0.06/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.06/0.13	% Command    : do_cvc5 %s %d
0.12/0.34	% Computer   : n005.cluster.edu
0.12/0.34	% Model      : x86_64 x86_64
0.12/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.34	% Memory     : 8042.1875MB
0.12/0.34	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.34	% CPULimit   : 1200
0.12/0.34	% WCLimit    : 120
0.12/0.34	% DateTime   : Tue Jul 13 12:51:33 EDT 2021
0.12/0.34	% CPUTime    : 
0.19/0.51	%----THF division
0.19/0.51	------- cvc5-thf casc 28 : /export/starexec/sandbox2/benchmark/theBenchmark.p at 120...
0.19/0.51	--- Run --ho-elim --full-saturate-quant at 10...
0.35/0.77	% SZS status Theorem for theBenchmark
0.35/0.78	% SZS output start Proof for theBenchmark
0.35/0.78	(proof
0.35/0.78	(let ((_let_1 (= ((polyno1934269411ymul_a p) q) ((polyno1934269411ymul_a q) p)))) (let ((_let_2 (= (forall ((Bs list_a)) (let ((_let_1 (polyno422358502poly_a Bs))) (= (_let_1 ((polyno1934269411ymul_a p) q)) (_let_1 ((polyno1934269411ymul_a q) p))))) _let_1))) (let ((_let_3 (forall ((Bs2 list_a) (P polyno727731844poly_a) (Q polyno727731844poly_a)) (let ((_let_1 (polyno422358502poly_a Bs2))) (= (_let_1 ((polyno1934269411ymul_a P) Q)) ((times_times_a (_let_1 P)) (_let_1 Q))))))) (let ((_let_4 (= times_times_a (lambda ((A2 a) (B2 a)) ((times_times_a B2) A2))))) (let ((_let_5 (not _let_1))) (let ((_let_6 (not (= zero_zero_nat one_one_nat)))) (let ((_let_7 (= k_58 k_61))) (let ((_let_8 (ho_69 (ho_68 k_133 p) q))) (let ((_let_9 (ho_122 k_121 skv_173))) (let ((_let_10 (ho_123 _let_9 _let_8))) (let ((_let_11 (ho_69 (ho_68 k_133 q) p))) (let ((_let_12 (ho_123 _let_9 _let_11))) (let ((_let_13 (= _let_12 _let_10))) (let ((_let_14 (ho_123 _let_9 q))) (let ((_let_15 (ho_123 _let_9 p))) (let ((_let_16 (ho_60 (ho_59 k_61 _let_15) _let_14))) (let ((_let_17 (= _let_10 _let_16))) (let ((_let_18 (= _let_12 (ho_60 (ho_59 k_61 _let_14) _let_15)))) (let ((_let_19 (= _let_16 (ho_60 (ho_59 k_58 _let_14) _let_15)))) (let ((_let_20 (= times_times_a ll_32))) (let ((_let_21 (EQ_RESOLVE (ASSUME |:args| (_let_4)) (TRANS (PREPROCESS |:args| ((= _let_4 _let_20))) (PREPROCESS |:args| ((= _let_20 _let_7))))))) (let ((_let_22 (forall ((Bs list_a)) (let ((_let_1 (ho_122 k_121 Bs))) (= (ho_123 _let_1 (ho_69 (ho_68 k_133 q) p)) (ho_123 _let_1 (ho_69 (ho_68 k_133 p) q))))))) (let ((_let_23 (not _let_13))) (let ((_let_24 (= _let_11 _let_8))) (let ((_let_25 (not _let_22))) (let ((_let_26 (20))) (let ((_let_27 (_let_23))) (let ((_let_28 (_let_25))) (let ((_let_29 (forall ((Bs2 list_a) (P polyno727731844poly_a) (Q polyno727731844poly_a)) (let ((_let_1 (ho_122 k_121 Bs2))) (= (ho_60 (ho_59 k_61 (ho_123 _let_1 P)) (ho_123 _let_1 Q)) (ho_123 _let_1 (ho_69 (ho_68 k_133 P) Q))))))) (let ((_let_30 (EQ_RESOLVE (ASSUME |:args| (_let_3)) (PREPROCESS |:args| ((= _let_3 _let_29)))))) (let ((_let_31 (_let_29))) (let ((_let_32 (forall ((BOUND_VARIABLE_7232 a) (BOUND_VARIABLE_7233 a)) (= (ho_60 (ho_59 k_58 BOUND_VARIABLE_7232) BOUND_VARIABLE_7233) (ho_60 (ho_59 k_61 BOUND_VARIABLE_7233) BOUND_VARIABLE_7232))))) (let ((_let_33 (forall ((u |u_(-> polyno1532895200ly_nat nat polyno1532895200ly_nat)|) (e |u_(-> nat polyno1532895200ly_nat)|) (i polyno1532895200ly_nat)) (not (forall ((v |u_(-> polyno1532895200ly_nat nat polyno1532895200ly_nat)|)) (not (forall ((ii polyno1532895200ly_nat)) (= (ho_91 v ii) (ite (= i ii) e (ho_91 u ii)))))))))) (let ((_let_34 (forall ((x |u_(-> polyno1532895200ly_nat nat polyno1532895200ly_nat)|) (y |u_(-> polyno1532895200ly_nat nat polyno1532895200ly_nat)|)) (or (not (forall ((z polyno1532895200ly_nat)) (= (ho_91 x z) (ho_91 y z)))) (= x y))))) (let ((_let_35 (forall ((u |u_(-> a a)|) (e a) (i a)) (not (forall ((v |u_(-> a a)|)) (not (forall ((ii a)) (= (ho_60 v ii) (ite (= i ii) e (ho_60 u ii)))))))))) (let ((_let_36 (forall ((x |u_(-> a a)|) (y |u_(-> a a)|)) (or (not (forall ((z a)) (= (ho_60 x z) (ho_60 y z)))) (= x y))))) (let ((_let_37 (forall ((u |u_(-> polyno1532895200ly_nat nat nat)|) (e |u_(-> nat nat)|) (i polyno1532895200ly_nat)) (not (forall ((v |u_(-> polyno1532895200ly_nat nat nat)|)) (not (forall ((ii polyno1532895200ly_nat)) (= (ho_104 v ii) (ite (= i ii) e (ho_104 u ii)))))))))) (let ((_let_38 (forall ((x |u_(-> polyno1532895200ly_nat nat nat)|) (y |u_(-> polyno1532895200ly_nat nat nat)|)) (or (not (forall ((z polyno1532895200ly_nat)) (= (ho_104 x z) (ho_104 y z)))) (= x y))))) (let ((_let_39 (forall ((u |u_(-> a nat polyno727731844poly_a)|) (e |u_(-> nat polyno727731844poly_a)|) (i a)) (not (forall ((v |u_(-> a nat polyno727731844poly_a)|)) (not (forall ((ii a)) (= (ho_86 v ii) (ite (= i ii) e (ho_86 u ii)))))))))) (let ((_let_40 (forall ((x |u_(-> a nat polyno727731844poly_a)|) (y |u_(-> a nat polyno727731844poly_a)|)) (or (not (forall ((z a)) (= (ho_86 x z) (ho_86 y z)))) (= x y))))) (let ((_let_41 (forall ((u |u_(-> a polyno727731844poly_a)|) (e polyno727731844poly_a) (i a)) (not (forall ((v |u_(-> a polyno727731844poly_a)|)) (not (forall ((ii a)) (= (ho_88 v ii) (ite (= i ii) e (ho_88 u ii)))))))))) (let ((_let_42 (forall ((x |u_(-> a polyno727731844poly_a)|) (y |u_(-> a polyno727731844poly_a)|)) (or (not (forall ((z a)) (= (ho_88 x z) (ho_88 y z)))) (= x y))))) (let ((_let_43 (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_76 v ii) (ite (= ii i) e (ho_76 u ii)))))))))) (let ((_let_44 (forall ((x |u_(-> Bool nat nat nat)|) (y |u_(-> Bool nat nat nat)|)) (or (not (forall ((z Bool)) (= (ho_76 x z) (ho_76 y z)))) (= x y))))) (let ((_let_45 (forall ((u |u_(-> nat nat)|) (e nat) (i nat)) (not (forall ((v |u_(-> nat nat)|)) (not (forall ((ii nat)) (= (ho_41 v ii) (ite (= i ii) e (ho_41 u ii)))))))))) (let ((_let_46 (forall ((x |u_(-> nat nat)|) (y |u_(-> nat nat)|)) (or (not (forall ((z nat)) (= (ho_41 x z) (ho_41 y z)))) (= x y))))) (let ((_let_47 (forall ((u |u_(-> polyno727731844poly_a nat polyno727731844poly_a polyno727731844poly_a)|) (e |u_(-> nat polyno727731844poly_a polyno727731844poly_a)|) (i polyno727731844poly_a)) (not (forall ((v |u_(-> polyno727731844poly_a nat polyno727731844poly_a polyno727731844poly_a)|)) (not (forall ((ii polyno727731844poly_a)) (= (ho_119 v ii) (ite (= i ii) e (ho_119 u ii)))))))))) (let ((_let_48 (forall ((x |u_(-> polyno727731844poly_a nat polyno727731844poly_a polyno727731844poly_a)|) (y |u_(-> polyno727731844poly_a nat polyno727731844poly_a polyno727731844poly_a)|)) (or (not (forall ((z polyno727731844poly_a)) (= (ho_119 x z) (ho_119 y z)))) (= x y))))) (let ((_let_49 (forall ((u |u_(-> _u_(-> polyno1532895200ly_nat polyno1532895200ly_nat)_ polyno1532895200ly_nat polyno1532895200ly_nat)|) (e |u_(-> polyno1532895200ly_nat polyno1532895200ly_nat)|) (i |u_(-> polyno1532895200ly_nat polyno1532895200ly_nat)|)) (not (forall ((v |u_(-> _u_(-> polyno1532895200ly_nat polyno1532895200ly_nat)_ polyno1532895200ly_nat polyno1532895200ly_nat)|)) (not (forall ((ii |u_(-> polyno1532895200ly_nat polyno1532895200ly_nat)|)) (= (ho_162 v ii) (ite (= i ii) e (ho_162 u ii)))))))))) (let ((_let_50 (forall ((x |u_(-> _u_(-> polyno1532895200ly_nat polyno1532895200ly_nat)_ polyno1532895200ly_nat polyno1532895200ly_nat)|) (y |u_(-> _u_(-> polyno1532895200ly_nat polyno1532895200ly_nat)_ polyno1532895200ly_nat polyno1532895200ly_nat)|)) (or (not (forall ((z |u_(-> polyno1532895200ly_nat polyno1532895200ly_nat)|)) (= (ho_162 x z) (ho_162 y z)))) (= x y))))) (let ((_let_51 (forall ((u |u_(-> nat polyno727731844poly_a polyno727731844poly_a)|) (e |u_(-> polyno727731844poly_a polyno727731844poly_a)|) (i nat)) (not (forall ((v |u_(-> nat polyno727731844poly_a polyno727731844poly_a)|)) (not (forall ((ii nat)) (= (ho_120 v ii) (ite (= i ii) e (ho_120 u ii)))))))))) (let ((_let_52 (forall ((x |u_(-> nat polyno727731844poly_a polyno727731844poly_a)|) (y |u_(-> nat polyno727731844poly_a polyno727731844poly_a)|)) (or (not (forall ((z nat)) (= (ho_120 x z) (ho_120 y z)))) (= x y))))) (let ((_let_53 (forall ((u |u_(-> nat Bool)|) (e Bool) (i nat)) (not (forall ((v |u_(-> nat Bool)|)) (not (forall ((ii nat)) (= (ho_97 v ii) (ite (= i ii) e (ho_97 u ii)))))))))) (let ((_let_54 (forall ((x |u_(-> nat Bool)|) (y |u_(-> nat Bool)|)) (or (not (forall ((z nat)) (= (ho_97 x z) (ho_97 y z)))) (= x y))))) (let ((_let_55 (forall ((u |u_(-> nat polyno1532895200ly_nat)|) (e polyno1532895200ly_nat) (i nat)) (not (forall ((v |u_(-> nat polyno1532895200ly_nat)|)) (not (forall ((ii nat)) (= (ho_47 v ii) (ite (= i ii) e (ho_47 u ii)))))))))) (let ((_let_56 (forall ((x |u_(-> nat polyno1532895200ly_nat)|) (y |u_(-> nat polyno1532895200ly_nat)|)) (or (not (forall ((z nat)) (= (ho_47 x z) (ho_47 y z)))) (= x y))))) (let ((_let_57 (forall ((u |u_(-> nat polyno1532895200ly_nat polyno1532895200ly_nat)|) (e |u_(-> polyno1532895200ly_nat polyno1532895200ly_nat)|) (i nat)) (not (forall ((v |u_(-> nat polyno1532895200ly_nat polyno1532895200ly_nat)|)) (not (forall ((ii nat)) (= (ho_126 v ii) (ite (= i ii) e (ho_126 u ii)))))))))) (let ((_let_58 (forall ((x |u_(-> nat polyno1532895200ly_nat polyno1532895200ly_nat)|) (y |u_(-> nat polyno1532895200ly_nat polyno1532895200ly_nat)|)) (or (not (forall ((z nat)) (= (ho_126 x z) (ho_126 y z)))) (= x y))))) (let ((_let_59 (forall ((u |u_(-> nat nat Bool)|) (e |u_(-> nat Bool)|) (i nat)) (not (forall ((v |u_(-> nat nat Bool)|)) (not (forall ((ii nat)) (= (ho_171 v ii) (ite (= i ii) e (ho_171 u ii)))))))))) (let ((_let_60 (forall ((x |u_(-> nat nat Bool)|) (y |u_(-> nat nat Bool)|)) (or (not (forall ((z nat)) (= (ho_171 x z) (ho_171 y z)))) (= x y))))) (let ((_let_61 (forall ((u |u_(-> polyno1532895200ly_nat nat nat nat)|) (e |u_(-> nat nat nat)|) (i polyno1532895200ly_nat)) (not (forall ((v |u_(-> polyno1532895200ly_nat nat nat nat)|)) (not (forall ((ii polyno1532895200ly_nat)) (= (ho_102 v ii) (ite (= i ii) e (ho_102 u ii)))))))))) (let ((_let_62 (forall ((x |u_(-> polyno1532895200ly_nat nat nat nat)|) (y |u_(-> polyno1532895200ly_nat nat nat nat)|)) (or (not (forall ((z polyno1532895200ly_nat)) (= (ho_102 x z) (ho_102 y z)))) (= x y))))) (let ((_let_63 (forall ((u |u_(-> polyno1532895200ly_nat polyno1532895200ly_nat polyno1532895200ly_nat)|) (e |u_(-> polyno1532895200ly_nat polyno1532895200ly_nat)|) (i polyno1532895200ly_nat)) (not (forall ((v |u_(-> polyno1532895200ly_nat polyno1532895200ly_nat polyno1532895200ly_nat)|)) (not (forall ((ii polyno1532895200ly_nat)) (= (ho_93 v ii) (ite (= i ii) e (ho_93 u ii)))))))))) (let ((_let_64 (forall ((x |u_(-> polyno1532895200ly_nat polyno1532895200ly_nat polyno1532895200ly_nat)|) (y |u_(-> polyno1532895200ly_nat polyno1532895200ly_nat polyno1532895200ly_nat)|)) (or (not (forall ((z polyno1532895200ly_nat)) (= (ho_93 x z) (ho_93 y z)))) (= x y))))) (let ((_let_65 (forall ((u |u_(-> polyno727731844poly_a nat nat nat)|) (e |u_(-> nat nat nat)|) (i polyno727731844poly_a)) (not (forall ((v |u_(-> polyno727731844poly_a nat nat nat)|)) (not (forall ((ii polyno727731844poly_a)) (= (ho_71 v ii) (ite (= i ii) e (ho_71 u ii)))))))))) (let ((_let_66 (forall ((x |u_(-> polyno727731844poly_a nat nat nat)|) (y |u_(-> polyno727731844poly_a nat nat nat)|)) (or (not (forall ((z polyno727731844poly_a)) (= (ho_71 x z) (ho_71 y z)))) (= x y))))) (let ((_let_67 (forall ((u |u_(-> polyno727731844poly_a nat Bool)|) (e |u_(-> nat Bool)|) (i polyno727731844poly_a)) (not (forall ((v |u_(-> polyno727731844poly_a nat Bool)|)) (not (forall ((ii polyno727731844poly_a)) (= (ho_131 v ii) (ite (= i ii) e (ho_131 u ii)))))))))) (let ((_let_68 (forall ((x |u_(-> polyno727731844poly_a nat Bool)|) (y |u_(-> polyno727731844poly_a nat Bool)|)) (or (not (forall ((z polyno727731844poly_a)) (= (ho_131 x z) (ho_131 y z)))) (= x y))))) (let ((_let_69 (forall ((u |u_(-> polyno1532895200ly_nat polyno1532895200ly_nat)|) (e polyno1532895200ly_nat) (i polyno1532895200ly_nat)) (not (forall ((v |u_(-> polyno1532895200ly_nat polyno1532895200ly_nat)|)) (not (forall ((ii polyno1532895200ly_nat)) (= (ho_51 v ii) (ite (= i ii) e (ho_51 u ii)))))))))) (let ((_let_70 (forall ((x |u_(-> polyno1532895200ly_nat polyno1532895200ly_nat)|) (y |u_(-> polyno1532895200ly_nat polyno1532895200ly_nat)|)) (or (not (forall ((z polyno1532895200ly_nat)) (= (ho_51 x z) (ho_51 y z)))) (= x y))))) (let ((_let_71 (forall ((u |u_(-> polyno1532895200ly_nat polyno1532895200ly_nat nat polyno1532895200ly_nat)|) (e |u_(-> polyno1532895200ly_nat nat polyno1532895200ly_nat)|) (i polyno1532895200ly_nat)) (not (forall ((v |u_(-> polyno1532895200ly_nat polyno1532895200ly_nat nat polyno1532895200ly_nat)|)) (not (forall ((ii polyno1532895200ly_nat)) (= (ho_90 v ii) (ite (= i ii) e (ho_90 u ii)))))))))) (let ((_let_72 (forall ((x |u_(-> polyno1532895200ly_nat polyno1532895200ly_nat nat polyno1532895200ly_nat)|) (y |u_(-> polyno1532895200ly_nat polyno1532895200ly_nat nat polyno1532895200ly_nat)|)) (or (not (forall ((z polyno1532895200ly_nat)) (= (ho_90 x z) (ho_90 y z)))) (= x y))))) (let ((_let_73 (forall ((u |u_(-> nat nat nat)|) (e |u_(-> nat nat)|) (i nat)) (not (forall ((v |u_(-> nat nat nat)|)) (not (forall ((ii nat)) (= (ho_43 v ii) (ite (= i ii) e (ho_43 u ii)))))))))) (let ((_let_74 (forall ((x |u_(-> nat nat nat)|) (y |u_(-> nat nat nat)|)) (or (not (forall ((z nat)) (= (ho_43 x z) (ho_43 y z)))) (= x y))))) (let ((_let_75 (forall ((u |u_(-> polyno727731844poly_a polyno727731844poly_a)|) (e polyno727731844poly_a) (i polyno727731844poly_a)) (not (forall ((v |u_(-> polyno727731844poly_a polyno727731844poly_a)|)) (not (forall ((ii polyno727731844poly_a)) (= (ho_69 v ii) (ite (= i ii) e (ho_69 u ii)))))))))) (let ((_let_76 (forall ((x |u_(-> polyno727731844poly_a polyno727731844poly_a)|) (y |u_(-> polyno727731844poly_a polyno727731844poly_a)|)) (or (not (forall ((z polyno727731844poly_a)) (= (ho_69 x z) (ho_69 y z)))) (= x y))))) (let ((_let_77 (forall ((u |u_(-> polyno727731844poly_a nat nat)|) (e |u_(-> nat nat)|) (i polyno727731844poly_a)) (not (forall ((v |u_(-> polyno727731844poly_a nat nat)|)) (not (forall ((ii polyno727731844poly_a)) (= (ho_73 v ii) (ite (= i ii) e (ho_73 u ii)))))))))) (let ((_let_78 (forall ((x |u_(-> polyno727731844poly_a nat nat)|) (y |u_(-> polyno727731844poly_a nat nat)|)) (or (not (forall ((z polyno727731844poly_a)) (= (ho_73 x z) (ho_73 y z)))) (= x y))))) (let ((_let_79 (forall ((u |u_(-> list_nat polyno1532895200ly_nat Bool)|) (e |u_(-> polyno1532895200ly_nat Bool)|) (i list_nat)) (not (forall ((v |u_(-> list_nat polyno1532895200ly_nat Bool)|)) (not (forall ((ii list_nat)) (= (ho_169 v ii) (ite (= i ii) e (ho_169 u ii)))))))))) (let ((_let_80 (forall ((x |u_(-> list_nat polyno1532895200ly_nat Bool)|) (y |u_(-> list_nat polyno1532895200ly_nat Bool)|)) (or (not (forall ((z list_nat)) (= (ho_169 x z) (ho_169 y z)))) (= x y))))) (let ((_let_81 (forall ((u |u_(-> nat nat polyno1532895200ly_nat)|) (e |u_(-> nat polyno1532895200ly_nat)|) (i nat)) (not (forall ((v |u_(-> nat nat polyno1532895200ly_nat)|)) (not (forall ((ii nat)) (= (ho_46 v ii) (ite (= i ii) e (ho_46 u ii)))))))))) (let ((_let_82 (forall ((x |u_(-> nat nat polyno1532895200ly_nat)|) (y |u_(-> nat nat polyno1532895200ly_nat)|)) (or (not (forall ((z nat)) (= (ho_46 x z) (ho_46 y z)))) (= x y))))) (let ((_let_83 (forall ((u |u_(-> nat polyno727731844poly_a)|) (e polyno727731844poly_a) (i nat)) (not (forall ((v |u_(-> nat polyno727731844poly_a)|)) (not (forall ((ii nat)) (= (ho_54 v ii) (ite (= i ii) e (ho_54 u ii)))))))))) (let ((_let_84 (forall ((x |u_(-> nat polyno727731844poly_a)|) (y |u_(-> nat polyno727731844poly_a)|)) (or (not (forall ((z nat)) (= (ho_54 x z) (ho_54 y z)))) (= x y))))) (let ((_let_85 (forall ((u |u_(-> _u_(-> polyno727731844poly_a polyno727731844poly_a)_ polyno727731844poly_a polyno727731844poly_a)|) (e |u_(-> polyno727731844poly_a polyno727731844poly_a)|) (i |u_(-> polyno727731844poly_a polyno727731844poly_a)|)) (not (forall ((v |u_(-> _u_(-> polyno727731844poly_a polyno727731844poly_a)_ polyno727731844poly_a polyno727731844poly_a)|)) (not (forall ((ii |u_(-> polyno727731844poly_a polyno727731844poly_a)|)) (= (ho_142 v ii) (ite (= i ii) e (ho_142 u ii)))))))))) (let ((_let_86 (forall ((x |u_(-> _u_(-> polyno727731844poly_a polyno727731844poly_a)_ polyno727731844poly_a polyno727731844poly_a)|) (y |u_(-> _u_(-> polyno727731844poly_a polyno727731844poly_a)_ polyno727731844poly_a polyno727731844poly_a)|)) (or (not (forall ((z |u_(-> polyno727731844poly_a polyno727731844poly_a)|)) (= (ho_142 x z) (ho_142 y z)))) (= x y))))) (let ((_let_87 (forall ((u |u_(-> nat nat polyno727731844poly_a)|) (e |u_(-> nat polyno727731844poly_a)|) (i nat)) (not (forall ((v |u_(-> nat nat polyno727731844poly_a)|)) (not (forall ((ii nat)) (= (ho_53 v ii) (ite (= i ii) e (ho_53 u ii)))))))))) (let ((_let_88 (forall ((x |u_(-> nat nat polyno727731844poly_a)|) (y |u_(-> nat nat polyno727731844poly_a)|)) (or (not (forall ((z nat)) (= (ho_53 x z) (ho_53 y z)))) (= x y))))) (let ((_let_89 (forall ((u |u_(-> polyno727731844poly_a Bool)|) (e Bool) (i polyno727731844poly_a)) (not (forall ((v |u_(-> polyno727731844poly_a Bool)|)) (not (forall ((ii polyno727731844poly_a)) (= (ho_152 v ii) (ite (= i ii) e (ho_152 u ii)))))))))) (let ((_let_90 (forall ((x |u_(-> polyno727731844poly_a Bool)|) (y |u_(-> polyno727731844poly_a Bool)|)) (or (not (forall ((z polyno727731844poly_a)) (= (ho_152 x z) (ho_152 y z)))) (= x y))))) (let ((_let_91 (forall ((u |u_(-> polyno727731844poly_a polyno727731844poly_a polyno727731844poly_a)|) (e |u_(-> polyno727731844poly_a polyno727731844poly_a)|) (i polyno727731844poly_a)) (not (forall ((v |u_(-> polyno727731844poly_a polyno727731844poly_a polyno727731844poly_a)|)) (not (forall ((ii polyno727731844poly_a)) (= (ho_68 v ii) (ite (= i ii) e (ho_68 u ii)))))))))) (let ((_let_92 (forall ((x |u_(-> polyno727731844poly_a polyno727731844poly_a polyno727731844poly_a)|) (y |u_(-> polyno727731844poly_a polyno727731844poly_a polyno727731844poly_a)|)) (or (not (forall ((z polyno727731844poly_a)) (= (ho_68 x z) (ho_68 y z)))) (= x y))))) (let ((_let_93 (forall ((u |u_(-> polyno727731844poly_a a)|) (e a) (i polyno727731844poly_a)) (not (forall ((v |u_(-> polyno727731844poly_a a)|)) (not (forall ((ii polyno727731844poly_a)) (= (ho_123 v ii) (ite (= i ii) e (ho_123 u ii)))))))))) (let ((_let_94 (forall ((x |u_(-> polyno727731844poly_a a)|) (y |u_(-> polyno727731844poly_a a)|)) (or (not (forall ((z polyno727731844poly_a)) (= (ho_123 x z) (ho_123 y z)))) (= x y))))) (let ((_let_95 (forall ((u |u_(-> a a a)|) (e |u_(-> a a)|) (i a)) (not (forall ((v |u_(-> a a a)|)) (not (forall ((ii a)) (= (ho_59 v ii) (ite (= i ii) e (ho_59 u ii)))))))))) (let ((_let_96 (forall ((x |u_(-> a a a)|) (y |u_(-> a a a)|)) (or (not (forall ((z a)) (= (ho_59 x z) (ho_59 y z)))) (= x y))))) (let ((_let_97 (forall ((u |u_(-> polyno727731844poly_a nat polyno727731844poly_a)|) (e |u_(-> nat polyno727731844poly_a)|) (i polyno727731844poly_a)) (not (forall ((v |u_(-> polyno727731844poly_a nat polyno727731844poly_a)|)) (not (forall ((ii polyno727731844poly_a)) (= (ho_66 v ii) (ite (= i ii) e (ho_66 u ii)))))))))) (let ((_let_98 (forall ((x |u_(-> polyno727731844poly_a nat polyno727731844poly_a)|) (y |u_(-> polyno727731844poly_a nat polyno727731844poly_a)|)) (or (not (forall ((z polyno727731844poly_a)) (= (ho_66 x z) (ho_66 y z)))) (= x y))))) (let ((_let_99 (forall ((u |u_(-> list_a polyno727731844poly_a a)|) (e |u_(-> polyno727731844poly_a a)|) (i list_a)) (not (forall ((v |u_(-> list_a polyno727731844poly_a a)|)) (not (forall ((ii list_a)) (= (ho_122 v ii) (ite (= i ii) e (ho_122 u ii)))))))))) (let ((_let_100 (forall ((x |u_(-> list_a polyno727731844poly_a a)|) (y |u_(-> list_a polyno727731844poly_a a)|)) (or (not (forall ((z list_a)) (= (ho_122 x z) (ho_122 y z)))) (= x y))))) (let ((_let_101 (forall ((u |u_(-> polyno727731844poly_a polyno727731844poly_a nat polyno727731844poly_a)|) (e |u_(-> polyno727731844poly_a nat polyno727731844poly_a)|) (i polyno727731844poly_a)) (not (forall ((v |u_(-> polyno727731844poly_a polyno727731844poly_a nat polyno727731844poly_a)|)) (not (forall ((ii polyno727731844poly_a)) (= (ho_65 v ii) (ite (= i ii) e (ho_65 u ii)))))))))) (let ((_let_102 (forall ((x |u_(-> polyno727731844poly_a polyno727731844poly_a nat polyno727731844poly_a)|) (y |u_(-> polyno727731844poly_a polyno727731844poly_a nat polyno727731844poly_a)|)) (or (not (forall ((z polyno727731844poly_a)) (= (ho_65 x z) (ho_65 y z)))) (= x y))))) (let ((_let_103 (forall ((u |u_(-> polyno1532895200ly_nat nat polyno1532895200ly_nat polyno1532895200ly_nat)|) (e |u_(-> nat polyno1532895200ly_nat polyno1532895200ly_nat)|) (i polyno1532895200ly_nat)) (not (forall ((v |u_(-> polyno1532895200ly_nat nat polyno1532895200ly_nat polyno1532895200ly_nat)|)) (not (forall ((ii polyno1532895200ly_nat)) (= (ho_125 v ii) (ite (= i ii) e (ho_125 u ii)))))))))) (let ((_let_104 (forall ((x |u_(-> polyno1532895200ly_nat nat polyno1532895200ly_nat polyno1532895200ly_nat)|) (y |u_(-> polyno1532895200ly_nat nat polyno1532895200ly_nat polyno1532895200ly_nat)|)) (or (not (forall ((z polyno1532895200ly_nat)) (= (ho_125 x z) (ho_125 y z)))) (= x y))))) (let ((_let_105 (forall ((u |u_(-> a polyno727731844poly_a polyno727731844poly_a)|) (e |u_(-> polyno727731844poly_a polyno727731844poly_a)|) (i a)) (not (forall ((v |u_(-> a polyno727731844poly_a polyno727731844poly_a)|)) (not (forall ((ii a)) (= (ho_135 v ii) (ite (= i ii) e (ho_135 u ii)))))))))) (let ((_let_106 (forall ((x |u_(-> a polyno727731844poly_a polyno727731844poly_a)|) (y |u_(-> a polyno727731844poly_a polyno727731844poly_a)|)) (or (not (forall ((z a)) (= (ho_135 x z) (ho_135 y z)))) (= x y))))) (let ((_let_107 (forall ((u |u_(-> nat _u_(-> polyno1532895200ly_nat polyno1532895200ly_nat)_ polyno1532895200ly_nat polyno1532895200ly_nat)|) (e |u_(-> _u_(-> polyno1532895200ly_nat polyno1532895200ly_nat)_ polyno1532895200ly_nat polyno1532895200ly_nat)|) (i nat)) (not (forall ((v |u_(-> nat _u_(-> polyno1532895200ly_nat polyno1532895200ly_nat)_ polyno1532895200ly_nat polyno1532895200ly_nat)|)) (not (forall ((ii nat)) (= (ho_161 v ii) (ite (= i ii) e (ho_161 u ii)))))))))) (let ((_let_108 (forall ((x |u_(-> nat _u_(-> polyno1532895200ly_nat polyno1532895200ly_nat)_ polyno1532895200ly_nat polyno1532895200ly_nat)|) (y |u_(-> nat _u_(-> polyno1532895200ly_nat polyno1532895200ly_nat)_ polyno1532895200ly_nat polyno1532895200ly_nat)|)) (or (not (forall ((z nat)) (= (ho_161 x z) (ho_161 y z)))) (= x y))))) (let ((_let_109 (forall ((u |u_(-> polyno727731844poly_a nat)|) (e nat) (i polyno727731844poly_a)) (not (forall ((v |u_(-> polyno727731844poly_a nat)|)) (not (forall ((ii polyno727731844poly_a)) (= (ho_137 v ii) (ite (= i ii) e (ho_137 u ii)))))))))) (let ((_let_110 (forall ((x |u_(-> polyno727731844poly_a nat)|) (y |u_(-> polyno727731844poly_a nat)|)) (or (not (forall ((z polyno727731844poly_a)) (= (ho_137 x z) (ho_137 y z)))) (= x y))))) (let ((_let_111 (forall ((u |u_(-> nat _u_(-> polyno727731844poly_a polyno727731844poly_a)_ polyno727731844poly_a polyno727731844poly_a)|) (e |u_(-> _u_(-> polyno727731844poly_a polyno727731844poly_a)_ polyno727731844poly_a polyno727731844poly_a)|) (i nat)) (not (forall ((v |u_(-> nat _u_(-> polyno727731844poly_a polyno727731844poly_a)_ polyno727731844poly_a polyno727731844poly_a)|)) (not (forall ((ii nat)) (= (ho_141 v ii) (ite (= i ii) e (ho_141 u ii)))))))))) (let ((_let_112 (forall ((x |u_(-> nat _u_(-> polyno727731844poly_a polyno727731844poly_a)_ polyno727731844poly_a polyno727731844poly_a)|) (y |u_(-> nat _u_(-> polyno727731844poly_a polyno727731844poly_a)_ polyno727731844poly_a polyno727731844poly_a)|)) (or (not (forall ((z nat)) (= (ho_141 x z) (ho_141 y z)))) (= x y))))) (let ((_let_113 (forall ((u |u_(-> list_a polyno727731844poly_a Bool)|) (e |u_(-> polyno727731844poly_a Bool)|) (i list_a)) (not (forall ((v |u_(-> list_a polyno727731844poly_a Bool)|)) (not (forall ((ii list_a)) (= (ho_151 v ii) (ite (= i ii) e (ho_151 u ii)))))))))) (let ((_let_114 (forall ((x |u_(-> list_a polyno727731844poly_a Bool)|) (y |u_(-> list_a polyno727731844poly_a Bool)|)) (or (not (forall ((z list_a)) (= (ho_151 x z) (ho_151 y z)))) (= x y))))) (let ((_let_115 (forall ((u |u_(-> polyno1532895200ly_nat nat Bool)|) (e |u_(-> nat Bool)|) (i polyno1532895200ly_nat)) (not (forall ((v |u_(-> polyno1532895200ly_nat nat Bool)|)) (not (forall ((ii polyno1532895200ly_nat)) (= (ho_156 v ii) (ite (= i ii) e (ho_156 u ii)))))))))) (let ((_let_116 (forall ((x |u_(-> polyno1532895200ly_nat nat Bool)|) (y |u_(-> polyno1532895200ly_nat nat Bool)|)) (or (not (forall ((z polyno1532895200ly_nat)) (= (ho_156 x z) (ho_156 y z)))) (= x y))))) (let ((_let_117 (forall ((u |u_(-> polyno1532895200ly_nat nat)|) (e nat) (i polyno1532895200ly_nat)) (not (forall ((v |u_(-> polyno1532895200ly_nat nat)|)) (not (forall ((ii polyno1532895200ly_nat)) (= (ho_158 v ii) (ite (= i ii) e (ho_158 u ii)))))))))) (let ((_let_118 (forall ((x |u_(-> polyno1532895200ly_nat nat)|) (y |u_(-> polyno1532895200ly_nat nat)|)) (or (not (forall ((z polyno1532895200ly_nat)) (= (ho_158 x z) (ho_158 y z)))) (= x y))))) (let ((_let_119 (forall ((u |u_(-> polyno1532895200ly_nat Bool)|) (e Bool) (i polyno1532895200ly_nat)) (not (forall ((v |u_(-> polyno1532895200ly_nat Bool)|)) (not (forall ((ii polyno1532895200ly_nat)) (= (ho_170 v ii) (ite (= i ii) e (ho_170 u ii)))))))))) (let ((_let_120 (forall ((x |u_(-> polyno1532895200ly_nat Bool)|) (y |u_(-> polyno1532895200ly_nat Bool)|)) (or (not (forall ((z polyno1532895200ly_nat)) (= (ho_170 x z) (ho_170 y z)))) (= x y))))) (let ((_let_121 (forall ((BOUND_VARIABLE_7279 nat)) (= zero_zero_nat (ho_41 k_40 BOUND_VARIABLE_7279))))) (let ((_let_122 (forall ((BOUND_VARIABLE_7271 nat) (BOUND_VARIABLE_7272 nat)) (= (ho_41 (ho_43 k_42 BOUND_VARIABLE_7271) BOUND_VARIABLE_7272) (ho_41 (ho_43 k_44 BOUND_VARIABLE_7272) BOUND_VARIABLE_7271))))) (let ((_let_123 (forall ((BOUND_VARIABLE_7264 nat) (BOUND_VARIABLE_7265 nat)) (= (ho_47 (ho_46 k_45 BOUND_VARIABLE_7264) BOUND_VARIABLE_7265) (ho_47 k_48 BOUND_VARIABLE_7264))))) (let ((_let_124 (forall ((BOUND_VARIABLE_7259 nat)) (= zero_zero_nat (ho_41 k_49 BOUND_VARIABLE_7259))))) (let ((_let_125 (forall ((BOUND_VARIABLE_7254 polyno1532895200ly_nat)) (= (ho_51 k_50 BOUND_VARIABLE_7254) (ho_47 k_48 one_one_nat))))) (let ((_let_126 (forall ((BOUND_VARIABLE_7247 nat) (BOUND_VARIABLE_7248 nat)) (= (ho_54 (ho_53 k_52 BOUND_VARIABLE_7247) BOUND_VARIABLE_7248) (ho_54 k_55 BOUND_VARIABLE_7247))))) (let ((_let_127 (forall ((BOUND_VARIABLE_7240 nat) (BOUND_VARIABLE_7241 nat)) (= (ho_47 (ho_46 k_56 BOUND_VARIABLE_7240) BOUND_VARIABLE_7241) (ho_47 k_57 BOUND_VARIABLE_7240))))) (let ((_let_128 (forall ((BOUND_VARIABLE_7227 nat)) (= zero_zero_nat (ho_41 k_62 BOUND_VARIABLE_7227))))) (let ((_let_129 (forall ((BOUND_VARIABLE_7222 nat)) (= zero_zero_nat (ho_41 k_63 BOUND_VARIABLE_7222))))) (let ((_let_130 (forall ((BOUND_VARIABLE_7213 polyno727731844poly_a) (BOUND_VARIABLE_7214 polyno727731844poly_a) (BOUND_VARIABLE_7215 nat)) (= (ho_54 (ho_66 (ho_65 k_64 BOUND_VARIABLE_7213) BOUND_VARIABLE_7214) BOUND_VARIABLE_7215) (ho_69 (ho_68 k_67 BOUND_VARIABLE_7213) BOUND_VARIABLE_7214))))) (let ((_let_131 (forall ((BOUND_VARIABLE_7199 polyno727731844poly_a) (BOUND_VARIABLE_7200 nat) (BOUND_VARIABLE_7201 nat)) (= (ho_41 (ho_43 (ho_71 k_70 BOUND_VARIABLE_7199) BOUND_VARIABLE_7200) BOUND_VARIABLE_7201) (ho_41 (ho_43 (ho_76 k_75 (= BOUND_VARIABLE_7200 BOUND_VARIABLE_7201)) (ho_41 (ho_43 k_74 one_one_nat) (ho_41 (ho_73 k_72 BOUND_VARIABLE_7199) BOUND_VARIABLE_7200))) zero_zero_nat))))) (let ((_let_132 (forall ((BOUND_VARIABLE_7194 nat)) (= zero_zero_nat (ho_41 k_77 BOUND_VARIABLE_7194))))) (let ((_let_133 (forall ((BOUND_VARIABLE_7189 nat)) (= zero_zero_nat (ho_41 k_78 BOUND_VARIABLE_7189))))) (let ((_let_134 (forall ((BOUND_VARIABLE_7184 nat)) (= zero_zero_nat (ho_41 k_79 BOUND_VARIABLE_7184))))) (let ((_let_135 (forall ((BOUND_VARIABLE_7179 nat)) (= zero_zero_nat (ho_41 k_80 BOUND_VARIABLE_7179))))) (let ((_let_136 (forall ((BOUND_VARIABLE_7174 nat)) (= zero_zero_nat (ho_41 k_81 BOUND_VARIABLE_7174))))) (let ((_let_137 (forall ((BOUND_VARIABLE_7169 nat)) (= zero_zero_nat (ho_41 k_82 BOUND_VARIABLE_7169))))) (let ((_let_138 (forall ((BOUND_VARIABLE_7164 nat)) (= zero_zero_nat (ho_41 k_83 BOUND_VARIABLE_7164))))) (let ((_let_139 (forall ((BOUND_VARIABLE_7156 nat) (BOUND_VARIABLE_7157 nat)) (= (ho_41 (ho_43 k_84 BOUND_VARIABLE_7156) BOUND_VARIABLE_7157) (ho_41 (ho_43 k_74 BOUND_VARIABLE_7157) BOUND_VARIABLE_7156))))) (let ((_let_140 (forall ((BOUND_VARIABLE_7149 a) (BOUND_VARIABLE_7150 nat)) (= (ho_54 (ho_86 k_85 BOUND_VARIABLE_7149) BOUND_VARIABLE_7150) (ho_88 k_87 BOUND_VARIABLE_7149))))) (let ((_let_141 (forall ((BOUND_VARIABLE_7140 polyno1532895200ly_nat) (BOUND_VARIABLE_7141 polyno1532895200ly_nat) (BOUND_VARIABLE_7142 nat)) (= (ho_47 (ho_91 (ho_90 k_89 BOUND_VARIABLE_7140) BOUND_VARIABLE_7141) BOUND_VARIABLE_7142) (ho_51 (ho_93 k_92 BOUND_VARIABLE_7140) BOUND_VARIABLE_7141))))) (let ((_let_142 (forall ((BOUND_VARIABLE_7135 polyno727731844poly_a)) (= (ho_69 k_94 BOUND_VARIABLE_7135) (ho_88 k_87 one_one_a))))) (let ((_let_143 (forall ((BOUND_VARIABLE_7130 nat)) (= zero_zero_nat (ho_41 k_95 BOUND_VARIABLE_7130))))) (let ((_let_144 (forall ((BOUND_VARIABLE_7125 nat)) (not (ho_97 k_96 BOUND_VARIABLE_7125))))) (let ((_let_145 (forall ((BOUND_VARIABLE_7120 nat)) (= zero_zero_nat (ho_41 k_98 BOUND_VARIABLE_7120))))) (let ((_let_146 (forall ((BOUND_VARIABLE_7115 nat)) (ho_97 k_99 BOUND_VARIABLE_7115)))) (let ((_let_147 (forall ((BOUND_VARIABLE_7110 nat)) (= zero_zero_nat (ho_41 k_100 BOUND_VARIABLE_7110))))) (let ((_let_148 (forall ((BOUND_VARIABLE_7096 polyno1532895200ly_nat) (BOUND_VARIABLE_7097 nat) (BOUND_VARIABLE_7098 nat)) (= (ho_41 (ho_43 (ho_102 k_101 BOUND_VARIABLE_7096) BOUND_VARIABLE_7097) BOUND_VARIABLE_7098) (ho_41 (ho_43 (ho_76 k_75 (= BOUND_VARIABLE_7097 BOUND_VARIABLE_7098)) (ho_41 (ho_43 k_74 one_one_nat) (ho_41 (ho_104 k_103 BOUND_VARIABLE_7096) BOUND_VARIABLE_7097))) zero_zero_nat))))) (let ((_let_149 (forall ((BOUND_VARIABLE_7091 nat)) (= zero_zero_nat (ho_41 k_105 BOUND_VARIABLE_7091))))) (let ((_let_150 (forall ((BOUND_VARIABLE_7086 nat)) (= zero_zero_nat (ho_41 k_106 BOUND_VARIABLE_7086))))) (let ((_let_151 (forall ((BOUND_VARIABLE_7081 nat)) (= zero_zero_nat (ho_41 k_107 BOUND_VARIABLE_7081))))) (let ((_let_152 (forall ((BOUND_VARIABLE_7076 nat)) (= zero_zero_nat (ho_41 k_108 BOUND_VARIABLE_7076))))) (let ((_let_153 (forall ((BOUND_VARIABLE_7071 nat)) (= zero_zero_nat (ho_41 k_109 BOUND_VARIABLE_7071))))) (let ((_let_154 (forall ((BOUND_VARIABLE_7066 nat)) (= zero_zero_nat (ho_41 k_110 BOUND_VARIABLE_7066))))) (let ((_let_155 (forall ((BOUND_VARIABLE_7061 nat)) (= zero_zero_nat (ho_41 k_111 BOUND_VARIABLE_7061))))) (let ((_let_156 (forall ((BOUND_VARIABLE_7052 polyno1532895200ly_nat) (BOUND_VARIABLE_7053 polyno1532895200ly_nat) (BOUND_VARIABLE_7054 nat)) (= (ho_47 (ho_91 (ho_90 k_112 BOUND_VARIABLE_7052) BOUND_VARIABLE_7053) BOUND_VARIABLE_7054) (ho_51 (ho_93 k_113 BOUND_VARIABLE_7052) BOUND_VARIABLE_7053))))) (let ((_let_157 (forall ((BOUND_VARIABLE_7043 polyno727731844poly_a) (BOUND_VARIABLE_7044 polyno727731844poly_a) (BOUND_VARIABLE_7045 nat)) (= (ho_54 (ho_66 (ho_65 k_114 BOUND_VARIABLE_7043) BOUND_VARIABLE_7044) BOUND_VARIABLE_7045) (ho_69 (ho_68 k_115 BOUND_VARIABLE_7043) BOUND_VARIABLE_7044))))) (let ((_let_158 (forall ((BOUND_VARIABLE_7038 nat)) (= zero_zero_nat (ho_41 k_116 BOUND_VARIABLE_7038))))) (let ((_let_159 (not (= one_one_nat zero_zero_nat)))) (let ((_let_160 (forall ((BOUND_VARIABLE_7279 nat)) (= zero_zero_nat (ll_39 BOUND_VARIABLE_7279))))) (let ((_let_161 (forall ((BOUND_VARIABLE_7271 nat) (BOUND_VARIABLE_7272 nat)) (= ((times_times_nat BOUND_VARIABLE_7272) BOUND_VARIABLE_7271) (ll_38 BOUND_VARIABLE_7271 BOUND_VARIABLE_7272))))) (let ((_let_162 (forall ((BOUND_VARIABLE_7264 nat) (BOUND_VARIABLE_7265 nat)) (= (polyno2122022170_C_nat BOUND_VARIABLE_7264) (ll_37 BOUND_VARIABLE_7264 BOUND_VARIABLE_7265))))) (let ((_let_163 (forall ((BOUND_VARIABLE_7259 nat)) (= zero_zero_nat (ll_36 BOUND_VARIABLE_7259))))) (let ((_let_164 (forall ((BOUND_VARIABLE_7254 polyno1532895200ly_nat)) (= (polyno2122022170_C_nat one_one_nat) (ll_35 BOUND_VARIABLE_7254))))) (let ((_let_165 (forall ((BOUND_VARIABLE_7247 nat) (BOUND_VARIABLE_7248 nat)) (= (polyno2024845497ound_a BOUND_VARIABLE_7247) (ll_34 BOUND_VARIABLE_7247 BOUND_VARIABLE_7248))))) (let ((_let_166 (forall ((BOUND_VARIABLE_7240 nat) (BOUND_VARIABLE_7241 nat)) (= (polyno1999838549nd_nat BOUND_VARIABLE_7240) (ll_33 BOUND_VARIABLE_7240 BOUND_VARIABLE_7241))))) (let ((_let_167 (forall ((BOUND_VARIABLE_7232 a) (BOUND_VARIABLE_7233 a)) (= ((times_times_a BOUND_VARIABLE_7233) BOUND_VARIABLE_7232) (ll_32 BOUND_VARIABLE_7232 BOUND_VARIABLE_7233))))) (let ((_let_168 (forall ((BOUND_VARIABLE_7227 nat)) (= zero_zero_nat (ll_31 BOUND_VARIABLE_7227))))) (let ((_let_169 (forall ((BOUND_VARIABLE_7222 nat)) (= zero_zero_nat (ll_30 BOUND_VARIABLE_7222))))) (let ((_let_170 (forall ((BOUND_VARIABLE_7213 polyno727731844poly_a) (BOUND_VARIABLE_7214 polyno727731844poly_a) (BOUND_VARIABLE_7215 nat)) (= ((polyno1623170614_Add_a BOUND_VARIABLE_7213) BOUND_VARIABLE_7214) (ll_29 BOUND_VARIABLE_7213 BOUND_VARIABLE_7214 BOUND_VARIABLE_7215))))) (let ((_let_171 (forall ((BOUND_VARIABLE_7199 polyno727731844poly_a) (BOUND_VARIABLE_7200 nat) (BOUND_VARIABLE_7201 nat)) (= (((if_nat (= BOUND_VARIABLE_7200 BOUND_VARIABLE_7201)) ((plus_plus_nat one_one_nat) ((polyno1674775833reen_a BOUND_VARIABLE_7199) BOUND_VARIABLE_7200))) zero_zero_nat) (ll_28 BOUND_VARIABLE_7199 BOUND_VARIABLE_7200 BOUND_VARIABLE_7201))))) (let ((_let_172 (forall ((BOUND_VARIABLE_7194 nat)) (= zero_zero_nat (ll_27 BOUND_VARIABLE_7194))))) (let ((_let_173 (forall ((BOUND_VARIABLE_7189 nat)) (= zero_zero_nat (ll_26 BOUND_VARIABLE_7189))))) (let ((_let_174 (forall ((BOUND_VARIABLE_7184 nat)) (= zero_zero_nat (ll_25 BOUND_VARIABLE_7184))))) (let ((_let_175 (forall ((BOUND_VARIABLE_7179 nat)) (= zero_zero_nat (ll_24 BOUND_VARIABLE_7179))))) (let ((_let_176 (forall ((BOUND_VARIABLE_7174 nat)) (= zero_zero_nat (ll_23 BOUND_VARIABLE_7174))))) (let ((_let_177 (forall ((BOUND_VARIABLE_7169 nat)) (= zero_zero_nat (ll_22 BOUND_VARIABLE_7169))))) (let ((_let_178 (forall ((BOUND_VARIABLE_7164 nat)) (= zero_zero_nat (ll_21 BOUND_VARIABLE_7164))))) (let ((_let_179 (forall ((BOUND_VARIABLE_7156 nat) (BOUND_VARIABLE_7157 nat)) (= ((plus_plus_nat BOUND_VARIABLE_7157) BOUND_VARIABLE_7156) (ll_20 BOUND_VARIABLE_7156 BOUND_VARIABLE_7157))))) (let ((_let_180 (forall ((BOUND_VARIABLE_7149 a) (BOUND_VARIABLE_7150 nat)) (= (polyno439679028le_C_a BOUND_VARIABLE_7149) (ll_19 BOUND_VARIABLE_7149 BOUND_VARIABLE_7150))))) (let ((_let_181 (forall ((BOUND_VARIABLE_7140 polyno1532895200ly_nat) (BOUND_VARIABLE_7141 polyno1532895200ly_nat) (BOUND_VARIABLE_7142 nat)) (= ((polyno1222032024dd_nat BOUND_VARIABLE_7140) BOUND_VARIABLE_7141) (ll_18 BOUND_VARIABLE_7140 BOUND_VARIABLE_7141 BOUND_VARIABLE_7142))))) (let ((_let_182 (forall ((BOUND_VARIABLE_7135 polyno727731844poly_a)) (= (polyno439679028le_C_a one_one_a) (ll_17 BOUND_VARIABLE_7135))))) (let ((_let_183 (forall ((BOUND_VARIABLE_7130 nat)) (= zero_zero_nat (ll_16 BOUND_VARIABLE_7130))))) (let ((_let_184 (forall ((BOUND_VARIABLE_7125 nat)) (not (ll_15 BOUND_VARIABLE_7125))))) (let ((_let_185 (forall ((BOUND_VARIABLE_7120 nat)) (= zero_zero_nat (ll_14 BOUND_VARIABLE_7120))))) (let ((_let_186 (forall ((BOUND_VARIABLE_7115 nat)) (ll_13 BOUND_VARIABLE_7115)))) (let ((_let_187 (forall ((BOUND_VARIABLE_7110 nat)) (= zero_zero_nat (ll_12 BOUND_VARIABLE_7110))))) (let ((_let_188 (forall ((BOUND_VARIABLE_7096 polyno1532895200ly_nat) (BOUND_VARIABLE_7097 nat) (BOUND_VARIABLE_7098 nat)) (= (((if_nat (= BOUND_VARIABLE_7097 BOUND_VARIABLE_7098)) ((plus_plus_nat one_one_nat) ((polyno1779722485en_nat BOUND_VARIABLE_7096) BOUND_VARIABLE_7097))) zero_zero_nat) (ll_11 BOUND_VARIABLE_7096 BOUND_VARIABLE_7097 BOUND_VARIABLE_7098))))) (let ((_let_189 (forall ((BOUND_VARIABLE_7091 nat)) (= zero_zero_nat (ll_10 BOUND_VARIABLE_7091))))) (let ((_let_190 (forall ((BOUND_VARIABLE_7086 nat)) (= zero_zero_nat (ll_9 BOUND_VARIABLE_7086))))) (let ((_let_191 (forall ((BOUND_VARIABLE_7081 nat)) (= zero_zero_nat (ll_8 BOUND_VARIABLE_7081))))) (let ((_let_192 (forall ((BOUND_VARIABLE_7076 nat)) (= zero_zero_nat (ll_7 BOUND_VARIABLE_7076))))) (let ((_let_193 (forall ((BOUND_VARIABLE_7071 nat)) (= zero_zero_nat (ll_6 BOUND_VARIABLE_7071))))) (let ((_let_194 (forall ((BOUND_VARIABLE_7066 nat)) (= zero_zero_nat (ll_5 BOUND_VARIABLE_7066))))) (let ((_let_195 (forall ((BOUND_VARIABLE_7061 nat)) (= zero_zero_nat (ll_4 BOUND_VARIABLE_7061))))) (let ((_let_196 (forall ((BOUND_VARIABLE_7052 polyno1532895200ly_nat) (BOUND_VARIABLE_7053 polyno1532895200ly_nat) (BOUND_VARIABLE_7054 nat)) (= ((polyno1415441627ul_nat BOUND_VARIABLE_7052) BOUND_VARIABLE_7053) (ll_3 BOUND_VARIABLE_7052 BOUND_VARIABLE_7053 BOUND_VARIABLE_7054))))) (let ((_let_197 (forall ((BOUND_VARIABLE_7043 polyno727731844poly_a) (BOUND_VARIABLE_7044 polyno727731844poly_a) (BOUND_VARIABLE_7045 nat)) (= ((polyno1491482291_Mul_a BOUND_VARIABLE_7043) BOUND_VARIABLE_7044) (ll_2 BOUND_VARIABLE_7043 BOUND_VARIABLE_7044 BOUND_VARIABLE_7045))))) (let ((_let_198 (forall ((BOUND_VARIABLE_7038 nat)) (= zero_zero_nat (ll_1 BOUND_VARIABLE_7038))))) (let ((_let_199 (and _let_159 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160))) (let ((_let_200 (_let_32))) (let ((_let_201 (not _let_19))) (let ((_let_202 (not _let_18))) (let ((_let_203 (not _let_17))) (let ((_let_204 (not _let_7))) (let ((_let_205 (and _let_18 _let_7 _let_23 _let_17))) (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG |:args| (_let_205)) (IMPLIES_ELIM (SCOPE (FALSE_ELIM (MACRO_SR_PRED_TRANSFORM (TRANS (CONG (TRANS (CONG (CONG (SYMM (SYMM _let_21)) (REFL |:args| (_let_14)) |:args| (23 ho_59)) (REFL |:args| (_let_15)) |:args| (23 ho_60)) (SYMM (ASSUME |:args| (_let_18)))) (SYMM (ASSUME |:args| (_let_17))) |:args| (6)) (FALSE_INTRO (ASSUME |:args| _let_27))) |:args| ((= _let_19 false)))) |:args| (_let_18 _let_7 _let_23 _let_17))) |:args| (true _let_205)) (CONG (REFL |:args| (_let_202)) (REFL |:args| (_let_204)) (MACRO_SR_PRED_INTRO |:args| ((= (not _let_23) _let_13))) (REFL |:args| (_let_203)) (REFL |:args| (_let_201)) |:args| _let_26)) |:args| ((or _let_204 _let_13 _let_203 _let_202 _let_201))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME |:args| _let_200) |:args| (_let_14 _let_15)) |:args| _let_200))) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (MACRO_SR_PRED_TRANSFORM (AND_INTRO (SYMM (ASSUME |:args| (_let_6))) (PREPROCESS |:args| ((and _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160)))) |:args| (_let_199)) (PREPROCESS |:args| ((= _let_199 (and _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_32 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121))))) (PREPROCESS |:args| ((and _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)))) |:args| ((and _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_32 _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))) |:args| (32)) |:args| (_let_19 false _let_32)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_30 |:args| (skv_173 q p)) |:args| _let_31))) _let_30 |:args| (_let_18 false _let_29)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_30 |:args| (skv_173 p q)) |:args| _let_31))) _let_30 |:args| (_let_17 false _let_29)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME |:args| _let_28)) |:args| _let_28)) (CONG (MACRO_SR_PRED_INTRO |:args| ((= (not _let_25) _let_22))) (REFL |:args| _let_27) |:args| _let_26)) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (EQ_RESOLVE (ASSUME |:args| (_let_2)) (PREPROCESS |:args| ((= _let_2 (= _let_22 _let_24)))))) |:args| ((or _let_24 _let_25))) (EQ_RESOLVE (ASSUME |:args| (_let_5)) (PREPROCESS |:args| ((= _let_5 (not _let_24))))) |:args| (_let_25 true _let_24)) |:args| (_let_23 true _let_22)) _let_21 |:args| (false false _let_19 false _let_18 false _let_17 true _let_13 false _let_7)) |:args| (_let_6 (forall ((V polyno1532895200ly_nat) (Va polyno1532895200ly_nat)) (= (polyno1779722485en_nat ((polyno1222032024dd_nat V) Va)) (lambda ((M2 nat)) zero_zero_nat))) (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)))))) (= polyno1013235523ly_nat (lambda ((P2 polyno1532895200ly_nat)) ((polyno892049031yh_nat P2) zero_zero_nat))) (forall ((R a) (A a) (B a) (C a) (D a)) (let ((_let_1 (times_times_a R))) (=> (not (= R zero_zero_a)) (=> (and (= A B) (not (= C D))) (not (= ((plus_plus_a A) (_let_1 C)) ((plus_plus_a B) (_let_1 D)))))))) (forall ((A a) (C a)) (= (= ((times_times_a A) C) C) (or (= A one_one_a) (= C zero_zero_a)))) (forall ((X31 polyno727731844poly_a) (X32 polyno727731844poly_a) (X81 polyno727731844poly_a) (X82 nat) (X83 polyno727731844poly_a)) (not (= ((polyno1623170614_Add_a X31) X32) (((polyno1057396216e_CN_a X81) X82) X83)))) (forall ((Bs2 list_a) (P polyno727731844poly_a)) (let ((_let_1 (polyno422358502poly_a Bs2))) (= (_let_1 (polyno784948432ift1_a P)) (_let_1 ((polyno1491482291_Mul_a (polyno2024845497ound_a zero_zero_nat)) P))))) (forall ((X31 polyno1532895200ly_nat) (X32 polyno1532895200ly_nat) (Y31 polyno1532895200ly_nat) (Y32 polyno1532895200ly_nat)) (= (= ((polyno1222032024dd_nat X31) X32) ((polyno1222032024dd_nat Y31) Y32)) (and (= X31 Y31) (= X32 Y32)))) (forall ((A nat)) (= ((times_times_nat A) one_one_nat) A)) (forall ((A a) (B a) (C a)) (let ((_let_1 (times_times_a A))) (= ((times_times_a (_let_1 B)) C) (_let_1 ((times_times_a B) C))))) (forall ((A a) (B a) (C a)) (let ((_let_1 (times_times_a A))) (= (_let_1 ((plus_plus_a B) C)) ((plus_plus_a (_let_1 B)) (_let_1 C))))) (forall ((M nat) (N nat)) (= (= ((times_times_nat M) N) one_one_nat) (and (= N one_one_nat) (= M one_one_nat)))) (forall ((X81 polyno1532895200ly_nat) (X82 nat) (X83 polyno1532895200ly_nat) (Y81 polyno1532895200ly_nat) (Y82 nat) (Y83 polyno1532895200ly_nat)) (= (= (((polyno720942678CN_nat X81) X82) X83) (((polyno720942678CN_nat Y81) Y82) Y83)) (and (= X83 Y83) (= X82 Y82) (= X81 Y81)))) (forall ((V polyno727731844poly_a) (Va polyno727731844poly_a)) (= (polyno567601229eadn_a ((polyno1491482291_Mul_a V) Va)) (lambda ((M2 nat)) ((polyno1491482291_Mul_a V) Va)))) (forall ((C nat) (C2 polyno1532895200ly_nat) (N2 nat) (P3 polyno1532895200ly_nat)) (let ((_let_1 (polyno929799083ul_nat (polyno2122022170_C_nat C)))) (let ((_let_2 (_let_1 (((polyno720942678CN_nat C2) N2) P3)))) (let ((_let_3 (= C zero_zero_nat))) (and (=> (not _let_3) (= _let_2 (((polyno720942678CN_nat (_let_1 C2)) N2) (_let_1 P3)))) (=> _let_3 (= _let_2 (polyno2122022170_C_nat zero_zero_nat)))))))) (forall ((V polyno1532895200ly_nat) (Va polyno1532895200ly_nat)) (= (polyno544860353dn_nat ((polyno1415441627ul_nat V) Va)) (lambda ((M2 nat)) ((polyno1415441627ul_nat V) Va)))) (forall ((P polyno727731844poly_a) (N0 nat) (M nat)) (let ((_let_1 (polyno439679028le_C_a zero_zero_a))) (=> ((polyno1372495879olyh_a P) N0) (= (= ((polyno567601229eadn_a P) M) _let_1) (= P _let_1))))) (forall ((Y a) (V polyno727731844poly_a) (Va nat)) (let ((_let_1 ((polyno1538138524e_Pw_a V) Va))) (= ((polyno562434098cmul_a Y) _let_1) ((polyno1934269411ymul_a (polyno439679028le_C_a Y)) _let_1)))) (forall ((C polyno727731844poly_a) (N nat) (P polyno727731844poly_a) (N0 nat)) (=> ((polyno1372495879olyh_a (((polyno1057396216e_CN_a C) N) P)) N0) (= (polyno578545843gree_a C) zero_zero_nat))) (forall ((V polyno1532895200ly_nat) (Va nat) (B polyno1532895200ly_nat)) (let ((_let_1 ((polyno359287218Pw_nat V) Va))) (= ((polyno929799083ul_nat _let_1) B) ((polyno1415441627ul_nat _let_1) B)))) (forall ((Y a) (X a)) (= ((polyno562434098cmul_a Y) (polyno439679028le_C_a X)) (polyno439679028le_C_a ((times_times_a Y) X)))) (forall ((V polyno727731844poly_a) (Va polyno727731844poly_a)) (= (polyno1465139388head_a ((polyno1623170614_Add_a V) Va)) (polyno439679028le_C_a zero_zero_a))) (forall ((Bs2 list_a) (N nat) (P polyno727731844poly_a)) (let ((_let_1 ((compow1114216044poly_a N) polyno784948432ift1_a))) (let ((_let_2 (polyno422358502poly_a Bs2))) (= (_let_2 (_let_1 P)) (_let_2 ((polyno1934269411ymul_a (_let_1 (polyno439679028le_C_a one_one_a))) P)))))) (forall ((A nat) (B nat)) (= (= ((plus_plus_nat A) B) A) (= B zero_zero_nat))) (forall ((I nat) (J nat) (K2 nat) (L nat)) (=> (and (= K2 L) (= I J)) (= ((plus_plus_nat I) K2) ((plus_plus_nat J) L)))) (forall ((C a) (C2 polyno727731844poly_a) (N2 nat) (P3 polyno727731844poly_a)) (let ((_let_1 (polyno1934269411ymul_a (polyno439679028le_C_a C)))) (let ((_let_2 (_let_1 (((polyno1057396216e_CN_a C2) N2) P3)))) (let ((_let_3 (= C zero_zero_a))) (and (=> (not _let_3) (= _let_2 (((polyno1057396216e_CN_a (_let_1 C2)) N2) (_let_1 P3)))) (=> _let_3 (= _let_2 (polyno439679028le_C_a zero_zero_a)))))))) (forall ((C polyno1532895200ly_nat) (P polyno1532895200ly_nat)) (= (polyno1952548879ad_nat (((polyno720942678CN_nat C) zero_zero_nat) P)) (polyno1952548879ad_nat P))) (forall ((Y a) (V polyno727731844poly_a)) (let ((_let_1 (polyno96675367_Neg_a V))) (= ((polyno562434098cmul_a Y) _let_1) ((polyno1934269411ymul_a (polyno439679028le_C_a Y)) _let_1)))) (forall ((N nat)) (= ((times_times_nat zero_zero_nat) N) zero_zero_nat)) (forall ((P polyno727731844poly_a) (N0 nat)) (let ((_let_1 (polyno439679028le_C_a zero_zero_a))) (=> ((polyno1372495879olyh_a P) N0) (= ((polyno1934269411ymul_a _let_1) P) _let_1)))) (forall ((B nat) (A nat)) (= (= B ((plus_plus_nat B) A)) (= A zero_zero_nat))) (forall ((P polyno727731844poly_a) (Q polyno727731844poly_a)) (= (polyno955999183nate_a ((polyno1491482291_Mul_a P) Q)) ((polyno1934269411ymul_a (polyno955999183nate_a P)) (polyno955999183nate_a Q)))) (forall ((A polyno1532895200ly_nat) (V polyno1532895200ly_nat) (Va nat)) (let ((_let_1 ((polyno359287218Pw_nat V) Va))) (= ((polyno929799083ul_nat A) _let_1) ((polyno1415441627ul_nat A) _let_1)))) (forall ((X nat) (Y nat)) (= (= zero_zero_nat ((plus_plus_nat X) Y)) (and (= X zero_zero_nat) (= Y zero_zero_nat)))) (forall ((X31 polyno727731844poly_a) (X32 polyno727731844poly_a) (Y31 polyno727731844poly_a) (Y32 polyno727731844poly_a)) (= (= ((polyno1623170614_Add_a X31) X32) ((polyno1623170614_Add_a Y31) Y32)) (and (= X31 Y31) (= X32 Y32)))) (forall ((A a) (B a) (C a)) (let ((_let_1 (times_times_a A))) (= (_let_1 ((plus_plus_a B) C)) ((plus_plus_a (_let_1 B)) (_let_1 C))))) (forall ((V polyno727731844poly_a) (Va polyno727731844poly_a)) (= (polyno578545843gree_a ((polyno1491482291_Mul_a V) Va)) zero_zero_nat)) (forall ((B3 nat) (K2 nat) (B nat) (A nat)) (let ((_let_1 (plus_plus_nat A))) (let ((_let_2 (plus_plus_nat K2))) (=> (= B3 (_let_2 B)) (= (_let_1 B3) (_let_2 (_let_1 B))))))) (forall ((T polyno1532895200ly_nat) (A polyno1532895200ly_nat) (B polyno1532895200ly_nat)) (let ((_let_1 (polyno336795754t0_nat T))) (= (_let_1 ((polyno1415441627ul_nat A) B)) ((polyno1415441627ul_nat (_let_1 A)) (_let_1 B))))) (forall ((A nat)) (= ((plus_plus_nat A) zero_zero_nat) A)) (forall ((V nat)) (let ((_let_1 (polyno2122022170_C_nat V))) (= (polyno1952548879ad_nat _let_1) _let_1))) (forall ((X1 nat) (X51 polyno1532895200ly_nat) (X52 polyno1532895200ly_nat)) (not (= (polyno2122022170_C_nat X1) ((polyno1415441627ul_nat X51) X52)))) (forall ((X1 a) (X51 polyno727731844poly_a) (X52 polyno727731844poly_a)) (not (= (polyno439679028le_C_a X1) ((polyno1491482291_Mul_a X51) X52)))) (forall ((V polyno1532895200ly_nat)) (= (polyno587244178ad_nat (polyno1366804583eg_nat V)) (polyno2122022170_C_nat zero_zero_nat))) (forall ((X polyno1532895200ly_nat) (Y (-> nat nat))) (=> (= (polyno1779722485en_nat X) Y) (=> (forall ((C3 polyno1532895200ly_nat) (N3 nat) (P4 polyno1532895200ly_nat)) (=> (= X (((polyno720942678CN_nat C3) N3) P4)) (not (= Y (lambda ((M2 nat)) (((if_nat (= N3 M2)) ((plus_plus_nat one_one_nat) ((polyno1779722485en_nat P4) N3))) zero_zero_nat)))))) (=> (=> (exists ((V2 nat)) (= X (polyno2122022170_C_nat V2))) (not (= Y (lambda ((M2 nat)) zero_zero_nat)))) (=> (=> (exists ((V2 nat)) (= X (polyno1999838549nd_nat V2))) (not (= Y (lambda ((M2 nat)) zero_zero_nat)))) (=> (=> (exists ((V2 polyno1532895200ly_nat) (Va2 polyno1532895200ly_nat)) (= X ((polyno1222032024dd_nat V2) Va2))) (not (= Y (lambda ((M2 nat)) zero_zero_nat)))) (=> (=> (exists ((V2 polyno1532895200ly_nat) (Va2 polyno1532895200ly_nat)) (= X ((polyno1921014231ub_nat V2) Va2))) (not (= Y (lambda ((M2 nat)) zero_zero_nat)))) (=> (=> (exists ((V2 polyno1532895200ly_nat) (Va2 polyno1532895200ly_nat)) (= X ((polyno1415441627ul_nat V2) Va2))) (not (= Y (lambda ((M2 nat)) zero_zero_nat)))) (=> (=> (exists ((V2 polyno1532895200ly_nat)) (= X (polyno1366804583eg_nat V2))) (not (= Y (lambda ((M2 nat)) zero_zero_nat)))) (not (=> (exists ((V2 polyno1532895200ly_nat) (Va2 nat)) (= X ((polyno359287218Pw_nat V2) Va2))) (not (= Y (lambda ((M2 nat)) zero_zero_nat)))))))))))))) (forall ((Bs2 list_a) (P polyno727731844poly_a) (Q polyno727731844poly_a)) (let ((_let_1 (polyno896877631f_bs_a Bs2))) (=> (_let_1 P) (=> (_let_1 Q) (_let_1 ((polyno1418491367ysub_a P) Q)))))) (forall ((T polyno727731844poly_a) (A polyno727731844poly_a) (B polyno727731844poly_a)) (let ((_let_1 (polyno1397854436bst0_a T))) (= (_let_1 ((polyno1491482291_Mul_a A) B)) ((polyno1491482291_Mul_a (_let_1 A)) (_let_1 B))))) (forall ((V polyno727731844poly_a) (Va polyno727731844poly_a)) (= (polyno1465139388head_a ((polyno1491482291_Mul_a V) Va)) (polyno439679028le_C_a zero_zero_a))) (forall ((V nat)) (let ((_let_1 (polyno1999838549nd_nat V))) (= (polyno1952548879ad_nat _let_1) _let_1))) (forall ((A a) (C a) (B a)) (= (= ((times_times_a A) C) ((times_times_a B) C)) (or (= C zero_zero_a) (= A B)))) (forall ((Vc polyno1532895200ly_nat) (Vd polyno1532895200ly_nat) (V polyno1532895200ly_nat) (Va nat) (Vb polyno1532895200ly_nat)) (let ((_let_1 (((polyno720942678CN_nat V) Va) Vb))) (let ((_let_2 ((polyno1222032024dd_nat Vc) Vd))) (= ((polyno929799083ul_nat _let_2) _let_1) ((polyno1415441627ul_nat _let_2) _let_1))))) (forall ((A polyno727731844poly_a) (V nat)) (let ((_let_1 (polyno2024845497ound_a V))) (= ((polyno1934269411ymul_a A) _let_1) ((polyno1491482291_Mul_a A) _let_1)))) (forall ((V polyno727731844poly_a) (Va polyno727731844poly_a)) (= (polyno1674775833reen_a ((polyno1623170614_Add_a V) Va)) (lambda ((M2 nat)) zero_zero_nat))) (forall ((A a) (B a) (C a)) (= ((times_times_a ((plus_plus_a A) B)) C) ((plus_plus_a ((times_times_a A) C)) ((times_times_a B) C)))) (forall ((C nat) (C2 nat)) (= ((polyno929799083ul_nat (polyno2122022170_C_nat C)) (polyno2122022170_C_nat C2)) (polyno2122022170_C_nat ((times_times_nat C) C2)))) (forall ((C a)) (= (polyno1372495879olyh_a (polyno439679028le_C_a C)) (lambda ((K nat)) true))) (forall ((V polyno727731844poly_a) (Va polyno727731844poly_a)) (= (polyno1674775833reen_a ((polyno1491482291_Mul_a V) Va)) (lambda ((M2 nat)) zero_zero_nat))) (forall ((B nat) (A nat)) (= (= ((plus_plus_nat B) A) A) (= B zero_zero_nat))) (forall ((T polyno727731844poly_a) (C a)) (let ((_let_1 (polyno439679028le_C_a C))) (= ((polyno1397854436bst0_a T) _let_1) _let_1))) (forall ((V nat)) (= (polyno1465139388head_a (polyno2024845497ound_a V)) (polyno439679028le_C_a zero_zero_a))) (forall ((P polyno727731844poly_a) (N nat) (K2 nat)) (=> ((polyno1372495879olyh_a P) N) ((polyno1372495879olyh_a ((polyno1371724751ypow_a K2) P)) N))) (forall ((A a) (B a)) (=> (= ((times_times_a A) B) zero_zero_a) (or (= A zero_zero_a) (= B zero_zero_a)))) (forall ((A nat)) (= ((plus_plus_nat A) zero_zero_nat) A)) (forall ((M nat) (N nat)) (= (= ((plus_plus_nat M) N) zero_zero_nat) (and (= M zero_zero_nat) (= N zero_zero_nat)))) (forall ((X a)) (= (= zero_zero_a X) (= X zero_zero_a))) (forall ((V nat)) (= (polyno892049031yh_nat (polyno1999838549nd_nat V)) (lambda ((K nat)) false))) (forall ((X nat) (Y nat)) (= (= ((plus_plus_nat X) Y) zero_zero_nat) (and (= X zero_zero_nat) (= Y zero_zero_nat)))) (forall ((N nat) (T polyno727731844poly_a) (C polyno727731844poly_a) (P polyno727731844poly_a)) (let ((_let_1 (polyno1397854436bst0_a T))) (let ((_let_2 (_let_1 P))) (let ((_let_3 (_let_1 C))) (let ((_let_4 (_let_1 (((polyno1057396216e_CN_a C) N) P)))) (let ((_let_5 (= N zero_zero_nat))) (and (=> (not _let_5) (= _let_4 (((polyno1057396216e_CN_a _let_3) N) _let_2))) (=> _let_5 (= _let_4 ((polyno1623170614_Add_a _let_3) ((polyno1491482291_Mul_a T) _let_2))))))))))) (forall ((P polyno1532895200ly_nat) (N0 nat)) (=> ((polyno892049031yh_nat P) N0) (= (= (polyno524777654st_nat P) zero_zero_nat) (= P (polyno2122022170_C_nat zero_zero_nat))))) (forall ((V nat)) (= (polyno1779722485en_nat (polyno1999838549nd_nat V)) (lambda ((M2 nat)) zero_zero_nat))) (= (polyno1371724751ypow_a zero_zero_nat) (lambda ((P2 polyno727731844poly_a)) (polyno439679028le_C_a one_one_a))) (forall ((Y a) (V nat)) (let ((_let_1 (polyno2024845497ound_a V))) (= ((polyno562434098cmul_a Y) _let_1) ((polyno1934269411ymul_a (polyno439679028le_C_a Y)) _let_1)))) (forall ((V polyno1532895200ly_nat) (Va nat) (Vb polyno1532895200ly_nat) (Vc polyno1532895200ly_nat) (Vd polyno1532895200ly_nat)) (let ((_let_1 ((polyno1415441627ul_nat Vc) Vd))) (let ((_let_2 (((polyno720942678CN_nat V) Va) Vb))) (= ((polyno929799083ul_nat _let_2) _let_1) ((polyno1415441627ul_nat _let_2) _let_1))))) (forall ((A a) (B a)) (=> (not (= ((times_times_a A) B) zero_zero_a)) (and (not (= A zero_zero_a)) (not (= B zero_zero_a))))) (forall ((A a) (B a) (C a) (D a)) (let ((_let_1 (times_times_a B))) (let ((_let_2 (times_times_a A))) (= (and (not (= A B)) (not (= C D))) (not (= ((plus_plus_a (_let_2 C)) (_let_1 D)) ((plus_plus_a (_let_2 D)) (_let_1 C)))))))) (forall ((P polyno1532895200ly_nat) (N nat) (M nat)) (let ((_let_1 (polyno2122022170_C_nat zero_zero_nat))) (=> ((polyno892049031yh_nat P) N) (=> (not (= P _let_1)) (not (= ((polyno544860353dn_nat P) M) _let_1)))))) (forall ((V polyno1532895200ly_nat) (Va polyno1532895200ly_nat)) (= (polyno544860353dn_nat ((polyno1222032024dd_nat V) Va)) (lambda ((M2 nat)) ((polyno1222032024dd_nat V) Va)))) (forall ((P polyno727731844poly_a)) (polyno190918219poly_a (polyno955999183nate_a P))) (forall ((C polyno727731844poly_a) (N nat) (P polyno727731844poly_a)) (= (polyno2115742616onst_a (((polyno1057396216e_CN_a C) N) P)) (polyno2115742616onst_a P))) (forall ((V a)) (= (polyno578545843gree_a (polyno439679028le_C_a V)) zero_zero_nat)) (forall ((X51 polyno1532895200ly_nat) (X52 polyno1532895200ly_nat) (X81 polyno1532895200ly_nat) (X82 nat) (X83 polyno1532895200ly_nat)) (not (= ((polyno1415441627ul_nat X51) X52) (((polyno720942678CN_nat X81) X82) X83)))) (forall ((W a) (Y a) (X a) (Z a)) (let ((_let_1 (times_times_a X))) (let ((_let_2 (times_times_a W))) (= (= ((plus_plus_a (_let_2 Y)) (_let_1 Z)) ((plus_plus_a (_let_2 Z)) (_let_1 Y))) (or (= W X) (= Y Z)))))) (forall ((T polyno727731844poly_a) (A polyno727731844poly_a) (B polyno727731844poly_a)) (let ((_let_1 (polyno1397854436bst0_a T))) (= (_let_1 ((polyno1623170614_Add_a A) B)) ((polyno1623170614_Add_a (_let_1 A)) (_let_1 B))))) (forall ((N nat) (F (-> polyno1532895200ly_nat polyno1532895200ly_nat)) (P polyno1532895200ly_nat) (K2 nat)) (=> (forall ((P4 polyno1532895200ly_nat)) (=> ((polyno892049031yh_nat P4) N) ((polyno892049031yh_nat (F P4)) N))) (=> ((polyno892049031yh_nat P) N) ((polyno892049031yh_nat (((compow808008746ly_nat K2) F) P)) N)))) (forall ((V nat)) (let ((_let_1 (polyno2024845497ound_a V))) (= (polyno1884029055head_a _let_1) _let_1))) (forall ((A a)) (= ((times_times_a A) one_one_a) A)) (forall ((V polyno727731844poly_a) (Va nat)) (= (polyno212464073eriv_a ((polyno1538138524e_Pw_a V) Va)) (polyno439679028le_C_a zero_zero_a))) (forall ((A polyno1532895200ly_nat) (V polyno1532895200ly_nat) (Va polyno1532895200ly_nat)) (let ((_let_1 ((polyno1222032024dd_nat V) Va))) (= ((polyno929799083ul_nat A) _let_1) ((polyno1415441627ul_nat A) _let_1)))) (forall ((A3 nat) (K2 nat) (A nat) (B nat)) (let ((_let_1 (plus_plus_nat K2))) (=> (= A3 (_let_1 A)) (= ((plus_plus_nat A3) B) (_let_1 ((plus_plus_nat A) B)))))) (forall ((A nat) (B nat) (C nat)) (= ((times_times_nat ((plus_plus_nat A) B)) C) ((plus_plus_nat ((times_times_nat A) C)) ((times_times_nat B) C)))) (forall ((A a)) (= ((times_times_a one_one_a) A) A)) (forall ((C a) (A a) (B a)) (let ((_let_1 (times_times_a C))) (= (= (_let_1 A) (_let_1 B)) (or (= C zero_zero_a) (= A B))))) (forall ((F (-> polyno727731844poly_a polyno727731844poly_a)) (N nat) (X polyno727731844poly_a)) (let ((_let_1 ((compow1114216044poly_a N) F))) (= (F (_let_1 X)) (_let_1 (F X))))) (forall ((Bs2 list_a) (P polyno727731844poly_a)) (let ((_let_1 (polyno422358502poly_a Bs2))) (= (_let_1 (polyno955999183nate_a P)) (_let_1 P)))) (forall ((V nat) (B polyno727731844poly_a)) (let ((_let_1 (polyno2024845497ound_a V))) (= ((polyno1934269411ymul_a _let_1) B) ((polyno1491482291_Mul_a _let_1) B)))) (forall ((P polyno727731844poly_a) (N nat) (Bs2 list_a)) (let ((_let_1 (polyno422358502poly_a Bs2))) (=> ((polyno1372495879olyh_a P) N) (= (_let_1 ((polyno1623170614_Add_a ((polyno1491482291_Mul_a (polyno1884029055head_a P)) ((polyno1538138524e_Pw_a (polyno2024845497ound_a zero_zero_nat)) (polyno578545843gree_a P)))) (polyno1465139388head_a P))) (_let_1 P))))) (forall ((V a)) (= (polyno567601229eadn_a (polyno439679028le_C_a V)) (lambda ((M2 nat)) (polyno439679028le_C_a V)))) (forall ((V polyno727731844poly_a) (Va polyno727731844poly_a)) (= (polyno212464073eriv_a ((polyno1623170614_Add_a V) Va)) (polyno439679028le_C_a zero_zero_a))) (forall ((V polyno727731844poly_a) (Va nat)) (= (polyno1465139388head_a ((polyno1538138524e_Pw_a V) Va)) (polyno439679028le_C_a zero_zero_a))) (forall ((V polyno727731844poly_a) (Va polyno727731844poly_a)) (= (polyno578545843gree_a ((polyno1623170614_Add_a V) Va)) zero_zero_nat)) (forall ((Vc polyno727731844poly_a) (Vd nat) (V polyno727731844poly_a) (Va nat) (Vb polyno727731844poly_a)) (let ((_let_1 (((polyno1057396216e_CN_a V) Va) Vb))) (let ((_let_2 ((polyno1538138524e_Pw_a Vc) Vd))) (= ((polyno1934269411ymul_a _let_2) _let_1) ((polyno1491482291_Mul_a _let_2) _let_1))))) (forall ((N nat)) ((polyno892049031yh_nat (polyno2122022170_C_nat one_one_nat)) N)) (forall ((X a)) (= (= one_one_a X) (= X one_one_a))) (forall ((V polyno727731844poly_a) (Va polyno727731844poly_a)) (= (polyno212464073eriv_a ((polyno975704247_Sub_a V) Va)) (polyno439679028le_C_a zero_zero_a))) (forall ((N nat)) (= ((times_times_nat one_one_nat) N) N)) (forall ((A nat) (B nat) (C nat)) (let ((_let_1 (plus_plus_nat A))) (= ((plus_plus_nat (_let_1 B)) C) (_let_1 ((plus_plus_nat B) C))))) (forall ((C a) (A a) (B a)) (=> (not (= C zero_zero_a)) (= (= ((times_times_a A) C) ((times_times_a B) C)) (= A B)))) (forall ((Vc polyno1532895200ly_nat) (Vd polyno1532895200ly_nat) (V polyno1532895200ly_nat) (Va nat) (Vb polyno1532895200ly_nat)) (let ((_let_1 (((polyno720942678CN_nat V) Va) Vb))) (let ((_let_2 ((polyno1415441627ul_nat Vc) Vd))) (= ((polyno929799083ul_nat _let_2) _let_1) ((polyno1415441627ul_nat _let_2) _let_1))))) (forall ((V polyno1532895200ly_nat) (Va polyno1532895200ly_nat)) (= (polyno587244178ad_nat ((polyno1222032024dd_nat V) Va)) (polyno2122022170_C_nat zero_zero_nat))) (forall ((V polyno1532895200ly_nat) (Va polyno1532895200ly_nat)) (= (polyno220183259ee_nat ((polyno1415441627ul_nat V) Va)) zero_zero_nat)) (forall ((V polyno727731844poly_a) (Va polyno727731844poly_a)) (let ((_let_1 ((polyno1623170614_Add_a V) Va))) (= (polyno1884029055head_a _let_1) _let_1))) (forall ((V polyno1532895200ly_nat) (Va polyno1532895200ly_nat)) (let ((_let_1 ((polyno1222032024dd_nat V) Va))) (= (polyno1952548879ad_nat _let_1) _let_1))) (forall ((V polyno727731844poly_a)) (= (polyno212464073eriv_a (polyno96675367_Neg_a V)) (polyno439679028le_C_a zero_zero_a))) (forall ((X31 polyno1532895200ly_nat) (X32 polyno1532895200ly_nat) (X51 polyno1532895200ly_nat) (X52 polyno1532895200ly_nat)) (not (= ((polyno1222032024dd_nat X31) X32) ((polyno1415441627ul_nat X51) X52)))) (forall ((A a) (E a) (B a) (C a)) (= ((plus_plus_a ((times_times_a A) E)) ((plus_plus_a ((times_times_a B) E)) C)) ((plus_plus_a ((times_times_a ((plus_plus_a A) B)) E)) C))) (forall ((V nat)) (= (polyno220183259ee_nat (polyno1999838549nd_nat V)) zero_zero_nat)) (forall ((M nat) (N nat)) (=> (= ((plus_plus_nat M) N) M) (= N zero_zero_nat))) (forall ((Y nat) (V polyno1532895200ly_nat) (Va polyno1532895200ly_nat)) (let ((_let_1 ((polyno1415441627ul_nat V) Va))) (= ((polyno1467023772ul_nat Y) _let_1) ((polyno929799083ul_nat (polyno2122022170_C_nat Y)) _let_1)))) (forall ((X51 polyno1532895200ly_nat) (X52 polyno1532895200ly_nat) (Y51 polyno1532895200ly_nat) (Y52 polyno1532895200ly_nat)) (= (= ((polyno1415441627ul_nat X51) X52) ((polyno1415441627ul_nat Y51) Y52)) (and (= X51 Y51) (= X52 Y52)))) (forall ((V nat)) (= (polyno587244178ad_nat (polyno2122022170_C_nat V)) (polyno2122022170_C_nat zero_zero_nat))) (forall ((Bs2 list_a) (N nat) (P polyno727731844poly_a)) (let ((_let_1 (polyno422358502poly_a Bs2))) (= (_let_1 (((compow1114216044poly_a N) polyno784948432ift1_a) P)) (_let_1 ((polyno1491482291_Mul_a ((polyno1538138524e_Pw_a (polyno2024845497ound_a zero_zero_nat)) N)) P))))) (forall ((P polyno727731844poly_a) (N0 nat)) (=> ((polyno1372495879olyh_a P) N0) (=> (not (= P (polyno439679028le_C_a zero_zero_a))) ((polyno1372495879olyh_a (polyno784948432ift1_a P)) zero_zero_nat)))) (forall ((V polyno727731844poly_a) (Va polyno727731844poly_a)) (= (polyno1372495879olyh_a ((polyno1623170614_Add_a V) Va)) (lambda ((K nat)) false))) (forall ((P polyno727731844poly_a) (N0 nat)) (=> ((polyno1372495879olyh_a P) N0) (=> (forall ((Bs3 list_a)) (=> ((polyno896877631f_bs_a Bs3) P) (= ((polyno422358502poly_a Bs3) P) zero_zero_a))) (= P (polyno439679028le_C_a zero_zero_a))))) (forall ((M nat)) (= ((plus_plus_nat M) zero_zero_nat) M)) (forall ((Y a) (V polyno727731844poly_a) (Va polyno727731844poly_a)) (let ((_let_1 ((polyno1623170614_Add_a V) Va))) (= ((polyno562434098cmul_a Y) _let_1) ((polyno1934269411ymul_a (polyno439679028le_C_a Y)) _let_1)))) (forall ((W nat) (Y nat) (X nat) (Z nat)) (let ((_let_1 (times_times_nat X))) (let ((_let_2 (times_times_nat W))) (= (= ((plus_plus_nat (_let_2 Y)) (_let_1 Z)) ((plus_plus_nat (_let_2 Z)) (_let_1 Y))) (or (= W X) (= Y Z)))))) ((polyno1372495879olyh_a p) n0) (forall ((Bs2 list_a) (A polyno727731844poly_a) (B polyno727731844poly_a)) (let ((_let_1 (polyno422358502poly_a Bs2))) (= (_let_1 ((polyno1491482291_Mul_a A) B)) ((times_times_a (_let_1 A)) (_let_1 B))))) (forall ((N a) (V a)) (let ((_let_1 (polyno439679028le_C_a V))) (= ((polyno1006823949_aux_a N) _let_1) ((polyno562434098cmul_a N) _let_1)))) (forall ((C a) (B a)) (= (= C ((times_times_a C) B)) (or (= C zero_zero_a) (= B one_one_a)))) (forall ((V a)) (let ((_let_1 (polyno439679028le_C_a V))) (= (polyno1884029055head_a _let_1) _let_1))) (forall ((A a) (B a)) (=> (not (= A zero_zero_a)) (=> (not (= B zero_zero_a)) (not (= ((times_times_a A) B) zero_zero_a))))) (forall ((P polyno727731844poly_a) (N0 nat)) (let ((_let_1 (polyno439679028le_C_a zero_zero_a))) (=> ((polyno1372495879olyh_a P) N0) (= (= (polyno1884029055head_a P) _let_1) (= P _let_1))))) (forall ((Bs2 list_a) (P polyno727731844poly_a) (Q polyno727731844poly_a)) (let ((_let_1 (polyno896877631f_bs_a Bs2))) (=> (_let_1 P) (=> (_let_1 Q) (_let_1 ((polyno1934269411ymul_a P) Q)))))) (= plus_plus_nat (lambda ((A2 nat) (B2 nat)) ((plus_plus_nat B2) A2))) (forall ((X1 a) (X2 nat)) (not (= (polyno439679028le_C_a X1) (polyno2024845497ound_a X2)))) (forall ((K2 nat) (M nat) (N nat)) (let ((_let_1 (times_times_nat K2))) (= (= (_let_1 M) (_let_1 N)) (or (= M N) (= K2 zero_zero_nat))))) (forall ((A nat) (B nat)) (=> (not (= ((times_times_nat A) B) zero_zero_nat)) (and (not (= A zero_zero_nat)) (not (= B zero_zero_nat))))) (forall ((M nat) (N nat) (K2 nat)) (= ((times_times_nat ((plus_plus_nat M) N)) K2) ((plus_plus_nat ((times_times_nat M) K2)) ((times_times_nat N) K2)))) (forall ((Bs2 list_nat) (P polyno1532895200ly_nat) (Q polyno1532895200ly_nat)) (let ((_let_1 (polyno1438831695bs_nat Bs2))) (=> (_let_1 P) (=> (_let_1 Q) (_let_1 ((polyno929799083ul_nat P) Q)))))) (forall ((Y a) (V polyno727731844poly_a) (Va polyno727731844poly_a)) (let ((_let_1 ((polyno975704247_Sub_a V) Va))) (= ((polyno562434098cmul_a Y) _let_1) ((polyno1934269411ymul_a (polyno439679028le_C_a Y)) _let_1)))) (forall ((F (-> polyno1532895200ly_nat polyno1532895200ly_nat)) (N nat) (X polyno1532895200ly_nat)) (let ((_let_1 ((compow808008746ly_nat N) F))) (= (F (_let_1 X)) (_let_1 (F X))))) (forall ((A polyno727731844poly_a) (V polyno727731844poly_a) (Va polyno727731844poly_a)) (let ((_let_1 ((polyno1623170614_Add_a V) Va))) (= ((polyno1934269411ymul_a A) _let_1) ((polyno1491482291_Mul_a A) _let_1)))) (forall ((A nat) (B nat) (C nat)) (let ((_let_1 (plus_plus_nat A))) (= (= (_let_1 B) (_let_1 C)) (= B C)))) (forall ((P polyno727731844poly_a)) (not (= (polyno784948432ift1_a P) (polyno439679028le_C_a zero_zero_a)))) (forall ((C polyno727731844poly_a) (N nat) (P polyno727731844poly_a) (N0 nat)) (=> ((polyno1372495879olyh_a (((polyno1057396216e_CN_a C) N) P)) N0) (= ((polyno1674775833reen_a C) N) zero_zero_nat))) (forall ((Vc nat) (V polyno727731844poly_a) (Va nat) (Vb polyno727731844poly_a)) (let ((_let_1 (((polyno1057396216e_CN_a V) Va) Vb))) (let ((_let_2 (polyno2024845497ound_a Vc))) (= ((polyno1934269411ymul_a _let_2) _let_1) ((polyno1491482291_Mul_a _let_2) _let_1))))) (forall ((P polyno1532895200ly_nat) (N0 nat) (M nat)) (let ((_let_1 (polyno2122022170_C_nat zero_zero_nat))) (=> ((polyno892049031yh_nat P) N0) (= (= ((polyno544860353dn_nat P) M) _let_1) (= P _let_1))))) (forall ((Vc nat) (V polyno1532895200ly_nat) (Va nat) (Vb polyno1532895200ly_nat)) (let ((_let_1 (((polyno720942678CN_nat V) Va) Vb))) (let ((_let_2 (polyno1999838549nd_nat Vc))) (= ((polyno929799083ul_nat _let_2) _let_1) ((polyno1415441627ul_nat _let_2) _let_1))))) (forall ((X1 nat) (X2 nat)) (not (= (polyno2122022170_C_nat X1) (polyno1999838549nd_nat X2)))) (forall ((X1 nat) (X71 polyno1532895200ly_nat) (X72 nat)) (not (= (polyno2122022170_C_nat X1) ((polyno359287218Pw_nat X71) X72)))) (= polyno1884029055head_a (lambda ((P2 polyno727731844poly_a)) ((polyno567601229eadn_a P2) zero_zero_nat))) (forall ((Bs2 list_a) (A polyno727731844poly_a) (B polyno727731844poly_a)) (let ((_let_1 (polyno422358502poly_a Bs2))) (= (_let_1 ((polyno1623170614_Add_a A) B)) ((plus_plus_a (_let_1 A)) (_let_1 B))))) (forall ((T polyno1532895200ly_nat) (A polyno1532895200ly_nat) (B polyno1532895200ly_nat)) (let ((_let_1 (polyno336795754t0_nat T))) (= (_let_1 ((polyno1222032024dd_nat A) B)) ((polyno1222032024dd_nat (_let_1 A)) (_let_1 B))))) (forall ((Y nat) (V polyno1532895200ly_nat) (Va nat)) (let ((_let_1 ((polyno359287218Pw_nat V) Va))) (= ((polyno1467023772ul_nat Y) _let_1) ((polyno929799083ul_nat (polyno2122022170_C_nat Y)) _let_1)))) (forall ((N nat) (F (-> polyno727731844poly_a polyno727731844poly_a)) (P polyno727731844poly_a) (K2 nat)) (=> (forall ((P4 polyno727731844poly_a)) (=> ((polyno1372495879olyh_a P4) N) ((polyno1372495879olyh_a (F P4)) N))) (=> ((polyno1372495879olyh_a P) N) ((polyno1372495879olyh_a (((compow1114216044poly_a K2) F) P)) N)))) (forall ((X polyno727731844poly_a) (Y (-> nat nat))) (=> (= (polyno1674775833reen_a X) Y) (=> (forall ((C3 polyno727731844poly_a) (N3 nat) (P4 polyno727731844poly_a)) (=> (= X (((polyno1057396216e_CN_a C3) N3) P4)) (not (= Y (lambda ((M2 nat)) (((if_nat (= N3 M2)) ((plus_plus_nat one_one_nat) ((polyno1674775833reen_a P4) N3))) zero_zero_nat)))))) (=> (=> (exists ((V2 a)) (= X (polyno439679028le_C_a V2))) (not (= Y (lambda ((M2 nat)) zero_zero_nat)))) (=> (=> (exists ((V2 nat)) (= X (polyno2024845497ound_a V2))) (not (= Y (lambda ((M2 nat)) zero_zero_nat)))) (=> (=> (exists ((V2 polyno727731844poly_a) (Va2 polyno727731844poly_a)) (= X ((polyno1623170614_Add_a V2) Va2))) (not (= Y (lambda ((M2 nat)) zero_zero_nat)))) (=> (=> (exists ((V2 polyno727731844poly_a) (Va2 polyno727731844poly_a)) (= X ((polyno975704247_Sub_a V2) Va2))) (not (= Y (lambda ((M2 nat)) zero_zero_nat)))) (=> (=> (exists ((V2 polyno727731844poly_a) (Va2 polyno727731844poly_a)) (= X ((polyno1491482291_Mul_a V2) Va2))) (not (= Y (lambda ((M2 nat)) zero_zero_nat)))) (=> (=> (exists ((V2 polyno727731844poly_a)) (= X (polyno96675367_Neg_a V2))) (not (= Y (lambda ((M2 nat)) zero_zero_nat)))) (not (=> (exists ((V2 polyno727731844poly_a) (Va2 nat)) (= X ((polyno1538138524e_Pw_a V2) Va2))) (not (= Y (lambda ((M2 nat)) zero_zero_nat)))))))))))))) (forall ((X nat)) (= (= zero_zero_nat X) (= X zero_zero_nat))) (forall ((C polyno1532895200ly_nat) (N nat) (P polyno1532895200ly_nat) (N0 nat)) (=> ((polyno892049031yh_nat (((polyno720942678CN_nat C) N) P)) N0) (= ((polyno1779722485en_nat C) N) zero_zero_nat))) (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 ((X nat) (Y nat)) (= (((if_nat true) X) Y) X)) (forall ((P polyno727731844poly_a) (N0 nat) (Q polyno727731844poly_a) (N1 nat)) (=> ((polyno1372495879olyh_a P) N0) (=> ((polyno1372495879olyh_a Q) N1) (= (= ((polyno1418491367ysub_a P) Q) (polyno439679028le_C_a zero_zero_a)) (= P Q))))) (forall ((P5 (-> nat nat Bool)) (A nat) (B nat)) (=> (forall ((A4 nat) (B4 nat)) (= ((P5 A4) B4) ((P5 B4) A4))) (=> (forall ((A4 nat)) ((P5 A4) zero_zero_nat)) (=> (forall ((A4 nat) (B4 nat)) (let ((_let_1 (P5 A4))) (=> (_let_1 B4) (_let_1 ((plus_plus_nat A4) B4))))) ((P5 A) B))))) (forall ((M nat) (N nat)) (=> (= M ((times_times_nat M) N)) (or (= N one_one_nat) (= M zero_zero_nat)))) (forall ((N nat)) ((polyno1372495879olyh_a (polyno439679028le_C_a one_one_a)) N)) (forall ((C2 a) (C polyno727731844poly_a) (N nat) (P polyno727731844poly_a)) (let ((_let_1 (polyno439679028le_C_a C2))) (let ((_let_2 ((polyno1934269411ymul_a (((polyno1057396216e_CN_a C) N) P)) _let_1))) (let ((_let_3 (= C2 zero_zero_a))) (and (=> (not _let_3) (= _let_2 (((polyno1057396216e_CN_a ((polyno1934269411ymul_a C) _let_1)) N) ((polyno1934269411ymul_a P) _let_1)))) (=> _let_3 (= _let_2 (polyno439679028le_C_a zero_zero_a)))))))) (forall ((V polyno1532895200ly_nat) (Va nat) (Vb polyno1532895200ly_nat) (Vc polyno1532895200ly_nat) (Vd nat)) (let ((_let_1 ((polyno359287218Pw_nat Vc) Vd))) (let ((_let_2 (((polyno720942678CN_nat V) Va) Vb))) (= ((polyno929799083ul_nat _let_2) _let_1) ((polyno1415441627ul_nat _let_2) _let_1))))) (forall ((A a)) (= ((times_times_a zero_zero_a) A) zero_zero_a)) (forall ((V polyno1532895200ly_nat) (Va polyno1532895200ly_nat)) (= (polyno587244178ad_nat ((polyno1415441627ul_nat V) Va)) (polyno2122022170_C_nat zero_zero_nat))) (forall ((X51 polyno727731844poly_a) (X52 polyno727731844poly_a) (Y51 polyno727731844poly_a) (Y52 polyno727731844poly_a)) (= (= ((polyno1491482291_Mul_a X51) X52) ((polyno1491482291_Mul_a Y51) Y52)) (and (= X51 Y51) (= X52 Y52)))) (forall ((K2 nat) (M nat) (N nat)) (let ((_let_1 (times_times_nat K2))) (= (= (_let_1 M) (_let_1 N)) (or (= M N) (= K2 zero_zero_nat))))) (forall ((V polyno727731844poly_a) (Va polyno727731844poly_a) (B polyno727731844poly_a)) (let ((_let_1 ((polyno1491482291_Mul_a V) Va))) (= ((polyno1934269411ymul_a _let_1) B) ((polyno1491482291_Mul_a _let_1) B)))) (forall ((V a)) (= (polyno212464073eriv_a (polyno439679028le_C_a V)) (polyno439679028le_C_a zero_zero_a))) (forall ((K2 nat) (M nat) (N nat)) (let ((_let_1 (times_times_nat K2))) (= (_let_1 ((plus_plus_nat M) N)) ((plus_plus_nat (_let_1 M)) (_let_1 N))))) (forall ((B nat) (A nat) (C nat)) (= (= ((plus_plus_nat B) A) ((plus_plus_nat C) A)) (= B C))) (forall ((A nat)) (= ((times_times_nat A) zero_zero_nat) zero_zero_nat)) _let_5 (forall ((R nat) (A nat) (B nat) (C nat) (D nat)) (let ((_let_1 (times_times_nat R))) (=> (not (= R zero_zero_nat)) (=> (and (not (= C D)) (= A B)) (not (= ((plus_plus_nat A) (_let_1 C)) ((plus_plus_nat B) (_let_1 D)))))))) (forall ((V polyno727731844poly_a) (Va polyno727731844poly_a)) (= (polyno1465139388head_a ((polyno975704247_Sub_a V) Va)) (polyno439679028le_C_a zero_zero_a))) (forall ((V a)) (= (polyno1465139388head_a (polyno439679028le_C_a V)) (polyno439679028le_C_a zero_zero_a))) (forall ((A nat) (B nat) (C nat)) (= ((times_times_nat ((plus_plus_nat A) B)) C) ((plus_plus_nat ((times_times_nat A) C)) ((times_times_nat B) C)))) (forall ((A nat)) (= ((times_times_nat one_one_nat) A) A)) (forall ((M nat)) (= ((times_times_nat M) zero_zero_nat) zero_zero_nat)) (forall ((V nat)) (= (polyno578545843gree_a (polyno2024845497ound_a V)) zero_zero_nat)) (forall ((T polyno1532895200ly_nat) (C nat)) (let ((_let_1 (polyno2122022170_C_nat C))) (= ((polyno336795754t0_nat T) _let_1) _let_1))) (forall ((P polyno727731844poly_a) (N nat)) (=> ((polyno1372495879olyh_a P) N) ((polyno1372495879olyh_a (polyno1465139388head_a P)) N))) (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 ((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 ((V polyno727731844poly_a) (Va polyno727731844poly_a)) (= (polyno567601229eadn_a ((polyno1623170614_Add_a V) Va)) (lambda ((M2 nat)) ((polyno1623170614_Add_a V) Va)))) (forall ((A nat)) (= ((plus_plus_nat zero_zero_nat) A) A)) (forall ((C2 nat) (C polyno1532895200ly_nat) (N nat) (P polyno1532895200ly_nat)) (let ((_let_1 (polyno2122022170_C_nat C2))) (let ((_let_2 ((polyno929799083ul_nat (((polyno720942678CN_nat C) N) P)) _let_1))) (let ((_let_3 (= C2 zero_zero_nat))) (and (=> (not _let_3) (= _let_2 (((polyno720942678CN_nat ((polyno929799083ul_nat C) _let_1)) N) ((polyno929799083ul_nat P) _let_1)))) (=> _let_3 (= _let_2 (polyno2122022170_C_nat zero_zero_nat)))))))) (forall ((X1 nat) (X31 polyno1532895200ly_nat) (X32 polyno1532895200ly_nat)) (not (= (polyno2122022170_C_nat X1) ((polyno1222032024dd_nat X31) X32)))) (forall ((P polyno727731844poly_a) (N0 nat) (Q polyno727731844poly_a) (N1 nat)) (=> ((polyno1372495879olyh_a P) N0) (=> ((polyno1372495879olyh_a Q) N1) (= (forall ((Bs list_a)) (let ((_let_1 (polyno422358502poly_a Bs))) (= (_let_1 P) (_let_1 Q)))) (= P Q))))) (forall ((A polyno1532895200ly_nat) (V nat)) (let ((_let_1 (polyno1999838549nd_nat V))) (= ((polyno929799083ul_nat A) _let_1) ((polyno1415441627ul_nat A) _let_1)))) (forall ((P polyno727731844poly_a) (N0 nat)) (=> ((polyno1372495879olyh_a P) N0) (= (= (polyno2115742616onst_a P) zero_zero_a) (= P (polyno439679028le_C_a zero_zero_a))))) (forall ((P polyno1532895200ly_nat) (N0 nat)) (=> ((polyno892049031yh_nat P) N0) (=> (not (= P (polyno2122022170_C_nat zero_zero_nat))) ((polyno892049031yh_nat (polyno1964927358t1_nat P)) zero_zero_nat)))) (forall ((M nat) (N nat)) (= (= one_one_nat ((times_times_nat M) N)) (and (= N one_one_nat) (= M one_one_nat)))) (forall ((V polyno1532895200ly_nat) (Va polyno1532895200ly_nat)) (= (polyno1779722485en_nat ((polyno1415441627ul_nat V) Va)) (lambda ((M2 nat)) zero_zero_nat))) (forall ((P polyno727731844poly_a) (N nat)) (=> (polyno190918219poly_a P) (=> (not (= P (polyno439679028le_C_a zero_zero_a))) (polyno190918219poly_a (((compow1114216044poly_a N) polyno784948432ift1_a) P))))) (forall ((V polyno727731844poly_a) (Va polyno727731844poly_a) (B polyno727731844poly_a)) (let ((_let_1 ((polyno1623170614_Add_a V) Va))) (= ((polyno1934269411ymul_a _let_1) B) ((polyno1491482291_Mul_a _let_1) B)))) (forall ((A nat) (C nat) (B nat)) (= (= ((times_times_nat A) C) ((times_times_nat B) C)) (or (= A B) (= C zero_zero_nat)))) (forall ((X2 nat) (X51 polyno727731844poly_a) (X52 polyno727731844poly_a)) (not (= (polyno2024845497ound_a X2) ((polyno1491482291_Mul_a X51) X52)))) (forall ((X2 nat) (X51 polyno1532895200ly_nat) (X52 polyno1532895200ly_nat)) (not (= (polyno1999838549nd_nat X2) ((polyno1415441627ul_nat X51) X52)))) (forall ((F (-> polyno727731844poly_a polyno727731844poly_a)) (X polyno727731844poly_a)) (= (((compow1114216044poly_a zero_zero_nat) F) X) X)) (forall ((C a)) (let ((_let_1 (polyno439679028le_C_a C))) (= (polyno955999183nate_a _let_1) _let_1))) (forall ((V polyno727731844poly_a) (Va polyno727731844poly_a)) (let ((_let_1 ((polyno1491482291_Mul_a V) Va))) (= (polyno1884029055head_a _let_1) _let_1))) (forall ((N nat) (T polyno1532895200ly_nat)) (let ((_let_1 (polyno1999838549nd_nat N))) (let ((_let_2 ((polyno336795754t0_nat T) _let_1))) (let ((_let_3 (= N zero_zero_nat))) (and (=> _let_3 (= _let_2 T)) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((X1 a) (X31 polyno727731844poly_a) (X32 polyno727731844poly_a)) (not (= (polyno439679028le_C_a X1) ((polyno1623170614_Add_a X31) X32)))) (forall ((X1 nat) (Y1 nat)) (= (= (polyno2122022170_C_nat X1) (polyno2122022170_C_nat Y1)) (= X1 Y1))) (forall ((A a) (B a) (C a)) (= ((times_times_a ((plus_plus_a A) B)) C) ((plus_plus_a ((times_times_a A) C)) ((times_times_a B) C)))) (forall ((V nat)) (= (polyno1674775833reen_a (polyno2024845497ound_a V)) (lambda ((M2 nat)) zero_zero_nat))) (forall ((V polyno727731844poly_a) (Va nat) (Vb polyno727731844poly_a) (Vc nat)) (let ((_let_1 (polyno2024845497ound_a Vc))) (let ((_let_2 (((polyno1057396216e_CN_a V) Va) Vb))) (= ((polyno1934269411ymul_a _let_2) _let_1) ((polyno1491482291_Mul_a _let_2) _let_1))))) (forall ((C a) (A a)) (= (= ((times_times_a C) A) C) (or (= A one_one_a) (= C zero_zero_a)))) (forall ((X nat) (Y nat)) (= (((if_nat false) X) Y) Y)) (forall ((V nat)) (= (polyno587244178ad_nat (polyno1999838549nd_nat V)) (polyno2122022170_C_nat zero_zero_nat))) (= polyno1952548879ad_nat (lambda ((P2 polyno1532895200ly_nat)) ((polyno544860353dn_nat P2) zero_zero_nat))) (forall ((P polyno727731844poly_a) (N0 nat)) (=> ((polyno1372495879olyh_a P) N0) (= ((polyno1934269411ymul_a P) (polyno439679028le_C_a one_one_a)) P))) (forall ((A nat) (B nat)) (=> (= ((times_times_nat A) B) zero_zero_nat) (or (= A zero_zero_nat) (= B zero_zero_nat)))) (forall ((V polyno1532895200ly_nat) (Va polyno1532895200ly_nat)) (let ((_let_1 ((polyno1415441627ul_nat V) Va))) (= (polyno1952548879ad_nat _let_1) _let_1))) (forall ((Y nat) (X nat)) (= ((polyno1467023772ul_nat Y) (polyno2122022170_C_nat X)) (polyno2122022170_C_nat ((times_times_nat Y) X)))) (forall ((V polyno727731844poly_a) (Va nat)) (= (polyno1372495879olyh_a ((polyno1538138524e_Pw_a V) Va)) (lambda ((K nat)) false))) (forall ((P polyno727731844poly_a) (N0 nat)) (=> ((polyno1372495879olyh_a P) N0) (= ((polyno1934269411ymul_a (polyno439679028le_C_a one_one_a)) P) P))) (forall ((P5 Bool)) (or (= P5 false) (= P5 true))) (forall ((C polyno727731844poly_a) (P polyno727731844poly_a)) (= (polyno1884029055head_a (((polyno1057396216e_CN_a C) zero_zero_nat) P)) (polyno1884029055head_a P))) _let_4 (forall ((V nat)) (= (polyno1372495879olyh_a (polyno2024845497ound_a V)) (lambda ((K nat)) false))) (forall ((V polyno1532895200ly_nat) (Va polyno1532895200ly_nat) (B polyno1532895200ly_nat)) (let ((_let_1 ((polyno1222032024dd_nat V) Va))) (= ((polyno929799083ul_nat _let_1) B) ((polyno1415441627ul_nat _let_1) B)))) (forall ((A polyno1532895200ly_nat) (V polyno1532895200ly_nat) (Va polyno1532895200ly_nat)) (let ((_let_1 ((polyno1415441627ul_nat V) Va))) (= ((polyno929799083ul_nat A) _let_1) ((polyno1415441627ul_nat A) _let_1)))) (forall ((A nat) (B nat)) (= (= A ((plus_plus_nat A) B)) (= B zero_zero_nat))) (forall ((A a) (B a)) (= (= ((times_times_a A) B) zero_zero_a) (or (= A zero_zero_a) (= B zero_zero_a)))) (forall ((M nat) (K2 nat) (N nat)) (= (= ((times_times_nat M) K2) ((times_times_nat N) K2)) (or (= K2 zero_zero_nat) (= M N)))) (forall ((X51 polyno727731844poly_a) (X52 polyno727731844poly_a) (X81 polyno727731844poly_a) (X82 nat) (X83 polyno727731844poly_a)) (not (= ((polyno1491482291_Mul_a X51) X52) (((polyno1057396216e_CN_a X81) X82) X83)))) (forall ((A nat) (E nat) (B nat) (C nat)) (= ((plus_plus_nat ((times_times_nat A) E)) ((plus_plus_nat ((times_times_nat B) E)) C)) ((plus_plus_nat ((times_times_nat ((plus_plus_nat A) B)) E)) C))) (forall ((C a) (A a) (B a)) (let ((_let_1 (times_times_a C))) (=> (not (= C zero_zero_a)) (= (= (_let_1 A) (_let_1 B)) (= A B))))) (= polyno190918219poly_a (lambda ((P2 polyno727731844poly_a)) ((polyno1372495879olyh_a P2) zero_zero_nat))) (= polyno784948432ift1_a ((polyno1057396216e_CN_a (polyno439679028le_C_a zero_zero_a)) zero_zero_nat)) (forall ((A a)) (= ((times_times_a A) one_one_a) A)) (forall ((V nat)) (= (polyno544860353dn_nat (polyno1999838549nd_nat V)) (lambda ((M2 nat)) (polyno1999838549nd_nat V)))) (forall ((V nat)) (= (polyno567601229eadn_a (polyno2024845497ound_a V)) (lambda ((M2 nat)) (polyno2024845497ound_a V)))) (forall ((Y nat) (V polyno1532895200ly_nat) (Va polyno1532895200ly_nat)) (let ((_let_1 ((polyno1222032024dd_nat V) Va))) (= ((polyno1467023772ul_nat Y) _let_1) ((polyno929799083ul_nat (polyno2122022170_C_nat Y)) _let_1)))) (forall ((A a) (B a) (C a)) (= ((times_times_a ((plus_plus_a A) B)) C) ((plus_plus_a ((times_times_a A) C)) ((times_times_a B) C)))) _let_3 (forall ((P polyno1532895200ly_nat) (N0 nat)) (let ((_let_1 (polyno2122022170_C_nat zero_zero_nat))) (=> ((polyno892049031yh_nat P) N0) (= (= (polyno1952548879ad_nat P) _let_1) (= P _let_1))))) (forall ((N nat)) (= (polyno524777654st_nat (polyno2122022170_C_nat N)) N)) (= (polyno1510045887ow_nat zero_zero_nat) (lambda ((P2 polyno1532895200ly_nat)) (polyno2122022170_C_nat one_one_nat))) (forall ((N nat)) (= ((times_times_nat N) one_one_nat) N)) (forall ((N nat) (M nat) (F (-> polyno1532895200ly_nat polyno1532895200ly_nat))) (= ((compow808008746ly_nat N) ((compow808008746ly_nat M) F)) ((compow808008746ly_nat ((times_times_nat M) N)) F))) (forall ((C nat)) (= (polyno892049031yh_nat (polyno2122022170_C_nat C)) (lambda ((K nat)) true))) (forall ((C a) (C2 a)) (= ((polyno1934269411ymul_a (polyno439679028le_C_a C)) (polyno439679028le_C_a C2)) (polyno439679028le_C_a ((times_times_a C) C2)))) (forall ((Bs2 list_a) (C a) (P polyno727731844poly_a)) (let ((_let_1 (polyno422358502poly_a Bs2))) (= (_let_1 ((polyno562434098cmul_a C) P)) (_let_1 ((polyno1491482291_Mul_a (polyno439679028le_C_a C)) P))))) (forall ((N nat)) ((polyno1372495879olyh_a (polyno439679028le_C_a zero_zero_a)) N)) (forall ((V nat)) (= (polyno212464073eriv_a (polyno2024845497ound_a V)) (polyno439679028le_C_a zero_zero_a))) (forall ((A nat)) (= ((times_times_nat A) one_one_nat) A)) (forall ((I nat) (U nat) (J nat) (K2 nat)) (= ((plus_plus_nat ((times_times_nat I) U)) ((plus_plus_nat ((times_times_nat J) U)) K2)) ((plus_plus_nat ((times_times_nat ((plus_plus_nat I) J)) U)) K2))) (forall ((V a)) (= (polyno1674775833reen_a (polyno439679028le_C_a V)) (lambda ((M2 nat)) zero_zero_nat))) (forall ((Y nat) (C polyno1532895200ly_nat) (N nat) (P polyno1532895200ly_nat)) (let ((_let_1 (polyno1467023772ul_nat Y))) (= (_let_1 (((polyno720942678CN_nat C) N) P)) (((polyno720942678CN_nat (_let_1 C)) N) (_let_1 P))))) ((polyno1372495879olyh_a q) n1) (forall ((N a)) (= (polyno2115742616onst_a (polyno439679028le_C_a N)) N)) (forall ((X nat)) (= (= one_one_nat X) (= X one_one_nat))) (forall ((X1 a) (X81 polyno727731844poly_a) (X82 nat) (X83 polyno727731844poly_a)) (not (= (polyno439679028le_C_a X1) (((polyno1057396216e_CN_a X81) X82) X83)))) (forall ((V polyno727731844poly_a) (Va nat) (Vb polyno727731844poly_a) (Vc polyno727731844poly_a) (Vd polyno727731844poly_a)) (let ((_let_1 ((polyno1491482291_Mul_a Vc) Vd))) (let ((_let_2 (((polyno1057396216e_CN_a V) Va) Vb))) (= ((polyno1934269411ymul_a _let_2) _let_1) ((polyno1491482291_Mul_a _let_2) _let_1))))) (forall ((Y nat) (V nat)) (let ((_let_1 (polyno1999838549nd_nat V))) (= ((polyno1467023772ul_nat Y) _let_1) ((polyno929799083ul_nat (polyno2122022170_C_nat Y)) _let_1)))) (forall ((C nat) (A nat) (B nat)) (let ((_let_1 (times_times_nat C))) (= (= (_let_1 A) (_let_1 B)) (or (= A B) (= C zero_zero_nat))))) (forall ((P polyno727731844poly_a) (N0 nat) (Q polyno727731844poly_a) (N1 nat)) (let ((_let_1 (polyno439679028le_C_a zero_zero_a))) (=> ((polyno1372495879olyh_a P) N0) (=> ((polyno1372495879olyh_a Q) N1) (= (= ((polyno1934269411ymul_a P) Q) _let_1) (or (= P _let_1) (= Q _let_1))))))) (forall ((B a) (A a) (C a)) (let ((_let_1 (times_times_a B))) (let ((_let_2 (times_times_a A))) (= (_let_1 (_let_2 C)) (_let_2 (_let_1 C)))))) (forall ((C polyno727731844poly_a) (N nat) (P polyno727731844poly_a)) (= (polyno955999183nate_a (((polyno1057396216e_CN_a C) N) P)) (polyno955999183nate_a ((polyno1623170614_Add_a C) ((polyno1491482291_Mul_a (polyno2024845497ound_a N)) P))))) (forall ((V polyno727731844poly_a) (Va polyno727731844poly_a)) (= (polyno1372495879olyh_a ((polyno1491482291_Mul_a V) Va)) (lambda ((K nat)) false))) (forall ((V nat)) (= (polyno544860353dn_nat (polyno2122022170_C_nat V)) (lambda ((M2 nat)) (polyno2122022170_C_nat V)))) (forall ((X31 polyno727731844poly_a) (X32 polyno727731844poly_a) (X51 polyno727731844poly_a) (X52 polyno727731844poly_a)) (not (= ((polyno1623170614_Add_a X31) X32) ((polyno1491482291_Mul_a X51) X52)))) (forall ((X1 a) (Y1 a)) (= (= (polyno439679028le_C_a X1) (polyno439679028le_C_a Y1)) (= X1 Y1))) (forall ((N nat)) (= ((plus_plus_nat zero_zero_nat) N) N)) (forall ((Vc polyno1532895200ly_nat) (Vd nat) (V polyno1532895200ly_nat) (Va nat) (Vb polyno1532895200ly_nat)) (let ((_let_1 (((polyno720942678CN_nat V) Va) Vb))) (let ((_let_2 ((polyno359287218Pw_nat Vc) Vd))) (= ((polyno929799083ul_nat _let_2) _let_1) ((polyno1415441627ul_nat _let_2) _let_1))))) (forall ((P polyno727731844poly_a) (N0 nat)) (let ((_let_1 (polyno439679028le_C_a zero_zero_a))) (=> ((polyno1372495879olyh_a P) N0) (= ((polyno1934269411ymul_a P) _let_1) _let_1)))) (forall ((N nat) (T polyno1532895200ly_nat) (C polyno1532895200ly_nat) (P polyno1532895200ly_nat)) (let ((_let_1 (polyno336795754t0_nat T))) (let ((_let_2 (_let_1 P))) (let ((_let_3 (_let_1 C))) (let ((_let_4 (_let_1 (((polyno720942678CN_nat C) N) P)))) (let ((_let_5 (= N zero_zero_nat))) (and (=> _let_5 (= _let_4 ((polyno1222032024dd_nat _let_3) ((polyno1415441627ul_nat T) _let_2)))) (=> (not _let_5) (= _let_4 (((polyno720942678CN_nat _let_3) N) _let_2)))))))))) (forall ((C polyno1532895200ly_nat) (N nat) (P polyno1532895200ly_nat)) (= (polyno524777654st_nat (((polyno720942678CN_nat C) N) P)) (polyno524777654st_nat P))) (forall ((B nat) (A nat) (C nat)) (=> (= ((plus_plus_nat B) A) ((plus_plus_nat C) A)) (= B C))) (forall ((V polyno727731844poly_a) (Va nat) (Vb polyno727731844poly_a) (Vc polyno727731844poly_a) (Vd polyno727731844poly_a)) (let ((_let_1 ((polyno1623170614_Add_a Vc) Vd))) (let ((_let_2 (((polyno1057396216e_CN_a V) Va) Vb))) (= ((polyno1934269411ymul_a _let_2) _let_1) ((polyno1491482291_Mul_a _let_2) _let_1))))) (forall ((V polyno1532895200ly_nat) (Va nat)) (= (polyno587244178ad_nat ((polyno359287218Pw_nat V) Va)) (polyno2122022170_C_nat zero_zero_nat))) (forall ((A a) (B a) (C a)) (let ((_let_1 (times_times_a A))) (= ((times_times_a (_let_1 B)) C) (_let_1 ((times_times_a B) C))))) (forall ((V polyno727731844poly_a) (Va polyno727731844poly_a) (B polyno727731844poly_a)) (let ((_let_1 ((polyno975704247_Sub_a V) Va))) (= ((polyno1934269411ymul_a _let_1) B) ((polyno1491482291_Mul_a _let_1) B)))) (forall ((Y nat) (V polyno1532895200ly_nat) (Va polyno1532895200ly_nat)) (let ((_let_1 ((polyno1921014231ub_nat V) Va))) (= ((polyno1467023772ul_nat Y) _let_1) ((polyno929799083ul_nat (polyno2122022170_C_nat Y)) _let_1)))) (forall ((A nat) (B nat) (C nat)) (let ((_let_1 (plus_plus_nat A))) (=> (= (_let_1 B) (_let_1 C)) (= B C)))) (forall ((Bs2 list_a) (C a)) (= ((polyno422358502poly_a Bs2) (polyno439679028le_C_a C)) C)) (forall ((X31 polyno1532895200ly_nat) (X32 polyno1532895200ly_nat) (X81 polyno1532895200ly_nat) (X82 nat) (X83 polyno1532895200ly_nat)) (not (= ((polyno1222032024dd_nat X31) X32) (((polyno720942678CN_nat X81) X82) X83)))) (forall ((A a)) (= ((times_times_a A) zero_zero_a) zero_zero_a)) (forall ((A nat)) (= ((times_times_nat one_one_nat) A) A)) (forall ((V polyno1532895200ly_nat) (Va polyno1532895200ly_nat)) (= (polyno220183259ee_nat ((polyno1222032024dd_nat V) Va)) zero_zero_nat)) (forall ((C polyno1532895200ly_nat) (N nat) (P polyno1532895200ly_nat) (N0 nat)) (=> ((polyno892049031yh_nat (((polyno720942678CN_nat C) N) P)) N0) (= (polyno220183259ee_nat C) zero_zero_nat))) (forall ((V polyno727731844poly_a) (Va nat) (B polyno727731844poly_a)) (let ((_let_1 ((polyno1538138524e_Pw_a V) Va))) (= ((polyno1934269411ymul_a _let_1) B) ((polyno1491482291_Mul_a _let_1) B)))) (forall ((V polyno1532895200ly_nat) (Va nat) (Vb polyno1532895200ly_nat) (Vc polyno1532895200ly_nat) (Vd polyno1532895200ly_nat)) (let ((_let_1 ((polyno1222032024dd_nat Vc) Vd))) (let ((_let_2 (((polyno720942678CN_nat V) Va) Vb))) (= ((polyno929799083ul_nat _let_2) _let_1) ((polyno1415441627ul_nat _let_2) _let_1))))) (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 nat)) (= ((plus_plus_nat A) zero_zero_nat) A)) (forall ((M nat) (N nat)) (= (= ((times_times_nat M) N) zero_zero_nat) (or (= M zero_zero_nat) (= N zero_zero_nat)))) (forall ((P polyno1532895200ly_nat)) (=> (polyno1013235523ly_nat P) (=> (not (= P (polyno2122022170_C_nat zero_zero_nat))) (polyno1013235523ly_nat (polyno1964927358t1_nat P))))) (forall ((A nat) (B nat) (C nat)) (let ((_let_1 (plus_plus_nat A))) (= ((plus_plus_nat (_let_1 B)) C) (_let_1 ((plus_plus_nat B) C))))) (forall ((C polyno727731844poly_a) (P polyno727731844poly_a)) (= (polyno212464073eriv_a (((polyno1057396216e_CN_a C) zero_zero_nat) P)) ((polyno1006823949_aux_a one_one_a) P))) (forall ((V polyno1532895200ly_nat) (Va polyno1532895200ly_nat)) (= (polyno587244178ad_nat ((polyno1921014231ub_nat V) Va)) (polyno2122022170_C_nat zero_zero_nat))) (forall ((X81 polyno727731844poly_a) (X82 nat) (X83 polyno727731844poly_a) (Y81 polyno727731844poly_a) (Y82 nat) (Y83 polyno727731844poly_a)) (= (= (((polyno1057396216e_CN_a X81) X82) X83) (((polyno1057396216e_CN_a Y81) Y82) Y83)) (and (= X81 Y81) (= X82 Y82) (= X83 Y83)))) (forall ((P polyno1532895200ly_nat) (N0 nat)) (=> ((polyno892049031yh_nat P) N0) ((polyno892049031yh_nat (polyno1952548879ad_nat P)) N0))) (forall ((P polyno727731844poly_a) (Q polyno727731844poly_a)) (=> (polyno190918219poly_a P) (=> (polyno190918219poly_a Q) (polyno190918219poly_a ((polyno1934269411ymul_a P) Q))))) (forall ((X2 nat) (Y2 nat)) (= (= (polyno2024845497ound_a X2) (polyno2024845497ound_a Y2)) (= X2 Y2))) (not (= zero_zero_a one_one_a)) (forall ((P polyno1532895200ly_nat) (N nat)) (=> (polyno1013235523ly_nat P) (=> (not (= P (polyno2122022170_C_nat zero_zero_nat))) (polyno1013235523ly_nat (((compow808008746ly_nat N) polyno1964927358t1_nat) P))))) (forall ((A nat) (B nat)) (= (= ((times_times_nat A) B) zero_zero_nat) (or (= A zero_zero_nat) (= B zero_zero_nat)))) (forall ((V polyno1532895200ly_nat) (Va nat) (Vb polyno1532895200ly_nat) (Vc nat)) (let ((_let_1 (polyno1999838549nd_nat Vc))) (let ((_let_2 (((polyno720942678CN_nat V) Va) Vb))) (= ((polyno929799083ul_nat _let_2) _let_1) ((polyno1415441627ul_nat _let_2) _let_1))))) (forall ((V nat) (B polyno1532895200ly_nat)) (let ((_let_1 (polyno1999838549nd_nat V))) (= ((polyno929799083ul_nat _let_1) B) ((polyno1415441627ul_nat _let_1) B)))) (forall ((V polyno727731844poly_a) (Va polyno727731844poly_a)) (= (polyno212464073eriv_a ((polyno1491482291_Mul_a V) Va)) (polyno439679028le_C_a zero_zero_a))) (forall ((V nat)) (= (polyno220183259ee_nat (polyno2122022170_C_nat V)) zero_zero_nat)) (forall ((V polyno727731844poly_a) (Va nat) (Vb polyno727731844poly_a) (Vc polyno727731844poly_a) (Vd nat)) (let ((_let_1 ((polyno1538138524e_Pw_a Vc) Vd))) (let ((_let_2 (((polyno1057396216e_CN_a V) Va) Vb))) (= ((polyno1934269411ymul_a _let_2) _let_1) ((polyno1491482291_Mul_a _let_2) _let_1))))) (= polyno1964927358t1_nat ((polyno720942678CN_nat (polyno2122022170_C_nat zero_zero_nat)) zero_zero_nat)) (forall ((C a) (B a)) (= (= C ((times_times_a B) C)) (or (= B one_one_a) (= C zero_zero_a)))) (forall ((N nat) (T polyno727731844poly_a)) (let ((_let_1 (polyno2024845497ound_a N))) (let ((_let_2 ((polyno1397854436bst0_a T) _let_1))) (let ((_let_3 (= N zero_zero_nat))) (and (=> _let_3 (= _let_2 T)) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((X2 nat) (Y2 nat)) (= (= (polyno1999838549nd_nat X2) (polyno1999838549nd_nat Y2)) (= X2 Y2))) (forall ((A nat) (B nat) (C nat) (D nat)) (let ((_let_1 (times_times_nat B))) (let ((_let_2 (times_times_nat A))) (= (and (not (= A B)) (not (= C D))) (not (= ((plus_plus_nat (_let_2 C)) (_let_1 D)) ((plus_plus_nat (_let_2 D)) (_let_1 C)))))))) (forall ((X1 nat) (X81 polyno1532895200ly_nat) (X82 nat) (X83 polyno1532895200ly_nat)) (not (= (polyno2122022170_C_nat X1) (((polyno720942678CN_nat X81) X82) X83)))) (forall ((N nat)) ((polyno892049031yh_nat (polyno2122022170_C_nat zero_zero_nat)) N)) (forall ((V polyno1532895200ly_nat) (Va polyno1532895200ly_nat) (B polyno1532895200ly_nat)) (let ((_let_1 ((polyno1921014231ub_nat V) Va))) (= ((polyno929799083ul_nat _let_1) B) ((polyno1415441627ul_nat _let_1) B)))) (forall ((Vc polyno727731844poly_a) (Vd polyno727731844poly_a) (V polyno727731844poly_a) (Va nat) (Vb polyno727731844poly_a)) (let ((_let_1 (((polyno1057396216e_CN_a V) Va) Vb))) (let ((_let_2 ((polyno1623170614_Add_a Vc) Vd))) (= ((polyno1934269411ymul_a _let_2) _let_1) ((polyno1491482291_Mul_a _let_2) _let_1))))) _let_2 (forall ((X1 a) (X71 polyno727731844poly_a) (X72 nat)) (not (= (polyno439679028le_C_a X1) ((polyno1538138524e_Pw_a X71) X72)))) (forall ((X2 nat) (X31 polyno727731844poly_a) (X32 polyno727731844poly_a)) (not (= (polyno2024845497ound_a X2) ((polyno1623170614_Add_a X31) X32)))) (forall ((X51 polyno727731844poly_a) (X52 polyno727731844poly_a) (X71 polyno727731844poly_a) (X72 nat)) (not (= ((polyno1491482291_Mul_a X51) X52) ((polyno1538138524e_Pw_a X71) X72)))) (forall ((A nat)) (= ((plus_plus_nat zero_zero_nat) A) A)) (forall ((A polyno727731844poly_a) (V polyno727731844poly_a) (Va nat)) (let ((_let_1 ((polyno1538138524e_Pw_a V) Va))) (= ((polyno1934269411ymul_a A) _let_1) ((polyno1491482291_Mul_a A) _let_1)))) (forall ((A nat)) (= ((times_times_nat zero_zero_nat) A) zero_zero_nat)) (forall ((X2 nat) (X81 polyno727731844poly_a) (X82 nat) (X83 polyno727731844poly_a)) (not (= (polyno2024845497ound_a X2) (((polyno1057396216e_CN_a X81) X82) X83)))) (forall ((A nat) (B nat) (C nat)) (let ((_let_1 (times_times_nat A))) (= (_let_1 ((plus_plus_nat B) C)) ((plus_plus_nat (_let_1 B)) (_let_1 C))))) (forall ((Y a) (V polyno727731844poly_a) (Va polyno727731844poly_a)) (let ((_let_1 ((polyno1491482291_Mul_a V) Va))) (= ((polyno562434098cmul_a Y) _let_1) ((polyno1934269411ymul_a (polyno439679028le_C_a Y)) _let_1)))) (forall ((P polyno727731844poly_a) (N nat) (M nat)) (let ((_let_1 (polyno439679028le_C_a zero_zero_a))) (=> ((polyno1372495879olyh_a P) N) (=> (not (= P _let_1)) (not (= ((polyno567601229eadn_a P) M) _let_1)))))) (forall ((X2 nat) (X31 polyno1532895200ly_nat) (X32 polyno1532895200ly_nat)) (not (= (polyno1999838549nd_nat X2) ((polyno1222032024dd_nat X31) X32)))) (forall ((A polyno727731844poly_a) (V polyno727731844poly_a) (Va polyno727731844poly_a)) (let ((_let_1 ((polyno1491482291_Mul_a V) Va))) (= ((polyno1934269411ymul_a A) _let_1) ((polyno1491482291_Mul_a A) _let_1)))) (forall ((P polyno727731844poly_a) (N0 nat)) (=> ((polyno1372495879olyh_a P) N0) (= ((polyno1418491367ysub_a P) P) (polyno439679028le_C_a zero_zero_a)))) (forall ((P polyno727731844poly_a)) (=> (polyno190918219poly_a P) (=> (not (= P (polyno439679028le_C_a zero_zero_a))) (polyno190918219poly_a (polyno784948432ift1_a P))))) (forall ((Vc polyno727731844poly_a) (Vd polyno727731844poly_a) (V polyno727731844poly_a) (Va nat) (Vb polyno727731844poly_a)) (let ((_let_1 (((polyno1057396216e_CN_a V) Va) Vb))) (let ((_let_2 ((polyno1491482291_Mul_a Vc) Vd))) (= ((polyno1934269411ymul_a _let_2) _let_1) ((polyno1491482291_Mul_a _let_2) _let_1))))) (forall ((N a) (V polyno727731844poly_a) (Va polyno727731844poly_a)) (let ((_let_1 ((polyno1491482291_Mul_a V) Va))) (= ((polyno1006823949_aux_a N) _let_1) ((polyno562434098cmul_a N) _let_1)))) (= times_times_nat (lambda ((A2 nat) (B2 nat)) ((times_times_nat B2) A2))) (forall ((V nat)) (= (polyno1779722485en_nat (polyno2122022170_C_nat V)) (lambda ((M2 nat)) zero_zero_nat))) (forall ((A a)) (= ((times_times_a one_one_a) A) A)) (forall ((B nat) (A nat) (C nat)) (let ((_let_1 (plus_plus_nat B))) (let ((_let_2 (plus_plus_nat A))) (= (_let_1 (_let_2 C)) (_let_2 (_let_1 C)))))) (forall ((C nat) (A nat) (B nat)) (=> (not (= C zero_zero_nat)) (= (= ((times_times_nat A) C) ((times_times_nat B) C)) (= A B)))) (forall ((Y nat) (V polyno1532895200ly_nat)) (let ((_let_1 (polyno1366804583eg_nat V))) (= ((polyno1467023772ul_nat Y) _let_1) ((polyno929799083ul_nat (polyno2122022170_C_nat Y)) _let_1)))) (forall ((P polyno727731844poly_a) (N0 nat)) (=> ((polyno1372495879olyh_a P) N0) ((polyno1372495879olyh_a (polyno1884029055head_a P)) N0))) (forall ((F (-> polyno1532895200ly_nat polyno1532895200ly_nat)) (X polyno1532895200ly_nat)) (= (((compow808008746ly_nat zero_zero_nat) F) X) X)) (forall ((A nat) (B nat)) (= (= A ((plus_plus_nat B) A)) (= B zero_zero_nat))) (forall ((V polyno1532895200ly_nat) (Va polyno1532895200ly_nat)) (= (polyno892049031yh_nat ((polyno1222032024dd_nat V) Va)) (lambda ((K nat)) false))) (forall ((V polyno727731844poly_a)) (= (polyno1465139388head_a (polyno96675367_Neg_a V)) (polyno439679028le_C_a zero_zero_a))) (forall ((P polyno727731844poly_a) (Q polyno727731844poly_a)) (=> (polyno190918219poly_a P) (=> (polyno190918219poly_a Q) (polyno190918219poly_a ((polyno1418491367ysub_a P) Q))))) (forall ((X2 nat) (X81 polyno1532895200ly_nat) (X82 nat) (X83 polyno1532895200ly_nat)) (not (= (polyno1999838549nd_nat X2) (((polyno720942678CN_nat X81) X82) X83)))) (forall ((N nat)) (= (polyno955999183nate_a (polyno2024845497ound_a N)) (((polyno1057396216e_CN_a (polyno439679028le_C_a zero_zero_a)) N) (polyno439679028le_C_a one_one_a)))) (forall ((V polyno1532895200ly_nat) (Va polyno1532895200ly_nat) (B polyno1532895200ly_nat)) (let ((_let_1 ((polyno1415441627ul_nat V) Va))) (= ((polyno929799083ul_nat _let_1) B) ((polyno1415441627ul_nat _let_1) B)))) (forall ((P polyno1532895200ly_nat)) (not (= (polyno1964927358t1_nat P) (polyno2122022170_C_nat zero_zero_nat)))) (forall ((V polyno1532895200ly_nat) (Va polyno1532895200ly_nat)) (= (polyno892049031yh_nat ((polyno1415441627ul_nat V) Va)) (lambda ((K nat)) false))) (forall ((N nat) (M nat) (F (-> polyno727731844poly_a polyno727731844poly_a))) (= ((compow1114216044poly_a N) ((compow1114216044poly_a M) F)) ((compow1114216044poly_a ((times_times_nat M) N)) F))) (forall ((Y a) (C polyno727731844poly_a) (N nat) (P polyno727731844poly_a)) (let ((_let_1 (polyno562434098cmul_a Y))) (= (_let_1 (((polyno1057396216e_CN_a C) N) P)) (((polyno1057396216e_CN_a (_let_1 C)) N) (_let_1 P))))) (not false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
0.35/0.78	)
0.35/0.78	% SZS output end Proof for theBenchmark
0.35/0.79	EOF