0.00/0.08	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.09	% Command    : do_cvc5 %s %d
0.09/0.28	% Computer   : n003.cluster.edu
0.09/0.28	% Model      : x86_64 x86_64
0.09/0.28	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.09/0.28	% Memory     : 8042.1875MB
0.09/0.28	% OS         : Linux 3.10.0-693.el7.x86_64
0.09/0.28	% CPULimit   : 1200
0.09/0.28	% WCLimit    : 120
0.09/0.28	% DateTime   : Tue Jul 13 16:02:39 EDT 2021
0.09/0.28	% CPUTime    : 
0.13/0.40	%----THF division
0.13/0.40	------- cvc5-thf casc 28 : /export/starexec/sandbox2/benchmark/theBenchmark.p at 120...
0.13/0.40	--- Run --ho-elim --full-saturate-quant at 10...
10.32/10.52	--- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
20.42/20.65	--- Run --ho-elim --no-e-matching --fs-sum --full-saturate-quant at 10...
30.50/30.77	--- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
35.54/35.87	--- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5...
38.22/38.49	--- Run --no-ho-matching --full-saturate-quant --fs-interleave --ho-elim-store-ax at 10...
38.74/39.07	--- Run --no-ho-matching --full-saturate-quant --macros-quant-mode=all at 10...
49.35/49.69	--- Run --ho-elim --full-saturate-quant --fs-interleave at 10...
59.43/59.74	--- Run --no-ho-matching --full-saturate-quant --ho-elim-store-ax at 10...
69.91/70.31	--- Run --ho-elim --no-ho-elim-store-ax --full-saturate-quant...
86.49/87.06	% SZS status Theorem for theBenchmark
86.55/87.10	% SZS output start Proof for theBenchmark
86.55/87.10	(proof
86.55/87.10	(let ((_let_1 (getRel904497637nt_a_b standard_S_Idt_a))) (let ((_let_2 (_let_1 g))) (let ((_let_3 (labele1424214014nt_a_b g))) (let ((_let_4 (f y))) (let ((_let_5 (f x))) (let ((_let_6 ((product_Pair_b_b _let_5) _let_4))) (let ((_let_7 (forall ((X b)) (= (= ((image_b_b ((getRel904497637nt_a_b standard_S_Idt_a) g)) ((insert_b X) bot_bot_set_b)) bot_bot_set_b) (not ((member_b X) (labele1424214014nt_a_b g))))))) (let ((_let_8 (= (id_on_689842066_a_nat bot_bo2122869057_a_nat) bot_bo1836341171_a_nat))) (let ((_let_9 (= agree_221379389_a_b_b (lambda ((G4 labele1159362096nt_a_b) (F_1 set_Product_prod_b_b) (F_2 set_Product_prod_b_b)) (forall ((X5 b)) (let ((_let_1 ((insert_b X5) bot_bot_set_b))) (=> ((member_b X5) (labele1424214014nt_a_b G4)) (= ((image_b_b F_1) _let_1) ((image_b_b F_2) _let_1))))))))) (let ((_let_10 (= p (lambda ((X5 b) (Y4 b)) ((member_b Y4) ((image_b_b ((getRel904497637nt_a_b standard_S_Idt_a) g)) ((insert_b X5) bot_bot_set_b))))))) (let ((_let_11 (= ord_less_eq_set_b (lambda ((A7 set_b) (B7 set_b)) (forall ((T b)) (let ((_let_1 (member_b T))) (=> (_let_1 A7) (_let_1 B7)))))))) (let ((_let_12 ((member_b _let_5) _let_3))) (let ((_let_13 ((map_gr926947118tant_a ((bNF_Gr_b_b _let_3) f)) g))) (let ((_let_14 (labele1424214014nt_a_b _let_13))) (let ((_let_15 (forall ((X b) (Y b)) (= (((if_b true) X) Y) X)))) (let ((_let_16 (= f (lambda ((X5 b)) (((if_b (= ((image_b_b ((getRel904497637nt_a_b standard_S_Idt_a) g)) ((insert_b X5) bot_bot_set_b)) bot_bot_set_b)) X5) (hilbert_Eps_b (p X5))))))) (let ((_let_17 (= (id_on_b bot_bot_set_b) bot_bo1343651123od_b_b))) (let ((_let_18 (= ord_le1036320359od_b_b (lambda ((A7 set_Product_prod_b_b) (B7 set_Product_prod_b_b)) (forall ((X5 product_prod_b_b)) (let ((_let_1 (member1285940496od_b_b X5))) (=> (_let_1 A7) (_let_1 B7)))))))) (let ((_let_19 (= (id_on_1651096324_a_nat bot_bo1836341171_a_nat) bot_bo1973379891_a_nat))) (let ((_let_20 (= ord_le123089219od_b_b (lambda ((A7 set_Pr1324126435od_b_b) (B7 set_Pr1324126435od_b_b)) (forall ((X5 produc1213276845od_b_b)) (let ((_let_1 (member1516365892od_b_b X5))) (=> (_let_1 A7) (_let_1 B7)))))))) (let ((_let_21 (not ((member_b x) _let_3)))) (let ((_let_22 (forall ((X1 b) (X22 b) (R set_Product_prod_b_b) (S set_Product_prod_b_b) (P (-> b b Bool))) (=> ((member1285940496od_b_b ((product_Pair_b_b X1) X22)) ((relcomp_b_b_b R) S)) (=> (forall ((A4 b) (B5 b) (C2 b)) (=> ((member1285940496od_b_b ((product_Pair_b_b A4) B5)) R) (=> ((member1285940496od_b_b ((product_Pair_b_b B5) C2)) S) ((P A4) C2)))) ((P X1) X22)))))) (let ((_let_23 (forall ((X b)) (= (= bot_bot_set_b (ho_30 (ho_35 k_34 (ho_33 (ho_32 k_31 standard_S_Idt_a) g)) (ho_30 (ho_29 k_28 X) bot_bot_set_b))) (not (ho_38 (ho_37 k_36 X) (ho_113 k_112 g))))))) (let ((_let_24 (ho_113 k_112 g))) (let ((_let_25 (ho_38 (ho_37 k_36 x) _let_24))) (let ((_let_26 (not _let_25))) (let ((_let_27 (= bot_bot_set_b (ho_30 (ho_35 k_34 (ho_33 (ho_32 k_31 standard_S_Idt_a) g)) (ho_30 (ho_29 k_28 x) bot_bot_set_b))))) (let ((_let_28 (= _let_27 _let_26))) (let ((_let_29 (EQ_RESOLVE (ASSUME |:args| (_let_7)) (TRANS (MACRO_SR_EQ_INTRO |:args| (_let_7 7 12)) (PREPROCESS |:args| ((= (forall ((X b)) (= (= bot_bot_set_b ((image_b_b ((getRel904497637nt_a_b standard_S_Idt_a) g)) ((insert_b X) bot_bot_set_b))) (not ((member_b X) (labele1424214014nt_a_b g))))) _let_23))))))) (let ((_let_30 (not _let_28))) (let ((_let_31 (ho_69 k_68 k_67))) (let ((_let_32 (ho_73 (ho_72 (ho_71 k_70 BOOLEAN_TERM_VARIABLE_20487) x) _let_31))) (let ((_let_33 (= x _let_32))) (let ((_let_34 (= x (ho_73 (ho_72 (ho_71 k_70 BOOLEAN_TERM_VARIABLE_32961) x) _let_31)))) (let ((_let_35 (not BOOLEAN_TERM_VARIABLE_20487))) (let ((_let_36 ((= BOOLEAN_TERM_VARIABLE_32961 true)))) (let ((_let_37 (ho_86 k_85 _let_24))) (let ((_let_38 (ho_41 _let_37 x))) (let ((_let_39 (ho_41 _let_37 _let_32))) (let ((_let_40 (not _let_33))) (let ((_let_41 (= _let_38 _let_25))) (let ((_let_42 (not _let_38))) (let ((_let_43 (forall ((BOUND_VARIABLE_10842 set_b) (BOUND_VARIABLE_10843 b)) (= (ho_41 (ho_86 k_85 BOUND_VARIABLE_10842) BOUND_VARIABLE_10843) (ho_38 (ho_37 k_36 BOUND_VARIABLE_10843) BOUND_VARIABLE_10842))))) (let ((_let_44 (forall ((x |u_(-> produc1990339951od_b_b set_Pr2134561957od_b_b Bool)|) (y |u_(-> produc1990339951od_b_b set_Pr2134561957od_b_b Bool)|)) (or (not (forall ((z produc1990339951od_b_b)) (= (ho_249 x z) (ho_249 y z)))) (= x y))))) (let ((_let_45 (forall ((x |u_(-> set_St761939237tant_a _u_(-> standard_Constant_a product_prod_b_b)_ set_Pr1324126435od_b_b)|) (y |u_(-> set_St761939237tant_a _u_(-> standard_Constant_a product_prod_b_b)_ set_Pr1324126435od_b_b)|)) (or (not (forall ((z set_St761939237tant_a)) (= (ho_227 x z) (ho_227 y z)))) (= x y))))) (let ((_let_46 (forall ((x |u_(-> produc1213276845od_b_b product_prod_b_b produc1990339951od_b_b)|) (y |u_(-> produc1213276845od_b_b product_prod_b_b produc1990339951od_b_b)|)) (or (not (forall ((z produc1213276845od_b_b)) (= (ho_246 x z) (ho_246 y z)))) (= x y))))) (let ((_let_47 (forall ((x |u_(-> set_Pr1324126435od_b_b set_Product_prod_b_b)|) (y |u_(-> set_Pr1324126435od_b_b set_Product_prod_b_b)|)) (or (not (forall ((z set_Pr1324126435od_b_b)) (= (ho_244 x z) (ho_244 y z)))) (= x y))))) (let ((_let_48 (forall ((x |u_(-> _u_(-> produc1871334759_a_nat Bool)_ set_Pr1987088711_a_nat)|) (y |u_(-> _u_(-> produc1871334759_a_nat Bool)_ set_Pr1987088711_a_nat)|)) (or (not (forall ((z |u_(-> produc1871334759_a_nat Bool)|)) (= (ho_289 x z) (ho_289 y z)))) (= x y))))) (let ((_let_49 (forall ((x |u_(-> produc90515391tant_a set_Pr154086431tant_a Bool)|) (y |u_(-> produc90515391tant_a set_Pr154086431tant_a Bool)|)) (or (not (forall ((z produc90515391tant_a)) (= (ho_235 x z) (ho_235 y z)))) (= x y))))) (let ((_let_50 (forall ((x |u_(-> standard_Constant_a standard_Constant_a produc90515391tant_a)|) (y |u_(-> standard_Constant_a standard_Constant_a produc90515391tant_a)|)) (or (not (forall ((z standard_Constant_a)) (= (ho_232 x z) (ho_232 y z)))) (= x y))))) (let ((_let_51 (forall ((x |u_(-> set_Pr154086431tant_a Bool)|) (y |u_(-> set_Pr154086431tant_a Bool)|)) (or (not (forall ((z set_Pr154086431tant_a)) (= (ho_236 x z) (ho_236 y z)))) (= x y))))) (let ((_let_52 (forall ((x |u_(-> product_prod_b_b produc1485083751od_b_b)|) (y |u_(-> product_prod_b_b produc1485083751od_b_b)|)) (or (not (forall ((z product_prod_b_b)) (= (ho_394 x z) (ho_394 y z)))) (= x y))))) (let ((_let_53 (forall ((x |u_(-> produc1213276845od_b_b produc1213276845od_b_b produc970027067od_b_b)|) (y |u_(-> produc1213276845od_b_b produc1213276845od_b_b produc970027067od_b_b)|)) (or (not (forall ((z produc1213276845od_b_b)) (= (ho_216 x z) (ho_216 y z)))) (= x y))))) (let ((_let_54 (forall ((x |u_(-> standard_Constant_a set_St761939237tant_a Bool)|) (y |u_(-> standard_Constant_a set_St761939237tant_a Bool)|)) (or (not (forall ((z standard_Constant_a)) (= (ho_210 x z) (ho_210 y z)))) (= x y))))) (let ((_let_55 (forall ((x |u_(-> standard_Constant_a produc90515391tant_a)|) (y |u_(-> standard_Constant_a produc90515391tant_a)|)) (or (not (forall ((z standard_Constant_a)) (= (ho_233 x z) (ho_233 y z)))) (= x y))))) (let ((_let_56 (forall ((x |u_(-> set_St761939237tant_a set_Pr1987088711_a_nat)|) (y |u_(-> set_St761939237tant_a set_Pr1987088711_a_nat)|)) (or (not (forall ((z set_St761939237tant_a)) (= (ho_208 x z) (ho_208 y z)))) (= x y))))) (let ((_let_57 (forall ((x |u_(-> standard_Constant_a product_prod_b_b produc1213276845od_b_b)|) (y |u_(-> standard_Constant_a product_prod_b_b produc1213276845od_b_b)|)) (or (not (forall ((z standard_Constant_a)) (= (ho_205 x z) (ho_205 y z)))) (= x y))))) (let ((_let_58 (forall ((x |u_(-> product_prod_b_b produc1213276845od_b_b)|) (y |u_(-> product_prod_b_b produc1213276845od_b_b)|)) (or (not (forall ((z product_prod_b_b)) (= (ho_206 x z) (ho_206 y z)))) (= x y))))) (let ((_let_59 (forall ((x |u_(-> _u_(-> produc1213276845od_b_b b)_ set_Pr1906739389_b_b_b)|) (y |u_(-> _u_(-> produc1213276845od_b_b b)_ set_Pr1906739389_b_b_b)|)) (or (not (forall ((z |u_(-> produc1213276845od_b_b b)|)) (= (ho_309 x z) (ho_309 y z)))) (= x y))))) (let ((_let_60 (forall ((x |u_(-> labele1159362096nt_a_b labele1159362096nt_a_b labele1159362096nt_a_b)|) (y |u_(-> labele1159362096nt_a_b labele1159362096nt_a_b labele1159362096nt_a_b)|)) (or (not (forall ((z labele1159362096nt_a_b)) (= (ho_201 x z) (ho_201 y z)))) (= x y))))) (let ((_let_61 (forall ((x |u_(-> labele1159362096nt_a_b set_Pr1324126435od_b_b)|) (y |u_(-> labele1159362096nt_a_b set_Pr1324126435od_b_b)|)) (or (not (forall ((z labele1159362096nt_a_b)) (= (ho_199 x z) (ho_199 y z)))) (= x y))))) (let ((_let_62 (forall ((x |u_(-> set_Pr1324126435od_b_b set_b labele1159362096nt_a_b)|) (y |u_(-> set_Pr1324126435od_b_b set_b labele1159362096nt_a_b)|)) (or (not (forall ((z set_Pr1324126435od_b_b)) (= (ho_196 x z) (ho_196 y z)))) (= x y))))) (let ((_let_63 (forall ((x |u_(-> set_b labele1159362096nt_a_b)|) (y |u_(-> set_b labele1159362096nt_a_b)|)) (or (not (forall ((z set_b)) (= (ho_197 x z) (ho_197 y z)))) (= x y))))) (let ((_let_64 (forall ((x |u_(-> labele1159362096nt_a_b Bool)|) (y |u_(-> labele1159362096nt_a_b Bool)|)) (or (not (forall ((z labele1159362096nt_a_b)) (= (ho_129 x z) (ho_129 y z)))) (= x y))))) (let ((_let_65 (forall ((x |u_(-> produc276146823_b_b_b set_Pr1906739389_b_b_b Bool)|) (y |u_(-> produc276146823_b_b_b set_Pr1906739389_b_b_b Bool)|)) (or (not (forall ((z produc276146823_b_b_b)) (= (ho_193 x z) (ho_193 y z)))) (= x y))))) (let ((_let_66 (forall ((x |u_(-> labele935650037_a_nat labele935650037_a_nat)|) (y |u_(-> labele935650037_a_nat labele935650037_a_nat)|)) (or (not (forall ((z labele935650037_a_nat)) (= (ho_290 x z) (ho_290 y z)))) (= x y))))) (let ((_let_67 (forall ((x |u_(-> set_Pr1021918435od_b_b set_Pr1324126435od_b_b Bool)|) (y |u_(-> set_Pr1021918435od_b_b set_Pr1324126435od_b_b Bool)|)) (or (not (forall ((z set_Pr1021918435od_b_b)) (= (ho_369 x z) (ho_369 y z)))) (= x y))))) (let ((_let_68 (forall ((x |u_(-> produc1213276845od_b_b b produc276146823_b_b_b)|) (y |u_(-> produc1213276845od_b_b b produc276146823_b_b_b)|)) (or (not (forall ((z produc1213276845od_b_b)) (= (ho_190 x z) (ho_190 y z)))) (= x y))))) (let ((_let_69 (forall ((x |u_(-> produc1213276845od_b_b produc970027067od_b_b)|) (y |u_(-> produc1213276845od_b_b produc970027067od_b_b)|)) (or (not (forall ((z produc1213276845od_b_b)) (= (ho_217 x z) (ho_217 y z)))) (= x y))))) (let ((_let_70 (forall ((x |u_(-> b produc276146823_b_b_b)|) (y |u_(-> b produc276146823_b_b_b)|)) (or (not (forall ((z b)) (= (ho_191 x z) (ho_191 y z)))) (= x y))))) (let ((_let_71 (forall ((x |u_(-> set_Pr812188767_nat_b set_Pr1987088711_a_nat set_b)|) (y |u_(-> set_Pr812188767_nat_b set_Pr1987088711_a_nat set_b)|)) (or (not (forall ((z set_Pr812188767_nat_b)) (= (ho_361 x z) (ho_361 y z)))) (= x y))))) (let ((_let_72 (forall ((x |u_(-> set_Pr1906739389_b_b_b Bool)|) (y |u_(-> set_Pr1906739389_b_b_b Bool)|)) (or (not (forall ((z set_Pr1906739389_b_b_b)) (= (ho_194 x z) (ho_194 y z)))) (= x y))))) (let ((_let_73 (forall ((x |u_(-> set_Pr1906739389_b_b_b set_Pr1324126435od_b_b set_b)|) (y |u_(-> set_Pr1906739389_b_b_b set_Pr1324126435od_b_b set_b)|)) (or (not (forall ((z set_Pr1906739389_b_b_b)) (= (ho_187 x z) (ho_187 y z)))) (= x y))))) (let ((_let_74 (forall ((x |u_(-> standard_Constant_a labele1835558936od_b_b set_Pr2007082183od_b_b)|) (y |u_(-> standard_Constant_a labele1835558936od_b_b set_Pr2007082183od_b_b)|)) (or (not (forall ((z standard_Constant_a)) (= (ho_184 x z) (ho_184 y z)))) (= x y))))) (let ((_let_75 (forall ((x |u_(-> set_St761939237tant_a set_Product_prod_b_b)|) (y |u_(-> set_St761939237tant_a set_Product_prod_b_b)|)) (or (not (forall ((z set_St761939237tant_a)) (= (ho_214 x z) (ho_214 y z)))) (= x y))))) (let ((_let_76 (forall ((x |u_(-> labele1835558936od_b_b set_Pr2007082183od_b_b)|) (y |u_(-> labele1835558936od_b_b set_Pr2007082183od_b_b)|)) (or (not (forall ((z labele1835558936od_b_b)) (= (ho_185 x z) (ho_185 y z)))) (= x y))))) (let ((_let_77 (forall ((x |u_(-> set_la1083530965_a_nat set_Pr1987088711_a_nat)|) (y |u_(-> set_la1083530965_a_nat set_Pr1987088711_a_nat)|)) (or (not (forall ((z set_la1083530965_a_nat)) (= (ho_97 x z) (ho_97 y z)))) (= x y))))) (let ((_let_78 (forall ((x |u_(-> produc970027067od_b_b set_Pr2109276827od_b_b Bool)|) (y |u_(-> produc970027067od_b_b set_Pr2109276827od_b_b Bool)|)) (or (not (forall ((z produc970027067od_b_b)) (= (ho_219 x z) (ho_219 y z)))) (= x y))))) (let ((_let_79 (forall ((x |u_(-> _u_(-> product_prod_b_b b)_ set_Pr357419743_b_b_b)|) (y |u_(-> _u_(-> product_prod_b_b b)_ set_Pr357419743_b_b_b)|)) (or (not (forall ((z |u_(-> product_prod_b_b b)|)) (= (ho_179 x z) (ho_179 y z)))) (= x y))))) (let ((_let_80 (forall ((x |u_(-> labele1835558936od_b_b labele1159362096nt_a_b)|) (y |u_(-> labele1835558936od_b_b labele1159362096nt_a_b)|)) (or (not (forall ((z labele1835558936od_b_b)) (= (ho_182 x z) (ho_182 y z)))) (= x y))))) (let ((_let_81 (forall ((x |u_(-> produc1871334759_a_nat b produc845793663_nat_b)|) (y |u_(-> produc1871334759_a_nat b produc845793663_nat_b)|)) (or (not (forall ((z produc1871334759_a_nat)) (= (ho_356 x z) (ho_356 y z)))) (= x y))))) (let ((_let_82 (forall ((x |u_(-> set_St761939237tant_a Bool)|) (y |u_(-> set_St761939237tant_a Bool)|)) (or (not (forall ((z set_St761939237tant_a)) (= (ho_211 x z) (ho_211 y z)))) (= x y))))) (let ((_let_83 (forall ((x |u_(-> set_Product_prod_b_b set_Pr2007082183od_b_b Bool)|) (y |u_(-> set_Product_prod_b_b set_Pr2007082183od_b_b Bool)|)) (or (not (forall ((z set_Product_prod_b_b)) (= (ho_173 x z) (ho_173 y z)))) (= x y))))) (let ((_let_84 (forall ((x |u_(-> b set_b Bool)|) (y |u_(-> b set_b Bool)|)) (or (not (forall ((z b)) (= (ho_37 x z) (ho_37 y z)))) (= x y))))) (let ((_let_85 (forall ((x |u_(-> product_prod_b_b produc1168037607od_b_b)|) (y |u_(-> product_prod_b_b produc1168037607od_b_b)|)) (or (not (forall ((z product_prod_b_b)) (= (ho_168 x z) (ho_168 y z)))) (= x y))))) (let ((_let_86 (forall ((x |u_(-> set_Pr357419743_b_b_b labele1835558936od_b_b labele1159362096nt_a_b)|) (y |u_(-> set_Pr357419743_b_b_b labele1835558936od_b_b labele1159362096nt_a_b)|)) (or (not (forall ((z set_Pr357419743_b_b_b)) (= (ho_181 x z) (ho_181 y z)))) (= x y))))) (let ((_let_87 (forall ((x |u_(-> set_Pr2007082183od_b_b Bool)|) (y |u_(-> set_Pr2007082183od_b_b Bool)|)) (or (not (forall ((z set_Pr2007082183od_b_b)) (= (ho_171 x z) (ho_171 y z)))) (= x y))))) (let ((_let_88 (forall ((x |u_(-> labele1835558936od_b_b set_Product_prod_b_b)|) (y |u_(-> labele1835558936od_b_b set_Product_prod_b_b)|)) (or (not (forall ((z labele1835558936od_b_b)) (= (ho_176 x z) (ho_176 y z)))) (= x y))))) (let ((_let_89 (forall ((x |u_(-> labele1159362096nt_a_b set_Product_prod_b_b Bool)|) (y |u_(-> labele1159362096nt_a_b set_Product_prod_b_b Bool)|)) (or (not (forall ((z labele1159362096nt_a_b)) (= (ho_165 x z) (ho_165 y z)))) (= x y))))) (let ((_let_90 (forall ((x |u_(-> set_b set_Pr1324126435od_b_b)|) (y |u_(-> set_b set_Pr1324126435od_b_b)|)) (or (not (forall ((z set_b)) (= (ho_268 x z) (ho_268 y z)))) (= x y))))) (let ((_let_91 (forall ((x |u_(-> labele935650037_a_nat produc1871334759_a_nat)|) (y |u_(-> labele935650037_a_nat produc1871334759_a_nat)|)) (or (not (forall ((z labele935650037_a_nat)) (= (ho_161 x z) (ho_161 y z)))) (= x y))))) (let ((_let_92 (forall ((x |u_(-> Bool b b b)|) (y |u_(-> Bool b b b)|)) (or (not (forall ((z Bool)) (= (ho_71 x z) (ho_71 y z)))) (= x y))))) (let ((_let_93 (forall ((x |u_(-> set_Product_prod_b_b _u_(-> product_prod_b_b b)_ set_Pr357419743_b_b_b)|) (y |u_(-> set_Product_prod_b_b _u_(-> product_prod_b_b b)_ set_Pr357419743_b_b_b)|)) (or (not (forall ((z set_Product_prod_b_b)) (= (ho_178 x z) (ho_178 y z)))) (= x y))))) (let ((_let_94 (forall ((x |u_(-> standard_Constant_a product_prod_b_b Bool)|) (y |u_(-> standard_Constant_a product_prod_b_b Bool)|)) (or (not (forall ((z standard_Constant_a)) (= (ho_335 x z) (ho_335 y z)))) (= x y))))) (let ((_let_95 (forall ((x |u_(-> produc398057191_a_nat set_Pr924198087_a_nat Bool)|) (y |u_(-> produc398057191_a_nat set_Pr924198087_a_nat Bool)|)) (or (not (forall ((z produc398057191_a_nat)) (= (ho_151 x z) (ho_151 y z)))) (= x y))))) (let ((_let_96 (forall ((x |u_(-> set_Pr1324126435od_b_b _u_(-> produc1213276845od_b_b b)_ set_Pr1906739389_b_b_b)|) (y |u_(-> set_Pr1324126435od_b_b _u_(-> produc1213276845od_b_b b)_ set_Pr1906739389_b_b_b)|)) (or (not (forall ((z set_Pr1324126435od_b_b)) (= (ho_308 x z) (ho_308 y z)))) (= x y))))) (let ((_let_97 (forall ((x |u_(-> set_Pr924198087_a_nat set_Pr1987088711_a_nat set_Pr1987088711_a_nat)|) (y |u_(-> set_Pr924198087_a_nat set_Pr1987088711_a_nat set_Pr1987088711_a_nat)|)) (or (not (forall ((z set_Pr924198087_a_nat)) (= (ho_147 x z) (ho_147 y z)))) (= x y))))) (let ((_let_98 (forall ((x |u_(-> produc255402447od_b_b set_Pr621705391od_b_b Bool)|) (y |u_(-> produc255402447od_b_b set_Pr621705391od_b_b Bool)|)) (or (not (forall ((z produc255402447od_b_b)) (= (ho_144 x z) (ho_144 y z)))) (= x y))))) (let ((_let_99 (forall ((x |u_(-> set_Pr1324126435od_b_b set_Pr2109276827od_b_b Bool)|) (y |u_(-> set_Pr1324126435od_b_b set_Pr2109276827od_b_b Bool)|)) (or (not (forall ((z set_Pr1324126435od_b_b)) (= (ho_224 x z) (ho_224 y z)))) (= x y))))) (let ((_let_100 (forall ((x |u_(-> set_Pr357419743_b_b_b Bool)|) (y |u_(-> set_Pr357419743_b_b_b Bool)|)) (or (not (forall ((z set_Pr357419743_b_b_b)) (= (ho_352 x z) (ho_352 y z)))) (= x y))))) (let ((_let_101 (forall ((x |u_(-> product_prod_b_b b)|) (y |u_(-> product_prod_b_b b)|)) (or (not (forall ((z product_prod_b_b)) (= (ho_174 x z) (ho_174 y z)))) (= x y))))) (let ((_let_102 (forall ((x |u_(-> produc1485083751od_b_b set_Pr667377223od_b_b Bool)|) (y |u_(-> produc1485083751od_b_b set_Pr667377223od_b_b Bool)|)) (or (not (forall ((z produc1485083751od_b_b)) (= (ho_396 x z) (ho_396 y z)))) (= x y))))) (let ((_let_103 (forall ((x |u_(-> b product_prod_b_b produc255402447od_b_b)|) (y |u_(-> b product_prod_b_b produc255402447od_b_b)|)) (or (not (forall ((z b)) (= (ho_141 x z) (ho_141 y z)))) (= x y))))) (let ((_let_104 (forall ((x |u_(-> set_Pr2109276827od_b_b Bool)|) (y |u_(-> set_Pr2109276827od_b_b Bool)|)) (or (not (forall ((z set_Pr2109276827od_b_b)) (= (ho_220 x z) (ho_220 y z)))) (= x y))))) (let ((_let_105 (forall ((x |u_(-> set_Pr1954438265od_b_b set_Pr1987088711_a_nat set_Pr1324126435od_b_b)|) (y |u_(-> set_Pr1954438265od_b_b set_Pr1987088711_a_nat set_Pr1324126435od_b_b)|)) (or (not (forall ((z set_Pr1954438265od_b_b)) (= (ho_333 x z) (ho_333 y z)))) (= x y))))) (let ((_let_106 (forall ((x |u_(-> set_b b Bool)|) (y |u_(-> set_b b Bool)|)) (or (not (forall ((z set_b)) (= (ho_86 x z) (ho_86 y z)))) (= x y))))) (let ((_let_107 (forall ((x |u_(-> set_Pr1324126435od_b_b produc1213276845od_b_b Bool)|) (y |u_(-> set_Pr1324126435od_b_b produc1213276845od_b_b Bool)|)) (or (not (forall ((z set_Pr1324126435od_b_b)) (= (ho_78 x z) (ho_78 y z)))) (= x y))))) (let ((_let_108 (forall ((x |u_(-> produc1398946881nt_a_b labele1159362096nt_a_b set_Product_prod_b_b Bool)|) (y |u_(-> produc1398946881nt_a_b labele1159362096nt_a_b set_Product_prod_b_b Bool)|)) (or (not (forall ((z produc1398946881nt_a_b)) (= (ho_325 x z) (ho_325 y z)))) (= x y))))) (let ((_let_109 (forall ((x |u_(-> produc1213276845od_b_b Bool)|) (y |u_(-> produc1213276845od_b_b Bool)|)) (or (not (forall ((z produc1213276845od_b_b)) (= (ho_79 x z) (ho_79 y z)))) (= x y))))) (let ((_let_110 (forall ((x |u_(-> set_Pr1324126435od_b_b set_Pr2109276827od_b_b)|) (y |u_(-> set_Pr1324126435od_b_b set_Pr2109276827od_b_b)|)) (or (not (forall ((z set_Pr1324126435od_b_b)) (= (ho_252 x z) (ho_252 y z)))) (= x y))))) (let ((_let_111 (forall ((x |u_(-> b b b)|) (y |u_(-> b b b)|)) (or (not (forall ((z b)) (= (ho_72 x z) (ho_72 y z)))) (= x y))))) (let ((_let_112 (forall ((x |u_(-> b set_b set_b)|) (y |u_(-> b set_b set_b)|)) (or (not (forall ((z b)) (= (ho_29 x z) (ho_29 y z)))) (= x y))))) (let ((_let_113 (forall ((x |u_(-> b b)|) (y |u_(-> b b)|)) (or (not (forall ((z b)) (= (ho_73 x z) (ho_73 y z)))) (= x y))))) (let ((_let_114 (forall ((x |u_(-> produc1168037607od_b_b set_Pr2007082183od_b_b Bool)|) (y |u_(-> produc1168037607od_b_b set_Pr2007082183od_b_b Bool)|)) (or (not (forall ((z produc1168037607od_b_b)) (= (ho_170 x z) (ho_170 y z)))) (= x y))))) (let ((_let_115 (forall ((x |u_(-> labele1159362096nt_a_b set_Pr2106913242_nat_b Bool)|) (y |u_(-> labele1159362096nt_a_b set_Pr2106913242_nat_b Bool)|)) (or (not (forall ((z labele1159362096nt_a_b)) (= (ho_158 x z) (ho_158 y z)))) (= x y))))) (let ((_let_116 (forall ((x |u_(-> set_Pr1021918435od_b_b Bool)|) (y |u_(-> set_Pr1021918435od_b_b Bool)|)) (or (not (forall ((z set_Pr1021918435od_b_b)) (= (ho_375 x z) (ho_375 y z)))) (= x y))))) (let ((_let_117 (forall ((x |u_(-> set_Pr2106913242_nat_b set_Pr2106913242_nat_b Bool)|) (y |u_(-> set_Pr2106913242_nat_b set_Pr2106913242_nat_b Bool)|)) (or (not (forall ((z set_Pr2106913242_nat_b)) (= (ho_154 x z) (ho_154 y z)))) (= x y))))) (let ((_let_118 (forall ((x |u_(-> b product_prod_b_b)|) (y |u_(-> b product_prod_b_b)|)) (or (not (forall ((z b)) (= (ho_81 x z) (ho_81 y z)))) (= x y))))) (let ((_let_119 (forall ((x |u_(-> b set_b)|) (y |u_(-> b set_b)|)) (or (not (forall ((z b)) (= (ho_65 x z) (ho_65 y z)))) (= x y))))) (let ((_let_120 (forall ((x |u_(-> standard_Constant_a b set_b)|) (y |u_(-> standard_Constant_a b set_b)|)) (or (not (forall ((z standard_Constant_a)) (= (ho_64 x z) (ho_64 y z)))) (= x y))))) (let ((_let_121 (forall ((x |u_(-> b produc2112523263_b_b_b)|) (y |u_(-> b produc2112523263_b_b_b)|)) (or (not (forall ((z b)) (= (ho_349 x z) (ho_349 y z)))) (= x y))))) (let ((_let_122 (forall ((x |u_(-> set_Product_prod_b_b labele1159362096nt_a_b labele1159362096nt_a_b)|) (y |u_(-> set_Product_prod_b_b labele1159362096nt_a_b labele1159362096nt_a_b)|)) (or (not (forall ((z set_Product_prod_b_b)) (= (ho_118 x z) (ho_118 y z)))) (= x y))))) (let ((_let_123 (forall ((x |u_(-> standard_Constant_a product_prod_b_b)|) (y |u_(-> standard_Constant_a product_prod_b_b)|)) (or (not (forall ((z standard_Constant_a)) (= (ho_225 x z) (ho_225 y z)))) (= x y))))) (let ((_let_124 (forall ((x |u_(-> produc1871334759_a_nat set_Pr1987088711_a_nat Bool)|) (y |u_(-> produc1871334759_a_nat set_Pr1987088711_a_nat Bool)|)) (or (not (forall ((z produc1871334759_a_nat)) (= (ho_135 x z) (ho_135 y z)))) (= x y))))) (let ((_let_125 (forall ((x |u_(-> set_Product_prod_b_b set_Product_prod_b_b Bool)|) (y |u_(-> set_Product_prod_b_b set_Product_prod_b_b Bool)|)) (or (not (forall ((z set_Product_prod_b_b)) (= (ho_55 x z) (ho_55 y z)))) (= x y))))) (let ((_let_126 (forall ((x |u_(-> _u_(-> b set_b)_ Bool)|) (y |u_(-> _u_(-> b set_b)_ Bool)|)) (or (not (forall ((z |u_(-> b set_b)|)) (= (ho_407 x z) (ho_407 y z)))) (= x y))))) (let ((_let_127 (forall ((x |u_(-> standard_Constant_a labele1159362096nt_a_b set_Product_prod_b_b)|) (y |u_(-> standard_Constant_a labele1159362096nt_a_b set_Product_prod_b_b)|)) (or (not (forall ((z standard_Constant_a)) (= (ho_32 x z) (ho_32 y z)))) (= x y))))) (let ((_let_128 (forall ((x |u_(-> product_prod_b_b Bool)|) (y |u_(-> product_prod_b_b Bool)|)) (or (not (forall ((z product_prod_b_b)) (= (ho_59 x z) (ho_59 y z)))) (= x y))))) (let ((_let_129 (forall ((x |u_(-> product_prod_b_b produc255402447od_b_b)|) (y |u_(-> product_prod_b_b produc255402447od_b_b)|)) (or (not (forall ((z product_prod_b_b)) (= (ho_142 x z) (ho_142 y z)))) (= x y))))) (let ((_let_130 (forall ((x |u_(-> set_Pr2109276827od_b_b set_Pr1324126435od_b_b set_Pr1324126435od_b_b)|) (y |u_(-> set_Pr2109276827od_b_b set_Pr1324126435od_b_b set_Pr1324126435od_b_b)|)) (or (not (forall ((z set_Pr2109276827od_b_b)) (= (ho_222 x z) (ho_222 y z)))) (= x y))))) (let ((_let_131 (forall ((x |u_(-> set_Pr1987088711_a_nat set_b)|) (y |u_(-> set_Pr1987088711_a_nat set_b)|)) (or (not (forall ((z set_Pr1987088711_a_nat)) (= (ho_362 x z) (ho_362 y z)))) (= x y))))) (let ((_let_132 (forall ((x |u_(-> set_b set_Product_prod_b_b Bool)|) (y |u_(-> set_b set_Product_prod_b_b Bool)|)) (or (not (forall ((z set_b)) (= (ho_203 x z) (ho_203 y z)))) (= x y))))) (let ((_let_133 (forall ((x |u_(-> labele1644675410od_b_b set_Pr2109276827od_b_b)|) (y |u_(-> labele1644675410od_b_b set_Pr2109276827od_b_b)|)) (or (not (forall ((z labele1644675410od_b_b)) (= (ho_388 x z) (ho_388 y z)))) (= x y))))) (let ((_let_134 (forall ((x |u_(-> set_Product_prod_b_b product_prod_b_b Bool)|) (y |u_(-> set_Product_prod_b_b product_prod_b_b Bool)|)) (or (not (forall ((z set_Product_prod_b_b)) (= (ho_58 x z) (ho_58 y z)))) (= x y))))) (let ((_let_135 (forall ((x |u_(-> set_b set_b)|) (y |u_(-> set_b set_b)|)) (or (not (forall ((z set_b)) (= (ho_30 x z) (ho_30 y z)))) (= x y))))) (let ((_let_136 (forall ((x |u_(-> set_Pr1649131859tant_a set_Pr1324126435od_b_b set_Pr621705391od_b_b)|) (y |u_(-> set_Pr1649131859tant_a set_Pr1324126435od_b_b set_Pr621705391od_b_b)|)) (or (not (forall ((z set_Pr1649131859tant_a)) (= (ho_381 x z) (ho_381 y z)))) (= x y))))) (let ((_let_137 (forall ((x |u_(-> set_b Bool)|) (y |u_(-> set_b Bool)|)) (or (not (forall ((z set_b)) (= (ho_38 x z) (ho_38 y z)))) (= x y))))) (let ((_let_138 (forall ((x |u_(-> set_Pr1324126435od_b_b set_Pr1324126435od_b_b Bool)|) (y |u_(-> set_Pr1324126435od_b_b set_Pr1324126435od_b_b Bool)|)) (or (not (forall ((z set_Pr1324126435od_b_b)) (= (ho_48 x z) (ho_48 y z)))) (= x y))))) (let ((_let_139 (forall ((x |u_(-> _u_(-> standard_Constant_a product_prod_b_b)_ set_Pr1324126435od_b_b)|) (y |u_(-> _u_(-> standard_Constant_a product_prod_b_b)_ set_Pr1324126435od_b_b)|)) (or (not (forall ((z |u_(-> standard_Constant_a product_prod_b_b)|)) (= (ho_228 x z) (ho_228 y z)))) (= x y))))) (let ((_let_140 (forall ((x |u_(-> set_b _u_(-> b b)_ set_Product_prod_b_b)|) (y |u_(-> set_b _u_(-> b b)_ set_Product_prod_b_b)|)) (or (not (forall ((z set_b)) (= (ho_115 x z) (ho_115 y z)))) (= x y))))) (let ((_let_141 (forall ((x |u_(-> product_prod_b_b set_Product_prod_b_b Bool)|) (y |u_(-> product_prod_b_b set_Product_prod_b_b Bool)|)) (or (not (forall ((z product_prod_b_b)) (= (ho_52 x z) (ho_52 y z)))) (= x y))))) (let ((_let_142 (forall ((x |u_(-> set_Pr1987088711_a_nat set_Pr924198087_a_nat Bool)|) (y |u_(-> set_Pr1987088711_a_nat set_Pr924198087_a_nat Bool)|)) (or (not (forall ((z set_Pr1987088711_a_nat)) (= (ho_110 x z) (ho_110 y z)))) (= x y))))) (let ((_let_143 (forall ((x |u_(-> set_Pr1324126435od_b_b Bool)|) (y |u_(-> set_Pr1324126435od_b_b Bool)|)) (or (not (forall ((z set_Pr1324126435od_b_b)) (= (ho_46 x z) (ho_46 y z)))) (= x y))))) (let ((_let_144 (forall ((x |u_(-> set_Pr1324126435od_b_b set_St761939237tant_a set_Product_prod_b_b)|) (y |u_(-> set_Pr1324126435od_b_b set_St761939237tant_a set_Product_prod_b_b)|)) (or (not (forall ((z set_Pr1324126435od_b_b)) (= (ho_213 x z) (ho_213 y z)))) (= x y))))) (let ((_let_145 (forall ((x |u_(-> produc1871334759_a_nat set_Pr1987088711_a_nat set_Pr1987088711_a_nat)|) (y |u_(-> produc1871334759_a_nat set_Pr1987088711_a_nat set_Pr1987088711_a_nat)|)) (or (not (forall ((z produc1871334759_a_nat)) (= (ho_107 x z) (ho_107 y z)))) (= x y))))) (let ((_let_146 (forall ((x |u_(-> labele1159362096nt_a_b labele1159362096nt_a_b set_Product_prod_b_b Bool)|) (y |u_(-> labele1159362096nt_a_b labele1159362096nt_a_b set_Product_prod_b_b Bool)|)) (or (not (forall ((z labele1159362096nt_a_b)) (= (ho_164 x z) (ho_164 y z)))) (= x y))))) (let ((_let_147 (forall ((x |u_(-> set_Product_prod_b_b set_b set_b)|) (y |u_(-> set_Product_prod_b_b set_b set_b)|)) (or (not (forall ((z set_Product_prod_b_b)) (= (ho_35 x z) (ho_35 y z)))) (= x y))))) (let ((_let_148 (forall ((x |u_(-> set_St761939237tant_a set_St761939237tant_a)|) (y |u_(-> set_St761939237tant_a set_St761939237tant_a)|)) (or (not (forall ((z set_St761939237tant_a)) (= (ho_284 x z) (ho_284 y z)))) (= x y))))) (let ((_let_149 (forall ((x |u_(-> set_Pr154086431tant_a set_Pr1324126435od_b_b set_Pr1324126435od_b_b)|) (y |u_(-> set_Pr154086431tant_a set_Pr1324126435od_b_b set_Pr1324126435od_b_b)|)) (or (not (forall ((z set_Pr154086431tant_a)) (= (ho_238 x z) (ho_238 y z)))) (= x y))))) (let ((_let_150 (forall ((x |u_(-> labele1159362096nt_a_b labele1159362096nt_a_b)|) (y |u_(-> labele1159362096nt_a_b labele1159362096nt_a_b)|)) (or (not (forall ((z labele1159362096nt_a_b)) (= (ho_119 x z) (ho_119 y z)))) (= x y))))) (let ((_let_151 (forall ((x |u_(-> produc1871334759_a_nat labele1159362096nt_a_b Bool)|) (y |u_(-> produc1871334759_a_nat labele1159362096nt_a_b Bool)|)) (or (not (forall ((z produc1871334759_a_nat)) (= (ho_128 x z) (ho_128 y z)))) (= x y))))) (let ((_let_152 (forall ((x |u_(-> _u_(-> b Bool)_ b)|) (y |u_(-> _u_(-> b Bool)_ b)|)) (or (not (forall ((z |u_(-> b Bool)|)) (= (ho_69 x z) (ho_69 y z)))) (= x y))))) (let ((_let_153 (forall ((x |u_(-> product_prod_b_b product_prod_b_b produc1168037607od_b_b)|) (y |u_(-> product_prod_b_b product_prod_b_b produc1168037607od_b_b)|)) (or (not (forall ((z product_prod_b_b)) (= (ho_167 x z) (ho_167 y z)))) (= x y))))) (let ((_let_154 (forall ((x |u_(-> _u_(-> b b)_ set_Product_prod_b_b)|) (y |u_(-> _u_(-> b b)_ set_Product_prod_b_b)|)) (or (not (forall ((z |u_(-> b b)|)) (= (ho_116 x z) (ho_116 y z)))) (= x y))))) (let ((_let_155 (forall ((x |u_(-> set_b set_Product_prod_b_b)|) (y |u_(-> set_b set_Product_prod_b_b)|)) (or (not (forall ((z set_b)) (= (ho_139 x z) (ho_139 y z)))) (= x y))))) (let ((_let_156 (forall ((x |u_(-> set_b set_b Bool)|) (y |u_(-> set_b set_b Bool)|)) (or (not (forall ((z set_b)) (= (ho_61 x z) (ho_61 y z)))) (= x y))))) (let ((_let_157 (forall ((x |u_(-> labele1159362096nt_a_b allego510293162tant_a set_Product_prod_b_b)|) (y |u_(-> labele1159362096nt_a_b allego510293162tant_a set_Product_prod_b_b)|)) (or (not (forall ((z labele1159362096nt_a_b)) (= (ho_121 x z) (ho_121 y z)))) (= x y))))) (let ((_let_158 (forall ((x |u_(-> set_Pr1646010159_a_nat set_b set_Pr1987088711_a_nat)|) (y |u_(-> set_Pr1646010159_a_nat set_b set_Pr1987088711_a_nat)|)) (or (not (forall ((z set_Pr1646010159_a_nat)) (= (ho_240 x z) (ho_240 y z)))) (= x y))))) (let ((_let_159 (forall ((x |u_(-> set_b set_Pr1987088711_a_nat)|) (y |u_(-> set_b set_Pr1987088711_a_nat)|)) (or (not (forall ((z set_b)) (= (ho_241 x z) (ho_241 y z)))) (= x y))))) (let ((_let_160 (forall ((x |u_(-> set_Pr667377223od_b_b set_Pr1987088711_a_nat set_Product_prod_b_b)|) (y |u_(-> set_Pr667377223od_b_b set_Pr1987088711_a_nat set_Product_prod_b_b)|)) (or (not (forall ((z set_Pr667377223od_b_b)) (= (ho_399 x z) (ho_399 y z)))) (= x y))))) (let ((_let_161 (forall ((x |u_(-> labele935650037_a_nat labele1159362096nt_a_b set_Pr2106913242_nat_b Bool)|) (y |u_(-> labele935650037_a_nat labele1159362096nt_a_b set_Pr2106913242_nat_b Bool)|)) (or (not (forall ((z labele935650037_a_nat)) (= (ho_157 x z) (ho_157 y z)))) (= x y))))) (let ((_let_162 (forall ((x |u_(-> produc1213276845od_b_b produc1605346267od_b_b)|) (y |u_(-> produc1213276845od_b_b produc1605346267od_b_b)|)) (or (not (forall ((z produc1213276845od_b_b)) (= (ho_271 x z) (ho_271 y z)))) (= x y))))) (let ((_let_163 (forall ((x |u_(-> set_Product_prod_b_b Bool)|) (y |u_(-> set_Product_prod_b_b Bool)|)) (or (not (forall ((z set_Product_prod_b_b)) (= (ho_53 x z) (ho_53 y z)))) (= x y))))) (let ((_let_164 (forall ((x |u_(-> produc1213276845od_b_b set_Pr1324126435od_b_b Bool)|) (y |u_(-> produc1213276845od_b_b set_Pr1324126435od_b_b Bool)|)) (or (not (forall ((z produc1213276845od_b_b)) (= (ho_45 x z) (ho_45 y z)))) (= x y))))) (let ((_let_165 (forall ((x |u_(-> produc1213276845od_b_b produc1169496899od_b_b)|) (y |u_(-> produc1213276845od_b_b produc1169496899od_b_b)|)) (or (not (forall ((z produc1213276845od_b_b)) (= (ho_328 x z) (ho_328 y z)))) (= x y))))) (let ((_let_166 (forall ((x |u_(-> b b Bool)|) (y |u_(-> b b Bool)|)) (or (not (forall ((z b)) (= (ho_40 x z) (ho_40 y z)))) (= x y))))) (let ((_let_167 (forall ((x |u_(-> b Bool)|) (y |u_(-> b Bool)|)) (or (not (forall ((z b)) (= (ho_41 x z) (ho_41 y z)))) (= x y))))) (let ((_let_168 (forall ((x |u_(-> b b product_prod_b_b)|) (y |u_(-> b b product_prod_b_b)|)) (or (not (forall ((z b)) (= (ho_83 x z) (ho_83 y z)))) (= x y))))) (let ((_let_169 (forall ((x |u_(-> set_Product_prod_b_b set_Product_prod_b_b)|) (y |u_(-> set_Product_prod_b_b set_Product_prod_b_b)|)) (or (not (forall ((z set_Product_prod_b_b)) (= (ho_95 x z) (ho_95 y z)))) (= x y))))) (let ((_let_170 (forall ((x |u_(-> set_Pr1906739389_b_b_b set_Pr1190604087od_b_b set_Pr1324126435od_b_b Bool)|) (y |u_(-> set_Pr1906739389_b_b_b set_Pr1190604087od_b_b set_Pr1324126435od_b_b Bool)|)) (or (not (forall ((z set_Pr1906739389_b_b_b)) (= (ho_311 x z) (ho_311 y z)))) (= x y))))) (let ((_let_171 (forall ((x |u_(-> set_Product_prod_b_b set_Product_prod_b_b set_Product_prod_b_b)|) (y |u_(-> set_Product_prod_b_b set_Product_prod_b_b set_Product_prod_b_b)|)) (or (not (forall ((z set_Product_prod_b_b)) (= (ho_94 x z) (ho_94 y z)))) (= x y))))) (let ((_let_172 (forall ((x |u_(-> set_Pr1987088711_a_nat set_Pr924198087_a_nat)|) (y |u_(-> set_Pr1987088711_a_nat set_Pr924198087_a_nat)|)) (or (not (forall ((z set_Pr1987088711_a_nat)) (= (ho_99 x z) (ho_99 y z)))) (= x y))))) (let ((_let_173 (forall ((x |u_(-> set_Pr1987088711_a_nat Bool)|) (y |u_(-> set_Pr1987088711_a_nat Bool)|)) (or (not (forall ((z set_Pr1987088711_a_nat)) (= (ho_136 x z) (ho_136 y z)))) (= x y))))) (let ((_let_174 (forall ((x |u_(-> set_la1083530965_a_nat set_Pr1987088711_a_nat Bool)|) (y |u_(-> set_la1083530965_a_nat set_Pr1987088711_a_nat Bool)|)) (or (not (forall ((z set_la1083530965_a_nat)) (= (ho_300 x z) (ho_300 y z)))) (= x y))))) (let ((_let_175 (forall ((x |u_(-> labele935650037_a_nat labele935650037_a_nat produc1871334759_a_nat)|) (y |u_(-> labele935650037_a_nat labele935650037_a_nat produc1871334759_a_nat)|)) (or (not (forall ((z labele935650037_a_nat)) (= (ho_160 x z) (ho_160 y z)))) (= x y))))) (let ((_let_176 (forall ((x |u_(-> set_Pr924198087_a_nat Bool)|) (y |u_(-> set_Pr924198087_a_nat Bool)|)) (or (not (forall ((z set_Pr924198087_a_nat)) (= (ho_111 x z) (ho_111 y z)))) (= x y))))) (let ((_let_177 (forall ((x |u_(-> set_Pr924198087_a_nat set_Pr924198087_a_nat)|) (y |u_(-> set_Pr924198087_a_nat set_Pr924198087_a_nat)|)) (or (not (forall ((z set_Pr924198087_a_nat)) (= (ho_105 x z) (ho_105 y z)))) (= x y))))) (let ((_let_178 (forall ((x |u_(-> set_Pr2134561957od_b_b Bool)|) (y |u_(-> set_Pr2134561957od_b_b Bool)|)) (or (not (forall ((z set_Pr2134561957od_b_b)) (= (ho_250 x z) (ho_250 y z)))) (= x y))))) (let ((_let_179 (forall ((x |u_(-> _u_(-> b product_prod_b_b)_ set_b set_Product_prod_b_b)|) (y |u_(-> _u_(-> b product_prod_b_b)_ set_b set_Product_prod_b_b)|)) (or (not (forall ((z |u_(-> b product_prod_b_b)|)) (= (ho_341 x z) (ho_341 y z)))) (= x y))))) (let ((_let_180 (forall ((x |u_(-> product_prod_b_b set_Product_prod_b_b set_Product_prod_b_b)|) (y |u_(-> product_prod_b_b set_Product_prod_b_b set_Product_prod_b_b)|)) (or (not (forall ((z product_prod_b_b)) (= (ho_230 x z) (ho_230 y z)))) (= x y))))) (let ((_let_181 (forall ((x |u_(-> produc1871334759_a_nat produc398057191_a_nat)|) (y |u_(-> produc1871334759_a_nat produc398057191_a_nat)|)) (or (not (forall ((z produc1871334759_a_nat)) (= (ho_102 x z) (ho_102 y z)))) (= x y))))) (let ((_let_182 (forall ((x |u_(-> standard_Constant_a produc970027067od_b_b produc1084374401od_b_b)|) (y |u_(-> standard_Constant_a produc970027067od_b_b produc1084374401od_b_b)|)) (or (not (forall ((z standard_Constant_a)) (= (ho_314 x z) (ho_314 y z)))) (= x y))))) (let ((_let_183 (forall ((x |u_(-> produc1871334759_a_nat produc1871334759_a_nat produc398057191_a_nat)|) (y |u_(-> produc1871334759_a_nat produc1871334759_a_nat produc398057191_a_nat)|)) (or (not (forall ((z produc1871334759_a_nat)) (= (ho_101 x z) (ho_101 y z)))) (= x y))))) (let ((_let_184 (forall ((x |u_(-> product_prod_b_b produc1990339951od_b_b)|) (y |u_(-> product_prod_b_b produc1990339951od_b_b)|)) (or (not (forall ((z product_prod_b_b)) (= (ho_247 x z) (ho_247 y z)))) (= x y))))) (let ((_let_185 (forall ((x |u_(-> set_Pr621705391od_b_b Bool)|) (y |u_(-> set_Pr621705391od_b_b Bool)|)) (or (not (forall ((z set_Pr621705391od_b_b)) (= (ho_145 x z) (ho_145 y z)))) (= x y))))) (let ((_let_186 (forall ((x |u_(-> _u_(-> b Bool)_ set_b)|) (y |u_(-> _u_(-> b Bool)_ set_b)|)) (or (not (forall ((z |u_(-> b Bool)|)) (= (ho_320 x z) (ho_320 y z)))) (= x y))))) (let ((_let_187 (forall ((x |u_(-> set_Pr1987088711_a_nat set_Pr1987088711_a_nat)|) (y |u_(-> set_Pr1987088711_a_nat set_Pr1987088711_a_nat)|)) (or (not (forall ((z set_Pr1987088711_a_nat)) (= (ho_108 x z) (ho_108 y z)))) (= x y))))) (let ((_let_188 (forall ((x |u_(-> produc398057191_a_nat set_Pr924198087_a_nat set_Pr924198087_a_nat)|) (y |u_(-> produc398057191_a_nat set_Pr924198087_a_nat set_Pr924198087_a_nat)|)) (or (not (forall ((z produc398057191_a_nat)) (= (ho_104 x z) (ho_104 y z)))) (= x y))))) (let ((_let_189 (forall ((x |u_(-> standard_Constant_a produc1871334759_a_nat)|) (y |u_(-> standard_Constant_a produc1871334759_a_nat)|)) (or (not (forall ((z standard_Constant_a)) (= (ho_131 x z) (ho_131 y z)))) (= x y))))) (let ((_let_190 (forall ((x |u_(-> set_Pr2106913242_nat_b Bool)|) (y |u_(-> set_Pr2106913242_nat_b Bool)|)) (or (not (forall ((z set_Pr2106913242_nat_b)) (= (ho_155 x z) (ho_155 y z)))) (= x y))))) (let ((_let_191 (forall ((x |u_(-> produc2112523263_b_b_b set_Pr357419743_b_b_b Bool)|) (y |u_(-> produc2112523263_b_b_b set_Pr357419743_b_b_b Bool)|)) (or (not (forall ((z produc2112523263_b_b_b)) (= (ho_351 x z) (ho_351 y z)))) (= x y))))) (let ((_let_192 (forall ((x |u_(-> labele1159362096nt_a_b set_Product_prod_b_b)|) (y |u_(-> labele1159362096nt_a_b set_Product_prod_b_b)|)) (or (not (forall ((z labele1159362096nt_a_b)) (= (ho_33 x z) (ho_33 y z)))) (= x y))))) (let ((_let_193 (forall ((x |u_(-> allego510293162tant_a set_Product_prod_b_b)|) (y |u_(-> allego510293162tant_a set_Product_prod_b_b)|)) (or (not (forall ((z allego510293162tant_a)) (= (ho_122 x z) (ho_122 y z)))) (= x y))))) (let ((_let_194 (forall ((x |u_(-> product_prod_b_b b produc2112523263_b_b_b)|) (y |u_(-> product_prod_b_b b produc2112523263_b_b_b)|)) (or (not (forall ((z product_prod_b_b)) (= (ho_348 x z) (ho_348 y z)))) (= x y))))) (let ((_let_195 (forall ((x |u_(-> labele1159362096nt_a_b set_b)|) (y |u_(-> labele1159362096nt_a_b set_b)|)) (or (not (forall ((z labele1159362096nt_a_b)) (= (ho_113 x z) (ho_113 y z)))) (= x y))))) (let ((_let_196 (forall ((x |u_(-> set_Pr2134561957od_b_b set_Pr1324126435od_b_b set_Product_prod_b_b)|) (y |u_(-> set_Pr2134561957od_b_b set_Pr1324126435od_b_b set_Product_prod_b_b)|)) (or (not (forall ((z set_Pr2134561957od_b_b)) (= (ho_243 x z) (ho_243 y z)))) (= x y))))) (let ((_let_197 (forall ((x |u_(-> set_Pr1324126435od_b_b set_Pr1324126435od_b_b)|) (y |u_(-> set_Pr1324126435od_b_b set_Pr1324126435od_b_b)|)) (or (not (forall ((z set_Pr1324126435od_b_b)) (= (ho_126 x z) (ho_126 y z)))) (= x y))))) (let ((_let_198 (forall ((x |u_(-> produc1213276845od_b_b set_Pr1324126435od_b_b set_Pr1324126435od_b_b)|) (y |u_(-> produc1213276845od_b_b set_Pr1324126435od_b_b set_Pr1324126435od_b_b)|)) (or (not (forall ((z produc1213276845od_b_b)) (= (ho_125 x z) (ho_125 y z)))) (= x y))))) (let ((_let_199 (forall ((x |u_(-> set_Pr1324126435od_b_b set_Pr621705391od_b_b)|) (y |u_(-> set_Pr1324126435od_b_b set_Pr621705391od_b_b)|)) (or (not (forall ((z set_Pr1324126435od_b_b)) (= (ho_382 x z) (ho_382 y z)))) (= x y))))) (let ((_let_200 (forall ((x |u_(-> set_Pr1324126435od_b_b set_b)|) (y |u_(-> set_Pr1324126435od_b_b set_b)|)) (or (not (forall ((z set_Pr1324126435od_b_b)) (= (ho_188 x z) (ho_188 y z)))) (= x y))))) (let ((_let_201 (forall ((x |u_(-> set_Pr357419743_b_b_b set_Product_prod_b_b set_b)|) (y |u_(-> set_Pr357419743_b_b_b set_Product_prod_b_b set_b)|)) (or (not (forall ((z set_Pr357419743_b_b_b)) (= (ho_345 x z) (ho_345 y z)))) (= x y))))) (let ((_let_202 (forall ((x |u_(-> set_Pr621705391od_b_b set_b set_Product_prod_b_b)|) (y |u_(-> set_Pr621705391od_b_b set_b set_Product_prod_b_b)|)) (or (not (forall ((z set_Pr621705391od_b_b)) (= (ho_138 x z) (ho_138 y z)))) (= x y))))) (let ((_let_203 (forall ((x |u_(-> set_Pr1987088711_a_nat set_Pr1987088711_a_nat Bool)|) (y |u_(-> set_Pr1987088711_a_nat set_Pr1987088711_a_nat Bool)|)) (or (not (forall ((z set_Pr1987088711_a_nat)) (= (ho_149 x z) (ho_149 y z)))) (= x y))))) (let ((_let_204 (forall ((x |u_(-> set_Pr1071216121od_b_b Bool)|) (y |u_(-> set_Pr1071216121od_b_b Bool)|)) (or (not (forall ((z set_Pr1071216121od_b_b)) (= (ho_258 x z) (ho_258 y z)))) (= x y))))) (let ((_let_205 (forall ((x |u_(-> set_Pr1987088711_a_nat set_Pr1987088711_a_nat set_Pr1987088711_a_nat)|) (y |u_(-> set_Pr1987088711_a_nat set_Pr1987088711_a_nat set_Pr1987088711_a_nat)|)) (or (not (forall ((z set_Pr1987088711_a_nat)) (= (ho_402 x z) (ho_402 y z)))) (= x y))))) (let ((_let_206 (forall ((x |u_(-> produc1213276845od_b_b produc1052326083od_b_b)|) (y |u_(-> produc1213276845od_b_b produc1052326083od_b_b)|)) (or (not (forall ((z produc1213276845od_b_b)) (= (ho_255 x z) (ho_255 y z)))) (= x y))))) (let ((_let_207 (forall ((x |u_(-> product_prod_b_b produc1213276845od_b_b produc1052326083od_b_b)|) (y |u_(-> product_prod_b_b produc1213276845od_b_b produc1052326083od_b_b)|)) (or (not (forall ((z product_prod_b_b)) (= (ho_254 x z) (ho_254 y z)))) (= x y))))) (let ((_let_208 (forall ((x |u_(-> produc1052326083od_b_b set_Pr1071216121od_b_b Bool)|) (y |u_(-> produc1052326083od_b_b set_Pr1071216121od_b_b Bool)|)) (or (not (forall ((z produc1052326083od_b_b)) (= (ho_257 x z) (ho_257 y z)))) (= x y))))) (let ((_let_209 (forall ((x |u_(-> set_b _u_(-> b standard_Constant_a)_ set_Pr1649131859tant_a)|) (y |u_(-> set_b _u_(-> b standard_Constant_a)_ set_Pr1649131859tant_a)|)) (or (not (forall ((z set_b)) (= (ho_378 x z) (ho_378 y z)))) (= x y))))) (let ((_let_210 (forall ((x |u_(-> set_Product_prod_b_b set_Pr1324126435od_b_b)|) (y |u_(-> set_Product_prod_b_b set_Pr1324126435od_b_b)|)) (or (not (forall ((z set_Product_prod_b_b)) (= (ho_261 x z) (ho_261 y z)))) (= x y))))) (let ((_let_211 (forall ((x |u_(-> set_la1083530965_a_nat set_la1083530965_a_nat)|) (y |u_(-> set_la1083530965_a_nat set_la1083530965_a_nat)|)) (or (not (forall ((z set_la1083530965_a_nat)) (= (ho_298 x z) (ho_298 y z)))) (= x y))))) (let ((_let_212 (forall ((x |u_(-> set_Pr1071216121od_b_b set_Product_prod_b_b set_Pr1324126435od_b_b)|) (y |u_(-> set_Pr1071216121od_b_b set_Product_prod_b_b set_Pr1324126435od_b_b)|)) (or (not (forall ((z set_Pr1071216121od_b_b)) (= (ho_260 x z) (ho_260 y z)))) (= x y))))) (let ((_let_213 (forall ((x |u_(-> set_Pr2007082183od_b_b set_Pr1324126435od_b_b)|) (y |u_(-> set_Pr2007082183od_b_b set_Pr1324126435od_b_b)|)) (or (not (forall ((z set_Pr2007082183od_b_b)) (= (ho_264 x z) (ho_264 y z)))) (= x y))))) (let ((_let_214 (forall ((x |u_(-> set_Pr1906739389_b_b_b labele1644675410od_b_b labele1159362096nt_a_b)|) (y |u_(-> set_Pr1906739389_b_b_b labele1644675410od_b_b labele1159362096nt_a_b)|)) (or (not (forall ((z set_Pr1906739389_b_b_b)) (= (ho_384 x z) (ho_384 y z)))) (= x y))))) (let ((_let_215 (forall ((x |u_(-> set_Pr1324126435od_b_b set_Pr2007082183od_b_b set_Pr1324126435od_b_b)|) (y |u_(-> set_Pr1324126435od_b_b set_Pr2007082183od_b_b set_Pr1324126435od_b_b)|)) (or (not (forall ((z set_Pr1324126435od_b_b)) (= (ho_263 x z) (ho_263 y z)))) (= x y))))) (let ((_let_216 (forall ((x |u_(-> set_Pr2060523537od_b_b set_b set_Pr1324126435od_b_b)|) (y |u_(-> set_Pr2060523537od_b_b set_b set_Pr1324126435od_b_b)|)) (or (not (forall ((z set_Pr2060523537od_b_b)) (= (ho_267 x z) (ho_267 y z)))) (= x y))))) (let ((_let_217 (forall ((x |u_(-> set_Pr2060523537od_b_b Bool)|) (y |u_(-> set_Pr2060523537od_b_b Bool)|)) (or (not (forall ((z set_Pr2060523537od_b_b)) (= (ho_274 x z) (ho_274 y z)))) (= x y))))) (let ((_let_218 (forall ((x |u_(-> b produc1213276845od_b_b produc1605346267od_b_b)|) (y |u_(-> b produc1213276845od_b_b produc1605346267od_b_b)|)) (or (not (forall ((z b)) (= (ho_270 x z) (ho_270 y z)))) (= x y))))) (let ((_let_219 (forall ((x |u_(-> produc1605346267od_b_b set_Pr2060523537od_b_b Bool)|) (y |u_(-> produc1605346267od_b_b set_Pr2060523537od_b_b Bool)|)) (or (not (forall ((z produc1605346267od_b_b)) (= (ho_273 x z) (ho_273 y z)))) (= x y))))) (let ((_let_220 (forall ((x |u_(-> set_Product_prod_b_b _u_(-> b set_b)_ Bool)|) (y |u_(-> set_Product_prod_b_b _u_(-> b set_b)_ Bool)|)) (or (not (forall ((z set_Product_prod_b_b)) (= (ho_406 x z) (ho_406 y z)))) (= x y))))) (let ((_let_221 (forall ((x |u_(-> set_Pr812188767_nat_b Bool)|) (y |u_(-> set_Pr812188767_nat_b Bool)|)) (or (not (forall ((z set_Pr812188767_nat_b)) (= (ho_281 x z) (ho_281 y z)))) (= x y))))) (let ((_let_222 (forall ((x |u_(-> labele1159362096nt_a_b set_Pr812188767_nat_b Bool)|) (y |u_(-> labele1159362096nt_a_b set_Pr812188767_nat_b Bool)|)) (or (not (forall ((z labele1159362096nt_a_b)) (= (ho_280 x z) (ho_280 y z)))) (= x y))))) (let ((_let_223 (forall ((x |u_(-> set_Pr1987088711_a_nat labele1322729112_a_nat)|) (y |u_(-> set_Pr1987088711_a_nat labele1322729112_a_nat)|)) (or (not (forall ((z set_Pr1987088711_a_nat)) (= (ho_277 x z) (ho_277 y z)))) (= x y))))) (let ((_let_224 (forall ((x |u_(-> labele1159362096nt_a_b labele1159362096nt_a_b produc1398946881nt_a_b)|) (y |u_(-> labele1159362096nt_a_b labele1159362096nt_a_b produc1398946881nt_a_b)|)) (or (not (forall ((z labele1159362096nt_a_b)) (= (ho_322 x z) (ho_322 y z)))) (= x y))))) (let ((_let_225 (forall ((x |u_(-> set_Pr197580003_a_nat set_Pr1987088711_a_nat labele1322729112_a_nat)|) (y |u_(-> set_Pr197580003_a_nat set_Pr1987088711_a_nat labele1322729112_a_nat)|)) (or (not (forall ((z set_Pr197580003_a_nat)) (= (ho_276 x z) (ho_276 y z)))) (= x y))))) (let ((_let_226 (forall ((x |u_(-> labele1322729112_a_nat labele1159362096nt_a_b set_Pr812188767_nat_b Bool)|) (y |u_(-> labele1322729112_a_nat labele1159362096nt_a_b set_Pr812188767_nat_b Bool)|)) (or (not (forall ((z labele1322729112_a_nat)) (= (ho_279 x z) (ho_279 y z)))) (= x y))))) (let ((_let_227 (forall ((x |u_(-> standard_Constant_a set_St761939237tant_a set_St761939237tant_a)|) (y |u_(-> standard_Constant_a set_St761939237tant_a set_St761939237tant_a)|)) (or (not (forall ((z standard_Constant_a)) (= (ho_283 x z) (ho_283 y z)))) (= x y))))) (let ((_let_228 (forall ((x |u_(-> set_Product_prod_b_b set_Pr2007082183od_b_b)|) (y |u_(-> set_Product_prod_b_b set_Pr2007082183od_b_b)|)) (or (not (forall ((z set_Product_prod_b_b)) (= (ho_286 x z) (ho_286 y z)))) (= x y))))) (let ((_let_229 (forall ((x |u_(-> produc1871334759_a_nat Bool)|) (y |u_(-> produc1871334759_a_nat Bool)|)) (or (not (forall ((z produc1871334759_a_nat)) (= (ho_287 x z) (ho_287 y z)))) (= x y))))) (let ((_let_230 (forall ((x |u_(-> _u_(-> labele935650037_a_nat labele935650037_a_nat)_ set_Pr1987088711_a_nat)|) (y |u_(-> _u_(-> labele935650037_a_nat labele935650037_a_nat)_ set_Pr1987088711_a_nat)|)) (or (not (forall ((z |u_(-> labele935650037_a_nat labele935650037_a_nat)|)) (= (ho_293 x z) (ho_293 y z)))) (= x y))))) (let ((_let_231 (forall ((x |u_(-> set_la1083530965_a_nat _u_(-> labele935650037_a_nat labele935650037_a_nat)_ set_Pr1987088711_a_nat)|) (y |u_(-> set_la1083530965_a_nat _u_(-> labele935650037_a_nat labele935650037_a_nat)_ set_Pr1987088711_a_nat)|)) (or (not (forall ((z set_la1083530965_a_nat)) (= (ho_292 x z) (ho_292 y z)))) (= x y))))) (let ((_let_232 (forall ((x |u_(-> produc1871334759_a_nat labele1159362096nt_a_b set_Pr2106913242_nat_b Bool)|) (y |u_(-> produc1871334759_a_nat labele1159362096nt_a_b set_Pr2106913242_nat_b Bool)|)) (or (not (forall ((z produc1871334759_a_nat)) (= (ho_295 x z) (ho_295 y z)))) (= x y))))) (let ((_let_233 (forall ((x |u_(-> labele935650037_a_nat set_la1083530965_a_nat set_la1083530965_a_nat)|) (y |u_(-> labele935650037_a_nat set_la1083530965_a_nat set_la1083530965_a_nat)|)) (or (not (forall ((z labele935650037_a_nat)) (= (ho_297 x z) (ho_297 y z)))) (= x y))))) (let ((_let_234 (forall ((x |u_(-> labele1644675410od_b_b set_Pr1190604087od_b_b)|) (y |u_(-> labele1644675410od_b_b set_Pr1190604087od_b_b)|)) (or (not (forall ((z labele1644675410od_b_b)) (= (ho_303 x z) (ho_303 y z)))) (= x y))))) (let ((_let_235 (forall ((x |u_(-> set_Pr1190604087od_b_b set_Pr1324126435od_b_b Bool)|) (y |u_(-> set_Pr1190604087od_b_b set_Pr1324126435od_b_b Bool)|)) (or (not (forall ((z set_Pr1190604087od_b_b)) (= (ho_312 x z) (ho_312 y z)))) (= x y))))) (let ((_let_236 (forall ((x |u_(-> produc1213276845od_b_b b)|) (y |u_(-> produc1213276845od_b_b b)|)) (or (not (forall ((z produc1213276845od_b_b)) (= (ho_304 x z) (ho_304 y z)))) (= x y))))) (let ((_let_237 (forall ((x |u_(-> labele1644675410od_b_b set_Pr1324126435od_b_b)|) (y |u_(-> labele1644675410od_b_b set_Pr1324126435od_b_b)|)) (or (not (forall ((z labele1644675410od_b_b)) (= (ho_306 x z) (ho_306 y z)))) (= x y))))) (let ((_let_238 (forall ((x |u_(-> set_Pr1190604087od_b_b Bool)|) (y |u_(-> set_Pr1190604087od_b_b Bool)|)) (or (not (forall ((z set_Pr1190604087od_b_b)) (= (ho_318 x z) (ho_318 y z)))) (= x y))))) (let ((_let_239 (forall ((x |u_(-> produc970027067od_b_b produc1084374401od_b_b)|) (y |u_(-> produc970027067od_b_b produc1084374401od_b_b)|)) (or (not (forall ((z produc970027067od_b_b)) (= (ho_315 x z) (ho_315 y z)))) (= x y))))) (let ((_let_240 (forall ((x |u_(-> produc1084374401od_b_b set_Pr1190604087od_b_b Bool)|) (y |u_(-> produc1084374401od_b_b set_Pr1190604087od_b_b Bool)|)) (or (not (forall ((z produc1084374401od_b_b)) (= (ho_317 x z) (ho_317 y z)))) (= x y))))) (let ((_let_241 (forall ((x |u_(-> labele1159362096nt_a_b produc1398946881nt_a_b)|) (y |u_(-> labele1159362096nt_a_b produc1398946881nt_a_b)|)) (or (not (forall ((z labele1159362096nt_a_b)) (= (ho_323 x z) (ho_323 y z)))) (= x y))))) (let ((_let_242 (forall ((x |u_(-> set_Pr2007082183od_b_b set_Product_prod_b_b set_Product_prod_b_b)|) (y |u_(-> set_Pr2007082183od_b_b set_Product_prod_b_b set_Product_prod_b_b)|)) (or (not (forall ((z set_Pr2007082183od_b_b)) (= (ho_343 x z) (ho_343 y z)))) (= x y))))) (let ((_let_243 (forall ((x |u_(-> set_Pr1954438265od_b_b Bool)|) (y |u_(-> set_Pr1954438265od_b_b Bool)|)) (or (not (forall ((z set_Pr1954438265od_b_b)) (= (ho_331 x z) (ho_331 y z)))) (= x y))))) (let ((_let_244 (forall ((x |u_(-> produc1871334759_a_nat produc1213276845od_b_b produc1169496899od_b_b)|) (y |u_(-> produc1871334759_a_nat produc1213276845od_b_b produc1169496899od_b_b)|)) (or (not (forall ((z produc1871334759_a_nat)) (= (ho_327 x z) (ho_327 y z)))) (= x y))))) (let ((_let_245 (forall ((x |u_(-> produc1169496899od_b_b set_Pr1954438265od_b_b Bool)|) (y |u_(-> produc1169496899od_b_b set_Pr1954438265od_b_b Bool)|)) (or (not (forall ((z produc1169496899od_b_b)) (= (ho_330 x z) (ho_330 y z)))) (= x y))))) (let ((_let_246 (forall ((x |u_(-> set_Pr1987088711_a_nat set_Pr1324126435od_b_b)|) (y |u_(-> set_Pr1987088711_a_nat set_Pr1324126435od_b_b)|)) (or (not (forall ((z set_Pr1987088711_a_nat)) (= (ho_334 x z) (ho_334 y z)))) (= x y))))) (let ((_let_247 (forall ((x |u_(-> set_Pr924198087_a_nat set_Pr924198087_a_nat Bool)|) (y |u_(-> set_Pr924198087_a_nat set_Pr924198087_a_nat Bool)|)) (or (not (forall ((z set_Pr924198087_a_nat)) (= (ho_337 x z) (ho_337 y z)))) (= x y))))) (let ((_let_248 (forall ((x |u_(-> set_Pr1987088711_a_nat labele1159362096nt_a_b Bool)|) (y |u_(-> set_Pr1987088711_a_nat labele1159362096nt_a_b Bool)|)) (or (not (forall ((z set_Pr1987088711_a_nat)) (= (ho_339 x z) (ho_339 y z)))) (= x y))))) (let ((_let_249 (forall ((x |u_(-> set_Product_prod_b_b set_b)|) (y |u_(-> set_Product_prod_b_b set_b)|)) (or (not (forall ((z set_Product_prod_b_b)) (= (ho_346 x z) (ho_346 y z)))) (= x y))))) (let ((_let_250 (forall ((x |u_(-> set_Product_prod_b_b set_Pr1324126435od_b_b set_Pr1324126435od_b_b Bool)|) (y |u_(-> set_Product_prod_b_b set_Pr1324126435od_b_b set_Pr1324126435od_b_b Bool)|)) (or (not (forall ((z set_Product_prod_b_b)) (= (ho_354 x z) (ho_354 y z)))) (= x y))))) (let ((_let_251 (forall ((x |u_(-> b produc845793663_nat_b)|) (y |u_(-> b produc845793663_nat_b)|)) (or (not (forall ((z b)) (= (ho_357 x z) (ho_357 y z)))) (= x y))))) (let ((_let_252 (forall ((x |u_(-> produc845793663_nat_b set_Pr812188767_nat_b Bool)|) (y |u_(-> produc845793663_nat_b set_Pr812188767_nat_b Bool)|)) (or (not (forall ((z produc845793663_nat_b)) (= (ho_359 x z) (ho_359 y z)))) (= x y))))) (let ((_let_253 (forall ((x |u_(-> _u_(-> produc1213276845od_b_b Bool)_ set_Pr1324126435od_b_b)|) (y |u_(-> _u_(-> produc1213276845od_b_b Bool)_ set_Pr1324126435od_b_b)|)) (or (not (forall ((z |u_(-> produc1213276845od_b_b Bool)|)) (= (ho_364 x z) (ho_364 y z)))) (= x y))))) (let ((_let_254 (forall ((x |u_(-> labele1835558936od_b_b set_Pr1021918435od_b_b)|) (y |u_(-> labele1835558936od_b_b set_Pr1021918435od_b_b)|)) (or (not (forall ((z labele1835558936od_b_b)) (= (ho_366 x z) (ho_366 y z)))) (= x y))))) (let ((_let_255 (forall ((x |u_(-> set_Pr357419743_b_b_b set_Pr1021918435od_b_b set_Pr1324126435od_b_b Bool)|) (y |u_(-> set_Pr357419743_b_b_b set_Pr1021918435od_b_b set_Pr1324126435od_b_b Bool)|)) (or (not (forall ((z set_Pr357419743_b_b_b)) (= (ho_368 x z) (ho_368 y z)))) (= x y))))) (let ((_let_256 (forall ((x |u_(-> produc1168037607od_b_b produc644633773od_b_b)|) (y |u_(-> produc1168037607od_b_b produc644633773od_b_b)|)) (or (not (forall ((z produc1168037607od_b_b)) (= (ho_372 x z) (ho_372 y z)))) (= x y))))) (let ((_let_257 (forall ((x |u_(-> b standard_Constant_a)|) (y |u_(-> b standard_Constant_a)|)) (or (not (forall ((z b)) (= (ho_376 x z) (ho_376 y z)))) (= x y))))) (let ((_let_258 (forall ((x |u_(-> standard_Constant_a produc1168037607od_b_b produc644633773od_b_b)|) (y |u_(-> standard_Constant_a produc1168037607od_b_b produc644633773od_b_b)|)) (or (not (forall ((z standard_Constant_a)) (= (ho_371 x z) (ho_371 y z)))) (= x y))))) (let ((_let_259 (forall ((x |u_(-> produc644633773od_b_b set_Pr1021918435od_b_b Bool)|) (y |u_(-> produc644633773od_b_b set_Pr1021918435od_b_b Bool)|)) (or (not (forall ((z produc644633773od_b_b)) (= (ho_374 x z) (ho_374 y z)))) (= x y))))) (let ((_let_260 (forall ((x |u_(-> _u_(-> b standard_Constant_a)_ set_Pr1649131859tant_a)|) (y |u_(-> _u_(-> b standard_Constant_a)_ set_Pr1649131859tant_a)|)) (or (not (forall ((z |u_(-> b standard_Constant_a)|)) (= (ho_379 x z) (ho_379 y z)))) (= x y))))) (let ((_let_261 (forall ((x |u_(-> labele1644675410od_b_b labele1159362096nt_a_b)|) (y |u_(-> labele1644675410od_b_b labele1159362096nt_a_b)|)) (or (not (forall ((z labele1644675410od_b_b)) (= (ho_385 x z) (ho_385 y z)))) (= x y))))) (let ((_let_262 (forall ((x |u_(-> standard_Constant_a labele1644675410od_b_b set_Pr2109276827od_b_b)|) (y |u_(-> standard_Constant_a labele1644675410od_b_b set_Pr2109276827od_b_b)|)) (or (not (forall ((z standard_Constant_a)) (= (ho_387 x z) (ho_387 y z)))) (= x y))))) (let ((_let_263 (forall ((x |u_(-> produc1398946881nt_a_b labele1159362096nt_a_b Bool)|) (y |u_(-> produc1398946881nt_a_b labele1159362096nt_a_b Bool)|)) (or (not (forall ((z produc1398946881nt_a_b)) (= (ho_390 x z) (ho_390 y z)))) (= x y))))) (let ((_let_264 (forall ((x |u_(-> set_Pr667377223od_b_b Bool)|) (y |u_(-> set_Pr667377223od_b_b Bool)|)) (or (not (forall ((z set_Pr667377223od_b_b)) (= (ho_397 x z) (ho_397 y z)))) (= x y))))) (let ((_let_265 (forall ((x |u_(-> produc1871334759_a_nat product_prod_b_b produc1485083751od_b_b)|) (y |u_(-> produc1871334759_a_nat product_prod_b_b produc1485083751od_b_b)|)) (or (not (forall ((z produc1871334759_a_nat)) (= (ho_393 x z) (ho_393 y z)))) (= x y))))) (let ((_let_266 (forall ((x |u_(-> set_Pr1987088711_a_nat set_Product_prod_b_b)|) (y |u_(-> set_Pr1987088711_a_nat set_Product_prod_b_b)|)) (or (not (forall ((z set_Pr1987088711_a_nat)) (= (ho_400 x z) (ho_400 y z)))) (= x y))))) (let ((_let_267 (forall ((x |u_(-> _u_(-> product_prod_b_b Bool)_ set_Product_prod_b_b)|) (y |u_(-> _u_(-> product_prod_b_b Bool)_ set_Product_prod_b_b)|)) (or (not (forall ((z |u_(-> product_prod_b_b Bool)|)) (= (ho_404 x z) (ho_404 y z)))) (= x y))))) (let ((_let_268 (forall ((x |u_(-> set_Pr1987088711_a_nat set_la1083530965_a_nat set_la1083530965_a_nat)|) (y |u_(-> set_Pr1987088711_a_nat set_la1083530965_a_nat set_la1083530965_a_nat)|)) (or (not (forall ((z set_Pr1987088711_a_nat)) (= (ho_409 x z) (ho_409 y z)))) (= x y))))) (let ((_let_269 (forall ((BOUND_VARIABLE_11059 b) (BOUND_VARIABLE_11060 b)) (= (ho_41 (ho_40 k_39 BOUND_VARIABLE_11059) BOUND_VARIABLE_11060) (ho_38 (ho_37 k_36 BOUND_VARIABLE_11060) (ho_30 (ho_35 k_34 (ho_33 (ho_32 k_31 standard_S_Idt_a) g)) (ho_30 (ho_29 k_28 BOUND_VARIABLE_11059) bot_bot_set_b))))))) (let ((_let_270 (forall ((BOUND_VARIABLE_11048 b) (BOUND_VARIABLE_11049 b)) (= (ho_41 (ho_40 k_42 BOUND_VARIABLE_11048) BOUND_VARIABLE_11049) (ho_38 (ho_37 k_36 BOUND_VARIABLE_11049) (ho_30 (ho_35 k_34 (ho_33 (ho_32 k_31 standard_S_Idt_a) g)) (ho_30 (ho_29 k_28 BOUND_VARIABLE_11048) bot_bot_set_b))))))) (let ((_let_271 (forall ((BOUND_VARIABLE_11037 b) (BOUND_VARIABLE_11038 b)) (= (ho_41 (ho_40 k_43 BOUND_VARIABLE_11037) BOUND_VARIABLE_11038) (ho_38 (ho_37 k_36 BOUND_VARIABLE_11038) (ho_30 (ho_35 k_34 (ho_33 (ho_32 k_31 standard_S_Idt_a) g)) (ho_30 (ho_29 k_28 BOUND_VARIABLE_11037) bot_bot_set_b))))))) (let ((_let_272 (forall ((BOUND_VARIABLE_11026 set_Pr1324126435od_b_b) (BOUND_VARIABLE_11027 set_Pr1324126435od_b_b)) (= (ho_46 (ho_48 k_47 BOUND_VARIABLE_11026) BOUND_VARIABLE_11027) (forall ((X5 produc1213276845od_b_b)) (let ((_let_1 (ho_45 k_44 X5))) (or (not (ho_46 _let_1 BOUND_VARIABLE_11026)) (ho_46 _let_1 BOUND_VARIABLE_11027)))))))) (let ((_let_273 (forall ((BOUND_VARIABLE_11015 set_Pr1324126435od_b_b) (BOUND_VARIABLE_11016 set_Pr1324126435od_b_b)) (= (ho_46 (ho_48 k_49 BOUND_VARIABLE_11015) BOUND_VARIABLE_11016) (forall ((T produc1213276845od_b_b)) (let ((_let_1 (ho_45 k_44 T))) (or (not (ho_46 _let_1 BOUND_VARIABLE_11015)) (ho_46 _let_1 BOUND_VARIABLE_11016)))))))) (let ((_let_274 (forall ((BOUND_VARIABLE_11004 b) (BOUND_VARIABLE_11005 b)) (= (ho_41 (ho_40 k_50 BOUND_VARIABLE_11004) BOUND_VARIABLE_11005) (ho_38 (ho_37 k_36 BOUND_VARIABLE_11005) (ho_30 (ho_35 k_34 (ho_33 (ho_32 k_31 standard_S_Idt_a) g)) (ho_30 (ho_29 k_28 BOUND_VARIABLE_11004) bot_bot_set_b))))))) (let ((_let_275 (forall ((BOUND_VARIABLE_10993 set_Product_prod_b_b) (BOUND_VARIABLE_10994 set_Product_prod_b_b)) (= (ho_53 (ho_55 k_54 BOUND_VARIABLE_10993) BOUND_VARIABLE_10994) (forall ((X5 product_prod_b_b)) (let ((_let_1 (ho_52 k_51 X5))) (or (not (ho_53 _let_1 BOUND_VARIABLE_10993)) (ho_53 _let_1 BOUND_VARIABLE_10994)))))))) (let ((_let_276 (forall ((BOUND_VARIABLE_10982 set_Product_prod_b_b) (BOUND_VARIABLE_10983 set_Product_prod_b_b)) (= (ho_53 (ho_55 k_56 BOUND_VARIABLE_10982) BOUND_VARIABLE_10983) (forall ((T product_prod_b_b)) (let ((_let_1 (ho_52 k_51 T))) (or (not (ho_53 _let_1 BOUND_VARIABLE_10982)) (ho_53 _let_1 BOUND_VARIABLE_10983)))))))) (let ((_let_277 (forall ((BOUND_VARIABLE_10974 set_Product_prod_b_b) (BOUND_VARIABLE_10975 product_prod_b_b)) (= (ho_59 (ho_58 k_57 BOUND_VARIABLE_10974) BOUND_VARIABLE_10975) (ho_53 (ho_52 k_51 BOUND_VARIABLE_10975) BOUND_VARIABLE_10974))))) (let ((_let_278 (forall ((BOUND_VARIABLE_10963 set_b) (BOUND_VARIABLE_10964 set_b)) (= (ho_38 (ho_61 k_60 BOUND_VARIABLE_10963) BOUND_VARIABLE_10964) (forall ((T b)) (let ((_let_1 (ho_37 k_36 T))) (or (not (ho_38 _let_1 BOUND_VARIABLE_10963)) (ho_38 _let_1 BOUND_VARIABLE_10964)))))))) (let ((_let_279 (forall ((BOUND_VARIABLE_10952 set_b) (BOUND_VARIABLE_10953 set_b)) (= (ho_38 (ho_61 k_62 BOUND_VARIABLE_10952) BOUND_VARIABLE_10953) (forall ((X5 b)) (let ((_let_1 (ho_37 k_36 X5))) (or (not (ho_38 _let_1 BOUND_VARIABLE_10952)) (ho_38 _let_1 BOUND_VARIABLE_10953)))))))) (let ((_let_280 (forall ((BOUND_VARIABLE_10940 standard_Constant_a) (BOUND_VARIABLE_10941 b)) (= (ho_65 (ho_64 k_63 BOUND_VARIABLE_10940) BOUND_VARIABLE_10941) (ho_30 (ho_35 k_34 (ho_33 (ho_32 k_31 BOUND_VARIABLE_10940) g)) (ho_30 (ho_29 k_28 BOUND_VARIABLE_10941) bot_bot_set_b)))))) (let ((_let_281 (forall ((BOUND_VARIABLE_10929 b) (BOUND_VARIABLE_10930 b)) (= (ho_41 (ho_40 k_66 BOUND_VARIABLE_10929) BOUND_VARIABLE_10930) (ho_38 (ho_37 k_36 BOUND_VARIABLE_10930) (ho_30 (ho_35 k_34 (ho_33 (ho_32 k_31 standard_S_Idt_a) g)) (ho_30 (ho_29 k_28 BOUND_VARIABLE_10929) bot_bot_set_b))))))) (let ((_let_282 (forall ((BOUND_VARIABLE_10922 b)) (= (ho_41 k_67 BOUND_VARIABLE_10922) (ho_38 (ho_37 k_36 BOUND_VARIABLE_10922) (ho_30 (ho_35 k_34 (ho_33 (ho_32 k_31 standard_S_Idt_a) g)) (ho_30 (ho_29 k_28 x) bot_bot_set_b))))))) (let ((_let_283 (forall ((BOUND_VARIABLE_10894 b)) (= (ho_73 (ho_72 (ho_71 k_70 (= bot_bot_set_b (ho_30 (ho_35 k_34 (ho_33 (ho_32 k_31 standard_S_Idt_a) g)) (ho_30 (ho_29 k_28 BOUND_VARIABLE_10894) bot_bot_set_b)))) BOUND_VARIABLE_10894) (ho_69 k_68 (ho_40 k_39 BOUND_VARIABLE_10894))) (ho_73 k_74 BOUND_VARIABLE_10894))))) (let ((_let_284 (forall ((BOUND_VARIABLE_10883 b) (BOUND_VARIABLE_10884 b)) (= (ho_41 (ho_40 k_75 BOUND_VARIABLE_10883) BOUND_VARIABLE_10884) (ho_38 (ho_37 k_36 BOUND_VARIABLE_10884) (ho_30 (ho_35 k_34 (ho_33 (ho_32 k_31 standard_S_Idt_a) g)) (ho_30 (ho_29 k_28 BOUND_VARIABLE_10883) bot_bot_set_b))))))) (let ((_let_285 (forall ((BOUND_VARIABLE_10872 b) (BOUND_VARIABLE_10873 b)) (= (ho_41 (ho_40 k_76 BOUND_VARIABLE_10872) BOUND_VARIABLE_10873) (ho_38 (ho_37 k_36 BOUND_VARIABLE_10873) (ho_30 (ho_35 k_34 (ho_33 (ho_32 k_31 standard_S_Idt_a) g)) (ho_30 (ho_29 k_28 BOUND_VARIABLE_10872) bot_bot_set_b))))))) (let ((_let_286 (forall ((BOUND_VARIABLE_10864 set_Pr1324126435od_b_b) (BOUND_VARIABLE_10865 produc1213276845od_b_b)) (= (ho_79 (ho_78 k_77 BOUND_VARIABLE_10864) BOUND_VARIABLE_10865) (ho_46 (ho_45 k_44 BOUND_VARIABLE_10865) BOUND_VARIABLE_10864))))) (let ((_let_287 (forall ((BOUND_VARIABLE_10857 b)) (= (ho_81 k_80 BOUND_VARIABLE_10857) (ho_81 (ho_83 k_82 BOUND_VARIABLE_10857) BOUND_VARIABLE_10857))))) (let ((_let_288 (forall ((BOUND_VARIABLE_10850 b)) (= (ho_41 k_84 BOUND_VARIABLE_10850) (ho_38 (ho_37 k_36 BOUND_VARIABLE_10850) (ho_30 (ho_35 k_34 (ho_33 (ho_32 k_31 standard_S_Idt_a) g)) (ho_30 (ho_29 k_28 y) bot_bot_set_b))))))) (let ((_let_289 (forall ((BOUND_VARIABLE_10831 b) (BOUND_VARIABLE_10832 b)) (= (ho_41 (ho_40 k_87 BOUND_VARIABLE_10831) BOUND_VARIABLE_10832) (ho_38 (ho_37 k_36 BOUND_VARIABLE_10832) (ho_30 (ho_35 k_34 (ho_33 (ho_32 k_31 standard_S_Idt_a) g)) (ho_30 (ho_29 k_28 BOUND_VARIABLE_10831) bot_bot_set_b))))))) (let ((_let_290 (forall ((BOUND_VARIABLE_10820 b) (BOUND_VARIABLE_10821 b)) (= (ho_41 (ho_40 k_88 BOUND_VARIABLE_10820) BOUND_VARIABLE_10821) (ho_38 (ho_37 k_36 BOUND_VARIABLE_10821) (ho_30 (ho_35 k_34 (ho_33 (ho_32 k_31 standard_S_Idt_a) g)) (ho_30 (ho_29 k_28 BOUND_VARIABLE_10820) bot_bot_set_b))))))) (let ((_let_291 (forall ((BOUND_VARIABLE_10787 b) (BOUND_VARIABLE_10788 b)) (= (ho_41 (ho_40 k_89 BOUND_VARIABLE_10787) BOUND_VARIABLE_10788) (ho_38 (ho_37 k_36 BOUND_VARIABLE_10788) (ho_30 (ho_35 k_34 (ho_33 (ho_32 k_31 standard_S_Idt_a) g)) (ho_30 (ho_29 k_28 (ho_69 k_68 (ho_40 k_42 BOUND_VARIABLE_10787))) bot_bot_set_b))))))) (let ((_let_292 (forall ((BOUND_VARIABLE_10776 b) (BOUND_VARIABLE_10777 b)) (= (ho_41 (ho_40 k_90 BOUND_VARIABLE_10776) BOUND_VARIABLE_10777) (ho_38 (ho_37 k_36 BOUND_VARIABLE_10777) (ho_30 (ho_35 k_34 (ho_33 (ho_32 k_31 standard_S_Idt_a) g)) (ho_30 (ho_29 k_28 BOUND_VARIABLE_10776) bot_bot_set_b))))))) (let ((_let_293 (forall ((BOUND_VARIABLE_10765 b) (BOUND_VARIABLE_10766 b)) (= (ho_41 (ho_40 k_91 BOUND_VARIABLE_10765) BOUND_VARIABLE_10766) (ho_38 (ho_37 k_36 BOUND_VARIABLE_10766) (ho_30 (ho_35 k_34 (ho_33 (ho_32 k_31 standard_S_Idt_a) g)) (ho_30 (ho_29 k_28 BOUND_VARIABLE_10765) bot_bot_set_b))))))) (let ((_let_294 (forall ((BOUND_VARIABLE_10737 b)) (= (ho_73 (ho_72 (ho_71 k_70 (= bot_bot_set_b (ho_30 (ho_35 k_34 (ho_33 (ho_32 k_31 standard_S_Idt_a) g)) (ho_30 (ho_29 k_28 BOUND_VARIABLE_10737) bot_bot_set_b)))) BOUND_VARIABLE_10737) (ho_69 k_68 (ho_40 k_43 BOUND_VARIABLE_10737))) (ho_73 k_92 BOUND_VARIABLE_10737))))) (let ((_let_295 (forall ((X1 b) (X22 b) (R set_Product_prod_b_b) (S set_Product_prod_b_b) (BOUND_VARIABLE_11526 |u_(-> b b Bool)|)) (or (not (ho_53 (ho_52 k_51 (ho_81 (ho_83 k_82 X1) X22)) (ho_95 (ho_94 k_93 R) S))) (not (forall ((A4 b) (B5 b) (C2 b)) (or (not (ho_53 (ho_52 k_51 (ho_81 (ho_83 k_82 A4) B5)) R)) (not (ho_53 (ho_52 k_51 (ho_81 (ho_83 k_82 B5) C2)) S)) (ho_41 (ho_40 BOUND_VARIABLE_11526 A4) C2)))) (ho_41 (ho_40 BOUND_VARIABLE_11526 X1) X22))))) (let ((_let_296 (forall ((BOUND_VARIABLE_11059 b) (BOUND_VARIABLE_11060 b)) (= (ll_27 BOUND_VARIABLE_11059 BOUND_VARIABLE_11060) ((member_b BOUND_VARIABLE_11060) ((image_b_b ((getRel904497637nt_a_b standard_S_Idt_a) g)) ((insert_b BOUND_VARIABLE_11059) bot_bot_set_b))))))) (let ((_let_297 (forall ((BOUND_VARIABLE_11048 b) (BOUND_VARIABLE_11049 b)) (= (ll_26 BOUND_VARIABLE_11048 BOUND_VARIABLE_11049) ((member_b BOUND_VARIABLE_11049) ((image_b_b ((getRel904497637nt_a_b standard_S_Idt_a) g)) ((insert_b BOUND_VARIABLE_11048) bot_bot_set_b))))))) (let ((_let_298 (forall ((BOUND_VARIABLE_11037 b) (BOUND_VARIABLE_11038 b)) (= (ll_25 BOUND_VARIABLE_11037 BOUND_VARIABLE_11038) ((member_b BOUND_VARIABLE_11038) ((image_b_b ((getRel904497637nt_a_b standard_S_Idt_a) g)) ((insert_b BOUND_VARIABLE_11037) bot_bot_set_b))))))) (let ((_let_299 (forall ((BOUND_VARIABLE_11026 set_Pr1324126435od_b_b) (BOUND_VARIABLE_11027 set_Pr1324126435od_b_b)) (= (ll_24 BOUND_VARIABLE_11026 BOUND_VARIABLE_11027) (forall ((X5 produc1213276845od_b_b)) (let ((_let_1 (member1516365892od_b_b X5))) (or (not (_let_1 BOUND_VARIABLE_11026)) (_let_1 BOUND_VARIABLE_11027)))))))) (let ((_let_300 (forall ((BOUND_VARIABLE_11015 set_Pr1324126435od_b_b) (BOUND_VARIABLE_11016 set_Pr1324126435od_b_b)) (= (ll_23 BOUND_VARIABLE_11015 BOUND_VARIABLE_11016) (forall ((T produc1213276845od_b_b)) (let ((_let_1 (member1516365892od_b_b T))) (or (not (_let_1 BOUND_VARIABLE_11015)) (_let_1 BOUND_VARIABLE_11016)))))))) (let ((_let_301 (forall ((BOUND_VARIABLE_11004 b) (BOUND_VARIABLE_11005 b)) (= (ll_22 BOUND_VARIABLE_11004 BOUND_VARIABLE_11005) ((member_b BOUND_VARIABLE_11005) ((image_b_b ((getRel904497637nt_a_b standard_S_Idt_a) g)) ((insert_b BOUND_VARIABLE_11004) bot_bot_set_b))))))) (let ((_let_302 (forall ((BOUND_VARIABLE_10993 set_Product_prod_b_b) (BOUND_VARIABLE_10994 set_Product_prod_b_b)) (= (ll_21 BOUND_VARIABLE_10993 BOUND_VARIABLE_10994) (forall ((X5 product_prod_b_b)) (let ((_let_1 (member1285940496od_b_b X5))) (or (not (_let_1 BOUND_VARIABLE_10993)) (_let_1 BOUND_VARIABLE_10994)))))))) (let ((_let_303 (forall ((BOUND_VARIABLE_10982 set_Product_prod_b_b) (BOUND_VARIABLE_10983 set_Product_prod_b_b)) (= (ll_20 BOUND_VARIABLE_10982 BOUND_VARIABLE_10983) (forall ((T product_prod_b_b)) (let ((_let_1 (member1285940496od_b_b T))) (or (not (_let_1 BOUND_VARIABLE_10982)) (_let_1 BOUND_VARIABLE_10983)))))))) (let ((_let_304 (forall ((BOUND_VARIABLE_10974 set_Product_prod_b_b) (BOUND_VARIABLE_10975 product_prod_b_b)) (= (ll_19 BOUND_VARIABLE_10974 BOUND_VARIABLE_10975) ((member1285940496od_b_b BOUND_VARIABLE_10975) BOUND_VARIABLE_10974))))) (let ((_let_305 (forall ((BOUND_VARIABLE_10963 set_b) (BOUND_VARIABLE_10964 set_b)) (= (ll_18 BOUND_VARIABLE_10963 BOUND_VARIABLE_10964) (forall ((T b)) (let ((_let_1 (member_b T))) (or (not (_let_1 BOUND_VARIABLE_10963)) (_let_1 BOUND_VARIABLE_10964)))))))) (let ((_let_306 (forall ((BOUND_VARIABLE_10952 set_b) (BOUND_VARIABLE_10953 set_b)) (= (ll_17 BOUND_VARIABLE_10952 BOUND_VARIABLE_10953) (forall ((X5 b)) (let ((_let_1 (member_b X5))) (or (not (_let_1 BOUND_VARIABLE_10952)) (_let_1 BOUND_VARIABLE_10953)))))))) (let ((_let_307 (forall ((BOUND_VARIABLE_10940 standard_Constant_a) (BOUND_VARIABLE_10941 b)) (= ((image_b_b ((getRel904497637nt_a_b BOUND_VARIABLE_10940) g)) ((insert_b BOUND_VARIABLE_10941) bot_bot_set_b)) (ll_16 BOUND_VARIABLE_10940 BOUND_VARIABLE_10941))))) (let ((_let_308 (forall ((BOUND_VARIABLE_10929 b) (BOUND_VARIABLE_10930 b)) (= (ll_15 BOUND_VARIABLE_10929 BOUND_VARIABLE_10930) ((member_b BOUND_VARIABLE_10930) ((image_b_b ((getRel904497637nt_a_b standard_S_Idt_a) g)) ((insert_b BOUND_VARIABLE_10929) bot_bot_set_b))))))) (let ((_let_309 (forall ((BOUND_VARIABLE_10922 b)) (= (ll_14 BOUND_VARIABLE_10922) ((member_b BOUND_VARIABLE_10922) ((image_b_b ((getRel904497637nt_a_b standard_S_Idt_a) g)) ((insert_b x) bot_bot_set_b))))))) (let ((_let_310 (forall ((BOUND_VARIABLE_10894 b)) (= (ll_13 BOUND_VARIABLE_10894) (((if_b (= bot_bot_set_b ((image_b_b ((getRel904497637nt_a_b standard_S_Idt_a) g)) ((insert_b BOUND_VARIABLE_10894) bot_bot_set_b)))) BOUND_VARIABLE_10894) (hilbert_Eps_b (ll_27 BOUND_VARIABLE_10894))))))) (let ((_let_311 (forall ((BOUND_VARIABLE_10883 b) (BOUND_VARIABLE_10884 b)) (= (ll_12 BOUND_VARIABLE_10883 BOUND_VARIABLE_10884) ((member_b BOUND_VARIABLE_10884) ((image_b_b ((getRel904497637nt_a_b standard_S_Idt_a) g)) ((insert_b BOUND_VARIABLE_10883) bot_bot_set_b))))))) (let ((_let_312 (forall ((BOUND_VARIABLE_10872 b) (BOUND_VARIABLE_10873 b)) (= (ll_11 BOUND_VARIABLE_10872 BOUND_VARIABLE_10873) ((member_b BOUND_VARIABLE_10873) ((image_b_b ((getRel904497637nt_a_b standard_S_Idt_a) g)) ((insert_b BOUND_VARIABLE_10872) bot_bot_set_b))))))) (let ((_let_313 (forall ((BOUND_VARIABLE_10864 set_Pr1324126435od_b_b) (BOUND_VARIABLE_10865 produc1213276845od_b_b)) (= (ll_10 BOUND_VARIABLE_10864 BOUND_VARIABLE_10865) ((member1516365892od_b_b BOUND_VARIABLE_10865) BOUND_VARIABLE_10864))))) (let ((_let_314 (forall ((BOUND_VARIABLE_10857 b)) (= ((product_Pair_b_b BOUND_VARIABLE_10857) BOUND_VARIABLE_10857) (ll_9 BOUND_VARIABLE_10857))))) (let ((_let_315 (forall ((BOUND_VARIABLE_10850 b)) (= (ll_8 BOUND_VARIABLE_10850) ((member_b BOUND_VARIABLE_10850) ((image_b_b ((getRel904497637nt_a_b standard_S_Idt_a) g)) ((insert_b y) bot_bot_set_b))))))) (let ((_let_316 (forall ((BOUND_VARIABLE_10842 set_b) (BOUND_VARIABLE_10843 b)) (= (ll_7 BOUND_VARIABLE_10842 BOUND_VARIABLE_10843) ((member_b BOUND_VARIABLE_10843) BOUND_VARIABLE_10842))))) (let ((_let_317 (forall ((BOUND_VARIABLE_10831 b) (BOUND_VARIABLE_10832 b)) (= (ll_6 BOUND_VARIABLE_10831 BOUND_VARIABLE_10832) ((member_b BOUND_VARIABLE_10832) ((image_b_b ((getRel904497637nt_a_b standard_S_Idt_a) g)) ((insert_b BOUND_VARIABLE_10831) bot_bot_set_b))))))) (let ((_let_318 (forall ((BOUND_VARIABLE_10820 b) (BOUND_VARIABLE_10821 b)) (= (ll_5 BOUND_VARIABLE_10820 BOUND_VARIABLE_10821) ((member_b BOUND_VARIABLE_10821) ((image_b_b ((getRel904497637nt_a_b standard_S_Idt_a) g)) ((insert_b BOUND_VARIABLE_10820) bot_bot_set_b))))))) (let ((_let_319 (forall ((BOUND_VARIABLE_10787 b) (BOUND_VARIABLE_10788 b)) (= (ll_4 BOUND_VARIABLE_10787 BOUND_VARIABLE_10788) ((member_b BOUND_VARIABLE_10788) ((image_b_b ((getRel904497637nt_a_b standard_S_Idt_a) g)) ((insert_b (hilbert_Eps_b (ll_26 BOUND_VARIABLE_10787))) bot_bot_set_b))))))) (let ((_let_320 (forall ((BOUND_VARIABLE_10776 b) (BOUND_VARIABLE_10777 b)) (= (ll_3 BOUND_VARIABLE_10776 BOUND_VARIABLE_10777) ((member_b BOUND_VARIABLE_10777) ((image_b_b ((getRel904497637nt_a_b standard_S_Idt_a) g)) ((insert_b BOUND_VARIABLE_10776) bot_bot_set_b))))))) (let ((_let_321 (forall ((BOUND_VARIABLE_10765 b) (BOUND_VARIABLE_10766 b)) (= (ll_2 BOUND_VARIABLE_10765 BOUND_VARIABLE_10766) ((member_b BOUND_VARIABLE_10766) ((image_b_b ((getRel904497637nt_a_b standard_S_Idt_a) g)) ((insert_b BOUND_VARIABLE_10765) bot_bot_set_b))))))) (let ((_let_322 (forall ((BOUND_VARIABLE_10737 b)) (= (ll_1 BOUND_VARIABLE_10737) (((if_b (= bot_bot_set_b ((image_b_b ((getRel904497637nt_a_b standard_S_Idt_a) g)) ((insert_b BOUND_VARIABLE_10737) bot_bot_set_b)))) BOUND_VARIABLE_10737) (hilbert_Eps_b (ll_25 BOUND_VARIABLE_10737))))))) (let ((_let_323 (and (forall ((X1 b) (X22 b) (R set_Product_prod_b_b) (S set_Product_prod_b_b) (P (-> b b Bool))) (or (not ((member1285940496od_b_b ((product_Pair_b_b X1) X22)) ((relcomp_b_b_b R) S))) (not (forall ((A4 b) (B5 b) (C2 b)) (or (not ((member1285940496od_b_b ((product_Pair_b_b A4) B5)) R)) (not ((member1285940496od_b_b ((product_Pair_b_b B5) C2)) S)) ((P A4) C2)))) ((P X1) X22))) _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296))) (let ((_let_324 (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME |:args| (_let_22)) (MACRO_SR_EQ_INTRO |:args| (_let_22 7 12))) (PREPROCESS |:args| ((and _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296)))) |:args| (_let_323)) (PREPROCESS |:args| ((= _let_323 (and _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_43 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269))))) (PREPROCESS |:args| ((and _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119 _let_118 _let_117 _let_116 _let_115 _let_114 _let_113 _let_112 _let_111 _let_110 _let_109 _let_108 _let_107 _let_106 _let_105 _let_104 _let_103 _let_102 _let_101 _let_100 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(labele1424214014nt_a_b G))) (= G (restri446606278nt_a_b G)))) (= ((graph_1309249505nt_a_b _let_13) g) g) (forall ((X produc1871334759_a_nat) (A set_Pr1987088711_a_nat)) (=> ((member832397200_a_nat X) A) (not (forall ((B8 set_Pr1987088711_a_nat)) (=> (= A ((insert1574423351_a_nat X) B8)) ((member832397200_a_nat X) B8)))))) (forall ((Y b) (Z b) (L standard_Constant_a) (G labele1159362096nt_a_b) (G3 labele1159362096nt_a_b)) (let ((_let_1 (getRel904497637nt_a_b L))) (let ((_let_2 (member1285940496od_b_b ((product_Pair_b_b Y) Z)))) (=> (_let_2 (_let_1 G)) (=> (((graph_222606102_a_b_b G) G3) (id_on_b (labele1424214014nt_a_b G))) (_let_2 (_let_1 G3))))))) (forall ((A set_b)) ((refl_on_b A) (id_on_b A))) (forall ((G_1 labele1159362096nt_a_b) (G_2 labele1159362096nt_a_b)) (let ((_let_1 (labele1424214014nt_a_b G_1))) (=> (= G_1 (restri446606278nt_a_b G_1)) (=> (= G_2 (restri446606278nt_a_b G_2)) (= (((graph_222606102_a_b_b G_1) G_2) (id_on_b _let_1)) (and ((ord_le123089219od_b_b (labele1741081071nt_a_b G_1)) (labele1741081071nt_a_b G_2)) ((ord_less_eq_set_b _let_1) (labele1424214014nt_a_b G_2)))))))) (forall ((A set_Product_prod_b_b)) (=> (forall ((Y3 product_prod_b_b)) (not ((member1285940496od_b_b Y3) A))) (= A bot_bo1343651123od_b_b))) (forall ((P (-> produc1213276845od_b_b Bool)) (X produc1213276845od_b_b)) (=> (forall ((A4 standard_Constant_a) (B5 b) (C2 b)) (P ((produc1432590431od_b_b A4) ((product_Pair_b_b B5) C2)))) (P X))) (forall ((A2 b) (A set_b)) (=> ((member_b A2) A) ((member1285940496od_b_b ((product_Pair_b_b A2) A2)) (id_on_b A)))) (forall ((A set_Pr1324126435od_b_b)) (= (forall ((X5 produc1213276845od_b_b)) (not ((member1516365892od_b_b X5) A))) (= A bot_bo1664927607od_b_b))) (forall ((X2 produc1871334759_a_nat)) (=> ((member832397200_a_nat X2) (standa1568205540ules_a l)) ((mainta1604381365_nat_b X2) g))) (forall ((A22 b) (G labele1159362096nt_a_b) (B2 b) (L standard_Constant_a) (F (-> b b)) (A2 b) (B3 b)) (let ((_let_1 (labele1424214014nt_a_b G))) (let ((_let_2 (getRel904497637nt_a_b L))) (=> ((member_b A22) _let_1) (=> ((member_b B2) _let_1) (=> ((member1285940496od_b_b ((product_Pair_b_b A22) B2)) (_let_2 G)) (=> (= (F A22) A2) (=> (= (F B2) B3) ((member1285940496od_b_b ((product_Pair_b_b A2) B3)) (_let_2 ((map_gr926947118tant_a ((bNF_Gr_b_b _let_1) F)) G))))))))))) (forall ((B3 product_prod_b_b) (R set_Pr1324126435od_b_b) (A set_St761939237tant_a)) (= ((member1285940496od_b_b B3) ((image_1916422435od_b_b R) A)) (exists ((X5 standard_Constant_a)) (and ((member1632892294tant_a X5) A) ((member1516365892od_b_b ((produc1432590431od_b_b X5) B3)) R))))) (forall ((A set_Pr1324126435od_b_b) (R set_Pr2109276827od_b_b) (B3 produc1213276845od_b_b) (A2 produc1213276845od_b_b)) (let ((_let_1 (image_763305007od_b_b R))) (=> ((equiv_2048442231od_b_b A) R) (=> ((ord_le123089219od_b_b (_let_1 ((insert2037698781od_b_b B3) bot_bo1664927607od_b_b))) (_let_1 ((insert2037698781od_b_b A2) bot_bo1664927607od_b_b))) (=> ((member1516365892od_b_b B3) A) ((member1086024932od_b_b ((produc449289715od_b_b A2) B3)) R)))))) (forall ((X b) (A set_b)) (let ((_let_1 (insert_b X))) (let ((_let_2 (_let_1 A))) (= (_let_1 _let_2) _let_2)))) (forall ((R2 set_Pr924198087_a_nat)) (= ((image_1168831379_a_nat R2) bot_bo1836341171_a_nat) bot_bo1836341171_a_nat)) (forall ((A2 standard_Constant_a) (B3 product_prod_b_b) (A3 standard_Constant_a) (B4 product_prod_b_b)) (= (= ((produc1432590431od_b_b A2) B3) ((produc1432590431od_b_b A3) B4)) (and (= A2 A3) (= B3 B4)))) (forall ((A2 standard_Constant_a) (B3 product_prod_b_b) (R set_Pr1324126435od_b_b) (A set_St761939237tant_a)) (=> ((member1516365892od_b_b ((produc1432590431od_b_b A2) B3)) R) (=> ((member1632892294tant_a A2) A) ((member1285940496od_b_b B3) ((image_1916422435od_b_b R) A))))) ((refl_on_b bot_bot_set_b) bot_bo1343651123od_b_b) (forall ((A set_Pr1324126435od_b_b) (A2 produc1213276845od_b_b)) (=> (= A bot_bo1664927607od_b_b) (not ((member1516365892od_b_b A2) A)))) (forall ((X produc1213276845od_b_b) (A set_Pr1324126435od_b_b) (B set_Pr1324126435od_b_b)) (let ((_let_1 (insert2037698781od_b_b X))) (let ((_let_2 (member1516365892od_b_b X))) (=> (not (_let_2 A)) (=> (not (_let_2 B)) (= (= (_let_1 A) (_let_1 B)) (= A B))))))) (forall ((X standard_Constant_a) (F2 set_St761939237tant_a) (F (-> standard_Constant_a product_prod_b_b)) (Y product_prod_b_b)) (=> (or (not (= (F X) Y)) (not ((member1632892294tant_a X) F2))) (not ((member1516365892od_b_b ((produc1432590431od_b_b X) Y)) ((bNF_Gr1272216980od_b_b F2) F))))) (forall ((P2 produc1213276845od_b_b)) (exists ((X4 standard_Constant_a) (Y3 product_prod_b_b)) (= P2 ((produc1432590431od_b_b X4) Y3)))) (forall ((A2 standard_Constant_a) (B3 product_prod_b_b) (A3 standard_Constant_a) (B4 product_prod_b_b)) (=> (= ((produc1432590431od_b_b A2) B3) ((produc1432590431od_b_b A3) B4)) (not (=> (= A2 A3) (not (= B3 B4)))))) (forall ((A2 b) (B3 product_prod_b_b) (R set_Pr621705391od_b_b) (A set_b)) (=> ((member641857272od_b_b ((produc1257047359od_b_b A2) B3)) R) (=> ((member_b A2) A) ((member1285940496od_b_b B3) ((image_1177096571od_b_b R) A))))) (forall ((A2 produc1871334759_a_nat) (A set_Pr1987088711_a_nat)) (not (= ((insert1574423351_a_nat A2) A) bot_bo1836341171_a_nat))) (forall ((A2 product_prod_b_b)) ((member1285940496od_b_b A2) ((insert1952693431od_b_b A2) bot_bo1343651123od_b_b))) (forall ((Xz produc1213276845od_b_b) (R set_Pr154086431tant_a) (S set_Pr1324126435od_b_b)) (=> ((member1516365892od_b_b Xz) ((relcom883816262od_b_b R) S)) (not (forall ((X4 standard_Constant_a) (Y3 standard_Constant_a) (Z2 product_prod_b_b)) (=> (= Xz ((produc1432590431od_b_b X4) Z2)) (=> ((member1214736488tant_a ((produc342647tant_a X4) Y3)) R) (not ((member1516365892od_b_b ((produc1432590431od_b_b Y3) Z2)) S)))))))) _let_20 _let_19 (forall ((B3 product_prod_b_b) (R set_Pr1324126435od_b_b) (A set_St761939237tant_a)) (=> ((member1285940496od_b_b B3) ((image_1916422435od_b_b R) A)) (not (forall ((X4 standard_Constant_a)) (=> ((member1516365892od_b_b ((produc1432590431od_b_b X4) B3)) R) (not ((member1632892294tant_a X4) A))))))) (forall ((A2 b) (A set_b)) (=> ((member_b A2) A) (= ((insert_b A2) A) A))) (forall ((R2 set_Pr1646010159_a_nat)) (= ((image_1749766139_a_nat R2) bot_bot_set_b) bot_bo1836341171_a_nat)) (forall ((A set_Product_prod_b_b)) (= (forall ((X5 product_prod_b_b)) (not ((member1285940496od_b_b X5) A))) (= A bot_bo1343651123od_b_b))) (forall ((A2 produc1213276845od_b_b) (A set_Pr1324126435od_b_b) (B3 produc1213276845od_b_b) (R set_Pr2109276827od_b_b)) (=> ((member1516365892od_b_b A2) A) (=> ((member1086024932od_b_b ((produc449289715od_b_b A2) B3)) R) ((member1516365892od_b_b B3) ((image_763305007od_b_b R) A))))) (forall ((A2 labele1159362096nt_a_b)) (let ((_let_1 (restri446606278nt_a_b A2))) (((graph_222606102_a_b_b _let_1) _let_1) (id_on_b (labele1424214014nt_a_b A2))))) (forall ((A2 produc1213276845od_b_b) (A set_Pr1324126435od_b_b) (B3 product_prod_b_b) (R set_Pr2134561957od_b_b)) (=> ((member1516365892od_b_b A2) A) (=> ((member942707974od_b_b ((produc1597690145od_b_b A2) B3)) R) ((member1285940496od_b_b B3) ((image_1397930469od_b_b R) A))))) (forall ((B3 product_prod_b_b) (R set_Pr621705391od_b_b) (A2 b)) (= ((member1285940496od_b_b B3) ((image_1177096571od_b_b R) ((insert_b A2) bot_bot_set_b))) ((member641857272od_b_b ((produc1257047359od_b_b A2) B3)) R))) (forall ((A set_Product_prod_b_b) (B set_Product_prod_b_b) (C product_prod_b_b)) (let ((_let_1 (member1285940496od_b_b C))) (=> ((ord_le1036320359od_b_b A) B) (=> (_let_1 A) (_let_1 B))))) (forall ((P (-> product_prod_b_b Bool)) (P2 product_prod_b_b)) (=> (forall ((A4 b) (B5 b)) (P ((product_Pair_b_b A4) B5))) (P P2))) (forall ((R3 set_Product_prod_b_b) (R set_Product_prod_b_b) (A6 set_b) (A set_b)) (=> ((ord_le1036320359od_b_b R3) R) (=> ((ord_less_eq_set_b A6) A) ((ord_less_eq_set_b ((image_b_b R3) A6)) ((image_b_b R) A))))) (forall ((B3 produc1871334759_a_nat) (A2 produc1871334759_a_nat) (A set_Pr1987088711_a_nat)) (let ((_let_1 ((insert1574423351_a_nat B3) bot_bo1836341171_a_nat))) (= (= _let_1 ((insert1574423351_a_nat A2) A)) (and (= A2 B3) ((ord_le1718765799_a_nat A) _let_1))))) (forall ((A2 produc1213276845od_b_b) (B3 produc1213276845od_b_b) (A set_Pr1324126435od_b_b)) (let ((_let_1 (member1516365892od_b_b A2))) (=> (_let_1 ((insert2037698781od_b_b B3) A)) (=> (not (= A2 B3)) (_let_1 A))))) (forall ((A2 produc1213276845od_b_b) (A set_Pr1324126435od_b_b)) (=> ((member1516365892od_b_b A2) A) ((member1086024932od_b_b ((produc449289715od_b_b A2) A2)) (id_on_250271696od_b_b A)))) (forall ((Labeled_graph labele1159362096nt_a_b) (Labeled_graph2 labele1159362096nt_a_b)) (=> (and (= (labele1424214014nt_a_b Labeled_graph) (labele1424214014nt_a_b Labeled_graph2)) (= (labele1741081071nt_a_b Labeled_graph) (labele1741081071nt_a_b Labeled_graph2))) (= Labeled_graph Labeled_graph2))) (forall ((A set_Pr1987088711_a_nat)) (= (forall ((X5 produc1871334759_a_nat)) (not ((member832397200_a_nat X5) A))) (= A bot_bo1836341171_a_nat))) (forall ((C produc970027067od_b_b) (A set_Pr1324126435od_b_b)) (=> ((member1086024932od_b_b C) (id_on_250271696od_b_b A)) (not (forall ((X4 produc1213276845od_b_b)) (=> ((member1516365892od_b_b X4) A) (not (= C ((produc449289715od_b_b X4) X4)))))))) (forall ((A2 produc1213276845od_b_b) (B3 produc1213276845od_b_b) (A set_Pr1324126435od_b_b)) (=> (= A2 B3) (=> ((member1516365892od_b_b A2) A) ((member1086024932od_b_b ((produc449289715od_b_b A2) B3)) (id_on_250271696od_b_b A))))) (forall ((X b) (Y b) (A set_b) (F (-> b b))) (= ((member1285940496od_b_b ((product_Pair_b_b X) Y)) ((bNF_Gr_b_b A) F)) (and (= (F X) Y) ((member_b X) A)))) (forall ((A labele1159362096nt_a_b) (B labele1159362096nt_a_b) (X3 labele1159362096nt_a_b) (H set_Product_prod_b_b)) (let ((_let_1 (graph_222606102_a_b_b X3))) (=> (((graph_222606102_a_b_b A) B) (id_on_b (labele1424214014nt_a_b A))) (=> ((_let_1 A) H) ((_let_1 B) H))))) (forall ((A set_b) (R set_Product_prod_b_b) (X b) (Y b)) (=> ((refl_on_b A) R) (=> ((member1285940496od_b_b ((product_Pair_b_b X) Y)) R) ((member_b X) A)))) (forall ((B3 produc1213276845od_b_b) (R set_Pr1071216121od_b_b) (A set_Product_prod_b_b)) (=> ((member1516365892od_b_b B3) ((image_532916993od_b_b R) A)) (not (forall ((X4 product_prod_b_b)) (=> ((member4694106od_b_b ((produc732676669od_b_b X4) B3)) R) (not ((member1285940496od_b_b X4) A))))))) (forall ((A2 b) (A set_b)) (=> ((member_b A2) A) (exists ((B8 set_b)) (and (= A ((insert_b A2) B8)) (not ((member_b A2) B8)))))) (forall ((G labele1159362096nt_a_b) (F (-> b b)) (G2 (-> b b))) (let ((_let_1 (bNF_Gr_b_b (labele1424214014nt_a_b G)))) (=> (forall ((X4 b)) (=> ((member_b X4) (labele1424214014nt_a_b G)) (= (F X4) (G2 X4)))) (= ((map_gr926947118tant_a (_let_1 F)) G) ((map_gr926947118tant_a (_let_1 G2)) G))))) (forall ((X produc1213276845od_b_b) (A set_Pr1324126435od_b_b)) (=> ((member1516365892od_b_b X) A) (not (forall ((B8 set_Pr1324126435od_b_b)) (=> (= A ((insert2037698781od_b_b X) B8)) ((member1516365892od_b_b X) B8)))))) (forall ((A set_Pr1987088711_a_nat)) (= ((ord_le1718765799_a_nat A) bot_bo1836341171_a_nat) (= A bot_bo1836341171_a_nat))) ((refl_on_b _let_3) _let_2) (forall ((A2 b) (B3 b) (R set_Product_prod_b_b) (C b) (S set_Product_prod_b_b)) (let ((_let_1 (product_Pair_b_b A2))) (=> ((member1285940496od_b_b (_let_1 B3)) R) (=> ((member1285940496od_b_b ((product_Pair_b_b B3) C)) S) ((member1285940496od_b_b (_let_1 C)) ((relcomp_b_b_b R) S)))))) (forall ((X produc1213276845od_b_b) (A set_Pr1324126435od_b_b) (B set_Pr1324126435od_b_b)) (= ((ord_le123089219od_b_b ((insert2037698781od_b_b X) A)) B) (and ((ord_le123089219od_b_b A) B) ((member1516365892od_b_b X) B)))) (forall ((A1 standard_Constant_a) (A22 product_prod_b_b) (R set_Pr1324126435od_b_b) (S set_Pr2007082183od_b_b)) (=> ((member1516365892od_b_b ((produc1432590431od_b_b A1) A22)) ((relcom1823941168od_b_b R) S)) (not (forall ((B5 product_prod_b_b)) (=> ((member1516365892od_b_b ((produc1432590431od_b_b A1) B5)) R) (not ((member1652792080od_b_b ((produc546497367od_b_b B5) A22)) S))))))) (forall ((G_1 labele1159362096nt_a_b) (G_2 labele1159362096nt_a_b)) (= (= ((graph_1309249505nt_a_b G_1) G_2) G_2) (and ((ord_le123089219od_b_b (labele1741081071nt_a_b G_1)) (labele1741081071nt_a_b G_2)) ((ord_less_eq_set_b (labele1424214014nt_a_b G_1)) (labele1424214014nt_a_b G_2))))) (forall ((A2 b) (B3 b) (A3 b) (B4 b)) (=> (= ((product_Pair_b_b A2) B3) ((product_Pair_b_b A3) B4)) (not (=> (= A2 A3) (not (= B3 B4)))))) (forall ((A set_Product_prod_b_b) (R set_Pr2007082183od_b_b) (A2 product_prod_b_b)) (=> ((refl_o2134473190od_b_b A) R) (=> ((member1285940496od_b_b A2) A) ((member1652792080od_b_b ((produc546497367od_b_b A2) A2)) R)))) (forall ((A2 b) (B3 b) (A set_b)) (=> (= A2 B3) (=> ((member_b A2) A) ((member1285940496od_b_b ((product_Pair_b_b A2) B3)) (id_on_b A))))) (forall ((A set_b) (R set_Product_prod_b_b) (A2 b) (B3 b)) (let ((_let_1 (image_b_b R))) (=> ((equiv_equiv_b A) R) (=> ((member1285940496od_b_b ((product_Pair_b_b A2) B3)) R) ((ord_less_eq_set_b (_let_1 ((insert_b A2) bot_bot_set_b))) (_let_1 ((insert_b B3) bot_bot_set_b))))))) (forall ((A2 b) (B3 b) (A3 b) (B4 b)) (= (= ((product_Pair_b_b A2) B3) ((product_Pair_b_b A3) B4)) (and (= A2 A3) (= B3 B4)))) (forall ((A2 b) (B3 b) (A set_b)) (let ((_let_1 (member_b A2))) (= (_let_1 ((insert_b B3) A)) (or (_let_1 A) (= A2 B3))))) (forall ((A2 produc1871334759_a_nat) (B set_Pr1987088711_a_nat)) ((member832397200_a_nat A2) ((insert1574423351_a_nat A2) B))) (forall ((A2 produc1871334759_a_nat) (A set_Pr1987088711_a_nat)) (=> ((member832397200_a_nat A2) A) (= ((insert1574423351_a_nat A2) A) A))) (forall ((X standard_Constant_a) (Fx product_prod_b_b) (A set_St761939237tant_a) (F (-> standard_Constant_a product_prod_b_b))) (=> ((member1516365892od_b_b ((produc1432590431od_b_b X) Fx)) ((bNF_Gr1272216980od_b_b A) F)) (= (F X) Fx))) (forall ((A labele1159362096nt_a_b) (B labele1159362096nt_a_b) (F set_Product_prod_b_b) (A2 b) (B3 b) (E allego510293162tant_a) (A3 b) (B4 b)) (let ((_let_1 (product_Pair_b_b A2))) (=> (((graph_222606102_a_b_b A) B) F) (=> ((member1285940496od_b_b (_let_1 B3)) ((semant55076487nt_a_b A) E)) (=> ((member1285940496od_b_b (_let_1 A3)) F) (=> ((member1285940496od_b_b ((product_Pair_b_b B3) B4)) F) ((member1285940496od_b_b ((product_Pair_b_b A3) B4)) ((semant55076487nt_a_b B) E)))))))) (forall ((A2 b) (A set_b) (B3 b)) (let ((_let_1 ((insert_b B3) bot_bot_set_b))) (= (= ((insert_b A2) A) _let_1) (and (= A2 B3) ((ord_less_eq_set_b A) _let_1))))) (forall ((X b) (Fx b) (A set_b) (F (-> b b))) (=> ((member1285940496od_b_b ((product_Pair_b_b X) Fx)) ((bNF_Gr_b_b A) F)) ((member_b X) A))) (forall ((A2 b) (A set_b) (B3 produc1213276845od_b_b) (R set_Pr2060523537od_b_b)) (=> ((member_b A2) A) (=> ((member599505522od_b_b ((produc800495189od_b_b A2) B3)) R) ((member1516365892od_b_b B3) ((image_984343321od_b_b R) A))))) (forall ((A2 b) (A set_b)) (not (= ((insert_b A2) A) bot_bot_set_b))) (forall ((A2 product_prod_b_b) (B set_Product_prod_b_b) (B3 product_prod_b_b)) (let ((_let_1 (member1285940496od_b_b A2))) (=> (=> (not (_let_1 B)) (= A2 B3)) (_let_1 ((insert1952693431od_b_b B3) B))))) (forall ((A set_b) (R set_Product_prod_b_b) (A2 b)) (=> ((refl_on_b A) R) (=> ((member_b A2) A) ((member1285940496od_b_b ((product_Pair_b_b A2) A2)) R)))) (forall ((X labele1159362096nt_a_b)) (let ((_let_1 (restri446606278nt_a_b X))) (= (restri446606278nt_a_b _let_1) _let_1))) (forall ((R2 labele935650037_a_nat) (G labele1159362096nt_a_b)) ((mainta1604381365_nat_b ((produc1676969687_a_nat R2) R2)) G)) (forall ((G labele1159362096nt_a_b) (F set_Pr812188767_nat_b)) (= (((graph_726202286_nat_b ((labele27098724_a_nat bot_bo1653310327_a_nat) bot_bo1836341171_a_nat)) G) F) (and (= F bot_bo1113554635_nat_b) (= G (restri446606278nt_a_b G))))) (forall ((B3 produc1213276845od_b_b) (R set_Pr2060523537od_b_b) (A set_b)) (=> ((member1516365892od_b_b B3) ((image_984343321od_b_b R) A)) (not (forall ((X4 b)) (=> ((member599505522od_b_b ((produc800495189od_b_b X4) B3)) R) (not ((member_b X4) A))))))) (forall ((X b) (A set_b)) (=> ((member_b X) A) (not (forall ((B8 set_b)) (=> (= A ((insert_b X) B8)) ((member_b X) B8)))))) _let_18 (forall ((X standard_Constant_a) (F2 set_St761939237tant_a) (F (-> standard_Constant_a product_prod_b_b))) (= ((bNF_Gr1272216980od_b_b ((insert1909710879tant_a X) F2)) F) ((insert2037698781od_b_b ((produc1432590431od_b_b X) (F X))) ((bNF_Gr1272216980od_b_b F2) F)))) (forall ((G labele1159362096nt_a_b) (F (-> b b))) (let ((_let_1 ((map_gr926947118tant_a ((bNF_Gr_b_b (labele1424214014nt_a_b G)) F)) G))) (= _let_1 (restri446606278nt_a_b _let_1)))) (forall ((G_1 labele1159362096nt_a_b) (G_2 labele1159362096nt_a_b)) (let ((_let_1 ((graph_1309249505nt_a_b G_1) G_2))) (=> (= G_1 (restri446606278nt_a_b G_1)) (=> (= G_2 (restri446606278nt_a_b G_2)) (= _let_1 (restri446606278nt_a_b _let_1)))))) (forall ((A1 standard_Constant_a) (A22 product_prod_b_b) (R set_Pr154086431tant_a) (S set_Pr1324126435od_b_b)) (=> ((member1516365892od_b_b ((produc1432590431od_b_b A1) A22)) ((relcom883816262od_b_b R) S)) (not (forall ((B5 standard_Constant_a)) (=> ((member1214736488tant_a ((produc342647tant_a A1) B5)) R) (not ((member1516365892od_b_b ((produc1432590431od_b_b B5) A22)) S))))))) (forall ((A2 produc1213276845od_b_b) (A set_Pr1324126435od_b_b) (B3 produc1213276845od_b_b) (B set_Pr1324126435od_b_b)) (let ((_let_1 (= A2 B3))) (=> (not ((member1516365892od_b_b A2) A)) (=> (not ((member1516365892od_b_b B3) B)) (= (= ((insert2037698781od_b_b A2) A) ((insert2037698781od_b_b B3) B)) (and (=> (not _let_1) (exists ((C4 set_Pr1324126435od_b_b)) (and (= A ((insert2037698781od_b_b B3) C4)) (not ((member1516365892od_b_b B3) C4)) (= B ((insert2037698781od_b_b A2) C4)) (not ((member1516365892od_b_b A2) C4))))) (=> _let_1 (= A B)))))))) (forall ((G_1 labele1159362096nt_a_b) (G_2 labele1159362096nt_a_b)) (=> ((ord_le123089219od_b_b (labele1741081071nt_a_b G_1)) (labele1741081071nt_a_b G_2)) (=> ((ord_less_eq_set_b (labele1424214014nt_a_b G_1)) (labele1424214014nt_a_b G_2)) (= ((graph_1309249505nt_a_b G_1) G_2) G_2)))) (forall ((A22 product_prod_b_b) (G labele1835558936od_b_b) (B2 product_prod_b_b) (L standard_Constant_a) (F (-> product_prod_b_b b)) (A2 b) (B3 b)) (let ((_let_1 (labele442485990od_b_b G))) (=> ((member1285940496od_b_b A22) _let_1) (=> ((member1285940496od_b_b B2) _let_1) (=> ((member1652792080od_b_b ((produc546497367od_b_b A22) B2)) ((getRel118493133od_b_b L) G)) (=> (= (F A22) A2) (=> (= (F B2) B3) ((member1285940496od_b_b ((product_Pair_b_b A2) B3)) ((getRel904497637nt_a_b L) ((map_gr1314489926tant_a ((bNF_Gr521784954_b_b_b _let_1) F)) G)))))))))) (forall ((X3 labele1159362096nt_a_b)) (= ((map_gr926947118tant_a (id_on_b (labele1424214014nt_a_b X3))) X3) (restri446606278nt_a_b X3))) (forall ((G_1 labele1159362096nt_a_b) (G_2 labele1159362096nt_a_b) (G_3 labele1159362096nt_a_b)) (let ((_let_1 (id_on_b (labele1424214014nt_a_b G_1)))) (let ((_let_2 (graph_222606102_a_b_b G_1))) (=> ((_let_2 G_2) _let_1) (=> (((graph_222606102_a_b_b G_2) G_3) (id_on_b (labele1424214014nt_a_b G_2))) ((_let_2 G_3) _let_1)))))) (forall ((A set_Product_prod_b_b) (B set_Product_prod_b_b) (X product_prod_b_b)) (let ((_let_1 (member1285940496od_b_b X))) (=> ((ord_le1036320359od_b_b A) B) (=> (_let_1 A) (_let_1 B))))) (forall ((A2 labele1159362096nt_a_b) (B3 labele1159362096nt_a_b) (F set_Product_prod_b_b) (Aa b) (Ba b)) (let ((_let_1 (member1285940496od_b_b ((product_Pair_b_b Aa) Ba)))) (=> (((graph_222606102_a_b_b A2) B3) F) (=> (_let_1 F) (_let_1 ((relcomp_b_b_b F) (id_on_b (labele1424214014nt_a_b B3)))))))) (forall ((A set_Product_prod_b_b)) (= (exists ((X5 product_prod_b_b)) ((member1285940496od_b_b X5) A)) (not (= A bot_bo1343651123od_b_b)))) (forall ((X product_prod_b_b) (Y product_prod_b_b) (A set_Product_prod_b_b)) (= ((member1652792080od_b_b ((produc546497367od_b_b X) Y)) (id_on_2019020932od_b_b A)) (and (= X Y) ((member1285940496od_b_b X) A)))) (forall ((F set_Product_prod_b_b) (G labele1159362096nt_a_b)) (= (labele1424214014nt_a_b ((map_gr926947118tant_a F) G)) ((image_b_b F) (labele1424214014nt_a_b G)))) (forall ((A2 product_prod_b_b) (B set_Product_prod_b_b)) ((member1285940496od_b_b A2) ((insert1952693431od_b_b A2) B))) (forall ((A2 product_prod_b_b) (B set_Product_prod_b_b) (B3 product_prod_b_b)) (let ((_let_1 (member1285940496od_b_b A2))) (=> (_let_1 B) (_let_1 ((insert1952693431od_b_b B3) B))))) (forall ((A set_Product_prod_b_b) (R set_Pr2007082183od_b_b) (X product_prod_b_b) (Y product_prod_b_b)) (=> ((refl_o2134473190od_b_b A) R) (=> ((member1652792080od_b_b ((produc546497367od_b_b X) Y)) R) ((member1285940496od_b_b Y) A)))) _let_17 (forall ((L standard_Constant_a) (X b) (Y b)) (let ((_let_1 (labele1741081071nt_a_b g))) (let ((_let_2 (produc1432590431od_b_b L))) (let ((_let_3 (labele1424214014nt_a_b g))) (=> ((member1516365892od_b_b (_let_2 ((product_Pair_b_b X) Y))) _let_1) (=> ((member_b X) _let_3) (=> ((member_b Y) _let_3) ((member1516365892od_b_b (_let_2 ((product_Pair_b_b (f X)) (f Y)))) _let_1)))))))) (forall ((A2 produc1871334759_a_nat) (B3 produc1871334759_a_nat)) (=> (= ((insert1574423351_a_nat A2) bot_bo1836341171_a_nat) ((insert1574423351_a_nat B3) bot_bo1836341171_a_nat)) (= A2 B3))) (forall ((A set_b) (R set_Product_prod_b_b) (B3 b) (A2 b)) (let ((_let_1 (image_b_b R))) (=> ((equiv_equiv_b A) R) (=> ((ord_less_eq_set_b (_let_1 ((insert_b B3) bot_bot_set_b))) (_let_1 ((insert_b A2) bot_bot_set_b))) (=> ((member_b B3) A) ((member1285940496od_b_b ((product_Pair_b_b A2) B3)) R)))))) (forall ((A2 b) (B set_b) (B3 b)) (let ((_let_1 (member_b A2))) (=> (_let_1 B) (_let_1 ((insert_b B3) B))))) (forall ((P (-> produc1871334759_a_nat Bool))) (= (= bot_bo1836341171_a_nat (collec357096914_a_nat P)) (forall ((X5 produc1871334759_a_nat)) (not (P X5))))) (forall ((F (-> labele935650037_a_nat labele935650037_a_nat))) (= ((bNF_Gr996500706_a_nat bot_bo2122869057_a_nat) F) bot_bo1836341171_a_nat)) (forall ((R2 set_Product_prod_b_b)) (= ((image_b_b R2) bot_bot_set_b) bot_bot_set_b)) (forall ((R set_Pr1324126435od_b_b) (S set_Pr1324126435od_b_b)) (=> (forall ((X4 standard_Constant_a) (Y3 product_prod_b_b)) (let ((_let_1 (member1516365892od_b_b ((produc1432590431od_b_b X4) Y3)))) (=> (_let_1 R) (_let_1 S)))) ((ord_le123089219od_b_b R) S))) (forall ((A labele935650037_a_nat) (B labele935650037_a_nat) (G labele1159362096nt_a_b) (F set_Pr2106913242_nat_b)) (let ((_let_1 ((produc1676969687_a_nat A) B))) (=> ((mainta1604381365_nat_b _let_1) G) (=> (((graph_714568023_nat_b A) G) F) (((extens1554515172_nat_b _let_1) G) F))))) (forall ((X b)) (let ((_let_1 (hilbert_Eps_b (p X)))) (=> (not (= ((image_b_b ((getRel904497637nt_a_b standard_S_Idt_a) g)) ((insert_b X) bot_bot_set_b)) bot_bot_set_b)) (= (hilbert_Eps_b (p _let_1)) _let_1)))) (forall ((A set_Product_prod_b_b) (R set_Pr2007082183od_b_b) (A2 product_prod_b_b) (B3 product_prod_b_b)) (=> ((refl_o2134473190od_b_b A) R) (=> ((member1652792080od_b_b ((produc546497367od_b_b A2) B3)) R) (and ((member1285940496od_b_b A2) A) ((member1285940496od_b_b B3) A))))) (forall ((A2 standard_Constant_a) (C product_prod_b_b) (R set_Pr1324126435od_b_b) (S set_Pr2007082183od_b_b)) (=> ((member1516365892od_b_b ((produc1432590431od_b_b A2) C)) ((relcom1823941168od_b_b R) S)) (not (forall ((B5 product_prod_b_b)) (=> ((member1516365892od_b_b ((produc1432590431od_b_b A2) B5)) R) (not ((member1652792080od_b_b ((produc546497367od_b_b B5) C)) S))))))) (forall ((A set_Pr1324126435od_b_b)) (=> (forall ((Y3 produc1213276845od_b_b)) (not ((member1516365892od_b_b Y3) A))) (= A bot_bo1664927607od_b_b))) (forall ((A2 b) (B3 b) (C b) (D b)) (= (= ((insert_b A2) ((insert_b B3) bot_bot_set_b)) ((insert_b C) ((insert_b D) bot_bot_set_b))) (or (and (= A2 C) (= B3 D)) (and (= B3 C) (= A2 D))))) (forall ((Xa b)) (let ((_let_1 (labele1424214014nt_a_b g))) (=> ((member_b (f Xa)) _let_1) ((member_b Xa) _let_1)))) (forall ((X labele935650037_a_nat)) ((refl_o1031343860_a_nat ((insert1167839429_a_nat X) bot_bo2122869057_a_nat)) ((insert1574423351_a_nat ((produc1676969687_a_nat X) X)) bot_bo1836341171_a_nat))) (forall ((A2 b) (B3 b)) (=> (= ((insert_b A2) bot_bot_set_b) ((insert_b B3) bot_bot_set_b)) (= A2 B3))) (forall ((G labele1159362096nt_a_b)) (= (labele1424214014nt_a_b (restri446606278nt_a_b G)) (labele1424214014nt_a_b G))) (forall ((A set_b)) ((ord_less_eq_set_b bot_bot_set_b) A)) (forall ((A2 produc1213276845od_b_b) (B3 produc1213276845od_b_b) (R set_Pr2109276827od_b_b) (A set_Pr1324126435od_b_b)) (=> ((member1086024932od_b_b ((produc449289715od_b_b A2) B3)) R) (=> ((member1516365892od_b_b A2) A) ((member1516365892od_b_b B3) ((image_763305007od_b_b R) A))))) (forall ((A set_Pr1324126435od_b_b) (R set_Pr2109276827od_b_b) (X produc1213276845od_b_b) (Y produc1213276845od_b_b)) (=> ((refl_o1921098222od_b_b A) R) (=> ((member1086024932od_b_b ((produc449289715od_b_b X) Y)) R) ((member1516365892od_b_b Y) A)))) (forall ((A set_b)) (= ((ord_less_eq_set_b A) bot_bot_set_b) (= A bot_bot_set_b))) (forall ((A2 produc1213276845od_b_b) (B3 produc1213276845od_b_b) (A set_Pr1324126435od_b_b)) (let ((_let_1 (member1516365892od_b_b A2))) (= (_let_1 ((insert2037698781od_b_b B3) A)) (or (_let_1 A) (= A2 B3))))) (forall ((P (-> produc1213276845od_b_b Bool)) (Prod produc1213276845od_b_b)) (=> (forall ((A4 standard_Constant_a) (B5 product_prod_b_b)) (P ((produc1432590431od_b_b A4) B5))) (P Prod))) (forall ((A2 b)) ((member_b A2) ((insert_b A2) bot_bot_set_b))) (forall ((X3 labele1644675410od_b_b) (F (-> produc1213276845od_b_b b)) (Y2 set_Pr1324126435od_b_b)) (=> (forall ((L2 standard_Constant_a) (X4 produc1213276845od_b_b) (Y3 produc1213276845od_b_b)) (let ((_let_1 (labele595103470od_b_b X3))) (=> ((member147868824od_b_b ((produc1788032435od_b_b L2) ((produc449289715od_b_b X4) Y3))) (labele2032816061od_b_b X3)) (=> ((member1516365892od_b_b X4) _let_1) (=> ((member1516365892od_b_b Y3) _let_1) ((member1516365892od_b_b ((produc1432590431od_b_b L2) ((product_Pair_b_b (F X4)) (F Y3)))) Y2)))))) (((edge_p1817988046tant_a ((bNF_Gr492676974_b_b_b (labele595103470od_b_b X3)) F)) (labele2032816061od_b_b X3)) Y2))) (forall ((P (-> b Bool))) (= (= bot_bot_set_b (collect_b P)) (forall ((X5 b)) (not (P X5))))) (forall ((B3 product_prod_b_b) (R set_Pr2134561957od_b_b) (A set_Pr1324126435od_b_b)) (=> ((member1285940496od_b_b B3) ((image_1397930469od_b_b R) A)) (not (forall ((X4 produc1213276845od_b_b)) (=> ((member942707974od_b_b ((produc1597690145od_b_b X4) B3)) R) (not ((member1516365892od_b_b X4) A))))))) (forall ((Y product_prod_b_b)) (not (forall ((A4 b) (B5 b)) (not (= Y ((product_Pair_b_b A4) B5)))))) (forall ((G labele1159362096nt_a_b) (L standard_Constant_a)) (=> (= G (restri446606278nt_a_b G)) (=> ((mainta1604381365_nat_b (standa63370785tant_a L)) G) ((refl_on_b (labele1424214014nt_a_b G)) ((getRel904497637nt_a_b L) G))))) (forall ((A set_b)) (= (collect_b (lambda ((X5 b)) ((member_b X5) A))) A)) (forall ((R2 labele1159362096nt_a_b) (G labele1159362096nt_a_b) (F set_Product_prod_b_b)) (=> (((graph_222606102_a_b_b R2) G) F) (((extens1779443913_a_b_b ((produc1569511545nt_a_b R2) R2)) G) F))) (forall ((A set_Pr1324126435od_b_b) (R set_Pr2109276827od_b_b) (X produc1213276845od_b_b) (Y produc1213276845od_b_b)) (=> ((refl_o1921098222od_b_b A) R) (=> ((member1086024932od_b_b ((produc449289715od_b_b X) Y)) R) ((member1516365892od_b_b X) A)))) (forall ((Xz product_prod_b_b) (R set_Product_prod_b_b) (S set_Product_prod_b_b)) (=> ((member1285940496od_b_b Xz) ((relcomp_b_b_b R) S)) (not (forall ((X4 b) (Y3 b) (Z2 b)) (let ((_let_1 (product_Pair_b_b X4))) (=> (= Xz (_let_1 Z2)) (=> ((member1285940496od_b_b (_let_1 Y3)) R) (not ((member1285940496od_b_b ((product_Pair_b_b Y3) Z2)) S))))))))) (forall ((A2 b) (A set_b) (B3 b) (R set_Product_prod_b_b)) (=> ((member_b A2) A) (=> ((member1285940496od_b_b ((product_Pair_b_b A2) B3)) R) ((member_b B3) ((image_b_b R) A))))) (forall ((B3 produc1213276845od_b_b) (R set_Pr1954438265od_b_b) (A2 produc1871334759_a_nat)) (= ((member1516365892od_b_b B3) ((image_480774529od_b_b R) ((insert1574423351_a_nat A2) bot_bo1836341171_a_nat))) ((member1533761242od_b_b ((produc401731773od_b_b A2) B3)) R))) ((member_b _let_4) _let_3) (forall ((X1 standard_Constant_a) (X22 product_prod_b_b) (R set_Pr1324126435od_b_b) (S set_Pr2007082183od_b_b) (P (-> standard_Constant_a product_prod_b_b Bool))) (=> ((member1516365892od_b_b ((produc1432590431od_b_b X1) X22)) ((relcom1823941168od_b_b R) S)) (=> (forall ((A4 standard_Constant_a) (B5 product_prod_b_b) (C2 product_prod_b_b)) (=> ((member1516365892od_b_b ((produc1432590431od_b_b A4) B5)) R) (=> ((member1652792080od_b_b ((produc546497367od_b_b B5) C2)) S) ((P A4) C2)))) ((P X1) X22)))) (forall ((X labele935650037_a_nat) (F2 set_la1083530965_a_nat) (F (-> labele935650037_a_nat labele935650037_a_nat))) (= ((bNF_Gr996500706_a_nat ((insert1167839429_a_nat X) F2)) F) ((insert1574423351_a_nat ((produc1676969687_a_nat X) (F X))) ((bNF_Gr996500706_a_nat F2) F)))) (forall ((R2 set_Pr924198087_a_nat) (S2 set_Pr924198087_a_nat) (A set_Pr1987088711_a_nat) (A2 produc1871334759_a_nat)) (let ((_let_1 ((insert1574423351_a_nat A2) bot_bo1836341171_a_nat))) (let ((_let_2 (image_1168831379_a_nat S2))) (let ((_let_3 (equiv_291114781_a_nat A))) (=> ((ord_le107617383_a_nat R2) S2) (=> (_let_3 R2) (=> (_let_3 S2) (= (_let_2 ((image_1168831379_a_nat R2) _let_1)) (_let_2 _let_1))))))))) (forall ((A2 product_prod_b_b) (A set_Product_prod_b_b) (B3 product_prod_b_b) (B set_Product_prod_b_b)) (let ((_let_1 (= A2 B3))) (=> (not ((member1285940496od_b_b A2) A)) (=> (not ((member1285940496od_b_b B3) B)) (= (= ((insert1952693431od_b_b A2) A) ((insert1952693431od_b_b B3) B)) (and (=> _let_1 (= A B)) (=> (not _let_1) (exists ((C4 set_Product_prod_b_b)) (and (= A ((insert1952693431od_b_b B3) C4)) (= B ((insert1952693431od_b_b A2) C4)) (not ((member1285940496od_b_b A2) C4)) (not ((member1285940496od_b_b B3) C4))))))))))) (forall ((X b) (Y b) (A set_b)) (= ((member1285940496od_b_b ((product_Pair_b_b X) Y)) (id_on_b A)) (and ((member_b X) A) (= X Y)))) (forall ((Rs set_Pr1987088711_a_nat) (G labele1159362096nt_a_b) (R2 produc1871334759_a_nat)) (=> ((conseq956760372_nat_b Rs) G) (=> ((member832397200_a_nat R2) Rs) ((mainta1604381365_nat_b R2) G)))) (forall ((A2 product_prod_b_b) (B3 product_prod_b_b) (A set_Product_prod_b_b)) (=> (= A2 B3) (=> ((member1285940496od_b_b A2) A) ((member1652792080od_b_b ((produc546497367od_b_b A2) B3)) (id_on_2019020932od_b_b A))))) (forall ((P (-> produc1871334759_a_nat Bool))) (= (= (collec357096914_a_nat P) bot_bo1836341171_a_nat) (forall ((X5 produc1871334759_a_nat)) (not (P X5))))) (= (_let_1 _let_13) ((image_1683732397od_b_b (lambda ((X5 b)) ((product_Pair_b_b X5) X5))) _let_14)) (forall ((A2 product_prod_b_b) (A set_Product_prod_b_b) (B3 product_prod_b_b) (R set_Pr2007082183od_b_b)) (=> ((member1285940496od_b_b A2) A) (=> ((member1652792080od_b_b ((produc546497367od_b_b A2) B3)) R) ((member1285940496od_b_b B3) ((image_1928024979od_b_b R) A))))) (forall ((A set_Pr1324126435od_b_b) (R set_Pr2109276827od_b_b) (A2 produc1213276845od_b_b)) (=> ((refl_o1921098222od_b_b A) R) (=> ((member1516365892od_b_b A2) A) ((member1086024932od_b_b ((produc449289715od_b_b A2) A2)) R)))) (forall ((G_1 labele1159362096nt_a_b) (G_2 labele1159362096nt_a_b)) (let ((_let_1 (labele1424214014nt_a_b G_1))) (=> (((graph_222606102_a_b_b G_1) G_2) (id_on_b _let_1)) ((ord_less_eq_set_b _let_1) (labele1424214014nt_a_b G_2))))) _let_16 (forall ((A2 product_prod_b_b)) (not ((member1285940496od_b_b A2) bot_bo1343651123od_b_b))) (forall ((P Bool)) (or (= P true) (= P false))) (forall ((A2 b) (B3 b) (A set_b)) (let ((_let_1 (member_b A2))) (=> (_let_1 ((insert_b B3) A)) (=> (not (= A2 B3)) (_let_1 A))))) (forall ((A2 product_prod_b_b) (A set_Product_prod_b_b) (B3 b) (R set_Pr357419743_b_b_b)) (=> ((member1285940496od_b_b A2) A) (=> ((member351494440_b_b_b ((produc1001682799_b_b_b A2) B3)) R) ((member_b B3) ((image_921732011_b_b_b R) A))))) (forall ((B3 produc1213276845od_b_b) (R set_Pr2060523537od_b_b) (A2 b)) (= ((member1516365892od_b_b B3) ((image_984343321od_b_b R) ((insert_b A2) bot_bot_set_b))) ((member599505522od_b_b ((produc800495189od_b_b A2) B3)) R))) (forall ((Y b) (Z b) (L standard_Constant_a) (G labele1159362096nt_a_b) (U b) (F set_Product_prod_b_b) (V b)) (let ((_let_1 (getRel904497637nt_a_b L))) (let ((_let_2 (product_Pair_b_b Y))) (=> ((member1285940496od_b_b (_let_2 Z)) (_let_1 G)) (=> ((member1285940496od_b_b (_let_2 U)) F) (=> ((member1285940496od_b_b ((product_Pair_b_b Z) V)) F) ((member1285940496od_b_b ((product_Pair_b_b U) V)) (_let_1 ((map_gr926947118tant_a F) G))))))))) (forall ((P (-> b Bool))) (= (= (collect_b P) bot_bot_set_b) (forall ((X5 b)) (not (P X5))))) (forall ((P2 product_prod_b_b)) (exists ((X4 b) (Y3 b)) (= P2 ((product_Pair_b_b X4) Y3)))) (forall ((F set_Product_prod_b_b) (G labele1159362096nt_a_b)) (((edge_p1384198690tant_a F) (labele1741081071nt_a_b G)) (labele1741081071nt_a_b ((map_gr926947118tant_a F) G)))) (forall ((A labele1159362096nt_a_b) (A2 b) (B3 b) (E allego510293162tant_a)) (=> (= A (restri446606278nt_a_b A)) (=> ((member1285940496od_b_b ((product_Pair_b_b A2) B3)) ((semant55076487nt_a_b A) E)) ((member_b B3) (labele1424214014nt_a_b A))))) (forall ((C produc1213276845od_b_b)) (not ((member1516365892od_b_b C) bot_bo1664927607od_b_b))) (forall ((A set_b)) (= (forall ((X5 b)) (not ((member_b X5) A))) (= A bot_bot_set_b))) (forall ((B3 b) (R set_Pr812188767_nat_b) (A2 produc1871334759_a_nat)) (= ((member_b B3) ((image_924992811_nat_b R) ((insert1574423351_a_nat A2) bot_bo1836341171_a_nat))) ((member1544800936_nat_b ((produc2059954415_nat_b A2) B3)) R))) (forall ((G labele1159362096nt_a_b) (F set_Product_prod_b_b)) (let ((_let_1 ((map_gr926947118tant_a F) G))) (=> (= G (restri446606278nt_a_b G)) (= _let_1 (restri446606278nt_a_b _let_1))))) (forall ((X produc1213276845od_b_b) (Y produc1213276845od_b_b) (A set_Pr1324126435od_b_b)) (= ((member1086024932od_b_b ((produc449289715od_b_b X) Y)) (id_on_250271696od_b_b A)) (and (= X Y) ((member1516365892od_b_b X) A)))) (forall ((A set_Pr1324126435od_b_b)) (= (collec279084418od_b_b (lambda ((X5 produc1213276845od_b_b)) ((member1516365892od_b_b X5) A))) A)) (forall ((P (-> produc1213276845od_b_b Bool)) (P2 produc1213276845od_b_b)) (=> (forall ((A4 standard_Constant_a) (B5 product_prod_b_b)) (P ((produc1432590431od_b_b A4) B5))) (P P2))) (forall ((A set_b) (R set_Product_prod_b_b) (A2 b) (B3 b)) (=> ((refl_on_b A) R) (=> ((member1285940496od_b_b ((product_Pair_b_b A2) B3)) R) (and ((member_b A2) A) ((member_b B3) A))))) (forall ((A2 produc1213276845od_b_b) (B3 product_prod_b_b) (R set_Pr2134561957od_b_b) (A set_Pr1324126435od_b_b)) (=> ((member942707974od_b_b ((produc1597690145od_b_b A2) B3)) R) (=> ((member1516365892od_b_b A2) A) ((member1285940496od_b_b B3) ((image_1397930469od_b_b R) A))))) (forall ((X3 labele1835558936od_b_b) (F (-> product_prod_b_b b)) (Y2 set_Pr1324126435od_b_b)) (=> (forall ((L2 standard_Constant_a) (X4 product_prod_b_b) (Y3 product_prod_b_b)) (let ((_let_1 (labele442485990od_b_b X3))) (=> ((member1744485444od_b_b ((produc618266719od_b_b L2) ((produc546497367od_b_b X4) Y3))) (labele372159959od_b_b X3)) (=> ((member1285940496od_b_b X4) _let_1) (=> ((member1285940496od_b_b Y3) _let_1) ((member1516365892od_b_b ((produc1432590431od_b_b L2) ((product_Pair_b_b (F X4)) (F Y3)))) Y2)))))) (((edge_p1969196346tant_a ((bNF_Gr521784954_b_b_b (labele442485990od_b_b X3)) F)) (labele372159959od_b_b X3)) Y2))) (forall ((C produc1871334759_a_nat)) (not ((member832397200_a_nat C) bot_bo1836341171_a_nat))) (forall ((A2 product_prod_b_b) (A set_Product_prod_b_b)) (=> ((member1285940496od_b_b A2) A) (exists ((B8 set_Product_prod_b_b)) (and (= A ((insert1952693431od_b_b A2) B8)) (not ((member1285940496od_b_b A2) B8)))))) (forall ((X b) (G labele1159362096nt_a_b) (A2 (-> b b)) (Y b) (B3 set_Product_prod_b_b)) (let ((_let_1 (labele1424214014nt_a_b G))) (=> ((member_b X) _let_1) (=> ((member1285940496od_b_b ((product_Pair_b_b (A2 X)) Y)) B3) ((member1285940496od_b_b ((product_Pair_b_b X) Y)) ((relcomp_b_b_b ((bNF_Gr_b_b _let_1) A2)) B3)))))) (forall ((C product_prod_b_b) (A set_b)) (=> ((member1285940496od_b_b C) (id_on_b A)) (not (forall ((X4 b)) (=> ((member_b X4) A) (not (= C ((product_Pair_b_b X4) X4)))))))) (forall ((A2 b) (A set_b) (B3 b) (B set_b)) (let ((_let_1 (= A2 B3))) (=> (not ((member_b A2) A)) (=> (not ((member_b B3) B)) (= (= ((insert_b A2) A) ((insert_b B3) B)) (and (=> (not _let_1) (exists ((C4 set_b)) (and (= A ((insert_b B3) C4)) (not ((member_b A2) C4)) (= B ((insert_b A2) C4)) (not ((member_b B3) C4))))) (=> _let_1 (= A B)))))))) (forall ((X1 set_Pr1324126435od_b_b) (X22 set_b)) (= (labele1424214014nt_a_b ((labele1230159100nt_a_b X1) X22)) X22)) (forall ((X b) (Fx b) (A set_b) (F (-> b b))) (=> ((member1285940496od_b_b ((product_Pair_b_b X) Fx)) ((bNF_Gr_b_b A) F)) (= (F X) Fx))) (forall ((A2 produc1213276845od_b_b) (P (-> produc1213276845od_b_b Bool))) (= ((member1516365892od_b_b A2) (collec279084418od_b_b P)) (P A2))) (forall ((A1 b) (A22 b) (R set_Product_prod_b_b) (S set_Product_prod_b_b)) (=> ((member1285940496od_b_b ((product_Pair_b_b A1) A22)) ((relcomp_b_b_b R) S)) (not (forall ((B5 b)) (=> ((member1285940496od_b_b ((product_Pair_b_b A1) B5)) R) (not ((member1285940496od_b_b ((product_Pair_b_b B5) A22)) S))))))) (forall ((X b) (F2 set_b) (F (-> b b))) (= ((bNF_Gr_b_b ((insert_b X) F2)) F) ((insert1952693431od_b_b ((product_Pair_b_b X) (F X))) ((bNF_Gr_b_b F2) F)))) (forall ((X b) (G labele1159362096nt_a_b) (A2 (-> b standard_Constant_a)) (Y product_prod_b_b) (B3 set_Pr1324126435od_b_b)) (let ((_let_1 (labele1424214014nt_a_b G))) (=> ((member_b X) _let_1) (=> ((member1516365892od_b_b ((produc1432590431od_b_b (A2 X)) Y)) B3) ((member641857272od_b_b ((produc1257047359od_b_b X) Y)) ((relcom112561144od_b_b ((bNF_Gr230160332tant_a _let_1) A2)) B3)))))) (forall ((A set_Pr1987088711_a_nat)) ((ord_le1718765799_a_nat bot_bo1836341171_a_nat) A)) (forall ((Labeled_graph labele1159362096nt_a_b)) (= Labeled_graph ((labele1230159100nt_a_b (labele1741081071nt_a_b Labeled_graph)) (labele1424214014nt_a_b Labeled_graph)))) (forall ((Y produc1213276845od_b_b) (Z produc1213276845od_b_b) (L standard_Constant_a) (G labele1644675410od_b_b) (F (-> produc1213276845od_b_b b))) (let ((_let_1 (labele595103470od_b_b G))) (=> ((member1086024932od_b_b ((produc449289715od_b_b Y) Z)) ((getRel59882567od_b_b L) G)) (=> ((member1516365892od_b_b Y) _let_1) (=> ((member1516365892od_b_b Z) _let_1) ((member1285940496od_b_b ((product_Pair_b_b (F Y)) (F Z))) ((getRel904497637nt_a_b L) ((map_gr1495881666tant_a ((bNF_Gr492676974_b_b_b _let_1) F)) G)))))))) (forall ((B3 product_prod_b_b) (R set_Pr1324126435od_b_b) (A2 standard_Constant_a)) (= ((member1285940496od_b_b B3) ((image_1916422435od_b_b R) ((insert1909710879tant_a A2) bot_bo1160111033tant_a))) ((member1516365892od_b_b ((produc1432590431od_b_b A2) B3)) R))) (forall ((A labele1159362096nt_a_b) (B labele1159362096nt_a_b)) (let ((_let_1 (graph_1309249505nt_a_b A))) (let ((_let_2 (_let_1 B))) (= (_let_1 _let_2) _let_2)))) (forall ((A labele1159362096nt_a_b)) (= ((graph_1309249505nt_a_b A) A) A)) (forall ((A2 produc1871334759_a_nat)) (not ((member832397200_a_nat A2) bot_bo1836341171_a_nat))) (forall ((A2 produc1213276845od_b_b)) ((member1516365892od_b_b A2) ((insert2037698781od_b_b A2) bot_bo1664927607od_b_b))) (forall ((A set_b) (A2 b)) (=> (= A bot_bot_set_b) (not ((member_b A2) A)))) (forall ((V set_b)) (let ((_let_1 ((labele1230159100nt_a_b bot_bo1664927607od_b_b) V))) (= _let_1 (restri446606278nt_a_b _let_1)))) (forall ((A2 product_prod_b_b) (B3 b) (R set_Pr357419743_b_b_b) (A set_Product_prod_b_b)) (=> ((member351494440_b_b_b ((produc1001682799_b_b_b A2) B3)) R) (=> ((member1285940496od_b_b A2) A) ((member_b B3) ((image_921732011_b_b_b R) A))))) (forall ((X b) (F2 set_b) (F (-> b b)) (Y b)) (=> (or (not ((member_b X) F2)) (not (= (F X) Y))) (not ((member1285940496od_b_b ((product_Pair_b_b X) Y)) ((bNF_Gr_b_b F2) F))))) (forall ((P (-> product_prod_b_b Bool)) (Prod product_prod_b_b)) (=> (forall ((A4 b) (B5 b)) (P ((product_Pair_b_b A4) B5))) (P Prod))) (forall ((G labele1159362096nt_a_b)) (let ((_let_1 (restri446606278nt_a_b G))) (=> ((ord_le123089219od_b_b (labele1741081071nt_a_b G)) (labele1741081071nt_a_b _let_1)) (= G _let_1)))) (forall ((G_1 labele1159362096nt_a_b) (G_2 labele1159362096nt_a_b)) (= (((graph_222606102_a_b_b G_1) G_2) (id_on_b (labele1424214014nt_a_b G_1))) (and (= G_1 (restri446606278nt_a_b G_1)) (= ((graph_1309249505nt_a_b G_1) G_2) G_2) (= G_2 (restri446606278nt_a_b G_2))))) (forall ((A labele1159362096nt_a_b) (G labele1159362096nt_a_b) (B labele1159362096nt_a_b)) (=> (forall ((F3 set_Product_prod_b_b)) (=> (((graph_222606102_a_b_b A) G) F3) (((extens1779443913_a_b_b ((produc1569511545nt_a_b A) B)) G) F3))) ((mainta374363448_a_b_b ((produc1569511545nt_a_b A) B)) G))) (forall ((X b)) ((refl_on_b ((insert_b X) bot_bot_set_b)) ((insert1952693431od_b_b ((product_Pair_b_b X) X)) bot_bo1343651123od_b_b))) (forall ((A1 standard_Constant_a) (A22 product_prod_b_b) (R set_Pr1324126435od_b_b) (S set_Pr2007082183od_b_b)) (= ((member1516365892od_b_b ((produc1432590431od_b_b A1) A22)) ((relcom1823941168od_b_b R) S)) (exists ((A5 standard_Constant_a) (B6 product_prod_b_b) (C3 product_prod_b_b)) (and ((member1516365892od_b_b ((produc1432590431od_b_b A5) B6)) R) ((member1652792080od_b_b ((produc546497367od_b_b B6) C3)) S) (= A22 C3) (= A1 A5))))) (forall ((G labele1159362096nt_a_b)) (let ((_let_1 (restri446606278nt_a_b G))) (= (((graph_222606102_a_b_b G) _let_1) (id_on_b (labele1424214014nt_a_b G))) (= G _let_1)))) (forall ((A2 b) (B set_b) (B3 b)) (let ((_let_1 (member_b A2))) (=> (=> (not (_let_1 B)) (= A2 B3)) (_let_1 ((insert_b B3) B))))) (forall ((A labele1159362096nt_a_b) (B labele1159362096nt_a_b) (R2 set_Product_prod_b_b) (F (-> b b))) (let ((_let_1 ((bNF_Gr_b_b (labele1424214014nt_a_b B)) F))) (let ((_let_2 (graph_222606102_a_b_b A))) (=> ((_let_2 B) R2) ((_let_2 ((map_gr926947118tant_a _let_1) B)) ((relcomp_b_b_b R2) _let_1)))))) (forall ((X3 labele1159362096nt_a_b) (F (-> b b)) (Y2 set_Pr1324126435od_b_b)) (=> (forall ((L2 standard_Constant_a) (X4 b) (Y3 b)) (let ((_let_1 (produc1432590431od_b_b L2))) (let ((_let_2 (labele1424214014nt_a_b X3))) (=> ((member1516365892od_b_b (_let_1 ((product_Pair_b_b X4) Y3))) (labele1741081071nt_a_b X3)) (=> ((member_b X4) _let_2) (=> ((member_b Y3) _let_2) ((member1516365892od_b_b (_let_1 ((product_Pair_b_b (F X4)) (F Y3)))) Y2))))))) (((edge_p1384198690tant_a ((bNF_Gr_b_b (labele1424214014nt_a_b X3)) F)) (labele1741081071nt_a_b X3)) Y2))) _let_15 (forall ((A set_b)) (=> (forall ((Y3 b)) (not ((member_b Y3) A))) (= A bot_bot_set_b))) (forall ((X b) (Y b)) (=> ((member1516365892od_b_b ((produc1432590431od_b_b standard_S_Idt_a) ((product_Pair_b_b X) Y))) (labele1741081071nt_a_b g)) (= (hilbert_Eps_b (p X)) (hilbert_Eps_b (p Y))))) (forall ((R2 set_Product_prod_b_b) (S2 set_Product_prod_b_b) (A set_b) (A2 b)) (let ((_let_1 ((insert_b A2) bot_bot_set_b))) (let ((_let_2 (image_b_b S2))) (let ((_let_3 (equiv_equiv_b A))) (=> ((ord_le1036320359od_b_b R2) S2) (=> (_let_3 R2) (=> (_let_3 S2) (= (_let_2 ((image_b_b R2) _let_1)) (_let_2 _let_1))))))))) (forall ((G labele1159362096nt_a_b) (F set_Product_prod_b_b)) (= (((graph_222606102_a_b_b ((labele1230159100nt_a_b bot_bo1664927607od_b_b) bot_bot_set_b)) G) F) (and (= F bot_bo1343651123od_b_b) (= G (restri446606278nt_a_b G))))) (forall ((X standard_Constant_a) (Y product_prod_b_b) (A set_St761939237tant_a) (F (-> standard_Constant_a product_prod_b_b))) (= ((member1516365892od_b_b ((produc1432590431od_b_b X) Y)) ((bNF_Gr1272216980od_b_b A) F)) (and ((member1632892294tant_a X) A) (= (F X) Y)))) (forall ((A2 produc1871334759_a_nat) (A set_Pr1987088711_a_nat)) (=> ((member832397200_a_nat A2) A) (exists ((B8 set_Pr1987088711_a_nat)) (and (= A ((insert1574423351_a_nat A2) B8)) (not ((member832397200_a_nat A2) B8)))))) (((graph_222606102_a_b_b _let_13) g) (id_on_b _let_14)) (= f (lambda ((X5 b)) (((if_b (= ((image_b_b ((getRel904497637nt_a_b standard_S_Idt_a) g)) ((insert_b X5) bot_bot_set_b)) bot_bot_set_b)) X5) (hilbert_Eps_b (p X5))))) (forall ((A2 produc1213276845od_b_b) (A set_Pr1324126435od_b_b)) (=> ((member1516365892od_b_b A2) A) (exists ((B8 set_Pr1324126435od_b_b)) (and (not ((member1516365892od_b_b A2) B8)) (= A ((insert2037698781od_b_b A2) B8)))))) (forall ((X1 standard_Constant_a) (X22 product_prod_b_b) (Y1 standard_Constant_a) (Y22 product_prod_b_b)) (= (= ((produc1432590431od_b_b X1) X22) ((produc1432590431od_b_b Y1) Y22)) (and (= X22 Y22) (= X1 Y1)))) (forall ((X produc1871334759_a_nat) (A set_Pr1987088711_a_nat) (B set_Pr1987088711_a_nat)) (let ((_let_1 (insert1574423351_a_nat X))) (let ((_let_2 (member832397200_a_nat X))) (=> (not (_let_2 A)) (=> (not (_let_2 B)) (= (= (_let_1 A) (_let_1 B)) (= A B))))))) (forall ((B3 b) (R set_Pr1906739389_b_b_b) (A set_Pr1324126435od_b_b)) (=> ((member_b B3) ((image_1764625405_b_b_b R) A)) (not (forall ((X4 produc1213276845od_b_b)) (=> ((member1417789726_b_b_b ((produc1580777273_b_b_b X4) B3)) R) (not ((member1516365892od_b_b X4) A))))))) (forall ((A set_Product_prod_b_b) (R set_Pr2007082183od_b_b) (B3 product_prod_b_b) (A2 product_prod_b_b)) (let ((_let_1 (image_1928024979od_b_b R))) (=> ((equiv_1125628061od_b_b A) R) (=> ((ord_le1036320359od_b_b (_let_1 ((insert1952693431od_b_b B3) bot_bo1343651123od_b_b))) (_let_1 ((insert1952693431od_b_b A2) bot_bo1343651123od_b_b))) (=> ((member1285940496od_b_b B3) A) ((member1652792080od_b_b ((produc546497367od_b_b A2) B3)) R)))))) (forall ((A2 standard_Constant_a) (B3 product_prod_b_b) (R set_Pr1324126435od_b_b) (C product_prod_b_b) (S set_Pr2007082183od_b_b)) (let ((_let_1 (produc1432590431od_b_b A2))) (=> ((member1516365892od_b_b (_let_1 B3)) R) (=> ((member1652792080od_b_b ((produc546497367od_b_b B3) C)) S) ((member1516365892od_b_b (_let_1 C)) ((relcom1823941168od_b_b R) S)))))) (forall ((A2 b) (B set_b)) ((member_b A2) ((insert_b A2) B))) (forall ((A2 standard_Constant_a) (B3 standard_Constant_a) (R set_Pr154086431tant_a) (C product_prod_b_b) (S set_Pr1324126435od_b_b)) (=> ((member1214736488tant_a ((produc342647tant_a A2) B3)) R) (=> ((member1516365892od_b_b ((produc1432590431od_b_b B3) C)) S) ((member1516365892od_b_b ((produc1432590431od_b_b A2) C)) ((relcom883816262od_b_b R) S))))) (forall ((A labele1159362096nt_a_b) (A2 b) (B3 b) (E allego510293162tant_a)) (=> (= A (restri446606278nt_a_b A)) (=> ((member1285940496od_b_b ((product_Pair_b_b A2) B3)) ((semant55076487nt_a_b A) E)) ((member_b A2) (labele1424214014nt_a_b A))))) (forall ((B3 product_prod_b_b) (R set_Pr667377223od_b_b) (A2 produc1871334759_a_nat)) (= ((member1285940496od_b_b B3) ((image_1214223635od_b_b R) ((insert1574423351_a_nat A2) bot_bo1836341171_a_nat))) ((member301892752od_b_b ((produc590959831od_b_b A2) B3)) R))) (forall ((R2 set_Pr1987088711_a_nat)) (= ((relcom1338300020_a_nat R2) bot_bo1836341171_a_nat) bot_bo1836341171_a_nat)) (forall ((A set_b) (B set_b)) (=> (forall ((X4 b)) (let ((_let_1 (member_b X4))) (=> (_let_1 A) (_let_1 B)))) ((ord_less_eq_set_b A) B))) _let_12 (forall ((C produc1168037607od_b_b) (A set_Product_prod_b_b)) (=> ((member1652792080od_b_b C) (id_on_2019020932od_b_b A)) (not (forall ((X4 product_prod_b_b)) (=> ((member1285940496od_b_b X4) A) (not (= C ((produc546497367od_b_b X4) X4)))))))) _let_11 (forall ((Labeled_graph labele1159362096nt_a_b)) (= ((labele1230159100nt_a_b (labele1741081071nt_a_b Labeled_graph)) (labele1424214014nt_a_b Labeled_graph)) Labeled_graph)) (forall ((G labele1159362096nt_a_b) (A2 b) (B3 b) (L standard_Constant_a)) (=> (= G (restri446606278nt_a_b G)) (=> ((member1285940496od_b_b ((product_Pair_b_b A2) B3)) ((getRel904497637nt_a_b L) G)) ((member_b B3) (labele1424214014nt_a_b G))))) (forall ((A set_Pr1987088711_a_nat)) (= (exists ((X5 produc1871334759_a_nat)) ((member832397200_a_nat X5) A)) (not (= A bot_bo1836341171_a_nat)))) (forall ((A2 product_prod_b_b) (A set_Product_prod_b_b)) (=> ((member1285940496od_b_b A2) A) (= ((insert1952693431od_b_b A2) A) A))) (forall ((A labele1159362096nt_a_b) (B labele1159362096nt_a_b) (G labele1159362096nt_a_b) (F set_Product_prod_b_b)) (let ((_let_1 ((produc1569511545nt_a_b A) B))) (=> ((mainta374363448_a_b_b _let_1) G) (=> (((graph_222606102_a_b_b A) G) F) (((extens1779443913_a_b_b _let_1) G) F))))) (forall ((A2 produc1871334759_a_nat) (A set_Pr1987088711_a_nat) (B3 produc1871334759_a_nat) (B set_Pr1987088711_a_nat)) (let ((_let_1 (= A2 B3))) (=> (not ((member832397200_a_nat A2) A)) (=> (not ((member832397200_a_nat B3) B)) (= (= ((insert1574423351_a_nat A2) A) ((insert1574423351_a_nat B3) B)) (and (=> (not _let_1) (exists ((C4 set_Pr1987088711_a_nat)) (and (= A ((insert1574423351_a_nat B3) C4)) (not ((member832397200_a_nat A2) C4)) (= B ((insert1574423351_a_nat A2) C4)) (not ((member832397200_a_nat B3) C4))))) (=> _let_1 (= A B)))))))) (forall ((X b)) (let ((_let_1 (labele1424214014nt_a_b g))) (=> ((member_b X) _let_1) ((member_b (f X)) _let_1)))) (forall ((X produc1871334759_a_nat) (A set_Pr1987088711_a_nat)) (let ((_let_1 (insert1574423351_a_nat X))) (let ((_let_2 (_let_1 A))) (= (_let_1 _let_2) _let_2)))) (forall ((A labele935650037_a_nat) (G labele1159362096nt_a_b) (B labele935650037_a_nat)) (=> (forall ((F3 set_Pr2106913242_nat_b)) (=> (((graph_714568023_nat_b A) G) F3) (((extens1554515172_nat_b ((produc1676969687_a_nat A) B)) G) F3))) ((mainta1604381365_nat_b ((produc1676969687_a_nat A) B)) G))) (forall ((A2 product_prod_b_b) (P (-> product_prod_b_b Bool))) (= ((member1285940496od_b_b A2) (collec1481886546od_b_b P)) (P A2))) _let_10 (forall ((X b) (A set_b) (B set_b)) (let ((_let_1 (insert_b X))) (let ((_let_2 (member_b X))) (=> (not (_let_2 A)) (=> (not (_let_2 B)) (= (= (_let_1 A) (_let_1 B)) (= A B))))))) (forall ((X b) (Y b) (L standard_Constant_a)) (=> ((member1285940496od_b_b ((product_Pair_b_b X) Y)) ((getRel904497637nt_a_b L) g)) ((equiv_1821124534_set_b ((getRel904497637nt_a_b standard_S_Idt_a) g)) (lambda ((V3 b)) ((image_b_b ((getRel904497637nt_a_b L) g)) ((insert_b V3) bot_bot_set_b)))))) (forall ((A2 standard_Constant_a) (A set_St761939237tant_a) (B3 product_prod_b_b) (R set_Pr1324126435od_b_b)) (=> ((member1632892294tant_a A2) A) (=> ((member1516365892od_b_b ((produc1432590431od_b_b A2) B3)) R) ((member1285940496od_b_b B3) ((image_1916422435od_b_b R) A))))) (forall ((A2 b)) (not ((member_b A2) bot_bot_set_b))) (forall ((B3 produc1213276845od_b_b) (R set_Pr2109276827od_b_b) (A set_Pr1324126435od_b_b)) (=> ((member1516365892od_b_b B3) ((image_763305007od_b_b R) A)) (not (forall ((X4 produc1213276845od_b_b)) (=> ((member1086024932od_b_b ((produc449289715od_b_b X4) B3)) R) (not ((member1516365892od_b_b X4) A))))))) ((refl_o1031343860_a_nat bot_bo2122869057_a_nat) bot_bo1836341171_a_nat) (forall ((A labele1159362096nt_a_b) (B labele1159362096nt_a_b) (G labele1159362096nt_a_b) (F set_Product_prod_b_b)) (=> (((graph_222606102_a_b_b ((graph_1309249505nt_a_b A) B)) G) F) (=> (= A (restri446606278nt_a_b A)) (((graph_222606102_a_b_b A) G) ((relcomp_b_b_b (id_on_b (labele1424214014nt_a_b A))) F))))) (forall ((A set_Product_prod_b_b) (B set_Product_prod_b_b)) (=> (forall ((X4 product_prod_b_b)) (let ((_let_1 (member1285940496od_b_b X4))) (=> (_let_1 A) (_let_1 B)))) ((ord_le1036320359od_b_b A) B))) (forall ((A2 product_prod_b_b) (B3 product_prod_b_b) (A set_Product_prod_b_b)) (let ((_let_1 (member1285940496od_b_b A2))) (= (_let_1 ((insert1952693431od_b_b B3) A)) (or (= A2 B3) (_let_1 A))))) (forall ((X produc1871334759_a_nat) (Y produc1871334759_a_nat) (A set_Pr1987088711_a_nat)) (let ((_let_1 (insert1574423351_a_nat X))) (let ((_let_2 (insert1574423351_a_nat Y))) (= (_let_1 (_let_2 A)) (_let_2 (_let_1 A)))))) (forall ((X produc1871334759_a_nat) (A set_Pr1987088711_a_nat) (B set_Pr1987088711_a_nat)) (= ((ord_le1718765799_a_nat ((insert1574423351_a_nat X) A)) B) (and ((ord_le1718765799_a_nat A) B) ((member832397200_a_nat X) B)))) (forall ((A2 labele1159362096nt_a_b) (B3 labele1159362096nt_a_b) (X set_Product_prod_b_b) (C labele1159362096nt_a_b) (Y set_Product_prod_b_b)) (let ((_let_1 (graph_222606102_a_b_b A2))) (=> ((_let_1 B3) X) (=> (((graph_222606102_a_b_b B3) C) Y) ((_let_1 C) ((relcomp_b_b_b X) Y)))))) (forall ((A2 produc1213276845od_b_b) (B set_Pr1324126435od_b_b)) ((member1516365892od_b_b A2) ((insert2037698781od_b_b A2) B))) (forall ((Y produc1213276845od_b_b)) (not (forall ((A4 standard_Constant_a) (B5 b) (C2 b)) (not (= Y ((produc1432590431od_b_b A4) ((product_Pair_b_b B5) C2))))))) (forall ((X product_prod_b_b) (A set_Product_prod_b_b) (B set_Product_prod_b_b)) (= ((ord_le1036320359od_b_b ((insert1952693431od_b_b X) A)) B) (and ((ord_le1036320359od_b_b A) B) ((member1285940496od_b_b X) B)))) (forall ((A2 standard_Constant_a) (B3 b) (C b)) (let ((_let_1 ((labele1230159100nt_a_b ((insert2037698781od_b_b ((produc1432590431od_b_b A2) ((product_Pair_b_b B3) C))) bot_bo1664927607od_b_b)) ((insert_b B3) ((insert_b C) bot_bot_set_b))))) (= _let_1 (restri446606278nt_a_b _let_1)))) (forall ((X b) (Y b) (A set_b)) (let ((_let_1 (insert_b X))) (let ((_let_2 (insert_b Y))) (= (_let_1 (_let_2 A)) (_let_2 (_let_1 A)))))) (= ord_less_eq_set_b (lambda ((A7 set_b) (B7 set_b)) (forall ((X5 b)) (let ((_let_1 (member_b X5))) (=> (_let_1 A7) (_let_1 B7)))))) (forall ((A22 produc1213276845od_b_b) (G labele1644675410od_b_b) (B2 produc1213276845od_b_b) (L standard_Constant_a) (F (-> produc1213276845od_b_b b)) (A2 b) (B3 b)) (let ((_let_1 (labele595103470od_b_b G))) (=> ((member1516365892od_b_b A22) _let_1) (=> ((member1516365892od_b_b B2) _let_1) (=> ((member1086024932od_b_b ((produc449289715od_b_b A22) B2)) ((getRel59882567od_b_b L) G)) (=> (= (F A22) A2) (=> (= (F B2) B3) ((member1285940496od_b_b ((product_Pair_b_b A2) B3)) ((getRel904497637nt_a_b L) ((map_gr1495881666tant_a ((bNF_Gr492676974_b_b_b _let_1) F)) G)))))))))) (forall ((G labele1159362096nt_a_b) (F (-> b b))) (let ((_let_1 ((bNF_Gr_b_b (labele1424214014nt_a_b G)) F))) (=> (= G (restri446606278nt_a_b G)) (((graph_222606102_a_b_b G) ((map_gr926947118tant_a _let_1) G)) _let_1)))) (forall ((B3 product_prod_b_b) (R set_Pr2007082183od_b_b) (A set_Product_prod_b_b)) (=> ((member1285940496od_b_b B3) ((image_1928024979od_b_b R) A)) (not (forall ((X4 product_prod_b_b)) (=> ((member1652792080od_b_b ((produc546497367od_b_b X4) B3)) R) (not ((member1285940496od_b_b X4) A))))))) (forall ((A2 product_prod_b_b) (B3 produc1213276845od_b_b) (R set_Pr1071216121od_b_b) (A set_Product_prod_b_b)) (=> ((member4694106od_b_b ((produc732676669od_b_b A2) B3)) R) (=> ((member1285940496od_b_b A2) A) ((member1516365892od_b_b B3) ((image_532916993od_b_b R) A))))) _let_9 (forall ((A labele1159362096nt_a_b) (B labele1159362096nt_a_b) (A2 b) (B3 b) (E allego510293162tant_a)) (let ((_let_1 (member1285940496od_b_b ((product_Pair_b_b A2) B3)))) (=> (((graph_222606102_a_b_b A) B) (id_on_b (labele1424214014nt_a_b A))) (=> (_let_1 ((semant55076487nt_a_b A) E)) (_let_1 ((semant55076487nt_a_b B) E)))))) (forall ((A2 labele1159362096nt_a_b) (B3 labele1159362096nt_a_b) (F set_Product_prod_b_b) (Aa b) (Ba b)) (let ((_let_1 (member1285940496od_b_b ((product_Pair_b_b Aa) Ba)))) (=> (((graph_222606102_a_b_b A2) B3) F) (=> (_let_1 F) (_let_1 ((relcomp_b_b_b (id_on_b (labele1424214014nt_a_b A2))) F)))))) (forall ((X b)) (= ((member_b X) (labele1424214014nt_a_b g)) ((p X) X))) (forall ((G labele1159362096nt_a_b) (A2 b) (B3 b) (L standard_Constant_a)) (=> (= G (restri446606278nt_a_b G)) (=> ((member1285940496od_b_b ((product_Pair_b_b A2) B3)) ((getRel904497637nt_a_b L) G)) ((member_b A2) (labele1424214014nt_a_b G))))) (forall ((A labele1159362096nt_a_b) (B labele1159362096nt_a_b) (G labele1159362096nt_a_b) (F set_Product_prod_b_b)) (=> ((mainta374363448_a_b_b ((produc1569511545nt_a_b A) B)) G) (=> (((graph_222606102_a_b_b A) G) F) (not (forall ((G5 set_Product_prod_b_b)) (=> (((graph_222606102_a_b_b B) G) G5) (not ((ord_le1036320359od_b_b F) G5)))))))) (forall ((R set_Product_prod_b_b) (S set_Product_prod_b_b)) (=> (forall ((X4 b) (Y3 b)) (let ((_let_1 (member1285940496od_b_b ((product_Pair_b_b X4) Y3)))) (=> (_let_1 R) (_let_1 S)))) ((ord_le1036320359od_b_b R) S))) (forall ((Y b) (Z b) (L standard_Constant_a) (G labele1159362096nt_a_b) (F (-> b b))) (let ((_let_1 (labele1424214014nt_a_b G))) (let ((_let_2 (getRel904497637nt_a_b L))) (=> ((member1285940496od_b_b ((product_Pair_b_b Y) Z)) (_let_2 G)) (=> ((member_b Y) _let_1) (=> ((member_b Z) _let_1) ((member1285940496od_b_b ((product_Pair_b_b (F Y)) (F Z))) (_let_2 ((map_gr926947118tant_a ((bNF_Gr_b_b _let_1) F)) G))))))))) (forall ((A2 produc1871334759_a_nat) (B set_Pr1987088711_a_nat) (B3 produc1871334759_a_nat)) (let ((_let_1 (member832397200_a_nat A2))) (=> (=> (not (_let_1 B)) (= A2 B3)) (_let_1 ((insert1574423351_a_nat B3) B))))) (forall ((A1 standard_Constant_a) (A22 product_prod_b_b) (R set_Pr154086431tant_a) (S set_Pr1324126435od_b_b)) (= ((member1516365892od_b_b ((produc1432590431od_b_b A1) A22)) ((relcom883816262od_b_b R) S)) (exists ((A5 standard_Constant_a) (B6 standard_Constant_a) (C3 product_prod_b_b)) (and (= A1 A5) ((member1214736488tant_a ((produc342647tant_a A5) B6)) R) ((member1516365892od_b_b ((produc1432590431od_b_b B6) C3)) S) (= A22 C3))))) (forall ((A2 product_prod_b_b) (B3 product_prod_b_b) (A set_Product_prod_b_b)) (let ((_let_1 (member1285940496od_b_b A2))) (=> (_let_1 ((insert1952693431od_b_b B3) A)) (=> (not (= A2 B3)) (_let_1 A))))) (forall ((A set_Product_prod_b_b)) (= (collec1481886546od_b_b (lambda ((X5 product_prod_b_b)) ((member1285940496od_b_b X5) A))) A)) (forall ((A set_Pr1987088711_a_nat) (A2 produc1871334759_a_nat)) (=> (= A bot_bo1836341171_a_nat) (not ((member832397200_a_nat A2) A)))) (forall ((A2 produc1213276845od_b_b) (A set_Pr1324126435od_b_b)) (=> ((member1516365892od_b_b A2) A) (= ((insert2037698781od_b_b A2) A) A))) (forall ((X product_prod_b_b) (A set_Product_prod_b_b)) (=> ((member1285940496od_b_b X) A) (not (forall ((B8 set_Product_prod_b_b)) (=> (= A ((insert1952693431od_b_b X) B8)) ((member1285940496od_b_b X) B8)))))) (forall ((R22 labele1159362096nt_a_b) (G labele1159362096nt_a_b) (G2 set_Product_prod_b_b) (R1 labele1159362096nt_a_b) (F set_Product_prod_b_b)) (=> (((graph_222606102_a_b_b R22) G) G2) (=> (((agree_221379389_a_b_b R1) F) G2) (((extens1779443913_a_b_b ((produc1569511545nt_a_b R1) R22)) G) F)))) (forall ((H1 set_Product_prod_b_b) (E1 set_Pr1324126435od_b_b) (E2 set_Pr1324126435od_b_b) (V1 b) (V12 b) (V2 b) (V22 b) (K standard_Constant_a)) (let ((_let_1 (produc1432590431od_b_b K))) (let ((_let_2 (product_Pair_b_b V1))) (=> (((edge_p1384198690tant_a H1) E1) E2) (=> ((member1285940496od_b_b (_let_2 V12)) H1) (=> ((member1285940496od_b_b ((product_Pair_b_b V2) V22)) H1) (=> ((member1516365892od_b_b (_let_1 (_let_2 V2))) E1) ((member1516365892od_b_b (_let_1 ((product_Pair_b_b V12) V22))) E2)))))))) (forall ((A2 produc1871334759_a_nat) (B set_Pr1987088711_a_nat) (B3 produc1871334759_a_nat)) (let ((_let_1 (member832397200_a_nat A2))) (=> (_let_1 B) (_let_1 ((insert1574423351_a_nat B3) B))))) (forall ((A2 produc1871334759_a_nat) (B3 produc1871334759_a_nat) (A set_Pr1987088711_a_nat)) (let ((_let_1 (member832397200_a_nat A2))) (= (_let_1 ((insert1574423351_a_nat B3) A)) (or (= A2 B3) (_let_1 A))))) (forall ((X standard_Constant_a) (Fx product_prod_b_b) (A set_St761939237tant_a) (F (-> standard_Constant_a product_prod_b_b))) (=> ((member1516365892od_b_b ((produc1432590431od_b_b X) Fx)) ((bNF_Gr1272216980od_b_b A) F)) ((member1632892294tant_a X) A))) (forall ((A labele1159362096nt_a_b) (B labele1159362096nt_a_b)) (let ((_let_1 ((graph_1309249505nt_a_b B) A))) (= ((graph_1309249505nt_a_b A) _let_1) _let_1))) (forall ((A2 b) (C b) (R set_Product_prod_b_b) (S set_Product_prod_b_b)) (=> ((member1285940496od_b_b ((product_Pair_b_b A2) C)) ((relcomp_b_b_b R) S)) (not (forall ((B5 b)) (=> ((member1285940496od_b_b ((product_Pair_b_b A2) B5)) R) (not ((member1285940496od_b_b ((product_Pair_b_b B5) C)) S))))))) (forall ((A set_Pr1324126435od_b_b) (B set_Pr1324126435od_b_b)) (=> (forall ((X4 produc1213276845od_b_b)) (let ((_let_1 (member1516365892od_b_b X4))) (=> (_let_1 A) (_let_1 B)))) ((ord_le123089219od_b_b A) B))) (forall ((C product_prod_b_b)) (not ((member1285940496od_b_b C) bot_bo1343651123od_b_b))) (= ord_le1036320359od_b_b (lambda ((A7 set_Product_prod_b_b) (B7 set_Product_prod_b_b)) (forall ((T product_prod_b_b)) (let ((_let_1 (member1285940496od_b_b T))) (=> (_let_1 A7) (_let_1 B7)))))) (forall ((A2 product_prod_b_b) (B3 product_prod_b_b) (R set_Pr2007082183od_b_b) (A set_Product_prod_b_b)) (=> ((member1652792080od_b_b ((produc546497367od_b_b A2) B3)) R) (=> ((member1285940496od_b_b A2) A) ((member1285940496od_b_b B3) ((image_1928024979od_b_b R) A))))) (forall ((X b) (Y b)) (= (((if_b false) X) Y) Y)) (forall ((E_1 set_Pr1324126435od_b_b) (V set_b) (G labele1159362096nt_a_b) (F set_Product_prod_b_b) (E_2 set_Pr1324126435od_b_b)) (let ((_let_1 ((labele1230159100nt_a_b E_2) V))) (let ((_let_2 ((labele1230159100nt_a_b E_1) V))) (=> (((graph_222606102_a_b_b _let_2) G) F) (= (((extens1779443913_a_b_b ((produc1569511545nt_a_b _let_2) _let_1)) G) F) (((graph_222606102_a_b_b _let_1) G) F)))))) (forall ((A labele1159362096nt_a_b) (B labele1159362096nt_a_b) (F set_Product_prod_b_b)) (let ((_let_1 (map_gr926947118tant_a F))) (let ((_let_2 (_let_1 A))) (=> (((graph_222606102_a_b_b A) B) (id_on_b (labele1424214014nt_a_b A))) (((graph_222606102_a_b_b _let_2) (_let_1 B)) (id_on_b (labele1424214014nt_a_b _let_2))))))) (forall ((X3 set_b)) (= ((image_b_b bot_bo1343651123od_b_b) X3) bot_bot_set_b)) (forall ((A set_Pr1324126435od_b_b) (B set_Pr1324126435od_b_b) (C produc1213276845od_b_b)) (let ((_let_1 (member1516365892od_b_b C))) (=> ((ord_le123089219od_b_b A) B) (=> (_let_1 A) (_let_1 B))))) (forall ((A set_Pr1987088711_a_nat) (R set_Pr924198087_a_nat) (B3 produc1871334759_a_nat) (A2 produc1871334759_a_nat)) (let ((_let_1 (image_1168831379_a_nat R))) (=> ((equiv_291114781_a_nat A) R) (=> ((ord_le1718765799_a_nat (_let_1 ((insert1574423351_a_nat B3) bot_bo1836341171_a_nat))) (_let_1 ((insert1574423351_a_nat A2) bot_bo1836341171_a_nat))) (=> ((member832397200_a_nat B3) A) ((member584645392_a_nat ((produc1677124439_a_nat A2) B3)) R)))))) (forall ((X product_prod_b_b) (A set_Product_prod_b_b) (B set_Product_prod_b_b)) (let ((_let_1 (insert1952693431od_b_b X))) (let ((_let_2 (member1285940496od_b_b X))) (=> (not (_let_2 A)) (=> (not (_let_2 B)) (= (= (_let_1 A) (_let_1 B)) (= A B))))))) (forall ((A set_Product_prod_b_b) (A2 product_prod_b_b)) (=> (= A bot_bo1343651123od_b_b) (not ((member1285940496od_b_b A2) A)))) (forall ((F (-> b b))) (= ((bNF_Gr_b_b bot_bot_set_b) F) bot_bo1343651123od_b_b)) (forall ((A2 produc1213276845od_b_b)) (not ((member1516365892od_b_b A2) bot_bo1664927607od_b_b))) (forall ((B3 b) (R set_Pr357419743_b_b_b) (A set_Product_prod_b_b)) (=> ((member_b B3) ((image_921732011_b_b_b R) A)) (not (forall ((X4 product_prod_b_b)) (=> ((member351494440_b_b_b ((produc1001682799_b_b_b X4) B3)) R) (not ((member1285940496od_b_b X4) A))))))) (forall ((A2 produc1213276845od_b_b) (B3 b) (R set_Pr1906739389_b_b_b) (A set_Pr1324126435od_b_b)) (=> ((member1417789726_b_b_b ((produc1580777273_b_b_b A2) B3)) R) (=> ((member1516365892od_b_b A2) A) ((member_b B3) ((image_1764625405_b_b_b R) A))))) (forall ((X3 set_la1083530965_a_nat)) (= ((image_1971191571_a_nat bot_bo1836341171_a_nat) X3) bot_bo2122869057_a_nat)) (forall ((A set_Pr1324126435od_b_b) (R set_Pr2109276827od_b_b) (A2 produc1213276845od_b_b) (B3 produc1213276845od_b_b)) (=> ((refl_o1921098222od_b_b A) R) (=> ((member1086024932od_b_b ((produc449289715od_b_b A2) B3)) R) (and ((member1516365892od_b_b A2) A) ((member1516365892od_b_b B3) A))))) (forall ((G_1 labele1159362096nt_a_b) (G_2 labele1159362096nt_a_b)) (=> (((graph_222606102_a_b_b G_1) G_2) (id_on_b (labele1424214014nt_a_b G_1))) ((ord_le123089219od_b_b (labele1741081071nt_a_b (restri446606278nt_a_b G_1))) (labele1741081071nt_a_b G_2)))) (forall ((X b)) (=> ((member_b X) (labele1424214014nt_a_b g)) ((member1285940496od_b_b ((product_Pair_b_b X) (hilbert_Eps_b (p X)))) ((getRel904497637nt_a_b standard_S_Idt_a) g)))) (forall ((R2 set_Pr812188767_nat_b)) (= ((image_924992811_nat_b R2) bot_bo1836341171_a_nat) bot_bot_set_b)) (forall ((A2 product_prod_b_b) (A set_Product_prod_b_b) (B3 produc1213276845od_b_b) (R set_Pr1071216121od_b_b)) (=> ((member1285940496od_b_b A2) A) (=> ((member4694106od_b_b ((produc732676669od_b_b A2) B3)) R) ((member1516365892od_b_b B3) ((image_532916993od_b_b R) A))))) (forall ((A set_Pr1324126435od_b_b)) (= (exists ((X5 produc1213276845od_b_b)) ((member1516365892od_b_b X5) A)) (not (= A bot_bo1664927607od_b_b)))) (forall ((Xz produc1213276845od_b_b) (R set_Pr1324126435od_b_b) (S set_Pr2007082183od_b_b)) (=> ((member1516365892od_b_b Xz) ((relcom1823941168od_b_b R) S)) (not (forall ((X4 standard_Constant_a) (Y3 product_prod_b_b) (Z2 product_prod_b_b)) (let ((_let_1 (produc1432590431od_b_b X4))) (=> (= Xz (_let_1 Z2)) (=> ((member1516365892od_b_b (_let_1 Y3)) R) (not ((member1652792080od_b_b ((produc546497367od_b_b Y3) Z2)) S))))))))) (forall ((A2 produc1871334759_a_nat) (A set_Pr1987088711_a_nat) (B3 produc1871334759_a_nat)) (let ((_let_1 ((insert1574423351_a_nat B3) bot_bo1836341171_a_nat))) (= (= ((insert1574423351_a_nat A2) A) _let_1) (and (= A2 B3) ((ord_le1718765799_a_nat A) _let_1))))) (forall ((A2 b) (B3 produc1213276845od_b_b) (R set_Pr2060523537od_b_b) (A set_b)) (=> ((member599505522od_b_b ((produc800495189od_b_b A2) B3)) R) (=> ((member_b A2) A) ((member1516365892od_b_b B3) ((image_984343321od_b_b R) A))))) (forall ((A2 produc1213276845od_b_b) (B set_Pr1324126435od_b_b) (B3 produc1213276845od_b_b)) (let ((_let_1 (member1516365892od_b_b A2))) (=> (=> (not (_let_1 B)) (= A2 B3)) (_let_1 ((insert2037698781od_b_b B3) B))))) (forall ((A set_b)) (= (exists ((X5 b)) ((member_b X5) A)) (not (= A bot_bot_set_b)))) (forall ((A2 b) (P (-> b Bool))) (= ((member_b A2) (collect_b P)) (P A2))) (forall ((X1 b) (X22 b) (Y1 b) (Y22 b)) (= (= ((product_Pair_b_b X1) X22) ((product_Pair_b_b Y1) Y22)) (and (= X22 Y22) (= X1 Y1)))) _let_8 _let_7 (forall ((X3 set_Product_prod_b_b) (Y2 set_Product_prod_b_b) (Z3 set_b)) (= ((image_b_b ((relcomp_b_b_b X3) Y2)) Z3) ((image_b_b Y2) ((image_b_b X3) Z3)))) (forall ((A2 produc1871334759_a_nat) (B3 produc1871334759_a_nat) (C produc1871334759_a_nat) (D produc1871334759_a_nat)) (= (= ((insert1574423351_a_nat A2) ((insert1574423351_a_nat B3) bot_bo1836341171_a_nat)) ((insert1574423351_a_nat C) ((insert1574423351_a_nat D) bot_bo1836341171_a_nat))) (or (and (= B3 D) (= A2 C)) (and (= A2 D) (= B3 C))))) (forall ((A2 b) (B3 b) (R set_Product_prod_b_b) (A set_b)) (=> ((member1285940496od_b_b ((product_Pair_b_b A2) B3)) R) (=> ((member_b A2) A) ((member_b B3) ((image_b_b R) A))))) (forall ((B3 b) (R set_Product_prod_b_b) (A set_b)) (=> ((member_b B3) ((image_b_b R) A)) (not (forall ((X4 b)) (=> ((member1285940496od_b_b ((product_Pair_b_b X4) B3)) R) (not ((member_b X4) A))))))) ((member1285940496od_b_b _let_6) ((getRel904497637nt_a_b l2) g)) (forall ((A2 produc1871334759_a_nat)) ((member832397200_a_nat A2) ((insert1574423351_a_nat A2) bot_bo1836341171_a_nat))) (= ord_le123089219od_b_b (lambda ((A7 set_Pr1324126435od_b_b) (B7 set_Pr1324126435od_b_b)) (forall ((T produc1213276845od_b_b)) (let ((_let_1 (member1516365892od_b_b T))) (=> (_let_1 A7) (_let_1 B7)))))) (forall ((Y produc1213276845od_b_b)) (not (forall ((A4 standard_Constant_a) (B5 product_prod_b_b)) (not (= Y ((produc1432590431od_b_b A4) B5)))))) (forall ((X1 standard_Constant_a) (X22 product_prod_b_b) (R set_Pr154086431tant_a) (S set_Pr1324126435od_b_b) (P (-> standard_Constant_a product_prod_b_b Bool))) (=> ((member1516365892od_b_b ((produc1432590431od_b_b X1) X22)) ((relcom883816262od_b_b R) S)) (=> (forall ((A4 standard_Constant_a) (B5 standard_Constant_a) (C2 product_prod_b_b)) (=> ((member1214736488tant_a ((produc342647tant_a A4) B5)) R) (=> ((member1516365892od_b_b ((produc1432590431od_b_b B5) C2)) S) ((P A4) C2)))) ((P X1) X22)))) (forall ((X b) (A set_b) (B set_b)) (= ((ord_less_eq_set_b ((insert_b X) A)) B) (and ((member_b X) B) ((ord_less_eq_set_b A) B)))) (forall ((B3 b) (R set_Product_prod_b_b) (A set_b)) (= ((member_b B3) ((image_b_b R) A)) (exists ((X5 b)) (and ((member1285940496od_b_b ((product_Pair_b_b X5) B3)) R) ((member_b X5) A))))) (forall ((A2 standard_Constant_a) (C product_prod_b_b) (R set_Pr154086431tant_a) (S set_Pr1324126435od_b_b)) (=> ((member1516365892od_b_b ((produc1432590431od_b_b A2) C)) ((relcom883816262od_b_b R) S)) (not (forall ((B5 standard_Constant_a)) (=> ((member1214736488tant_a ((produc342647tant_a A2) B5)) R) (not ((member1516365892od_b_b ((produc1432590431od_b_b B5) C)) S))))))) ((member1516365892od_b_b ((produc1432590431od_b_b l2) _let_6)) (labele1741081071nt_a_b g)) (forall ((X b)) (=> ((member_b X) (labele1424214014nt_a_b g)) ((member1285940496od_b_b ((product_Pair_b_b X) X)) ((getRel904497637nt_a_b standard_S_Idt_a) g)))) (forall ((A2 product_prod_b_b) (A set_Product_prod_b_b)) (=> ((member1285940496od_b_b A2) A) ((member1652792080od_b_b ((produc546497367od_b_b A2) A2)) (id_on_2019020932od_b_b A)))) (forall ((B3 product_prod_b_b) (R set_Pr621705391od_b_b) (A set_b)) (=> ((member1285940496od_b_b B3) ((image_1177096571od_b_b R) A)) (not (forall ((X4 b)) (=> ((member641857272od_b_b ((produc1257047359od_b_b X4) B3)) R) (not ((member_b X4) A))))))) ((equiv_equiv_b _let_3) _let_2) (forall ((A set_b) (R set_Product_prod_b_b) (X b) (Y b)) (=> ((refl_on_b A) R) (=> ((member1285940496od_b_b ((product_Pair_b_b X) Y)) R) ((member_b Y) A)))) ((refl_o1213627494_a_nat bot_bo1836341171_a_nat) bot_bo1973379891_a_nat) (forall ((R2 set_Pr1987088711_a_nat)) (= ((relcom1338300020_a_nat bot_bo1836341171_a_nat) R2) bot_bo1836341171_a_nat)) (forall ((A set_Pr1324126435od_b_b) (B set_Pr1324126435od_b_b) (X produc1213276845od_b_b)) (let ((_let_1 (member1516365892od_b_b X))) (=> ((ord_le123089219od_b_b A) B) (=> (_let_1 A) (_let_1 B))))) (forall ((A labele1159362096nt_a_b) (B labele1159362096nt_a_b) (G labele1159362096nt_a_b) (F set_Product_prod_b_b)) (=> (((graph_222606102_a_b_b ((graph_1309249505nt_a_b A) B)) G) F) (=> (= B (restri446606278nt_a_b B)) (((graph_222606102_a_b_b B) G) ((relcomp_b_b_b (id_on_b (labele1424214014nt_a_b B))) F))))) (= g (restri446606278nt_a_b g)) (not false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
86.55/87.10	)
86.55/87.10	% SZS output end Proof for theBenchmark
86.55/87.11	EOF