0.07/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.13	% Command    : do_cvc5 %s %d
0.13/0.33	% Computer   : n010.cluster.edu
0.13/0.33	% Model      : x86_64 x86_64
0.13/0.33	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.33	% Memory     : 8042.1875MB
0.13/0.33	% OS         : Linux 3.10.0-693.el7.x86_64
0.19/0.33	% CPULimit   : 1200
0.19/0.33	% WCLimit    : 120
0.19/0.33	% DateTime   : Tue Jul 13 13:30:21 EDT 2021
0.19/0.34	% CPUTime    : 
0.19/0.48	%----THF division
0.19/0.49	------- cvc5-thf casc 28 : /export/starexec/sandbox2/benchmark/theBenchmark.p at 120...
0.19/0.49	--- Run --ho-elim --full-saturate-quant at 10...
0.56/0.81	% SZS status Theorem for theBenchmark
0.65/0.83	% SZS output start Proof for theBenchmark
0.65/0.83	(proof
0.65/0.83	(let ((_let_1 (forall ((A set_real) (B a) (C set_real) (D a)) (= ((plus_p1582417306real_a ((produc617496131real_a A) B)) ((produc617496131real_a C) D)) ((produc617496131real_a ((plus_plus_set_real A) C)) ((plus_plus_a B) D)))))) (let ((_let_2 ((member449909584od_a_a ((product_Pair_a_a x) y)) relation))) (let ((_let_3 (ord_less_real one_one_real))) (let ((_let_4 (ord_less_eq_real zero_zero_real))) (let ((_let_5 (forall ((A real) (B real)) (= (= A ((plus_plus_real A) B)) (= B zero_zero_real))))) (let ((_let_6 ((plus_plus_real u) v))) (let ((_let_7 (= _let_6 one_one_real))) (let ((_let_8 (= zero_z1937883107real_a ((produc1430099868real_a zero_z659284464l_real) zero_zero_a)))) (let ((_let_9 ((member449909584od_a_a ((product_Pair_a_a ((plus_plus_a ((real_V1035702895aleR_a u) x)) ((real_V1035702895aleR_a v) y))) y)) relation))) (let ((_let_10 (= u zero_zero_real))) (let ((_let_11 (=> (and (not _let_10) (not (= u one_one_real))) _let_9))) (let ((_let_12 (= zero_z659284464l_real ((produc705216881l_real zero_zero_real) zero_zero_real)))) (let ((_let_13 (forall ((X a)) (= ((real_V1035702895aleR_a one_one_real) X) X)))) (let ((_let_14 (forall ((A real) (X a)) (= (= ((real_V1035702895aleR_a A) X) zero_zero_a) (or (= A zero_zero_real) (= X zero_zero_a)))))) (let ((_let_15 (ord_less_real zero_zero_real))) (let ((_let_16 (=> _let_10 _let_9))) (let ((_let_17 (= zero_z590476811l_real ((produc1926903988l_real zero_zero_real) zero_z659284464l_real)))) (let ((_let_18 (= zero_z950819678od_a_a ((product_Pair_a_a zero_zero_a) zero_zero_a)))) (let ((_let_19 (= prefer529818233pref_a (lambda ((Pr2 set_Product_prod_a_a)) (forall ((X3 a) (Y5 a)) (=> ((member449909584od_a_a ((product_Pair_a_a X3) Y5)) Pr2) (forall ((Alpha2 real) (Beta2 real)) (let ((_let_1 (ord_less_real zero_zero_real))) (=> (and (= ((plus_plus_real Alpha2) Beta2) one_one_real) (_let_1 Alpha2) (_let_1 Beta2)) ((member449909584od_a_a ((product_Pair_a_a ((plus_plus_a ((real_V1035702895aleR_a Alpha2) X3)) ((real_V1035702895aleR_a Beta2) Y5))) Y5)) Pr2)))))))))) (let ((_let_20 (= zero_z2135370393l_real ((produc64206290l_real zero_zero_a) zero_z659284464l_real)))) (let ((_let_21 (= zero_z342251165l_real ((produc1175086478l_real zero_z659284464l_real) zero_zero_real)))) (let ((_let_22 (= zero_z53797895od_a_a ((produc1299253312od_a_a zero_zero_a) zero_z950819678od_a_a)))) (let ((_let_23 (forall ((A a)) (= ((plus_plus_a A) zero_zero_a) A)))) (let ((_let_24 (= prefer1247792113f_real (lambda ((Pr2 set_Pr147102617l_real)) (forall ((X3 real) (Y5 real)) (=> ((member1068169442l_real ((produc705216881l_real X3) Y5)) Pr2) (forall ((Alpha2 real) (Beta2 real)) (let ((_let_1 (ord_less_real zero_zero_real))) (=> (and (_let_1 Beta2) (_let_1 Alpha2) (= ((plus_plus_real Alpha2) Beta2) one_one_real)) ((member1068169442l_real ((produc705216881l_real ((plus_plus_real ((real_V453051771R_real Alpha2) X3)) ((real_V453051771R_real Beta2) Y5))) Y5)) Pr2)))))))))) (let ((_let_25 (= ord_le1824328871od_a_a (lambda ((A6 set_Product_prod_a_a) (B6 set_Product_prod_a_a)) (forall ((T product_prod_a_a)) (let ((_let_1 (member449909584od_a_a T))) (=> (_let_1 A6) (_let_1 B6)))))))) (let ((_let_26 (not _let_9))) (let ((_let_27 (= plus_plus_a (lambda ((A4 a) (B3 a)) ((plus_plus_a B3) A4))))) (let ((_let_28 (ord_less_eq_real one_one_real))) (let ((_let_29 (= zero_z396988537od_a_a ((produc454550562od_a_a zero_zero_real) zero_z950819678od_a_a)))) (let ((_let_30 (= zero_z705155042a_real ((product_Pair_a_real zero_zero_a) zero_zero_real)))) (let ((_let_31 (= zero_z1407338960real_a ((product_Pair_real_a zero_zero_real) zero_zero_a)))) (let ((_let_32 (= k_32 k_35))) (let ((_let_33 (ho_38 (ho_37 k_39 u) v))) (let ((_let_34 (= u _let_33))) (let ((_let_35 (ho_34 (ho_64 k_63 u) x))) (let ((_let_36 (ho_33 k_35 _let_35))) (let ((_let_37 (= _let_35 (ho_34 _let_36 zero_zero_a)))) (let ((_let_38 (ho_34 (ho_64 k_63 v) y))) (let ((_let_39 (ho_67 (ho_66 k_65 (ho_34 _let_36 _let_38)) y))) (let ((_let_40 (ho_41 k_40 relation))) (let ((_let_41 (ho_42 _let_40 _let_39))) (let ((_let_42 (ho_67 (ho_66 k_65 x) y))) (let ((_let_43 (ho_42 _let_40 _let_42))) (let ((_let_44 (= zero_zero_a _let_38))) (let ((_let_45 (= x (ho_34 (ho_64 k_63 _let_33) x)))) (let ((_let_46 (= plus_plus_a ll_5))) (let ((_let_47 (EQ_RESOLVE (ASSUME |:args| (_let_27)) (TRANS (PREPROCESS |:args| ((= _let_27 _let_46))) (PREPROCESS |:args| ((= _let_46 _let_32))))))) (let ((_let_48 (not _let_34))) (let ((_let_49 (= zero_zero_real u))) (let ((_let_50 (not _let_49))) (let ((_let_51 (and _let_50 _let_48))) (let ((_let_52 (ho_15 (ho_14 k_13 _let_39) relation))) (let ((_let_53 (not _let_51))) (let ((_let_54 (EQ_RESOLVE (ASSUME |:args| (_let_26)) (PREPROCESS |:args| ((= _let_26 (not _let_52))))))) (let ((_let_55 (SYMM (ASSUME |:args| (_let_7))))) (let ((_let_56 (ASSUME |:args| (_let_8)))) (let ((_let_57 (ASSUME |:args| (_let_17)))) (let ((_let_58 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_19)) (MACRO_SR_EQ_INTRO |:args| (_let_19 7 12))) (MACRO_SR_EQ_INTRO _let_57 _let_56 _let_55 |:args| ((= prefer529818233pref_a (lambda ((Pr2 set_Product_prod_a_a)) (forall ((X3 a) (Y5 a) (BOUND_VARIABLE_5727 real) (BOUND_VARIABLE_5725 real)) (let ((_let_1 (ord_less_real zero_zero_real))) (or (not ((member449909584od_a_a ((product_Pair_a_a X3) Y5)) Pr2)) (not (= one_one_real ((plus_plus_real BOUND_VARIABLE_5725) BOUND_VARIABLE_5727))) (not (_let_1 BOUND_VARIABLE_5725)) (not (_let_1 BOUND_VARIABLE_5727)) ((member449909584od_a_a ((product_Pair_a_a ((plus_plus_a ((real_V1035702895aleR_a BOUND_VARIABLE_5725) X3)) ((real_V1035702895aleR_a BOUND_VARIABLE_5727) Y5))) Y5)) Pr2)))))) 7 12))))) (let ((_let_59 (ASSUME |:args| (_let_21)))) (let ((_let_60 (ASSUME |:args| (_let_18)))) (let ((_let_61 (EQ_RESOLVE (EQ_RESOLVE (ASSUME |:args| (_let_24)) (MACRO_SR_EQ_INTRO |:args| (_let_24 7 12))) (MACRO_SR_EQ_INTRO _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 |:args| ((= prefer1247792113f_real (lambda ((Pr2 set_Pr147102617l_real)) (forall ((X3 real) (Y5 real) (BOUND_VARIABLE_6127 real) (BOUND_VARIABLE_6125 real)) (let ((_let_1 (ord_less_real zero_zero_real))) (or (not ((member1068169442l_real ((produc705216881l_real X3) Y5)) Pr2)) (not (_let_1 BOUND_VARIABLE_6127)) (not (_let_1 BOUND_VARIABLE_6125)) (not (= one_one_real ((plus_plus_real BOUND_VARIABLE_6125) BOUND_VARIABLE_6127))) ((member1068169442l_real ((produc705216881l_real ((plus_plus_real ((real_V453051771R_real BOUND_VARIABLE_6125) X3)) ((real_V453051771R_real BOUND_VARIABLE_6127) Y5))) Y5)) Pr2)))))) 7 12))))) (let ((_let_62 (EQ_RESOLVE (ASSUME |:args| (_let_25)) (MACRO_SR_EQ_INTRO |:args| (_let_25 7 12))))) (let ((_let_63 (ASSUME |:args| (_let_20)))) (let ((_let_64 (ASSUME |:args| (_let_12)))) (let ((_let_65 (EQ_RESOLVE (ASSUME |:args| (_let_29)) (MACRO_SR_EQ_INTRO _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 |:args| (_let_29 7 12))))) (let ((_let_66 (EQ_RESOLVE (ASSUME |:args| (_let_22)) (MACRO_SR_EQ_INTRO _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 |:args| (_let_22 7 12))))) (let ((_let_67 (ASSUME |:args| (_let_30)))) (let ((_let_68 (ASSUME |:args| (_let_31)))) (let ((_let_69 (20))) (let ((_let_70 (_let_51))) (let ((_let_71 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG |:args| _let_70) (CONG (REFL |:args| _let_70) (MACRO_SR_PRED_INTRO |:args| ((= (not _let_50) _let_49))) (MACRO_SR_PRED_INTRO |:args| ((= (not _let_48) _let_34))) |:args| _let_69)) |:args| ((or _let_49 _let_34 _let_51))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (ASSUME |:args| (_let_16)) (TRANS (MACRO_SR_EQ_INTRO |:args| (_let_16 7 12)) (PREPROCESS |:args| ((= (=> _let_49 _let_9) (=> _let_49 _let_52))))))) _let_54 |:args| (_let_50 true _let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (EQ_RESOLVE (ASSUME |:args| (_let_11)) (TRANS (MACRO_SR_EQ_INTRO |:args| (_let_11 7 12)) (MACRO_SR_EQ_INTRO _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 |:args| ((=> (and _let_50 (not (= one_one_real u))) _let_9) 7 12)) (PREPROCESS |:args| ((= (=> (and _let_50 (not (= u _let_6))) _let_9) (=> _let_51 _let_52))))))) |:args| ((or _let_52 _let_53))) _let_54 |:args| (_let_53 true _let_52)) |:args| (_let_34 true _let_49 true _let_51)))) (let ((_let_72 (forall ((A a)) (= A (ho_34 (ho_33 k_35 A) zero_zero_a))))) (let ((_let_73 (EQ_RESOLVE (ASSUME |:args| (_let_23)) (TRANS (MACRO_SR_EQ_INTRO |:args| (_let_23 7 12)) (PREPROCESS |:args| ((= (forall ((A a)) (= A ((plus_plus_a A) zero_zero_a))) _let_72))))))) (let ((_let_74 (_let_35))) (let ((_let_75 (= _let_41 _let_52))) (let ((_let_76 (not _let_41))) (let ((_let_77 (forall ((BOUND_VARIABLE_7928 set_Product_prod_a_a) (BOUND_VARIABLE_7929 product_prod_a_a)) (= (ho_42 (ho_41 k_40 BOUND_VARIABLE_7928) BOUND_VARIABLE_7929) (ho_15 (ho_14 k_13 BOUND_VARIABLE_7929) BOUND_VARIABLE_7928))))) (let ((_let_78 (forall ((u |u_(-> product_prod_a_set_a product_prod_a_set_a)|) (e product_prod_a_set_a) (i product_prod_a_set_a)) (not (forall ((v |u_(-> product_prod_a_set_a product_prod_a_set_a)|)) (not (forall ((ii product_prod_a_set_a)) (= (ho_114 v ii) (ite (= i ii) e (ho_114 u ii)))))))))) (let ((_let_79 (forall ((x |u_(-> product_prod_a_set_a product_prod_a_set_a)|) (y |u_(-> product_prod_a_set_a product_prod_a_set_a)|)) (or (not (forall ((z product_prod_a_set_a)) (= (ho_114 x z) (ho_114 y z)))) (= x y))))) (let ((_let_80 (forall ((u |u_(-> set_a set_set_a Bool)|) (e |u_(-> set_set_a Bool)|) (i set_a)) (not (forall ((v |u_(-> set_a set_set_a Bool)|)) (not (forall ((ii set_a)) (= (ho_160 v ii) (ite (= i ii) e (ho_160 u ii)))))))))) (let ((_let_81 (forall ((x |u_(-> set_a set_set_a Bool)|) (y |u_(-> set_a set_set_a Bool)|)) (or (not (forall ((z set_a)) (= (ho_160 x z) (ho_160 y z)))) (= x y))))) (let ((_let_82 (forall ((u |u_(-> a set_a product_prod_a_set_a)|) (e |u_(-> set_a product_prod_a_set_a)|) (i a)) (not (forall ((v |u_(-> a set_a product_prod_a_set_a)|)) (not (forall ((ii a)) (= (ho_110 v ii) (ite (= i ii) e (ho_110 u ii)))))))))) (let ((_let_83 (forall ((x |u_(-> a set_a product_prod_a_set_a)|) (y |u_(-> a set_a product_prod_a_set_a)|)) (or (not (forall ((z a)) (= (ho_110 x z) (ho_110 y z)))) (= x y))))) (let ((_let_84 (forall ((u |u_(-> set_a product_prod_a_set_a)|) (e product_prod_a_set_a) (i set_a)) (not (forall ((v |u_(-> set_a product_prod_a_set_a)|)) (not (forall ((ii set_a)) (= (ho_111 v ii) (ite (= i ii) e (ho_111 u ii)))))))))) (let ((_let_85 (forall ((x |u_(-> set_a product_prod_a_set_a)|) (y |u_(-> set_a product_prod_a_set_a)|)) (or (not (forall ((z set_a)) (= (ho_111 x z) (ho_111 y z)))) (= x y))))) (let ((_let_86 (forall ((u |u_(-> product_prod_a_a produc1572603623od_a_a)|) (e produc1572603623od_a_a) (i product_prod_a_a)) (not (forall ((v |u_(-> product_prod_a_a produc1572603623od_a_a)|)) (not (forall ((ii product_prod_a_a)) (= (ho_95 v ii) (ite (= i ii) e (ho_95 u ii)))))))))) (let ((_let_87 (forall ((x |u_(-> product_prod_a_a produc1572603623od_a_a)|) (y |u_(-> product_prod_a_a produc1572603623od_a_a)|)) (or (not (forall ((z product_prod_a_a)) (= (ho_95 x z) (ho_95 y z)))) (= x y))))) (let ((_let_88 (forall ((u |u_(-> product_prod_a_a produc1921647824od_a_a)|) (e produc1921647824od_a_a) (i product_prod_a_a)) (not (forall ((v |u_(-> product_prod_a_a produc1921647824od_a_a)|)) (not (forall ((ii product_prod_a_a)) (= (ho_174 v ii) (ite (= i ii) e (ho_174 u ii)))))))))) (let ((_let_89 (forall ((x |u_(-> product_prod_a_a produc1921647824od_a_a)|) (y |u_(-> product_prod_a_a produc1921647824od_a_a)|)) (or (not (forall ((z product_prod_a_a)) (= (ho_174 x z) (ho_174 y z)))) (= x y))))) (let ((_let_90 (forall ((u |u_(-> set_se1596668135od_a_a set_se1596668135od_a_a set_se1596668135od_a_a)|) (e |u_(-> set_se1596668135od_a_a set_se1596668135od_a_a)|) (i set_se1596668135od_a_a)) (not (forall ((v |u_(-> set_se1596668135od_a_a set_se1596668135od_a_a set_se1596668135od_a_a)|)) (not (forall ((ii set_se1596668135od_a_a)) (= (ho_211 v ii) (ite (= i ii) e (ho_211 u ii)))))))))) (let ((_let_91 (forall ((x |u_(-> set_se1596668135od_a_a set_se1596668135od_a_a set_se1596668135od_a_a)|) (y |u_(-> set_se1596668135od_a_a set_se1596668135od_a_a set_se1596668135od_a_a)|)) (or (not (forall ((z set_se1596668135od_a_a)) (= (ho_211 x z) (ho_211 y z)))) (= x y))))) (let ((_let_92 (forall ((u |u_(-> set_a set_a)|) (e set_a) (i set_a)) (not (forall ((v |u_(-> set_a set_a)|)) (not (forall ((ii set_a)) (= (ho_108 v ii) (ite (= i ii) e (ho_108 u ii)))))))))) (let ((_let_93 (forall ((x |u_(-> set_a set_a)|) (y |u_(-> set_a set_a)|)) (or (not (forall ((z set_a)) (= (ho_108 x z) (ho_108 y z)))) (= x y))))) (let ((_let_94 (forall ((u |u_(-> real produc957004601l_real)|) (e produc957004601l_real) (i real)) (not (forall ((v |u_(-> real produc957004601l_real)|)) (not (forall ((ii real)) (= (ho_103 v ii) (ite (= i ii) e (ho_103 u ii)))))))))) (let ((_let_95 (forall ((x |u_(-> real produc957004601l_real)|) (y |u_(-> real produc957004601l_real)|)) (or (not (forall ((z real)) (= (ho_103 x z) (ho_103 y z)))) (= x y))))) (let ((_let_96 (forall ((u |u_(-> _u_(-> real Bool)_ set_real)|) (e set_real) (i |u_(-> real Bool)|)) (not (forall ((v |u_(-> _u_(-> real Bool)_ set_real)|)) (not (forall ((ii |u_(-> real Bool)|)) (= (ho_99 v ii) (ite (= i ii) e (ho_99 u ii)))))))))) (let ((_let_97 (forall ((x |u_(-> _u_(-> real Bool)_ set_real)|) (y |u_(-> _u_(-> real Bool)_ set_real)|)) (or (not (forall ((z |u_(-> real Bool)|)) (= (ho_99 x z) (ho_99 y z)))) (= x y))))) (let ((_let_98 (forall ((u |u_(-> produc2096821232od_a_a produc2096821232od_a_a)|) (e produc2096821232od_a_a) (i produc2096821232od_a_a)) (not (forall ((v |u_(-> produc2096821232od_a_a produc2096821232od_a_a)|)) (not (forall ((ii produc2096821232od_a_a)) (= (ho_135 v ii) (ite (= i ii) e (ho_135 u ii)))))))))) (let ((_let_99 (forall ((x |u_(-> produc2096821232od_a_a produc2096821232od_a_a)|) (y |u_(-> produc2096821232od_a_a produc2096821232od_a_a)|)) (or (not (forall ((z produc2096821232od_a_a)) (= (ho_135 x z) (ho_135 y z)))) (= x y))))) (let ((_let_100 (forall ((u |u_(-> produc1396156303t_real produc1396156303t_real produc1396156303t_real)|) (e |u_(-> produc1396156303t_real produc1396156303t_real)|) (i produc1396156303t_real)) (not (forall ((v |u_(-> produc1396156303t_real produc1396156303t_real produc1396156303t_real)|)) (not (forall ((ii produc1396156303t_real)) (= (ho_194 v ii) (ite (= i ii) e (ho_194 u ii)))))))))) (let ((_let_101 (forall ((x |u_(-> produc1396156303t_real produc1396156303t_real produc1396156303t_real)|) (y |u_(-> produc1396156303t_real produc1396156303t_real produc1396156303t_real)|)) (or (not (forall ((z produc1396156303t_real)) (= (ho_194 x z) (ho_194 y z)))) (= x y))))) (let ((_let_102 (forall ((u |u_(-> real real produc957004601l_real)|) (e |u_(-> real produc957004601l_real)|) (i real)) (not (forall ((v |u_(-> real real produc957004601l_real)|)) (not (forall ((ii real)) (= (ho_102 v ii) (ite (= i ii) e (ho_102 u ii)))))))))) (let ((_let_103 (forall ((x |u_(-> real real produc957004601l_real)|) (y |u_(-> real real produc957004601l_real)|)) (or (not (forall ((z real)) (= (ho_102 x z) (ho_102 y z)))) (= x y))))) (let ((_let_104 (forall ((u |u_(-> produc1572603623od_a_a set_Pr1948701895od_a_a Bool)|) (e |u_(-> set_Pr1948701895od_a_a Bool)|) (i produc1572603623od_a_a)) (not (forall ((v |u_(-> produc1572603623od_a_a set_Pr1948701895od_a_a Bool)|)) (not (forall ((ii produc1572603623od_a_a)) (= (ho_97 v ii) (ite (= i ii) e (ho_97 u ii)))))))))) (let ((_let_105 (forall ((x |u_(-> produc1572603623od_a_a set_Pr1948701895od_a_a Bool)|) (y |u_(-> produc1572603623od_a_a set_Pr1948701895od_a_a Bool)|)) (or (not (forall ((z produc1572603623od_a_a)) (= (ho_97 x z) (ho_97 y z)))) (= x y))))) (let ((_let_106 (forall ((u |u_(-> real product_prod_a_a product_prod_a_a)|) (e |u_(-> product_prod_a_a product_prod_a_a)|) (i real)) (not (forall ((v |u_(-> real product_prod_a_a product_prod_a_a)|)) (not (forall ((ii real)) (= (ho_92 v ii) (ite (= i ii) e (ho_92 u ii)))))))))) (let ((_let_107 (forall ((x |u_(-> real product_prod_a_a product_prod_a_a)|) (y |u_(-> real product_prod_a_a product_prod_a_a)|)) (or (not (forall ((z real)) (= (ho_92 x z) (ho_92 y z)))) (= x y))))) (let ((_let_108 (forall ((u |u_(-> produc443621487t_real produc443621487t_real produc443621487t_real)|) (e |u_(-> produc443621487t_real produc443621487t_real)|) (i produc443621487t_real)) (not (forall ((v |u_(-> produc443621487t_real produc443621487t_real produc443621487t_real)|)) (not (forall ((ii produc443621487t_real)) (= (ho_188 v ii) (ite (= i ii) e (ho_188 u ii)))))))))) (let ((_let_109 (forall ((x |u_(-> produc443621487t_real produc443621487t_real produc443621487t_real)|) (y |u_(-> produc443621487t_real produc443621487t_real produc443621487t_real)|)) (or (not (forall ((z produc443621487t_real)) (= (ho_188 x z) (ho_188 y z)))) (= x y))))) (let ((_let_110 (forall ((u |u_(-> set_se1596668135od_a_a Bool)|) (e Bool) (i set_se1596668135od_a_a)) (not (forall ((v |u_(-> set_se1596668135od_a_a Bool)|)) (not (forall ((ii set_se1596668135od_a_a)) (= (ho_215 v ii) (ite (= i ii) e (ho_215 u ii)))))))))) (let ((_let_111 (forall ((x |u_(-> set_se1596668135od_a_a Bool)|) (y |u_(-> set_se1596668135od_a_a Bool)|)) (or (not (forall ((z set_se1596668135od_a_a)) (= (ho_215 x z) (ho_215 y z)))) (= x y))))) (let ((_let_112 (forall ((u |u_(-> real produc957004601l_real produc957004601l_real)|) (e |u_(-> produc957004601l_real produc957004601l_real)|) (i real)) (not (forall ((v |u_(-> real produc957004601l_real produc957004601l_real)|)) (not (forall ((ii real)) (= (ho_105 v ii) (ite (= i ii) e (ho_105 u ii)))))))))) (let ((_let_113 (forall ((x |u_(-> real produc957004601l_real produc957004601l_real)|) (y |u_(-> real produc957004601l_real produc957004601l_real)|)) (or (not (forall ((z real)) (= (ho_105 x z) (ho_105 y z)))) (= x y))))) (let ((_let_114 (forall ((u |u_(-> set_Pr147102617l_real set_Pr147102617l_real)|) (e set_Pr147102617l_real) (i set_Pr147102617l_real)) (not (forall ((v |u_(-> set_Pr147102617l_real set_Pr147102617l_real)|)) (not (forall ((ii set_Pr147102617l_real)) (= (ho_88 v ii) (ite (= i ii) e (ho_88 u ii)))))))))) (let ((_let_115 (forall ((x |u_(-> set_Pr147102617l_real set_Pr147102617l_real)|) (y |u_(-> set_Pr147102617l_real set_Pr147102617l_real)|)) (or (not (forall ((z set_Pr147102617l_real)) (= (ho_88 x z) (ho_88 y z)))) (= x y))))) (let ((_let_116 (forall ((u |u_(-> a product_prod_a_a produc1921647824od_a_a)|) (e |u_(-> product_prod_a_a produc1921647824od_a_a)|) (i a)) (not (forall ((v |u_(-> a product_prod_a_a produc1921647824od_a_a)|)) (not (forall ((ii a)) (= (ho_173 v ii) (ite (= i ii) e (ho_173 u ii)))))))))) (let ((_let_117 (forall ((x |u_(-> a product_prod_a_a produc1921647824od_a_a)|) (y |u_(-> a product_prod_a_a produc1921647824od_a_a)|)) (or (not (forall ((z a)) (= (ho_173 x z) (ho_173 y z)))) (= x y))))) (let ((_let_118 (forall ((u |u_(-> set_Product_prod_a_a set_Product_prod_a_a set_Product_prod_a_a)|) (e |u_(-> set_Product_prod_a_a set_Product_prod_a_a)|) (i set_Product_prod_a_a)) (not (forall ((v |u_(-> set_Product_prod_a_a set_Product_prod_a_a set_Product_prod_a_a)|)) (not (forall ((ii set_Product_prod_a_a)) (= (ho_84 v ii) (ite (= i ii) e (ho_84 u ii)))))))))) (let ((_let_119 (forall ((x |u_(-> set_Product_prod_a_a set_Product_prod_a_a set_Product_prod_a_a)|) (y |u_(-> set_Product_prod_a_a set_Product_prod_a_a set_Product_prod_a_a)|)) (or (not (forall ((z set_Product_prod_a_a)) (= (ho_84 x z) (ho_84 y z)))) (= x y))))) (let ((_let_120 (forall ((u |u_(-> set_Product_prod_a_a set_Product_prod_a_a)|) (e set_Product_prod_a_a) (i set_Product_prod_a_a)) (not (forall ((v |u_(-> set_Product_prod_a_a set_Product_prod_a_a)|)) (not (forall ((ii set_Product_prod_a_a)) (= (ho_85 v ii) (ite (= i ii) e (ho_85 u ii)))))))))) (let ((_let_121 (forall ((x |u_(-> set_Product_prod_a_a set_Product_prod_a_a)|) (y |u_(-> set_Product_prod_a_a set_Product_prod_a_a)|)) (or (not (forall ((z set_Product_prod_a_a)) (= (ho_85 x z) (ho_85 y z)))) (= x y))))) (let ((_let_122 (forall ((u |u_(-> set_real produc443621487t_real)|) (e produc443621487t_real) (i set_real)) (not (forall ((v |u_(-> set_real produc443621487t_real)|)) (not (forall ((ii set_real)) (= (ho_186 v ii) (ite (= i ii) e (ho_186 u ii)))))))))) (let ((_let_123 (forall ((x |u_(-> set_real produc443621487t_real)|) (y |u_(-> set_real produc443621487t_real)|)) (or (not (forall ((z set_real)) (= (ho_186 x z) (ho_186 y z)))) (= x y))))) (let ((_let_124 (forall ((u |u_(-> produc957004601l_real produc957004601l_real)|) (e produc957004601l_real) (i produc957004601l_real)) (not (forall ((v |u_(-> produc957004601l_real produc957004601l_real)|)) (not (forall ((ii produc957004601l_real)) (= (ho_82 v ii) (ite (= i ii) e (ho_82 u ii)))))))))) (let ((_let_125 (forall ((x |u_(-> produc957004601l_real produc957004601l_real)|) (y |u_(-> produc957004601l_real produc957004601l_real)|)) (or (not (forall ((z produc957004601l_real)) (= (ho_82 x z) (ho_82 y z)))) (= x y))))) (let ((_let_126 (forall ((u |u_(-> set_Pr1948701895od_a_a Bool)|) (e Bool) (i set_Pr1948701895od_a_a)) (not (forall ((v |u_(-> set_Pr1948701895od_a_a Bool)|)) (not (forall ((ii set_Pr1948701895od_a_a)) (= (ho_90 v ii) (ite (= i ii) e (ho_90 u ii)))))))))) (let ((_let_127 (forall ((x |u_(-> set_Pr1948701895od_a_a Bool)|) (y |u_(-> set_Pr1948701895od_a_a Bool)|)) (or (not (forall ((z set_Pr1948701895od_a_a)) (= (ho_90 x z) (ho_90 y z)))) (= x y))))) (let ((_let_128 (forall ((u |u_(-> produc391212143l_real produc391212143l_real produc391212143l_real)|) (e |u_(-> produc391212143l_real produc391212143l_real)|) (i produc391212143l_real)) (not (forall ((v |u_(-> produc391212143l_real produc391212143l_real produc391212143l_real)|)) (not (forall ((ii produc391212143l_real)) (= (ho_75 v ii) (ite (= i ii) e (ho_75 u ii)))))))))) (let ((_let_129 (forall ((x |u_(-> produc391212143l_real produc391212143l_real produc391212143l_real)|) (y |u_(-> produc391212143l_real produc391212143l_real produc391212143l_real)|)) (or (not (forall ((z produc391212143l_real)) (= (ho_75 x z) (ho_75 y z)))) (= x y))))) (let ((_let_130 (forall ((u |u_(-> _u_(-> produc957004601l_real Bool)_ set_Pr147102617l_real)|) (e set_Pr147102617l_real) (i |u_(-> produc957004601l_real Bool)|)) (not (forall ((v |u_(-> _u_(-> produc957004601l_real Bool)_ set_Pr147102617l_real)|)) (not (forall ((ii |u_(-> produc957004601l_real Bool)|)) (= (ho_200 v ii) (ite (= i ii) e (ho_200 u ii)))))))))) (let ((_let_131 (forall ((x |u_(-> _u_(-> produc957004601l_real Bool)_ set_Pr147102617l_real)|) (y |u_(-> _u_(-> produc957004601l_real Bool)_ set_Pr147102617l_real)|)) (or (not (forall ((z |u_(-> produc957004601l_real Bool)|)) (= (ho_200 x z) (ho_200 y z)))) (= x y))))) (let ((_let_132 (forall ((u |u_(-> product_prod_a_a product_prod_a_a product_prod_a_a)|) (e |u_(-> product_prod_a_a product_prod_a_a)|) (i product_prod_a_a)) (not (forall ((v |u_(-> product_prod_a_a product_prod_a_a product_prod_a_a)|)) (not (forall ((ii product_prod_a_a)) (= (ho_69 v ii) (ite (= i ii) e (ho_69 u ii)))))))))) (let ((_let_133 (forall ((x |u_(-> product_prod_a_a product_prod_a_a product_prod_a_a)|) (y |u_(-> product_prod_a_a product_prod_a_a product_prod_a_a)|)) (or (not (forall ((z product_prod_a_a)) (= (ho_69 x z) (ho_69 y z)))) (= x y))))) (let ((_let_134 (forall ((u |u_(-> product_prod_a_a product_prod_a_a)|) (e product_prod_a_a) (i product_prod_a_a)) (not (forall ((v |u_(-> product_prod_a_a product_prod_a_a)|)) (not (forall ((ii product_prod_a_a)) (= (ho_70 v ii) (ite (= i ii) e (ho_70 u ii)))))))))) (let ((_let_135 (forall ((x |u_(-> product_prod_a_a product_prod_a_a)|) (y |u_(-> product_prod_a_a product_prod_a_a)|)) (or (not (forall ((z product_prod_a_a)) (= (ho_70 x z) (ho_70 y z)))) (= x y))))) (let ((_let_136 (forall ((u |u_(-> real produc348734722a_real produc348734722a_real)|) (e |u_(-> produc348734722a_real produc348734722a_real)|) (i real)) (not (forall ((v |u_(-> real produc348734722a_real produc348734722a_real)|)) (not (forall ((ii real)) (= (ho_125 v ii) (ite (= i ii) e (ho_125 u ii)))))))))) (let ((_let_137 (forall ((x |u_(-> real produc348734722a_real produc348734722a_real)|) (y |u_(-> real produc348734722a_real produc348734722a_real)|)) (or (not (forall ((z real)) (= (ho_125 x z) (ho_125 y z)))) (= x y))))) (let ((_let_138 (forall ((u |u_(-> a a product_prod_a_a)|) (e |u_(-> a product_prod_a_a)|) (i a)) (not (forall ((v |u_(-> a a product_prod_a_a)|)) (not (forall ((ii a)) (= (ho_66 v ii) (ite (= i ii) e (ho_66 u ii)))))))))) (let ((_let_139 (forall ((x |u_(-> a a product_prod_a_a)|) (y |u_(-> a a product_prod_a_a)|)) (or (not (forall ((z a)) (= (ho_66 x z) (ho_66 y z)))) (= x y))))) (let ((_let_140 (forall ((u |u_(-> set_a set_a set_a)|) (e |u_(-> set_a set_a)|) (i set_a)) (not (forall ((v |u_(-> set_a set_a set_a)|)) (not (forall ((ii set_a)) (= (ho_107 v ii) (ite (= i ii) e (ho_107 u ii)))))))))) (let ((_let_141 (forall ((x |u_(-> set_a set_a set_a)|) (y |u_(-> set_a set_a set_a)|)) (or (not (forall ((z set_a)) (= (ho_107 x z) (ho_107 y z)))) (= x y))))) (let ((_let_142 (forall ((u |u_(-> real produc348734722a_real)|) (e produc348734722a_real) (i real)) (not (forall ((v |u_(-> real produc348734722a_real)|)) (not (forall ((ii real)) (= (ho_123 v ii) (ite (= i ii) e (ho_123 u ii)))))))))) (let ((_let_143 (forall ((x |u_(-> real produc348734722a_real)|) (y |u_(-> real produc348734722a_real)|)) (or (not (forall ((z real)) (= (ho_123 x z) (ho_123 y z)))) (= x y))))) (let ((_let_144 (forall ((u |u_(-> product_prod_a_a set_Product_prod_a_a Bool)|) (e |u_(-> set_Product_prod_a_a Bool)|) (i product_prod_a_a)) (not (forall ((v |u_(-> product_prod_a_a set_Product_prod_a_a Bool)|)) (not (forall ((ii product_prod_a_a)) (= (ho_14 v ii) (ite (= i ii) e (ho_14 u ii)))))))))) (let ((_let_145 (forall ((x |u_(-> product_prod_a_a set_Product_prod_a_a Bool)|) (y |u_(-> product_prod_a_a set_Product_prod_a_a Bool)|)) (or (not (forall ((z product_prod_a_a)) (= (ho_14 x z) (ho_14 y z)))) (= x y))))) (let ((_let_146 (forall ((u |u_(-> set_a a Bool)|) (e |u_(-> a Bool)|) (i set_a)) (not (forall ((v |u_(-> set_a a Bool)|)) (not (forall ((ii set_a)) (= (ho_47 v ii) (ite (= i ii) e (ho_47 u ii)))))))))) (let ((_let_147 (forall ((x |u_(-> set_a a Bool)|) (y |u_(-> set_a a Bool)|)) (or (not (forall ((z set_a)) (= (ho_47 x z) (ho_47 y z)))) (= x y))))) (let ((_let_148 (forall ((u |u_(-> produc391212143l_real produc391212143l_real)|) (e produc391212143l_real) (i produc391212143l_real)) (not (forall ((v |u_(-> produc391212143l_real produc391212143l_real)|)) (not (forall ((ii produc391212143l_real)) (= (ho_76 v ii) (ite (= i ii) e (ho_76 u ii)))))))))) (let ((_let_149 (forall ((x |u_(-> produc391212143l_real produc391212143l_real)|) (y |u_(-> produc391212143l_real produc391212143l_real)|)) (or (not (forall ((z produc391212143l_real)) (= (ho_76 x z) (ho_76 y z)))) (= x y))))) (let ((_let_150 (forall ((u |u_(-> set_se1596668135od_a_a set_se1596668135od_a_a)|) (e set_se1596668135od_a_a) (i set_se1596668135od_a_a)) (not (forall ((v |u_(-> set_se1596668135od_a_a set_se1596668135od_a_a)|)) (not (forall ((ii set_se1596668135od_a_a)) (= (ho_212 v ii) (ite (= i ii) e (ho_212 u ii)))))))))) (let ((_let_151 (forall ((x |u_(-> set_se1596668135od_a_a set_se1596668135od_a_a)|) (y |u_(-> set_se1596668135od_a_a set_se1596668135od_a_a)|)) (or (not (forall ((z set_se1596668135od_a_a)) (= (ho_212 x z) (ho_212 y z)))) (= x y))))) (let ((_let_152 (forall ((u |u_(-> a product_prod_a_a)|) (e product_prod_a_a) (i a)) (not (forall ((v |u_(-> a product_prod_a_a)|)) (not (forall ((ii a)) (= (ho_67 v ii) (ite (= i ii) e (ho_67 u ii)))))))))) (let ((_let_153 (forall ((x |u_(-> a product_prod_a_a)|) (y |u_(-> a product_prod_a_a)|)) (or (not (forall ((z a)) (= (ho_67 x z) (ho_67 y z)))) (= x y))))) (let ((_let_154 (forall ((u |u_(-> real product_prod_a_real)|) (e product_prod_a_real) (i real)) (not (forall ((v |u_(-> real product_prod_a_real)|)) (not (forall ((ii real)) (= (ho_140 v ii) (ite (= i ii) e (ho_140 u ii)))))))))) (let ((_let_155 (forall ((x |u_(-> real product_prod_a_real)|) (y |u_(-> real product_prod_a_real)|)) (or (not (forall ((z real)) (= (ho_140 x z) (ho_140 y z)))) (= x y))))) (let ((_let_156 (forall ((u |u_(-> set_Pr147102617l_real produc957004601l_real Bool)|) (e |u_(-> produc957004601l_real Bool)|) (i set_Pr147102617l_real)) (not (forall ((v |u_(-> set_Pr147102617l_real produc957004601l_real Bool)|)) (not (forall ((ii set_Pr147102617l_real)) (= (ho_28 v ii) (ite (= i ii) e (ho_28 u ii)))))))))) (let ((_let_157 (forall ((x |u_(-> set_Pr147102617l_real produc957004601l_real Bool)|) (y |u_(-> set_Pr147102617l_real produc957004601l_real Bool)|)) (or (not (forall ((z set_Pr147102617l_real)) (= (ho_28 x z) (ho_28 y z)))) (= x y))))) (let ((_let_158 (forall ((u |u_(-> a a)|) (e a) (i a)) (not (forall ((v |u_(-> a a)|)) (not (forall ((ii a)) (= (ho_34 v ii) (ite (= i ii) e (ho_34 u ii)))))))))) (let ((_let_159 (forall ((x |u_(-> a a)|) (y |u_(-> a a)|)) (or (not (forall ((z a)) (= (ho_34 x z) (ho_34 y z)))) (= x y))))) (let ((_let_160 (forall ((u |u_(-> set_Product_prod_a_a Bool)|) (e Bool) (i set_Product_prod_a_a)) (not (forall ((v |u_(-> set_Product_prod_a_a Bool)|)) (not (forall ((ii set_Product_prod_a_a)) (= (ho_15 v ii) (ite (= i ii) e (ho_15 u ii)))))))))) (let ((_let_161 (forall ((x |u_(-> set_Product_prod_a_a Bool)|) (y |u_(-> set_Product_prod_a_a Bool)|)) (or (not (forall ((z set_Product_prod_a_a)) (= (ho_15 x z) (ho_15 y z)))) (= x y))))) (let ((_let_162 (forall ((u |u_(-> set_a Bool)|) (e Bool) (i set_a)) (not (forall ((v |u_(-> set_a Bool)|)) (not (forall ((ii set_a)) (= (ho_45 v ii) (ite (= i ii) e (ho_45 u ii)))))))))) (let ((_let_163 (forall ((x |u_(-> set_a Bool)|) (y |u_(-> set_a Bool)|)) (or (not (forall ((z set_a)) (= (ho_45 x z) (ho_45 y z)))) (= x y))))) (let ((_let_164 (forall ((u |u_(-> product_prod_a_a product_prod_a_a produc1572603623od_a_a)|) (e |u_(-> product_prod_a_a produc1572603623od_a_a)|) (i product_prod_a_a)) (not (forall ((v |u_(-> product_prod_a_a product_prod_a_a produc1572603623od_a_a)|)) (not (forall ((ii product_prod_a_a)) (= (ho_94 v ii) (ite (= i ii) e (ho_94 u ii)))))))))) (let ((_let_165 (forall ((x |u_(-> product_prod_a_a product_prod_a_a produc1572603623od_a_a)|) (y |u_(-> product_prod_a_a product_prod_a_a produc1572603623od_a_a)|)) (or (not (forall ((z product_prod_a_a)) (= (ho_94 x z) (ho_94 y z)))) (= x y))))) (let ((_let_166 (forall ((u |u_(-> real real real)|) (e |u_(-> real real)|) (i real)) (not (forall ((v |u_(-> real real real)|)) (not (forall ((ii real)) (= (ho_37 v ii) (ite (= i ii) e (ho_37 u ii)))))))))) (let ((_let_167 (forall ((x |u_(-> real real real)|) (y |u_(-> real real real)|)) (or (not (forall ((z real)) (= (ho_37 x z) (ho_37 y z)))) (= x y))))) (let ((_let_168 (forall ((u |u_(-> produc957004601l_real set_Pr147102617l_real Bool)|) (e |u_(-> set_Pr147102617l_real Bool)|) (i produc957004601l_real)) (not (forall ((v |u_(-> produc957004601l_real set_Pr147102617l_real Bool)|)) (not (forall ((ii produc957004601l_real)) (= (ho_25 v ii) (ite (= i ii) e (ho_25 u ii)))))))))) (let ((_let_169 (forall ((x |u_(-> produc957004601l_real set_Pr147102617l_real Bool)|) (y |u_(-> produc957004601l_real set_Pr147102617l_real Bool)|)) (or (not (forall ((z produc957004601l_real)) (= (ho_25 x z) (ho_25 y z)))) (= x y))))) (let ((_let_170 (forall ((u |u_(-> produc1572603623od_a_a produc1572603623od_a_a)|) (e produc1572603623od_a_a) (i produc1572603623od_a_a)) (not (forall ((v |u_(-> produc1572603623od_a_a produc1572603623od_a_a)|)) (not (forall ((ii produc1572603623od_a_a)) (= (ho_198 v ii) (ite (= i ii) e (ho_198 u ii)))))))))) (let ((_let_171 (forall ((x |u_(-> produc1572603623od_a_a produc1572603623od_a_a)|) (y |u_(-> produc1572603623od_a_a produc1572603623od_a_a)|)) (or (not (forall ((z produc1572603623od_a_a)) (= (ho_198 x z) (ho_198 y z)))) (= x y))))) (let ((_let_172 (forall ((u |u_(-> set_real real produc391212143l_real)|) (e |u_(-> real produc391212143l_real)|) (i set_real)) (not (forall ((v |u_(-> set_real real produc391212143l_real)|)) (not (forall ((ii set_real)) (= (ho_72 v ii) (ite (= i ii) e (ho_72 u ii)))))))))) (let ((_let_173 (forall ((x |u_(-> set_real real produc391212143l_real)|) (y |u_(-> set_real real produc391212143l_real)|)) (or (not (forall ((z set_real)) (= (ho_72 x z) (ho_72 y z)))) (= x y))))) (let ((_let_174 (forall ((u |u_(-> a a a)|) (e |u_(-> a a)|) (i a)) (not (forall ((v |u_(-> a a a)|)) (not (forall ((ii a)) (= (ho_33 v ii) (ite (= i ii) e (ho_33 u ii)))))))))) (let ((_let_175 (forall ((x |u_(-> a a a)|) (y |u_(-> a a a)|)) (or (not (forall ((z a)) (= (ho_33 x z) (ho_33 y z)))) (= x y))))) (let ((_let_176 (forall ((u |u_(-> set_Product_prod_a_a product_prod_a_a Bool)|) (e |u_(-> product_prod_a_a Bool)|) (i set_Product_prod_a_a)) (not (forall ((v |u_(-> set_Product_prod_a_a product_prod_a_a Bool)|)) (not (forall ((ii set_Product_prod_a_a)) (= (ho_41 v ii) (ite (= i ii) e (ho_41 u ii)))))))))) (let ((_let_177 (forall ((x |u_(-> set_Product_prod_a_a product_prod_a_a Bool)|) (y |u_(-> set_Product_prod_a_a product_prod_a_a Bool)|)) (or (not (forall ((z set_Product_prod_a_a)) (= (ho_41 x z) (ho_41 y z)))) (= x y))))) (let ((_let_178 (forall ((u |u_(-> real set_real Bool)|) (e |u_(-> set_real Bool)|) (i real)) (not (forall ((v |u_(-> real set_real Bool)|)) (not (forall ((ii real)) (= (ho_50 v ii) (ite (= i ii) e (ho_50 u ii)))))))))) (let ((_let_179 (forall ((x |u_(-> real set_real Bool)|) (y |u_(-> real set_real Bool)|)) (or (not (forall ((z real)) (= (ho_50 x z) (ho_50 y z)))) (= x y))))) (let ((_let_180 (forall ((u |u_(-> real real)|) (e real) (i real)) (not (forall ((v |u_(-> real real)|)) (not (forall ((ii real)) (= (ho_38 v ii) (ite (= i ii) e (ho_38 u ii)))))))))) (let ((_let_181 (forall ((x |u_(-> real real)|) (y |u_(-> real real)|)) (or (not (forall ((z real)) (= (ho_38 x z) (ho_38 y z)))) (= x y))))) (let ((_let_182 (forall ((u |u_(-> produc957004601l_real produc957004601l_real produc957004601l_real)|) (e |u_(-> produc957004601l_real produc957004601l_real)|) (i produc957004601l_real)) (not (forall ((v |u_(-> produc957004601l_real produc957004601l_real produc957004601l_real)|)) (not (forall ((ii produc957004601l_real)) (= (ho_81 v ii) (ite (= i ii) e (ho_81 u ii)))))))))) (let ((_let_183 (forall ((x |u_(-> produc957004601l_real produc957004601l_real produc957004601l_real)|) (y |u_(-> produc957004601l_real produc957004601l_real produc957004601l_real)|)) (or (not (forall ((z produc957004601l_real)) (= (ho_81 x z) (ho_81 y z)))) (= x y))))) (let ((_let_184 (forall ((u |u_(-> real product_prod_a_real product_prod_a_real)|) (e |u_(-> product_prod_a_real product_prod_a_real)|) (i real)) (not (forall ((v |u_(-> real product_prod_a_real product_prod_a_real)|)) (not (forall ((ii real)) (= (ho_147 v ii) (ite (= i ii) e (ho_147 u ii)))))))))) (let ((_let_185 (forall ((x |u_(-> real product_prod_a_real product_prod_a_real)|) (y |u_(-> real product_prod_a_real product_prod_a_real)|)) (or (not (forall ((z real)) (= (ho_147 x z) (ho_147 y z)))) (= x y))))) (let ((_let_186 (forall ((u |u_(-> produc957004601l_real produc957004601l_real Bool)|) (e |u_(-> produc957004601l_real Bool)|) (i produc957004601l_real)) (not (forall ((v |u_(-> produc957004601l_real produc957004601l_real Bool)|)) (not (forall ((ii produc957004601l_real)) (= (ho_79 v ii) (ite (= i ii) e (ho_79 u ii)))))))))) (let ((_let_187 (forall ((x |u_(-> produc957004601l_real produc957004601l_real Bool)|) (y |u_(-> produc957004601l_real produc957004601l_real Bool)|)) (or (not (forall ((z produc957004601l_real)) (= (ho_79 x z) (ho_79 y z)))) (= x y))))) (let ((_let_188 (forall ((u |u_(-> set_real Bool)|) (e Bool) (i set_real)) (not (forall ((v |u_(-> set_real Bool)|)) (not (forall ((ii set_real)) (= (ho_51 v ii) (ite (= i ii) e (ho_51 u ii)))))))))) (let ((_let_189 (forall ((x |u_(-> set_real Bool)|) (y |u_(-> set_real Bool)|)) (or (not (forall ((z set_real)) (= (ho_51 x z) (ho_51 y z)))) (= x y))))) (let ((_let_190 (forall ((u |u_(-> real set_real produc443621487t_real)|) (e |u_(-> set_real produc443621487t_real)|) (i real)) (not (forall ((v |u_(-> real set_real produc443621487t_real)|)) (not (forall ((ii real)) (= (ho_185 v ii) (ite (= i ii) e (ho_185 u ii)))))))))) (let ((_let_191 (forall ((x |u_(-> real set_real produc443621487t_real)|) (y |u_(-> real set_real produc443621487t_real)|)) (or (not (forall ((z real)) (= (ho_185 x z) (ho_185 y z)))) (= x y))))) (let ((_let_192 (forall ((u |u_(-> real real Bool)|) (e |u_(-> real Bool)|) (i real)) (not (forall ((v |u_(-> real real Bool)|)) (not (forall ((ii real)) (= (ho_20 v ii) (ite (= i ii) e (ho_20 u ii)))))))))) (let ((_let_193 (forall ((x |u_(-> real real Bool)|) (y |u_(-> real real Bool)|)) (or (not (forall ((z real)) (= (ho_20 x z) (ho_20 y z)))) (= x y))))) (let ((_let_194 (forall ((u |u_(-> a produc1016684094_a_a_a)|) (e produc1016684094_a_a_a) (i a)) (not (forall ((v |u_(-> a produc1016684094_a_a_a)|)) (not (forall ((ii a)) (= (ho_168 v ii) (ite (= i ii) e (ho_168 u ii)))))))))) (let ((_let_195 (forall ((x |u_(-> a produc1016684094_a_a_a)|) (y |u_(-> a produc1016684094_a_a_a)|)) (or (not (forall ((z a)) (= (ho_168 x z) (ho_168 y z)))) (= x y))))) (let ((_let_196 (forall ((u |u_(-> set_Pr147102617l_real set_Pr147102617l_real set_Pr147102617l_real)|) (e |u_(-> set_Pr147102617l_real set_Pr147102617l_real)|) (i set_Pr147102617l_real)) (not (forall ((v |u_(-> set_Pr147102617l_real set_Pr147102617l_real set_Pr147102617l_real)|)) (not (forall ((ii set_Pr147102617l_real)) (= (ho_87 v ii) (ite (= i ii) e (ho_87 u ii)))))))))) (let ((_let_197 (forall ((x |u_(-> set_Pr147102617l_real set_Pr147102617l_real set_Pr147102617l_real)|) (y |u_(-> set_Pr147102617l_real set_Pr147102617l_real set_Pr147102617l_real)|)) (or (not (forall ((z set_Pr147102617l_real)) (= (ho_87 x z) (ho_87 y z)))) (= x y))))) (let ((_let_198 (forall ((u |u_(-> real produc391212143l_real)|) (e produc391212143l_real) (i real)) (not (forall ((v |u_(-> real produc391212143l_real)|)) (not (forall ((ii real)) (= (ho_73 v ii) (ite (= i ii) e (ho_73 u ii)))))))))) (let ((_let_199 (forall ((x |u_(-> real produc391212143l_real)|) (y |u_(-> real produc391212143l_real)|)) (or (not (forall ((z real)) (= (ho_73 x z) (ho_73 y z)))) (= x y))))) (let ((_let_200 (forall ((u |u_(-> produc1923333543_set_a produc1923333543_set_a produc1923333543_set_a)|) (e |u_(-> produc1923333543_set_a produc1923333543_set_a)|) (i produc1923333543_set_a)) (not (forall ((v |u_(-> produc1923333543_set_a produc1923333543_set_a produc1923333543_set_a)|)) (not (forall ((ii produc1923333543_set_a)) (= (ho_119 v ii) (ite (= i ii) e (ho_119 u ii)))))))))) (let ((_let_201 (forall ((x |u_(-> produc1923333543_set_a produc1923333543_set_a produc1923333543_set_a)|) (y |u_(-> produc1923333543_set_a produc1923333543_set_a produc1923333543_set_a)|)) (or (not (forall ((z produc1923333543_set_a)) (= (ho_119 x z) (ho_119 y z)))) (= x y))))) (let ((_let_202 (forall ((u |u_(-> real Bool)|) (e Bool) (i real)) (not (forall ((v |u_(-> real Bool)|)) (not (forall ((ii real)) (= (ho_21 v ii) (ite (= i ii) e (ho_21 u ii)))))))))) (let ((_let_203 (forall ((x |u_(-> real Bool)|) (y |u_(-> real Bool)|)) (or (not (forall ((z real)) (= (ho_21 x z) (ho_21 y z)))) (= x y))))) (let ((_let_204 (forall ((u |u_(-> set_Product_prod_a_a set_Product_prod_a_a Bool)|) (e |u_(-> set_Product_prod_a_a Bool)|) (i set_Product_prod_a_a)) (not (forall ((v |u_(-> set_Product_prod_a_a set_Product_prod_a_a Bool)|)) (not (forall ((ii set_Product_prod_a_a)) (= (ho_17 v ii) (ite (= i ii) e (ho_17 u ii)))))))))) (let ((_let_205 (forall ((x |u_(-> set_Product_prod_a_a set_Product_prod_a_a Bool)|) (y |u_(-> set_Product_prod_a_a set_Product_prod_a_a Bool)|)) (or (not (forall ((z set_Product_prod_a_a)) (= (ho_17 x z) (ho_17 y z)))) (= x y))))) (let ((_let_206 (forall ((u |u_(-> set_real set_real)|) (e set_real) (i set_real)) (not (forall ((v |u_(-> set_real set_real)|)) (not (forall ((ii set_real)) (= (ho_56 v ii) (ite (= i ii) e (ho_56 u ii)))))))))) (let ((_let_207 (forall ((x |u_(-> set_real set_real)|) (y |u_(-> set_real set_real)|)) (or (not (forall ((z set_real)) (= (ho_56 x z) (ho_56 y z)))) (= x y))))) (let ((_let_208 (forall ((u |u_(-> set_real set_real set_real)|) (e |u_(-> set_real set_real)|) (i set_real)) (not (forall ((v |u_(-> set_real set_real set_real)|)) (not (forall ((ii set_real)) (= (ho_55 v ii) (ite (= i ii) e (ho_55 u ii)))))))))) (let ((_let_209 (forall ((x |u_(-> set_real set_real set_real)|) (y |u_(-> set_real set_real set_real)|)) (or (not (forall ((z set_real)) (= (ho_55 x z) (ho_55 y z)))) (= x y))))) (let ((_let_210 (forall ((u |u_(-> set_Pr1928503567a_real Bool)|) (e Bool) (i set_Pr1928503567a_real)) (not (forall ((v |u_(-> set_Pr1928503567a_real Bool)|)) (not (forall ((ii set_Pr1928503567a_real)) (= (ho_206 v ii) (ite (= i ii) e (ho_206 u ii)))))))))) (let ((_let_211 (forall ((x |u_(-> set_Pr1928503567a_real Bool)|) (y |u_(-> set_Pr1928503567a_real Bool)|)) (or (not (forall ((z set_Pr1928503567a_real)) (= (ho_206 x z) (ho_206 y z)))) (= x y))))) (let ((_let_212 (forall ((u |u_(-> product_prod_a_a Bool)|) (e Bool) (i product_prod_a_a)) (not (forall ((v |u_(-> product_prod_a_a Bool)|)) (not (forall ((ii product_prod_a_a)) (= (ho_42 v ii) (ite (= i ii) e (ho_42 u ii)))))))))) (let ((_let_213 (forall ((x |u_(-> product_prod_a_a Bool)|) (y |u_(-> product_prod_a_a Bool)|)) (or (not (forall ((z product_prod_a_a)) (= (ho_42 x z) (ho_42 y z)))) (= x y))))) (let ((_let_214 (forall ((u |u_(-> produc1232925073real_a produc1232925073real_a produc1232925073real_a)|) (e |u_(-> produc1232925073real_a produc1232925073real_a)|) (i produc1232925073real_a)) (not (forall ((v |u_(-> produc1232925073real_a produc1232925073real_a produc1232925073real_a)|)) (not (forall ((ii produc1232925073real_a)) (= (ho_61 v ii) (ite (= i ii) e (ho_61 u ii)))))))))) (let ((_let_215 (forall ((x |u_(-> produc1232925073real_a produc1232925073real_a produc1232925073real_a)|) (y |u_(-> produc1232925073real_a produc1232925073real_a produc1232925073real_a)|)) (or (not (forall ((z produc1232925073real_a)) (= (ho_61 x z) (ho_61 y z)))) (= x y))))) (let ((_let_216 (forall ((u |u_(-> a set_a Bool)|) (e |u_(-> set_a Bool)|) (i a)) (not (forall ((v |u_(-> a set_a Bool)|)) (not (forall ((ii a)) (= (ho_44 v ii) (ite (= i ii) e (ho_44 u ii)))))))))) (let ((_let_217 (forall ((x |u_(-> a set_a Bool)|) (y |u_(-> a set_a Bool)|)) (or (not (forall ((z a)) (= (ho_44 x z) (ho_44 y z)))) (= x y))))) (let ((_let_218 (forall ((u |u_(-> a Bool)|) (e Bool) (i a)) (not (forall ((v |u_(-> a Bool)|)) (not (forall ((ii a)) (= (ho_48 v ii) (ite (= i ii) e (ho_48 u ii)))))))))) (let ((_let_219 (forall ((x |u_(-> a Bool)|) (y |u_(-> a Bool)|)) (or (not (forall ((z a)) (= (ho_48 x z) (ho_48 y z)))) (= x y))))) (let ((_let_220 (forall ((u |u_(-> product_prod_a_set_a product_prod_a_set_a product_prod_a_set_a)|) (e |u_(-> product_prod_a_set_a product_prod_a_set_a)|) (i product_prod_a_set_a)) (not (forall ((v |u_(-> product_prod_a_set_a product_prod_a_set_a product_prod_a_set_a)|)) (not (forall ((ii product_prod_a_set_a)) (= (ho_113 v ii) (ite (= i ii) e (ho_113 u ii)))))))))) (let ((_let_221 (forall ((x |u_(-> product_prod_a_set_a product_prod_a_set_a product_prod_a_set_a)|) (y |u_(-> product_prod_a_set_a product_prod_a_set_a product_prod_a_set_a)|)) (or (not (forall ((z product_prod_a_set_a)) (= (ho_113 x z) (ho_113 y z)))) (= x y))))) (let ((_let_222 (forall ((u |u_(-> set_real real Bool)|) (e |u_(-> real Bool)|) (i set_real)) (not (forall ((v |u_(-> set_real real Bool)|)) (not (forall ((ii set_real)) (= (ho_53 v ii) (ite (= i ii) e (ho_53 u ii)))))))))) (let ((_let_223 (forall ((x |u_(-> set_real real Bool)|) (y |u_(-> set_real real Bool)|)) (or (not (forall ((z set_real)) (= (ho_53 x z) (ho_53 y z)))) (= x y))))) (let ((_let_224 (forall ((u |u_(-> produc957004601l_real Bool)|) (e Bool) (i produc957004601l_real)) (not (forall ((v |u_(-> produc957004601l_real Bool)|)) (not (forall ((ii produc957004601l_real)) (= (ho_29 v ii) (ite (= i ii) e (ho_29 u ii)))))))))) (let ((_let_225 (forall ((x |u_(-> produc957004601l_real Bool)|) (y |u_(-> produc957004601l_real Bool)|)) (or (not (forall ((z produc957004601l_real)) (= (ho_29 x z) (ho_29 y z)))) (= x y))))) (let ((_let_226 (forall ((u |u_(-> a produc1232925073real_a)|) (e produc1232925073real_a) (i a)) (not (forall ((v |u_(-> a produc1232925073real_a)|)) (not (forall ((ii a)) (= (ho_59 v ii) (ite (= i ii) e (ho_59 u ii)))))))))) (let ((_let_227 (forall ((x |u_(-> a produc1232925073real_a)|) (y |u_(-> a produc1232925073real_a)|)) (or (not (forall ((z a)) (= (ho_59 x z) (ho_59 y z)))) (= x y))))) (let ((_let_228 (forall ((u |u_(-> set_Pr147102617l_real Bool)|) (e Bool) (i set_Pr147102617l_real)) (not (forall ((v |u_(-> set_Pr147102617l_real Bool)|)) (not (forall ((ii set_Pr147102617l_real)) (= (ho_26 v ii) (ite (= i ii) e (ho_26 u ii)))))))))) (let ((_let_229 (forall ((x |u_(-> set_Pr147102617l_real Bool)|) (y |u_(-> set_Pr147102617l_real Bool)|)) (or (not (forall ((z set_Pr147102617l_real)) (= (ho_26 x z) (ho_26 y z)))) (= x y))))) (let ((_let_230 (forall ((u |u_(-> set_real a produc1232925073real_a)|) (e |u_(-> a produc1232925073real_a)|) (i set_real)) (not (forall ((v |u_(-> set_real a produc1232925073real_a)|)) (not (forall ((ii set_real)) (= (ho_58 v ii) (ite (= i ii) e (ho_58 u ii)))))))))) (let ((_let_231 (forall ((x |u_(-> set_real a produc1232925073real_a)|) (y |u_(-> set_real a produc1232925073real_a)|)) (or (not (forall ((z set_real)) (= (ho_58 x z) (ho_58 y z)))) (= x y))))) (let ((_let_232 (forall ((u |u_(-> produc1232925073real_a produc1232925073real_a)|) (e produc1232925073real_a) (i produc1232925073real_a)) (not (forall ((v |u_(-> produc1232925073real_a produc1232925073real_a)|)) (not (forall ((ii produc1232925073real_a)) (= (ho_62 v ii) (ite (= i ii) e (ho_62 u ii)))))))))) (let ((_let_233 (forall ((x |u_(-> produc1232925073real_a produc1232925073real_a)|) (y |u_(-> produc1232925073real_a produc1232925073real_a)|)) (or (not (forall ((z produc1232925073real_a)) (= (ho_62 x z) (ho_62 y z)))) (= x y))))) (let ((_let_234 (forall ((u |u_(-> real a a)|) (e |u_(-> a a)|) (i real)) (not (forall ((v |u_(-> real a a)|)) (not (forall ((ii real)) (= (ho_64 v ii) (ite (= i ii) e (ho_64 u ii)))))))))) (let ((_let_235 (forall ((x |u_(-> real a a)|) (y |u_(-> real a a)|)) (or (not (forall ((z real)) (= (ho_64 x z) (ho_64 y z)))) (= x y))))) (let ((_let_236 (forall ((u |u_(-> set_a produc1923333543_set_a)|) (e produc1923333543_set_a) (i set_a)) (not (forall ((v |u_(-> set_a produc1923333543_set_a)|)) (not (forall ((ii set_a)) (= (ho_117 v ii) (ite (= i ii) e (ho_117 u ii)))))))))) (let ((_let_237 (forall ((x |u_(-> set_a produc1923333543_set_a)|) (y |u_(-> set_a produc1923333543_set_a)|)) (or (not (forall ((z set_a)) (= (ho_117 x z) (ho_117 y z)))) (= x y))))) (let ((_let_238 (forall ((u |u_(-> real produc1921647824od_a_a produc1921647824od_a_a)|) (e |u_(-> produc1921647824od_a_a produc1921647824od_a_a)|) (i real)) (not (forall ((v |u_(-> real produc1921647824od_a_a produc1921647824od_a_a)|)) (not (forall ((ii real)) (= (ho_176 v ii) (ite (= i ii) e (ho_176 u ii)))))))))) (let ((_let_239 (forall ((x |u_(-> real produc1921647824od_a_a produc1921647824od_a_a)|) (y |u_(-> real produc1921647824od_a_a produc1921647824od_a_a)|)) (or (not (forall ((z real)) (= (ho_176 x z) (ho_176 y z)))) (= x y))))) (let ((_let_240 (forall ((u |u_(-> real set_a produc1923333543_set_a)|) (e |u_(-> set_a produc1923333543_set_a)|) (i real)) (not (forall ((v |u_(-> real set_a produc1923333543_set_a)|)) (not (forall ((ii real)) (= (ho_116 v ii) (ite (= i ii) e (ho_116 u ii)))))))))) (let ((_let_241 (forall ((x |u_(-> real set_a produc1923333543_set_a)|) (y |u_(-> real set_a produc1923333543_set_a)|)) (or (not (forall ((z real)) (= (ho_116 x z) (ho_116 y z)))) (= x y))))) (let ((_let_242 (forall ((u |u_(-> produc1923333543_set_a produc1923333543_set_a)|) (e produc1923333543_set_a) (i produc1923333543_set_a)) (not (forall ((v |u_(-> produc1923333543_set_a produc1923333543_set_a)|)) (not (forall ((ii produc1923333543_set_a)) (= (ho_120 v ii) (ite (= i ii) e (ho_120 u ii)))))))))) (let ((_let_243 (forall ((x |u_(-> produc1923333543_set_a produc1923333543_set_a)|) (y |u_(-> produc1923333543_set_a produc1923333543_set_a)|)) (or (not (forall ((z produc1923333543_set_a)) (= (ho_120 x z) (ho_120 y z)))) (= x y))))) (let ((_let_244 (forall ((u |u_(-> product_prod_a_a real produc348734722a_real)|) (e |u_(-> real produc348734722a_real)|) (i product_prod_a_a)) (not (forall ((v |u_(-> product_prod_a_a real produc348734722a_real)|)) (not (forall ((ii product_prod_a_a)) (= (ho_122 v ii) (ite (= i ii) e (ho_122 u ii)))))))))) (let ((_let_245 (forall ((x |u_(-> product_prod_a_a real produc348734722a_real)|) (y |u_(-> product_prod_a_a real produc348734722a_real)|)) (or (not (forall ((z product_prod_a_a)) (= (ho_122 x z) (ho_122 y z)))) (= x y))))) (let ((_let_246 (forall ((u |u_(-> produc348734722a_real produc348734722a_real)|) (e produc348734722a_real) (i produc348734722a_real)) (not (forall ((v |u_(-> produc348734722a_real produc348734722a_real)|)) (not (forall ((ii produc348734722a_real)) (= (ho_126 v ii) (ite (= i ii) e (ho_126 u ii)))))))))) (let ((_let_247 (forall ((x |u_(-> produc348734722a_real produc348734722a_real)|) (y |u_(-> produc348734722a_real produc348734722a_real)|)) (or (not (forall ((z produc348734722a_real)) (= (ho_126 x z) (ho_126 y z)))) (= x y))))) (let ((_let_248 (forall ((u |u_(-> a product_prod_real_a)|) (e product_prod_real_a) (i a)) (not (forall ((v |u_(-> a product_prod_real_a)|)) (not (forall ((ii a)) (= (ho_129 v ii) (ite (= i ii) e (ho_129 u ii)))))))))) (let ((_let_249 (forall ((x |u_(-> a product_prod_real_a)|) (y |u_(-> a product_prod_real_a)|)) (or (not (forall ((z a)) (= (ho_129 x z) (ho_129 y z)))) (= x y))))) (let ((_let_250 (forall ((u |u_(-> real a product_prod_real_a)|) (e |u_(-> a product_prod_real_a)|) (i real)) (not (forall ((v |u_(-> real a product_prod_real_a)|)) (not (forall ((ii real)) (= (ho_128 v ii) (ite (= i ii) e (ho_128 u ii)))))))))) (let ((_let_251 (forall ((x |u_(-> real a product_prod_real_a)|) (y |u_(-> real a product_prod_real_a)|)) (or (not (forall ((z real)) (= (ho_128 x z) (ho_128 y z)))) (= x y))))) (let ((_let_252 (forall ((u |u_(-> set_set_a set_set_a)|) (e set_set_a) (i set_set_a)) (not (forall ((v |u_(-> set_set_a set_set_a)|)) (not (forall ((ii set_set_a)) (= (ho_158 v ii) (ite (= i ii) e (ho_158 u ii)))))))))) (let ((_let_253 (forall ((x |u_(-> set_set_a set_set_a)|) (y |u_(-> set_set_a set_set_a)|)) (or (not (forall ((z set_set_a)) (= (ho_158 x z) (ho_158 y z)))) (= x y))))) (let ((_let_254 (forall ((u |u_(-> product_prod_a_a produc2096821232od_a_a)|) (e produc2096821232od_a_a) (i product_prod_a_a)) (not (forall ((v |u_(-> product_prod_a_a produc2096821232od_a_a)|)) (not (forall ((ii product_prod_a_a)) (= (ho_132 v ii) (ite (= i ii) e (ho_132 u ii)))))))))) (let ((_let_255 (forall ((x |u_(-> product_prod_a_a produc2096821232od_a_a)|) (y |u_(-> product_prod_a_a produc2096821232od_a_a)|)) (or (not (forall ((z product_prod_a_a)) (= (ho_132 x z) (ho_132 y z)))) (= x y))))) (let ((_let_256 (forall ((u |u_(-> _u_(-> product_prod_a_a Bool)_ set_Product_prod_a_a)|) (e set_Product_prod_a_a) (i |u_(-> product_prod_a_a Bool)|)) (not (forall ((v |u_(-> _u_(-> product_prod_a_a Bool)_ set_Product_prod_a_a)|)) (not (forall ((ii |u_(-> product_prod_a_a Bool)|)) (= (ho_165 v ii) (ite (= i ii) e (ho_165 u ii)))))))))) (let ((_let_257 (forall ((x |u_(-> _u_(-> product_prod_a_a Bool)_ set_Product_prod_a_a)|) (y |u_(-> _u_(-> product_prod_a_a Bool)_ set_Product_prod_a_a)|)) (or (not (forall ((z |u_(-> product_prod_a_a Bool)|)) (= (ho_165 x z) (ho_165 y z)))) (= x y))))) (let ((_let_258 (forall ((u |u_(-> real product_prod_a_a produc2096821232od_a_a)|) (e |u_(-> product_prod_a_a produc2096821232od_a_a)|) (i real)) (not (forall ((v |u_(-> real product_prod_a_a produc2096821232od_a_a)|)) (not (forall ((ii real)) (= (ho_131 v ii) (ite (= i ii) e (ho_131 u ii)))))))))) (let ((_let_259 (forall ((x |u_(-> real product_prod_a_a produc2096821232od_a_a)|) (y |u_(-> real product_prod_a_a produc2096821232od_a_a)|)) (or (not (forall ((z real)) (= (ho_131 x z) (ho_131 y z)))) (= x y))))) (let ((_let_260 (forall ((u |u_(-> produc443621487t_real produc443621487t_real)|) (e produc443621487t_real) (i produc443621487t_real)) (not (forall ((v |u_(-> produc443621487t_real produc443621487t_real)|)) (not (forall ((ii produc443621487t_real)) (= (ho_189 v ii) (ite (= i ii) e (ho_189 u ii)))))))))) (let ((_let_261 (forall ((x |u_(-> produc443621487t_real produc443621487t_real)|) (y |u_(-> produc443621487t_real produc443621487t_real)|)) (or (not (forall ((z produc443621487t_real)) (= (ho_189 x z) (ho_189 y z)))) (= x y))))) (let ((_let_262 (forall ((u |u_(-> real produc2096821232od_a_a produc2096821232od_a_a)|) (e |u_(-> produc2096821232od_a_a produc2096821232od_a_a)|) (i real)) (not (forall ((v |u_(-> real produc2096821232od_a_a produc2096821232od_a_a)|)) (not (forall ((ii real)) (= (ho_134 v ii) (ite (= i ii) e (ho_134 u ii)))))))))) (let ((_let_263 (forall ((x |u_(-> real produc2096821232od_a_a produc2096821232od_a_a)|) (y |u_(-> real produc2096821232od_a_a produc2096821232od_a_a)|)) (or (not (forall ((z real)) (= (ho_134 x z) (ho_134 y z)))) (= x y))))) (let ((_let_264 (forall ((u |u_(-> _u_(-> a Bool)_ set_a)|) (e set_a) (i |u_(-> a Bool)|)) (not (forall ((v |u_(-> _u_(-> a Bool)_ set_a)|)) (not (forall ((ii |u_(-> a Bool)|)) (= (ho_137 v ii) (ite (= i ii) e (ho_137 u ii)))))))))) (let ((_let_265 (forall ((x |u_(-> _u_(-> a Bool)_ set_a)|) (y |u_(-> _u_(-> a Bool)_ set_a)|)) (or (not (forall ((z |u_(-> a Bool)|)) (= (ho_137 x z) (ho_137 y z)))) (= x y))))) (let ((_let_266 (forall ((u |u_(-> a real product_prod_a_real)|) (e |u_(-> real product_prod_a_real)|) (i a)) (not (forall ((v |u_(-> a real product_prod_a_real)|)) (not (forall ((ii a)) (= (ho_139 v ii) (ite (= i ii) e (ho_139 u ii)))))))))) (let ((_let_267 (forall ((x |u_(-> a real product_prod_a_real)|) (y |u_(-> a real product_prod_a_real)|)) (or (not (forall ((z a)) (= (ho_139 x z) (ho_139 y z)))) (= x y))))) (let ((_let_268 (forall ((u |u_(-> product_prod_a_real product_prod_a_real)|) (e product_prod_a_real) (i product_prod_a_real)) (not (forall ((v |u_(-> product_prod_a_real product_prod_a_real)|)) (not (forall ((ii product_prod_a_real)) (= (ho_143 v ii) (ite (= i ii) e (ho_143 u ii)))))))))) (let ((_let_269 (forall ((x |u_(-> product_prod_a_real product_prod_a_real)|) (y |u_(-> product_prod_a_real product_prod_a_real)|)) (or (not (forall ((z product_prod_a_real)) (= (ho_143 x z) (ho_143 y z)))) (= x y))))) (let ((_let_270 (forall ((u |u_(-> product_prod_a_real product_prod_a_real product_prod_a_real)|) (e |u_(-> product_prod_a_real product_prod_a_real)|) (i product_prod_a_real)) (not (forall ((v |u_(-> product_prod_a_real product_prod_a_real product_prod_a_real)|)) (not (forall ((ii product_prod_a_real)) (= (ho_142 v ii) (ite (= i ii) e (ho_142 u ii)))))))))) (let ((_let_271 (forall ((x |u_(-> product_prod_a_real product_prod_a_real product_prod_a_real)|) (y |u_(-> product_prod_a_real product_prod_a_real product_prod_a_real)|)) (or (not (forall ((z product_prod_a_real)) (= (ho_142 x z) (ho_142 y z)))) (= x y))))) (let ((_let_272 (forall ((u |u_(-> set_Pr1741234931a_real Bool)|) (e Bool) (i set_Pr1741234931a_real)) (not (forall ((v |u_(-> set_Pr1741234931a_real Bool)|)) (not (forall ((ii set_Pr1741234931a_real)) (= (ho_145 v ii) (ite (= i ii) e (ho_145 u ii)))))))))) (let ((_let_273 (forall ((x |u_(-> set_Pr1741234931a_real Bool)|) (y |u_(-> set_Pr1741234931a_real Bool)|)) (or (not (forall ((z set_Pr1741234931a_real)) (= (ho_145 x z) (ho_145 y z)))) (= x y))))) (let ((_let_274 (forall ((u |u_(-> product_prod_a_real produc1826081171a_real)|) (e produc1826081171a_real) (i product_prod_a_real)) (not (forall ((v |u_(-> product_prod_a_real produc1826081171a_real)|)) (not (forall ((ii product_prod_a_real)) (= (ho_150 v ii) (ite (= i ii) e (ho_150 u ii)))))))))) (let ((_let_275 (forall ((x |u_(-> product_prod_a_real produc1826081171a_real)|) (y |u_(-> product_prod_a_real produc1826081171a_real)|)) (or (not (forall ((z product_prod_a_real)) (= (ho_150 x z) (ho_150 y z)))) (= x y))))) (let ((_let_276 (forall ((u |u_(-> product_prod_a_real product_prod_a_real produc1826081171a_real)|) (e |u_(-> product_prod_a_real produc1826081171a_real)|) (i product_prod_a_real)) (not (forall ((v |u_(-> product_prod_a_real product_prod_a_real produc1826081171a_real)|)) (not (forall ((ii product_prod_a_real)) (= (ho_149 v ii) (ite (= i ii) e (ho_149 u ii)))))))))) (let ((_let_277 (forall ((x |u_(-> product_prod_a_real product_prod_a_real produc1826081171a_real)|) (y |u_(-> product_prod_a_real product_prod_a_real produc1826081171a_real)|)) (or (not (forall ((z product_prod_a_real)) (= (ho_149 x z) (ho_149 y z)))) (= x y))))) (let ((_let_278 (forall ((u |u_(-> produc1826081171a_real set_Pr1741234931a_real Bool)|) (e |u_(-> set_Pr1741234931a_real Bool)|) (i produc1826081171a_real)) (not (forall ((v |u_(-> produc1826081171a_real set_Pr1741234931a_real Bool)|)) (not (forall ((ii produc1826081171a_real)) (= (ho_152 v ii) (ite (= i ii) e (ho_152 u ii)))))))))) (let ((_let_279 (forall ((x |u_(-> produc1826081171a_real set_Pr1741234931a_real Bool)|) (y |u_(-> produc1826081171a_real set_Pr1741234931a_real Bool)|)) (or (not (forall ((z produc1826081171a_real)) (= (ho_152 x z) (ho_152 y z)))) (= x y))))) (let ((_let_280 (forall ((u |u_(-> product_prod_real_a product_prod_real_a)|) (e product_prod_real_a) (i product_prod_real_a)) (not (forall ((v |u_(-> product_prod_real_a product_prod_real_a)|)) (not (forall ((ii product_prod_real_a)) (= (ho_155 v ii) (ite (= i ii) e (ho_155 u ii)))))))))) (let ((_let_281 (forall ((x |u_(-> product_prod_real_a product_prod_real_a)|) (y |u_(-> product_prod_real_a product_prod_real_a)|)) (or (not (forall ((z product_prod_real_a)) (= (ho_155 x z) (ho_155 y z)))) (= x y))))) (let ((_let_282 (forall ((u |u_(-> product_prod_real_a product_prod_real_a product_prod_real_a)|) (e |u_(-> product_prod_real_a product_prod_real_a)|) (i product_prod_real_a)) (not (forall ((v |u_(-> product_prod_real_a product_prod_real_a product_prod_real_a)|)) (not (forall ((ii product_prod_real_a)) (= (ho_154 v ii) (ite (= i ii) e (ho_154 u ii)))))))))) (let ((_let_283 (forall ((x |u_(-> product_prod_real_a product_prod_real_a product_prod_real_a)|) (y |u_(-> product_prod_real_a product_prod_real_a product_prod_real_a)|)) (or (not (forall ((z product_prod_real_a)) (= (ho_154 x z) (ho_154 y z)))) (= x y))))) (let ((_let_284 (forall ((u |u_(-> set_set_a set_set_a set_set_a)|) (e |u_(-> set_set_a set_set_a)|) (i set_set_a)) (not (forall ((v |u_(-> set_set_a set_set_a set_set_a)|)) (not (forall ((ii set_set_a)) (= (ho_157 v ii) (ite (= i ii) e (ho_157 u ii)))))))))) (let ((_let_285 (forall ((x |u_(-> set_set_a set_set_a set_set_a)|) (y |u_(-> set_set_a set_set_a set_set_a)|)) (or (not (forall ((z set_set_a)) (= (ho_157 x z) (ho_157 y z)))) (= x y))))) (let ((_let_286 (forall ((u |u_(-> set_set_a Bool)|) (e Bool) (i set_set_a)) (not (forall ((v |u_(-> set_set_a Bool)|)) (not (forall ((ii set_set_a)) (= (ho_161 v ii) (ite (= i ii) e (ho_161 u ii)))))))))) (let ((_let_287 (forall ((x |u_(-> set_set_a Bool)|) (y |u_(-> set_set_a Bool)|)) (or (not (forall ((z set_set_a)) (= (ho_161 x z) (ho_161 y z)))) (= x y))))) (let ((_let_288 (forall ((u |u_(-> set_real set_real Bool)|) (e |u_(-> set_real Bool)|) (i set_real)) (not (forall ((v |u_(-> set_real set_real Bool)|)) (not (forall ((ii set_real)) (= (ho_163 v ii) (ite (= i ii) e (ho_163 u ii)))))))))) (let ((_let_289 (forall ((x |u_(-> set_real set_real Bool)|) (y |u_(-> set_real set_real Bool)|)) (or (not (forall ((z set_real)) (= (ho_163 x z) (ho_163 y z)))) (= x y))))) (let ((_let_290 (forall ((u |u_(-> product_prod_a_a a produc1016684094_a_a_a)|) (e |u_(-> a produc1016684094_a_a_a)|) (i product_prod_a_a)) (not (forall ((v |u_(-> product_prod_a_a a produc1016684094_a_a_a)|)) (not (forall ((ii product_prod_a_a)) (= (ho_167 v ii) (ite (= i ii) e (ho_167 u ii)))))))))) (let ((_let_291 (forall ((x |u_(-> product_prod_a_a a produc1016684094_a_a_a)|) (y |u_(-> product_prod_a_a a produc1016684094_a_a_a)|)) (or (not (forall ((z product_prod_a_a)) (= (ho_167 x z) (ho_167 y z)))) (= x y))))) (let ((_let_292 (forall ((u |u_(-> produc1016684094_a_a_a produc1016684094_a_a_a)|) (e produc1016684094_a_a_a) (i produc1016684094_a_a_a)) (not (forall ((v |u_(-> produc1016684094_a_a_a produc1016684094_a_a_a)|)) (not (forall ((ii produc1016684094_a_a_a)) (= (ho_171 v ii) (ite (= i ii) e (ho_171 u ii)))))))))) (let ((_let_293 (forall ((x |u_(-> produc1016684094_a_a_a produc1016684094_a_a_a)|) (y |u_(-> produc1016684094_a_a_a produc1016684094_a_a_a)|)) (or (not (forall ((z produc1016684094_a_a_a)) (= (ho_171 x z) (ho_171 y z)))) (= x y))))) (let ((_let_294 (forall ((u |u_(-> real produc1016684094_a_a_a produc1016684094_a_a_a)|) (e |u_(-> produc1016684094_a_a_a produc1016684094_a_a_a)|) (i real)) (not (forall ((v |u_(-> real produc1016684094_a_a_a produc1016684094_a_a_a)|)) (not (forall ((ii real)) (= (ho_170 v ii) (ite (= i ii) e (ho_170 u ii)))))))))) (let ((_let_295 (forall ((x |u_(-> real produc1016684094_a_a_a produc1016684094_a_a_a)|) (y |u_(-> real produc1016684094_a_a_a produc1016684094_a_a_a)|)) (or (not (forall ((z real)) (= (ho_170 x z) (ho_170 y z)))) (= x y))))) (let ((_let_296 (forall ((u |u_(-> produc1921647824od_a_a produc1921647824od_a_a)|) (e produc1921647824od_a_a) (i produc1921647824od_a_a)) (not (forall ((v |u_(-> produc1921647824od_a_a produc1921647824od_a_a)|)) (not (forall ((ii produc1921647824od_a_a)) (= (ho_177 v ii) (ite (= i ii) e (ho_177 u ii)))))))))) (let ((_let_297 (forall ((x |u_(-> produc1921647824od_a_a produc1921647824od_a_a)|) (y |u_(-> produc1921647824od_a_a produc1921647824od_a_a)|)) (or (not (forall ((z produc1921647824od_a_a)) (= (ho_177 x z) (ho_177 y z)))) (= x y))))) (let ((_let_298 (forall ((u |u_(-> set_real set_set_real Bool)|) (e |u_(-> set_set_real Bool)|) (i set_real)) (not (forall ((v |u_(-> set_real set_set_real Bool)|)) (not (forall ((ii set_real)) (= (ho_182 v ii) (ite (= i ii) e (ho_182 u ii)))))))))) (let ((_let_299 (forall ((x |u_(-> set_real set_set_real Bool)|) (y |u_(-> set_real set_set_real Bool)|)) (or (not (forall ((z set_real)) (= (ho_182 x z) (ho_182 y z)))) (= x y))))) (let ((_let_300 (forall ((u |u_(-> set_Pr1928503567a_real set_Pr1928503567a_real)|) (e set_Pr1928503567a_real) (i set_Pr1928503567a_real)) (not (forall ((v |u_(-> set_Pr1928503567a_real set_Pr1928503567a_real)|)) (not (forall ((ii set_Pr1928503567a_real)) (= (ho_203 v ii) (ite (= i ii) e (ho_203 u ii)))))))))) (let ((_let_301 (forall ((x |u_(-> set_Pr1928503567a_real set_Pr1928503567a_real)|) (y |u_(-> set_Pr1928503567a_real set_Pr1928503567a_real)|)) (or (not (forall ((z set_Pr1928503567a_real)) (= (ho_203 x z) (ho_203 y z)))) (= x y))))) (let ((_let_302 (forall ((u |u_(-> set_set_real set_set_real)|) (e set_set_real) (i set_set_real)) (not (forall ((v |u_(-> set_set_real set_set_real)|)) (not (forall ((ii set_set_real)) (= (ho_180 v ii) (ite (= i ii) e (ho_180 u ii)))))))))) (let ((_let_303 (forall ((x |u_(-> set_set_real set_set_real)|) (y |u_(-> set_set_real set_set_real)|)) (or (not (forall ((z set_set_real)) (= (ho_180 x z) (ho_180 y z)))) (= x y))))) (let ((_let_304 (forall ((u |u_(-> set_set_real set_set_real set_set_real)|) (e |u_(-> set_set_real set_set_real)|) (i set_set_real)) (not (forall ((v |u_(-> set_set_real set_set_real set_set_real)|)) (not (forall ((ii set_set_real)) (= (ho_179 v ii) (ite (= i ii) e (ho_179 u ii)))))))))) (let ((_let_305 (forall ((x |u_(-> set_set_real set_set_real set_set_real)|) (y |u_(-> set_set_real set_set_real set_set_real)|)) (or (not (forall ((z set_set_real)) (= (ho_179 x z) (ho_179 y z)))) (= x y))))) (let ((_let_306 (forall ((u |u_(-> set_set_real Bool)|) (e Bool) (i set_set_real)) (not (forall ((v |u_(-> set_set_real Bool)|)) (not (forall ((ii set_set_real)) (= (ho_183 v ii) (ite (= i ii) e (ho_183 u ii)))))))))) (let ((_let_307 (forall ((x |u_(-> set_set_real Bool)|) (y |u_(-> set_set_real Bool)|)) (or (not (forall ((z set_set_real)) (= (ho_183 x z) (ho_183 y z)))) (= x y))))) (let ((_let_308 (forall ((u |u_(-> set_real produc1396156303t_real)|) (e produc1396156303t_real) (i set_real)) (not (forall ((v |u_(-> set_real produc1396156303t_real)|)) (not (forall ((ii set_real)) (= (ho_192 v ii) (ite (= i ii) e (ho_192 u ii)))))))))) (let ((_let_309 (forall ((x |u_(-> set_real produc1396156303t_real)|) (y |u_(-> set_real produc1396156303t_real)|)) (or (not (forall ((z set_real)) (= (ho_192 x z) (ho_192 y z)))) (= x y))))) (let ((_let_310 (forall ((u |u_(-> a set_real produc1396156303t_real)|) (e |u_(-> set_real produc1396156303t_real)|) (i a)) (not (forall ((v |u_(-> a set_real produc1396156303t_real)|)) (not (forall ((ii a)) (= (ho_191 v ii) (ite (= i ii) e (ho_191 u ii)))))))))) (let ((_let_311 (forall ((x |u_(-> a set_real produc1396156303t_real)|) (y |u_(-> a set_real produc1396156303t_real)|)) (or (not (forall ((z a)) (= (ho_191 x z) (ho_191 y z)))) (= x y))))) (let ((_let_312 (forall ((u |u_(-> produc1396156303t_real produc1396156303t_real)|) (e produc1396156303t_real) (i produc1396156303t_real)) (not (forall ((v |u_(-> produc1396156303t_real produc1396156303t_real)|)) (not (forall ((ii produc1396156303t_real)) (= (ho_195 v ii) (ite (= i ii) e (ho_195 u ii)))))))))) (let ((_let_313 (forall ((x |u_(-> produc1396156303t_real produc1396156303t_real)|) (y |u_(-> produc1396156303t_real produc1396156303t_real)|)) (or (not (forall ((z produc1396156303t_real)) (= (ho_195 x z) (ho_195 y z)))) (= x y))))) (let ((_let_314 (forall ((u |u_(-> real produc1572603623od_a_a produc1572603623od_a_a)|) (e |u_(-> produc1572603623od_a_a produc1572603623od_a_a)|) (i real)) (not (forall ((v |u_(-> real produc1572603623od_a_a produc1572603623od_a_a)|)) (not (forall ((ii real)) (= (ho_197 v ii) (ite (= i ii) e (ho_197 u ii)))))))))) (let ((_let_315 (forall ((x |u_(-> real produc1572603623od_a_a produc1572603623od_a_a)|) (y |u_(-> real produc1572603623od_a_a produc1572603623od_a_a)|)) (or (not (forall ((z real)) (= (ho_197 x z) (ho_197 y z)))) (= x y))))) (let ((_let_316 (forall ((u |u_(-> set_Pr1928503567a_real set_Pr1928503567a_real set_Pr1928503567a_real)|) (e |u_(-> set_Pr1928503567a_real set_Pr1928503567a_real)|) (i set_Pr1928503567a_real)) (not (forall ((v |u_(-> set_Pr1928503567a_real set_Pr1928503567a_real set_Pr1928503567a_real)|)) (not (forall ((ii set_Pr1928503567a_real)) (= (ho_202 v ii) (ite (= i ii) e (ho_202 u ii)))))))))) (let ((_let_317 (forall ((x |u_(-> set_Pr1928503567a_real set_Pr1928503567a_real set_Pr1928503567a_real)|) (y |u_(-> set_Pr1928503567a_real set_Pr1928503567a_real set_Pr1928503567a_real)|)) (or (not (forall ((z set_Pr1928503567a_real)) (= (ho_202 x z) (ho_202 y z)))) (= x y))))) (let ((_let_318 (forall ((u |u_(-> product_prod_a_real set_Pr1928503567a_real Bool)|) (e |u_(-> set_Pr1928503567a_real Bool)|) (i product_prod_a_real)) (not (forall ((v |u_(-> product_prod_a_real set_Pr1928503567a_real Bool)|)) (not (forall ((ii product_prod_a_real)) (= (ho_205 v ii) (ite (= i ii) e (ho_205 u ii)))))))))) (let ((_let_319 (forall ((x |u_(-> product_prod_a_real set_Pr1928503567a_real Bool)|) (y |u_(-> product_prod_a_real set_Pr1928503567a_real Bool)|)) (or (not (forall ((z product_prod_a_real)) (= (ho_205 x z) (ho_205 y z)))) (= x y))))) (let ((_let_320 (forall ((u |u_(-> real product_prod_real_a product_prod_real_a)|) (e |u_(-> product_prod_real_a product_prod_real_a)|) (i real)) (not (forall ((v |u_(-> real product_prod_real_a product_prod_real_a)|)) (not (forall ((ii real)) (= (ho_208 v ii) (ite (= i ii) e (ho_208 u ii)))))))))) (let ((_let_321 (forall ((x |u_(-> real product_prod_real_a product_prod_real_a)|) (y |u_(-> real product_prod_real_a product_prod_real_a)|)) (or (not (forall ((z real)) (= (ho_208 x z) (ho_208 y z)))) (= x y))))) (let ((_let_322 (forall ((u |u_(-> set_Product_prod_a_a set_se1596668135od_a_a Bool)|) (e |u_(-> set_se1596668135od_a_a Bool)|) (i set_Product_prod_a_a)) (not (forall ((v |u_(-> set_Product_prod_a_a set_se1596668135od_a_a Bool)|)) (not (forall ((ii set_Product_prod_a_a)) (= (ho_214 v ii) (ite (= i ii) e (ho_214 u ii)))))))))) (let ((_let_323 (forall ((x |u_(-> set_Product_prod_a_a set_se1596668135od_a_a Bool)|) (y |u_(-> set_Product_prod_a_a set_se1596668135od_a_a Bool)|)) (or (not (forall ((z set_Product_prod_a_a)) (= (ho_214 x z) (ho_214 y z)))) (= x y))))) (let ((_let_324 (forall ((BOUND_VARIABLE_8007 set_Product_prod_a_a) (BOUND_VARIABLE_8008 set_Product_prod_a_a)) (= (ho_15 (ho_17 k_16 BOUND_VARIABLE_8007) BOUND_VARIABLE_8008) (forall ((T product_prod_a_a)) (let ((_let_1 (ho_14 k_13 T))) (or (not (ho_15 _let_1 BOUND_VARIABLE_8007)) (ho_15 _let_1 BOUND_VARIABLE_8008)))))))) (let ((_let_325 (forall ((BOUND_VARIABLE_7996 set_Product_prod_a_a) (BOUND_VARIABLE_7997 set_Product_prod_a_a)) (= (ho_15 (ho_17 k_18 BOUND_VARIABLE_7996) BOUND_VARIABLE_7997) (forall ((X3 product_prod_a_a)) (let ((_let_1 (ho_14 k_13 X3))) (or (not (ho_15 _let_1 BOUND_VARIABLE_7996)) (ho_15 _let_1 BOUND_VARIABLE_7997)))))))) (let ((_let_326 (forall ((BOUND_VARIABLE_7989 real) (BOUND_VARIABLE_7990 real)) (= (ho_21 (ho_20 k_19 BOUND_VARIABLE_7989) BOUND_VARIABLE_7990) (= BOUND_VARIABLE_7989 BOUND_VARIABLE_7990))))) (let ((_let_327 (forall ((BOUND_VARIABLE_7978 real) (BOUND_VARIABLE_7979 real)) (= (ho_21 (ho_20 k_23 BOUND_VARIABLE_7978) BOUND_VARIABLE_7979) (and (ho_21 (ho_20 k_22 BOUND_VARIABLE_7979) BOUND_VARIABLE_7978) (ho_21 (ho_20 k_22 BOUND_VARIABLE_7978) BOUND_VARIABLE_7979)))))) (let ((_let_328 (forall ((BOUND_VARIABLE_7970 set_Pr147102617l_real) (BOUND_VARIABLE_7971 produc957004601l_real)) (= (ho_29 (ho_28 k_27 BOUND_VARIABLE_7970) BOUND_VARIABLE_7971) (ho_26 (ho_25 k_24 BOUND_VARIABLE_7971) BOUND_VARIABLE_7970))))) (let ((_let_329 (forall ((BOUND_VARIABLE_7963 real) (BOUND_VARIABLE_7964 real)) (= (ho_21 (ho_20 k_30 BOUND_VARIABLE_7963) BOUND_VARIABLE_7964) (= BOUND_VARIABLE_7963 BOUND_VARIABLE_7964))))) (let ((_let_330 (forall ((BOUND_VARIABLE_7952 real) (BOUND_VARIABLE_7953 real)) (= (ho_21 (ho_20 k_31 BOUND_VARIABLE_7952) BOUND_VARIABLE_7953) (and (ho_21 (ho_20 k_22 BOUND_VARIABLE_7952) BOUND_VARIABLE_7953) (ho_21 (ho_20 k_22 BOUND_VARIABLE_7953) BOUND_VARIABLE_7952)))))) (let ((_let_331 (forall ((BOUND_VARIABLE_7944 a) (BOUND_VARIABLE_7945 a)) (= (ho_34 (ho_33 k_32 BOUND_VARIABLE_7944) BOUND_VARIABLE_7945) (ho_34 (ho_33 k_35 BOUND_VARIABLE_7945) BOUND_VARIABLE_7944))))) (let ((_let_332 (forall ((BOUND_VARIABLE_7936 real) (BOUND_VARIABLE_7937 real)) (= (ho_38 (ho_37 k_36 BOUND_VARIABLE_7936) BOUND_VARIABLE_7937) (ho_38 (ho_37 k_39 BOUND_VARIABLE_7937) BOUND_VARIABLE_7936))))) (let ((_let_333 (forall ((BOUND_VARIABLE_7920 set_a) (BOUND_VARIABLE_7921 a)) (= (ho_48 (ho_47 k_46 BOUND_VARIABLE_7920) BOUND_VARIABLE_7921) (ho_45 (ho_44 k_43 BOUND_VARIABLE_7921) BOUND_VARIABLE_7920))))) (let ((_let_334 (forall ((BOUND_VARIABLE_7912 set_real) (BOUND_VARIABLE_7913 real)) (= (ho_21 (ho_53 k_52 BOUND_VARIABLE_7912) BOUND_VARIABLE_7913) (ho_51 (ho_50 k_49 BOUND_VARIABLE_7913) BOUND_VARIABLE_7912))))) (let ((_let_335 (forall ((A set_real) (B a) (C set_real) (D a)) (= (ho_59 (ho_58 k_57 (ho_56 (ho_55 k_54 A) C)) (ho_34 (ho_33 k_35 B) D)) (ho_62 (ho_61 k_60 (ho_59 (ho_58 k_57 A) B)) (ho_59 (ho_58 k_57 C) D)))))) (let ((_let_336 (forall ((BOUND_VARIABLE_8007 set_Product_prod_a_a) (BOUND_VARIABLE_8008 set_Product_prod_a_a)) (= (ll_12 BOUND_VARIABLE_8007 BOUND_VARIABLE_8008) (forall ((T product_prod_a_a)) (let ((_let_1 (member449909584od_a_a T))) (or (not (_let_1 BOUND_VARIABLE_8007)) (_let_1 BOUND_VARIABLE_8008)))))))) (let ((_let_337 (forall ((BOUND_VARIABLE_7996 set_Product_prod_a_a) (BOUND_VARIABLE_7997 set_Product_prod_a_a)) (= (ll_11 BOUND_VARIABLE_7996 BOUND_VARIABLE_7997) (forall ((X3 product_prod_a_a)) (let ((_let_1 (member449909584od_a_a X3))) (or (not (_let_1 BOUND_VARIABLE_7996)) (_let_1 BOUND_VARIABLE_7997)))))))) (let ((_let_338 (forall ((BOUND_VARIABLE_7989 real) (BOUND_VARIABLE_7990 real)) (= (ll_10 BOUND_VARIABLE_7989 BOUND_VARIABLE_7990) (= BOUND_VARIABLE_7989 BOUND_VARIABLE_7990))))) (let ((_let_339 (forall ((BOUND_VARIABLE_7978 real) (BOUND_VARIABLE_7979 real)) (= (ll_9 BOUND_VARIABLE_7978 BOUND_VARIABLE_7979) (and ((ord_less_eq_real BOUND_VARIABLE_7979) BOUND_VARIABLE_7978) ((ord_less_eq_real BOUND_VARIABLE_7978) BOUND_VARIABLE_7979)))))) (let ((_let_340 (forall ((BOUND_VARIABLE_7970 set_Pr147102617l_real) (BOUND_VARIABLE_7971 produc957004601l_real)) (= (ll_8 BOUND_VARIABLE_7970 BOUND_VARIABLE_7971) ((member1068169442l_real BOUND_VARIABLE_7971) BOUND_VARIABLE_7970))))) (let ((_let_341 (forall ((BOUND_VARIABLE_7963 real) (BOUND_VARIABLE_7964 real)) (= (ll_7 BOUND_VARIABLE_7963 BOUND_VARIABLE_7964) (= BOUND_VARIABLE_7963 BOUND_VARIABLE_7964))))) (let ((_let_342 (forall ((BOUND_VARIABLE_7952 real) (BOUND_VARIABLE_7953 real)) (= (ll_6 BOUND_VARIABLE_7952 BOUND_VARIABLE_7953) (and ((ord_less_eq_real BOUND_VARIABLE_7952) BOUND_VARIABLE_7953) ((ord_less_eq_real BOUND_VARIABLE_7953) BOUND_VARIABLE_7952)))))) (let ((_let_343 (forall ((BOUND_VARIABLE_7944 a) (BOUND_VARIABLE_7945 a)) (= ((plus_plus_a BOUND_VARIABLE_7945) BOUND_VARIABLE_7944) (ll_5 BOUND_VARIABLE_7944 BOUND_VARIABLE_7945))))) (let ((_let_344 (forall ((BOUND_VARIABLE_7936 real) (BOUND_VARIABLE_7937 real)) (= ((plus_plus_real BOUND_VARIABLE_7937) BOUND_VARIABLE_7936) (ll_4 BOUND_VARIABLE_7936 BOUND_VARIABLE_7937))))) (let ((_let_345 (forall ((BOUND_VARIABLE_7928 set_Product_prod_a_a) (BOUND_VARIABLE_7929 product_prod_a_a)) (= (ll_3 BOUND_VARIABLE_7928 BOUND_VARIABLE_7929) ((member449909584od_a_a BOUND_VARIABLE_7929) BOUND_VARIABLE_7928))))) (let ((_let_346 (forall ((BOUND_VARIABLE_7920 set_a) (BOUND_VARIABLE_7921 a)) (= (ll_2 BOUND_VARIABLE_7920 BOUND_VARIABLE_7921) ((member_a BOUND_VARIABLE_7921) BOUND_VARIABLE_7920))))) (let ((_let_347 (forall ((BOUND_VARIABLE_7912 set_real) (BOUND_VARIABLE_7913 real)) (= (ll_1 BOUND_VARIABLE_7912 BOUND_VARIABLE_7913) ((member_real BOUND_VARIABLE_7913) BOUND_VARIABLE_7912))))) (let ((_let_348 (and _let_1 _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 ((_let_349 (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (MACRO_SR_PRED_TRANSFORM (AND_INTRO (ASSUME |:args| (_let_1)) (PREPROCESS |:args| ((and _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336)))) |:args| (_let_348)) (PREPROCESS |:args| ((= _let_348 (and _let_335 _let_334 _let_333 _let_77 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324))))) (PREPROCESS |:args| ((and _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119 _let_118 _let_117 _let_116 _let_115 _let_114 _let_113 _let_112 _let_111 _let_110 _let_109 _let_108 _let_107 _let_106 _let_105 _let_104 _let_103 _let_102 _let_101 _let_100 _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78)))) |:args| ((and _let_335 _let_334 _let_333 _let_77 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119 _let_118 _let_117 _let_116 _let_115 _let_114 _let_113 _let_112 _let_111 _let_110 _let_109 _let_108 _let_107 _let_106 _let_105 _let_104 _let_103 _let_102 _let_101 _let_100 _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78))) |:args| (3)))) (let ((_let_350 (_let_77))) (let ((_let_351 (ASSUME |:args| _let_350))) (let ((_let_352 (ho_15 (ho_14 k_13 _let_42) relation))) (let ((_let_353 (= _let_43 _let_352))) (let ((_let_354 (= zero_zero_real v))) (let ((_let_355 (or _let_354 (= zero_zero_a y)))) (let ((_let_356 (= _let_44 _let_355))) (let ((_let_357 (forall ((A real) (X a)) (= (= zero_zero_a (ho_34 (ho_64 k_63 A) X)) (or (= zero_zero_real A) (= zero_zero_a X)))))) (let ((_let_358 (EQ_RESOLVE (ASSUME |:args| (_let_14)) (TRANS (MACRO_SR_EQ_INTRO |:args| (_let_14 7 12)) (PREPROCESS |:args| ((= (forall ((A real) (X a)) (= (= zero_zero_a ((real_V1035702895aleR_a A) X)) (or (= zero_zero_real A) (= zero_zero_a X)))) _let_357))))))) (let ((_let_359 (= _let_33 (ho_38 (ho_37 k_39 _let_33) v)))) (let ((_let_360 (= _let_359 _let_354))) (let ((_let_361 (forall ((A real) (B real)) (= (= A (ho_38 (ho_37 k_39 A) B)) (= zero_zero_real B))))) (let ((_let_362 (EQ_RESOLVE (ASSUME |:args| (_let_5)) (TRANS (MACRO_SR_EQ_INTRO |:args| (_let_5 7 12)) (PREPROCESS |:args| ((= (forall ((A real) (B real)) (= (= A ((plus_plus_real A) B)) (= zero_zero_real B))) _let_361))))))) (let ((_let_363 (_let_34))) (let ((_let_364 (SYMM (SYMM (ASSUME |:args| _let_363))))) (let ((_let_365 (forall ((X a)) (= X (ho_34 (ho_64 k_63 (ho_38 (ho_37 k_39 u) v)) X))))) (let ((_let_366 (EQ_RESOLVE (ASSUME |:args| (_let_13)) (TRANS (MACRO_SR_EQ_INTRO |:args| (_let_13 7 12)) (MACRO_SR_EQ_INTRO _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 |:args| ((forall ((X a)) (= X ((real_V1035702895aleR_a one_one_real) X))) 7 12)) (PREPROCESS |:args| ((= (forall ((X a)) (= X ((real_V1035702895aleR_a ((plus_plus_real u) v)) X))) _let_365))))))) (let ((_let_367 (x))) (let ((_let_368 (not _let_45))) (let ((_let_369 (not _let_37))) (let ((_let_370 (not _let_44))) (let ((_let_371 (not _let_43))) (let ((_let_372 (not _let_32))) (let ((_let_373 (23 ho_34))) (let ((_let_374 (CONG (SYMM (SYMM _let_47)) (REFL |:args| _let_74) |:args| (23 ho_33)))) (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO (ASSUME |:args| (_let_76)))) (CONG (REFL |:args| (_let_40)) (CONG (CONG (REFL |:args| (k_65)) (TRANS (CONG (SYMM _let_374) (REFL |:args| (_let_38)) |:args| _let_373) (CONG _let_374 (SYMM (ASSUME |:args| (_let_44))) |:args| _let_373) (SYMM (ASSUME |:args| (_let_37))) (CONG (CONG (REFL |:args| (k_63)) _let_364 |:args| (23 ho_64)) (REFL |:args| _let_367) |:args| _let_373) (SYMM (ASSUME |:args| (_let_45)))) |:args| (23 ho_66)) (REFL |:args| (y)) |:args| (23 ho_67)) |:args| (23 ho_42)) (TRUE_INTRO (ASSUME |:args| (_let_43))))) |:args| (_let_43 _let_45 _let_34 _let_37 _let_32 _let_44 _let_76))) (CONG (REFL |:args| (_let_371)) (REFL |:args| (_let_368)) (REFL |:args| (_let_48)) (REFL |:args| (_let_369)) (REFL |:args| (_let_372)) (REFL |:args| (_let_370)) (MACRO_SR_PRED_INTRO |:args| ((= (not _let_76) _let_41))) |:args| _let_69)) |:args| ((or _let_48 _let_372 _let_41 _let_371 _let_370 _let_369 _let_368))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_366 |:args| _let_367) |:args| (_let_365))) _let_366 |:args| (_let_45 false _let_365)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 |:args| (_let_356)) |:args| ((or _let_44 (not _let_355) (not _let_356)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_NEG |:args| (_let_355 0)) |:args| ((or (not _let_354) _let_355))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 |:args| (_let_360)) |:args| ((or _let_354 (not _let_359) (not _let_360)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (CONG (CONG (REFL |:args| (k_39)) _let_364 |:args| (23 ho_37)) (REFL |:args| (v)) |:args| (23 ho_38)) |:args| _let_363)) _let_71 |:args| (_let_359 false _let_34)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_362 |:args| (_let_33 v)) |:args| (_let_361))) _let_362 |:args| (_let_360 false _let_361)) |:args| (_let_354 false _let_359 false _let_360)) |:args| (_let_355 false _let_354)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_358 |:args| (v y)) |:args| (_let_357))) _let_358 |:args| (_let_356 false _let_357)) |:args| (_let_44 false _let_355 false _let_356)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 |:args| (_let_353)) |:args| ((or (not _let_352) _let_43 (not _let_353)))) (EQ_RESOLVE (ASSUME |:args| (_let_2)) (PREPROCESS |:args| ((= _let_2 _let_352)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_351 |:args| (relation _let_42)) |:args| _let_350)) _let_349 |:args| (_let_353 false _let_77)) |:args| (_let_43 false _let_352 false _let_353)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 |:args| (_let_75)) |:args| ((or _let_52 _let_76 (not _let_75)))) _let_54 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_351 |:args| (relation _let_39)) |:args| _let_350)) _let_349 |:args| (_let_75 false _let_77)) |:args| (_let_76 true _let_52 false _let_75)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_73 |:args| _let_74) |:args| (_let_72))) _let_73 |:args| (_let_37 false _let_72)) _let_71 _let_47 |:args| (false false _let_45 false _let_44 false _let_43 true _let_41 false _let_37 false _let_34 false _let_32)) |:args| ((not false) (_let_15 ((plus_plus_real one_one_real) one_one_real)) (forall ((B real) (A real)) (= ((ord_less_real ((plus_plus_real B) A)) B) ((ord_less_real A) zero_zero_real))) (forall ((A a) (B a)) (= (= ((plus_plus_a A) B) A) (= B zero_zero_a))) (forall ((X produc957004601l_real)) (= (= zero_z659284464l_real X) (= X zero_z659284464l_real))) (forall ((X1 a) (X2 real) (Y1 a) (Y2 real)) (= (= ((product_Pair_a_real X1) X2) ((product_Pair_a_real Y1) Y2)) (and (= X2 Y2) (= X1 Y1)))) (prefer529818233pref_a relation) (forall ((B real) (U real) (A real)) (let ((_let_1 (real_V453051771R_real U))) (= (= ((plus_plus_real B) (_let_1 A)) ((plus_plus_real A) (_let_1 B))) (or (= U one_one_real) (= A B))))) (forall ((U real) (B a) (V real) (A a)) (let ((_let_1 (real_V1035702895aleR_a V))) (let ((_let_2 (real_V1035702895aleR_a U))) (=> (= ((plus_plus_a (_let_2 B)) (_let_1 A)) ((plus_plus_a (_let_2 A)) (_let_1 B))) (=> (not (= U V)) (= A B)))))) (forall ((A real) (B real)) (= (= ((plus_plus_real A) B) A) (= B zero_zero_real))) (forall ((B product_prod_a_a) (A product_prod_a_a) (C product_prod_a_a)) (= (= ((plus_p1505579230od_a_a B) A) ((plus_p1505579230od_a_a C) A)) (= B C))) (forall ((A a)) (= ((plus_plus_a zero_zero_a) A) A)) (forall ((A real) (B real)) (= ((ord_less_eq_real A) ((plus_plus_real A) B)) ((ord_less_eq_real zero_zero_real) B))) (forall ((A real) (X real)) (=> ((ord_less_eq_real zero_zero_real) A) (=> ((ord_less_eq_real X) zero_zero_real) ((ord_less_eq_real ((real_V453051771R_real A) X)) zero_zero_real)))) (forall ((A real)) (= (= ((plus_plus_real A) A) zero_zero_real) (= A zero_zero_real))) (forall ((C real) (A real) (B real)) (let ((_let_1 (plus_plus_real C))) (=> ((ord_less_eq_real (_let_1 A)) (_let_1 B)) ((ord_less_eq_real A) B)))) (forall ((C real) (X real) (D real) (Y real)) (let ((_let_1 ((real_V453051771R_real C) X))) (let ((_let_2 ((real_V453051771R_real D) Y))) (= ((plus_plus_real _let_1) _let_2) ((plus_plus_real _let_2) _let_1))))) _let_31 (forall ((A3 set_Product_prod_a_a) (B4 set_Product_prod_a_a) (C product_prod_a_a)) (let ((_let_1 (member449909584od_a_a C))) (=> ((ord_le108336051od_a_a A3) B4) (=> (_let_1 A3) (_let_1 B4))))) (forall ((A real)) (= ((real_V1035702895aleR_a A) zero_zero_a) zero_zero_a)) (forall ((A product_prod_a_real)) (= ((plus_p541014626a_real zero_z705155042a_real) A) A)) _let_30 (forall ((X real) (A product_prod_a_a) (B a)) (= ((real_V1538726831_a_a_a X) ((produc2061588782_a_a_a A) B)) ((produc2061588782_a_a_a ((real_V543523736od_a_a X) A)) ((real_V1035702895aleR_a X) B)))) (forall ((A a) (P (-> a Bool))) (= ((member_a A) (collect_a P)) (P A))) _let_29 (forall ((X1 a) (X2 a) (Y1 a) (Y2 a)) (= (= ((product_Pair_a_a X1) X2) ((product_Pair_a_a Y1) Y2)) (and (= X2 Y2) (= X1 Y1)))) (forall ((B real) (A real) (C real)) (let ((_let_1 (plus_plus_real B))) (let ((_let_2 (plus_plus_real A))) (= (_let_1 (_let_2 C)) (_let_2 (_let_1 C)))))) (forall ((A a) (B real) (C a) (D real)) (= ((plus_p541014626a_real ((product_Pair_a_real A) B)) ((product_Pair_a_real C) D)) ((product_Pair_a_real ((plus_plus_a A) C)) ((plus_plus_real B) D)))) (forall ((A a) (B a) (C a)) (let ((_let_1 (plus_plus_a A))) (= ((plus_plus_a (_let_1 B)) C) (_let_1 ((plus_plus_a B) C))))) (forall ((I real) (J real) (K real) (L real)) (=> (and (= K L) ((ord_less_eq_real I) J)) ((ord_less_eq_real ((plus_plus_real I) K)) ((plus_plus_real J) L)))) (forall ((A real) (B real) (C real)) (=> ((ord_less_eq_real A) B) ((ord_less_eq_real ((plus_plus_real A) C)) ((plus_plus_real B) C)))) (forall ((A product_prod_a_a)) (= ((plus_p1505579230od_a_a A) zero_z950819678od_a_a) A)) (forall ((B produc957004601l_real) (A produc957004601l_real)) (= (= ((plus_p77862768l_real B) A) A) (= B zero_z659284464l_real))) (forall ((A produc957004601l_real) (B produc957004601l_real) (C produc957004601l_real)) (let ((_let_1 (ord_le1342644953l_real B))) (=> ((ord_le1342644953l_real zero_z659284464l_real) A) (=> (_let_1 C) (_let_1 ((plus_p77862768l_real A) C)))))) (forall ((A a) (B a) (C a)) (let ((_let_1 (plus_plus_a A))) (=> (= (_let_1 B) (_let_1 C)) (= B C)))) (forall ((P2 product_prod_a_a)) (exists ((X4 a) (Y3 a)) (= P2 ((product_Pair_a_a X4) Y3)))) (forall ((A real) (X a) (Y a)) (let ((_let_1 (real_V1035702895aleR_a A))) (= (_let_1 ((plus_plus_a X) Y)) ((plus_plus_a (_let_1 X)) (_let_1 Y))))) (forall ((C real) (X real) (Y real)) (let ((_let_1 (real_V453051771R_real C))) (= (_let_1 ((plus_plus_real X) Y)) ((plus_plus_real (_let_1 X)) (_let_1 Y))))) (forall ((C real) (X real) (W real) (D real) (Y real) (Z real)) (let ((_let_1 ((plus_plus_real ((real_V453051771R_real D) Y)) Z))) (let ((_let_2 (plus_plus_real ((real_V453051771R_real C) X)))) (= ((plus_plus_real (_let_2 W)) _let_1) (_let_2 ((plus_plus_real W) _let_1)))))) (forall ((A a)) (= ((plus_plus_a A) zero_zero_a) A)) (forall ((A produc957004601l_real) (B produc957004601l_real) (C produc957004601l_real)) (let ((_let_1 (plus_p77862768l_real C))) (=> ((ord_le1342644953l_real A) B) ((ord_le1342644953l_real (_let_1 A)) (_let_1 B))))) (forall ((Y product_prod_a_a)) (not (forall ((A5 a) (B5 a)) (not (= Y ((product_Pair_a_a A5) B5)))))) (forall ((B a) (A a) (C a)) (let ((_let_1 (plus_plus_a B))) (let ((_let_2 (plus_plus_a A))) (= (_let_1 (_let_2 C)) (_let_2 (_let_1 C)))))) (forall ((A3 real) (K real) (A real) (B real)) (let ((_let_1 (plus_plus_real K))) (=> (= A3 (_let_1 A)) (= ((plus_plus_real A3) B) (_let_1 ((plus_plus_real A) B)))))) (forall ((C produc957004601l_real) (A produc957004601l_real) (B produc957004601l_real)) (let ((_let_1 (plus_p77862768l_real C))) (=> ((ord_le1342644953l_real (_let_1 A)) (_let_1 B)) ((ord_le1342644953l_real A) B)))) (forall ((C real) (X real) (W real) (D real) (Z real)) (= ((plus_plus_real ((plus_plus_real ((real_V453051771R_real C) X)) W)) ((plus_plus_real ((real_V453051771R_real D) X)) Z)) ((plus_plus_real ((real_V453051771R_real ((plus_plus_real C) D)) X)) ((plus_plus_real W) Z)))) (forall ((A product_prod_a_real) (C2 set_Pr1928503567a_real) (B product_prod_a_real) (D2 set_Pr1928503567a_real)) (=> ((member1103263856a_real A) C2) (=> ((member1103263856a_real B) D2) ((member1103263856a_real ((plus_p541014626a_real A) B)) ((plus_p130512152a_real C2) D2))))) (forall ((C real) (X real) (Z real) (D real) (Y real)) (let ((_let_1 ((real_V453051771R_real D) Y))) (let ((_let_2 (plus_plus_real ((real_V453051771R_real C) X)))) (= ((plus_plus_real (_let_2 Z)) _let_1) (_let_2 ((plus_plus_real Z) _let_1)))))) (forall ((A real) (B real)) (=> ((ord_less_eq_real A) zero_zero_real) (=> ((ord_less_real B) zero_zero_real) ((ord_less_real ((plus_plus_real A) B)) zero_zero_real)))) (forall ((A product_prod_a_real) (B product_prod_a_real) (C product_prod_a_real)) (let ((_let_1 (plus_p541014626a_real A))) (= (= (_let_1 B) (_let_1 C)) (= B C)))) (forall ((B real) (A real) (C real)) (=> ((ord_less_eq_real B) A) (=> ((ord_less_eq_real C) zero_zero_real) ((ord_less_eq_real ((real_V453051771R_real A) C)) ((real_V453051771R_real B) C))))) (not (_let_28 zero_zero_real)) (forall ((A real) (X real)) (let ((_let_1 (ord_less_eq_real zero_zero_real))) (=> (or (and ((ord_less_eq_real X) zero_zero_real) (_let_1 A)) (and (_let_1 X) ((ord_less_eq_real A) zero_zero_real))) ((ord_less_eq_real ((real_V453051771R_real A) X)) zero_zero_real)))) (forall ((A real) (B real) (C real) (D real)) (=> ((ord_less_real A) B) (=> ((ord_less_eq_real C) D) ((ord_less_real ((plus_plus_real A) C)) ((plus_plus_real B) D))))) (forall ((C real) (X real) (D real) (Z real)) (= ((plus_plus_real ((real_V453051771R_real C) X)) ((plus_plus_real ((real_V453051771R_real D) X)) Z)) ((plus_plus_real ((real_V453051771R_real ((plus_plus_real C) D)) X)) Z))) (_let_28 one_one_real) (forall ((X1 real) (X2 a) (Y1 real) (Y2 a)) (= (= ((product_Pair_real_a X1) X2) ((product_Pair_real_a Y1) Y2)) (and (= X2 Y2) (= X1 Y1)))) (forall ((A product_prod_a_a) (B product_prod_a_a)) (= (= A ((plus_p1505579230od_a_a A) B)) (= B zero_z950819678od_a_a))) (forall ((X a)) (= ((real_V1035702895aleR_a zero_zero_real) X) zero_zero_a)) (forall ((A real) (B real)) (=> ((ord_less_eq_real A) zero_zero_real) (=> ((ord_less_eq_real B) zero_zero_real) ((ord_less_eq_real ((plus_plus_real A) B)) zero_zero_real)))) (forall ((A real) (B real) (C real) (D real)) (= ((ord_le1342644953l_real ((produc705216881l_real A) B)) ((produc705216881l_real C) D)) (and ((ord_less_eq_real A) C) ((ord_less_eq_real B) D)))) (forall ((U real) (B real) (V real) (A real)) (let ((_let_1 (real_V453051771R_real V))) (let ((_let_2 (real_V453051771R_real U))) (=> (= ((plus_plus_real (_let_2 B)) (_let_1 A)) ((plus_plus_real (_let_2 A)) (_let_1 B))) (=> (not (= U V)) (= A B)))))) (forall ((X a)) (= (= zero_zero_a X) (= X zero_zero_a))) (forall ((P (-> product_prod_a_a Bool)) (Q (-> product_prod_a_a Bool))) (=> (forall ((X4 product_prod_a_a)) (= (P X4) (Q X4))) (= (collec645855634od_a_a P) (collec645855634od_a_a Q)))) (forall ((X real) (Y real)) (let ((_let_1 (ord_less_eq_real zero_zero_real))) (=> (_let_1 X) (=> (_let_1 Y) (= (= ((plus_plus_real X) Y) zero_zero_real) (and (= Y zero_zero_real) (= X zero_zero_real))))))) (forall ((A product_prod_a_real) (B product_prod_a_real)) (= (= A ((plus_p541014626a_real B) A)) (= B zero_z705155042a_real))) (not (_let_3 zero_zero_real)) (forall ((X real) (Y real)) (=> ((ord_less_eq_real X) zero_zero_real) (=> ((ord_less_eq_real Y) zero_zero_real) (= (= ((plus_plus_real X) Y) zero_zero_real) (and (= Y zero_zero_real) (= X zero_zero_real)))))) (forall ((A a)) (= ((plus_plus_a zero_zero_a) A) A)) (forall ((A produc957004601l_real)) (= ((plus_p77862768l_real zero_z659284464l_real) A) A)) (forall ((A produc957004601l_real) (P (-> produc957004601l_real Bool))) (= ((member1068169442l_real A) (collec1300223524l_real P)) (P A))) (forall ((A a) (B a) (A2 a) (B2 a)) (= (= ((product_Pair_a_a A) B) ((product_Pair_a_a A2) B2)) (and (= B B2) (= A A2)))) (forall ((A set_real)) (= ((plus_plus_set_real zero_zero_set_real) A) A)) (forall ((A real) (X a) (Y a)) (let ((_let_1 (real_V1035702895aleR_a A))) (=> (not (= A zero_zero_real)) (=> (= (_let_1 X) (_let_1 Y)) (= X Y))))) (forall ((A product_prod_a_real)) (= ((plus_p541014626a_real A) zero_z705155042a_real) A)) (forall ((X real) (Y real) (Z real)) (let ((_let_1 (ord_less_eq_real X))) (let ((_let_2 (_let_1 Y))) (let ((_let_3 (ord_less_eq_real Z))) (let ((_let_4 (_let_3 X))) (let ((_let_5 (ord_less_eq_real Y))) (let ((_let_6 (_let_5 Z))) (let ((_let_7 (_let_5 X))) (let ((_let_8 (_let_3 Y))) (let ((_let_9 (_let_1 Z))) (=> (=> _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 ((A real) (B real)) (= ((ord_less_real A) ((plus_plus_real B) A)) ((ord_less_real zero_zero_real) B))) (forall ((X real) (A product_prod_a_a) (B product_prod_a_a)) (let ((_let_1 (real_V543523736od_a_a X))) (= ((real_V368978776od_a_a X) ((produc1474507607od_a_a A) B)) ((produc1474507607od_a_a (_let_1 A)) (_let_1 B))))) (forall ((R real) (A a) (B product_prod_a_a)) (= ((real_V296206913od_a_a R) ((produc1299253312od_a_a A) B)) ((produc1299253312od_a_a ((real_V1035702895aleR_a R) A)) ((real_V543523736od_a_a R) B)))) (forall ((X real) (Y real)) (=> (= X Y) ((ord_less_eq_real X) Y))) (forall ((X real) (A real) (B a)) (= ((real_V1214981142real_a X) ((product_Pair_real_a A) B)) ((product_Pair_real_a ((real_V453051771R_real X) A)) ((real_V1035702895aleR_a X) B)))) (forall ((A set_a)) (= ((plus_plus_set_a A) zero_zero_set_a) A)) (forall ((A real) (X real) (B real)) (= (= ((real_V453051771R_real A) X) ((real_V453051771R_real B) X)) (or (= A B) (= X zero_zero_real)))) _let_27 (forall ((B real) (A real)) (= ((ord_less_eq_real ((plus_plus_real B) A)) B) ((ord_less_eq_real A) zero_zero_real))) (forall ((A produc957004601l_real) (B produc957004601l_real) (C produc957004601l_real) (D produc957004601l_real)) (=> ((ord_le1342644953l_real A) B) (=> ((ord_le1342644953l_real C) D) ((ord_le1342644953l_real ((plus_p77862768l_real A) C)) ((plus_p77862768l_real B) D))))) (forall ((A real) (B real) (C real)) (let ((_let_1 (plus_plus_real A))) (= ((plus_plus_real (_let_1 B)) C) (_let_1 ((plus_plus_real B) C))))) _let_26 (forall ((I real) (J real) (K real) (L real)) (=> (and (= I J) ((ord_less_eq_real K) L)) ((ord_less_eq_real ((plus_plus_real I) K)) ((plus_plus_real J) L)))) (forall ((A3 set_Product_prod_a_a) (B4 set_Product_prod_a_a)) (=> (forall ((X4 product_prod_a_a)) (let ((_let_1 (member449909584od_a_a X4))) (=> (_let_1 A3) (_let_1 B4)))) ((ord_le1824328871od_a_a A3) B4))) (forall ((A real) (X a) (Y a)) (let ((_let_1 (real_V1035702895aleR_a A))) (= (= (_let_1 X) (_let_1 Y)) (or (= X Y) (= A zero_zero_real))))) _let_25 (not (_let_15 zero_zero_real)) (forall ((A real) (B real) (C real)) (let ((_let_1 (plus_plus_real A))) (= (= (_let_1 B) (_let_1 C)) (= B C)))) (forall ((X real)) (= ((plus_plus_real X) zero_zero_real) X)) _let_24 (forall ((A real) (B real) (A2 real) (B2 real)) (= (= ((produc705216881l_real A) B) ((produc705216881l_real A2) B2)) (and (= A A2) (= B B2)))) (forall ((A produc957004601l_real)) (= ((plus_p77862768l_real A) zero_z659284464l_real) A)) (forall ((A real) (F2 (-> real real)) (B real) (C real)) (=> (= A (F2 B)) (=> ((ord_less_eq_real B) C) (=> (forall ((X4 real) (Y3 real)) (=> ((ord_less_eq_real X4) Y3) ((ord_less_eq_real (F2 X4)) (F2 Y3)))) ((ord_less_eq_real A) (F2 C)))))) (forall ((A a) (B set_real) (C a) (D set_real)) (= ((plus_p1745648536t_real ((produc1391501065t_real A) B)) ((produc1391501065t_real C) D)) ((produc1391501065t_real ((plus_plus_a A) C)) ((plus_plus_set_real B) D)))) (forall ((C real) (X real) (D real) (Y real)) (let ((_let_1 ((plus_plus_real ((real_V453051771R_real C) X)) ((real_V453051771R_real D) Y)))) (= _let_1 _let_1))) (forall ((R real) (A a) (B a)) (let ((_let_1 (real_V1035702895aleR_a R))) (= ((real_V543523736od_a_a R) ((product_Pair_a_a A) B)) ((product_Pair_a_a (_let_1 A)) (_let_1 B))))) (forall ((X a) (Y a) (Z a)) (let ((_let_1 (product_Pair_a_a Z))) (let ((_let_2 (product_Pair_a_a X))) (let ((_let_3 (product_Pair_a_a Y))) (=> (and (not ((member449909584od_a_a (_let_3 X)) relation)) ((member449909584od_a_a (_let_2 Y)) relation)) (=> (and ((member449909584od_a_a (_let_3 Z)) relation) (not ((member449909584od_a_a (_let_1 Y)) relation))) (and ((member449909584od_a_a (_let_2 Z)) relation) (not ((member449909584od_a_a (_let_1 X)) relation))))))))) (= plus_plus_real (lambda ((A4 real) (B3 real)) ((plus_plus_real B3) A4))) (forall ((A real) (B set_real) (C real) (D set_real)) (= ((plus_p2005278886t_real ((produc247649703t_real A) B)) ((produc247649703t_real C) D)) ((produc247649703t_real ((plus_plus_real A) C)) ((plus_plus_set_real B) D)))) (forall ((A real) (B real) (C real)) (let ((_let_1 (plus_plus_real C))) (=> ((ord_less_eq_real A) B) ((ord_less_eq_real (_let_1 A)) (_let_1 B))))) (forall ((C2 set_Product_prod_a_a) (D2 set_Product_prod_a_a) (E set_Product_prod_a_a) (F set_Product_prod_a_a) (X product_prod_a_a)) (let ((_let_1 (member449909584od_a_a X))) (=> ((ord_le1824328871od_a_a C2) D2) (=> ((ord_le1824328871od_a_a E) F) (=> (_let_1 ((plus_p634297534od_a_a C2) E)) (_let_1 ((plus_p634297534od_a_a D2) F))))))) _let_23 (forall ((X produc957004601l_real) (Y produc957004601l_real)) (=> ((ord_le1342644953l_real X) zero_z659284464l_real) (=> ((ord_le1342644953l_real Y) zero_z659284464l_real) (= (= ((plus_p77862768l_real X) Y) zero_z659284464l_real) (and (= X zero_z659284464l_real) (= Y zero_z659284464l_real)))))) (forall ((A set_real) (C2 set_set_real) (B set_real) (D2 set_set_real)) (=> ((member_set_real A) C2) (=> ((member_set_real B) D2) ((member_set_real ((plus_plus_set_real A) B)) ((plus_p768704801t_real C2) D2))))) (forall ((X real) (Y real)) (=> (forall ((E2 real)) (=> ((ord_less_real zero_zero_real) E2) ((ord_less_eq_real X) ((plus_plus_real Y) E2)))) ((ord_less_eq_real X) Y))) _let_22 (forall ((A real) (B real) (C real)) (let ((_let_1 (ord_less_eq_real A))) (=> (_let_1 B) (=> ((ord_less_eq_real B) C) (_let_1 C))))) (forall ((A real) (B real) (F2 (-> real real)) (C real)) (=> ((ord_less_eq_real A) B) (=> (= (F2 B) C) (=> (forall ((X4 real) (Y3 real)) (=> ((ord_less_eq_real X4) Y3) ((ord_less_eq_real (F2 X4)) (F2 Y3)))) ((ord_less_eq_real (F2 A)) C))))) (forall ((A real) (B real)) (let ((_let_1 (ord_less_real zero_zero_real))) (=> ((ord_less_eq_real zero_zero_real) A) (=> (_let_1 B) (_let_1 ((plus_plus_real A) B)))))) (forall ((X real) (A a) (B a)) (let ((_let_1 (real_V1035702895aleR_a X))) (= ((real_V543523736od_a_a X) ((product_Pair_a_a A) B)) ((product_Pair_a_a (_let_1 A)) (_let_1 B))))) (forall ((Pr set_Product_prod_a_a)) (=> (forall ((X4 a) (Y3 a)) (=> ((member449909584od_a_a ((product_Pair_a_a X4) Y3)) Pr) (forall ((Alpha real) (Beta real)) (let ((_let_1 (ord_less_eq_real zero_zero_real))) (=> (and (_let_1 Alpha) (_let_1 Beta) (= ((plus_plus_real Alpha) Beta) one_one_real)) ((member449909584od_a_a ((product_Pair_a_a ((plus_plus_a ((real_V1035702895aleR_a Alpha) X4)) ((real_V1035702895aleR_a Beta) Y3))) Y3)) Pr)))))) (prefer529818233pref_a Pr))) (forall ((A real) (B real) (C real)) (let ((_let_1 (plus_plus_real C))) (=> ((ord_less_real A) B) ((ord_less_real (_let_1 A)) (_let_1 B))))) (forall ((A product_prod_a_a) (P (-> product_prod_a_a Bool))) (= ((member449909584od_a_a A) (collec645855634od_a_a P)) (P A))) (forall ((A real) (B real)) (=> ((ord_less_eq_real A) zero_zero_real) (=> ((ord_less_eq_real B) zero_zero_real) ((ord_less_eq_real zero_zero_real) ((real_V453051771R_real A) B))))) (forall ((C real) (X real) (D real)) (= ((plus_plus_real ((real_V453051771R_real C) X)) ((real_V453051771R_real D) X)) ((real_V453051771R_real ((plus_plus_real C) D)) X))) (forall ((C real) (A real) (B real)) (let ((_let_1 (plus_plus_real C))) (=> ((ord_less_real (_let_1 A)) (_let_1 B)) ((ord_less_real A) B)))) (forall ((A produc957004601l_real) (C produc957004601l_real) (B produc957004601l_real)) (=> ((ord_le1342644953l_real A) zero_z659284464l_real) (=> ((ord_le1342644953l_real C) B) ((ord_le1342644953l_real ((plus_p77862768l_real A) C)) B)))) (forall ((X real) (Y real) (A real)) (let ((_let_1 (real_V453051771R_real A))) (=> ((ord_less_eq_real X) Y) (=> ((ord_less_eq_real zero_zero_real) A) ((ord_less_eq_real (_let_1 X)) (_let_1 Y)))))) (forall ((A real) (B real)) (let ((_let_1 (ord_less_real zero_zero_real))) (=> (_let_1 A) (=> ((ord_less_eq_real zero_zero_real) B) (_let_1 ((plus_plus_real A) B)))))) _let_21 (forall ((B real) (A real)) (= (= ((plus_plus_real B) A) A) (= B zero_zero_real))) (forall ((A a) (C2 set_a) (B a) (D2 set_a)) (=> ((member_a A) C2) (=> ((member_a B) D2) ((member_a ((plus_plus_a A) B)) ((plus_plus_set_a C2) D2))))) (not (= zero_zero_real one_one_real)) (forall ((A a) (B a) (C a)) (let ((_let_1 (plus_plus_a A))) (= (= (_let_1 B) (_let_1 C)) (= B C)))) (forall ((A product_prod_a_a) (B product_prod_a_a)) (= (= ((plus_p1505579230od_a_a A) B) A) (= B zero_z950819678od_a_a))) (forall ((Pr set_Pr147102617l_real)) (=> (forall ((X4 real) (Y3 real)) (=> ((member1068169442l_real ((produc705216881l_real X4) Y3)) Pr) (forall ((Alpha real) (Beta real)) (let ((_let_1 (ord_less_eq_real zero_zero_real))) (=> (and (= ((plus_plus_real Alpha) Beta) one_one_real) (_let_1 Alpha) (_let_1 Beta)) ((member1068169442l_real ((produc705216881l_real ((plus_plus_real ((real_V453051771R_real Alpha) X4)) ((real_V453051771R_real Beta) Y3))) Y3)) Pr)))))) (prefer1247792113f_real Pr))) (forall ((X real)) (= (= zero_zero_real X) (= X zero_zero_real))) (forall ((A real) (X real)) (=> ((ord_less_eq_real A) zero_zero_real) (=> ((ord_less_eq_real zero_zero_real) X) ((ord_less_eq_real ((real_V453051771R_real A) X)) zero_zero_real)))) (forall ((A real) (B real) (X a)) (let ((_let_1 (real_V1035702895aleR_a A))) (let ((_let_2 (real_V1035702895aleR_a B))) (= (_let_1 (_let_2 X)) (_let_2 (_let_1 X)))))) (forall ((A produc957004601l_real) (B produc957004601l_real)) (= ((ord_le1342644953l_real A) ((plus_p77862768l_real A) B)) ((ord_le1342644953l_real zero_z659284464l_real) B))) (forall ((A real) (C2 set_real) (B real) (D2 set_real)) (=> ((member_real A) C2) (=> ((member_real B) D2) ((member_real ((plus_plus_real A) B)) ((plus_plus_set_real C2) D2))))) (forall ((A real) (B real) (F2 (-> real real)) (C real)) (=> ((ord_less_eq_real A) B) (=> ((ord_less_eq_real (F2 B)) C) (=> (forall ((X4 real) (Y3 real)) (=> ((ord_less_eq_real X4) Y3) ((ord_less_eq_real (F2 X4)) (F2 Y3)))) ((ord_less_eq_real (F2 A)) C))))) (forall ((A real) (C real) (B real)) (=> ((ord_less_eq_real ((plus_plus_real A) C)) ((plus_plus_real B) C)) ((ord_less_eq_real A) B))) (forall ((R real) (A product_prod_a_a) (B a)) (= ((real_V1538726831_a_a_a R) ((produc2061588782_a_a_a A) B)) ((produc2061588782_a_a_a ((real_V543523736od_a_a R) A)) ((real_V1035702895aleR_a R) B)))) (forall ((A real) (C real) (B real)) (= ((ord_less_real ((plus_plus_real A) C)) ((plus_plus_real B) C)) ((ord_less_real A) B))) (forall ((A real)) (= ((plus_plus_real A) zero_zero_real) A)) (forall ((A3 set_Product_prod_a_a)) (= (collec645855634od_a_a (lambda ((X3 product_prod_a_a)) ((member449909584od_a_a X3) A3))) A3)) (forall ((X real) (X5 real) (Y real) (Y4 real)) (=> ((ord_less_eq_real X) X5) (=> ((ord_less_eq_real Y) Y4) ((ord_le1342644953l_real ((produc705216881l_real X) Y)) ((produc705216881l_real X5) Y4))))) (forall ((X product_prod_a_a)) (= (= zero_z950819678od_a_a X) (= X zero_z950819678od_a_a))) (forall ((B product_prod_a_a) (A product_prod_a_a)) (= (= ((plus_p1505579230od_a_a B) A) A) (= B zero_z950819678od_a_a))) (forall ((R real) (A a) (B real)) (= ((real_V512797224a_real R) ((product_Pair_a_real A) B)) ((product_Pair_a_real ((real_V1035702895aleR_a R) A)) ((real_V453051771R_real R) B)))) (forall ((A set_a)) (= ((plus_plus_set_a zero_zero_set_a) A) A)) (forall ((A3 set_Product_prod_a_a) (B4 set_Product_prod_a_a) (X product_prod_a_a)) (let ((_let_1 (member449909584od_a_a X))) (=> ((ord_le1824328871od_a_a A3) B4) (=> (_let_1 A3) (_let_1 B4))))) (forall ((P (-> product_prod_a_a Bool)) (Prod product_prod_a_a)) (=> (forall ((A5 a) (B5 a)) (P ((product_Pair_a_a A5) B5))) (P Prod))) (forall ((A real) (P (-> real Bool))) (= ((member_real A) (collect_real P)) (P A))) (forall ((A3 set_real) (B4 set_real)) (=> ((member_real zero_zero_real) A3) ((ord_less_eq_set_real B4) ((plus_plus_set_real A3) B4)))) (forall ((A produc957004601l_real)) (= ((plus_p77862768l_real A) zero_z659284464l_real) A)) _let_20 (forall ((A real)) (= (= zero_zero_real ((plus_plus_real A) A)) (= A zero_zero_real))) (forall ((A set_a) (C2 set_set_a) (B set_a) (D2 set_set_a)) (=> ((member_set_a A) C2) (=> ((member_set_a B) D2) ((member_set_a ((plus_plus_set_a A) B)) ((plus_plus_set_set_a C2) D2))))) (forall ((A real) (B real)) (let ((_let_1 (ord_less_eq_real zero_zero_real))) (=> (or (and ((ord_less_eq_real A) zero_zero_real) ((ord_less_eq_real B) zero_zero_real)) (and (_let_1 B) (_let_1 A))) (_let_1 ((real_V453051771R_real A) B))))) (forall ((C produc957004601l_real) (B produc957004601l_real) (A produc957004601l_real)) (let ((_let_1 (ord_le1342644953l_real B))) (=> ((ord_le1342644953l_real zero_z659284464l_real) C) (=> (_let_1 A) (_let_1 ((plus_p77862768l_real A) C)))))) (forall ((X real) (A3 set_real) (B4 set_real)) (=> ((member_real X) ((plus_plus_set_real A3) B4)) (not (forall ((A5 real) (B5 real)) (=> (= X ((plus_plus_real A5) B5)) (=> ((member_real A5) A3) (not ((member_real B5) B4)))))))) (forall ((A real) (B real) (C real) (D real)) (= ((plus_p77862768l_real ((produc705216881l_real A) B)) ((produc705216881l_real C) D)) ((produc705216881l_real ((plus_plus_real A) C)) ((plus_plus_real B) D)))) _let_19 (forall ((A real)) (= ((real_V453051771R_real A) zero_zero_real) zero_zero_real)) (forall ((A real) (X real)) (= (= ((real_V453051771R_real A) X) zero_zero_real) (or (= A zero_zero_real) (= X zero_zero_real)))) (forall ((A real) (X real) (Y real)) (let ((_let_1 (real_V453051771R_real A))) (= (_let_1 ((plus_plus_real X) Y)) ((plus_plus_real (_let_1 X)) (_let_1 Y))))) _let_18 (forall ((B4 a) (K a) (B a) (A a)) (let ((_let_1 (plus_plus_a A))) (let ((_let_2 (plus_plus_a K))) (=> (= B4 (_let_2 B)) (= (_let_1 B4) (_let_2 (_let_1 B))))))) (forall ((A real) (B real) (C real) (D real)) (=> ((ord_less_real A) B) (=> ((ord_less_real C) D) ((ord_less_real ((plus_plus_real A) C)) ((plus_plus_real B) D))))) (forall ((B real) (A real) (C real)) (= (= ((plus_plus_real B) A) ((plus_plus_real C) A)) (= B C))) (forall ((A product_prod_a_a) (B product_prod_a_a) (C product_prod_a_a)) (let ((_let_1 (plus_p1505579230od_a_a A))) (= (= (_let_1 B) (_let_1 C)) (= B C)))) _let_17 (forall ((C real) (A real) (B real)) (=> ((ord_less_eq_real C) zero_zero_real) (=> ((ord_less_eq_real A) B) ((ord_less_eq_real ((plus_plus_real A) C)) B)))) (forall ((X real)) (= ((real_V453051771R_real zero_zero_real) X) zero_zero_real)) (forall ((X real) (Y real)) (=> (not ((ord_less_eq_real X) Y)) ((ord_less_eq_real Y) X))) (forall ((X real)) (= (= one_one_real X) (= X one_one_real))) (forall ((A product_prod_a_real) (B product_prod_a_real)) (= (= ((plus_p541014626a_real A) B) A) (= B zero_z705155042a_real))) (forall ((A real) (C real) (B real)) (=> ((ord_less_real ((plus_plus_real A) C)) ((plus_plus_real B) C)) ((ord_less_real A) B))) (forall ((X a) (Y a)) (let ((_let_1 ((member449909584od_a_a ((product_Pair_a_a X) Y)) relation))) (=> (and ((member449909584od_a_a ((product_Pair_a_a Y) X)) relation) _let_1) _let_1))) (forall ((X real) (Y real)) (=> ((ord_less_eq_real X) Y) (=> ((ord_less_eq_real Y) X) (= X Y)))) _let_16 (forall ((R real) (A product_prod_a_a) (B real)) (= ((real_V195069393a_real R) ((produc454274172a_real A) B)) ((produc454274172a_real ((real_V543523736od_a_a R) A)) ((real_V453051771R_real R) B)))) (forall ((X produc957004601l_real) (Y produc957004601l_real)) (let ((_let_1 (ord_le1342644953l_real zero_z659284464l_real))) (=> (_let_1 X) (=> (_let_1 Y) (= (= ((plus_p77862768l_real X) Y) zero_z659284464l_real) (and (= X zero_z659284464l_real) (= Y zero_z659284464l_real))))))) (forall ((Pr set_Pr1741234931a_real)) (=> (forall ((X4 product_prod_a_real) (Y3 product_prod_a_real)) (=> ((member384820540a_real ((produc886678603a_real X4) Y3)) Pr) (forall ((Alpha real) (Beta real)) (let ((_let_1 (ord_less_eq_real zero_zero_real))) (=> (and (_let_1 Alpha) (_let_1 Beta) (= ((plus_plus_real Alpha) Beta) one_one_real)) ((member384820540a_real ((produc886678603a_real ((plus_p541014626a_real ((real_V512797224a_real Alpha) X4)) ((real_V512797224a_real Beta) Y3))) Y3)) Pr)))))) (prefer1113819806a_real Pr))) (_let_4 one_one_real) (forall ((C real) (X real) (W real) (D real) (Y real) (Z real)) (let ((_let_1 (plus_plus_real ((plus_plus_real ((real_V453051771R_real C) X)) W)))) (let ((_let_2 (plus_plus_real ((real_V453051771R_real D) Y)))) (= (_let_1 (_let_2 Z)) (_let_2 (_let_1 Z)))))) (forall ((A real) (B real) (C real)) (let ((_let_1 (ord_less_real B))) (=> ((ord_less_real zero_zero_real) A) (=> (_let_1 C) (_let_1 ((plus_plus_real A) C)))))) (forall ((B4 real) (K real) (B real) (A real)) (let ((_let_1 (plus_plus_real A))) (let ((_let_2 (plus_plus_real K))) (=> (= B4 (_let_2 B)) (= (_let_1 B4) (_let_2 (_let_1 B))))))) (forall ((B real) (A real) (C real)) (let ((_let_1 (real_V453051771R_real C))) (=> ((ord_less_eq_real B) A) (=> ((ord_less_eq_real C) zero_zero_real) ((ord_less_eq_real (_let_1 A)) (_let_1 B)))))) (forall ((B product_prod_a_real) (A product_prod_a_real) (C product_prod_a_real)) (= (= ((plus_p541014626a_real B) A) ((plus_p541014626a_real C) A)) (= B C))) (forall ((A produc957004601l_real) (B produc957004601l_real)) (= (= ((plus_p77862768l_real A) B) A) (= B zero_z659284464l_real))) (forall ((I real) (J real) (K real) (L real)) (=> (and ((ord_less_eq_real K) L) ((ord_less_eq_real I) J)) ((ord_less_eq_real ((plus_plus_real I) K)) ((plus_plus_real J) L)))) (_let_15 one_one_real) (forall ((A real)) (let ((_let_1 (ord_less_eq_real zero_zero_real))) (= (_let_1 ((plus_plus_real A) A)) (_let_1 A)))) (forall ((C real) (X real) (Z real) (D real) (Y real)) (let ((_let_1 ((plus_plus_real ((real_V453051771R_real C) X)) Z))) (let ((_let_2 ((real_V453051771R_real D) Y))) (= ((plus_plus_real _let_1) _let_2) ((plus_plus_real _let_2) _let_1))))) (forall ((A produc957004601l_real) (B produc957004601l_real)) (= ((ord_le1342644953l_real ((plus_p77862768l_real A) B)) B) ((ord_le1342644953l_real A) zero_z659284464l_real))) _let_14 (forall ((X real) (Y real) (Xa real)) (= ((real_V453051771R_real ((plus_plus_real X) Y)) Xa) ((plus_plus_real ((real_V453051771R_real X) Xa)) ((real_V453051771R_real Y) Xa)))) (forall ((C real) (A real) (B real)) (let ((_let_1 (real_V453051771R_real C))) (=> ((ord_less_real zero_zero_real) C) (= ((ord_less_eq_real (_let_1 A)) (_let_1 B)) ((ord_less_eq_real A) B))))) (forall ((A real) (B a) (C real) (D a)) (= ((plus_p1243198544real_a ((product_Pair_real_a A) B)) ((product_Pair_real_a C) D)) ((product_Pair_real_a ((plus_plus_real A) C)) ((plus_plus_a B) D)))) (forall ((X real) (Y real)) (=> ((ord_less_real ((plus_plus_real X) Y)) zero_zero_real) (or ((ord_less_real X) zero_zero_real) ((ord_less_real Y) zero_zero_real)))) (forall ((A product_prod_a_a) (B product_prod_a_a)) (= (= A ((plus_p1505579230od_a_a B) A)) (= B zero_z950819678od_a_a))) (forall ((A real) (C real) (B real)) (=> ((ord_less_eq_real A) zero_zero_real) (=> ((ord_less_eq_real C) B) ((ord_less_eq_real ((plus_plus_real A) C)) B)))) (forall ((A real)) (= ((plus_plus_real zero_zero_real) A) A)) (forall ((A3 set_a)) (= (collect_a (lambda ((X3 a)) ((member_a X3) A3))) A3)) (forall ((A set_Product_prod_a_a) (C2 set_se1596668135od_a_a) (B set_Product_prod_a_a) (D2 set_se1596668135od_a_a)) (=> ((member1838126896od_a_a A) C2) (=> ((member1838126896od_a_a B) D2) ((member1838126896od_a_a ((plus_p634297534od_a_a A) B)) ((plus_p1613276318od_a_a C2) D2))))) (forall ((A real) (C real) (B real)) (= ((ord_less_eq_real ((plus_plus_real A) C)) ((plus_plus_real B) C)) ((ord_less_eq_real A) B))) (forall ((X real) (A a) (B product_prod_a_a)) (= ((real_V296206913od_a_a X) ((produc1299253312od_a_a A) B)) ((produc1299253312od_a_a ((real_V1035702895aleR_a X) A)) ((real_V543523736od_a_a X) B)))) (forall ((A product_prod_a_a) (C2 set_Product_prod_a_a) (B product_prod_a_a) (D2 set_Product_prod_a_a)) (=> ((member449909584od_a_a A) C2) (=> ((member449909584od_a_a B) D2) ((member449909584od_a_a ((plus_p1505579230od_a_a A) B)) ((plus_p634297534od_a_a C2) D2))))) (forall ((A set_a)) (= ((plus_plus_set_a A) zero_zero_set_a) A)) (forall ((A real) (X a) (B real)) (= (= ((real_V1035702895aleR_a A) X) ((real_V1035702895aleR_a B) X)) (or (= X zero_zero_a) (= A B)))) (forall ((A real)) ((ord_less_real A) ((plus_plus_real A) one_one_real))) (forall ((A3 set_Product_prod_a_a) (B4 set_Product_prod_a_a) (C product_prod_a_a)) (let ((_let_1 (member449909584od_a_a C))) (=> ((ord_le1824328871od_a_a A3) B4) (=> (_let_1 A3) (_let_1 B4))))) (forall ((A a) (B a) (C a)) (let ((_let_1 (plus_plus_a A))) (= ((plus_plus_a (_let_1 B)) C) (_let_1 ((plus_plus_a B) C))))) (forall ((A set_real)) (= ((plus_plus_set_real A) zero_zero_set_real) A)) (forall ((C real) (X real) (D real) (Y real) (Z real)) (let ((_let_1 ((plus_plus_real ((real_V453051771R_real C) X)) ((plus_plus_real ((real_V453051771R_real D) Y)) Z)))) (= _let_1 _let_1))) (forall ((X real) (A real) (B product_prod_a_a)) (= ((real_V1943155903od_a_a X) ((produc454550562od_a_a A) B)) ((produc454550562od_a_a ((real_V453051771R_real X) A)) ((real_V543523736od_a_a X) B)))) (forall ((A produc957004601l_real)) (= ((plus_p77862768l_real zero_z659284464l_real) A) A)) (forall ((C real) (B real) (A real)) (let ((_let_1 (ord_less_eq_real B))) (=> ((ord_less_eq_real zero_zero_real) C) (=> (_let_1 A) (_let_1 ((plus_plus_real A) C)))))) (forall ((A real) (X real)) (let ((_let_1 (ord_less_eq_real zero_zero_real))) (=> (_let_1 A) (=> (_let_1 X) (_let_1 ((real_V453051771R_real A) X)))))) (forall ((A real) (B real)) (=> ((ord_less_real A) zero_zero_real) (=> ((ord_less_eq_real B) zero_zero_real) ((ord_less_real ((plus_plus_real A) B)) zero_zero_real)))) (forall ((X produc957004601l_real)) (= ((real_V1139189034l_real zero_zero_real) X) zero_z659284464l_real)) (forall ((A real) (B real) (X real)) (= ((real_V453051771R_real ((plus_plus_real A) B)) X) ((plus_plus_real ((real_V453051771R_real A) X)) ((real_V453051771R_real B) X)))) (forall ((A set_Product_prod_a_a)) (= ((plus_p634297534od_a_a zero_z257140542od_a_a) A) A)) (forall ((X real)) (= ((plus_plus_real zero_zero_real) X) X)) (forall ((A real) (B a) (A2 real) (B2 a)) (= (= ((product_Pair_real_a A) B) ((product_Pair_real_a A2) B2)) (and (= A A2) (= B B2)))) (forall ((X a) (Y a) (Z a)) (let ((_let_1 (product_Pair_a_a Z))) (let ((_let_2 (product_Pair_a_a X))) (let ((_let_3 (product_Pair_a_a Y))) (=> (and ((member449909584od_a_a (_let_3 X)) relation) ((member449909584od_a_a (_let_2 Y)) relation)) (=> (and ((member449909584od_a_a (_let_1 Y)) relation) ((member449909584od_a_a (_let_3 Z)) relation)) (and ((member449909584od_a_a (_let_2 Z)) relation) ((member449909584od_a_a (_let_1 X)) relation)))))))) (forall ((A real) (B real)) (let ((_let_1 (ord_less_eq_real zero_zero_real))) (=> (_let_1 A) (=> (_let_1 B) (_let_1 ((plus_plus_real A) B)))))) (forall ((A produc957004601l_real) (B produc957004601l_real)) (=> ((ord_le1342644953l_real A) zero_z659284464l_real) (=> ((ord_le1342644953l_real B) zero_z659284464l_real) ((ord_le1342644953l_real ((plus_p77862768l_real A) B)) zero_z659284464l_real)))) (forall ((A real) (B real) (X real) (Y real)) (let ((_let_1 (ord_less_eq_real zero_zero_real))) (=> ((ord_less_eq_real A) B) (=> ((ord_less_eq_real X) Y) (=> (_let_1 B) (=> (_let_1 X) ((ord_less_eq_real ((real_V453051771R_real A) X)) ((real_V453051771R_real B) Y)))))))) (forall ((X real) (A product_prod_a_a) (B real)) (= ((real_V195069393a_real X) ((produc454274172a_real A) B)) ((produc454274172a_real ((real_V543523736od_a_a X) A)) ((real_V453051771R_real X) B)))) (forall ((B a) (A a) (C a)) (= (= ((plus_plus_a B) A) ((plus_plus_a C) A)) (= B C))) (forall ((A a)) (= ((plus_plus_a zero_zero_a) A) A)) (= (lambda ((Y6 real) (Z2 real)) (= Y6 Z2)) (lambda ((X3 real) (Y5 real)) (and ((ord_less_eq_real X3) Y5) ((ord_less_eq_real Y5) X3)))) (forall ((A real) (B set_a) (C real) (D set_a)) (= ((plus_p125342128_set_a ((produc1872317017_set_a A) B)) ((produc1872317017_set_a C) D)) ((produc1872317017_set_a ((plus_plus_real A) C)) ((plus_plus_set_a B) D)))) (forall ((A produc957004601l_real) (B produc957004601l_real) (C produc957004601l_real)) (=> ((ord_le1342644953l_real A) B) ((ord_le1342644953l_real ((plus_p77862768l_real A) C)) ((plus_p77862768l_real B) C)))) (forall ((X real) (A a) (B real)) (= ((real_V512797224a_real X) ((product_Pair_a_real A) B)) ((product_Pair_a_real ((real_V1035702895aleR_a X) A)) ((real_V453051771R_real X) B)))) (forall ((X real) (A real) (B real)) (let ((_let_1 (real_V453051771R_real X))) (= ((real_V1139189034l_real X) ((produc705216881l_real A) B)) ((produc705216881l_real (_let_1 A)) (_let_1 B))))) (forall ((B produc957004601l_real) (A produc957004601l_real)) (= ((ord_le1342644953l_real ((plus_p77862768l_real B) A)) B) ((ord_le1342644953l_real A) zero_z659284464l_real))) (forall ((X a) (A3 set_a) (B4 set_a)) (=> ((member_a X) ((plus_plus_set_a A3) B4)) (not (forall ((A5 a) (B5 a)) (=> (= X ((plus_plus_a A5) B5)) (=> ((member_a A5) A3) (not ((member_a B5) B4)))))))) (forall ((A a) (B a) (A2 a) (B2 a)) (=> (= ((product_Pair_a_a A) B) ((product_Pair_a_a A2) B2)) (not (=> (= A A2) (not (= B B2)))))) (forall ((I produc957004601l_real) (J produc957004601l_real) (K produc957004601l_real) (L produc957004601l_real)) (=> (and ((ord_le1342644953l_real I) J) ((ord_le1342644953l_real K) L)) ((ord_le1342644953l_real ((plus_p77862768l_real I) K)) ((plus_p77862768l_real J) L)))) (forall ((A a) (B set_a) (C a) (D set_a)) (= ((plus_p1265825342_set_a ((product_Pair_a_set_a A) B)) ((product_Pair_a_set_a C) D)) ((product_Pair_a_set_a ((plus_plus_a A) C)) ((plus_plus_set_a B) D)))) _let_13 (forall ((A real) (B real) (C real)) (let ((_let_1 (ord_less_real B))) (=> ((ord_less_eq_real zero_zero_real) A) (=> (_let_1 C) (_let_1 ((plus_plus_real A) C)))))) (forall ((X real) (Y real)) (= ((plus_plus_real ((real_V453051771R_real zero_zero_real) X)) Y) Y)) (forall ((A product_prod_a_a)) (= ((plus_p1505579230od_a_a zero_z950819678od_a_a) A) A)) (forall ((X a) (Y a)) (let ((_let_1 ((member449909584od_a_a ((product_Pair_a_a Y) X)) relation))) (=> (and _let_1 ((member449909584od_a_a ((product_Pair_a_a X) Y)) relation)) _let_1))) (forall ((A real) (B real)) (= ((ord_less_eq_real ((plus_plus_real A) B)) B) ((ord_less_eq_real A) zero_zero_real))) (forall ((C real) (A real) (B real)) (let ((_let_1 (real_V453051771R_real C))) (= ((ord_less_eq_real (_let_1 A)) (_let_1 B)) (and (=> ((ord_less_real zero_zero_real) C) ((ord_less_eq_real A) B)) (=> ((ord_less_real C) zero_zero_real) ((ord_less_eq_real B) A)))))) (forall ((A produc957004601l_real) (B produc957004601l_real)) (= ((ord_le1342644953l_real A) ((plus_p77862768l_real B) A)) ((ord_le1342644953l_real zero_z659284464l_real) B))) (forall ((I produc957004601l_real) (J produc957004601l_real) (K produc957004601l_real) (L produc957004601l_real)) (=> (and (= I J) ((ord_le1342644953l_real K) L)) ((ord_le1342644953l_real ((plus_p77862768l_real I) K)) ((plus_p77862768l_real J) L)))) (forall ((A3 set_Product_prod_a_a) (B4 set_Product_prod_a_a)) (=> ((member449909584od_a_a zero_z950819678od_a_a) A3) ((ord_le1824328871od_a_a B4) ((plus_p634297534od_a_a A3) B4)))) (forall ((P (-> product_prod_a_a Bool)) (P2 product_prod_a_a)) (=> (forall ((A5 a) (B5 a)) (P ((product_Pair_a_a A5) B5))) (P P2))) _let_12 (forall ((A real) (B real) (C real)) (let ((_let_1 (plus_plus_real A))) (=> (= (_let_1 B) (_let_1 C)) (= B C)))) (forall ((A real) (B real) (C real)) (let ((_let_1 (plus_plus_real A))) (= ((plus_plus_real (_let_1 B)) C) (_let_1 ((plus_plus_real B) C))))) (forall ((A real) (B real) (C real)) (=> ((ord_less_real zero_zero_real) A) (=> ((ord_less_eq_real B) C) ((ord_less_real B) ((plus_plus_real A) C))))) _let_11 (forall ((A real) (B real)) (=> ((ord_less_real A) zero_zero_real) (=> ((ord_less_real B) zero_zero_real) ((ord_less_real ((plus_plus_real A) B)) zero_zero_real)))) (forall ((A real)) (= ((plus_plus_real zero_zero_real) A) A)) (forall ((A real) (B real)) (= ((ord_less_real A) ((plus_plus_real A) B)) ((ord_less_real zero_zero_real) B))) (forall ((Pr set_Product_prod_a_a) (X a) (Y a) (U real) (V real)) (let ((_let_1 (ord_less_real zero_zero_real))) (=> (prefer529818233pref_a Pr) (=> ((member449909584od_a_a ((product_Pair_a_a X) Y)) Pr) (=> (_let_1 U) (=> (_let_1 V) (=> (= ((plus_plus_real U) V) one_one_real) ((member449909584od_a_a ((product_Pair_a_a ((plus_plus_a ((real_V1035702895aleR_a U) X)) ((real_V1035702895aleR_a V) Y))) Y)) Pr)))))))) _let_8 (forall ((A3 a) (K a) (A a) (B a)) (let ((_let_1 (plus_plus_a K))) (=> (= A3 (_let_1 A)) (= ((plus_plus_a A3) B) (_let_1 ((plus_plus_a A) B)))))) (forall ((A real) (B real) (C real)) (let ((_let_1 (plus_plus_real A))) (= ((plus_plus_real (_let_1 B)) C) (_let_1 ((plus_plus_real B) C))))) (forall ((I real) (J real) (K real) (L real)) (=> (and ((ord_less_real I) J) (= K L)) ((ord_less_real ((plus_plus_real I) K)) ((plus_plus_real J) L)))) (forall ((I real) (J real) (K real) (L real)) (=> (and ((ord_less_real K) L) (= I J)) ((ord_less_real ((plus_plus_real I) K)) ((plus_plus_real J) L)))) (forall ((R real) (A real) (B real)) (let ((_let_1 (real_V453051771R_real R))) (= ((real_V1139189034l_real R) ((produc705216881l_real A) B)) ((produc705216881l_real (_let_1 A)) (_let_1 B))))) (forall ((A real) (F2 (-> real real)) (B real) (C real)) (let ((_let_1 (ord_less_eq_real A))) (=> (_let_1 (F2 B)) (=> ((ord_less_eq_real B) C) (=> (forall ((X4 real) (Y3 real)) (=> ((ord_less_eq_real X4) Y3) ((ord_less_eq_real (F2 X4)) (F2 Y3)))) (_let_1 (F2 C))))))) (forall ((I real) (J real) (K real) (L real)) (=> (and ((ord_less_eq_real K) L) ((ord_less_real I) J)) ((ord_less_real ((plus_plus_real I) K)) ((plus_plus_real J) L)))) (forall ((A real) (B real) (X real)) (=> ((ord_less_eq_real A) B) (=> ((ord_less_eq_real zero_zero_real) X) ((ord_less_eq_real ((real_V453051771R_real A) X)) ((real_V453051771R_real B) X))))) (forall ((A real)) (= ((plus_plus_real A) zero_zero_real) A)) (forall ((C real) (X real) (D real) (Y real) (Z real)) (let ((_let_1 (plus_plus_real ((real_V453051771R_real C) X)))) (let ((_let_2 (plus_plus_real ((real_V453051771R_real D) Y)))) (= (_let_1 (_let_2 Z)) (_let_2 (_let_1 Z)))))) (forall ((A real) (B real)) (= ((ord_less_eq_real ((real_V453051771R_real A) B)) zero_zero_real) (or (and ((ord_less_real zero_zero_real) A) ((ord_less_eq_real B) zero_zero_real)) (and ((ord_less_real A) zero_zero_real) ((ord_less_eq_real zero_zero_real) B)) (= A zero_zero_real)))) (forall ((A real) (B real) (C real)) (let ((_let_1 (ord_less_eq_real B))) (=> ((ord_less_eq_real zero_zero_real) A) (=> (_let_1 C) (_let_1 ((plus_plus_real A) C)))))) (forall ((C produc957004601l_real) (A produc957004601l_real) (B produc957004601l_real)) (let ((_let_1 (plus_p77862768l_real C))) (= ((ord_le1342644953l_real (_let_1 A)) (_let_1 B)) ((ord_le1342644953l_real A) B)))) (forall ((A product_prod_a_real)) (= ((plus_p541014626a_real zero_z705155042a_real) A) A)) (forall ((R real) (A real) (B product_prod_a_a)) (= ((real_V1943155903od_a_a R) ((produc454550562od_a_a A) B)) ((produc454550562od_a_a ((real_V453051771R_real R) A)) ((real_V543523736od_a_a R) B)))) (forall ((I produc957004601l_real) (J produc957004601l_real) (K produc957004601l_real) (L produc957004601l_real)) (=> (and (= K L) ((ord_le1342644953l_real I) J)) ((ord_le1342644953l_real ((plus_p77862768l_real I) K)) ((plus_p77862768l_real J) L)))) (forall ((R real) (A real) (B a)) (= ((real_V1214981142real_a R) ((product_Pair_real_a A) B)) ((product_Pair_real_a ((real_V453051771R_real R) A)) ((real_V1035702895aleR_a R) B)))) (forall ((X1 real) (X2 real) (Y1 real) (Y2 real)) (= (= ((produc705216881l_real X1) X2) ((produc705216881l_real Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))) (forall ((A a) (B a)) (= (= A ((plus_plus_a A) B)) (= B zero_zero_a))) (forall ((Y real) (X real)) (=> ((ord_less_eq_real Y) X) (= ((ord_less_eq_real X) Y) (= X Y)))) (forall ((X real) (A real)) (=> ((ord_less_eq_real zero_zero_real) X) (=> ((ord_less_eq_real A) one_one_real) ((ord_less_eq_real ((real_V453051771R_real A) X)) X)))) (forall ((B real) (A real) (C real)) (= (= ((plus_plus_real B) A) ((plus_plus_real C) A)) (= B C))) (forall ((A real) (B real) (C real) (D real)) (let ((_let_1 (ord_less_eq_real zero_zero_real))) (=> ((ord_less_eq_real A) B) (=> ((ord_less_eq_real C) D) (=> (_let_1 A) (=> (_let_1 C) ((ord_less_eq_real ((real_V453051771R_real A) C)) ((real_V453051771R_real B) D)))))))) (forall ((A real) (B real) (C real) (D real)) (=> ((ord_less_eq_real A) B) (=> ((ord_less_real C) D) ((ord_less_real ((plus_plus_real A) C)) ((plus_plus_real B) D))))) (forall ((A produc957004601l_real) (B produc957004601l_real)) (= (= A ((plus_p77862768l_real A) B)) (= B zero_z659284464l_real))) (forall ((I real) (J real) (K real) (L real)) (=> (and (= K L) (= I J)) (= ((plus_plus_real I) K) ((plus_plus_real J) L)))) (forall ((X real) (A real) (B real)) (=> (not (= X zero_zero_real)) (=> (= ((real_V453051771R_real A) X) ((real_V453051771R_real B) X)) (= A B)))) (_let_4 v) (forall ((C real) (A real) (B real)) (let ((_let_1 (real_V453051771R_real C))) (=> ((ord_less_real C) zero_zero_real) (= ((ord_less_eq_real (_let_1 A)) (_let_1 B)) ((ord_less_eq_real B) A))))) (forall ((A real)) (let ((_let_1 (ord_less_real zero_zero_real))) (= (_let_1 ((plus_plus_real A) A)) (_let_1 A)))) (forall ((B a) (U real) (A a)) (let ((_let_1 (real_V1035702895aleR_a U))) (= (= ((plus_plus_a B) (_let_1 A)) ((plus_plus_a A) (_let_1 B))) (or (= U one_one_real) (= A B))))) (forall ((C real) (A real) (B real)) (let ((_let_1 (plus_plus_real C))) (= ((ord_less_real (_let_1 A)) (_let_1 B)) ((ord_less_real A) B)))) (forall ((A real) (B real)) (let ((_let_1 (ord_less_real zero_zero_real))) (=> (_let_1 A) (=> (_let_1 B) (_let_1 ((plus_plus_real A) B)))))) (forall ((A real) (B real) (C real) (D real)) (=> ((ord_less_eq_real A) B) (=> ((ord_less_eq_real C) D) ((ord_less_eq_real ((plus_plus_real A) C)) ((plus_plus_real B) D))))) (forall ((B real) (A real) (C real)) (=> (= ((plus_plus_real B) A) ((plus_plus_real C) A)) (= B C))) (forall ((X product_prod_a_a) (A3 set_Product_prod_a_a) (B4 set_Product_prod_a_a)) (=> ((member449909584od_a_a X) ((plus_p634297534od_a_a A3) B4)) (not (forall ((A5 product_prod_a_a) (B5 product_prod_a_a)) (=> (= X ((plus_p1505579230od_a_a A5) B5)) (=> ((member449909584od_a_a A5) A3) (not ((member449909584od_a_a B5) B4)))))))) (forall ((A real) (B real)) (= ((ord_less_real ((plus_plus_real A) B)) B) ((ord_less_real A) zero_zero_real))) _let_7 (forall ((A produc957004601l_real) (B produc957004601l_real)) (let ((_let_1 (ord_le1342644953l_real zero_z659284464l_real))) (=> (_let_1 A) (=> (_let_1 B) (_let_1 ((plus_p77862768l_real A) B)))))) (forall ((X real)) ((ord_less_eq_real X) X)) (forall ((Pr set_Pr147102617l_real) (X real) (Y real) (U real) (V real)) (let ((_let_1 (ord_less_real zero_zero_real))) (=> (prefer1247792113f_real Pr) (=> ((member1068169442l_real ((produc705216881l_real X) Y)) Pr) (=> (_let_1 U) (=> (_let_1 V) (=> (= ((plus_plus_real U) V) one_one_real) ((member1068169442l_real ((produc705216881l_real ((plus_plus_real ((real_V453051771R_real U) X)) ((real_V453051771R_real V) Y))) Y)) Pr)))))))) (forall ((A real) (B real) (C real)) (=> ((ord_less_real A) B) ((ord_less_real ((plus_plus_real A) C)) ((plus_plus_real B) C)))) (_let_4 u) (forall ((A real) (B real)) (=> ((ord_less_real A) B) ((ord_less_real ((plus_plus_real A) one_one_real)) ((plus_plus_real B) one_one_real)))) (forall ((A3 set_real)) (= (collect_real (lambda ((X3 real)) ((member_real X3) A3))) A3)) (forall ((A product_prod_a_real) (B product_prod_a_real)) (= (= A ((plus_p541014626a_real A) B)) (= B zero_z705155042a_real))) _let_5 (forall ((A product_prod_a_a)) (= ((plus_p1505579230od_a_a A) zero_z950819678od_a_a) A)) (forall ((I real) (J real) (K real) (L real)) (=> (and ((ord_less_real K) L) ((ord_less_real I) J)) ((ord_less_real ((plus_plus_real I) K)) ((plus_plus_real J) L)))) (forall ((R real) (A product_prod_a_a) (B product_prod_a_a)) (let ((_let_1 (real_V543523736od_a_a R))) (= ((real_V368978776od_a_a R) ((produc1474507607od_a_a A) B)) ((produc1474507607od_a_a (_let_1 A)) (_let_1 B))))) (forall ((A real) (B real) (X a)) (= ((real_V1035702895aleR_a ((plus_plus_real A) B)) X) ((plus_plus_a ((real_V1035702895aleR_a A) X)) ((real_V1035702895aleR_a B) X)))) (forall ((Pr set_Pr1948701895od_a_a)) (=> (forall ((X4 product_prod_a_a) (Y3 product_prod_a_a)) (=> ((member2057358096od_a_a ((produc1474507607od_a_a X4) Y3)) Pr) (forall ((Alpha real) (Beta real)) (let ((_let_1 (ord_less_eq_real zero_zero_real))) (=> (and (= ((plus_plus_real Alpha) Beta) one_one_real) (_let_1 Alpha) (_let_1 Beta)) ((member2057358096od_a_a ((produc1474507607od_a_a ((plus_p1505579230od_a_a ((real_V543523736od_a_a Alpha) X4)) ((real_V543523736od_a_a Beta) Y3))) Y3)) Pr)))))) (prefer225425826od_a_a Pr))) (forall ((A produc957004601l_real) (B produc957004601l_real)) (= (= A ((plus_p77862768l_real B) A)) (= B zero_z659284464l_real))) (forall ((B a) (A a)) (= (= ((plus_plus_a B) A) A) (= B zero_zero_a))) (forall ((B a) (A a) (C a)) (= (= ((plus_plus_a B) A) ((plus_plus_a C) A)) (= B C))) (forall ((B product_prod_a_real) (A product_prod_a_real)) (= (= ((plus_p541014626a_real B) A) A) (= B zero_z705155042a_real))) (forall ((A real)) (= ((ord_less_eq_real ((plus_plus_real A) A)) zero_zero_real) ((ord_less_eq_real A) zero_zero_real))) (forall ((A product_prod_a_a)) (= ((plus_p1505579230od_a_a zero_z950819678od_a_a) A) A)) (forall ((X real) (Y real)) (or ((ord_less_eq_real X) Y) ((ord_less_eq_real Y) X))) (forall ((I real) (J real) (K real) (L real)) (=> (and ((ord_less_eq_real I) J) ((ord_less_real K) L)) ((ord_less_real ((plus_plus_real I) K)) ((plus_plus_real J) L)))) (forall ((C real) (X real) (Z real) (D real)) (= ((plus_plus_real ((plus_plus_real ((real_V453051771R_real C) X)) Z)) ((real_V453051771R_real D) X)) ((plus_plus_real ((real_V453051771R_real ((plus_plus_real C) D)) X)) Z))) (forall ((A produc957004601l_real) (C2 set_Pr147102617l_real) (B produc957004601l_real) (D2 set_Pr147102617l_real)) (=> ((member1068169442l_real A) C2) (=> ((member1068169442l_real B) D2) ((member1068169442l_real ((plus_p77862768l_real A) B)) ((plus_p1708760016l_real C2) D2))))) (forall ((A real) (B real)) (= (= A ((plus_plus_real B) A)) (= B zero_zero_real))) (forall ((C real)) (= ((real_V453051771R_real C) zero_zero_real) zero_zero_real)) (forall ((A set_Product_prod_a_a)) (= ((plus_p634297534od_a_a A) zero_z257140542od_a_a) A)) (forall ((C real) (A real) (B real)) (let ((_let_1 (plus_plus_real C))) (= ((ord_less_eq_real (_let_1 A)) (_let_1 B)) ((ord_less_eq_real A) B)))) (_let_4 zero_zero_real) (= ord_le1824328871od_a_a (lambda ((A6 set_Product_prod_a_a) (B6 set_Product_prod_a_a)) (forall ((X3 product_prod_a_a)) (let ((_let_1 (member449909584od_a_a X3))) (=> (_let_1 A6) (_let_1 B6)))))) (forall ((A real) (B real)) (let ((_let_1 (ord_less_eq_real zero_zero_real))) (= (_let_1 ((real_V453051771R_real A) B)) (or (= A zero_zero_real) (and ((ord_less_eq_real B) zero_zero_real) ((ord_less_real A) zero_zero_real)) (and (_let_1 B) ((ord_less_real zero_zero_real) A)))))) (forall ((A real) (B real)) (= ((ord_less_eq_real A) ((plus_plus_real B) A)) ((ord_less_eq_real zero_zero_real) B))) (forall ((A real) (B real) (C real)) (let ((_let_1 (plus_plus_real A))) (= (= (_let_1 B) (_let_1 C)) (= B C)))) (forall ((X a) (A real) (B real)) (=> (not (= X zero_zero_a)) (=> (= ((real_V1035702895aleR_a A) X) ((real_V1035702895aleR_a B) X)) (= A B)))) (forall ((A produc957004601l_real) (C produc957004601l_real) (B produc957004601l_real)) (= ((ord_le1342644953l_real ((plus_p77862768l_real A) C)) ((plus_p77862768l_real B) C)) ((ord_le1342644953l_real A) B))) (forall ((A a) (B real) (A2 a) (B2 real)) (= (= ((product_Pair_a_real A) B) ((product_Pair_a_real A2) B2)) (and (= A A2) (= B B2)))) (= (lambda ((Y6 real) (Z2 real)) (= Y6 Z2)) (lambda ((A4 real) (B3 real)) (and ((ord_less_eq_real B3) A4) ((ord_less_eq_real A4) B3)))) (forall ((A a) (B a) (C a)) (let ((_let_1 (plus_plus_a A))) (= (= (_let_1 B) (_let_1 C)) (= B C)))) (forall ((C produc957004601l_real) (A produc957004601l_real) (B produc957004601l_real)) (=> ((ord_le1342644953l_real C) zero_z659284464l_real) (=> ((ord_le1342644953l_real A) B) ((ord_le1342644953l_real ((plus_p77862768l_real A) C)) B)))) (forall ((Pr set_Product_prod_a_a)) (=> (forall ((X4 a) (Y3 a) (Alpha real) (Beta real)) (let ((_let_1 (ord_less_real zero_zero_real))) (=> ((member449909584od_a_a ((product_Pair_a_a X4) Y3)) Pr) (=> (= ((plus_plus_real Alpha) Beta) one_one_real) (=> (_let_1 Alpha) (=> (_let_1 Beta) ((member449909584od_a_a ((product_Pair_a_a ((plus_plus_a ((real_V1035702895aleR_a Alpha) X4)) ((real_V1035702895aleR_a Beta) Y3))) Y3)) Pr))))))) (prefer529818233pref_a Pr))) (forall ((A real)) (= ((ord_less_real ((plus_plus_real A) A)) zero_zero_real) ((ord_less_real A) zero_zero_real))) (forall ((X real)) (= ((real_V453051771R_real zero_zero_real) X) zero_zero_real)) (not (_let_3 one_one_real)) (forall ((A a) (B a)) (= (= A ((plus_plus_a B) A)) (= B zero_zero_a))) (forall ((A set_real) (B real) (C set_real) (D real)) (= ((plus_p1952869542l_real ((produc1812461223l_real A) B)) ((produc1812461223l_real C) D)) ((produc1812461223l_real ((plus_plus_set_real A) C)) ((plus_plus_real B) D)))) _let_2 (forall ((A a) (B a) (C a) (D a)) (= ((plus_p1505579230od_a_a ((product_Pair_a_a A) B)) ((product_Pair_a_a C) D)) ((product_Pair_a_a ((plus_plus_a A) C)) ((plus_plus_a B) D)))) (forall ((A produc957004601l_real) (C produc957004601l_real) (B produc957004601l_real)) (=> ((ord_le1342644953l_real ((plus_p77862768l_real A) C)) ((plus_p77862768l_real B) C)) ((ord_le1342644953l_real A) B))) (forall ((A3 set_Pr147102617l_real)) (= (collec1300223524l_real (lambda ((X3 produc957004601l_real)) ((member1068169442l_real X3) A3))) A3)) (forall ((X real) (Y real) (Xa a)) (= ((real_V1035702895aleR_a ((plus_plus_real X) Y)) Xa) ((plus_plus_a ((real_V1035702895aleR_a X) Xa)) ((real_V1035702895aleR_a Y) Xa)))) (forall ((Pr set_Pr147102617l_real)) (=> (forall ((X4 real) (Y3 real) (Alpha real) (Beta real)) (let ((_let_1 (ord_less_real zero_zero_real))) (=> ((member1068169442l_real ((produc705216881l_real X4) Y3)) Pr) (=> (= ((plus_plus_real Alpha) Beta) one_one_real) (=> (_let_1 Alpha) (=> (_let_1 Beta) ((member1068169442l_real ((produc705216881l_real ((plus_plus_real ((real_V453051771R_real Alpha) X4)) ((real_V453051771R_real Beta) Y3))) Y3)) Pr))))))) (prefer1247792113f_real Pr))) (forall ((B a) (A a) (C a)) (=> (= ((plus_plus_a B) A) ((plus_plus_a C) A)) (= B C))) (forall ((A real)) (= ((plus_plus_real zero_zero_real) A) A)) _let_1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
0.65/0.83	)
0.65/0.83	% SZS output end Proof for theBenchmark
0.65/0.83	EOF