0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.13 % Command : do_cvc5 %s %d 0.13/0.35 % Computer : n015.cluster.edu 0.13/0.35 % Model : x86_64 x86_64 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.35 % Memory : 8042.1875MB 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.35 % CPULimit : 1200 0.13/0.35 % WCLimit : 120 0.13/0.35 % DateTime : Tue Jul 13 12:37:50 EDT 2021 0.13/0.35 % CPUTime : 0.20/0.52 %----THF division 0.20/0.53 ------- cvc5-thf casc 28 : /export/starexec/sandbox2/benchmark/theBenchmark.p at 120... 0.20/0.53 --- Run --ho-elim --full-saturate-quant at 10... 10.34/10.60 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10... 20.41/20.64 --- Run --ho-elim --no-e-matching --fs-sum --full-saturate-quant at 10... 30.50/30.69 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5... 35.51/35.75 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5... 35.69/35.96 --- Run --no-ho-matching --full-saturate-quant --fs-interleave --ho-elim-store-ax at 10... 35.78/36.17 --- Run --no-ho-matching --full-saturate-quant --macros-quant-mode=all at 10... 36.18/36.38 --- Run --ho-elim --full-saturate-quant --fs-interleave at 10... 46.24/46.49 --- Run --no-ho-matching --full-saturate-quant --ho-elim-store-ax at 10... 46.64/46.86 --- Run --ho-elim --no-ho-elim-store-ax --full-saturate-quant... 73.50/73.70 % SZS status Theorem for theBenchmark 73.50/73.72 % SZS output start Proof for theBenchmark 73.50/73.72 (proof 73.50/73.72 (let ((_let_1 (forall ((A nat) (B nat)) (=> ((ord_less_eq_nat A) B) (not (forall ((C3 nat)) (not (= B ((plus_plus_nat A) C3))))))))) (let ((_let_2 (= ord_less_eq_nat (lambda ((M2 nat) (N2 nat)) (or ((ord_less_nat M2) N2) (= M2 N2)))))) (let ((_let_3 (isPath_a c2))) (let ((_let_4 (= reachableNodes_a (lambda ((C2 (-> product_prod_nat_nat a)) (U2 nat)) (collect_nat ((connected_a C2) U2)))))) (let ((_let_5 (isPath_capacity c))) (let ((_let_6 (((_let_5 ua) p2_a) t))) (let ((_let_7 (forall ((I nat) (J nat) (K nat) (L nat)) (=> (and ((ord_less_nat K) L) ((ord_less_eq_nat I) J)) ((ord_less_nat ((plus_plus_nat I) K)) ((plus_plus_nat J) L)))))) (let ((_let_8 (= isShor1936442771pacity (lambda ((C2 (-> product_prod_nat_nat capacity)) (U2 nat) (P list_P559422087at_nat) (V4 nat)) (and (= (size_s1990949619at_nat P) (((min_dist_capacity C2) U2) V4)) ((((isPath_capacity C2) U2) P) V4)))))) (let ((_let_9 (forall ((I nat) (J nat) (K nat) (L nat)) (=> (and ((ord_less_nat I) J) ((ord_less_eq_nat K) L)) ((ord_less_nat ((plus_plus_nat I) K)) ((plus_plus_nat J) L)))))) (let ((_let_10 (= dist_a (lambda ((C2 (-> product_prod_nat_nat a)) (V4 nat) (D4 nat) (V5 nat)) (exists ((P list_P559422087at_nat)) (and ((((isPath_a C2) V4) P) V5) (= (size_s1990949619at_nat P) D4))))))) (let ((_let_11 (size_s1990949619at_nat p2_a))) (let ((_let_12 (min_dist_capacity c))) (let ((_let_13 ((_let_12 ua) t))) (let ((_let_14 (= connected_a (lambda ((C2 (-> product_prod_nat_nat a)) (U2 nat) (V4 nat)) (exists ((P list_P559422087at_nat)) ((((isPath_a C2) U2) P) V4)))))) (let ((_let_15 (forall ((C (-> product_prod_nat_nat capacity)) (U nat) (P2 list_P559422087at_nat) (V nat)) (=> ((((isPath_capacity C) U) P2) V) ((((dist_capacity C) U) (size_s1990949619at_nat P2)) V))))) (let ((_let_16 (= reacha1693770334pacity (lambda ((C2 (-> product_prod_nat_nat capacity)) (U2 nat)) (collect_nat ((connected_capacity C2) U2)))))) (let ((_let_17 (_let_5 s))) (let ((_let_18 (size_s1990949619at_nat p1a))) (let ((_let_19 ((plus_plus_nat _let_18) _let_11))) (let ((_let_20 (_let_12 s))) (let ((_let_21 (_let_20 t))) (let ((_let_22 (not ((ord_less_nat _let_21) _let_19)))) (let ((_let_23 (= min_dist_a (lambda ((C2 (-> product_prod_nat_nat a)) (V4 nat) (V5 nat)) (ord_Least_nat (lambda ((D4 nat)) ((((dist_a C2) V4) D4) V5))))))) (let ((_let_24 (= dist_capacity (lambda ((C2 (-> product_prod_nat_nat capacity)) (V4 nat) (D4 nat) (V5 nat)) (exists ((P list_P559422087at_nat)) (and (= (size_s1990949619at_nat P) D4) ((((isPath_capacity C2) V4) P) V5))))))) (let ((_let_25 (= isShortestPath_a (lambda ((C2 (-> product_prod_nat_nat a)) (U2 nat) (P list_P559422087at_nat) (V4 nat)) (and ((((isPath_a C2) U2) P) V4) (= (size_s1990949619at_nat P) (((min_dist_a C2) U2) V4))))))) (let ((_let_26 (= ord_less_nat (lambda ((M2 nat) (N2 nat)) (and ((ord_less_eq_nat M2) N2) (not (= M2 N2))))))) (let ((_let_27 (_let_20 ua))) (let ((_let_28 ((ord_less_nat _let_27) _let_18))) (let ((_let_29 (= connected_capacity (lambda ((C2 (-> product_prod_nat_nat capacity)) (V4 nat) (V5 nat)) (exists ((D4 nat)) ((((dist_capacity C2) V4) D4) V5)))))) (let ((_let_30 (forall ((P5 (-> nat Bool)) (K nat)) (=> (P5 K) ((ord_less_eq_nat (ord_Least_nat P5)) K))))) (let ((_let_31 (= _let_21 ((plus_plus_nat _let_27) _let_13)))) (let ((_let_32 (= min_dist_capacity (lambda ((C2 (-> product_prod_nat_nat capacity)) (V4 nat) (V5 nat)) (ord_Least_nat (lambda ((D4 nat)) ((((dist_capacity C2) V4) D4) V5))))))) (let ((_let_33 (ho_119 k_118 p2_a))) (let ((_let_34 (ho_117 k_160 _let_33))) (let ((_let_35 (forall ((BOUND_VARIABLE_12086 list_P559422087at_nat)) (or (not (= (ho_119 k_118 BOUND_VARIABLE_12086) (ho_119 k_118 p2_a))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 k_139) ua) BOUND_VARIABLE_12086) t)))))) (let ((_let_36 (not _let_35))) (let ((_let_37 (= _let_34 _let_36))) (let ((_let_38 (ho_154 k_153 k_160))) (let ((_let_39 (= _let_33 _let_38))) (let ((_let_40 (ho_117 (ho_123 k_141 _let_38) _let_33))) (let ((_let_41 (not _let_34))) (let ((_let_42 (or _let_41 _let_40 _let_39))) (let ((_let_43 (forall ((BOUND_VARIABLE_32686 |u_(-> nat Bool)|) (K nat)) (let ((_let_1 (ho_154 k_153 BOUND_VARIABLE_32686))) (or (not (ho_117 BOUND_VARIABLE_32686 K)) (ho_117 (ho_123 k_141 _let_1) K) (= K _let_1)))))) (let ((_let_44 (ASSUME |:args| (_let_2)))) (let ((_let_45 (ASSUME |:args| (_let_8)))) (let ((_let_46 (EQ_RESOLVE (ASSUME |:args| (_let_14)) (MACRO_SR_EQ_INTRO |:args| (_let_14 7 12))))) (let ((_let_47 (ASSUME |:args| (_let_23)))) (let ((_let_48 (EQ_RESOLVE (ASSUME |:args| (_let_24)) (MACRO_SR_EQ_INTRO |:args| (_let_24 7 12))))) (let ((_let_49 (EQ_RESOLVE (ASSUME |:args| (_let_25)) (TRUST_SUBS_MAP _let_48 _let_47 _let_46 _let_45 _let_44 |:args| ((= _let_25 (= isShortestPath_a (lambda ((C2 (-> product_prod_nat_nat a)) (U2 nat) (P list_P559422087at_nat) (V4 nat)) (and ((((isPath_a C2) U2) P) V4) (= (size_s1990949619at_nat P) (ord_Least_nat (lambda ((BOUND_VARIABLE_7173 nat)) ((((dist_a C2) U2) BOUND_VARIABLE_7173) V4))))))))))))) (let ((_let_50 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_29)) (MACRO_SR_EQ_INTRO |:args| (_let_29 7 12))) (MACRO_SR_EQ_INTRO _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 |:args| ((= connected_capacity (lambda ((C2 (-> product_prod_nat_nat capacity)) (V4 nat) (V5 nat)) (not (forall ((D4 nat)) (not ((((dist_capacity C2) V4) D4) V5)))))) 7 12))))) (let ((_let_51 (EQ_RESOLVE (ASSUME |:args| (_let_16)) (MACRO_SR_EQ_INTRO _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 |:args| (_let_16 7 12))))) (let ((_let_52 (EQ_RESOLVE (ASSUME |:args| (_let_4)) (MACRO_SR_EQ_INTRO _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 |:args| (_let_4 7 12))))) (let ((_let_53 (EQ_RESOLVE (ASSUME |:args| (_let_32)) (MACRO_SR_EQ_INTRO _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 |:args| (_let_32 7 12))))) (let ((_let_54 (EQ_RESOLVE (ASSUME |:args| (_let_10)) (MACRO_SR_EQ_INTRO |:args| (_let_10 7 12))))) (let ((_let_55 (EQ_RESOLVE (ASSUME |:args| (_let_30)) (TRANS (MACRO_SR_EQ_INTRO |:args| (_let_30 7 12)) (MACRO_SR_EQ_INTRO _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 |:args| ((forall ((P5 (-> nat Bool)) (K nat)) (or (not (P5 K)) ((ord_less_eq_nat (ord_Least_nat P5)) K))) 7 12)) (PREPROCESS |:args| ((= (forall ((P5 (-> nat Bool)) (K nat)) (let ((_let_1 (ord_Least_nat P5))) (or (not (P5 K)) ((ord_less_nat _let_1) K) (= K _let_1)))) _let_43))))))) (let ((_let_56 (not _let_39))) (let ((_let_57 (not _let_40))) (let ((_let_58 (and _let_57 _let_56))) (let ((_let_59 (ho_119 k_118 p1a))) (let ((_let_60 (ho_137 (ho_136 k_135 _let_59) _let_33))) (let ((_let_61 (ho_154 k_153 k_159))) (let ((_let_62 (ho_137 (ho_136 k_135 _let_61) _let_38))) (let ((_let_63 (ho_117 (ho_123 k_141 _let_62) _let_60))) (let ((_let_64 (ho_117 (ho_123 k_141 _let_61) _let_59))) (let ((_let_65 (not _let_64))) (let ((_let_66 (or _let_65 _let_58 _let_63))) (let ((_let_67 (forall ((I nat) (J nat) (K nat) (L nat)) (or (not (ho_117 (ho_123 k_141 I) J)) (and (not (ho_117 (ho_123 k_141 K) L)) (not (= K L))) (ho_117 (ho_123 k_141 (ho_137 (ho_136 k_135 I) K)) (ho_137 (ho_136 k_135 J) L)))))) (let ((_let_68 (EQ_RESOLVE (ASSUME |:args| (_let_9)) (TRANS (MACRO_SR_EQ_INTRO |:args| (_let_9 7 12)) (MACRO_SR_EQ_INTRO _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 |:args| ((forall ((I nat) (J nat) (K nat) (L nat)) (or (not ((ord_less_nat I) J)) (not ((ord_less_eq_nat K) L)) ((ord_less_nat ((plus_plus_nat I) K)) ((plus_plus_nat J) L)))) 7 12)) (PREPROCESS |:args| ((= (forall ((I nat) (J nat) (K nat) (L nat)) (or (not ((ord_less_nat I) J)) (and (not ((ord_less_nat K) L)) (not (= K L))) ((ord_less_nat ((plus_plus_nat I) K)) ((plus_plus_nat J) L)))) _let_67))))))) (let ((_let_69 (_let_61 _let_59 _let_38 _let_33))) (let ((_let_70 (ho_154 k_153 k_158))) (let ((_let_71 (= _let_70 _let_62))) (let ((_let_72 (= k_141 k_204))) (let ((_let_73 (ho_117 (ho_123 k_141 _let_70) _let_60))) (let ((_let_74 (not _let_63))) (let ((_let_75 (ord_Least_nat ll_94))) (let ((_let_76 (ord_Least_nat ll_93))) (let ((_let_77 (= ((plus_plus_nat _let_76) (ord_Least_nat ll_92)) _let_75))) (let ((_let_78 (ord_Least_nat (lambda ((BOUND_VARIABLE_12049 nat)) (not (forall ((BOUND_VARIABLE_12050 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_12049 (size_s1990949619at_nat BOUND_VARIABLE_12050))) (not ((((isPath_capacity c) s) BOUND_VARIABLE_12050) ua))))))))) (let ((_let_79 (ord_Least_nat (lambda ((BOUND_VARIABLE_12033 nat)) (not (forall ((BOUND_VARIABLE_12034 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_12033 (size_s1990949619at_nat BOUND_VARIABLE_12034))) (not ((((isPath_capacity c) s) BOUND_VARIABLE_12034) t))))))))) (let ((_let_80 (EQ_RESOLVE (ASSUME |:args| (_let_31)) (TRANS (MACRO_SR_EQ_INTRO _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 |:args| (_let_31 7 12)) (PREPROCESS |:args| ((= (= _let_79 ((plus_plus_nat _let_78) (ord_Least_nat (lambda ((BOUND_VARIABLE_12085 nat)) (not (forall ((BOUND_VARIABLE_12086 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_12085 (size_s1990949619at_nat BOUND_VARIABLE_12086))) (not ((((isPath_capacity c) ua) BOUND_VARIABLE_12086) t))))))))) _let_77))) (PREPROCESS |:args| ((= _let_77 _let_71))))))) (let ((_let_81 (= ord_less_nat ll_51))) (let ((_let_82 (EQ_RESOLVE (ASSUME |:args| (_let_26)) (TRANS (MACRO_SR_EQ_INTRO _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 |:args| (_let_26 7 12)) (PREPROCESS |:args| ((= (= ord_less_nat (lambda ((M2 nat) (N2 nat)) (let ((_let_1 (= M2 N2))) (and (or ((ord_less_nat M2) N2) _let_1) (not _let_1))))) _let_81))) (PREPROCESS |:args| ((= _let_81 _let_72))))))) (let ((_let_83 (not _let_73))) (let ((_let_84 (not ((ord_less_nat _let_75) _let_19)))) (let ((_let_85 (EQ_RESOLVE (ASSUME |:args| (_let_22)) (TRANS (MACRO_SR_EQ_INTRO _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 |:args| (_let_22 7 12)) (PREPROCESS |:args| ((= (not ((ord_less_nat _let_79) _let_19)) _let_84))) (PREPROCESS |:args| ((= _let_84 _let_83))))))) (let ((_let_86 (20))) (let ((_let_87 (and _let_83 _let_72 _let_71))) (let ((_let_88 (23 ho_117))) (let ((_let_89 (REFL |:args| (_let_60)))) (let ((_let_90 (23 ho_123))) (let ((_let_91 (CONG (SYMM _let_82) (REFL |:args| (_let_70)) |:args| _let_90))) (let ((_let_92 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG |:args| (_let_87)) (IMPLIES_ELIM (SCOPE (FALSE_ELIM (TRANS (CONG (TRANS (CONG (REFL |:args| (k_141)) (SYMM _let_80) |:args| _let_90) (SYMM _let_91)) _let_89 |:args| _let_88) (CONG _let_91 _let_89 |:args| _let_88) (FALSE_INTRO _let_85))) |:args| (_let_83 _let_72 _let_71))) |:args| (true _let_87)) (CONG (MACRO_SR_PRED_INTRO |:args| ((= (not _let_83) _let_73))) (REFL |:args| ((not _let_72))) (REFL |:args| ((not _let_71))) (REFL |:args| (_let_74)) |:args| _let_86)) _let_85 _let_82 _let_80 |:args| (_let_74 true _let_73 false _let_72 false _let_71)))) (let ((_let_93 ((ord_less_nat _let_76) _let_18))) (let ((_let_94 (EQ_RESOLVE (ASSUME |:args| (_let_28)) (TRANS (MACRO_SR_EQ_INTRO _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 |:args| (_let_28 7 12)) (PREPROCESS |:args| ((= ((ord_less_nat _let_78) _let_18) _let_93))) (PREPROCESS |:args| ((= _let_93 _let_64))))))) (let ((_let_95 (and _let_65 (not (= _let_61 _let_59))))) (let ((_let_96 (or _let_57 _let_95 _let_63))) (let ((_let_97 (forall ((I nat) (J nat) (K nat) (L nat)) (or (not (ho_117 (ho_123 k_141 K) L)) (and (not (ho_117 (ho_123 k_141 I) J)) (not (= I J))) (ho_117 (ho_123 k_141 (ho_137 (ho_136 k_135 I) K)) (ho_137 (ho_136 k_135 J) L)))))) (let ((_let_98 (EQ_RESOLVE (ASSUME |:args| (_let_7)) (TRANS (MACRO_SR_EQ_INTRO |:args| (_let_7 7 12)) (MACRO_SR_EQ_INTRO _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 |:args| ((forall ((I nat) (J nat) (K nat) (L nat)) (or (not ((ord_less_nat K) L)) (not ((ord_less_eq_nat I) J)) ((ord_less_nat ((plus_plus_nat I) K)) ((plus_plus_nat J) L)))) 7 12)) (PREPROCESS |:args| ((= (forall ((I nat) (J nat) (K nat) (L nat)) (or (not ((ord_less_nat K) L)) (and (not ((ord_less_nat I) J)) (not (= I J))) ((ord_less_nat ((plus_plus_nat I) K)) ((plus_plus_nat J) L)))) _let_97))))))) (let ((_let_99 (not _let_95))) (let ((_let_100 (forall ((BOUND_VARIABLE_17355 list_P559422087at_nat)) (or (not (= (ho_119 k_118 p2_a) (ho_119 k_118 BOUND_VARIABLE_17355))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 k_139) ua) BOUND_VARIABLE_17355) t)))))) (let ((_let_101 (not _let_100))) (let ((_let_102 (ho_117 (ho_116 (ho_115 (ho_114 k_113 k_139) ua) p2_a) t))) (let ((_let_103 (not _let_102))) (let ((_let_104 (or _let_103 _let_101))) (let ((_let_105 (forall ((BOUND_VARIABLE_30791 |u_(-> product_prod_nat_nat capacity)|) (U nat) (P2 list_P559422087at_nat) (V nat)) (or (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 BOUND_VARIABLE_30791) U) P2) V)) (not (forall ((BOUND_VARIABLE_17355 list_P559422087at_nat)) (or (not (= (ho_119 k_118 BOUND_VARIABLE_17355) (ho_119 k_118 P2))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 BOUND_VARIABLE_30791) U) BOUND_VARIABLE_17355) V))))))))) (let ((_let_106 (EQ_RESOLVE (ASSUME |:args| (_let_15)) (TRANS (MACRO_SR_EQ_INTRO |:args| (_let_15 7 12)) (MACRO_SR_EQ_INTRO _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 |:args| ((forall ((C (-> product_prod_nat_nat capacity)) (U nat) (P2 list_P559422087at_nat) (V nat)) (or (not ((((isPath_capacity C) U) P2) V)) ((((dist_capacity C) U) (size_s1990949619at_nat P2)) V))) 7 12)) (PREPROCESS |:args| ((= (forall ((C (-> product_prod_nat_nat capacity)) (U nat) (P2 list_P559422087at_nat) (V nat)) (or (not ((((isPath_capacity C) U) P2) V)) (not (forall ((BOUND_VARIABLE_17355 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat P2) (size_s1990949619at_nat BOUND_VARIABLE_17355))) (not ((((isPath_capacity C) U) BOUND_VARIABLE_17355) V))))))) _let_105))))))) (let ((_let_107 (forall ((BOUND_VARIABLE_26036 nat)) (= (ho_117 k_160 BOUND_VARIABLE_26036) (not (forall ((BOUND_VARIABLE_12086 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_26036 (ho_119 k_118 BOUND_VARIABLE_12086))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 k_139) ua) BOUND_VARIABLE_12086) t))))))))) (let ((_let_108 (forall ((x |u_(-> _u_(-> product_prod_nat_nat a)_ nat nat Bool)|) (y |u_(-> _u_(-> product_prod_nat_nat a)_ nat nat Bool)|)) (or (not (forall ((z |u_(-> product_prod_nat_nat a)|)) (= (ho_133 x z) (ho_133 y z)))) (= x y))))) (let ((_let_109 (forall ((x |u_(-> nat Bool)|) (y |u_(-> nat Bool)|)) (or (not (forall ((z nat)) (= (ho_117 x z) (ho_117 y z)))) (= x y))))) (let ((_let_110 (forall ((x |u_(-> _u_(-> product_prod_nat_nat a)_ nat list_P559422087at_nat nat Bool)|) (y |u_(-> _u_(-> product_prod_nat_nat a)_ nat list_P559422087at_nat nat Bool)|)) (or (not (forall ((z |u_(-> product_prod_nat_nat a)|)) (= (ho_126 x z) (ho_126 y z)))) (= x y))))) (let ((_let_111 (forall ((x |u_(-> list_P559422087at_nat nat Bool)|) (y |u_(-> list_P559422087at_nat nat Bool)|)) (or (not (forall ((z list_P559422087at_nat)) (= (ho_116 x z) (ho_116 y z)))) (= x y))))) (let ((_let_112 (forall ((x |u_(-> product_prod_nat_nat a)|) (y |u_(-> product_prod_nat_nat a)|)) (or (not (forall ((z product_prod_nat_nat)) (= (ho_124 x z) (ho_124 y z)))) (= x y))))) (let ((_let_113 (forall ((x |u_(-> _u_(-> product_prod_nat_nat capacity)_ nat nat nat Bool)|) (y |u_(-> _u_(-> product_prod_nat_nat capacity)_ nat nat nat Bool)|)) (or (not (forall ((z |u_(-> product_prod_nat_nat capacity)|)) (= (ho_121 x z) (ho_121 y z)))) (= x y))))) (let ((_let_114 (forall ((x |u_(-> nat list_P559422087at_nat nat Bool)|) (y |u_(-> nat list_P559422087at_nat nat Bool)|)) (or (not (forall ((z nat)) (= (ho_115 x z) (ho_115 y z)))) (= x y))))) (let ((_let_115 (forall ((x |u_(-> nat nat Bool)|) (y |u_(-> nat nat Bool)|)) (or (not (forall ((z nat)) (= (ho_123 x z) (ho_123 y z)))) (= x y))))) (let ((_let_116 (forall ((x |u_(-> _u_(-> product_prod_nat_nat capacity)_ nat nat Bool)|) (y |u_(-> _u_(-> product_prod_nat_nat capacity)_ nat nat Bool)|)) (or (not (forall ((z |u_(-> product_prod_nat_nat capacity)|)) (= (ho_182 x z) (ho_182 y z)))) (= x y))))) (let ((_let_117 (forall ((x |u_(-> list_P559422087at_nat nat)|) (y |u_(-> list_P559422087at_nat nat)|)) (or (not (forall ((z list_P559422087at_nat)) (= (ho_119 x z) (ho_119 y z)))) (= x y))))) (let ((_let_118 (forall ((x |u_(-> nat nat nat Bool)|) (y |u_(-> nat nat nat Bool)|)) (or (not (forall ((z nat)) (= (ho_122 x z) (ho_122 y z)))) (= x y))))) (let ((_let_119 (forall ((x |u_(-> product_prod_nat_nat capacity)|) (y |u_(-> product_prod_nat_nat capacity)|)) (or (not (forall ((z product_prod_nat_nat)) (= (ho_112 x z) (ho_112 y z)))) (= x y))))) (let ((_let_120 (forall ((x |u_(-> _u_(-> nat Bool)_ Bool)|) (y |u_(-> _u_(-> nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> nat Bool)|)) (= (ho_179 x z) (ho_179 y z)))) (= x y))))) (let ((_let_121 (forall ((x |u_(-> _u_(-> product_prod_nat_nat capacity)_ nat list_P559422087at_nat nat Bool)|) (y |u_(-> _u_(-> product_prod_nat_nat capacity)_ nat list_P559422087at_nat nat Bool)|)) (or (not (forall ((z |u_(-> product_prod_nat_nat capacity)|)) (= (ho_114 x z) (ho_114 y z)))) (= x y))))) (let ((_let_122 (forall ((x |u_(-> _u_(-> product_prod_nat_nat a)_ nat nat nat Bool)|) (y |u_(-> _u_(-> product_prod_nat_nat a)_ nat nat nat Bool)|)) (or (not (forall ((z |u_(-> product_prod_nat_nat a)|)) (= (ho_128 x z) (ho_128 y z)))) (= x y))))) (let ((_let_123 (forall ((x |u_(-> set_nat Bool)|) (y |u_(-> set_nat Bool)|)) (or (not (forall ((z set_nat)) (= (ho_146 x z) (ho_146 y z)))) (= x y))))) (let ((_let_124 (forall ((x |u_(-> nat nat)|) (y |u_(-> nat nat)|)) (or (not (forall ((z nat)) (= (ho_137 x z) (ho_137 y z)))) (= x y))))) (let ((_let_125 (forall ((x |u_(-> set_nat nat Bool)|) (y |u_(-> set_nat nat Bool)|)) (or (not (forall ((z set_nat)) (= (ho_148 x z) (ho_148 y z)))) (= x y))))) (let ((_let_126 (forall ((x |u_(-> _u_(-> nat Bool)_ nat)|) (y |u_(-> _u_(-> nat Bool)_ nat)|)) (or (not (forall ((z |u_(-> nat Bool)|)) (= (ho_154 x z) (ho_154 y z)))) (= x y))))) (let ((_let_127 (forall ((x |u_(-> nat nat nat)|) (y |u_(-> nat nat nat)|)) (or (not (forall ((z nat)) (= (ho_136 x z) (ho_136 y z)))) (= x y))))) (let ((_let_128 (forall ((x |u_(-> nat set_nat Bool)|) (y |u_(-> nat set_nat Bool)|)) (or (not (forall ((z nat)) (= (ho_145 x z) (ho_145 y z)))) (= x y))))) (let ((_let_129 (forall ((x |u_(-> _u_(-> nat Bool)_ set_nat)|) (y |u_(-> _u_(-> nat Bool)_ set_nat)|)) (or (not (forall ((z |u_(-> nat Bool)|)) (= (ho_256 x z) (ho_256 y z)))) (= x y))))) (let ((_let_130 (forall ((BOUND_VARIABLE_26955 |u_(-> product_prod_nat_nat capacity)|) (BOUND_VARIABLE_26358 nat) (BOUND_VARIABLE_26359 nat) (BOUND_VARIABLE_26360 nat)) (= (ho_117 (ho_123 (ho_122 (ho_121 k_120 BOUND_VARIABLE_26955) BOUND_VARIABLE_26358) BOUND_VARIABLE_26359) BOUND_VARIABLE_26360) (not (forall ((BOUND_VARIABLE_12388 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_26360 (ho_119 k_118 BOUND_VARIABLE_12388))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 BOUND_VARIABLE_26955) BOUND_VARIABLE_26358) BOUND_VARIABLE_12388) BOUND_VARIABLE_26359))))))))) (let ((_let_131 (forall ((BOUND_VARIABLE_27022 |u_(-> product_prod_nat_nat a)|) (BOUND_VARIABLE_26340 nat) (BOUND_VARIABLE_26341 nat) (BOUND_VARIABLE_26342 nat)) (= (ho_117 (ho_123 (ho_122 (ho_128 k_127 BOUND_VARIABLE_27022) BOUND_VARIABLE_26340) BOUND_VARIABLE_26341) BOUND_VARIABLE_26342) (not (forall ((BOUND_VARIABLE_20120 list_P559422087at_nat)) (or (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 BOUND_VARIABLE_27022) BOUND_VARIABLE_26340) BOUND_VARIABLE_20120) BOUND_VARIABLE_26341)) (not (= BOUND_VARIABLE_26342 (ho_119 k_118 BOUND_VARIABLE_20120)))))))))) (let ((_let_132 (forall ((BOUND_VARIABLE_27056 |u_(-> product_prod_nat_nat capacity)|) (BOUND_VARIABLE_26322 nat) (BOUND_VARIABLE_26323 nat) (BOUND_VARIABLE_26324 nat)) (= (ho_117 (ho_123 (ho_122 (ho_121 k_129 BOUND_VARIABLE_27056) BOUND_VARIABLE_26322) BOUND_VARIABLE_26323) BOUND_VARIABLE_26324) (not (forall ((BOUND_VARIABLE_12326 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_26324 (ho_119 k_118 BOUND_VARIABLE_12326))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 BOUND_VARIABLE_27056) BOUND_VARIABLE_26322) BOUND_VARIABLE_12326) BOUND_VARIABLE_26323))))))))) (let ((_let_133 (forall ((BOUND_VARIABLE_27083 |u_(-> product_prod_nat_nat a)|) (BOUND_VARIABLE_26304 nat) (BOUND_VARIABLE_26305 nat) (BOUND_VARIABLE_26306 nat)) (= (ho_117 (ho_123 (ho_122 (ho_128 k_130 BOUND_VARIABLE_27083) BOUND_VARIABLE_26304) BOUND_VARIABLE_26305) BOUND_VARIABLE_26306) (not (forall ((BOUND_VARIABLE_14014 list_P559422087at_nat)) (or (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 BOUND_VARIABLE_27083) BOUND_VARIABLE_26304) BOUND_VARIABLE_14014) BOUND_VARIABLE_26305)) (not (= BOUND_VARIABLE_26306 (ho_119 k_118 BOUND_VARIABLE_14014)))))))))) (let ((_let_134 (forall ((BOUND_VARIABLE_27107 |u_(-> product_prod_nat_nat a)|) (BOUND_VARIABLE_26286 nat) (BOUND_VARIABLE_26287 nat) (BOUND_VARIABLE_26288 nat)) (= (ho_117 (ho_123 (ho_122 (ho_128 k_131 BOUND_VARIABLE_27107) BOUND_VARIABLE_26286) BOUND_VARIABLE_26287) BOUND_VARIABLE_26288) (not (forall ((BOUND_VARIABLE_18276 list_P559422087at_nat)) (or (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 BOUND_VARIABLE_27107) BOUND_VARIABLE_26286) BOUND_VARIABLE_18276) BOUND_VARIABLE_26287)) (not (= BOUND_VARIABLE_26288 (ho_119 k_118 BOUND_VARIABLE_18276)))))))))) (let ((_let_135 (forall ((BOUND_VARIABLE_27128 |u_(-> product_prod_nat_nat a)|) (BOUND_VARIABLE_26272 nat) (BOUND_VARIABLE_26273 nat)) (= (ho_117 (ho_123 (ho_133 k_132 BOUND_VARIABLE_27128) BOUND_VARIABLE_26272) BOUND_VARIABLE_26273) (not (forall ((P list_P559422087at_nat)) (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 BOUND_VARIABLE_27128) BOUND_VARIABLE_26272) P) BOUND_VARIABLE_26273)))))))) (let ((_let_136 (forall ((BOUND_VARIABLE_27151 |u_(-> product_prod_nat_nat a)|) (BOUND_VARIABLE_26258 nat) (BOUND_VARIABLE_26259 nat)) (= (ho_117 (ho_123 (ho_133 k_134 BOUND_VARIABLE_27151) BOUND_VARIABLE_26258) BOUND_VARIABLE_26259) (not (forall ((BOUND_VARIABLE_13581 list_P559422087at_nat)) (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 BOUND_VARIABLE_27151) BOUND_VARIABLE_26258) BOUND_VARIABLE_13581) BOUND_VARIABLE_26259)))))))) (let ((_let_137 (forall ((BOUND_VARIABLE_26245 nat) (BOUND_VARIABLE_26246 nat)) (= (ho_117 (ho_123 k_138 BOUND_VARIABLE_26245) BOUND_VARIABLE_26246) (not (forall ((K2 nat)) (not (= BOUND_VARIABLE_26246 (ho_137 (ho_136 k_135 BOUND_VARIABLE_26245) K2))))))))) (let ((_let_138 (forall ((BOUND_VARIABLE_26229 nat) (BOUND_VARIABLE_26230 nat) (BOUND_VARIABLE_26231 nat)) (= (ho_117 (ho_123 (ho_122 k_140 BOUND_VARIABLE_26229) BOUND_VARIABLE_26230) BOUND_VARIABLE_26231) (not (forall ((BOUND_VARIABLE_13256 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_26231 (ho_119 k_118 BOUND_VARIABLE_13256))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 k_139) BOUND_VARIABLE_26229) BOUND_VARIABLE_13256) BOUND_VARIABLE_26230))))))))) (let ((_let_139 (forall ((BOUND_VARIABLE_27212 |u_(-> product_prod_nat_nat a)|) (BOUND_VARIABLE_26208 nat) (BOUND_VARIABLE_26209 list_P559422087at_nat) (BOUND_VARIABLE_26210 nat)) (= (ho_117 (ho_116 (ho_115 (ho_126 k_142 BOUND_VARIABLE_27212) BOUND_VARIABLE_26208) BOUND_VARIABLE_26209) BOUND_VARIABLE_26210) (and (forall ((P4 list_P559422087at_nat)) (let ((_let_1 (ho_119 k_118 P4))) (let ((_let_2 (ho_119 k_118 BOUND_VARIABLE_26209))) (or (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 BOUND_VARIABLE_27212) BOUND_VARIABLE_26208) P4) BOUND_VARIABLE_26210)) (ho_117 (ho_123 k_141 _let_2) _let_1) (= _let_2 _let_1))))) (ho_117 (ho_116 (ho_115 (ho_126 k_125 BOUND_VARIABLE_27212) BOUND_VARIABLE_26208) BOUND_VARIABLE_26209) BOUND_VARIABLE_26210)))))) (let ((_let_140 (forall ((BOUND_VARIABLE_27244 |u_(-> product_prod_nat_nat a)|) (BOUND_VARIABLE_26190 nat) (BOUND_VARIABLE_26191 nat) (BOUND_VARIABLE_26192 nat)) (= (ho_117 (ho_123 (ho_122 (ho_128 k_143 BOUND_VARIABLE_27244) BOUND_VARIABLE_26190) BOUND_VARIABLE_26191) BOUND_VARIABLE_26192) (not (forall ((BOUND_VARIABLE_22784 list_P559422087at_nat)) (or (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 BOUND_VARIABLE_27244) BOUND_VARIABLE_26190) BOUND_VARIABLE_22784) BOUND_VARIABLE_26191)) (not (= BOUND_VARIABLE_26192 (ho_119 k_118 BOUND_VARIABLE_22784)))))))))) (let ((_let_141 (forall ((BOUND_VARIABLE_26181 set_nat) (BOUND_VARIABLE_26182 nat)) (= (ho_117 (ho_148 k_147 BOUND_VARIABLE_26181) BOUND_VARIABLE_26182) (ho_146 (ho_145 k_144 BOUND_VARIABLE_26182) BOUND_VARIABLE_26181))))) (let ((_let_142 (forall ((BOUND_VARIABLE_27290 |u_(-> product_prod_nat_nat a)|) (BOUND_VARIABLE_26164 nat) (BOUND_VARIABLE_26165 nat) (BOUND_VARIABLE_26166 nat)) (= (ho_117 (ho_123 (ho_122 (ho_128 k_149 BOUND_VARIABLE_27290) BOUND_VARIABLE_26164) BOUND_VARIABLE_26165) BOUND_VARIABLE_26166) (not (forall ((BOUND_VARIABLE_22343 list_P559422087at_nat)) (or (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 BOUND_VARIABLE_27290) BOUND_VARIABLE_26164) BOUND_VARIABLE_22343) BOUND_VARIABLE_26165)) (not (= BOUND_VARIABLE_26166 (ho_119 k_118 BOUND_VARIABLE_22343)))))))))) (let ((_let_143 (forall ((BOUND_VARIABLE_26147 nat) (BOUND_VARIABLE_26148 nat) (BOUND_VARIABLE_26149 nat)) (= (ho_117 (ho_123 (ho_122 k_151 BOUND_VARIABLE_26147) BOUND_VARIABLE_26148) BOUND_VARIABLE_26149) (not (forall ((BOUND_VARIABLE_22192 list_P559422087at_nat)) (or (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 k_150) BOUND_VARIABLE_26147) BOUND_VARIABLE_22192) BOUND_VARIABLE_26148)) (not (= BOUND_VARIABLE_26149 (ho_119 k_118 BOUND_VARIABLE_22192)))))))))) (let ((_let_144 (forall ((BOUND_VARIABLE_26131 nat) (BOUND_VARIABLE_26132 nat) (BOUND_VARIABLE_26133 nat)) (= (ho_117 (ho_123 (ho_122 k_152 BOUND_VARIABLE_26131) BOUND_VARIABLE_26132) BOUND_VARIABLE_26133) (not (forall ((BOUND_VARIABLE_22229 list_P559422087at_nat)) (or (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 k_150) BOUND_VARIABLE_26131) BOUND_VARIABLE_22229) BOUND_VARIABLE_26132)) (not (= BOUND_VARIABLE_26133 (ho_119 k_118 BOUND_VARIABLE_22229)))))))))) (let ((_let_145 (forall ((BOUND_VARIABLE_27351 |u_(-> product_prod_nat_nat capacity)|) (BOUND_VARIABLE_26085 nat) (BOUND_VARIABLE_26086 list_P559422087at_nat) (BOUND_VARIABLE_26087 nat)) (= (ho_117 (ho_116 (ho_115 (ho_114 k_156 BOUND_VARIABLE_27351) BOUND_VARIABLE_26085) BOUND_VARIABLE_26086) BOUND_VARIABLE_26087) (and (ho_117 (ho_116 (ho_115 (ho_114 k_155 BOUND_VARIABLE_27351) BOUND_VARIABLE_26085) BOUND_VARIABLE_26086) BOUND_VARIABLE_26087) (= (ho_154 k_153 (ho_123 (ho_122 (ho_121 k_120 BOUND_VARIABLE_27351) BOUND_VARIABLE_26085) BOUND_VARIABLE_26087)) (ho_119 k_118 BOUND_VARIABLE_26086))))))) (let ((_let_146 (forall ((BOUND_VARIABLE_27385 |u_(-> product_prod_nat_nat a)|) (BOUND_VARIABLE_26067 nat) (BOUND_VARIABLE_26068 nat) (BOUND_VARIABLE_26069 nat)) (= (ho_117 (ho_123 (ho_122 (ho_128 k_157 BOUND_VARIABLE_27385) BOUND_VARIABLE_26067) BOUND_VARIABLE_26068) BOUND_VARIABLE_26069) (not (forall ((BOUND_VARIABLE_22005 list_P559422087at_nat)) (or (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 BOUND_VARIABLE_27385) BOUND_VARIABLE_26067) BOUND_VARIABLE_22005) BOUND_VARIABLE_26068)) (not (= BOUND_VARIABLE_26069 (ho_119 k_118 BOUND_VARIABLE_22005)))))))))) (let ((_let_147 (forall ((BOUND_VARIABLE_26056 nat)) (= (ho_117 k_158 BOUND_VARIABLE_26056) (not (forall ((BOUND_VARIABLE_12034 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_26056 (ho_119 k_118 BOUND_VARIABLE_12034))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 k_139) s) BOUND_VARIABLE_12034) t))))))))) (let ((_let_148 (forall ((BOUND_VARIABLE_26046 nat)) (= (ho_117 k_159 BOUND_VARIABLE_26046) (not (forall ((BOUND_VARIABLE_12050 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_26046 (ho_119 k_118 BOUND_VARIABLE_12050))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 k_139) s) BOUND_VARIABLE_12050) ua))))))))) (let ((_let_149 (forall ((BOUND_VARIABLE_26020 nat) (BOUND_VARIABLE_26021 nat) (BOUND_VARIABLE_26022 nat)) (= (ho_117 (ho_123 (ho_122 k_161 BOUND_VARIABLE_26020) BOUND_VARIABLE_26021) BOUND_VARIABLE_26022) (not (forall ((BOUND_VARIABLE_21770 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_26022 (ho_119 k_118 BOUND_VARIABLE_21770))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 k_139) BOUND_VARIABLE_26020) BOUND_VARIABLE_21770) BOUND_VARIABLE_26021))))))))) (let ((_let_150 (forall ((BOUND_VARIABLE_26010 nat)) (= (ho_117 k_162 BOUND_VARIABLE_26010) (not (forall ((BOUND_VARIABLE_21694 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_26010 (ho_119 k_118 BOUND_VARIABLE_21694))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 k_139) s) BOUND_VARIABLE_21694) t))))))))) (let ((_let_151 (forall ((BOUND_VARIABLE_27486 |u_(-> product_prod_nat_nat a)|) (BOUND_VARIABLE_25993 nat) (BOUND_VARIABLE_25994 nat) (BOUND_VARIABLE_25995 nat)) (= (ho_117 (ho_123 (ho_122 (ho_128 k_163 BOUND_VARIABLE_27486) BOUND_VARIABLE_25993) BOUND_VARIABLE_25994) BOUND_VARIABLE_25995) (not (forall ((BOUND_VARIABLE_21502 list_P559422087at_nat)) (or (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 BOUND_VARIABLE_27486) BOUND_VARIABLE_25993) BOUND_VARIABLE_21502) BOUND_VARIABLE_25994)) (not (= BOUND_VARIABLE_25995 (ho_119 k_118 BOUND_VARIABLE_21502)))))))))) (let ((_let_152 (forall ((BOUND_VARIABLE_27507 |u_(-> product_prod_nat_nat capacity)|) (BOUND_VARIABLE_25975 nat) (BOUND_VARIABLE_25976 nat) (BOUND_VARIABLE_25977 nat)) (= (ho_117 (ho_123 (ho_122 (ho_121 k_164 BOUND_VARIABLE_27507) BOUND_VARIABLE_25975) BOUND_VARIABLE_25976) BOUND_VARIABLE_25977) (not (forall ((BOUND_VARIABLE_21353 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_25977 (ho_119 k_118 BOUND_VARIABLE_21353))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 BOUND_VARIABLE_27507) BOUND_VARIABLE_25975) BOUND_VARIABLE_21353) BOUND_VARIABLE_25976))))))))) (let ((_let_153 (forall ((BOUND_VARIABLE_27531 |u_(-> product_prod_nat_nat capacity)|) (BOUND_VARIABLE_25957 nat) (BOUND_VARIABLE_25958 nat) (BOUND_VARIABLE_25959 nat)) (= (ho_117 (ho_123 (ho_122 (ho_121 k_165 BOUND_VARIABLE_27531) BOUND_VARIABLE_25957) BOUND_VARIABLE_25958) BOUND_VARIABLE_25959) (not (forall ((BOUND_VARIABLE_21280 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_25959 (ho_119 k_118 BOUND_VARIABLE_21280))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 BOUND_VARIABLE_27531) BOUND_VARIABLE_25957) BOUND_VARIABLE_21280) BOUND_VARIABLE_25958))))))))) (let ((_let_154 (forall ((BOUND_VARIABLE_27558 |u_(-> product_prod_nat_nat a)|) (BOUND_VARIABLE_25939 nat) (BOUND_VARIABLE_25940 nat) (BOUND_VARIABLE_25941 nat)) (= (ho_117 (ho_123 (ho_122 (ho_128 k_166 BOUND_VARIABLE_27558) BOUND_VARIABLE_25939) BOUND_VARIABLE_25940) BOUND_VARIABLE_25941) (not (forall ((BOUND_VARIABLE_21120 list_P559422087at_nat)) (or (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 BOUND_VARIABLE_27558) BOUND_VARIABLE_25939) BOUND_VARIABLE_21120) BOUND_VARIABLE_25940)) (not (= BOUND_VARIABLE_25941 (ho_119 k_118 BOUND_VARIABLE_21120)))))))))) (let ((_let_155 (forall ((BOUND_VARIABLE_27582 |u_(-> product_prod_nat_nat a)|) (BOUND_VARIABLE_25921 nat) (BOUND_VARIABLE_25922 nat) (BOUND_VARIABLE_25923 nat)) (= (ho_117 (ho_123 (ho_122 (ho_128 k_167 BOUND_VARIABLE_27582) BOUND_VARIABLE_25921) BOUND_VARIABLE_25922) BOUND_VARIABLE_25923) (not (forall ((BOUND_VARIABLE_21141 list_P559422087at_nat)) (or (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 BOUND_VARIABLE_27582) BOUND_VARIABLE_25921) BOUND_VARIABLE_21141) BOUND_VARIABLE_25922)) (not (= BOUND_VARIABLE_25923 (ho_119 k_118 BOUND_VARIABLE_21141)))))))))) (let ((_let_156 (forall ((BOUND_VARIABLE_25904 nat) (BOUND_VARIABLE_25905 nat) (BOUND_VARIABLE_25906 nat)) (= (ho_117 (ho_123 (ho_122 k_168 BOUND_VARIABLE_25904) BOUND_VARIABLE_25905) BOUND_VARIABLE_25906) (not (forall ((BOUND_VARIABLE_21012 list_P559422087at_nat)) (or (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 k_150) BOUND_VARIABLE_25904) BOUND_VARIABLE_21012) BOUND_VARIABLE_25905)) (not (= BOUND_VARIABLE_25906 (ho_119 k_118 BOUND_VARIABLE_21012)))))))))) (let ((_let_157 (forall ((BOUND_VARIABLE_27622 |u_(-> product_prod_nat_nat capacity)|) (BOUND_VARIABLE_25887 nat) (BOUND_VARIABLE_25888 nat) (BOUND_VARIABLE_25889 nat)) (= (ho_117 (ho_123 (ho_122 (ho_121 k_169 BOUND_VARIABLE_27622) BOUND_VARIABLE_25887) BOUND_VARIABLE_25888) BOUND_VARIABLE_25889) (not (forall ((BOUND_VARIABLE_20791 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_25889 (ho_119 k_118 BOUND_VARIABLE_20791))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 BOUND_VARIABLE_27622) BOUND_VARIABLE_25887) BOUND_VARIABLE_20791) BOUND_VARIABLE_25888))))))))) (let ((_let_158 (forall ((BOUND_VARIABLE_27646 |u_(-> product_prod_nat_nat capacity)|) (BOUND_VARIABLE_25869 nat) (BOUND_VARIABLE_25870 nat) (BOUND_VARIABLE_25871 nat)) (= (ho_117 (ho_123 (ho_122 (ho_121 k_170 BOUND_VARIABLE_27646) BOUND_VARIABLE_25869) BOUND_VARIABLE_25870) BOUND_VARIABLE_25871) (not (forall ((BOUND_VARIABLE_20810 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_25871 (ho_119 k_118 BOUND_VARIABLE_20810))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 BOUND_VARIABLE_27646) BOUND_VARIABLE_25869) BOUND_VARIABLE_20810) BOUND_VARIABLE_25870))))))))) (let ((_let_159 (forall ((BOUND_VARIABLE_27670 |u_(-> product_prod_nat_nat capacity)|) (BOUND_VARIABLE_25851 nat) (BOUND_VARIABLE_25852 nat) (BOUND_VARIABLE_25853 nat)) (= (ho_117 (ho_123 (ho_122 (ho_121 k_171 BOUND_VARIABLE_27670) BOUND_VARIABLE_25851) BOUND_VARIABLE_25852) BOUND_VARIABLE_25853) (not (forall ((BOUND_VARIABLE_20637 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_25853 (ho_119 k_118 BOUND_VARIABLE_20637))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 BOUND_VARIABLE_27670) BOUND_VARIABLE_25851) BOUND_VARIABLE_20637) BOUND_VARIABLE_25852))))))))) (let ((_let_160 (forall ((BOUND_VARIABLE_27694 |u_(-> product_prod_nat_nat capacity)|) (BOUND_VARIABLE_25833 nat) (BOUND_VARIABLE_25834 nat) (BOUND_VARIABLE_25835 nat)) (= (ho_117 (ho_123 (ho_122 (ho_121 k_172 BOUND_VARIABLE_27694) BOUND_VARIABLE_25833) BOUND_VARIABLE_25834) BOUND_VARIABLE_25835) (not (forall ((BOUND_VARIABLE_20675 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_25835 (ho_119 k_118 BOUND_VARIABLE_20675))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 BOUND_VARIABLE_27694) BOUND_VARIABLE_25833) BOUND_VARIABLE_20675) BOUND_VARIABLE_25834))))))))) (let ((_let_161 (forall ((BOUND_VARIABLE_25816 nat) (BOUND_VARIABLE_25817 nat) (BOUND_VARIABLE_25818 nat)) (= (ho_117 (ho_123 (ho_122 k_173 BOUND_VARIABLE_25816) BOUND_VARIABLE_25817) BOUND_VARIABLE_25818) (not (forall ((BOUND_VARIABLE_20368 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_25818 (ho_119 k_118 BOUND_VARIABLE_20368))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 k_139) BOUND_VARIABLE_25816) BOUND_VARIABLE_20368) BOUND_VARIABLE_25817))))))))) (let ((_let_162 (forall ((BOUND_VARIABLE_25800 nat) (BOUND_VARIABLE_25801 nat) (BOUND_VARIABLE_25802 nat)) (= (ho_117 (ho_123 (ho_122 k_174 BOUND_VARIABLE_25800) BOUND_VARIABLE_25801) BOUND_VARIABLE_25802) (not (forall ((BOUND_VARIABLE_20406 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_25802 (ho_119 k_118 BOUND_VARIABLE_20406))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 k_139) BOUND_VARIABLE_25800) BOUND_VARIABLE_20406) BOUND_VARIABLE_25801))))))))) (let ((_let_163 (forall ((BOUND_VARIABLE_25784 nat) (BOUND_VARIABLE_25785 nat) (BOUND_VARIABLE_25786 nat)) (= (ho_117 (ho_123 (ho_122 k_175 BOUND_VARIABLE_25784) BOUND_VARIABLE_25785) BOUND_VARIABLE_25786) (not (forall ((BOUND_VARIABLE_20271 list_P559422087at_nat)) (or (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 k_150) BOUND_VARIABLE_25784) BOUND_VARIABLE_20271) BOUND_VARIABLE_25785)) (not (= BOUND_VARIABLE_25786 (ho_119 k_118 BOUND_VARIABLE_20271)))))))))) (let ((_let_164 (forall ((BOUND_VARIABLE_25768 nat) (BOUND_VARIABLE_25769 nat) (BOUND_VARIABLE_25770 nat)) (= (ho_117 (ho_123 (ho_122 k_176 BOUND_VARIABLE_25768) BOUND_VARIABLE_25769) BOUND_VARIABLE_25770) (not (forall ((BOUND_VARIABLE_20292 list_P559422087at_nat)) (or (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 k_150) BOUND_VARIABLE_25768) BOUND_VARIABLE_20292) BOUND_VARIABLE_25769)) (not (= BOUND_VARIABLE_25770 (ho_119 k_118 BOUND_VARIABLE_20292)))))))))) (let ((_let_165 (forall ((BOUND_VARIABLE_25752 nat) (BOUND_VARIABLE_25753 nat) (BOUND_VARIABLE_25754 nat)) (= (ho_117 (ho_123 (ho_122 k_177 BOUND_VARIABLE_25752) BOUND_VARIABLE_25753) BOUND_VARIABLE_25754) (not (forall ((BOUND_VARIABLE_20190 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_25754 (ho_119 k_118 BOUND_VARIABLE_20190))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 k_139) BOUND_VARIABLE_25752) BOUND_VARIABLE_20190) BOUND_VARIABLE_25753))))))))) (let ((_let_166 (forall ((BOUND_VARIABLE_27813 |u_(-> nat Bool)|)) (= (ho_179 k_178 BOUND_VARIABLE_27813) (not (forall ((X4 nat)) (not (ho_117 BOUND_VARIABLE_27813 X4)))))))) (let ((_let_167 (forall ((BOUND_VARIABLE_27829 |u_(-> nat Bool)|)) (= (ho_179 k_180 BOUND_VARIABLE_27829) (not (forall ((N2 nat)) (or (not (forall ((M2 nat)) (or (not (ho_117 (ho_123 k_141 M2) N2)) (not (ho_117 BOUND_VARIABLE_27829 M2))))) (not (ho_117 BOUND_VARIABLE_27829 N2))))))))) (let ((_let_168 (forall ((BOUND_VARIABLE_27849 |u_(-> product_prod_nat_nat capacity)|) (BOUND_VARIABLE_25715 nat) (BOUND_VARIABLE_25716 nat)) (= (ho_117 (ho_123 (ho_182 k_181 BOUND_VARIABLE_27849) BOUND_VARIABLE_25715) BOUND_VARIABLE_25716) (not (forall ((P list_P559422087at_nat)) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 BOUND_VARIABLE_27849) BOUND_VARIABLE_25715) P) BOUND_VARIABLE_25716)))))))) (let ((_let_169 (forall ((BOUND_VARIABLE_27872 |u_(-> product_prod_nat_nat capacity)|) (BOUND_VARIABLE_25701 nat) (BOUND_VARIABLE_25702 nat)) (= (ho_117 (ho_123 (ho_182 k_183 BOUND_VARIABLE_27872) BOUND_VARIABLE_25701) BOUND_VARIABLE_25702) (not (forall ((BOUND_VARIABLE_8474 list_P559422087at_nat)) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 BOUND_VARIABLE_27872) BOUND_VARIABLE_25701) BOUND_VARIABLE_8474) BOUND_VARIABLE_25702)))))))) (let ((_let_170 (forall ((BOUND_VARIABLE_27890 |u_(-> product_prod_nat_nat a)|) (BOUND_VARIABLE_25654 nat) (BOUND_VARIABLE_25655 list_P559422087at_nat) (BOUND_VARIABLE_25656 nat)) (= (ho_117 (ho_116 (ho_115 (ho_126 k_185 BOUND_VARIABLE_27890) BOUND_VARIABLE_25654) BOUND_VARIABLE_25655) BOUND_VARIABLE_25656) (and (= (ho_154 k_153 (ho_123 (ho_122 (ho_128 k_127 BOUND_VARIABLE_27890) BOUND_VARIABLE_25654) BOUND_VARIABLE_25656)) (ho_119 k_118 BOUND_VARIABLE_25655)) (ho_117 (ho_116 (ho_115 (ho_126 k_184 BOUND_VARIABLE_27890) BOUND_VARIABLE_25654) BOUND_VARIABLE_25655) BOUND_VARIABLE_25656)))))) (let ((_let_171 (forall ((BOUND_VARIABLE_27915 |u_(-> product_prod_nat_nat capacity)|) (BOUND_VARIABLE_25636 nat) (BOUND_VARIABLE_25637 nat) (BOUND_VARIABLE_25638 nat)) (= (ho_117 (ho_123 (ho_122 (ho_121 k_186 BOUND_VARIABLE_27915) BOUND_VARIABLE_25636) BOUND_VARIABLE_25637) BOUND_VARIABLE_25638) (not (forall ((BOUND_VARIABLE_20011 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_25638 (ho_119 k_118 BOUND_VARIABLE_20011))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 BOUND_VARIABLE_27915) BOUND_VARIABLE_25636) BOUND_VARIABLE_20011) BOUND_VARIABLE_25637))))))))) (let ((_let_172 (forall ((BOUND_VARIABLE_27939 |u_(-> product_prod_nat_nat capacity)|) (BOUND_VARIABLE_25618 nat) (BOUND_VARIABLE_25619 nat) (BOUND_VARIABLE_25620 nat)) (= (ho_117 (ho_123 (ho_122 (ho_121 k_187 BOUND_VARIABLE_27939) BOUND_VARIABLE_25618) BOUND_VARIABLE_25619) BOUND_VARIABLE_25620) (not (forall ((BOUND_VARIABLE_20029 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_25620 (ho_119 k_118 BOUND_VARIABLE_20029))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 BOUND_VARIABLE_27939) BOUND_VARIABLE_25618) BOUND_VARIABLE_20029) BOUND_VARIABLE_25619))))))))) (let ((_let_173 (forall ((BOUND_VARIABLE_27966 |u_(-> product_prod_nat_nat a)|) (BOUND_VARIABLE_25600 nat) (BOUND_VARIABLE_25601 nat) (BOUND_VARIABLE_25602 nat)) (= (ho_117 (ho_123 (ho_122 (ho_128 k_188 BOUND_VARIABLE_27966) BOUND_VARIABLE_25600) BOUND_VARIABLE_25601) BOUND_VARIABLE_25602) (not (forall ((BOUND_VARIABLE_19899 list_P559422087at_nat)) (or (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 BOUND_VARIABLE_27966) BOUND_VARIABLE_25600) BOUND_VARIABLE_19899) BOUND_VARIABLE_25601)) (not (= BOUND_VARIABLE_25602 (ho_119 k_118 BOUND_VARIABLE_19899)))))))))) (let ((_let_174 (forall ((BOUND_VARIABLE_27990 |u_(-> product_prod_nat_nat a)|) (BOUND_VARIABLE_25582 nat) (BOUND_VARIABLE_25583 nat) (BOUND_VARIABLE_25584 nat)) (= (ho_117 (ho_123 (ho_122 (ho_128 k_189 BOUND_VARIABLE_27990) BOUND_VARIABLE_25582) BOUND_VARIABLE_25583) BOUND_VARIABLE_25584) (not (forall ((BOUND_VARIABLE_19917 list_P559422087at_nat)) (or (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 BOUND_VARIABLE_27990) BOUND_VARIABLE_25582) BOUND_VARIABLE_19917) BOUND_VARIABLE_25583)) (not (= BOUND_VARIABLE_25584 (ho_119 k_118 BOUND_VARIABLE_19917)))))))))) (let ((_let_175 (forall ((BOUND_VARIABLE_25569 nat) (BOUND_VARIABLE_25570 nat)) (= (ho_117 (ho_123 k_190 BOUND_VARIABLE_25569) BOUND_VARIABLE_25570) (not (forall ((BOUND_VARIABLE_9148 list_P559422087at_nat)) (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 k_150) BOUND_VARIABLE_25569) BOUND_VARIABLE_9148) BOUND_VARIABLE_25570)))))))) (let ((_let_176 (forall ((BOUND_VARIABLE_25557 nat) (BOUND_VARIABLE_25558 nat)) (= (ho_117 (ho_123 k_191 BOUND_VARIABLE_25557) BOUND_VARIABLE_25558) (not (forall ((BOUND_VARIABLE_19828 list_P559422087at_nat)) (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 k_150) BOUND_VARIABLE_25557) BOUND_VARIABLE_19828) BOUND_VARIABLE_25558)))))))) (let ((_let_177 (forall ((BOUND_VARIABLE_25541 nat) (BOUND_VARIABLE_25542 nat) (BOUND_VARIABLE_25543 nat)) (= (ho_117 (ho_123 (ho_122 k_192 BOUND_VARIABLE_25541) BOUND_VARIABLE_25542) BOUND_VARIABLE_25543) (not (forall ((BOUND_VARIABLE_9095 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_25543 (ho_119 k_118 BOUND_VARIABLE_9095))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 k_139) BOUND_VARIABLE_25541) BOUND_VARIABLE_9095) BOUND_VARIABLE_25542))))))))) (let ((_let_178 (forall ((BOUND_VARIABLE_25525 nat) (BOUND_VARIABLE_25526 nat) (BOUND_VARIABLE_25527 nat)) (= (ho_117 (ho_123 (ho_122 k_193 BOUND_VARIABLE_25525) BOUND_VARIABLE_25526) BOUND_VARIABLE_25527) (not (forall ((BOUND_VARIABLE_19789 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_25527 (ho_119 k_118 BOUND_VARIABLE_19789))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 k_139) BOUND_VARIABLE_25525) BOUND_VARIABLE_19789) BOUND_VARIABLE_25526))))))))) (let ((_let_179 (forall ((BOUND_VARIABLE_25509 nat) (BOUND_VARIABLE_25510 nat) (BOUND_VARIABLE_25511 nat)) (= (ho_117 (ho_123 (ho_122 k_194 BOUND_VARIABLE_25509) BOUND_VARIABLE_25510) BOUND_VARIABLE_25511) (not (forall ((BOUND_VARIABLE_19725 list_P559422087at_nat)) (or (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 k_150) BOUND_VARIABLE_25509) BOUND_VARIABLE_19725) BOUND_VARIABLE_25510)) (not (= BOUND_VARIABLE_25511 (ho_119 k_118 BOUND_VARIABLE_19725)))))))))) (let ((_let_180 (forall ((BOUND_VARIABLE_28097 |u_(-> product_prod_nat_nat a)|) (BOUND_VARIABLE_25492 nat) (BOUND_VARIABLE_25493 nat) (BOUND_VARIABLE_25494 nat)) (= (ho_117 (ho_123 (ho_122 (ho_128 k_195 BOUND_VARIABLE_28097) BOUND_VARIABLE_25492) BOUND_VARIABLE_25493) BOUND_VARIABLE_25494) (not (forall ((BOUND_VARIABLE_19510 list_P559422087at_nat)) (or (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 BOUND_VARIABLE_28097) BOUND_VARIABLE_25492) BOUND_VARIABLE_19510) BOUND_VARIABLE_25493)) (not (= BOUND_VARIABLE_25494 (ho_119 k_118 BOUND_VARIABLE_19510)))))))))) (let ((_let_181 (forall ((BOUND_VARIABLE_28121 |u_(-> product_prod_nat_nat a)|) (BOUND_VARIABLE_25474 nat) (BOUND_VARIABLE_25475 nat) (BOUND_VARIABLE_25476 nat)) (= (ho_117 (ho_123 (ho_122 (ho_128 k_196 BOUND_VARIABLE_28121) BOUND_VARIABLE_25474) BOUND_VARIABLE_25475) BOUND_VARIABLE_25476) (not (forall ((BOUND_VARIABLE_19529 list_P559422087at_nat)) (or (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 BOUND_VARIABLE_28121) BOUND_VARIABLE_25474) BOUND_VARIABLE_19529) BOUND_VARIABLE_25475)) (not (= BOUND_VARIABLE_25476 (ho_119 k_118 BOUND_VARIABLE_19529)))))))))) (let ((_let_182 (forall ((BOUND_VARIABLE_28142 |u_(-> product_prod_nat_nat capacity)|) (BOUND_VARIABLE_25452 nat) (BOUND_VARIABLE_25453 list_P559422087at_nat) (BOUND_VARIABLE_25454 nat)) (= (ho_117 (ho_116 (ho_115 (ho_114 k_197 BOUND_VARIABLE_28142) BOUND_VARIABLE_25452) BOUND_VARIABLE_25453) BOUND_VARIABLE_25454) (and (forall ((P4 list_P559422087at_nat)) (let ((_let_1 (ho_119 k_118 P4))) (let ((_let_2 (ho_119 k_118 BOUND_VARIABLE_25453))) (or (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 BOUND_VARIABLE_28142) BOUND_VARIABLE_25452) P4) BOUND_VARIABLE_25454)) (ho_117 (ho_123 k_141 _let_2) _let_1) (= _let_2 _let_1))))) (ho_117 (ho_116 (ho_115 (ho_114 k_113 BOUND_VARIABLE_28142) BOUND_VARIABLE_25452) BOUND_VARIABLE_25453) BOUND_VARIABLE_25454)))))) (let ((_let_183 (forall ((BOUND_VARIABLE_28170 |u_(-> product_prod_nat_nat capacity)|) (BOUND_VARIABLE_25407 nat) (BOUND_VARIABLE_25408 list_P559422087at_nat) (BOUND_VARIABLE_25409 nat)) (= (ho_117 (ho_116 (ho_115 (ho_114 k_198 BOUND_VARIABLE_28170) BOUND_VARIABLE_25407) BOUND_VARIABLE_25408) BOUND_VARIABLE_25409) (and (= (ho_154 k_153 (ho_123 (ho_122 (ho_121 k_129 BOUND_VARIABLE_28170) BOUND_VARIABLE_25407) BOUND_VARIABLE_25409)) (ho_119 k_118 BOUND_VARIABLE_25408)) (ho_117 (ho_116 (ho_115 (ho_114 k_113 BOUND_VARIABLE_28170) BOUND_VARIABLE_25407) BOUND_VARIABLE_25408) BOUND_VARIABLE_25409)))))) (let ((_let_184 (forall ((BOUND_VARIABLE_25390 nat) (BOUND_VARIABLE_25391 nat) (BOUND_VARIABLE_25392 nat)) (= (ho_117 (ho_123 (ho_122 k_199 BOUND_VARIABLE_25390) BOUND_VARIABLE_25391) BOUND_VARIABLE_25392) (not (forall ((BOUND_VARIABLE_19130 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_25392 (ho_119 k_118 BOUND_VARIABLE_19130))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 k_139) BOUND_VARIABLE_25390) BOUND_VARIABLE_19130) BOUND_VARIABLE_25391))))))))) (let ((_let_185 (forall ((BOUND_VARIABLE_25374 nat) (BOUND_VARIABLE_25375 nat) (BOUND_VARIABLE_25376 nat)) (= (ho_117 (ho_123 (ho_122 k_200 BOUND_VARIABLE_25374) BOUND_VARIABLE_25375) BOUND_VARIABLE_25376) (not (forall ((BOUND_VARIABLE_19149 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_25376 (ho_119 k_118 BOUND_VARIABLE_19149))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 k_139) BOUND_VARIABLE_25374) BOUND_VARIABLE_19149) BOUND_VARIABLE_25375))))))))) (let ((_let_186 (forall ((BOUND_VARIABLE_25358 nat) (BOUND_VARIABLE_25359 nat) (BOUND_VARIABLE_25360 nat)) (= (ho_117 (ho_123 (ho_122 k_201 BOUND_VARIABLE_25358) BOUND_VARIABLE_25359) BOUND_VARIABLE_25360) (not (forall ((BOUND_VARIABLE_19053 list_P559422087at_nat)) (or (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 k_150) BOUND_VARIABLE_25358) BOUND_VARIABLE_19053) BOUND_VARIABLE_25359)) (not (= BOUND_VARIABLE_25360 (ho_119 k_118 BOUND_VARIABLE_19053)))))))))) (let ((_let_187 (forall ((BOUND_VARIABLE_25346 nat) (BOUND_VARIABLE_25347 nat)) (= (ho_117 (ho_123 k_202 BOUND_VARIABLE_25346) BOUND_VARIABLE_25347) (not (forall ((BOUND_VARIABLE_18903 list_P559422087at_nat)) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 k_139) BOUND_VARIABLE_25346) BOUND_VARIABLE_18903) BOUND_VARIABLE_25347)))))))) (let ((_let_188 (forall ((BOUND_VARIABLE_25334 nat) (BOUND_VARIABLE_25335 nat)) (= (ho_117 (ho_123 k_203 BOUND_VARIABLE_25334) BOUND_VARIABLE_25335) (not (forall ((BOUND_VARIABLE_18916 list_P559422087at_nat)) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 k_139) BOUND_VARIABLE_25334) BOUND_VARIABLE_18916) BOUND_VARIABLE_25335)))))))) (let ((_let_189 (forall ((BOUND_VARIABLE_25322 nat) (BOUND_VARIABLE_25323 nat)) (let ((_let_1 (= BOUND_VARIABLE_25322 BOUND_VARIABLE_25323))) (= (ho_117 (ho_123 k_204 BOUND_VARIABLE_25322) BOUND_VARIABLE_25323) (and (or (ho_117 (ho_123 k_141 BOUND_VARIABLE_25322) BOUND_VARIABLE_25323) _let_1) (not _let_1))))))) (let ((_let_190 (forall ((BOUND_VARIABLE_25306 nat) (BOUND_VARIABLE_25307 nat) (BOUND_VARIABLE_25308 nat)) (= (ho_117 (ho_123 (ho_122 k_205 BOUND_VARIABLE_25306) BOUND_VARIABLE_25307) BOUND_VARIABLE_25308) (not (forall ((BOUND_VARIABLE_18797 list_P559422087at_nat)) (or (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 k_150) BOUND_VARIABLE_25306) BOUND_VARIABLE_18797) BOUND_VARIABLE_25307)) (not (= BOUND_VARIABLE_25308 (ho_119 k_118 BOUND_VARIABLE_18797)))))))))) (let ((_let_191 (forall ((BOUND_VARIABLE_25290 nat) (BOUND_VARIABLE_25291 nat) (BOUND_VARIABLE_25292 nat)) (= (ho_117 (ho_123 (ho_122 k_206 BOUND_VARIABLE_25290) BOUND_VARIABLE_25291) BOUND_VARIABLE_25292) (not (forall ((BOUND_VARIABLE_18816 list_P559422087at_nat)) (or (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 k_150) BOUND_VARIABLE_25290) BOUND_VARIABLE_18816) BOUND_VARIABLE_25291)) (not (= BOUND_VARIABLE_25292 (ho_119 k_118 BOUND_VARIABLE_18816)))))))))) (let ((_let_192 (forall ((BOUND_VARIABLE_25278 nat) (BOUND_VARIABLE_25279 nat)) (= (ho_117 (ho_123 k_207 BOUND_VARIABLE_25278) BOUND_VARIABLE_25279) (not (forall ((C2 nat)) (not (= BOUND_VARIABLE_25279 (ho_137 (ho_136 k_135 BOUND_VARIABLE_25278) C2))))))))) (let ((_let_193 (forall ((BOUND_VARIABLE_25262 nat) (BOUND_VARIABLE_25263 nat) (BOUND_VARIABLE_25264 nat)) (= (ho_117 (ho_123 (ho_122 k_208 BOUND_VARIABLE_25262) BOUND_VARIABLE_25263) BOUND_VARIABLE_25264) (not (forall ((BOUND_VARIABLE_18642 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_25264 (ho_119 k_118 BOUND_VARIABLE_18642))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 k_139) BOUND_VARIABLE_25262) BOUND_VARIABLE_18642) BOUND_VARIABLE_25263))))))))) (let ((_let_194 (forall ((BOUND_VARIABLE_25246 nat) (BOUND_VARIABLE_25247 nat) (BOUND_VARIABLE_25248 nat)) (= (ho_117 (ho_123 (ho_122 k_209 BOUND_VARIABLE_25246) BOUND_VARIABLE_25247) BOUND_VARIABLE_25248) (not (forall ((BOUND_VARIABLE_18549 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_25248 (ho_119 k_118 BOUND_VARIABLE_18549))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 k_139) BOUND_VARIABLE_25246) BOUND_VARIABLE_18549) BOUND_VARIABLE_25247))))))))) (let ((_let_195 (forall ((BOUND_VARIABLE_28377 |u_(-> product_prod_nat_nat capacity)|) (BOUND_VARIABLE_25229 nat) (BOUND_VARIABLE_25230 nat) (BOUND_VARIABLE_25231 nat)) (= (ho_117 (ho_123 (ho_122 (ho_121 k_210 BOUND_VARIABLE_28377) BOUND_VARIABLE_25229) BOUND_VARIABLE_25230) BOUND_VARIABLE_25231) (not (forall ((BOUND_VARIABLE_18431 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_25231 (ho_119 k_118 BOUND_VARIABLE_18431))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 BOUND_VARIABLE_28377) BOUND_VARIABLE_25229) BOUND_VARIABLE_18431) BOUND_VARIABLE_25230))))))))) (let ((_let_196 (forall ((BOUND_VARIABLE_28401 |u_(-> product_prod_nat_nat a)|) (BOUND_VARIABLE_25184 nat) (BOUND_VARIABLE_25185 list_P559422087at_nat) (BOUND_VARIABLE_25186 nat)) (= (ho_117 (ho_116 (ho_115 (ho_126 k_211 BOUND_VARIABLE_28401) BOUND_VARIABLE_25184) BOUND_VARIABLE_25185) BOUND_VARIABLE_25186) (and (ho_117 (ho_116 (ho_115 (ho_126 k_125 BOUND_VARIABLE_28401) BOUND_VARIABLE_25184) BOUND_VARIABLE_25185) BOUND_VARIABLE_25186) (= (ho_154 k_153 (ho_123 (ho_122 (ho_128 k_130 BOUND_VARIABLE_28401) BOUND_VARIABLE_25184) BOUND_VARIABLE_25186)) (ho_119 k_118 BOUND_VARIABLE_25185))))))) (let ((_let_197 (forall ((BOUND_VARIABLE_28425 |u_(-> product_prod_nat_nat a)|) (BOUND_VARIABLE_25139 nat) (BOUND_VARIABLE_25140 list_P559422087at_nat) (BOUND_VARIABLE_25141 nat)) (= (ho_117 (ho_116 (ho_115 (ho_126 k_212 BOUND_VARIABLE_28425) BOUND_VARIABLE_25139) BOUND_VARIABLE_25140) BOUND_VARIABLE_25141) (and (ho_117 (ho_116 (ho_115 (ho_126 k_125 BOUND_VARIABLE_28425) BOUND_VARIABLE_25139) BOUND_VARIABLE_25140) BOUND_VARIABLE_25141) (= (ho_154 k_153 (ho_123 (ho_122 (ho_128 k_131 BOUND_VARIABLE_28425) BOUND_VARIABLE_25139) BOUND_VARIABLE_25141)) (ho_119 k_118 BOUND_VARIABLE_25140))))))) (let ((_let_198 (forall ((BOUND_VARIABLE_25128 nat) (BOUND_VARIABLE_25129 nat)) (= (ho_117 (ho_123 k_213 BOUND_VARIABLE_25128) BOUND_VARIABLE_25129) (or (ho_117 (ho_123 k_141 BOUND_VARIABLE_25128) BOUND_VARIABLE_25129) (= BOUND_VARIABLE_25128 BOUND_VARIABLE_25129)))))) (let ((_let_199 (forall ((BOUND_VARIABLE_25118 nat) (BOUND_VARIABLE_25119 nat)) (= (ho_117 (ho_123 k_214 BOUND_VARIABLE_25118) BOUND_VARIABLE_25119) (or (ho_117 (ho_123 k_141 BOUND_VARIABLE_25118) BOUND_VARIABLE_25119) (= BOUND_VARIABLE_25118 BOUND_VARIABLE_25119)))))) (let ((_let_200 (forall ((BOUND_VARIABLE_25106 nat) (BOUND_VARIABLE_25107 nat)) (let ((_let_1 (= BOUND_VARIABLE_25106 BOUND_VARIABLE_25107))) (= (ho_117 (ho_123 k_215 BOUND_VARIABLE_25106) BOUND_VARIABLE_25107) (and (or (ho_117 (ho_123 k_141 BOUND_VARIABLE_25106) BOUND_VARIABLE_25107) _let_1) (not _let_1))))))) (let ((_let_201 (forall ((BOUND_VARIABLE_25090 nat) (BOUND_VARIABLE_25091 nat) (BOUND_VARIABLE_25092 nat)) (= (ho_117 (ho_123 (ho_122 k_216 BOUND_VARIABLE_25090) BOUND_VARIABLE_25091) BOUND_VARIABLE_25092) (not (forall ((BOUND_VARIABLE_18152 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_25092 (ho_119 k_118 BOUND_VARIABLE_18152))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 k_139) BOUND_VARIABLE_25090) BOUND_VARIABLE_18152) BOUND_VARIABLE_25091))))))))) (let ((_let_202 (forall ((BOUND_VARIABLE_25074 nat) (BOUND_VARIABLE_25075 nat) (BOUND_VARIABLE_25076 nat)) (= (ho_117 (ho_123 (ho_122 k_217 BOUND_VARIABLE_25074) BOUND_VARIABLE_25075) BOUND_VARIABLE_25076) (not (forall ((BOUND_VARIABLE_18182 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_25076 (ho_119 k_118 BOUND_VARIABLE_18182))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 k_139) BOUND_VARIABLE_25074) BOUND_VARIABLE_18182) BOUND_VARIABLE_25075))))))))) (let ((_let_203 (forall ((BOUND_VARIABLE_25058 nat) (BOUND_VARIABLE_25059 nat) (BOUND_VARIABLE_25060 nat)) (= (ho_117 (ho_123 (ho_122 k_218 BOUND_VARIABLE_25058) BOUND_VARIABLE_25059) BOUND_VARIABLE_25060) (not (forall ((BOUND_VARIABLE_18063 list_P559422087at_nat)) (or (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 k_150) BOUND_VARIABLE_25058) BOUND_VARIABLE_18063) BOUND_VARIABLE_25059)) (not (= BOUND_VARIABLE_25060 (ho_119 k_118 BOUND_VARIABLE_18063)))))))))) (let ((_let_204 (forall ((BOUND_VARIABLE_25042 nat) (BOUND_VARIABLE_25043 nat) (BOUND_VARIABLE_25044 nat)) (= (ho_117 (ho_123 (ho_122 k_219 BOUND_VARIABLE_25042) BOUND_VARIABLE_25043) BOUND_VARIABLE_25044) (not (forall ((BOUND_VARIABLE_17857 list_P559422087at_nat)) (or (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 k_150) BOUND_VARIABLE_25042) BOUND_VARIABLE_17857) BOUND_VARIABLE_25043)) (not (= BOUND_VARIABLE_25044 (ho_119 k_118 BOUND_VARIABLE_17857)))))))))) (let ((_let_205 (forall ((BOUND_VARIABLE_25026 nat) (BOUND_VARIABLE_25027 nat) (BOUND_VARIABLE_25028 nat)) (= (ho_117 (ho_123 (ho_122 k_220 BOUND_VARIABLE_25026) BOUND_VARIABLE_25027) BOUND_VARIABLE_25028) (not (forall ((BOUND_VARIABLE_17895 list_P559422087at_nat)) (or (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 k_150) BOUND_VARIABLE_25026) BOUND_VARIABLE_17895) BOUND_VARIABLE_25027)) (not (= BOUND_VARIABLE_25028 (ho_119 k_118 BOUND_VARIABLE_17895)))))))))) (let ((_let_206 (forall ((BOUND_VARIABLE_25019 nat) (BOUND_VARIABLE_25020 nat)) (= (ho_117 (ho_123 k_221 BOUND_VARIABLE_25019) BOUND_VARIABLE_25020) (= BOUND_VARIABLE_25019 BOUND_VARIABLE_25020))))) (let ((_let_207 (forall ((BOUND_VARIABLE_25005 nat) (BOUND_VARIABLE_25006 nat)) (let ((_let_1 (= BOUND_VARIABLE_25005 BOUND_VARIABLE_25006))) (= (ho_117 (ho_123 k_222 BOUND_VARIABLE_25005) BOUND_VARIABLE_25006) (and (or (ho_117 (ho_123 k_141 BOUND_VARIABLE_25006) BOUND_VARIABLE_25005) _let_1) (or (ho_117 (ho_123 k_141 BOUND_VARIABLE_25005) BOUND_VARIABLE_25006) _let_1))))))) (let ((_let_208 (forall ((BOUND_VARIABLE_28599 |u_(-> product_prod_nat_nat a)|) (BOUND_VARIABLE_24988 nat) (BOUND_VARIABLE_24989 nat) (BOUND_VARIABLE_24990 nat)) (= (ho_117 (ho_123 (ho_122 (ho_128 k_223 BOUND_VARIABLE_28599) BOUND_VARIABLE_24988) BOUND_VARIABLE_24989) BOUND_VARIABLE_24990) (not (forall ((BOUND_VARIABLE_17552 list_P559422087at_nat)) (or (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 BOUND_VARIABLE_28599) BOUND_VARIABLE_24988) BOUND_VARIABLE_17552) BOUND_VARIABLE_24989)) (not (= BOUND_VARIABLE_24990 (ho_119 k_118 BOUND_VARIABLE_17552)))))))))) (let ((_let_209 (forall ((BOUND_VARIABLE_24971 nat) (BOUND_VARIABLE_24972 nat) (BOUND_VARIABLE_24973 nat)) (= (ho_117 (ho_123 (ho_122 k_224 BOUND_VARIABLE_24971) BOUND_VARIABLE_24972) BOUND_VARIABLE_24973) (not (forall ((BOUND_VARIABLE_17260 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_24973 (ho_119 k_118 BOUND_VARIABLE_17260))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 k_139) BOUND_VARIABLE_24971) BOUND_VARIABLE_17260) BOUND_VARIABLE_24972))))))))) (let ((_let_210 (forall ((BOUND_VARIABLE_24955 nat) (BOUND_VARIABLE_24956 nat) (BOUND_VARIABLE_24957 nat)) (= (ho_117 (ho_123 (ho_122 k_225 BOUND_VARIABLE_24955) BOUND_VARIABLE_24956) BOUND_VARIABLE_24957) (not (forall ((BOUND_VARIABLE_17090 list_P559422087at_nat)) (or (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 k_150) BOUND_VARIABLE_24955) BOUND_VARIABLE_17090) BOUND_VARIABLE_24956)) (not (= BOUND_VARIABLE_24957 (ho_119 k_118 BOUND_VARIABLE_17090)))))))))) (let ((_let_211 (forall ((BOUND_VARIABLE_24939 nat) (BOUND_VARIABLE_24940 nat) (BOUND_VARIABLE_24941 nat)) (= (ho_117 (ho_123 (ho_122 k_226 BOUND_VARIABLE_24939) BOUND_VARIABLE_24940) BOUND_VARIABLE_24941) (not (forall ((BOUND_VARIABLE_17138 list_P559422087at_nat)) (or (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 k_150) BOUND_VARIABLE_24939) BOUND_VARIABLE_17138) BOUND_VARIABLE_24940)) (not (= BOUND_VARIABLE_24941 (ho_119 k_118 BOUND_VARIABLE_17138)))))))))) (let ((_let_212 (forall ((BOUND_VARIABLE_24923 nat) (BOUND_VARIABLE_24924 nat) (BOUND_VARIABLE_24925 nat)) (= (ho_117 (ho_123 (ho_122 k_227 BOUND_VARIABLE_24923) BOUND_VARIABLE_24924) BOUND_VARIABLE_24925) (not (forall ((BOUND_VARIABLE_16994 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_24925 (ho_119 k_118 BOUND_VARIABLE_16994))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 k_139) BOUND_VARIABLE_24923) BOUND_VARIABLE_16994) BOUND_VARIABLE_24924))))))))) (let ((_let_213 (forall ((BOUND_VARIABLE_24907 nat) (BOUND_VARIABLE_24908 nat) (BOUND_VARIABLE_24909 nat)) (= (ho_117 (ho_123 (ho_122 k_228 BOUND_VARIABLE_24907) BOUND_VARIABLE_24908) BOUND_VARIABLE_24909) (not (forall ((BOUND_VARIABLE_17021 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_24909 (ho_119 k_118 BOUND_VARIABLE_17021))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 k_139) BOUND_VARIABLE_24907) BOUND_VARIABLE_17021) BOUND_VARIABLE_24908))))))))) (let ((_let_214 (forall ((BOUND_VARIABLE_24891 nat) (BOUND_VARIABLE_24892 nat) (BOUND_VARIABLE_24893 nat)) (= (ho_117 (ho_123 (ho_122 k_229 BOUND_VARIABLE_24891) BOUND_VARIABLE_24892) BOUND_VARIABLE_24893) (not (forall ((BOUND_VARIABLE_16909 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_24893 (ho_119 k_118 BOUND_VARIABLE_16909))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 k_139) BOUND_VARIABLE_24891) BOUND_VARIABLE_16909) BOUND_VARIABLE_24892))))))))) (let ((_let_215 (forall ((BOUND_VARIABLE_24875 nat) (BOUND_VARIABLE_24876 nat) (BOUND_VARIABLE_24877 nat)) (= (ho_117 (ho_123 (ho_122 k_230 BOUND_VARIABLE_24875) BOUND_VARIABLE_24876) BOUND_VARIABLE_24877) (not (forall ((BOUND_VARIABLE_16654 list_P559422087at_nat)) (or (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 k_150) BOUND_VARIABLE_24875) BOUND_VARIABLE_16654) BOUND_VARIABLE_24876)) (not (= BOUND_VARIABLE_24877 (ho_119 k_118 BOUND_VARIABLE_16654)))))))))) (let ((_let_216 (forall ((BOUND_VARIABLE_24859 nat) (BOUND_VARIABLE_24860 nat) (BOUND_VARIABLE_24861 nat)) (= (ho_117 (ho_123 (ho_122 k_231 BOUND_VARIABLE_24859) BOUND_VARIABLE_24860) BOUND_VARIABLE_24861) (not (forall ((BOUND_VARIABLE_16672 list_P559422087at_nat)) (or (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 k_150) BOUND_VARIABLE_24859) BOUND_VARIABLE_16672) BOUND_VARIABLE_24860)) (not (= BOUND_VARIABLE_24861 (ho_119 k_118 BOUND_VARIABLE_16672)))))))))) (let ((_let_217 (forall ((BOUND_VARIABLE_28772 |u_(-> product_prod_nat_nat capacity)|) (BOUND_VARIABLE_24842 nat) (BOUND_VARIABLE_24843 nat) (BOUND_VARIABLE_24844 nat)) (= (ho_117 (ho_123 (ho_122 (ho_121 k_232 BOUND_VARIABLE_28772) BOUND_VARIABLE_24842) BOUND_VARIABLE_24843) BOUND_VARIABLE_24844) (not (forall ((BOUND_VARIABLE_16573 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_24844 (ho_119 k_118 BOUND_VARIABLE_16573))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 BOUND_VARIABLE_28772) BOUND_VARIABLE_24842) BOUND_VARIABLE_16573) BOUND_VARIABLE_24843))))))))) (let ((_let_218 (forall ((BOUND_VARIABLE_24825 nat) (BOUND_VARIABLE_24826 nat) (BOUND_VARIABLE_24827 nat)) (= (ho_117 (ho_123 (ho_122 k_233 BOUND_VARIABLE_24825) BOUND_VARIABLE_24826) BOUND_VARIABLE_24827) (not (forall ((BOUND_VARIABLE_16401 list_P559422087at_nat)) (or (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 k_150) BOUND_VARIABLE_24825) BOUND_VARIABLE_16401) BOUND_VARIABLE_24826)) (not (= BOUND_VARIABLE_24827 (ho_119 k_118 BOUND_VARIABLE_16401)))))))))) (let ((_let_219 (forall ((BOUND_VARIABLE_28815 |u_(-> product_prod_nat_nat capacity)|) (BOUND_VARIABLE_24808 nat) (BOUND_VARIABLE_24809 nat) (BOUND_VARIABLE_24810 nat)) (= (ho_117 (ho_123 (ho_122 (ho_121 k_234 BOUND_VARIABLE_28815) BOUND_VARIABLE_24808) BOUND_VARIABLE_24809) BOUND_VARIABLE_24810) (not (forall ((BOUND_VARIABLE_15965 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_24810 (ho_119 k_118 BOUND_VARIABLE_15965))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 BOUND_VARIABLE_28815) BOUND_VARIABLE_24808) BOUND_VARIABLE_15965) BOUND_VARIABLE_24809))))))))) (let ((_let_220 (forall ((BOUND_VARIABLE_24791 nat) (BOUND_VARIABLE_24792 nat) (BOUND_VARIABLE_24793 nat)) (= (ho_117 (ho_123 (ho_122 k_235 BOUND_VARIABLE_24791) BOUND_VARIABLE_24792) BOUND_VARIABLE_24793) (not (forall ((BOUND_VARIABLE_15764 list_P559422087at_nat)) (or (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 k_150) BOUND_VARIABLE_24791) BOUND_VARIABLE_15764) BOUND_VARIABLE_24792)) (not (= BOUND_VARIABLE_24793 (ho_119 k_118 BOUND_VARIABLE_15764)))))))))) (let ((_let_221 (forall ((BOUND_VARIABLE_24775 nat) (BOUND_VARIABLE_24776 nat) (BOUND_VARIABLE_24777 nat)) (= (ho_117 (ho_123 (ho_122 k_236 BOUND_VARIABLE_24775) BOUND_VARIABLE_24776) BOUND_VARIABLE_24777) (not (forall ((BOUND_VARIABLE_15647 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_24777 (ho_119 k_118 BOUND_VARIABLE_15647))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 k_139) BOUND_VARIABLE_24775) BOUND_VARIABLE_15647) BOUND_VARIABLE_24776))))))))) (let ((_let_222 (forall ((BOUND_VARIABLE_24759 nat) (BOUND_VARIABLE_24760 nat) (BOUND_VARIABLE_24761 nat)) (= (ho_117 (ho_123 (ho_122 k_237 BOUND_VARIABLE_24759) BOUND_VARIABLE_24760) BOUND_VARIABLE_24761) (not (forall ((BOUND_VARIABLE_15684 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_24761 (ho_119 k_118 BOUND_VARIABLE_15684))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 k_139) BOUND_VARIABLE_24759) BOUND_VARIABLE_15684) BOUND_VARIABLE_24760))))))))) (let ((_let_223 (forall ((BOUND_VARIABLE_24749 nat)) (= (ho_117 k_238 BOUND_VARIABLE_24749) (not (forall ((BOUND_VARIABLE_15563 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_24749 (ho_119 k_118 BOUND_VARIABLE_15563))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 k_139) ua) BOUND_VARIABLE_15563) t))))))))) (let ((_let_224 (forall ((BOUND_VARIABLE_24733 nat) (BOUND_VARIABLE_24734 nat) (BOUND_VARIABLE_24735 nat)) (= (ho_117 (ho_123 (ho_122 k_239 BOUND_VARIABLE_24733) BOUND_VARIABLE_24734) BOUND_VARIABLE_24735) (not (forall ((BOUND_VARIABLE_15512 list_P559422087at_nat)) (or (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 k_150) BOUND_VARIABLE_24733) BOUND_VARIABLE_15512) BOUND_VARIABLE_24734)) (not (= BOUND_VARIABLE_24735 (ho_119 k_118 BOUND_VARIABLE_15512)))))))))) (let ((_let_225 (forall ((BOUND_VARIABLE_24726 nat) (BOUND_VARIABLE_24727 nat)) (= (ho_117 (ho_123 k_240 BOUND_VARIABLE_24726) BOUND_VARIABLE_24727) (= BOUND_VARIABLE_24726 BOUND_VARIABLE_24727))))) (let ((_let_226 (forall ((BOUND_VARIABLE_24712 nat) (BOUND_VARIABLE_24713 nat)) (let ((_let_1 (= BOUND_VARIABLE_24712 BOUND_VARIABLE_24713))) (= (ho_117 (ho_123 k_241 BOUND_VARIABLE_24712) BOUND_VARIABLE_24713) (and (or (ho_117 (ho_123 k_141 BOUND_VARIABLE_24712) BOUND_VARIABLE_24713) _let_1) (or (ho_117 (ho_123 k_141 BOUND_VARIABLE_24713) BOUND_VARIABLE_24712) _let_1))))))) (let ((_let_227 (forall ((BOUND_VARIABLE_24696 nat) (BOUND_VARIABLE_24697 nat) (BOUND_VARIABLE_24698 nat)) (= (ho_117 (ho_123 (ho_122 k_242 BOUND_VARIABLE_24696) BOUND_VARIABLE_24697) BOUND_VARIABLE_24698) (not (forall ((BOUND_VARIABLE_15231 list_P559422087at_nat)) (or (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 k_150) BOUND_VARIABLE_24696) BOUND_VARIABLE_15231) BOUND_VARIABLE_24697)) (not (= BOUND_VARIABLE_24698 (ho_119 k_118 BOUND_VARIABLE_15231)))))))))) (let ((_let_228 (forall ((BOUND_VARIABLE_24680 nat) (BOUND_VARIABLE_24681 nat) (BOUND_VARIABLE_24682 nat)) (= (ho_117 (ho_123 (ho_122 k_243 BOUND_VARIABLE_24680) BOUND_VARIABLE_24681) BOUND_VARIABLE_24682) (not (forall ((BOUND_VARIABLE_15269 list_P559422087at_nat)) (or (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 k_150) BOUND_VARIABLE_24680) BOUND_VARIABLE_15269) BOUND_VARIABLE_24681)) (not (= BOUND_VARIABLE_24682 (ho_119 k_118 BOUND_VARIABLE_15269)))))))))) (let ((_let_229 (forall ((BOUND_VARIABLE_24673 nat) (BOUND_VARIABLE_24674 nat)) (= (ho_117 (ho_123 k_244 BOUND_VARIABLE_24673) BOUND_VARIABLE_24674) (= BOUND_VARIABLE_24673 BOUND_VARIABLE_24674))))) (let ((_let_230 (forall ((BOUND_VARIABLE_24659 nat) (BOUND_VARIABLE_24660 nat)) (let ((_let_1 (= BOUND_VARIABLE_24659 BOUND_VARIABLE_24660))) (= (ho_117 (ho_123 k_245 BOUND_VARIABLE_24659) BOUND_VARIABLE_24660) (and (or (ho_117 (ho_123 k_141 BOUND_VARIABLE_24660) BOUND_VARIABLE_24659) _let_1) (or (ho_117 (ho_123 k_141 BOUND_VARIABLE_24659) BOUND_VARIABLE_24660) _let_1))))))) (let ((_let_231 (forall ((BOUND_VARIABLE_24651 nat) (BOUND_VARIABLE_24652 nat)) (= (ho_137 (ho_136 k_246 BOUND_VARIABLE_24651) BOUND_VARIABLE_24652) (ho_137 (ho_136 k_135 BOUND_VARIABLE_24652) BOUND_VARIABLE_24651))))) (let ((_let_232 (forall ((BOUND_VARIABLE_29018 |u_(-> product_prod_nat_nat capacity)|) (BOUND_VARIABLE_24634 nat) (BOUND_VARIABLE_24635 nat) (BOUND_VARIABLE_24636 nat)) (= (ho_117 (ho_123 (ho_122 (ho_121 k_247 BOUND_VARIABLE_29018) BOUND_VARIABLE_24634) BOUND_VARIABLE_24635) BOUND_VARIABLE_24636) (not (forall ((BOUND_VARIABLE_14986 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_24636 (ho_119 k_118 BOUND_VARIABLE_14986))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 BOUND_VARIABLE_29018) BOUND_VARIABLE_24634) BOUND_VARIABLE_14986) BOUND_VARIABLE_24635))))))))) (let ((_let_233 (forall ((BOUND_VARIABLE_29042 |u_(-> product_prod_nat_nat capacity)|) (BOUND_VARIABLE_24616 nat) (BOUND_VARIABLE_24617 nat) (BOUND_VARIABLE_24618 nat)) (= (ho_117 (ho_123 (ho_122 (ho_121 k_248 BOUND_VARIABLE_29042) BOUND_VARIABLE_24616) BOUND_VARIABLE_24617) BOUND_VARIABLE_24618) (not (forall ((BOUND_VARIABLE_14748 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_24618 (ho_119 k_118 BOUND_VARIABLE_14748))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 BOUND_VARIABLE_29042) BOUND_VARIABLE_24616) BOUND_VARIABLE_14748) BOUND_VARIABLE_24617))))))))) (let ((_let_234 (forall ((BOUND_VARIABLE_29066 |u_(-> product_prod_nat_nat capacity)|) (BOUND_VARIABLE_24598 nat) (BOUND_VARIABLE_24599 nat) (BOUND_VARIABLE_24600 nat)) (= (ho_117 (ho_123 (ho_122 (ho_121 k_249 BOUND_VARIABLE_29066) BOUND_VARIABLE_24598) BOUND_VARIABLE_24599) BOUND_VARIABLE_24600) (not (forall ((BOUND_VARIABLE_14778 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_24600 (ho_119 k_118 BOUND_VARIABLE_14778))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 BOUND_VARIABLE_29066) BOUND_VARIABLE_24598) BOUND_VARIABLE_14778) BOUND_VARIABLE_24599))))))))) (let ((_let_235 (forall ((BOUND_VARIABLE_29093 |u_(-> product_prod_nat_nat a)|) (BOUND_VARIABLE_24580 nat) (BOUND_VARIABLE_24581 nat) (BOUND_VARIABLE_24582 nat)) (= (ho_117 (ho_123 (ho_122 (ho_128 k_250 BOUND_VARIABLE_29093) BOUND_VARIABLE_24580) BOUND_VARIABLE_24581) BOUND_VARIABLE_24582) (not (forall ((BOUND_VARIABLE_14423 list_P559422087at_nat)) (or (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 BOUND_VARIABLE_29093) BOUND_VARIABLE_24580) BOUND_VARIABLE_14423) BOUND_VARIABLE_24581)) (not (= BOUND_VARIABLE_24582 (ho_119 k_118 BOUND_VARIABLE_14423)))))))))) (let ((_let_236 (forall ((BOUND_VARIABLE_29117 |u_(-> product_prod_nat_nat a)|) (BOUND_VARIABLE_24562 nat) (BOUND_VARIABLE_24563 nat) (BOUND_VARIABLE_24564 nat)) (= (ho_117 (ho_123 (ho_122 (ho_128 k_251 BOUND_VARIABLE_29117) BOUND_VARIABLE_24562) BOUND_VARIABLE_24563) BOUND_VARIABLE_24564) (not (forall ((BOUND_VARIABLE_14461 list_P559422087at_nat)) (or (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 BOUND_VARIABLE_29117) BOUND_VARIABLE_24562) BOUND_VARIABLE_14461) BOUND_VARIABLE_24563)) (not (= BOUND_VARIABLE_24564 (ho_119 k_118 BOUND_VARIABLE_14461)))))))))) (let ((_let_237 (forall ((BOUND_VARIABLE_29141 |u_(-> product_prod_nat_nat a)|) (BOUND_VARIABLE_24544 nat) (BOUND_VARIABLE_24545 nat) (BOUND_VARIABLE_24546 nat)) (= (ho_117 (ho_123 (ho_122 (ho_128 k_252 BOUND_VARIABLE_29141) BOUND_VARIABLE_24544) BOUND_VARIABLE_24545) BOUND_VARIABLE_24546) (not (forall ((BOUND_VARIABLE_14124 list_P559422087at_nat)) (or (not (ho_117 (ho_116 (ho_115 (ho_126 k_125 BOUND_VARIABLE_29141) BOUND_VARIABLE_24544) BOUND_VARIABLE_14124) BOUND_VARIABLE_24545)) (not (= BOUND_VARIABLE_24546 (ho_119 k_118 BOUND_VARIABLE_14124)))))))))) (let ((_let_238 (forall ((BOUND_VARIABLE_24527 nat) (BOUND_VARIABLE_24528 nat) (BOUND_VARIABLE_24529 nat)) (= (ho_117 (ho_123 (ho_122 k_253 BOUND_VARIABLE_24527) BOUND_VARIABLE_24528) BOUND_VARIABLE_24529) (not (forall ((BOUND_VARIABLE_13856 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_24529 (ho_119 k_118 BOUND_VARIABLE_13856))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 k_139) BOUND_VARIABLE_24527) BOUND_VARIABLE_13856) BOUND_VARIABLE_24528))))))))) (let ((_let_239 (forall ((BOUND_VARIABLE_24511 nat) (BOUND_VARIABLE_24512 nat) (BOUND_VARIABLE_24513 nat)) (= (ho_117 (ho_123 (ho_122 k_254 BOUND_VARIABLE_24511) BOUND_VARIABLE_24512) BOUND_VARIABLE_24513) (not (forall ((BOUND_VARIABLE_13893 list_P559422087at_nat)) (or (not (= BOUND_VARIABLE_24513 (ho_119 k_118 BOUND_VARIABLE_13893))) (not (ho_117 (ho_116 (ho_115 (ho_114 k_113 k_139) BOUND_VARIABLE_24511) BOUND_VARIABLE_13893) BOUND_VARIABLE_24512))))))))) (let ((_let_240 (forall ((BOUND_VARIABLE_13659 nat)) (not (forall ((C3 nat)) (not (= BOUND_VARIABLE_13659 (ho_137 (ho_136 k_135 BOUND_VARIABLE_13659) C3)))))))) (let ((_let_241 (forall ((BOUND_VARIABLE_13641 nat) (BOUND_VARIABLE_13643 nat)) (or (not (ho_117 (ho_123 k_141 BOUND_VARIABLE_13641) BOUND_VARIABLE_13643)) (not (forall ((C3 nat)) (not (= BOUND_VARIABLE_13643 (ho_137 (ho_136 k_135 BOUND_VARIABLE_13641) C3))))))))) (let ((_let_242 (forall ((BOUND_VARIABLE_26357 (-> product_prod_nat_nat capacity)) (BOUND_VARIABLE_26358 nat) (BOUND_VARIABLE_26359 nat) (BOUND_VARIABLE_26360 nat)) (= (ll_111 BOUND_VARIABLE_26357 BOUND_VARIABLE_26358 BOUND_VARIABLE_26359 BOUND_VARIABLE_26360) (not (forall ((BOUND_VARIABLE_12388 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_12388) BOUND_VARIABLE_26360)) (not ((((isPath_capacity BOUND_VARIABLE_26357) BOUND_VARIABLE_26358) BOUND_VARIABLE_12388) BOUND_VARIABLE_26359))))))))) (let ((_let_243 (forall ((BOUND_VARIABLE_26339 (-> product_prod_nat_nat a)) (BOUND_VARIABLE_26340 nat) (BOUND_VARIABLE_26341 nat) (BOUND_VARIABLE_26342 nat)) (= (ll_110 BOUND_VARIABLE_26339 BOUND_VARIABLE_26340 BOUND_VARIABLE_26341 BOUND_VARIABLE_26342) (not (forall ((BOUND_VARIABLE_20120 list_P559422087at_nat)) (or (not ((((isPath_a BOUND_VARIABLE_26339) BOUND_VARIABLE_26340) BOUND_VARIABLE_20120) BOUND_VARIABLE_26341)) (not (= (size_s1990949619at_nat BOUND_VARIABLE_20120) BOUND_VARIABLE_26342))))))))) (let ((_let_244 (forall ((BOUND_VARIABLE_26321 (-> product_prod_nat_nat capacity)) (BOUND_VARIABLE_26322 nat) (BOUND_VARIABLE_26323 nat) (BOUND_VARIABLE_26324 nat)) (= (ll_109 BOUND_VARIABLE_26321 BOUND_VARIABLE_26322 BOUND_VARIABLE_26323 BOUND_VARIABLE_26324) (not (forall ((BOUND_VARIABLE_12326 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_12326) BOUND_VARIABLE_26324)) (not ((((isPath_capacity BOUND_VARIABLE_26321) BOUND_VARIABLE_26322) BOUND_VARIABLE_12326) BOUND_VARIABLE_26323))))))))) (let ((_let_245 (forall ((BOUND_VARIABLE_26303 (-> product_prod_nat_nat a)) (BOUND_VARIABLE_26304 nat) (BOUND_VARIABLE_26305 nat) (BOUND_VARIABLE_26306 nat)) (= (ll_108 BOUND_VARIABLE_26303 BOUND_VARIABLE_26304 BOUND_VARIABLE_26305 BOUND_VARIABLE_26306) (not (forall ((BOUND_VARIABLE_14014 list_P559422087at_nat)) (or (not ((((isPath_a BOUND_VARIABLE_26303) BOUND_VARIABLE_26304) BOUND_VARIABLE_14014) BOUND_VARIABLE_26305)) (not (= (size_s1990949619at_nat BOUND_VARIABLE_14014) BOUND_VARIABLE_26306))))))))) (let ((_let_246 (forall ((BOUND_VARIABLE_26285 (-> product_prod_nat_nat a)) (BOUND_VARIABLE_26286 nat) (BOUND_VARIABLE_26287 nat) (BOUND_VARIABLE_26288 nat)) (= (ll_107 BOUND_VARIABLE_26285 BOUND_VARIABLE_26286 BOUND_VARIABLE_26287 BOUND_VARIABLE_26288) (not (forall ((BOUND_VARIABLE_18276 list_P559422087at_nat)) (or (not ((((isPath_a BOUND_VARIABLE_26285) BOUND_VARIABLE_26286) BOUND_VARIABLE_18276) BOUND_VARIABLE_26287)) (not (= (size_s1990949619at_nat BOUND_VARIABLE_18276) BOUND_VARIABLE_26288))))))))) (let ((_let_247 (forall ((BOUND_VARIABLE_26271 (-> product_prod_nat_nat a)) (BOUND_VARIABLE_26272 nat) (BOUND_VARIABLE_26273 nat)) (= (ll_106 BOUND_VARIABLE_26271 BOUND_VARIABLE_26272 BOUND_VARIABLE_26273) (not (forall ((P list_P559422087at_nat)) (not ((((isPath_a BOUND_VARIABLE_26271) BOUND_VARIABLE_26272) P) BOUND_VARIABLE_26273)))))))) (let ((_let_248 (forall ((BOUND_VARIABLE_26257 (-> product_prod_nat_nat a)) (BOUND_VARIABLE_26258 nat) (BOUND_VARIABLE_26259 nat)) (= (ll_105 BOUND_VARIABLE_26257 BOUND_VARIABLE_26258 BOUND_VARIABLE_26259) (not (forall ((BOUND_VARIABLE_13581 list_P559422087at_nat)) (not ((((isPath_a BOUND_VARIABLE_26257) BOUND_VARIABLE_26258) BOUND_VARIABLE_13581) BOUND_VARIABLE_26259)))))))) (let ((_let_249 (forall ((BOUND_VARIABLE_26245 nat) (BOUND_VARIABLE_26246 nat)) (= (ll_104 BOUND_VARIABLE_26245 BOUND_VARIABLE_26246) (not (forall ((K2 nat)) (not (= BOUND_VARIABLE_26246 ((plus_plus_nat BOUND_VARIABLE_26245) K2))))))))) (let ((_let_250 (forall ((BOUND_VARIABLE_26229 nat) (BOUND_VARIABLE_26230 nat) (BOUND_VARIABLE_26231 nat)) (= (ll_103 BOUND_VARIABLE_26229 BOUND_VARIABLE_26230 BOUND_VARIABLE_26231) (not (forall ((BOUND_VARIABLE_13256 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_13256) BOUND_VARIABLE_26231)) (not ((((isPath_capacity c) BOUND_VARIABLE_26229) BOUND_VARIABLE_13256) BOUND_VARIABLE_26230))))))))) (let ((_let_251 (forall ((BOUND_VARIABLE_26207 (-> product_prod_nat_nat a)) (BOUND_VARIABLE_26208 nat) (BOUND_VARIABLE_26209 list_P559422087at_nat) (BOUND_VARIABLE_26210 nat)) (= (ll_102 BOUND_VARIABLE_26207 BOUND_VARIABLE_26208 BOUND_VARIABLE_26209 BOUND_VARIABLE_26210) (and (forall ((P4 list_P559422087at_nat)) (let ((_let_1 (size_s1990949619at_nat BOUND_VARIABLE_26209))) (let ((_let_2 (size_s1990949619at_nat P4))) (or (not ((((isPath_a BOUND_VARIABLE_26207) BOUND_VARIABLE_26208) P4) BOUND_VARIABLE_26210)) ((ord_less_nat _let_1) _let_2) (= _let_2 _let_1))))) ((((isPath_a BOUND_VARIABLE_26207) BOUND_VARIABLE_26208) BOUND_VARIABLE_26209) BOUND_VARIABLE_26210)))))) (let ((_let_252 (forall ((BOUND_VARIABLE_26189 (-> product_prod_nat_nat a)) (BOUND_VARIABLE_26190 nat) (BOUND_VARIABLE_26191 nat) (BOUND_VARIABLE_26192 nat)) (= (ll_101 BOUND_VARIABLE_26189 BOUND_VARIABLE_26190 BOUND_VARIABLE_26191 BOUND_VARIABLE_26192) (not (forall ((BOUND_VARIABLE_22784 list_P559422087at_nat)) (or (not ((((isPath_a BOUND_VARIABLE_26189) BOUND_VARIABLE_26190) BOUND_VARIABLE_22784) BOUND_VARIABLE_26191)) (not (= (size_s1990949619at_nat BOUND_VARIABLE_22784) BOUND_VARIABLE_26192))))))))) (let ((_let_253 (forall ((BOUND_VARIABLE_26181 set_nat) (BOUND_VARIABLE_26182 nat)) (= (ll_100 BOUND_VARIABLE_26181 BOUND_VARIABLE_26182) ((member_nat BOUND_VARIABLE_26182) BOUND_VARIABLE_26181))))) (let ((_let_254 (forall ((BOUND_VARIABLE_26163 (-> product_prod_nat_nat a)) (BOUND_VARIABLE_26164 nat) (BOUND_VARIABLE_26165 nat) (BOUND_VARIABLE_26166 nat)) (= (ll_99 BOUND_VARIABLE_26163 BOUND_VARIABLE_26164 BOUND_VARIABLE_26165 BOUND_VARIABLE_26166) (not (forall ((BOUND_VARIABLE_22343 list_P559422087at_nat)) (or (not ((((isPath_a BOUND_VARIABLE_26163) BOUND_VARIABLE_26164) BOUND_VARIABLE_22343) BOUND_VARIABLE_26165)) (not (= (size_s1990949619at_nat BOUND_VARIABLE_22343) BOUND_VARIABLE_26166))))))))) (let ((_let_255 (forall ((BOUND_VARIABLE_26147 nat) (BOUND_VARIABLE_26148 nat) (BOUND_VARIABLE_26149 nat)) (= (ll_98 BOUND_VARIABLE_26147 BOUND_VARIABLE_26148 BOUND_VARIABLE_26149) (not (forall ((BOUND_VARIABLE_22192 list_P559422087at_nat)) (or (not ((((isPath_a c2) BOUND_VARIABLE_26147) BOUND_VARIABLE_22192) BOUND_VARIABLE_26148)) (not (= (size_s1990949619at_nat BOUND_VARIABLE_22192) BOUND_VARIABLE_26149))))))))) (let ((_let_256 (forall ((BOUND_VARIABLE_26131 nat) (BOUND_VARIABLE_26132 nat) (BOUND_VARIABLE_26133 nat)) (= (ll_97 BOUND_VARIABLE_26131 BOUND_VARIABLE_26132 BOUND_VARIABLE_26133) (not (forall ((BOUND_VARIABLE_22229 list_P559422087at_nat)) (or (not ((((isPath_a c2) BOUND_VARIABLE_26131) BOUND_VARIABLE_22229) BOUND_VARIABLE_26132)) (not (= (size_s1990949619at_nat BOUND_VARIABLE_22229) BOUND_VARIABLE_26133))))))))) (let ((_let_257 (forall ((BOUND_VARIABLE_26084 (-> product_prod_nat_nat capacity)) (BOUND_VARIABLE_26085 nat) (BOUND_VARIABLE_26086 list_P559422087at_nat) (BOUND_VARIABLE_26087 nat)) (= (ll_96 BOUND_VARIABLE_26084 BOUND_VARIABLE_26085 BOUND_VARIABLE_26086 BOUND_VARIABLE_26087) (and ((((isSimp1359852763pacity BOUND_VARIABLE_26084) BOUND_VARIABLE_26085) BOUND_VARIABLE_26086) BOUND_VARIABLE_26087) (= (size_s1990949619at_nat BOUND_VARIABLE_26086) (ord_Least_nat (((ll_111 BOUND_VARIABLE_26084) BOUND_VARIABLE_26085) BOUND_VARIABLE_26087)))))))) (let ((_let_258 (forall ((BOUND_VARIABLE_26066 (-> product_prod_nat_nat a)) (BOUND_VARIABLE_26067 nat) (BOUND_VARIABLE_26068 nat) (BOUND_VARIABLE_26069 nat)) (= (ll_95 BOUND_VARIABLE_26066 BOUND_VARIABLE_26067 BOUND_VARIABLE_26068 BOUND_VARIABLE_26069) (not (forall ((BOUND_VARIABLE_22005 list_P559422087at_nat)) (or (not ((((isPath_a BOUND_VARIABLE_26066) BOUND_VARIABLE_26067) BOUND_VARIABLE_22005) BOUND_VARIABLE_26068)) (not (= (size_s1990949619at_nat BOUND_VARIABLE_22005) BOUND_VARIABLE_26069))))))))) (let ((_let_259 (forall ((BOUND_VARIABLE_26056 nat)) (= (ll_94 BOUND_VARIABLE_26056) (not (forall ((BOUND_VARIABLE_12034 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_12034) BOUND_VARIABLE_26056)) (not ((((isPath_capacity c) s) BOUND_VARIABLE_12034) t))))))))) (let ((_let_260 (forall ((BOUND_VARIABLE_26046 nat)) (= (ll_93 BOUND_VARIABLE_26046) (not (forall ((BOUND_VARIABLE_12050 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_12050) BOUND_VARIABLE_26046)) (not ((((isPath_capacity c) s) BOUND_VARIABLE_12050) ua))))))))) (let ((_let_261 (forall ((BOUND_VARIABLE_26036 nat)) (= (ll_92 BOUND_VARIABLE_26036) (not (forall ((BOUND_VARIABLE_12086 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_12086) BOUND_VARIABLE_26036)) (not ((((isPath_capacity c) ua) BOUND_VARIABLE_12086) t))))))))) (let ((_let_262 (forall ((BOUND_VARIABLE_26020 nat) (BOUND_VARIABLE_26021 nat) (BOUND_VARIABLE_26022 nat)) (= (ll_91 BOUND_VARIABLE_26020 BOUND_VARIABLE_26021 BOUND_VARIABLE_26022) (not (forall ((BOUND_VARIABLE_21770 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_21770) BOUND_VARIABLE_26022)) (not ((((isPath_capacity c) BOUND_VARIABLE_26020) BOUND_VARIABLE_21770) BOUND_VARIABLE_26021))))))))) (let ((_let_263 (forall ((BOUND_VARIABLE_26010 nat)) (= (ll_90 BOUND_VARIABLE_26010) (not (forall ((BOUND_VARIABLE_21694 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_21694) BOUND_VARIABLE_26010)) (not ((((isPath_capacity c) s) BOUND_VARIABLE_21694) t))))))))) (let ((_let_264 (forall ((BOUND_VARIABLE_25992 (-> product_prod_nat_nat a)) (BOUND_VARIABLE_25993 nat) (BOUND_VARIABLE_25994 nat) (BOUND_VARIABLE_25995 nat)) (= (ll_89 BOUND_VARIABLE_25992 BOUND_VARIABLE_25993 BOUND_VARIABLE_25994 BOUND_VARIABLE_25995) (not (forall ((BOUND_VARIABLE_21502 list_P559422087at_nat)) (or (not ((((isPath_a BOUND_VARIABLE_25992) BOUND_VARIABLE_25993) BOUND_VARIABLE_21502) BOUND_VARIABLE_25994)) (not (= (size_s1990949619at_nat BOUND_VARIABLE_21502) BOUND_VARIABLE_25995))))))))) (let ((_let_265 (forall ((BOUND_VARIABLE_25974 (-> product_prod_nat_nat capacity)) (BOUND_VARIABLE_25975 nat) (BOUND_VARIABLE_25976 nat) (BOUND_VARIABLE_25977 nat)) (= (ll_88 BOUND_VARIABLE_25974 BOUND_VARIABLE_25975 BOUND_VARIABLE_25976 BOUND_VARIABLE_25977) (not (forall ((BOUND_VARIABLE_21353 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_21353) BOUND_VARIABLE_25977)) (not ((((isPath_capacity BOUND_VARIABLE_25974) BOUND_VARIABLE_25975) BOUND_VARIABLE_21353) BOUND_VARIABLE_25976))))))))) (let ((_let_266 (forall ((BOUND_VARIABLE_25956 (-> product_prod_nat_nat capacity)) (BOUND_VARIABLE_25957 nat) (BOUND_VARIABLE_25958 nat) (BOUND_VARIABLE_25959 nat)) (= (ll_87 BOUND_VARIABLE_25956 BOUND_VARIABLE_25957 BOUND_VARIABLE_25958 BOUND_VARIABLE_25959) (not (forall ((BOUND_VARIABLE_21280 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_21280) BOUND_VARIABLE_25959)) (not ((((isPath_capacity BOUND_VARIABLE_25956) BOUND_VARIABLE_25957) BOUND_VARIABLE_21280) BOUND_VARIABLE_25958))))))))) (let ((_let_267 (forall ((BOUND_VARIABLE_25938 (-> product_prod_nat_nat a)) (BOUND_VARIABLE_25939 nat) (BOUND_VARIABLE_25940 nat) (BOUND_VARIABLE_25941 nat)) (= (ll_86 BOUND_VARIABLE_25938 BOUND_VARIABLE_25939 BOUND_VARIABLE_25940 BOUND_VARIABLE_25941) (not (forall ((BOUND_VARIABLE_21120 list_P559422087at_nat)) (or (not ((((isPath_a BOUND_VARIABLE_25938) BOUND_VARIABLE_25939) BOUND_VARIABLE_21120) BOUND_VARIABLE_25940)) (not (= (size_s1990949619at_nat BOUND_VARIABLE_21120) BOUND_VARIABLE_25941))))))))) (let ((_let_268 (forall ((BOUND_VARIABLE_25920 (-> product_prod_nat_nat a)) (BOUND_VARIABLE_25921 nat) (BOUND_VARIABLE_25922 nat) (BOUND_VARIABLE_25923 nat)) (= (ll_85 BOUND_VARIABLE_25920 BOUND_VARIABLE_25921 BOUND_VARIABLE_25922 BOUND_VARIABLE_25923) (not (forall ((BOUND_VARIABLE_21141 list_P559422087at_nat)) (or (not ((((isPath_a BOUND_VARIABLE_25920) BOUND_VARIABLE_25921) BOUND_VARIABLE_21141) BOUND_VARIABLE_25922)) (not (= (size_s1990949619at_nat BOUND_VARIABLE_21141) BOUND_VARIABLE_25923))))))))) (let ((_let_269 (forall ((BOUND_VARIABLE_25904 nat) (BOUND_VARIABLE_25905 nat) (BOUND_VARIABLE_25906 nat)) (= (ll_84 BOUND_VARIABLE_25904 BOUND_VARIABLE_25905 BOUND_VARIABLE_25906) (not (forall ((BOUND_VARIABLE_21012 list_P559422087at_nat)) (or (not ((((isPath_a c2) BOUND_VARIABLE_25904) BOUND_VARIABLE_21012) BOUND_VARIABLE_25905)) (not (= (size_s1990949619at_nat BOUND_VARIABLE_21012) BOUND_VARIABLE_25906))))))))) (let ((_let_270 (forall ((BOUND_VARIABLE_25886 (-> product_prod_nat_nat capacity)) (BOUND_VARIABLE_25887 nat) (BOUND_VARIABLE_25888 nat) (BOUND_VARIABLE_25889 nat)) (= (ll_83 BOUND_VARIABLE_25886 BOUND_VARIABLE_25887 BOUND_VARIABLE_25888 BOUND_VARIABLE_25889) (not (forall ((BOUND_VARIABLE_20791 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_20791) BOUND_VARIABLE_25889)) (not ((((isPath_capacity BOUND_VARIABLE_25886) BOUND_VARIABLE_25887) BOUND_VARIABLE_20791) BOUND_VARIABLE_25888))))))))) (let ((_let_271 (forall ((BOUND_VARIABLE_25868 (-> product_prod_nat_nat capacity)) (BOUND_VARIABLE_25869 nat) (BOUND_VARIABLE_25870 nat) (BOUND_VARIABLE_25871 nat)) (= (ll_82 BOUND_VARIABLE_25868 BOUND_VARIABLE_25869 BOUND_VARIABLE_25870 BOUND_VARIABLE_25871) (not (forall ((BOUND_VARIABLE_20810 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_20810) BOUND_VARIABLE_25871)) (not ((((isPath_capacity BOUND_VARIABLE_25868) BOUND_VARIABLE_25869) BOUND_VARIABLE_20810) BOUND_VARIABLE_25870))))))))) (let ((_let_272 (forall ((BOUND_VARIABLE_25850 (-> product_prod_nat_nat capacity)) (BOUND_VARIABLE_25851 nat) (BOUND_VARIABLE_25852 nat) (BOUND_VARIABLE_25853 nat)) (= (ll_81 BOUND_VARIABLE_25850 BOUND_VARIABLE_25851 BOUND_VARIABLE_25852 BOUND_VARIABLE_25853) (not (forall ((BOUND_VARIABLE_20637 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_20637) BOUND_VARIABLE_25853)) (not ((((isPath_capacity BOUND_VARIABLE_25850) BOUND_VARIABLE_25851) BOUND_VARIABLE_20637) BOUND_VARIABLE_25852))))))))) (let ((_let_273 (forall ((BOUND_VARIABLE_25832 (-> product_prod_nat_nat capacity)) (BOUND_VARIABLE_25833 nat) (BOUND_VARIABLE_25834 nat) (BOUND_VARIABLE_25835 nat)) (= (ll_80 BOUND_VARIABLE_25832 BOUND_VARIABLE_25833 BOUND_VARIABLE_25834 BOUND_VARIABLE_25835) (not (forall ((BOUND_VARIABLE_20675 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_20675) BOUND_VARIABLE_25835)) (not ((((isPath_capacity BOUND_VARIABLE_25832) BOUND_VARIABLE_25833) BOUND_VARIABLE_20675) BOUND_VARIABLE_25834))))))))) (let ((_let_274 (forall ((BOUND_VARIABLE_25816 nat) (BOUND_VARIABLE_25817 nat) (BOUND_VARIABLE_25818 nat)) (= (ll_79 BOUND_VARIABLE_25816 BOUND_VARIABLE_25817 BOUND_VARIABLE_25818) (not (forall ((BOUND_VARIABLE_20368 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_20368) BOUND_VARIABLE_25818)) (not ((((isPath_capacity c) BOUND_VARIABLE_25816) BOUND_VARIABLE_20368) BOUND_VARIABLE_25817))))))))) (let ((_let_275 (forall ((BOUND_VARIABLE_25800 nat) (BOUND_VARIABLE_25801 nat) (BOUND_VARIABLE_25802 nat)) (= (ll_78 BOUND_VARIABLE_25800 BOUND_VARIABLE_25801 BOUND_VARIABLE_25802) (not (forall ((BOUND_VARIABLE_20406 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_20406) BOUND_VARIABLE_25802)) (not ((((isPath_capacity c) BOUND_VARIABLE_25800) BOUND_VARIABLE_20406) BOUND_VARIABLE_25801))))))))) (let ((_let_276 (forall ((BOUND_VARIABLE_25784 nat) (BOUND_VARIABLE_25785 nat) (BOUND_VARIABLE_25786 nat)) (= (ll_77 BOUND_VARIABLE_25784 BOUND_VARIABLE_25785 BOUND_VARIABLE_25786) (not (forall ((BOUND_VARIABLE_20271 list_P559422087at_nat)) (or (not ((((isPath_a c2) BOUND_VARIABLE_25784) BOUND_VARIABLE_20271) BOUND_VARIABLE_25785)) (not (= (size_s1990949619at_nat BOUND_VARIABLE_20271) BOUND_VARIABLE_25786))))))))) (let ((_let_277 (forall ((BOUND_VARIABLE_25768 nat) (BOUND_VARIABLE_25769 nat) (BOUND_VARIABLE_25770 nat)) (= (ll_76 BOUND_VARIABLE_25768 BOUND_VARIABLE_25769 BOUND_VARIABLE_25770) (not (forall ((BOUND_VARIABLE_20292 list_P559422087at_nat)) (or (not ((((isPath_a c2) BOUND_VARIABLE_25768) BOUND_VARIABLE_20292) BOUND_VARIABLE_25769)) (not (= (size_s1990949619at_nat BOUND_VARIABLE_20292) BOUND_VARIABLE_25770))))))))) (let ((_let_278 (forall ((BOUND_VARIABLE_25752 nat) (BOUND_VARIABLE_25753 nat) (BOUND_VARIABLE_25754 nat)) (= (ll_75 BOUND_VARIABLE_25752 BOUND_VARIABLE_25753 BOUND_VARIABLE_25754) (not (forall ((BOUND_VARIABLE_20190 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_20190) BOUND_VARIABLE_25754)) (not ((((isPath_capacity c) BOUND_VARIABLE_25752) BOUND_VARIABLE_20190) BOUND_VARIABLE_25753))))))))) (let ((_let_279 (forall ((BOUND_VARIABLE_25743 (-> nat Bool))) (= (ll_74 BOUND_VARIABLE_25743) (not (forall ((X4 nat)) (not (BOUND_VARIABLE_25743 X4)))))))) (let ((_let_280 (forall ((BOUND_VARIABLE_25728 (-> nat Bool))) (= (ll_73 BOUND_VARIABLE_25728) (not (forall ((N2 nat)) (or (not (forall ((M2 nat)) (or (not ((ord_less_nat M2) N2)) (not (BOUND_VARIABLE_25728 M2))))) (not (BOUND_VARIABLE_25728 N2))))))))) (let ((_let_281 (forall ((BOUND_VARIABLE_25714 (-> product_prod_nat_nat capacity)) (BOUND_VARIABLE_25715 nat) (BOUND_VARIABLE_25716 nat)) (= (ll_72 BOUND_VARIABLE_25714 BOUND_VARIABLE_25715 BOUND_VARIABLE_25716) (not (forall ((P list_P559422087at_nat)) (not ((((isPath_capacity BOUND_VARIABLE_25714) BOUND_VARIABLE_25715) P) BOUND_VARIABLE_25716)))))))) (let ((_let_282 (forall ((BOUND_VARIABLE_25700 (-> product_prod_nat_nat capacity)) (BOUND_VARIABLE_25701 nat) (BOUND_VARIABLE_25702 nat)) (= (ll_71 BOUND_VARIABLE_25700 BOUND_VARIABLE_25701 BOUND_VARIABLE_25702) (not (forall ((BOUND_VARIABLE_8474 list_P559422087at_nat)) (not ((((isPath_capacity BOUND_VARIABLE_25700) BOUND_VARIABLE_25701) BOUND_VARIABLE_8474) BOUND_VARIABLE_25702)))))))) (let ((_let_283 (forall ((BOUND_VARIABLE_25653 (-> product_prod_nat_nat a)) (BOUND_VARIABLE_25654 nat) (BOUND_VARIABLE_25655 list_P559422087at_nat) (BOUND_VARIABLE_25656 nat)) (= (ll_70 BOUND_VARIABLE_25653 BOUND_VARIABLE_25654 BOUND_VARIABLE_25655 BOUND_VARIABLE_25656) (and (= (size_s1990949619at_nat BOUND_VARIABLE_25655) (ord_Least_nat (((ll_110 BOUND_VARIABLE_25653) BOUND_VARIABLE_25654) BOUND_VARIABLE_25656))) ((((isSimplePath_a BOUND_VARIABLE_25653) BOUND_VARIABLE_25654) BOUND_VARIABLE_25655) BOUND_VARIABLE_25656)))))) (let ((_let_284 (forall ((BOUND_VARIABLE_25635 (-> product_prod_nat_nat capacity)) (BOUND_VARIABLE_25636 nat) (BOUND_VARIABLE_25637 nat) (BOUND_VARIABLE_25638 nat)) (= (ll_69 BOUND_VARIABLE_25635 BOUND_VARIABLE_25636 BOUND_VARIABLE_25637 BOUND_VARIABLE_25638) (not (forall ((BOUND_VARIABLE_20011 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_20011) BOUND_VARIABLE_25638)) (not ((((isPath_capacity BOUND_VARIABLE_25635) BOUND_VARIABLE_25636) BOUND_VARIABLE_20011) BOUND_VARIABLE_25637))))))))) (let ((_let_285 (forall ((BOUND_VARIABLE_25617 (-> product_prod_nat_nat capacity)) (BOUND_VARIABLE_25618 nat) (BOUND_VARIABLE_25619 nat) (BOUND_VARIABLE_25620 nat)) (= (ll_68 BOUND_VARIABLE_25617 BOUND_VARIABLE_25618 BOUND_VARIABLE_25619 BOUND_VARIABLE_25620) (not (forall ((BOUND_VARIABLE_20029 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_20029) BOUND_VARIABLE_25620)) (not ((((isPath_capacity BOUND_VARIABLE_25617) BOUND_VARIABLE_25618) BOUND_VARIABLE_20029) BOUND_VARIABLE_25619))))))))) (let ((_let_286 (forall ((BOUND_VARIABLE_25599 (-> product_prod_nat_nat a)) (BOUND_VARIABLE_25600 nat) (BOUND_VARIABLE_25601 nat) (BOUND_VARIABLE_25602 nat)) (= (ll_67 BOUND_VARIABLE_25599 BOUND_VARIABLE_25600 BOUND_VARIABLE_25601 BOUND_VARIABLE_25602) (not (forall ((BOUND_VARIABLE_19899 list_P559422087at_nat)) (or (not ((((isPath_a BOUND_VARIABLE_25599) BOUND_VARIABLE_25600) BOUND_VARIABLE_19899) BOUND_VARIABLE_25601)) (not (= (size_s1990949619at_nat BOUND_VARIABLE_19899) BOUND_VARIABLE_25602))))))))) (let ((_let_287 (forall ((BOUND_VARIABLE_25581 (-> product_prod_nat_nat a)) (BOUND_VARIABLE_25582 nat) (BOUND_VARIABLE_25583 nat) (BOUND_VARIABLE_25584 nat)) (= (ll_66 BOUND_VARIABLE_25581 BOUND_VARIABLE_25582 BOUND_VARIABLE_25583 BOUND_VARIABLE_25584) (not (forall ((BOUND_VARIABLE_19917 list_P559422087at_nat)) (or (not ((((isPath_a BOUND_VARIABLE_25581) BOUND_VARIABLE_25582) BOUND_VARIABLE_19917) BOUND_VARIABLE_25583)) (not (= (size_s1990949619at_nat BOUND_VARIABLE_19917) BOUND_VARIABLE_25584))))))))) (let ((_let_288 (forall ((BOUND_VARIABLE_25569 nat) (BOUND_VARIABLE_25570 nat)) (= (ll_65 BOUND_VARIABLE_25569 BOUND_VARIABLE_25570) (not (forall ((BOUND_VARIABLE_9148 list_P559422087at_nat)) (not ((((isPath_a c2) BOUND_VARIABLE_25569) BOUND_VARIABLE_9148) BOUND_VARIABLE_25570)))))))) (let ((_let_289 (forall ((BOUND_VARIABLE_25557 nat) (BOUND_VARIABLE_25558 nat)) (= (ll_64 BOUND_VARIABLE_25557 BOUND_VARIABLE_25558) (not (forall ((BOUND_VARIABLE_19828 list_P559422087at_nat)) (not ((((isPath_a c2) BOUND_VARIABLE_25557) BOUND_VARIABLE_19828) BOUND_VARIABLE_25558)))))))) (let ((_let_290 (forall ((BOUND_VARIABLE_25541 nat) (BOUND_VARIABLE_25542 nat) (BOUND_VARIABLE_25543 nat)) (= (ll_63 BOUND_VARIABLE_25541 BOUND_VARIABLE_25542 BOUND_VARIABLE_25543) (not (forall ((BOUND_VARIABLE_9095 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_9095) BOUND_VARIABLE_25543)) (not ((((isPath_capacity c) BOUND_VARIABLE_25541) BOUND_VARIABLE_9095) BOUND_VARIABLE_25542))))))))) (let ((_let_291 (forall ((BOUND_VARIABLE_25525 nat) (BOUND_VARIABLE_25526 nat) (BOUND_VARIABLE_25527 nat)) (= (ll_62 BOUND_VARIABLE_25525 BOUND_VARIABLE_25526 BOUND_VARIABLE_25527) (not (forall ((BOUND_VARIABLE_19789 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_19789) BOUND_VARIABLE_25527)) (not ((((isPath_capacity c) BOUND_VARIABLE_25525) BOUND_VARIABLE_19789) BOUND_VARIABLE_25526))))))))) (let ((_let_292 (forall ((BOUND_VARIABLE_25509 nat) (BOUND_VARIABLE_25510 nat) (BOUND_VARIABLE_25511 nat)) (= (ll_61 BOUND_VARIABLE_25509 BOUND_VARIABLE_25510 BOUND_VARIABLE_25511) (not (forall ((BOUND_VARIABLE_19725 list_P559422087at_nat)) (or (not ((((isPath_a c2) BOUND_VARIABLE_25509) BOUND_VARIABLE_19725) BOUND_VARIABLE_25510)) (not (= (size_s1990949619at_nat BOUND_VARIABLE_19725) BOUND_VARIABLE_25511))))))))) (let ((_let_293 (forall ((BOUND_VARIABLE_25491 (-> product_prod_nat_nat a)) (BOUND_VARIABLE_25492 nat) (BOUND_VARIABLE_25493 nat) (BOUND_VARIABLE_25494 nat)) (= (ll_60 BOUND_VARIABLE_25491 BOUND_VARIABLE_25492 BOUND_VARIABLE_25493 BOUND_VARIABLE_25494) (not (forall ((BOUND_VARIABLE_19510 list_P559422087at_nat)) (or (not ((((isPath_a BOUND_VARIABLE_25491) BOUND_VARIABLE_25492) BOUND_VARIABLE_19510) BOUND_VARIABLE_25493)) (not (= (size_s1990949619at_nat BOUND_VARIABLE_19510) BOUND_VARIABLE_25494))))))))) (let ((_let_294 (forall ((BOUND_VARIABLE_25473 (-> product_prod_nat_nat a)) (BOUND_VARIABLE_25474 nat) (BOUND_VARIABLE_25475 nat) (BOUND_VARIABLE_25476 nat)) (= (ll_59 BOUND_VARIABLE_25473 BOUND_VARIABLE_25474 BOUND_VARIABLE_25475 BOUND_VARIABLE_25476) (not (forall ((BOUND_VARIABLE_19529 list_P559422087at_nat)) (or (not ((((isPath_a BOUND_VARIABLE_25473) BOUND_VARIABLE_25474) BOUND_VARIABLE_19529) BOUND_VARIABLE_25475)) (not (= (size_s1990949619at_nat BOUND_VARIABLE_19529) BOUND_VARIABLE_25476))))))))) (let ((_let_295 (forall ((BOUND_VARIABLE_25451 (-> product_prod_nat_nat capacity)) (BOUND_VARIABLE_25452 nat) (BOUND_VARIABLE_25453 list_P559422087at_nat) (BOUND_VARIABLE_25454 nat)) (= (ll_58 BOUND_VARIABLE_25451 BOUND_VARIABLE_25452 BOUND_VARIABLE_25453 BOUND_VARIABLE_25454) (and (forall ((P4 list_P559422087at_nat)) (let ((_let_1 (size_s1990949619at_nat BOUND_VARIABLE_25453))) (let ((_let_2 (size_s1990949619at_nat P4))) (or (not ((((isPath_capacity BOUND_VARIABLE_25451) BOUND_VARIABLE_25452) P4) BOUND_VARIABLE_25454)) ((ord_less_nat _let_1) _let_2) (= _let_2 _let_1))))) ((((isPath_capacity BOUND_VARIABLE_25451) BOUND_VARIABLE_25452) BOUND_VARIABLE_25453) BOUND_VARIABLE_25454)))))) (let ((_let_296 (forall ((BOUND_VARIABLE_25406 (-> product_prod_nat_nat capacity)) (BOUND_VARIABLE_25407 nat) (BOUND_VARIABLE_25408 list_P559422087at_nat) (BOUND_VARIABLE_25409 nat)) (= (ll_57 BOUND_VARIABLE_25406 BOUND_VARIABLE_25407 BOUND_VARIABLE_25408 BOUND_VARIABLE_25409) (and (= (size_s1990949619at_nat BOUND_VARIABLE_25408) (ord_Least_nat (((ll_109 BOUND_VARIABLE_25406) BOUND_VARIABLE_25407) BOUND_VARIABLE_25409))) ((((isPath_capacity BOUND_VARIABLE_25406) BOUND_VARIABLE_25407) BOUND_VARIABLE_25408) BOUND_VARIABLE_25409)))))) (let ((_let_297 (forall ((BOUND_VARIABLE_25390 nat) (BOUND_VARIABLE_25391 nat) (BOUND_VARIABLE_25392 nat)) (= (ll_56 BOUND_VARIABLE_25390 BOUND_VARIABLE_25391 BOUND_VARIABLE_25392) (not (forall ((BOUND_VARIABLE_19130 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_19130) BOUND_VARIABLE_25392)) (not ((((isPath_capacity c) BOUND_VARIABLE_25390) BOUND_VARIABLE_19130) BOUND_VARIABLE_25391))))))))) (let ((_let_298 (forall ((BOUND_VARIABLE_25374 nat) (BOUND_VARIABLE_25375 nat) (BOUND_VARIABLE_25376 nat)) (= (ll_55 BOUND_VARIABLE_25374 BOUND_VARIABLE_25375 BOUND_VARIABLE_25376) (not (forall ((BOUND_VARIABLE_19149 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_19149) BOUND_VARIABLE_25376)) (not ((((isPath_capacity c) BOUND_VARIABLE_25374) BOUND_VARIABLE_19149) BOUND_VARIABLE_25375))))))))) (let ((_let_299 (forall ((BOUND_VARIABLE_25358 nat) (BOUND_VARIABLE_25359 nat) (BOUND_VARIABLE_25360 nat)) (= (ll_54 BOUND_VARIABLE_25358 BOUND_VARIABLE_25359 BOUND_VARIABLE_25360) (not (forall ((BOUND_VARIABLE_19053 list_P559422087at_nat)) (or (not ((((isPath_a c2) BOUND_VARIABLE_25358) BOUND_VARIABLE_19053) BOUND_VARIABLE_25359)) (not (= (size_s1990949619at_nat BOUND_VARIABLE_19053) BOUND_VARIABLE_25360))))))))) (let ((_let_300 (forall ((BOUND_VARIABLE_25346 nat) (BOUND_VARIABLE_25347 nat)) (= (ll_53 BOUND_VARIABLE_25346 BOUND_VARIABLE_25347) (not (forall ((BOUND_VARIABLE_18903 list_P559422087at_nat)) (not ((((isPath_capacity c) BOUND_VARIABLE_25346) BOUND_VARIABLE_18903) BOUND_VARIABLE_25347)))))))) (let ((_let_301 (forall ((BOUND_VARIABLE_25334 nat) (BOUND_VARIABLE_25335 nat)) (= (ll_52 BOUND_VARIABLE_25334 BOUND_VARIABLE_25335) (not (forall ((BOUND_VARIABLE_18916 list_P559422087at_nat)) (not ((((isPath_capacity c) BOUND_VARIABLE_25334) BOUND_VARIABLE_18916) BOUND_VARIABLE_25335)))))))) (let ((_let_302 (forall ((BOUND_VARIABLE_25322 nat) (BOUND_VARIABLE_25323 nat)) (let ((_let_1 (= BOUND_VARIABLE_25322 BOUND_VARIABLE_25323))) (= (ll_51 BOUND_VARIABLE_25322 BOUND_VARIABLE_25323) (and (or ((ord_less_nat BOUND_VARIABLE_25322) BOUND_VARIABLE_25323) _let_1) (not _let_1))))))) (let ((_let_303 (forall ((BOUND_VARIABLE_25306 nat) (BOUND_VARIABLE_25307 nat) (BOUND_VARIABLE_25308 nat)) (= (ll_50 BOUND_VARIABLE_25306 BOUND_VARIABLE_25307 BOUND_VARIABLE_25308) (not (forall ((BOUND_VARIABLE_18797 list_P559422087at_nat)) (or (not ((((isPath_a c2) BOUND_VARIABLE_25306) BOUND_VARIABLE_18797) BOUND_VARIABLE_25307)) (not (= (size_s1990949619at_nat BOUND_VARIABLE_18797) BOUND_VARIABLE_25308))))))))) (let ((_let_304 (forall ((BOUND_VARIABLE_25290 nat) (BOUND_VARIABLE_25291 nat) (BOUND_VARIABLE_25292 nat)) (= (ll_49 BOUND_VARIABLE_25290 BOUND_VARIABLE_25291 BOUND_VARIABLE_25292) (not (forall ((BOUND_VARIABLE_18816 list_P559422087at_nat)) (or (not ((((isPath_a c2) BOUND_VARIABLE_25290) BOUND_VARIABLE_18816) BOUND_VARIABLE_25291)) (not (= (size_s1990949619at_nat BOUND_VARIABLE_18816) BOUND_VARIABLE_25292))))))))) (let ((_let_305 (forall ((BOUND_VARIABLE_25278 nat) (BOUND_VARIABLE_25279 nat)) (= (ll_48 BOUND_VARIABLE_25278 BOUND_VARIABLE_25279) (not (forall ((C2 nat)) (not (= BOUND_VARIABLE_25279 ((plus_plus_nat BOUND_VARIABLE_25278) C2))))))))) (let ((_let_306 (forall ((BOUND_VARIABLE_25262 nat) (BOUND_VARIABLE_25263 nat) (BOUND_VARIABLE_25264 nat)) (= (ll_47 BOUND_VARIABLE_25262 BOUND_VARIABLE_25263 BOUND_VARIABLE_25264) (not (forall ((BOUND_VARIABLE_18642 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_18642) BOUND_VARIABLE_25264)) (not ((((isPath_capacity c) BOUND_VARIABLE_25262) BOUND_VARIABLE_18642) BOUND_VARIABLE_25263))))))))) (let ((_let_307 (forall ((BOUND_VARIABLE_25246 nat) (BOUND_VARIABLE_25247 nat) (BOUND_VARIABLE_25248 nat)) (= (ll_46 BOUND_VARIABLE_25246 BOUND_VARIABLE_25247 BOUND_VARIABLE_25248) (not (forall ((BOUND_VARIABLE_18549 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_18549) BOUND_VARIABLE_25248)) (not ((((isPath_capacity c) BOUND_VARIABLE_25246) BOUND_VARIABLE_18549) BOUND_VARIABLE_25247))))))))) (let ((_let_308 (forall ((BOUND_VARIABLE_25228 (-> product_prod_nat_nat capacity)) (BOUND_VARIABLE_25229 nat) (BOUND_VARIABLE_25230 nat) (BOUND_VARIABLE_25231 nat)) (= (ll_45 BOUND_VARIABLE_25228 BOUND_VARIABLE_25229 BOUND_VARIABLE_25230 BOUND_VARIABLE_25231) (not (forall ((BOUND_VARIABLE_18431 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_18431) BOUND_VARIABLE_25231)) (not ((((isPath_capacity BOUND_VARIABLE_25228) BOUND_VARIABLE_25229) BOUND_VARIABLE_18431) BOUND_VARIABLE_25230))))))))) (let ((_let_309 (forall ((BOUND_VARIABLE_25183 (-> product_prod_nat_nat a)) (BOUND_VARIABLE_25184 nat) (BOUND_VARIABLE_25185 list_P559422087at_nat) (BOUND_VARIABLE_25186 nat)) (= (ll_44 BOUND_VARIABLE_25183 BOUND_VARIABLE_25184 BOUND_VARIABLE_25185 BOUND_VARIABLE_25186) (and ((((isPath_a BOUND_VARIABLE_25183) BOUND_VARIABLE_25184) BOUND_VARIABLE_25185) BOUND_VARIABLE_25186) (= (size_s1990949619at_nat BOUND_VARIABLE_25185) (ord_Least_nat (((ll_108 BOUND_VARIABLE_25183) BOUND_VARIABLE_25184) BOUND_VARIABLE_25186)))))))) (let ((_let_310 (forall ((BOUND_VARIABLE_25138 (-> product_prod_nat_nat a)) (BOUND_VARIABLE_25139 nat) (BOUND_VARIABLE_25140 list_P559422087at_nat) (BOUND_VARIABLE_25141 nat)) (= (ll_43 BOUND_VARIABLE_25138 BOUND_VARIABLE_25139 BOUND_VARIABLE_25140 BOUND_VARIABLE_25141) (and ((((isPath_a BOUND_VARIABLE_25138) BOUND_VARIABLE_25139) BOUND_VARIABLE_25140) BOUND_VARIABLE_25141) (= (size_s1990949619at_nat BOUND_VARIABLE_25140) (ord_Least_nat (((ll_107 BOUND_VARIABLE_25138) BOUND_VARIABLE_25139) BOUND_VARIABLE_25141)))))))) (let ((_let_311 (forall ((BOUND_VARIABLE_25128 nat) (BOUND_VARIABLE_25129 nat)) (= (ll_42 BOUND_VARIABLE_25128 BOUND_VARIABLE_25129) (or ((ord_less_nat BOUND_VARIABLE_25128) BOUND_VARIABLE_25129) (= BOUND_VARIABLE_25128 BOUND_VARIABLE_25129)))))) (let ((_let_312 (forall ((BOUND_VARIABLE_25118 nat) (BOUND_VARIABLE_25119 nat)) (= (ll_41 BOUND_VARIABLE_25118 BOUND_VARIABLE_25119) (or ((ord_less_nat BOUND_VARIABLE_25118) BOUND_VARIABLE_25119) (= BOUND_VARIABLE_25118 BOUND_VARIABLE_25119)))))) (let ((_let_313 (forall ((BOUND_VARIABLE_25106 nat) (BOUND_VARIABLE_25107 nat)) (let ((_let_1 (= BOUND_VARIABLE_25106 BOUND_VARIABLE_25107))) (= (ll_40 BOUND_VARIABLE_25106 BOUND_VARIABLE_25107) (and (or ((ord_less_nat BOUND_VARIABLE_25106) BOUND_VARIABLE_25107) _let_1) (not _let_1))))))) (let ((_let_314 (forall ((BOUND_VARIABLE_25090 nat) (BOUND_VARIABLE_25091 nat) (BOUND_VARIABLE_25092 nat)) (= (ll_39 BOUND_VARIABLE_25090 BOUND_VARIABLE_25091 BOUND_VARIABLE_25092) (not (forall ((BOUND_VARIABLE_18152 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_18152) BOUND_VARIABLE_25092)) (not ((((isPath_capacity c) BOUND_VARIABLE_25090) BOUND_VARIABLE_18152) BOUND_VARIABLE_25091))))))))) (let ((_let_315 (forall ((BOUND_VARIABLE_25074 nat) (BOUND_VARIABLE_25075 nat) (BOUND_VARIABLE_25076 nat)) (= (ll_38 BOUND_VARIABLE_25074 BOUND_VARIABLE_25075 BOUND_VARIABLE_25076) (not (forall ((BOUND_VARIABLE_18182 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_18182) BOUND_VARIABLE_25076)) (not ((((isPath_capacity c) BOUND_VARIABLE_25074) BOUND_VARIABLE_18182) BOUND_VARIABLE_25075))))))))) (let ((_let_316 (forall ((BOUND_VARIABLE_25058 nat) (BOUND_VARIABLE_25059 nat) (BOUND_VARIABLE_25060 nat)) (= (ll_37 BOUND_VARIABLE_25058 BOUND_VARIABLE_25059 BOUND_VARIABLE_25060) (not (forall ((BOUND_VARIABLE_18063 list_P559422087at_nat)) (or (not ((((isPath_a c2) BOUND_VARIABLE_25058) BOUND_VARIABLE_18063) BOUND_VARIABLE_25059)) (not (= (size_s1990949619at_nat BOUND_VARIABLE_18063) BOUND_VARIABLE_25060))))))))) (let ((_let_317 (forall ((BOUND_VARIABLE_25042 nat) (BOUND_VARIABLE_25043 nat) (BOUND_VARIABLE_25044 nat)) (= (ll_36 BOUND_VARIABLE_25042 BOUND_VARIABLE_25043 BOUND_VARIABLE_25044) (not (forall ((BOUND_VARIABLE_17857 list_P559422087at_nat)) (or (not ((((isPath_a c2) BOUND_VARIABLE_25042) BOUND_VARIABLE_17857) BOUND_VARIABLE_25043)) (not (= (size_s1990949619at_nat BOUND_VARIABLE_17857) BOUND_VARIABLE_25044))))))))) (let ((_let_318 (forall ((BOUND_VARIABLE_25026 nat) (BOUND_VARIABLE_25027 nat) (BOUND_VARIABLE_25028 nat)) (= (ll_35 BOUND_VARIABLE_25026 BOUND_VARIABLE_25027 BOUND_VARIABLE_25028) (not (forall ((BOUND_VARIABLE_17895 list_P559422087at_nat)) (or (not ((((isPath_a c2) BOUND_VARIABLE_25026) BOUND_VARIABLE_17895) BOUND_VARIABLE_25027)) (not (= (size_s1990949619at_nat BOUND_VARIABLE_17895) BOUND_VARIABLE_25028))))))))) (let ((_let_319 (forall ((BOUND_VARIABLE_25019 nat) (BOUND_VARIABLE_25020 nat)) (= (ll_34 BOUND_VARIABLE_25019 BOUND_VARIABLE_25020) (= BOUND_VARIABLE_25019 BOUND_VARIABLE_25020))))) (let ((_let_320 (forall ((BOUND_VARIABLE_25005 nat) (BOUND_VARIABLE_25006 nat)) (let ((_let_1 (= BOUND_VARIABLE_25005 BOUND_VARIABLE_25006))) (= (ll_33 BOUND_VARIABLE_25005 BOUND_VARIABLE_25006) (and (or ((ord_less_nat BOUND_VARIABLE_25006) BOUND_VARIABLE_25005) _let_1) (or ((ord_less_nat BOUND_VARIABLE_25005) BOUND_VARIABLE_25006) _let_1))))))) (let ((_let_321 (forall ((BOUND_VARIABLE_24987 (-> product_prod_nat_nat a)) (BOUND_VARIABLE_24988 nat) (BOUND_VARIABLE_24989 nat) (BOUND_VARIABLE_24990 nat)) (= (ll_32 BOUND_VARIABLE_24987 BOUND_VARIABLE_24988 BOUND_VARIABLE_24989 BOUND_VARIABLE_24990) (not (forall ((BOUND_VARIABLE_17552 list_P559422087at_nat)) (or (not ((((isPath_a BOUND_VARIABLE_24987) BOUND_VARIABLE_24988) BOUND_VARIABLE_17552) BOUND_VARIABLE_24989)) (not (= (size_s1990949619at_nat BOUND_VARIABLE_17552) BOUND_VARIABLE_24990))))))))) (let ((_let_322 (forall ((BOUND_VARIABLE_24971 nat) (BOUND_VARIABLE_24972 nat) (BOUND_VARIABLE_24973 nat)) (= (ll_31 BOUND_VARIABLE_24971 BOUND_VARIABLE_24972 BOUND_VARIABLE_24973) (not (forall ((BOUND_VARIABLE_17260 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_17260) BOUND_VARIABLE_24973)) (not ((((isPath_capacity c) BOUND_VARIABLE_24971) BOUND_VARIABLE_17260) BOUND_VARIABLE_24972))))))))) (let ((_let_323 (forall ((BOUND_VARIABLE_24955 nat) (BOUND_VARIABLE_24956 nat) (BOUND_VARIABLE_24957 nat)) (= (ll_30 BOUND_VARIABLE_24955 BOUND_VARIABLE_24956 BOUND_VARIABLE_24957) (not (forall ((BOUND_VARIABLE_17090 list_P559422087at_nat)) (or (not ((((isPath_a c2) BOUND_VARIABLE_24955) BOUND_VARIABLE_17090) BOUND_VARIABLE_24956)) (not (= (size_s1990949619at_nat BOUND_VARIABLE_17090) BOUND_VARIABLE_24957))))))))) (let ((_let_324 (forall ((BOUND_VARIABLE_24939 nat) (BOUND_VARIABLE_24940 nat) (BOUND_VARIABLE_24941 nat)) (= (ll_29 BOUND_VARIABLE_24939 BOUND_VARIABLE_24940 BOUND_VARIABLE_24941) (not (forall ((BOUND_VARIABLE_17138 list_P559422087at_nat)) (or (not ((((isPath_a c2) BOUND_VARIABLE_24939) BOUND_VARIABLE_17138) BOUND_VARIABLE_24940)) (not (= (size_s1990949619at_nat BOUND_VARIABLE_17138) BOUND_VARIABLE_24941))))))))) (let ((_let_325 (forall ((BOUND_VARIABLE_24923 nat) (BOUND_VARIABLE_24924 nat) (BOUND_VARIABLE_24925 nat)) (= (ll_28 BOUND_VARIABLE_24923 BOUND_VARIABLE_24924 BOUND_VARIABLE_24925) (not (forall ((BOUND_VARIABLE_16994 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_16994) BOUND_VARIABLE_24925)) (not ((((isPath_capacity c) BOUND_VARIABLE_24923) BOUND_VARIABLE_16994) BOUND_VARIABLE_24924))))))))) (let ((_let_326 (forall ((BOUND_VARIABLE_24907 nat) (BOUND_VARIABLE_24908 nat) (BOUND_VARIABLE_24909 nat)) (= (ll_27 BOUND_VARIABLE_24907 BOUND_VARIABLE_24908 BOUND_VARIABLE_24909) (not (forall ((BOUND_VARIABLE_17021 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_17021) BOUND_VARIABLE_24909)) (not ((((isPath_capacity c) BOUND_VARIABLE_24907) BOUND_VARIABLE_17021) BOUND_VARIABLE_24908))))))))) (let ((_let_327 (forall ((BOUND_VARIABLE_24891 nat) (BOUND_VARIABLE_24892 nat) (BOUND_VARIABLE_24893 nat)) (= (ll_26 BOUND_VARIABLE_24891 BOUND_VARIABLE_24892 BOUND_VARIABLE_24893) (not (forall ((BOUND_VARIABLE_16909 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_16909) BOUND_VARIABLE_24893)) (not ((((isPath_capacity c) BOUND_VARIABLE_24891) BOUND_VARIABLE_16909) BOUND_VARIABLE_24892))))))))) (let ((_let_328 (forall ((BOUND_VARIABLE_24875 nat) (BOUND_VARIABLE_24876 nat) (BOUND_VARIABLE_24877 nat)) (= (ll_25 BOUND_VARIABLE_24875 BOUND_VARIABLE_24876 BOUND_VARIABLE_24877) (not (forall ((BOUND_VARIABLE_16654 list_P559422087at_nat)) (or (not ((((isPath_a c2) BOUND_VARIABLE_24875) BOUND_VARIABLE_16654) BOUND_VARIABLE_24876)) (not (= (size_s1990949619at_nat BOUND_VARIABLE_16654) BOUND_VARIABLE_24877))))))))) (let ((_let_329 (forall ((BOUND_VARIABLE_24859 nat) (BOUND_VARIABLE_24860 nat) (BOUND_VARIABLE_24861 nat)) (= (ll_24 BOUND_VARIABLE_24859 BOUND_VARIABLE_24860 BOUND_VARIABLE_24861) (not (forall ((BOUND_VARIABLE_16672 list_P559422087at_nat)) (or (not ((((isPath_a c2) BOUND_VARIABLE_24859) BOUND_VARIABLE_16672) BOUND_VARIABLE_24860)) (not (= (size_s1990949619at_nat BOUND_VARIABLE_16672) BOUND_VARIABLE_24861))))))))) (let ((_let_330 (forall ((BOUND_VARIABLE_24841 (-> product_prod_nat_nat capacity)) (BOUND_VARIABLE_24842 nat) (BOUND_VARIABLE_24843 nat) (BOUND_VARIABLE_24844 nat)) (= (ll_23 BOUND_VARIABLE_24841 BOUND_VARIABLE_24842 BOUND_VARIABLE_24843 BOUND_VARIABLE_24844) (not (forall ((BOUND_VARIABLE_16573 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_16573) BOUND_VARIABLE_24844)) (not ((((isPath_capacity BOUND_VARIABLE_24841) BOUND_VARIABLE_24842) BOUND_VARIABLE_16573) BOUND_VARIABLE_24843))))))))) (let ((_let_331 (forall ((BOUND_VARIABLE_24825 nat) (BOUND_VARIABLE_24826 nat) (BOUND_VARIABLE_24827 nat)) (= (ll_22 BOUND_VARIABLE_24825 BOUND_VARIABLE_24826 BOUND_VARIABLE_24827) (not (forall ((BOUND_VARIABLE_16401 list_P559422087at_nat)) (or (not ((((isPath_a c2) BOUND_VARIABLE_24825) BOUND_VARIABLE_16401) BOUND_VARIABLE_24826)) (not (= (size_s1990949619at_nat BOUND_VARIABLE_16401) BOUND_VARIABLE_24827))))))))) (let ((_let_332 (forall ((BOUND_VARIABLE_24807 (-> product_prod_nat_nat capacity)) (BOUND_VARIABLE_24808 nat) (BOUND_VARIABLE_24809 nat) (BOUND_VARIABLE_24810 nat)) (= (ll_21 BOUND_VARIABLE_24807 BOUND_VARIABLE_24808 BOUND_VARIABLE_24809 BOUND_VARIABLE_24810) (not (forall ((BOUND_VARIABLE_15965 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_15965) BOUND_VARIABLE_24810)) (not ((((isPath_capacity BOUND_VARIABLE_24807) BOUND_VARIABLE_24808) BOUND_VARIABLE_15965) BOUND_VARIABLE_24809))))))))) (let ((_let_333 (forall ((BOUND_VARIABLE_24791 nat) (BOUND_VARIABLE_24792 nat) (BOUND_VARIABLE_24793 nat)) (= (ll_20 BOUND_VARIABLE_24791 BOUND_VARIABLE_24792 BOUND_VARIABLE_24793) (not (forall ((BOUND_VARIABLE_15764 list_P559422087at_nat)) (or (not ((((isPath_a c2) BOUND_VARIABLE_24791) BOUND_VARIABLE_15764) BOUND_VARIABLE_24792)) (not (= (size_s1990949619at_nat BOUND_VARIABLE_15764) BOUND_VARIABLE_24793))))))))) (let ((_let_334 (forall ((BOUND_VARIABLE_24775 nat) (BOUND_VARIABLE_24776 nat) (BOUND_VARIABLE_24777 nat)) (= (ll_19 BOUND_VARIABLE_24775 BOUND_VARIABLE_24776 BOUND_VARIABLE_24777) (not (forall ((BOUND_VARIABLE_15647 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_15647) BOUND_VARIABLE_24777)) (not ((((isPath_capacity c) BOUND_VARIABLE_24775) BOUND_VARIABLE_15647) BOUND_VARIABLE_24776))))))))) (let ((_let_335 (forall ((BOUND_VARIABLE_24759 nat) (BOUND_VARIABLE_24760 nat) (BOUND_VARIABLE_24761 nat)) (= (ll_18 BOUND_VARIABLE_24759 BOUND_VARIABLE_24760 BOUND_VARIABLE_24761) (not (forall ((BOUND_VARIABLE_15684 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_15684) BOUND_VARIABLE_24761)) (not ((((isPath_capacity c) BOUND_VARIABLE_24759) BOUND_VARIABLE_15684) BOUND_VARIABLE_24760))))))))) (let ((_let_336 (forall ((BOUND_VARIABLE_24749 nat)) (= (ll_17 BOUND_VARIABLE_24749) (not (forall ((BOUND_VARIABLE_15563 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_15563) BOUND_VARIABLE_24749)) (not ((((isPath_capacity c) ua) BOUND_VARIABLE_15563) t))))))))) (let ((_let_337 (forall ((BOUND_VARIABLE_24733 nat) (BOUND_VARIABLE_24734 nat) (BOUND_VARIABLE_24735 nat)) (= (ll_16 BOUND_VARIABLE_24733 BOUND_VARIABLE_24734 BOUND_VARIABLE_24735) (not (forall ((BOUND_VARIABLE_15512 list_P559422087at_nat)) (or (not ((((isPath_a c2) BOUND_VARIABLE_24733) BOUND_VARIABLE_15512) BOUND_VARIABLE_24734)) (not (= (size_s1990949619at_nat BOUND_VARIABLE_15512) BOUND_VARIABLE_24735))))))))) (let ((_let_338 (forall ((BOUND_VARIABLE_24726 nat) (BOUND_VARIABLE_24727 nat)) (= (ll_15 BOUND_VARIABLE_24726 BOUND_VARIABLE_24727) (= BOUND_VARIABLE_24726 BOUND_VARIABLE_24727))))) (let ((_let_339 (forall ((BOUND_VARIABLE_24712 nat) (BOUND_VARIABLE_24713 nat)) (let ((_let_1 (= BOUND_VARIABLE_24712 BOUND_VARIABLE_24713))) (= (ll_14 BOUND_VARIABLE_24712 BOUND_VARIABLE_24713) (and (or ((ord_less_nat BOUND_VARIABLE_24712) BOUND_VARIABLE_24713) _let_1) (or ((ord_less_nat BOUND_VARIABLE_24713) BOUND_VARIABLE_24712) _let_1))))))) (let ((_let_340 (forall ((BOUND_VARIABLE_24696 nat) (BOUND_VARIABLE_24697 nat) (BOUND_VARIABLE_24698 nat)) (= (ll_13 BOUND_VARIABLE_24696 BOUND_VARIABLE_24697 BOUND_VARIABLE_24698) (not (forall ((BOUND_VARIABLE_15231 list_P559422087at_nat)) (or (not ((((isPath_a c2) BOUND_VARIABLE_24696) BOUND_VARIABLE_15231) BOUND_VARIABLE_24697)) (not (= (size_s1990949619at_nat BOUND_VARIABLE_15231) BOUND_VARIABLE_24698))))))))) (let ((_let_341 (forall ((BOUND_VARIABLE_24680 nat) (BOUND_VARIABLE_24681 nat) (BOUND_VARIABLE_24682 nat)) (= (ll_12 BOUND_VARIABLE_24680 BOUND_VARIABLE_24681 BOUND_VARIABLE_24682) (not (forall ((BOUND_VARIABLE_15269 list_P559422087at_nat)) (or (not ((((isPath_a c2) BOUND_VARIABLE_24680) BOUND_VARIABLE_15269) BOUND_VARIABLE_24681)) (not (= (size_s1990949619at_nat BOUND_VARIABLE_15269) BOUND_VARIABLE_24682))))))))) (let ((_let_342 (forall ((BOUND_VARIABLE_24673 nat) (BOUND_VARIABLE_24674 nat)) (= (ll_11 BOUND_VARIABLE_24673 BOUND_VARIABLE_24674) (= BOUND_VARIABLE_24673 BOUND_VARIABLE_24674))))) (let ((_let_343 (forall ((BOUND_VARIABLE_24659 nat) (BOUND_VARIABLE_24660 nat)) (let ((_let_1 (= BOUND_VARIABLE_24659 BOUND_VARIABLE_24660))) (= (ll_10 BOUND_VARIABLE_24659 BOUND_VARIABLE_24660) (and (or ((ord_less_nat BOUND_VARIABLE_24660) BOUND_VARIABLE_24659) _let_1) (or ((ord_less_nat BOUND_VARIABLE_24659) BOUND_VARIABLE_24660) _let_1))))))) (let ((_let_344 (forall ((BOUND_VARIABLE_24651 nat) (BOUND_VARIABLE_24652 nat)) (= ((plus_plus_nat BOUND_VARIABLE_24652) BOUND_VARIABLE_24651) (ll_9 BOUND_VARIABLE_24651 BOUND_VARIABLE_24652))))) (let ((_let_345 (forall ((BOUND_VARIABLE_24633 (-> product_prod_nat_nat capacity)) (BOUND_VARIABLE_24634 nat) (BOUND_VARIABLE_24635 nat) (BOUND_VARIABLE_24636 nat)) (= (ll_8 BOUND_VARIABLE_24633 BOUND_VARIABLE_24634 BOUND_VARIABLE_24635 BOUND_VARIABLE_24636) (not (forall ((BOUND_VARIABLE_14986 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_14986) BOUND_VARIABLE_24636)) (not ((((isPath_capacity BOUND_VARIABLE_24633) BOUND_VARIABLE_24634) BOUND_VARIABLE_14986) BOUND_VARIABLE_24635))))))))) (let ((_let_346 (forall ((BOUND_VARIABLE_24615 (-> product_prod_nat_nat capacity)) (BOUND_VARIABLE_24616 nat) (BOUND_VARIABLE_24617 nat) (BOUND_VARIABLE_24618 nat)) (= (ll_7 BOUND_VARIABLE_24615 BOUND_VARIABLE_24616 BOUND_VARIABLE_24617 BOUND_VARIABLE_24618) (not (forall ((BOUND_VARIABLE_14748 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_14748) BOUND_VARIABLE_24618)) (not ((((isPath_capacity BOUND_VARIABLE_24615) BOUND_VARIABLE_24616) BOUND_VARIABLE_14748) BOUND_VARIABLE_24617))))))))) (let ((_let_347 (forall ((BOUND_VARIABLE_24597 (-> product_prod_nat_nat capacity)) (BOUND_VARIABLE_24598 nat) (BOUND_VARIABLE_24599 nat) (BOUND_VARIABLE_24600 nat)) (= (ll_6 BOUND_VARIABLE_24597 BOUND_VARIABLE_24598 BOUND_VARIABLE_24599 BOUND_VARIABLE_24600) (not (forall ((BOUND_VARIABLE_14778 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_14778) BOUND_VARIABLE_24600)) (not ((((isPath_capacity BOUND_VARIABLE_24597) BOUND_VARIABLE_24598) BOUND_VARIABLE_14778) BOUND_VARIABLE_24599))))))))) (let ((_let_348 (forall ((BOUND_VARIABLE_24579 (-> product_prod_nat_nat a)) (BOUND_VARIABLE_24580 nat) (BOUND_VARIABLE_24581 nat) (BOUND_VARIABLE_24582 nat)) (= (ll_5 BOUND_VARIABLE_24579 BOUND_VARIABLE_24580 BOUND_VARIABLE_24581 BOUND_VARIABLE_24582) (not (forall ((BOUND_VARIABLE_14423 list_P559422087at_nat)) (or (not ((((isPath_a BOUND_VARIABLE_24579) BOUND_VARIABLE_24580) BOUND_VARIABLE_14423) BOUND_VARIABLE_24581)) (not (= (size_s1990949619at_nat BOUND_VARIABLE_14423) BOUND_VARIABLE_24582))))))))) (let ((_let_349 (forall ((BOUND_VARIABLE_24561 (-> product_prod_nat_nat a)) (BOUND_VARIABLE_24562 nat) (BOUND_VARIABLE_24563 nat) (BOUND_VARIABLE_24564 nat)) (= (ll_4 BOUND_VARIABLE_24561 BOUND_VARIABLE_24562 BOUND_VARIABLE_24563 BOUND_VARIABLE_24564) (not (forall ((BOUND_VARIABLE_14461 list_P559422087at_nat)) (or (not ((((isPath_a BOUND_VARIABLE_24561) BOUND_VARIABLE_24562) BOUND_VARIABLE_14461) BOUND_VARIABLE_24563)) (not (= (size_s1990949619at_nat BOUND_VARIABLE_14461) BOUND_VARIABLE_24564))))))))) (let ((_let_350 (forall ((BOUND_VARIABLE_24543 (-> product_prod_nat_nat a)) (BOUND_VARIABLE_24544 nat) (BOUND_VARIABLE_24545 nat) (BOUND_VARIABLE_24546 nat)) (= (ll_3 BOUND_VARIABLE_24543 BOUND_VARIABLE_24544 BOUND_VARIABLE_24545 BOUND_VARIABLE_24546) (not (forall ((BOUND_VARIABLE_14124 list_P559422087at_nat)) (or (not ((((isPath_a BOUND_VARIABLE_24543) BOUND_VARIABLE_24544) BOUND_VARIABLE_14124) BOUND_VARIABLE_24545)) (not (= (size_s1990949619at_nat BOUND_VARIABLE_14124) BOUND_VARIABLE_24546))))))))) (let ((_let_351 (forall ((BOUND_VARIABLE_24527 nat) (BOUND_VARIABLE_24528 nat) (BOUND_VARIABLE_24529 nat)) (= (ll_2 BOUND_VARIABLE_24527 BOUND_VARIABLE_24528 BOUND_VARIABLE_24529) (not (forall ((BOUND_VARIABLE_13856 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_13856) BOUND_VARIABLE_24529)) (not ((((isPath_capacity c) BOUND_VARIABLE_24527) BOUND_VARIABLE_13856) BOUND_VARIABLE_24528))))))))) (let ((_let_352 (forall ((BOUND_VARIABLE_24511 nat) (BOUND_VARIABLE_24512 nat) (BOUND_VARIABLE_24513 nat)) (= (ll_1 BOUND_VARIABLE_24511 BOUND_VARIABLE_24512 BOUND_VARIABLE_24513) (not (forall ((BOUND_VARIABLE_13893 list_P559422087at_nat)) (or (not (= (size_s1990949619at_nat BOUND_VARIABLE_13893) BOUND_VARIABLE_24513)) (not ((((isPath_capacity c) BOUND_VARIABLE_24511) BOUND_VARIABLE_13893) BOUND_VARIABLE_24512))))))))) (let ((_let_353 (and (forall ((BOUND_VARIABLE_13641 nat) (BOUND_VARIABLE_13643 nat)) (or (not ((ord_less_nat BOUND_VARIABLE_13641) BOUND_VARIABLE_13643)) (not (forall ((C3 nat)) (not (= BOUND_VARIABLE_13643 ((plus_plus_nat BOUND_VARIABLE_13641) C3))))))) (forall ((BOUND_VARIABLE_13659 nat)) (not (forall ((C3 nat)) (not (= BOUND_VARIABLE_13659 ((plus_plus_nat BOUND_VARIABLE_13659) C3)))))) _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 ((_let_354 (_let_107))) (let ((_let_355 (not _let_37))) (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 |:args| (_let_37)) (CONG (REFL |:args| (_let_355)) (REFL |:args| (_let_34)) (MACRO_SR_PRED_INTRO |:args| ((= (not _let_36) _let_35))) |:args| _let_86)) |:args| ((or _let_34 _let_35 _let_355))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME |:args| _let_354) |:args| (_let_33)) |:args| _let_354))) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME |:args| (_let_1)) (TRANS (MACRO_SR_EQ_INTRO |:args| (_let_1 7 12)) (MACRO_SR_EQ_INTRO _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 |:args| ((forall ((A nat) (B nat)) (or (not ((ord_less_eq_nat A) B)) (not (forall ((C3 nat)) (not (= B ((plus_plus_nat A) C3))))))) 7 12)))) (PREPROCESS |:args| ((and _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)))) |:args| (_let_353)) (PREPROCESS |:args| ((= _let_353 (and _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_107 _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))))) (PREPROCESS |:args| ((and _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)))) |:args| ((and _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_107 _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))) |:args| (93)) |:args| (_let_37 false _let_107)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (THEORY_LEMMA |:args| ((= _let_35 _let_100) 12))) |:args| ((or _let_100 _let_36))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS |:args| (_let_104)) |:args| ((or _let_103 _let_101 (not _let_104)))) (EQ_RESOLVE (ASSUME |:args| (_let_6)) (PREPROCESS |:args| ((= _let_6 _let_102)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_106 |:args| (k_139 ua p2_a t)) |:args| (_let_105)))) _let_106 |:args| (_let_104 false _let_105)) |:args| (_let_101 false _let_102 false _let_104)) |:args| (_let_36 true _let_100)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS |:args| (_let_42)) |:args| ((or _let_40 _let_39 _let_41 (not _let_42)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS |:args| (_let_96)) |:args| ((or _let_95 _let_57 _let_63 (not _let_96)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS |:args| (_let_95 0)) |:args| ((or _let_65 _let_99))) _let_94 |:args| (_let_99 false _let_64)) _let_92 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_98 |:args| _let_69) |:args| (_let_97))) _let_98 |:args| (_let_96 false _let_97)) |:args| (_let_57 true _let_95 true _let_63 false _let_96)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS |:args| (_let_58 1)) |:args| ((or _let_56 (not _let_58)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS |:args| (_let_66)) |:args| ((or _let_65 _let_63 _let_58 (not _let_66)))) _let_94 _let_92 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_68 |:args| _let_69) |:args| (_let_67)))) _let_68 |:args| (_let_66 false _let_67)) |:args| (_let_58 false _let_64 true _let_63 false _let_66)) |:args| (_let_56 false _let_58)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_55 |:args| (k_160 _let_33)) |:args| (_let_43))) _let_55 |:args| (_let_42 false _let_43)) |:args| (_let_41 true _let_40 true _let_39 false _let_42)) |:args| (false false _let_37 true _let_35 true _let_34)) |:args| ((not false) (forall ((U nat) (P2 list_P559422087at_nat) (V nat)) (=> ((((isPath_capacity c) U) P2) V) ((((dist_capacity c) U) (size_s1990949619at_nat P2)) V))) (= ord_less_eq_nat (lambda ((M2 nat) (N2 nat)) (exists ((K2 nat)) (= N2 ((plus_plus_nat M2) K2))))) (forall ((A nat) (F (-> nat nat)) (B nat) (C nat)) (=> (= A (F B)) (=> ((ord_less_eq_nat B) C) (=> (forall ((X nat) (Y nat)) (=> ((ord_less_eq_nat X) Y) ((ord_less_eq_nat (F X)) (F Y)))) ((ord_less_eq_nat A) (F C)))))) (= connected_a connected_a) (((_let_3 u) p2) t) (forall ((I nat) (J nat) (K nat)) (=> ((ord_less_nat I) J) ((ord_less_nat ((plus_plus_nat I) K)) ((plus_plus_nat J) K)))) (forall ((B nat) (A nat) (C nat)) (let ((_let_1 (ord_less_nat C))) (=> ((ord_less_nat B) A) (=> (_let_1 B) (_let_1 A))))) (forall ((P5 (-> nat Bool)) (K nat) (B nat)) (=> (P5 K) (=> (forall ((Y nat)) (=> (P5 Y) ((ord_less_eq_nat Y) B))) (exists ((X nat)) (and (forall ((Y2 nat)) (=> (P5 Y2) ((ord_less_eq_nat Y2) X))) (P5 X)))))) (forall ((X3 nat) (Y3 nat) (Z2 nat)) (let ((_let_1 (ord_less_eq_nat X3))) (let ((_let_2 (_let_1 Y3))) (let ((_let_3 (ord_less_eq_nat Z2))) (let ((_let_4 (_let_3 X3))) (let ((_let_5 (ord_less_eq_nat Y3))) (let ((_let_6 (_let_5 Z2))) (let ((_let_7 (_let_5 X3))) (let ((_let_8 (_let_3 Y3))) (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 ((C (-> product_prod_nat_nat capacity)) (V nat)) (((connected_capacity C) V) V)) (forall ((X3 nat) (Y3 nat)) (=> ((ord_less_nat X3) Y3) (not (= Y3 X3)))) (forall ((A nat)) (not ((ord_less_nat A) A))) (forall ((P5 (-> nat nat Bool)) (A nat) (B nat)) (=> (forall ((A4 nat) (B4 nat)) (=> ((ord_less_nat A4) B4) ((P5 A4) B4))) (=> (forall ((A4 nat)) ((P5 A4) A4)) (=> (forall ((A4 nat) (B4 nat)) (=> ((P5 B4) A4) ((P5 A4) B4))) ((P5 A) B))))) (forall ((A3 set_nat)) (= (collect_nat (lambda ((X2 nat)) ((member_nat X2) A3))) A3)) (forall ((V nat)) (((connected_a c2) V) V)) (forall ((V nat) (D nat) (V3 nat)) (=> ((((dist_a c2) V) D) V3) (((connected_a c2) V) V3))) (forall ((A nat) (C nat) (B nat)) (= ((ord_less_eq_nat ((plus_plus_nat A) C)) ((plus_plus_nat B) C)) ((ord_less_eq_nat A) B))) (forall ((C (-> product_prod_nat_nat a)) (V nat) (D nat) (V3 nat)) (=> ((((dist_a C) V) D) V3) ((ord_less_eq_nat (((min_dist_a C) V) V3)) D))) ((((isShor1936442771pacity c) s) p) t) (forall ((C (-> product_prod_nat_nat a)) (V nat) (D nat) (V3 nat)) (=> ((((dist_a C) V) D) V3) (((connected_a C) V) V3))) (forall ((A nat) (B nat) (C nat)) (let ((_let_1 (plus_plus_nat C))) (=> ((ord_less_eq_nat A) B) ((ord_less_eq_nat (_let_1 A)) (_let_1 B))))) (forall ((C (-> product_prod_nat_nat a)) (V nat) (V3 nat)) (=> (((connected_a C) V) V3) ((((dist_a C) V) (((min_dist_a C) V) V3)) V3))) (forall ((Y3 nat) (X3 nat)) (=> (not ((ord_less_nat Y3) X3)) (= (not ((ord_less_nat X3) Y3)) (= X3 Y3)))) (forall ((V nat) (V3 nat)) (= (((connected_a c2) V) V3) (exists ((D4 nat)) ((((dist_a c2) V) D4) V3)))) (forall ((A nat) (B nat) (C nat)) (let ((_let_1 (plus_plus_nat A))) (= ((plus_plus_nat (_let_1 B)) C) (_let_1 ((plus_plus_nat B) C))))) _let_32 (= isShor1936442771pacity isShor1936442771pacity) (forall ((I nat) (J nat) (M nat)) (let ((_let_1 (ord_less_eq_nat I))) (=> (_let_1 J) (_let_1 ((plus_plus_nat J) M))))) (forall ((C (-> product_prod_nat_nat capacity)) (S nat) (P2 list_P559422087at_nat) (T nat)) (=> ((((isShor1936442771pacity C) S) P2) T) ((((isSimp1359852763pacity C) S) P2) T))) (forall ((C (-> product_prod_nat_nat a)) (Src nat) (V nat) (D3 nat)) (=> (((connected_a C) Src) V) (=> ((ord_less_eq_nat D3) (((min_dist_a C) Src) V)) (exists ((V2 nat)) (and (((connected_a C) Src) V2) (= (((min_dist_a C) Src) V2) D3)))))) (forall ((V nat) (D nat) (V3 nat)) (=> ((((dist_a c2) V) D) V3) (=> (forall ((D5 nat)) (=> ((((dist_a c2) V) D5) V3) ((ord_less_eq_nat D) D5))) (= (((min_dist_a c2) V) V3) D)))) (forall ((A nat) (B nat) (F (-> nat nat)) (C nat)) (=> ((ord_less_nat A) B) (=> ((ord_less_nat (F B)) C) (=> (forall ((X nat) (Y nat)) (=> ((ord_less_nat X) Y) ((ord_less_nat (F X)) (F Y)))) ((ord_less_nat (F A)) C))))) (= isShortestPath_a (lambda ((C2 (-> product_prod_nat_nat a)) (U2 nat) (P list_P559422087at_nat) (V4 nat)) (and (forall ((P4 list_P559422087at_nat)) (=> ((((isPath_a C2) U2) P4) V4) ((ord_less_eq_nat (size_s1990949619at_nat P)) (size_s1990949619at_nat P4)))) ((((isPath_a C2) U2) P) V4)))) (forall ((C (-> product_prod_nat_nat a)) (S nat) (P2 list_P559422087at_nat) (T nat)) (=> ((((isPath_a C) S) P2) T) (exists ((P6 list_P559422087at_nat)) ((((isSimplePath_a C) S) P6) T)))) (forall ((M nat) (K nat) (N nat)) (=> ((ord_less_eq_nat ((plus_plus_nat M) K)) N) ((ord_less_eq_nat K) N))) (forall ((C (-> product_prod_nat_nat capacity)) (U nat) (D1 nat) (W nat) (D2 nat) (V nat)) (let ((_let_1 ((min_dist_capacity C) U))) (let ((_let_2 (dist_capacity C))) (=> (((_let_2 U) D1) W) (=> (((_let_2 W) D2) V) (=> (= (_let_1 V) ((plus_plus_nat D1) D2)) (= (_let_1 W) D1))))))) (forall ((C (-> product_prod_nat_nat capacity)) (U nat) (D1 nat) (W nat) (D2 nat) (V nat)) (let ((_let_1 (min_dist_capacity C))) (let ((_let_2 (dist_capacity C))) (=> (((_let_2 U) D1) W) (=> (((_let_2 W) D2) V) (=> (= ((_let_1 U) V) ((plus_plus_nat D1) D2)) (= ((_let_1 W) V) D2))))))) (forall ((Y3 nat) (X3 nat)) (=> ((ord_less_eq_nat Y3) X3) (= ((ord_less_eq_nat X3) Y3) (= X3 Y3)))) (forall ((C (-> product_prod_nat_nat a)) (U nat) (P2 list_P559422087at_nat) (V nat)) (=> ((((isShortestPath_a C) U) P2) V) ((((isPath_a C) U) P2) V))) _let_31 (forall ((X3 nat)) (not ((ord_less_nat X3) X3))) (forall ((N nat) (M nat)) ((ord_less_eq_nat N) ((plus_plus_nat M) N))) (forall ((X3 nat) (Y3 nat)) (= (not (= X3 Y3)) (or ((ord_less_nat Y3) X3) ((ord_less_nat X3) Y3)))) (forall ((M nat) (N nat)) (= (not (= M N)) (or ((ord_less_nat M) N) ((ord_less_nat N) M)))) (forall ((U nat) (D1 nat) (W nat) (D2 nat) (V nat)) (let ((_let_1 (min_dist_capacity c))) (let ((_let_2 (dist_capacity c))) (=> (((_let_2 U) D1) W) (=> (((_let_2 W) D2) V) (=> (= ((_let_1 U) V) ((plus_plus_nat D1) D2)) (= ((_let_1 W) V) D2))))))) (forall ((N nat)) ((ord_less_eq_nat N) N)) (forall ((Src nat) (V nat) (D3 nat)) (=> (((connected_a c2) Src) V) (=> ((ord_less_eq_nat D3) (((min_dist_a c2) Src) V)) (exists ((V2 nat)) (and (((connected_a c2) Src) V2) (= (((min_dist_a c2) Src) V2) D3)))))) (forall ((A nat) (B nat) (F (-> nat nat)) (C nat)) (=> ((ord_less_eq_nat A) B) (=> ((ord_less_eq_nat (F B)) C) (=> (forall ((X nat) (Y nat)) (=> ((ord_less_eq_nat X) Y) ((ord_less_eq_nat (F X)) (F Y)))) ((ord_less_eq_nat (F A)) C))))) (= min_dist_capacity min_dist_capacity) (forall ((I nat) (J nat) (M nat)) (let ((_let_1 (ord_less_eq_nat I))) (=> (_let_1 J) (_let_1 ((plus_plus_nat M) J))))) (forall ((A nat) (B nat) (C nat) (D nat)) (=> ((ord_less_eq_nat A) B) (=> ((ord_less_nat C) D) ((ord_less_nat ((plus_plus_nat A) C)) ((plus_plus_nat B) D))))) (forall ((A nat) (B nat)) (=> ((ord_less_nat A) B) (not (= A B)))) (forall ((M nat) (N nat)) (=> ((ord_less_eq_nat M) N) (=> (not (= M N)) ((ord_less_nat M) N)))) (forall ((S nat) (T nat)) (=> ((ord_less_nat S) T) (not (= S T)))) (forall ((I nat) (J nat) (K nat) (L nat)) (=> (and (= I J) ((ord_less_nat K) L)) ((ord_less_nat ((plus_plus_nat I) K)) ((plus_plus_nat J) L)))) (= connected_capacity (lambda ((C2 (-> product_prod_nat_nat capacity)) (U2 nat) (V4 nat)) (exists ((P list_P559422087at_nat)) ((((isPath_capacity C2) U2) P) V4)))) (forall ((C nat) (A nat) (B nat)) (let ((_let_1 (plus_plus_nat C))) (=> ((ord_less_nat (_let_1 A)) (_let_1 B)) ((ord_less_nat A) B)))) (= isShortestPath_a (lambda ((C2 (-> product_prod_nat_nat a)) (U2 nat) (P list_P559422087at_nat) (V4 nat)) (and (= (size_s1990949619at_nat P) (((min_dist_a C2) U2) V4)) ((((isSimplePath_a C2) U2) P) V4)))) (forall ((X3 nat) (Y3 nat)) (= (not ((ord_less_nat X3) Y3)) (or ((ord_less_nat Y3) X3) (= X3 Y3)))) (forall ((C (-> product_prod_nat_nat capacity)) (Src nat) (V nat) (D nat) (D3 nat)) (=> (((connected_capacity C) Src) V) (=> (= (((min_dist_capacity C) Src) V) D) (=> ((ord_less_nat D3) D) (exists ((V2 nat)) (and (= (((min_dist_capacity C) Src) V2) D3) (((connected_capacity C) Src) V2))))))) (forall ((X3 nat)) (exists ((X_1 nat)) ((ord_less_nat X3) X_1))) (forall ((C (-> product_prod_nat_nat a)) (Src nat) (V nat) (D nat) (D3 nat)) (=> (((connected_a C) Src) V) (=> (= (((min_dist_a C) Src) V) D) (=> ((ord_less_nat D3) D) (exists ((V2 nat)) (and (((connected_a C) Src) V2) (= (((min_dist_a C) Src) V2) D3))))))) (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)))) (= (lambda ((P7 (-> nat Bool))) (exists ((X4 nat)) (P7 X4))) (lambda ((P8 (-> nat Bool))) (exists ((N2 nat)) (and (forall ((M2 nat)) (=> ((ord_less_nat M2) N2) (not (P8 M2)))) (P8 N2))))) (forall ((C (-> product_prod_nat_nat a)) (V nat)) (((connected_a C) V) V)) (forall ((N nat)) (not ((ord_less_nat N) N))) (forall ((A nat) (F (-> nat nat)) (B nat) (C nat)) (=> (= A (F B)) (=> ((ord_less_nat B) C) (=> (forall ((X nat) (Y nat)) (=> ((ord_less_nat X) Y) ((ord_less_nat (F X)) (F Y)))) ((ord_less_nat A) (F C)))))) (forall ((B nat) (A nat)) (=> ((ord_less_nat B) A) (not ((ord_less_nat A) B)))) (forall ((V nat) (V3 nat)) (= (((min_dist_capacity c) V) V3) (ord_Least_nat (lambda ((D4 nat)) ((((dist_capacity c) V) D4) V3))))) (forall ((A nat) (B nat)) (=> ((ord_less_eq_nat A) B) (=> ((ord_less_eq_nat B) A) (= A B)))) (forall ((X3 nat) (Y3 nat)) (=> ((ord_less_eq_nat X3) Y3) (=> ((ord_less_eq_nat Y3) X3) (= X3 Y3)))) (forall ((M nat) (N nat)) (=> ((ord_less_nat M) N) ((ord_less_eq_nat M) N))) (forall ((M nat) (N nat)) (=> (= M N) ((ord_less_eq_nat M) N))) (forall ((V nat) (D nat) (V3 nat)) (=> ((((dist_capacity c) V) D) V3) (=> (forall ((D5 nat)) (=> ((((dist_capacity c) V) D5) V3) ((ord_less_eq_nat D) D5))) (= (((min_dist_capacity c) V) V3) D)))) ((_let_17 p1) v) _let_30 (forall ((A nat) (C nat) (B nat)) (=> ((ord_less_eq_nat ((plus_plus_nat A) C)) ((plus_plus_nat B) C)) ((ord_less_eq_nat A) B))) (forall ((I nat) (J nat) (K nat) (L nat)) (=> (and ((ord_less_eq_nat K) L) ((ord_less_eq_nat I) J)) ((ord_less_eq_nat ((plus_plus_nat I) K)) ((plus_plus_nat J) L)))) _let_29 (((_let_3 ua) p2_a) t) (forall ((U nat) (P2 list_P559422087at_nat) (V nat)) (= ((((isShortestPath_a c2) U) P2) V) (and (= (size_s1990949619at_nat P2) (((min_dist_a c2) U) V)) ((((isPath_a c2) U) P2) V)))) (forall ((I nat) (J nat) (K nat) (L nat)) (=> (and (= I J) ((ord_less_eq_nat K) L)) ((ord_less_eq_nat ((plus_plus_nat I) K)) ((plus_plus_nat J) L)))) _let_28 (forall ((A3 nat) (K nat) (A nat) (B nat)) (let ((_let_1 (plus_plus_nat K))) (=> (= A3 (_let_1 A)) (= ((plus_plus_nat A3) B) (_let_1 ((plus_plus_nat A) B)))))) (forall ((X3 nat) (Y3 nat)) (or ((ord_less_nat X3) Y3) ((ord_less_nat Y3) X3) (= X3 Y3))) (forall ((U nat) (D1 nat) (W nat) (D2 nat) (V nat)) (let ((_let_1 ((min_dist_capacity c) U))) (let ((_let_2 (dist_capacity c))) (=> (((_let_2 U) D1) W) (=> (((_let_2 W) D2) V) (=> (= (_let_1 V) ((plus_plus_nat D1) D2)) (= (_let_1 W) D1))))))) (forall ((B nat) (A nat) (C nat)) (let ((_let_1 (ord_less_eq_nat C))) (=> ((ord_less_eq_nat B) A) (=> (_let_1 B) (_let_1 A))))) (forall ((A nat) (B nat) (C nat)) (let ((_let_1 (ord_less_eq_nat A))) (=> (_let_1 B) (=> (= B C) (_let_1 C))))) (forall ((V nat) (D nat) (V3 nat)) (=> ((((dist_a c2) V) D) V3) ((ord_less_eq_nat (((min_dist_a c2) V) V3)) D))) (forall ((I nat) (J nat) (M nat)) (let ((_let_1 (ord_less_nat I))) (=> (_let_1 J) (_let_1 ((plus_plus_nat M) J))))) (forall ((A nat) (F (-> nat nat)) (B nat) (C nat)) (let ((_let_1 (ord_less_eq_nat A))) (=> (_let_1 (F B)) (=> ((ord_less_eq_nat B) C) (=> (forall ((X nat) (Y nat)) (=> ((ord_less_eq_nat X) Y) ((ord_less_eq_nat (F X)) (F Y)))) (_let_1 (F C))))))) (forall ((C nat) (A nat) (B nat)) (let ((_let_1 (plus_plus_nat C))) (= ((ord_less_nat (_let_1 A)) (_let_1 B)) ((ord_less_nat A) B)))) (forall ((V nat) (D nat) (V3 nat)) (= ((((dist_a c2) V) D) V3) (exists ((P list_P559422087at_nat)) (and ((((isPath_a c2) V) P) V3) (= (size_s1990949619at_nat P) D))))) (((connected_capacity c) s) ua) (forall ((X3 nat) (Y3 nat)) (=> ((ord_less_nat X3) Y3) (not ((ord_less_nat Y3) X3)))) (forall ((U nat)) (= ((reacha1693770334pacity c) U) (collect_nat ((connected_capacity c) U)))) _let_26 (forall ((P5 (-> nat Bool)) (Q (-> nat Bool))) (=> (forall ((X nat)) (= (P5 X) (Q X))) (= (collect_nat P5) (collect_nat Q)))) (forall ((P5 (-> nat Bool))) (=> (exists ((X_12 nat)) (P5 X_12)) (P5 (ord_Least_nat P5)))) (forall ((C nat) (A nat) (B nat)) (let ((_let_1 (plus_plus_nat C))) (= ((ord_less_eq_nat (_let_1 A)) (_let_1 B)) ((ord_less_eq_nat A) B)))) (forall ((X3 list_P559422087at_nat) (Y3 list_P559422087at_nat)) (=> (not (= (size_s1990949619at_nat X3) (size_s1990949619at_nat Y3))) (not (= X3 Y3)))) (forall ((C (-> product_prod_nat_nat capacity)) (U nat) (D1 nat) (W nat) (D2 nat) (V nat)) (let ((_let_1 (dist_capacity C))) (let ((_let_2 (_let_1 U))) (=> ((_let_2 D1) W) (=> (((_let_1 W) D2) V) ((_let_2 ((plus_plus_nat D1) D2)) V)))))) (forall ((A nat)) ((ord_less_eq_nat A) A)) (forall ((S nat) (P2 list_P559422087at_nat) (T nat)) (=> ((((isShor1936442771pacity c) S) P2) T) ((((isSimp1359852763pacity c) S) P2) T))) (forall ((K nat) (L nat) (M nat) (N nat)) (=> ((ord_less_nat K) L) (=> (= ((plus_plus_nat M) L) ((plus_plus_nat K) N)) ((ord_less_nat M) N)))) (= isShor1936442771pacity (lambda ((C2 (-> product_prod_nat_nat capacity)) (U2 nat) (P list_P559422087at_nat) (V4 nat)) (and ((((isSimp1359852763pacity C2) U2) P) V4) (= (size_s1990949619at_nat P) (((min_dist_capacity C2) U2) V4))))) (forall ((B nat) (A nat)) (=> ((ord_less_eq_nat B) A) (=> ((ord_less_eq_nat A) B) (= A B)))) (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 ((A nat) (B nat)) (=> (not (= A B)) (=> ((ord_less_eq_nat A) B) ((ord_less_nat A) B)))) (forall ((F (-> nat nat)) (I nat) (J nat)) (=> (forall ((I2 nat) (J2 nat)) (=> ((ord_less_nat I2) J2) ((ord_less_nat (F I2)) (F J2)))) (=> ((ord_less_eq_nat I) J) ((ord_less_eq_nat (F I)) (F J))))) (forall ((U nat) (V nat)) (=> (((connected_capacity c) U) V) (not (forall ((P3 list_P559422087at_nat)) (not ((((isShor1936442771pacity c) U) P3) V)))))) (forall ((P5 (-> nat Bool)) (A nat)) (=> (forall ((X nat)) (=> (forall ((Y2 nat)) (=> ((ord_less_nat Y2) X) (P5 Y2))) (P5 X))) (P5 A))) (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 ((C (-> product_prod_nat_nat capacity)) (U nat) (V nat)) (=> (((connected_capacity C) U) V) (not (forall ((P3 list_P559422087at_nat)) (not ((((isShor1936442771pacity C) U) P3) V)))))) (forall ((P5 (-> nat Bool)) (Q (-> nat Bool))) (=> (exists ((X_12 nat)) (P5 X_12)) (=> (forall ((X nat)) (=> (P5 X) (Q X))) (Q (ord_Least_nat P5))))) (forall ((M nat) (N nat)) (=> (or (= M N) ((ord_less_nat M) N)) ((ord_less_eq_nat M) N))) (forall ((B3 nat) (K nat) (B nat) (A nat)) (let ((_let_1 (plus_plus_nat A))) (let ((_let_2 (plus_plus_nat K))) (=> (= B3 (_let_2 B)) (= (_let_1 B3) (_let_2 (_let_1 B))))))) _let_25 (= ord_less_eq_nat (lambda ((B2 nat) (A2 nat)) (or ((ord_less_nat B2) A2) (= A2 B2)))) (forall ((P5 (-> nat Bool)) (N nat)) (=> (forall ((N3 nat)) (=> (not (P5 N3)) (exists ((M3 nat)) (and (not (P5 M3)) ((ord_less_nat M3) N3))))) (P5 N))) (= ord_less_nat (lambda ((B2 nat) (A2 nat)) (and ((ord_less_eq_nat B2) A2) (not (= A2 B2))))) (forall ((A nat) (B nat) (C nat)) (let ((_let_1 (ord_less_nat A))) (=> (_let_1 B) (=> (= B C) (_let_1 C))))) (forall ((Src nat) (V nat) (D3 nat)) (=> (((connected_capacity c) Src) V) (=> ((ord_less_eq_nat D3) (((min_dist_capacity c) Src) V)) (exists ((V2 nat)) (and (((connected_capacity c) Src) V2) (= (((min_dist_capacity c) Src) V2) D3)))))) (forall ((C (-> product_prod_nat_nat a)) (U nat) (V nat)) (=> (((connected_a C) U) V) (not (forall ((P3 list_P559422087at_nat)) (not ((((isShortestPath_a C) U) P3) V)))))) (forall ((A nat) (C nat) (B nat)) (=> ((ord_less_nat ((plus_plus_nat A) C)) ((plus_plus_nat B) C)) ((ord_less_nat A) B))) (forall ((I nat) (J nat) (K nat) (L nat)) (=> (and ((ord_less_nat I) J) ((ord_less_nat K) L)) ((ord_less_nat ((plus_plus_nat I) K)) ((plus_plus_nat J) L)))) (= reacha1693770334pacity reacha1693770334pacity) _let_24 (forall ((S nat) (P2 list_P559422087at_nat) (T nat)) (=> ((((isShortestPath_a c2) S) P2) T) ((((isSimplePath_a c2) S) P2) T))) (forall ((I nat) (J nat) (K nat)) (=> ((ord_less_nat ((plus_plus_nat I) J)) K) ((ord_less_nat I) K))) (forall ((U nat) (P2 list_P559422087at_nat) (V nat)) (=> ((((isShor1936442771pacity c) U) P2) V) ((((isPath_capacity c) U) P2) V))) (forall ((X3 nat) (Y3 nat)) (=> (not ((ord_less_nat X3) Y3)) (=> (not (= X3 Y3)) ((ord_less_nat Y3) X3)))) (forall ((A nat) (B nat) (C nat)) (let ((_let_1 (plus_plus_nat C))) (=> ((ord_less_nat A) B) ((ord_less_nat (_let_1 A)) (_let_1 B))))) (forall ((J nat) (I nat)) (not ((ord_less_nat ((plus_plus_nat J) I)) I))) _let_23 (forall ((X3 nat) (Y3 nat)) (=> ((ord_less_nat X3) Y3) (not ((ord_less_nat Y3) X3)))) (forall ((B nat) (A nat) (C nat)) (let ((_let_1 (plus_plus_nat B))) (let ((_let_2 (plus_plus_nat A))) (= (_let_1 (_let_2 C)) (_let_2 (_let_1 C)))))) (forall ((X3 nat) (Y3 nat)) (=> ((ord_less_nat X3) Y3) (not ((ord_less_nat Y3) X3)))) (forall ((S nat) (P2 list_P559422087at_nat) (T nat)) (=> ((((isPath_a c2) S) P2) T) (exists ((P6 list_P559422087at_nat)) ((((isSimplePath_a c2) S) P6) T)))) (forall ((A nat) (B nat) (C nat) (D nat)) (=> ((ord_less_nat A) B) (=> ((ord_less_eq_nat C) D) ((ord_less_nat ((plus_plus_nat A) C)) ((plus_plus_nat B) D))))) (forall ((C (-> product_prod_nat_nat capacity)) (V nat) (D nat) (V3 nat)) (=> ((((dist_capacity C) V) D) V3) (((connected_capacity C) V) V3))) (forall ((U nat) (P2 list_P559422087at_nat) (V nat)) (= ((((isShortestPath_a c2) U) P2) V) (and ((((isSimplePath_a c2) U) P2) V) (= (size_s1990949619at_nat P2) (((min_dist_a c2) U) V))))) (forall ((B nat) (A nat)) (=> ((ord_less_nat B) A) ((ord_less_eq_nat B) A))) (forall ((X3 nat) (Y3 nat)) (=> (not (= X3 Y3)) (=> (not ((ord_less_nat X3) Y3)) ((ord_less_nat Y3) X3)))) (forall ((U nat) (D1 nat) (W nat) (D2 nat) (V nat)) (let ((_let_1 (dist_capacity c))) (let ((_let_2 (_let_1 U))) (=> ((_let_2 D1) W) (=> (((_let_1 W) D2) V) ((_let_2 ((plus_plus_nat D1) D2)) V)))))) (= (lambda ((Y4 nat) (Z nat)) (= Y4 Z)) (lambda ((X2 nat) (Y5 nat)) (and ((ord_less_eq_nat Y5) X2) ((ord_less_eq_nat X2) Y5)))) (forall ((C nat) (A nat) (B nat)) (let ((_let_1 (plus_plus_nat C))) (=> ((ord_less_eq_nat (_let_1 A)) (_let_1 B)) ((ord_less_eq_nat A) B)))) (= isShortestPath_a isShortestPath_a) (forall ((C (-> product_prod_nat_nat a)) (V nat) (D nat) (V3 nat)) (=> ((((dist_a C) V) D) V3) (=> (forall ((D5 nat)) (=> ((((dist_a C) V) D5) V3) ((ord_less_eq_nat D) D5))) (= (((min_dist_a C) V) V3) D)))) (forall ((A nat) (B nat)) (=> ((ord_less_nat A) B) (not ((ord_less_nat B) A)))) (forall ((U nat) (V nat)) (= (((connected_a c2) U) V) (exists ((P list_P559422087at_nat)) ((((isPath_a c2) U) P) V)))) (forall ((A nat) (B nat) (C nat) (D nat)) (=> ((ord_less_eq_nat A) B) (=> ((ord_less_eq_nat C) D) ((ord_less_eq_nat ((plus_plus_nat A) C)) ((plus_plus_nat B) D))))) (forall ((C (-> product_prod_nat_nat a)) (V nat) (V3 nat) (Q (-> nat Bool))) (=> (((connected_a C) V) V3) (=> (forall ((D6 nat)) (=> ((((dist_a C) V) D6) V3) (=> (forall ((D7 nat)) (=> ((((dist_a C) V) D7) V3) ((ord_less_eq_nat D6) D7))) (Q D6)))) (Q (((min_dist_a C) V) V3))))) (forall ((X3 nat) (Y3 nat)) (=> (not (= X3 Y3)) (=> (not ((ord_less_nat X3) Y3)) ((ord_less_nat Y3) X3)))) (forall ((P5 (-> nat Bool)) (N nat)) (=> (forall ((N3 nat)) (=> (forall ((M3 nat)) (=> ((ord_less_nat M3) N3) (P5 M3))) (P5 N3))) (P5 N))) (= connected_a (lambda ((C2 (-> product_prod_nat_nat a)) (V4 nat) (V5 nat)) (exists ((D4 nat)) ((((dist_a C2) V4) D4) V5)))) (= connected_capacity connected_capacity) (forall ((I nat) (J nat) (K nat) (L nat)) (=> (and ((ord_less_nat I) J) (= K L)) ((ord_less_nat ((plus_plus_nat I) K)) ((plus_plus_nat J) L)))) (forall ((V nat) (V3 nat)) (= (((min_dist_a c2) V) V3) (ord_Least_nat (lambda ((D4 nat)) ((((dist_a c2) V) D4) V3))))) (forall ((X3 nat) (Y3 nat)) (=> ((ord_less_nat X3) Y3) (not (= X3 Y3)))) (forall ((C (-> product_prod_nat_nat a)) (U nat) (P2 list_P559422087at_nat) (V nat)) (=> ((((isPath_a C) U) P2) V) ((((dist_a C) U) (size_s1990949619at_nat P2)) V))) _let_22 (forall ((Src nat) (V nat) (D nat) (D3 nat)) (=> (((connected_capacity c) Src) V) (=> (= (((min_dist_capacity c) Src) V) D) (=> ((ord_less_nat D3) D) (exists ((V2 nat)) (and (((connected_capacity c) Src) V2) (= (((min_dist_capacity c) Src) V2) D3))))))) (forall ((V nat) (V3 nat) (Q (-> nat Bool))) (=> (((connected_capacity c) V) V3) (=> (forall ((D6 nat)) (=> ((((dist_capacity c) V) D6) V3) (=> (forall ((D7 nat)) (=> ((((dist_capacity c) V) D7) V3) ((ord_less_eq_nat D6) D7))) (Q D6)))) (Q (((min_dist_capacity c) V) V3))))) ((_let_17 p1a) va) (forall ((Src nat) (V nat) (D nat) (D3 nat)) (=> (((connected_a c2) Src) V) (=> (= (((min_dist_a c2) Src) V) D) (=> ((ord_less_nat D3) D) (exists ((V2 nat)) (and (((connected_a c2) Src) V2) (= (((min_dist_a c2) Src) V2) D3))))))) (forall ((I nat) (J nat) (K nat) (L nat)) (=> ((ord_less_eq_nat I) J) (=> ((ord_less_eq_nat K) L) ((ord_less_eq_nat ((plus_plus_nat I) K)) ((plus_plus_nat J) L))))) _let_16 (forall ((U nat) (D1 nat) (W nat) (D2 nat) (V nat)) (let ((_let_1 ((min_dist_a c2) U))) (let ((_let_2 (dist_a c2))) (=> (((_let_2 U) D1) W) (=> (((_let_2 W) D2) V) (=> (= (_let_1 V) ((plus_plus_nat D1) D2)) (= (_let_1 W) D1))))))) (forall ((C (-> product_prod_nat_nat capacity)) (V nat) (D nat) (V3 nat)) (=> ((((dist_capacity C) V) D) V3) ((ord_less_eq_nat (((min_dist_capacity C) V) V3)) D))) (forall ((V nat) (V3 nat) (Q (-> nat Bool))) (=> (((connected_a c2) V) V3) (=> (forall ((D6 nat)) (=> ((((dist_a c2) V) D6) V3) (=> (forall ((D7 nat)) (=> ((((dist_a c2) V) D7) V3) ((ord_less_eq_nat D6) D7))) (Q D6)))) (Q (((min_dist_a c2) V) V3))))) (forall ((A nat) (B nat) (C nat)) (let ((_let_1 (plus_plus_nat A))) (= (= (_let_1 B) (_let_1 C)) (= B C)))) (forall ((A nat) (B nat) (C nat)) (=> ((ord_less_eq_nat A) B) ((ord_less_eq_nat ((plus_plus_nat A) C)) ((plus_plus_nat B) C)))) (forall ((A nat) (B nat) (F (-> nat nat)) (C nat)) (=> ((ord_less_nat A) B) (=> (= (F B) C) (=> (forall ((X nat) (Y nat)) (=> ((ord_less_nat X) Y) ((ord_less_nat (F X)) (F Y)))) ((ord_less_nat (F A)) C))))) (forall ((X3 nat) (Y3 nat)) (=> (not ((ord_less_eq_nat X3) Y3)) ((ord_less_eq_nat Y3) X3))) (= dist_a dist_a) (= min_dist_a min_dist_a) _let_15 (forall ((C (-> product_prod_nat_nat a)) (U nat) (D1 nat) (W nat) (D2 nat) (V nat)) (let ((_let_1 (dist_a C))) (let ((_let_2 (_let_1 U))) (=> ((_let_2 D1) W) (=> (((_let_1 W) D2) V) ((_let_2 ((plus_plus_nat D1) D2)) V)))))) (forall ((C (-> product_prod_nat_nat capacity)) (S nat) (P2 list_P559422087at_nat) (T nat)) (=> ((((isPath_capacity C) S) P2) T) (exists ((P6 list_P559422087at_nat)) ((((isSimp1359852763pacity C) S) P6) T)))) (forall ((I nat) (J nat)) (not ((ord_less_nat ((plus_plus_nat I) J)) I))) (forall ((A nat) (B nat) (C nat)) (=> (= A B) (=> ((ord_less_eq_nat B) C) ((ord_less_eq_nat A) C)))) (= isPath_capacity isPath_capacity) (= dist_capacity dist_capacity) _let_14 (forall ((P5 (-> nat Bool)) (A nat) (Q (-> nat Bool))) (=> (P5 A) (=> (forall ((X nat)) (=> (P5 X) (Q X))) (Q (ord_Least_nat P5))))) (forall ((U nat) (P2 list_P559422087at_nat) (V nat)) (= ((((isShor1936442771pacity c) U) P2) V) (and ((((isSimp1359852763pacity c) U) P2) V) (= (size_s1990949619at_nat P2) (((min_dist_capacity c) U) V))))) ((ord_less_eq_nat _let_13) _let_11) (forall ((M nat) (N nat)) (=> ((ord_less_eq_nat M) N) (=> ((ord_less_eq_nat N) M) (= M N)))) _let_10 _let_9 (forall ((B nat) (A nat) (C nat)) (=> (= ((plus_plus_nat B) A) ((plus_plus_nat C) A)) (= B C))) _let_8 (forall ((I nat) (J nat) (K nat) (L nat)) (=> ((ord_less_nat I) J) (=> ((ord_less_nat K) L) ((ord_less_nat ((plus_plus_nat I) K)) ((plus_plus_nat J) L))))) (forall ((A nat) (B nat)) (=> ((ord_less_nat A) B) ((ord_less_eq_nat A) B))) (forall ((A nat) (B nat) (C nat)) (let ((_let_1 (ord_less_nat A))) (=> (_let_1 B) (=> ((ord_less_nat B) C) (_let_1 C))))) (forall ((S nat) (P2 list_P559422087at_nat) (T nat)) (=> ((((isPath_capacity c) S) P2) T) (exists ((P6 list_P559422087at_nat)) ((((isSimp1359852763pacity c) S) P6) T)))) (forall ((V nat) (D nat) (V3 nat)) (=> ((((dist_capacity c) V) D) V3) (((connected_capacity c) V) V3))) (forall ((U nat) (V nat)) (=> (((connected_a c2) U) V) (not (forall ((P3 list_P559422087at_nat)) (not ((((isShortestPath_a c2) U) P3) V)))))) (forall ((I nat) (J nat) (K nat)) (=> ((ord_less_eq_nat I) J) ((ord_less_eq_nat ((plus_plus_nat I) K)) ((plus_plus_nat J) K)))) (forall ((C (-> product_prod_nat_nat capacity)) (U nat) (P2 list_P559422087at_nat) (V nat)) (=> ((((isShor1936442771pacity C) U) P2) V) ((((isPath_capacity C) U) P2) V))) (= (lambda ((Y4 nat) (Z nat)) (= Y4 Z)) (lambda ((A2 nat) (B2 nat)) (and ((ord_less_eq_nat A2) B2) ((ord_less_eq_nat B2) A2)))) (= isShor1936442771pacity (lambda ((C2 (-> product_prod_nat_nat capacity)) (U2 nat) (P list_P559422087at_nat) (V4 nat)) (and (forall ((P4 list_P559422087at_nat)) (=> ((((isPath_capacity C2) U2) P4) V4) ((ord_less_eq_nat (size_s1990949619at_nat P)) (size_s1990949619at_nat P4)))) ((((isPath_capacity C2) U2) P) V4)))) (forall ((N nat) (M nat)) (=> ((ord_less_nat N) M) (not (= M N)))) (forall ((V nat)) (((connected_capacity c) V) V)) (forall ((V nat) (V3 nat)) (= (((connected_capacity c) V) V3) (exists ((D4 nat)) ((((dist_capacity c) V) D4) V3)))) (forall ((V nat) (D nat) (V3 nat)) (=> ((((dist_capacity c) V) D) V3) ((ord_less_eq_nat (((min_dist_capacity c) V) V3)) D))) (forall ((X3 nat) (Y3 nat)) (or ((ord_less_eq_nat X3) Y3) ((ord_less_eq_nat Y3) X3))) (forall ((N nat)) (not ((ord_less_nat N) N))) (= isSimp1359852763pacity isSimp1359852763pacity) (forall ((X3 nat) (Y3 nat) (Z2 nat)) (let ((_let_1 (ord_less_eq_nat X3))) (=> (_let_1 Y3) (=> ((ord_less_eq_nat Y3) Z2) (_let_1 Z2))))) (forall ((U nat) (D1 nat) (W nat) (D2 nat) (V nat)) (let ((_let_1 (min_dist_a c2))) (let ((_let_2 (dist_a c2))) (=> (((_let_2 U) D1) W) (=> (((_let_2 W) D2) V) (=> (= ((_let_1 U) V) ((plus_plus_nat D1) D2)) (= ((_let_1 W) V) D2))))))) (forall ((P5 (-> nat Bool)) (K nat)) (=> (P5 K) (P5 (ord_Least_nat P5)))) (forall ((C (-> product_prod_nat_nat capacity)) (V nat) (V3 nat) (Q (-> nat Bool))) (=> (((connected_capacity C) V) V3) (=> (forall ((D6 nat)) (=> ((((dist_capacity C) V) D6) V3) (=> (forall ((D7 nat)) (=> ((((dist_capacity C) V) D7) V3) ((ord_less_eq_nat D6) D7))) (Q D6)))) (Q (((min_dist_capacity C) V) V3))))) (forall ((C (-> product_prod_nat_nat capacity)) (V nat) (D nat) (V3 nat)) (=> ((((dist_capacity C) V) D) V3) (=> (forall ((D5 nat)) (=> ((((dist_capacity C) V) D5) V3) ((ord_less_eq_nat D) D5))) (= (((min_dist_capacity C) V) V3) D)))) (forall ((A nat) (B nat) (C nat)) (=> (= A B) (=> ((ord_less_nat B) C) ((ord_less_nat A) C)))) (forall ((U nat)) (= ((reachableNodes_a c2) U) (collect_nat ((connected_a c2) U)))) (forall ((B nat) (A nat)) (=> ((ord_less_nat B) A) (not (= A B)))) (= (lambda ((Y4 nat) (Z nat)) (= Y4 Z)) (lambda ((A2 nat) (B2 nat)) (and ((ord_less_eq_nat B2) A2) ((ord_less_eq_nat A2) B2)))) _let_7 (forall ((V nat) (D nat) (V3 nat)) (= ((((dist_capacity c) V) D) V3) (exists ((P list_P559422087at_nat)) (and (= (size_s1990949619at_nat P) D) ((((isPath_capacity c) V) P) V3))))) (forall ((B nat) (A nat) (C nat)) (= (= ((plus_plus_nat B) A) ((plus_plus_nat C) A)) (= B C))) (forall ((U nat) (P2 list_P559422087at_nat) (V nat)) (= ((((isShortestPath_a c2) U) P2) V) (and (forall ((P4 list_P559422087at_nat)) (=> ((((isPath_a c2) U) P4) V) ((ord_less_eq_nat (size_s1990949619at_nat P2)) (size_s1990949619at_nat P4)))) ((((isPath_a c2) U) P2) V)))) (forall ((A nat) (B nat) (C nat)) (let ((_let_1 (plus_plus_nat A))) (= ((plus_plus_nat (_let_1 B)) C) (_let_1 ((plus_plus_nat B) C))))) (forall ((A nat) (B nat)) (=> ((ord_less_nat A) B) (not ((ord_less_nat B) A)))) (forall ((I nat) (J nat) (K nat)) (let ((_let_1 (ord_less_eq_nat I))) (=> (_let_1 J) (=> ((ord_less_eq_nat J) K) (_let_1 K))))) (forall ((V nat) (V3 nat)) (=> (((connected_a c2) V) V3) ((((dist_a c2) V) (((min_dist_a c2) V) V3)) V3))) (forall ((I nat) (J nat) (K nat) (L nat)) (=> (and ((ord_less_eq_nat I) J) (= K L)) ((ord_less_eq_nat ((plus_plus_nat I) K)) ((plus_plus_nat J) L)))) (forall ((A nat) (B nat) (C nat)) (=> ((ord_less_nat A) B) ((ord_less_nat ((plus_plus_nat A) C)) ((plus_plus_nat B) C)))) (forall ((M nat) (K nat) (N nat)) (=> ((ord_less_eq_nat ((plus_plus_nat M) K)) N) ((ord_less_eq_nat M) N))) (forall ((U nat) (D1 nat) (W nat) (D2 nat) (V nat)) (let ((_let_1 (dist_a c2))) (let ((_let_2 (_let_1 U))) (=> ((_let_2 D1) W) (=> (((_let_1 W) D2) V) ((_let_2 ((plus_plus_nat D1) D2)) V)))))) (= plus_plus_nat (lambda ((A2 nat) (B2 nat)) ((plus_plus_nat B2) A2))) _let_6 (forall ((C (-> product_prod_nat_nat a)) (U nat) (D1 nat) (W nat) (D2 nat) (V nat)) (let ((_let_1 ((min_dist_a C) U))) (let ((_let_2 (dist_a C))) (=> (((_let_2 U) D1) W) (=> (((_let_2 W) D2) V) (=> (= (_let_1 V) ((plus_plus_nat D1) D2)) (= (_let_1 W) D1))))))) (= isSimplePath_a isSimplePath_a) (forall ((X3 nat) (Y3 nat)) (=> ((ord_less_nat X3) Y3) (not (= X3 Y3)))) _let_4 (forall ((C (-> product_prod_nat_nat capacity)) (V nat) (V3 nat)) (=> (((connected_capacity C) V) V3) ((((dist_capacity C) V) (((min_dist_capacity C) V) V3)) V3))) (forall ((U nat) (V nat)) (= (((connected_capacity c) U) V) (exists ((P list_P559422087at_nat)) ((((isPath_capacity c) U) P) V)))) (forall ((I nat) (J nat) (M nat)) (let ((_let_1 (ord_less_nat I))) (=> (_let_1 J) (_let_1 ((plus_plus_nat J) M))))) (forall ((A nat) (F (-> nat nat)) (B nat) (C nat)) (let ((_let_1 (ord_less_nat A))) (=> (_let_1 (F B)) (=> ((ord_less_nat B) C) (=> (forall ((X nat) (Y nat)) (=> ((ord_less_nat X) Y) ((ord_less_nat (F X)) (F Y)))) (_let_1 (F C))))))) (forall ((A nat) (B nat) (C nat) (D nat)) (=> ((ord_less_nat A) B) (=> ((ord_less_nat C) D) ((ord_less_nat ((plus_plus_nat A) C)) ((plus_plus_nat B) D))))) (= ord_less_eq_nat (lambda ((A2 nat) (B2 nat)) (exists ((C2 nat)) (= B2 ((plus_plus_nat A2) C2))))) (forall ((X3 nat) (Y3 nat) (P5 Bool)) (=> ((ord_less_nat X3) Y3) (=> ((ord_less_nat Y3) X3) P5))) (forall ((K nat) (P5 (-> nat Bool))) (=> ((ord_less_nat K) (ord_Least_nat P5)) (not (P5 K)))) (forall ((I nat) (J nat) (K nat) (L nat)) (=> (and (= K L) (= I J)) (= ((plus_plus_nat I) K) ((plus_plus_nat J) L)))) (forall ((X3 nat) (Y3 nat) (Z2 nat)) (let ((_let_1 (ord_less_nat X3))) (=> (_let_1 Y3) (=> ((ord_less_nat Y3) Z2) (_let_1 Z2))))) (((_let_3 s) p3) t) (= isPath_a isPath_a) (forall ((C (-> product_prod_nat_nat capacity)) (Src nat) (V nat) (D3 nat)) (=> (((connected_capacity C) Src) V) (=> ((ord_less_eq_nat D3) (((min_dist_capacity C) Src) V)) (exists ((V2 nat)) (and (((connected_capacity C) Src) V2) (= (((min_dist_capacity C) Src) V2) D3)))))) (forall ((X3 nat)) ((ord_less_eq_nat X3) X3)) (forall ((A nat) (B nat) (C nat)) (let ((_let_1 (ord_less_eq_nat A))) (=> (_let_1 B) (=> ((ord_less_eq_nat B) C) (_let_1 C))))) (forall ((A nat) (C nat) (B nat)) (= ((ord_less_nat ((plus_plus_nat A) C)) ((plus_plus_nat B) C)) ((ord_less_nat A) B))) (forall ((A nat) (B nat) (F (-> nat nat)) (C nat)) (=> ((ord_less_eq_nat A) B) (=> (= (F B) C) (=> (forall ((X nat) (Y nat)) (=> ((ord_less_eq_nat X) Y) ((ord_less_eq_nat (F X)) (F Y)))) ((ord_less_eq_nat (F A)) C))))) (forall ((V nat) (V3 nat)) (=> (((connected_capacity c) V) V3) ((((dist_capacity c) V) (((min_dist_capacity c) V) V3)) V3))) (forall ((U nat) (P2 list_P559422087at_nat) (V nat)) (=> ((((isShortestPath_a c2) U) P2) V) ((((isPath_a c2) U) P2) V))) _let_2 (forall ((K nat) (L nat)) (=> ((ord_less_eq_nat K) L) (exists ((N3 nat)) (= L ((plus_plus_nat K) N3))))) (forall ((C (-> product_prod_nat_nat a)) (U nat) (D1 nat) (W nat) (D2 nat) (V nat)) (let ((_let_1 (min_dist_a C))) (let ((_let_2 (dist_a C))) (=> (((_let_2 U) D1) W) (=> (((_let_2 W) D2) V) (=> (= ((_let_1 U) V) ((plus_plus_nat D1) D2)) (= ((_let_1 W) V) D2))))))) (forall ((X3 nat) (Y3 nat)) (=> (= X3 Y3) ((ord_less_eq_nat X3) Y3))) (forall ((A nat) (B nat) (C nat)) (let ((_let_1 (plus_plus_nat A))) (=> (= (_let_1 B) (_let_1 C)) (= B C)))) (= reachableNodes_a reachableNodes_a) (forall ((A nat) (P5 (-> nat Bool))) (= ((member_nat A) (collect_nat P5)) (P5 A))) (forall ((C (-> product_prod_nat_nat a)) (S nat) (P2 list_P559422087at_nat) (T nat)) (=> ((((isShortestPath_a C) S) P2) T) ((((isSimplePath_a C) S) P2) T))) (forall ((F (-> nat nat)) (M nat) (K nat)) (=> (forall ((M4 nat) (N3 nat)) (=> ((ord_less_nat M4) N3) ((ord_less_nat (F M4)) (F N3)))) ((ord_less_eq_nat ((plus_plus_nat (F M)) K)) (F ((plus_plus_nat M) K))))) (forall ((P5 (-> nat nat Bool)) (A nat) (B nat)) (=> (forall ((A4 nat) (B4 nat)) (=> ((ord_less_eq_nat A4) B4) ((P5 A4) B4))) (=> (forall ((A4 nat) (B4 nat)) (=> ((P5 B4) A4) ((P5 A4) B4))) ((P5 A) B)))) (forall ((M nat) (N nat)) (or ((ord_less_eq_nat M) N) ((ord_less_eq_nat N) M))) (forall ((N nat) (M nat)) ((ord_less_eq_nat N) ((plus_plus_nat N) M))) (forall ((U nat) (P2 list_P559422087at_nat) (V nat)) (= ((((isShor1936442771pacity c) U) P2) V) (and (= (size_s1990949619at_nat P2) (((min_dist_capacity c) U) V)) ((((isPath_capacity c) U) P2) V)))) (forall ((U nat) (P2 list_P559422087at_nat) (V nat)) (= ((((isShor1936442771pacity c) U) P2) V) (and ((((isPath_capacity c) U) P2) V) (forall ((P4 list_P559422087at_nat)) (=> ((((isPath_capacity c) U) P4) V) ((ord_less_eq_nat (size_s1990949619at_nat P2)) (size_s1990949619at_nat P4))))))) (forall ((U nat) (P2 list_P559422087at_nat) (V nat)) (=> ((((isPath_a c2) U) P2) V) ((((dist_a c2) U) (size_s1990949619at_nat P2)) V))) _let_1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 73.50/73.72 ) 73.50/73.72 % SZS output end Proof for theBenchmark 73.55/73.73 EOF