i ii) e (ho_584 u ii)))))))))) (let ((_let_108 (forall ((x |u_(-> set_na1064332610at_nat Bool)|) (y |u_(-> set_na1064332610at_nat Bool)|)) (or (not (forall ((z set_na1064332610at_nat)) (= (ho_584 x z) (ho_584 y z)))) (= x y))))) (let ((_let_109 (forall ((u |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)_ _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (e |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (i |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)_ _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|)) (= (ho_427 v ii) (ite (= i ii) e (ho_427 u ii)))))))))) (let ((_let_110 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)_ _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)_ _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|)) (= (ho_427 x z) (ho_427 y z)))) (= x y))))) (let ((_let_111 (forall ((u |u_(-> set_nat_nat_nat_nat3 _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (e |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (i set_nat_nat_nat_nat3)) (not (forall ((v |u_(-> set_nat_nat_nat_nat3 _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|)) (not (forall ((ii set_nat_nat_nat_nat3)) (= (ho_404 v ii) (ite (= i ii) e (ho_404 u ii)))))))))) (let ((_let_112 (forall ((x |u_(-> set_nat_nat_nat_nat3 _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (y |u_(-> set_nat_nat_nat_nat3 _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|)) (or (not (forall ((z set_nat_nat_nat_nat3)) (= (ho_404 x z) (ho_404 y z)))) (= x y))))) (let ((_let_113 (forall ((u |u_(-> _u_(-> nat Bool)_ nat nat Bool)|) (e |u_(-> nat nat Bool)|) (i |u_(-> nat Bool)|)) (not (forall ((v |u_(-> _u_(-> nat Bool)_ nat nat Bool)|)) (not (forall ((ii |u_(-> nat Bool)|)) (= (ho_422 v ii) (ite (= i ii) e (ho_422 u ii)))))))))) (let ((_let_114 (forall ((x |u_(-> _u_(-> nat Bool)_ nat nat Bool)|) (y |u_(-> _u_(-> nat Bool)_ nat nat Bool)|)) (or (not (forall ((z |u_(-> nat Bool)|)) (= (ho_422 x z) (ho_422 y z)))) (= x y))))) (let ((_let_115 (forall ((u |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (e Bool) (i |u_(-> _u_(-> nat nat)_ nat)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> nat nat)_ nat)|)) (= (ho_215 v ii) (ite (= i ii) e (ho_215 u ii)))))))))) (let ((_let_116 (forall ((x |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> nat nat)_ nat)|)) (= (ho_215 x z) (ho_215 y z)))) (= x y))))) (let ((_let_117 (forall ((u |u_(-> _u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ nat)_ Bool)|) (e Bool) (i |u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ nat)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ nat)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ nat)|)) (= (ho_440 v ii) (ite (= i ii) e (ho_440 u ii)))))))))) (let ((_let_118 (forall ((x |u_(-> _u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ nat)|)) (= (ho_440 x z) (ho_440 y z)))) (= x y))))) (let ((_let_119 (forall ((u |u_(-> set_nat_nat_nat2 set_nat _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ Bool)|) (e |u_(-> set_nat _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ Bool)|) (i set_nat_nat_nat2)) (not (forall ((v |u_(-> set_nat_nat_nat2 set_nat _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ Bool)|)) (not (forall ((ii set_nat_nat_nat2)) (= (ho_418 v ii) (ite (= i ii) e (ho_418 u ii)))))))))) (let ((_let_120 (forall ((x |u_(-> set_nat_nat_nat2 set_nat _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ Bool)|) (y |u_(-> set_nat_nat_nat2 set_nat _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ Bool)|)) (or (not (forall ((z set_nat_nat_nat2)) (= (ho_418 x z) (ho_418 y z)))) (= x y))))) (let ((_let_121 (forall ((u |u_(-> set_nat_nat_nat2 _u_(-> nat _u_(-> nat nat)_ nat)_ Bool)|) (e |u_(-> _u_(-> nat _u_(-> nat nat)_ nat)_ Bool)|) (i set_nat_nat_nat2)) (not (forall ((v |u_(-> set_nat_nat_nat2 _u_(-> nat _u_(-> nat nat)_ nat)_ Bool)|)) (not (forall ((ii set_nat_nat_nat2)) (= (ho_305 v ii) (ite (= i ii) e (ho_305 u ii)))))))))) (let ((_let_122 (forall ((x |u_(-> set_nat_nat_nat2 _u_(-> nat _u_(-> nat nat)_ nat)_ Bool)|) (y |u_(-> set_nat_nat_nat2 _u_(-> nat _u_(-> nat nat)_ nat)_ Bool)|)) (or (not (forall ((z set_nat_nat_nat2)) (= (ho_305 x z) (ho_305 y z)))) (= x y))))) (let ((_let_123 (forall ((u |u_(-> _u_(-> nat nat)_ set_nat_nat Bool)|) (e |u_(-> set_nat_nat Bool)|) (i |u_(-> nat nat)|)) (not (forall ((v |u_(-> _u_(-> nat nat)_ set_nat_nat Bool)|)) (not (forall ((ii |u_(-> nat nat)|)) (= (ho_198 v ii) (ite (= i ii) e (ho_198 u ii)))))))))) (let ((_let_124 (forall ((x |u_(-> _u_(-> nat nat)_ set_nat_nat Bool)|) (y |u_(-> _u_(-> nat nat)_ set_nat_nat Bool)|)) (or (not (forall ((z |u_(-> nat nat)|)) (= (ho_198 x z) (ho_198 y z)))) (= x y))))) (let ((_let_125 (forall ((u |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ Bool)|) (e Bool) (i |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)|)) (= (ho_420 v ii) (ite (= i ii) e (ho_420 u ii)))))))))) (let ((_let_126 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)|)) (= (ho_420 x z) (ho_420 y z)))) (= x y))))) (let ((_let_127 (forall ((u |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)|) (e nat) (i |u_(-> _u_(-> nat nat)_ nat)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)|)) (not (forall ((ii |u_(-> _u_(-> nat nat)_ nat)|)) (= (ho_415 v ii) (ite (= i ii) e (ho_415 u ii)))))))))) (let ((_let_128 (forall ((x |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)|) (y |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)|)) (or (not (forall ((z |u_(-> _u_(-> nat nat)_ nat)|)) (= (ho_415 x z) (ho_415 y z)))) (= x y))))) (let ((_let_129 (forall ((u |u_(-> set_nat _u_(-> nat nat Bool)_ nat nat Bool)|) (e |u_(-> _u_(-> nat nat Bool)_ nat nat Bool)|) (i set_nat)) (not (forall ((v |u_(-> set_nat _u_(-> nat nat Bool)_ nat nat Bool)|)) (not (forall ((ii set_nat)) (= (ho_347 v ii) (ite (= i ii) e (ho_347 u ii)))))))))) (let ((_let_130 (forall ((x |u_(-> set_nat _u_(-> nat nat Bool)_ nat nat Bool)|) (y |u_(-> set_nat _u_(-> nat nat Bool)_ nat nat Bool)|)) (or (not (forall ((z set_nat)) (= (ho_347 x z) (ho_347 y z)))) (= x y))))) (let ((_let_131 (forall ((u |u_(-> _u_(-> _u_(-> nat nat nat)_ nat Bool)_ nat set_nat_nat_nat _u_(-> nat nat nat)_ Bool)|) (e |u_(-> nat set_nat_nat_nat _u_(-> nat nat nat)_ Bool)|) (i |u_(-> _u_(-> nat nat nat)_ nat Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> nat nat nat)_ nat Bool)_ nat set_nat_nat_nat _u_(-> nat nat nat)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> nat nat nat)_ nat Bool)|)) (= (ho_412 v ii) (ite (= i ii) e (ho_412 u ii)))))))))) (let ((_let_132 (forall ((x |u_(-> _u_(-> _u_(-> nat nat nat)_ nat Bool)_ nat set_nat_nat_nat _u_(-> nat nat nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> nat nat nat)_ nat Bool)_ nat set_nat_nat_nat _u_(-> nat nat nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> nat nat nat)_ nat Bool)|)) (= (ho_412 x z) (ho_412 y z)))) (= x y))))) (let ((_let_133 (forall ((u |u_(-> _u_(-> nat nat)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (e |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (i |u_(-> nat nat)|)) (not (forall ((v |u_(-> _u_(-> nat nat)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (not (forall ((ii |u_(-> nat nat)|)) (= (ho_450 v ii) (ite (= i ii) e (ho_450 u ii)))))))))) (let ((_let_134 (forall ((x |u_(-> _u_(-> nat nat)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (y |u_(-> _u_(-> nat nat)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (or (not (forall ((z |u_(-> nat nat)|)) (= (ho_450 x z) (ho_450 y z)))) (= x y))))) (let ((_let_135 (forall ((u |u_(-> nat set_nat_nat_nat _u_(-> nat nat nat)_ Bool)|) (e |u_(-> set_nat_nat_nat _u_(-> nat nat nat)_ Bool)|) (i nat)) (not (forall ((v |u_(-> nat set_nat_nat_nat _u_(-> nat nat nat)_ Bool)|)) (not (forall ((ii nat)) (= (ho_413 v ii) (ite (= i ii) e (ho_413 u ii)))))))))) (let ((_let_136 (forall ((x |u_(-> nat set_nat_nat_nat _u_(-> nat nat nat)_ Bool)|) (y |u_(-> nat set_nat_nat_nat _u_(-> nat nat nat)_ Bool)|)) (or (not (forall ((z nat)) (= (ho_413 x z) (ho_413 y z)))) (= x y))))) (let ((_let_137 (forall ((u |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ nat)_ set_nat_nat_nat_nat3 _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (e |u_(-> set_nat_nat_nat_nat3 _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (i |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ nat)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ nat)_ set_nat_nat_nat_nat3 _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ nat)|)) (= (ho_407 v ii) (ite (= i ii) e (ho_407 u ii)))))))))) (let ((_let_138 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ nat)_ set_nat_nat_nat_nat3 _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ nat)_ set_nat_nat_nat_nat3 _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ nat)|)) (= (ho_407 x z) (ho_407 y z)))) (= x y))))) (let ((_let_139 (forall ((u |u_(-> set_nat_nat set_nat_nat_nat _u_(-> _u_(-> nat nat)_ nat nat nat)_ Bool)|) (e |u_(-> set_nat_nat_nat _u_(-> _u_(-> nat nat)_ nat nat nat)_ Bool)|) (i set_nat_nat)) (not (forall ((v |u_(-> set_nat_nat set_nat_nat_nat _u_(-> _u_(-> nat nat)_ nat nat nat)_ Bool)|)) (not (forall ((ii set_nat_nat)) (= (ho_392 v ii) (ite (= i ii) e (ho_392 u ii)))))))))) (let ((_let_140 (forall ((x |u_(-> set_nat_nat set_nat_nat_nat _u_(-> _u_(-> nat nat)_ nat nat nat)_ Bool)|) (y |u_(-> set_nat_nat set_nat_nat_nat _u_(-> _u_(-> nat nat)_ nat nat nat)_ Bool)|)) (or (not (forall ((z set_nat_nat)) (= (ho_392 x z) (ho_392 y z)))) (= x y))))) (let ((_let_141 (forall ((u |u_(-> set_nat_nat_nat _u_(-> _u_(-> nat nat)_ nat nat nat)_ Bool)|) (e |u_(-> _u_(-> _u_(-> nat nat)_ nat nat nat)_ Bool)|) (i set_nat_nat_nat)) (not (forall ((v |u_(-> set_nat_nat_nat _u_(-> _u_(-> nat nat)_ nat nat nat)_ Bool)|)) (not (forall ((ii set_nat_nat_nat)) (= (ho_393 v ii) (ite (= i ii) e (ho_393 u ii)))))))))) (let ((_let_142 (forall ((x |u_(-> set_nat_nat_nat _u_(-> _u_(-> nat nat)_ nat nat nat)_ Bool)|) (y |u_(-> set_nat_nat_nat _u_(-> _u_(-> nat nat)_ nat nat nat)_ Bool)|)) (or (not (forall ((z set_nat_nat_nat)) (= (ho_393 x z) (ho_393 y z)))) (= x y))))) (let ((_let_143 (forall ((u |u_(-> _u_(-> nat nat)_ Bool)|) (e Bool) (i |u_(-> nat nat)|)) (not (forall ((v |u_(-> _u_(-> nat nat)_ Bool)|)) (not (forall ((ii |u_(-> nat nat)|)) (= (ho_202 v ii) (ite (= i ii) e (ho_202 u ii)))))))))) (let ((_let_144 (forall ((x |u_(-> _u_(-> nat nat)_ Bool)|) (y |u_(-> _u_(-> nat nat)_ Bool)|)) (or (not (forall ((z |u_(-> nat nat)|)) (= (ho_202 x z) (ho_202 y z)))) (= x y))))) (let ((_let_145 (forall ((u |u_(-> set_nat_nat_nat _u_(-> _u_(-> nat nat nat)_ nat)_ _u_(-> _u_(-> nat nat nat)_ nat)_ _u_(-> nat nat nat)_ Bool)|) (e |u_(-> _u_(-> _u_(-> nat nat nat)_ nat)_ _u_(-> _u_(-> nat nat nat)_ nat)_ _u_(-> nat nat nat)_ Bool)|) (i set_nat_nat_nat)) (not (forall ((v |u_(-> set_nat_nat_nat _u_(-> _u_(-> nat nat nat)_ nat)_ _u_(-> _u_(-> nat nat nat)_ nat)_ _u_(-> nat nat nat)_ Bool)|)) (not (forall ((ii set_nat_nat_nat)) (= (ho_382 v ii) (ite (= i ii) e (ho_382 u ii)))))))))) (let ((_let_146 (forall ((x |u_(-> set_nat_nat_nat _u_(-> _u_(-> nat nat nat)_ nat)_ _u_(-> _u_(-> nat nat nat)_ nat)_ _u_(-> nat nat nat)_ Bool)|) (y |u_(-> set_nat_nat_nat _u_(-> _u_(-> nat nat nat)_ nat)_ _u_(-> _u_(-> nat nat nat)_ nat)_ _u_(-> nat nat nat)_ Bool)|)) (or (not (forall ((z set_nat_nat_nat)) (= (ho_382 x z) (ho_382 y z)))) (= x y))))) (let ((_let_147 (forall ((u |u_(-> _u_(-> _u_(-> nat nat nat)_ nat)_ _u_(-> _u_(-> nat nat nat)_ nat)_ _u_(-> nat nat nat)_ Bool)|) (e |u_(-> _u_(-> _u_(-> nat nat nat)_ nat)_ _u_(-> nat nat nat)_ Bool)|) (i |u_(-> _u_(-> nat nat nat)_ nat)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> nat nat nat)_ nat)_ _u_(-> _u_(-> nat nat nat)_ nat)_ _u_(-> nat nat nat)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> nat nat nat)_ nat)|)) (= (ho_383 v ii) (ite (= i ii) e (ho_383 u ii)))))))))) (let ((_let_148 (forall ((x |u_(-> _u_(-> _u_(-> nat nat nat)_ nat)_ _u_(-> _u_(-> nat nat nat)_ nat)_ _u_(-> nat nat nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> nat nat nat)_ nat)_ _u_(-> _u_(-> nat nat nat)_ nat)_ _u_(-> nat nat nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> nat nat nat)_ nat)|)) (= (ho_383 x z) (ho_383 y z)))) (= x y))))) (let ((_let_149 (forall ((u |u_(-> _u_(-> nat nat nat)_ Bool)|) (e Bool) (i |u_(-> nat nat nat)|)) (not (forall ((v |u_(-> _u_(-> nat nat nat)_ Bool)|)) (not (forall ((ii |u_(-> nat nat nat)|)) (= (ho_221 v ii) (ite (= i ii) e (ho_221 u ii)))))))))) (let ((_let_150 (forall ((x |u_(-> _u_(-> nat nat nat)_ Bool)|) (y |u_(-> _u_(-> nat nat nat)_ Bool)|)) (or (not (forall ((z |u_(-> nat nat nat)|)) (= (ho_221 x z) (ho_221 y z)))) (= x y))))) (let ((_let_151 (forall ((u |u_(-> _u_(-> _u_(-> nat nat nat)_ nat)_ _u_(-> nat nat nat)_ Bool)|) (e |u_(-> _u_(-> nat nat nat)_ Bool)|) (i |u_(-> _u_(-> nat nat nat)_ nat)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> nat nat nat)_ nat)_ _u_(-> nat nat nat)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> nat nat nat)_ nat)|)) (= (ho_380 v ii) (ite (= i ii) e (ho_380 u ii)))))))))) (let ((_let_152 (forall ((x |u_(-> _u_(-> _u_(-> nat nat nat)_ nat)_ _u_(-> nat nat nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> nat nat nat)_ nat)_ _u_(-> nat nat nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> nat nat nat)_ nat)|)) (= (ho_380 x z) (ho_380 y z)))) (= x y))))) (let ((_let_153 (forall ((u |u_(-> _u_(-> _u_(-> nat nat nat)_ Bool)_ set_nat_nat_nat)|) (e set_nat_nat_nat) (i |u_(-> _u_(-> nat nat nat)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> nat nat nat)_ Bool)_ set_nat_nat_nat)|)) (not (forall ((ii |u_(-> _u_(-> nat nat nat)_ Bool)|)) (= (ho_550 v ii) (ite (= i ii) e (ho_550 u ii)))))))))) (let ((_let_154 (forall ((x |u_(-> _u_(-> _u_(-> nat nat nat)_ Bool)_ set_nat_nat_nat)|) (y |u_(-> _u_(-> _u_(-> nat nat nat)_ Bool)_ set_nat_nat_nat)|)) (or (not (forall ((z |u_(-> _u_(-> nat nat nat)_ Bool)|)) (= (ho_550 x z) (ho_550 y z)))) (= x y))))) (let ((_let_155 (forall ((u |u_(-> nat set_nat_nat_nat2 set_nat _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ Bool)|) (e |u_(-> set_nat_nat_nat2 set_nat _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ Bool)|) (i nat)) (not (forall ((v |u_(-> nat set_nat_nat_nat2 set_nat _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ Bool)|)) (not (forall ((ii nat)) (= (ho_417 v ii) (ite (= i ii) e (ho_417 u ii)))))))))) (let ((_let_156 (forall ((x |u_(-> nat set_nat_nat_nat2 set_nat _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ Bool)|) (y |u_(-> nat set_nat_nat_nat2 set_nat _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ Bool)|)) (or (not (forall ((z nat)) (= (ho_417 x z) (ho_417 y z)))) (= x y))))) (let ((_let_157 (forall ((u |u_(-> _u_(-> nat nat nat)_ nat)|) (e nat) (i |u_(-> nat nat nat)|)) (not (forall ((v |u_(-> _u_(-> nat nat nat)_ nat)|)) (not (forall ((ii |u_(-> nat nat nat)|)) (= (ho_375 v ii) (ite (= i ii) e (ho_375 u ii)))))))))) (let ((_let_158 (forall ((x |u_(-> _u_(-> nat nat nat)_ nat)|) (y |u_(-> _u_(-> nat nat nat)_ nat)|)) (or (not (forall ((z |u_(-> nat nat nat)|)) (= (ho_375 x z) (ho_375 y z)))) (= x y))))) (let ((_let_159 (forall ((u |u_(-> set_nat_nat_nat2 _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (e |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (i set_nat_nat_nat2)) (not (forall ((v |u_(-> set_nat_nat_nat2 _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (not (forall ((ii set_nat_nat_nat2)) (= (ho_371 v ii) (ite (= i ii) e (ho_371 u ii)))))))))) (let ((_let_160 (forall ((x |u_(-> set_nat_nat_nat2 _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (y |u_(-> set_nat_nat_nat2 _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (or (not (forall ((z set_nat_nat_nat2)) (= (ho_371 x z) (ho_371 y z)))) (= x y))))) (let ((_let_161 (forall ((u |u_(-> _u_(-> _u_(-> nat nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ Bool)_ Bool)|) (e |u_(-> _u_(-> _u_(-> nat nat)_ Bool)_ Bool)|) (i |u_(-> _u_(-> nat nat)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> nat nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ Bool)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> nat nat)_ Bool)|)) (= (ho_363 v ii) (ite (= i ii) e (ho_363 u ii)))))))))) (let ((_let_162 (forall ((x |u_(-> _u_(-> _u_(-> nat nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> nat nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> nat nat)_ Bool)|)) (= (ho_363 x z) (ho_363 y z)))) (= x y))))) (let ((_let_163 (forall ((u |u_(-> set_nat_nat _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ nat)_ Bool)|) (e |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ nat)_ Bool)|) (i set_nat_nat)) (not (forall ((v |u_(-> set_nat_nat _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ nat)_ Bool)|)) (not (forall ((ii set_nat_nat)) (= (ho_438 v ii) (ite (= i ii) e (ho_438 u ii)))))))))) (let ((_let_164 (forall ((x |u_(-> set_nat_nat _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ nat)_ Bool)|) (y |u_(-> set_nat_nat _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ nat)_ Bool)|)) (or (not (forall ((z set_nat_nat)) (= (ho_438 x z) (ho_438 y z)))) (= x y))))) (let ((_let_165 (forall ((u |u_(-> _u_(-> nat Bool)_ nat Bool)|) (e |u_(-> nat Bool)|) (i |u_(-> nat Bool)|)) (not (forall ((v |u_(-> _u_(-> nat Bool)_ nat Bool)|)) (not (forall ((ii |u_(-> nat Bool)|)) (= (ho_206 v ii) (ite (= i ii) e (ho_206 u ii)))))))))) (let ((_let_166 (forall ((x |u_(-> _u_(-> nat Bool)_ nat Bool)|) (y |u_(-> _u_(-> nat Bool)_ nat Bool)|)) (or (not (forall ((z |u_(-> nat Bool)|)) (= (ho_206 x z) (ho_206 y z)))) (= x y))))) (let ((_let_167 (forall ((u |u_(-> _u_(-> _u_(-> nat nat)_ Bool)_ Bool)|) (e Bool) (i |u_(-> _u_(-> nat nat)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> nat nat)_ Bool)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> nat nat)_ Bool)|)) (= (ho_364 v ii) (ite (= i ii) e (ho_364 u ii)))))))))) (let ((_let_168 (forall ((x |u_(-> _u_(-> _u_(-> nat nat)_ Bool)_ Bool)|) (y |u_(-> _u_(-> _u_(-> nat nat)_ Bool)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> nat nat)_ Bool)|)) (= (ho_364 x z) (ho_364 y z)))) (= x y))))) (let ((_let_169 (forall ((u |u_(-> set_nat_nat_nat2 set_nat_nat_nat2 Bool)|) (e |u_(-> set_nat_nat_nat2 Bool)|) (i set_nat_nat_nat2)) (not (forall ((v |u_(-> set_nat_nat_nat2 set_nat_nat_nat2 Bool)|)) (not (forall ((ii set_nat_nat_nat2)) (= (ho_358 v ii) (ite (= i ii) e (ho_358 u ii)))))))))) (let ((_let_170 (forall ((x |u_(-> set_nat_nat_nat2 set_nat_nat_nat2 Bool)|) (y |u_(-> set_nat_nat_nat2 set_nat_nat_nat2 Bool)|)) (or (not (forall ((z set_nat_nat_nat2)) (= (ho_358 x z) (ho_358 y z)))) (= x y))))) (let ((_let_171 (forall ((u |u_(-> set_nat_nat_nat _u_(-> _u_(-> nat nat nat)_ Bool)_ _u_(-> nat nat nat)_ Bool)|) (e |u_(-> _u_(-> _u_(-> nat nat nat)_ Bool)_ _u_(-> nat nat nat)_ Bool)|) (i set_nat_nat_nat)) (not (forall ((v |u_(-> set_nat_nat_nat _u_(-> _u_(-> nat nat nat)_ Bool)_ _u_(-> nat nat nat)_ Bool)|)) (not (forall ((ii set_nat_nat_nat)) (= (ho_240 v ii) (ite (= i ii) e (ho_240 u ii)))))))))) (let ((_let_172 (forall ((x |u_(-> set_nat_nat_nat _u_(-> _u_(-> nat nat nat)_ Bool)_ _u_(-> nat nat nat)_ Bool)|) (y |u_(-> set_nat_nat_nat _u_(-> _u_(-> nat nat nat)_ Bool)_ _u_(-> nat nat nat)_ Bool)|)) (or (not (forall ((z set_nat_nat_nat)) (= (ho_240 x z) (ho_240 y z)))) (= x y))))) (let ((_let_173 (forall ((u |u_(-> _u_(-> nat _u_(-> nat nat nat)_ Bool)_ _u_(-> nat nat nat)_ set_nat nat Bool)|) (e |u_(-> _u_(-> nat nat nat)_ set_nat nat Bool)|) (i |u_(-> nat _u_(-> nat nat nat)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> nat _u_(-> nat nat nat)_ Bool)_ _u_(-> nat nat nat)_ set_nat nat Bool)|)) (not (forall ((ii |u_(-> nat _u_(-> nat nat nat)_ Bool)|)) (= (ho_337 v ii) (ite (= i ii) e (ho_337 u ii)))))))))) (let ((_let_174 (forall ((x |u_(-> _u_(-> nat _u_(-> nat nat nat)_ Bool)_ _u_(-> nat nat nat)_ set_nat nat Bool)|) (y |u_(-> _u_(-> nat _u_(-> nat nat nat)_ Bool)_ _u_(-> nat nat nat)_ set_nat nat Bool)|)) (or (not (forall ((z |u_(-> nat _u_(-> nat nat nat)_ Bool)|)) (= (ho_337 x z) (ho_337 y z)))) (= x y))))) (let ((_let_175 (forall ((u |u_(-> set_nat_nat _u_(-> nat nat nat)_ Bool)|) (e |u_(-> _u_(-> nat nat nat)_ Bool)|) (i set_nat_nat)) (not (forall ((v |u_(-> set_nat_nat _u_(-> nat nat nat)_ Bool)|)) (not (forall ((ii set_nat_nat)) (= (ho_483 v ii) (ite (= i ii) e (ho_483 u ii)))))))))) (let ((_let_176 (forall ((x |u_(-> set_nat_nat _u_(-> nat nat nat)_ Bool)|) (y |u_(-> set_nat_nat _u_(-> nat nat nat)_ Bool)|)) (or (not (forall ((z set_nat_nat)) (= (ho_483 x z) (ho_483 y z)))) (= x y))))) (let ((_let_177 (forall ((u |u_(-> _u_(-> nat nat nat)_ set_nat_nat set_nat_nat_nat _u_(-> _u_(-> nat nat)_ nat nat nat)_ Bool)|) (e |u_(-> set_nat_nat set_nat_nat_nat _u_(-> _u_(-> nat nat)_ nat nat nat)_ Bool)|) (i |u_(-> nat nat nat)|)) (not (forall ((v |u_(-> _u_(-> nat nat nat)_ set_nat_nat set_nat_nat_nat _u_(-> _u_(-> nat nat)_ nat nat nat)_ Bool)|)) (not (forall ((ii |u_(-> nat nat nat)|)) (= (ho_391 v ii) (ite (= i ii) e (ho_391 u ii)))))))))) (let ((_let_178 (forall ((x |u_(-> _u_(-> nat nat nat)_ set_nat_nat set_nat_nat_nat _u_(-> _u_(-> nat nat)_ nat nat nat)_ Bool)|) (y |u_(-> _u_(-> nat nat nat)_ set_nat_nat set_nat_nat_nat _u_(-> _u_(-> nat nat)_ nat nat nat)_ Bool)|)) (or (not (forall ((z |u_(-> nat nat nat)|)) (= (ho_391 x z) (ho_391 y z)))) (= x y))))) (let ((_let_179 (forall ((u |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ set_nat_nat_nat2 _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (e |u_(-> set_nat_nat_nat2 _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (i |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ set_nat_nat_nat2 _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (= (ho_370 v ii) (ite (= i ii) e (ho_370 u ii)))))))))) (let ((_let_180 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ set_nat_nat_nat2 _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ set_nat_nat_nat2 _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (= (ho_370 x z) (ho_370 y z)))) (= x y))))) (let ((_let_181 (forall ((u |u_(-> set_nat _u_(-> nat _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat)_ nat Bool)|) (e |u_(-> _u_(-> nat _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat)_ nat Bool)|) (i set_nat)) (not (forall ((v |u_(-> set_nat _u_(-> nat _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat)_ nat Bool)|)) (not (forall ((ii set_nat)) (= (ho_444 v ii) (ite (= i ii) e (ho_444 u ii)))))))))) (let ((_let_182 (forall ((x |u_(-> set_nat _u_(-> nat _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat)_ nat Bool)|) (y |u_(-> set_nat _u_(-> nat _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat)_ nat Bool)|)) (or (not (forall ((z set_nat)) (= (ho_444 x z) (ho_444 y z)))) (= x y))))) (let ((_let_183 (forall ((u |u_(-> _u_(-> nat nat nat)_ set_nat nat Bool)|) (e |u_(-> set_nat nat Bool)|) (i |u_(-> nat nat nat)|)) (not (forall ((v |u_(-> _u_(-> nat nat nat)_ set_nat nat Bool)|)) (not (forall ((ii |u_(-> nat nat nat)|)) (= (ho_338 v ii) (ite (= i ii) e (ho_338 u ii)))))))))) (let ((_let_184 (forall ((x |u_(-> _u_(-> nat nat nat)_ set_nat nat Bool)|) (y |u_(-> _u_(-> nat nat nat)_ set_nat nat Bool)|)) (or (not (forall ((z |u_(-> nat nat nat)|)) (= (ho_338 x z) (ho_338 y z)))) (= x y))))) (let ((_let_185 (forall ((u |u_(-> set_nat _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ Bool)|) (e |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ Bool)|) (i set_nat)) (not (forall ((v |u_(-> set_nat _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ Bool)|)) (not (forall ((ii set_nat)) (= (ho_419 v ii) (ite (= i ii) e (ho_419 u ii)))))))))) (let ((_let_186 (forall ((x |u_(-> set_nat _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ Bool)|) (y |u_(-> set_nat _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ Bool)|)) (or (not (forall ((z set_nat)) (= (ho_419 x z) (ho_419 y z)))) (= x y))))) (let ((_let_187 (forall ((u |u_(-> nat _u_(-> nat nat nat)_ Bool)|) (e |u_(-> _u_(-> nat nat nat)_ Bool)|) (i nat)) (not (forall ((v |u_(-> nat _u_(-> nat nat nat)_ Bool)|)) (not (forall ((ii nat)) (= (ho_335 v ii) (ite (= i ii) e (ho_335 u ii)))))))))) (let ((_let_188 (forall ((x |u_(-> nat _u_(-> nat nat nat)_ Bool)|) (y |u_(-> nat _u_(-> nat nat nat)_ Bool)|)) (or (not (forall ((z nat)) (= (ho_335 x z) (ho_335 y z)))) (= x y))))) (let ((_let_189 (forall ((u |u_(-> set_nat set_nat nat _u_(-> nat nat)_ Bool)|) (e |u_(-> set_nat nat _u_(-> nat nat)_ Bool)|) (i set_nat)) (not (forall ((v |u_(-> set_nat set_nat nat _u_(-> nat nat)_ Bool)|)) (not (forall ((ii set_nat)) (= (ho_333 v ii) (ite (= i ii) e (ho_333 u ii)))))))))) (let ((_let_190 (forall ((x |u_(-> set_nat set_nat nat _u_(-> nat nat)_ Bool)|) (y |u_(-> set_nat set_nat nat _u_(-> nat nat)_ Bool)|)) (or (not (forall ((z set_nat)) (= (ho_333 x z) (ho_333 y z)))) (= x y))))) (let ((_let_191 (forall ((u |u_(-> _u_(-> _u_(-> nat nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ Bool)_ _u_(-> nat nat)_ Bool)|) (e |u_(-> _u_(-> _u_(-> nat nat)_ Bool)_ _u_(-> nat nat)_ Bool)|) (i |u_(-> _u_(-> nat nat)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> nat nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ Bool)_ _u_(-> nat nat)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> nat nat)_ Bool)|)) (= (ho_397 v ii) (ite (= i ii) e (ho_397 u ii)))))))))) (let ((_let_192 (forall ((x |u_(-> _u_(-> _u_(-> nat nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ Bool)_ _u_(-> nat nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> nat nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ Bool)_ _u_(-> nat nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> nat nat)_ Bool)|)) (= (ho_397 x z) (ho_397 y z)))) (= x y))))) (let ((_let_193 (forall ((u |u_(-> set_nat nat _u_(-> nat nat)_ Bool)|) (e |u_(-> nat _u_(-> nat nat)_ Bool)|) (i set_nat)) (not (forall ((v |u_(-> set_nat nat _u_(-> nat nat)_ Bool)|)) (not (forall ((ii set_nat)) (= (ho_334 v ii) (ite (= i ii) e (ho_334 u ii)))))))))) (let ((_let_194 (forall ((x |u_(-> set_nat nat _u_(-> nat nat)_ Bool)|) (y |u_(-> set_nat nat _u_(-> nat nat)_ Bool)|)) (or (not (forall ((z set_nat)) (= (ho_334 x z) (ho_334 y z)))) (= x y))))) (let ((_let_195 (forall ((u |u_(-> set_nat_nat_nat set_nat _u_(-> nat nat nat)_ _u_(-> nat nat nat nat)_ Bool)|) (e |u_(-> set_nat _u_(-> nat nat nat)_ _u_(-> nat nat nat nat)_ Bool)|) (i set_nat_nat_nat)) (not (forall ((v |u_(-> set_nat_nat_nat set_nat _u_(-> nat nat nat)_ _u_(-> nat nat nat nat)_ Bool)|)) (not (forall ((ii set_nat_nat_nat)) (= (ho_244 v ii) (ite (= i ii) e (ho_244 u ii)))))))))) (let ((_let_196 (forall ((x |u_(-> set_nat_nat_nat set_nat _u_(-> nat nat nat)_ _u_(-> nat nat nat nat)_ Bool)|) (y |u_(-> set_nat_nat_nat set_nat _u_(-> nat nat nat)_ _u_(-> nat nat nat nat)_ Bool)|)) (or (not (forall ((z set_nat_nat_nat)) (= (ho_244 x z) (ho_244 y z)))) (= x y))))) (let ((_let_197 (forall ((u |u_(-> _u_(-> _u_(-> nat nat nat)_ Bool)_ set_nat_nat_nat _u_(-> nat nat nat)_ Bool)|) (e |u_(-> set_nat_nat_nat _u_(-> nat nat nat)_ Bool)|) (i |u_(-> _u_(-> nat nat nat)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> nat nat nat)_ Bool)_ set_nat_nat_nat _u_(-> nat nat nat)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> nat nat nat)_ Bool)|)) (= (ho_330 v ii) (ite (= i ii) e (ho_330 u ii)))))))))) (let ((_let_198 (forall ((x |u_(-> _u_(-> _u_(-> nat nat nat)_ Bool)_ set_nat_nat_nat _u_(-> nat nat nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> nat nat nat)_ Bool)_ set_nat_nat_nat _u_(-> nat nat nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> nat nat nat)_ Bool)|)) (= (ho_330 x z) (ho_330 y z)))) (= x y))))) (let ((_let_199 (forall ((u |u_(-> _u_(-> nat nat nat)_ nat Bool)|) (e |u_(-> nat Bool)|) (i |u_(-> nat nat nat)|)) (not (forall ((v |u_(-> _u_(-> nat nat nat)_ nat Bool)|)) (not (forall ((ii |u_(-> nat nat nat)|)) (= (ho_410 v ii) (ite (= i ii) e (ho_410 u ii)))))))))) (let ((_let_200 (forall ((x |u_(-> _u_(-> nat nat nat)_ nat Bool)|) (y |u_(-> _u_(-> nat nat nat)_ nat Bool)|)) (or (not (forall ((z |u_(-> nat nat nat)|)) (= (ho_410 x z) (ho_410 y z)))) (= x y))))) (let ((_let_201 (forall ((u |u_(-> set_set_nat Bool)|) (e Bool) (i set_set_nat)) (not (forall ((v |u_(-> set_set_nat Bool)|)) (not (forall ((ii set_set_nat)) (= (ho_576 v ii) (ite (= i ii) e (ho_576 u ii)))))))))) (let ((_let_202 (forall ((x |u_(-> set_set_nat Bool)|) (y |u_(-> set_set_nat Bool)|)) (or (not (forall ((z set_set_nat)) (= (ho_576 x z) (ho_576 y z)))) (= x y))))) (let ((_let_203 (forall ((u |u_(-> set_nat_nat_nat_nat3 set_nat_nat_nat_nat3 Bool)|) (e |u_(-> set_nat_nat_nat_nat3 Bool)|) (i set_nat_nat_nat_nat3)) (not (forall ((v |u_(-> set_nat_nat_nat_nat3 set_nat_nat_nat_nat3 Bool)|)) (not (forall ((ii set_nat_nat_nat_nat3)) (= (ho_387 v ii) (ite (= i ii) e (ho_387 u ii)))))))))) (let ((_let_204 (forall ((x |u_(-> set_nat_nat_nat_nat3 set_nat_nat_nat_nat3 Bool)|) (y |u_(-> set_nat_nat_nat_nat3 set_nat_nat_nat_nat3 Bool)|)) (or (not (forall ((z set_nat_nat_nat_nat3)) (= (ho_387 x z) (ho_387 y z)))) (= x y))))) (let ((_let_205 (forall ((u |u_(-> set_nat_nat_nat _u_(-> nat nat nat)_ Bool)|) (e |u_(-> _u_(-> nat nat nat)_ Bool)|) (i set_nat_nat_nat)) (not (forall ((v |u_(-> set_nat_nat_nat _u_(-> nat nat nat)_ Bool)|)) (not (forall ((ii set_nat_nat_nat)) (= (ho_331 v ii) (ite (= i ii) e (ho_331 u ii)))))))))) (let ((_let_206 (forall ((x |u_(-> set_nat_nat_nat _u_(-> nat nat nat)_ Bool)|) (y |u_(-> set_nat_nat_nat _u_(-> nat nat nat)_ Bool)|)) (or (not (forall ((z set_nat_nat_nat)) (= (ho_331 x z) (ho_331 y z)))) (= x y))))) (let ((_let_207 (forall ((u |u_(-> set_nat_nat _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> nat nat)_ Bool)|) (e |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> nat nat)_ Bool)|) (i set_nat_nat)) (not (forall ((v |u_(-> set_nat_nat _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> nat nat)_ Bool)|)) (not (forall ((ii set_nat_nat)) (= (ho_326 v ii) (ite (= i ii) e (ho_326 u ii)))))))))) (let ((_let_208 (forall ((x |u_(-> set_nat_nat _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> nat nat)_ Bool)|) (y |u_(-> set_nat_nat _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> nat nat)_ Bool)|)) (or (not (forall ((z set_nat_nat)) (= (ho_326 x z) (ho_326 y z)))) (= x y))))) (let ((_let_209 (forall ((u |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat Bool)|) (e |u_(-> nat Bool)|) (i |u_(-> _u_(-> nat nat)_ nat)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat Bool)|)) (not (forall ((ii |u_(-> _u_(-> nat nat)_ nat)|)) (= (ho_446 v ii) (ite (= i ii) e (ho_446 u ii)))))))))) (let ((_let_210 (forall ((x |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat Bool)|) (y |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat Bool)|)) (or (not (forall ((z |u_(-> _u_(-> nat nat)_ nat)|)) (= (ho_446 x z) (ho_446 y z)))) (= x y))))) (let ((_let_211 (forall ((u |u_(-> set_nat_nat_nat2 _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (e |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (i set_nat_nat_nat2)) (not (forall ((v |u_(-> set_nat_nat_nat2 _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (not (forall ((ii set_nat_nat_nat2)) (= (ho_520 v ii) (ite (= i ii) e (ho_520 u ii)))))))))) (let ((_let_212 (forall ((x |u_(-> set_nat_nat_nat2 _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (y |u_(-> set_nat_nat_nat2 _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (or (not (forall ((z set_nat_nat_nat2)) (= (ho_520 x z) (ho_520 y z)))) (= x y))))) (let ((_let_213 (forall ((u |u_(-> _u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ Bool)_ set_nat_nat_nat_nat5)|) (e set_nat_nat_nat_nat5) (i |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ Bool)_ set_nat_nat_nat_nat5)|)) (not (forall ((ii |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ Bool)|)) (= (ho_578 v ii) (ite (= i ii) e (ho_578 u ii)))))))))) (let ((_let_214 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ Bool)_ set_nat_nat_nat_nat5)|) (y |u_(-> _u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ Bool)_ set_nat_nat_nat_nat5)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ Bool)|)) (= (ho_578 x z) (ho_578 y z)))) (= x y))))) (let ((_let_215 (forall ((u |u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ nat)|) (e |u_(-> _u_(-> nat nat)_ nat)|) (i |u_(-> nat nat)|)) (not (forall ((v |u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ nat)|)) (not (forall ((ii |u_(-> nat nat)|)) (= (ho_435 v ii) (ite (= i ii) e (ho_435 u ii)))))))))) (let ((_let_216 (forall ((x |u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ nat)|) (y |u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ nat)|)) (or (not (forall ((z |u_(-> nat nat)|)) (= (ho_435 x z) (ho_435 y z)))) (= x y))))) (let ((_let_217 (forall ((u |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> nat nat)_ Bool)|) (e |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> nat nat)_ Bool)|) (i |u_(-> _u_(-> nat nat)_ nat)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> nat nat)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> nat nat)_ nat)|)) (= (ho_327 v ii) (ite (= i ii) e (ho_327 u ii)))))))))) (let ((_let_218 (forall ((x |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> nat nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> nat nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> nat nat)_ nat)|)) (= (ho_327 x z) (ho_327 y z)))) (= x y))))) (let ((_let_219 (forall ((u |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> nat nat)_ Bool)|) (e |u_(-> _u_(-> nat nat)_ Bool)|) (i |u_(-> _u_(-> nat nat)_ nat)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> nat nat)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> nat nat)_ nat)|)) (= (ho_323 v ii) (ite (= i ii) e (ho_323 u ii)))))))))) (let ((_let_220 (forall ((x |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> nat nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> nat nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> nat nat)_ nat)|)) (= (ho_323 x z) (ho_323 y z)))) (= x y))))) (let ((_let_221 (forall ((u |u_(-> _u_(-> nat nat)_ set_nat set_nat_nat _u_(-> nat nat nat)_ Bool)|) (e |u_(-> set_nat set_nat_nat _u_(-> nat nat nat)_ Bool)|) (i |u_(-> nat nat)|)) (not (forall ((v |u_(-> _u_(-> nat nat)_ set_nat set_nat_nat _u_(-> nat nat nat)_ Bool)|)) (not (forall ((ii |u_(-> nat nat)|)) (= (ho_481 v ii) (ite (= i ii) e (ho_481 u ii)))))))))) (let ((_let_222 (forall ((x |u_(-> _u_(-> nat nat)_ set_nat set_nat_nat _u_(-> nat nat nat)_ Bool)|) (y |u_(-> _u_(-> nat nat)_ set_nat set_nat_nat _u_(-> nat nat nat)_ Bool)|)) (or (not (forall ((z |u_(-> nat nat)|)) (= (ho_481 x z) (ho_481 y z)))) (= x y))))) (let ((_let_223 (forall ((u |u_(-> _u_(-> nat Bool)_ _u_(-> nat Bool)_ Bool)|) (e |u_(-> _u_(-> nat Bool)_ Bool)|) (i |u_(-> nat Bool)|)) (not (forall ((v |u_(-> _u_(-> nat Bool)_ _u_(-> nat Bool)_ Bool)|)) (not (forall ((ii |u_(-> nat Bool)|)) (= (ho_311 v ii) (ite (= i ii) e (ho_311 u ii)))))))))) (let ((_let_224 (forall ((x |u_(-> _u_(-> nat Bool)_ _u_(-> nat Bool)_ Bool)|) (y |u_(-> _u_(-> nat Bool)_ _u_(-> nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> nat Bool)|)) (= (ho_311 x z) (ho_311 y z)))) (= x y))))) (let ((_let_225 (forall ((u |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ set_nat_nat_nat2 _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (e |u_(-> set_nat_nat_nat2 _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (i |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ set_nat_nat_nat2 _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)|)) (= (ho_523 v ii) (ite (= i ii) e (ho_523 u ii)))))))))) (let ((_let_226 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ set_nat_nat_nat2 _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ set_nat_nat_nat2 _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)|)) (= (ho_523 x z) (ho_523 y z)))) (= x y))))) (let ((_let_227 (forall ((u |u_(-> _u_(-> nat Bool)_ Bool)|) (e Bool) (i |u_(-> nat Bool)|)) (not (forall ((v |u_(-> _u_(-> nat Bool)_ Bool)|)) (not (forall ((ii |u_(-> nat Bool)|)) (= (ho_312 v ii) (ite (= i ii) e (ho_312 u ii)))))))))) (let ((_let_228 (forall ((x |u_(-> _u_(-> nat Bool)_ Bool)|) (y |u_(-> _u_(-> nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> nat Bool)|)) (= (ho_312 x z) (ho_312 y z)))) (= x y))))) (let ((_let_229 (forall ((u |u_(-> _u_(-> nat nat)_ nat Bool)|) (e |u_(-> nat Bool)|) (i |u_(-> nat nat)|)) (not (forall ((v |u_(-> _u_(-> nat nat)_ nat Bool)|)) (not (forall ((ii |u_(-> nat nat)|)) (= (ho_308 v ii) (ite (= i ii) e (ho_308 u ii)))))))))) (let ((_let_230 (forall ((x |u_(-> _u_(-> nat nat)_ nat Bool)|) (y |u_(-> _u_(-> nat nat)_ nat Bool)|)) (or (not (forall ((z |u_(-> nat nat)|)) (= (ho_308 x z) (ho_308 y z)))) (= x y))))) (let ((_let_231 (forall ((u |u_(-> set_nat_nat_nat2 _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (e |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (i set_nat_nat_nat2)) (not (forall ((v |u_(-> set_nat_nat_nat2 _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (not (forall ((ii set_nat_nat_nat2)) (= (ho_525 v ii) (ite (= i ii) e (ho_525 u ii)))))))))) (let ((_let_232 (forall ((x |u_(-> set_nat_nat_nat2 _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (y |u_(-> set_nat_nat_nat2 _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (or (not (forall ((z set_nat_nat_nat2)) (= (ho_525 x z) (ho_525 y z)))) (= x y))))) (let ((_let_233 (forall ((u |u_(-> _u_(-> nat nat)_ nat nat nat)|) (e |u_(-> nat nat nat)|) (i |u_(-> nat nat)|)) (not (forall ((v |u_(-> _u_(-> nat nat)_ nat nat nat)|)) (not (forall ((ii |u_(-> nat nat)|)) (= (ho_389 v ii) (ite (= i ii) e (ho_389 u ii)))))))))) (let ((_let_234 (forall ((x |u_(-> _u_(-> nat nat)_ nat nat nat)|) (y |u_(-> _u_(-> nat nat)_ nat nat nat)|)) (or (not (forall ((z |u_(-> nat nat)|)) (= (ho_389 x z) (ho_389 y z)))) (= x y))))) (let ((_let_235 (forall ((u |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ set_nat set_nat_nat_nat2 _u_(-> nat _u_(-> nat nat)_ nat)_ Bool)|) (e |u_(-> set_nat set_nat_nat_nat2 _u_(-> nat _u_(-> nat nat)_ nat)_ Bool)|) (i |u_(-> _u_(-> nat nat)_ nat)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ set_nat set_nat_nat_nat2 _u_(-> nat _u_(-> nat nat)_ nat)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> nat nat)_ nat)|)) (= (ho_303 v ii) (ite (= i ii) e (ho_303 u ii)))))))))) (let ((_let_236 (forall ((x |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ set_nat set_nat_nat_nat2 _u_(-> nat _u_(-> nat nat)_ nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ set_nat set_nat_nat_nat2 _u_(-> nat _u_(-> nat nat)_ nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> nat nat)_ nat)|)) (= (ho_303 x z) (ho_303 y z)))) (= x y))))) (let ((_let_237 (forall ((u |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ set_nat_nat_nat_nat3 Bool)|) (e |u_(-> set_nat_nat_nat_nat3 Bool)|) (i |u_(-> _u_(-> nat nat)_ nat nat)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ set_nat_nat_nat_nat3 Bool)|)) (not (forall ((ii |u_(-> _u_(-> nat nat)_ nat nat)|)) (= (ho_296 v ii) (ite (= i ii) e (ho_296 u ii)))))))))) (let ((_let_238 (forall ((x |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ set_nat_nat_nat_nat3 Bool)|) (y |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ set_nat_nat_nat_nat3 Bool)|)) (or (not (forall ((z |u_(-> _u_(-> nat nat)_ nat nat)|)) (= (ho_296 x z) (ho_296 y z)))) (= x y))))) (let ((_let_239 (forall ((u |u_(-> set_nat set_nat_nat_nat2 _u_(-> nat _u_(-> nat nat)_ nat)_ Bool)|) (e |u_(-> set_nat_nat_nat2 _u_(-> nat _u_(-> nat nat)_ nat)_ Bool)|) (i set_nat)) (not (forall ((v |u_(-> set_nat set_nat_nat_nat2 _u_(-> nat _u_(-> nat nat)_ nat)_ Bool)|)) (not (forall ((ii set_nat)) (= (ho_304 v ii) (ite (= i ii) e (ho_304 u ii)))))))))) (let ((_let_240 (forall ((x |u_(-> set_nat set_nat_nat_nat2 _u_(-> nat _u_(-> nat nat)_ nat)_ Bool)|) (y |u_(-> set_nat set_nat_nat_nat2 _u_(-> nat _u_(-> nat nat)_ nat)_ Bool)|)) (or (not (forall ((z set_nat)) (= (ho_304 x z) (ho_304 y z)))) (= x y))))) (let ((_let_241 (forall ((u |u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ set_nat nat Bool)|) (e |u_(-> _u_(-> nat nat)_ set_nat nat Bool)|) (i |u_(-> nat nat)|)) (not (forall ((v |u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ set_nat nat Bool)|)) (not (forall ((ii |u_(-> nat nat)|)) (= (ho_259 v ii) (ite (= i ii) e (ho_259 u ii)))))))))) (let ((_let_242 (forall ((x |u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ set_nat nat Bool)|) (y |u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ set_nat nat Bool)|)) (or (not (forall ((z |u_(-> nat nat)|)) (= (ho_259 x z) (ho_259 y z)))) (= x y))))) (let ((_let_243 (forall ((u |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (e Bool) (i |u_(-> _u_(-> nat nat)_ nat nat)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> nat nat)_ nat nat)|)) (= (ho_231 v ii) (ite (= i ii) e (ho_231 u ii)))))))))) (let ((_let_244 (forall ((x |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> nat nat)_ nat nat)|)) (= (ho_231 x z) (ho_231 y z)))) (= x y))))) (let ((_let_245 (forall ((u |u_(-> set_nat_nat_nat2 _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (e |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (i set_nat_nat_nat2)) (not (forall ((v |u_(-> set_nat_nat_nat2 _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (not (forall ((ii set_nat_nat_nat2)) (= (ho_266 v ii) (ite (= i ii) e (ho_266 u ii)))))))))) (let ((_let_246 (forall ((x |u_(-> set_nat_nat_nat2 _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (y |u_(-> set_nat_nat_nat2 _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (or (not (forall ((z set_nat_nat_nat2)) (= (ho_266 x z) (ho_266 y z)))) (= x y))))) (let ((_let_247 (forall ((u |u_(-> _u_(-> nat nat)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (e |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (i |u_(-> nat nat)|)) (not (forall ((v |u_(-> _u_(-> nat nat)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|)) (not (forall ((ii |u_(-> nat nat)|)) (= (ho_230 v ii) (ite (= i ii) e (ho_230 u ii)))))))))) (let ((_let_248 (forall ((x |u_(-> _u_(-> nat nat)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (y |u_(-> _u_(-> nat nat)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|)) (or (not (forall ((z |u_(-> nat nat)|)) (= (ho_230 x z) (ho_230 y z)))) (= x y))))) (let ((_let_249 (forall ((u |u_(-> nat nat _u_(-> nat nat)_ Bool)|) (e |u_(-> nat _u_(-> nat nat)_ Bool)|) (i nat)) (not (forall ((v |u_(-> nat nat _u_(-> nat nat)_ Bool)|)) (not (forall ((ii nat)) (= (ho_282 v ii) (ite (= i ii) e (ho_282 u ii)))))))))) (let ((_let_250 (forall ((x |u_(-> nat nat _u_(-> nat nat)_ Bool)|) (y |u_(-> nat nat _u_(-> nat nat)_ Bool)|)) (or (not (forall ((z nat)) (= (ho_282 x z) (ho_282 y z)))) (= x y))))) (let ((_let_251 (forall ((u |u_(-> _u_(-> nat nat Bool)_ nat nat Bool)|) (e |u_(-> nat nat Bool)|) (i |u_(-> nat nat Bool)|)) (not (forall ((v |u_(-> _u_(-> nat nat Bool)_ nat nat Bool)|)) (not (forall ((ii |u_(-> nat nat Bool)|)) (= (ho_348 v ii) (ite (= i ii) e (ho_348 u ii)))))))))) (let ((_let_252 (forall ((x |u_(-> _u_(-> nat nat Bool)_ nat nat Bool)|) (y |u_(-> _u_(-> nat nat Bool)_ nat nat Bool)|)) (or (not (forall ((z |u_(-> nat nat Bool)|)) (= (ho_348 x z) (ho_348 y z)))) (= x y))))) (let ((_let_253 (forall ((u |u_(-> _u_(-> _u_(-> nat nat nat)_ nat)_ Bool)|) (e Bool) (i |u_(-> _u_(-> nat nat nat)_ nat)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> nat nat nat)_ nat)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> nat nat nat)_ nat)|)) (= (ho_461 v ii) (ite (= i ii) e (ho_461 u ii)))))))))) (let ((_let_254 (forall ((x |u_(-> _u_(-> _u_(-> nat nat nat)_ nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> nat nat nat)_ nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> nat nat nat)_ nat)|)) (= (ho_461 x z) (ho_461 y z)))) (= x y))))) (let ((_let_255 (forall ((u |u_(-> nat nat)|) (e nat) (i nat)) (not (forall ((v |u_(-> nat nat)|)) (not (forall ((ii nat)) (= (ho_196 v ii) (ite (= i ii) e (ho_196 u ii)))))))))) (let ((_let_256 (forall ((x |u_(-> nat nat)|) (y |u_(-> nat nat)|)) (or (not (forall ((z nat)) (= (ho_196 x z) (ho_196 y z)))) (= x y))))) (let ((_let_257 (forall ((u |u_(-> nat nat nat nat)|) (e |u_(-> nat nat nat)|) (i nat)) (not (forall ((v |u_(-> nat nat nat nat)|)) (not (forall ((ii nat)) (= (ho_242 v ii) (ite (= i ii) e (ho_242 u ii)))))))))) (let ((_let_258 (forall ((x |u_(-> nat nat nat nat)|) (y |u_(-> nat nat nat nat)|)) (or (not (forall ((z nat)) (= (ho_242 x z) (ho_242 y z)))) (= x y))))) (let ((_let_259 (forall ((u |u_(-> nat set_nat_nat_nat2 _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (e |u_(-> set_nat_nat_nat2 _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (i nat)) (not (forall ((v |u_(-> nat set_nat_nat_nat2 _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (not (forall ((ii nat)) (= (ho_518 v ii) (ite (= i ii) e (ho_518 u ii)))))))))) (let ((_let_260 (forall ((x |u_(-> nat set_nat_nat_nat2 _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (y |u_(-> nat set_nat_nat_nat2 _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (or (not (forall ((z nat)) (= (ho_518 x z) (ho_518 y z)))) (= x y))))) (let ((_let_261 (forall ((u |u_(-> _u_(-> nat nat)_ nat nat)|) (e |u_(-> nat nat)|) (i |u_(-> nat nat)|)) (not (forall ((v |u_(-> _u_(-> nat nat)_ nat nat)|)) (not (forall ((ii |u_(-> nat nat)|)) (= (ho_226 v ii) (ite (= i ii) e (ho_226 u ii)))))))))) (let ((_let_262 (forall ((x |u_(-> _u_(-> nat nat)_ nat nat)|) (y |u_(-> _u_(-> nat nat)_ nat nat)|)) (or (not (forall ((z |u_(-> nat nat)|)) (= (ho_226 x z) (ho_226 y z)))) (= x y))))) (let ((_let_263 (forall ((u |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (e |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (i |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)|)) (= (ho_521 v ii) (ite (= i ii) e (ho_521 u ii)))))))))) (let ((_let_264 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)|)) (= (ho_521 x z) (ho_521 y z)))) (= x y))))) (let ((_let_265 (forall ((u |u_(-> set_nat_nat _u_(-> _u_(-> nat nat)_ _u_(-> nat nat nat)_ Bool)_ _u_(-> nat nat nat)_ _u_(-> nat nat)_ Bool)|) (e |u_(-> _u_(-> _u_(-> nat nat)_ _u_(-> nat nat nat)_ Bool)_ _u_(-> nat nat nat)_ _u_(-> nat nat)_ Bool)|) (i set_nat_nat)) (not (forall ((v |u_(-> set_nat_nat _u_(-> _u_(-> nat nat)_ _u_(-> nat nat nat)_ Bool)_ _u_(-> nat nat nat)_ _u_(-> nat nat)_ Bool)|)) (not (forall ((ii set_nat_nat)) (= (ho_223 v ii) (ite (= i ii) e (ho_223 u ii)))))))))) (let ((_let_266 (forall ((x |u_(-> set_nat_nat _u_(-> _u_(-> nat nat)_ _u_(-> nat nat nat)_ Bool)_ _u_(-> nat nat nat)_ _u_(-> nat nat)_ Bool)|) (y |u_(-> set_nat_nat _u_(-> _u_(-> nat nat)_ _u_(-> nat nat nat)_ Bool)_ _u_(-> nat nat nat)_ _u_(-> nat nat)_ Bool)|)) (or (not (forall ((z set_nat_nat)) (= (ho_223 x z) (ho_223 y z)))) (= x y))))) (let ((_let_267 (forall ((u |u_(-> set_nat_nat_nat2 Bool)|) (e Bool) (i set_nat_nat_nat2)) (not (forall ((v |u_(-> set_nat_nat_nat2 Bool)|)) (not (forall ((ii set_nat_nat_nat2)) (= (ho_264 v ii) (ite (= i ii) e (ho_264 u ii)))))))))) (let ((_let_268 (forall ((x |u_(-> set_nat_nat_nat2 Bool)|) (y |u_(-> set_nat_nat_nat2 Bool)|)) (or (not (forall ((z set_nat_nat_nat2)) (= (ho_264 x z) (ho_264 y z)))) (= x y))))) (let ((_let_269 (forall ((u |u_(-> _u_(-> _u_(-> nat nat)_ _u_(-> nat nat nat)_ Bool)_ _u_(-> nat nat nat)_ _u_(-> nat nat)_ Bool)|) (e |u_(-> _u_(-> nat nat nat)_ _u_(-> nat nat)_ Bool)|) (i |u_(-> _u_(-> nat nat)_ _u_(-> nat nat nat)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> nat nat)_ _u_(-> nat nat nat)_ Bool)_ _u_(-> nat nat nat)_ _u_(-> nat nat)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> nat nat)_ _u_(-> nat nat nat)_ Bool)|)) (= (ho_224 v ii) (ite (= i ii) e (ho_224 u ii)))))))))) (let ((_let_270 (forall ((x |u_(-> _u_(-> _u_(-> nat nat)_ _u_(-> nat nat nat)_ Bool)_ _u_(-> nat nat nat)_ _u_(-> nat nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> nat nat)_ _u_(-> nat nat nat)_ Bool)_ _u_(-> nat nat nat)_ _u_(-> nat nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> nat nat)_ _u_(-> nat nat nat)_ Bool)|)) (= (ho_224 x z) (ho_224 y z)))) (= x y))))) (let ((_let_271 (forall ((u |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (e |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (i |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|)) (= (ho_300 v ii) (ite (= i ii) e (ho_300 u ii)))))))))) (let ((_let_272 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|)) (= (ho_300 x z) (ho_300 y z)))) (= x y))))) (let ((_let_273 (forall ((u |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (e |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (i |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ nat)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ nat)|)) (= (ho_405 v ii) (ite (= i ii) e (ho_405 u ii)))))))))) (let ((_let_274 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ nat)|)) (= (ho_405 x z) (ho_405 y z)))) (= x y))))) (let ((_let_275 (forall ((u |u_(-> set_nat _u_(-> nat nat nat)_ _u_(-> nat nat nat nat)_ Bool)|) (e |u_(-> _u_(-> nat nat nat)_ _u_(-> nat nat nat nat)_ Bool)|) (i set_nat)) (not (forall ((v |u_(-> set_nat _u_(-> nat nat nat)_ _u_(-> nat nat nat nat)_ Bool)|)) (not (forall ((ii set_nat)) (= (ho_245 v ii) (ite (= i ii) e (ho_245 u ii)))))))))) (let ((_let_276 (forall ((x |u_(-> set_nat _u_(-> nat nat nat)_ _u_(-> nat nat nat nat)_ Bool)|) (y |u_(-> set_nat _u_(-> nat nat nat)_ _u_(-> nat nat nat nat)_ Bool)|)) (or (not (forall ((z set_nat)) (= (ho_245 x z) (ho_245 y z)))) (= x y))))) (let ((_let_277 (forall ((u |u_(-> nat nat nat)|) (e |u_(-> nat nat)|) (i nat)) (not (forall ((v |u_(-> nat nat nat)|)) (not (forall ((ii nat)) (= (ho_219 v ii) (ite (= i ii) e (ho_219 u ii)))))))))) (let ((_let_278 (forall ((x |u_(-> nat nat nat)|) (y |u_(-> nat nat nat)|)) (or (not (forall ((z nat)) (= (ho_219 x z) (ho_219 y z)))) (= x y))))) (let ((_let_279 (forall ((u |u_(-> set_nat_nat_nat_nat3 _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (e |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (i set_nat_nat_nat_nat3)) (not (forall ((v |u_(-> set_nat_nat_nat_nat3 _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|)) (not (forall ((ii set_nat_nat_nat_nat3)) (= (ho_351 v ii) (ite (= i ii) e (ho_351 u ii)))))))))) (let ((_let_280 (forall ((x |u_(-> set_nat_nat_nat_nat3 _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (y |u_(-> set_nat_nat_nat_nat3 _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|)) (or (not (forall ((z set_nat_nat_nat_nat3)) (= (ho_351 x z) (ho_351 y z)))) (= x y))))) (let ((_let_281 (forall ((u |u_(-> set_nat_nat Bool)|) (e Bool) (i set_nat_nat)) (not (forall ((v |u_(-> set_nat_nat Bool)|)) (not (forall ((ii set_nat_nat)) (= (ho_199 v ii) (ite (= i ii) e (ho_199 u ii)))))))))) (let ((_let_282 (forall ((x |u_(-> set_nat_nat Bool)|) (y |u_(-> set_nat_nat Bool)|)) (or (not (forall ((z set_nat_nat)) (= (ho_199 x z) (ho_199 y z)))) (= x y))))) (let ((_let_283 (forall ((u |u_(-> set_nat_nat _u_(-> nat nat)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (e |u_(-> _u_(-> nat nat)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (i set_nat_nat)) (not (forall ((v |u_(-> set_nat_nat _u_(-> nat nat)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|)) (not (forall ((ii set_nat_nat)) (= (ho_229 v ii) (ite (= i ii) e (ho_229 u ii)))))))))) (let ((_let_284 (forall ((x |u_(-> set_nat_nat _u_(-> nat nat)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (y |u_(-> set_nat_nat _u_(-> nat nat)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|)) (or (not (forall ((z set_nat_nat)) (= (ho_229 x z) (ho_229 y z)))) (= x y))))) (let ((_let_285 (forall ((u |u_(-> _u_(-> nat _u_(-> nat nat)_ nat)_ Bool)|) (e Bool) (i |u_(-> nat _u_(-> nat nat)_ nat)|)) (not (forall ((v |u_(-> _u_(-> nat _u_(-> nat nat)_ nat)_ Bool)|)) (not (forall ((ii |u_(-> nat _u_(-> nat nat)_ nat)|)) (= (ho_306 v ii) (ite (= i ii) e (ho_306 u ii)))))))))) (let ((_let_286 (forall ((x |u_(-> _u_(-> nat _u_(-> nat nat)_ nat)_ Bool)|) (y |u_(-> _u_(-> nat _u_(-> nat nat)_ nat)_ Bool)|)) (or (not (forall ((z |u_(-> nat _u_(-> nat nat)_ nat)|)) (= (ho_306 x z) (ho_306 y z)))) (= x y))))) (let ((_let_287 (forall ((u |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ nat)_ Bool)|) (e |u_(-> _u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ nat)_ Bool)|) (i |u_(-> _u_(-> nat nat)_ nat)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ nat)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> nat nat)_ nat)|)) (= (ho_439 v ii) (ite (= i ii) e (ho_439 u ii)))))))))) (let ((_let_288 (forall ((x |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> nat nat)_ nat)|)) (= (ho_439 x z) (ho_439 y z)))) (= x y))))) (let ((_let_289 (forall ((u |u_(-> set_nat _u_(-> nat Bool)_ nat Bool)|) (e |u_(-> _u_(-> nat Bool)_ nat Bool)|) (i set_nat)) (not (forall ((v |u_(-> set_nat _u_(-> nat Bool)_ nat Bool)|)) (not (forall ((ii set_nat)) (= (ho_205 v ii) (ite (= i ii) e (ho_205 u ii)))))))))) (let ((_let_290 (forall ((x |u_(-> set_nat _u_(-> nat Bool)_ nat Bool)|) (y |u_(-> set_nat _u_(-> nat Bool)_ nat Bool)|)) (or (not (forall ((z set_nat)) (= (ho_205 x z) (ho_205 y z)))) (= x y))))) (let ((_let_291 (forall ((u |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (e |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (i |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (= (ho_217 v ii) (ite (= i ii) e (ho_217 u ii)))))))))) (let ((_let_292 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (= (ho_217 x z) (ho_217 y z)))) (= x y))))) (let ((_let_293 (forall ((u |u_(-> _u_(-> _u_(-> nat nat)_ Bool)_ set_nat_nat)|) (e set_nat_nat) (i |u_(-> _u_(-> nat nat)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> nat nat)_ Bool)_ set_nat_nat)|)) (not (forall ((ii |u_(-> _u_(-> nat nat)_ Bool)|)) (= (ho_547 v ii) (ite (= i ii) e (ho_547 u ii)))))))))) (let ((_let_294 (forall ((x |u_(-> _u_(-> _u_(-> nat nat)_ Bool)_ set_nat_nat)|) (y |u_(-> _u_(-> _u_(-> nat nat)_ Bool)_ set_nat_nat)|)) (or (not (forall ((z |u_(-> _u_(-> nat nat)_ Bool)|)) (= (ho_547 x z) (ho_547 y z)))) (= x y))))) (let ((_let_295 (forall ((u |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)_ set_nat_nat_nat_nat3 _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (e |u_(-> set_nat_nat_nat_nat3 _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (i |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)_ set_nat_nat_nat_nat3 _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|)) (= (ho_350 v ii) (ite (= i ii) e (ho_350 u ii)))))))))) (let ((_let_296 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)_ set_nat_nat_nat_nat3 _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)_ set_nat_nat_nat_nat3 _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|)) (= (ho_350 x z) (ho_350 y z)))) (= x y))))) (let ((_let_297 (forall ((u |u_(-> set_nat_nat_nat_nat Bool)|) (e Bool) (i set_nat_nat_nat_nat)) (not (forall ((v |u_(-> set_nat_nat_nat_nat Bool)|)) (not (forall ((ii set_nat_nat_nat_nat)) (= (ho_603 v ii) (ite (= i ii) e (ho_603 u ii)))))))))) (let ((_let_298 (forall ((x |u_(-> set_nat_nat_nat_nat Bool)|) (y |u_(-> set_nat_nat_nat_nat Bool)|)) (or (not (forall ((z set_nat_nat_nat_nat)) (= (ho_603 x z) (ho_603 y z)))) (= x y))))) (let ((_let_299 (forall ((u |u_(-> set_nat Bool)|) (e Bool) (i set_nat)) (not (forall ((v |u_(-> set_nat Bool)|)) (not (forall ((ii set_nat)) (= (ho_188 v ii) (ite (= i ii) e (ho_188 u ii)))))))))) (let ((_let_300 (forall ((x |u_(-> set_nat Bool)|) (y |u_(-> set_nat Bool)|)) (or (not (forall ((z set_nat)) (= (ho_188 x z) (ho_188 y z)))) (= x y))))) (let ((_let_301 (forall ((u |u_(-> _u_(-> _u_(-> nat nat nat)_ nat)_ set_nat_nat_nat _u_(-> nat nat nat)_ Bool)|) (e |u_(-> set_nat_nat_nat _u_(-> nat nat nat)_ Bool)|) (i |u_(-> _u_(-> nat nat nat)_ nat)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> nat nat nat)_ nat)_ set_nat_nat_nat _u_(-> nat nat nat)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> nat nat nat)_ nat)|)) (= (ho_377 v ii) (ite (= i ii) e (ho_377 u ii)))))))))) (let ((_let_302 (forall ((x |u_(-> _u_(-> _u_(-> nat nat nat)_ nat)_ set_nat_nat_nat _u_(-> nat nat nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> nat nat nat)_ nat)_ set_nat_nat_nat _u_(-> nat nat nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> nat nat nat)_ nat)|)) (= (ho_377 x z) (ho_377 y z)))) (= x y))))) (let ((_let_303 (forall ((u |u_(-> set_nat_nat set_nat_nat _u_(-> nat nat)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (e |u_(-> set_nat_nat _u_(-> nat nat)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (i set_nat_nat)) (not (forall ((v |u_(-> set_nat_nat set_nat_nat _u_(-> nat nat)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|)) (not (forall ((ii set_nat_nat)) (= (ho_228 v ii) (ite (= i ii) e (ho_228 u ii)))))))))) (let ((_let_304 (forall ((x |u_(-> set_nat_nat set_nat_nat _u_(-> nat nat)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (y |u_(-> set_nat_nat set_nat_nat _u_(-> nat nat)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|)) (or (not (forall ((z set_nat_nat)) (= (ho_228 x z) (ho_228 y z)))) (= x y))))) (let ((_let_305 (forall ((u |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ nat)_ _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ nat)_ set_nat_nat_nat_nat3 _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (e |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ nat)_ set_nat_nat_nat_nat3 _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (i |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ nat)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ nat)_ _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ nat)_ set_nat_nat_nat_nat3 _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ nat)|)) (= (ho_409 v ii) (ite (= i ii) e (ho_409 u ii)))))))))) (let ((_let_306 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ nat)_ _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ nat)_ set_nat_nat_nat_nat3 _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ nat)_ _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ nat)_ set_nat_nat_nat_nat3 _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ nat)|)) (= (ho_409 x z) (ho_409 y z)))) (= x y))))) (let ((_let_307 (forall ((u |u_(-> nat set_nat Bool)|) (e |u_(-> set_nat Bool)|) (i nat)) (not (forall ((v |u_(-> nat set_nat Bool)|)) (not (forall ((ii nat)) (= (ho_187 v ii) (ite (= i ii) e (ho_187 u ii)))))))))) (let ((_let_308 (forall ((x |u_(-> nat set_nat Bool)|) (y |u_(-> nat set_nat Bool)|)) (or (not (forall ((z nat)) (= (ho_187 x z) (ho_187 y z)))) (= x y))))) (let ((_let_309 (forall ((u |u_(-> _u_(-> _u_(-> nat nat)_ nat Bool)_ nat set_nat_nat _u_(-> nat nat)_ Bool)|) (e |u_(-> nat set_nat_nat _u_(-> nat nat)_ Bool)|) (i |u_(-> _u_(-> nat nat)_ nat Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> nat nat)_ nat Bool)_ nat set_nat_nat _u_(-> nat nat)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> nat nat)_ nat Bool)|)) (= (ho_455 v ii) (ite (= i ii) e (ho_455 u ii)))))))))) (let ((_let_310 (forall ((x |u_(-> _u_(-> _u_(-> nat nat)_ nat Bool)_ nat set_nat_nat _u_(-> nat nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> nat nat)_ nat Bool)_ nat set_nat_nat _u_(-> nat nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> nat nat)_ nat Bool)|)) (= (ho_455 x z) (ho_455 y z)))) (= x y))))) (let ((_let_311 (forall ((u |u_(-> set_nat nat Bool)|) (e |u_(-> nat Bool)|) (i set_nat)) (not (forall ((v |u_(-> set_nat nat Bool)|)) (not (forall ((ii set_nat)) (= (ho_190 v ii) (ite (= i ii) e (ho_190 u ii)))))))))) (let ((_let_312 (forall ((x |u_(-> set_nat nat Bool)|) (y |u_(-> set_nat nat Bool)|)) (or (not (forall ((z set_nat)) (= (ho_190 x z) (ho_190 y z)))) (= x y))))) (let ((_let_313 (forall ((u |u_(-> nat Bool)|) (e Bool) (i nat)) (not (forall ((v |u_(-> nat Bool)|)) (not (forall ((ii nat)) (= (ho_191 v ii) (ite (= i ii) e (ho_191 u ii)))))))))) (let ((_let_314 (forall ((x |u_(-> nat Bool)|) (y |u_(-> nat Bool)|)) (or (not (forall ((z nat)) (= (ho_191 x z) (ho_191 y z)))) (= x y))))) (let ((_let_315 (forall ((u |u_(-> _u_(-> nat Bool)_ set_nat nat Bool)|) (e |u_(-> set_nat nat Bool)|) (i |u_(-> nat Bool)|)) (not (forall ((v |u_(-> _u_(-> nat Bool)_ set_nat nat Bool)|)) (not (forall ((ii |u_(-> nat Bool)|)) (= (ho_194 v ii) (ite (= i ii) e (ho_194 u ii)))))))))) (let ((_let_316 (forall ((x |u_(-> _u_(-> nat Bool)_ set_nat nat Bool)|) (y |u_(-> _u_(-> nat Bool)_ set_nat nat Bool)|)) (or (not (forall ((z |u_(-> nat Bool)|)) (= (ho_194 x z) (ho_194 y z)))) (= x y))))) (let ((_let_317 (forall ((u |u_(-> _u_(-> nat nat nat)_ _u_(-> nat nat)_ Bool)|) (e |u_(-> _u_(-> nat nat)_ Bool)|) (i |u_(-> nat nat nat)|)) (not (forall ((v |u_(-> _u_(-> nat nat nat)_ _u_(-> nat nat)_ Bool)|)) (not (forall ((ii |u_(-> nat nat nat)|)) (= (ho_225 v ii) (ite (= i ii) e (ho_225 u ii)))))))))) (let ((_let_318 (forall ((x |u_(-> _u_(-> nat nat nat)_ _u_(-> nat nat)_ Bool)|) (y |u_(-> _u_(-> nat nat nat)_ _u_(-> nat nat)_ Bool)|)) (or (not (forall ((z |u_(-> nat nat nat)|)) (= (ho_225 x z) (ho_225 y z)))) (= x y))))) (let ((_let_319 (forall ((u |u_(-> set_nat_nat_nat Bool)|) (e Bool) (i set_nat_nat_nat)) (not (forall ((v |u_(-> set_nat_nat_nat Bool)|)) (not (forall ((ii set_nat_nat_nat)) (= (ho_238 v ii) (ite (= i ii) e (ho_238 u ii)))))))))) (let ((_let_320 (forall ((x |u_(-> set_nat_nat_nat Bool)|) (y |u_(-> set_nat_nat_nat Bool)|)) (or (not (forall ((z set_nat_nat_nat)) (= (ho_238 x z) (ho_238 y z)))) (= x y))))) (let ((_let_321 (forall ((u |u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ Bool)|) (e |u_(-> _u_(-> nat nat)_ Bool)|) (i |u_(-> nat nat)|)) (not (forall ((v |u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ Bool)|)) (not (forall ((ii |u_(-> nat nat)|)) (= (ho_291 v ii) (ite (= i ii) e (ho_291 u ii)))))))))) (let ((_let_322 (forall ((x |u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ Bool)|) (y |u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ Bool)|)) (or (not (forall ((z |u_(-> nat nat)|)) (= (ho_291 x z) (ho_291 y z)))) (= x y))))) (let ((_let_323 (forall ((u |u_(-> set_nat_nat _u_(-> _u_(-> nat nat)_ Bool)_ _u_(-> nat nat)_ Bool)|) (e |u_(-> _u_(-> _u_(-> nat nat)_ Bool)_ _u_(-> nat nat)_ Bool)|) (i set_nat_nat)) (not (forall ((v |u_(-> set_nat_nat _u_(-> _u_(-> nat nat)_ Bool)_ _u_(-> nat nat)_ Bool)|)) (not (forall ((ii set_nat_nat)) (= (ho_268 v ii) (ite (= i ii) e (ho_268 u ii)))))))))) (let ((_let_324 (forall ((x |u_(-> set_nat_nat _u_(-> _u_(-> nat nat)_ Bool)_ _u_(-> nat nat)_ Bool)|) (y |u_(-> set_nat_nat _u_(-> _u_(-> nat nat)_ Bool)_ _u_(-> nat nat)_ Bool)|)) (or (not (forall ((z set_nat_nat)) (= (ho_268 x z) (ho_268 y z)))) (= x y))))) (let ((_let_325 (forall ((u |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (e |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (i |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (= (ho_218 v ii) (ite (= i ii) e (ho_218 u ii)))))))))) (let ((_let_326 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (= (ho_218 x z) (ho_218 y z)))) (= x y))))) (let ((_let_327 (forall ((u |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ set_nat_nat_nat2)|) (e set_nat_nat_nat2) (i |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ set_nat_nat_nat2)|)) (not (forall ((ii |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (= (ho_537 v ii) (ite (= i ii) e (ho_537 u ii)))))))))) (let ((_let_328 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ set_nat_nat_nat2)|) (y |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)_ set_nat_nat_nat2)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (= (ho_537 x z) (ho_537 y z)))) (= x y))))) (let ((_let_329 (forall ((u |u_(-> nat nat Bool)|) (e |u_(-> nat Bool)|) (i nat)) (not (forall ((v |u_(-> nat nat Bool)|)) (not (forall ((ii nat)) (= (ho_233 v ii) (ite (= i ii) e (ho_233 u ii)))))))))) (let ((_let_330 (forall ((x |u_(-> nat nat Bool)|) (y |u_(-> nat nat Bool)|)) (or (not (forall ((z nat)) (= (ho_233 x z) (ho_233 y z)))) (= x y))))) (let ((_let_331 (forall ((u |u_(-> _u_(-> nat nat)_ _u_(-> nat nat nat)_ Bool)|) (e |u_(-> _u_(-> nat nat nat)_ Bool)|) (i |u_(-> nat nat)|)) (not (forall ((v |u_(-> _u_(-> nat nat)_ _u_(-> nat nat nat)_ Bool)|)) (not (forall ((ii |u_(-> nat nat)|)) (= (ho_220 v ii) (ite (= i ii) e (ho_220 u ii)))))))))) (let ((_let_332 (forall ((x |u_(-> _u_(-> nat nat)_ _u_(-> nat nat nat)_ Bool)|) (y |u_(-> _u_(-> nat nat)_ _u_(-> nat nat nat)_ Bool)|)) (or (not (forall ((z |u_(-> nat nat)|)) (= (ho_220 x z) (ho_220 y z)))) (= x y))))) (let ((_let_333 (forall ((u |u_(-> _u_(-> _u_(-> nat nat nat)_ Bool)_ _u_(-> _u_(-> nat nat nat)_ Bool)_ _u_(-> nat nat nat)_ Bool)|) (e |u_(-> _u_(-> _u_(-> nat nat nat)_ Bool)_ _u_(-> nat nat nat)_ Bool)|) (i |u_(-> _u_(-> nat nat nat)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> nat nat nat)_ Bool)_ _u_(-> _u_(-> nat nat nat)_ Bool)_ _u_(-> nat nat nat)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> nat nat nat)_ Bool)|)) (= (ho_318 v ii) (ite (= i ii) e (ho_318 u ii)))))))))) (let ((_let_334 (forall ((x |u_(-> _u_(-> _u_(-> nat nat nat)_ Bool)_ _u_(-> _u_(-> nat nat nat)_ Bool)_ _u_(-> nat nat nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> nat nat nat)_ Bool)_ _u_(-> _u_(-> nat nat nat)_ Bool)_ _u_(-> nat nat nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> nat nat nat)_ Bool)|)) (= (ho_318 x z) (ho_318 y z)))) (= x y))))) (let ((_let_335 (forall ((u |u_(-> set_nat_nat_nat_nat3 Bool)|) (e Bool) (i set_nat_nat_nat_nat3)) (not (forall ((v |u_(-> set_nat_nat_nat_nat3 Bool)|)) (not (forall ((ii set_nat_nat_nat_nat3)) (= (ho_297 v ii) (ite (= i ii) e (ho_297 u ii)))))))))) (let ((_let_336 (forall ((x |u_(-> set_nat_nat_nat_nat3 Bool)|) (y |u_(-> set_nat_nat_nat_nat3 Bool)|)) (or (not (forall ((z set_nat_nat_nat_nat3)) (= (ho_297 x z) (ho_297 y z)))) (= x y))))) (let ((_let_337 (forall ((u |u_(-> nat _u_(-> nat nat)_ nat)|) (e |u_(-> _u_(-> nat nat)_ nat)|) (i nat)) (not (forall ((v |u_(-> nat _u_(-> nat nat)_ nat)|)) (not (forall ((ii nat)) (= (ho_301 v ii) (ite (= i ii) e (ho_301 u ii)))))))))) (let ((_let_338 (forall ((x |u_(-> nat _u_(-> nat nat)_ nat)|) (y |u_(-> nat _u_(-> nat nat)_ nat)|)) (or (not (forall ((z nat)) (= (ho_301 x z) (ho_301 y z)))) (= x y))))) (let ((_let_339 (forall ((u |u_(-> set_nat_nat _u_(-> nat nat)_ Bool)|) (e |u_(-> _u_(-> nat nat)_ Bool)|) (i set_nat_nat)) (not (forall ((v |u_(-> set_nat_nat _u_(-> nat nat)_ Bool)|)) (not (forall ((ii set_nat_nat)) (= (ho_201 v ii) (ite (= i ii) e (ho_201 u ii)))))))))) (let ((_let_340 (forall ((x |u_(-> set_nat_nat _u_(-> nat nat)_ Bool)|) (y |u_(-> set_nat_nat _u_(-> nat nat)_ Bool)|)) (or (not (forall ((z set_nat_nat)) (= (ho_201 x z) (ho_201 y z)))) (= x y))))) (let ((_let_341 (forall ((u |u_(-> _u_(-> nat nat)_ nat)|) (e nat) (i |u_(-> nat nat)|)) (not (forall ((v |u_(-> _u_(-> nat nat)_ nat)|)) (not (forall ((ii |u_(-> nat nat)|)) (= (ho_214 v ii) (ite (= i ii) e (ho_214 u ii)))))))))) (let ((_let_342 (forall ((x |u_(-> _u_(-> nat nat)_ nat)|) (y |u_(-> _u_(-> nat nat)_ nat)|)) (or (not (forall ((z |u_(-> nat nat)|)) (= (ho_214 x z) (ho_214 y z)))) (= x y))))) (let ((_let_343 (forall ((u |u_(-> _u_(-> nat nat nat)_ set_nat_nat_nat Bool)|) (e |u_(-> set_nat_nat_nat Bool)|) (i |u_(-> nat nat nat)|)) (not (forall ((v |u_(-> _u_(-> nat nat nat)_ set_nat_nat_nat Bool)|)) (not (forall ((ii |u_(-> nat nat nat)|)) (= (ho_237 v ii) (ite (= i ii) e (ho_237 u ii)))))))))) (let ((_let_344 (forall ((x |u_(-> _u_(-> nat nat nat)_ set_nat_nat_nat Bool)|) (y |u_(-> _u_(-> nat nat nat)_ set_nat_nat_nat Bool)|)) (or (not (forall ((z |u_(-> nat nat nat)|)) (= (ho_237 x z) (ho_237 y z)))) (= x y))))) (let ((_let_345 (forall ((u |u_(-> _u_(-> _u_(-> nat nat)_ nat nat nat)_ Bool)|) (e Bool) (i |u_(-> _u_(-> nat nat)_ nat nat nat)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> nat nat)_ nat nat nat)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> nat nat)_ nat nat nat)|)) (= (ho_394 v ii) (ite (= i ii) e (ho_394 u ii)))))))))) (let ((_let_346 (forall ((x |u_(-> _u_(-> _u_(-> nat nat)_ nat nat nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> nat nat)_ nat nat nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> nat nat)_ nat nat nat)|)) (= (ho_394 x z) (ho_394 y z)))) (= x y))))) (let ((_let_347 (forall ((u |u_(-> _u_(-> nat Bool)_ _u_(-> nat Bool)_ nat Bool)|) (e |u_(-> _u_(-> nat Bool)_ nat Bool)|) (i |u_(-> nat Bool)|)) (not (forall ((v |u_(-> _u_(-> nat Bool)_ _u_(-> nat Bool)_ nat Bool)|)) (not (forall ((ii |u_(-> nat Bool)|)) (= (ho_212 v ii) (ite (= i ii) e (ho_212 u ii)))))))))) (let ((_let_348 (forall ((x |u_(-> _u_(-> nat Bool)_ _u_(-> nat Bool)_ nat Bool)|) (y |u_(-> _u_(-> nat Bool)_ _u_(-> nat Bool)_ nat Bool)|)) (or (not (forall ((z |u_(-> nat Bool)|)) (= (ho_212 x z) (ho_212 y z)))) (= x y))))) (let ((_let_349 (forall ((u |u_(-> _u_(-> _u_(-> nat nat nat)_ Bool)_ _u_(-> nat nat nat)_ Bool)|) (e |u_(-> _u_(-> nat nat nat)_ Bool)|) (i |u_(-> _u_(-> nat nat nat)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> nat nat nat)_ Bool)_ _u_(-> nat nat nat)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> nat nat nat)_ Bool)|)) (= (ho_241 v ii) (ite (= i ii) e (ho_241 u ii)))))))))) (let ((_let_350 (forall ((x |u_(-> _u_(-> _u_(-> nat nat nat)_ Bool)_ _u_(-> nat nat nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> nat nat nat)_ Bool)_ _u_(-> nat nat nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> nat nat nat)_ Bool)|)) (= (ho_241 x z) (ho_241 y z)))) (= x y))))) (let ((_let_351 (forall ((u |u_(-> _u_(-> nat nat nat nat)_ Bool)|) (e Bool) (i |u_(-> nat nat nat nat)|)) (not (forall ((v |u_(-> _u_(-> nat nat nat nat)_ Bool)|)) (not (forall ((ii |u_(-> nat nat nat nat)|)) (= (ho_247 v ii) (ite (= i ii) e (ho_247 u ii)))))))))) (let ((_let_352 (forall ((x |u_(-> _u_(-> nat nat nat nat)_ Bool)|) (y |u_(-> _u_(-> nat nat nat nat)_ Bool)|)) (or (not (forall ((z |u_(-> nat nat nat nat)|)) (= (ho_247 x z) (ho_247 y z)))) (= x y))))) (let ((_let_353 (forall ((u |u_(-> set_nat_nat_nat2 set_nat_nat _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ nat)_ Bool)|) (e |u_(-> set_nat_nat _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ nat)_ Bool)|) (i set_nat_nat_nat2)) (not (forall ((v |u_(-> set_nat_nat_nat2 set_nat_nat _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ nat)_ Bool)|)) (not (forall ((ii set_nat_nat_nat2)) (= (ho_437 v ii) (ite (= i ii) e (ho_437 u ii)))))))))) (let ((_let_354 (forall ((x |u_(-> set_nat_nat_nat2 set_nat_nat _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ nat)_ Bool)|) (y |u_(-> set_nat_nat_nat2 set_nat_nat _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ nat)_ Bool)|)) (or (not (forall ((z set_nat_nat_nat2)) (= (ho_437 x z) (ho_437 y z)))) (= x y))))) (let ((_let_355 (forall ((u |u_(-> _u_(-> nat nat nat)_ _u_(-> nat nat nat nat)_ Bool)|) (e |u_(-> _u_(-> nat nat nat nat)_ Bool)|) (i |u_(-> nat nat nat)|)) (not (forall ((v |u_(-> _u_(-> nat nat nat)_ _u_(-> nat nat nat nat)_ Bool)|)) (not (forall ((ii |u_(-> nat nat nat)|)) (= (ho_246 v ii) (ite (= i ii) e (ho_246 u ii)))))))))) (let ((_let_356 (forall ((x |u_(-> _u_(-> nat nat nat)_ _u_(-> nat nat nat nat)_ Bool)|) (y |u_(-> _u_(-> nat nat nat)_ _u_(-> nat nat nat nat)_ Bool)|)) (or (not (forall ((z |u_(-> nat nat nat)|)) (= (ho_246 x z) (ho_246 y z)))) (= x y))))) (let ((_let_357 (forall ((u |u_(-> set_nat_nat set_nat_nat Bool)|) (e |u_(-> set_nat_nat Bool)|) (i set_nat_nat)) (not (forall ((v |u_(-> set_nat_nat set_nat_nat Bool)|)) (not (forall ((ii set_nat_nat)) (= (ho_251 v ii) (ite (= i ii) e (ho_251 u ii)))))))))) (let ((_let_358 (forall ((x |u_(-> set_nat_nat set_nat_nat Bool)|) (y |u_(-> set_nat_nat set_nat_nat Bool)|)) (or (not (forall ((z set_nat_nat)) (= (ho_251 x z) (ho_251 y z)))) (= x y))))) (let ((_let_359 (forall ((u |u_(-> _u_(-> nat nat)_ set_nat nat Bool)|) (e |u_(-> set_nat nat Bool)|) (i |u_(-> nat nat)|)) (not (forall ((v |u_(-> _u_(-> nat nat)_ set_nat nat Bool)|)) (not (forall ((ii |u_(-> nat nat)|)) (= (ho_255 v ii) (ite (= i ii) e (ho_255 u ii)))))))))) (let ((_let_360 (forall ((x |u_(-> _u_(-> nat nat)_ set_nat nat Bool)|) (y |u_(-> _u_(-> nat nat)_ set_nat nat Bool)|)) (or (not (forall ((z |u_(-> nat nat)|)) (= (ho_255 x z) (ho_255 y z)))) (= x y))))) (let ((_let_361 (forall ((u |u_(-> nat set_nat_nat set_nat _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (e |u_(-> set_nat_nat set_nat _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (i nat)) (not (forall ((v |u_(-> nat set_nat_nat set_nat _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (not (forall ((ii nat)) (= (ho_485 v ii) (ite (= i ii) e (ho_485 u ii)))))))))) (let ((_let_362 (forall ((x |u_(-> nat set_nat_nat set_nat _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (y |u_(-> nat set_nat_nat set_nat _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (or (not (forall ((z nat)) (= (ho_485 x z) (ho_485 y z)))) (= x y))))) (let ((_let_363 (forall ((u |u_(-> set_nat_nat set_set_nat_nat Bool)|) (e |u_(-> set_set_nat_nat Bool)|) (i set_nat_nat)) (not (forall ((v |u_(-> set_nat_nat set_set_nat_nat Bool)|)) (not (forall ((ii set_nat_nat)) (= (ho_543 v ii) (ite (= i ii) e (ho_543 u ii)))))))))) (let ((_let_364 (forall ((x |u_(-> set_nat_nat set_set_nat_nat Bool)|) (y |u_(-> set_nat_nat set_set_nat_nat Bool)|)) (or (not (forall ((z set_nat_nat)) (= (ho_543 x z) (ho_543 y z)))) (= x y))))) (let ((_let_365 (forall ((u |u_(-> set_nat_nat _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> nat nat)_ Bool)|) (e |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> nat nat)_ Bool)|) (i set_nat_nat)) (not (forall ((v |u_(-> set_nat_nat _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> nat nat)_ Bool)|)) (not (forall ((ii set_nat_nat)) (= (ho_322 v ii) (ite (= i ii) e (ho_322 u ii)))))))))) (let ((_let_366 (forall ((x |u_(-> set_nat_nat _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> nat nat)_ Bool)|) (y |u_(-> set_nat_nat _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> nat nat)_ Bool)|)) (or (not (forall ((z set_nat_nat)) (= (ho_322 x z) (ho_322 y z)))) (= x y))))) (let ((_let_367 (forall ((u |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ set_nat_nat_nat2 Bool)|) (e |u_(-> set_nat_nat_nat2 Bool)|) (i |u_(-> _u_(-> nat nat)_ nat)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ set_nat_nat_nat2 Bool)|)) (not (forall ((ii |u_(-> _u_(-> nat nat)_ nat)|)) (= (ho_263 v ii) (ite (= i ii) e (ho_263 u ii)))))))))) (let ((_let_368 (forall ((x |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ set_nat_nat_nat2 Bool)|) (y |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ set_nat_nat_nat2 Bool)|)) (or (not (forall ((z |u_(-> _u_(-> nat nat)_ nat)|)) (= (ho_263 x z) (ho_263 y z)))) (= x y))))) (let ((_let_369 (forall ((u |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ nat)|) (e nat) (i |u_(-> _u_(-> nat nat)_ nat nat)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ nat)|)) (not (forall ((ii |u_(-> _u_(-> nat nat)_ nat nat)|)) (= (ho_402 v ii) (ite (= i ii) e (ho_402 u ii)))))))))) (let ((_let_370 (forall ((x |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ nat)|) (y |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ nat)|)) (or (not (forall ((z |u_(-> _u_(-> nat nat)_ nat nat)|)) (= (ho_402 x z) (ho_402 y z)))) (= x y))))) (let ((_let_371 (forall ((u |u_(-> set_nat _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (e |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (i set_nat)) (not (forall ((v |u_(-> set_nat _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (not (forall ((ii set_nat)) (= (ho_487 v ii) (ite (= i ii) e (ho_487 u ii)))))))))) (let ((_let_372 (forall ((x |u_(-> set_nat _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (y |u_(-> set_nat _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (or (not (forall ((z set_nat)) (= (ho_487 x z) (ho_487 y z)))) (= x y))))) (let ((_let_373 (forall ((u |u_(-> _u_(-> nat nat)_ set_nat_nat _u_(-> nat nat)_ Bool)|) (e |u_(-> set_nat_nat _u_(-> nat nat)_ Bool)|) (i |u_(-> nat nat)|)) (not (forall ((v |u_(-> _u_(-> nat nat)_ set_nat_nat _u_(-> nat nat)_ Bool)|)) (not (forall ((ii |u_(-> nat nat)|)) (= (ho_294 v ii) (ite (= i ii) e (ho_294 u ii)))))))))) (let ((_let_374 (forall ((x |u_(-> _u_(-> nat nat)_ set_nat_nat _u_(-> nat nat)_ Bool)|) (y |u_(-> _u_(-> nat nat)_ set_nat_nat _u_(-> nat nat)_ Bool)|)) (or (not (forall ((z |u_(-> nat nat)|)) (= (ho_294 x z) (ho_294 y z)))) (= x y))))) (let ((_let_375 (forall ((u |u_(-> _u_(-> _u_(-> nat nat)_ Bool)_ _u_(-> nat nat)_ Bool)|) (e |u_(-> _u_(-> nat nat)_ Bool)|) (i |u_(-> _u_(-> nat nat)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> nat nat)_ Bool)_ _u_(-> nat nat)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> nat nat)_ Bool)|)) (= (ho_269 v ii) (ite (= i ii) e (ho_269 u ii)))))))))) (let ((_let_376 (forall ((x |u_(-> _u_(-> _u_(-> nat nat)_ Bool)_ _u_(-> nat nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> nat nat)_ Bool)_ _u_(-> nat nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> nat nat)_ Bool)|)) (= (ho_269 x z) (ho_269 y z)))) (= x y))))) (let ((_let_377 (forall ((u |u_(-> _u_(-> nat Bool)_ set_nat)|) (e set_nat) (i |u_(-> nat Bool)|)) (not (forall ((v |u_(-> _u_(-> nat Bool)_ set_nat)|)) (not (forall ((ii |u_(-> nat Bool)|)) (= (ho_271 v ii) (ite (= i ii) e (ho_271 u ii)))))))))) (let ((_let_378 (forall ((x |u_(-> _u_(-> nat Bool)_ set_nat)|) (y |u_(-> _u_(-> nat Bool)_ set_nat)|)) (or (not (forall ((z |u_(-> nat Bool)|)) (= (ho_271 x z) (ho_271 y z)))) (= x y))))) (let ((_let_379 (forall ((u |u_(-> set_nat set_nat Bool)|) (e |u_(-> set_nat Bool)|) (i set_nat)) (not (forall ((v |u_(-> set_nat set_nat Bool)|)) (not (forall ((ii set_nat)) (= (ho_277 v ii) (ite (= i ii) e (ho_277 u ii)))))))))) (let ((_let_380 (forall ((x |u_(-> set_nat set_nat Bool)|) (y |u_(-> set_nat set_nat Bool)|)) (or (not (forall ((z set_nat)) (= (ho_277 x z) (ho_277 y z)))) (= x y))))) (let ((_let_381 (forall ((u |u_(-> set_nat_nat_nat _u_(-> _u_(-> nat nat nat)_ nat)_ _u_(-> nat nat nat)_ Bool)|) (e |u_(-> _u_(-> _u_(-> nat nat nat)_ nat)_ _u_(-> nat nat nat)_ Bool)|) (i set_nat_nat_nat)) (not (forall ((v |u_(-> set_nat_nat_nat _u_(-> _u_(-> nat nat nat)_ nat)_ _u_(-> nat nat nat)_ Bool)|)) (not (forall ((ii set_nat_nat_nat)) (= (ho_379 v ii) (ite (= i ii) e (ho_379 u ii)))))))))) (let ((_let_382 (forall ((x |u_(-> set_nat_nat_nat _u_(-> _u_(-> nat nat nat)_ nat)_ _u_(-> nat nat nat)_ Bool)|) (y |u_(-> set_nat_nat_nat _u_(-> _u_(-> nat nat nat)_ nat)_ _u_(-> nat nat nat)_ Bool)|)) (or (not (forall ((z set_nat_nat_nat)) (= (ho_379 x z) (ho_379 y z)))) (= x y))))) (let ((_let_383 (forall ((u |u_(-> _u_(-> set_nat_nat Bool)_ set_set_nat_nat)|) (e set_set_nat_nat) (i |u_(-> set_nat_nat Bool)|)) (not (forall ((v |u_(-> _u_(-> set_nat_nat Bool)_ set_set_nat_nat)|)) (not (forall ((ii |u_(-> set_nat_nat Bool)|)) (= (ho_599 v ii) (ite (= i ii) e (ho_599 u ii)))))))))) (let ((_let_384 (forall ((x |u_(-> _u_(-> set_nat_nat Bool)_ set_set_nat_nat)|) (y |u_(-> _u_(-> set_nat_nat Bool)_ set_set_nat_nat)|)) (or (not (forall ((z |u_(-> set_nat_nat Bool)|)) (= (ho_599 x z) (ho_599 y z)))) (= x y))))) (let ((_let_385 (forall ((u |u_(-> nat _u_(-> nat nat)_ Bool)|) (e |u_(-> _u_(-> nat nat)_ Bool)|) (i nat)) (not (forall ((v |u_(-> nat _u_(-> nat nat)_ Bool)|)) (not (forall ((ii nat)) (= (ho_283 v ii) (ite (= i ii) e (ho_283 u ii)))))))))) (let ((_let_386 (forall ((x |u_(-> nat _u_(-> nat nat)_ Bool)|) (y |u_(-> nat _u_(-> nat nat)_ Bool)|)) (or (not (forall ((z nat)) (= (ho_283 x z) (ho_283 y z)))) (= x y))))) (let ((_let_387 (forall ((u |u_(-> set_nat_nat_nat_nat3 _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (e |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (i set_nat_nat_nat_nat3)) (not (forall ((v |u_(-> set_nat_nat_nat_nat3 _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|)) (not (forall ((ii set_nat_nat_nat_nat3)) (= (ho_299 v ii) (ite (= i ii) e (ho_299 u ii)))))))))) (let ((_let_388 (forall ((x |u_(-> set_nat_nat_nat_nat3 _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (y |u_(-> set_nat_nat_nat_nat3 _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|)) (or (not (forall ((z set_nat_nat_nat_nat3)) (= (ho_299 x z) (ho_299 y z)))) (= x y))))) (let ((_let_389 (forall ((u |u_(-> nat set_nat_nat _u_(-> nat nat)_ Bool)|) (e |u_(-> set_nat_nat _u_(-> nat nat)_ Bool)|) (i nat)) (not (forall ((v |u_(-> nat set_nat_nat _u_(-> nat nat)_ Bool)|)) (not (forall ((ii nat)) (= (ho_456 v ii) (ite (= i ii) e (ho_456 u ii)))))))))) (let ((_let_390 (forall ((x |u_(-> nat set_nat_nat _u_(-> nat nat)_ Bool)|) (y |u_(-> nat set_nat_nat _u_(-> nat nat)_ Bool)|)) (or (not (forall ((z nat)) (= (ho_456 x z) (ho_456 y z)))) (= x y))))) (let ((_let_391 (forall ((u |u_(-> _u_(-> nat nat)_ nat nat Bool)|) (e |u_(-> nat nat Bool)|) (i |u_(-> nat nat)|)) (not (forall ((v |u_(-> _u_(-> nat nat)_ nat nat Bool)|)) (not (forall ((ii |u_(-> nat nat)|)) (= (ho_514 v ii) (ite (= i ii) e (ho_514 u ii)))))))))) (let ((_let_392 (forall ((x |u_(-> _u_(-> nat nat)_ nat nat Bool)|) (y |u_(-> _u_(-> nat nat)_ nat nat Bool)|)) (or (not (forall ((z |u_(-> nat nat)|)) (= (ho_514 x z) (ho_514 y z)))) (= x y))))) (let ((_let_393 (forall ((u |u_(-> set_nat _u_(-> _u_(-> nat nat nat)_ nat)_ Bool)|) (e |u_(-> _u_(-> _u_(-> nat nat nat)_ nat)_ Bool)|) (i set_nat)) (not (forall ((v |u_(-> set_nat _u_(-> _u_(-> nat nat nat)_ nat)_ Bool)|)) (not (forall ((ii set_nat)) (= (ho_460 v ii) (ite (= i ii) e (ho_460 u ii)))))))))) (let ((_let_394 (forall ((x |u_(-> set_nat _u_(-> _u_(-> nat nat nat)_ nat)_ Bool)|) (y |u_(-> set_nat _u_(-> _u_(-> nat nat nat)_ nat)_ Bool)|)) (or (not (forall ((z set_nat)) (= (ho_460 x z) (ho_460 y z)))) (= x y))))) (let ((_let_395 (forall ((u |u_(-> set_nat_nat_nat set_nat _u_(-> _u_(-> nat nat nat)_ nat)_ Bool)|) (e |u_(-> set_nat _u_(-> _u_(-> nat nat nat)_ nat)_ Bool)|) (i set_nat_nat_nat)) (not (forall ((v |u_(-> set_nat_nat_nat set_nat _u_(-> _u_(-> nat nat nat)_ nat)_ Bool)|)) (not (forall ((ii set_nat_nat_nat)) (= (ho_459 v ii) (ite (= i ii) e (ho_459 u ii)))))))))) (let ((_let_396 (forall ((x |u_(-> set_nat_nat_nat set_nat _u_(-> _u_(-> nat nat nat)_ nat)_ Bool)|) (y |u_(-> set_nat_nat_nat set_nat _u_(-> _u_(-> nat nat nat)_ nat)_ Bool)|)) (or (not (forall ((z set_nat_nat_nat)) (= (ho_459 x z) (ho_459 y z)))) (= x y))))) (let ((_let_397 (forall ((u |u_(-> _u_(-> set_nat_nat_nat2 Bool)_ set_set_nat_nat_nat2)|) (e set_set_nat_nat_nat2) (i |u_(-> set_nat_nat_nat2 Bool)|)) (not (forall ((v |u_(-> _u_(-> set_nat_nat_nat2 Bool)_ set_set_nat_nat_nat2)|)) (not (forall ((ii |u_(-> set_nat_nat_nat2 Bool)|)) (= (ho_591 v ii) (ite (= i ii) e (ho_591 u ii)))))))))) (let ((_let_398 (forall ((x |u_(-> _u_(-> set_nat_nat_nat2 Bool)_ set_set_nat_nat_nat2)|) (y |u_(-> _u_(-> set_nat_nat_nat2 Bool)_ set_set_nat_nat_nat2)|)) (or (not (forall ((z |u_(-> set_nat_nat_nat2 Bool)|)) (= (ho_591 x z) (ho_591 y z)))) (= x y))))) (let ((_let_399 (forall ((u |u_(-> nat set_nat_nat_nat set_nat _u_(-> _u_(-> nat nat nat)_ nat)_ Bool)|) (e |u_(-> set_nat_nat_nat set_nat _u_(-> _u_(-> nat nat nat)_ nat)_ Bool)|) (i nat)) (not (forall ((v |u_(-> nat set_nat_nat_nat set_nat _u_(-> _u_(-> nat nat nat)_ nat)_ Bool)|)) (not (forall ((ii nat)) (= (ho_458 v ii) (ite (= i ii) e (ho_458 u ii)))))))))) (let ((_let_400 (forall ((x |u_(-> nat set_nat_nat_nat set_nat _u_(-> _u_(-> nat nat nat)_ nat)_ Bool)|) (y |u_(-> nat set_nat_nat_nat set_nat _u_(-> _u_(-> nat nat nat)_ nat)_ Bool)|)) (or (not (forall ((z nat)) (= (ho_458 x z) (ho_458 y z)))) (= x y))))) (let ((_let_401 (forall ((u |u_(-> _u_(-> nat _u_(-> nat nat)_ Bool)_ _u_(-> nat nat)_ nat Bool)|) (e |u_(-> _u_(-> nat nat)_ nat Bool)|) (i |u_(-> nat _u_(-> nat nat)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> nat _u_(-> nat nat)_ Bool)_ _u_(-> nat nat)_ nat Bool)|)) (not (forall ((ii |u_(-> nat _u_(-> nat nat)_ Bool)|)) (= (ho_479 v ii) (ite (= i ii) e (ho_479 u ii)))))))))) (let ((_let_402 (forall ((x |u_(-> _u_(-> nat _u_(-> nat nat)_ Bool)_ _u_(-> nat nat)_ nat Bool)|) (y |u_(-> _u_(-> nat _u_(-> nat nat)_ Bool)_ _u_(-> nat nat)_ nat Bool)|)) (or (not (forall ((z |u_(-> nat _u_(-> nat nat)_ Bool)|)) (= (ho_479 x z) (ho_479 y z)))) (= x y))))) (let ((_let_403 (forall ((u |u_(-> set_nat _u_(-> nat _u_(-> nat nat)_ Bool)_ _u_(-> nat nat)_ nat Bool)|) (e |u_(-> _u_(-> nat _u_(-> nat nat)_ Bool)_ _u_(-> nat nat)_ nat Bool)|) (i set_nat)) (not (forall ((v |u_(-> set_nat _u_(-> nat _u_(-> nat nat)_ Bool)_ _u_(-> nat nat)_ nat Bool)|)) (not (forall ((ii set_nat)) (= (ho_478 v ii) (ite (= i ii) e (ho_478 u ii)))))))))) (let ((_let_404 (forall ((x |u_(-> set_nat _u_(-> nat _u_(-> nat nat)_ Bool)_ _u_(-> nat nat)_ nat Bool)|) (y |u_(-> set_nat _u_(-> nat _u_(-> nat nat)_ Bool)_ _u_(-> nat nat)_ nat Bool)|)) (or (not (forall ((z set_nat)) (= (ho_478 x z) (ho_478 y z)))) (= x y))))) (let ((_let_405 (forall ((u |u_(-> set_nat set_nat_nat _u_(-> nat nat nat)_ Bool)|) (e |u_(-> set_nat_nat _u_(-> nat nat nat)_ Bool)|) (i set_nat)) (not (forall ((v |u_(-> set_nat set_nat_nat _u_(-> nat nat nat)_ Bool)|)) (not (forall ((ii set_nat)) (= (ho_482 v ii) (ite (= i ii) e (ho_482 u ii)))))))))) (let ((_let_406 (forall ((x |u_(-> set_nat set_nat_nat _u_(-> nat nat nat)_ Bool)|) (y |u_(-> set_nat set_nat_nat _u_(-> nat nat nat)_ Bool)|)) (or (not (forall ((z set_nat)) (= (ho_482 x z) (ho_482 y z)))) (= x y))))) (let ((_let_407 (forall ((u |u_(-> set_nat_nat set_nat _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (e |u_(-> set_nat _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (i set_nat_nat)) (not (forall ((v |u_(-> set_nat_nat set_nat _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (not (forall ((ii set_nat_nat)) (= (ho_486 v ii) (ite (= i ii) e (ho_486 u ii)))))))))) (let ((_let_408 (forall ((x |u_(-> set_nat_nat set_nat _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (y |u_(-> set_nat_nat set_nat _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (or (not (forall ((z set_nat_nat)) (= (ho_486 x z) (ho_486 y z)))) (= x y))))) (let ((_let_409 (forall ((u |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat Bool)_ nat set_nat_nat_nat2 _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (e |u_(-> nat set_nat_nat_nat2 _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (i |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat Bool)_ nat set_nat_nat_nat2 _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat Bool)|)) (= (ho_517 v ii) (ite (= i ii) e (ho_517 u ii)))))))))) (let ((_let_410 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat Bool)_ nat set_nat_nat_nat2 _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat Bool)_ nat set_nat_nat_nat2 _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat Bool)|)) (= (ho_517 x z) (ho_517 y z)))) (= x y))))) (let ((_let_411 (forall ((u |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (e |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (i |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)|)) (= (ho_526 v ii) (ite (= i ii) e (ho_526 u ii)))))))))) (let ((_let_412 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ _u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)|)) (= (ho_526 x z) (ho_526 y z)))) (= x y))))) (let ((_let_413 (forall ((u |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)_ set_nat_nat_nat_nat3)|) (e set_nat_nat_nat_nat3) (i |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)_ set_nat_nat_nat_nat3)|)) (not (forall ((ii |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|)) (= (ho_540 v ii) (ite (= i ii) e (ho_540 u ii)))))))))) (let ((_let_414 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)_ set_nat_nat_nat_nat3)|) (y |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)_ set_nat_nat_nat_nat3)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|)) (= (ho_540 x z) (ho_540 y z)))) (= x y))))) (let ((_let_415 (forall ((u |u_(-> set_set_nat_nat Bool)|) (e Bool) (i set_set_nat_nat)) (not (forall ((v |u_(-> set_set_nat_nat Bool)|)) (not (forall ((ii set_set_nat_nat)) (= (ho_544 v ii) (ite (= i ii) e (ho_544 u ii)))))))))) (let ((_let_416 (forall ((x |u_(-> set_set_nat_nat Bool)|) (y |u_(-> set_set_nat_nat Bool)|)) (or (not (forall ((z set_set_nat_nat)) (= (ho_544 x z) (ho_544 y z)))) (= x y))))) (let ((_let_417 (forall ((u |u_(-> set_nat_nat set_nat_nat)|) (e set_nat_nat) (i set_nat_nat)) (not (forall ((v |u_(-> set_nat_nat set_nat_nat)|)) (not (forall ((ii set_nat_nat)) (= (ho_552 v ii) (ite (= i ii) e (ho_552 u ii)))))))))) (let ((_let_418 (forall ((x |u_(-> set_nat_nat set_nat_nat)|) (y |u_(-> set_nat_nat set_nat_nat)|)) (or (not (forall ((z set_nat_nat)) (= (ho_552 x z) (ho_552 y z)))) (= x y))))) (let ((_let_419 (forall ((u |u_(-> set_nat_nat nat)|) (e nat) (i set_nat_nat)) (not (forall ((v |u_(-> set_nat_nat nat)|)) (not (forall ((ii set_nat_nat)) (= (ho_553 v ii) (ite (= i ii) e (ho_553 u ii)))))))))) (let ((_let_420 (forall ((x |u_(-> set_nat_nat nat)|) (y |u_(-> set_nat_nat nat)|)) (or (not (forall ((z set_nat_nat)) (= (ho_553 x z) (ho_553 y z)))) (= x y))))) (let ((_let_421 (forall ((u |u_(-> _u_(-> set_nat Bool)_ set_set_nat)|) (e set_set_nat) (i |u_(-> set_nat Bool)|)) (not (forall ((v |u_(-> _u_(-> set_nat Bool)_ set_set_nat)|)) (not (forall ((ii |u_(-> set_nat Bool)|)) (= (ho_574 v ii) (ite (= i ii) e (ho_574 u ii)))))))))) (let ((_let_422 (forall ((x |u_(-> _u_(-> set_nat Bool)_ set_set_nat)|) (y |u_(-> _u_(-> set_nat Bool)_ set_set_nat)|)) (or (not (forall ((z |u_(-> set_nat Bool)|)) (= (ho_574 x z) (ho_574 y z)))) (= x y))))) (let ((_let_423 (forall ((u |u_(-> nat set_nat_nat)|) (e set_nat_nat) (i nat)) (not (forall ((v |u_(-> nat set_nat_nat)|)) (not (forall ((ii nat)) (= (ho_554 v ii) (ite (= i ii) e (ho_554 u ii)))))))))) (let ((_let_424 (forall ((x |u_(-> nat set_nat_nat)|) (y |u_(-> nat set_nat_nat)|)) (or (not (forall ((z nat)) (= (ho_554 x z) (ho_554 y z)))) (= x y))))) (let ((_let_425 (forall ((u |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (e |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (i |u_(-> _u_(-> nat nat)_ nat nat)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> nat nat)_ nat nat)|)) (= (ho_556 v ii) (ite (= i ii) e (ho_556 u ii)))))))))) (let ((_let_426 (forall ((x |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> nat nat)_ nat nat)|)) (= (ho_556 x z) (ho_556 y z)))) (= x y))))) (let ((_let_427 (forall ((u |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (e |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (i |u_(-> _u_(-> nat nat)_ nat)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (not (forall ((ii |u_(-> _u_(-> nat nat)_ nat)|)) (= (ho_558 v ii) (ite (= i ii) e (ho_558 u ii)))))))))) (let ((_let_428 (forall ((x |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (y |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (or (not (forall ((z |u_(-> _u_(-> nat nat)_ nat)|)) (= (ho_558 x z) (ho_558 y z)))) (= x y))))) (let ((_let_429 (forall ((u |u_(-> _u_(-> _u_(-> _u_(-> nat nat nat)_ nat)_ Bool)_ set_nat_nat_nat_nat4)|) (e set_nat_nat_nat_nat4) (i |u_(-> _u_(-> _u_(-> nat nat nat)_ nat)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> _u_(-> nat nat nat)_ nat)_ Bool)_ set_nat_nat_nat_nat4)|)) (not (forall ((ii |u_(-> _u_(-> _u_(-> nat nat nat)_ nat)_ Bool)|)) (= (ho_560 v ii) (ite (= i ii) e (ho_560 u ii)))))))))) (let ((_let_430 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> nat nat nat)_ nat)_ Bool)_ set_nat_nat_nat_nat4)|) (y |u_(-> _u_(-> _u_(-> _u_(-> nat nat nat)_ nat)_ Bool)_ set_nat_nat_nat_nat4)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> nat nat nat)_ nat)_ Bool)|)) (= (ho_560 x z) (ho_560 y z)))) (= x y))))) (let ((_let_431 (forall ((u |u_(-> set_nat_nat_nat_nat4 Bool)|) (e Bool) (i set_nat_nat_nat_nat4)) (not (forall ((v |u_(-> set_nat_nat_nat_nat4 Bool)|)) (not (forall ((ii set_nat_nat_nat_nat4)) (= (ho_562 v ii) (ite (= i ii) e (ho_562 u ii)))))))))) (let ((_let_432 (forall ((x |u_(-> set_nat_nat_nat_nat4 Bool)|) (y |u_(-> set_nat_nat_nat_nat4 Bool)|)) (or (not (forall ((z set_nat_nat_nat_nat4)) (= (ho_562 x z) (ho_562 y z)))) (= x y))))) (let ((_let_433 (forall ((u |u_(-> _u_(-> set_nat_nat_nat Bool)_ set_set_nat_nat_nat)|) (e set_set_nat_nat_nat) (i |u_(-> set_nat_nat_nat Bool)|)) (not (forall ((v |u_(-> _u_(-> set_nat_nat_nat Bool)_ set_set_nat_nat_nat)|)) (not (forall ((ii |u_(-> set_nat_nat_nat Bool)|)) (= (ho_564 v ii) (ite (= i ii) e (ho_564 u ii)))))))))) (let ((_let_434 (forall ((x |u_(-> _u_(-> set_nat_nat_nat Bool)_ set_set_nat_nat_nat)|) (y |u_(-> _u_(-> set_nat_nat_nat Bool)_ set_set_nat_nat_nat)|)) (or (not (forall ((z |u_(-> set_nat_nat_nat Bool)|)) (= (ho_564 x z) (ho_564 y z)))) (= x y))))) (let ((_let_435 (forall ((u |u_(-> set_set_nat_nat_nat Bool)|) (e Bool) (i set_set_nat_nat_nat)) (not (forall ((v |u_(-> set_set_nat_nat_nat Bool)|)) (not (forall ((ii set_set_nat_nat_nat)) (= (ho_566 v ii) (ite (= i ii) e (ho_566 u ii)))))))))) (let ((_let_436 (forall ((x |u_(-> set_set_nat_nat_nat Bool)|) (y |u_(-> set_set_nat_nat_nat Bool)|)) (or (not (forall ((z set_set_nat_nat_nat)) (= (ho_566 x z) (ho_566 y z)))) (= x y))))) (let ((_let_437 (forall ((u |u_(-> _u_(-> nat nat nat)_ _u_(-> nat nat nat)_ Bool)|) (e |u_(-> _u_(-> nat nat nat)_ Bool)|) (i |u_(-> nat nat nat)|)) (not (forall ((v |u_(-> _u_(-> nat nat nat)_ _u_(-> nat nat nat)_ Bool)|)) (not (forall ((ii |u_(-> nat nat nat)|)) (= (ho_568 v ii) (ite (= i ii) e (ho_568 u ii)))))))))) (let ((_let_438 (forall ((x |u_(-> _u_(-> nat nat nat)_ _u_(-> nat nat nat)_ Bool)|) (y |u_(-> _u_(-> nat nat nat)_ _u_(-> nat nat nat)_ Bool)|)) (or (not (forall ((z |u_(-> nat nat nat)|)) (= (ho_568 x z) (ho_568 y z)))) (= x y))))) (let ((_let_439 (forall ((u |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ nat)_ Bool)_ set_na1201295426at_nat)|) (e set_na1201295426at_nat) (i |u_(-> _u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ nat)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ nat)_ Bool)_ set_na1201295426at_nat)|)) (not (forall ((ii |u_(-> _u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ nat)_ Bool)|)) (= (ho_570 v ii) (ite (= i ii) e (ho_570 u ii)))))))))) (let ((_let_440 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ nat)_ Bool)_ set_na1201295426at_nat)|) (y |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ nat)_ Bool)_ set_na1201295426at_nat)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ nat)_ Bool)|)) (= (ho_570 x z) (ho_570 y z)))) (= x y))))) (let ((_let_441 (forall ((u |u_(-> set_na1201295426at_nat Bool)|) (e Bool) (i set_na1201295426at_nat)) (not (forall ((v |u_(-> set_na1201295426at_nat Bool)|)) (not (forall ((ii set_na1201295426at_nat)) (= (ho_572 v ii) (ite (= i ii) e (ho_572 u ii)))))))))) (let ((_let_442 (forall ((x |u_(-> set_na1201295426at_nat Bool)|) (y |u_(-> set_na1201295426at_nat Bool)|)) (or (not (forall ((z set_na1201295426at_nat)) (= (ho_572 x z) (ho_572 y z)))) (= x y))))) (let ((_let_443 (forall ((u |u_(-> set_nat_nat_nat_nat5 Bool)|) (e Bool) (i set_nat_nat_nat_nat5)) (not (forall ((v |u_(-> set_nat_nat_nat_nat5 Bool)|)) (not (forall ((ii set_nat_nat_nat_nat5)) (= (ho_580 v ii) (ite (= i ii) e (ho_580 u ii)))))))))) (let ((_let_444 (forall ((x |u_(-> set_nat_nat_nat_nat5 Bool)|) (y |u_(-> set_nat_nat_nat_nat5 Bool)|)) (or (not (forall ((z set_nat_nat_nat_nat5)) (= (ho_580 x z) (ho_580 y z)))) (= x y))))) (let ((_let_445 (forall ((u |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat nat nat)_ Bool)_ set_na1064332610at_nat)|) (e set_na1064332610at_nat) (i |u_(-> _u_(-> _u_(-> nat nat)_ nat nat nat)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat nat nat)_ Bool)_ set_na1064332610at_nat)|)) (not (forall ((ii |u_(-> _u_(-> _u_(-> nat nat)_ nat nat nat)_ Bool)|)) (= (ho_582 v ii) (ite (= i ii) e (ho_582 u ii)))))))))) (let ((_let_446 (forall ((x |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat nat nat)_ Bool)_ set_na1064332610at_nat)|) (y |u_(-> _u_(-> _u_(-> _u_(-> nat nat)_ nat nat nat)_ Bool)_ set_na1064332610at_nat)|)) (or (not (forall ((z |u_(-> _u_(-> _u_(-> nat nat)_ nat nat nat)_ Bool)|)) (= (ho_582 x z) (ho_582 y z)))) (= x y))))) (let ((_let_447 (forall ((u |u_(-> _u_(-> set_nat_nat_nat_nat3 Bool)_ set_se1657353at_nat)|) (e set_se1657353at_nat) (i |u_(-> set_nat_nat_nat_nat3 Bool)|)) (not (forall ((v |u_(-> _u_(-> set_nat_nat_nat_nat3 Bool)_ set_se1657353at_nat)|)) (not (forall ((ii |u_(-> set_nat_nat_nat_nat3 Bool)|)) (= (ho_586 v ii) (ite (= i ii) e (ho_586 u ii)))))))))) (let ((_let_448 (forall ((x |u_(-> _u_(-> set_nat_nat_nat_nat3 Bool)_ set_se1657353at_nat)|) (y |u_(-> _u_(-> set_nat_nat_nat_nat3 Bool)_ set_se1657353at_nat)|)) (or (not (forall ((z |u_(-> set_nat_nat_nat_nat3 Bool)|)) (= (ho_586 x z) (ho_586 y z)))) (= x y))))) (let ((_let_449 (forall ((u |u_(-> set_se1657353at_nat Bool)|) (e Bool) (i set_se1657353at_nat)) (not (forall ((v |u_(-> set_se1657353at_nat Bool)|)) (not (forall ((ii set_se1657353at_nat)) (= (ho_588 v ii) (ite (= i ii) e (ho_588 u ii)))))))))) (let ((_let_450 (forall ((x |u_(-> set_se1657353at_nat Bool)|) (y |u_(-> set_se1657353at_nat Bool)|)) (or (not (forall ((z set_se1657353at_nat)) (= (ho_588 x z) (ho_588 y z)))) (= x y))))) (let ((_let_451 (forall ((u |u_(-> set_set_nat_nat_nat2 Bool)|) (e Bool) (i set_set_nat_nat_nat2)) (not (forall ((v |u_(-> set_set_nat_nat_nat2 Bool)|)) (not (forall ((ii set_set_nat_nat_nat2)) (= (ho_593 v ii) (ite (= i ii) e (ho_593 u ii)))))))))) (let ((_let_452 (forall ((x |u_(-> set_set_nat_nat_nat2 Bool)|) (y |u_(-> set_set_nat_nat_nat2 Bool)|)) (or (not (forall ((z set_set_nat_nat_nat2)) (= (ho_593 x z) (ho_593 y z)))) (= x y))))) (let ((_let_453 (forall ((u |u_(-> _u_(-> _u_(-> nat _u_(-> nat nat)_ nat)_ Bool)_ set_nat_nat_nat_nat2)|) (e set_nat_nat_nat_nat2) (i |u_(-> _u_(-> nat _u_(-> nat nat)_ nat)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> nat _u_(-> nat nat)_ nat)_ Bool)_ set_nat_nat_nat_nat2)|)) (not (forall ((ii |u_(-> _u_(-> nat _u_(-> nat nat)_ nat)_ Bool)|)) (= (ho_595 v ii) (ite (= i ii) e (ho_595 u ii)))))))))) (let ((_let_454 (forall ((x |u_(-> _u_(-> _u_(-> nat _u_(-> nat nat)_ nat)_ Bool)_ set_nat_nat_nat_nat2)|) (y |u_(-> _u_(-> _u_(-> nat _u_(-> nat nat)_ nat)_ Bool)_ set_nat_nat_nat_nat2)|)) (or (not (forall ((z |u_(-> _u_(-> nat _u_(-> nat nat)_ nat)_ Bool)|)) (= (ho_595 x z) (ho_595 y z)))) (= x y))))) (let ((_let_455 (forall ((u |u_(-> set_nat_nat_nat_nat2 Bool)|) (e Bool) (i set_nat_nat_nat_nat2)) (not (forall ((v |u_(-> set_nat_nat_nat_nat2 Bool)|)) (not (forall ((ii set_nat_nat_nat_nat2)) (= (ho_597 v ii) (ite (= i ii) e (ho_597 u ii)))))))))) (let ((_let_456 (forall ((x |u_(-> set_nat_nat_nat_nat2 Bool)|) (y |u_(-> set_nat_nat_nat_nat2 Bool)|)) (or (not (forall ((z set_nat_nat_nat_nat2)) (= (ho_597 x z) (ho_597 y z)))) (= x y))))) (let ((_let_457 (forall ((u |u_(-> _u_(-> _u_(-> nat nat nat nat)_ Bool)_ set_nat_nat_nat_nat)|) (e set_nat_nat_nat_nat) (i |u_(-> _u_(-> nat nat nat nat)_ Bool)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> nat nat nat nat)_ Bool)_ set_nat_nat_nat_nat)|)) (not (forall ((ii |u_(-> _u_(-> nat nat nat nat)_ Bool)|)) (= (ho_601 v ii) (ite (= i ii) e (ho_601 u ii)))))))))) (let ((_let_458 (forall ((x |u_(-> _u_(-> _u_(-> nat nat nat nat)_ Bool)_ set_nat_nat_nat_nat)|) (y |u_(-> _u_(-> _u_(-> nat nat nat nat)_ Bool)_ set_nat_nat_nat_nat)|)) (or (not (forall ((z |u_(-> _u_(-> nat nat nat nat)_ Bool)|)) (= (ho_601 x z) (ho_601 y z)))) (= x y))))) (let ((_let_459 (forall ((BOUND_VARIABLE_21846 set_nat) (BOUND_VARIABLE_21847 nat)) (= (ho_191 (ho_190 k_189 BOUND_VARIABLE_21846) BOUND_VARIABLE_21847) (ho_188 (ho_187 k_186 BOUND_VARIABLE_21847) BOUND_VARIABLE_21846))))) (let ((_let_460 (forall ((BOUND_VARIABLE_21838 set_nat) (BOUND_VARIABLE_21839 nat)) (= (ho_191 (ho_190 k_192 BOUND_VARIABLE_21838) BOUND_VARIABLE_21839) (ho_188 (ho_187 k_186 BOUND_VARIABLE_21839) BOUND_VARIABLE_21838))))) (let ((_let_461 (forall ((BOUND_VARIABLE_21899 |u_(-> nat Bool)|) (BOUND_VARIABLE_21828 set_nat) (BOUND_VARIABLE_21829 nat)) (= (ho_191 (ho_190 (ho_194 k_193 BOUND_VARIABLE_21899) BOUND_VARIABLE_21828) BOUND_VARIABLE_21829) (and (ho_191 BOUND_VARIABLE_21899 BOUND_VARIABLE_21829) (ho_188 (ho_187 k_186 BOUND_VARIABLE_21829) BOUND_VARIABLE_21828)))))) (let ((_let_462 (forall ((BOUND_VARIABLE_21919 |u_(-> nat Bool)|) (BOUND_VARIABLE_21817 set_nat) (BOUND_VARIABLE_21818 nat)) (= (ho_191 (ho_190 (ho_194 k_195 BOUND_VARIABLE_21919) BOUND_VARIABLE_21817) BOUND_VARIABLE_21818) (and (ho_191 BOUND_VARIABLE_21919 BOUND_VARIABLE_21818) (ho_188 (ho_187 k_186 BOUND_VARIABLE_21818) BOUND_VARIABLE_21817)))))) (let ((_let_463 (forall ((BOUND_VARIABLE_21808 set_nat_nat) (BOUND_VARIABLE_21934 |u_(-> nat nat)|)) (= (ho_202 (ho_201 k_200 BOUND_VARIABLE_21808) BOUND_VARIABLE_21934) (ho_199 (ho_198 k_197 BOUND_VARIABLE_21934) BOUND_VARIABLE_21808))))) (let ((_let_464 (forall ((BOUND_VARIABLE_21800 set_nat_nat) (BOUND_VARIABLE_21967 |u_(-> nat nat)|)) (= (ho_202 (ho_201 k_203 BOUND_VARIABLE_21800) BOUND_VARIABLE_21967) (ho_199 (ho_198 k_197 BOUND_VARIABLE_21967) BOUND_VARIABLE_21800))))) (let ((_let_465 (forall ((BOUND_VARIABLE_21789 set_nat) (BOUND_VARIABLE_21978 |u_(-> nat Bool)|) (BOUND_VARIABLE_21791 nat)) (= (ho_191 (ho_206 (ho_205 k_204 BOUND_VARIABLE_21789) BOUND_VARIABLE_21978) BOUND_VARIABLE_21791) (and (ho_188 (ho_187 k_186 BOUND_VARIABLE_21791) BOUND_VARIABLE_21789) (ho_191 BOUND_VARIABLE_21978 BOUND_VARIABLE_21791)))))) (let ((_let_466 (forall ((BOUND_VARIABLE_21781 set_nat) (BOUND_VARIABLE_21782 nat)) (= (ho_191 (ho_190 k_207 BOUND_VARIABLE_21781) BOUND_VARIABLE_21782) (ho_188 (ho_187 k_186 BOUND_VARIABLE_21782) BOUND_VARIABLE_21781))))) (let ((_let_467 (forall ((BOUND_VARIABLE_21773 set_nat) (BOUND_VARIABLE_21774 nat)) (= (ho_191 (ho_190 k_208 BOUND_VARIABLE_21773) BOUND_VARIABLE_21774) (ho_188 (ho_187 k_186 BOUND_VARIABLE_21774) BOUND_VARIABLE_21773))))) (let ((_let_468 (forall ((BOUND_VARIABLE_22022 |u_(-> nat Bool)|) (BOUND_VARIABLE_21763 set_nat) (BOUND_VARIABLE_21764 nat)) (= (ho_191 (ho_190 (ho_194 k_209 BOUND_VARIABLE_22022) BOUND_VARIABLE_21763) BOUND_VARIABLE_21764) (and (ho_191 BOUND_VARIABLE_22022 BOUND_VARIABLE_21764) (ho_188 (ho_187 k_186 BOUND_VARIABLE_21764) BOUND_VARIABLE_21763)))))) (let ((_let_469 (forall ((BOUND_VARIABLE_21751 set_nat) (BOUND_VARIABLE_22035 |u_(-> nat Bool)|) (BOUND_VARIABLE_21753 nat)) (= (ho_191 (ho_206 (ho_205 k_210 BOUND_VARIABLE_21751) BOUND_VARIABLE_22035) BOUND_VARIABLE_21753) (and (ho_188 (ho_187 k_186 BOUND_VARIABLE_21753) BOUND_VARIABLE_21751) (ho_191 BOUND_VARIABLE_22035 BOUND_VARIABLE_21753)))))) (let ((_let_470 (forall ((BOUND_VARIABLE_22052 |u_(-> nat Bool)|) (BOUND_VARIABLE_22050 |u_(-> nat Bool)|) (BOUND_VARIABLE_21743 nat)) (= (ho_191 (ho_206 (ho_212 k_211 BOUND_VARIABLE_22052) BOUND_VARIABLE_22050) BOUND_VARIABLE_21743) (and (ho_191 BOUND_VARIABLE_22052 BOUND_VARIABLE_21743) (ho_191 BOUND_VARIABLE_22050 BOUND_VARIABLE_21743)))))) (let ((_let_471 (forall ((BOUND_VARIABLE_22072 |u_(-> nat Bool)|) (BOUND_VARIABLE_21731 set_nat) (BOUND_VARIABLE_21732 nat)) (= (ho_191 (ho_190 (ho_194 k_213 BOUND_VARIABLE_22072) BOUND_VARIABLE_21731) BOUND_VARIABLE_21732) (and (ho_191 BOUND_VARIABLE_22072 BOUND_VARIABLE_21732) (ho_188 (ho_187 k_186 BOUND_VARIABLE_21732) BOUND_VARIABLE_21731)))))) (let ((_let_472 (forall ((BOUND_VARIABLE_22098 |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (BOUND_VARIABLE_22094 |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (BOUND_VARIABLE_22088 |u_(-> _u_(-> nat nat)_ nat)|)) (= (ho_215 (ho_218 (ho_217 k_216 BOUND_VARIABLE_22098) BOUND_VARIABLE_22094) BOUND_VARIABLE_22088) (or (ho_215 BOUND_VARIABLE_22098 BOUND_VARIABLE_22088) (ho_215 BOUND_VARIABLE_22094 BOUND_VARIABLE_22088)))))) (let ((_let_473 (forall ((BOUND_VARIABLE_21707 set_nat_nat) (BOUND_VARIABLE_22129 |u_(-> _u_(-> nat nat)_ _u_(-> nat nat nat)_ Bool)|) (BOUND_VARIABLE_22122 |u_(-> nat nat nat)|) (BOUND_VARIABLE_22125 |u_(-> nat nat)|)) (= (ho_202 (ho_225 (ho_224 (ho_223 k_222 BOUND_VARIABLE_21707) BOUND_VARIABLE_22129) BOUND_VARIABLE_22122) BOUND_VARIABLE_22125) (and (ho_199 (ho_198 k_197 BOUND_VARIABLE_22125) BOUND_VARIABLE_21707) (ho_221 (ho_220 BOUND_VARIABLE_22129 BOUND_VARIABLE_22125) BOUND_VARIABLE_22122)))))) (let ((_let_474 (forall ((BOUND_VARIABLE_21686 set_nat_nat) (BOUND_VARIABLE_21687 set_nat_nat) (BOUND_VARIABLE_22176 |u_(-> nat nat)|) (BOUND_VARIABLE_22172 |u_(-> _u_(-> nat nat)_ nat nat)|)) (= (ho_231 (ho_230 (ho_229 (ho_228 k_227 BOUND_VARIABLE_21686) BOUND_VARIABLE_21687) BOUND_VARIABLE_22176) BOUND_VARIABLE_22172) (and (forall ((BOUND_VARIABLE_22183 |u_(-> nat nat)|)) (or (not (ho_199 (ho_198 k_197 BOUND_VARIABLE_22183) BOUND_VARIABLE_21687)) (ho_199 (ho_198 k_197 (ho_226 BOUND_VARIABLE_22172 BOUND_VARIABLE_22183)) BOUND_VARIABLE_21686))) (forall ((BOUND_VARIABLE_22169 |u_(-> nat nat)|)) (or (ho_199 (ho_198 k_197 BOUND_VARIABLE_22169) BOUND_VARIABLE_21687) (= (ho_226 BOUND_VARIABLE_22172 BOUND_VARIABLE_22169) BOUND_VARIABLE_22176)))))))) (let ((_let_475 (forall ((BOUND_VARIABLE_21674 set_nat)) (= (ho_188 k_234 BOUND_VARIABLE_21674) (not (forall ((M2 nat)) (not (forall ((X nat)) (or (not (ho_188 (ho_187 k_186 X) BOUND_VARIABLE_21674)) (ho_191 (ho_233 k_232 X) M2)))))))))) (let ((_let_476 (forall ((BOUND_VARIABLE_21662 set_nat)) (= (ho_188 k_235 BOUND_VARIABLE_21662) (not (forall ((M2 nat)) (not (forall ((X nat)) (or (not (ho_188 (ho_187 k_186 X) BOUND_VARIABLE_21662)) (= M2 X) (ho_191 (ho_233 k_232 X) M2)))))))))) (let ((_let_477 (forall ((BOUND_VARIABLE_21651 set_nat_nat_nat) (BOUND_VARIABLE_22262 |u_(-> _u_(-> nat nat nat)_ Bool)|) (BOUND_VARIABLE_22261 |u_(-> nat nat nat)|)) (= (ho_221 (ho_241 (ho_240 k_239 BOUND_VARIABLE_21651) BOUND_VARIABLE_22262) BOUND_VARIABLE_22261) (and (ho_238 (ho_237 k_236 BOUND_VARIABLE_22261) BOUND_VARIABLE_21651) (ho_221 BOUND_VARIABLE_22262 BOUND_VARIABLE_22261)))))) (let ((_let_478 (forall ((BOUND_VARIABLE_21630 set_nat_nat_nat) (BOUND_VARIABLE_21631 set_nat) (BOUND_VARIABLE_22302 |u_(-> nat nat nat)|) (BOUND_VARIABLE_22298 |u_(-> nat nat nat nat)|)) (= (ho_247 (ho_246 (ho_245 (ho_244 k_243 BOUND_VARIABLE_21630) BOUND_VARIABLE_21631) BOUND_VARIABLE_22302) BOUND_VARIABLE_22298) (and (forall ((BOUND_VARIABLE_8781 nat)) (or (not (ho_188 (ho_187 k_186 BOUND_VARIABLE_8781) BOUND_VARIABLE_21631)) (ho_238 (ho_237 k_236 (ho_242 BOUND_VARIABLE_22298 BOUND_VARIABLE_8781)) BOUND_VARIABLE_21630))) (forall ((BOUND_VARIABLE_8792 nat)) (or (ho_188 (ho_187 k_186 BOUND_VARIABLE_8792) BOUND_VARIABLE_21631) (= (ho_242 BOUND_VARIABLE_22298 BOUND_VARIABLE_8792) BOUND_VARIABLE_22302)))))))) (let ((_let_479 (forall ((BOUND_VARIABLE_21623 nat) (BOUND_VARIABLE_21624 nat)) (= (ho_191 (ho_233 k_248 BOUND_VARIABLE_21623) BOUND_VARIABLE_21624) (= BOUND_VARIABLE_21623 BOUND_VARIABLE_21624))))) (let ((_let_480 (forall ((BOUND_VARIABLE_21609 nat) (BOUND_VARIABLE_21610 nat)) (let ((_let_1 (= BOUND_VARIABLE_21609 BOUND_VARIABLE_21610))) (= (ho_191 (ho_233 k_249 BOUND_VARIABLE_21609) BOUND_VARIABLE_21610) (and (or _let_1 (ho_191 (ho_233 k_232 BOUND_VARIABLE_21610) BOUND_VARIABLE_21609)) (or _let_1 (ho_191 (ho_233 k_232 BOUND_VARIABLE_21609) BOUND_VARIABLE_21610)))))))) (let ((_let_481 (forall ((BOUND_VARIABLE_21602 set_nat_nat) (BOUND_VARIABLE_21603 set_nat_nat)) (= (ho_199 (ho_251 k_250 BOUND_VARIABLE_21602) BOUND_VARIABLE_21603) (= BOUND_VARIABLE_21602 BOUND_VARIABLE_21603))))) (let ((_let_482 (forall ((BOUND_VARIABLE_21588 set_nat_nat) (BOUND_VARIABLE_21589 set_nat_nat)) (let ((_let_1 (= BOUND_VARIABLE_21588 BOUND_VARIABLE_21589))) (= (ho_199 (ho_251 k_253 BOUND_VARIABLE_21588) BOUND_VARIABLE_21589) (and (or _let_1 (ho_199 (ho_251 k_252 BOUND_VARIABLE_21589) BOUND_VARIABLE_21588)) (or _let_1 (ho_199 (ho_251 k_252 BOUND_VARIABLE_21588) BOUND_VARIABLE_21589)))))))) (let ((_let_483 (forall ((BOUND_VARIABLE_22398 |u_(-> nat nat)|) (BOUND_VARIABLE_21576 set_nat) (BOUND_VARIABLE_21577 nat)) (= (ho_191 (ho_190 (ho_255 k_254 BOUND_VARIABLE_22398) BOUND_VARIABLE_21576) BOUND_VARIABLE_21577) (and (not (= zero_zero_nat (ho_196 BOUND_VARIABLE_22398 BOUND_VARIABLE_21577))) (ho_188 (ho_187 k_186 BOUND_VARIABLE_21577) BOUND_VARIABLE_21576)))))) (let ((_let_484 (forall ((BOUND_VARIABLE_22420 |u_(-> nat nat)|) (BOUND_VARIABLE_21563 set_nat) (BOUND_VARIABLE_21564 nat)) (= (ho_191 (ho_190 (ho_255 k_256 BOUND_VARIABLE_22420) BOUND_VARIABLE_21563) BOUND_VARIABLE_21564) (and (not (= zero_zero_nat (ho_196 BOUND_VARIABLE_22420 BOUND_VARIABLE_21564))) (ho_188 (ho_187 k_186 BOUND_VARIABLE_21564) BOUND_VARIABLE_21563)))))) (let ((_let_485 (forall ((BOUND_VARIABLE_22439 |u_(-> nat nat)|) (BOUND_VARIABLE_22437 |u_(-> nat nat)|) (BOUND_VARIABLE_21547 set_nat) (BOUND_VARIABLE_21548 nat)) (= (ho_191 (ho_190 (ho_255 (ho_259 k_258 BOUND_VARIABLE_22439) BOUND_VARIABLE_22437) BOUND_VARIABLE_21547) BOUND_VARIABLE_21548) (and (not (= zero_zero_nat (ho_196 (ho_219 k_257 (ho_196 BOUND_VARIABLE_22439 BOUND_VARIABLE_21548)) (ho_196 BOUND_VARIABLE_22437 BOUND_VARIABLE_21548)))) (ho_188 (ho_187 k_186 BOUND_VARIABLE_21548) BOUND_VARIABLE_21547)))))) (let ((_let_486 (forall ((BOUND_VARIABLE_21537 set_nat) (BOUND_VARIABLE_21538 nat)) (= (ho_191 (ho_190 k_260 BOUND_VARIABLE_21537) BOUND_VARIABLE_21538) (ho_188 (ho_187 k_186 BOUND_VARIABLE_21538) BOUND_VARIABLE_21537))))) (let ((_let_487 (forall ((BOUND_VARIABLE_21529 set_nat) (BOUND_VARIABLE_21530 nat)) (= (ho_191 (ho_190 k_261 BOUND_VARIABLE_21529) BOUND_VARIABLE_21530) (ho_188 (ho_187 k_186 BOUND_VARIABLE_21530) BOUND_VARIABLE_21529))))) (let ((_let_488 (forall ((BOUND_VARIABLE_21518 set_nat_nat_nat2) (BOUND_VARIABLE_22483 |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (BOUND_VARIABLE_22482 |u_(-> _u_(-> nat nat)_ nat)|)) (= (ho_215 (ho_218 (ho_266 k_265 BOUND_VARIABLE_21518) BOUND_VARIABLE_22483) BOUND_VARIABLE_22482) (and (ho_264 (ho_263 k_262 BOUND_VARIABLE_22482) BOUND_VARIABLE_21518) (ho_215 BOUND_VARIABLE_22483 BOUND_VARIABLE_22482)))))) (let ((_let_489 (forall ((BOUND_VARIABLE_21507 set_nat_nat) (BOUND_VARIABLE_22514 |u_(-> _u_(-> nat nat)_ Bool)|) (BOUND_VARIABLE_22513 |u_(-> nat nat)|)) (= (ho_202 (ho_269 (ho_268 k_267 BOUND_VARIABLE_21507) BOUND_VARIABLE_22514) BOUND_VARIABLE_22513) (and (ho_199 (ho_198 k_197 BOUND_VARIABLE_22513) BOUND_VARIABLE_21507) (ho_202 BOUND_VARIABLE_22514 BOUND_VARIABLE_22513)))))) (let ((_let_490 (forall ((BOUND_VARIABLE_22538 |u_(-> nat Bool)|) (BOUND_VARIABLE_21499 nat)) (= (ho_191 (ho_206 k_272 BOUND_VARIABLE_22538) BOUND_VARIABLE_21499) (ho_188 (ho_187 k_186 BOUND_VARIABLE_21499) (ho_271 k_270 BOUND_VARIABLE_22538)))))) (let ((_let_491 (forall ((BOUND_VARIABLE_22556 |u_(-> nat Bool)|) (BOUND_VARIABLE_21490 nat)) (= (ho_191 (ho_206 k_273 BOUND_VARIABLE_22556) BOUND_VARIABLE_21490) (ho_188 (ho_187 k_186 BOUND_VARIABLE_21490) (ho_271 k_270 BOUND_VARIABLE_22556)))))) (let ((_let_492 (forall ((BOUND_VARIABLE_21481 set_nat) (BOUND_VARIABLE_21482 nat)) (= (ho_191 (ho_190 k_274 BOUND_VARIABLE_21481) BOUND_VARIABLE_21482) (ho_188 (ho_187 k_186 BOUND_VARIABLE_21482) BOUND_VARIABLE_21481))))) (let ((_let_493 (forall ((BOUND_VARIABLE_21469 nat) (BOUND_VARIABLE_21470 nat)) (= (ho_191 (ho_233 k_275 BOUND_VARIABLE_21469) BOUND_VARIABLE_21470) (not (forall ((C2 nat)) (not (= BOUND_VARIABLE_21470 (ho_196 (ho_219 k_257 BOUND_VARIABLE_21469) C2))))))))) (let ((_let_494 (forall ((BOUND_VARIABLE_21458 set_nat) (BOUND_VARIABLE_21459 set_nat)) (= (ho_188 (ho_277 k_276 BOUND_VARIABLE_21458) BOUND_VARIABLE_21459) (forall ((T2 nat)) (let ((_let_1 (ho_187 k_186 T2))) (or (not (ho_188 _let_1 BOUND_VARIABLE_21458)) (ho_188 _let_1 BOUND_VARIABLE_21459)))))))) (let ((_let_495 (forall ((BOUND_VARIABLE_21448 nat) (BOUND_VARIABLE_21449 nat)) (= (ho_191 (ho_233 k_278 BOUND_VARIABLE_21448) BOUND_VARIABLE_21449) (or (ho_191 (ho_233 k_232 BOUND_VARIABLE_21448) BOUND_VARIABLE_21449) (= BOUND_VARIABLE_21448 BOUND_VARIABLE_21449)))))) (let ((_let_496 (forall ((BOUND_VARIABLE_21438 set_nat_nat) (BOUND_VARIABLE_21439 set_nat_nat)) (= (ho_199 (ho_251 k_279 BOUND_VARIABLE_21438) BOUND_VARIABLE_21439) (or (= BOUND_VARIABLE_21438 BOUND_VARIABLE_21439) (ho_199 (ho_251 k_252 BOUND_VARIABLE_21439) BOUND_VARIABLE_21438)))))) (let ((_let_497 (forall ((BOUND_VARIABLE_21426 nat) (BOUND_VARIABLE_21427 nat)) (= (ho_191 (ho_233 k_280 BOUND_VARIABLE_21426) BOUND_VARIABLE_21427) (not (forall ((K2 nat)) (not (= BOUND_VARIABLE_21427 (ho_196 (ho_219 k_257 BOUND_VARIABLE_21426) K2))))))))) (let ((_let_498 (forall ((BOUND_VARIABLE_21403 nat) (BOUND_VARIABLE_21404 nat) (BOUND_VARIABLE_22640 |u_(-> nat nat)|)) (= (ho_202 (ho_283 (ho_282 k_281 BOUND_VARIABLE_21403) BOUND_VARIABLE_21404) BOUND_VARIABLE_22640) (and (forall ((I nat)) (let ((_let_1 (ho_196 BOUND_VARIABLE_22640 I))) (or (= BOUND_VARIABLE_21403 _let_1) (ho_191 (ho_233 k_232 _let_1) BOUND_VARIABLE_21403)))) (= zero_zero_nat (ho_196 BOUND_VARIABLE_22640 BOUND_VARIABLE_21404)) (forall ((BOUND_VARIABLE_14242 nat)) (or (not (ho_191 (ho_233 k_232 BOUND_VARIABLE_21404) BOUND_VARIABLE_14242)) (= zero_zero_nat (ho_196 BOUND_VARIABLE_22640 BOUND_VARIABLE_14242))))))))) (let ((_let_499 (forall ((BOUND_VARIABLE_22680 |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (BOUND_VARIABLE_22678 |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (BOUND_VARIABLE_22677 |u_(-> _u_(-> nat nat)_ nat)|)) (= (ho_215 (ho_218 (ho_217 k_284 BOUND_VARIABLE_22680) BOUND_VARIABLE_22678) BOUND_VARIABLE_22677) (and (ho_215 BOUND_VARIABLE_22680 BOUND_VARIABLE_22677) (ho_215 BOUND_VARIABLE_22678 BOUND_VARIABLE_22677)))))) (let ((_let_500 (forall ((BOUND_VARIABLE_21381 nat) (BOUND_VARIABLE_21382 nat)) (let ((_let_1 (= BOUND_VARIABLE_21381 BOUND_VARIABLE_21382))) (= (ho_191 (ho_233 k_285 BOUND_VARIABLE_21381) BOUND_VARIABLE_21382) (and (or _let_1 (ho_191 (ho_233 k_232 BOUND_VARIABLE_21381) BOUND_VARIABLE_21382)) (not _let_1))))))) (let ((_let_501 (forall ((BOUND_VARIABLE_22706 |u_(-> nat Bool)|) (BOUND_VARIABLE_22704 |u_(-> nat Bool)|) (BOUND_VARIABLE_21373 nat)) (= (ho_191 (ho_206 (ho_212 k_286 BOUND_VARIABLE_22706) BOUND_VARIABLE_22704) BOUND_VARIABLE_21373) (or (ho_191 BOUND_VARIABLE_22706 BOUND_VARIABLE_21373) (ho_191 BOUND_VARIABLE_22704 BOUND_VARIABLE_21373)))))) (let ((_let_502 (forall ((BOUND_VARIABLE_21363 set_nat) (BOUND_VARIABLE_21364 nat)) (= (ho_191 (ho_190 k_287 BOUND_VARIABLE_21363) BOUND_VARIABLE_21364) (ho_188 (ho_187 k_186 BOUND_VARIABLE_21364) BOUND_VARIABLE_21363))))) (let ((_let_503 (forall ((BOUND_VARIABLE_21355 set_nat) (BOUND_VARIABLE_21356 nat)) (= (ho_191 (ho_190 k_288 BOUND_VARIABLE_21355) BOUND_VARIABLE_21356) (ho_188 (ho_187 k_186 BOUND_VARIABLE_21356) BOUND_VARIABLE_21355))))) (let ((_let_504 (forall ((BOUND_VARIABLE_21347 set_nat) (BOUND_VARIABLE_21348 nat)) (= (ho_191 (ho_190 k_289 BOUND_VARIABLE_21347) BOUND_VARIABLE_21348) (ho_188 (ho_187 k_186 BOUND_VARIABLE_21348) BOUND_VARIABLE_21347))))) (let ((_let_505 (forall ((BOUND_VARIABLE_21339 set_nat) (BOUND_VARIABLE_21340 nat)) (= (ho_191 (ho_190 k_290 BOUND_VARIABLE_21339) BOUND_VARIABLE_21340) (ho_188 (ho_187 k_186 BOUND_VARIABLE_21340) BOUND_VARIABLE_21339))))) (let ((_let_506 (forall ((BOUND_VARIABLE_22762 |u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ Bool)|) (BOUND_VARIABLE_22758 |u_(-> nat nat)|) (BOUND_VARIABLE_21328 set_nat_nat) (BOUND_VARIABLE_22755 |u_(-> nat nat)|)) (= (ho_202 (ho_201 (ho_294 (ho_293 k_292 BOUND_VARIABLE_22762) BOUND_VARIABLE_22758) BOUND_VARIABLE_21328) BOUND_VARIABLE_22755) (and (ho_202 (ho_291 BOUND_VARIABLE_22762 BOUND_VARIABLE_22755) BOUND_VARIABLE_22758) (ho_199 (ho_198 k_197 BOUND_VARIABLE_22755) BOUND_VARIABLE_21328)))))) (let ((_let_507 (forall ((BOUND_VARIABLE_21315 set_nat_nat_nat_nat3) (BOUND_VARIABLE_22791 |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (BOUND_VARIABLE_22790 |u_(-> _u_(-> nat nat)_ nat nat)|)) (= (ho_231 (ho_300 (ho_299 k_298 BOUND_VARIABLE_21315) BOUND_VARIABLE_22791) BOUND_VARIABLE_22790) (and (ho_297 (ho_296 k_295 BOUND_VARIABLE_22790) BOUND_VARIABLE_21315) (ho_231 BOUND_VARIABLE_22791 BOUND_VARIABLE_22790)))))) (let ((_let_508 (forall ((BOUND_VARIABLE_22840 |u_(-> _u_(-> nat nat)_ nat)|) (BOUND_VARIABLE_21295 set_nat) (BOUND_VARIABLE_21296 set_nat_nat_nat2) (BOUND_VARIABLE_22828 |u_(-> nat _u_(-> nat nat)_ nat)|)) (= (ho_306 (ho_305 (ho_304 (ho_303 k_302 BOUND_VARIABLE_22840) BOUND_VARIABLE_21295) BOUND_VARIABLE_21296) BOUND_VARIABLE_22828) (and (forall ((BOUND_VARIABLE_8260 nat)) (or (ho_188 (ho_187 k_186 BOUND_VARIABLE_8260) BOUND_VARIABLE_21295) (= (ho_301 BOUND_VARIABLE_22828 BOUND_VARIABLE_8260) BOUND_VARIABLE_22840))) (forall ((BOUND_VARIABLE_8269 nat)) (or (not (ho_188 (ho_187 k_186 BOUND_VARIABLE_8269) BOUND_VARIABLE_21295)) (ho_264 (ho_263 k_262 (ho_301 BOUND_VARIABLE_22828 BOUND_VARIABLE_8269)) BOUND_VARIABLE_21296)))))))) (let ((_let_509 (forall ((BOUND_VARIABLE_21259 set_nat) (BOUND_VARIABLE_21260 set_nat)) (= (ho_188 (ho_277 k_313 BOUND_VARIABLE_21259) BOUND_VARIABLE_21260) (ho_312 (ho_311 k_310 (ho_190 k_189 BOUND_VARIABLE_21259)) (ho_190 k_192 BOUND_VARIABLE_21260)))))) (let ((_let_510 (forall ((BOUND_VARIABLE_21248 set_nat) (BOUND_VARIABLE_21249 set_nat)) (= (ho_188 (ho_277 k_314 BOUND_VARIABLE_21248) BOUND_VARIABLE_21249) (forall ((X nat)) (let ((_let_1 (ho_187 k_186 X))) (or (not (ho_188 _let_1 BOUND_VARIABLE_21248)) (ho_188 _let_1 BOUND_VARIABLE_21249)))))))) (let ((_let_511 (forall ((BOUND_VARIABLE_21237 set_nat_nat) (BOUND_VARIABLE_22930 |u_(-> _u_(-> nat nat)_ Bool)|) (BOUND_VARIABLE_22929 |u_(-> nat nat)|)) (= (ho_202 (ho_269 (ho_268 k_315 BOUND_VARIABLE_21237) BOUND_VARIABLE_22930) BOUND_VARIABLE_22929) (and (ho_199 (ho_198 k_197 BOUND_VARIABLE_22929) BOUND_VARIABLE_21237) (ho_202 BOUND_VARIABLE_22930 BOUND_VARIABLE_22929)))))) (let ((_let_512 (forall ((BOUND_VARIABLE_21226 set_nat_nat) (BOUND_VARIABLE_22946 |u_(-> _u_(-> nat nat)_ Bool)|) (BOUND_VARIABLE_22945 |u_(-> nat nat)|)) (= (ho_202 (ho_269 (ho_268 k_316 BOUND_VARIABLE_21226) BOUND_VARIABLE_22946) BOUND_VARIABLE_22945) (and (ho_199 (ho_198 k_197 BOUND_VARIABLE_22945) BOUND_VARIABLE_21226) (ho_202 BOUND_VARIABLE_22946 BOUND_VARIABLE_22945)))))) (let ((_let_513 (forall ((BOUND_VARIABLE_22964 |u_(-> _u_(-> nat nat nat)_ Bool)|) (BOUND_VARIABLE_22962 |u_(-> _u_(-> nat nat nat)_ Bool)|) (BOUND_VARIABLE_22961 |u_(-> nat nat nat)|)) (= (ho_221 (ho_241 (ho_318 k_317 BOUND_VARIABLE_22964) BOUND_VARIABLE_22962) BOUND_VARIABLE_22961) (and (ho_221 BOUND_VARIABLE_22964 BOUND_VARIABLE_22961) (ho_221 BOUND_VARIABLE_22962 BOUND_VARIABLE_22961)))))) (let ((_let_514 (forall ((BOUND_VARIABLE_22982 |u_(-> nat Bool)|) (BOUND_VARIABLE_21208 nat)) (= (ho_191 (ho_206 k_319 BOUND_VARIABLE_22982) BOUND_VARIABLE_21208) (ho_188 (ho_187 k_186 BOUND_VARIABLE_21208) (ho_271 k_270 BOUND_VARIABLE_22982)))))) (let ((_let_515 (forall ((BOUND_VARIABLE_22994 |u_(-> nat Bool)|) (BOUND_VARIABLE_21199 nat)) (= (ho_191 (ho_206 k_320 BOUND_VARIABLE_22994) BOUND_VARIABLE_21199) (ho_188 (ho_187 k_186 BOUND_VARIABLE_21199) (ho_271 k_270 BOUND_VARIABLE_22994)))))) (let ((_let_516 (forall ((BOUND_VARIABLE_21185 set_nat_nat) (BOUND_VARIABLE_23007 |u_(-> _u_(-> nat nat)_ nat)|) (BOUND_VARIABLE_23006 |u_(-> nat nat)|)) (= (ho_202 (ho_323 (ho_322 k_321 BOUND_VARIABLE_21185) BOUND_VARIABLE_23007) BOUND_VARIABLE_23006) (and (ho_199 (ho_198 k_197 BOUND_VARIABLE_23006) BOUND_VARIABLE_21185) (not (= zero_zero_nat (ho_214 BOUND_VARIABLE_23007 BOUND_VARIABLE_23006)))))))) (let ((_let_517 (forall ((BOUND_VARIABLE_21172 set_nat_nat) (BOUND_VARIABLE_23035 |u_(-> _u_(-> nat nat)_ nat)|) (BOUND_VARIABLE_23034 |u_(-> nat nat)|)) (= (ho_202 (ho_323 (ho_322 k_324 BOUND_VARIABLE_21172) BOUND_VARIABLE_23035) BOUND_VARIABLE_23034) (and (ho_199 (ho_198 k_197 BOUND_VARIABLE_23034) BOUND_VARIABLE_21172) (not (= zero_zero_nat (ho_214 BOUND_VARIABLE_23035 BOUND_VARIABLE_23034)))))))) (let ((_let_518 (forall ((BOUND_VARIABLE_21155 set_nat_nat) (BOUND_VARIABLE_23055 |u_(-> _u_(-> nat nat)_ nat)|) (BOUND_VARIABLE_23053 |u_(-> _u_(-> nat nat)_ nat)|) (BOUND_VARIABLE_23052 |u_(-> nat nat)|)) (= (ho_202 (ho_323 (ho_327 (ho_326 k_325 BOUND_VARIABLE_21155) BOUND_VARIABLE_23055) BOUND_VARIABLE_23053) BOUND_VARIABLE_23052) (and (ho_199 (ho_198 k_197 BOUND_VARIABLE_23052) BOUND_VARIABLE_21155) (not (= zero_zero_nat (ho_196 (ho_219 k_257 (ho_214 BOUND_VARIABLE_23055 BOUND_VARIABLE_23052)) (ho_214 BOUND_VARIABLE_23053 BOUND_VARIABLE_23052))))))))) (let ((_let_519 (forall ((BOUND_VARIABLE_21143 set_nat_nat) (BOUND_VARIABLE_21144 set_nat_nat)) (let ((_let_1 (= BOUND_VARIABLE_21143 BOUND_VARIABLE_21144))) (= (ho_199 (ho_251 k_328 BOUND_VARIABLE_21143) BOUND_VARIABLE_21144) (and (or _let_1 (ho_199 (ho_251 k_252 BOUND_VARIABLE_21143) BOUND_VARIABLE_21144)) (not _let_1))))))) (let ((_let_520 (forall ((BOUND_VARIABLE_23100 |u_(-> _u_(-> nat nat nat)_ Bool)|) (BOUND_VARIABLE_21133 set_nat_nat_nat) (BOUND_VARIABLE_23097 |u_(-> nat nat nat)|)) (= (ho_221 (ho_331 (ho_330 k_329 BOUND_VARIABLE_23100) BOUND_VARIABLE_21133) BOUND_VARIABLE_23097) (and (ho_221 BOUND_VARIABLE_23100 BOUND_VARIABLE_23097) (ho_238 (ho_237 k_236 BOUND_VARIABLE_23097) BOUND_VARIABLE_21133)))))) (let ((_let_521 (forall ((BOUND_VARIABLE_21111 set_nat) (BOUND_VARIABLE_21112 set_nat) (BOUND_VARIABLE_21113 nat) (BOUND_VARIABLE_23123 |u_(-> nat nat)|)) (= (ho_202 (ho_283 (ho_334 (ho_333 k_332 BOUND_VARIABLE_21111) BOUND_VARIABLE_21112) BOUND_VARIABLE_21113) BOUND_VARIABLE_23123) (and (forall ((BOUND_VARIABLE_8077 nat)) (or (not (ho_188 (ho_187 k_186 BOUND_VARIABLE_8077) BOUND_VARIABLE_21112)) (ho_188 (ho_187 k_186 (ho_196 BOUND_VARIABLE_23123 BOUND_VARIABLE_8077)) BOUND_VARIABLE_21111))) (forall ((BOUND_VARIABLE_8088 nat)) (or (ho_188 (ho_187 k_186 BOUND_VARIABLE_8088) BOUND_VARIABLE_21112) (= BOUND_VARIABLE_21113 (ho_196 BOUND_VARIABLE_23123 BOUND_VARIABLE_8088))))))))) (let ((_let_522 (forall ((BOUND_VARIABLE_23167 |u_(-> nat _u_(-> nat nat nat)_ Bool)|) (BOUND_VARIABLE_23163 |u_(-> nat nat nat)|) (BOUND_VARIABLE_21100 set_nat) (BOUND_VARIABLE_21101 nat)) (= (ho_191 (ho_190 (ho_338 (ho_337 k_336 BOUND_VARIABLE_23167) BOUND_VARIABLE_23163) BOUND_VARIABLE_21100) BOUND_VARIABLE_21101) (and (ho_221 (ho_335 BOUND_VARIABLE_23167 BOUND_VARIABLE_21101) BOUND_VARIABLE_23163) (ho_188 (ho_187 k_186 BOUND_VARIABLE_21101) BOUND_VARIABLE_21100)))))) (let ((_let_523 (forall ((BOUND_VARIABLE_21090 set_nat) (BOUND_VARIABLE_21091 nat)) (= (ho_191 (ho_190 k_339 BOUND_VARIABLE_21090) BOUND_VARIABLE_21091) (ho_188 (ho_187 k_186 BOUND_VARIABLE_21091) BOUND_VARIABLE_21090))))) (let ((_let_524 (forall ((BOUND_VARIABLE_21082 set_nat) (BOUND_VARIABLE_21083 nat)) (= (ho_191 (ho_190 k_340 BOUND_VARIABLE_21082) BOUND_VARIABLE_21083) (ho_188 (ho_187 k_186 BOUND_VARIABLE_21083) BOUND_VARIABLE_21082))))) (let ((_let_525 (forall ((BOUND_VARIABLE_23215 |u_(-> nat Bool)|) (BOUND_VARIABLE_23213 |u_(-> nat Bool)|) (BOUND_VARIABLE_21074 nat)) (= (ho_191 (ho_206 (ho_212 k_341 BOUND_VARIABLE_23215) BOUND_VARIABLE_23213) BOUND_VARIABLE_21074) (and (ho_191 BOUND_VARIABLE_23215 BOUND_VARIABLE_21074) (ho_191 BOUND_VARIABLE_23213 BOUND_VARIABLE_21074)))))) (let ((_let_526 (forall ((BOUND_VARIABLE_21064 set_nat_nat) (BOUND_VARIABLE_23228 |u_(-> nat nat)|)) (= (ho_202 (ho_201 k_342 BOUND_VARIABLE_21064) BOUND_VARIABLE_23228) (ho_199 (ho_198 k_197 BOUND_VARIABLE_23228) BOUND_VARIABLE_21064))))) (let ((_let_527 (forall ((BOUND_VARIABLE_21056 set_nat_nat) (BOUND_VARIABLE_23239 |u_(-> nat nat)|)) (= (ho_202 (ho_201 k_343 BOUND_VARIABLE_21056) BOUND_VARIABLE_23239) (ho_199 (ho_198 k_197 BOUND_VARIABLE_23239) BOUND_VARIABLE_21056))))) (let ((_let_528 (forall ((BOUND_VARIABLE_21046 nat) (BOUND_VARIABLE_21047 nat)) (= (ho_191 (ho_233 k_344 BOUND_VARIABLE_21046) BOUND_VARIABLE_21047) (or (ho_191 (ho_233 k_232 BOUND_VARIABLE_21046) BOUND_VARIABLE_21047) (= BOUND_VARIABLE_21046 BOUND_VARIABLE_21047)))))) (let ((_let_529 (forall ((BOUND_VARIABLE_21036 nat) (BOUND_VARIABLE_21037 nat)) (= (ho_191 (ho_233 k_345 BOUND_VARIABLE_21036) BOUND_VARIABLE_21037) (or (= BOUND_VARIABLE_21036 BOUND_VARIABLE_21037) (ho_191 (ho_233 k_232 BOUND_VARIABLE_21036) BOUND_VARIABLE_21037)))))) (let ((_let_530 (forall ((BOUND_VARIABLE_21023 set_nat) (BOUND_VARIABLE_23270 |u_(-> nat nat Bool)|) (BOUND_VARIABLE_21025 nat) (BOUND_VARIABLE_21026 nat)) (= (ho_191 (ho_233 (ho_348 (ho_347 k_346 BOUND_VARIABLE_21023) BOUND_VARIABLE_23270) BOUND_VARIABLE_21025) BOUND_VARIABLE_21026) (and (ho_188 (ho_187 k_186 BOUND_VARIABLE_21026) BOUND_VARIABLE_21023) (ho_191 (ho_233 BOUND_VARIABLE_23270 BOUND_VARIABLE_21026) BOUND_VARIABLE_21025)))))) (let ((_let_531 (forall ((BOUND_VARIABLE_23301 |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (BOUND_VARIABLE_21013 set_nat_nat_nat_nat3) (BOUND_VARIABLE_23298 |u_(-> _u_(-> nat nat)_ nat nat)|)) (= (ho_231 (ho_351 (ho_350 k_349 BOUND_VARIABLE_23301) BOUND_VARIABLE_21013) BOUND_VARIABLE_23298) (and (ho_231 BOUND_VARIABLE_23301 BOUND_VARIABLE_23298) (ho_297 (ho_296 k_295 BOUND_VARIABLE_23298) BOUND_VARIABLE_21013)))))) (let ((_let_532 (forall ((BOUND_VARIABLE_21002 nat) (BOUND_VARIABLE_21003 nat)) (= (ho_191 (ho_233 k_352 BOUND_VARIABLE_21002) BOUND_VARIABLE_21003) (or (= BOUND_VARIABLE_21002 BOUND_VARIABLE_21003) (ho_191 (ho_233 k_232 BOUND_VARIABLE_21003) BOUND_VARIABLE_21002)))))) (let ((_let_533 (forall ((BOUND_VARIABLE_20994 set_nat) (BOUND_VARIABLE_20995 nat)) (= (ho_191 (ho_190 k_353 BOUND_VARIABLE_20994) BOUND_VARIABLE_20995) (ho_188 (ho_187 k_186 BOUND_VARIABLE_20995) BOUND_VARIABLE_20994))))) (let ((_let_534 (forall ((BOUND_VARIABLE_20986 set_nat) (BOUND_VARIABLE_20987 nat)) (= (ho_191 (ho_190 k_354 BOUND_VARIABLE_20986) BOUND_VARIABLE_20987) (ho_188 (ho_187 k_186 BOUND_VARIABLE_20987) BOUND_VARIABLE_20986))))) (let ((_let_535 (forall ((BOUND_VARIABLE_23352 |u_(-> nat Bool)|) (BOUND_VARIABLE_20959 set_nat) (BOUND_VARIABLE_20960 nat)) (= (ho_191 (ho_190 (ho_194 k_355 BOUND_VARIABLE_23352) BOUND_VARIABLE_20959) BOUND_VARIABLE_20960) (ho_188 (ho_187 k_186 BOUND_VARIABLE_20960) (ho_271 k_270 (ho_190 (ho_194 k_193 BOUND_VARIABLE_23352) BOUND_VARIABLE_20959))))))) (let ((_let_536 (forall ((BOUND_VARIABLE_23368 |u_(-> nat Bool)|) (BOUND_VARIABLE_20931 set_nat) (BOUND_VARIABLE_20932 nat)) (= (ho_191 (ho_190 (ho_194 k_356 BOUND_VARIABLE_23368) BOUND_VARIABLE_20931) BOUND_VARIABLE_20932) (ho_188 (ho_187 k_186 BOUND_VARIABLE_20932) (ho_271 k_270 (ho_190 (ho_194 k_195 BOUND_VARIABLE_23368) BOUND_VARIABLE_20931))))))) (let ((_let_537 (forall ((BOUND_VARIABLE_20922 set_nat_nat_nat2) (BOUND_VARIABLE_20923 set_nat_nat_nat2)) (= (ho_264 (ho_358 k_359 BOUND_VARIABLE_20922) BOUND_VARIABLE_20923) (ho_264 (ho_358 k_357 BOUND_VARIABLE_20923) BOUND_VARIABLE_20922))))) (let ((_let_538 (forall ((BOUND_VARIABLE_20914 set_nat_nat) (BOUND_VARIABLE_23398 |u_(-> nat nat)|)) (= (ho_202 (ho_201 k_360 BOUND_VARIABLE_20914) BOUND_VARIABLE_23398) (ho_199 (ho_198 k_197 BOUND_VARIABLE_23398) BOUND_VARIABLE_20914))))) (let ((_let_539 (forall ((BOUND_VARIABLE_20906 set_nat_nat_nat) (BOUND_VARIABLE_23409 |u_(-> nat nat nat)|)) (= (ho_221 (ho_331 k_361 BOUND_VARIABLE_20906) BOUND_VARIABLE_23409) (ho_238 (ho_237 k_236 BOUND_VARIABLE_23409) BOUND_VARIABLE_20906))))) (let ((_let_540 (forall ((BOUND_VARIABLE_20878 set_nat_nat) (BOUND_VARIABLE_20879 set_nat_nat)) (= (ho_199 (ho_251 k_365 BOUND_VARIABLE_20878) BOUND_VARIABLE_20879) (ho_364 (ho_363 k_362 (ho_201 k_200 BOUND_VARIABLE_20878)) (ho_201 k_203 BOUND_VARIABLE_20879)))))) (let ((_let_541 (forall ((BOUND_VARIABLE_20867 set_nat_nat) (BOUND_VARIABLE_20868 set_nat_nat)) (= (ho_199 (ho_251 k_366 BOUND_VARIABLE_20867) BOUND_VARIABLE_20868) (forall ((BOUND_VARIABLE_23442 |u_(-> nat nat)|)) (let ((_let_1 (ho_198 k_197 BOUND_VARIABLE_23442))) (or (not (ho_199 _let_1 BOUND_VARIABLE_20867)) (ho_199 _let_1 BOUND_VARIABLE_20868)))))))) (let ((_let_542 (forall ((BOUND_VARIABLE_20859 set_nat) (BOUND_VARIABLE_20860 nat)) (= (ho_191 (ho_190 k_367 BOUND_VARIABLE_20859) BOUND_VARIABLE_20860) (ho_188 (ho_187 k_186 BOUND_VARIABLE_20860) BOUND_VARIABLE_20859))))) (let ((_let_543 (forall ((BOUND_VARIABLE_20831 set_nat) (BOUND_VARIABLE_23466 |u_(-> nat Bool)|) (BOUND_VARIABLE_20833 nat)) (= (ho_191 (ho_206 (ho_205 k_368 BOUND_VARIABLE_20831) BOUND_VARIABLE_23466) BOUND_VARIABLE_20833) (ho_188 (ho_187 k_186 BOUND_VARIABLE_20833) (ho_271 k_270 (ho_206 (ho_205 k_204 BOUND_VARIABLE_20831) BOUND_VARIABLE_23466))))))) (let ((_let_544 (forall ((BOUND_VARIABLE_23485 |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (BOUND_VARIABLE_20821 set_nat_nat_nat2) (BOUND_VARIABLE_23482 |u_(-> _u_(-> nat nat)_ nat)|)) (= (ho_215 (ho_371 (ho_370 k_369 BOUND_VARIABLE_23485) BOUND_VARIABLE_20821) BOUND_VARIABLE_23482) (and (ho_215 BOUND_VARIABLE_23485 BOUND_VARIABLE_23482) (ho_264 (ho_263 k_262 BOUND_VARIABLE_23482) BOUND_VARIABLE_20821)))))) (let ((_let_545 (forall ((BOUND_VARIABLE_20809 set_nat_nat_nat2) (BOUND_VARIABLE_23509 |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (BOUND_VARIABLE_23508 |u_(-> _u_(-> nat nat)_ nat)|)) (= (ho_215 (ho_218 (ho_266 k_372 BOUND_VARIABLE_20809) BOUND_VARIABLE_23509) BOUND_VARIABLE_23508) (and (ho_264 (ho_263 k_262 BOUND_VARIABLE_23508) BOUND_VARIABLE_20809) (ho_215 BOUND_VARIABLE_23509 BOUND_VARIABLE_23508)))))) (let ((_let_546 (forall ((BOUND_VARIABLE_23524 |u_(-> nat nat)|)) (= (ho_202 k_373 BOUND_VARIABLE_23524) (ho_191 (ho_308 k_307 BOUND_VARIABLE_23524) n))))) (let ((_let_547 (forall ((BOUND_VARIABLE_23533 |u_(-> nat nat)|)) (= (ho_202 k_374 BOUND_VARIABLE_23533) (and (forall ((I nat)) (let ((_let_1 (ho_196 BOUND_VARIABLE_23533 I))) (or (= n _let_1) (ho_191 (ho_233 k_232 _let_1) n)))) (= zero_zero_nat (ho_196 BOUND_VARIABLE_23533 (ho_196 (ho_219 k_257 n) one_one_nat))) (forall ((BOUND_VARIABLE_12178 nat)) (or (not (ho_191 (ho_233 k_232 (ho_196 (ho_219 k_257 n) one_one_nat)) BOUND_VARIABLE_12178)) (= zero_zero_nat (ho_196 BOUND_VARIABLE_23533 BOUND_VARIABLE_12178))))))))) (let ((_let_548 (forall ((BOUND_VARIABLE_23564 |u_(-> _u_(-> nat nat nat)_ nat)|) (BOUND_VARIABLE_20772 set_nat_nat_nat) (BOUND_VARIABLE_23558 |u_(-> nat nat nat)|)) (= (ho_221 (ho_331 (ho_377 k_376 BOUND_VARIABLE_23564) BOUND_VARIABLE_20772) BOUND_VARIABLE_23558) (and (not (= zero_zero_nat (ho_375 BOUND_VARIABLE_23564 BOUND_VARIABLE_23558))) (ho_238 (ho_237 k_236 BOUND_VARIABLE_23558) BOUND_VARIABLE_20772)))))) (let ((_let_549 (forall ((BOUND_VARIABLE_20758 set_nat_nat_nat) (BOUND_VARIABLE_23587 |u_(-> _u_(-> nat nat nat)_ nat)|) (BOUND_VARIABLE_23586 |u_(-> nat nat nat)|)) (= (ho_221 (ho_380 (ho_379 k_378 BOUND_VARIABLE_20758) BOUND_VARIABLE_23587) BOUND_VARIABLE_23586) (and (ho_238 (ho_237 k_236 BOUND_VARIABLE_23586) BOUND_VARIABLE_20758) (not (= zero_zero_nat (ho_375 BOUND_VARIABLE_23587 BOUND_VARIABLE_23586)))))))) (let ((_let_550 (forall ((BOUND_VARIABLE_20741 set_nat_nat_nat) (BOUND_VARIABLE_23617 |u_(-> _u_(-> nat nat nat)_ nat)|) (BOUND_VARIABLE_23615 |u_(-> _u_(-> nat nat nat)_ nat)|) (BOUND_VARIABLE_23614 |u_(-> nat nat nat)|)) (= (ho_221 (ho_380 (ho_383 (ho_382 k_381 BOUND_VARIABLE_20741) BOUND_VARIABLE_23617) BOUND_VARIABLE_23615) BOUND_VARIABLE_23614) (and (ho_238 (ho_237 k_236 BOUND_VARIABLE_23614) BOUND_VARIABLE_20741) (not (= zero_zero_nat (ho_196 (ho_219 k_257 (ho_375 BOUND_VARIABLE_23617 BOUND_VARIABLE_23614)) (ho_375 BOUND_VARIABLE_23615 BOUND_VARIABLE_23614))))))))) (let ((_let_551 (forall ((BOUND_VARIABLE_20733 set_nat) (BOUND_VARIABLE_20734 nat)) (= (ho_191 (ho_190 k_384 BOUND_VARIABLE_20733) BOUND_VARIABLE_20734) (ho_188 (ho_187 k_186 BOUND_VARIABLE_20734) BOUND_VARIABLE_20733))))) (let ((_let_552 (forall ((BOUND_VARIABLE_20725 set_nat) (BOUND_VARIABLE_20726 nat)) (= (ho_191 (ho_190 k_385 BOUND_VARIABLE_20725) BOUND_VARIABLE_20726) (ho_188 (ho_187 k_186 BOUND_VARIABLE_20726) BOUND_VARIABLE_20725))))) (let ((_let_553 (forall ((BOUND_VARIABLE_20717 set_nat_nat_nat_nat3) (BOUND_VARIABLE_20718 set_nat_nat_nat_nat3)) (= (ho_297 (ho_387 k_388 BOUND_VARIABLE_20717) BOUND_VARIABLE_20718) (ho_297 (ho_387 k_386 BOUND_VARIABLE_20718) BOUND_VARIABLE_20717))))) (let ((_let_554 (forall ((BOUND_VARIABLE_23698 |u_(-> nat nat nat)|) (BOUND_VARIABLE_20697 set_nat_nat) (BOUND_VARIABLE_20698 set_nat_nat_nat) (BOUND_VARIABLE_23684 |u_(-> _u_(-> nat nat)_ nat nat nat)|)) (= (ho_394 (ho_393 (ho_392 (ho_391 k_390 BOUND_VARIABLE_23698) BOUND_VARIABLE_20697) BOUND_VARIABLE_20698) BOUND_VARIABLE_23684) (and (forall ((BOUND_VARIABLE_23696 |u_(-> nat nat)|)) (or (ho_199 (ho_198 k_197 BOUND_VARIABLE_23696) BOUND_VARIABLE_20697) (= (ho_389 BOUND_VARIABLE_23684 BOUND_VARIABLE_23696) BOUND_VARIABLE_23698))) (forall ((BOUND_VARIABLE_23680 |u_(-> nat nat)|)) (or (not (ho_199 (ho_198 k_197 BOUND_VARIABLE_23680) BOUND_VARIABLE_20697)) (ho_238 (ho_237 k_236 (ho_389 BOUND_VARIABLE_23684 BOUND_VARIABLE_23680)) BOUND_VARIABLE_20698)))))))) (let ((_let_555 (forall ((BOUND_VARIABLE_20686 set_nat_nat) (BOUND_VARIABLE_20687 set_nat_nat)) (= (ho_199 (ho_251 k_395 BOUND_VARIABLE_20686) BOUND_VARIABLE_20687) (or (ho_199 (ho_251 k_252 BOUND_VARIABLE_20686) BOUND_VARIABLE_20687) (= BOUND_VARIABLE_20686 BOUND_VARIABLE_20687)))))) (let ((_let_556 (forall ((BOUND_VARIABLE_23751 |u_(-> _u_(-> nat nat)_ Bool)|) (BOUND_VARIABLE_23749 |u_(-> _u_(-> nat nat)_ Bool)|) (BOUND_VARIABLE_23748 |u_(-> nat nat)|)) (= (ho_202 (ho_269 (ho_397 k_396 BOUND_VARIABLE_23751) BOUND_VARIABLE_23749) BOUND_VARIABLE_23748) (and (ho_202 BOUND_VARIABLE_23751 BOUND_VARIABLE_23748) (ho_202 BOUND_VARIABLE_23749 BOUND_VARIABLE_23748)))))) (let ((_let_557 (forall ((BOUND_VARIABLE_20668 set_nat) (BOUND_VARIABLE_20669 nat)) (= (ho_191 (ho_190 k_398 BOUND_VARIABLE_20668) BOUND_VARIABLE_20669) (ho_188 (ho_187 k_186 BOUND_VARIABLE_20669) BOUND_VARIABLE_20668))))) (let ((_let_558 (forall ((BOUND_VARIABLE_20660 set_nat) (BOUND_VARIABLE_20661 nat)) (= (ho_191 (ho_190 k_399 BOUND_VARIABLE_20660) BOUND_VARIABLE_20661) (ho_188 (ho_187 k_186 BOUND_VARIABLE_20661) BOUND_VARIABLE_20660))))) (let ((_let_559 (forall ((BOUND_VARIABLE_23790 |u_(-> _u_(-> nat nat nat)_ Bool)|) (BOUND_VARIABLE_23788 |u_(-> _u_(-> nat nat nat)_ Bool)|) (BOUND_VARIABLE_23787 |u_(-> nat nat nat)|)) (= (ho_221 (ho_241 (ho_318 k_400 BOUND_VARIABLE_23790) BOUND_VARIABLE_23788) BOUND_VARIABLE_23787) (or (ho_221 BOUND_VARIABLE_23790 BOUND_VARIABLE_23787) (ho_221 BOUND_VARIABLE_23788 BOUND_VARIABLE_23787)))))) (let ((_let_560 (forall ((BOUND_VARIABLE_23803 |u_(-> nat nat)|) (BOUND_VARIABLE_20643 nat)) (= (ho_191 (ho_308 k_401 BOUND_VARIABLE_23803) BOUND_VARIABLE_20643) (ho_191 (ho_233 k_232 zero_zero_nat) (ho_196 BOUND_VARIABLE_23803 BOUND_VARIABLE_20643)))))) (let ((_let_561 (forall ((BOUND_VARIABLE_20629 set_nat_nat_nat_nat3) (BOUND_VARIABLE_23819 |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ nat)|) (BOUND_VARIABLE_23815 |u_(-> _u_(-> nat nat)_ nat nat)|)) (= (ho_231 (ho_405 (ho_404 k_403 BOUND_VARIABLE_20629) BOUND_VARIABLE_23819) BOUND_VARIABLE_23815) (and (ho_297 (ho_296 k_295 BOUND_VARIABLE_23815) BOUND_VARIABLE_20629) (not (= zero_zero_nat (ho_402 BOUND_VARIABLE_23819 BOUND_VARIABLE_23815)))))))) (let ((_let_562 (forall ((BOUND_VARIABLE_23851 |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ nat)|) (BOUND_VARIABLE_20617 set_nat_nat_nat_nat3) (BOUND_VARIABLE_23848 |u_(-> _u_(-> nat nat)_ nat nat)|)) (= (ho_231 (ho_351 (ho_407 k_406 BOUND_VARIABLE_23851) BOUND_VARIABLE_20617) BOUND_VARIABLE_23848) (and (not (= zero_zero_nat (ho_402 BOUND_VARIABLE_23851 BOUND_VARIABLE_23848))) (ho_297 (ho_296 k_295 BOUND_VARIABLE_23848) BOUND_VARIABLE_20617)))))) (let ((_let_563 (forall ((BOUND_VARIABLE_23876 |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ nat)|) (BOUND_VARIABLE_23874 |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ nat)|) (BOUND_VARIABLE_20601 set_nat_nat_nat_nat3) (BOUND_VARIABLE_23871 |u_(-> _u_(-> nat nat)_ nat nat)|)) (= (ho_231 (ho_351 (ho_407 (ho_409 k_408 BOUND_VARIABLE_23876) BOUND_VARIABLE_23874) BOUND_VARIABLE_20601) BOUND_VARIABLE_23871) (and (not (= zero_zero_nat (ho_196 (ho_219 k_257 (ho_402 BOUND_VARIABLE_23876 BOUND_VARIABLE_23871)) (ho_402 BOUND_VARIABLE_23874 BOUND_VARIABLE_23871)))) (ho_297 (ho_296 k_295 BOUND_VARIABLE_23871) BOUND_VARIABLE_20601)))))) (let ((_let_564 (forall ((BOUND_VARIABLE_23906 |u_(-> _u_(-> nat nat nat)_ nat Bool)|) (BOUND_VARIABLE_20587 nat) (BOUND_VARIABLE_20588 set_nat_nat_nat) (BOUND_VARIABLE_23900 |u_(-> nat nat nat)|)) (= (ho_221 (ho_331 (ho_413 (ho_412 k_411 BOUND_VARIABLE_23906) BOUND_VARIABLE_20587) BOUND_VARIABLE_20588) BOUND_VARIABLE_23900) (and (ho_191 (ho_410 BOUND_VARIABLE_23906 BOUND_VARIABLE_23900) BOUND_VARIABLE_20587) (ho_238 (ho_237 k_236 BOUND_VARIABLE_23900) BOUND_VARIABLE_20588)))))) (let ((_let_565 (forall ((BOUND_VARIABLE_20578 nat) (BOUND_VARIABLE_20579 nat)) (= (ho_196 (ho_219 k_414 BOUND_VARIABLE_20578) BOUND_VARIABLE_20579) (ho_196 (ho_219 k_257 BOUND_VARIABLE_20579) BOUND_VARIABLE_20578))))) (let ((_let_566 (forall ((BOUND_VARIABLE_20557 nat) (BOUND_VARIABLE_20558 set_nat_nat_nat2) (BOUND_VARIABLE_20559 set_nat) (BOUND_VARIABLE_23947 |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)|)) (= (ho_420 (ho_419 (ho_418 (ho_417 k_416 BOUND_VARIABLE_20557) BOUND_VARIABLE_20558) BOUND_VARIABLE_20559) BOUND_VARIABLE_23947) (and (forall ((BOUND_VARIABLE_23959 |u_(-> _u_(-> nat nat)_ nat)|)) (or (ho_264 (ho_263 k_262 BOUND_VARIABLE_23959) BOUND_VARIABLE_20558) (= BOUND_VARIABLE_20557 (ho_415 BOUND_VARIABLE_23947 BOUND_VARIABLE_23959)))) (forall ((BOUND_VARIABLE_23943 |u_(-> _u_(-> nat nat)_ nat)|)) (or (not (ho_264 (ho_263 k_262 BOUND_VARIABLE_23943) BOUND_VARIABLE_20558)) (ho_188 (ho_187 k_186 (ho_415 BOUND_VARIABLE_23947 BOUND_VARIABLE_23943)) BOUND_VARIABLE_20559)))))))) (let ((_let_567 (forall ((BOUND_VARIABLE_24002 |u_(-> nat Bool)|) (BOUND_VARIABLE_20547 nat) (BOUND_VARIABLE_20548 nat)) (= (ho_191 (ho_233 (ho_422 k_421 BOUND_VARIABLE_24002) BOUND_VARIABLE_20547) BOUND_VARIABLE_20548) (and (ho_191 BOUND_VARIABLE_24002 BOUND_VARIABLE_20548) (ho_191 (ho_233 k_232 BOUND_VARIABLE_20548) BOUND_VARIABLE_20547)))))) (let ((_let_568 (forall ((BOUND_VARIABLE_20538 set_nat) (BOUND_VARIABLE_20539 nat)) (= (ho_191 (ho_190 k_423 BOUND_VARIABLE_20538) BOUND_VARIABLE_20539) (ho_188 (ho_187 k_186 BOUND_VARIABLE_20539) BOUND_VARIABLE_20538))))) (let ((_let_569 (forall ((BOUND_VARIABLE_20530 set_nat) (BOUND_VARIABLE_20531 nat)) (= (ho_191 (ho_190 k_424 BOUND_VARIABLE_20530) BOUND_VARIABLE_20531) (ho_188 (ho_187 k_186 BOUND_VARIABLE_20531) BOUND_VARIABLE_20530))))) (let ((_let_570 (forall ((BOUND_VARIABLE_20518 nat) (BOUND_VARIABLE_20519 nat)) (let ((_let_1 (= BOUND_VARIABLE_20518 BOUND_VARIABLE_20519))) (= (ho_191 (ho_233 k_425 BOUND_VARIABLE_20518) BOUND_VARIABLE_20519) (and (or _let_1 (ho_191 (ho_233 k_232 BOUND_VARIABLE_20518) BOUND_VARIABLE_20519)) (not _let_1))))))) (let ((_let_571 (forall ((BOUND_VARIABLE_24052 |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (BOUND_VARIABLE_24050 |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (BOUND_VARIABLE_24049 |u_(-> _u_(-> nat nat)_ nat nat)|)) (= (ho_231 (ho_300 (ho_427 k_426 BOUND_VARIABLE_24052) BOUND_VARIABLE_24050) BOUND_VARIABLE_24049) (or (ho_231 BOUND_VARIABLE_24052 BOUND_VARIABLE_24049) (ho_231 BOUND_VARIABLE_24050 BOUND_VARIABLE_24049)))))) (let ((_let_572 (forall ((BOUND_VARIABLE_20501 set_nat_nat) (BOUND_VARIABLE_20502 set_nat_nat)) (= (ho_199 (ho_251 k_428 BOUND_VARIABLE_20501) BOUND_VARIABLE_20502) (= BOUND_VARIABLE_20501 BOUND_VARIABLE_20502))))) (let ((_let_573 (forall ((BOUND_VARIABLE_20487 set_nat_nat) (BOUND_VARIABLE_20488 set_nat_nat)) (let ((_let_1 (= BOUND_VARIABLE_20487 BOUND_VARIABLE_20488))) (= (ho_199 (ho_251 k_429 BOUND_VARIABLE_20487) BOUND_VARIABLE_20488) (and (or _let_1 (ho_199 (ho_251 k_252 BOUND_VARIABLE_20488) BOUND_VARIABLE_20487)) (or _let_1 (ho_199 (ho_251 k_252 BOUND_VARIABLE_20487) BOUND_VARIABLE_20488)))))))) (let ((_let_574 (forall ((BOUND_VARIABLE_20479 set_nat_nat_nat_nat3) (BOUND_VARIABLE_24091 |u_(-> _u_(-> nat nat)_ nat nat)|)) (= (ho_231 (ho_351 k_430 BOUND_VARIABLE_20479) BOUND_VARIABLE_24091) (ho_297 (ho_296 k_295 BOUND_VARIABLE_24091) BOUND_VARIABLE_20479))))) (let ((_let_575 (forall ((BOUND_VARIABLE_20451 set_nat) (BOUND_VARIABLE_20452 set_nat)) (= (ho_188 (ho_277 k_431 BOUND_VARIABLE_20451) BOUND_VARIABLE_20452) (ho_312 (ho_311 k_310 (ho_190 k_207 BOUND_VARIABLE_20452)) (ho_190 k_208 BOUND_VARIABLE_20451)))))) (let ((_let_576 (forall ((BOUND_VARIABLE_24116 |u_(-> _u_(-> nat nat nat)_ Bool)|) (BOUND_VARIABLE_24114 |u_(-> _u_(-> nat nat nat)_ Bool)|) (BOUND_VARIABLE_24113 |u_(-> nat nat nat)|)) (= (ho_221 (ho_241 (ho_318 k_432 BOUND_VARIABLE_24116) BOUND_VARIABLE_24114) BOUND_VARIABLE_24113) (and (ho_221 BOUND_VARIABLE_24116 BOUND_VARIABLE_24113) (ho_221 BOUND_VARIABLE_24114 BOUND_VARIABLE_24113)))))) (let ((_let_577 (forall ((BOUND_VARIABLE_20433 nat) (BOUND_VARIABLE_20434 nat)) (= (ho_191 (ho_233 k_433 BOUND_VARIABLE_20433) BOUND_VARIABLE_20434) (ho_191 (ho_233 k_232 BOUND_VARIABLE_20434) BOUND_VARIABLE_20433))))) (let ((_let_578 (forall ((BOUND_VARIABLE_20425 set_nat_nat_nat2) (BOUND_VARIABLE_24138 |u_(-> _u_(-> nat nat)_ nat)|)) (= (ho_215 (ho_371 k_434 BOUND_VARIABLE_20425) BOUND_VARIABLE_24138) (ho_264 (ho_263 k_262 BOUND_VARIABLE_24138) BOUND_VARIABLE_20425))))) (let ((_let_579 (forall ((BOUND_VARIABLE_20404 set_nat_nat_nat2) (BOUND_VARIABLE_20405 set_nat_nat) (BOUND_VARIABLE_24157 |u_(-> _u_(-> nat nat)_ nat)|) (BOUND_VARIABLE_24153 |u_(-> _u_(-> nat nat)_ _u_(-> nat nat)_ nat)|)) (= (ho_440 (ho_439 (ho_438 (ho_437 k_436 BOUND_VARIABLE_20404) BOUND_VARIABLE_20405) BOUND_VARIABLE_24157) BOUND_VARIABLE_24153) (and (forall ((BOUND_VARIABLE_24164 |u_(-> nat nat)|)) (or (not (ho_199 (ho_198 k_197 BOUND_VARIABLE_24164) BOUND_VARIABLE_20405)) (ho_264 (ho_263 k_262 (ho_435 BOUND_VARIABLE_24153 BOUND_VARIABLE_24164)) BOUND_VARIABLE_20404))) (forall ((BOUND_VARIABLE_24149 |u_(-> nat nat)|)) (or (ho_199 (ho_198 k_197 BOUND_VARIABLE_24149) BOUND_VARIABLE_20405) (= (ho_435 BOUND_VARIABLE_24153 BOUND_VARIABLE_24149) BOUND_VARIABLE_24157)))))))) (let ((_let_580 (forall ((BOUND_VARIABLE_20392 nat) (BOUND_VARIABLE_20393 nat)) (let ((_let_1 (= BOUND_VARIABLE_20392 BOUND_VARIABLE_20393))) (= (ho_191 (ho_233 k_441 BOUND_VARIABLE_20392) BOUND_VARIABLE_20393) (and (not _let_1) (or _let_1 (ho_191 (ho_233 k_232 BOUND_VARIABLE_20392) BOUND_VARIABLE_20393)))))))) (let ((_let_581 (forall ((BOUND_VARIABLE_20379 set_nat) (BOUND_VARIABLE_24222 |u_(-> nat _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (BOUND_VARIABLE_24218 |u_(-> _u_(-> nat nat)_ nat)|) (BOUND_VARIABLE_20382 nat)) (= (ho_191 (ho_446 (ho_445 (ho_444 k_443 BOUND_VARIABLE_20379) BOUND_VARIABLE_24222) BOUND_VARIABLE_24218) BOUND_VARIABLE_20382) (and (ho_188 (ho_187 k_186 BOUND_VARIABLE_20382) BOUND_VARIABLE_20379) (ho_215 (ho_442 BOUND_VARIABLE_24222 BOUND_VARIABLE_20382) BOUND_VARIABLE_24218)))))) (let ((_let_582 (forall ((BOUND_VARIABLE_20371 set_nat_nat_nat) (BOUND_VARIABLE_20372 set_nat_nat_nat)) (= (ho_238 (ho_448 k_449 BOUND_VARIABLE_20371) BOUND_VARIABLE_20372) (ho_238 (ho_448 k_447 BOUND_VARIABLE_20372) BOUND_VARIABLE_20371))))) (let ((_let_583 (forall ((BOUND_VARIABLE_20358 set_nat_nat) (BOUND_VARIABLE_24276 |u_(-> _u_(-> nat nat)_ _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (BOUND_VARIABLE_24271 |u_(-> _u_(-> nat nat)_ nat)|) (BOUND_VARIABLE_24272 |u_(-> nat nat)|)) (= (ho_202 (ho_323 (ho_453 (ho_452 k_451 BOUND_VARIABLE_20358) BOUND_VARIABLE_24276) BOUND_VARIABLE_24271) BOUND_VARIABLE_24272) (and (ho_199 (ho_198 k_197 BOUND_VARIABLE_24272) BOUND_VARIABLE_20358) (ho_215 (ho_450 BOUND_VARIABLE_24276 BOUND_VARIABLE_24272) BOUND_VARIABLE_24271)))))) (let ((_let_584 (forall ((BOUND_VARIABLE_24309 |u_(-> _u_(-> nat nat)_ nat Bool)|) (BOUND_VARIABLE_20346 nat) (BOUND_VARIABLE_20347 set_nat_nat) (BOUND_VARIABLE_24306 |u_(-> nat nat)|)) (= (ho_202 (ho_201 (ho_456 (ho_455 k_454 BOUND_VARIABLE_24309) BOUND_VARIABLE_20346) BOUND_VARIABLE_20347) BOUND_VARIABLE_24306) (and (ho_191 (ho_308 BOUND_VARIABLE_24309 BOUND_VARIABLE_24306) BOUND_VARIABLE_20346) (ho_199 (ho_198 k_197 BOUND_VARIABLE_24306) BOUND_VARIABLE_20347)))))) (let ((_let_585 (forall ((BOUND_VARIABLE_20324 nat) (BOUND_VARIABLE_20325 set_nat_nat_nat) (BOUND_VARIABLE_20326 set_nat) (BOUND_VARIABLE_24336 |u_(-> _u_(-> nat nat nat)_ nat)|)) (= (ho_461 (ho_460 (ho_459 (ho_458 k_457 BOUND_VARIABLE_20324) BOUND_VARIABLE_20325) BOUND_VARIABLE_20326) BOUND_VARIABLE_24336) (and (forall ((BOUND_VARIABLE_24346 |u_(-> nat nat nat)|)) (or (ho_238 (ho_237 k_236 BOUND_VARIABLE_24346) BOUND_VARIABLE_20325) (= BOUND_VARIABLE_20324 (ho_375 BOUND_VARIABLE_24336 BOUND_VARIABLE_24346)))) (forall ((BOUND_VARIABLE_24335 |u_(-> nat nat nat)|)) (or (not (ho_238 (ho_237 k_236 BOUND_VARIABLE_24335) BOUND_VARIABLE_20325)) (ho_188 (ho_187 k_186 (ho_375 BOUND_VARIABLE_24336 BOUND_VARIABLE_24335)) BOUND_VARIABLE_20326)))))))) (let ((_let_586 (forall ((BOUND_VARIABLE_20316 set_nat) (BOUND_VARIABLE_20317 nat)) (= (ho_191 (ho_190 k_462 BOUND_VARIABLE_20316) BOUND_VARIABLE_20317) (ho_188 (ho_187 k_186 BOUND_VARIABLE_20317) BOUND_VARIABLE_20316))))) (let ((_let_587 (forall ((BOUND_VARIABLE_20308 set_nat) (BOUND_VARIABLE_20309 nat)) (= (ho_191 (ho_190 k_463 BOUND_VARIABLE_20308) BOUND_VARIABLE_20309) (ho_188 (ho_187 k_186 BOUND_VARIABLE_20309) BOUND_VARIABLE_20308))))) (let ((_let_588 (forall ((BOUND_VARIABLE_20300 set_nat) (BOUND_VARIABLE_20301 nat)) (= (ho_191 (ho_190 k_464 BOUND_VARIABLE_20300) BOUND_VARIABLE_20301) (ho_188 (ho_187 k_186 BOUND_VARIABLE_20301) BOUND_VARIABLE_20300))))) (let ((_let_589 (forall ((BOUND_VARIABLE_24414 |u_(-> nat Bool)|) (BOUND_VARIABLE_20273 set_nat) (BOUND_VARIABLE_20274 nat)) (= (ho_191 (ho_190 (ho_194 k_465 BOUND_VARIABLE_24414) BOUND_VARIABLE_20273) BOUND_VARIABLE_20274) (ho_188 (ho_187 k_186 BOUND_VARIABLE_20274) (ho_271 k_270 (ho_190 (ho_194 k_209 BOUND_VARIABLE_24414) BOUND_VARIABLE_20273))))))) (let ((_let_590 (forall ((BOUND_VARIABLE_20262 set_nat_nat) (BOUND_VARIABLE_20263 set_nat_nat)) (= (ho_199 (ho_251 k_466 BOUND_VARIABLE_20262) BOUND_VARIABLE_20263) (or (= BOUND_VARIABLE_20262 BOUND_VARIABLE_20263) (ho_199 (ho_251 k_252 BOUND_VARIABLE_20262) BOUND_VARIABLE_20263)))))) (let ((_let_591 (forall ((BOUND_VARIABLE_20251 set_nat_nat) (BOUND_VARIABLE_20252 set_nat_nat)) (= (ho_199 (ho_251 k_467 BOUND_VARIABLE_20251) BOUND_VARIABLE_20252) (forall ((BOUND_VARIABLE_24440 |u_(-> nat nat)|)) (let ((_let_1 (ho_198 k_197 BOUND_VARIABLE_24440))) (or (not (ho_199 _let_1 BOUND_VARIABLE_20251)) (ho_199 _let_1 BOUND_VARIABLE_20252)))))))) (let ((_let_592 (forall ((BOUND_VARIABLE_24455 |u_(-> nat nat)|)) (= (ho_202 k_468 BOUND_VARIABLE_24455) (and (forall ((I nat)) (let ((_let_1 (ho_196 BOUND_VARIABLE_24455 I))) (or (= n _let_1) (ho_191 (ho_233 k_232 _let_1) n)))) (= zero_zero_nat (ho_196 BOUND_VARIABLE_24455 (ho_196 (ho_219 k_257 n) one_one_nat))) (forall ((BOUND_VARIABLE_10295 nat)) (or (not (ho_191 (ho_233 k_232 (ho_196 (ho_219 k_257 n) one_one_nat)) BOUND_VARIABLE_10295)) (= zero_zero_nat (ho_196 BOUND_VARIABLE_24455 BOUND_VARIABLE_10295))))))))) (let ((_let_593 (forall ((BOUND_VARIABLE_20222 set_nat_nat_nat_nat3) (BOUND_VARIABLE_24478 |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (BOUND_VARIABLE_24477 |u_(-> _u_(-> nat nat)_ nat nat)|)) (= (ho_231 (ho_300 (ho_299 k_469 BOUND_VARIABLE_20222) BOUND_VARIABLE_24478) BOUND_VARIABLE_24477) (and (ho_297 (ho_296 k_295 BOUND_VARIABLE_24477) BOUND_VARIABLE_20222) (ho_231 BOUND_VARIABLE_24478 BOUND_VARIABLE_24477)))))) (let ((_let_594 (forall ((BOUND_VARIABLE_24496 |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (BOUND_VARIABLE_20212 set_nat_nat_nat_nat3) (BOUND_VARIABLE_24493 |u_(-> _u_(-> nat nat)_ nat nat)|)) (= (ho_231 (ho_351 (ho_350 k_470 BOUND_VARIABLE_24496) BOUND_VARIABLE_20212) BOUND_VARIABLE_24493) (and (ho_231 BOUND_VARIABLE_24496 BOUND_VARIABLE_24493) (ho_297 (ho_296 k_295 BOUND_VARIABLE_24493) BOUND_VARIABLE_20212)))))) (let ((_let_595 (forall ((BOUND_VARIABLE_20200 set_nat_nat_nat) (BOUND_VARIABLE_24510 |u_(-> _u_(-> nat nat nat)_ Bool)|) (BOUND_VARIABLE_24509 |u_(-> nat nat nat)|)) (= (ho_221 (ho_241 (ho_240 k_471 BOUND_VARIABLE_20200) BOUND_VARIABLE_24510) BOUND_VARIABLE_24509) (and (ho_238 (ho_237 k_236 BOUND_VARIABLE_24509) BOUND_VARIABLE_20200) (ho_221 BOUND_VARIABLE_24510 BOUND_VARIABLE_24509)))))) (let ((_let_596 (forall ((BOUND_VARIABLE_24528 |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (BOUND_VARIABLE_24526 |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (BOUND_VARIABLE_24525 |u_(-> _u_(-> nat nat)_ nat nat)|)) (= (ho_231 (ho_300 (ho_427 k_472 BOUND_VARIABLE_24528) BOUND_VARIABLE_24526) BOUND_VARIABLE_24525) (and (ho_231 BOUND_VARIABLE_24528 BOUND_VARIABLE_24525) (ho_231 BOUND_VARIABLE_24526 BOUND_VARIABLE_24525)))))) (let ((_let_597 (forall ((BOUND_VARIABLE_20178 set_nat_nat) (BOUND_VARIABLE_20179 set_nat_nat)) (let ((_let_1 (= BOUND_VARIABLE_20178 BOUND_VARIABLE_20179))) (= (ho_199 (ho_251 k_473 BOUND_VARIABLE_20178) BOUND_VARIABLE_20179) (and (or _let_1 (ho_199 (ho_251 k_252 BOUND_VARIABLE_20178) BOUND_VARIABLE_20179)) (not _let_1))))))) (let ((_let_598 (forall ((BOUND_VARIABLE_20150 set_nat) (BOUND_VARIABLE_24552 |u_(-> nat Bool)|) (BOUND_VARIABLE_20152 nat)) (= (ho_191 (ho_206 (ho_205 k_474 BOUND_VARIABLE_20150) BOUND_VARIABLE_24552) BOUND_VARIABLE_20152) (ho_188 (ho_187 k_186 BOUND_VARIABLE_20152) (ho_271 k_270 (ho_206 (ho_205 k_210 BOUND_VARIABLE_20150) BOUND_VARIABLE_24552))))))) (let ((_let_599 (forall ((BOUND_VARIABLE_20142 set_nat) (BOUND_VARIABLE_20143 nat)) (= (ho_191 (ho_190 k_475 BOUND_VARIABLE_20142) BOUND_VARIABLE_20143) (ho_188 (ho_187 k_186 BOUND_VARIABLE_20143) BOUND_VARIABLE_20142))))) (let ((_let_600 (forall ((BOUND_VARIABLE_24580 |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (BOUND_VARIABLE_20132 set_nat_nat_nat_nat3) (BOUND_VARIABLE_24577 |u_(-> _u_(-> nat nat)_ nat nat)|)) (= (ho_231 (ho_351 (ho_350 k_476 BOUND_VARIABLE_24580) BOUND_VARIABLE_20132) BOUND_VARIABLE_24577) (and (ho_231 BOUND_VARIABLE_24580 BOUND_VARIABLE_24577) (ho_297 (ho_296 k_295 BOUND_VARIABLE_24577) BOUND_VARIABLE_20132)))))) (let ((_let_601 (forall ((BOUND_VARIABLE_20118 set_nat) (BOUND_VARIABLE_24594 |u_(-> nat _u_(-> nat nat)_ Bool)|) (BOUND_VARIABLE_24593 |u_(-> nat nat)|) (BOUND_VARIABLE_20121 nat)) (= (ho_191 (ho_308 (ho_479 (ho_478 k_477 BOUND_VARIABLE_20118) BOUND_VARIABLE_24594) BOUND_VARIABLE_24593) BOUND_VARIABLE_20121) (and (ho_188 (ho_187 k_186 BOUND_VARIABLE_20121) BOUND_VARIABLE_20118) (ho_202 (ho_283 BOUND_VARIABLE_24594 BOUND_VARIABLE_20121) BOUND_VARIABLE_24593)))))) (let ((_let_602 (forall ((BOUND_VARIABLE_24632 |u_(-> nat nat)|) (BOUND_VARIABLE_20098 set_nat) (BOUND_VARIABLE_20099 set_nat_nat) (BOUND_VARIABLE_24622 |u_(-> nat nat nat)|)) (= (ho_221 (ho_483 (ho_482 (ho_481 k_480 BOUND_VARIABLE_24632) BOUND_VARIABLE_20098) BOUND_VARIABLE_20099) BOUND_VARIABLE_24622) (and (forall ((BOUND_VARIABLE_6601 nat)) (or (ho_188 (ho_187 k_186 BOUND_VARIABLE_6601) BOUND_VARIABLE_20098) (= (ho_219 BOUND_VARIABLE_24622 BOUND_VARIABLE_6601) BOUND_VARIABLE_24632))) (forall ((BOUND_VARIABLE_6610 nat)) (or (not (ho_188 (ho_187 k_186 BOUND_VARIABLE_6610) BOUND_VARIABLE_20098)) (ho_199 (ho_198 k_197 (ho_219 BOUND_VARIABLE_24622 BOUND_VARIABLE_6610)) BOUND_VARIABLE_20099)))))))) (let ((_let_603 (forall ((BOUND_VARIABLE_20076 nat) (BOUND_VARIABLE_20077 set_nat_nat) (BOUND_VARIABLE_20078 set_nat) (BOUND_VARIABLE_24667 |u_(-> _u_(-> nat nat)_ nat)|)) (= (ho_215 (ho_487 (ho_486 (ho_485 k_484 BOUND_VARIABLE_20076) BOUND_VARIABLE_20077) BOUND_VARIABLE_20078) BOUND_VARIABLE_24667) (and (forall ((BOUND_VARIABLE_24677 |u_(-> nat nat)|)) (or (ho_199 (ho_198 k_197 BOUND_VARIABLE_24677) BOUND_VARIABLE_20077) (= BOUND_VARIABLE_20076 (ho_214 BOUND_VARIABLE_24667 BOUND_VARIABLE_24677)))) (forall ((BOUND_VARIABLE_24666 |u_(-> nat nat)|)) (or (not (ho_199 (ho_198 k_197 BOUND_VARIABLE_24666) BOUND_VARIABLE_20077)) (ho_188 (ho_187 k_186 (ho_214 BOUND_VARIABLE_24667 BOUND_VARIABLE_24666)) BOUND_VARIABLE_20078)))))))) (let ((_let_604 (forall ((BOUND_VARIABLE_24716 |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (BOUND_VARIABLE_24714 |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (BOUND_VARIABLE_24713 |u_(-> _u_(-> nat nat)_ nat)|)) (= (ho_215 (ho_218 (ho_217 k_488 BOUND_VARIABLE_24716) BOUND_VARIABLE_24714) BOUND_VARIABLE_24713) (and (ho_215 BOUND_VARIABLE_24716 BOUND_VARIABLE_24713) (ho_215 BOUND_VARIABLE_24714 BOUND_VARIABLE_24713)))))) (let ((_let_605 (forall ((BOUND_VARIABLE_20055 set_nat_nat_nat2) (BOUND_VARIABLE_24730 |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (BOUND_VARIABLE_24729 |u_(-> _u_(-> nat nat)_ nat)|)) (= (ho_215 (ho_218 (ho_266 k_489 BOUND_VARIABLE_20055) BOUND_VARIABLE_24730) BOUND_VARIABLE_24729) (and (ho_264 (ho_263 k_262 BOUND_VARIABLE_24729) BOUND_VARIABLE_20055) (ho_215 BOUND_VARIABLE_24730 BOUND_VARIABLE_24729)))))) (let ((_let_606 (forall ((BOUND_VARIABLE_20048 set_nat_nat) (BOUND_VARIABLE_20049 set_nat_nat)) (= (ho_199 (ho_251 k_490 BOUND_VARIABLE_20048) BOUND_VARIABLE_20049) (= BOUND_VARIABLE_20048 BOUND_VARIABLE_20049))))) (let ((_let_607 (forall ((BOUND_VARIABLE_20034 set_nat_nat) (BOUND_VARIABLE_20035 set_nat_nat)) (let ((_let_1 (= BOUND_VARIABLE_20034 BOUND_VARIABLE_20035))) (= (ho_199 (ho_251 k_491 BOUND_VARIABLE_20034) BOUND_VARIABLE_20035) (and (or _let_1 (ho_199 (ho_251 k_252 BOUND_VARIABLE_20034) BOUND_VARIABLE_20035)) (or _let_1 (ho_199 (ho_251 k_252 BOUND_VARIABLE_20035) BOUND_VARIABLE_20034)))))))) (let ((_let_608 (forall ((BOUND_VARIABLE_20023 set_nat_nat_nat) (BOUND_VARIABLE_24767 |u_(-> _u_(-> nat nat nat)_ Bool)|) (BOUND_VARIABLE_24766 |u_(-> nat nat nat)|)) (= (ho_221 (ho_241 (ho_240 k_492 BOUND_VARIABLE_20023) BOUND_VARIABLE_24767) BOUND_VARIABLE_24766) (and (ho_238 (ho_237 k_236 BOUND_VARIABLE_24766) BOUND_VARIABLE_20023) (ho_221 BOUND_VARIABLE_24767 BOUND_VARIABLE_24766)))))) (let ((_let_609 (forall ((BOUND_VARIABLE_24785 |u_(-> _u_(-> nat nat nat)_ Bool)|) (BOUND_VARIABLE_20013 set_nat_nat_nat) (BOUND_VARIABLE_24782 |u_(-> nat nat nat)|)) (= (ho_221 (ho_331 (ho_330 k_493 BOUND_VARIABLE_24785) BOUND_VARIABLE_20013) BOUND_VARIABLE_24782) (and (ho_221 BOUND_VARIABLE_24785 BOUND_VARIABLE_24782) (ho_238 (ho_237 k_236 BOUND_VARIABLE_24782) BOUND_VARIABLE_20013)))))) (let ((_let_610 (forall ((BOUND_VARIABLE_20001 set_nat_nat) (BOUND_VARIABLE_24799 |u_(-> _u_(-> nat nat)_ Bool)|) (BOUND_VARIABLE_24798 |u_(-> nat nat)|)) (= (ho_202 (ho_269 (ho_268 k_494 BOUND_VARIABLE_20001) BOUND_VARIABLE_24799) BOUND_VARIABLE_24798) (and (ho_199 (ho_198 k_197 BOUND_VARIABLE_24798) BOUND_VARIABLE_20001) (ho_202 BOUND_VARIABLE_24799 BOUND_VARIABLE_24798)))))) (let ((_let_611 (forall ((BOUND_VARIABLE_19994 set_nat_nat) (BOUND_VARIABLE_19995 set_nat_nat)) (= (ho_199 (ho_251 k_495 BOUND_VARIABLE_19994) BOUND_VARIABLE_19995) (= BOUND_VARIABLE_19994 BOUND_VARIABLE_19995))))) (let ((_let_612 (forall ((BOUND_VARIABLE_19980 set_nat_nat) (BOUND_VARIABLE_19981 set_nat_nat)) (let ((_let_1 (= BOUND_VARIABLE_19980 BOUND_VARIABLE_19981))) (= (ho_199 (ho_251 k_496 BOUND_VARIABLE_19980) BOUND_VARIABLE_19981) (and (or _let_1 (ho_199 (ho_251 k_252 BOUND_VARIABLE_19981) BOUND_VARIABLE_19980)) (or _let_1 (ho_199 (ho_251 k_252 BOUND_VARIABLE_19980) BOUND_VARIABLE_19981)))))))) (let ((_let_613 (forall ((BOUND_VARIABLE_19972 set_nat) (BOUND_VARIABLE_19973 nat)) (= (ho_191 (ho_190 k_497 BOUND_VARIABLE_19972) BOUND_VARIABLE_19973) (ho_188 (ho_187 k_186 BOUND_VARIABLE_19973) BOUND_VARIABLE_19972))))) (let ((_let_614 (forall ((BOUND_VARIABLE_24845 |u_(-> nat Bool)|) (BOUND_VARIABLE_24844 |u_(-> nat Bool)|) (BOUND_VARIABLE_19946 nat)) (= (ho_191 (ho_206 (ho_212 k_498 BOUND_VARIABLE_24845) BOUND_VARIABLE_24844) BOUND_VARIABLE_19946) (ho_188 (ho_187 k_186 BOUND_VARIABLE_19946) (ho_271 k_270 (ho_206 (ho_212 k_211 BOUND_VARIABLE_24845) BOUND_VARIABLE_24844))))))) (let ((_let_615 (forall ((BOUND_VARIABLE_19936 set_nat) (BOUND_VARIABLE_19937 nat)) (= (ho_191 (ho_190 k_499 BOUND_VARIABLE_19936) BOUND_VARIABLE_19937) (ho_188 (ho_187 k_186 BOUND_VARIABLE_19937) BOUND_VARIABLE_19936))))) (let ((_let_616 (forall ((BOUND_VARIABLE_24870 |u_(-> nat Bool)|) (BOUND_VARIABLE_19928 nat)) (= (ho_191 (ho_206 k_500 BOUND_VARIABLE_24870) BOUND_VARIABLE_19928) (ho_188 (ho_187 k_186 BOUND_VARIABLE_19928) (ho_271 k_270 BOUND_VARIABLE_24870)))))) (let ((_let_617 (forall ((BOUND_VARIABLE_19919 set_nat) (BOUND_VARIABLE_19920 nat)) (= (ho_191 (ho_190 k_501 BOUND_VARIABLE_19919) BOUND_VARIABLE_19920) (ho_188 (ho_187 k_186 BOUND_VARIABLE_19920) BOUND_VARIABLE_19919))))) (let ((_let_618 (forall ((BOUND_VARIABLE_24891 |u_(-> nat Bool)|) (BOUND_VARIABLE_19911 nat)) (= (ho_191 (ho_206 k_502 BOUND_VARIABLE_24891) BOUND_VARIABLE_19911) (ho_188 (ho_187 k_186 BOUND_VARIABLE_19911) (ho_271 k_270 BOUND_VARIABLE_24891)))))) (let ((_let_619 (forall ((BOUND_VARIABLE_19903 nat) (BOUND_VARIABLE_19904 nat)) (= (ho_191 (ho_233 k_503 BOUND_VARIABLE_19903) BOUND_VARIABLE_19904) (= BOUND_VARIABLE_19903 BOUND_VARIABLE_19904))))) (let ((_let_620 (forall ((BOUND_VARIABLE_19889 nat) (BOUND_VARIABLE_19890 nat)) (let ((_let_1 (= BOUND_VARIABLE_19889 BOUND_VARIABLE_19890))) (= (ho_191 (ho_233 k_504 BOUND_VARIABLE_19889) BOUND_VARIABLE_19890) (and (or _let_1 (ho_191 (ho_233 k_232 BOUND_VARIABLE_19890) BOUND_VARIABLE_19889)) (or _let_1 (ho_191 (ho_233 k_232 BOUND_VARIABLE_19889) BOUND_VARIABLE_19890)))))))) (let ((_let_621 (forall ((BOUND_VARIABLE_19882 nat) (BOUND_VARIABLE_19883 nat)) (= (ho_191 (ho_233 k_505 BOUND_VARIABLE_19882) BOUND_VARIABLE_19883) (= BOUND_VARIABLE_19882 BOUND_VARIABLE_19883))))) (let ((_let_622 (forall ((BOUND_VARIABLE_19868 nat) (BOUND_VARIABLE_19869 nat)) (let ((_let_1 (= BOUND_VARIABLE_19868 BOUND_VARIABLE_19869))) (= (ho_191 (ho_233 k_506 BOUND_VARIABLE_19868) BOUND_VARIABLE_19869) (and (or _let_1 (ho_191 (ho_233 k_232 BOUND_VARIABLE_19869) BOUND_VARIABLE_19868)) (or _let_1 (ho_191 (ho_233 k_232 BOUND_VARIABLE_19868) BOUND_VARIABLE_19869)))))))) (let ((_let_623 (forall ((BOUND_VARIABLE_19857 set_nat_nat) (BOUND_VARIABLE_24946 |u_(-> _u_(-> nat nat)_ Bool)|) (BOUND_VARIABLE_24945 |u_(-> nat nat)|)) (= (ho_202 (ho_269 (ho_268 k_507 BOUND_VARIABLE_19857) BOUND_VARIABLE_24946) BOUND_VARIABLE_24945) (and (ho_199 (ho_198 k_197 BOUND_VARIABLE_24945) BOUND_VARIABLE_19857) (ho_202 BOUND_VARIABLE_24946 BOUND_VARIABLE_24945)))))) (let ((_let_624 (forall ((BOUND_VARIABLE_24964 |u_(-> _u_(-> nat nat)_ Bool)|) (BOUND_VARIABLE_19847 set_nat_nat) (BOUND_VARIABLE_24961 |u_(-> nat nat)|)) (= (ho_202 (ho_201 (ho_509 k_508 BOUND_VARIABLE_24964) BOUND_VARIABLE_19847) BOUND_VARIABLE_24961) (and (ho_202 BOUND_VARIABLE_24964 BOUND_VARIABLE_24961) (ho_199 (ho_198 k_197 BOUND_VARIABLE_24961) BOUND_VARIABLE_19847)))))) (let ((_let_625 (forall ((BOUND_VARIABLE_19835 set_nat_nat) (BOUND_VARIABLE_24983 |u_(-> _u_(-> nat nat)_ Bool)|) (BOUND_VARIABLE_24982 |u_(-> nat nat)|)) (= (ho_202 (ho_269 (ho_268 k_510 BOUND_VARIABLE_19835) BOUND_VARIABLE_24983) BOUND_VARIABLE_24982) (and (ho_199 (ho_198 k_197 BOUND_VARIABLE_24982) BOUND_VARIABLE_19835) (ho_202 BOUND_VARIABLE_24983 BOUND_VARIABLE_24982)))))) (let ((_let_626 (forall ((BOUND_VARIABLE_19827 set_nat) (BOUND_VARIABLE_19828 nat)) (= (ho_191 (ho_190 k_511 BOUND_VARIABLE_19827) BOUND_VARIABLE_19828) (ho_188 (ho_187 k_186 BOUND_VARIABLE_19828) BOUND_VARIABLE_19827))))) (let ((_let_627 (forall ((BOUND_VARIABLE_19819 set_nat) (BOUND_VARIABLE_19820 nat)) (= (ho_191 (ho_190 k_512 BOUND_VARIABLE_19819) BOUND_VARIABLE_19820) (ho_188 (ho_187 k_186 BOUND_VARIABLE_19820) BOUND_VARIABLE_19819))))) (let ((_let_628 (forall ((BOUND_VARIABLE_25016 |u_(-> nat nat)|) (BOUND_VARIABLE_19808 nat) (BOUND_VARIABLE_19809 nat)) (let ((_let_1 (ho_196 BOUND_VARIABLE_25016 BOUND_VARIABLE_19809))) (= (ho_191 (ho_233 (ho_514 k_513 BOUND_VARIABLE_25016) BOUND_VARIABLE_19808) BOUND_VARIABLE_19809) (or (= BOUND_VARIABLE_19808 _let_1) (ho_191 (ho_233 k_232 _let_1) BOUND_VARIABLE_19808))))))) (let ((_let_629 (forall ((BOUND_VARIABLE_25040 |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (BOUND_VARIABLE_19797 set_nat_nat_nat2) (BOUND_VARIABLE_25037 |u_(-> _u_(-> nat nat)_ nat)|)) (= (ho_215 (ho_371 (ho_370 k_515 BOUND_VARIABLE_25040) BOUND_VARIABLE_19797) BOUND_VARIABLE_25037) (and (ho_215 BOUND_VARIABLE_25040 BOUND_VARIABLE_25037) (ho_264 (ho_263 k_262 BOUND_VARIABLE_25037) BOUND_VARIABLE_19797)))))) (let ((_let_630 (forall ((BOUND_VARIABLE_25056 |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat Bool)|) (BOUND_VARIABLE_19784 nat) (BOUND_VARIABLE_19785 set_nat_nat_nat2) (BOUND_VARIABLE_25053 |u_(-> _u_(-> nat nat)_ nat)|)) (= (ho_215 (ho_371 (ho_518 (ho_517 k_516 BOUND_VARIABLE_25056) BOUND_VARIABLE_19784) BOUND_VARIABLE_19785) BOUND_VARIABLE_25053) (and (ho_191 (ho_446 BOUND_VARIABLE_25056 BOUND_VARIABLE_25053) BOUND_VARIABLE_19784) (ho_264 (ho_263 k_262 BOUND_VARIABLE_25053) BOUND_VARIABLE_19785)))))) (let ((_let_631 (forall ((BOUND_VARIABLE_19770 set_nat_nat_nat2) (BOUND_VARIABLE_25083 |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)|) (BOUND_VARIABLE_25082 |u_(-> _u_(-> nat nat)_ nat)|)) (= (ho_215 (ho_521 (ho_520 k_519 BOUND_VARIABLE_19770) BOUND_VARIABLE_25083) BOUND_VARIABLE_25082) (and (ho_264 (ho_263 k_262 BOUND_VARIABLE_25082) BOUND_VARIABLE_19770) (not (= zero_zero_nat (ho_415 BOUND_VARIABLE_25083 BOUND_VARIABLE_25082)))))))) (let ((_let_632 (forall ((BOUND_VARIABLE_25113 |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)|) (BOUND_VARIABLE_19758 set_nat_nat_nat2) (BOUND_VARIABLE_25110 |u_(-> _u_(-> nat nat)_ nat)|)) (= (ho_215 (ho_371 (ho_523 k_522 BOUND_VARIABLE_25113) BOUND_VARIABLE_19758) BOUND_VARIABLE_25110) (and (not (= zero_zero_nat (ho_415 BOUND_VARIABLE_25113 BOUND_VARIABLE_25110))) (ho_264 (ho_263 k_262 BOUND_VARIABLE_25110) BOUND_VARIABLE_19758)))))) (let ((_let_633 (forall ((BOUND_VARIABLE_19740 set_nat_nat_nat2) (BOUND_VARIABLE_25136 |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)|) (BOUND_VARIABLE_25134 |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ nat)|) (BOUND_VARIABLE_25133 |u_(-> _u_(-> nat nat)_ nat)|)) (= (ho_215 (ho_521 (ho_526 (ho_525 k_524 BOUND_VARIABLE_19740) BOUND_VARIABLE_25136) BOUND_VARIABLE_25134) BOUND_VARIABLE_25133) (and (ho_264 (ho_263 k_262 BOUND_VARIABLE_25133) BOUND_VARIABLE_19740) (not (= zero_zero_nat (ho_196 (ho_219 k_257 (ho_415 BOUND_VARIABLE_25136 BOUND_VARIABLE_25133)) (ho_415 BOUND_VARIABLE_25134 BOUND_VARIABLE_25133))))))))) (let ((_let_634 (forall ((BOUND_VARIABLE_25170 |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (BOUND_VARIABLE_19730 set_nat_nat_nat_nat3) (BOUND_VARIABLE_25167 |u_(-> _u_(-> nat nat)_ nat nat)|)) (= (ho_231 (ho_351 (ho_350 k_527 BOUND_VARIABLE_25170) BOUND_VARIABLE_19730) BOUND_VARIABLE_25167) (and (ho_231 BOUND_VARIABLE_25170 BOUND_VARIABLE_25167) (ho_297 (ho_296 k_295 BOUND_VARIABLE_25167) BOUND_VARIABLE_19730)))))) (let ((_let_635 (forall ((BOUND_VARIABLE_25186 |u_(-> _u_(-> nat nat)_ Bool)|) (BOUND_VARIABLE_25184 |u_(-> _u_(-> nat nat)_ Bool)|) (BOUND_VARIABLE_25183 |u_(-> nat nat)|)) (= (ho_202 (ho_269 (ho_397 k_528 BOUND_VARIABLE_25186) BOUND_VARIABLE_25184) BOUND_VARIABLE_25183) (or (ho_202 BOUND_VARIABLE_25186 BOUND_VARIABLE_25183) (ho_202 BOUND_VARIABLE_25184 BOUND_VARIABLE_25183)))))) (let ((_let_636 (forall ((BOUND_VARIABLE_25202 |u_(-> _u_(-> nat nat nat)_ Bool)|) (BOUND_VARIABLE_19709 set_nat_nat_nat) (BOUND_VARIABLE_25199 |u_(-> nat nat nat)|)) (= (ho_221 (ho_331 (ho_330 k_529 BOUND_VARIABLE_25202) BOUND_VARIABLE_19709) BOUND_VARIABLE_25199) (and (ho_221 BOUND_VARIABLE_25202 BOUND_VARIABLE_25199) (ho_238 (ho_237 k_236 BOUND_VARIABLE_25199) BOUND_VARIABLE_19709)))))) (let ((_let_637 (forall ((BOUND_VARIABLE_19703 nat)) (= zero_zero_nat (ho_196 k_530 BOUND_VARIABLE_19703))))) (let ((_let_638 (forall ((BOUND_VARIABLE_25223 |u_(-> _u_(-> nat nat)_ Bool)|) (BOUND_VARIABLE_25221 |u_(-> _u_(-> nat nat)_ Bool)|) (BOUND_VARIABLE_25220 |u_(-> nat nat)|)) (= (ho_202 (ho_269 (ho_397 k_531 BOUND_VARIABLE_25223) BOUND_VARIABLE_25221) BOUND_VARIABLE_25220) (and (ho_202 BOUND_VARIABLE_25223 BOUND_VARIABLE_25220) (ho_202 BOUND_VARIABLE_25221 BOUND_VARIABLE_25220)))))) (let ((_let_639 (forall ((BOUND_VARIABLE_25239 |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (BOUND_VARIABLE_25237 |u_(-> _u_(-> _u_(-> nat nat)_ nat nat)_ Bool)|) (BOUND_VARIABLE_25236 |u_(-> _u_(-> nat nat)_ nat nat)|)) (= (ho_231 (ho_300 (ho_427 k_532 BOUND_VARIABLE_25239) BOUND_VARIABLE_25237) BOUND_VARIABLE_25236) (and (ho_231 BOUND_VARIABLE_25239 BOUND_VARIABLE_25236) (ho_231 BOUND_VARIABLE_25237 BOUND_VARIABLE_25236)))))) (let ((_let_640 (forall ((BOUND_VARIABLE_25255 |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (BOUND_VARIABLE_19673 set_nat_nat_nat2) (BOUND_VARIABLE_25252 |u_(-> _u_(-> nat nat)_ nat)|)) (= (ho_215 (ho_371 (ho_370 k_533 BOUND_VARIABLE_25255) BOUND_VARIABLE_19673) BOUND_VARIABLE_25252) (and (ho_215 BOUND_VARIABLE_25255 BOUND_VARIABLE_25252) (ho_264 (ho_263 k_262 BOUND_VARIABLE_25252) BOUND_VARIABLE_19673)))))) (let ((_let_641 (forall ((BOUND_VARIABLE_25268 |u_(-> nat Bool)|) (BOUND_VARIABLE_19645 set_nat) (BOUND_VARIABLE_19646 nat)) (= (ho_191 (ho_190 (ho_194 k_534 BOUND_VARIABLE_25268) BOUND_VARIABLE_19645) BOUND_VARIABLE_19646) (ho_188 (ho_187 k_186 BOUND_VARIABLE_19646) (ho_271 k_270 (ho_190 (ho_194 k_213 BOUND_VARIABLE_25268) BOUND_VARIABLE_19645))))))) (let ((_let_642 (forall ((BOUND_VARIABLE_19636 set_nat) (BOUND_VARIABLE_19637 nat)) (= (ho_191 (ho_190 k_535 BOUND_VARIABLE_19636) BOUND_VARIABLE_19637) (ho_188 (ho_187 k_186 BOUND_VARIABLE_19637) BOUND_VARIABLE_19636))))) (let ((_let_643 (forall ((BOUND_VARIABLE_25301 |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)|) (BOUND_VARIABLE_25293 |u_(-> _u_(-> _u_(-> nat nat)_ nat)_ Bool)|)) (or (not (forall ((BOUND_VARIABLE_25304 |u_(-> _u_(-> nat nat)_ nat)|)) (= (ho_215 BOUND_VARIABLE_25301 BOUND_VARIABLE_25304) (ho_215 BOUND_VARIABLE_25293 BOUND_VARIABLE_25304)))) (= (ho_537 k_536 BOUND_VARIABLE_25293) (ho_537 k_536 BOUND_VARIABLE_25301)))))) (let ((_let_644 (forall ((BOUND_VARIABLE_21846 set_nat) (BOUND_VARIABLE_21847 nat)) (= (ll_185 BOUND_VARIABLE_21846 BOUND_VARIABLE_21847) ((member_nat BOUND_VARIABLE_21847) BOUND_VARIABLE_21846))))) (let ((_let_645 (forall ((BOUND_VARIABLE_21838 set_nat) (BOUND_VARIABLE_21839 nat)) (= (ll_184 BOUND_VARIABLE_21838 BOUND_VARIABLE_21839) ((member_nat BOUND_VARIABLE_21839) BOUND_VARIABLE_21838))))) (let ((_let_646 (forall ((BOUND_VARIABLE_21827 (-> nat Bool)) (BOUND_VARIABLE_21828 set_nat) (BOUND_VARIABLE_21829 nat)) (= (ll_183 BOUND_VARIABLE_21827 BOUND_VARIABLE_21828 BOUND_VARIABLE_21829) (and (BOUND_VARIABLE_21827 BOUND_VARIABLE_21829) ((member_nat BOUND_VARIABLE_21829) BOUND_VARIABLE_21828)))))) (let ((_let_647 (forall ((BOUND_VARIABLE_21816 (-> nat Bool)) (BOUND_VARIABLE_21817 set_nat) (BOUND_VARIABLE_21818 nat)) (= (ll_182 BOUND_VARIABLE_21816 BOUND_VARIABLE_21817 BOUND_VARIABLE_21818) (and (BOUND_VARIABLE_21816 BOUND_VARIABLE_21818) ((member_nat BOUND_VARIABLE_21818) BOUND_VARIABLE_21817)))))) (let ((_let_648 (forall ((BOUND_VARIABLE_21808 set_nat_nat) (BOUND_VARIABLE_21809 (-> nat nat))) (= (ll_181 BOUND_VARIABLE_21808 BOUND_VARIABLE_21809) ((member_nat_nat BOUND_VARIABLE_21809) BOUND_VARIABLE_21808))))) (let ((_let_649 (forall ((BOUND_VARIABLE_21800 set_nat_nat) (BOUND_VARIABLE_21801 (-> nat nat))) (= (ll_180 BOUND_VARIABLE_21800 BOUND_VARIABLE_21801) ((member_nat_nat BOUND_VARIABLE_21801) BOUND_VARIABLE_21800))))) (let ((_let_650 (forall ((BOUND_VARIABLE_21789 set_nat) (BOUND_VARIABLE_21790 (-> nat Bool)) (BOUND_VARIABLE_21791 nat)) (= (ll_179 BOUND_VARIABLE_21789 BOUND_VARIABLE_21790 BOUND_VARIABLE_21791) (and ((member_nat BOUND_VARIABLE_21791) BOUND_VARIABLE_21789) (BOUND_VARIABLE_21790 BOUND_VARIABLE_21791)))))) (let ((_let_651 (forall ((BOUND_VARIABLE_21781 set_nat) (BOUND_VARIABLE_21782 nat)) (= (ll_178 BOUND_VARIABLE_21781 BOUND_VARIABLE_21782) ((member_nat BOUND_VARIABLE_21782) BOUND_VARIABLE_21781))))) (let ((_let_652 (forall ((BOUND_VARIABLE_21773 set_nat) (BOUND_VARIABLE_21774 nat)) (= (ll_177 BOUND_VARIABLE_21773 BOUND_VARIABLE_21774) ((member_nat BOUND_VARIABLE_21774) BOUND_VARIABLE_21773))))) (let ((_let_653 (forall ((BOUND_VARIABLE_21762 (-> nat Bool)) (BOUND_VARIABLE_21763 set_nat) (BOUND_VARIABLE_21764 nat)) (= (ll_176 BOUND_VARIABLE_21762 BOUND_VARIABLE_21763 BOUND_VARIABLE_21764) (and (BOUND_VARIABLE_21762 BOUND_VARIABLE_21764) ((member_nat BOUND_VARIABLE_21764) BOUND_VARIABLE_21763)))))) (let ((_let_654 (forall ((BOUND_VARIABLE_21751 set_nat) (BOUND_VARIABLE_21752 (-> nat Bool)) (BOUND_VARIABLE_21753 nat)) (= (ll_175 BOUND_VARIABLE_21751 BOUND_VARIABLE_21752 BOUND_VARIABLE_21753) (and ((member_nat BOUND_VARIABLE_21753) BOUND_VARIABLE_21751) (BOUND_VARIABLE_21752 BOUND_VARIABLE_21753)))))) (let ((_let_655 (forall ((BOUND_VARIABLE_21741 (-> nat Bool)) (BOUND_VARIABLE_21742 (-> nat Bool)) (BOUND_VARIABLE_21743 nat)) (= (ll_174 BOUND_VARIABLE_21741 BOUND_VARIABLE_21742 BOUND_VARIABLE_21743) (and (BOUND_VARIABLE_21741 BOUND_VARIABLE_21743) (BOUND_VARIABLE_21742 BOUND_VARIABLE_21743)))))) (let ((_let_656 (forall ((BOUND_VARIABLE_21730 (-> nat Bool)) (BOUND_VARIABLE_21731 set_nat) (BOUND_VARIABLE_21732 nat)) (= (ll_173 BOUND_VARIABLE_21730 BOUND_VARIABLE_21731 BOUND_VARIABLE_21732) (and (BOUND_VARIABLE_21730 BOUND_VARIABLE_21732) ((member_nat BOUND_VARIABLE_21732) BOUND_VARIABLE_21731)))))) (let ((_let_657 (forall ((BOUND_VARIABLE_21720 (-> (-> (-> nat nat) nat) Bool)) (BOUND_VARIABLE_21721 (-> (-> (-> nat nat) nat) Bool)) (BOUND_VARIABLE_21722 (-> (-> nat nat) nat))) (= (ll_172 BOUND_VARIABLE_21720 BOUND_VARIABLE_21721 BOUND_VARIABLE_21722) (or (BOUND_VARIABLE_21720 BOUND_VARIABLE_21722) (BOUND_VARIABLE_21721 BOUND_VARIABLE_21722)))))) (let ((_let_658 (forall ((BOUND_VARIABLE_21707 set_nat_nat) (BOUND_VARIABLE_21708 (-> (-> nat nat) (-> nat nat nat) Bool)) (BOUND_VARIABLE_21709 (-> nat nat nat)) (BOUND_VARIABLE_21710 (-> nat nat))) (= (ll_171 BOUND_VARIABLE_21707 BOUND_VARIABLE_21708 BOUND_VARIABLE_21709 BOUND_VARIABLE_21710) (and ((member_nat_nat BOUND_VARIABLE_21710) BOUND_VARIABLE_21707) ((BOUND_VARIABLE_21708 BOUND_VARIABLE_21710) BOUND_VARIABLE_21709)))))) (let ((_let_659 (forall ((BOUND_VARIABLE_21686 set_nat_nat) (BOUND_VARIABLE_21687 set_nat_nat) (BOUND_VARIABLE_21688 (-> nat nat)) (BOUND_VARIABLE_21689 (-> (-> nat nat) nat nat))) (= (ll_170 BOUND_VARIABLE_21686 BOUND_VARIABLE_21687 BOUND_VARIABLE_21688 BOUND_VARIABLE_21689) (and (forall ((BOUND_VARIABLE_8892 (-> nat nat))) (or (not ((member_nat_nat BOUND_VARIABLE_8892) BOUND_VARIABLE_21687)) ((member_nat_nat (BOUND_VARIABLE_21689 BOUND_VARIABLE_8892)) BOUND_VARIABLE_21686))) (forall ((BOUND_VARIABLE_8903 (-> nat nat))) (or ((member_nat_nat BOUND_VARIABLE_8903) BOUND_VARIABLE_21687) (= BOUND_VARIABLE_21688 (BOUND_VARIABLE_21689 BOUND_VARIABLE_8903))))))))) (let ((_let_660 (forall ((BOUND_VARIABLE_21674 set_nat)) (= (ll_169 BOUND_VARIABLE_21674) (not (forall ((M2 nat)) (not (forall ((X nat)) (or (not ((member_nat X) BOUND_VARIABLE_21674)) ((ord_less_nat X) M2)))))))))) (let ((_let_661 (forall ((BOUND_VARIABLE_21662 set_nat)) (= (ll_168 BOUND_VARIABLE_21662) (not (forall ((M2 nat)) (not (forall ((X nat)) (or (not ((member_nat X) BOUND_VARIABLE_21662)) (= M2 X) ((ord_less_nat X) M2)))))))))) (let ((_let_662 (forall ((BOUND_VARIABLE_21651 set_nat_nat_nat) (BOUND_VARIABLE_21652 (-> (-> nat nat nat) Bool)) (BOUND_VARIABLE_21653 (-> nat nat nat))) (= (ll_167 BOUND_VARIABLE_21651 BOUND_VARIABLE_21652 BOUND_VARIABLE_21653) (and ((member_nat_nat_nat2 BOUND_VARIABLE_21653) BOUND_VARIABLE_21651) (BOUND_VARIABLE_21652 BOUND_VARIABLE_21653)))))) (let ((_let_663 (forall ((BOUND_VARIABLE_21630 set_nat_nat_nat) (BOUND_VARIABLE_21631 set_nat) (BOUND_VARIABLE_21632 (-> nat nat nat)) (BOUND_VARIABLE_21633 (-> nat nat nat nat))) (= (ll_166 BOUND_VARIABLE_21630 BOUND_VARIABLE_21631 BOUND_VARIABLE_21632 BOUND_VARIABLE_21633) (and (forall ((BOUND_VARIABLE_8781 nat)) (or (not ((member_nat BOUND_VARIABLE_8781) BOUND_VARIABLE_21631)) ((member_nat_nat_nat2 (BOUND_VARIABLE_21633 BOUND_VARIABLE_8781)) BOUND_VARIABLE_21630))) (forall ((BOUND_VARIABLE_8792 nat)) (or ((member_nat BOUND_VARIABLE_8792) BOUND_VARIABLE_21631) (= BOUND_VARIABLE_21632 (BOUND_VARIABLE_21633 BOUND_VARIABLE_8792))))))))) (let ((_let_664 (forall ((BOUND_VARIABLE_21623 nat) (BOUND_VARIABLE_21624 nat)) (= (ll_165 BOUND_VARIABLE_21623 BOUND_VARIABLE_21624) (= BOUND_VARIABLE_21623 BOUND_VARIABLE_21624))))) (let ((_let_665 (forall ((BOUND_VARIABLE_21609 nat) (BOUND_VARIABLE_21610 nat)) (let ((_let_1 (= BOUND_VARIABLE_21609 BOUND_VARIABLE_21610))) (= (ll_164 BOUND_VARIABLE_21609 BOUND_VARIABLE_21610) (and (or _let_1 ((ord_less_nat BOUND_VARIABLE_21610) BOUND_VARIABLE_21609)) (or _let_1 ((ord_less_nat BOUND_VARIABLE_21609) BOUND_VARIABLE_21610)))))))) (let ((_let_666 (forall ((BOUND_VARIABLE_21602 set_nat_nat) (BOUND_VARIABLE_21603 set_nat_nat)) (= (ll_163 BOUND_VARIABLE_21602 BOUND_VARIABLE_21603) (= BOUND_VARIABLE_21602 BOUND_VARIABLE_21603))))) (let ((_let_667 (forall ((BOUND_VARIABLE_21588 set_nat_nat) (BOUND_VARIABLE_21589 set_nat_nat)) (let ((_let_1 (= BOUND_VARIABLE_21588 BOUND_VARIABLE_21589))) (= (ll_162 BOUND_VARIABLE_21588 BOUND_VARIABLE_21589) (and (or _let_1 ((ord_less_set_nat_nat BOUND_VARIABLE_21589) BOUND_VARIABLE_21588)) (or _let_1 ((ord_less_set_nat_nat BOUND_VARIABLE_21588) BOUND_VARIABLE_21589)))))))) (let ((_let_668 (forall ((BOUND_VARIABLE_21575 (-> nat nat)) (BOUND_VARIABLE_21576 set_nat) (BOUND_VARIABLE_21577 nat)) (= (ll_161 BOUND_VARIABLE_21575 BOUND_VARIABLE_21576 BOUND_VARIABLE_21577) (and (not (= zero_zero_nat (BOUND_VARIABLE_21575 BOUND_VARIABLE_21577))) ((member_nat BOUND_VARIABLE_21577) BOUND_VARIABLE_21576)))))) (let ((_let_669 (forall ((BOUND_VARIABLE_21562 (-> nat nat)) (BOUND_VARIABLE_21563 set_nat) (BOUND_VARIABLE_21564 nat)) (= (ll_160 BOUND_VARIABLE_21562 BOUND_VARIABLE_21563 BOUND_VARIABLE_21564) (and (not (= zero_zero_nat (BOUND_VARIABLE_21562 BOUND_VARIABLE_21564))) ((member_nat BOUND_VARIABLE_21564) BOUND_VARIABLE_21563)))))) (let ((_let_670 (forall ((BOUND_VARIABLE_21545 (-> nat nat)) (BOUND_VARIABLE_21546 (-> nat nat)) (BOUND_VARIABLE_21547 set_nat) (BOUND_VARIABLE_21548 nat)) (= (ll_159 BOUND_VARIABLE_21545 BOUND_VARIABLE_21546 BOUND_VARIABLE_21547 BOUND_VARIABLE_21548) (and (not (= zero_zero_nat ((plus_plus_nat (BOUND_VARIABLE_21545 BOUND_VARIABLE_21548)) (BOUND_VARIABLE_21546 BOUND_VARIABLE_21548)))) ((member_nat BOUND_VARIABLE_21548) BOUND_VARIABLE_21547)))))) (let ((_let_671 (forall ((BOUND_VARIABLE_21537 set_nat) (BOUND_VARIABLE_21538 nat)) (= (ll_158 BOUND_VARIABLE_21537 BOUND_VARIABLE_21538) ((member_nat BOUND_VARIABLE_21538) BOUND_VARIABLE_21537))))) (let ((_let_672 (forall ((BOUND_VARIABLE_21529 set_nat) (BOUND_VARIABLE_21530 nat)) (= (ll_157 BOUND_VARIABLE_21529 BOUND_VARIABLE_21530) ((member_nat BOUND_VARIABLE_21530) BOUND_VARIABLE_21529))))) (let ((_let_673 (forall ((BOUND_VARIABLE_21518 set_nat_nat_nat2) (BOUND_VARIABLE_21519 (-> (-> (-> nat nat) nat) Bool)) (BOUND_VARIABLE_21520 (-> (-> nat nat) nat))) (= (ll_156 BOUND_VARIABLE_21518 BOUND_VARIABLE_21519 BOUND_VARIABLE_21520) (and ((member_nat_nat_nat BOUND_VARIABLE_21520) BOUND_VARIABLE_21518) (BOUND_VARIABLE_21519 BOUND_VARIABLE_21520)))))) (let ((_let_674 (forall ((BOUND_VARIABLE_21507 set_nat_nat) (BOUND_VARIABLE_21508 (-> (-> nat nat) Bool)) (BOUND_VARIABLE_21509 (-> nat nat))) (= (ll_155 BOUND_VARIABLE_21507 BOUND_VARIABLE_21508 BOUND_VARIABLE_21509) (and ((member_nat_nat BOUND_VARIABLE_21509) BOUND_VARIABLE_21507) (BOUND_VARIABLE_21508 BOUND_VARIABLE_21509)))))) (let ((_let_675 (forall ((BOUND_VARIABLE_21498 (-> nat Bool)) (BOUND_VARIABLE_21499 nat)) (= (ll_154 BOUND_VARIABLE_21498 BOUND_VARIABLE_21499) ((member_nat BOUND_VARIABLE_21499) (collect_nat BOUND_VARIABLE_21498)))))) (let ((_let_676 (forall ((BOUND_VARIABLE_21489 (-> nat Bool)) (BOUND_VARIABLE_21490 nat)) (= (ll_153 BOUND_VARIABLE_21489 BOUND_VARIABLE_21490) ((member_nat BOUND_VARIABLE_21490) (collect_nat BOUND_VARIABLE_21489)))))) (let ((_let_677 (forall ((BOUND_VARIABLE_21481 set_nat) (BOUND_VARIABLE_21482 nat)) (= (ll_152 BOUND_VARIABLE_21481 BOUND_VARIABLE_21482) ((member_nat BOUND_VARIABLE_21482) BOUND_VARIABLE_21481))))) (let ((_let_678 (forall ((BOUND_VARIABLE_21469 nat) (BOUND_VARIABLE_21470 nat)) (= (ll_151 BOUND_VARIABLE_21469 BOUND_VARIABLE_21470) (not (forall ((C2 nat)) (not (= BOUND_VARIABLE_21470 ((plus_plus_nat BOUND_VARIABLE_21469) C2))))))))) (let ((_let_679 (forall ((BOUND_VARIABLE_21458 set_nat) (BOUND_VARIABLE_21459 set_nat)) (= (ll_150 BOUND_VARIABLE_21458 BOUND_VARIABLE_21459) (forall ((T2 nat)) (let ((_let_1 (member_nat T2))) (or (not (_let_1 BOUND_VARIABLE_21458)) (_let_1 BOUND_VARIABLE_21459)))))))) (let ((_let_680 (forall ((BOUND_VARIABLE_21448 nat) (BOUND_VARIABLE_21449 nat)) (= (ll_149 BOUND_VARIABLE_21448 BOUND_VARIABLE_21449) (or ((ord_less_nat BOUND_VARIABLE_21448) BOUND_VARIABLE_21449) (= BOUND_VARIABLE_21448 BOUND_VARIABLE_21449)))))) (let ((_let_681 (forall ((BOUND_VARIABLE_21438 set_nat_nat) (BOUND_VARIABLE_21439 set_nat_nat)) (= (ll_148 BOUND_VARIABLE_21438 BOUND_VARIABLE_21439) (or (= BOUND_VARIABLE_21438 BOUND_VARIABLE_21439) ((ord_less_set_nat_nat BOUND_VARIABLE_21439) BOUND_VARIABLE_21438)))))) (let ((_let_682 (forall ((BOUND_VARIABLE_21426 nat) (BOUND_VARIABLE_21427 nat)) (= (ll_147 BOUND_VARIABLE_21426 BOUND_VARIABLE_21427) (not (forall ((K2 nat)) (not (= BOUND_VARIABLE_21427 ((plus_plus_nat BOUND_VARIABLE_21426) K2))))))))) (let ((_let_683 (forall ((BOUND_VARIABLE_21403 nat) (BOUND_VARIABLE_21404 nat) (BOUND_VARIABLE_21405 (-> nat nat))) (= (ll_146 BOUND_VARIABLE_21403 BOUND_VARIABLE_21404 BOUND_VARIABLE_21405) (and (forall ((I nat)) (let ((_let_1 (BOUND_VARIABLE_21405 I))) (or (= BOUND_VARIABLE_21403 _let_1) ((ord_less_nat _let_1) BOUND_VARIABLE_21403)))) (= zero_zero_nat (BOUND_VARIABLE_21405 BOUND_VARIABLE_21404)) (forall ((BOUND_VARIABLE_14242 nat)) (or (not ((ord_less_nat BOUND_VARIABLE_21404) BOUND_VARIABLE_14242)) (= zero_zero_nat (BOUND_VARIABLE_21405 BOUND_VARIABLE_14242))))))))) (let ((_let_684 (forall ((BOUND_VARIABLE_21393 (-> (-> (-> nat nat) nat) Bool)) (BOUND_VARIABLE_21394 (-> (-> (-> nat nat) nat) Bool)) (BOUND_VARIABLE_21395 (-> (-> nat nat) nat))) (= (ll_145 BOUND_VARIABLE_21393 BOUND_VARIABLE_21394 BOUND_VARIABLE_21395) (and (BOUND_VARIABLE_21393 BOUND_VARIABLE_21395) (BOUND_VARIABLE_21394 BOUND_VARIABLE_21395)))))) (let ((_let_685 (forall ((BOUND_VARIABLE_21381 nat) (BOUND_VARIABLE_21382 nat)) (let ((_let_1 (= BOUND_VARIABLE_21381 BOUND_VARIABLE_21382))) (= (ll_144 BOUND_VARIABLE_21381 BOUND_VARIABLE_21382) (and (or _let_1 ((ord_less_nat BOUND_VARIABLE_21381) BOUND_VARIABLE_21382)) (not _let_1))))))) (let ((_let_686 (forall ((BOUND_VARIABLE_21371 (-> nat Bool)) (BOUND_VARIABLE_21372 (-> nat Bool)) (BOUND_VARIABLE_21373 nat)) (= (ll_143 BOUND_VARIABLE_21371 BOUND_VARIABLE_21372 BOUND_VARIABLE_21373) (or (BOUND_VARIABLE_21371 BOUND_VARIABLE_21373) (BOUND_VARIABLE_21372 BOUND_VARIABLE_21373)))))) (let ((_let_687 (forall ((BOUND_VARIABLE_21363 set_nat) (BOUND_VARIABLE_21364 nat)) (= (ll_142 BOUND_VARIABLE_21363 BOUND_VARIABLE_21364) ((member_nat BOUND_VARIABLE_21364) BOUND_VARIABLE_21363))))) (let ((_let_688 (forall ((BOUND_VARIABLE_21355 set_nat) (BOUND_VARIABLE_21356 nat)) (= (ll_141 BOUND_VARIABLE_21355 BOUND_VARIABLE_21356) ((member_nat BOUND_VARIABLE_21356) BOUND_VARIABLE_21355))))) (let ((_let_689 (forall ((BOUND_VARIABLE_21347 set_nat) (BOUND_VARIABLE_21348 nat)) (= (ll_140 BOUND_VARIABLE_21347 BOUND_VARIABLE_21348) ((member_nat BOUND_VARIABLE_21348) BOUND_VARIABLE_21347))))) (let ((_let_690 (forall ((BOUND_VARIABLE_21339 set_nat) (BOUND_VARIABLE_21340 nat)) (= (ll_139 BOUND_VARIABLE_21339 BOUND_VARIABLE_21340) ((member_nat BOUND_VARIABLE_21340) BOUND_VARIABLE_21339))))) (let ((_let_691 (forall ((BOUND_VARIABLE_21326 (-> (-> nat nat) (-> nat nat) Bool)) (BOUND_VARIABLE_21327 (-> nat nat)) (BOUND_VARIABLE_21328 set_nat_nat) (BOUND_VARIABLE_21329 (-> nat nat))) (= (ll_138 BOUND_VARIABLE_21326 BOUND_VARIABLE_21327 BOUND_VARIABLE_21328 BOUND_VARIABLE_21329) (and ((BOUND_VARIABLE_21326 BOUND_VARIABLE_21329) BOUND_VARIABLE_21327) ((member_nat_nat BOUND_VARIABLE_21329) BOUND_VARIABLE_21328)))))) (let ((_let_692 (forall ((BOUND_VARIABLE_21315 set_nat_nat_nat_nat3) (BOUND_VARIABLE_21316 (-> (-> (-> nat nat) nat nat) Bool)) (BOUND_VARIABLE_21317 (-> (-> nat nat) nat nat))) (= (ll_137 BOUND_VARIABLE_21315 BOUND_VARIABLE_21316 BOUND_VARIABLE_21317) (and ((member1128122036at_nat BOUND_VARIABLE_21317) BOUND_VARIABLE_21315) (BOUND_VARIABLE_21316 BOUND_VARIABLE_21317)))))) (let ((_let_693 (forall ((BOUND_VARIABLE_21294 (-> (-> nat nat) nat)) (BOUND_VARIABLE_21295 set_nat) (BOUND_VARIABLE_21296 set_nat_nat_nat2) (BOUND_VARIABLE_21297 (-> nat (-> nat nat) nat))) (= (ll_136 BOUND_VARIABLE_21294 BOUND_VARIABLE_21295 BOUND_VARIABLE_21296 BOUND_VARIABLE_21297) (and (forall ((BOUND_VARIABLE_8260 nat)) (or ((member_nat BOUND_VARIABLE_8260) BOUND_VARIABLE_21295) (= BOUND_VARIABLE_21294 (BOUND_VARIABLE_21297 BOUND_VARIABLE_8260)))) (forall ((BOUND_VARIABLE_8269 nat)) (or (not ((member_nat BOUND_VARIABLE_8269) BOUND_VARIABLE_21295)) ((member_nat_nat_nat (BOUND_VARIABLE_21297 BOUND_VARIABLE_8269)) BOUND_VARIABLE_21296)))))))) (let ((_let_694 (forall ((BOUND_VARIABLE_21287 (-> nat nat))) (= (ll_135 BOUND_VARIABLE_21287) ((number1551313001itions BOUND_VARIABLE_21287) n))))) (let ((_let_695 (forall ((BOUND_VARIABLE_21259 set_nat) (BOUND_VARIABLE_21260 set_nat)) (= (ll_134 BOUND_VARIABLE_21259 BOUND_VARIABLE_21260) ((ord_less_eq_nat_o (ll_185 BOUND_VARIABLE_21259)) (ll_184 BOUND_VARIABLE_21260)))))) (let ((_let_696 (forall ((BOUND_VARIABLE_21248 set_nat) (BOUND_VARIABLE_21249 set_nat)) (= (ll_133 BOUND_VARIABLE_21248 BOUND_VARIABLE_21249) (forall ((X nat)) (let ((_let_1 (member_nat X))) (or (not (_let_1 BOUND_VARIABLE_21248)) (_let_1 BOUND_VARIABLE_21249)))))))) (let ((_let_697 (forall ((BOUND_VARIABLE_21237 set_nat_nat) (BOUND_VARIABLE_21238 (-> (-> nat nat) Bool)) (BOUND_VARIABLE_21239 (-> nat nat))) (= (ll_132 BOUND_VARIABLE_21237 BOUND_VARIABLE_21238 BOUND_VARIABLE_21239) (and ((member_nat_nat BOUND_VARIABLE_21239) BOUND_VARIABLE_21237) (BOUND_VARIABLE_21238 BOUND_VARIABLE_21239)))))) (let ((_let_698 (forall ((BOUND_VARIABLE_21226 set_nat_nat) (BOUND_VARIABLE_21227 (-> (-> nat nat) Bool)) (BOUND_VARIABLE_21228 (-> nat nat))) (= (ll_131 BOUND_VARIABLE_21226 BOUND_VARIABLE_21227 BOUND_VARIABLE_21228) (and ((member_nat_nat BOUND_VARIABLE_21228) BOUND_VARIABLE_21226) (BOUND_VARIABLE_21227 BOUND_VARIABLE_21228)))))) (let ((_let_699 (forall ((BOUND_VARIABLE_21216 (-> (-> nat nat nat) Bool)) (BOUND_VARIABLE_21217 (-> (-> nat nat nat) Bool)) (BOUND_VARIABLE_21218 (-> nat nat nat))) (= (ll_130 BOUND_VARIABLE_21216 BOUND_VARIABLE_21217 BOUND_VARIABLE_21218) (and (BOUND_VARIABLE_21216 BOUND_VARIABLE_21218) (BOUND_VARIABLE_21217 BOUND_VARIABLE_21218)))))) (let ((_let_700 (forall ((BOUND_VARIABLE_21207 (-> nat Bool)) (BOUND_VARIABLE_21208 nat)) (= (ll_129 BOUND_VARIABLE_21207 BOUND_VARIABLE_21208) ((member_nat BOUND_VARIABLE_21208) (collect_nat BOUND_VARIABLE_21207)))))) (let ((_let_701 (forall ((BOUND_VARIABLE_21198 (-> nat Bool)) (BOUND_VARIABLE_21199 nat)) (= (ll_128 BOUND_VARIABLE_21198 BOUND_VARIABLE_21199) ((member_nat BOUND_VARIABLE_21199) (collect_nat BOUND_VARIABLE_21198)))))) (let ((_let_702 (forall ((BOUND_VARIABLE_21185 set_nat_nat) (BOUND_VARIABLE_21186 (-> (-> nat nat) nat)) (BOUND_VARIABLE_21187 (-> nat nat))) (= (ll_127 BOUND_VARIABLE_21185 BOUND_VARIABLE_21186 BOUND_VARIABLE_21187) (and ((member_nat_nat BOUND_VARIABLE_21187) BOUND_VARIABLE_21185) (not (= zero_zero_nat (BOUND_VARIABLE_21186 BOUND_VARIABLE_21187)))))))) (let ((_let_703 (forall ((BOUND_VARIABLE_21172 set_nat_nat) (BOUND_VARIABLE_21173 (-> (-> nat nat) nat)) (BOUND_VARIABLE_21174 (-> nat nat))) (= (ll_126 BOUND_VARIABLE_21172 BOUND_VARIABLE_21173 BOUND_VARIABLE_21174) (and ((member_nat_nat BOUND_VARIABLE_21174) BOUND_VARIABLE_21172) (not (= zero_zero_nat (BOUND_VARIABLE_21173 BOUND_VARIABLE_21174)))))))) (let ((_let_704 (forall ((BOUND_VARIABLE_21155 set_nat_nat) (BOUND_VARIABLE_21156 (-> (-> nat nat) nat)) (BOUND_VARIABLE_21157 (-> (-> nat nat) nat)) (BOUND_VARIABLE_21158 (-> nat nat))) (= (ll_125 BOUND_VARIABLE_21155 BOUND_VARIABLE_21156 BOUND_VARIABLE_21157 BOUND_VARIABLE_21158) (and ((member_nat_nat BOUND_VARIABLE_21158) BOUND_VARIABLE_21155) (not (= zero_zero_nat ((plus_plus_nat (BOUND_VARIABLE_21156 BOUND_VARIABLE_21158)) (BOUND_VARIABLE_21157 BOUND_VARIABLE_21158))))))))) (let ((_let_705 (forall ((BOUND_VARIABLE_21143 set_nat_nat) (BOUND_VARIABLE_21144 set_nat_nat)) (let ((_let_1 (= BOUND_VARIABLE_21143 BOUND_VARIABLE_21144))) (= (ll_124 BOUND_VARIABLE_21143 BOUND_VARIABLE_21144) (and (or _let_1 ((ord_less_set_nat_nat BOUND_VARIABLE_21143) BOUND_VARIABLE_21144)) (not _let_1))))))) (let ((_let_706 (forall ((BOUND_VARIABLE_21132 (-> (-> nat nat nat) Bool)) (BOUND_VARIABLE_21133 set_nat_nat_nat) (BOUND_VARIABLE_21134 (-> nat nat nat))) (= (ll_123 BOUND_VARIABLE_21132 BOUND_VARIABLE_21133 BOUND_VARIABLE_21134) (and (BOUND_VARIABLE_21132 BOUND_VARIABLE_21134) ((member_nat_nat_nat2 BOUND_VARIABLE_21134) BOUND_VARIABLE_21133)))))) (let ((_let_707 (forall ((BOUND_VARIABLE_21111 set_nat) (BOUND_VARIABLE_21112 set_nat) (BOUND_VARIABLE_21113 nat) (BOUND_VARIABLE_21114 (-> nat nat))) (= (ll_122 BOUND_VARIABLE_21111 BOUND_VARIABLE_21112 BOUND_VARIABLE_21113 BOUND_VARIABLE_21114) (and (forall ((BOUND_VARIABLE_8077 nat)) (or (not ((member_nat BOUND_VARIABLE_8077) BOUND_VARIABLE_21112)) ((member_nat (BOUND_VARIABLE_21114 BOUND_VARIABLE_8077)) BOUND_VARIABLE_21111))) (forall ((BOUND_VARIABLE_8088 nat)) (or ((member_nat BOUND_VARIABLE_8088) BOUND_VARIABLE_21112) (= BOUND_VARIABLE_21113 (BOUND_VARIABLE_21114 BOUND_VARIABLE_8088))))))))) (let ((_let_708 (forall ((BOUND_VARIABLE_21098 (-> nat (-> nat nat nat) Bool)) (BOUND_VARIABLE_21099 (-> nat nat nat)) (BOUND_VARIABLE_21100 set_nat) (BOUND_VARIABLE_21101 nat)) (= (ll_121 BOUND_VARIABLE_21098 BOUND_VARIABLE_21099 BOUND_VARIABLE_21100 BOUND_VARIABLE_21101) (and ((BOUND_VARIABLE_21098 BOUND_VARIABLE_21101) BOUND_VARIABLE_21099) ((member_nat BOUND_VARIABLE_21101) BOUND_VARIABLE_21100)))))) (let ((_let_709 (forall ((BOUND_VARIABLE_21090 set_nat) (BOUND_VARIABLE_21091 nat)) (= (ll_120 BOUND_VARIABLE_21090 BOUND_VARIABLE_21091) ((member_nat BOUND_VARIABLE_21091) BOUND_VARIABLE_21090))))) (let ((_let_710 (forall ((BOUND_VARIABLE_21082 set_nat) (BOUND_VARIABLE_21083 nat)) (= (ll_119 BOUND_VARIABLE_21082 BOUND_VARIABLE_21083) ((member_nat BOUND_VARIABLE_21083) BOUND_VARIABLE_21082))))) (let ((_let_711 (forall ((BOUND_VARIABLE_21072 (-> nat Bool)) (BOUND_VARIABLE_21073 (-> nat Bool)) (BOUND_VARIABLE_21074 nat)) (= (ll_118 BOUND_VARIABLE_21072 BOUND_VARIABLE_21073 BOUND_VARIABLE_21074) (and (BOUND_VARIABLE_21072 BOUND_VARIABLE_21074) (BOUND_VARIABLE_21073 BOUND_VARIABLE_21074)))))) (let ((_let_712 (forall ((BOUND_VARIABLE_21064 set_nat_nat) (BOUND_VARIABLE_21065 (-> nat nat))) (= (ll_117 BOUND_VARIABLE_21064 BOUND_VARIABLE_21065) ((member_nat_nat BOUND_VARIABLE_21065) BOUND_VARIABLE_21064))))) (let ((_let_713 (forall ((BOUND_VARIABLE_21056 set_nat_nat) (BOUND_VARIABLE_21057 (-> nat nat))) (= (ll_116 BOUND_VARIABLE_21056 BOUND_VARIABLE_21057) ((member_nat_nat BOUND_VARIABLE_21057) BOUND_VARIABLE_21056))))) (let ((_let_714 (forall ((BOUND_VARIABLE_21046 nat) (BOUND_VARIABLE_21047 nat)) (= (ll_115 BOUND_VARIABLE_21046 BOUND_VARIABLE_21047) (or ((ord_less_nat BOUND_VARIABLE_21046) BOUND_VARIABLE_21047) (= BOUND_VARIABLE_21046 BOUND_VARIABLE_21047)))))) (let ((_let_715 (forall ((BOUND_VARIABLE_21036 nat) (BOUND_VARIABLE_21037 nat)) (= (ll_114 BOUND_VARIABLE_21036 BOUND_VARIABLE_21037) (or (= BOUND_VARIABLE_21036 BOUND_VARIABLE_21037) ((ord_less_nat BOUND_VARIABLE_21036) BOUND_VARIABLE_21037)))))) (let ((_let_716 (forall ((BOUND_VARIABLE_21023 set_nat) (BOUND_VARIABLE_21024 (-> nat nat Bool)) (BOUND_VARIABLE_21025 nat) (BOUND_VARIABLE_21026 nat)) (= (ll_113 BOUND_VARIABLE_21023 BOUND_VARIABLE_21024 BOUND_VARIABLE_21025 BOUND_VARIABLE_21026) (and ((member_nat BOUND_VARIABLE_21026) BOUND_VARIABLE_21023) ((BOUND_VARIABLE_21024 BOUND_VARIABLE_21026) BOUND_VARIABLE_21025)))))) (let ((_let_717 (forall ((BOUND_VARIABLE_21012 (-> (-> (-> nat nat) nat nat) Bool)) (BOUND_VARIABLE_21013 set_nat_nat_nat_nat3) (BOUND_VARIABLE_21014 (-> (-> nat nat) nat nat))) (= (ll_112 BOUND_VARIABLE_21012 BOUND_VARIABLE_21013 BOUND_VARIABLE_21014) (and (BOUND_VARIABLE_21012 BOUND_VARIABLE_21014) ((member1128122036at_nat BOUND_VARIABLE_21014) BOUND_VARIABLE_21013)))))) (let ((_let_718 (forall ((BOUND_VARIABLE_21002 nat) (BOUND_VARIABLE_21003 nat)) (= (ll_111 BOUND_VARIABLE_21002 BOUND_VARIABLE_21003) (or (= BOUND_VARIABLE_21002 BOUND_VARIABLE_21003) ((ord_less_nat BOUND_VARIABLE_21003) BOUND_VARIABLE_21002)))))) (let ((_let_719 (forall ((BOUND_VARIABLE_20994 set_nat) (BOUND_VARIABLE_20995 nat)) (= (ll_110 BOUND_VARIABLE_20994 BOUND_VARIABLE_20995) ((member_nat BOUND_VARIABLE_20995) BOUND_VARIABLE_20994))))) (let ((_let_720 (forall ((BOUND_VARIABLE_20986 set_nat) (BOUND_VARIABLE_20987 nat)) (= (ll_109 BOUND_VARIABLE_20986 BOUND_VARIABLE_20987) ((member_nat BOUND_VARIABLE_20987) BOUND_VARIABLE_20986))))) (let ((_let_721 (forall ((BOUND_VARIABLE_20958 (-> nat Bool)) (BOUND_VARIABLE_20959 set_nat) (BOUND_VARIABLE_20960 nat)) (= (ll_108 BOUND_VARIABLE_20958 BOUND_VARIABLE_20959 BOUND_VARIABLE_20960) ((member_nat BOUND_VARIABLE_20960) (collect_nat ((ll_183 BOUND_VARIABLE_20958) BOUND_VARIABLE_20959))))))) (let ((_let_722 (forall ((BOUND_VARIABLE_20930 (-> nat Bool)) (BOUND_VARIABLE_20931 set_nat) (BOUND_VARIABLE_20932 nat)) (= (ll_107 BOUND_VARIABLE_20930 BOUND_VARIABLE_20931 BOUND_VARIABLE_20932) ((member_nat BOUND_VARIABLE_20932) (collect_nat ((ll_182 BOUND_VARIABLE_20930) BOUND_VARIABLE_20931))))))) (let ((_let_723 (forall ((BOUND_VARIABLE_20922 set_nat_nat_nat2) (BOUND_VARIABLE_20923 set_nat_nat_nat2)) (= (ll_106 BOUND_VARIABLE_20922 BOUND_VARIABLE_20923) ((ord_le633272388at_nat BOUND_VARIABLE_20923) BOUND_VARIABLE_20922))))) (let ((_let_724 (forall ((BOUND_VARIABLE_20914 set_nat_nat) (BOUND_VARIABLE_20915 (-> nat nat))) (= (ll_105 BOUND_VARIABLE_20914 BOUND_VARIABLE_20915) ((member_nat_nat BOUND_VARIABLE_20915) BOUND_VARIABLE_20914))))) (let ((_let_725 (forall ((BOUND_VARIABLE_20906 set_nat_nat_nat) (BOUND_VARIABLE_20907 (-> nat nat nat))) (= (ll_104 BOUND_VARIABLE_20906 BOUND_VARIABLE_20907) ((member_nat_nat_nat2 BOUND_VARIABLE_20907) BOUND_VARIABLE_20906))))) (let ((_let_726 (forall ((BOUND_VARIABLE_20878 set_nat_nat) (BOUND_VARIABLE_20879 set_nat_nat)) (= (ll_103 BOUND_VARIABLE_20878 BOUND_VARIABLE_20879) ((ord_le2026740592_nat_o (ll_181 BOUND_VARIABLE_20878)) (ll_180 BOUND_VARIABLE_20879)))))) (let ((_let_727 (forall ((BOUND_VARIABLE_20867 set_nat_nat) (BOUND_VARIABLE_20868 set_nat_nat)) (= (ll_102 BOUND_VARIABLE_20867 BOUND_VARIABLE_20868) (forall ((X (-> nat nat))) (let ((_let_1 (member_nat_nat X))) (or (not (_let_1 BOUND_VARIABLE_20867)) (_let_1 BOUND_VARIABLE_20868)))))))) (let ((_let_728 (forall ((BOUND_VARIABLE_20859 set_nat) (BOUND_VARIABLE_20860 nat)) (= (ll_101 BOUND_VARIABLE_20859 BOUND_VARIABLE_20860) ((member_nat BOUND_VARIABLE_20860) BOUND_VARIABLE_20859))))) (let ((_let_729 (forall ((BOUND_VARIABLE_20831 set_nat) (BOUND_VARIABLE_20832 (-> nat Bool)) (BOUND_VARIABLE_20833 nat)) (= (ll_100 BOUND_VARIABLE_20831 BOUND_VARIABLE_20832 BOUND_VARIABLE_20833) ((member_nat BOUND_VARIABLE_20833) (collect_nat ((ll_179 BOUND_VARIABLE_20831) BOUND_VARIABLE_20832))))))) (let ((_let_730 (forall ((BOUND_VARIABLE_20820 (-> (-> (-> nat nat) nat) Bool)) (BOUND_VARIABLE_20821 set_nat_nat_nat2) (BOUND_VARIABLE_20822 (-> (-> nat nat) nat))) (= (ll_99 BOUND_VARIABLE_20820 BOUND_VARIABLE_20821 BOUND_VARIABLE_20822) (and (BOUND_VARIABLE_20820 BOUND_VARIABLE_20822) ((member_nat_nat_nat BOUND_VARIABLE_20822) BOUND_VARIABLE_20821)))))) (let ((_let_731 (forall ((BOUND_VARIABLE_20809 set_nat_nat_nat2) (BOUND_VARIABLE_20810 (-> (-> (-> nat nat) nat) Bool)) (BOUND_VARIABLE_20811 (-> (-> nat nat) nat))) (= (ll_98 BOUND_VARIABLE_20809 BOUND_VARIABLE_20810 BOUND_VARIABLE_20811) (and ((member_nat_nat_nat BOUND_VARIABLE_20811) BOUND_VARIABLE_20809) (BOUND_VARIABLE_20810 BOUND_VARIABLE_20811)))))) (let ((_let_732 (forall ((BOUND_VARIABLE_20802 (-> nat nat))) (= (ll_97 BOUND_VARIABLE_20802) ((number1551313001itions BOUND_VARIABLE_20802) n))))) (let ((_let_733 (forall ((BOUND_VARIABLE_20784 (-> nat nat))) (= (ll_96 BOUND_VARIABLE_20784) (and (forall ((I nat)) (let ((_let_1 (BOUND_VARIABLE_20784 I))) (or (= n _let_1) ((ord_less_nat _let_1) n)))) (= zero_zero_nat (BOUND_VARIABLE_20784 ((plus_plus_nat n) one_one_nat))) (forall ((BOUND_VARIABLE_12178 nat)) (or (not ((ord_less_nat ((plus_plus_nat n) one_one_nat)) BOUND_VARIABLE_12178)) (= zero_zero_nat (BOUND_VARIABLE_20784 BOUND_VARIABLE_12178))))))))) (let ((_let_734 (forall ((BOUND_VARIABLE_20771 (-> (-> nat nat nat) nat)) (BOUND_VARIABLE_20772 set_nat_nat_nat) (BOUND_VARIABLE_20773 (-> nat nat nat))) (= (ll_95 BOUND_VARIABLE_20771 BOUND_VARIABLE_20772 BOUND_VARIABLE_20773) (and (not (= zero_zero_nat (BOUND_VARIABLE_20771 BOUND_VARIABLE_20773))) ((member_nat_nat_nat2 BOUND_VARIABLE_20773) BOUND_VARIABLE_20772)))))) (let ((_let_735 (forall ((BOUND_VARIABLE_20758 set_nat_nat_nat) (BOUND_VARIABLE_20759 (-> (-> nat nat nat) nat)) (BOUND_VARIABLE_20760 (-> nat nat nat))) (= (ll_94 BOUND_VARIABLE_20758 BOUND_VARIABLE_20759 BOUND_VARIABLE_20760) (and ((member_nat_nat_nat2 BOUND_VARIABLE_20760) BOUND_VARIABLE_20758) (not (= zero_zero_nat (BOUND_VARIABLE_20759 BOUND_VARIABLE_20760)))))))) (let ((_let_736 (forall ((BOUND_VARIABLE_20741 set_nat_nat_nat) (BOUND_VARIABLE_20742 (-> (-> nat nat nat) nat)) (BOUND_VARIABLE_20743 (-> (-> nat nat nat) nat)) (BOUND_VARIABLE_20744 (-> nat nat nat))) (= (ll_93 BOUND_VARIABLE_20741 BOUND_VARIABLE_20742 BOUND_VARIABLE_20743 BOUND_VARIABLE_20744) (and ((member_nat_nat_nat2 BOUND_VARIABLE_20744) BOUND_VARIABLE_20741) (not (= zero_zero_nat ((plus_plus_nat (BOUND_VARIABLE_20742 BOUND_VARIABLE_20744)) (BOUND_VARIABLE_20743 BOUND_VARIABLE_20744))))))))) (let ((_let_737 (forall ((BOUND_VARIABLE_20733 set_nat) (BOUND_VARIABLE_20734 nat)) (= (ll_92 BOUND_VARIABLE_20733 BOUND_VARIABLE_20734) ((member_nat BOUND_VARIABLE_20734) BOUND_VARIABLE_20733))))) (let ((_let_738 (forall ((BOUND_VARIABLE_20725 set_nat) (BOUND_VARIABLE_20726 nat)) (= (ll_91 BOUND_VARIABLE_20725 BOUND_VARIABLE_20726) ((member_nat BOUND_VARIABLE_20726) BOUND_VARIABLE_20725))))) (let ((_let_739 (forall ((BOUND_VARIABLE_20717 set_nat_nat_nat_nat3) (BOUND_VARIABLE_20718 set_nat_nat_nat_nat3)) (= (ll_90 BOUND_VARIABLE_20717 BOUND_VARIABLE_20718) ((ord_le2040082867at_nat BOUND_VARIABLE_20718) BOUND_VARIABLE_20717))))) (let ((_let_740 (forall ((BOUND_VARIABLE_20696 (-> nat nat nat)) (BOUND_VARIABLE_20697 set_nat_nat) (BOUND_VARIABLE_20698 set_nat_nat_nat) (BOUND_VARIABLE_20699 (-> (-> nat nat) nat nat nat))) (= (ll_89 BOUND_VARIABLE_20696 BOUND_VARIABLE_20697 BOUND_VARIABLE_20698 BOUND_VARIABLE_20699) (and (forall ((BOUND_VARIABLE_7497 (-> nat nat))) (or ((member_nat_nat BOUND_VARIABLE_7497) BOUND_VARIABLE_20697) (= BOUND_VARIABLE_20696 (BOUND_VARIABLE_20699 BOUND_VARIABLE_7497)))) (forall ((BOUND_VARIABLE_7506 (-> nat nat))) (or (not ((member_nat_nat BOUND_VARIABLE_7506) BOUND_VARIABLE_20697)) ((member_nat_nat_nat2 (BOUND_VARIABLE_20699 BOUND_VARIABLE_7506)) BOUND_VARIABLE_20698)))))))) (let ((_let_741 (forall ((BOUND_VARIABLE_20686 set_nat_nat) (BOUND_VARIABLE_20687 set_nat_nat)) (= (ll_88 BOUND_VARIABLE_20686 BOUND_VARIABLE_20687) (or ((ord_less_set_nat_nat BOUND_VARIABLE_20686) BOUND_VARIABLE_20687) (= BOUND_VARIABLE_20686 BOUND_VARIABLE_20687)))))) (let ((_let_742 (forall ((BOUND_VARIABLE_20676 (-> (-> nat nat) Bool)) (BOUND_VARIABLE_20677 (-> (-> nat nat) Bool)) (BOUND_VARIABLE_20678 (-> nat nat))) (= (ll_87 BOUND_VARIABLE_20676 BOUND_VARIABLE_20677 BOUND_VARIABLE_20678) (and (BOUND_VARIABLE_20676 BOUND_VARIABLE_20678) (BOUND_VARIABLE_20677 BOUND_VARIABLE_20678)))))) (let ((_let_743 (forall ((BOUND_VARIABLE_20668 set_nat) (BOUND_VARIABLE_20669 nat)) (= (ll_86 BOUND_VARIABLE_20668 BOUND_VARIABLE_20669) ((member_nat BOUND_VARIABLE_20669) BOUND_VARIABLE_20668))))) (let ((_let_744 (forall ((BOUND_VARIABLE_20660 set_nat) (BOUND_VARIABLE_20661 nat)) (= (ll_85 BOUND_VARIABLE_20660 BOUND_VARIABLE_20661) ((member_nat BOUND_VARIABLE_20661) BOUND_VARIABLE_20660))))) (let ((_let_745 (forall ((BOUND_VARIABLE_20650 (-> (-> nat nat nat) Bool)) (BOUND_VARIABLE_20651 (-> (-> nat nat nat) Bool)) (BOUND_VARIABLE_20652 (-> nat nat nat))) (= (ll_84 BOUND_VARIABLE_20650 BOUND_VARIABLE_20651 BOUND_VARIABLE_20652) (or (BOUND_VARIABLE_20650 BOUND_VARIABLE_20652) (BOUND_VARIABLE_20651 BOUND_VARIABLE_20652)))))) (let ((_let_746 (forall ((BOUND_VARIABLE_20642 (-> nat nat)) (BOUND_VARIABLE_20643 nat)) (= (ll_83 BOUND_VARIABLE_20642 BOUND_VARIABLE_20643) ((ord_less_nat zero_zero_nat) (BOUND_VARIABLE_20642 BOUND_VARIABLE_20643)))))) (let ((_let_747 (forall ((BOUND_VARIABLE_20629 set_nat_nat_nat_nat3) (BOUND_VARIABLE_20630 (-> (-> (-> nat nat) nat nat) nat)) (BOUND_VARIABLE_20631 (-> (-> nat nat) nat nat))) (= (ll_82 BOUND_VARIABLE_20629 BOUND_VARIABLE_20630 BOUND_VARIABLE_20631) (and ((member1128122036at_nat BOUND_VARIABLE_20631) BOUND_VARIABLE_20629) (not (= zero_zero_nat (BOUND_VARIABLE_20630 BOUND_VARIABLE_20631)))))))) (let ((_let_748 (forall ((BOUND_VARIABLE_20616 (-> (-> (-> nat nat) nat nat) nat)) (BOUND_VARIABLE_20617 set_nat_nat_nat_nat3) (BOUND_VARIABLE_20618 (-> (-> nat nat) nat nat))) (= (ll_81 BOUND_VARIABLE_20616 BOUND_VARIABLE_20617 BOUND_VARIABLE_20618) (and (not (= zero_zero_nat (BOUND_VARIABLE_20616 BOUND_VARIABLE_20618))) ((member1128122036at_nat BOUND_VARIABLE_20618) BOUND_VARIABLE_20617)))))) (let ((_let_749 (forall ((BOUND_VARIABLE_20599 (-> (-> (-> nat nat) nat nat) nat)) (BOUND_VARIABLE_20600 (-> (-> (-> nat nat) nat nat) nat)) (BOUND_VARIABLE_20601 set_nat_nat_nat_nat3) (BOUND_VARIABLE_20602 (-> (-> nat nat) nat nat))) (= (ll_80 BOUND_VARIABLE_20599 BOUND_VARIABLE_20600 BOUND_VARIABLE_20601 BOUND_VARIABLE_20602) (and (not (= zero_zero_nat ((plus_plus_nat (BOUND_VARIABLE_20599 BOUND_VARIABLE_20602)) (BOUND_VARIABLE_20600 BOUND_VARIABLE_20602)))) ((member1128122036at_nat BOUND_VARIABLE_20602) BOUND_VARIABLE_20601)))))) (let ((_let_750 (forall ((BOUND_VARIABLE_20586 (-> (-> nat nat nat) nat Bool)) (BOUND_VARIABLE_20587 nat) (BOUND_VARIABLE_20588 set_nat_nat_nat) (BOUND_VARIABLE_20589 (-> nat nat nat))) (= (ll_79 BOUND_VARIABLE_20586 BOUND_VARIABLE_20587 BOUND_VARIABLE_20588 BOUND_VARIABLE_20589) (and ((BOUND_VARIABLE_20586 BOUND_VARIABLE_20589) BOUND_VARIABLE_20587) ((member_nat_nat_nat2 BOUND_VARIABLE_20589) BOUND_VARIABLE_20588)))))) (let ((_let_751 (forall ((BOUND_VARIABLE_20578 nat) (BOUND_VARIABLE_20579 nat)) (= ((plus_plus_nat BOUND_VARIABLE_20579) BOUND_VARIABLE_20578) (ll_78 BOUND_VARIABLE_20578 BOUND_VARIABLE_20579))))) (let ((_let_752 (forall ((BOUND_VARIABLE_20557 nat) (BOUND_VARIABLE_20558 set_nat_nat_nat2) (BOUND_VARIABLE_20559 set_nat) (BOUND_VARIABLE_20560 (-> (-> (-> nat nat) nat) nat))) (= (ll_77 BOUND_VARIABLE_20557 BOUND_VARIABLE_20558 BOUND_VARIABLE_20559 BOUND_VARIABLE_20560) (and (forall ((BOUND_VARIABLE_7227 (-> (-> nat nat) nat))) (or ((member_nat_nat_nat BOUND_VARIABLE_7227) BOUND_VARIABLE_20558) (= BOUND_VARIABLE_20557 (BOUND_VARIABLE_20560 BOUND_VARIABLE_7227)))) (forall ((BOUND_VARIABLE_7236 (-> (-> nat nat) nat))) (or (not ((member_nat_nat_nat BOUND_VARIABLE_7236) BOUND_VARIABLE_20558)) ((member_nat (BOUND_VARIABLE_20560 BOUND_VARIABLE_7236)) BOUND_VARIABLE_20559)))))))) (let ((_let_753 (forall ((BOUND_VARIABLE_20546 (-> nat Bool)) (BOUND_VARIABLE_20547 nat) (BOUND_VARIABLE_20548 nat)) (= (ll_76 BOUND_VARIABLE_20546 BOUND_VARIABLE_20547 BOUND_VARIABLE_20548) (and (BOUND_VARIABLE_20546 BOUND_VARIABLE_20548) ((ord_less_nat BOUND_VARIABLE_20548) BOUND_VARIABLE_20547)))))) (let ((_let_754 (forall ((BOUND_VARIABLE_20538 set_nat) (BOUND_VARIABLE_20539 nat)) (= (ll_75 BOUND_VARIABLE_20538 BOUND_VARIABLE_20539) ((member_nat BOUND_VARIABLE_20539) BOUND_VARIABLE_20538))))) (let ((_let_755 (forall ((BOUND_VARIABLE_20530 set_nat) (BOUND_VARIABLE_20531 nat)) (= (ll_74 BOUND_VARIABLE_20530 BOUND_VARIABLE_20531) ((member_nat BOUND_VARIABLE_20531) BOUND_VARIABLE_20530))))) (let ((_let_756 (forall ((BOUND_VARIABLE_20518 nat) (BOUND_VARIABLE_20519 nat)) (let ((_let_1 (= BOUND_VARIABLE_20518 BOUND_VARIABLE_20519))) (= (ll_73 BOUND_VARIABLE_20518 BOUND_VARIABLE_20519) (and (or _let_1 ((ord_less_nat BOUND_VARIABLE_20518) BOUND_VARIABLE_20519)) (not _let_1))))))) (let ((_let_757 (forall ((BOUND_VARIABLE_20508 (-> (-> (-> nat nat) nat nat) Bool)) (BOUND_VARIABLE_20509 (-> (-> (-> nat nat) nat nat) Bool)) (BOUND_VARIABLE_20510 (-> (-> nat nat) nat nat))) (= (ll_72 BOUND_VARIABLE_20508 BOUND_VARIABLE_20509 BOUND_VARIABLE_20510) (or (BOUND_VARIABLE_20508 BOUND_VARIABLE_20510) (BOUND_VARIABLE_20509 BOUND_VARIABLE_20510)))))) (let ((_let_758 (forall ((BOUND_VARIABLE_20501 set_nat_nat) (BOUND_VARIABLE_20502 set_nat_nat)) (= (ll_71 BOUND_VARIABLE_20501 BOUND_VARIABLE_20502) (= BOUND_VARIABLE_20501 BOUND_VARIABLE_20502))))) (let ((_let_759 (forall ((BOUND_VARIABLE_20487 set_nat_nat) (BOUND_VARIABLE_20488 set_nat_nat)) (let ((_let_1 (= BOUND_VARIABLE_20487 BOUND_VARIABLE_20488))) (= (ll_70 BOUND_VARIABLE_20487 BOUND_VARIABLE_20488) (and (or _let_1 ((ord_less_set_nat_nat BOUND_VARIABLE_20488) BOUND_VARIABLE_20487)) (or _let_1 ((ord_less_set_nat_nat BOUND_VARIABLE_20487) BOUND_VARIABLE_20488)))))))) (let ((_let_760 (forall ((BOUND_VARIABLE_20479 set_nat_nat_nat_nat3) (BOUND_VARIABLE_20480 (-> (-> nat nat) nat nat))) (= (ll_69 BOUND_VARIABLE_20479 BOUND_VARIABLE_20480) ((member1128122036at_nat BOUND_VARIABLE_20480) BOUND_VARIABLE_20479))))) (let ((_let_761 (forall ((BOUND_VARIABLE_20451 set_nat) (BOUND_VARIABLE_20452 set_nat)) (= (ll_68 BOUND_VARIABLE_20451 BOUND_VARIABLE_20452) ((ord_less_eq_nat_o (ll_178 BOUND_VARIABLE_20452)) (ll_177 BOUND_VARIABLE_20451)))))) (let ((_let_762 (forall ((BOUND_VARIABLE_20441 (-> (-> nat nat nat) Bool)) (BOUND_VARIABLE_20442 (-> (-> nat nat nat) Bool)) (BOUND_VARIABLE_20443 (-> nat nat nat))) (= (ll_67 BOUND_VARIABLE_20441 BOUND_VARIABLE_20442 BOUND_VARIABLE_20443) (and (BOUND_VARIABLE_20441 BOUND_VARIABLE_20443) (BOUND_VARIABLE_20442 BOUND_VARIABLE_20443)))))) (let ((_let_763 (forall ((BOUND_VARIABLE_20433 nat) (BOUND_VARIABLE_20434 nat)) (= (ll_66 BOUND_VARIABLE_20433 BOUND_VARIABLE_20434) ((ord_less_nat BOUND_VARIABLE_20434) BOUND_VARIABLE_20433))))) (let ((_let_764 (forall ((BOUND_VARIABLE_20425 set_nat_nat_nat2) (BOUND_VARIABLE_20426 (-> (-> nat nat) nat))) (= (ll_65 BOUND_VARIABLE_20425 BOUND_VARIABLE_20426) ((member_nat_nat_nat BOUND_VARIABLE_20426) BOUND_VARIABLE_20425))))) (let ((_let_765 (forall ((BOUND_VARIABLE_20404 set_nat_nat_nat2) (BOUND_VARIABLE_20405 set_nat_nat) (BOUND_VARIABLE_20406 (-> (-> nat nat) nat)) (BOUND_VARIABLE_20407 (-> (-> nat nat) (-> nat nat) nat))) (= (ll_64 BOUND_VARIABLE_20404 BOUND_VARIABLE_20405 BOUND_VARIABLE_20406 BOUND_VARIABLE_20407) (and (forall ((BOUND_VARIABLE_7067 (-> nat nat))) (or (not ((member_nat_nat BOUND_VARIABLE_7067) BOUND_VARIABLE_20405)) ((member_nat_nat_nat (BOUND_VARIABLE_20407 BOUND_VARIABLE_7067)) BOUND_VARIABLE_20404))) (forall ((BOUND_VARIABLE_7078 (-> nat nat))) (or ((member_nat_nat BOUND_VARIABLE_7078) BOUND_VARIABLE_20405) (= BOUND_VARIABLE_20406 (BOUND_VARIABLE_20407 BOUND_VARIABLE_7078))))))))) (let ((_let_766 (forall ((BOUND_VARIABLE_20392 nat) (BOUND_VARIABLE_20393 nat)) (let ((_let_1 (= BOUND_VARIABLE_20392 BOUND_VARIABLE_20393))) (= (ll_63 BOUND_VARIABLE_20392 BOUND_VARIABLE_20393) (and (not _let_1) (or _let_1 ((ord_less_nat BOUND_VARIABLE_20392) BOUND_VARIABLE_20393)))))))) (let ((_let_767 (forall ((BOUND_VARIABLE_20379 set_nat) (BOUND_VARIABLE_20380 (-> nat (-> (-> nat nat) nat) Bool)) (BOUND_VARIABLE_20381 (-> (-> nat nat) nat)) (BOUND_VARIABLE_20382 nat)) (= (ll_62 BOUND_VARIABLE_20379 BOUND_VARIABLE_20380 BOUND_VARIABLE_20381 BOUND_VARIABLE_20382) (and ((member_nat BOUND_VARIABLE_20382) BOUND_VARIABLE_20379) ((BOUND_VARIABLE_20380 BOUND_VARIABLE_20382) BOUND_VARIABLE_20381)))))) (let ((_let_768 (forall ((BOUND_VARIABLE_20371 set_nat_nat_nat) (BOUND_VARIABLE_20372 set_nat_nat_nat)) (= (ll_61 BOUND_VARIABLE_20371 BOUND_VARIABLE_20372) ((ord_le940807492at_nat BOUND_VARIABLE_20372) BOUND_VARIABLE_20371))))) (let ((_let_769 (forall ((BOUND_VARIABLE_20358 set_nat_nat) (BOUND_VARIABLE_20359 (-> (-> nat nat) (-> (-> nat nat) nat) Bool)) (BOUND_VARIABLE_20360 (-> (-> nat nat) nat)) (BOUND_VARIABLE_20361 (-> nat nat))) (= (ll_60 BOUND_VARIABLE_20358 BOUND_VARIABLE_20359 BOUND_VARIABLE_20360 BOUND_VARIABLE_20361) (and ((member_nat_nat BOUND_VARIABLE_20361) BOUND_VARIABLE_20358) ((BOUND_VARIABLE_20359 BOUND_VARIABLE_20361) BOUND_VARIABLE_20360)))))) (let ((_let_770 (forall ((BOUND_VARIABLE_20345 (-> (-> nat nat) nat Bool)) (BOUND_VARIABLE_20346 nat) (BOUND_VARIABLE_20347 set_nat_nat) (BOUND_VARIABLE_20348 (-> nat nat))) (= (ll_59 BOUND_VARIABLE_20345 BOUND_VARIABLE_20346 BOUND_VARIABLE_20347 BOUND_VARIABLE_20348) (and ((BOUND_VARIABLE_20345 BOUND_VARIABLE_20348) BOUND_VARIABLE_20346) ((member_nat_nat BOUND_VARIABLE_20348) BOUND_VARIABLE_20347)))))) (let ((_let_771 (forall ((BOUND_VARIABLE_20324 nat) (BOUND_VARIABLE_20325 set_nat_nat_nat) (BOUND_VARIABLE_20326 set_nat) (BOUND_VARIABLE_20327 (-> (-> nat nat nat) nat))) (= (ll_58 BOUND_VARIABLE_20324 BOUND_VARIABLE_20325 BOUND_VARIABLE_20326 BOUND_VARIABLE_20327) (and (forall ((BOUND_VARIABLE_6864 (-> nat nat nat))) (or ((member_nat_nat_nat2 BOUND_VARIABLE_6864) BOUND_VARIABLE_20325) (= BOUND_VARIABLE_20324 (BOUND_VARIABLE_20327 BOUND_VARIABLE_6864)))) (forall ((BOUND_VARIABLE_6873 (-> nat nat nat))) (or (not ((member_nat_nat_nat2 BOUND_VARIABLE_6873) BOUND_VARIABLE_20325)) ((member_nat (BOUND_VARIABLE_20327 BOUND_VARIABLE_6873)) BOUND_VARIABLE_20326)))))))) (let ((_let_772 (forall ((BOUND_VARIABLE_20316 set_nat) (BOUND_VARIABLE_20317 nat)) (= (ll_57 BOUND_VARIABLE_20316 BOUND_VARIABLE_20317) ((member_nat BOUND_VARIABLE_20317) BOUND_VARIABLE_20316))))) (let ((_let_773 (forall ((BOUND_VARIABLE_20308 set_nat) (BOUND_VARIABLE_20309 nat)) (= (ll_56 BOUND_VARIABLE_20308 BOUND_VARIABLE_20309) ((member_nat BOUND_VARIABLE_20309) BOUND_VARIABLE_20308))))) (let ((_let_774 (forall ((BOUND_VARIABLE_20300 set_nat) (BOUND_VARIABLE_20301 nat)) (= (ll_55 BOUND_VARIABLE_20300 BOUND_VARIABLE_20301) ((member_nat BOUND_VARIABLE_20301) BOUND_VARIABLE_20300))))) (let ((_let_775 (forall ((BOUND_VARIABLE_20272 (-> nat Bool)) (BOUND_VARIABLE_20273 set_nat) (BOUND_VARIABLE_20274 nat)) (= (ll_54 BOUND_VARIABLE_20272 BOUND_VARIABLE_20273 BOUND_VARIABLE_20274) ((member_nat BOUND_VARIABLE_20274) (collect_nat ((ll_176 BOUND_VARIABLE_20272) BOUND_VARIABLE_20273))))))) (let ((_let_776 (forall ((BOUND_VARIABLE_20262 set_nat_nat) (BOUND_VARIABLE_20263 set_nat_nat)) (= (ll_53 BOUND_VARIABLE_20262 BOUND_VARIABLE_20263) (or (= BOUND_VARIABLE_20262 BOUND_VARIABLE_20263) ((ord_less_set_nat_nat BOUND_VARIABLE_20262) BOUND_VARIABLE_20263)))))) (let ((_let_777 (forall ((BOUND_VARIABLE_20251 set_nat_nat) (BOUND_VARIABLE_20252 set_nat_nat)) (= (ll_52 BOUND_VARIABLE_20251 BOUND_VARIABLE_20252) (forall ((T2 (-> nat nat))) (let ((_let_1 (member_nat_nat T2))) (or (not (_let_1 BOUND_VARIABLE_20251)) (_let_1 BOUND_VARIABLE_20252)))))))) (let ((_let_778 (forall ((BOUND_VARIABLE_20233 (-> nat nat))) (= (ll_51 BOUND_VARIABLE_20233) (and (forall ((I nat)) (let ((_let_1 (BOUND_VARIABLE_20233 I))) (or (= n _let_1) ((ord_less_nat _let_1) n)))) (= zero_zero_nat (BOUND_VARIABLE_20233 ((plus_plus_nat n) one_one_nat))) (forall ((BOUND_VARIABLE_10295 nat)) (or (not ((ord_less_nat ((plus_plus_nat n) one_one_nat)) BOUND_VARIABLE_10295)) (= zero_zero_nat (BOUND_VARIABLE_20233 BOUND_VARIABLE_10295))))))))) (let ((_let_779 (forall ((BOUND_VARIABLE_20222 set_nat_nat_nat_nat3) (BOUND_VARIABLE_20223 (-> (-> (-> nat nat) nat nat) Bool)) (BOUND_VARIABLE_20224 (-> (-> nat nat) nat nat))) (= (ll_50 BOUND_VARIABLE_20222 BOUND_VARIABLE_20223 BOUND_VARIABLE_20224) (and ((member1128122036at_nat BOUND_VARIABLE_20224) BOUND_VARIABLE_20222) (BOUND_VARIABLE_20223 BOUND_VARIABLE_20224)))))) (let ((_let_780 (forall ((BOUND_VARIABLE_20211 (-> (-> (-> nat nat) nat nat) Bool)) (BOUND_VARIABLE_20212 set_nat_nat_nat_nat3) (BOUND_VARIABLE_20213 (-> (-> nat nat) nat nat))) (= (ll_49 BOUND_VARIABLE_20211 BOUND_VARIABLE_20212 BOUND_VARIABLE_20213) (and (BOUND_VARIABLE_20211 BOUND_VARIABLE_20213) ((member1128122036at_nat BOUND_VARIABLE_20213) BOUND_VARIABLE_20212)))))) (let ((_let_781 (forall ((BOUND_VARIABLE_20200 set_nat_nat_nat) (BOUND_VARIABLE_20201 (-> (-> nat nat nat) Bool)) (BOUND_VARIABLE_20202 (-> nat nat nat))) (= (ll_48 BOUND_VARIABLE_20200 BOUND_VARIABLE_20201 BOUND_VARIABLE_20202) (and ((member_nat_nat_nat2 BOUND_VARIABLE_20202) BOUND_VARIABLE_20200) (BOUND_VARIABLE_20201 BOUND_VARIABLE_20202)))))) (let ((_let_782 (forall ((BOUND_VARIABLE_20190 (-> (-> (-> nat nat) nat nat) Bool)) (BOUND_VARIABLE_20191 (-> (-> (-> nat nat) nat nat) Bool)) (BOUND_VARIABLE_20192 (-> (-> nat nat) nat nat))) (= (ll_47 BOUND_VARIABLE_20190 BOUND_VARIABLE_20191 BOUND_VARIABLE_20192) (and (BOUND_VARIABLE_20190 BOUND_VARIABLE_20192) (BOUND_VARIABLE_20191 BOUND_VARIABLE_20192)))))) (let ((_let_783 (forall ((BOUND_VARIABLE_20178 set_nat_nat) (BOUND_VARIABLE_20179 set_nat_nat)) (let ((_let_1 (= BOUND_VARIABLE_20178 BOUND_VARIABLE_20179))) (= (ll_46 BOUND_VARIABLE_20178 BOUND_VARIABLE_20179) (and (or _let_1 ((ord_less_set_nat_nat BOUND_VARIABLE_20178) BOUND_VARIABLE_20179)) (not _let_1))))))) (let ((_let_784 (forall ((BOUND_VARIABLE_20150 set_nat) (BOUND_VARIABLE_20151 (-> nat Bool)) (BOUND_VARIABLE_20152 nat)) (= (ll_45 BOUND_VARIABLE_20150 BOUND_VARIABLE_20151 BOUND_VARIABLE_20152) ((member_nat BOUND_VARIABLE_20152) (collect_nat ((ll_175 BOUND_VARIABLE_20150) BOUND_VARIABLE_20151))))))) (let ((_let_785 (forall ((BOUND_VARIABLE_20142 set_nat) (BOUND_VARIABLE_20143 nat)) (= (ll_44 BOUND_VARIABLE_20142 BOUND_VARIABLE_20143) ((member_nat BOUND_VARIABLE_20143) BOUND_VARIABLE_20142))))) (let ((_let_786 (forall ((BOUND_VARIABLE_20131 (-> (-> (-> nat nat) nat nat) Bool)) (BOUND_VARIABLE_20132 set_nat_nat_nat_nat3) (BOUND_VARIABLE_20133 (-> (-> nat nat) nat nat))) (= (ll_43 BOUND_VARIABLE_20131 BOUND_VARIABLE_20132 BOUND_VARIABLE_20133) (and (BOUND_VARIABLE_20131 BOUND_VARIABLE_20133) ((member1128122036at_nat BOUND_VARIABLE_20133) BOUND_VARIABLE_20132)))))) (let ((_let_787 (forall ((BOUND_VARIABLE_20118 set_nat) (BOUND_VARIABLE_20119 (-> nat (-> nat nat) Bool)) (BOUND_VARIABLE_20120 (-> nat nat)) (BOUND_VARIABLE_20121 nat)) (= (ll_42 BOUND_VARIABLE_20118 BOUND_VARIABLE_20119 BOUND_VARIABLE_20120 BOUND_VARIABLE_20121) (and ((member_nat BOUND_VARIABLE_20121) BOUND_VARIABLE_20118) ((BOUND_VARIABLE_20119 BOUND_VARIABLE_20121) BOUND_VARIABLE_20120)))))) (let ((_let_788 (forall ((BOUND_VARIABLE_20097 (-> nat nat)) (BOUND_VARIABLE_20098 set_nat) (BOUND_VARIABLE_20099 set_nat_nat) (BOUND_VARIABLE_20100 (-> nat nat nat))) (= (ll_41 BOUND_VARIABLE_20097 BOUND_VARIABLE_20098 BOUND_VARIABLE_20099 BOUND_VARIABLE_20100) (and (forall ((BOUND_VARIABLE_6601 nat)) (or ((member_nat BOUND_VARIABLE_6601) BOUND_VARIABLE_20098) (= BOUND_VARIABLE_20097 (BOUND_VARIABLE_20100 BOUND_VARIABLE_6601)))) (forall ((BOUND_VARIABLE_6610 nat)) (or (not ((member_nat BOUND_VARIABLE_6610) BOUND_VARIABLE_20098)) ((member_nat_nat (BOUND_VARIABLE_20100 BOUND_VARIABLE_6610)) BOUND_VARIABLE_20099)))))))) (let ((_let_789 (forall ((BOUND_VARIABLE_20076 nat) (BOUND_VARIABLE_20077 set_nat_nat) (BOUND_VARIABLE_20078 set_nat) (BOUND_VARIABLE_20079 (-> (-> nat nat) nat))) (= (ll_40 BOUND_VARIABLE_20076 BOUND_VARIABLE_20077 BOUND_VARIABLE_20078 BOUND_VARIABLE_20079) (and (forall ((BOUND_VARIABLE_6546 (-> nat nat))) (or ((member_nat_nat BOUND_VARIABLE_6546) BOUND_VARIABLE_20077) (= BOUND_VARIABLE_20076 (BOUND_VARIABLE_20079 BOUND_VARIABLE_6546)))) (forall ((BOUND_VARIABLE_6555 (-> nat nat))) (or (not ((member_nat_nat BOUND_VARIABLE_6555) BOUND_VARIABLE_20077)) ((member_nat (BOUND_VARIABLE_20079 BOUND_VARIABLE_6555)) BOUND_VARIABLE_20078)))))))) (let ((_let_790 (forall ((BOUND_VARIABLE_20066 (-> (-> (-> nat nat) nat) Bool)) (BOUND_VARIABLE_20067 (-> (-> (-> nat nat) nat) Bool)) (BOUND_VARIABLE_20068 (-> (-> nat nat) nat))) (= (ll_39 BOUND_VARIABLE_20066 BOUND_VARIABLE_20067 BOUND_VARIABLE_20068) (and (BOUND_VARIABLE_20066 BOUND_VARIABLE_20068) (BOUND_VARIABLE_20067 BOUND_VARIABLE_20068)))))) (let ((_let_791 (forall ((BOUND_VARIABLE_20055 set_nat_nat_nat2) (BOUND_VARIABLE_20056 (-> (-> (-> nat nat) nat) Bool)) (BOUND_VARIABLE_20057 (-> (-> nat nat) nat))) (= (ll_38 BOUND_VARIABLE_20055 BOUND_VARIABLE_20056 BOUND_VARIABLE_20057) (and ((member_nat_nat_nat BOUND_VARIABLE_20057) BOUND_VARIABLE_20055) (BOUND_VARIABLE_20056 BOUND_VARIABLE_20057)))))) (let ((_let_792 (forall ((BOUND_VARIABLE_20048 set_nat_nat) (BOUND_VARIABLE_20049 set_nat_nat)) (= (ll_37 BOUND_VARIABLE_20048 BOUND_VARIABLE_20049) (= BOUND_VARIABLE_20048 BOUND_VARIABLE_20049))))) (let ((_let_793 (forall ((BOUND_VARIABLE_20034 set_nat_nat) (BOUND_VARIABLE_20035 set_nat_nat)) (let ((_let_1 (= BOUND_VARIABLE_20034 BOUND_VARIABLE_20035))) (= (ll_36 BOUND_VARIABLE_20034 BOUND_VARIABLE_20035) (and (or _let_1 ((ord_less_set_nat_nat BOUND_VARIABLE_20034) BOUND_VARIABLE_20035)) (or _let_1 ((ord_less_set_nat_nat BOUND_VARIABLE_20035) BOUND_VARIABLE_20034)))))))) (let ((_let_794 (forall ((BOUND_VARIABLE_20023 set_nat_nat_nat) (BOUND_VARIABLE_20024 (-> (-> nat nat nat) Bool)) (BOUND_VARIABLE_20025 (-> nat nat nat))) (= (ll_35 BOUND_VARIABLE_20023 BOUND_VARIABLE_20024 BOUND_VARIABLE_20025) (and ((member_nat_nat_nat2 BOUND_VARIABLE_20025) BOUND_VARIABLE_20023) (BOUND_VARIABLE_20024 BOUND_VARIABLE_20025)))))) (let ((_let_795 (forall ((BOUND_VARIABLE_20012 (-> (-> nat nat nat) Bool)) (BOUND_VARIABLE_20013 set_nat_nat_nat) (BOUND_VARIABLE_20014 (-> nat nat nat))) (= (ll_34 BOUND_VARIABLE_20012 BOUND_VARIABLE_20013 BOUND_VARIABLE_20014) (and (BOUND_VARIABLE_20012 BOUND_VARIABLE_20014) ((member_nat_nat_nat2 BOUND_VARIABLE_20014) BOUND_VARIABLE_20013)))))) (let ((_let_796 (forall ((BOUND_VARIABLE_20001 set_nat_nat) (BOUND_VARIABLE_20002 (-> (-> nat nat) Bool)) (BOUND_VARIABLE_20003 (-> nat nat))) (= (ll_33 BOUND_VARIABLE_20001 BOUND_VARIABLE_20002 BOUND_VARIABLE_20003) (and ((member_nat_nat BOUND_VARIABLE_20003) BOUND_VARIABLE_20001) (BOUND_VARIABLE_20002 BOUND_VARIABLE_20003)))))) (let ((_let_797 (forall ((BOUND_VARIABLE_19994 set_nat_nat) (BOUND_VARIABLE_19995 set_nat_nat)) (= (ll_32 BOUND_VARIABLE_19994 BOUND_VARIABLE_19995) (= BOUND_VARIABLE_19994 BOUND_VARIABLE_19995))))) (let ((_let_798 (forall ((BOUND_VARIABLE_19980 set_nat_nat) (BOUND_VARIABLE_19981 set_nat_nat)) (let ((_let_1 (= BOUND_VARIABLE_19980 BOUND_VARIABLE_19981))) (= (ll_31 BOUND_VARIABLE_19980 BOUND_VARIABLE_19981) (and (or _let_1 ((ord_less_set_nat_nat BOUND_VARIABLE_19981) BOUND_VARIABLE_19980)) (or _let_1 ((ord_less_set_nat_nat BOUND_VARIABLE_19980) BOUND_VARIABLE_19981)))))))) (let ((_let_799 (forall ((BOUND_VARIABLE_19972 set_nat) (BOUND_VARIABLE_19973 nat)) (= (ll_30 BOUND_VARIABLE_19972 BOUND_VARIABLE_19973) ((member_nat BOUND_VARIABLE_19973) BOUND_VARIABLE_19972))))) (let ((_let_800 (forall ((BOUND_VARIABLE_19944 (-> nat Bool)) (BOUND_VARIABLE_19945 (-> nat Bool)) (BOUND_VARIABLE_19946 nat)) (= (ll_29 BOUND_VARIABLE_19944 BOUND_VARIABLE_19945 BOUND_VARIABLE_19946) ((member_nat BOUND_VARIABLE_19946) (collect_nat ((ll_174 BOUND_VARIABLE_19944) BOUND_VARIABLE_19945))))))) (let ((_let_801 (forall ((BOUND_VARIABLE_19936 set_nat) (BOUND_VARIABLE_19937 nat)) (= (ll_28 BOUND_VARIABLE_19936 BOUND_VARIABLE_19937) ((member_nat BOUND_VARIABLE_19937) BOUND_VARIABLE_19936))))) (let ((_let_802 (forall ((BOUND_VARIABLE_19927 (-> nat Bool)) (BOUND_VARIABLE_19928 nat)) (= (ll_27 BOUND_VARIABLE_19927 BOUND_VARIABLE_19928) ((member_nat BOUND_VARIABLE_19928) (collect_nat BOUND_VARIABLE_19927)))))) (let ((_let_803 (forall ((BOUND_VARIABLE_19919 set_nat) (BOUND_VARIABLE_19920 nat)) (= (ll_26 BOUND_VARIABLE_19919 BOUND_VARIABLE_19920) ((member_nat BOUND_VARIABLE_19920) BOUND_VARIABLE_19919))))) (let ((_let_804 (forall ((BOUND_VARIABLE_19910 (-> nat Bool)) (BOUND_VARIABLE_19911 nat)) (= (ll_25 BOUND_VARIABLE_19910 BOUND_VARIABLE_19911) ((member_nat BOUND_VARIABLE_19911) (collect_nat BOUND_VARIABLE_19910)))))) (let ((_let_805 (forall ((BOUND_VARIABLE_19903 nat) (BOUND_VARIABLE_19904 nat)) (= (ll_24 BOUND_VARIABLE_19903 BOUND_VARIABLE_19904) (= BOUND_VARIABLE_19903 BOUND_VARIABLE_19904))))) (let ((_let_806 (forall ((BOUND_VARIABLE_19889 nat) (BOUND_VARIABLE_19890 nat)) (let ((_let_1 (= BOUND_VARIABLE_19889 BOUND_VARIABLE_19890))) (= (ll_23 BOUND_VARIABLE_19889 BOUND_VARIABLE_19890) (and (or _let_1 ((ord_less_nat BOUND_VARIABLE_19890) BOUND_VARIABLE_19889)) (or _let_1 ((ord_less_nat BOUND_VARIABLE_19889) BOUND_VARIABLE_19890)))))))) (let ((_let_807 (forall ((BOUND_VARIABLE_19882 nat) (BOUND_VARIABLE_19883 nat)) (= (ll_22 BOUND_VARIABLE_19882 BOUND_VARIABLE_19883) (= BOUND_VARIABLE_19882 BOUND_VARIABLE_19883))))) (let ((_let_808 (forall ((BOUND_VARIABLE_19868 nat) (BOUND_VARIABLE_19869 nat)) (let ((_let_1 (= BOUND_VARIABLE_19868 BOUND_VARIABLE_19869))) (= (ll_21 BOUND_VARIABLE_19868 BOUND_VARIABLE_19869) (and (or _let_1 ((ord_less_nat BOUND_VARIABLE_19869) BOUND_VARIABLE_19868)) (or _let_1 ((ord_less_nat BOUND_VARIABLE_19868) BOUND_VARIABLE_19869)))))))) (let ((_let_809 (forall ((BOUND_VARIABLE_19857 set_nat_nat) (BOUND_VARIABLE_19858 (-> (-> nat nat) Bool)) (BOUND_VARIABLE_19859 (-> nat nat))) (= (ll_20 BOUND_VARIABLE_19857 BOUND_VARIABLE_19858 BOUND_VARIABLE_19859) (and ((member_nat_nat BOUND_VARIABLE_19859) BOUND_VARIABLE_19857) (BOUND_VARIABLE_19858 BOUND_VARIABLE_19859)))))) (let ((_let_810 (forall ((BOUND_VARIABLE_19846 (-> (-> nat nat) Bool)) (BOUND_VARIABLE_19847 set_nat_nat) (BOUND_VARIABLE_19848 (-> nat nat))) (= (ll_19 BOUND_VARIABLE_19846 BOUND_VARIABLE_19847 BOUND_VARIABLE_19848) (and (BOUND_VARIABLE_19846 BOUND_VARIABLE_19848) ((member_nat_nat BOUND_VARIABLE_19848) BOUND_VARIABLE_19847)))))) (let ((_let_811 (forall ((BOUND_VARIABLE_19835 set_nat_nat) (BOUND_VARIABLE_19836 (-> (-> nat nat) Bool)) (BOUND_VARIABLE_19837 (-> nat nat))) (= (ll_18 BOUND_VARIABLE_19835 BOUND_VARIABLE_19836 BOUND_VARIABLE_19837) (and ((member_nat_nat BOUND_VARIABLE_19837) BOUND_VARIABLE_19835) (BOUND_VARIABLE_19836 BOUND_VARIABLE_19837)))))) (let ((_let_812 (forall ((BOUND_VARIABLE_19827 set_nat) (BOUND_VARIABLE_19828 nat)) (= (ll_17 BOUND_VARIABLE_19827 BOUND_VARIABLE_19828) ((member_nat BOUND_VARIABLE_19828) BOUND_VARIABLE_19827))))) (let ((_let_813 (forall ((BOUND_VARIABLE_19819 set_nat) (BOUND_VARIABLE_19820 nat)) (= (ll_16 BOUND_VARIABLE_19819 BOUND_VARIABLE_19820) ((member_nat BOUND_VARIABLE_19820) BOUND_VARIABLE_19819))))) (let ((_let_814 (forall ((BOUND_VARIABLE_19807 (-> nat nat)) (BOUND_VARIABLE_19808 nat) (BOUND_VARIABLE_19809 nat)) (let ((_let_1 (BOUND_VARIABLE_19807 BOUND_VARIABLE_19809))) (= (ll_15 BOUND_VARIABLE_19807 BOUND_VARIABLE_19808 BOUND_VARIABLE_19809) (or (= BOUND_VARIABLE_19808 _let_1) ((ord_less_nat _let_1) BOUND_VARIABLE_19808))))))) (let ((_let_815 (forall ((BOUND_VARIABLE_19796 (-> (-> (-> nat nat) nat) Bool)) (BOUND_VARIABLE_19797 set_nat_nat_nat2) (BOUND_VARIABLE_19798 (-> (-> nat nat) nat))) (= (ll_14 BOUND_VARIABLE_19796 BOUND_VARIABLE_19797 BOUND_VARIABLE_19798) (and (BOUND_VARIABLE_19796 BOUND_VARIABLE_19798) ((member_nat_nat_nat BOUND_VARIABLE_19798) BOUND_VARIABLE_19797)))))) (let ((_let_816 (forall ((BOUND_VARIABLE_19783 (-> (-> (-> nat nat) nat) nat Bool)) (BOUND_VARIABLE_19784 nat) (BOUND_VARIABLE_19785 set_nat_nat_nat2) (BOUND_VARIABLE_19786 (-> (-> nat nat) nat))) (= (ll_13 BOUND_VARIABLE_19783 BOUND_VARIABLE_19784 BOUND_VARIABLE_19785 BOUND_VARIABLE_19786) (and ((BOUND_VARIABLE_19783 BOUND_VARIABLE_19786) BOUND_VARIABLE_19784) ((member_nat_nat_nat BOUND_VARIABLE_19786) BOUND_VARIABLE_19785)))))) (let ((_let_817 (forall ((BOUND_VARIABLE_19770 set_nat_nat_nat2) (BOUND_VARIABLE_19771 (-> (-> (-> nat nat) nat) nat)) (BOUND_VARIABLE_19772 (-> (-> nat nat) nat))) (= (ll_12 BOUND_VARIABLE_19770 BOUND_VARIABLE_19771 BOUND_VARIABLE_19772) (and ((member_nat_nat_nat BOUND_VARIABLE_19772) BOUND_VARIABLE_19770) (not (= zero_zero_nat (BOUND_VARIABLE_19771 BOUND_VARIABLE_19772)))))))) (let ((_let_818 (forall ((BOUND_VARIABLE_19757 (-> (-> (-> nat nat) nat) nat)) (BOUND_VARIABLE_19758 set_nat_nat_nat2) (BOUND_VARIABLE_19759 (-> (-> nat nat) nat))) (= (ll_11 BOUND_VARIABLE_19757 BOUND_VARIABLE_19758 BOUND_VARIABLE_19759) (and (not (= zero_zero_nat (BOUND_VARIABLE_19757 BOUND_VARIABLE_19759))) ((member_nat_nat_nat BOUND_VARIABLE_19759) BOUND_VARIABLE_19758)))))) (let ((_let_819 (forall ((BOUND_VARIABLE_19740 set_nat_nat_nat2) (BOUND_VARIABLE_19741 (-> (-> (-> nat nat) nat) nat)) (BOUND_VARIABLE_19742 (-> (-> (-> nat nat) nat) nat)) (BOUND_VARIABLE_19743 (-> (-> nat nat) nat))) (= (ll_10 BOUND_VARIABLE_19740 BOUND_VARIABLE_19741 BOUND_VARIABLE_19742 BOUND_VARIABLE_19743) (and ((member_nat_nat_nat BOUND_VARIABLE_19743) BOUND_VARIABLE_19740) (not (= zero_zero_nat ((plus_plus_nat (BOUND_VARIABLE_19741 BOUND_VARIABLE_19743)) (BOUND_VARIABLE_19742 BOUND_VARIABLE_19743))))))))) (let ((_let_820 (forall ((BOUND_VARIABLE_19729 (-> (-> (-> nat nat) nat nat) Bool)) (BOUND_VARIABLE_19730 set_nat_nat_nat_nat3) (BOUND_VARIABLE_19731 (-> (-> nat nat) nat nat))) (= (ll_9 BOUND_VARIABLE_19729 BOUND_VARIABLE_19730 BOUND_VARIABLE_19731) (and (BOUND_VARIABLE_19729 BOUND_VARIABLE_19731) ((member1128122036at_nat BOUND_VARIABLE_19731) BOUND_VARIABLE_19730)))))) (let ((_let_821 (forall ((BOUND_VARIABLE_19719 (-> (-> nat nat) Bool)) (BOUND_VARIABLE_19720 (-> (-> nat nat) Bool)) (BOUND_VARIABLE_19721 (-> nat nat))) (= (ll_8 BOUND_VARIABLE_19719 BOUND_VARIABLE_19720 BOUND_VARIABLE_19721) (or (BOUND_VARIABLE_19719 BOUND_VARIABLE_19721) (BOUND_VARIABLE_19720 BOUND_VARIABLE_19721)))))) (let ((_let_822 (forall ((BOUND_VARIABLE_19708 (-> (-> nat nat nat) Bool)) (BOUND_VARIABLE_19709 set_nat_nat_nat) (BOUND_VARIABLE_19710 (-> nat nat nat))) (= (ll_7 BOUND_VARIABLE_19708 BOUND_VARIABLE_19709 BOUND_VARIABLE_19710) (and (BOUND_VARIABLE_19708 BOUND_VARIABLE_19710) ((member_nat_nat_nat2 BOUND_VARIABLE_19710) BOUND_VARIABLE_19709)))))) (let ((_let_823 (forall ((BOUND_VARIABLE_19703 nat)) (= zero_zero_nat (ll_6 BOUND_VARIABLE_19703))))) (let ((_let_824 (forall ((BOUND_VARIABLE_19693 (-> (-> nat nat) Bool)) (BOUND_VARIABLE_19694 (-> (-> nat nat) Bool)) (BOUND_VARIABLE_19695 (-> nat nat))) (= (ll_5 BOUND_VARIABLE_19693 BOUND_VARIABLE_19694 BOUND_VARIABLE_19695) (and (BOUND_VARIABLE_19693 BOUND_VARIABLE_19695) (BOUND_VARIABLE_19694 BOUND_VARIABLE_19695)))))) (let ((_let_825 (forall ((BOUND_VARIABLE_19683 (-> (-> (-> nat nat) nat nat) Bool)) (BOUND_VARIABLE_19684 (-> (-> (-> nat nat) nat nat) Bool)) (BOUND_VARIABLE_19685 (-> (-> nat nat) nat nat))) (= (ll_4 BOUND_VARIABLE_19683 BOUND_VARIABLE_19684 BOUND_VARIABLE_19685) (and (BOUND_VARIABLE_19683 BOUND_VARIABLE_19685) (BOUND_VARIABLE_19684 BOUND_VARIABLE_19685)))))) (let ((_let_826 (forall ((BOUND_VARIABLE_19672 (-> (-> (-> nat nat) nat) Bool)) (BOUND_VARIABLE_19673 set_nat_nat_nat2) (BOUND_VARIABLE_19674 (-> (-> nat nat) nat))) (= (ll_3 BOUND_VARIABLE_19672 BOUND_VARIABLE_19673 BOUND_VARIABLE_19674) (and (BOUND_VARIABLE_19672 BOUND_VARIABLE_19674) ((member_nat_nat_nat BOUND_VARIABLE_19674) BOUND_VARIABLE_19673)))))) (let ((_let_827 (forall ((BOUND_VARIABLE_19644 (-> nat Bool)) (BOUND_VARIABLE_19645 set_nat) (BOUND_VARIABLE_19646 nat)) (= (ll_2 BOUND_VARIABLE_19644 BOUND_VARIABLE_19645 BOUND_VARIABLE_19646) ((member_nat BOUND_VARIABLE_19646) (collect_nat ((ll_173 BOUND_VARIABLE_19644) BOUND_VARIABLE_19645))))))) (let ((_let_828 (forall ((BOUND_VARIABLE_19636 set_nat) (BOUND_VARIABLE_19637 nat)) (= (ll_1 BOUND_VARIABLE_19636 BOUND_VARIABLE_19637) ((member_nat BOUND_VARIABLE_19637) BOUND_VARIABLE_19636))))) (let ((_let_829 (and (forall ((P2 (-> (-> (-> nat nat) nat) Bool)) (Q (-> (-> (-> nat nat) nat) Bool))) (or (not (forall ((X2 (-> (-> nat nat) nat))) (= (P2 X2) (Q X2)))) (= (collect_nat_nat_nat P2) (collect_nat_nat_nat Q)))) _let_828 _let_827 _let_826 _let_825 _let_824 _let_823 _let_822 _let_821 _let_820 _let_819 _let_818 _let_817 _let_816 _let_815 _let_814 _let_813 _let_812 _let_811 _let_810 _let_809 _let_808 _let_807 _let_806 _let_805 _let_804 _let_803 _let_802 _let_801 _let_800 _let_799 _let_798 _let_797 _let_796 _let_795 _let_794 _let_793 _let_792 _let_791 _let_790 _let_789 _let_788 _let_787 _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644))) (let ((_let_830 (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME |:args| (_let_21)) (MACRO_SR_EQ_INTRO |:args| (_let_21 7 12))) (PREPROCESS |:args| ((and _let_828 _let_827 _let_826 _let_825 _let_824 _let_823 _let_822 _let_821 _let_820 _let_819 _let_818 _let_817 _let_816 _let_815 _let_814 _let_813 _let_812 _let_811 _let_810 _let_809 _let_808 _let_807 _let_806 _let_805 _let_804 _let_803 _let_802 _let_801 _let_800 _let_799 _let_798 _let_797 _let_796 _let_795 _let_794 _let_793 _let_792 _let_791 _let_790 _let_789 _let_788 _let_787 _let_786 _let_785 _let_784 _let_783 _let_782 _let_781 _let_780 _let_779 _let_778 _let_777 _let_776 _let_775 _let_774 _let_773 _let_772 _let_771 _let_770 _let_769 _let_768 _let_767 _let_766 _let_765 _let_764 _let_763 _let_762 _let_761 _let_760 _let_759 _let_758 _let_757 _let_756 _let_755 _let_754 _let_753 _let_752 _let_751 _let_750 _let_749 _let_748 _let_747 _let_746 _let_745 _let_744 _let_743 _let_742 _let_741 _let_740 _let_739 _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644)))) |:args| (_let_829)) (PREPROCESS |:args| ((= _let_829 (and _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_92 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459))))) (PREPROCESS |:args| ((and _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119 _let_118 _let_117 _let_116 _let_115 _let_114 _let_113 _let_112 _let_111 _let_110 _let_109 _let_108 _let_107 _let_106 _let_105 _let_104 _let_103 _let_102 _let_101 _let_100 _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93)))) |:args| ((and _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_92 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482 _let_481 _let_480 _let_479 _let_478 _let_477 _let_476 _let_475 _let_474 _let_473 _let_472 _let_471 _let_470 _let_469 _let_468 _let_467 _let_466 _let_465 _let_464 _let_463 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434 _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119 _let_118 _let_117 _let_116 _let_115 _let_114 _let_113 _let_112 _let_111 _let_110 _let_109 _let_108 _let_107 _let_106 _let_105 _let_104 _let_103 _let_102 _let_101 _let_100 _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93))))) (let ((_let_831 (AND_ELIM _let_830 |:args| (135)))) (let ((_let_832 (_let_92))) (let ((_let_833 (ASSUME |:args| _let_832))) (let ((_let_834 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_833 |:args| _let_87) |:args| _let_832)) _let_831 |:args| (_let_75 false _let_92)))) (let ((_let_835 (not _let_75))) (let ((_let_836 (_let_75))) (let ((_let_837 (AND_ELIM _let_830 |:args| (97)))) (let ((_let_838 (_let_546))) (let ((_let_839 (ASSUME |:args| _let_838))) (let ((_let_840 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_839 |:args| _let_87) |:args| _let_838)) _let_837 |:args| (_let_79 false _let_546)))) (let ((_let_841 (not _let_79))) (let ((_let_842 (not _let_74))) (let ((_let_843 (_let_79))) (let ((_let_844 (forall ((BOUND_VARIABLE_29798 |u_(-> nat nat)|) (BOUND_VARIABLE_29799 |u_(-> _u_(-> nat nat)_ Bool)|)) (= (ho_199 (ho_198 k_197 BOUND_VARIABLE_29798) (ho_547 k_546 BOUND_VARIABLE_29799)) (ho_202 BOUND_VARIABLE_29799 BOUND_VARIABLE_29798))))) (let ((_let_845 (EQ_RESOLVE (ASSUME |:args| (_let_2)) (PREPROCESS |:args| ((= _let_2 _let_844)))))) (let ((_let_846 (_let_844))) (let ((_let_847 (and _let_77 _let_35))) (let ((_let_848 (23 ho_199))) (let ((_let_849 (SYMM (ASSUME |:args| (_let_35))))) (let ((_let_850 (20))) (let ((_let_851 (_let_56))) (let ((_let_852 (forall ((BOUND_VARIABLE_25601 |u_(-> _u_(-> nat nat)_ Bool)|) (BOUND_VARIABLE_25599 |u_(-> _u_(-> nat nat)_ Bool)|)) (or (not (forall ((BOUND_VARIABLE_25604 |u_(-> nat nat)|)) (= (ho_202 BOUND_VARIABLE_25601 BOUND_VARIABLE_25604) (ho_202 BOUND_VARIABLE_25599 BOUND_VARIABLE_25604)))) (= (ho_547 k_546 BOUND_VARIABLE_25599) (ho_547 k_546 BOUND_VARIABLE_25601)))))) (let ((_let_853 (EQ_RESOLVE (ASSUME |:args| (_let_19)) (TRANS (MACRO_SR_EQ_INTRO |:args| (_let_19 7 12)) (PREPROCESS |:args| ((= (forall ((P2 (-> (-> nat nat) Bool)) (Q (-> (-> nat nat) Bool))) (or (not (forall ((X2 (-> nat nat))) (= (P2 X2) (Q X2)))) (= (collect_nat_nat P2) (collect_nat_nat Q)))) _let_852))))))) (let ((_let_854 (_let_852))) (let ((_let_855 (ho_202 k_374 skv_609))) (let ((_let_856 (not _let_59))) (let ((_let_857 (or _let_856 _let_855))) (let ((_let_858 (ho_198 k_197 skv_609))) (let ((_let_859 (ho_199 _let_858 _let_24))) (let ((_let_860 (= _let_859 _let_59))) (let ((_let_861 (forall ((BOUND_VARIABLE_10295 nat)) (or (not (ho_191 (ho_233 k_232 (ho_196 (ho_219 k_257 n) one_one_nat)) BOUND_VARIABLE_10295)) (= zero_zero_nat (ho_196 skv_609 BOUND_VARIABLE_10295)))))) (let ((_let_862 (ho_196 (ho_219 k_257 n) one_one_nat))) (let ((_let_863 (= zero_zero_nat (ho_196 skv_609 _let_862)))) (let ((_let_864 (forall ((I nat)) (let ((_let_1 (ho_196 skv_609 I))) (or (= n _let_1) (ho_191 (ho_233 k_232 _let_1) n)))))) (let ((_let_865 (and _let_864 _let_863 _let_861))) (let ((_let_866 (= _let_58 _let_865))) (let ((_let_867 (forall ((I nat)) (let ((_let_1 (ho_196 skv_609 I))) (or (= n _let_1) (ho_191 (ho_233 k_232 _let_1) n)))))) (let ((_let_868 (forall ((BOUND_VARIABLE_12178 nat)) (or (not (ho_191 (ho_233 k_232 (ho_196 (ho_219 k_257 n) one_one_nat)) BOUND_VARIABLE_12178)) (= zero_zero_nat (ho_196 skv_609 BOUND_VARIABLE_12178)))))) (let ((_let_869 (and _let_867 _let_863 _let_868))) (let ((_let_870 (= _let_855 _let_869))) (let ((_let_871 (ho_199 _let_858 _let_30))) (let ((_let_872 (= _let_871 _let_855))) (let ((_let_873 (skv_609))) (let ((_let_874 (ho_191 (ho_308 k_307 skv_609) n))) (let ((_let_875 (= _let_59 _let_874))) (let ((_let_876 (ho_196 skv_609 skv_616))) (let ((_let_877 (ho_191 (ho_233 k_232 _let_876) n))) (let ((_let_878 (= n _let_876))) (let ((_let_879 (or _let_878 _let_877))) (let ((_let_880 (not _let_857))) (let ((_let_881 (_let_60))) (let ((_let_882 (AND_ELIM _let_830 |:args| (51)))) (let ((_let_883 (_let_592))) (let ((_let_884 (ASSUME |:args| _let_883))) (let ((_let_885 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_884 |:args| _let_873) |:args| _let_883)) _let_882 |:args| (_let_866 false _let_592)))) (let ((_let_886 (not _let_866))) (let ((_let_887 (not _let_865))) (let ((_let_888 (_let_866))) (let ((_let_889 (not _let_874))) (let ((_let_890 (or _let_889 _let_878 _let_877))) (let ((_let_891 (forall ((BOUND_VARIABLE_28102 |u_(-> nat nat)|) (N nat) (I2 nat)) (let ((_let_1 (ho_196 BOUND_VARIABLE_28102 I2))) (or (not (ho_191 (ho_308 k_307 BOUND_VARIABLE_28102) N)) (= N _let_1) (ho_191 (ho_233 k_232 _let_1) N)))))) (let ((_let_892 (EQ_RESOLVE (ASSUME |:args| (_let_10)) (TRANS (MACRO_SR_EQ_INTRO |:args| (_let_10 7 12)) (MACRO_SR_EQ_INTRO _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 |:args| ((forall ((P3 (-> nat nat)) (N nat) (I2 nat)) (or (not ((number1551313001itions P3) N)) ((ord_less_eq_nat (P3 I2)) N))) 7 12)) (PREPROCESS |:args| ((= (forall ((P3 (-> nat nat)) (N nat) (I2 nat)) (let ((_let_1 (P3 I2))) (or (not ((number1551313001itions P3) N)) (= N _let_1) ((ord_less_nat _let_1) N)))) _let_891))))))) (let ((_let_893 (AND_ELIM _let_830 |:args| (96)))) (let ((_let_894 (_let_547))) (let ((_let_895 (ASSUME |:args| _let_894))) (let ((_let_896 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_895 |:args| _let_873) |:args| _let_894)) _let_893 |:args| (_let_870 false _let_547)))) (let ((_let_897 (not _let_870))) (let ((_let_898 (not _let_855))) (let ((_let_899 (_let_870))) (let ((_let_900 (not _let_864))) (let ((_let_901 (_let_900))) (let ((_let_902 (not _let_869))) (let ((_let_903 (not _let_868))) (let ((_let_904 (THEORY_LEMMA |:args| ((= _let_868 _let_861) 12)))) (let ((_let_905 (not _let_859))) (let ((_let_906 (not _let_871))) (let ((_let_907 (REFL |:args| (_let_36)))) (let ((_let_908 (and _let_905 _let_35))) (let ((_let_909 (_let_64))) (let ((_let_910 (finite570312790at_nat (collect_nat_nat ll_51)))) (let ((_let_911 (EQ_RESOLVE (ASSUME |:args| (_let_11)) (TRANS (MACRO_SR_EQ_INTRO |:args| (_let_11 7 12)) (MACRO_SR_EQ_INTRO _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 |:args| ((finite570312790at_nat (collect_nat_nat (lambda ((F (-> nat nat))) (and (forall ((I nat)) (or (not ((ord_less_eq_nat ((plus_plus_nat n) one_one_nat)) I)) (= zero_zero_nat (F I)))) (forall ((I nat)) ((ord_less_eq_nat (F I)) n)))))) 7 12)) (PREPROCESS |:args| ((= (finite570312790at_nat (collect_nat_nat (lambda ((F (-> nat nat))) (and (forall ((I nat)) (let ((_let_1 (F I))) (or (= n _let_1) ((ord_less_nat _let_1) n)))) (= zero_zero_nat (F ((plus_plus_nat n) one_one_nat))) (forall ((BOUND_VARIABLE_10295 nat)) (or (not ((ord_less_nat ((plus_plus_nat n) one_one_nat)) BOUND_VARIABLE_10295)) (= zero_zero_nat (F BOUND_VARIABLE_10295)))))))) _let_910))) (PREPROCESS |:args| ((= _let_910 _let_66))))))) (let ((_let_912 (not _let_55))) (let ((_let_913 (not _let_63))) (let ((_let_914 (not _let_66))) (let ((_let_915 (MACRO_SR_PRED_INTRO |:args| ((= (not _let_27) _let_23))))) (let ((_let_916 (FALSE_INTRO _let_29))) (let ((_let_917 (REFL |:args| (k_548)))) (let ((_let_918 (TRUE_INTRO _let_911))) (let ((_let_919 (collect_nat_nat ll_96))) (let ((_let_920 (collect_nat_nat ll_97))) (let ((_let_921 (or (= _let_919 _let_920) ((ord_less_set_nat_nat _let_920) _let_919)))) (let ((_let_922 (collect_nat_nat (lambda ((F (-> nat nat))) (and (forall ((I nat)) (let ((_let_1 (F I))) (or (= n _let_1) ((ord_less_nat _let_1) n)))) (= zero_zero_nat (F ((plus_plus_nat n) one_one_nat))) (forall ((BOUND_VARIABLE_12178 nat)) (or (not ((ord_less_nat ((plus_plus_nat n) one_one_nat)) BOUND_VARIABLE_12178)) (= zero_zero_nat (F BOUND_VARIABLE_12178))))))))) (let ((_let_923 (collect_nat_nat (lambda ((BOUND_VARIABLE_12211 (-> nat nat))) ((number1551313001itions BOUND_VARIABLE_12211) n))))) (let ((_let_924 (= _let_62 _let_30))) (let ((_let_925 (forall ((BOUND_VARIABLE_25604 |u_(-> nat nat)|)) (= (ho_202 k_374 BOUND_VARIABLE_25604) (ho_202 k_468 BOUND_VARIABLE_25604))))) (let ((_let_926 (not _let_925))) (let ((_let_927 (or _let_926 _let_924))) (let ((_let_928 (ho_202 k_468 skv_618))) (let ((_let_929 (ho_202 k_374 skv_618))) (let ((_let_930 (= _let_929 _let_928))) (let ((_let_931 (forall ((BOUND_VARIABLE_12178 nat)) (or (not (ho_191 (ho_233 k_232 (ho_196 (ho_219 k_257 n) one_one_nat)) BOUND_VARIABLE_12178)) (= zero_zero_nat (ho_196 skv_618 BOUND_VARIABLE_12178)))))) (let ((_let_932 (= zero_zero_nat (ho_196 skv_618 _let_862)))) (let ((_let_933 (forall ((I nat)) (let ((_let_1 (ho_196 skv_618 I))) (or (= n _let_1) (ho_191 (ho_233 k_232 _let_1) n)))))) (let ((_let_934 (and _let_933 _let_932 _let_931))) (let ((_let_935 (= _let_929 _let_934))) (let ((_let_936 (forall ((BOUND_VARIABLE_10295 nat)) (or (not (ho_191 (ho_233 k_232 (ho_196 (ho_219 k_257 n) one_one_nat)) BOUND_VARIABLE_10295)) (= zero_zero_nat (ho_196 skv_618 BOUND_VARIABLE_10295)))))) (let ((_let_937 (forall ((I nat)) (let ((_let_1 (ho_196 skv_618 I))) (or (= n _let_1) (ho_191 (ho_233 k_232 _let_1) n)))))) (let ((_let_938 (and _let_937 _let_932 _let_936))) (let ((_let_939 (= _let_928 _let_938))) (let ((_let_940 (not _let_929))) (let ((_let_941 (_let_930))) (let ((_let_942 (skv_618))) (let ((_let_943 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_895 |:args| _let_942) |:args| _let_894)) _let_893 |:args| (_let_935 false _let_547)))) (let ((_let_944 (not _let_935))) (let ((_let_945 (_let_935))) (let ((_let_946 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_884 |:args| _let_942) |:args| _let_883)) _let_882 |:args| (_let_939 false _let_592)))) (let ((_let_947 (not _let_939))) (let ((_let_948 (not _let_938))) (let ((_let_949 (_let_939))) (let ((_let_950 (not _let_934))) (let ((_let_951 (THEORY_LEMMA |:args| ((= _let_937 _let_933) 12)))) (let ((_let_952 (THEORY_LEMMA |:args| ((= _let_936 _let_931) 12)))) (let ((_let_953 (not _let_936))) (let ((_let_954 (not _let_937))) (let ((_let_955 (_let_926))) (let ((_let_956 (and _let_66 _let_924))) (let ((_let_957 (forall ((BOUND_VARIABLE_25604 |u_(-> nat nat)|)) (= (ho_202 k_309 BOUND_VARIABLE_25604) (ho_202 k_373 BOUND_VARIABLE_25604))))) (let ((_let_958 (not _let_957))) (let ((_let_959 (or _let_958 _let_26))) (let ((_let_960 (ho_202 k_373 skv_619))) (let ((_let_961 (ho_202 k_309 skv_619))) (let ((_let_962 (= _let_961 _let_960))) (let ((_let_963 (ho_191 (ho_308 k_307 skv_619) n))) (let ((_let_964 (= _let_961 _let_963))) (let ((_let_965 (= _let_960 _let_963))) (let ((_let_966 (not _let_961))) (let ((_let_967 (_let_962))) (let ((_let_968 (skv_619))) (let ((_let_969 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_833 |:args| _let_968) |:args| _let_832)) _let_831 |:args| (_let_964 false _let_92)))) (let ((_let_970 (not _let_964))) (let ((_let_971 (_let_964))) (let ((_let_972 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_839 |:args| _let_968) |:args| _let_838)) _let_837 |:args| (_let_965 false _let_546)))) (let ((_let_973 (not _let_965))) (let ((_let_974 (not _let_963))) (let ((_let_975 (_let_965))) (let ((_let_976 (_let_958))) (let ((_let_977 (not _let_26))) (let ((_let_978 (not _let_25))) (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM _let_916) (CONG _let_917 (SYMM (ASSUME |:args| (_let_26))) |:args| _let_848) (TRUE_INTRO (ASSUME |:args| (_let_25))))) |:args| (_let_25 _let_26 _let_27))) (CONG (REFL |:args| (_let_978)) (REFL |:args| (_let_977)) _let_915 |:args| _let_850)) |:args| ((or _let_23 _let_978 _let_977))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS |:args| (_let_959)) |:args| ((or _let_958 _let_26 (not _let_959)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME |:args| _let_976)) |:args| _let_976)) (CONG (MACRO_SR_PRED_INTRO |:args| ((= (not _let_958) _let_957))) (REFL |:args| ((not _let_962))) |:args| _let_850)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 |:args| _let_975) |:args| ((or (not _let_960) _let_963 _let_973))) _let_972 (REORDERING (CNF_EQUIV_POS2 |:args| _let_971) |:args| ((or _let_961 _let_974 _let_970))) _let_969 (REORDERING (CNF_EQUIV_NEG1 |:args| _let_967) |:args| ((or _let_961 _let_960 _let_962))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 |:args| _let_975) |:args| ((or _let_960 _let_974 _let_973))) _let_972 (REORDERING (CNF_EQUIV_POS1 |:args| _let_971) |:args| ((or _let_966 _let_963 _let_970))) _let_969 (CNF_EQUIV_NEG2 |:args| _let_967) |:args| ((or _let_962 _let_966) false _let_965 false _let_963 false _let_964 true _let_960)) |:args| (_let_962 false _let_965 true _let_963 false _let_964 false _let_960 true _let_961)) |:args| (_let_957 false _let_962)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_853 |:args| (k_309 k_373)) |:args| _let_854)) _let_853 |:args| (_let_959 false _let_852)) |:args| (_let_26 false _let_957 false _let_959)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS |:args| (_let_38)) |:args| ((or _let_25 _let_32 _let_37 (not _let_38)))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG |:args| (_let_956)) (IMPLIES_ELIM (SCOPE (TRUE_ELIM (TRANS (CONG _let_917 (SYMM (ASSUME |:args| (_let_924))) |:args| _let_848) _let_918)) |:args| (_let_66 _let_924))) |:args| (true _let_956)) |:args| ((or _let_914 _let_31 (not _let_924)))) _let_911 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS |:args| (_let_927)) |:args| ((or _let_926 _let_924 (not _let_927)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME |:args| _let_955)) |:args| _let_955)) (CONG (MACRO_SR_PRED_INTRO |:args| ((= (not _let_926) _let_925))) (REFL |:args| ((not _let_930))) |:args| _let_850)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 _let_952) |:args| ((or _let_931 _let_953))) (CNF_AND_NEG |:args| (_let_934)) (REORDERING (EQUIV_ELIM1 _let_951) |:args| ((or _let_933 _let_954))) (REORDERING (CNF_AND_POS |:args| (_let_938 2)) |:args| ((or _let_936 _let_948))) (REORDERING (CNF_AND_POS |:args| (_let_938 1)) |:args| ((or _let_932 _let_948))) (REORDERING (CNF_AND_POS |:args| (_let_938 0)) |:args| ((or _let_937 _let_948))) (REORDERING (CNF_EQUIV_POS1 |:args| _let_949) |:args| ((or (not _let_928) _let_938 _let_947))) _let_946 (REORDERING (CNF_EQUIV_POS2 |:args| _let_945) |:args| ((or _let_929 _let_950 _let_944))) _let_943 (REORDERING (CNF_EQUIV_NEG1 |:args| _let_941) |:args| ((or _let_929 _let_928 _let_930))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG |:args| (_let_938)) |:args| ((or _let_938 (not _let_932) _let_954 _let_953))) (EQUIV_ELIM2 _let_952) (EQUIV_ELIM2 _let_951) (REORDERING (CNF_AND_POS |:args| (_let_934 2)) |:args| ((or _let_931 _let_950))) (REORDERING (CNF_AND_POS |:args| (_let_934 1)) |:args| ((or _let_932 _let_950))) (REORDERING (CNF_AND_POS |:args| (_let_934 0)) |:args| ((or _let_933 _let_950))) (REORDERING (CNF_EQUIV_POS2 |:args| _let_949) |:args| ((or _let_928 _let_948 _let_947))) _let_946 (REORDERING (CNF_EQUIV_POS1 |:args| _let_945) |:args| ((or _let_940 _let_934 _let_944))) _let_943 (CNF_EQUIV_NEG2 |:args| _let_941) |:args| ((or _let_930 _let_940) false _let_936 false _let_937 false _let_931 false _let_932 false _let_933 true _let_938 false _let_939 false _let_934 false _let_935 true _let_928)) |:args| (_let_930 true _let_931 false _let_933 false _let_936 false _let_932 false _let_937 false _let_938 false _let_939 true _let_934 false _let_935 false _let_928 true _let_929)) |:args| (_let_925 false _let_930)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_853 |:args| (k_374 k_468)) |:args| _let_854)) _let_853 |:args| (_let_927 false _let_852)) |:args| (_let_924 false _let_925 false _let_927)) |:args| (_let_31 false _let_66 false _let_924)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS |:args| (_let_37 1)) |:args| ((or _let_34 _let_50))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (ASSUME |:args| (_let_9)) (TRANS (MACRO_SR_EQ_INTRO |:args| (_let_9 7 12)) (MACRO_SR_EQ_INTRO _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 |:args| ((_let_8 (collect_nat_nat (lambda ((F (-> nat nat))) (and (forall ((I nat)) (or (not ((ord_less_eq_nat ((plus_plus_nat n) one_one_nat)) I)) (= zero_zero_nat (F I)))) (forall ((I nat)) ((ord_less_eq_nat (F I)) n)))))) 7 12)) (PREPROCESS |:args| ((= (or (= _let_922 _let_923) ((ord_less_set_nat_nat _let_923) _let_922)) _let_921))) (PREPROCESS |:args| ((= _let_921 _let_67))))) |:args| ((or _let_33 _let_35))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM _let_918) (CONG _let_917 (TRANS (SYMM (SYMM (ASSUME |:args| (_let_63)))) _let_849) |:args| _let_848) (CONG _let_917 (SYMM (SYMM (ASSUME |:args| (_let_55)))) |:args| _let_848) _let_916)) |:args| (_let_27 _let_55 _let_35 _let_63 _let_66))) (CONG _let_915 (REFL |:args| (_let_912)) _let_907 (REFL |:args| (_let_913)) (REFL |:args| (_let_914)) |:args| _let_850)) |:args| ((or _let_23 _let_914 _let_36 _let_913 _let_912))) _let_29 _let_911 (REORDERING (CNF_OR_POS |:args| (_let_65)) |:args| ((or _let_64 _let_63 (not _let_65)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_853 |:args| (k_373 k_468)) |:args| _let_854)) _let_853 |:args| (_let_65 false _let_852)) (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME |:args| _let_909)) |:args| _let_909)) (CONG (MACRO_SR_PRED_INTRO |:args| ((= (not _let_64) _let_61))) (REFL |:args| ((not _let_60))) |:args| _let_850)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG |:args| (_let_908)) (IMPLIES_ELIM (SCOPE (FALSE_ELIM (TRANS (CONG (REFL |:args| (_let_858)) (SYMM _let_849) |:args| _let_848) (FALSE_INTRO (ASSUME |:args| (_let_905))))) |:args| (_let_905 _let_35))) |:args| (true _let_908)) (CONG (MACRO_SR_PRED_INTRO |:args| ((= (not _let_905) _let_859))) _let_907 (REFL |:args| (_let_906)) |:args| _let_850)) |:args| ((or _let_36 _let_859 _let_906))) (REORDERING (CNF_EQUIV_POS2 |:args| (_let_872)) |:args| ((or _let_898 _let_871 (not _let_872)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_845 |:args| (skv_609 k_374)) |:args| _let_846)) _let_845 |:args| (_let_872 false _let_844)) (REORDERING (CNF_EQUIV_POS2 |:args| _let_899) |:args| ((or _let_855 _let_902 _let_897))) _let_896 (REORDERING (CNF_AND_NEG |:args| (_let_869)) |:args| ((or (not _let_863) _let_869 (not _let_867) _let_903))) (REORDERING (EQUIV_ELIM2 _let_904) |:args| ((or (not _let_861) _let_868))) (REORDERING (EQUIV_ELIM2 (THEORY_LEMMA |:args| ((= _let_867 _let_864) 12))) |:args| ((or _let_900 _let_867))) (REORDERING (CNF_AND_POS |:args| (_let_865 2)) |:args| ((or _let_861 _let_887))) (REORDERING (CNF_AND_POS |:args| (_let_865 1)) |:args| ((or _let_863 _let_887))) (REORDERING (CNF_AND_POS |:args| (_let_865 0)) |:args| ((or _let_864 _let_887))) (REORDERING (CNF_EQUIV_POS1 |:args| _let_888) |:args| ((or (not _let_58) _let_865 _let_886))) _let_885 (REORDERING (CNF_EQUIV_POS1 |:args| (_let_860)) |:args| ((or _let_59 _let_905 (not _let_860)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_845 |:args| (skv_609 k_373)) |:args| _let_846)) _let_845 |:args| (_let_860 false _let_844)) (REORDERING (CNF_EQUIV_NEG1 |:args| _let_881) |:args| ((or _let_59 _let_58 _let_60))) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 _let_904) |:args| ((or _let_861 _let_903))) (CNF_AND_NEG |:args| (_let_865)) (REORDERING (CNF_AND_POS |:args| (_let_869 2)) |:args| ((or _let_868 _let_902))) (REORDERING (CNF_AND_POS |:args| (_let_869 1)) |:args| ((or _let_863 _let_902))) (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME |:args| _let_901)) |:args| _let_901)) (CONG (MACRO_SR_PRED_INTRO |:args| ((= (not _let_900) _let_864))) (REFL |:args| ((not _let_879))) |:args| _let_850)) (REORDERING (CNF_EQUIV_POS1 |:args| _let_899) |:args| ((or _let_898 _let_869 _let_897))) _let_896 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS |:args| (_let_890)) |:args| ((or _let_889 _let_878 _let_877 (not _let_890)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_892 |:args| (skv_609 n skv_616)) |:args| (_let_891))) _let_892 |:args| (_let_890 false _let_891)) (CNF_OR_NEG |:args| (_let_879 1)) (CNF_OR_NEG |:args| (_let_879 0)) |:args| ((or _let_889 _let_879) false _let_890 true _let_877 true _let_878)) (REORDERING (CNF_EQUIV_POS2 |:args| _let_888) |:args| ((or _let_58 _let_887 _let_886))) _let_885 (REORDERING (CNF_OR_POS |:args| (_let_857)) |:args| ((or _let_856 _let_855 _let_880))) (REORDERING (CNF_EQUIV_POS1 |:args| (_let_875)) |:args| ((or _let_856 _let_874 (not _let_875)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_839 |:args| _let_873) |:args| _let_838)) _let_837 |:args| (_let_875 false _let_546)) (CNF_EQUIV_NEG2 |:args| _let_881) |:args| ((or _let_60 _let_856 _let_880) true _let_861 false _let_868 false _let_863 false _let_864 false _let_869 false _let_870 false _let_879 true _let_865 false _let_866 false _let_855 false _let_874 false _let_875 true _let_58)) (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_88 |:args| _let_873) |:args| _let_86)) _let_85 _let_84 _let_83 _let_82 |:args| ((or _let_36 _let_60) false _let_871 false _let_872 false _let_855 false _let_870 false _let_869 false _let_868 false _let_867 false _let_861 false _let_863 false _let_864 false _let_865 false _let_866 true _let_859 false _let_860 false _let_58 true _let_59 false _let_857 false _let_69 false _let_70 false _let_68 false _let_67)) (REORDERING (CNF_OR_POS |:args| (_let_57)) |:args| ((or _let_56 _let_55 (not _let_57)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_853 |:args| (k_309 k_374)) |:args| _let_854)) _let_853 |:args| (_let_57 false _let_852)) (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME |:args| _let_851)) |:args| _let_851)) (CONG (MACRO_SR_PRED_INTRO |:args| ((= (not _let_56) _let_54))) (REFL |:args| ((not _let_53))) |:args| _let_850)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG |:args| (_let_847)) (IMPLIES_ELIM (SCOPE (TRUE_ELIM (TRANS (CONG (REFL |:args| (_let_76)) _let_849 |:args| _let_848) (TRUE_INTRO (ASSUME |:args| (_let_77))))) |:args| (_let_77 _let_35))) |:args| (true _let_847)) |:args| ((or _let_36 (not _let_77) _let_80))) (REORDERING (CNF_EQUIV_POS1 |:args| (_let_81)) |:args| ((or _let_71 (not _let_80) (not _let_81)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_845 |:args| (skv_610 k_373)) |:args| _let_846)) _let_845 |:args| (_let_81 false _let_844)) (REORDERING (CNF_EQUIV_POS1 |:args| _let_843) |:args| ((or _let_74 _let_72 _let_841))) _let_840 (REORDERING (CNF_EQUIV_POS2 |:args| (_let_78)) |:args| ((or (not _let_51) _let_77 (not _let_78)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_845 |:args| (skv_610 k_374)) |:args| _let_846)) _let_845 |:args| (_let_78 false _let_844)) (REORDERING (CNF_EQUIV_POS2 |:args| _let_836) |:args| ((or _let_52 _let_842 _let_835))) _let_834 (REORDERING (CNF_EQUIV_NEG1 |:args| _let_91) |:args| ((or _let_52 _let_51 _let_53))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 |:args| _let_843) |:args| ((or _let_71 _let_842 _let_841))) _let_840 (REORDERING (CNF_OR_POS |:args| (_let_73)) |:args| ((or _let_51 _let_72 _let_89))) (REORDERING (CNF_EQUIV_POS1 |:args| _let_836) |:args| ((or _let_90 _let_74 _let_835))) _let_834 (CNF_EQUIV_NEG2 |:args| _let_91) |:args| ((or _let_53 _let_90 _let_89) false _let_79 true _let_71 false _let_74 false _let_75 true _let_51)) (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_88 |:args| _let_87) |:args| _let_86)) _let_85 _let_84 _let_83 _let_82 |:args| ((or _let_36 _let_53) true _let_80 false _let_81 true _let_71 false _let_79 false _let_77 false _let_78 true _let_74 false _let_75 false _let_51 true _let_52 false _let_73 false _let_69 false _let_70 false _let_68 false _let_67)) |:args| (_let_36 true _let_23 false _let_66 false _let_63 false _let_65 false _let_61 false _let_60 false _let_55 false _let_57 false _let_54 false _let_53)) |:args| (_let_33 true _let_35)) |:args| (_let_50 false _let_33)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_49 |:args| (_let_24 _let_30)) |:args| (_let_39)))) _let_49 |:args| (_let_38 false _let_39)) |:args| (_let_25 false _let_31 true _let_37 false _let_38)) _let_29 |:args| (false false _let_26 false _let_25 true _let_23)) |:args| (_let_21 (forall ((X5 set_nat) (P2 (-> nat Bool))) ((ord_less_eq_set_nat (collect_nat (lambda ((X nat)) (and (P2 X) ((member_nat X) X5))))) X5)) (forall ((A set_nat_nat) (B set_nat_nat) (C4 set_nat_nat)) (let ((_let_1 (ord_le1415039317at_nat A))) (=> (_let_1 B) (=> ((ord_le1415039317at_nat B) C4) (_let_1 C4))))) (forall ((B3 nat) (A3 nat) (C nat)) (let ((_let_1 (ord_less_eq_nat C))) (=> ((ord_less_eq_nat B3) A3) (=> (_let_1 B3) (_let_1 A3))))) (_let_15 zero_zero_nat) (forall ((A set_nat_nat_nat) (B set_nat_nat_nat)) (=> ((ord_le940807492at_nat A) B) (=> (finite2045569477at_nat B) (finite2045569477at_nat A)))) (forall ((A3 nat) (B3 nat) (C nat)) (let ((_let_1 (plus_plus_nat A3))) (=> (= (_let_1 B3) (_let_1 C)) (= B3 C)))) (forall ((A3 nat) (B3 nat)) (= ((ord_less_eq_nat A3) ((plus_plus_nat B3) A3)) ((ord_less_eq_nat zero_zero_nat) B3))) (forall ((X3 (-> (-> nat nat) nat)) (Z3 set_nat_nat_nat2) (X5 set_nat_nat_nat2) (P2 (-> (-> (-> nat nat) nat) Bool))) (=> ((member_nat_nat_nat X3) Z3) (=> ((ord_le633272388at_nat Z3) (collect_nat_nat_nat (lambda ((X (-> (-> nat nat) nat))) (and (P2 X) ((member_nat_nat_nat X) X5))))) (P2 X3)))) (forall ((P2 (-> (-> (-> nat nat) nat nat) Bool)) (Q (-> (-> (-> nat nat) nat nat) Bool))) (=> (or (finite1064868788at_nat (collec1610646258at_nat P2)) (finite1064868788at_nat (collec1610646258at_nat Q))) (finite1064868788at_nat (collec1610646258at_nat (lambda ((X (-> (-> nat nat) nat nat))) (and (P2 X) (Q X))))))) (forall ((A3 set_nat_nat) (B3 set_nat_nat)) (=> ((ord_le1415039317at_nat A3) B3) (=> ((ord_le1415039317at_nat B3) A3) (= A3 B3)))) (forall ((A set_set_nat_nat) (A3 set_nat_nat)) (=> (finite604103692at_nat A) (=> ((member_set_nat_nat A3) A) (exists ((X2 set_nat_nat)) (and (forall ((Xa set_nat_nat)) (=> ((member_set_nat_nat Xa) A) (=> ((ord_le1415039317at_nat X2) Xa) (= X2 Xa)))) ((ord_le1415039317at_nat A3) X2) ((member_set_nat_nat X2) A)))))) (forall ((P2 (-> (-> nat nat) Bool)) (Q (-> (-> nat nat) Bool))) (=> (or (finite570312790at_nat (collect_nat_nat P2)) (finite570312790at_nat (collect_nat_nat Q))) (finite570312790at_nat (collect_nat_nat (lambda ((X (-> nat nat))) (and (Q X) (P2 X))))))) (not (_let_12 zero_zero_nat)) _let_20 (forall ((A3 nat) (B3 nat)) (= ((ord_less_nat A3) ((plus_plus_nat A3) B3)) ((ord_less_nat zero_zero_nat) B3))) (forall ((P3 (-> nat nat))) (= ((number1551313001itions P3) zero_zero_nat) (= P3 (lambda ((I nat)) zero_zero_nat)))) (forall ((A set_nat_nat_nat) (P2 (-> (-> nat nat nat) Bool))) ((ord_le940807492at_nat (collect_nat_nat_nat2 (lambda ((X (-> nat nat nat))) (and (P2 X) ((member_nat_nat_nat2 X) A))))) A)) (forall ((P2 (-> (-> (-> nat nat) nat) Bool))) (=> (not (finite1440337093at_nat (collect_nat_nat_nat P2))) (exists ((X_1 (-> (-> nat nat) nat))) (P2 X_1)))) (forall ((S set_nat_nat_nat) (T set_nat_nat_nat)) (=> ((ord_le940807492at_nat S) T) (=> (not (finite2045569477at_nat S)) (not (finite2045569477at_nat T))))) _let_19 (forall ((N nat)) (= ((ord_less_eq_nat N) zero_zero_nat) (= N zero_zero_nat))) (forall ((P2 (-> (-> nat nat) Bool)) (Q (-> (-> nat nat) Bool))) (= (finite570312790at_nat (collect_nat_nat (lambda ((X (-> nat nat))) (or (Q X) (P2 X))))) (and (finite570312790at_nat (collect_nat_nat P2)) (finite570312790at_nat (collect_nat_nat Q))))) (forall ((N5 set_nat) (N nat)) (=> (forall ((X2 nat)) (=> ((member_nat X2) N5) ((ord_less_nat X2) N))) (finite_finite_nat N5))) (forall ((A set_nat_nat_nat_nat3) (P2 (-> (-> (-> nat nat) nat nat) Bool))) ((ord_le2040082867at_nat (collec1610646258at_nat (lambda ((X (-> (-> nat nat) nat nat))) (and (P2 X) ((member1128122036at_nat X) A))))) A)) (forall ((A3 (-> nat nat nat)) (P2 (-> (-> nat nat nat) Bool))) (= ((member_nat_nat_nat2 A3) (collect_nat_nat_nat2 P2)) (P2 A3))) (forall ((A3 set_nat_nat) (F2 (-> set_nat_nat set_nat_nat)) (B3 set_nat_nat) (C set_nat_nat)) (let ((_let_1 (ord_le1415039317at_nat A3))) (=> (_let_1 (F2 B3)) (=> ((ord_le1415039317at_nat B3) C) (=> (forall ((X2 set_nat_nat) (Y2 set_nat_nat)) (=> ((ord_le1415039317at_nat X2) Y2) ((ord_le1415039317at_nat (F2 X2)) (F2 Y2)))) (_let_1 (F2 C))))))) (forall ((B set_nat_nat_nat) (A set_nat_nat_nat)) (=> (finite2045569477at_nat B) (=> ((ord_le940807492at_nat A) B) (finite2045569477at_nat A)))) (forall ((I3 set_nat_nat_nat2) (X3 (-> (-> (-> nat nat) nat) nat)) (Y (-> (-> (-> nat nat) nat) nat))) (=> (finite1440337093at_nat (collect_nat_nat_nat (lambda ((I (-> (-> nat nat) nat))) (and ((member_nat_nat_nat I) I3) (not (= (X3 I) zero_zero_nat)))))) (=> (finite1440337093at_nat (collect_nat_nat_nat (lambda ((I (-> (-> nat nat) nat))) (and (not (= (Y I) zero_zero_nat)) ((member_nat_nat_nat I) I3))))) (finite1440337093at_nat (collect_nat_nat_nat (lambda ((I (-> (-> nat nat) nat))) (and ((member_nat_nat_nat I) I3) (not (= ((plus_plus_nat (X3 I)) (Y I)) zero_zero_nat))))))))) (forall ((A3 set_nat_nat) (B3 set_nat_nat) (F2 (-> set_nat_nat set_nat_nat)) (C set_nat_nat)) (=> ((ord_le1415039317at_nat A3) B3) (=> ((ord_le1415039317at_nat (F2 B3)) C) (=> (forall ((X2 set_nat_nat) (Y2 set_nat_nat)) (=> ((ord_le1415039317at_nat X2) Y2) ((ord_le1415039317at_nat (F2 X2)) (F2 Y2)))) ((ord_le1415039317at_nat (F2 A3)) C))))) (forall ((A3 nat)) ((ord_less_eq_nat zero_zero_nat) A3)) (forall ((A set_nat_nat_nat2) (B set_nat) (R (-> (-> (-> nat nat) nat) nat Bool))) (=> (not (finite1440337093at_nat A)) (=> (finite_finite_nat B) (=> (forall ((X2 (-> (-> nat nat) nat))) (=> ((member_nat_nat_nat X2) A) (exists ((Xa nat)) (and ((member_nat Xa) B) ((R X2) Xa))))) (exists ((X2 nat)) (and (not (finite1440337093at_nat (collect_nat_nat_nat (lambda ((A2 (-> (-> nat nat) nat))) (and ((R A2) X2) ((member_nat_nat_nat A2) A)))))) ((member_nat X2) B))))))) (forall ((A3 set_nat_nat) (B3 set_nat_nat) (F2 (-> set_nat_nat nat)) (C nat)) (=> ((ord_le1415039317at_nat A3) B3) (=> ((ord_less_eq_nat (F2 B3)) C) (=> (forall ((X2 set_nat_nat) (Y2 set_nat_nat)) (=> ((ord_le1415039317at_nat X2) Y2) ((ord_less_eq_nat (F2 X2)) (F2 Y2)))) ((ord_less_eq_nat (F2 A3)) C))))) (forall ((N nat)) ((ord_less_eq_nat N) N)) (forall ((B set_nat_nat_nat2) (A set_nat_nat_nat2) (P2 (-> (-> (-> nat nat) nat) Bool))) (let ((_let_1 (ord_le633272388at_nat B))) (=> (_let_1 A) (= (_let_1 (collect_nat_nat_nat (lambda ((X (-> (-> nat nat) nat))) (and (P2 X) ((member_nat_nat_nat X) A))))) (forall ((X (-> (-> nat nat) nat))) (=> ((member_nat_nat_nat X) B) (P2 X))))))) (forall ((X3 nat)) ((ord_less_eq_nat X3) X3)) (forall ((A3 nat) (B3 nat)) (= ((ord_less_eq_nat ((plus_plus_nat A3) B3)) B3) ((ord_less_eq_nat A3) zero_zero_nat))) (forall ((A set_nat_nat) (B set_nat_nat)) (=> (= A B) ((ord_le1415039317at_nat A) B))) (forall ((A3 nat) (B3 nat)) (=> ((ord_less_eq_nat A3) B3) (not (forall ((C3 nat)) (not (= B3 ((plus_plus_nat A3) C3))))))) (forall ((X3 nat)) (= (= one_one_nat X3) (= X3 one_one_nat))) (forall ((K nat) (L nat)) (=> ((ord_less_eq_nat K) L) (exists ((N3 nat)) (= L ((plus_plus_nat K) N3))))) (forall ((S set_nat_nat_nat2) (T set_nat_nat_nat2)) (=> ((ord_le633272388at_nat S) T) (=> (not (finite1440337093at_nat S)) (not (finite1440337093at_nat T))))) (forall ((B set_nat_nat_nat_nat3) (A set_nat_nat_nat_nat3)) (=> (finite1064868788at_nat B) (=> ((ord_le2040082867at_nat A) B) (finite1064868788at_nat A)))) (forall ((M nat) (N nat)) (=> (or (= M N) ((ord_less_nat M) N)) ((ord_less_eq_nat M) N))) (forall ((X3 set_nat_nat)) ((ord_le1415039317at_nat X3) X3)) (forall ((F2 (-> nat nat)) (U nat)) (=> (forall ((N3 nat)) ((ord_less_eq_nat N3) (F2 N3))) (finite_finite_nat (collect_nat (lambda ((N2 nat)) ((ord_less_eq_nat (F2 N2)) U)))))) (forall ((A set_nat) (B set_nat) (C nat)) (let ((_let_1 (member_nat C))) (=> ((ord_less_eq_set_nat A) B) (=> (_let_1 A) (_let_1 B))))) (forall ((P2 (-> (-> nat nat nat) Bool)) (Q (-> (-> nat nat nat) Bool))) (=> (forall ((X2 (-> nat nat nat))) (= (P2 X2) (Q X2))) (= (collect_nat_nat_nat2 P2) (collect_nat_nat_nat2 Q)))) (forall ((N nat)) ((ord_less_eq_nat zero_zero_nat) N)) (forall ((A3 nat) (B3 nat) (F2 (-> nat set_nat_nat)) (C set_nat_nat)) (=> ((ord_less_eq_nat A3) B3) (=> ((ord_le1415039317at_nat (F2 B3)) C) (=> (forall ((X2 nat) (Y2 nat)) (=> ((ord_less_eq_nat X2) Y2) ((ord_le1415039317at_nat (F2 X2)) (F2 Y2)))) ((ord_le1415039317at_nat (F2 A3)) C))))) (forall ((P2 (-> (-> (-> nat nat) nat nat) Bool)) (Q (-> (-> (-> nat nat) nat nat) Bool))) (= ((ord_le2040082867at_nat (collec1610646258at_nat P2)) (collec1610646258at_nat Q)) (forall ((X (-> (-> nat nat) nat nat))) (=> (P2 X) (Q X))))) (forall ((A set_nat_nat) (P2 (-> (-> nat nat) Bool))) ((ord_le1415039317at_nat (collect_nat_nat (lambda ((X (-> nat nat))) (and ((member_nat_nat X) A) (P2 X))))) A)) _let_18 (forall ((A3 set_nat_nat) (B3 set_nat_nat) (F2 (-> set_nat_nat nat)) (C nat)) (=> ((ord_le1415039317at_nat A3) B3) (=> (= (F2 B3) C) (=> (forall ((X2 set_nat_nat) (Y2 set_nat_nat)) (=> ((ord_le1415039317at_nat X2) Y2) ((ord_less_eq_nat (F2 X2)) (F2 Y2)))) ((ord_less_eq_nat (F2 A3)) C))))) (forall ((B set_nat_nat) (A set_nat_nat) (Q (-> (-> nat nat) Bool)) (P2 (-> (-> nat nat) Bool))) (=> ((ord_le1415039317at_nat B) A) (=> (forall ((X2 (-> nat nat))) (=> ((member_nat_nat X2) B) (=> (Q X2) (P2 X2)))) ((ord_le1415039317at_nat (collect_nat_nat (lambda ((X (-> nat nat))) (and ((member_nat_nat X) B) (Q X))))) (collect_nat_nat (lambda ((X (-> nat nat))) (and (P2 X) ((member_nat_nat X) A)))))))) (forall ((N nat)) (= ((ord_less_nat N) one_one_nat) (= N zero_zero_nat))) (= (lambda ((Y4 nat) (Z nat)) (= Y4 Z)) (lambda ((A2 nat) (B4 nat)) (and ((ord_less_eq_nat B4) A2) ((ord_less_eq_nat A2) B4)))) (= (lambda ((Y4 nat) (Z nat)) (= Y4 Z)) (lambda ((A2 nat) (B4 nat)) (and ((ord_less_eq_nat B4) A2) ((ord_less_eq_nat A2) B4)))) (forall ((A3 nat) (B3 nat)) (= (= A3 ((plus_plus_nat B3) A3)) (= B3 zero_zero_nat))) (forall ((A3 nat) (C nat) (B3 nat)) (= ((ord_less_eq_nat ((plus_plus_nat A3) C)) ((plus_plus_nat B3) C)) ((ord_less_eq_nat A3) B3))) (forall ((A set_nat) (P2 (-> nat Bool)) (Q (-> nat Bool))) (let ((_let_1 (ord_less_eq_set_nat A))) (= (_let_1 (collect_nat (lambda ((X nat)) (and (P2 X) (Q X))))) (and (_let_1 (collect_nat P2)) (_let_1 (collect_nat Q)))))) (forall ((M nat) (K nat) (N nat)) (=> ((ord_less_eq_nat ((plus_plus_nat M) K)) N) ((ord_less_eq_nat K) N))) _let_17 (forall ((A3 nat) (B3 nat) (C nat)) (let ((_let_1 (ord_less_eq_nat B3))) (=> ((ord_less_eq_nat zero_zero_nat) A3) (=> (_let_1 C) (_let_1 ((plus_plus_nat A3) C)))))) (forall ((M nat)) (= ((plus_plus_nat M) zero_zero_nat) M)) (forall ((P2 (-> nat nat Bool)) (A3 nat) (B3 nat)) (=> (forall ((A4 nat) (B5 nat)) (= ((P2 A4) B5) ((P2 B5) A4))) (=> (forall ((A4 nat)) ((P2 A4) zero_zero_nat)) (=> (forall ((A4 nat) (B5 nat)) (let ((_let_1 (P2 A4))) (=> (_let_1 B5) (_let_1 ((plus_plus_nat A4) B5))))) ((P2 A3) B3))))) (= (lambda ((Y4 set_nat_nat) (Z set_nat_nat)) (= Y4 Z)) (lambda ((X set_nat_nat) (Y5 set_nat_nat)) (and ((ord_le1415039317at_nat Y5) X) ((ord_le1415039317at_nat X) Y5)))) _let_16 (forall ((A set_nat_nat_nat_nat3) (A3 (-> (-> nat nat) nat nat))) (=> (finite1064868788at_nat A) (=> ((member1128122036at_nat A3) A) (exists ((X2 (-> (-> nat nat) nat nat))) (and (forall ((Xa (-> (-> nat nat) nat nat))) (=> ((member1128122036at_nat Xa) A) (=> ((ord_le2059018749at_nat X2) Xa) (= X2 Xa)))) ((ord_le2059018749at_nat A3) X2) ((member1128122036at_nat X2) A)))))) (forall ((A3 set_nat_nat) (F2 (-> nat set_nat_nat)) (B3 nat) (C nat)) (=> (= A3 (F2 B3)) (=> ((ord_less_eq_nat B3) C) (=> (forall ((X2 nat) (Y2 nat)) (=> ((ord_less_eq_nat X2) Y2) ((ord_le1415039317at_nat (F2 X2)) (F2 Y2)))) ((ord_le1415039317at_nat A3) (F2 C)))))) (forall ((X3 (-> nat nat)) (Z3 set_nat_nat) (X5 set_nat_nat) (P2 (-> (-> nat nat) Bool))) (=> ((member_nat_nat X3) Z3) (=> ((ord_le1415039317at_nat Z3) (collect_nat_nat (lambda ((X (-> nat nat))) (and ((member_nat_nat X) X5) (P2 X))))) (P2 X3)))) (forall ((B set_nat_nat_nat) (A set_nat_nat_nat) (Q (-> (-> nat nat nat) Bool)) (P2 (-> (-> nat nat nat) Bool))) (=> ((ord_le940807492at_nat B) A) (=> (forall ((X2 (-> nat nat nat))) (=> ((member_nat_nat_nat2 X2) B) (=> (Q X2) (P2 X2)))) ((ord_le940807492at_nat (collect_nat_nat_nat2 (lambda ((X (-> nat nat nat))) (and ((member_nat_nat_nat2 X) B) (Q X))))) (collect_nat_nat_nat2 (lambda ((X (-> nat nat nat))) (and (P2 X) ((member_nat_nat_nat2 X) A)))))))) (forall ((X3 nat) (Y nat)) (=> (not ((ord_less_eq_nat X3) Y)) ((ord_less_eq_nat Y) X3))) (forall ((P2 (-> (-> (-> nat nat) nat) Bool)) (Q (-> (-> (-> nat nat) nat) Bool))) (= ((ord_le633272388at_nat (collect_nat_nat_nat P2)) (collect_nat_nat_nat Q)) (forall ((X (-> (-> nat nat) nat))) (=> (P2 X) (Q X))))) (forall ((X3 nat) (Y nat)) (= (= ((plus_plus_nat X3) Y) zero_zero_nat) (and (= Y zero_zero_nat) (= X3 zero_zero_nat)))) (forall ((A3 nat) (B3 nat)) (let ((_let_1 (ord_less_eq_nat zero_zero_nat))) (=> (_let_1 A3) (=> (_let_1 B3) (_let_1 ((plus_plus_nat A3) B3)))))) (= (lambda ((Y4 set_nat_nat) (Z set_nat_nat)) (= Y4 Z)) (lambda ((A2 set_nat_nat) (B4 set_nat_nat)) (and ((ord_le1415039317at_nat A2) B4) ((ord_le1415039317at_nat B4) A2)))) (_let_15 one_one_nat) _let_14 (forall ((A set_nat_nat_nat2) (P2 (-> (-> (-> nat nat) nat) Bool))) ((ord_le633272388at_nat (collect_nat_nat_nat (lambda ((X (-> (-> nat nat) nat))) (and ((member_nat_nat_nat X) A) (P2 X))))) A)) (forall ((X3 set_nat_nat) (Y set_nat_nat)) (=> ((ord_le1415039317at_nat X3) Y) (=> ((ord_le1415039317at_nat Y) X3) (= X3 Y)))) (forall ((A set_nat_nat_nat2) (P2 (-> (-> (-> nat nat) nat) Bool)) (Q (-> (-> (-> nat nat) nat) Bool))) (let ((_let_1 (ord_le633272388at_nat A))) (= (_let_1 (collect_nat_nat_nat (lambda ((X (-> (-> nat nat) nat))) (and (Q X) (P2 X))))) (and (_let_1 (collect_nat_nat_nat P2)) (_let_1 (collect_nat_nat_nat Q)))))) (forall ((A set_nat_nat) (B set_nat) (D nat)) (=> (finite570312790at_nat A) (=> (finite_finite_nat B) (finite1440337093at_nat (collect_nat_nat_nat (lambda ((F (-> (-> nat nat) nat))) (forall ((X (-> nat nat))) (let ((_let_1 (F X))) (let ((_let_2 ((member_nat_nat X) A))) (and (=> (not _let_2) (= _let_1 D)) (=> _let_2 ((member_nat _let_1) B)))))))))))) (forall ((A3 nat) (B3 nat) (C nat) (D nat)) (=> ((ord_less_nat A3) B3) (=> ((ord_less_eq_nat C) D) ((ord_less_nat ((plus_plus_nat A3) C)) ((plus_plus_nat B3) D))))) (forall ((P2 (-> nat Bool))) (=> (not (finite_finite_nat (collect_nat P2))) (exists ((X_1 nat)) (P2 X_1)))) (forall ((A set_nat) (B set_nat_nat) (D (-> nat nat))) (=> (finite_finite_nat A) (=> (finite570312790at_nat B) (finite2045569477at_nat (collect_nat_nat_nat2 (lambda ((F (-> nat nat nat))) (forall ((X nat)) (let ((_let_1 (F X))) (let ((_let_2 ((member_nat X) A))) (and (=> (not _let_2) (= _let_1 D)) (=> _let_2 ((member_nat_nat _let_1) B)))))))))))) (forall ((A set_nat) (B set_nat_nat) (R (-> nat (-> nat nat) Bool))) (=> (not (finite_finite_nat A)) (=> (finite570312790at_nat B) (=> (forall ((X2 nat)) (=> ((member_nat X2) A) (exists ((Xa (-> nat nat))) (and ((R X2) Xa) ((member_nat_nat Xa) B))))) (exists ((X2 (-> nat nat))) (and ((member_nat_nat X2) B) (not (finite_finite_nat (collect_nat (lambda ((A2 nat)) (and ((member_nat A2) A) ((R A2) X2)))))))))))) (forall ((N nat) (M nat)) ((ord_less_eq_nat N) ((plus_plus_nat N) M))) (forall ((B set_nat_nat_nat_nat3) (A set_nat_nat_nat_nat3) (P2 (-> (-> (-> nat nat) nat nat) Bool))) (let ((_let_1 (ord_le2040082867at_nat B))) (=> (_let_1 A) (= (_let_1 (collec1610646258at_nat (lambda ((X (-> (-> nat nat) nat nat))) (and (P2 X) ((member1128122036at_nat X) A))))) (forall ((X (-> (-> nat nat) nat nat))) (=> ((member1128122036at_nat X) B) (P2 X))))))) (forall ((I2 nat) (J nat) (K nat) (L nat)) (=> (and ((ord_less_eq_nat K) L) ((ord_less_eq_nat I2) J)) ((ord_less_eq_nat ((plus_plus_nat I2) K)) ((plus_plus_nat J) L)))) (forall ((A3 nat) (C nat) (B3 nat)) (=> ((ord_less_eq_nat ((plus_plus_nat A3) C)) ((plus_plus_nat B3) C)) ((ord_less_eq_nat A3) B3))) (forall ((X3 set_nat_nat) (Y set_nat_nat)) (=> (= X3 Y) ((ord_le1415039317at_nat X3) Y))) _let_13 (forall ((N nat)) (= ((ord_less_eq_nat N) zero_zero_nat) (= N zero_zero_nat))) (forall ((B3 set_nat_nat) (A3 set_nat_nat)) (=> ((ord_le1415039317at_nat B3) A3) (=> ((ord_le1415039317at_nat A3) B3) (= A3 B3)))) (forall ((A set_nat) (P2 (-> nat Bool))) ((ord_less_eq_set_nat (collect_nat (lambda ((X nat)) (and ((member_nat X) A) (P2 X))))) A)) (forall ((A3 nat)) (= ((plus_plus_nat A3) zero_zero_nat) A3)) (forall ((X3 nat) (Y nat)) (=> ((ord_less_eq_nat X3) zero_zero_nat) (=> ((ord_less_eq_nat Y) zero_zero_nat) (= (= ((plus_plus_nat X3) Y) zero_zero_nat) (and (= X3 zero_zero_nat) (= Y zero_zero_nat)))))) (_let_12 one_one_nat) (forall ((A3 nat)) (= ((plus_plus_nat A3) zero_zero_nat) A3)) (forall ((A set_nat) (A3 nat)) (=> (finite_finite_nat A) (=> ((member_nat A3) A) (exists ((X2 nat)) (and ((ord_less_eq_nat A3) X2) (forall ((Xa nat)) (=> ((member_nat Xa) A) (=> ((ord_less_eq_nat X2) Xa) (= X2 Xa)))) ((member_nat X2) A)))))) (forall ((B3 nat) (A3 nat)) (= ((ord_less_nat ((plus_plus_nat B3) A3)) B3) ((ord_less_nat A3) zero_zero_nat))) (= ord_less_set_nat_nat (lambda ((A2 set_nat_nat) (B4 set_nat_nat)) (and ((ord_le1415039317at_nat A2) B4) (not (= A2 B4))))) (forall ((A set_nat_nat_nat2) (A3 (-> (-> nat nat) nat))) (=> (finite1440337093at_nat A) (=> ((member_nat_nat_nat A3) A) (exists ((X2 (-> (-> nat nat) nat))) (and ((ord_le809907342at_nat X2) A3) (forall ((Xa (-> (-> nat nat) nat))) (=> ((member_nat_nat_nat Xa) A) (=> ((ord_le809907342at_nat Xa) X2) (= X2 Xa)))) ((member_nat_nat_nat X2) A)))))) (forall ((A set_nat_nat_nat_nat3) (P2 (-> (-> (-> nat nat) nat nat) Bool)) (Q (-> (-> (-> nat nat) nat nat) Bool))) (let ((_let_1 (ord_le2040082867at_nat A))) (= (_let_1 (collec1610646258at_nat (lambda ((X (-> (-> nat nat) nat nat))) (and (Q X) (P2 X))))) (and (_let_1 (collec1610646258at_nat Q)) (_let_1 (collec1610646258at_nat P2)))))) (forall ((B set_nat_nat_nat) (A set_nat_nat_nat) (P2 (-> (-> nat nat nat) Bool))) (let ((_let_1 (ord_le940807492at_nat B))) (=> (_let_1 A) (= (_let_1 (collect_nat_nat_nat2 (lambda ((X (-> nat nat nat))) (and ((member_nat_nat_nat2 X) A) (P2 X))))) (forall ((X (-> nat nat nat))) (=> ((member_nat_nat_nat2 X) B) (P2 X))))))) (forall ((B set_nat_nat_nat_nat3) (A set_nat_nat_nat_nat3) (Q (-> (-> (-> nat nat) nat nat) Bool)) (P2 (-> (-> (-> nat nat) nat nat) Bool))) (=> ((ord_le2040082867at_nat B) A) (=> (forall ((X2 (-> (-> nat nat) nat nat))) (=> ((member1128122036at_nat X2) B) (=> (Q X2) (P2 X2)))) ((ord_le2040082867at_nat (collec1610646258at_nat (lambda ((X (-> (-> nat nat) nat nat))) (and ((member1128122036at_nat X) B) (Q X))))) (collec1610646258at_nat (lambda ((X (-> (-> nat nat) nat nat))) (and (P2 X) ((member1128122036at_nat X) A)))))))) _let_11 (forall ((A3 nat) (B3 nat) (C nat)) (=> (= A3 B3) (=> ((ord_less_eq_nat B3) C) ((ord_less_eq_nat A3) C)))) (= ord_le1415039317at_nat (lambda ((A5 set_nat_nat) (B2 set_nat_nat)) (forall ((T2 (-> nat nat))) (let ((_let_1 (member_nat_nat T2))) (=> (_let_1 A5) (_let_1 B2)))))) (forall ((B set_nat) (A set_nat) (P2 (-> nat Bool))) (let ((_let_1 (ord_less_eq_set_nat B))) (=> (_let_1 A) (= (_let_1 (collect_nat (lambda ((X nat)) (and (P2 X) ((member_nat X) A))))) (forall ((X nat)) (=> ((member_nat X) B) (P2 X))))))) (forall ((A set_nat_nat_nat) (B set_nat) (D nat)) (=> (finite2045569477at_nat A) (=> (finite_finite_nat B) (finite2081887156at_nat (collec480180978at_nat (lambda ((F (-> (-> nat nat nat) nat))) (forall ((X (-> nat nat nat))) (let ((_let_1 (F X))) (let ((_let_2 ((member_nat_nat_nat2 X) A))) (and (=> (not _let_2) (= _let_1 D)) (=> _let_2 ((member_nat _let_1) B)))))))))))) (forall ((A set_nat) (A3 nat)) (=> (finite_finite_nat A) (=> ((member_nat A3) A) (exists ((X2 nat)) (and ((member_nat X2) A) (forall ((Xa nat)) (=> ((member_nat Xa) A) (=> ((ord_less_eq_nat Xa) X2) (= X2 Xa)))) ((ord_less_eq_nat X2) A3)))))) (forall ((Y nat) (X3 nat)) (=> ((ord_less_eq_nat Y) X3) (= ((ord_less_eq_nat X3) Y) (= X3 Y)))) (forall ((A3 nat) (B3 nat) (C nat)) (let ((_let_1 (plus_plus_nat A3))) (= (= (_let_1 B3) (_let_1 C)) (= B3 C)))) (forall ((A set_nat_nat) (B set_nat) (R (-> (-> nat nat) nat Bool))) (=> (not (finite570312790at_nat A)) (=> (finite_finite_nat B) (=> (forall ((X2 (-> nat nat))) (=> ((member_nat_nat X2) A) (exists ((Xa nat)) (and ((member_nat Xa) B) ((R X2) Xa))))) (exists ((X2 nat)) (and (not (finite570312790at_nat (collect_nat_nat (lambda ((A2 (-> nat nat))) (and ((R A2) X2) ((member_nat_nat A2) A)))))) ((member_nat X2) B))))))) (forall ((A set_nat_nat) (B set_nat_nat_nat2) (R (-> (-> nat nat) (-> (-> nat nat) nat) Bool))) (=> (not (finite570312790at_nat A)) (=> (finite1440337093at_nat B) (=> (forall ((X2 (-> nat nat))) (=> ((member_nat_nat X2) A) (exists ((Xa (-> (-> nat nat) nat))) (and ((R X2) Xa) ((member_nat_nat_nat Xa) B))))) (exists ((X2 (-> (-> nat nat) nat))) (and (not (finite570312790at_nat (collect_nat_nat (lambda ((A2 (-> nat nat))) (and ((member_nat_nat A2) A) ((R A2) X2)))))) ((member_nat_nat_nat X2) B))))))) (forall ((A set_nat_nat_nat)) (=> (finite2045569477at_nat A) (finite137548155at_nat (collec617280953at_nat (lambda ((B2 set_nat_nat_nat)) ((ord_le940807492at_nat B2) A)))))) (forall ((A set_nat) (B set_nat_nat_nat2) (R (-> nat (-> (-> nat nat) nat) Bool))) (=> (not (finite_finite_nat A)) (=> (finite1440337093at_nat B) (=> (forall ((X2 nat)) (=> ((member_nat X2) A) (exists ((Xa (-> (-> nat nat) nat))) (and ((member_nat_nat_nat Xa) B) ((R X2) Xa))))) (exists ((X2 (-> (-> nat nat) nat))) (and ((member_nat_nat_nat X2) B) (not (finite_finite_nat (collect_nat (lambda ((A2 nat)) (and ((member_nat A2) A) ((R A2) X2)))))))))))) (forall ((A set_nat_nat_nat) (A3 (-> nat nat nat))) (=> (finite2045569477at_nat A) (=> ((member_nat_nat_nat2 A3) A) (exists ((X2 (-> nat nat nat))) (and ((member_nat_nat_nat2 X2) A) (forall ((Xa (-> nat nat nat))) (=> ((member_nat_nat_nat2 Xa) A) (=> ((ord_le1415139726at_nat X2) Xa) (= X2 Xa)))) ((ord_le1415139726at_nat A3) X2)))))) (forall ((A3 nat) (B3 nat)) (= ((ord_less_eq_nat A3) ((plus_plus_nat A3) B3)) ((ord_less_eq_nat zero_zero_nat) B3))) (= ord_less_nat (lambda ((M2 nat) (N2 nat)) (and (not (= M2 N2)) ((ord_less_eq_nat M2) N2)))) (forall ((A3 nat) (B3 nat) (C nat) (D nat)) (=> ((ord_less_eq_nat A3) B3) (=> ((ord_less_eq_nat C) D) ((ord_less_eq_nat ((plus_plus_nat A3) C)) ((plus_plus_nat B3) D))))) (forall ((A set_nat_nat) (B set_nat_nat_nat2) (D (-> (-> nat nat) nat))) (=> (finite570312790at_nat A) (=> (finite1440337093at_nat B) (finite1090277411at_nat (collec6783585at_nat (lambda ((F (-> (-> nat nat) (-> nat nat) nat))) (forall ((X (-> nat nat))) (let ((_let_1 (F X))) (let ((_let_2 ((member_nat_nat X) A))) (and (=> _let_2 ((member_nat_nat_nat _let_1) B)) (=> (not _let_2) (= _let_1 D)))))))))))) (forall ((B3 set_nat_nat) (A3 set_nat_nat) (C set_nat_nat)) (let ((_let_1 (ord_le1415039317at_nat C))) (=> ((ord_le1415039317at_nat B3) A3) (=> (_let_1 B3) (_let_1 A3))))) (forall ((A3 nat) (B3 nat) (C nat) (D nat)) (=> ((ord_less_eq_nat A3) B3) (=> ((ord_less_nat C) D) ((ord_less_nat ((plus_plus_nat A3) C)) ((plus_plus_nat B3) D))))) (forall ((Y set_nat_nat) (X3 set_nat_nat)) (=> ((ord_le1415039317at_nat Y) X3) (= ((ord_le1415039317at_nat X3) Y) (= X3 Y)))) (forall ((A set_nat_nat_nat2)) (= (collect_nat_nat_nat (lambda ((X (-> (-> nat nat) nat))) ((member_nat_nat_nat X) A))) A)) (forall ((F2 (-> nat nat)) (I2 nat) (J nat)) (=> (forall ((I4 nat) (J2 nat)) (=> ((ord_less_nat I4) J2) ((ord_less_nat (F2 I4)) (F2 J2)))) (=> ((ord_less_eq_nat I2) J) ((ord_less_eq_nat (F2 I2)) (F2 J))))) (forall ((P2 (-> (-> (-> nat nat) nat nat) Bool))) (=> (not (finite1064868788at_nat (collec1610646258at_nat P2))) (exists ((X_1 (-> (-> nat nat) nat nat))) (P2 X_1)))) (forall ((K nat)) (finite_finite_nat (collect_nat (lambda ((N2 nat)) ((ord_less_nat N2) K))))) (forall ((P2 (-> (-> (-> nat nat) nat nat) Bool)) (Q (-> (-> (-> nat nat) nat nat) Bool))) (=> (forall ((X2 (-> (-> nat nat) nat nat))) (= (P2 X2) (Q X2))) (= (collec1610646258at_nat P2) (collec1610646258at_nat Q)))) (forall ((A set_nat_nat_nat) (P2 (-> (-> nat nat nat) Bool)) (Q (-> (-> nat nat nat) Bool))) (let ((_let_1 (ord_le940807492at_nat A))) (= (_let_1 (collect_nat_nat_nat2 (lambda ((X (-> nat nat nat))) (and (Q X) (P2 X))))) (and (_let_1 (collect_nat_nat_nat2 P2)) (_let_1 (collect_nat_nat_nat2 Q)))))) (forall ((A set_nat)) (=> (finite_finite_nat A) (finite2012248349et_nat (collect_set_nat (lambda ((B2 set_nat)) ((ord_less_eq_set_nat B2) A)))))) (forall ((A3 nat) (B3 nat) (F2 (-> nat nat)) (C nat)) (=> ((ord_less_eq_nat A3) B3) (=> (= (F2 B3) C) (=> (forall ((X2 nat) (Y2 nat)) (=> ((ord_less_eq_nat X2) Y2) ((ord_less_eq_nat (F2 X2)) (F2 Y2)))) ((ord_less_eq_nat (F2 A3)) C))))) (forall ((M nat) (N nat)) (=> ((ord_less_eq_nat M) N) (=> ((ord_less_eq_nat N) M) (= M N)))) (forall ((A set_nat_nat_nat_nat3)) (= (collec1610646258at_nat (lambda ((X (-> (-> nat nat) nat nat))) ((member1128122036at_nat X) A))) A)) (= (lambda ((Y4 set_nat_nat) (Z set_nat_nat)) (= Y4 Z)) (lambda ((A5 set_nat_nat) (B2 set_nat_nat)) (and ((ord_le1415039317at_nat B2) A5) ((ord_le1415039317at_nat A5) B2)))) (forall ((P2 (-> (-> (-> nat nat) nat nat) Bool)) (Q (-> (-> (-> nat nat) nat nat) Bool))) (= (finite1064868788at_nat (collec1610646258at_nat (lambda ((X (-> (-> nat nat) nat nat))) (or (Q X) (P2 X))))) (and (finite1064868788at_nat (collec1610646258at_nat Q)) (finite1064868788at_nat (collec1610646258at_nat P2))))) (= ord_less_nat (lambda ((A2 nat) (B4 nat)) (and ((ord_less_eq_nat A2) B4) (not (= A2 B4))))) (forall ((A3 nat) (B3 nat) (C nat)) (let ((_let_1 (ord_less_eq_nat A3))) (=> (_let_1 B3) (=> ((ord_less_eq_nat B3) C) (_let_1 C))))) (forall ((B set_nat) (A set_nat)) (=> (finite_finite_nat B) (=> ((ord_less_eq_set_nat A) B) (finite_finite_nat A)))) (forall ((P2 (-> nat Bool)) (I2 nat)) (finite_finite_nat (collect_nat (lambda ((K2 nat)) (and (P2 K2) ((ord_less_nat K2) I2)))))) (forall ((X3 nat) (Y nat)) (or ((ord_less_eq_nat X3) Y) ((ord_less_eq_nat Y) X3))) (forall ((B3 set_nat_nat) (A3 set_nat_nat) (C set_nat_nat)) (=> ((ord_less_set_nat_nat B3) A3) (=> ((ord_le1415039317at_nat C) B3) ((ord_less_set_nat_nat C) A3)))) (forall ((N nat)) (= ((plus_plus_nat zero_zero_nat) N) N)) (forall ((X3 nat) (Y nat)) (=> (= X3 Y) ((ord_less_eq_nat X3) Y))) (forall ((A set_nat_nat_nat2) (B set_nat) (D nat)) (=> (finite1440337093at_nat A) (=> (finite_finite_nat B) (finite1526199988at_nat (collec2071977458at_nat (lambda ((F (-> (-> (-> nat nat) nat) nat))) (forall ((X (-> (-> nat nat) nat))) (let ((_let_1 (F X))) (let ((_let_2 ((member_nat_nat_nat X) A))) (and (=> (not _let_2) (= _let_1 D)) (=> _let_2 ((member_nat _let_1) B)))))))))))) (forall ((A3 nat)) (= ((plus_plus_nat zero_zero_nat) A3) A3)) (forall ((A set_nat_nat_nat_nat3) (B set_nat_nat_nat_nat3)) (=> ((ord_le2040082867at_nat A) B) (=> (finite1064868788at_nat B) (finite1064868788at_nat A)))) (forall ((A3 nat) (B3 nat)) (= ((ord_less_nat ((plus_plus_nat A3) B3)) B3) ((ord_less_nat A3) zero_zero_nat))) (= plus_plus_nat (lambda ((A2 nat) (B4 nat)) ((plus_plus_nat B4) A2))) (forall ((B3 nat) (A3 nat) (C nat)) (= (= ((plus_plus_nat B3) A3) ((plus_plus_nat C) A3)) (= B3 C))) (forall ((A3 nat) (B3 nat)) (= (= ((plus_plus_nat A3) B3) A3) (= B3 zero_zero_nat))) (forall ((I2 nat) (J nat) (K nat) (L nat)) (=> (and ((ord_less_eq_nat I2) J) ((ord_less_nat K) L)) ((ord_less_nat ((plus_plus_nat I2) K)) ((plus_plus_nat J) L)))) (forall ((A set_nat_nat_nat) (B set_nat) (R (-> (-> nat nat nat) nat Bool))) (=> (not (finite2045569477at_nat A)) (=> (finite_finite_nat B) (=> (forall ((X2 (-> nat nat nat))) (=> ((member_nat_nat_nat2 X2) A) (exists ((Xa nat)) (and ((R X2) Xa) ((member_nat Xa) B))))) (exists ((X2 nat)) (and ((member_nat X2) B) (not (finite2045569477at_nat (collect_nat_nat_nat2 (lambda ((A2 (-> nat nat nat))) (and ((R A2) X2) ((member_nat_nat_nat2 A2) A)))))))))))) (forall ((I2 nat) (J nat) (M nat)) (let ((_let_1 (ord_less_eq_nat I2))) (=> (_let_1 J) (_let_1 ((plus_plus_nat M) J))))) (forall ((B3 nat) (A3 nat)) (=> ((ord_less_nat B3) A3) ((ord_less_eq_nat B3) A3))) (forall ((A3 set_nat_nat) (F2 (-> nat set_nat_nat)) (B3 nat) (C nat)) (let ((_let_1 (ord_le1415039317at_nat A3))) (=> (_let_1 (F2 B3)) (=> ((ord_less_eq_nat B3) C) (=> (forall ((X2 nat) (Y2 nat)) (=> ((ord_less_eq_nat X2) Y2) ((ord_le1415039317at_nat (F2 X2)) (F2 Y2)))) (_let_1 (F2 C))))))) (forall ((A3 nat) (B3 nat) (C nat)) (let ((_let_1 (ord_less_nat B3))) (=> ((ord_less_nat zero_zero_nat) A3) (=> (_let_1 C) (_let_1 ((plus_plus_nat A3) C)))))) (forall ((I3 set_nat_nat_nat_nat3) (X3 (-> (-> (-> nat nat) nat nat) nat)) (Y (-> (-> (-> nat nat) nat nat) nat))) (=> (finite1064868788at_nat (collec1610646258at_nat (lambda ((I (-> (-> nat nat) nat nat))) (and ((member1128122036at_nat I) I3) (not (= (X3 I) zero_zero_nat)))))) (=> (finite1064868788at_nat (collec1610646258at_nat (lambda ((I (-> (-> nat nat) nat nat))) (and (not (= (Y I) zero_zero_nat)) ((member1128122036at_nat I) I3))))) (finite1064868788at_nat (collec1610646258at_nat (lambda ((I (-> (-> nat nat) nat nat))) (and (not (= ((plus_plus_nat (X3 I)) (Y I)) zero_zero_nat)) ((member1128122036at_nat I) I3)))))))) (forall ((A3 set_nat_nat)) ((ord_le1415039317at_nat A3) A3)) (forall ((N nat) (M nat)) ((ord_less_eq_nat N) ((plus_plus_nat M) N))) (forall ((M nat) (N nat)) (=> ((ord_less_nat M) N) ((ord_less_eq_nat M) N))) (forall ((A3 set_nat_nat) (B3 set_nat_nat) (C set_nat_nat)) (let ((_let_1 (ord_le1415039317at_nat A3))) (=> (_let_1 B3) (=> (= B3 C) (_let_1 C))))) (forall ((I2 nat) (J nat) (K nat) (L nat)) (=> (and (= I2 J) ((ord_less_eq_nat K) L)) ((ord_less_eq_nat ((plus_plus_nat I2) K)) ((plus_plus_nat J) L)))) (forall ((P3 (-> nat nat)) (N nat)) (=> ((number1551313001itions P3) N) (finite_finite_nat (collect_nat (lambda ((I nat)) ((ord_less_nat zero_zero_nat) (P3 I))))))) (forall ((P2 (-> (-> nat nat nat) Bool)) (Q (-> (-> nat nat nat) Bool))) (= (finite2045569477at_nat (collect_nat_nat_nat2 (lambda ((X (-> nat nat nat))) (or (P2 X) (Q X))))) (and (finite2045569477at_nat (collect_nat_nat_nat2 P2)) (finite2045569477at_nat (collect_nat_nat_nat2 Q))))) (forall ((A set_nat) (B set_nat)) (=> (forall ((X2 nat)) (let ((_let_1 (member_nat X2))) (=> (_let_1 A) (_let_1 B)))) ((ord_less_eq_set_nat A) B))) (forall ((A3 set_nat_nat) (B3 set_nat_nat) (C set_nat_nat)) (let ((_let_1 (ord_less_set_nat_nat A3))) (=> (_let_1 B3) (=> ((ord_le1415039317at_nat B3) C) (_let_1 C))))) (forall ((A set_nat_nat_nat2) (A3 (-> (-> nat nat) nat))) (=> (finite1440337093at_nat A) (=> ((member_nat_nat_nat A3) A) (exists ((X2 (-> (-> nat nat) nat))) (and (forall ((Xa (-> (-> nat nat) nat))) (=> ((member_nat_nat_nat Xa) A) (=> ((ord_le809907342at_nat X2) Xa) (= X2 Xa)))) ((ord_le809907342at_nat A3) X2) ((member_nat_nat_nat X2) A)))))) (forall ((N nat)) ((ord_less_eq_nat zero_zero_nat) N)) (forall ((A3 nat)) (=> ((ord_less_eq_nat A3) zero_zero_nat) (= A3 zero_zero_nat))) (forall ((A set_nat_nat) (P2 (-> (-> nat nat) Bool)) (Q (-> (-> nat nat) Bool))) (let ((_let_1 (ord_le1415039317at_nat A))) (= (_let_1 (collect_nat_nat (lambda ((X (-> nat nat))) (and (Q X) (P2 X))))) (and (_let_1 (collect_nat_nat P2)) (_let_1 (collect_nat_nat Q)))))) (forall ((A3 nat)) ((ord_less_eq_nat A3) A3)) (forall ((A set_nat_nat) (B set_nat_nat) (C (-> nat nat))) (let ((_let_1 (member_nat_nat C))) (=> ((ord_le1415039317at_nat A) B) (=> (_let_1 A) (_let_1 B))))) (forall ((A3 set_nat_nat) (B3 set_nat_nat) (C set_nat_nat)) (let ((_let_1 (ord_le1415039317at_nat A3))) (=> (_let_1 B3) (=> ((ord_le1415039317at_nat B3) C) (_let_1 C))))) (forall ((A3 nat) (B3 nat)) (=> ((ord_less_nat A3) B3) (not (forall ((C3 nat)) (=> (= B3 ((plus_plus_nat A3) C3)) (= C3 zero_zero_nat)))))) (forall ((A3 nat) (C nat) (B3 nat)) (= ((ord_less_nat ((plus_plus_nat A3) C)) ((plus_plus_nat B3) C)) ((ord_less_nat A3) B3))) (= ord_le1415039317at_nat (lambda ((A2 set_nat_nat) (B4 set_nat_nat)) (or ((ord_less_set_nat_nat A2) B4) (= A2 B4)))) (forall ((A3 nat) (P2 (-> nat Bool))) (= ((member_nat A3) (collect_nat P2)) (P2 A3))) (forall ((A set_nat_nat) (B set_nat_nat)) (=> ((ord_le1415039317at_nat A) B) (=> ((ord_le1415039317at_nat B) A) (= A B)))) (forall ((C nat) (A3 nat) (B3 nat)) (let ((_let_1 (plus_plus_nat C))) (= ((ord_less_nat (_let_1 A3)) (_let_1 B3)) ((ord_less_nat A3) B3)))) (forall ((A set_nat_nat) (B set_nat_nat_nat) (D (-> nat nat nat))) (=> (finite570312790at_nat A) (=> (finite2045569477at_nat B) (finite1397812515at_nat (collec314318689at_nat (lambda ((F (-> (-> nat nat) nat nat nat))) (forall ((X (-> nat nat))) (let ((_let_1 (F X))) (let ((_let_2 ((member_nat_nat X) A))) (and (=> (not _let_2) (= _let_1 D)) (=> _let_2 ((member_nat_nat_nat2 _let_1) B)))))))))))) (forall ((A3 nat)) (= ((ord_less_eq_nat A3) zero_zero_nat) (= A3 zero_zero_nat))) (forall ((A set_nat_nat_nat_nat3)) (=> (finite1064868788at_nat A) (finite547180394at_nat (collec1702444712at_nat (lambda ((B2 set_nat_nat_nat_nat3)) ((ord_le2040082867at_nat B2) A)))))) (forall ((K nat) (M nat) (N nat)) (let ((_let_1 (plus_plus_nat K))) (= ((ord_less_eq_nat (_let_1 M)) (_let_1 N)) ((ord_less_eq_nat M) N)))) (forall ((S set_nat) (T set_nat)) (=> ((ord_less_eq_set_nat S) T) (=> (not (finite_finite_nat S)) (not (finite_finite_nat T))))) _let_10 (forall ((A3 set_nat_nat) (B3 set_nat_nat)) (=> ((ord_less_set_nat_nat A3) B3) ((ord_le1415039317at_nat A3) B3))) (forall ((C nat) (B3 nat) (A3 nat)) (let ((_let_1 (ord_less_eq_nat B3))) (=> ((ord_less_eq_nat zero_zero_nat) C) (=> (_let_1 A3) (_let_1 ((plus_plus_nat A3) C)))))) (forall ((A set_nat_nat) (B set_nat_nat)) (=> (= A B) ((ord_le1415039317at_nat B) A))) (forall ((P2 (-> (-> nat nat nat) Bool)) (Q (-> (-> nat nat nat) Bool))) (=> (forall ((X2 (-> nat nat nat))) (=> (P2 X2) (Q X2))) ((ord_le940807492at_nat (collect_nat_nat_nat2 P2)) (collect_nat_nat_nat2 Q)))) (forall ((A3 nat) (B3 nat)) (= (= A3 ((plus_plus_nat A3) B3)) (= B3 zero_zero_nat))) (forall ((X3 nat) (Y nat) (Z2 nat)) (let ((_let_1 (ord_less_eq_nat X3))) (let ((_let_2 (_let_1 Y))) (let ((_let_3 (ord_less_eq_nat Z2))) (let ((_let_4 (_let_3 X3))) (let ((_let_5 (ord_less_eq_nat Y))) (let ((_let_6 (_let_5 Z2))) (let ((_let_7 (_let_5 X3))) (let ((_let_8 (_let_3 Y))) (let ((_let_9 (_let_1 Z2))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))) (forall ((A3 set_nat_nat) (B3 set_nat_nat) (C set_nat_nat)) (=> (= A3 B3) (=> ((ord_le1415039317at_nat B3) C) ((ord_le1415039317at_nat A3) C)))) (forall ((B3 nat) (A3 nat) (C nat)) (=> ((ord_less_nat B3) A3) (=> ((ord_less_eq_nat C) B3) ((ord_less_nat C) A3)))) (forall ((I3 set_nat_nat_nat) (X3 (-> (-> nat nat nat) nat)) (Y (-> (-> nat nat nat) nat))) (=> (finite2045569477at_nat (collect_nat_nat_nat2 (lambda ((I (-> nat nat nat))) (and (not (= (X3 I) zero_zero_nat)) ((member_nat_nat_nat2 I) I3))))) (=> (finite2045569477at_nat (collect_nat_nat_nat2 (lambda ((I (-> nat nat nat))) (and ((member_nat_nat_nat2 I) I3) (not (= (Y I) zero_zero_nat)))))) (finite2045569477at_nat (collect_nat_nat_nat2 (lambda ((I (-> nat nat nat))) (and ((member_nat_nat_nat2 I) I3) (not (= ((plus_plus_nat (X3 I)) (Y I)) zero_zero_nat))))))))) (forall ((X3 nat) (Y nat)) (=> ((ord_less_eq_nat X3) Y) (=> ((ord_less_eq_nat Y) X3) (= X3 Y)))) (forall ((P2 (-> (-> nat nat) Bool))) (=> (not (finite570312790at_nat (collect_nat_nat P2))) (exists ((X_1 (-> nat nat))) (P2 X_1)))) (forall ((I2 nat) (J nat) (K nat)) (=> ((ord_less_eq_nat I2) J) ((ord_less_eq_nat ((plus_plus_nat I2) K)) ((plus_plus_nat J) K)))) (forall ((A3 nat) (B3 nat)) (=> ((ord_less_eq_nat A3) B3) (=> ((ord_less_eq_nat B3) A3) (= A3 B3)))) _let_9 (forall ((B set_nat_nat_nat2) (A set_nat_nat_nat2) (Q (-> (-> (-> nat nat) nat) Bool)) (P2 (-> (-> (-> nat nat) nat) Bool))) (=> ((ord_le633272388at_nat B) A) (=> (forall ((X2 (-> (-> nat nat) nat))) (=> ((member_nat_nat_nat X2) B) (=> (Q X2) (P2 X2)))) ((ord_le633272388at_nat (collect_nat_nat_nat (lambda ((X (-> (-> nat nat) nat))) (and (Q X) ((member_nat_nat_nat X) B))))) (collect_nat_nat_nat (lambda ((X (-> (-> nat nat) nat))) (and ((member_nat_nat_nat X) A) (P2 X)))))))) (forall ((X3 nat) (Z3 set_nat) (X5 set_nat) (P2 (-> nat Bool))) (=> ((member_nat X3) Z3) (=> ((ord_less_eq_set_nat Z3) (collect_nat (lambda ((X nat)) (and ((member_nat X) X5) (P2 X))))) (P2 X3)))) (= ord_le1415039317at_nat (lambda ((A5 set_nat_nat) (B2 set_nat_nat)) (forall ((X (-> nat nat))) (let ((_let_1 (member_nat_nat X))) (=> (_let_1 A5) (_let_1 B2)))))) _let_7 (forall ((X3 set_nat_nat) (Y set_nat_nat) (Z2 set_nat_nat)) (let ((_let_1 (ord_le1415039317at_nat X3))) (=> (_let_1 Y) (=> ((ord_le1415039317at_nat Y) Z2) (_let_1 Z2))))) (forall ((A3 set_nat_nat) (F2 (-> set_nat_nat set_nat_nat)) (B3 set_nat_nat) (C set_nat_nat)) (=> (= A3 (F2 B3)) (=> ((ord_le1415039317at_nat B3) C) (=> (forall ((X2 set_nat_nat) (Y2 set_nat_nat)) (=> ((ord_le1415039317at_nat X2) Y2) ((ord_le1415039317at_nat (F2 X2)) (F2 Y2)))) ((ord_le1415039317at_nat A3) (F2 C)))))) (forall ((A3 nat) (F2 (-> set_nat_nat nat)) (B3 set_nat_nat) (C set_nat_nat)) (=> (= A3 (F2 B3)) (=> ((ord_le1415039317at_nat B3) C) (=> (forall ((X2 set_nat_nat) (Y2 set_nat_nat)) (=> ((ord_le1415039317at_nat X2) Y2) ((ord_less_eq_nat (F2 X2)) (F2 Y2)))) ((ord_less_eq_nat A3) (F2 C)))))) (= ord_le1415039317at_nat (lambda ((A5 set_nat_nat) (B2 set_nat_nat)) ((ord_le2026740592_nat_o (lambda ((X (-> nat nat))) ((member_nat_nat X) A5))) (lambda ((X (-> nat nat))) ((member_nat_nat X) B2))))) (forall ((A set_nat_nat_nat)) (= (collect_nat_nat_nat2 (lambda ((X (-> nat nat nat))) ((member_nat_nat_nat2 X) A))) A)) (forall ((A set_nat_nat) (A3 (-> nat nat))) (=> (finite570312790at_nat A) (=> ((member_nat_nat A3) A) (exists ((X2 (-> nat nat))) (and ((member_nat_nat X2) A) ((ord_less_eq_nat_nat A3) X2) (forall ((Xa (-> nat nat))) (=> ((member_nat_nat Xa) A) (=> ((ord_less_eq_nat_nat X2) Xa) (= X2 Xa))))))))) _let_6 (forall ((A3 (-> (-> nat nat) nat)) (P2 (-> (-> (-> nat nat) nat) Bool))) (= ((member_nat_nat_nat A3) (collect_nat_nat_nat P2)) (P2 A3))) (forall ((S set_nat_nat_nat_nat3) (T set_nat_nat_nat_nat3)) (=> ((ord_le2040082867at_nat S) T) (=> (not (finite1064868788at_nat S)) (not (finite1064868788at_nat T))))) (forall ((A set_nat_nat)) (= (collect_nat_nat (lambda ((X (-> nat nat))) ((member_nat_nat X) A))) A)) (forall ((N nat)) (not ((ord_less_nat N) zero_zero_nat))) (forall ((A set_nat_nat_nat2)) (=> (finite1440337093at_nat A) (finite1977496699at_nat (collec309745849at_nat (lambda ((B2 set_nat_nat_nat2)) ((ord_le633272388at_nat B2) A)))))) (forall ((C nat) (A3 nat) (B3 nat)) (let ((_let_1 (plus_plus_nat C))) (=> ((ord_less_eq_nat (_let_1 A3)) (_let_1 B3)) ((ord_less_eq_nat A3) B3)))) (forall ((B set_nat) (A set_nat) (Q (-> nat Bool)) (P2 (-> nat Bool))) (=> ((ord_less_eq_set_nat B) A) (=> (forall ((X2 nat)) (=> ((member_nat X2) B) (=> (Q X2) (P2 X2)))) ((ord_less_eq_set_nat (collect_nat (lambda ((X nat)) (and (Q X) ((member_nat X) B))))) (collect_nat (lambda ((X nat)) (and (P2 X) ((member_nat X) A)))))))) (forall ((K nat)) (finite_finite_nat (collect_nat (lambda ((N2 nat)) ((ord_less_eq_nat N2) K))))) (forall ((A3 nat) (C nat) (B3 nat)) (=> ((ord_less_eq_nat A3) zero_zero_nat) (=> ((ord_less_eq_nat C) B3) ((ord_less_eq_nat ((plus_plus_nat A3) C)) B3)))) (forall ((X3 nat) (Y nat)) (let ((_let_1 (ord_less_eq_nat zero_zero_nat))) (=> (_let_1 X3) (=> (_let_1 Y) (= (= ((plus_plus_nat X3) Y) zero_zero_nat) (and (= X3 zero_zero_nat) (= Y zero_zero_nat))))))) (forall ((A3 nat)) (= ((plus_plus_nat A3) zero_zero_nat) A3)) (forall ((X3 (-> (-> nat nat) nat nat)) (Z3 set_nat_nat_nat_nat3) (X5 set_nat_nat_nat_nat3) (P2 (-> (-> (-> nat nat) nat nat) Bool))) (=> ((member1128122036at_nat X3) Z3) (=> ((ord_le2040082867at_nat Z3) (collec1610646258at_nat (lambda ((X (-> (-> nat nat) nat nat))) (and (P2 X) ((member1128122036at_nat X) X5))))) (P2 X3)))) (forall ((A nat) (K nat) (A3 nat) (B3 nat)) (let ((_let_1 (plus_plus_nat K))) (=> (= A (_let_1 A3)) (= ((plus_plus_nat A) B3) (_let_1 ((plus_plus_nat A3) B3)))))) (forall ((A3 nat) (B3 nat) (F2 (-> nat set_nat_nat)) (C set_nat_nat)) (=> ((ord_less_eq_nat A3) B3) (=> (= (F2 B3) C) (=> (forall ((X2 nat) (Y2 nat)) (=> ((ord_less_eq_nat X2) Y2) ((ord_le1415039317at_nat (F2 X2)) (F2 Y2)))) ((ord_le1415039317at_nat (F2 A3)) C))))) (forall ((X3 nat) (Y nat) (Z2 nat)) (let ((_let_1 (ord_less_eq_nat X3))) (=> (_let_1 Y) (=> ((ord_less_eq_nat Y) Z2) (_let_1 Z2))))) (forall ((A3 nat) (B3 nat) (C nat)) (let ((_let_1 (ord_less_eq_nat A3))) (=> (_let_1 B3) (=> (= B3 C) (_let_1 C))))) (forall ((B3 nat) (A3 nat)) (= (= ((plus_plus_nat B3) A3) A3) (= B3 zero_zero_nat))) (forall ((A set_nat) (B set_nat) (R (-> nat nat Bool))) (=> (not (finite_finite_nat A)) (=> (finite_finite_nat B) (=> (forall ((X2 nat)) (=> ((member_nat X2) A) (exists ((Xa nat)) (and ((R X2) Xa) ((member_nat Xa) B))))) (exists ((X2 nat)) (and (not (finite_finite_nat (collect_nat (lambda ((A2 nat)) (and ((member_nat A2) A) ((R A2) X2)))))) ((member_nat X2) B))))))) (= ord_less_eq_nat (lambda ((M2 nat) (N2 nat)) (or ((ord_less_nat M2) N2) (= M2 N2)))) (forall ((A3 nat) (B3 nat) (F2 (-> nat nat)) (C nat)) (=> ((ord_less_eq_nat A3) B3) (=> ((ord_less_eq_nat (F2 B3)) C) (=> (forall ((X2 nat) (Y2 nat)) (=> ((ord_less_eq_nat X2) Y2) ((ord_less_eq_nat (F2 X2)) (F2 Y2)))) ((ord_less_eq_nat (F2 A3)) C))))) (forall ((R set_nat_nat) (S set_nat_nat)) (= ((ord_le2026740592_nat_o (lambda ((X (-> nat nat))) ((member_nat_nat X) R))) (lambda ((X (-> nat nat))) ((member_nat_nat X) S))) ((ord_le1415039317at_nat R) S))) (forall ((M nat) (N nat)) (= (= ((plus_plus_nat M) N) zero_zero_nat) (and (= N zero_zero_nat) (= M zero_zero_nat)))) (forall ((P2 (-> nat Bool)) (Q (-> nat Bool))) (=> (or (finite_finite_nat (collect_nat Q)) (finite_finite_nat (collect_nat P2))) (finite_finite_nat (collect_nat (lambda ((X nat)) (and (P2 X) (Q X))))))) (forall ((M nat) (K nat) (N nat)) (=> ((ord_less_eq_nat ((plus_plus_nat M) K)) N) (not (=> ((ord_less_eq_nat M) N) (not ((ord_less_eq_nat K) N)))))) (forall ((I2 nat) (J nat) (K nat)) (let ((_let_1 (ord_less_eq_nat I2))) (=> (_let_1 J) (=> ((ord_less_eq_nat J) K) (_let_1 K))))) (forall ((A set_nat_nat) (B set_nat_nat)) (=> (forall ((X2 (-> nat nat))) (let ((_let_1 (member_nat_nat X2))) (=> (_let_1 A) (_let_1 B)))) ((ord_le1415039317at_nat A) B))) (forall ((P2 (-> (-> nat nat) Bool)) (Q (-> (-> nat nat) Bool))) (=> (forall ((X2 (-> nat nat))) (=> (P2 X2) (Q X2))) ((ord_le1415039317at_nat (collect_nat_nat P2)) (collect_nat_nat Q)))) (forall ((M nat) (K nat) (N nat)) (=> ((ord_less_eq_nat ((plus_plus_nat M) K)) N) ((ord_less_eq_nat M) N))) (forall ((A set_nat) (B set_nat) (X3 nat)) (let ((_let_1 (member_nat X3))) (=> ((ord_less_eq_set_nat A) B) (=> (_let_1 A) (_let_1 B))))) (forall ((A3 nat) (B3 nat)) (=> ((ord_less_eq_nat A3) zero_zero_nat) (=> ((ord_less_eq_nat B3) zero_zero_nat) ((ord_less_eq_nat ((plus_plus_nat A3) B3)) zero_zero_nat)))) (forall ((C nat) (A3 nat) (B3 nat)) (let ((_let_1 (plus_plus_nat C))) (= ((ord_less_eq_nat (_let_1 A3)) (_let_1 B3)) ((ord_less_eq_nat A3) B3)))) (forall ((A set_nat) (B set_nat_nat_nat) (R (-> nat (-> nat nat nat) Bool))) (=> (not (finite_finite_nat A)) (=> (finite2045569477at_nat B) (=> (forall ((X2 nat)) (=> ((member_nat X2) A) (exists ((Xa (-> nat nat nat))) (and ((member_nat_nat_nat2 Xa) B) ((R X2) Xa))))) (exists ((X2 (-> nat nat nat))) (and (not (finite_finite_nat (collect_nat (lambda ((A2 nat)) (and ((R A2) X2) ((member_nat A2) A)))))) ((member_nat_nat_nat2 X2) B))))))) (forall ((A set_nat) (B set_nat) (D nat)) (=> (finite_finite_nat A) (=> (finite_finite_nat B) (finite570312790at_nat (collect_nat_nat (lambda ((F (-> nat nat))) (forall ((X nat)) (let ((_let_1 (F X))) (let ((_let_2 ((member_nat X) A))) (and (=> _let_2 ((member_nat _let_1) B)) (=> (not _let_2) (= _let_1 D)))))))))))) (forall ((B3 nat) (A3 nat)) (= (= B3 ((plus_plus_nat B3) A3)) (= A3 zero_zero_nat))) (forall ((X3 (-> nat nat nat)) (Z3 set_nat_nat_nat) (X5 set_nat_nat_nat) (P2 (-> (-> nat nat nat) Bool))) (=> ((member_nat_nat_nat2 X3) Z3) (=> ((ord_le940807492at_nat Z3) (collect_nat_nat_nat2 (lambda ((X (-> nat nat nat))) (and (P2 X) ((member_nat_nat_nat2 X) X5))))) (P2 X3)))) (= ord_less_set_nat_nat (lambda ((B4 set_nat_nat) (A2 set_nat_nat)) (and ((ord_le1415039317at_nat B4) A2) (not (= A2 B4))))) (forall ((B3 nat) (A3 nat)) (=> ((ord_less_eq_nat B3) A3) (=> ((ord_less_eq_nat A3) B3) (= A3 B3)))) (forall ((I3 set_nat_nat) (X3 (-> (-> nat nat) nat)) (Y (-> (-> nat nat) nat))) (=> (finite570312790at_nat (collect_nat_nat (lambda ((I (-> nat nat))) (and ((member_nat_nat I) I3) (not (= (X3 I) zero_zero_nat)))))) (=> (finite570312790at_nat (collect_nat_nat (lambda ((I (-> nat nat))) (and ((member_nat_nat I) I3) (not (= (Y I) zero_zero_nat)))))) (finite570312790at_nat (collect_nat_nat (lambda ((I (-> nat nat))) (and ((member_nat_nat I) I3) (not (= ((plus_plus_nat (X3 I)) (Y I)) zero_zero_nat))))))))) (forall ((A3 nat) (B3 nat)) (=> ((ord_less_nat A3) zero_zero_nat) (=> ((ord_less_nat B3) zero_zero_nat) ((ord_less_nat ((plus_plus_nat A3) B3)) zero_zero_nat)))) (forall ((P2 (-> nat Bool)) (Q (-> nat Bool))) (= ((ord_less_eq_set_nat (collect_nat P2)) (collect_nat Q)) (forall ((X nat)) (=> (P2 X) (Q X))))) (forall ((I2 nat) (J nat) (K nat) (L nat)) (=> ((ord_less_eq_nat I2) J) (=> ((ord_less_eq_nat K) L) ((ord_less_eq_nat ((plus_plus_nat I2) K)) ((plus_plus_nat J) L))))) (forall ((P2 (-> (-> nat nat nat) Bool)) (Q (-> (-> nat nat nat) Bool))) (=> (or (finite2045569477at_nat (collect_nat_nat_nat2 Q)) (finite2045569477at_nat (collect_nat_nat_nat2 P2))) (finite2045569477at_nat (collect_nat_nat_nat2 (lambda ((X (-> nat nat nat))) (and (P2 X) (Q X))))))) (forall ((P2 (-> nat Bool)) (Q (-> nat Bool))) (=> (forall ((X2 nat)) (= (P2 X2) (Q X2))) (= (collect_nat P2) (collect_nat Q)))) (forall ((B set_nat_nat) (A set_nat_nat) (P2 (-> (-> nat nat) Bool))) (let ((_let_1 (ord_le1415039317at_nat B))) (=> (_let_1 A) (= (_let_1 (collect_nat_nat (lambda ((X (-> nat nat))) (and ((member_nat_nat X) A) (P2 X))))) (forall ((X (-> nat nat))) (=> ((member_nat_nat X) B) (P2 X))))))) (not (= zero_zero_nat one_one_nat)) (forall ((A3 nat)) (= (not (= A3 zero_zero_nat)) ((ord_less_nat zero_zero_nat) A3))) (forall ((X3 nat) (Y nat)) (= (= zero_zero_nat ((plus_plus_nat X3) Y)) (and (= X3 zero_zero_nat) (= Y zero_zero_nat)))) (forall ((M nat) (N nat)) (=> (= M N) ((ord_less_eq_nat M) N))) (forall ((A3 nat) (B3 nat)) (= ((ord_less_nat A3) ((plus_plus_nat B3) A3)) ((ord_less_nat zero_zero_nat) B3))) (= ord_less_eq_set_nat (lambda ((A5 set_nat) (B2 set_nat)) (forall ((X nat)) (let ((_let_1 (member_nat X))) (=> (_let_1 A5) (_let_1 B2)))))) _let_5 (forall ((A3 nat) (F2 (-> nat nat)) (B3 nat) (C nat)) (let ((_let_1 (ord_less_eq_nat A3))) (=> (_let_1 (F2 B3)) (=> ((ord_less_eq_nat B3) C) (=> (forall ((X2 nat) (Y2 nat)) (=> ((ord_less_eq_nat X2) Y2) ((ord_less_eq_nat (F2 X2)) (F2 Y2)))) (_let_1 (F2 C))))))) (forall ((A set_nat) (B set_nat_nat_nat2) (D (-> (-> nat nat) nat))) (=> (finite_finite_nat A) (=> (finite1440337093at_nat B) (finite584233140at_nat (collec1130010610at_nat (lambda ((F (-> nat (-> nat nat) nat))) (forall ((X nat)) (let ((_let_1 (F X))) (let ((_let_2 ((member_nat X) A))) (and (=> (not _let_2) (= _let_1 D)) (=> _let_2 ((member_nat_nat_nat _let_1) B)))))))))))) (forall ((P2 (-> nat Bool)) (K nat) (B3 nat)) (=> (P2 K) (=> (forall ((Y2 nat)) (=> (P2 Y2) ((ord_less_eq_nat Y2) B3))) (exists ((X2 nat)) (and (forall ((Y3 nat)) (=> (P2 Y3) ((ord_less_eq_nat Y3) X2))) (P2 X2)))))) (forall ((A set_nat_nat) (B set_nat_nat)) (=> (= A B) (not (=> ((ord_le1415039317at_nat A) B) (not ((ord_le1415039317at_nat B) A)))))) (forall ((X5 set_nat_nat_nat_nat3) (P2 (-> (-> (-> nat nat) nat nat) Bool))) ((ord_le2040082867at_nat (collec1610646258at_nat (lambda ((X (-> (-> nat nat) nat nat))) (and ((member1128122036at_nat X) X5) (P2 X))))) X5)) (forall ((A set_nat_nat) (B set_nat_nat) (R (-> (-> nat nat) (-> nat nat) Bool))) (=> (not (finite570312790at_nat A)) (=> (finite570312790at_nat B) (=> (forall ((X2 (-> nat nat))) (=> ((member_nat_nat X2) A) (exists ((Xa (-> nat nat))) (and ((R X2) Xa) ((member_nat_nat Xa) B))))) (exists ((X2 (-> nat nat))) (and ((member_nat_nat X2) B) (not (finite570312790at_nat (collect_nat_nat (lambda ((A2 (-> nat nat))) (and ((R A2) X2) ((member_nat_nat A2) A)))))))))))) (forall ((R set_nat) (S set_nat)) (= ((ord_less_eq_nat_o (lambda ((X nat)) ((member_nat X) R))) (lambda ((X nat)) ((member_nat X) S))) ((ord_less_eq_set_nat R) S))) (forall ((P2 (-> nat Bool)) (Q (-> nat Bool))) (= (finite_finite_nat (collect_nat (lambda ((X nat)) (or (Q X) (P2 X))))) (and (finite_finite_nat (collect_nat P2)) (finite_finite_nat (collect_nat Q))))) (forall ((A3 nat) (B3 nat)) (let ((_let_1 (ord_less_nat zero_zero_nat))) (=> (_let_1 A3) (=> (_let_1 B3) (_let_1 ((plus_plus_nat A3) B3)))))) (= ord_less_nat (lambda ((B4 nat) (A2 nat)) (and ((ord_less_eq_nat B4) A2) (not (= A2 B4))))) (forall ((B3 nat) (A3 nat) (C nat)) (=> (= ((plus_plus_nat B3) A3) ((plus_plus_nat C) A3)) (= B3 C))) (forall ((P2 (-> (-> (-> nat nat) nat) Bool)) (Q (-> (-> (-> nat nat) nat) Bool))) (=> (or (finite1440337093at_nat (collect_nat_nat_nat Q)) (finite1440337093at_nat (collect_nat_nat_nat P2))) (finite1440337093at_nat (collect_nat_nat_nat (lambda ((X (-> (-> nat nat) nat))) (and (P2 X) (Q X))))))) (forall ((P2 (-> (-> (-> nat nat) nat) Bool)) (Q (-> (-> (-> nat nat) nat) Bool))) (=> (forall ((X2 (-> (-> nat nat) nat))) (=> (P2 X2) (Q X2))) ((ord_le633272388at_nat (collect_nat_nat_nat P2)) (collect_nat_nat_nat Q)))) (forall ((N nat) (M nat)) (finite570312790at_nat (collect_nat_nat (lambda ((F (-> nat nat))) (and (forall ((I nat)) (=> ((ord_less_eq_nat M) I) (= (F I) zero_zero_nat))) (forall ((I nat)) ((ord_less_eq_nat (F I)) N))))))) (= ord_less_eq_nat (lambda ((M2 nat) (N2 nat)) (exists ((K2 nat)) (= N2 ((plus_plus_nat M2) K2))))) (forall ((B3 nat) (A3 nat) (C nat)) (let ((_let_1 (ord_less_nat C))) (=> ((ord_less_eq_nat B3) A3) (=> (_let_1 B3) (_let_1 A3))))) (forall ((A set_nat_nat)) (=> (finite570312790at_nat A) (finite604103692at_nat (collect_set_nat_nat (lambda ((B2 set_nat_nat)) ((ord_le1415039317at_nat B2) A)))))) (forall ((B set_nat_nat_nat2) (A set_nat_nat_nat2)) (=> (finite1440337093at_nat B) (=> ((ord_le633272388at_nat A) B) (finite1440337093at_nat A)))) (forall ((A3 nat) (B3 nat) (C nat)) (let ((_let_1 (plus_plus_nat C))) (=> ((ord_less_eq_nat A3) B3) ((ord_less_eq_nat (_let_1 A3)) (_let_1 B3))))) _let_4 (forall ((M nat) (N nat)) (let ((_let_1 (ord_less_nat zero_zero_nat))) (= (_let_1 ((plus_plus_nat M) N)) (or (_let_1 M) (_let_1 N))))) (= ord_less_eq_nat (lambda ((A2 nat) (B4 nat)) (or ((ord_less_nat A2) B4) (= A2 B4)))) (forall ((M nat) (N nat)) (or ((ord_less_eq_nat M) N) ((ord_less_eq_nat N) M))) (forall ((B set_nat_nat) (A set_nat_nat)) (=> (finite570312790at_nat B) (=> ((ord_le1415039317at_nat A) B) (finite570312790at_nat A)))) (forall ((A set_nat_nat_nat2) (B set_nat_nat_nat2)) (=> ((ord_le633272388at_nat A) B) (=> (finite1440337093at_nat B) (finite1440337093at_nat A)))) (forall ((A3 nat) (F2 (-> set_nat_nat nat)) (B3 set_nat_nat) (C set_nat_nat)) (let ((_let_1 (ord_less_eq_nat A3))) (=> (_let_1 (F2 B3)) (=> ((ord_le1415039317at_nat B3) C) (=> (forall ((X2 set_nat_nat) (Y2 set_nat_nat)) (=> ((ord_le1415039317at_nat X2) Y2) ((ord_less_eq_nat (F2 X2)) (F2 Y2)))) (_let_1 (F2 C))))))) (forall ((A set_set_nat_nat) (A3 set_nat_nat)) (=> (finite604103692at_nat A) (=> ((member_set_nat_nat A3) A) (exists ((X2 set_nat_nat)) (and (forall ((Xa set_nat_nat)) (=> ((member_set_nat_nat Xa) A) (=> ((ord_le1415039317at_nat Xa) X2) (= X2 Xa)))) ((ord_le1415039317at_nat X2) A3) ((member_set_nat_nat X2) A)))))) _let_3 (forall ((A3 nat) (B3 nat)) (=> ((ord_less_nat A3) B3) ((ord_less_eq_nat A3) B3))) (forall ((C nat) (A3 nat) (B3 nat)) (=> ((ord_less_eq_nat C) zero_zero_nat) (=> ((ord_less_eq_nat A3) B3) ((ord_less_eq_nat ((plus_plus_nat A3) C)) B3)))) (forall ((K nat) (M nat) (N nat)) (let ((_let_1 (plus_plus_nat K))) (= ((ord_less_nat (_let_1 M)) (_let_1 N)) ((ord_less_nat M) N)))) (forall ((M nat) (N nat)) (=> (= ((plus_plus_nat M) N) M) (= N zero_zero_nat))) (forall ((A3 nat)) (= ((plus_plus_nat zero_zero_nat) A3) A3)) (forall ((A3 nat) (B3 nat) (C nat)) (let ((_let_1 (plus_plus_nat A3))) (= ((plus_plus_nat (_let_1 B3)) C) (_let_1 ((plus_plus_nat B3) C))))) (forall ((X3 nat)) ((ord_less_eq_nat zero_zero_nat) X3)) (forall ((I2 nat) (J nat) (K nat) (L nat)) (=> (and ((ord_less_nat I2) J) ((ord_less_eq_nat K) L)) ((ord_less_nat ((plus_plus_nat I2) K)) ((plus_plus_nat J) L)))) (forall ((B3 nat) (A3 nat)) (= ((ord_less_eq_nat ((plus_plus_nat B3) A3)) B3) ((ord_less_eq_nat A3) zero_zero_nat))) (forall ((A3 (-> (-> nat nat) nat nat)) (P2 (-> (-> (-> nat nat) nat nat) Bool))) (= ((member1128122036at_nat A3) (collec1610646258at_nat P2)) (P2 A3))) (= ord_less_eq_set_nat (lambda ((A5 set_nat) (B2 set_nat)) (forall ((T2 nat)) (let ((_let_1 (member_nat T2))) (=> (_let_1 A5) (_let_1 B2)))))) (= ord_less_eq_nat (lambda ((A2 nat) (B4 nat)) (exists ((C2 nat)) (= B4 ((plus_plus_nat A2) C2))))) (forall ((N nat)) (= (not (= N zero_zero_nat)) ((ord_less_nat zero_zero_nat) N))) (forall ((P2 (-> (-> (-> nat nat) nat nat) Bool)) (Q (-> (-> (-> nat nat) nat nat) Bool))) (=> (forall ((X2 (-> (-> nat nat) nat nat))) (=> (P2 X2) (Q X2))) ((ord_le2040082867at_nat (collec1610646258at_nat P2)) (collec1610646258at_nat Q)))) (forall ((I2 nat) (J nat) (M nat)) (let ((_let_1 (ord_less_eq_nat I2))) (=> (_let_1 J) (_let_1 ((plus_plus_nat J) M))))) (forall ((A set_nat)) (= (collect_nat (lambda ((X nat)) ((member_nat X) A))) A)) _let_2 (forall ((B3 set_nat_nat) (A3 set_nat_nat)) (=> ((ord_less_set_nat_nat B3) A3) ((ord_le1415039317at_nat B3) A3))) (forall ((P2 (-> nat Bool)) (Q (-> nat Bool))) (=> (forall ((X2 nat)) (=> (P2 X2) (Q X2))) ((ord_less_eq_set_nat (collect_nat P2)) (collect_nat Q)))) (forall ((A3 nat) (F2 (-> nat nat)) (B3 nat) (C nat)) (=> (= A3 (F2 B3)) (=> ((ord_less_eq_nat B3) C) (=> (forall ((X2 nat) (Y2 nat)) (=> ((ord_less_eq_nat X2) Y2) ((ord_less_eq_nat (F2 X2)) (F2 Y2)))) ((ord_less_eq_nat A3) (F2 C)))))) (forall ((P2 (-> (-> nat nat nat) Bool)) (Q (-> (-> nat nat nat) Bool))) (= ((ord_le940807492at_nat (collect_nat_nat_nat2 P2)) (collect_nat_nat_nat2 Q)) (forall ((X (-> nat nat nat))) (=> (P2 X) (Q X))))) (forall ((A set_nat_nat) (A3 (-> nat nat))) (=> (finite570312790at_nat A) (=> ((member_nat_nat A3) A) (exists ((X2 (-> nat nat))) (and ((ord_less_eq_nat_nat X2) A3) (forall ((Xa (-> nat nat))) (=> ((member_nat_nat Xa) A) (=> ((ord_less_eq_nat_nat Xa) X2) (= X2 Xa)))) ((member_nat_nat X2) A)))))) (forall ((X5 set_nat_nat) (P2 (-> (-> nat nat) Bool))) ((ord_le1415039317at_nat (collect_nat_nat (lambda ((X (-> nat nat))) (and ((member_nat_nat X) X5) (P2 X))))) X5)) (forall ((X5 set_nat_nat_nat2) (P2 (-> (-> (-> nat nat) nat) Bool))) ((ord_le633272388at_nat (collect_nat_nat_nat (lambda ((X (-> (-> nat nat) nat))) (and ((member_nat_nat_nat X) X5) (P2 X))))) X5)) _let_1 (forall ((A3 set_nat_nat) (B3 set_nat_nat)) (=> (not (= A3 B3)) (=> ((ord_le1415039317at_nat A3) B3) ((ord_less_set_nat_nat A3) B3)))) (forall ((A3 nat) (B3 nat) (C nat)) (let ((_let_1 (plus_plus_nat A3))) (= ((plus_plus_nat (_let_1 B3)) C) (_let_1 ((plus_plus_nat B3) C))))) (forall ((A3 nat) (B3 nat)) (or (= A3 B3) (not ((ord_less_eq_nat A3) B3)) (not ((ord_less_eq_nat B3) A3)))) (forall ((N nat)) (= (not ((ord_less_nat zero_zero_nat) N)) (= N zero_zero_nat))) (forall ((A set_nat_nat) (B set_nat_nat) (X3 (-> nat nat))) (let ((_let_1 (member_nat_nat X3))) (=> ((ord_le1415039317at_nat A) B) (=> (_let_1 A) (_let_1 B))))) (forall ((A3 nat) (B3 nat) (C nat)) (=> ((ord_less_eq_nat A3) B3) ((ord_less_eq_nat ((plus_plus_nat A3) C)) ((plus_plus_nat B3) C)))) (forall ((A set_nat) (B set_nat)) (=> ((ord_less_eq_set_nat A) B) (=> (finite_finite_nat B) (finite_finite_nat A)))) (forall ((P2 (-> (-> nat nat nat) Bool))) (=> (not (finite2045569477at_nat (collect_nat_nat_nat2 P2))) (exists ((X_1 (-> nat nat nat))) (P2 X_1)))) (forall ((S set_nat_nat) (T set_nat_nat)) (=> ((ord_le1415039317at_nat S) T) (=> (not (finite570312790at_nat S)) (not (finite570312790at_nat T))))) (forall ((I3 set_nat) (X3 (-> nat nat)) (Y (-> nat nat))) (=> (finite_finite_nat (collect_nat (lambda ((I nat)) (and (not (= (X3 I) zero_zero_nat)) ((member_nat I) I3))))) (=> (finite_finite_nat (collect_nat (lambda ((I nat)) (and (not (= (Y I) zero_zero_nat)) ((member_nat I) I3))))) (finite_finite_nat (collect_nat (lambda ((I nat)) (and (not (= ((plus_plus_nat (X3 I)) (Y I)) zero_zero_nat)) ((member_nat I) I3)))))))) (forall ((A set_nat_nat_nat_nat3) (A3 (-> (-> nat nat) nat nat))) (=> (finite1064868788at_nat A) (=> ((member1128122036at_nat A3) A) (exists ((X2 (-> (-> nat nat) nat nat))) (and ((member1128122036at_nat X2) A) ((ord_le2059018749at_nat X2) A3) (forall ((Xa (-> (-> nat nat) nat nat))) (=> ((member1128122036at_nat Xa) A) (=> ((ord_le2059018749at_nat Xa) X2) (= X2 Xa))))))))) (= (lambda ((Y4 set_nat_nat) (Z set_nat_nat)) (= Y4 Z)) (lambda ((A2 set_nat_nat) (B4 set_nat_nat)) (and ((ord_le1415039317at_nat B4) A2) ((ord_le1415039317at_nat A2) B4)))) (forall ((A3 nat) (B3 nat)) (=> (not (= A3 B3)) (=> ((ord_less_eq_nat A3) B3) ((ord_less_nat A3) B3)))) (forall ((I2 nat) (J nat) (K nat) (L nat)) (=> (and (= I2 J) (= K L)) (= ((plus_plus_nat I2) K) ((plus_plus_nat J) L)))) (= (lambda ((Y4 nat) (Z nat)) (= Y4 Z)) (lambda ((X nat) (Y5 nat)) (and ((ord_less_eq_nat Y5) X) ((ord_less_eq_nat X) Y5)))) (forall ((B3 nat) (A3 nat) (C nat)) (let ((_let_1 (plus_plus_nat B3))) (let ((_let_2 (plus_plus_nat A3))) (= (_let_1 (_let_2 C)) (_let_2 (_let_1 C)))))) (forall ((A set_nat_nat_nat) (A3 (-> nat nat nat))) (=> (finite2045569477at_nat A) (=> ((member_nat_nat_nat2 A3) A) (exists ((X2 (-> nat nat nat))) (and ((member_nat_nat_nat2 X2) A) ((ord_le1415139726at_nat X2) A3) (forall ((Xa (-> nat nat nat))) (=> ((member_nat_nat_nat2 Xa) A) (=> ((ord_le1415139726at_nat Xa) X2) (= X2 Xa))))))))) (forall ((M nat) (N nat)) (=> ((ord_less_eq_nat M) N) (=> (not (= M N)) ((ord_less_nat M) N)))) (forall ((A set_nat_nat)) ((ord_le1415039317at_nat A) A)) (forall ((X3 nat)) (= (= zero_zero_nat X3) (= X3 zero_zero_nat))) (forall ((A set_nat) (B set_nat_nat_nat) (D (-> nat nat nat))) (=> (finite_finite_nat A) (=> (finite2045569477at_nat B) (finite891768244at_nat (collec1437545714at_nat (lambda ((F (-> nat nat nat nat))) (forall ((X nat)) (let ((_let_1 (F X))) (let ((_let_2 ((member_nat X) A))) (and (=> _let_2 ((member_nat_nat_nat2 _let_1) B)) (=> (not _let_2) (= _let_1 D)))))))))))) (forall ((P2 (-> nat nat Bool)) (A3 nat) (B3 nat)) (=> (forall ((A4 nat) (B5 nat)) (=> ((ord_less_eq_nat A4) B5) ((P2 A4) B5))) (=> (forall ((A4 nat) (B5 nat)) (=> ((P2 B5) A4) ((P2 A4) B5))) ((P2 A3) B3)))) (forall ((I2 nat) (J nat) (K nat) (L nat)) (=> (and (= K L) ((ord_less_eq_nat I2) J)) ((ord_less_eq_nat ((plus_plus_nat I2) K)) ((plus_plus_nat J) L)))) (forall ((X5 set_nat_nat_nat) (P2 (-> (-> nat nat nat) Bool))) ((ord_le940807492at_nat (collect_nat_nat_nat2 (lambda ((X (-> nat nat nat))) (and ((member_nat_nat_nat2 X) X5) (P2 X))))) X5)) (= finite_finite_nat (lambda ((N4 set_nat)) (exists ((M2 nat)) (forall ((X nat)) (=> ((member_nat X) N4) ((ord_less_eq_nat X) M2)))))) (forall ((P2 (-> nat Bool)) (X3 nat) (M3 nat)) (=> (P2 X3) (=> (forall ((X2 nat)) (=> (P2 X2) ((ord_less_eq_nat X2) M3))) (not (forall ((M4 nat)) (=> (P2 M4) (not (forall ((X4 nat)) (=> (P2 X4) ((ord_less_eq_nat X4) M4)))))))))) (forall ((B3 set_nat_nat) (A3 set_nat_nat) (C set_nat_nat)) (let ((_let_1 (ord_less_set_nat_nat C))) (=> ((ord_le1415039317at_nat B3) A3) (=> (_let_1 B3) (_let_1 A3))))) (forall ((A set_nat_nat) (B set_nat_nat) (D (-> nat nat))) (=> (finite570312790at_nat A) (=> (finite570312790at_nat B) (finite1064868788at_nat (collec1610646258at_nat (lambda ((F (-> (-> nat nat) nat nat))) (forall ((X (-> nat nat))) (let ((_let_1 (F X))) (let ((_let_2 ((member_nat_nat X) A))) (and (=> _let_2 ((member_nat_nat _let_1) B)) (=> (not _let_2) (= _let_1 D)))))))))))) (forall ((A set_nat_nat) (B set_nat_nat_nat) (R (-> (-> nat nat) (-> nat nat nat) Bool))) (=> (not (finite570312790at_nat A)) (=> (finite2045569477at_nat B) (=> (forall ((X2 (-> nat nat))) (=> ((member_nat_nat X2) A) (exists ((Xa (-> nat nat nat))) (and ((R X2) Xa) ((member_nat_nat_nat2 Xa) B))))) (exists ((X2 (-> nat nat nat))) (and ((member_nat_nat_nat2 X2) B) (not (finite570312790at_nat (collect_nat_nat (lambda ((A2 (-> nat nat))) (and ((member_nat_nat A2) A) ((R A2) X2)))))))))))) (forall ((B nat) (K nat) (B3 nat) (A3 nat)) (let ((_let_1 (plus_plus_nat A3))) (let ((_let_2 (plus_plus_nat K))) (=> (= B (_let_2 B3)) (= (_let_1 B) (_let_2 (_let_1 B3))))))) (forall ((A3 set_nat_nat) (B3 set_nat_nat) (F2 (-> set_nat_nat set_nat_nat)) (C set_nat_nat)) (=> ((ord_le1415039317at_nat A3) B3) (=> (= (F2 B3) C) (=> (forall ((X2 set_nat_nat) (Y2 set_nat_nat)) (=> ((ord_le1415039317at_nat X2) Y2) ((ord_le1415039317at_nat (F2 X2)) (F2 Y2)))) ((ord_le1415039317at_nat (F2 A3)) C))))) (forall ((P2 (-> (-> (-> nat nat) nat) Bool)) (Q (-> (-> (-> nat nat) nat) Bool))) (= (finite1440337093at_nat (collect_nat_nat_nat (lambda ((X (-> (-> nat nat) nat))) (or (Q X) (P2 X))))) (and (finite1440337093at_nat (collect_nat_nat_nat P2)) (finite1440337093at_nat (collect_nat_nat_nat Q))))) (not false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
2.24/2.41	)
2.24/2.41	% SZS output end Proof for theBenchmark
2.24/2.42	EOF