0.07/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.13	% Command    : do_cvc5 %s %d
0.13/0.34	% Computer   : n020.cluster.edu
0.13/0.34	% Model      : x86_64 x86_64
0.13/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.34	% Memory     : 8042.1875MB
0.13/0.34	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.34	% CPULimit   : 1200
0.13/0.34	% WCLimit    : 120
0.13/0.34	% DateTime   : Tue Jul 13 15:13:36 EDT 2021
0.13/0.34	% CPUTime    : 
0.31/0.54	%----THF division
0.33/0.54	------- cvc5-thf casc 28 : /export/starexec/sandbox2/benchmark/theBenchmark.p at 120...
0.33/0.54	--- Run --ho-elim --full-saturate-quant at 10...
0.33/0.79	% SZS status Theorem for theBenchmark
0.33/0.80	% SZS output start Proof for theBenchmark
0.33/0.80	(proof
0.33/0.80	(let ((_let_1 (= funpow_complex compow1667379464omplex))) (let ((_let_2 (lambda ((Z2 complex)) one_one_complex))) (let ((_let_3 (deriv_complex id_complex))) (let ((_let_4 (= _let_3 _let_2))) (let ((_let_5 (image_real_real id_real))) (let ((_let_6 (= _let_5 id_set_real))) (let ((_let_7 (= (arcosh_real one_one_real) zero_zero_real))) (let ((_let_8 (_let_3 w))) (let ((_let_9 (not (= _let_8 one_one_complex)))) (let ((_let_10 (image_58037603omplex id_complex))) (let ((_let_11 (= _let_10 id_set_complex))) (let ((_let_12 (= funpow_real_real compow1723822618l_real))) (let ((_let_13 (lambda ((X complex)) X))) (let ((_let_14 (= id_complex _let_13))) (let ((_let_15 ((deriv_complex f) w))) (let ((_let_16 ((deriv_complex g) (f w)))) (let ((_let_17 ((times_times_complex _let_16) _let_15))) (let ((_let_18 ((times_times_complex _let_15) _let_16))) (let ((_let_19 (= funpow1854104714omplex compow1098280738omplex))) (let ((_let_20 (= (ln_ln_complex one_one_complex) zero_zero_complex))) (let ((_let_21 (= id_real (lambda ((X real)) X)))) (let ((_let_22 ((deriv_complex ((comp_c130555887omplex g) f)) w))) (let ((_let_23 (= comp_c130555887omplex (lambda ((F2 (-> complex complex)) (G (-> complex complex)) (X complex)) (F2 (G X)))))) (let ((_let_24 (= (comp_c130555887omplex id_complex) id_complex_complex))) (let ((_let_25 (= (image_944012797omplex id_complex_complex) id_set1618538368omplex))) (let ((_let_26 (= ord_le701908932omplex (lambda ((A5 set_complex) (B5 set_complex)) (forall ((X complex)) (let ((_let_1 (member_complex X))) (=> (_let_1 A5) (_let_1 B5)))))))) (let ((_let_27 (forall ((N nat) (M nat) (F (-> complex complex))) (= ((compow1667379464omplex N) ((compow1667379464omplex M) F)) ((compow1667379464omplex ((times_times_nat M) N)) F))))) (let ((_let_28 (forall ((BOUND_VARIABLE_12456 complex)) (= one_one_complex (ho_72 k_86 BOUND_VARIABLE_12456))))) (let ((_let_29 (= one_one_complex (ho_72 k_86 w)))) (let ((_let_30 (forall ((u |u_(-> _u_(-> _u_(-> real real)_ real real)_ _u_(-> real real)_ real real)|) (e |u_(-> _u_(-> real real)_ real real)|) (i |u_(-> _u_(-> real real)_ real real)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> real real)_ real real)_ _u_(-> real real)_ real real)|)) (not (forall ((ii |u_(-> _u_(-> real real)_ real real)|)) (= (ho_217 v ii) (ite (= i ii) e (ho_217 u ii)))))))))) (let ((_let_31 (forall ((x |u_(-> _u_(-> _u_(-> real real)_ real real)_ _u_(-> real real)_ real real)|) (y |u_(-> _u_(-> _u_(-> real real)_ real real)_ _u_(-> real real)_ real real)|)) (or (not (forall ((z |u_(-> _u_(-> real real)_ real real)|)) (= (ho_217 x z) (ho_217 y z)))) (= x y))))) (let ((_let_32 (forall ((u |u_(-> set_complex complex)|) (e complex) (i set_complex)) (not (forall ((v |u_(-> set_complex complex)|)) (not (forall ((ii set_complex)) (= (ho_214 v ii) (ite (= i ii) e (ho_214 u ii)))))))))) (let ((_let_33 (forall ((x |u_(-> set_complex complex)|) (y |u_(-> set_complex complex)|)) (or (not (forall ((z set_complex)) (= (ho_214 x z) (ho_214 y z)))) (= x y))))) (let ((_let_34 (forall ((u |u_(-> _u_(-> real complex complex)_ real real)|) (e |u_(-> real real)|) (i |u_(-> real complex complex)|)) (not (forall ((v |u_(-> _u_(-> real complex complex)_ real real)|)) (not (forall ((ii |u_(-> real complex complex)|)) (= (ho_213 v ii) (ite (= i ii) e (ho_213 u ii)))))))))) (let ((_let_35 (forall ((x |u_(-> _u_(-> real complex complex)_ real real)|) (y |u_(-> _u_(-> real complex complex)_ real real)|)) (or (not (forall ((z |u_(-> real complex complex)|)) (= (ho_213 x z) (ho_213 y z)))) (= x y))))) (let ((_let_36 (forall ((u |u_(-> _u_(-> real complex complex)_ _u_(-> _u_(-> complex complex)_ real)_ _u_(-> complex complex)_ complex complex)|) (e |u_(-> _u_(-> _u_(-> complex complex)_ real)_ _u_(-> complex complex)_ complex complex)|) (i |u_(-> real complex complex)|)) (not (forall ((v |u_(-> _u_(-> real complex complex)_ _u_(-> _u_(-> complex complex)_ real)_ _u_(-> complex complex)_ complex complex)|)) (not (forall ((ii |u_(-> real complex complex)|)) (= (ho_209 v ii) (ite (= i ii) e (ho_209 u ii)))))))))) (let ((_let_37 (forall ((x |u_(-> _u_(-> real complex complex)_ _u_(-> _u_(-> complex complex)_ real)_ _u_(-> complex complex)_ complex complex)|) (y |u_(-> _u_(-> real complex complex)_ _u_(-> _u_(-> complex complex)_ real)_ _u_(-> complex complex)_ complex complex)|)) (or (not (forall ((z |u_(-> real complex complex)|)) (= (ho_209 x z) (ho_209 y z)))) (= x y))))) (let ((_let_38 (forall ((u |u_(-> real complex complex)|) (e |u_(-> complex complex)|) (i real)) (not (forall ((v |u_(-> real complex complex)|)) (not (forall ((ii real)) (= (ho_207 v ii) (ite (= i ii) e (ho_207 u ii)))))))))) (let ((_let_39 (forall ((x |u_(-> real complex complex)|) (y |u_(-> real complex complex)|)) (or (not (forall ((z real)) (= (ho_207 x z) (ho_207 y z)))) (= x y))))) (let ((_let_40 (forall ((u |u_(-> _u_(-> _u_(-> complex complex)_ real)_ _u_(-> complex complex)_ complex complex)|) (e |u_(-> _u_(-> complex complex)_ complex complex)|) (i |u_(-> _u_(-> complex complex)_ real)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> complex complex)_ real)_ _u_(-> complex complex)_ complex complex)|)) (not (forall ((ii |u_(-> _u_(-> complex complex)_ real)|)) (= (ho_210 v ii) (ite (= i ii) e (ho_210 u ii)))))))))) (let ((_let_41 (forall ((x |u_(-> _u_(-> _u_(-> complex complex)_ real)_ _u_(-> complex complex)_ complex complex)|) (y |u_(-> _u_(-> _u_(-> complex complex)_ real)_ _u_(-> complex complex)_ complex complex)|)) (or (not (forall ((z |u_(-> _u_(-> complex complex)_ real)|)) (= (ho_210 x z) (ho_210 y z)))) (= x y))))) (let ((_let_42 (forall ((u |u_(-> _u_(-> complex complex)_ real)|) (e real) (i |u_(-> complex complex)|)) (not (forall ((v |u_(-> _u_(-> complex complex)_ real)|)) (not (forall ((ii |u_(-> complex complex)|)) (= (ho_206 v ii) (ite (= i ii) e (ho_206 u ii)))))))))) (let ((_let_43 (forall ((x |u_(-> _u_(-> complex complex)_ real)|) (y |u_(-> _u_(-> complex complex)_ real)|)) (or (not (forall ((z |u_(-> complex complex)|)) (= (ho_206 x z) (ho_206 y z)))) (= x y))))) (let ((_let_44 (forall ((u |u_(-> set_complex set_complex set_complex)|) (e |u_(-> set_complex set_complex)|) (i set_complex)) (not (forall ((v |u_(-> set_complex set_complex set_complex)|)) (not (forall ((ii set_complex)) (= (ho_203 v ii) (ite (= i ii) e (ho_203 u ii)))))))))) (let ((_let_45 (forall ((x |u_(-> set_complex set_complex set_complex)|) (y |u_(-> set_complex set_complex set_complex)|)) (or (not (forall ((z set_complex)) (= (ho_203 x z) (ho_203 y z)))) (= x y))))) (let ((_let_46 (forall ((u |u_(-> _u_(-> complex complex complex)_ _u_(-> _u_(-> complex complex)_ complex)_ _u_(-> complex complex)_ complex complex)|) (e |u_(-> _u_(-> _u_(-> complex complex)_ complex)_ _u_(-> complex complex)_ complex complex)|) (i |u_(-> complex complex complex)|)) (not (forall ((v |u_(-> _u_(-> complex complex complex)_ _u_(-> _u_(-> complex complex)_ complex)_ _u_(-> complex complex)_ complex complex)|)) (not (forall ((ii |u_(-> complex complex complex)|)) (= (ho_198 v ii) (ite (= i ii) e (ho_198 u ii)))))))))) (let ((_let_47 (forall ((x |u_(-> _u_(-> complex complex complex)_ _u_(-> _u_(-> complex complex)_ complex)_ _u_(-> complex complex)_ complex complex)|) (y |u_(-> _u_(-> complex complex complex)_ _u_(-> _u_(-> complex complex)_ complex)_ _u_(-> complex complex)_ complex complex)|)) (or (not (forall ((z |u_(-> complex complex complex)|)) (= (ho_198 x z) (ho_198 y z)))) (= x y))))) (let ((_let_48 (forall ((u |u_(-> Bool real real real)|) (e |u_(-> real real real)|) (i Bool)) (not (forall ((v |u_(-> Bool real real real)|)) (not (forall ((ii Bool)) (= (ho_201 v ii) (ite (= ii i) e (ho_201 u ii)))))))))) (let ((_let_49 (forall ((x |u_(-> Bool real real real)|) (y |u_(-> Bool real real real)|)) (or (not (forall ((z Bool)) (= (ho_201 x z) (ho_201 y z)))) (= x y))))) (let ((_let_50 (forall ((u |u_(-> _u_(-> complex complex complex)_ complex complex)|) (e |u_(-> complex complex)|) (i |u_(-> complex complex complex)|)) (not (forall ((v |u_(-> _u_(-> complex complex complex)_ complex complex)|)) (not (forall ((ii |u_(-> complex complex complex)|)) (= (ho_196 v ii) (ite (= i ii) e (ho_196 u ii)))))))))) (let ((_let_51 (forall ((x |u_(-> _u_(-> complex complex complex)_ complex complex)|) (y |u_(-> _u_(-> complex complex complex)_ complex complex)|)) (or (not (forall ((z |u_(-> complex complex complex)|)) (= (ho_196 x z) (ho_196 y z)))) (= x y))))) (let ((_let_52 (forall ((u |u_(-> Bool complex complex complex)|) (e |u_(-> complex complex complex)|) (i Bool)) (not (forall ((v |u_(-> Bool complex complex complex)|)) (not (forall ((ii Bool)) (= (ho_181 v ii) (ite (= ii i) e (ho_181 u ii)))))))))) (let ((_let_53 (forall ((x |u_(-> Bool complex complex complex)|) (y |u_(-> Bool complex complex complex)|)) (or (not (forall ((z Bool)) (= (ho_181 x z) (ho_181 y z)))) (= x y))))) (let ((_let_54 (forall ((u |u_(-> Bool nat nat nat)|) (e |u_(-> nat nat nat)|) (i Bool)) (not (forall ((v |u_(-> Bool nat nat nat)|)) (not (forall ((ii Bool)) (= (ho_192 v ii) (ite (= ii i) e (ho_192 u ii)))))))))) (let ((_let_55 (forall ((x |u_(-> Bool nat nat nat)|) (y |u_(-> Bool nat nat nat)|)) (or (not (forall ((z Bool)) (= (ho_192 x z) (ho_192 y z)))) (= x y))))) (let ((_let_56 (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_189 v ii) (ite (= i ii) e (ho_189 u ii)))))))))) (let ((_let_57 (forall ((x |u_(-> set_real set_real set_real)|) (y |u_(-> set_real set_real set_real)|)) (or (not (forall ((z set_real)) (= (ho_189 x z) (ho_189 y z)))) (= x y))))) (let ((_let_58 (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_190 v ii) (ite (= i ii) e (ho_190 u ii)))))))))) (let ((_let_59 (forall ((x |u_(-> set_real set_real)|) (y |u_(-> set_real set_real)|)) (or (not (forall ((z set_real)) (= (ho_190 x z) (ho_190 y z)))) (= x y))))) (let ((_let_60 (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_186 v ii) (ite (= i ii) e (ho_186 u ii)))))))))) (let ((_let_61 (forall ((x |u_(-> real set_real Bool)|) (y |u_(-> real set_real Bool)|)) (or (not (forall ((z real)) (= (ho_186 x z) (ho_186 y z)))) (= x y))))) (let ((_let_62 (forall ((u |u_(-> _u_(-> complex complex)_ _u_(-> complex complex)_ _u_(-> complex complex)_ complex complex)|) (e |u_(-> _u_(-> complex complex)_ _u_(-> complex complex)_ complex complex)|) (i |u_(-> complex complex)|)) (not (forall ((v |u_(-> _u_(-> complex complex)_ _u_(-> complex complex)_ _u_(-> complex complex)_ complex complex)|)) (not (forall ((ii |u_(-> complex complex)|)) (= (ho_83 v ii) (ite (= i ii) e (ho_83 u ii)))))))))) (let ((_let_63 (forall ((x |u_(-> _u_(-> complex complex)_ _u_(-> complex complex)_ _u_(-> complex complex)_ complex complex)|) (y |u_(-> _u_(-> complex complex)_ _u_(-> complex complex)_ _u_(-> complex complex)_ complex complex)|)) (or (not (forall ((z |u_(-> complex complex)|)) (= (ho_83 x z) (ho_83 y z)))) (= x y))))) (let ((_let_64 (forall ((u |u_(-> nat _u_(-> _u_(-> real real)_ real real)_ _u_(-> real real)_ real real)|) (e |u_(-> _u_(-> _u_(-> real real)_ real real)_ _u_(-> real real)_ real real)|) (i nat)) (not (forall ((v |u_(-> nat _u_(-> _u_(-> real real)_ real real)_ _u_(-> real real)_ real real)|)) (not (forall ((ii nat)) (= (ho_216 v ii) (ite (= i ii) e (ho_216 u ii)))))))))) (let ((_let_65 (forall ((x |u_(-> nat _u_(-> _u_(-> real real)_ real real)_ _u_(-> real real)_ real real)|) (y |u_(-> nat _u_(-> _u_(-> real real)_ real real)_ _u_(-> real real)_ real real)|)) (or (not (forall ((z nat)) (= (ho_216 x z) (ho_216 y z)))) (= x y))))) (let ((_let_66 (forall ((u |u_(-> set_real Bool)|) (e Bool) (i set_real)) (not (forall ((v |u_(-> set_real Bool)|)) (not (forall ((ii set_real)) (= (ho_187 v ii) (ite (= i ii) e (ho_187 u ii)))))))))) (let ((_let_67 (forall ((x |u_(-> set_real Bool)|) (y |u_(-> set_real Bool)|)) (or (not (forall ((z set_real)) (= (ho_187 x z) (ho_187 y z)))) (= x y))))) (let ((_let_68 (forall ((u |u_(-> _u_(-> _u_(-> complex complex)_ complex)_ _u_(-> complex complex complex)_ complex complex)|) (e |u_(-> _u_(-> complex complex complex)_ complex complex)|) (i |u_(-> _u_(-> complex complex)_ complex)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> complex complex)_ complex)_ _u_(-> complex complex complex)_ complex complex)|)) (not (forall ((ii |u_(-> _u_(-> complex complex)_ complex)|)) (= (ho_195 v ii) (ite (= i ii) e (ho_195 u ii)))))))))) (let ((_let_69 (forall ((x |u_(-> _u_(-> _u_(-> complex complex)_ complex)_ _u_(-> complex complex complex)_ complex complex)|) (y |u_(-> _u_(-> _u_(-> complex complex)_ complex)_ _u_(-> complex complex complex)_ complex complex)|)) (or (not (forall ((z |u_(-> _u_(-> complex complex)_ complex)|)) (= (ho_195 x z) (ho_195 y z)))) (= x y))))) (let ((_let_70 (forall ((u |u_(-> nat _u_(-> real real)_ real real)|) (e |u_(-> _u_(-> real real)_ real real)|) (i nat)) (not (forall ((v |u_(-> nat _u_(-> real real)_ real real)|)) (not (forall ((ii nat)) (= (ho_183 v ii) (ite (= i ii) e (ho_183 u ii)))))))))) (let ((_let_71 (forall ((x |u_(-> nat _u_(-> real real)_ real real)|) (y |u_(-> nat _u_(-> real real)_ real real)|)) (or (not (forall ((z nat)) (= (ho_183 x z) (ho_183 y z)))) (= x y))))) (let ((_let_72 (forall ((u |u_(-> _u_(-> complex Bool)_ set_complex)|) (e set_complex) (i |u_(-> complex Bool)|)) (not (forall ((v |u_(-> _u_(-> complex Bool)_ set_complex)|)) (not (forall ((ii |u_(-> complex Bool)|)) (= (ho_179 v ii) (ite (= i ii) e (ho_179 u ii)))))))))) (let ((_let_73 (forall ((x |u_(-> _u_(-> complex Bool)_ set_complex)|) (y |u_(-> _u_(-> complex Bool)_ set_complex)|)) (or (not (forall ((z |u_(-> complex Bool)|)) (= (ho_179 x z) (ho_179 y z)))) (= x y))))) (let ((_let_74 (forall ((u |u_(-> _u_(-> complex real)_ _u_(-> real complex)_ real real)|) (e |u_(-> _u_(-> real complex)_ real real)|) (i |u_(-> complex real)|)) (not (forall ((v |u_(-> _u_(-> complex real)_ _u_(-> real complex)_ real real)|)) (not (forall ((ii |u_(-> complex real)|)) (= (ho_174 v ii) (ite (= i ii) e (ho_174 u ii)))))))))) (let ((_let_75 (forall ((x |u_(-> _u_(-> complex real)_ _u_(-> real complex)_ real real)|) (y |u_(-> _u_(-> complex real)_ _u_(-> real complex)_ real real)|)) (or (not (forall ((z |u_(-> complex real)|)) (= (ho_174 x z) (ho_174 y z)))) (= x y))))) (let ((_let_76 (forall ((u |u_(-> _u_(-> real complex)_ real real)|) (e |u_(-> real real)|) (i |u_(-> real complex)|)) (not (forall ((v |u_(-> _u_(-> real complex)_ real real)|)) (not (forall ((ii |u_(-> real complex)|)) (= (ho_175 v ii) (ite (= i ii) e (ho_175 u ii)))))))))) (let ((_let_77 (forall ((x |u_(-> _u_(-> real complex)_ real real)|) (y |u_(-> _u_(-> real complex)_ real real)|)) (or (not (forall ((z |u_(-> real complex)|)) (= (ho_175 x z) (ho_175 y z)))) (= x y))))) (let ((_let_78 (forall ((u |u_(-> nat Bool)|) (e Bool) (i nat)) (not (forall ((v |u_(-> nat Bool)|)) (not (forall ((ii nat)) (= (ho_119 v ii) (ite (= i ii) e (ho_119 u ii)))))))))) (let ((_let_79 (forall ((x |u_(-> nat Bool)|) (y |u_(-> nat Bool)|)) (or (not (forall ((z nat)) (= (ho_119 x z) (ho_119 y z)))) (= x y))))) (let ((_let_80 (forall ((u |u_(-> real real real)|) (e |u_(-> real real)|) (i real)) (not (forall ((v |u_(-> real real real)|)) (not (forall ((ii real)) (= (ho_113 v ii) (ite (= i ii) e (ho_113 u ii)))))))))) (let ((_let_81 (forall ((x |u_(-> real real real)|) (y |u_(-> real real real)|)) (or (not (forall ((z real)) (= (ho_113 x z) (ho_113 y z)))) (= x y))))) (let ((_let_82 (forall ((u |u_(-> _u_(-> complex complex)_ set_complex Bool)|) (e |u_(-> set_complex Bool)|) (i |u_(-> complex complex)|)) (not (forall ((v |u_(-> _u_(-> complex complex)_ set_complex Bool)|)) (not (forall ((ii |u_(-> complex complex)|)) (= (ho_162 v ii) (ite (= i ii) e (ho_162 u ii)))))))))) (let ((_let_83 (forall ((x |u_(-> _u_(-> complex complex)_ set_complex Bool)|) (y |u_(-> _u_(-> complex complex)_ set_complex Bool)|)) (or (not (forall ((z |u_(-> complex complex)|)) (= (ho_162 x z) (ho_162 y z)))) (= x y))))) (let ((_let_84 (forall ((u |u_(-> set_nat Bool)|) (e Bool) (i set_nat)) (not (forall ((v |u_(-> set_nat Bool)|)) (not (forall ((ii set_nat)) (= (ho_220 v ii) (ite (= i ii) e (ho_220 u ii)))))))))) (let ((_let_85 (forall ((x |u_(-> set_nat Bool)|) (y |u_(-> set_nat Bool)|)) (or (not (forall ((z set_nat)) (= (ho_220 x z) (ho_220 y z)))) (= x y))))) (let ((_let_86 (forall ((u |u_(-> _u_(-> _u_(-> complex complex)_ real)_ _u_(-> real complex complex)_ real real)|) (e |u_(-> _u_(-> real complex complex)_ real real)|) (i |u_(-> _u_(-> complex complex)_ real)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> complex complex)_ real)_ _u_(-> real complex complex)_ real real)|)) (not (forall ((ii |u_(-> _u_(-> complex complex)_ real)|)) (= (ho_212 v ii) (ite (= i ii) e (ho_212 u ii)))))))))) (let ((_let_87 (forall ((x |u_(-> _u_(-> _u_(-> complex complex)_ real)_ _u_(-> real complex complex)_ real real)|) (y |u_(-> _u_(-> _u_(-> complex complex)_ real)_ _u_(-> real complex complex)_ real real)|)) (or (not (forall ((z |u_(-> _u_(-> complex complex)_ real)|)) (= (ho_212 x z) (ho_212 y z)))) (= x y))))) (let ((_let_88 (forall ((u |u_(-> _u_(-> _u_(-> complex complex)_ complex complex)_ _u_(-> complex complex)_ complex complex)|) (e |u_(-> _u_(-> complex complex)_ complex complex)|) (i |u_(-> _u_(-> complex complex)_ complex complex)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> complex complex)_ complex complex)_ _u_(-> complex complex)_ complex complex)|)) (not (forall ((ii |u_(-> _u_(-> complex complex)_ complex complex)|)) (= (ho_160 v ii) (ite (= i ii) e (ho_160 u ii)))))))))) (let ((_let_89 (forall ((x |u_(-> _u_(-> _u_(-> complex complex)_ complex complex)_ _u_(-> complex complex)_ complex complex)|) (y |u_(-> _u_(-> _u_(-> complex complex)_ complex complex)_ _u_(-> complex complex)_ complex complex)|)) (or (not (forall ((z |u_(-> _u_(-> complex complex)_ complex complex)|)) (= (ho_160 x z) (ho_160 y z)))) (= x y))))) (let ((_let_90 (forall ((u |u_(-> _u_(-> complex complex)_ complex)|) (e complex) (i |u_(-> complex complex)|)) (not (forall ((v |u_(-> _u_(-> complex complex)_ complex)|)) (not (forall ((ii |u_(-> complex complex)|)) (= (ho_193 v ii) (ite (= i ii) e (ho_193 u ii)))))))))) (let ((_let_91 (forall ((x |u_(-> _u_(-> complex complex)_ complex)|) (y |u_(-> _u_(-> complex complex)_ complex)|)) (or (not (forall ((z |u_(-> complex complex)|)) (= (ho_193 x z) (ho_193 y z)))) (= x y))))) (let ((_let_92 (forall ((u |u_(-> nat _u_(-> complex complex)_ complex complex)|) (e |u_(-> _u_(-> complex complex)_ complex complex)|) (i nat)) (not (forall ((v |u_(-> nat _u_(-> complex complex)_ complex complex)|)) (not (forall ((ii nat)) (= (ho_106 v ii) (ite (= i ii) e (ho_106 u ii)))))))))) (let ((_let_93 (forall ((x |u_(-> nat _u_(-> complex complex)_ complex complex)|) (y |u_(-> nat _u_(-> complex complex)_ complex complex)|)) (or (not (forall ((z nat)) (= (ho_106 x z) (ho_106 y z)))) (= x y))))) (let ((_let_94 (forall ((u |u_(-> complex complex complex)|) (e |u_(-> complex complex)|) (i complex)) (not (forall ((v |u_(-> complex complex complex)|)) (not (forall ((ii complex)) (= (ho_140 v ii) (ite (= i ii) e (ho_140 u ii)))))))))) (let ((_let_95 (forall ((x |u_(-> complex complex complex)|) (y |u_(-> complex complex complex)|)) (or (not (forall ((z complex)) (= (ho_140 x z) (ho_140 y z)))) (= x y))))) (let ((_let_96 (forall ((u |u_(-> set_complex complex Bool)|) (e |u_(-> complex Bool)|) (i set_complex)) (not (forall ((v |u_(-> set_complex complex Bool)|)) (not (forall ((ii set_complex)) (= (ho_151 v ii) (ite (= i ii) e (ho_151 u ii)))))))))) (let ((_let_97 (forall ((x |u_(-> set_complex complex Bool)|) (y |u_(-> set_complex complex Bool)|)) (or (not (forall ((z set_complex)) (= (ho_151 x z) (ho_151 y z)))) (= x y))))) (let ((_let_98 (forall ((u |u_(-> set_complex Bool)|) (e Bool) (i set_complex)) (not (forall ((v |u_(-> set_complex Bool)|)) (not (forall ((ii set_complex)) (= (ho_68 v ii) (ite (= i ii) e (ho_68 u ii)))))))))) (let ((_let_99 (forall ((x |u_(-> set_complex Bool)|) (y |u_(-> set_complex Bool)|)) (or (not (forall ((z set_complex)) (= (ho_68 x z) (ho_68 y z)))) (= x y))))) (let ((_let_100 (forall ((u |u_(-> nat _u_(-> complex complex)_ _u_(-> complex complex)_ complex complex)|) (e |u_(-> _u_(-> complex complex)_ _u_(-> complex complex)_ complex complex)|) (i nat)) (not (forall ((v |u_(-> nat _u_(-> complex complex)_ _u_(-> complex complex)_ complex complex)|)) (not (forall ((ii nat)) (= (ho_104 v ii) (ite (= i ii) e (ho_104 u ii)))))))))) (let ((_let_101 (forall ((x |u_(-> nat _u_(-> complex complex)_ _u_(-> complex complex)_ complex complex)|) (y |u_(-> nat _u_(-> complex complex)_ _u_(-> complex complex)_ complex complex)|)) (or (not (forall ((z nat)) (= (ho_104 x z) (ho_104 y z)))) (= x y))))) (let ((_let_102 (forall ((u |u_(-> set_nat set_nat)|) (e set_nat) (i set_nat)) (not (forall ((v |u_(-> set_nat set_nat)|)) (not (forall ((ii set_nat)) (= (ho_223 v ii) (ite (= i ii) e (ho_223 u ii)))))))))) (let ((_let_103 (forall ((x |u_(-> set_nat set_nat)|) (y |u_(-> set_nat set_nat)|)) (or (not (forall ((z set_nat)) (= (ho_223 x z) (ho_223 y z)))) (= x y))))) (let ((_let_104 (forall ((u |u_(-> nat set_nat Bool)|) (e |u_(-> set_nat Bool)|) (i nat)) (not (forall ((v |u_(-> nat set_nat Bool)|)) (not (forall ((ii nat)) (= (ho_219 v ii) (ite (= i ii) e (ho_219 u ii)))))))))) (let ((_let_105 (forall ((x |u_(-> nat set_nat Bool)|) (y |u_(-> nat set_nat Bool)|)) (or (not (forall ((z nat)) (= (ho_219 x z) (ho_219 y z)))) (= x y))))) (let ((_let_106 (forall ((u |u_(-> _u_(-> complex complex)_ _u_(-> complex complex)_ complex complex)|) (e |u_(-> _u_(-> complex complex)_ complex complex)|) (i |u_(-> complex complex)|)) (not (forall ((v |u_(-> _u_(-> complex complex)_ _u_(-> complex complex)_ complex complex)|)) (not (forall ((ii |u_(-> complex complex)|)) (= (ho_74 v ii) (ite (= i ii) e (ho_74 u ii)))))))))) (let ((_let_107 (forall ((x |u_(-> _u_(-> complex complex)_ _u_(-> complex complex)_ complex complex)|) (y |u_(-> _u_(-> complex complex)_ _u_(-> complex complex)_ complex complex)|)) (or (not (forall ((z |u_(-> complex complex)|)) (= (ho_74 x z) (ho_74 y z)))) (= x y))))) (let ((_let_108 (forall ((u |u_(-> real real Bool)|) (e |u_(-> real Bool)|) (i real)) (not (forall ((v |u_(-> real real Bool)|)) (not (forall ((ii real)) (= (ho_127 v ii) (ite (= i ii) e (ho_127 u ii)))))))))) (let ((_let_109 (forall ((x |u_(-> real real Bool)|) (y |u_(-> real real Bool)|)) (or (not (forall ((z real)) (= (ho_127 x z) (ho_127 y z)))) (= x y))))) (let ((_let_110 (forall ((u |u_(-> _u_(-> complex real)_ complex complex)|) (e |u_(-> complex complex)|) (i |u_(-> complex real)|)) (not (forall ((v |u_(-> _u_(-> complex real)_ complex complex)|)) (not (forall ((ii |u_(-> complex real)|)) (= (ho_172 v ii) (ite (= i ii) e (ho_172 u ii)))))))))) (let ((_let_111 (forall ((x |u_(-> _u_(-> complex real)_ complex complex)|) (y |u_(-> _u_(-> complex real)_ complex complex)|)) (or (not (forall ((z |u_(-> complex real)|)) (= (ho_172 x z) (ho_172 y z)))) (= x y))))) (let ((_let_112 (forall ((u |u_(-> set_complex set_complex Bool)|) (e |u_(-> set_complex Bool)|) (i set_complex)) (not (forall ((v |u_(-> set_complex set_complex Bool)|)) (not (forall ((ii set_complex)) (= (ho_70 v ii) (ite (= i ii) e (ho_70 u ii)))))))))) (let ((_let_113 (forall ((x |u_(-> set_complex set_complex Bool)|) (y |u_(-> set_complex set_complex Bool)|)) (or (not (forall ((z set_complex)) (= (ho_70 x z) (ho_70 y z)))) (= x y))))) (let ((_let_114 (forall ((u |u_(-> complex real)|) (e real) (i complex)) (not (forall ((v |u_(-> complex real)|)) (not (forall ((ii complex)) (= (ho_168 v ii) (ite (= i ii) e (ho_168 u ii)))))))))) (let ((_let_115 (forall ((x |u_(-> complex real)|) (y |u_(-> complex real)|)) (or (not (forall ((z complex)) (= (ho_168 x z) (ho_168 y z)))) (= x y))))) (let ((_let_116 (forall ((u |u_(-> set_real real)|) (e real) (i set_real)) (not (forall ((v |u_(-> set_real real)|)) (not (forall ((ii set_real)) (= (ho_226 v ii) (ite (= i ii) e (ho_226 u ii)))))))))) (let ((_let_117 (forall ((x |u_(-> set_real real)|) (y |u_(-> set_real real)|)) (or (not (forall ((z set_real)) (= (ho_226 x z) (ho_226 y z)))) (= x y))))) (let ((_let_118 (forall ((u |u_(-> nat nat Bool)|) (e |u_(-> nat Bool)|) (i nat)) (not (forall ((v |u_(-> nat nat Bool)|)) (not (forall ((ii nat)) (= (ho_118 v ii) (ite (= i ii) e (ho_118 u ii)))))))))) (let ((_let_119 (forall ((x |u_(-> nat nat Bool)|) (y |u_(-> nat nat Bool)|)) (or (not (forall ((z nat)) (= (ho_118 x z) (ho_118 y z)))) (= x y))))) (let ((_let_120 (forall ((u |u_(-> complex set_complex Bool)|) (e |u_(-> set_complex Bool)|) (i complex)) (not (forall ((v |u_(-> complex set_complex Bool)|)) (not (forall ((ii complex)) (= (ho_67 v ii) (ite (= i ii) e (ho_67 u ii)))))))))) (let ((_let_121 (forall ((x |u_(-> complex set_complex Bool)|) (y |u_(-> complex set_complex Bool)|)) (or (not (forall ((z complex)) (= (ho_67 x z) (ho_67 y z)))) (= x y))))) (let ((_let_122 (forall ((u |u_(-> _u_(-> _u_(-> complex complex)_ complex)_ _u_(-> complex complex)_ complex complex)|) (e |u_(-> _u_(-> complex complex)_ complex complex)|) (i |u_(-> _u_(-> complex complex)_ complex)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> complex complex)_ complex)_ _u_(-> complex complex)_ complex complex)|)) (not (forall ((ii |u_(-> _u_(-> complex complex)_ complex)|)) (= (ho_199 v ii) (ite (= i ii) e (ho_199 u ii)))))))))) (let ((_let_123 (forall ((x |u_(-> _u_(-> _u_(-> complex complex)_ complex)_ _u_(-> complex complex)_ complex complex)|) (y |u_(-> _u_(-> _u_(-> complex complex)_ complex)_ _u_(-> complex complex)_ complex complex)|)) (or (not (forall ((z |u_(-> _u_(-> complex complex)_ complex)|)) (= (ho_199 x z) (ho_199 y z)))) (= x y))))) (let ((_let_124 (forall ((u |u_(-> complex complex)|) (e complex) (i complex)) (not (forall ((v |u_(-> complex complex)|)) (not (forall ((ii complex)) (= (ho_72 v ii) (ite (= i ii) e (ho_72 u ii)))))))))) (let ((_let_125 (forall ((x |u_(-> complex complex)|) (y |u_(-> complex complex)|)) (or (not (forall ((z complex)) (= (ho_72 x z) (ho_72 y z)))) (= x y))))) (let ((_let_126 (forall ((u |u_(-> real real)|) (e real) (i real)) (not (forall ((v |u_(-> real real)|)) (not (forall ((ii real)) (= (ho_65 v ii) (ite (= i ii) e (ho_65 u ii)))))))))) (let ((_let_127 (forall ((x |u_(-> real real)|) (y |u_(-> real real)|)) (or (not (forall ((z real)) (= (ho_65 x z) (ho_65 y z)))) (= x y))))) (let ((_let_128 (forall ((u |u_(-> _u_(-> complex complex)_ complex complex)|) (e |u_(-> complex complex)|) (i |u_(-> complex complex)|)) (not (forall ((v |u_(-> _u_(-> complex complex)_ complex complex)|)) (not (forall ((ii |u_(-> complex complex)|)) (= (ho_75 v ii) (ite (= i ii) e (ho_75 u ii)))))))))) (let ((_let_129 (forall ((x |u_(-> _u_(-> complex complex)_ complex complex)|) (y |u_(-> _u_(-> complex complex)_ complex complex)|)) (or (not (forall ((z |u_(-> complex complex)|)) (= (ho_75 x z) (ho_75 y z)))) (= x y))))) (let ((_let_130 (forall ((u |u_(-> nat nat)|) (e nat) (i nat)) (not (forall ((v |u_(-> nat nat)|)) (not (forall ((ii nat)) (= (ho_124 v ii) (ite (= i ii) e (ho_124 u ii)))))))))) (let ((_let_131 (forall ((x |u_(-> nat nat)|) (y |u_(-> nat nat)|)) (or (not (forall ((z nat)) (= (ho_124 x z) (ho_124 y z)))) (= x y))))) (let ((_let_132 (forall ((u |u_(-> _u_(-> nat real)_ nat real)|) (e |u_(-> nat real)|) (i |u_(-> nat real)|)) (not (forall ((v |u_(-> _u_(-> nat real)_ nat real)|)) (not (forall ((ii |u_(-> nat real)|)) (= (ho_233 v ii) (ite (= i ii) e (ho_233 u ii)))))))))) (let ((_let_133 (forall ((x |u_(-> _u_(-> nat real)_ nat real)|) (y |u_(-> _u_(-> nat real)_ nat real)|)) (or (not (forall ((z |u_(-> nat real)|)) (= (ho_233 x z) (ho_233 y z)))) (= x y))))) (let ((_let_134 (forall ((u |u_(-> nat nat nat)|) (e |u_(-> nat nat)|) (i nat)) (not (forall ((v |u_(-> nat nat nat)|)) (not (forall ((ii nat)) (= (ho_123 v ii) (ite (= i ii) e (ho_123 u ii)))))))))) (let ((_let_135 (forall ((x |u_(-> nat nat nat)|) (y |u_(-> nat nat nat)|)) (or (not (forall ((z nat)) (= (ho_123 x z) (ho_123 y z)))) (= x y))))) (let ((_let_136 (forall ((u |u_(-> _u_(-> real real)_ real real)|) (e |u_(-> real real)|) (i |u_(-> real real)|)) (not (forall ((v |u_(-> _u_(-> real real)_ real real)|)) (not (forall ((ii |u_(-> real real)|)) (= (ho_177 v ii) (ite (= i ii) e (ho_177 u ii)))))))))) (let ((_let_137 (forall ((x |u_(-> _u_(-> real real)_ real real)|) (y |u_(-> _u_(-> real real)_ real real)|)) (or (not (forall ((z |u_(-> real real)|)) (= (ho_177 x z) (ho_177 y z)))) (= x y))))) (let ((_let_138 (forall ((u |u_(-> nat _u_(-> _u_(-> complex complex)_ complex complex)_ _u_(-> complex complex)_ complex complex)|) (e |u_(-> _u_(-> _u_(-> complex complex)_ complex complex)_ _u_(-> complex complex)_ complex complex)|) (i nat)) (not (forall ((v |u_(-> nat _u_(-> _u_(-> complex complex)_ complex complex)_ _u_(-> complex complex)_ complex complex)|)) (not (forall ((ii nat)) (= (ho_159 v ii) (ite (= i ii) e (ho_159 u ii)))))))))) (let ((_let_139 (forall ((x |u_(-> nat _u_(-> _u_(-> complex complex)_ complex complex)_ _u_(-> complex complex)_ complex complex)|) (y |u_(-> nat _u_(-> _u_(-> complex complex)_ complex complex)_ _u_(-> complex complex)_ complex complex)|)) (or (not (forall ((z nat)) (= (ho_159 x z) (ho_159 y z)))) (= x y))))) (let ((_let_140 (forall ((u |u_(-> set_complex set_complex)|) (e set_complex) (i set_complex)) (not (forall ((v |u_(-> set_complex set_complex)|)) (not (forall ((ii set_complex)) (= (ho_166 v ii) (ite (= i ii) e (ho_166 u ii)))))))))) (let ((_let_141 (forall ((x |u_(-> set_complex set_complex)|) (y |u_(-> set_complex set_complex)|)) (or (not (forall ((z set_complex)) (= (ho_166 x z) (ho_166 y z)))) (= x y))))) (let ((_let_142 (forall ((u |u_(-> complex Bool)|) (e Bool) (i complex)) (not (forall ((v |u_(-> complex Bool)|)) (not (forall ((ii complex)) (= (ho_152 v ii) (ite (= i ii) e (ho_152 u ii)))))))))) (let ((_let_143 (forall ((x |u_(-> complex Bool)|) (y |u_(-> complex Bool)|)) (or (not (forall ((z complex)) (= (ho_152 x z) (ho_152 y z)))) (= x y))))) (let ((_let_144 (forall ((u |u_(-> real complex)|) (e complex) (i real)) (not (forall ((v |u_(-> real complex)|)) (not (forall ((ii real)) (= (ho_169 v ii) (ite (= i ii) e (ho_169 u ii)))))))))) (let ((_let_145 (forall ((x |u_(-> real complex)|) (y |u_(-> real complex)|)) (or (not (forall ((z real)) (= (ho_169 x z) (ho_169 y z)))) (= x y))))) (let ((_let_146 (forall ((u |u_(-> real Bool)|) (e Bool) (i real)) (not (forall ((v |u_(-> real Bool)|)) (not (forall ((ii real)) (= (ho_128 v ii) (ite (= i ii) e (ho_128 u ii)))))))))) (let ((_let_147 (forall ((x |u_(-> real Bool)|) (y |u_(-> real Bool)|)) (or (not (forall ((z real)) (= (ho_128 x z) (ho_128 y z)))) (= x y))))) (let ((_let_148 (forall ((u |u_(-> _u_(-> complex complex)_ set_complex set_complex)|) (e |u_(-> set_complex set_complex)|) (i |u_(-> complex complex)|)) (not (forall ((v |u_(-> _u_(-> complex complex)_ set_complex set_complex)|)) (not (forall ((ii |u_(-> complex complex)|)) (= (ho_165 v ii) (ite (= i ii) e (ho_165 u ii)))))))))) (let ((_let_149 (forall ((x |u_(-> _u_(-> complex complex)_ set_complex set_complex)|) (y |u_(-> _u_(-> complex complex)_ set_complex set_complex)|)) (or (not (forall ((z |u_(-> complex complex)|)) (= (ho_165 x z) (ho_165 y z)))) (= x y))))) (let ((_let_150 (forall ((u |u_(-> _u_(-> real complex)_ _u_(-> complex real)_ complex complex)|) (e |u_(-> _u_(-> complex real)_ complex complex)|) (i |u_(-> real complex)|)) (not (forall ((v |u_(-> _u_(-> real complex)_ _u_(-> complex real)_ complex complex)|)) (not (forall ((ii |u_(-> real complex)|)) (= (ho_171 v ii) (ite (= i ii) e (ho_171 u ii)))))))))) (let ((_let_151 (forall ((x |u_(-> _u_(-> real complex)_ _u_(-> complex real)_ complex complex)|) (y |u_(-> _u_(-> real complex)_ _u_(-> complex real)_ complex complex)|)) (or (not (forall ((z |u_(-> real complex)|)) (= (ho_171 x z) (ho_171 y z)))) (= x y))))) (let ((_let_152 (forall ((u |u_(-> set_nat set_nat set_nat)|) (e |u_(-> set_nat set_nat)|) (i set_nat)) (not (forall ((v |u_(-> set_nat set_nat set_nat)|)) (not (forall ((ii set_nat)) (= (ho_222 v ii) (ite (= i ii) e (ho_222 u ii)))))))))) (let ((_let_153 (forall ((x |u_(-> set_nat set_nat set_nat)|) (y |u_(-> set_nat set_nat set_nat)|)) (or (not (forall ((z set_nat)) (= (ho_222 x z) (ho_222 y z)))) (= x y))))) (let ((_let_154 (forall ((u |u_(-> _u_(-> real real)_ set_real set_real)|) (e |u_(-> set_real set_real)|) (i |u_(-> real real)|)) (not (forall ((v |u_(-> _u_(-> real real)_ set_real set_real)|)) (not (forall ((ii |u_(-> real real)|)) (= (ho_225 v ii) (ite (= i ii) e (ho_225 u ii)))))))))) (let ((_let_155 (forall ((x |u_(-> _u_(-> real real)_ set_real set_real)|) (y |u_(-> _u_(-> real real)_ set_real set_real)|)) (or (not (forall ((z |u_(-> real real)|)) (= (ho_225 x z) (ho_225 y z)))) (= x y))))) (let ((_let_156 (forall ((u |u_(-> _u_(-> real real)_ _u_(-> real real)_ real real)|) (e |u_(-> _u_(-> real real)_ real real)|) (i |u_(-> real real)|)) (not (forall ((v |u_(-> _u_(-> real real)_ _u_(-> real real)_ real real)|)) (not (forall ((ii |u_(-> real real)|)) (= (ho_229 v ii) (ite (= i ii) e (ho_229 u ii)))))))))) (let ((_let_157 (forall ((x |u_(-> _u_(-> real real)_ _u_(-> real real)_ real real)|) (y |u_(-> _u_(-> real real)_ _u_(-> real real)_ real real)|)) (or (not (forall ((z |u_(-> real real)|)) (= (ho_229 x z) (ho_229 y z)))) (= x y))))) (let ((_let_158 (forall ((u |u_(-> nat real)|) (e real) (i nat)) (not (forall ((v |u_(-> nat real)|)) (not (forall ((ii nat)) (= (ho_230 v ii) (ite (= i ii) e (ho_230 u ii)))))))))) (let ((_let_159 (forall ((x |u_(-> nat real)|) (y |u_(-> nat real)|)) (or (not (forall ((z nat)) (= (ho_230 x z) (ho_230 y z)))) (= x y))))) (let ((_let_160 (forall ((u |u_(-> _u_(-> nat real)_ nat nat)|) (e |u_(-> nat nat)|) (i |u_(-> nat real)|)) (not (forall ((v |u_(-> _u_(-> nat real)_ nat nat)|)) (not (forall ((ii |u_(-> nat real)|)) (= (ho_231 v ii) (ite (= i ii) e (ho_231 u ii)))))))))) (let ((_let_161 (forall ((x |u_(-> _u_(-> nat real)_ nat nat)|) (y |u_(-> _u_(-> nat real)_ nat nat)|)) (or (not (forall ((z |u_(-> nat real)|)) (= (ho_231 x z) (ho_231 y z)))) (= x y))))) (let ((_let_162 (forall ((u |u_(-> _u_(-> nat real)_ Bool)|) (e Bool) (i |u_(-> nat real)|)) (not (forall ((v |u_(-> _u_(-> nat real)_ Bool)|)) (not (forall ((ii |u_(-> nat real)|)) (= (ho_232 v ii) (ite (= i ii) e (ho_232 u ii)))))))))) (let ((_let_163 (forall ((x |u_(-> _u_(-> nat real)_ Bool)|) (y |u_(-> _u_(-> nat real)_ Bool)|)) (or (not (forall ((z |u_(-> nat real)|)) (= (ho_232 x z) (ho_232 y z)))) (= x y))))) (let ((_let_164 (forall ((u |u_(-> _u_(-> _u_(-> complex complex)_ complex complex)_ _u_(-> _u_(-> complex complex)_ complex complex)_ _u_(-> complex complex)_ complex complex)|) (e |u_(-> _u_(-> _u_(-> complex complex)_ complex complex)_ _u_(-> complex complex)_ complex complex)|) (i |u_(-> _u_(-> complex complex)_ complex complex)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> complex complex)_ complex complex)_ _u_(-> _u_(-> complex complex)_ complex complex)_ _u_(-> complex complex)_ complex complex)|)) (not (forall ((ii |u_(-> _u_(-> complex complex)_ complex complex)|)) (= (ho_237 v ii) (ite (= i ii) e (ho_237 u ii)))))))))) (let ((_let_165 (forall ((x |u_(-> _u_(-> _u_(-> complex complex)_ complex complex)_ _u_(-> _u_(-> complex complex)_ complex complex)_ _u_(-> complex complex)_ complex complex)|) (y |u_(-> _u_(-> _u_(-> complex complex)_ complex complex)_ _u_(-> _u_(-> complex complex)_ complex complex)_ _u_(-> complex complex)_ complex complex)|)) (or (not (forall ((z |u_(-> _u_(-> complex complex)_ complex complex)|)) (= (ho_237 x z) (ho_237 y z)))) (= x y))))) (let ((_let_166 (forall ((u |u_(-> set_complex_complex set_complex_complex)|) (e set_complex_complex) (i set_complex_complex)) (not (forall ((v |u_(-> set_complex_complex set_complex_complex)|)) (not (forall ((ii set_complex_complex)) (= (ho_242 v ii) (ite (= i ii) e (ho_242 u ii)))))))))) (let ((_let_167 (forall ((x |u_(-> set_complex_complex set_complex_complex)|) (y |u_(-> set_complex_complex set_complex_complex)|)) (or (not (forall ((z set_complex_complex)) (= (ho_242 x z) (ho_242 y z)))) (= x y))))) (let ((_let_168 (forall ((u |u_(-> _u_(-> _u_(-> complex complex)_ complex complex)_ set_complex_complex set_complex_complex)|) (e |u_(-> set_complex_complex set_complex_complex)|) (i |u_(-> _u_(-> complex complex)_ complex complex)|)) (not (forall ((v |u_(-> _u_(-> _u_(-> complex complex)_ complex complex)_ set_complex_complex set_complex_complex)|)) (not (forall ((ii |u_(-> _u_(-> complex complex)_ complex complex)|)) (= (ho_241 v ii) (ite (= i ii) e (ho_241 u ii)))))))))) (let ((_let_169 (forall ((x |u_(-> _u_(-> _u_(-> complex complex)_ complex complex)_ set_complex_complex set_complex_complex)|) (y |u_(-> _u_(-> _u_(-> complex complex)_ complex complex)_ set_complex_complex set_complex_complex)|)) (or (not (forall ((z |u_(-> _u_(-> complex complex)_ complex complex)|)) (= (ho_241 x z) (ho_241 y z)))) (= x y))))) (let ((_let_170 (forall ((u |u_(-> set_complex_complex complex complex)|) (e |u_(-> complex complex)|) (i set_complex_complex)) (not (forall ((v |u_(-> set_complex_complex complex complex)|)) (not (forall ((ii set_complex_complex)) (= (ho_243 v ii) (ite (= i ii) e (ho_243 u ii)))))))))) (let ((_let_171 (forall ((x |u_(-> set_complex_complex complex complex)|) (y |u_(-> set_complex_complex complex complex)|)) (or (not (forall ((z set_complex_complex)) (= (ho_243 x z) (ho_243 y z)))) (= x y))))) (let ((_let_172 (forall ((BOUND_VARIABLE_12571 real)) (= BOUND_VARIABLE_12571 (ho_65 k_64 BOUND_VARIABLE_12571))))) (let ((_let_173 (forall ((BOUND_VARIABLE_12560 set_complex) (BOUND_VARIABLE_12561 set_complex)) (= (ho_68 (ho_70 k_69 BOUND_VARIABLE_12560) BOUND_VARIABLE_12561) (forall ((X complex)) (let ((_let_1 (ho_67 k_66 X))) (or (not (ho_68 _let_1 BOUND_VARIABLE_12560)) (ho_68 _let_1 BOUND_VARIABLE_12561)))))))) (let ((_let_174 (forall ((BOUND_VARIABLE_12549 set_complex) (BOUND_VARIABLE_12550 set_complex)) (= (ho_68 (ho_70 k_71 BOUND_VARIABLE_12549) BOUND_VARIABLE_12550) (forall ((T3 complex)) (let ((_let_1 (ho_67 k_66 T3))) (or (not (ho_68 _let_1 BOUND_VARIABLE_12549)) (ho_68 _let_1 BOUND_VARIABLE_12550)))))))) (let ((_let_175 (forall ((BOUND_VARIABLE_12740 |u_(-> complex complex)|) (BOUND_VARIABLE_12737 |u_(-> complex complex)|) (BOUND_VARIABLE_12542 complex)) (= (ho_72 (ho_75 (ho_74 k_73 BOUND_VARIABLE_12740) BOUND_VARIABLE_12737) BOUND_VARIABLE_12542) (ho_72 BOUND_VARIABLE_12740 (ho_72 BOUND_VARIABLE_12737 BOUND_VARIABLE_12542)))))) (let ((_let_176 (forall ((BOUND_VARIABLE_12763 |u_(-> complex complex)|) (BOUND_VARIABLE_12762 |u_(-> complex complex)|) (BOUND_VARIABLE_12533 complex)) (= (ho_72 (ho_75 (ho_74 k_76 BOUND_VARIABLE_12763) BOUND_VARIABLE_12762) BOUND_VARIABLE_12533) (ho_72 BOUND_VARIABLE_12763 (ho_72 BOUND_VARIABLE_12762 BOUND_VARIABLE_12533)))))) (let ((_let_177 (forall ((BOUND_VARIABLE_12775 |u_(-> complex complex)|) (BOUND_VARIABLE_12525 complex)) (= (ho_72 (ho_75 k_77 BOUND_VARIABLE_12775) BOUND_VARIABLE_12525) (ho_72 BOUND_VARIABLE_12775 BOUND_VARIABLE_12525))))) (let ((_let_178 (forall ((BOUND_VARIABLE_12787 |u_(-> complex complex)|) (BOUND_VARIABLE_12786 |u_(-> complex complex)|) (BOUND_VARIABLE_12517 complex)) (= (ho_72 (ho_75 (ho_74 k_78 BOUND_VARIABLE_12787) BOUND_VARIABLE_12786) BOUND_VARIABLE_12517) (ho_72 BOUND_VARIABLE_12787 (ho_72 BOUND_VARIABLE_12786 BOUND_VARIABLE_12517)))))) (let ((_let_179 (forall ((BOUND_VARIABLE_12801 |u_(-> complex complex)|) (BOUND_VARIABLE_12800 |u_(-> complex complex)|) (BOUND_VARIABLE_12508 complex)) (= (ho_72 (ho_75 (ho_74 k_79 BOUND_VARIABLE_12801) BOUND_VARIABLE_12800) BOUND_VARIABLE_12508) (ho_72 BOUND_VARIABLE_12801 (ho_72 BOUND_VARIABLE_12800 BOUND_VARIABLE_12508)))))) (let ((_let_180 (forall ((BOUND_VARIABLE_12815 |u_(-> complex complex)|) (BOUND_VARIABLE_12814 |u_(-> complex complex)|) (BOUND_VARIABLE_12499 complex)) (= (ho_72 (ho_75 (ho_74 k_80 BOUND_VARIABLE_12815) BOUND_VARIABLE_12814) BOUND_VARIABLE_12499) (ho_72 BOUND_VARIABLE_12815 (ho_72 BOUND_VARIABLE_12814 BOUND_VARIABLE_12499)))))) (let ((_let_181 (forall ((BOUND_VARIABLE_12827 |u_(-> complex complex)|) (BOUND_VARIABLE_12491 complex)) (= (ho_72 (ho_75 k_81 BOUND_VARIABLE_12827) BOUND_VARIABLE_12491) (ho_72 BOUND_VARIABLE_12827 BOUND_VARIABLE_12491))))) (let ((_let_182 (forall ((BOUND_VARIABLE_12841 |u_(-> complex complex)|) (BOUND_VARIABLE_12840 |u_(-> complex complex)|) (BOUND_VARIABLE_12839 |u_(-> complex complex)|) (BOUND_VARIABLE_12482 complex)) (= (ho_72 (ho_75 (ho_74 (ho_83 k_82 BOUND_VARIABLE_12841) BOUND_VARIABLE_12840) BOUND_VARIABLE_12839) BOUND_VARIABLE_12482) (ho_72 BOUND_VARIABLE_12841 (ho_72 BOUND_VARIABLE_12840 (ho_72 BOUND_VARIABLE_12839 BOUND_VARIABLE_12482))))))) (let ((_let_183 (forall ((BOUND_VARIABLE_12864 |u_(-> complex complex)|) (BOUND_VARIABLE_12863 |u_(-> complex complex)|) (BOUND_VARIABLE_12862 |u_(-> complex complex)|) (BOUND_VARIABLE_12471 complex)) (= (ho_72 (ho_75 (ho_74 (ho_83 k_84 BOUND_VARIABLE_12864) BOUND_VARIABLE_12863) BOUND_VARIABLE_12862) BOUND_VARIABLE_12471) (ho_72 BOUND_VARIABLE_12864 (ho_72 BOUND_VARIABLE_12863 (ho_72 BOUND_VARIABLE_12862 BOUND_VARIABLE_12471))))))) (let ((_let_184 (forall ((BOUND_VARIABLE_12878 |u_(-> complex complex)|) (BOUND_VARIABLE_12462 complex)) (= (ho_72 (ho_75 k_85 BOUND_VARIABLE_12878) BOUND_VARIABLE_12462) (ho_72 BOUND_VARIABLE_12878 BOUND_VARIABLE_12462))))) (let ((_let_185 (forall ((BOUND_VARIABLE_12895 |u_(-> complex complex)|) (BOUND_VARIABLE_12894 |u_(-> complex complex)|) (BOUND_VARIABLE_12449 complex)) (= (ho_72 (ho_75 (ho_74 k_87 BOUND_VARIABLE_12895) BOUND_VARIABLE_12894) BOUND_VARIABLE_12449) (ho_72 BOUND_VARIABLE_12895 (ho_72 BOUND_VARIABLE_12894 BOUND_VARIABLE_12449)))))) (let ((_let_186 (forall ((BOUND_VARIABLE_12909 |u_(-> complex complex)|) (BOUND_VARIABLE_12908 |u_(-> complex complex)|) (BOUND_VARIABLE_12440 complex)) (= (ho_72 (ho_75 (ho_74 k_88 BOUND_VARIABLE_12909) BOUND_VARIABLE_12908) BOUND_VARIABLE_12440) (ho_72 BOUND_VARIABLE_12909 (ho_72 BOUND_VARIABLE_12908 BOUND_VARIABLE_12440)))))) (let ((_let_187 (forall ((BOUND_VARIABLE_12925 |u_(-> complex complex)|) (BOUND_VARIABLE_12924 |u_(-> complex complex)|) (BOUND_VARIABLE_12923 |u_(-> complex complex)|) (BOUND_VARIABLE_12430 complex)) (= (ho_72 (ho_75 (ho_74 (ho_83 k_89 BOUND_VARIABLE_12925) BOUND_VARIABLE_12924) BOUND_VARIABLE_12923) BOUND_VARIABLE_12430) (ho_72 BOUND_VARIABLE_12925 (ho_72 BOUND_VARIABLE_12924 (ho_72 BOUND_VARIABLE_12923 BOUND_VARIABLE_12430))))))) (let ((_let_188 (forall ((BOUND_VARIABLE_12943 |u_(-> complex complex)|) (BOUND_VARIABLE_12942 |u_(-> complex complex)|) (BOUND_VARIABLE_12941 |u_(-> complex complex)|) (BOUND_VARIABLE_12419 complex)) (= (ho_72 (ho_75 (ho_74 (ho_83 k_90 BOUND_VARIABLE_12943) BOUND_VARIABLE_12942) BOUND_VARIABLE_12941) BOUND_VARIABLE_12419) (ho_72 BOUND_VARIABLE_12943 (ho_72 BOUND_VARIABLE_12942 (ho_72 BOUND_VARIABLE_12941 BOUND_VARIABLE_12419))))))) (let ((_let_189 (forall ((BOUND_VARIABLE_12961 |u_(-> complex complex)|) (BOUND_VARIABLE_12960 |u_(-> complex complex)|) (BOUND_VARIABLE_12959 |u_(-> complex complex)|) (BOUND_VARIABLE_12408 complex)) (= (ho_72 (ho_75 (ho_74 (ho_83 k_91 BOUND_VARIABLE_12961) BOUND_VARIABLE_12960) BOUND_VARIABLE_12959) BOUND_VARIABLE_12408) (ho_72 BOUND_VARIABLE_12961 (ho_72 BOUND_VARIABLE_12960 (ho_72 BOUND_VARIABLE_12959 BOUND_VARIABLE_12408))))))) (let ((_let_190 (forall ((BOUND_VARIABLE_12979 |u_(-> complex complex)|) (BOUND_VARIABLE_12978 |u_(-> complex complex)|) (BOUND_VARIABLE_12977 |u_(-> complex complex)|) (BOUND_VARIABLE_12397 complex)) (= (ho_72 (ho_75 (ho_74 (ho_83 k_92 BOUND_VARIABLE_12979) BOUND_VARIABLE_12978) BOUND_VARIABLE_12977) BOUND_VARIABLE_12397) (ho_72 BOUND_VARIABLE_12979 (ho_72 BOUND_VARIABLE_12978 (ho_72 BOUND_VARIABLE_12977 BOUND_VARIABLE_12397))))))) (let ((_let_191 (forall ((BOUND_VARIABLE_12995 |u_(-> complex complex)|) (BOUND_VARIABLE_12994 |u_(-> complex complex)|) (BOUND_VARIABLE_12387 complex)) (= (ho_72 (ho_75 (ho_74 k_93 BOUND_VARIABLE_12995) BOUND_VARIABLE_12994) BOUND_VARIABLE_12387) (ho_72 BOUND_VARIABLE_12995 (ho_72 BOUND_VARIABLE_12994 BOUND_VARIABLE_12387)))))) (let ((_let_192 (forall ((BOUND_VARIABLE_13009 |u_(-> complex complex)|) (BOUND_VARIABLE_13008 |u_(-> complex complex)|) (BOUND_VARIABLE_12378 complex)) (= (ho_72 (ho_75 (ho_74 k_94 BOUND_VARIABLE_13009) BOUND_VARIABLE_13008) BOUND_VARIABLE_12378) (ho_72 BOUND_VARIABLE_13009 (ho_72 BOUND_VARIABLE_13008 BOUND_VARIABLE_12378)))))) (let ((_let_193 (forall ((BOUND_VARIABLE_13023 |u_(-> complex complex)|) (BOUND_VARIABLE_13022 |u_(-> complex complex)|) (BOUND_VARIABLE_12369 complex)) (= (ho_72 (ho_75 (ho_74 k_95 BOUND_VARIABLE_13023) BOUND_VARIABLE_13022) BOUND_VARIABLE_12369) (ho_72 BOUND_VARIABLE_13023 (ho_72 BOUND_VARIABLE_13022 BOUND_VARIABLE_12369)))))) (let ((_let_194 (forall ((BOUND_VARIABLE_13037 |u_(-> complex complex)|) (BOUND_VARIABLE_13036 |u_(-> complex complex)|) (BOUND_VARIABLE_12360 complex)) (= (ho_72 (ho_75 (ho_74 k_96 BOUND_VARIABLE_13037) BOUND_VARIABLE_13036) BOUND_VARIABLE_12360) (ho_72 BOUND_VARIABLE_13037 (ho_72 BOUND_VARIABLE_13036 BOUND_VARIABLE_12360)))))) (let ((_let_195 (forall ((BOUND_VARIABLE_13051 |u_(-> complex complex)|) (BOUND_VARIABLE_13050 |u_(-> complex complex)|) (BOUND_VARIABLE_12351 complex)) (= (ho_72 (ho_75 (ho_74 k_97 BOUND_VARIABLE_13051) BOUND_VARIABLE_13050) BOUND_VARIABLE_12351) (ho_72 BOUND_VARIABLE_13051 (ho_72 BOUND_VARIABLE_13050 BOUND_VARIABLE_12351)))))) (let ((_let_196 (forall ((BOUND_VARIABLE_13065 |u_(-> complex complex)|) (BOUND_VARIABLE_13064 |u_(-> complex complex)|) (BOUND_VARIABLE_12342 complex)) (= (ho_72 (ho_75 (ho_74 k_98 BOUND_VARIABLE_13065) BOUND_VARIABLE_13064) BOUND_VARIABLE_12342) (ho_72 BOUND_VARIABLE_13065 (ho_72 BOUND_VARIABLE_13064 BOUND_VARIABLE_12342)))))) (let ((_let_197 (forall ((BOUND_VARIABLE_12335 complex)) (= BOUND_VARIABLE_12335 (ho_72 k_99 BOUND_VARIABLE_12335))))) (let ((_let_198 (forall ((BOUND_VARIABLE_13084 |u_(-> complex complex)|) (BOUND_VARIABLE_13083 |u_(-> complex complex)|) (BOUND_VARIABLE_12328 complex)) (= (ho_72 (ho_75 (ho_74 k_100 BOUND_VARIABLE_13084) BOUND_VARIABLE_13083) BOUND_VARIABLE_12328) (ho_72 BOUND_VARIABLE_13084 (ho_72 BOUND_VARIABLE_13083 BOUND_VARIABLE_12328)))))) (let ((_let_199 (forall ((BOUND_VARIABLE_13098 |u_(-> complex complex)|) (BOUND_VARIABLE_13097 |u_(-> complex complex)|) (BOUND_VARIABLE_12319 complex)) (= (ho_72 (ho_75 (ho_74 k_101 BOUND_VARIABLE_13098) BOUND_VARIABLE_13097) BOUND_VARIABLE_12319) (ho_72 BOUND_VARIABLE_13098 (ho_72 BOUND_VARIABLE_13097 BOUND_VARIABLE_12319)))))) (let ((_let_200 (forall ((BOUND_VARIABLE_13112 |u_(-> complex complex)|) (BOUND_VARIABLE_13111 |u_(-> complex complex)|) (BOUND_VARIABLE_12310 complex)) (= (ho_72 (ho_75 (ho_74 k_102 BOUND_VARIABLE_13112) BOUND_VARIABLE_13111) BOUND_VARIABLE_12310) (ho_72 BOUND_VARIABLE_13112 (ho_72 BOUND_VARIABLE_13111 BOUND_VARIABLE_12310)))))) (let ((_let_201 (forall ((BOUND_VARIABLE_12296 nat) (BOUND_VARIABLE_13127 |u_(-> complex complex)|) (BOUND_VARIABLE_13126 |u_(-> complex complex)|) (BOUND_VARIABLE_12299 complex)) (= (ho_72 (ho_75 (ho_74 (ho_104 k_103 BOUND_VARIABLE_12296) BOUND_VARIABLE_13127) BOUND_VARIABLE_13126) BOUND_VARIABLE_12299) (ho_72 (ho_75 (ho_106 k_105 BOUND_VARIABLE_12296) BOUND_VARIABLE_13127) (ho_72 BOUND_VARIABLE_13126 BOUND_VARIABLE_12299)))))) (let ((_let_202 (forall ((BOUND_VARIABLE_13153 |u_(-> complex complex)|) (BOUND_VARIABLE_12290 complex)) (= (ho_72 (ho_75 k_107 BOUND_VARIABLE_13153) BOUND_VARIABLE_12290) (ho_72 BOUND_VARIABLE_13153 BOUND_VARIABLE_12290))))) (let ((_let_203 (forall ((BOUND_VARIABLE_12282 set_complex) (BOUND_VARIABLE_12283 set_complex)) (= (ho_68 (ho_70 k_108 BOUND_VARIABLE_12282) BOUND_VARIABLE_12283) (= BOUND_VARIABLE_12282 BOUND_VARIABLE_12283))))) (let ((_let_204 (forall ((BOUND_VARIABLE_12265 set_complex) (BOUND_VARIABLE_12266 set_complex)) (= (ho_68 (ho_70 k_109 BOUND_VARIABLE_12265) BOUND_VARIABLE_12266) (and (forall ((BOUND_VARIABLE_8523 complex)) (let ((_let_1 (ho_67 k_66 BOUND_VARIABLE_8523))) (or (not (ho_68 _let_1 BOUND_VARIABLE_12265)) (ho_68 _let_1 BOUND_VARIABLE_12266)))) (forall ((BOUND_VARIABLE_8543 complex)) (let ((_let_1 (ho_67 k_66 BOUND_VARIABLE_8543))) (or (not (ho_68 _let_1 BOUND_VARIABLE_12266)) (ho_68 _let_1 BOUND_VARIABLE_12265))))))))) (let ((_let_205 (forall ((BOUND_VARIABLE_13194 |u_(-> complex complex)|) (BOUND_VARIABLE_13193 |u_(-> complex complex)|) (BOUND_VARIABLE_13192 |u_(-> complex complex)|) (BOUND_VARIABLE_12257 complex)) (= (ho_72 (ho_75 (ho_74 (ho_83 k_110 BOUND_VARIABLE_13194) BOUND_VARIABLE_13193) BOUND_VARIABLE_13192) BOUND_VARIABLE_12257) (ho_72 BOUND_VARIABLE_13194 (ho_72 BOUND_VARIABLE_13193 (ho_72 BOUND_VARIABLE_13192 BOUND_VARIABLE_12257))))))) (let ((_let_206 (forall ((BOUND_VARIABLE_13212 |u_(-> complex complex)|) (BOUND_VARIABLE_13211 |u_(-> complex complex)|) (BOUND_VARIABLE_13210 |u_(-> complex complex)|) (BOUND_VARIABLE_12246 complex)) (= (ho_72 (ho_75 (ho_74 (ho_83 k_111 BOUND_VARIABLE_13212) BOUND_VARIABLE_13211) BOUND_VARIABLE_13210) BOUND_VARIABLE_12246) (ho_72 BOUND_VARIABLE_13212 (ho_72 BOUND_VARIABLE_13211 (ho_72 BOUND_VARIABLE_13210 BOUND_VARIABLE_12246))))))) (let ((_let_207 (forall ((BOUND_VARIABLE_12235 real) (BOUND_VARIABLE_12236 real)) (= (ho_65 (ho_113 k_112 BOUND_VARIABLE_12235) BOUND_VARIABLE_12236) (ho_65 (ho_113 k_114 BOUND_VARIABLE_12236) BOUND_VARIABLE_12235))))) (let ((_let_208 (forall ((BOUND_VARIABLE_13242 |u_(-> complex complex)|) (BOUND_VARIABLE_13241 |u_(-> complex complex)|) (BOUND_VARIABLE_12228 complex)) (= (ho_72 (ho_75 (ho_74 k_115 BOUND_VARIABLE_13242) BOUND_VARIABLE_13241) BOUND_VARIABLE_12228) (ho_72 BOUND_VARIABLE_13242 (ho_72 BOUND_VARIABLE_13241 BOUND_VARIABLE_12228)))))) (let ((_let_209 (forall ((BOUND_VARIABLE_13254 |u_(-> complex complex)|) (BOUND_VARIABLE_12220 complex)) (= (ho_72 (ho_75 k_116 BOUND_VARIABLE_13254) BOUND_VARIABLE_12220) (ho_72 BOUND_VARIABLE_13254 BOUND_VARIABLE_12220))))) (let ((_let_210 (forall ((BOUND_VARIABLE_12212 nat) (BOUND_VARIABLE_12213 nat)) (= (ho_119 (ho_118 k_117 BOUND_VARIABLE_12212) BOUND_VARIABLE_12213) (= BOUND_VARIABLE_12212 BOUND_VARIABLE_12213))))) (let ((_let_211 (forall ((BOUND_VARIABLE_12201 nat) (BOUND_VARIABLE_12202 nat)) (= (ho_119 (ho_118 k_121 BOUND_VARIABLE_12201) BOUND_VARIABLE_12202) (and (ho_119 (ho_118 k_120 BOUND_VARIABLE_12201) BOUND_VARIABLE_12202) (ho_119 (ho_118 k_120 BOUND_VARIABLE_12202) BOUND_VARIABLE_12201)))))) (let ((_let_212 (forall ((BOUND_VARIABLE_12193 nat) (BOUND_VARIABLE_12194 nat)) (= (ho_124 (ho_123 k_122 BOUND_VARIABLE_12193) BOUND_VARIABLE_12194) (ho_124 (ho_123 k_125 BOUND_VARIABLE_12194) BOUND_VARIABLE_12193))))) (let ((_let_213 (forall ((BOUND_VARIABLE_12186 real) (BOUND_VARIABLE_12187 real)) (= (ho_128 (ho_127 k_126 BOUND_VARIABLE_12186) BOUND_VARIABLE_12187) (= BOUND_VARIABLE_12186 BOUND_VARIABLE_12187))))) (let ((_let_214 (forall ((BOUND_VARIABLE_12175 real) (BOUND_VARIABLE_12176 real)) (= (ho_128 (ho_127 k_130 BOUND_VARIABLE_12175) BOUND_VARIABLE_12176) (and (ho_128 (ho_127 k_129 BOUND_VARIABLE_12175) BOUND_VARIABLE_12176) (ho_128 (ho_127 k_129 BOUND_VARIABLE_12176) BOUND_VARIABLE_12175)))))) (let ((_let_215 (forall ((BOUND_VARIABLE_13340 |u_(-> complex complex)|) (BOUND_VARIABLE_13339 |u_(-> complex complex)|) (BOUND_VARIABLE_12168 complex)) (= (ho_72 (ho_75 (ho_74 k_131 BOUND_VARIABLE_13340) BOUND_VARIABLE_13339) BOUND_VARIABLE_12168) (ho_72 BOUND_VARIABLE_13340 (ho_72 BOUND_VARIABLE_13339 BOUND_VARIABLE_12168)))))) (let ((_let_216 (forall ((BOUND_VARIABLE_13354 |u_(-> complex complex)|) (BOUND_VARIABLE_13353 |u_(-> complex complex)|) (BOUND_VARIABLE_12159 complex)) (= (ho_72 (ho_75 (ho_74 k_132 BOUND_VARIABLE_13354) BOUND_VARIABLE_13353) BOUND_VARIABLE_12159) (ho_72 BOUND_VARIABLE_13354 (ho_72 BOUND_VARIABLE_13353 BOUND_VARIABLE_12159)))))) (let ((_let_217 (forall ((BOUND_VARIABLE_13368 |u_(-> complex complex)|) (BOUND_VARIABLE_13367 |u_(-> complex complex)|) (BOUND_VARIABLE_12150 complex)) (= (ho_72 (ho_75 (ho_74 k_133 BOUND_VARIABLE_13368) BOUND_VARIABLE_13367) BOUND_VARIABLE_12150) (ho_72 BOUND_VARIABLE_13368 (ho_72 BOUND_VARIABLE_13367 BOUND_VARIABLE_12150)))))) (let ((_let_218 (forall ((BOUND_VARIABLE_12141 set_complex) (BOUND_VARIABLE_12142 set_complex)) (= (ho_68 (ho_70 k_134 BOUND_VARIABLE_12141) BOUND_VARIABLE_12142) (= BOUND_VARIABLE_12141 BOUND_VARIABLE_12142))))) (let ((_let_219 (forall ((BOUND_VARIABLE_12124 set_complex) (BOUND_VARIABLE_12125 set_complex)) (= (ho_68 (ho_70 k_135 BOUND_VARIABLE_12124) BOUND_VARIABLE_12125) (and (forall ((BOUND_VARIABLE_7785 complex)) (let ((_let_1 (ho_67 k_66 BOUND_VARIABLE_7785))) (or (not (ho_68 _let_1 BOUND_VARIABLE_12124)) (ho_68 _let_1 BOUND_VARIABLE_12125)))) (forall ((BOUND_VARIABLE_7805 complex)) (let ((_let_1 (ho_67 k_66 BOUND_VARIABLE_7805))) (or (not (ho_68 _let_1 BOUND_VARIABLE_12125)) (ho_68 _let_1 BOUND_VARIABLE_12124))))))))) (let ((_let_220 (forall ((BOUND_VARIABLE_12117 complex)) (= (ho_72 k_136 BOUND_VARIABLE_12117) (ho_72 k_138 (ho_72 k_137 BOUND_VARIABLE_12117)))))) (let ((_let_221 (forall ((BOUND_VARIABLE_12109 complex) (BOUND_VARIABLE_12110 complex)) (= (ho_72 (ho_140 k_139 BOUND_VARIABLE_12109) BOUND_VARIABLE_12110) (ho_72 (ho_140 k_141 BOUND_VARIABLE_12110) BOUND_VARIABLE_12109))))) (let ((_let_222 (forall ((BOUND_VARIABLE_13430 |u_(-> complex complex)|) (BOUND_VARIABLE_12103 complex)) (= (ho_72 (ho_75 k_142 BOUND_VARIABLE_13430) BOUND_VARIABLE_12103) (ho_72 BOUND_VARIABLE_13430 BOUND_VARIABLE_12103))))) (let ((_let_223 (forall ((BOUND_VARIABLE_13440 |u_(-> complex complex)|) (BOUND_VARIABLE_12096 complex)) (= (ho_72 (ho_75 k_143 BOUND_VARIABLE_13440) BOUND_VARIABLE_12096) (ho_72 BOUND_VARIABLE_13440 BOUND_VARIABLE_12096))))) (let ((_let_224 (forall ((BOUND_VARIABLE_13454 |u_(-> complex complex)|) (BOUND_VARIABLE_13453 |u_(-> complex complex)|) (BOUND_VARIABLE_13452 |u_(-> complex complex)|) (BOUND_VARIABLE_12087 complex)) (= (ho_72 (ho_75 (ho_74 (ho_83 k_144 BOUND_VARIABLE_13454) BOUND_VARIABLE_13453) BOUND_VARIABLE_13452) BOUND_VARIABLE_12087) (ho_72 BOUND_VARIABLE_13454 (ho_72 BOUND_VARIABLE_13453 (ho_72 BOUND_VARIABLE_13452 BOUND_VARIABLE_12087))))))) (let ((_let_225 (forall ((BOUND_VARIABLE_13472 |u_(-> complex complex)|) (BOUND_VARIABLE_13471 |u_(-> complex complex)|) (BOUND_VARIABLE_13470 |u_(-> complex complex)|) (BOUND_VARIABLE_12076 complex)) (= (ho_72 (ho_75 (ho_74 (ho_83 k_145 BOUND_VARIABLE_13472) BOUND_VARIABLE_13471) BOUND_VARIABLE_13470) BOUND_VARIABLE_12076) (ho_72 BOUND_VARIABLE_13472 (ho_72 BOUND_VARIABLE_13471 (ho_72 BOUND_VARIABLE_13470 BOUND_VARIABLE_12076))))))) (let ((_let_226 (forall ((BOUND_VARIABLE_13488 |u_(-> complex complex)|) (BOUND_VARIABLE_13487 |u_(-> complex complex)|) (BOUND_VARIABLE_12066 complex)) (= (ho_72 (ho_75 (ho_74 k_146 BOUND_VARIABLE_13488) BOUND_VARIABLE_13487) BOUND_VARIABLE_12066) (ho_72 BOUND_VARIABLE_13488 (ho_72 BOUND_VARIABLE_13487 BOUND_VARIABLE_12066)))))) (let ((_let_227 (forall ((BOUND_VARIABLE_13502 |u_(-> complex complex)|) (BOUND_VARIABLE_13501 |u_(-> complex complex)|) (BOUND_VARIABLE_12057 complex)) (= (ho_72 (ho_75 (ho_74 k_147 BOUND_VARIABLE_13502) BOUND_VARIABLE_13501) BOUND_VARIABLE_12057) (ho_72 BOUND_VARIABLE_13502 (ho_72 BOUND_VARIABLE_13501 BOUND_VARIABLE_12057)))))) (let ((_let_228 (forall ((BOUND_VARIABLE_13518 |u_(-> complex complex)|) (BOUND_VARIABLE_13517 |u_(-> complex complex)|) (BOUND_VARIABLE_13516 |u_(-> complex complex)|) (BOUND_VARIABLE_12047 complex)) (= (ho_72 (ho_75 (ho_74 (ho_83 k_148 BOUND_VARIABLE_13518) BOUND_VARIABLE_13517) BOUND_VARIABLE_13516) BOUND_VARIABLE_12047) (ho_72 BOUND_VARIABLE_13518 (ho_72 BOUND_VARIABLE_13517 (ho_72 BOUND_VARIABLE_13516 BOUND_VARIABLE_12047))))))) (let ((_let_229 (forall ((BOUND_VARIABLE_13536 |u_(-> complex complex)|) (BOUND_VARIABLE_13535 |u_(-> complex complex)|) (BOUND_VARIABLE_13534 |u_(-> complex complex)|) (BOUND_VARIABLE_12036 complex)) (= (ho_72 (ho_75 (ho_74 (ho_83 k_149 BOUND_VARIABLE_13536) BOUND_VARIABLE_13535) BOUND_VARIABLE_13534) BOUND_VARIABLE_12036) (ho_72 BOUND_VARIABLE_13536 (ho_72 BOUND_VARIABLE_13535 (ho_72 BOUND_VARIABLE_13534 BOUND_VARIABLE_12036))))))) (let ((_let_230 (forall ((BOUND_VARIABLE_12025 set_complex) (BOUND_VARIABLE_12026 complex)) (= (ho_152 (ho_151 k_150 BOUND_VARIABLE_12025) BOUND_VARIABLE_12026) (ho_68 (ho_67 k_66 BOUND_VARIABLE_12026) BOUND_VARIABLE_12025))))) (let ((_let_231 (forall ((BOUND_VARIABLE_12020 real)) (= one_one_real (ho_65 k_153 BOUND_VARIABLE_12020))))) (let ((_let_232 (forall ((BOUND_VARIABLE_12015 real)) (= BOUND_VARIABLE_12015 (ho_65 k_154 BOUND_VARIABLE_12015))))) (let ((_let_233 (forall ((BOUND_VARIABLE_12010 complex)) (= BOUND_VARIABLE_12010 (ho_72 k_155 BOUND_VARIABLE_12010))))) (let ((_let_234 (forall ((N nat) (M nat) (BOUND_VARIABLE_13580 |u_(-> complex complex)|)) (= (ho_75 (ho_106 k_105 N) (ho_75 (ho_106 k_105 M) BOUND_VARIABLE_13580)) (ho_75 (ho_106 k_105 (ho_124 (ho_123 k_125 M) N)) BOUND_VARIABLE_13580))))) (let ((_let_235 (forall ((BOUND_VARIABLE_12571 real)) (= BOUND_VARIABLE_12571 (ll_63 BOUND_VARIABLE_12571))))) (let ((_let_236 (forall ((BOUND_VARIABLE_12560 set_complex) (BOUND_VARIABLE_12561 set_complex)) (= (ll_62 BOUND_VARIABLE_12560 BOUND_VARIABLE_12561) (forall ((X complex)) (let ((_let_1 (member_complex X))) (or (not (_let_1 BOUND_VARIABLE_12560)) (_let_1 BOUND_VARIABLE_12561)))))))) (let ((_let_237 (forall ((BOUND_VARIABLE_12549 set_complex) (BOUND_VARIABLE_12550 set_complex)) (= (ll_61 BOUND_VARIABLE_12549 BOUND_VARIABLE_12550) (forall ((T3 complex)) (let ((_let_1 (member_complex T3))) (or (not (_let_1 BOUND_VARIABLE_12549)) (_let_1 BOUND_VARIABLE_12550)))))))) (let ((_let_238 (forall ((BOUND_VARIABLE_12540 (-> complex complex)) (BOUND_VARIABLE_12541 (-> complex complex)) (BOUND_VARIABLE_12542 complex)) (= (BOUND_VARIABLE_12540 (BOUND_VARIABLE_12541 BOUND_VARIABLE_12542)) (ll_60 BOUND_VARIABLE_12540 BOUND_VARIABLE_12541 BOUND_VARIABLE_12542))))) (let ((_let_239 (forall ((BOUND_VARIABLE_12531 (-> complex complex)) (BOUND_VARIABLE_12532 (-> complex complex)) (BOUND_VARIABLE_12533 complex)) (= (BOUND_VARIABLE_12531 (BOUND_VARIABLE_12532 BOUND_VARIABLE_12533)) (ll_59 BOUND_VARIABLE_12531 BOUND_VARIABLE_12532 BOUND_VARIABLE_12533))))) (let ((_let_240 (forall ((BOUND_VARIABLE_12524 (-> complex complex)) (BOUND_VARIABLE_12525 complex)) (= (BOUND_VARIABLE_12524 BOUND_VARIABLE_12525) (ll_58 BOUND_VARIABLE_12524 BOUND_VARIABLE_12525))))) (let ((_let_241 (forall ((BOUND_VARIABLE_12515 (-> complex complex)) (BOUND_VARIABLE_12516 (-> complex complex)) (BOUND_VARIABLE_12517 complex)) (= (BOUND_VARIABLE_12515 (BOUND_VARIABLE_12516 BOUND_VARIABLE_12517)) (ll_57 BOUND_VARIABLE_12515 BOUND_VARIABLE_12516 BOUND_VARIABLE_12517))))) (let ((_let_242 (forall ((BOUND_VARIABLE_12506 (-> complex complex)) (BOUND_VARIABLE_12507 (-> complex complex)) (BOUND_VARIABLE_12508 complex)) (= (BOUND_VARIABLE_12506 (BOUND_VARIABLE_12507 BOUND_VARIABLE_12508)) (ll_56 BOUND_VARIABLE_12506 BOUND_VARIABLE_12507 BOUND_VARIABLE_12508))))) (let ((_let_243 (forall ((BOUND_VARIABLE_12497 (-> complex complex)) (BOUND_VARIABLE_12498 (-> complex complex)) (BOUND_VARIABLE_12499 complex)) (= (BOUND_VARIABLE_12497 (BOUND_VARIABLE_12498 BOUND_VARIABLE_12499)) (ll_55 BOUND_VARIABLE_12497 BOUND_VARIABLE_12498 BOUND_VARIABLE_12499))))) (let ((_let_244 (forall ((BOUND_VARIABLE_12490 (-> complex complex)) (BOUND_VARIABLE_12491 complex)) (= (BOUND_VARIABLE_12490 BOUND_VARIABLE_12491) (ll_54 BOUND_VARIABLE_12490 BOUND_VARIABLE_12491))))) (let ((_let_245 (forall ((BOUND_VARIABLE_12479 (-> complex complex)) (BOUND_VARIABLE_12480 (-> complex complex)) (BOUND_VARIABLE_12481 (-> complex complex)) (BOUND_VARIABLE_12482 complex)) (= (BOUND_VARIABLE_12479 (BOUND_VARIABLE_12480 (BOUND_VARIABLE_12481 BOUND_VARIABLE_12482))) (ll_53 BOUND_VARIABLE_12479 BOUND_VARIABLE_12480 BOUND_VARIABLE_12481 BOUND_VARIABLE_12482))))) (let ((_let_246 (forall ((BOUND_VARIABLE_12468 (-> complex complex)) (BOUND_VARIABLE_12469 (-> complex complex)) (BOUND_VARIABLE_12470 (-> complex complex)) (BOUND_VARIABLE_12471 complex)) (= (BOUND_VARIABLE_12468 (BOUND_VARIABLE_12469 (BOUND_VARIABLE_12470 BOUND_VARIABLE_12471))) (ll_52 BOUND_VARIABLE_12468 BOUND_VARIABLE_12469 BOUND_VARIABLE_12470 BOUND_VARIABLE_12471))))) (let ((_let_247 (forall ((BOUND_VARIABLE_12461 (-> complex complex)) (BOUND_VARIABLE_12462 complex)) (= (BOUND_VARIABLE_12461 BOUND_VARIABLE_12462) (ll_51 BOUND_VARIABLE_12461 BOUND_VARIABLE_12462))))) (let ((_let_248 (forall ((BOUND_VARIABLE_12456 complex)) (= one_one_complex (ll_50 BOUND_VARIABLE_12456))))) (let ((_let_249 (forall ((BOUND_VARIABLE_12447 (-> complex complex)) (BOUND_VARIABLE_12448 (-> complex complex)) (BOUND_VARIABLE_12449 complex)) (= (BOUND_VARIABLE_12447 (BOUND_VARIABLE_12448 BOUND_VARIABLE_12449)) (ll_49 BOUND_VARIABLE_12447 BOUND_VARIABLE_12448 BOUND_VARIABLE_12449))))) (let ((_let_250 (forall ((BOUND_VARIABLE_12438 (-> complex complex)) (BOUND_VARIABLE_12439 (-> complex complex)) (BOUND_VARIABLE_12440 complex)) (= (BOUND_VARIABLE_12438 (BOUND_VARIABLE_12439 BOUND_VARIABLE_12440)) (ll_48 BOUND_VARIABLE_12438 BOUND_VARIABLE_12439 BOUND_VARIABLE_12440))))) (let ((_let_251 (forall ((BOUND_VARIABLE_12427 (-> complex complex)) (BOUND_VARIABLE_12428 (-> complex complex)) (BOUND_VARIABLE_12429 (-> complex complex)) (BOUND_VARIABLE_12430 complex)) (= (BOUND_VARIABLE_12427 (BOUND_VARIABLE_12428 (BOUND_VARIABLE_12429 BOUND_VARIABLE_12430))) (ll_47 BOUND_VARIABLE_12427 BOUND_VARIABLE_12428 BOUND_VARIABLE_12429 BOUND_VARIABLE_12430))))) (let ((_let_252 (forall ((BOUND_VARIABLE_12416 (-> complex complex)) (BOUND_VARIABLE_12417 (-> complex complex)) (BOUND_VARIABLE_12418 (-> complex complex)) (BOUND_VARIABLE_12419 complex)) (= (BOUND_VARIABLE_12416 (BOUND_VARIABLE_12417 (BOUND_VARIABLE_12418 BOUND_VARIABLE_12419))) (ll_46 BOUND_VARIABLE_12416 BOUND_VARIABLE_12417 BOUND_VARIABLE_12418 BOUND_VARIABLE_12419))))) (let ((_let_253 (forall ((BOUND_VARIABLE_12405 (-> complex complex)) (BOUND_VARIABLE_12406 (-> complex complex)) (BOUND_VARIABLE_12407 (-> complex complex)) (BOUND_VARIABLE_12408 complex)) (= (BOUND_VARIABLE_12405 (BOUND_VARIABLE_12406 (BOUND_VARIABLE_12407 BOUND_VARIABLE_12408))) (ll_45 BOUND_VARIABLE_12405 BOUND_VARIABLE_12406 BOUND_VARIABLE_12407 BOUND_VARIABLE_12408))))) (let ((_let_254 (forall ((BOUND_VARIABLE_12394 (-> complex complex)) (BOUND_VARIABLE_12395 (-> complex complex)) (BOUND_VARIABLE_12396 (-> complex complex)) (BOUND_VARIABLE_12397 complex)) (= (BOUND_VARIABLE_12394 (BOUND_VARIABLE_12395 (BOUND_VARIABLE_12396 BOUND_VARIABLE_12397))) (ll_44 BOUND_VARIABLE_12394 BOUND_VARIABLE_12395 BOUND_VARIABLE_12396 BOUND_VARIABLE_12397))))) (let ((_let_255 (forall ((BOUND_VARIABLE_12385 (-> complex complex)) (BOUND_VARIABLE_12386 (-> complex complex)) (BOUND_VARIABLE_12387 complex)) (= (BOUND_VARIABLE_12385 (BOUND_VARIABLE_12386 BOUND_VARIABLE_12387)) (ll_43 BOUND_VARIABLE_12385 BOUND_VARIABLE_12386 BOUND_VARIABLE_12387))))) (let ((_let_256 (forall ((BOUND_VARIABLE_12376 (-> complex complex)) (BOUND_VARIABLE_12377 (-> complex complex)) (BOUND_VARIABLE_12378 complex)) (= (BOUND_VARIABLE_12376 (BOUND_VARIABLE_12377 BOUND_VARIABLE_12378)) (ll_42 BOUND_VARIABLE_12376 BOUND_VARIABLE_12377 BOUND_VARIABLE_12378))))) (let ((_let_257 (forall ((BOUND_VARIABLE_12367 (-> complex complex)) (BOUND_VARIABLE_12368 (-> complex complex)) (BOUND_VARIABLE_12369 complex)) (= (BOUND_VARIABLE_12367 (BOUND_VARIABLE_12368 BOUND_VARIABLE_12369)) (ll_41 BOUND_VARIABLE_12367 BOUND_VARIABLE_12368 BOUND_VARIABLE_12369))))) (let ((_let_258 (forall ((BOUND_VARIABLE_12358 (-> complex complex)) (BOUND_VARIABLE_12359 (-> complex complex)) (BOUND_VARIABLE_12360 complex)) (= (BOUND_VARIABLE_12358 (BOUND_VARIABLE_12359 BOUND_VARIABLE_12360)) (ll_40 BOUND_VARIABLE_12358 BOUND_VARIABLE_12359 BOUND_VARIABLE_12360))))) (let ((_let_259 (forall ((BOUND_VARIABLE_12349 (-> complex complex)) (BOUND_VARIABLE_12350 (-> complex complex)) (BOUND_VARIABLE_12351 complex)) (= (BOUND_VARIABLE_12349 (BOUND_VARIABLE_12350 BOUND_VARIABLE_12351)) (ll_39 BOUND_VARIABLE_12349 BOUND_VARIABLE_12350 BOUND_VARIABLE_12351))))) (let ((_let_260 (forall ((BOUND_VARIABLE_12340 (-> complex complex)) (BOUND_VARIABLE_12341 (-> complex complex)) (BOUND_VARIABLE_12342 complex)) (= (BOUND_VARIABLE_12340 (BOUND_VARIABLE_12341 BOUND_VARIABLE_12342)) (ll_38 BOUND_VARIABLE_12340 BOUND_VARIABLE_12341 BOUND_VARIABLE_12342))))) (let ((_let_261 (forall ((BOUND_VARIABLE_12335 complex)) (= BOUND_VARIABLE_12335 (ll_37 BOUND_VARIABLE_12335))))) (let ((_let_262 (forall ((BOUND_VARIABLE_12326 (-> complex complex)) (BOUND_VARIABLE_12327 (-> complex complex)) (BOUND_VARIABLE_12328 complex)) (= (BOUND_VARIABLE_12326 (BOUND_VARIABLE_12327 BOUND_VARIABLE_12328)) (ll_36 BOUND_VARIABLE_12326 BOUND_VARIABLE_12327 BOUND_VARIABLE_12328))))) (let ((_let_263 (forall ((BOUND_VARIABLE_12317 (-> complex complex)) (BOUND_VARIABLE_12318 (-> complex complex)) (BOUND_VARIABLE_12319 complex)) (= (BOUND_VARIABLE_12317 (BOUND_VARIABLE_12318 BOUND_VARIABLE_12319)) (ll_35 BOUND_VARIABLE_12317 BOUND_VARIABLE_12318 BOUND_VARIABLE_12319))))) (let ((_let_264 (forall ((BOUND_VARIABLE_12308 (-> complex complex)) (BOUND_VARIABLE_12309 (-> complex complex)) (BOUND_VARIABLE_12310 complex)) (= (BOUND_VARIABLE_12308 (BOUND_VARIABLE_12309 BOUND_VARIABLE_12310)) (ll_34 BOUND_VARIABLE_12308 BOUND_VARIABLE_12309 BOUND_VARIABLE_12310))))) (let ((_let_265 (forall ((BOUND_VARIABLE_12296 nat) (BOUND_VARIABLE_12297 (-> complex complex)) (BOUND_VARIABLE_12298 (-> complex complex)) (BOUND_VARIABLE_12299 complex)) (= (((funpow_complex BOUND_VARIABLE_12296) BOUND_VARIABLE_12297) (BOUND_VARIABLE_12298 BOUND_VARIABLE_12299)) (ll_33 BOUND_VARIABLE_12296 BOUND_VARIABLE_12297 BOUND_VARIABLE_12298 BOUND_VARIABLE_12299))))) (let ((_let_266 (forall ((BOUND_VARIABLE_12289 (-> complex complex)) (BOUND_VARIABLE_12290 complex)) (= (BOUND_VARIABLE_12289 BOUND_VARIABLE_12290) (ll_32 BOUND_VARIABLE_12289 BOUND_VARIABLE_12290))))) (let ((_let_267 (forall ((BOUND_VARIABLE_12282 set_complex) (BOUND_VARIABLE_12283 set_complex)) (= (ll_31 BOUND_VARIABLE_12282 BOUND_VARIABLE_12283) (= BOUND_VARIABLE_12282 BOUND_VARIABLE_12283))))) (let ((_let_268 (forall ((BOUND_VARIABLE_12265 set_complex) (BOUND_VARIABLE_12266 set_complex)) (= (ll_30 BOUND_VARIABLE_12265 BOUND_VARIABLE_12266) (and (forall ((BOUND_VARIABLE_8523 complex)) (let ((_let_1 (member_complex BOUND_VARIABLE_8523))) (or (not (_let_1 BOUND_VARIABLE_12265)) (_let_1 BOUND_VARIABLE_12266)))) (forall ((BOUND_VARIABLE_8543 complex)) (let ((_let_1 (member_complex BOUND_VARIABLE_8543))) (or (not (_let_1 BOUND_VARIABLE_12266)) (_let_1 BOUND_VARIABLE_12265))))))))) (let ((_let_269 (forall ((BOUND_VARIABLE_12254 (-> complex complex)) (BOUND_VARIABLE_12255 (-> complex complex)) (BOUND_VARIABLE_12256 (-> complex complex)) (BOUND_VARIABLE_12257 complex)) (= (BOUND_VARIABLE_12254 (BOUND_VARIABLE_12255 (BOUND_VARIABLE_12256 BOUND_VARIABLE_12257))) (ll_29 BOUND_VARIABLE_12254 BOUND_VARIABLE_12255 BOUND_VARIABLE_12256 BOUND_VARIABLE_12257))))) (let ((_let_270 (forall ((BOUND_VARIABLE_12243 (-> complex complex)) (BOUND_VARIABLE_12244 (-> complex complex)) (BOUND_VARIABLE_12245 (-> complex complex)) (BOUND_VARIABLE_12246 complex)) (= (BOUND_VARIABLE_12243 (BOUND_VARIABLE_12244 (BOUND_VARIABLE_12245 BOUND_VARIABLE_12246))) (ll_28 BOUND_VARIABLE_12243 BOUND_VARIABLE_12244 BOUND_VARIABLE_12245 BOUND_VARIABLE_12246))))) (let ((_let_271 (forall ((BOUND_VARIABLE_12235 real) (BOUND_VARIABLE_12236 real)) (= ((times_times_real BOUND_VARIABLE_12236) BOUND_VARIABLE_12235) (ll_27 BOUND_VARIABLE_12235 BOUND_VARIABLE_12236))))) (let ((_let_272 (forall ((BOUND_VARIABLE_12226 (-> complex complex)) (BOUND_VARIABLE_12227 (-> complex complex)) (BOUND_VARIABLE_12228 complex)) (= (BOUND_VARIABLE_12226 (BOUND_VARIABLE_12227 BOUND_VARIABLE_12228)) (ll_26 BOUND_VARIABLE_12226 BOUND_VARIABLE_12227 BOUND_VARIABLE_12228))))) (let ((_let_273 (forall ((BOUND_VARIABLE_12219 (-> complex complex)) (BOUND_VARIABLE_12220 complex)) (= (BOUND_VARIABLE_12219 BOUND_VARIABLE_12220) (ll_25 BOUND_VARIABLE_12219 BOUND_VARIABLE_12220))))) (let ((_let_274 (forall ((BOUND_VARIABLE_12212 nat) (BOUND_VARIABLE_12213 nat)) (= (ll_24 BOUND_VARIABLE_12212 BOUND_VARIABLE_12213) (= BOUND_VARIABLE_12212 BOUND_VARIABLE_12213))))) (let ((_let_275 (forall ((BOUND_VARIABLE_12201 nat) (BOUND_VARIABLE_12202 nat)) (= (ll_23 BOUND_VARIABLE_12201 BOUND_VARIABLE_12202) (and ((ord_less_eq_nat BOUND_VARIABLE_12201) BOUND_VARIABLE_12202) ((ord_less_eq_nat BOUND_VARIABLE_12202) BOUND_VARIABLE_12201)))))) (let ((_let_276 (forall ((BOUND_VARIABLE_12193 nat) (BOUND_VARIABLE_12194 nat)) (= ((times_times_nat BOUND_VARIABLE_12194) BOUND_VARIABLE_12193) (ll_22 BOUND_VARIABLE_12193 BOUND_VARIABLE_12194))))) (let ((_let_277 (forall ((BOUND_VARIABLE_12186 real) (BOUND_VARIABLE_12187 real)) (= (ll_21 BOUND_VARIABLE_12186 BOUND_VARIABLE_12187) (= BOUND_VARIABLE_12186 BOUND_VARIABLE_12187))))) (let ((_let_278 (forall ((BOUND_VARIABLE_12175 real) (BOUND_VARIABLE_12176 real)) (= (ll_20 BOUND_VARIABLE_12175 BOUND_VARIABLE_12176) (and ((ord_less_eq_real BOUND_VARIABLE_12175) BOUND_VARIABLE_12176) ((ord_less_eq_real BOUND_VARIABLE_12176) BOUND_VARIABLE_12175)))))) (let ((_let_279 (forall ((BOUND_VARIABLE_12166 (-> complex complex)) (BOUND_VARIABLE_12167 (-> complex complex)) (BOUND_VARIABLE_12168 complex)) (= (BOUND_VARIABLE_12166 (BOUND_VARIABLE_12167 BOUND_VARIABLE_12168)) (ll_19 BOUND_VARIABLE_12166 BOUND_VARIABLE_12167 BOUND_VARIABLE_12168))))) (let ((_let_280 (forall ((BOUND_VARIABLE_12157 (-> complex complex)) (BOUND_VARIABLE_12158 (-> complex complex)) (BOUND_VARIABLE_12159 complex)) (= (BOUND_VARIABLE_12157 (BOUND_VARIABLE_12158 BOUND_VARIABLE_12159)) (ll_18 BOUND_VARIABLE_12157 BOUND_VARIABLE_12158 BOUND_VARIABLE_12159))))) (let ((_let_281 (forall ((BOUND_VARIABLE_12148 (-> complex complex)) (BOUND_VARIABLE_12149 (-> complex complex)) (BOUND_VARIABLE_12150 complex)) (= (BOUND_VARIABLE_12148 (BOUND_VARIABLE_12149 BOUND_VARIABLE_12150)) (ll_17 BOUND_VARIABLE_12148 BOUND_VARIABLE_12149 BOUND_VARIABLE_12150))))) (let ((_let_282 (forall ((BOUND_VARIABLE_12141 set_complex) (BOUND_VARIABLE_12142 set_complex)) (= (ll_16 BOUND_VARIABLE_12141 BOUND_VARIABLE_12142) (= BOUND_VARIABLE_12141 BOUND_VARIABLE_12142))))) (let ((_let_283 (forall ((BOUND_VARIABLE_12124 set_complex) (BOUND_VARIABLE_12125 set_complex)) (= (ll_15 BOUND_VARIABLE_12124 BOUND_VARIABLE_12125) (and (forall ((BOUND_VARIABLE_7785 complex)) (let ((_let_1 (member_complex BOUND_VARIABLE_7785))) (or (not (_let_1 BOUND_VARIABLE_12124)) (_let_1 BOUND_VARIABLE_12125)))) (forall ((BOUND_VARIABLE_7805 complex)) (let ((_let_1 (member_complex BOUND_VARIABLE_7805))) (or (not (_let_1 BOUND_VARIABLE_12125)) (_let_1 BOUND_VARIABLE_12124))))))))) (let ((_let_284 (forall ((BOUND_VARIABLE_12117 complex)) (= (g (f BOUND_VARIABLE_12117)) (ll_14 BOUND_VARIABLE_12117))))) (let ((_let_285 (forall ((BOUND_VARIABLE_12109 complex) (BOUND_VARIABLE_12110 complex)) (= ((times_times_complex BOUND_VARIABLE_12110) BOUND_VARIABLE_12109) (ll_13 BOUND_VARIABLE_12109 BOUND_VARIABLE_12110))))) (let ((_let_286 (forall ((BOUND_VARIABLE_12102 (-> complex complex)) (BOUND_VARIABLE_12103 complex)) (= (BOUND_VARIABLE_12102 BOUND_VARIABLE_12103) (ll_12 BOUND_VARIABLE_12102 BOUND_VARIABLE_12103))))) (let ((_let_287 (forall ((BOUND_VARIABLE_12095 (-> complex complex)) (BOUND_VARIABLE_12096 complex)) (= (BOUND_VARIABLE_12095 BOUND_VARIABLE_12096) (ll_11 BOUND_VARIABLE_12095 BOUND_VARIABLE_12096))))) (let ((_let_288 (forall ((BOUND_VARIABLE_12084 (-> complex complex)) (BOUND_VARIABLE_12085 (-> complex complex)) (BOUND_VARIABLE_12086 (-> complex complex)) (BOUND_VARIABLE_12087 complex)) (= (BOUND_VARIABLE_12084 (BOUND_VARIABLE_12085 (BOUND_VARIABLE_12086 BOUND_VARIABLE_12087))) (ll_10 BOUND_VARIABLE_12084 BOUND_VARIABLE_12085 BOUND_VARIABLE_12086 BOUND_VARIABLE_12087))))) (let ((_let_289 (forall ((BOUND_VARIABLE_12073 (-> complex complex)) (BOUND_VARIABLE_12074 (-> complex complex)) (BOUND_VARIABLE_12075 (-> complex complex)) (BOUND_VARIABLE_12076 complex)) (= (BOUND_VARIABLE_12073 (BOUND_VARIABLE_12074 (BOUND_VARIABLE_12075 BOUND_VARIABLE_12076))) (ll_9 BOUND_VARIABLE_12073 BOUND_VARIABLE_12074 BOUND_VARIABLE_12075 BOUND_VARIABLE_12076))))) (let ((_let_290 (forall ((BOUND_VARIABLE_12064 (-> complex complex)) (BOUND_VARIABLE_12065 (-> complex complex)) (BOUND_VARIABLE_12066 complex)) (= (BOUND_VARIABLE_12064 (BOUND_VARIABLE_12065 BOUND_VARIABLE_12066)) (ll_8 BOUND_VARIABLE_12064 BOUND_VARIABLE_12065 BOUND_VARIABLE_12066))))) (let ((_let_291 (forall ((BOUND_VARIABLE_12055 (-> complex complex)) (BOUND_VARIABLE_12056 (-> complex complex)) (BOUND_VARIABLE_12057 complex)) (= (BOUND_VARIABLE_12055 (BOUND_VARIABLE_12056 BOUND_VARIABLE_12057)) (ll_7 BOUND_VARIABLE_12055 BOUND_VARIABLE_12056 BOUND_VARIABLE_12057))))) (let ((_let_292 (forall ((BOUND_VARIABLE_12044 (-> complex complex)) (BOUND_VARIABLE_12045 (-> complex complex)) (BOUND_VARIABLE_12046 (-> complex complex)) (BOUND_VARIABLE_12047 complex)) (= (BOUND_VARIABLE_12044 (BOUND_VARIABLE_12045 (BOUND_VARIABLE_12046 BOUND_VARIABLE_12047))) (ll_6 BOUND_VARIABLE_12044 BOUND_VARIABLE_12045 BOUND_VARIABLE_12046 BOUND_VARIABLE_12047))))) (let ((_let_293 (forall ((BOUND_VARIABLE_12033 (-> complex complex)) (BOUND_VARIABLE_12034 (-> complex complex)) (BOUND_VARIABLE_12035 (-> complex complex)) (BOUND_VARIABLE_12036 complex)) (= (BOUND_VARIABLE_12033 (BOUND_VARIABLE_12034 (BOUND_VARIABLE_12035 BOUND_VARIABLE_12036))) (ll_5 BOUND_VARIABLE_12033 BOUND_VARIABLE_12034 BOUND_VARIABLE_12035 BOUND_VARIABLE_12036))))) (let ((_let_294 (forall ((BOUND_VARIABLE_12025 set_complex) (BOUND_VARIABLE_12026 complex)) (= (ll_4 BOUND_VARIABLE_12025 BOUND_VARIABLE_12026) ((member_complex BOUND_VARIABLE_12026) BOUND_VARIABLE_12025))))) (let ((_let_295 (forall ((BOUND_VARIABLE_12020 real)) (= one_one_real (ll_3 BOUND_VARIABLE_12020))))) (let ((_let_296 (forall ((BOUND_VARIABLE_12015 real)) (= BOUND_VARIABLE_12015 (ll_2 BOUND_VARIABLE_12015))))) (let ((_let_297 (forall ((BOUND_VARIABLE_12010 complex)) (= BOUND_VARIABLE_12010 (ll_1 BOUND_VARIABLE_12010))))) (let ((_let_298 (and (forall ((N nat) (M nat) (F (-> complex complex))) (= ((funpow_complex ((times_times_nat M) N)) F) ((funpow_complex N) ((funpow_complex M) F)))) _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 ((_let_299 (EQ_RESOLVE (ASSUME |:args| (_let_26)) (MACRO_SR_EQ_INTRO |:args| (_let_26 7 12))))) (let ((_let_300 (SYMM (ASSUME |:args| (_let_25))))) (let ((_let_301 (SYMM (ASSUME |:args| (_let_24))))) (let ((_let_302 (ASSUME |:args| (_let_23)))) (let ((_let_303 (ASSUME |:args| (_let_21)))) (let ((_let_304 (SYMM (ASSUME |:args| (_let_20))))) (let ((_let_305 (SYMM (ASSUME |:args| (_let_19))))) (let ((_let_306 (ASSUME |:args| (_let_14)))) (let ((_let_307 (SYMM (ASSUME |:args| (_let_12))))) (let ((_let_308 (EQ_RESOLVE (SYMM (ASSUME |:args| (_let_11))) (MACRO_SR_EQ_INTRO _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 |:args| ((= id_set_complex _let_10) 7 12))))) (let ((_let_309 (SYMM (ASSUME |:args| (_let_7))))) (let ((_let_310 (EQ_RESOLVE (SYMM (ASSUME |:args| (_let_6))) (MACRO_SR_EQ_INTRO _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 |:args| ((= id_set_real _let_5) 7 12))))) (let ((_let_311 (SYMM (ASSUME |:args| (_let_1))))) (let ((_let_312 (ho_75 k_157 k_155))) (let ((_let_313 (= k_86 _let_312))) (let ((_let_314 (= one_one_complex (ho_72 _let_312 w)))) (let ((_let_315 (not _let_29))) (let ((_let_316 (deriv_complex ll_1))) (let ((_let_317 (= _let_316 ll_50))) (let ((_let_318 (deriv_complex _let_13))) (let ((_let_319 (EQ_RESOLVE (ASSUME |:args| (_let_4)) (TRANS (MACRO_SR_EQ_INTRO _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 |:args| (_let_4 7 12)) (PREPROCESS |:args| ((= (= _let_2 _let_318) _let_317))) (PREPROCESS |:args| ((= _let_317 _let_313))))))) (let ((_let_320 (not _let_314))) (let ((_let_321 (not (= one_one_complex (_let_316 w))))) (let ((_let_322 (EQ_RESOLVE (ASSUME |:args| (_let_9)) (TRANS (MACRO_SR_EQ_INTRO |:args| (_let_9 7 12)) (MACRO_SR_EQ_INTRO _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 |:args| ((not (= one_one_complex _let_8)) 7 12)) (PREPROCESS |:args| ((= (not (= one_one_complex (_let_318 w))) _let_321))) (PREPROCESS |:args| ((= _let_321 _let_320))))))) (let ((_let_323 (and _let_320 _let_313))) (let ((_let_324 (w))) (let ((_let_325 (_let_28))) (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME |:args| _let_325) |:args| _let_324) |:args| _let_325)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG |:args| (_let_323)) (IMPLIES_ELIM (SCOPE (FALSE_ELIM (TRANS (CONG (REFL |:args| (one_one_complex)) (CONG (SYMM (SYMM _let_319)) (REFL |:args| _let_324) |:args| (23 ho_72)) |:args| (6)) (FALSE_INTRO _let_322))) |:args| (_let_320 _let_313))) |:args| (true _let_323)) (CONG (MACRO_SR_PRED_INTRO |:args| ((= (not _let_320) _let_314))) (REFL |:args| ((not _let_313))) (REFL |:args| (_let_315)) |:args| (20))) _let_322 _let_319 |:args| (_let_315 true _let_314 false _let_313)) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME |:args| (_let_27)) (MACRO_SR_EQ_INTRO _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 |:args| (_let_27 7 12))) (PREPROCESS |:args| ((and _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)))) |:args| (_let_298)) (PREPROCESS |:args| ((= _let_298 (and _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_28 _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))))) (PREPROCESS |:args| ((and _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 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _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 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 _let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30)))) |:args| ((and _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_28 _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 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _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 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 _let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30))) |:args| (50)) |:args| (false true _let_29 false _let_28)) |:args| (_let_27 (forall ((C real) (A real)) (=> ((ord_less_eq_real C) one_one_real) (=> ((ord_less_eq_real zero_zero_real) A) ((ord_less_eq_real ((times_times_real A) C)) A)))) (forall ((B real) (A real) (C real)) (let ((_let_1 (ord_less_eq_real C))) (=> ((ord_less_eq_real B) A) (=> (_let_1 B) (_let_1 A))))) (forall ((I nat) (J nat) (K nat) (L nat)) (=> ((ord_less_eq_nat I) J) (=> ((ord_less_eq_nat K) L) ((ord_less_eq_nat ((times_times_nat I) K)) ((times_times_nat J) L))))) (forall ((F (-> complex complex)) (S set_complex) (N nat)) (=> ((comple372758642hic_on F) S) (=> (topolo935673511omplex S) ((comple372758642hic_on (((compow1098280738omplex N) deriv_complex) F)) S)))) (forall ((A nat) (B nat)) (=> ((ord_less_eq_nat zero_zero_nat) A) (=> ((ord_less_eq_nat B) zero_zero_nat) ((ord_less_eq_nat ((times_times_nat B) A)) zero_zero_nat)))) (forall ((F (-> complex complex)) (S2 set_complex) (G2 (-> complex complex)) (Z complex)) (=> ((comple372758642hic_on F) S2) (=> ((comple372758642hic_on G2) S2) (=> (topolo935673511omplex S2) (=> ((member_complex Z) S2) (=> (forall ((W complex)) (=> ((member_complex W) S2) (= (F W) (G2 W)))) (= ((deriv_complex F) Z) ((deriv_complex G2) Z)))))))) (forall ((Y real) (X2 real)) (=> (not ((ord_less_eq_real Y) X2)) ((ord_less_eq_real X2) Y))) (forall ((A2 set_complex) (B3 set_complex) (C2 set_complex)) (let ((_let_1 (ord_le701908932omplex A2))) (=> (_let_1 B3) (=> ((ord_le701908932omplex B3) C2) (_let_1 C2))))) (forall ((C real) (A real)) (= (= ((times_times_real C) A) C) (or (= A one_one_real) (= C zero_zero_real)))) (forall ((A2 set_complex) (B3 set_complex) (F (-> complex complex))) (let ((_let_1 (image_58037603omplex F))) (=> ((ord_le701908932omplex A2) B3) ((ord_le701908932omplex (_let_1 A2)) (_let_1 B3))))) (forall ((A2 set_complex) (B3 set_complex)) (=> (forall ((X3 complex)) (let ((_let_1 (member_complex X3))) (=> (_let_1 A2) (_let_1 B3)))) ((ord_le701908932omplex A2) B3))) (forall ((A complex) (B complex)) (=> (not (= ((times_times_complex A) B) zero_zero_complex)) (and (not (= A zero_zero_complex)) (not (= B zero_zero_complex))))) (forall ((F (-> complex real)) (G2 (-> real complex))) (= (and (= ((comp_c819638635l_real F) G2) id_real) (= ((comp_r667767405omplex G2) F) id_complex)) (and (forall ((X real)) (= (F (G2 X)) X)) (forall ((X complex)) (= (G2 (F X)) X))))) (forall ((A real) (B real)) (= (= ((times_times_real A) B) zero_zero_real) (or (= A zero_zero_real) (= B zero_zero_real)))) (= (deriv_real id_real) (lambda ((Z2 real)) one_one_real)) (forall ((C nat) (A nat) (B nat)) (=> (not (= C zero_zero_nat)) (= (= ((times_times_nat A) C) ((times_times_nat B) C)) (= A B)))) (forall ((F (-> complex complex)) (A2 set_complex) (B3 set_complex)) (= ((ord_le701908932omplex ((image_58037603omplex F) A2)) B3) (forall ((X complex)) (=> ((member_complex X) A2) ((member_complex (F X)) B3))))) (forall ((A2 set_complex)) (= (collect_complex (lambda ((X complex)) ((member_complex X) A2))) A2)) _let_26 (forall ((F (-> complex complex)) (G2 (-> complex complex)) (L1 (-> complex complex)) (L2 (-> complex complex)) (H (-> complex complex)) (R (-> complex complex))) (let ((_let_1 (comp_c130555887omplex L1))) (let ((_let_2 (comp_c130555887omplex F))) (=> (= (_let_2 G2) (_let_1 L2)) (=> (= ((comp_c130555887omplex L2) H) R) (= (_let_2 ((comp_c130555887omplex G2) H)) (_let_1 R))))))) (forall ((N nat)) (= ((times_times_nat N) one_one_nat) N)) (forall ((A complex) (B complex)) (=> (not (= A zero_zero_complex)) (=> (not (= B zero_zero_complex)) (not (= ((times_times_complex A) B) zero_zero_complex))))) (forall ((A complex) (P (-> complex Bool))) (= ((member_complex A) (collect_complex P)) (P A))) (forall ((F (-> complex complex)) (G2 (-> complex complex)) (L (-> complex complex)) (H (-> complex complex))) (let ((_let_1 (comp_c130555887omplex F))) (=> (= (_let_1 G2) L) (= (_let_1 ((comp_c130555887omplex G2) H)) ((comp_c130555887omplex L) H))))) (forall ((X2 set_complex)) ((ord_le701908932omplex X2) X2)) (forall ((X2 complex) (Y complex)) (= (((if_complex false) X2) Y) Y)) _let_25 (forall ((Z complex)) (let ((_let_1 ((((compow1098280738omplex one_one_nat) deriv_complex) id_complex) Z))) (let ((_let_2 (= one_one_nat zero_zero_nat))) (and (=> _let_2 (= _let_1 Z)) (=> (not _let_2) (= _let_1 one_one_complex)))))) _let_24 (forall ((G2 (-> complex complex))) (= ((comp_c130555887omplex id_complex) G2) G2)) (forall ((A nat) (B nat)) (= (= ((times_times_nat A) B) zero_zero_nat) (or (= B zero_zero_nat) (= A zero_zero_nat)))) (forall ((F (-> (-> complex complex) complex complex))) (= ((compow1098280738omplex zero_zero_nat) F) id_complex_complex)) (forall ((K nat) (M nat) (N nat)) (let ((_let_1 (times_times_nat K))) (= (= (_let_1 M) (_let_1 N)) (or (= K zero_zero_nat) (= M N))))) (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 ((C real) (A real) (B real)) (let ((_let_1 (times_times_real C))) (=> (not (= C zero_zero_real)) (= (= (_let_1 A) (_let_1 B)) (= A B))))) (forall ((A nat) (B nat) (C nat)) (let ((_let_1 (times_times_nat A))) (= ((times_times_nat (_let_1 B)) C) (_let_1 ((times_times_nat B) C))))) (forall ((A real) (B real) (X2 real)) (let ((_let_1 (times_times_real A))) (= (_let_1 ((times_times_real B) X2)) ((times_times_real (_let_1 B)) X2)))) (forall ((X2 real)) ((ord_less_eq_real X2) X2)) (forall ((F (-> complex complex))) (= ((compow1667379464omplex zero_zero_nat) F) id_complex)) (forall ((A2 set_complex) (F (-> complex complex)) (B3 set_complex)) (=> (forall ((X3 complex)) (=> ((member_complex X3) A2) ((member_complex (F X3)) B3))) ((ord_le701908932omplex ((image_58037603omplex F) A2)) B3))) (forall ((F (-> complex complex)) (N nat) (X2 complex)) (let ((_let_1 ((compow1667379464omplex N) F))) (= (F (_let_1 X2)) (_let_1 (F X2))))) (forall ((F (-> real real))) (= ((compow_real_real zero_zero_nat) F) id_real)) (= times_times_complex (lambda ((A3 complex) (B2 complex)) ((times_times_complex B2) A3))) (= _let_17 _let_22) (forall ((X2 real)) ((ord_less_eq_real X2) X2)) (forall ((P Bool)) (or (= P false) (= P true))) (forall ((F (-> complex complex)) (A2 set_complex) (P (-> complex Bool))) (=> (forall ((X3 complex)) (=> ((member_complex X3) ((image_58037603omplex F) A2)) (P X3))) (forall ((X4 complex)) (=> ((member_complex X4) A2) (P (F X4)))))) (forall ((X2 real)) (=> ((ord_less_eq_real one_one_real) X2) ((ord_less_eq_real zero_zero_real) (ln_ln_real X2)))) (forall ((A2 set_complex) (B3 set_complex) (X2 complex)) (let ((_let_1 (member_complex X2))) (=> ((ord_le701908932omplex A2) B3) (=> (_let_1 A2) (_let_1 B3))))) (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 ((times_times_real A) C)) ((times_times_real B) D)))))))) _let_23 (forall ((X2 complex) (Y complex)) (= (((if_complex true) X2) Y) X2)) (forall ((X2 real) (A2 set_real) (B3 set_real)) (=> ((member_real X2) ((times_times_set_real A2) B3)) (not (forall ((A4 real) (B4 real)) (=> (= X2 ((times_times_real A4) B4)) (=> ((member_real A4) A2) (not ((member_real B4) B3)))))))) (forall ((A complex)) (= ((times_times_complex one_one_complex) A) A)) (forall ((A real)) (= ((times_times_real zero_zero_real) A) zero_zero_real)) (forall ((X2 nat)) ((ord_less_eq_nat zero_zero_nat) X2)) (forall ((F (-> complex complex)) (X2 complex)) (= (((compow1667379464omplex zero_zero_nat) F) X2) X2)) (= (lambda ((Y2 set_complex) (Z4 set_complex)) (= Y2 Z4)) (lambda ((A5 set_complex) (B5 set_complex)) (and ((ord_le701908932omplex A5) B5) ((ord_le701908932omplex B5) A5)))) (forall ((X2 nat) (Y nat)) (= (((if_nat true) X2) Y) X2)) (forall ((A complex) (B complex) (C complex)) (let ((_let_1 (times_times_complex A))) (= ((times_times_complex (_let_1 B)) C) (_let_1 ((times_times_complex B) C))))) (forall ((C complex) (B complex)) (= (= C ((times_times_complex C) B)) (or (= B one_one_complex) (= C zero_zero_complex)))) (= _let_22 _let_8) (forall ((C nat) (A nat) (B nat)) (let ((_let_1 (times_times_nat C))) (= (= (_let_1 A) (_let_1 B)) (or (= C zero_zero_nat) (= A B))))) (forall ((M nat)) ((ord_less_eq_nat M) ((times_times_nat M) M))) (forall ((N nat)) (= ((ord_less_eq_nat N) zero_zero_nat) (= N zero_zero_nat))) (forall ((A nat) (B nat)) (=> ((ord_less_eq_nat A) B) (=> ((ord_less_eq_nat B) A) (= A B)))) (forall ((M2 set_complex) (N2 set_complex) (F (-> complex complex)) (G2 (-> complex complex))) (=> (= M2 N2) (=> (forall ((X3 complex)) (=> ((member_complex X3) N2) (= (F X3) (G2 X3)))) (= ((image_58037603omplex F) M2) ((image_58037603omplex G2) N2))))) (forall ((F (-> complex complex)) (G2 (-> complex complex)) (X2 complex)) (=> (= ((comp_c130555887omplex F) G2) id_complex) (= (F (G2 X2)) X2))) (forall ((F (-> complex complex complex)) (G2 (-> (-> complex complex) complex))) (= (and (= ((comp_c606622857omplex F) G2) id_complex_complex) (= ((comp_c881053372omplex G2) F) id_complex)) (and (forall ((X complex)) (= (G2 (F X)) X)) (forall ((X (-> complex complex))) (= (F (G2 X)) X))))) (forall ((A nat) (B nat)) (=> (not (= ((times_times_nat A) B) zero_zero_nat)) (and (not (= B zero_zero_nat)) (not (= A zero_zero_nat))))) (forall ((A real) (B real)) (=> (not (= ((times_times_real A) B) zero_zero_real)) (and (not (= A zero_zero_real)) (not (= B zero_zero_real))))) (= comp_c130555887omplex (lambda ((F2 (-> complex complex)) (G (-> complex complex)) (X complex)) (F2 (G X)))) (forall ((A real) (B real)) (let ((_let_1 (ord_less_eq_real zero_zero_real))) (=> (_let_1 A) (=> (_let_1 B) (_let_1 ((times_times_real A) B)))))) (forall ((A real) (X2 real) (Y real)) (let ((_let_1 (times_times_real A))) (=> (not (= A zero_zero_real)) (=> (= (_let_1 X2) (_let_1 Y)) (= X2 Y))))) (forall ((M nat) (N nat)) (=> (= M ((times_times_nat M) N)) (or (= M zero_zero_nat) (= N one_one_nat)))) (= (lambda ((Y2 real) (Z4 real)) (= Y2 Z4)) (lambda ((A3 real) (B2 real)) (and ((ord_less_eq_real A3) B2) ((ord_less_eq_real B2) A3)))) (forall ((A nat)) (= ((times_times_nat A) one_one_nat) A)) (forall ((A nat) (B nat)) (=> ((ord_less_eq_nat A) zero_zero_nat) (=> ((ord_less_eq_nat zero_zero_nat) B) ((ord_less_eq_nat ((times_times_nat A) B)) zero_zero_nat)))) (forall ((A complex) (X2 complex) (B complex)) (= (= ((times_times_complex A) X2) ((times_times_complex B) X2)) (or (= A B) (= X2 zero_zero_complex)))) (forall ((X2 real) (Y real)) (= (((if_real false) X2) Y) Y)) (forall ((X2 complex) (A2 set_complex) (B3 set_complex)) (=> ((member_complex X2) ((times_1316095593omplex A2) B3)) (not (forall ((A4 complex) (B4 complex)) (=> (= X2 ((times_times_complex A4) B4)) (=> ((member_complex A4) A2) (not ((member_complex B4) B3)))))))) (forall ((A (-> complex complex)) (B (-> complex complex)) (C (-> complex complex)) (V complex)) (=> (= ((comp_c130555887omplex A) B) C) (= (A (B V)) (C V)))) (= (arsinh_real zero_zero_real) zero_zero_real) (forall ((A real) (B real)) (=> ((ord_less_eq_real zero_zero_real) A) (=> ((ord_less_eq_real B) zero_zero_real) ((ord_less_eq_real ((times_times_real B) A)) zero_zero_real)))) (forall ((C complex) (A complex) (B complex)) (let ((_let_1 (times_times_complex C))) (=> (not (= C zero_zero_complex)) (= (= (_let_1 A) (_let_1 B)) (= A B))))) (forall ((C nat) (A nat) (B nat)) (let ((_let_1 (times_times_nat C))) (=> (not (= C zero_zero_nat)) (= (= (_let_1 A) (_let_1 B)) (= A B))))) (forall ((A real)) (= ((times_times_real A) zero_zero_real) zero_zero_real)) _let_21 (forall ((A complex) (C complex) (B complex)) (= (= ((times_times_complex A) C) ((times_times_complex B) C)) (or (= A B) (= C zero_zero_complex)))) (forall ((A real) (B real)) (let ((_let_1 (ord_less_eq_real zero_zero_real))) (= (_let_1 ((times_times_real A) B)) (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)))))) ((comple372758642hic_on f) s) ((comple372758642hic_on g) t) (= (artanh_complex zero_zero_complex) zero_zero_complex) (forall ((F (-> (-> complex complex) real)) (G2 (-> real complex complex)) (H (-> (-> complex complex) real))) (=> (= ((comp_c1884694328l_real F) G2) id_real) (=> (= ((comp_r2009261319omplex G2) H) id_complex_complex) (= F H)))) (= times_times_nat (lambda ((A3 nat) (B2 nat)) ((times_times_nat B2) A3))) (not (= zero_zero_nat one_one_nat)) (forall ((A real) (C2 set_real) (B real) (D2 set_real)) (=> ((member_real A) C2) (=> ((member_real B) D2) ((member_real ((times_times_real A) B)) ((times_times_set_real C2) D2))))) (forall ((Sup (-> set_complex complex)) (A2 set_complex)) (= (Sup ((image_58037603omplex id_complex) A2)) (Sup A2))) (forall ((N nat) (Z complex)) (let ((_let_1 ((((compow1098280738omplex N) deriv_complex) id_complex) Z))) (let ((_let_2 (= N zero_zero_nat))) (let ((_let_3 (= N one_one_nat))) (and (=> (not _let_2) (and (=> _let_3 (= _let_1 one_one_complex)) (=> (not _let_3) (= _let_1 zero_zero_complex)))) (=> _let_2 (= _let_1 Z))))))) (forall ((A real)) ((ord_less_eq_real A) A)) (forall ((A real) (C real)) (= (= ((times_times_real A) C) C) (or (= C zero_zero_real) (= A one_one_real)))) (forall ((A nat)) (= ((times_times_nat A) one_one_nat) A)) (forall ((B Bool) (X2 complex) (Y complex)) (let ((_let_1 ((times_times_complex (((if_complex B) X2) zero_zero_complex)) Y))) (and (=> B (= _let_1 ((times_times_complex X2) Y))) (=> (not B) (= _let_1 zero_zero_complex))))) _let_20 (forall ((K nat) (M nat) (N nat)) (let ((_let_1 (times_times_nat K))) (= (= (_let_1 M) (_let_1 N)) (or (= K zero_zero_nat) (= M N))))) (forall ((A real)) (= ((times_times_real one_one_real) A) A)) (forall ((X2 nat)) ((ord_less_eq_nat X2) X2)) (forall ((A nat) (B nat)) (=> ((ord_less_eq_nat zero_zero_nat) A) (=> ((ord_less_eq_nat A) one_one_nat) (=> ((ord_less_eq_nat B) one_one_nat) (= (= ((times_times_nat A) B) one_one_nat) (and (= A one_one_nat) (= B one_one_nat))))))) (= (lambda ((Y2 nat) (Z4 nat)) (= Y2 Z4)) (lambda ((A3 nat) (B2 nat)) (and ((ord_less_eq_nat A3) B2) ((ord_less_eq_nat B2) A3)))) (forall ((Z complex) (F (-> complex complex)) (A2 set_complex)) (= ((member_complex Z) ((image_58037603omplex F) A2)) (exists ((X complex)) (and (= Z (F X)) ((member_complex X) A2))))) (forall ((B complex) (F (-> complex complex)) (X2 complex) (A2 set_complex)) (=> (= B (F X2)) (=> ((member_complex X2) A2) ((member_complex B) ((image_58037603omplex F) A2))))) (forall ((C real) (B real)) (= (= C ((times_times_real B) C)) (or (= C zero_zero_real) (= B one_one_real)))) (forall ((A set_complex)) ((ord_le701908932omplex A) A)) (forall ((F (-> complex complex)) (S set_complex) (G2 (-> complex complex)) (Z complex) (I nat)) (let ((_let_1 ((compow1098280738omplex I) deriv_complex))) (=> ((comple372758642hic_on F) S) (=> ((comple372758642hic_on G2) S) (=> (topolo935673511omplex S) (=> ((member_complex Z) S) (=> (forall ((W complex)) (=> ((member_complex W) S) (= (F W) (G2 W)))) (= ((_let_1 F) Z) ((_let_1 G2) Z))))))))) (forall ((A2 set_complex) (B3 set_complex)) (=> (= A2 B3) (not (=> ((ord_le701908932omplex A2) B3) (not ((ord_le701908932omplex B3) A2)))))) (forall ((P Bool) (Q real)) (let ((_let_1 ((times_times_real (((if_real P) one_one_real) zero_zero_real)) Q))) (and (=> (not P) (= _let_1 zero_zero_real)) (=> P (= _let_1 Q))))) (forall ((X2 set_complex) (Y set_complex) (Z set_complex)) (let ((_let_1 (ord_le701908932omplex X2))) (=> (_let_1 Y) (=> ((ord_le701908932omplex Y) Z) (_let_1 Z))))) (forall ((A set_complex) (B set_complex)) (=> ((ord_le701908932omplex A) B) (=> ((ord_le701908932omplex B) A) (= A B)))) (forall ((N nat)) (= ((compow1098280738omplex N) id_complex_complex) id_complex_complex)) (= _let_18 _let_8) (forall ((X2 nat) (Y nat)) (= (((if_nat false) X2) Y) Y)) _let_19 (forall ((A nat)) (= ((times_times_nat one_one_nat) A) A)) (forall ((Z real)) (let ((_let_1 ((((compow1723822618l_real one_one_nat) deriv_real) id_real) Z))) (let ((_let_2 (= one_one_nat zero_zero_nat))) (and (=> (not _let_2) (= _let_1 one_one_real)) (=> _let_2 (= _let_1 Z)))))) (forall ((A complex) (C2 set_complex) (B complex) (D2 set_complex)) (=> ((member_complex A) C2) (=> ((member_complex B) D2) ((member_complex ((times_times_complex A) B)) ((times_1316095593omplex C2) D2))))) (not ((ord_less_eq_nat one_one_nat) zero_zero_nat)) (= _let_18 _let_17) (forall ((A nat) (B nat)) (=> (not (= A zero_zero_nat)) (=> (not (= B zero_zero_nat)) (not (= ((times_times_nat A) B) zero_zero_nat))))) (forall ((A (-> complex complex)) (B (-> complex complex)) (C (-> complex complex)) (V complex)) (=> (= ((comp_c130555887omplex A) B) ((comp_c130555887omplex id_complex) C)) (= (A (B V)) (C V)))) (forall ((A complex) (C complex)) (= (= ((times_times_complex A) C) C) (or (= A one_one_complex) (= C zero_zero_complex)))) (forall ((X2 nat) (A2 set_nat) (B3 set_nat)) (=> ((member_nat X2) ((times_times_set_nat A2) B3)) (not (forall ((A4 nat) (B4 nat)) (=> (= X2 ((times_times_nat A4) B4)) (=> ((member_nat A4) A2) (not ((member_nat B4) B3)))))))) (forall ((F (-> complex complex)) (S2 set_complex) (T set_complex)) (let ((_let_1 (comple372758642hic_on F))) (=> (_let_1 S2) (=> ((ord_le701908932omplex T) S2) (_let_1 T))))) (forall ((Sup (-> set_real real)) (A2 set_real)) (= (Sup ((image_real_real id_real) A2)) (Sup A2))) (forall ((A nat) (B nat)) (=> (= ((times_times_nat A) B) zero_zero_nat) (or (= A zero_zero_nat) (= B zero_zero_nat)))) (forall ((B Bool) (X2 nat) (Y nat)) (let ((_let_1 ((times_times_nat (((if_nat B) X2) zero_zero_nat)) Y))) (and (=> B (= _let_1 ((times_times_nat X2) Y))) (=> (not B) (= _let_1 zero_zero_nat))))) (forall ((F (-> real complex complex)) (G2 (-> (-> complex complex) real))) (= (and (= ((comp_r2009261319omplex F) G2) id_complex_complex) (= ((comp_c1884694328l_real G2) F) id_real)) (and (forall ((X real)) (= (G2 (F X)) X)) (forall ((X (-> complex complex))) (= (F (G2 X)) X))))) (forall ((F (-> real real))) (= (forall ((X real)) (= (F X) X)) (= F id_real))) (forall ((F (-> (-> real real) real real))) (= ((compow1723822618l_real zero_zero_nat) F) id_real_real)) (not ((ord_less_eq_real one_one_real) zero_zero_real)) (forall ((F (-> real complex complex)) (G2 (-> (-> complex complex) real)) (H (-> real complex complex))) (=> (= ((comp_r2009261319omplex F) G2) id_complex_complex) (=> (= ((comp_c1884694328l_real G2) H) id_real) (= F H)))) (forall ((F (-> complex real)) (G2 (-> real complex)) (H (-> complex real))) (=> (= ((comp_c819638635l_real F) G2) id_real) (=> (= ((comp_r667767405omplex G2) H) id_complex) (= F H)))) (forall ((A complex) (B complex) (C complex)) (let ((_let_1 (times_times_complex A))) (= ((times_times_complex (_let_1 B)) C) (_let_1 ((times_times_complex B) C))))) (forall ((A nat)) (= ((times_times_nat A) zero_zero_nat) zero_zero_nat)) (forall ((A complex) (B complex)) (= (= ((times_times_complex A) B) zero_zero_complex) (or (= B zero_zero_complex) (= A zero_zero_complex)))) ((ord_le701908932omplex ((image_58037603omplex f) s)) t) (= times_times_real (lambda ((A3 real) (B2 real)) ((times_times_real B2) A3))) (forall ((G2 (-> complex complex)) (F (-> complex complex)) (V (-> complex complex))) (let ((_let_1 (comp_c130555887omplex G2))) (= (_let_1 ((comp_c130555887omplex F) V)) ((comp_c130555887omplex (_let_1 F)) V)))) (forall ((X2 real) (Y real)) (= (((if_real true) X2) Y) X2)) (forall ((X2 complex) (A2 set_complex) (F (-> complex complex))) (=> ((member_complex X2) A2) ((member_complex (F X2)) ((image_58037603omplex F) A2)))) (forall ((F (-> (-> real real) real real)) (N nat) (X2 (-> real real))) (let ((_let_1 ((compow1723822618l_real N) F))) (= (F (_let_1 X2)) (_let_1 (F X2))))) (forall ((B set_complex) (A set_complex)) (=> ((ord_le701908932omplex B) A) (=> ((ord_le701908932omplex A) B) (= A B)))) (forall ((X2 complex)) (= ((times_times_complex zero_zero_complex) X2) zero_zero_complex)) (forall ((F (-> real real)) (G2 (-> real real)) (H (-> real real))) (=> (= ((comp_real_real_real F) G2) id_real) (=> (= ((comp_real_real_real G2) H) id_real) (= F H)))) (forall ((A complex) (B complex) (X2 complex)) (let ((_let_1 (times_times_complex A))) (let ((_let_2 (times_times_complex B))) (= (_let_1 (_let_2 X2)) (_let_2 (_let_1 X2)))))) (forall ((A complex)) (= ((times_times_complex zero_zero_complex) A) zero_zero_complex)) (forall ((B Bool) (X2 complex) (Y complex)) (let ((_let_1 (times_times_complex X2))) (let ((_let_2 (_let_1 (((if_complex B) Y) zero_zero_complex)))) (and (=> (not B) (= _let_2 zero_zero_complex)) (=> B (= _let_2 (_let_1 Y))))))) (forall ((A complex)) (= ((times_times_complex A) one_one_complex) A)) (forall ((N nat) (M nat) (F (-> (-> complex complex) complex complex))) (= ((compow1098280738omplex N) ((compow1098280738omplex M) F)) ((compow1098280738omplex ((times_times_nat M) N)) F))) (forall ((A nat)) ((ord_less_eq_nat zero_zero_nat) A)) (forall ((P Bool) (Q complex)) (let ((_let_1 ((times_times_complex (((if_complex P) one_one_complex) zero_zero_complex)) Q))) (and (=> (not P) (= _let_1 zero_zero_complex)) (=> P (= _let_1 Q))))) (forall ((C complex) (B complex)) (= (= C ((times_times_complex B) C)) (or (= B one_one_complex) (= C zero_zero_complex)))) (forall ((P (-> complex Bool)) (Q2 (-> complex Bool))) (= ((ord_le701908932omplex (collect_complex P)) (collect_complex Q2)) (forall ((X complex)) (=> (P X) (Q2 X))))) (forall ((A2 set_complex) (B3 set_complex)) (=> ((ord_le701908932omplex A2) B3) (=> ((ord_le701908932omplex B3) A2) (= A2 B3)))) (forall ((I nat) (J nat) (K nat)) (let ((_let_1 (ord_less_eq_nat I))) (=> (_let_1 J) (=> ((ord_less_eq_nat J) K) (_let_1 K))))) (forall ((F (-> real complex)) (G2 (-> complex real)) (H (-> real complex))) (=> (= ((comp_r667767405omplex F) G2) id_complex) (=> (= ((comp_c819638635l_real G2) H) id_real) (= F H)))) (= (lambda ((Y2 set_complex) (Z4 set_complex)) (= Y2 Z4)) (lambda ((A3 set_complex) (B2 set_complex)) (and ((ord_le701908932omplex A3) B2) ((ord_le701908932omplex B2) A3)))) (forall ((A complex)) (= ((times_times_complex A) one_one_complex) A)) (forall ((C complex) (A complex)) (= (= ((times_times_complex C) A) C) (or (= C zero_zero_complex) (= A one_one_complex)))) (forall ((N nat)) ((ord_less_eq_nat zero_zero_nat) N)) (forall ((C real) (B real)) (= (= C ((times_times_real C) B)) (or (= C zero_zero_real) (= B one_one_real)))) (forall ((M nat)) (let ((_let_1 (times_times_nat M))) ((ord_less_eq_nat M) (_let_1 (_let_1 M))))) (forall ((A nat)) (= ((ord_less_eq_nat A) zero_zero_nat) (= A zero_zero_nat))) (forall ((F (-> complex complex)) (S set_complex)) (=> ((comple372758642hic_on F) S) (=> (topolo935673511omplex S) ((comple372758642hic_on (deriv_complex F)) S)))) (forall ((A nat)) ((ord_less_eq_nat A) A)) _let_14 (forall ((A real) (B real)) (=> ((ord_less_eq_real zero_zero_real) A) (=> ((ord_less_eq_real A) one_one_real) (=> ((ord_less_eq_real B) one_one_real) (= (= ((times_times_real A) B) one_one_real) (and (= A one_one_real) (= B one_one_real))))))) (forall ((N nat)) (= ((compow1667379464omplex N) id_complex) id_complex)) (forall ((A complex) (B complex)) (=> (= ((times_times_complex A) B) zero_zero_complex) (or (= A zero_zero_complex) (= B zero_zero_complex)))) (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) ((times_times_real A) B))))) (forall ((A complex)) (= ((times_times_complex A) zero_zero_complex) zero_zero_complex)) ((member_complex w) s) (forall ((N nat) (Z real)) (let ((_let_1 ((((compow1723822618l_real N) deriv_real) id_real) Z))) (let ((_let_2 (= N zero_zero_nat))) (let ((_let_3 (= N one_one_nat))) (and (=> (not _let_2) (and (=> _let_3 (= _let_1 one_one_real)) (=> (not _let_3) (= _let_1 zero_zero_real)))) (=> _let_2 (= _let_1 Z))))))) (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 B) (=> (_let_1 C) ((ord_less_eq_real ((times_times_real A) C)) ((times_times_real B) D)))))))) (forall ((A nat)) (= ((times_times_nat one_one_nat) A) A)) (forall ((F (-> (-> real real) real real)) (X2 (-> real real))) (= (((compow1723822618l_real zero_zero_nat) F) X2) X2)) (forall ((F (-> complex complex complex)) (G2 (-> (-> complex complex) complex)) (H (-> complex complex complex))) (=> (= ((comp_c606622857omplex F) G2) id_complex_complex) (=> (= ((comp_c881053372omplex G2) H) id_complex) (= F H)))) (forall ((A nat) (B nat) (C nat)) (=> ((ord_less_eq_nat A) B) (=> ((ord_less_eq_nat zero_zero_nat) C) ((ord_less_eq_nat ((times_times_nat A) C)) ((times_times_nat B) C))))) (forall ((A nat)) (= ((times_times_nat zero_zero_nat) A) zero_zero_nat)) (forall ((Z complex)) (=> ((member_complex Z) s) (= (g (f Z)) Z))) (forall ((P (-> (-> nat real) Bool)) (F (-> (-> nat real) nat real)) (Q2 (-> nat Bool))) (=> (forall ((X3 (-> nat real))) (=> (P X3) (P (F X3)))) (=> (forall ((X3 (-> nat real))) (=> (P X3) (forall ((I2 nat)) (let ((_let_1 (X3 I2))) (=> (Q2 I2) (and ((ord_less_eq_real _let_1) one_one_real) ((ord_less_eq_real zero_zero_real) _let_1))))))) (exists ((L3 (-> (-> nat real) nat nat))) (and (forall ((X4 (-> nat real)) (I3 nat)) (=> (and (P X4) (= (X4 I3) zero_zero_real) (Q2 I3)) (= ((L3 X4) I3) zero_zero_nat))) (forall ((X4 (-> nat real)) (I3 nat)) (=> (and (P X4) (= ((L3 X4) I3) one_one_nat) (Q2 I3)) ((ord_less_eq_real ((F X4) I3)) (X4 I3)))) (forall ((X4 (-> nat real)) (I3 nat)) (=> (and (P X4) (Q2 I3) (= ((L3 X4) I3) zero_zero_nat)) ((ord_less_eq_real (X4 I3)) ((F X4) I3)))) (forall ((X4 (-> nat real)) (I3 nat)) (=> (and (P X4) (Q2 I3) (= (X4 I3) one_one_real)) (= ((L3 X4) I3) one_one_nat))) (forall ((X4 (-> nat real)) (I3 nat)) ((ord_less_eq_nat ((L3 X4) I3)) one_one_nat))))))) (forall ((A nat) (B nat)) (=> ((ord_less_eq_nat zero_zero_nat) A) (=> ((ord_less_eq_nat B) zero_zero_nat) ((ord_less_eq_nat ((times_times_nat A) B)) zero_zero_nat)))) (forall ((A real) (B real)) (=> (not (= A zero_zero_real)) (=> (not (= B zero_zero_real)) (not (= ((times_times_real A) B) zero_zero_real))))) (forall ((X2 real)) (= (= one_one_real X2) (= X2 one_one_real))) (forall ((C complex) (A complex) (B complex)) (let ((_let_1 (times_times_complex C))) (= (= (_let_1 A) (_let_1 B)) (or (= C zero_zero_complex) (= A B))))) (forall ((A real) (B real) (C real)) (=> ((ord_less_eq_real A) B) (=> ((ord_less_eq_real zero_zero_real) C) ((ord_less_eq_real ((times_times_real A) C)) ((times_times_real B) C))))) (forall ((B real) (A real) (C real)) (let ((_let_1 (times_times_real C))) (=> ((ord_less_eq_real B) A) (=> ((ord_less_eq_real zero_zero_real) C) ((ord_less_eq_real (_let_1 B)) (_let_1 A)))))) (forall ((X2 nat)) (= (= one_one_nat X2) (= X2 one_one_nat))) (forall ((X2 real)) (= ((times_times_real one_one_real) X2) X2)) (forall ((A nat)) (=> ((ord_less_eq_nat A) zero_zero_nat) (= A zero_zero_nat))) (forall ((A2 set_complex) (B3 set_complex)) (=> (= A2 B3) ((ord_le701908932omplex A2) B3))) _let_12 (forall ((A real) (B real) (X2 real)) (let ((_let_1 (times_times_real A))) (let ((_let_2 (times_times_real B))) (= (_let_1 (_let_2 X2)) (_let_2 (_let_1 X2)))))) _let_11 (forall ((P (-> nat nat Bool)) (A nat) (B nat)) (=> (forall ((A4 nat) (B4 nat)) (=> ((ord_less_eq_nat A4) B4) ((P A4) B4))) (=> (forall ((A4 nat) (B4 nat)) (=> ((P B4) A4) ((P A4) B4))) ((P A) B)))) (forall ((F (-> (-> complex complex) complex)) (G2 (-> complex complex complex)) (H (-> (-> complex complex) complex))) (=> (= ((comp_c881053372omplex F) G2) id_complex) (=> (= ((comp_c606622857omplex G2) H) id_complex_complex) (= F H)))) (forall ((F (-> (-> complex complex) complex complex))) (= (forall ((X (-> complex complex))) (= (F X) X)) (= F id_complex_complex))) (forall ((M nat)) (= ((times_times_nat M) zero_zero_nat) zero_zero_nat)) (forall ((X2 real) (Y real)) (let ((_let_1 (ord_less_eq_real zero_zero_real))) (=> (_let_1 X2) (=> (_let_1 Y) (=> ((ord_less_eq_real Y) one_one_real) ((ord_less_eq_real ((times_times_real Y) X2)) X2)))))) (forall ((F (-> (-> complex complex) complex complex)) (N nat) (X2 (-> complex complex))) (let ((_let_1 ((compow1098280738omplex N) F))) (= (F (_let_1 X2)) (_let_1 (F X2))))) (forall ((B Bool) (X2 real) (Y real)) (let ((_let_1 ((times_times_real (((if_real B) X2) zero_zero_real)) Y))) (and (=> (not B) (= _let_1 zero_zero_real)) (=> B (= _let_1 ((times_times_real X2) Y)))))) (forall ((X2 real) (A real) (B real)) (=> (not (= X2 zero_zero_real)) (=> (= ((times_times_real A) X2) ((times_times_real B) X2)) (= A B)))) (forall ((F (-> complex complex))) (= ((comp_c130555887omplex F) id_complex) F)) (forall ((N nat)) (= ((times_times_nat zero_zero_nat) N) zero_zero_nat)) (forall ((A real) (B real)) (let ((_let_1 (ord_less_eq_real zero_zero_real))) (= ((ord_less_eq_real ((times_times_real A) B)) zero_zero_real) (or (and (_let_1 A) ((ord_less_eq_real B) zero_zero_real)) (and (_let_1 B) ((ord_less_eq_real A) zero_zero_real)))))) (topolo935673511omplex t) (forall ((A nat) (B nat) (C nat) (D nat)) (let ((_let_1 (ord_less_eq_nat zero_zero_nat))) (=> ((ord_less_eq_nat A) B) (=> ((ord_less_eq_nat C) D) (=> (_let_1 B) (=> (_let_1 C) ((ord_less_eq_nat ((times_times_nat A) C)) ((times_times_nat B) D)))))))) (forall ((F (-> complex complex)) (S set_complex) (Z complex) (W2 complex)) (=> ((comple372758642hic_on F) S) (=> (topolo935673511omplex S) (=> (topolo2127351575omplex S) (=> (forall ((N3 nat)) (= ((((compow1098280738omplex N3) deriv_complex) F) Z) zero_zero_complex)) (=> ((member_complex Z) S) (=> ((member_complex W2) S) (= (F W2) zero_zero_complex)))))))) (forall ((A real) (B real)) (let ((_let_1 (ord_less_eq_real zero_zero_real))) (=> (or (and (_let_1 B) ((ord_less_eq_real A) zero_zero_real)) (and ((ord_less_eq_real B) zero_zero_real) (_let_1 A))) ((ord_less_eq_real ((times_times_real A) B)) zero_zero_real)))) (forall ((N nat) (F (-> complex complex))) (= ((compow1098280738omplex N) (comp_c130555887omplex F)) (comp_c130555887omplex ((compow1667379464omplex N) F)))) (forall ((F (-> real real)) (G2 (-> real real))) (= (and (= ((comp_real_real_real G2) F) id_real) (= ((comp_real_real_real F) G2) id_real)) (and (forall ((X real)) (= (F (G2 X)) X)) (forall ((X real)) (= (G2 (F X)) X))))) (forall ((F (-> complex complex)) (G2 (-> complex complex)) (R set_complex)) (= ((image_58037603omplex F) ((image_58037603omplex G2) R)) ((image_58037603omplex ((comp_c130555887omplex F) G2)) R))) (forall ((A real) (B real)) (=> (= ((times_times_real A) B) zero_zero_real) (or (= A zero_zero_real) (= B zero_zero_real)))) _let_9 (forall ((A nat) (B nat) (C nat)) (let ((_let_1 (ord_less_eq_nat A))) (=> (_let_1 B) (=> (= B C) (_let_1 C))))) (forall ((B Bool) (X2 real) (Y real)) (let ((_let_1 (times_times_real X2))) (let ((_let_2 (_let_1 (((if_real B) Y) zero_zero_real)))) (and (=> B (= _let_2 (_let_1 Y))) (=> (not B) (= _let_2 zero_zero_real)))))) (forall ((F (-> complex complex)) (S2 set_complex) (G2 (-> complex complex)) (T set_complex)) (=> ((comple372758642hic_on F) S2) (=> ((comple372758642hic_on G2) T) (=> ((ord_le701908932omplex ((image_58037603omplex F) S2)) T) ((comple372758642hic_on ((comp_c130555887omplex G2) F)) S2))))) (forall ((A nat) (B nat) (C nat)) (let ((_let_1 (times_times_nat A))) (= ((times_times_nat (_let_1 B)) C) (_let_1 ((times_times_nat B) C))))) (= id_complex (lambda ((X complex)) X)) (forall ((X2 real)) (= (= zero_zero_real X2) (= X2 zero_zero_real))) (forall ((C nat) (A nat)) (=> ((ord_less_eq_nat C) one_one_nat) (=> ((ord_less_eq_nat zero_zero_nat) A) ((ord_less_eq_nat ((times_times_nat A) C)) A)))) (forall ((A nat) (C2 set_nat) (B nat) (D2 set_nat)) (=> ((member_nat A) C2) (=> ((member_nat B) D2) ((member_nat ((times_times_nat A) B)) ((times_times_set_nat C2) D2))))) (forall ((A complex) (X2 complex) (Y complex)) (let ((_let_1 (times_times_complex A))) (= (= (_let_1 X2) (_let_1 Y)) (or (= A zero_zero_complex) (= X2 Y))))) (forall ((F (-> real complex)) (G2 (-> complex real))) (= (and (= ((comp_r667767405omplex F) G2) id_complex) (= ((comp_c819638635l_real G2) F) id_real)) (and (forall ((X real)) (= (G2 (F X)) X)) (forall ((X complex)) (= (F (G2 X)) X))))) (forall ((M nat) (N nat)) (or ((ord_less_eq_nat N) M) ((ord_less_eq_nat M) N))) ((ord_less_eq_nat zero_zero_nat) one_one_nat) (forall ((F (-> complex complex))) (= (forall ((X complex)) (= (F X) X)) (= F id_complex))) (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 ((times_times_real A) C)) ((times_times_real B) C))))) (forall ((B3 set_complex) (F (-> complex complex)) (A2 set_complex)) (=> ((ord_le701908932omplex B3) ((image_58037603omplex F) A2)) (not (forall ((C3 set_complex)) (=> ((ord_le701908932omplex C3) A2) (not (= B3 ((image_58037603omplex F) C3)))))))) (forall ((F (-> (-> complex complex) real)) (G2 (-> real complex complex))) (= (and (= ((comp_r2009261319omplex G2) F) id_complex_complex) (= ((comp_c1884694328l_real F) G2) id_real)) (and (forall ((X (-> complex complex))) (= (G2 (F X)) X)) (forall ((X real)) (= (F (G2 X)) X))))) (forall ((X2 real) (Y real)) (let ((_let_1 (ord_less_eq_real zero_zero_real))) (=> (_let_1 X2) (=> (_let_1 Y) (=> ((ord_less_eq_real Y) one_one_real) ((ord_less_eq_real ((times_times_real X2) Y)) X2)))))) (forall ((A complex) (B complex) (X2 complex)) (let ((_let_1 (times_times_complex A))) (= (_let_1 ((times_times_complex B) X2)) ((times_times_complex (_let_1 B)) X2)))) (forall ((F (-> (-> complex complex) complex complex)) (X2 (-> complex complex))) (= (((compow1098280738omplex zero_zero_nat) F) X2) X2)) (forall ((N nat)) ((ord_less_eq_nat N) N)) (forall ((F (-> (-> complex complex) complex)) (G2 (-> complex complex complex))) (= (and (= ((comp_c606622857omplex G2) F) id_complex_complex) (= ((comp_c881053372omplex F) G2) id_complex)) (and (forall ((X (-> complex complex))) (= (G2 (F X)) X)) (forall ((X complex)) (= (F (G2 X)) X))))) (not (= zero_zero_complex one_one_complex)) (forall ((A2 set_complex) (B3 set_complex) (C complex)) (let ((_let_1 (member_complex C))) (=> ((ord_le701908932omplex A2) B3) (=> (_let_1 A2) (_let_1 B3))))) (forall ((N nat) (F (-> real real))) (= ((compow1723822618l_real N) (comp_real_real_real F)) (comp_real_real_real ((compow_real_real N) F)))) (forall ((A real)) (= ((times_times_real A) one_one_real) A)) (forall ((A real) (B real) (C real)) (let ((_let_1 (times_times_real A))) (= ((times_times_real (_let_1 B)) C) (_let_1 ((times_times_real B) C))))) (forall ((A real) (B real)) (=> ((ord_less_eq_real A) B) (=> ((ord_less_eq_real B) A) (= A B)))) (forall ((A real) (C real) (B real)) (= (= ((times_times_real A) C) ((times_times_real B) C)) (or (= C zero_zero_real) (= A B)))) (forall ((A2 set_complex)) ((ord_le701908932omplex A2) A2)) (forall ((S2 set_complex) (T set_complex) (F (-> complex complex)) (G2 (-> complex complex))) (=> (= S2 T) (=> (forall ((X3 complex)) (=> ((member_complex X3) S2) (= (F X3) (G2 X3)))) (= ((comple372758642hic_on F) S2) ((comple372758642hic_on G2) T))))) _let_7 (forall ((B set_complex) (A set_complex) (C set_complex)) (let ((_let_1 (ord_le701908932omplex C))) (=> ((ord_le701908932omplex B) A) (=> (_let_1 B) (_let_1 A))))) (forall ((C complex) (A complex) (B complex)) (=> (not (= C zero_zero_complex)) (= (= ((times_times_complex A) C) ((times_times_complex B) C)) (= A B)))) (forall ((I nat) (J nat) (K nat)) (=> ((ord_less_eq_nat I) J) ((ord_less_eq_nat ((times_times_nat I) K)) ((times_times_nat J) K)))) (forall ((F (-> complex complex)) (G2 (-> complex complex))) (= (and (= ((comp_c130555887omplex F) G2) id_complex) (= ((comp_c130555887omplex G2) F) id_complex)) (and (forall ((X complex)) (= (G2 (F X)) X)) (forall ((X complex)) (= (F (G2 X)) X))))) (forall ((M nat) (N nat)) (= (= ((times_times_nat M) N) zero_zero_nat) (or (= M zero_zero_nat) (= N zero_zero_nat)))) (forall ((A nat) (B nat) (C nat)) (let ((_let_1 (times_times_nat C))) (=> ((ord_less_eq_nat A) B) (=> ((ord_less_eq_nat zero_zero_nat) C) ((ord_less_eq_nat (_let_1 A)) (_let_1 B)))))) (forall ((A real)) (= ((times_times_real A) one_one_real) A)) (forall ((A real)) (= ((times_times_real A) zero_zero_real) zero_zero_real)) (forall ((F (-> complex complex)) (S set_complex) (G2 (-> complex complex)) (T2 set_complex) (W2 complex)) (=> ((comple372758642hic_on F) S) (=> ((comple372758642hic_on G2) T2) (=> (topolo935673511omplex S) (=> (topolo935673511omplex T2) (=> ((ord_le701908932omplex ((image_58037603omplex F) S)) T2) (=> (forall ((Z3 complex)) (=> ((member_complex Z3) S) (= (G2 (F Z3)) Z3))) (=> ((member_complex W2) S) (= ((times_times_complex ((deriv_complex F) W2)) ((deriv_complex G2) (F W2))) one_one_complex))))))))) (forall ((A (-> complex complex)) (B (-> complex complex)) (C (-> complex complex)) (D (-> complex complex))) (=> (= ((comp_c130555887omplex A) B) ((comp_c130555887omplex C) D)) (forall ((V2 complex)) (= (A (B V2)) (C (D V2)))))) (forall ((A (-> complex complex)) (B (-> complex complex)) (C (-> complex complex)) (D (-> complex complex)) (V complex)) (=> (= ((comp_c130555887omplex A) B) ((comp_c130555887omplex C) D)) (= (A (B V)) (C (D V))))) (forall ((A real) (X2 real) (B real)) (= (= ((times_times_real A) X2) ((times_times_real B) X2)) (or (= X2 zero_zero_real) (= A B)))) (forall ((B real) (A real) (C real)) (let ((_let_1 (ord_less_eq_real C))) (=> ((ord_less_eq_real B) A) (=> (_let_1 B) (_let_1 A))))) (forall ((A real) (B real) (C real)) (let ((_let_1 (times_times_real A))) (= ((times_times_real (_let_1 B)) C) (_let_1 ((times_times_real B) C))))) (forall ((B real) (A real) (C real)) (let ((_let_1 (times_times_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 ((F (-> complex complex)) (G2 (-> complex complex)) (H (-> complex complex))) (let ((_let_1 (comp_c130555887omplex F))) (= ((comp_c130555887omplex (_let_1 G2)) H) (_let_1 ((comp_c130555887omplex G2) H))))) (forall ((M nat) (K nat) (N nat)) (= (= ((times_times_nat M) K) ((times_times_nat N) K)) (or (= M N) (= K zero_zero_nat)))) (forall ((S2 set_complex)) ((comple372758642hic_on id_complex) S2)) (forall ((X2 complex) (A complex) (B complex)) (=> (not (= X2 zero_zero_complex)) (=> (= ((times_times_complex A) X2) ((times_times_complex B) X2)) (= A B)))) (forall ((P Bool) (Q nat)) (let ((_let_1 ((times_times_nat (((if_nat P) one_one_nat) zero_zero_nat)) Q))) (and (=> (not P) (= _let_1 zero_zero_nat)) (=> P (= _let_1 Q))))) (forall ((A real) (B real) (C real)) (let ((_let_1 (times_times_real C))) (=> ((ord_less_eq_real A) B) (=> ((ord_less_eq_real zero_zero_real) C) ((ord_less_eq_real (_let_1 A)) (_let_1 B)))))) (forall ((G2 (-> complex complex)) (H (-> complex complex)) (R1 (-> complex complex)) (R2 (-> complex complex)) (F (-> complex complex)) (L (-> complex complex))) (let ((_let_1 (comp_c130555887omplex F))) (=> (= ((comp_c130555887omplex G2) H) ((comp_c130555887omplex R1) R2)) (=> (= (_let_1 R1) L) (= ((comp_c130555887omplex (_let_1 G2)) H) ((comp_c130555887omplex L) R2)))))) (forall ((N nat) (M nat) (F (-> (-> real real) real real))) (= ((compow1723822618l_real N) ((compow1723822618l_real M) F)) ((compow1723822618l_real ((times_times_nat M) N)) F))) (forall ((A nat) (B nat) (C nat) (D nat)) (let ((_let_1 (ord_less_eq_nat zero_zero_nat))) (=> ((ord_less_eq_nat A) B) (=> ((ord_less_eq_nat C) D) (=> (_let_1 A) (=> (_let_1 C) ((ord_less_eq_nat ((times_times_nat A) C)) ((times_times_nat B) D)))))))) (forall ((A real) (B real) (C real)) (=> ((ord_less_eq_real A) B) (=> ((ord_less_eq_real zero_zero_real) C) ((ord_less_eq_real ((times_times_real A) C)) ((times_times_real B) C))))) (forall ((A real) (B real) (C real)) (let ((_let_1 (times_times_real C))) (=> ((ord_less_eq_real A) B) (=> ((ord_less_eq_real zero_zero_real) C) ((ord_less_eq_real (_let_1 A)) (_let_1 B)))))) (forall ((A nat) (B nat)) (let ((_let_1 (ord_less_eq_nat zero_zero_nat))) (=> (_let_1 A) (=> (_let_1 B) (_let_1 ((times_times_nat A) B)))))) _let_6 (forall ((B Bool) (X2 nat) (Y nat)) (let ((_let_1 (times_times_nat X2))) (let ((_let_2 (_let_1 (((if_nat B) Y) zero_zero_nat)))) (and (=> (not B) (= _let_2 zero_zero_nat)) (=> B (= _let_2 (_let_1 Y))))))) _let_4 (forall ((T (-> complex complex))) (= ((comp_c130555887omplex id_complex) T) T)) (forall ((C2 set_complex) (D2 set_complex) (E set_complex) (F3 set_complex) (X2 complex)) (let ((_let_1 (member_complex X2))) (=> ((ord_le701908932omplex C2) D2) (=> ((ord_le701908932omplex E) F3) (=> (_let_1 ((times_1316095593omplex C2) E)) (_let_1 ((times_1316095593omplex D2) F3))))))) (forall ((M nat) (N nat)) (=> ((ord_less_eq_nat M) N) (=> ((ord_less_eq_nat N) M) (= M N)))) (forall ((B real) (A real) (C real)) (let ((_let_1 (times_times_real B))) (let ((_let_2 (times_times_real A))) (= (_let_1 (_let_2 C)) (_let_2 (_let_1 C)))))) (forall ((M nat) (N nat)) (= (= one_one_nat ((times_times_nat M) N)) (and (= N one_one_nat) (= M one_one_nat)))) (topolo935673511omplex s) (forall ((B real) (A real)) (=> ((ord_less_eq_real B) A) (=> ((ord_less_eq_real A) B) (= A B)))) (forall ((N nat)) (= ((times_times_nat one_one_nat) N) N)) (forall ((X2 real) (Y real)) (=> (not ((ord_less_eq_real X2) Y)) ((ord_less_eq_real Y) X2))) (forall ((A real) (B real)) (=> ((ord_less_eq_real A) one_one_real) (=> ((ord_less_eq_real zero_zero_real) B) (=> ((ord_less_eq_real B) one_one_real) ((ord_less_eq_real ((times_times_real A) B)) one_one_real))))) (forall ((G2 (-> complex complex)) (H (-> complex complex)) (R (-> complex complex)) (F (-> complex complex))) (let ((_let_1 (comp_c130555887omplex F))) (=> (= ((comp_c130555887omplex G2) H) R) (= ((comp_c130555887omplex (_let_1 G2)) H) (_let_1 R))))) (= id_complex_complex (lambda ((X (-> complex complex)) (__flatten_var_0 complex)) (X __flatten_var_0))) (forall ((A complex)) (= ((times_times_complex A) zero_zero_complex) zero_zero_complex)) (forall ((A real)) ((ord_less_eq_real zero_zero_real) ((times_times_real A) A))) (forall ((F (-> complex complex)) (S2 set_complex) (G2 (-> complex complex))) (=> ((comple372758642hic_on F) S2) (=> (forall ((X3 complex)) (=> ((member_complex X3) S2) (= (F X3) (G2 X3)))) ((comple372758642hic_on G2) S2)))) (forall ((A complex)) (= ((times_times_complex one_one_complex) A) A)) (forall ((A real)) (= ((times_times_real one_one_real) A) A)) (forall ((A complex) (X2 complex)) (= (= ((times_times_complex A) X2) zero_zero_complex) (or (= X2 zero_zero_complex) (= A zero_zero_complex)))) (forall ((A real) (B real) (C real)) (let ((_let_1 (times_times_real C))) (=> ((ord_less_eq_real A) B) (=> ((ord_less_eq_real zero_zero_real) C) ((ord_less_eq_real (_let_1 A)) (_let_1 B)))))) (forall ((B nat) (A nat)) (=> ((ord_less_eq_nat B) A) (=> ((ord_less_eq_nat A) B) (= A B)))) (forall ((C complex) (S2 set_complex)) ((comple372758642hic_on (times_times_complex C)) S2)) (forall ((M nat) (N nat)) (= (= ((times_times_nat M) N) one_one_nat) (and (= M one_one_nat) (= N one_one_nat)))) (forall ((X2 nat) (Y nat) (Z nat)) (let ((_let_1 (ord_less_eq_nat X2))) (=> (_let_1 Y) (=> ((ord_less_eq_nat Y) Z) (_let_1 Z))))) (forall ((F (-> complex complex)) (S2 set_complex) (G2 (-> complex complex))) (=> ((comple372758642hic_on F) S2) (=> ((comple372758642hic_on G2) ((image_58037603omplex F) S2)) ((comple372758642hic_on ((comp_c130555887omplex G2) F)) S2)))) (forall ((N nat)) ((ord_less_eq_nat zero_zero_nat) N)) (forall ((B complex) (A complex) (C complex)) (let ((_let_1 (times_times_complex B))) (let ((_let_2 (times_times_complex A))) (= (_let_1 (_let_2 C)) (_let_2 (_let_1 C)))))) (forall ((A real) (B real)) (=> ((ord_less_eq_real zero_zero_real) A) (=> ((ord_less_eq_real B) zero_zero_real) ((ord_less_eq_real ((times_times_real A) B)) zero_zero_real)))) (forall ((X2 complex)) (= (= zero_zero_complex X2) (= X2 zero_zero_complex))) (forall ((P (-> real real Bool)) (A real) (B real)) (=> (forall ((A4 real) (B4 real)) (=> ((ord_less_eq_real A4) B4) ((P A4) B4))) (=> (forall ((A4 real) (B4 real)) (=> ((P B4) A4) ((P A4) B4))) ((P A) B)))) (forall ((A real) (B real)) (let ((_let_1 (ord_less_eq_real zero_zero_real))) (=> (or (and (_let_1 A) (_let_1 B)) (and ((ord_less_eq_real B) zero_zero_real) ((ord_less_eq_real A) zero_zero_real))) (_let_1 ((times_times_real A) B))))) (forall ((F (-> complex complex)) (A2 set_complex) (P (-> complex Bool))) (=> (exists ((X4 complex)) (and ((member_complex X4) ((image_58037603omplex F) A2)) (P X4))) (exists ((X3 complex)) (and ((member_complex X3) A2) (P (F X3)))))) (forall ((X2 complex) (A2 set_complex) (B complex) (F (-> complex complex))) (=> ((member_complex X2) A2) (=> (= B (F X2)) ((member_complex B) ((image_58037603omplex F) A2))))) (forall ((N nat)) (= ((ord_less_eq_nat N) zero_zero_nat) (= N zero_zero_nat))) (forall ((A nat) (B nat)) (let ((_let_1 (ord_less_eq_nat zero_zero_nat))) (=> (or (and ((ord_less_eq_nat A) zero_zero_nat) (_let_1 B)) (and ((ord_less_eq_nat B) zero_zero_nat) (_let_1 A))) ((ord_less_eq_nat ((times_times_nat A) B)) zero_zero_nat)))) (forall ((A2 set_complex) (B3 set_complex)) (=> (= A2 B3) ((ord_le701908932omplex B3) A2))) (forall ((N nat)) (= ((compow_real_real N) id_real) id_real)) (forall ((B nat) (A nat) (C nat)) (let ((_let_1 (ord_less_eq_nat C))) (=> ((ord_less_eq_nat B) A) (=> (_let_1 B) (_let_1 A))))) (forall ((N nat)) (= ((compow1723822618l_real N) id_real_real) id_real_real)) (= (artanh_real zero_zero_real) zero_zero_real) (forall ((B nat) (A nat) (C nat)) (let ((_let_1 (times_times_nat B))) (let ((_let_2 (times_times_nat A))) (= (_let_1 (_let_2 C)) (_let_2 (_let_1 C)))))) (forall ((A nat) (C nat) (B nat)) (= (= ((times_times_nat A) C) ((times_times_nat B) C)) (or (= C zero_zero_nat) (= A B)))) _let_1 (forall ((C real) (A real) (B real)) (=> (not (= C zero_zero_real)) (= (= ((times_times_real A) C) ((times_times_real B) C)) (= A B)))) (forall ((A real) (B real) (C real)) (let ((_let_1 (ord_less_eq_real A))) (=> (_let_1 B) (=> (= B C) (_let_1 C))))) (forall ((F (-> (-> complex complex) complex complex)) (G2 (-> (-> complex complex) complex complex))) (= (and (= ((comp_c1610621014omplex F) G2) id_complex_complex) (= ((comp_c1610621014omplex G2) F) id_complex_complex)) (and (forall ((X (-> complex complex))) (= (F (G2 X)) X)) (forall ((X (-> complex complex))) (= (G2 (F X)) X))))) (forall ((F (-> complex complex)) (G2 (-> complex complex)) (H (-> complex complex))) (=> (= ((comp_c130555887omplex F) G2) id_complex) (=> (= ((comp_c130555887omplex G2) H) id_complex) (= F H)))) (not (= zero_zero_real one_one_real)) (forall ((I nat) (J nat) (K nat)) (let ((_let_1 (times_times_nat K))) (=> ((ord_less_eq_nat I) J) ((ord_less_eq_nat (_let_1 I)) (_let_1 J))))) (forall ((F (-> (-> complex complex) complex complex)) (G2 (-> (-> complex complex) complex complex)) (H (-> (-> complex complex) complex complex))) (=> (= ((comp_c1610621014omplex F) G2) id_complex_complex) (=> (= ((comp_c1610621014omplex G2) H) id_complex_complex) (= F H)))) (forall ((M nat) (N nat)) (=> (= M N) ((ord_less_eq_nat M) N))) (forall ((A real) (B real)) (=> ((ord_less_eq_real A) zero_zero_real) (=> ((ord_less_eq_real zero_zero_real) B) ((ord_less_eq_real ((times_times_real A) B)) zero_zero_real)))) (forall ((C2 set_complex) (D2 set_complex) (E set_complex) (F3 set_complex)) (=> ((ord_le701908932omplex C2) D2) (=> ((ord_le701908932omplex E) F3) ((ord_le701908932omplex ((times_1316095593omplex C2) E)) ((times_1316095593omplex D2) F3))))) (= (arsinh_complex zero_zero_complex) zero_zero_complex) (forall ((C real) (A real) (B real)) (let ((_let_1 (times_times_real C))) (= (= (_let_1 A) (_let_1 B)) (or (= A B) (= C zero_zero_real))))) (= id_complex_complex (lambda ((X (-> complex complex)) (__flatten_var_0 complex)) (X __flatten_var_0))) (forall ((F (-> complex complex)) (A2 set_complex) (G2 (-> complex complex)) (B3 set_complex) (H (-> complex complex))) (let ((_let_1 (comp_c130555887omplex H))) (=> (= ((image_58037603omplex F) A2) ((image_58037603omplex G2) B3)) (= ((image_58037603omplex (_let_1 F)) A2) ((image_58037603omplex (_let_1 G2)) B3))))) ((ord_less_eq_real zero_zero_real) one_one_real) (forall ((A real) (X2 real) (Y real)) (let ((_let_1 (times_times_real A))) (= (= (_let_1 X2) (_let_1 Y)) (or (= A zero_zero_real) (= X2 Y))))) (= (arcosh_complex one_one_complex) zero_zero_complex) (forall ((P (-> nat Bool)) (K nat) (B nat)) (=> (P K) (=> (forall ((Y3 nat)) (=> (P Y3) ((ord_less_eq_nat Y3) B))) (exists ((X3 nat)) (and (P X3) (forall ((Y4 nat)) (=> (P Y4) ((ord_less_eq_nat Y4) X3)))))))) (forall ((P (-> complex Bool)) (Q2 (-> complex Bool))) (=> (forall ((X3 complex)) (=> (P X3) (Q2 X3))) ((ord_le701908932omplex (collect_complex P)) (collect_complex Q2)))) (= ord_le701908932omplex (lambda ((A5 set_complex) (B5 set_complex)) (forall ((T3 complex)) (let ((_let_1 (member_complex T3))) (=> (_let_1 A5) (_let_1 B5)))))) (forall ((X2 complex)) (= (= one_one_complex X2) (= X2 one_one_complex))) (forall ((B real) (A real) (C real)) (=> ((ord_less_eq_real B) A) (=> ((ord_less_eq_real zero_zero_real) C) ((ord_less_eq_real ((times_times_real B) C)) ((times_times_real A) C))))) (forall ((X2 complex)) (= ((times_times_complex one_one_complex) X2) X2)) (forall ((A real) (X2 real)) (= (= ((times_times_real A) X2) zero_zero_real) (or (= A zero_zero_real) (= X2 zero_zero_real)))) (forall ((A nat) (B nat)) (=> ((ord_less_eq_nat A) one_one_nat) (=> ((ord_less_eq_nat zero_zero_nat) B) (=> ((ord_less_eq_nat B) one_one_nat) ((ord_less_eq_nat ((times_times_nat A) B)) one_one_nat))))) (forall ((Sup (-> set_complex_complex complex complex)) (A2 set_complex_complex)) (= (Sup ((image_944012797omplex id_complex_complex) A2)) (Sup A2))) (forall ((A nat) (B nat) (C nat)) (let ((_let_1 (times_times_nat C))) (=> ((ord_less_eq_nat A) B) (=> ((ord_less_eq_nat zero_zero_nat) C) ((ord_less_eq_nat (_let_1 A)) (_let_1 B)))))) (= id_real (lambda ((X real)) X)) (forall ((X2 real) (Y real) (Z real)) (let ((_let_1 (ord_less_eq_real X2))) (=> (_let_1 Y) (=> ((ord_less_eq_real Y) Z) (_let_1 Z))))) (forall ((X2 nat)) (= (= zero_zero_nat X2) (= X2 zero_zero_nat))) (forall ((X2 real)) (= ((times_times_real zero_zero_real) X2) zero_zero_real)) (forall ((A complex) (X2 complex) (Y complex)) (let ((_let_1 (times_times_complex A))) (=> (not (= A zero_zero_complex)) (=> (= (_let_1 X2) (_let_1 Y)) (= X2 Y))))) (forall ((B3 set_complex) (F (-> complex complex)) (A2 set_complex)) (= ((ord_le701908932omplex B3) ((image_58037603omplex F) A2)) (exists ((AA set_complex)) (and ((ord_le701908932omplex AA) A2) (= B3 ((image_58037603omplex F) AA)))))) (not false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
0.33/0.81	)
0.33/0.81	% SZS output end Proof for theBenchmark
0.33/0.81	EOF