%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP177^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:56:10 AM UTC 2026
% Result : Theorem 3.37s 1.80s
% Output : Refutation 3.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 105 ( 38 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 282 ( 10 ~; 5 |; 0 &; 264 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 53 ( 52 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 155 ( 152 usr; 17 con; 0-3 aty)
% Number of variables : 30 ( 23 ^; 7 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
set_St761939237tant_a: $tType ).
thf(type_def_6,type,
standard_Constant_a: $tType ).
thf(type_def_7,type,
product_prod_b_b: $tType ).
thf(type_def_9,type,
set_Pr1324126435od_b_b: $tType ).
thf(type_def_10,type,
set_la1083530965_a_nat: $tType ).
thf(type_def_11,type,
labele935650037_a_nat: $tType ).
thf(type_def_12,type,
set_Pr1987088711_a_nat: $tType ).
thf(type_def_13,type,
produc1213276845od_b_b: $tType ).
thf(type_def_14,type,
b: $tType ).
thf(type_def_15,type,
set_Pr1906739389_b_b_b: $tType ).
thf(type_def_16,type,
set_Product_prod_b_b: $tType ).
thf(type_def_17,type,
set_Pr357419743_b_b_b: $tType ).
thf(type_def_18,type,
set_b: $tType ).
thf(type_def_19,type,
set_Pr1649131859tant_a: $tType ).
thf(type_def_20,type,
set_Pr2109276827od_b_b: $tType ).
thf(type_def_21,type,
set_Pr924198087_a_nat: $tType ).
thf(type_def_22,type,
set_Pr2007082183od_b_b: $tType ).
thf(type_def_23,type,
labele1644675410od_b_b: $tType ).
thf(type_def_24,type,
labele1835558936od_b_b: $tType ).
thf(type_def_25,type,
labele1159362096nt_a_b: $tType ).
thf(type_def_26,type,
allego510293162tant_a: $tType ).
thf(type_def_27,type,
set_Pr1190604087od_b_b: $tType ).
thf(type_def_28,type,
set_Pr1021918435od_b_b: $tType ).
thf(type_def_29,type,
set_Pr2106913242_nat_b: $tType ).
thf(type_def_30,type,
labele1322729112_a_nat: $tType ).
thf(type_def_31,type,
set_Pr812188767_nat_b: $tType ).
thf(type_def_32,type,
set_Pr197580003_a_nat: $tType ).
thf(type_def_33,type,
produc90515391tant_a: $tType ).
thf(type_def_34,type,
produc970027067od_b_b: $tType ).
thf(type_def_35,type,
produc1084374401od_b_b: $tType ).
thf(type_def_36,type,
produc1168037607od_b_b: $tType ).
thf(type_def_37,type,
produc644633773od_b_b: $tType ).
thf(type_def_38,type,
produc1871334759_a_nat: $tType ).
thf(type_def_39,type,
produc1398946881nt_a_b: $tType ).
thf(type_def_40,type,
produc1990339951od_b_b: $tType ).
thf(type_def_41,type,
produc276146823_b_b_b: $tType ).
thf(type_def_42,type,
produc1169496899od_b_b: $tType ).
thf(type_def_43,type,
produc398057191_a_nat: $tType ).
thf(type_def_44,type,
produc1485083751od_b_b: $tType ).
thf(type_def_45,type,
produc845793663_nat_b: $tType ).
thf(type_def_46,type,
produc1052326083od_b_b: $tType ).
thf(type_def_47,type,
produc2112523263_b_b_b: $tType ).
thf(type_def_48,type,
produc1605346267od_b_b: $tType ).
thf(type_def_49,type,
produc255402447od_b_b: $tType ).
thf(type_def_50,type,
set_Pr2134561957od_b_b: $tType ).
thf(type_def_51,type,
set_Pr1954438265od_b_b: $tType ).
thf(type_def_52,type,
set_Pr667377223od_b_b: $tType ).
thf(type_def_53,type,
set_Pr1071216121od_b_b: $tType ).
thf(type_def_54,type,
set_Pr2060523537od_b_b: $tType ).
thf(type_def_55,type,
set_Pr1646010159_a_nat: $tType ).
thf(type_def_56,type,
set_Pr621705391od_b_b: $tType ).
thf(type_def_57,type,
set_Pr154086431tant_a: $tType ).
thf(func_def_0,type,
set_Pr197580003_a_nat: $tType ).
thf(func_def_1,type,
set_Pr924198087_a_nat: $tType ).
thf(func_def_2,type,
produc398057191_a_nat: $tType ).
thf(func_def_3,type,
set_Pr1954438265od_b_b: $tType ).
thf(func_def_4,type,
produc1169496899od_b_b: $tType ).
thf(func_def_5,type,
set_Pr1190604087od_b_b: $tType ).
thf(func_def_6,type,
produc1084374401od_b_b: $tType ).
thf(func_def_7,type,
labele1322729112_a_nat: $tType ).
thf(func_def_8,type,
set_Pr667377223od_b_b: $tType ).
thf(func_def_9,type,
produc1485083751od_b_b: $tType ).
thf(func_def_10,type,
set_Pr2109276827od_b_b: $tType ).
thf(func_def_11,type,
set_Pr1646010159_a_nat: $tType ).
thf(func_def_12,type,
set_Pr812188767_nat_b: $tType ).
thf(func_def_13,type,
produc970027067od_b_b: $tType ).
thf(func_def_14,type,
produc845793663_nat_b: $tType ).
thf(func_def_15,type,
set_Pr1987088711_a_nat: $tType ).
thf(func_def_16,type,
produc1871334759_a_nat: $tType ).
thf(func_def_17,type,
produc1398946881nt_a_b: $tType ).
thf(func_def_18,type,
labele1644675410od_b_b: $tType ).
thf(func_def_19,type,
set_Pr1071216121od_b_b: $tType ).
thf(func_def_20,type,
set_Pr2134561957od_b_b: $tType ).
thf(func_def_21,type,
set_Pr1021918435od_b_b: $tType ).
thf(func_def_22,type,
produc1052326083od_b_b: $tType ).
thf(func_def_23,type,
produc1990339951od_b_b: $tType ).
thf(func_def_24,type,
produc644633773od_b_b: $tType ).
thf(func_def_25,type,
set_Pr2060523537od_b_b: $tType ).
thf(func_def_26,type,
set_Pr1906739389_b_b_b: $tType ).
thf(func_def_27,type,
produc1605346267od_b_b: $tType ).
thf(func_def_28,type,
produc276146823_b_b_b: $tType ).
thf(func_def_29,type,
set_Pr154086431tant_a: $tType ).
thf(func_def_30,type,
set_Pr1324126435od_b_b: $tType ).
thf(func_def_31,type,
produc90515391tant_a: $tType ).
thf(func_def_32,type,
labele1835558936od_b_b: $tType ).
thf(func_def_33,type,
set_Pr2007082183od_b_b: $tType ).
thf(func_def_34,type,
produc1213276845od_b_b: $tType ).
thf(func_def_35,type,
set_la1083530965_a_nat: $tType ).
thf(func_def_36,type,
produc1168037607od_b_b: $tType ).
thf(func_def_37,type,
labele935650037_a_nat: $tType ).
thf(func_def_38,type,
set_Pr1649131859tant_a: $tType ).
thf(func_def_39,type,
allego510293162tant_a: $tType ).
thf(func_def_40,type,
labele1159362096nt_a_b: $tType ).
thf(func_def_41,type,
set_Pr621705391od_b_b: $tType ).
thf(func_def_42,type,
set_Pr357419743_b_b_b: $tType ).
thf(func_def_43,type,
produc255402447od_b_b: $tType ).
thf(func_def_44,type,
produc2112523263_b_b_b: $tType ).
thf(func_def_45,type,
set_St761939237tant_a: $tType ).
thf(func_def_46,type,
set_Pr2106913242_nat_b: $tType ).
thf(func_def_47,type,
set_Product_prod_b_b: $tType ).
thf(func_def_48,type,
standard_Constant_a: $tType ).
thf(func_def_49,type,
product_prod_b_b: $tType ).
thf(func_def_50,type,
set_b: $tType ).
thf(func_def_51,type,
b: $tType ).
thf(func_def_52,type,
bNF_Gr1272216980od_b_b: set_St761939237tant_a > ( standard_Constant_a > product_prod_b_b ) > set_Pr1324126435od_b_b ).
thf(func_def_53,type,
bNF_Gr996500706_a_nat: set_la1083530965_a_nat > ( labele935650037_a_nat > labele935650037_a_nat ) > set_Pr1987088711_a_nat ).
thf(func_def_54,type,
bNF_Gr492676974_b_b_b: set_Pr1324126435od_b_b > ( produc1213276845od_b_b > b ) > set_Pr1906739389_b_b_b ).
thf(func_def_55,type,
bNF_Gr521784954_b_b_b: set_Product_prod_b_b > ( product_prod_b_b > b ) > set_Pr357419743_b_b_b ).
thf(func_def_56,type,
bNF_Gr230160332tant_a: set_b > ( b > standard_Constant_a ) > set_Pr1649131859tant_a ).
thf(func_def_57,type,
bNF_Gr_b_b: set_b > ( b > b ) > set_Product_prod_b_b ).
thf(func_def_58,type,
equiv_1821124534_set_b: set_Product_prod_b_b > ( b > set_b ) > $o ).
thf(func_def_59,type,
equiv_2048442231od_b_b: set_Pr1324126435od_b_b > set_Pr2109276827od_b_b > $o ).
thf(func_def_60,type,
equiv_291114781_a_nat: set_Pr1987088711_a_nat > set_Pr924198087_a_nat > $o ).
thf(func_def_61,type,
equiv_1125628061od_b_b: set_Product_prod_b_b > set_Pr2007082183od_b_b > $o ).
thf(func_def_62,type,
equiv_equiv_b: set_b > set_Product_prod_b_b > $o ).
thf(func_def_63,type,
hilbert_Eps_b: ( b > $o ) > b ).
thf(func_def_64,type,
if_b: $o > b > b > b ).
thf(func_def_65,type,
standard_S_Idt_a: standard_Constant_a ).
thf(func_def_66,type,
getRel59882567od_b_b: standard_Constant_a > labele1644675410od_b_b > set_Pr2109276827od_b_b ).
thf(func_def_67,type,
getRel118493133od_b_b: standard_Constant_a > labele1835558936od_b_b > set_Pr2007082183od_b_b ).
thf(func_def_68,type,
getRel904497637nt_a_b: standard_Constant_a > labele1159362096nt_a_b > set_Product_prod_b_b ).
thf(func_def_69,type,
semant55076487nt_a_b: labele1159362096nt_a_b > allego510293162tant_a > set_Product_prod_b_b ).
thf(func_def_70,type,
edge_p1817988046tant_a: set_Pr1906739389_b_b_b > set_Pr1190604087od_b_b > set_Pr1324126435od_b_b > $o ).
thf(func_def_71,type,
edge_p1969196346tant_a: set_Pr357419743_b_b_b > set_Pr1021918435od_b_b > set_Pr1324126435od_b_b > $o ).
thf(func_def_72,type,
edge_p1384198690tant_a: set_Product_prod_b_b > set_Pr1324126435od_b_b > set_Pr1324126435od_b_b > $o ).
thf(func_def_73,type,
graph_714568023_nat_b: labele935650037_a_nat > labele1159362096nt_a_b > set_Pr2106913242_nat_b > $o ).
thf(func_def_74,type,
graph_726202286_nat_b: labele1322729112_a_nat > labele1159362096nt_a_b > set_Pr812188767_nat_b > $o ).
thf(func_def_75,type,
graph_222606102_a_b_b: labele1159362096nt_a_b > labele1159362096nt_a_b > set_Product_prod_b_b > $o ).
thf(func_def_76,type,
graph_1309249505nt_a_b: labele1159362096nt_a_b > labele1159362096nt_a_b > labele1159362096nt_a_b ).
thf(func_def_77,type,
labele27098724_a_nat: set_Pr197580003_a_nat > set_Pr1987088711_a_nat > labele1322729112_a_nat ).
thf(func_def_78,type,
labele1230159100nt_a_b: set_Pr1324126435od_b_b > set_b > labele1159362096nt_a_b ).
thf(func_def_79,type,
labele2032816061od_b_b: labele1644675410od_b_b > set_Pr1190604087od_b_b ).
thf(func_def_80,type,
labele372159959od_b_b: labele1835558936od_b_b > set_Pr1021918435od_b_b ).
thf(func_def_81,type,
labele1741081071nt_a_b: labele1159362096nt_a_b > set_Pr1324126435od_b_b ).
thf(func_def_82,type,
labele595103470od_b_b: labele1644675410od_b_b > set_Pr1324126435od_b_b ).
thf(func_def_83,type,
labele442485990od_b_b: labele1835558936od_b_b > set_Product_prod_b_b ).
thf(func_def_84,type,
labele1424214014nt_a_b: labele1159362096nt_a_b > set_b ).
thf(func_def_85,type,
map_gr1495881666tant_a: set_Pr1906739389_b_b_b > labele1644675410od_b_b > labele1159362096nt_a_b ).
thf(func_def_86,type,
map_gr1314489926tant_a: set_Pr357419743_b_b_b > labele1835558936od_b_b > labele1159362096nt_a_b ).
thf(func_def_87,type,
map_gr926947118tant_a: set_Product_prod_b_b > labele1159362096nt_a_b > labele1159362096nt_a_b ).
thf(func_def_88,type,
restri446606278nt_a_b: labele1159362096nt_a_b > labele1159362096nt_a_b ).
thf(func_def_89,type,
bot_bo1160111033tant_a: set_St761939237tant_a ).
thf(func_def_90,type,
bot_bo2122869057_a_nat: set_la1083530965_a_nat ).
thf(func_def_91,type,
bot_bo1653310327_a_nat: set_Pr197580003_a_nat ).
thf(func_def_92,type,
bot_bo1664927607od_b_b: set_Pr1324126435od_b_b ).
thf(func_def_93,type,
bot_bo1836341171_a_nat: set_Pr1987088711_a_nat ).
thf(func_def_94,type,
bot_bo1973379891_a_nat: set_Pr924198087_a_nat ).
thf(func_def_95,type,
bot_bo1113554635_nat_b: set_Pr812188767_nat_b ).
thf(func_def_96,type,
bot_bo1343651123od_b_b: set_Product_prod_b_b ).
thf(func_def_97,type,
bot_bot_set_b: set_b ).
thf(func_def_98,type,
ord_le123089219od_b_b: set_Pr1324126435od_b_b > set_Pr1324126435od_b_b > $o ).
thf(func_def_99,type,
ord_le1718765799_a_nat: set_Pr1987088711_a_nat > set_Pr1987088711_a_nat > $o ).
thf(func_def_100,type,
ord_le1484132922_nat_b: set_Pr2106913242_nat_b > set_Pr2106913242_nat_b > $o ).
thf(func_def_101,type,
ord_le107617383_a_nat: set_Pr924198087_a_nat > set_Pr924198087_a_nat > $o ).
thf(func_def_102,type,
ord_le1036320359od_b_b: set_Product_prod_b_b > set_Product_prod_b_b > $o ).
thf(func_def_103,type,
ord_less_eq_set_b: set_b > set_b > $o ).
thf(func_def_104,type,
produc342647tant_a: standard_Constant_a > standard_Constant_a > produc90515391tant_a ).
thf(func_def_105,type,
produc1788032435od_b_b: standard_Constant_a > produc970027067od_b_b > produc1084374401od_b_b ).
thf(func_def_106,type,
produc618266719od_b_b: standard_Constant_a > produc1168037607od_b_b > produc644633773od_b_b ).
thf(func_def_107,type,
produc1432590431od_b_b: standard_Constant_a > product_prod_b_b > produc1213276845od_b_b ).
thf(func_def_108,type,
produc1676969687_a_nat: labele935650037_a_nat > labele935650037_a_nat > produc1871334759_a_nat ).
thf(func_def_109,type,
produc1569511545nt_a_b: labele1159362096nt_a_b > labele1159362096nt_a_b > produc1398946881nt_a_b ).
thf(func_def_110,type,
produc449289715od_b_b: produc1213276845od_b_b > produc1213276845od_b_b > produc970027067od_b_b ).
thf(func_def_111,type,
produc1597690145od_b_b: produc1213276845od_b_b > product_prod_b_b > produc1990339951od_b_b ).
thf(func_def_112,type,
produc1580777273_b_b_b: produc1213276845od_b_b > b > produc276146823_b_b_b ).
thf(func_def_113,type,
produc401731773od_b_b: produc1871334759_a_nat > produc1213276845od_b_b > produc1169496899od_b_b ).
thf(func_def_114,type,
produc1677124439_a_nat: produc1871334759_a_nat > produc1871334759_a_nat > produc398057191_a_nat ).
thf(func_def_115,type,
produc590959831od_b_b: produc1871334759_a_nat > product_prod_b_b > produc1485083751od_b_b ).
thf(func_def_116,type,
produc2059954415_nat_b: produc1871334759_a_nat > b > produc845793663_nat_b ).
thf(func_def_117,type,
produc732676669od_b_b: product_prod_b_b > produc1213276845od_b_b > produc1052326083od_b_b ).
thf(func_def_118,type,
produc546497367od_b_b: product_prod_b_b > product_prod_b_b > produc1168037607od_b_b ).
thf(func_def_119,type,
produc1001682799_b_b_b: product_prod_b_b > b > produc2112523263_b_b_b ).
thf(func_def_120,type,
produc800495189od_b_b: b > produc1213276845od_b_b > produc1605346267od_b_b ).
thf(func_def_121,type,
produc1257047359od_b_b: b > product_prod_b_b > produc255402447od_b_b ).
thf(func_def_122,type,
product_Pair_b_b: b > b > product_prod_b_b ).
thf(func_def_123,type,
id_on_689842066_a_nat: set_la1083530965_a_nat > set_Pr1987088711_a_nat ).
thf(func_def_124,type,
id_on_250271696od_b_b: set_Pr1324126435od_b_b > set_Pr2109276827od_b_b ).
thf(func_def_125,type,
id_on_1651096324_a_nat: set_Pr1987088711_a_nat > set_Pr924198087_a_nat ).
thf(func_def_126,type,
id_on_2019020932od_b_b: set_Product_prod_b_b > set_Pr2007082183od_b_b ).
thf(func_def_127,type,
id_on_b: set_b > set_Product_prod_b_b ).
thf(func_def_128,type,
image_1916422435od_b_b: set_Pr1324126435od_b_b > set_St761939237tant_a > set_Product_prod_b_b ).
thf(func_def_129,type,
image_1971191571_a_nat: set_Pr1987088711_a_nat > set_la1083530965_a_nat > set_la1083530965_a_nat ).
thf(func_def_130,type,
image_763305007od_b_b: set_Pr2109276827od_b_b > set_Pr1324126435od_b_b > set_Pr1324126435od_b_b ).
thf(func_def_131,type,
image_1397930469od_b_b: set_Pr2134561957od_b_b > set_Pr1324126435od_b_b > set_Product_prod_b_b ).
thf(func_def_132,type,
image_1764625405_b_b_b: set_Pr1906739389_b_b_b > set_Pr1324126435od_b_b > set_b ).
thf(func_def_133,type,
image_480774529od_b_b: set_Pr1954438265od_b_b > set_Pr1987088711_a_nat > set_Pr1324126435od_b_b ).
thf(func_def_134,type,
image_1168831379_a_nat: set_Pr924198087_a_nat > set_Pr1987088711_a_nat > set_Pr1987088711_a_nat ).
thf(func_def_135,type,
image_1214223635od_b_b: set_Pr667377223od_b_b > set_Pr1987088711_a_nat > set_Product_prod_b_b ).
thf(func_def_136,type,
image_924992811_nat_b: set_Pr812188767_nat_b > set_Pr1987088711_a_nat > set_b ).
thf(func_def_137,type,
image_532916993od_b_b: set_Pr1071216121od_b_b > set_Product_prod_b_b > set_Pr1324126435od_b_b ).
thf(func_def_138,type,
image_1928024979od_b_b: set_Pr2007082183od_b_b > set_Product_prod_b_b > set_Product_prod_b_b ).
thf(func_def_139,type,
image_921732011_b_b_b: set_Pr357419743_b_b_b > set_Product_prod_b_b > set_b ).
thf(func_def_140,type,
image_984343321od_b_b: set_Pr2060523537od_b_b > set_b > set_Pr1324126435od_b_b ).
thf(func_def_141,type,
image_1749766139_a_nat: set_Pr1646010159_a_nat > set_b > set_Pr1987088711_a_nat ).
thf(func_def_142,type,
image_1177096571od_b_b: set_Pr621705391od_b_b > set_b > set_Product_prod_b_b ).
thf(func_def_143,type,
image_b_b: set_Product_prod_b_b > set_b > set_b ).
thf(func_def_144,type,
refl_o1031343860_a_nat: set_la1083530965_a_nat > set_Pr1987088711_a_nat > $o ).
thf(func_def_145,type,
refl_o1921098222od_b_b: set_Pr1324126435od_b_b > set_Pr2109276827od_b_b > $o ).
thf(func_def_146,type,
refl_o1213627494_a_nat: set_Pr1987088711_a_nat > set_Pr924198087_a_nat > $o ).
thf(func_def_147,type,
refl_o2134473190od_b_b: set_Product_prod_b_b > set_Pr2007082183od_b_b > $o ).
thf(func_def_148,type,
refl_on_b: set_b > set_Product_prod_b_b > $o ).
thf(func_def_149,type,
relcom883816262od_b_b: set_Pr154086431tant_a > set_Pr1324126435od_b_b > set_Pr1324126435od_b_b ).
thf(func_def_150,type,
relcom1823941168od_b_b: set_Pr1324126435od_b_b > set_Pr2007082183od_b_b > set_Pr1324126435od_b_b ).
thf(func_def_151,type,
relcom1338300020_a_nat: set_Pr1987088711_a_nat > set_Pr1987088711_a_nat > set_Pr1987088711_a_nat ).
thf(func_def_152,type,
relcom112561144od_b_b: set_Pr1649131859tant_a > set_Pr1324126435od_b_b > set_Pr621705391od_b_b ).
thf(func_def_153,type,
relcomp_b_b_b: set_Product_prod_b_b > set_Product_prod_b_b > set_Product_prod_b_b ).
thf(func_def_154,type,
agree_221379389_a_b_b: labele1159362096nt_a_b > set_Product_prod_b_b > set_Product_prod_b_b > $o ).
thf(func_def_155,type,
conseq956760372_nat_b: set_Pr1987088711_a_nat > labele1159362096nt_a_b > $o ).
thf(func_def_156,type,
extens1554515172_nat_b: produc1871334759_a_nat > labele1159362096nt_a_b > set_Pr2106913242_nat_b > $o ).
thf(func_def_157,type,
extens1779443913_a_b_b: produc1398946881nt_a_b > labele1159362096nt_a_b > set_Product_prod_b_b > $o ).
thf(func_def_158,type,
mainta1604381365_nat_b: produc1871334759_a_nat > labele1159362096nt_a_b > $o ).
thf(func_def_159,type,
mainta374363448_a_b_b: produc1398946881nt_a_b > labele1159362096nt_a_b > $o ).
thf(func_def_160,type,
collec279084418od_b_b: ( produc1213276845od_b_b > $o ) > set_Pr1324126435od_b_b ).
thf(func_def_161,type,
collec357096914_a_nat: ( produc1871334759_a_nat > $o ) > set_Pr1987088711_a_nat ).
thf(func_def_162,type,
collec1481886546od_b_b: ( product_prod_b_b > $o ) > set_Product_prod_b_b ).
thf(func_def_163,type,
collect_b: ( b > $o ) > set_b ).
thf(func_def_164,type,
image_1683732397od_b_b: ( b > product_prod_b_b ) > set_b > set_Product_prod_b_b ).
thf(func_def_165,type,
insert1909710879tant_a: standard_Constant_a > set_St761939237tant_a > set_St761939237tant_a ).
thf(func_def_166,type,
insert1167839429_a_nat: labele935650037_a_nat > set_la1083530965_a_nat > set_la1083530965_a_nat ).
thf(func_def_167,type,
insert2037698781od_b_b: produc1213276845od_b_b > set_Pr1324126435od_b_b > set_Pr1324126435od_b_b ).
thf(func_def_168,type,
insert1574423351_a_nat: produc1871334759_a_nat > set_Pr1987088711_a_nat > set_Pr1987088711_a_nat ).
thf(func_def_169,type,
insert1810136247_a_nat: produc398057191_a_nat > set_Pr924198087_a_nat > set_Pr924198087_a_nat ).
thf(func_def_170,type,
insert1952693431od_b_b: product_prod_b_b > set_Product_prod_b_b > set_Product_prod_b_b ).
thf(func_def_171,type,
insert_b: b > set_b > set_b ).
thf(func_def_172,type,
standa1568205540ules_a: set_St761939237tant_a > set_Pr1987088711_a_nat ).
thf(func_def_173,type,
standa63370785tant_a: standard_Constant_a > produc1871334759_a_nat ).
thf(func_def_174,type,
standa997693288tant_a: standard_Constant_a > produc1871334759_a_nat ).
thf(func_def_175,type,
standa1795879409tant_a: standard_Constant_a > produc1871334759_a_nat ).
thf(func_def_176,type,
member1632892294tant_a: standard_Constant_a > set_St761939237tant_a > $o ).
thf(func_def_177,type,
member1214736488tant_a: produc90515391tant_a > set_Pr154086431tant_a > $o ).
thf(func_def_178,type,
member147868824od_b_b: produc1084374401od_b_b > set_Pr1190604087od_b_b > $o ).
thf(func_def_179,type,
member1744485444od_b_b: produc644633773od_b_b > set_Pr1021918435od_b_b > $o ).
thf(func_def_180,type,
member1516365892od_b_b: produc1213276845od_b_b > set_Pr1324126435od_b_b > $o ).
thf(func_def_181,type,
member832397200_a_nat: produc1871334759_a_nat > set_Pr1987088711_a_nat > $o ).
thf(func_def_182,type,
member1086024932od_b_b: produc970027067od_b_b > set_Pr2109276827od_b_b > $o ).
thf(func_def_183,type,
member942707974od_b_b: produc1990339951od_b_b > set_Pr2134561957od_b_b > $o ).
thf(func_def_184,type,
member1417789726_b_b_b: produc276146823_b_b_b > set_Pr1906739389_b_b_b > $o ).
thf(func_def_185,type,
member1533761242od_b_b: produc1169496899od_b_b > set_Pr1954438265od_b_b > $o ).
thf(func_def_186,type,
member584645392_a_nat: produc398057191_a_nat > set_Pr924198087_a_nat > $o ).
thf(func_def_187,type,
member301892752od_b_b: produc1485083751od_b_b > set_Pr667377223od_b_b > $o ).
thf(func_def_188,type,
member1544800936_nat_b: produc845793663_nat_b > set_Pr812188767_nat_b > $o ).
thf(func_def_189,type,
member4694106od_b_b: produc1052326083od_b_b > set_Pr1071216121od_b_b > $o ).
thf(func_def_190,type,
member1652792080od_b_b: produc1168037607od_b_b > set_Pr2007082183od_b_b > $o ).
thf(func_def_191,type,
member351494440_b_b_b: produc2112523263_b_b_b > set_Pr357419743_b_b_b > $o ).
thf(func_def_192,type,
member599505522od_b_b: produc1605346267od_b_b > set_Pr2060523537od_b_b > $o ).
thf(func_def_193,type,
member641857272od_b_b: produc255402447od_b_b > set_Pr621705391od_b_b > $o ).
thf(func_def_194,type,
member1285940496od_b_b: product_prod_b_b > set_Product_prod_b_b > $o ).
thf(func_def_195,type,
member_b: b > set_b > $o ).
thf(func_def_196,type,
g: labele1159362096nt_a_b ).
thf(func_def_197,type,
l: set_St761939237tant_a ).
thf(func_def_198,type,
p: b > b > $o ).
thf(func_def_199,type,
f: b > b ).
thf(func_def_200,type,
l2: standard_Constant_a ).
thf(func_def_201,type,
x: b ).
thf(func_def_202,type,
y: b ).
thf(func_def_219,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f1039,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f1038,f973]) ).
thf(f973,plain,
( ( member_b @ x @ ( labele1424214014nt_a_b @ g ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f957]) ).
thf(f957,plain,
( ( member_b @ x @ ( labele1424214014nt_a_b @ g ) )
!= $true ),
inference(flattening,[status(thm)],[f884]) ).
thf(f884,plain,
( ( member_b @ x @ ( labele1424214014nt_a_b @ g ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f883]) ).
thf(f883,plain,
~ ( member_b @ x @ ( labele1424214014nt_a_b @ g ) ),
inference(rectify,[status(thm)],[f361]) ).
thf(f361,negated_conjecture,
~ ( member_b @ x @ ( labele1424214014nt_a_b @ g ) ),
inference(negated_conjecture,[status(cth)],[f360]) ).
thf(f360,conjecture,
member_b @ x @ ( labele1424214014nt_a_b @ g ),
file('/export/starexec/sandbox/tmp/tmp.XlSklPZmtK/DTF2THF_15787.p',conj_0) ).
thf(f1038,plain,
( ( member_b @ x @ ( labele1424214014nt_a_b @ g ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f1037]) ).
thf(f1037,plain,
( ( $true != $true )
| ( ( member_b @ x @ ( labele1424214014nt_a_b @ g ) )
= $true ) ),
inference(superposition,[status(thm)],[f1026,f1031]) ).
thf(f1031,plain,
( ( member_b
@ ( if_b
@ ( bot_bot_set_b
= ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ x @ bot_bot_set_b ) ) )
@ x
@ ( hilbert_Eps_b
@ ^ [Y0: b] : ( member_b @ Y0 @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ x @ bot_bot_set_b ) ) ) ) )
@ ( labele1424214014nt_a_b @ g ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1004]) ).
thf(f1004,plain,
( ( member_b
@ ( ^ [Y0: b] :
( if_b
@ ( bot_bot_set_b
= ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ Y0 @ bot_bot_set_b ) ) )
@ Y0
@ ( hilbert_Eps_b
@ ( ^ [Y1: b,Y2: b] : ( member_b @ Y2 @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ Y1 @ bot_bot_set_b ) ) )
@ Y0 ) ) )
@ x )
@ ( labele1424214014nt_a_b @ g ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f983,f997]) ).
thf(f997,plain,
( f
= ( ^ [Y0: b] :
( if_b
@ ( bot_bot_set_b
= ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ Y0 @ bot_bot_set_b ) ) )
@ Y0
@ ( hilbert_Eps_b
@ ( ^ [Y1: b,Y2: b] : ( member_b @ Y2 @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ Y1 @ bot_bot_set_b ) ) )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f982,f981]) ).
thf(f981,plain,
( p
= ( ^ [Y0: b,Y1: b] : ( member_b @ Y1 @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ Y0 @ bot_bot_set_b ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f550]) ).
thf(f550,plain,
( p
= ( ^ [Y0: b,Y1: b] : ( member_b @ Y1 @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ Y0 @ bot_bot_set_b ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f549]) ).
thf(f549,plain,
( p
= ( ^ [X0: b,X1: b] : ( member_b @ X1 @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ X0 @ bot_bot_set_b ) ) ) ) ),
inference(rectify,[status(thm)],[f354]) ).
thf(f354,axiom,
( p
= ( ^ [X26: b,X85: b] : ( member_b @ X85 @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ X26 @ bot_bot_set_b ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XlSklPZmtK/DTF2THF_15787.p',fact_353_P) ).
thf(f982,plain,
( f
= ( ^ [Y0: b] :
( if_b
@ ( bot_bot_set_b
= ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ Y0 @ bot_bot_set_b ) ) )
@ Y0
@ ( hilbert_Eps_b @ ( p @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f534]) ).
thf(f534,plain,
( f
= ( ^ [Y0: b] :
( if_b
@ ( bot_bot_set_b
= ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ Y0 @ bot_bot_set_b ) ) )
@ Y0
@ ( hilbert_Eps_b @ ( p @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f533]) ).
thf(f533,plain,
( ( ^ [X0: b] :
( if_b
@ ( bot_bot_set_b
= ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ X0 @ bot_bot_set_b ) ) )
@ X0
@ ( hilbert_Eps_b @ ( p @ X0 ) ) ) )
= f ),
inference(rectify,[status(thm)],[f353]) ).
thf(f353,axiom,
( ( ^ [X26: b] :
( if_b
@ ( bot_bot_set_b
= ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ X26 @ bot_bot_set_b ) ) )
@ X26
@ ( hilbert_Eps_b @ ( p @ X26 ) ) ) )
= f ),
file('/export/starexec/sandbox/tmp/tmp.XlSklPZmtK/DTF2THF_15787.p',fact_352_f) ).
thf(f983,plain,
( ( member_b @ ( f @ x ) @ ( labele1424214014nt_a_b @ g ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f442]) ).
thf(f442,plain,
( ( member_b @ ( f @ x ) @ ( labele1424214014nt_a_b @ g ) )
= $true ),
inference(fool_elimination,[status(thm)],[f441]) ).
thf(f441,plain,
member_b @ ( f @ x ) @ ( labele1424214014nt_a_b @ g ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
member_b @ ( f @ x ) @ ( labele1424214014nt_a_b @ g ),
file('/export/starexec/sandbox/tmp/tmp.XlSklPZmtK/DTF2THF_15787.p',fact_2_fv_I1_J) ).
thf(f1026,plain,
! [X0: b] :
( ( ( member_b
@ ( if_b
@ ( bot_bot_set_b
= ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ X0 @ bot_bot_set_b ) ) )
@ X0
@ ( hilbert_Eps_b
@ ^ [Y0: b] : ( member_b @ Y0 @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ X0 @ bot_bot_set_b ) ) ) ) )
@ ( labele1424214014nt_a_b @ g ) )
!= $true )
| ( ( member_b @ X0 @ ( labele1424214014nt_a_b @ g ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f1008]) ).
thf(f1008,plain,
! [X0: b] :
( ( ( member_b
@ ( ^ [Y0: b] :
( if_b
@ ( bot_bot_set_b
= ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ Y0 @ bot_bot_set_b ) ) )
@ Y0
@ ( hilbert_Eps_b
@ ( ^ [Y1: b,Y2: b] : ( member_b @ Y2 @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ Y1 @ bot_bot_set_b ) ) )
@ Y0 ) ) )
@ X0 )
@ ( labele1424214014nt_a_b @ g ) )
!= $true )
| ( ( member_b @ X0 @ ( labele1424214014nt_a_b @ g ) )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f989,f997]) ).
thf(f989,plain,
! [X0: b] :
( ( ( member_b @ ( f @ X0 ) @ ( labele1424214014nt_a_b @ g ) )
!= $true )
| ( ( member_b @ X0 @ ( labele1424214014nt_a_b @ g ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f970]) ).
thf(f970,plain,
! [X0: b] :
( ( ( member_b @ ( f @ X0 ) @ ( labele1424214014nt_a_b @ g ) )
!= $true )
| ( ( member_b @ X0 @ ( labele1424214014nt_a_b @ g ) )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f822]) ).
thf(f822,plain,
! [X0: b] :
( ( ( member_b @ ( f @ X0 ) @ ( labele1424214014nt_a_b @ g ) )
= $true )
=> ( ( member_b @ X0 @ ( labele1424214014nt_a_b @ g ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f821]) ).
thf(f821,plain,
! [X0: b] :
( ( member_b @ ( f @ X0 ) @ ( labele1424214014nt_a_b @ g ) )
=> ( member_b @ X0 @ ( labele1424214014nt_a_b @ g ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: b] :
( ( member_b @ ( f @ X0 ) @ ( labele1424214014nt_a_b @ g ) )
=> ( member_b @ X0 @ ( labele1424214014nt_a_b @ g ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XlSklPZmtK/DTF2THF_15787.p',fact_0__092_060open_062_092_060And_062xa_O_A_092_060lbrakk_062f_Axa_A_092_060in_062_Avertices_AG_059_Axa_A_092_060notin_062_Avertices_AG_092_060rbrakk_062_A_092_060Longrightarrow_062_AFalse_092_060close_062) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP177^1 : TPTP v9.2.1. Released v7.5.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n018.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 08:28:46 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.47 ---- Original DTF file ---
% 0.20/0.47 thf(spec,logic,$$dhol).
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 % File : ITP177^1 : TPTP v9.2.1. Released v7.5.0.
% 0.20/0.47 % Domain : Interactive Theorem Proving
% 0.20/0.47 % Problem : Sledgehammer StandardRules problem prob_340__5390244_1
% 0.20/0.47 % Version : Especial.
% 0.20/0.47 % English :
% 0.20/0.47
% 0.20/0.47 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.20/0.47 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.20/0.47 % Source : [Des21]
% 0.20/0.47 % Names : StandardRules/prob_340__5390244_1 [Des21]
% 0.20/0.47
% 0.20/0.47 % Status : Theorem
% 0.20/0.47 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.23 v8.1.0, 0.27 v7.5.0
% 0.20/0.47 % Syntax : Number of formulae : 563 ( 156 unt; 203 typ; 0 def)
% 0.20/0.47 % Number of atoms : 988 ( 324 equ; 0 cnn)
% 0.20/0.47 % Maximal formula atoms : 6 ( 2 avg)
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% 0.20/0.47 collec1481886546od_b_b: ( product_prod_b_b > $o ) > set_Product_prod_b_b ).
% 0.20/0.47
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% 0.20/0.47
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% 0.20/0.47 image_1683732397od_b_b: ( b > product_prod_b_b ) > set_b > set_Product_prod_b_b ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Set_Oinsert_001t__LabeledGraphSemantics__OStandard____Constant_Itf__a_J,type,
% 0.20/0.47 insert1909710879tant_a: standard_Constant_a > set_St761939237tant_a > set_St761939237tant_a ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Set_Oinsert_001t__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J,type,
% 0.20/0.47 insert1167839429_a_nat: labele935650037_a_nat > set_la1083530965_a_nat > set_la1083530965_a_nat ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_Itf__b_Mtf__b_J_J,type,
% 0.20/0.47 insert2037698781od_b_b: produc1213276845od_b_b > set_Pr1324126435od_b_b > set_Pr1324126435od_b_b ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J,type,
% 0.20/0.47 insert1574423351_a_nat: produc1871334759_a_nat > set_Pr1987088711_a_nat > set_Pr1987088711_a_nat ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_J,type,
% 0.20/0.47 insert1810136247_a_nat: produc398057191_a_nat > set_Pr924198087_a_nat > set_Pr924198087_a_nat ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_Itf__b_Mtf__b_J,type,
% 0.20/0.47 insert1952693431od_b_b: product_prod_b_b > set_Product_prod_b_b > set_Product_prod_b_b ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Set_Oinsert_001tf__b,type,
% 0.20/0.47 insert_b: b > set_b > set_b ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Oidentity__rules_001tf__a,type,
% 0.20/0.47 standa1568205540ules_a: set_St761939237tant_a > set_Pr1987088711_a_nat ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Oreflexivity__rule_001t__LabeledGraphSemantics__OStandard____Constant_Itf__a_J,type,
% 0.20/0.47 standa63370785tant_a: standard_Constant_a > produc1871334759_a_nat ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Osymmetry__rule_001t__LabeledGraphSemantics__OStandard____Constant_Itf__a_J,type,
% 0.20/0.47 standa997693288tant_a: standard_Constant_a > produc1871334759_a_nat ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Otransitive__rule_001t__LabeledGraphSemantics__OStandard____Constant_Itf__a_J,type,
% 0.20/0.47 standa1795879409tant_a: standard_Constant_a > produc1871334759_a_nat ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_member_001t__LabeledGraphSemantics__OStandard____Constant_Itf__a_J,type,
% 0.20/0.47 member1632892294tant_a: standard_Constant_a > set_St761939237tant_a > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_J,type,
% 0.20/0.47 member1214736488tant_a: produc90515391tant_a > set_Pr154086431tant_a > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_Itf__b_Mtf__b_J_J_Mt__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_Itf__b_Mtf__b_J_J_J_J,type,
% 0.20/0.47 member147868824od_b_b: produc1084374401od_b_b > set_Pr1190604087od_b_b > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b_Mtf__b_J_Mt__Product____Type__Oprod_Itf__b_Mtf__b_J_J_J,type,
% 0.20/0.47 member1744485444od_b_b: produc644633773od_b_b > set_Pr1021918435od_b_b > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_Itf__b_Mtf__b_J_J,type,
% 0.20/0.47 member1516365892od_b_b: produc1213276845od_b_b > set_Pr1324126435od_b_b > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J,type,
% 0.20/0.47 member832397200_a_nat: produc1871334759_a_nat > set_Pr1987088711_a_nat > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_Itf__b_Mtf__b_J_J_Mt__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_Itf__b_Mtf__b_J_J_J,type,
% 0.20/0.47 member1086024932od_b_b: produc970027067od_b_b > set_Pr2109276827od_b_b > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_Itf__b_Mtf__b_J_J_Mt__Product____Type__Oprod_Itf__b_Mtf__b_J_J,type,
% 0.20/0.47 member942707974od_b_b: produc1990339951od_b_b > set_Pr2134561957od_b_b > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_Itf__b_Mtf__b_J_J_Mtf__b_J,type,
% 0.20/0.47 member1417789726_b_b_b: produc276146823_b_b_b > set_Pr1906739389_b_b_b > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_Itf__b_Mtf__b_J_J_J,type,
% 0.20/0.47 member1533761242od_b_b: produc1169496899od_b_b > set_Pr1954438265od_b_b > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_J,type,
% 0.20/0.47 member584645392_a_nat: produc398057191_a_nat > set_Pr924198087_a_nat > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_Itf__b_Mtf__b_J_J,type,
% 0.20/0.47 member301892752od_b_b: produc1485083751od_b_b > set_Pr667377223od_b_b > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_Mtf__b_J,type,
% 0.20/0.47 member1544800936_nat_b: produc845793663_nat_b > set_Pr812188767_nat_b > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b_Mtf__b_J_Mt__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_Itf__b_Mtf__b_J_J_J,type,
% 0.20/0.47 member4694106od_b_b: produc1052326083od_b_b > set_Pr1071216121od_b_b > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b_Mtf__b_J_Mt__Product____Type__Oprod_Itf__b_Mtf__b_J_J,type,
% 0.20/0.47 member1652792080od_b_b: produc1168037607od_b_b > set_Pr2007082183od_b_b > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b_Mtf__b_J_Mtf__b_J,type,
% 0.20/0.47 member351494440_b_b_b: produc2112523263_b_b_b > set_Pr357419743_b_b_b > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_member_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_Itf__b_Mtf__b_J_J_J,type,
% 0.20/0.47 member599505522od_b_b: produc1605346267od_b_b > set_Pr2060523537od_b_b > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_member_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_Itf__b_Mtf__b_J_J,type,
% 0.20/0.47 member641857272od_b_b: produc255402447od_b_b > set_Pr621705391od_b_b > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_member_001t__Product____Type__Oprod_Itf__b_Mtf__b_J,type,
% 0.20/0.47 member1285940496od_b_b: product_prod_b_b > set_Product_prod_b_b > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_member_001tf__b,type,
% 0.20/0.47 member_b: b > set_b > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_v_G,type,
% 0.20/0.47 g: labele1159362096nt_a_b ).
% 0.20/0.47
% 0.20/0.47 thf(sy_v_L,type,
% 0.20/0.47 l: set_St761939237tant_a ).
% 0.20/0.47
% 0.20/0.47 thf(sy_v_P____,type,
% 0.20/0.47 p: b > b > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_v_f____,type,
% 0.20/0.47 f: b > b ).
% 0.20/0.47
% 0.20/0.47 thf(sy_v_l____,type,
% 0.20/0.47 l2: standard_Constant_a ).
% 0.20/0.47
% 0.20/0.47 thf(sy_v_x____,type,
% 0.20/0.47 x: b ).
% 0.20/0.47
% 0.20/0.47 thf(sy_v_y____,type,
% 0.20/0.47 y: b ).
% 0.20/0.47
% 0.20/0.47 % Relevant facts (356)
% 0.20/0.47 thf(fact_0__092_060open_062_092_060And_062xa_O_A_092_060lbrakk_062f_Axa_A_092_060in_062_Avertices_AG_059_Axa_A_092_060notin_062_Avertices_AG_092_060rbrakk_062_A_092_060Longrightarrow_062_AFalse_092_060close_062,axiom,
% 0.20/0.47 ! [Xa: b] :
% 0.20/0.47 ( ( member_b @ ( f @ Xa ) @ ( labele1424214014nt_a_b @ g ) )
% 0.20/0.47 => ( member_b @ Xa @ ( labele1424214014nt_a_b @ g ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % \<open>\<And>xa. \<lbrakk>f xa \<in> vertices G; xa \<notin> vertices G\<rbrakk> \<Longrightarrow> False\<close>
% 0.20/0.47 thf(fact_1_fv_I2_J,axiom,
% 0.20/0.47 member_b @ ( f @ y ) @ ( labele1424214014nt_a_b @ g ) ).
% 0.20/0.47
% 0.20/0.47 % fv(2)
% 0.20/0.47 thf(fact_2_fv_I1_J,axiom,
% 0.20/0.47 member_b @ ( f @ x ) @ ( labele1424214014nt_a_b @ g ) ).
% 0.20/0.47
% 0.20/0.47 % fv(1)
% 0.20/0.47 thf(fact_3_gu2,axiom,
% 0.20/0.47 ! [X: b] :
% 0.20/0.47 ( ( member_b @ X @ ( labele1424214014nt_a_b @ g ) )
% 0.20/0.47 => ( member_b @ ( f @ X ) @ ( labele1424214014nt_a_b @ g ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % gu2
% 0.20/0.47 thf(fact_4_assms_I1_J,axiom,
% 0.20/0.47 ( g
% 0.20/0.47 = ( restri446606278nt_a_b @ g ) ) ).
% 0.20/0.47
% 0.20/0.47 % assms(1)
% 0.20/0.47 thf(fact_5_r1,axiom,
% 0.20/0.47 ! [X: b] :
% 0.20/0.47 ( ( member_b @ X @ ( labele1424214014nt_a_b @ g ) )
% 0.20/0.47 = ( p @ X @ X ) ) ).
% 0.20/0.47
% 0.20/0.47 % r1
% 0.20/0.47 thf(fact_6_assms_I2_J,axiom,
% 0.20/0.47 ! [X2: produc1871334759_a_nat] :
% 0.20/0.47 ( ( member832397200_a_nat @ X2 @ ( standa1568205540ules_a @ l ) )
% 0.20/0.47 => ( mainta1604381365_nat_b @ X2 @ g ) ) ).
% 0.20/0.47
% 0.20/0.47 % assms(2)
% 0.20/0.47 thf(fact_7_gr,axiom,
% 0.20/0.47 member1285940496od_b_b @ ( product_Pair_b_b @ ( f @ x ) @ ( f @ y ) ) @ ( getRel904497637nt_a_b @ l2 @ g ) ).
% 0.20/0.47
% 0.20/0.47 % gr
% 0.20/0.47 thf(fact_8_a,axiom,
% 0.20/0.47 member1516365892od_b_b @ ( produc1432590431od_b_b @ l2 @ ( product_Pair_b_b @ ( f @ x ) @ ( f @ y ) ) ) @ ( labele1741081071nt_a_b @ g ) ).
% 0.20/0.47
% 0.20/0.47 % a
% 0.20/0.47 thf(fact_9_local_Orefl,axiom,
% 0.20/0.47 refl_on_b @ ( labele1424214014nt_a_b @ g ) @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) ).
% 0.20/0.47
% 0.20/0.47 % local.refl
% 0.20/0.47 thf(fact_10_equiv,axiom,
% 0.20/0.47 equiv_equiv_b @ ( labele1424214014nt_a_b @ g ) @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) ).
% 0.20/0.47
% 0.20/0.47 % equiv
% 0.20/0.47 thf(fact_11__092_060open_062graph__union_A_Imap__graph__fn_AG_Af_J_AG_A_061_AG_092_060close_062,axiom,
% 0.20/0.47 ( ( graph_1309249505nt_a_b @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ g ) @ f ) @ g ) @ g )
% 0.20/0.47 = g ) ).
% 0.20/0.47
% 0.20/0.47 % \<open>graph_union (map_graph_fn G f) G = G\<close>
% 0.20/0.47 thf(fact_12_gu1,axiom,
% 0.20/0.47 ! [L: standard_Constant_a,X: b,Y: b] :
% 0.20/0.47 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ L @ ( product_Pair_b_b @ X @ Y ) ) @ ( labele1741081071nt_a_b @ g ) )
% 0.20/0.47 => ( ( member_b @ X @ ( labele1424214014nt_a_b @ g ) )
% 0.20/0.47 => ( ( member_b @ Y @ ( labele1424214014nt_a_b @ g ) )
% 0.20/0.47 => ( member1516365892od_b_b @ ( produc1432590431od_b_b @ L @ ( product_Pair_b_b @ ( f @ X ) @ ( f @ Y ) ) ) @ ( labele1741081071nt_a_b @ g ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % gu1
% 0.20/0.47 thf(fact_13__092_060open_062_092_060And_062x_O_Ax_A_092_060in_062_Avertices_AG_A_092_060Longrightarrow_062_A_Ix_M_Ax_J_A_092_060in_062_AgetRel_AS__Idt_AG_092_060close_062,axiom,
% 0.20/0.47 ! [X: b] :
% 0.20/0.47 ( ( member_b @ X @ ( labele1424214014nt_a_b @ g ) )
% 0.20/0.47 => ( member1285940496od_b_b @ ( product_Pair_b_b @ X @ X ) @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % \<open>\<And>x. x \<in> vertices G \<Longrightarrow> (x, x) \<in> getRel S_Idt G\<close>
% 0.20/0.47 thf(fact_14_labeled__graph_Osel_I2_J,axiom,
% 0.20/0.47 ! [X1: set_Pr1324126435od_b_b,X22: set_b] :
% 0.20/0.47 ( ( labele1424214014nt_a_b @ ( labele1230159100nt_a_b @ X1 @ X22 ) )
% 0.20/0.47 = X22 ) ).
% 0.20/0.47
% 0.20/0.47 % labeled_graph.sel(2)
% 0.20/0.47 thf(fact_15_subg,axiom,
% 0.20/0.47 graph_222606102_a_b_b @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ g ) @ f ) @ g ) @ g @ ( id_on_b @ ( labele1424214014nt_a_b @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ g ) @ f ) @ g ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % subg
% 0.20/0.47 thf(fact_16_vertices__restrict,axiom,
% 0.20/0.47 ! [G: labele1159362096nt_a_b] :
% 0.20/0.47 ( ( labele1424214014nt_a_b @ ( restri446606278nt_a_b @ G ) )
% 0.20/0.47 = ( labele1424214014nt_a_b @ G ) ) ).
% 0.20/0.47
% 0.20/0.47 % vertices_restrict
% 0.20/0.47 thf(fact_17_restrict__idemp,axiom,
% 0.20/0.47 ! [X: labele1159362096nt_a_b] :
% 0.20/0.47 ( ( restri446606278nt_a_b @ ( restri446606278nt_a_b @ X ) )
% 0.20/0.47 = ( restri446606278nt_a_b @ X ) ) ).
% 0.20/0.47
% 0.20/0.47 % restrict_idemp
% 0.20/0.47 thf(fact_18_graph__union__idemp_I3_J,axiom,
% 0.20/0.47 ! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b] :
% 0.20/0.47 ( ( graph_1309249505nt_a_b @ A @ ( graph_1309249505nt_a_b @ B @ A ) )
% 0.20/0.47 = ( graph_1309249505nt_a_b @ B @ A ) ) ).
% 0.20/0.47
% 0.20/0.47 % graph_union_idemp(3)
% 0.20/0.47 thf(fact_19_graph__union__idemp_I2_J,axiom,
% 0.20/0.47 ! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b] :
% 0.20/0.47 ( ( graph_1309249505nt_a_b @ A @ ( graph_1309249505nt_a_b @ A @ B ) )
% 0.20/0.47 = ( graph_1309249505nt_a_b @ A @ B ) ) ).
% 0.20/0.47
% 0.20/0.47 % graph_union_idemp(2)
% 0.20/0.47 thf(fact_20_graph__union__idemp_I1_J,axiom,
% 0.20/0.47 ! [A: labele1159362096nt_a_b] :
% 0.20/0.47 ( ( graph_1309249505nt_a_b @ A @ A )
% 0.20/0.47 = A ) ).
% 0.20/0.47
% 0.20/0.47 % graph_union_idemp(1)
% 0.20/0.47 thf(fact_21_map__graph__preserves__restricted,axiom,
% 0.20/0.47 ! [G: labele1159362096nt_a_b,F: set_Product_prod_b_b] :
% 0.20/0.47 ( ( G
% 0.20/0.47 = ( restri446606278nt_a_b @ G ) )
% 0.20/0.47 => ( ( map_gr926947118tant_a @ F @ G )
% 0.20/0.47 = ( restri446606278nt_a_b @ ( map_gr926947118tant_a @ F @ G ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % map_graph_preserves_restricted
% 0.20/0.47 thf(fact_22_graph__union__preserves__restrict,axiom,
% 0.20/0.47 ! [G_1: labele1159362096nt_a_b,G_2: labele1159362096nt_a_b] :
% 0.20/0.47 ( ( G_1
% 0.20/0.47 = ( restri446606278nt_a_b @ G_1 ) )
% 0.20/0.47 => ( ( G_2
% 0.20/0.47 = ( restri446606278nt_a_b @ G_2 ) )
% 0.20/0.47 => ( ( graph_1309249505nt_a_b @ G_1 @ G_2 )
% 0.20/0.47 = ( restri446606278nt_a_b @ ( graph_1309249505nt_a_b @ G_1 @ G_2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % graph_union_preserves_restrict
% 0.20/0.47 thf(fact_23_labeled__graph_Ocollapse,axiom,
% 0.20/0.47 ! [Labeled_graph: labele1159362096nt_a_b] :
% 0.20/0.47 ( ( labele1230159100nt_a_b @ ( labele1741081071nt_a_b @ Labeled_graph ) @ ( labele1424214014nt_a_b @ Labeled_graph ) )
% 0.20/0.47 = Labeled_graph ) ).
% 0.20/0.47
% 0.20/0.47 % labeled_graph.collapse
% 0.20/0.47 thf(fact_24_subgraph__refl,axiom,
% 0.20/0.47 ! [G: labele1159362096nt_a_b] :
% 0.20/0.47 ( ( graph_222606102_a_b_b @ G @ G @ ( id_on_b @ ( labele1424214014nt_a_b @ G ) ) )
% 0.20/0.47 = ( G
% 0.20/0.47 = ( restri446606278nt_a_b @ G ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % subgraph_refl
% 0.20/0.47 thf(fact_25_subgraph__restrict,axiom,
% 0.20/0.47 ! [G: labele1159362096nt_a_b] :
% 0.20/0.47 ( ( graph_222606102_a_b_b @ G @ ( restri446606278nt_a_b @ G ) @ ( id_on_b @ ( labele1424214014nt_a_b @ G ) ) )
% 0.20/0.47 = ( G
% 0.20/0.47 = ( restri446606278nt_a_b @ G ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % subgraph_restrict
% 0.20/0.47 thf(fact_26_graph__homomorphism__Id,axiom,
% 0.20/0.47 ! [A2: labele1159362096nt_a_b] : ( graph_222606102_a_b_b @ ( restri446606278nt_a_b @ A2 ) @ ( restri446606278nt_a_b @ A2 ) @ ( id_on_b @ ( labele1424214014nt_a_b @ A2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % graph_homomorphism_Id
% 0.20/0.47 thf(fact_27_map__graph__preserves__subgraph,axiom,
% 0.20/0.47 ! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,F: set_Product_prod_b_b] :
% 0.20/0.47 ( ( graph_222606102_a_b_b @ A @ B @ ( id_on_b @ ( labele1424214014nt_a_b @ A ) ) )
% 0.20/0.47 => ( graph_222606102_a_b_b @ ( map_gr926947118tant_a @ F @ A ) @ ( map_gr926947118tant_a @ F @ B ) @ ( id_on_b @ ( labele1424214014nt_a_b @ ( map_gr926947118tant_a @ F @ A ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % map_graph_preserves_subgraph
% 0.20/0.47 thf(fact_28_map__graph__fn__id_I2_J,axiom,
% 0.20/0.47 ! [X3: labele1159362096nt_a_b] :
% 0.20/0.47 ( ( map_gr926947118tant_a @ ( id_on_b @ ( labele1424214014nt_a_b @ X3 ) ) @ X3 )
% 0.20/0.47 = ( restri446606278nt_a_b @ X3 ) ) ).
% 0.20/0.47
% 0.20/0.47 % map_graph_fn_id(2)
% 0.20/0.47 thf(fact_29_map__graph__fn__graphI,axiom,
% 0.20/0.47 ! [G: labele1159362096nt_a_b,F: b > b] :
% 0.20/0.47 ( ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ G ) @ F ) @ G )
% 0.20/0.47 = ( restri446606278nt_a_b @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ G ) @ F ) @ G ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % map_graph_fn_graphI
% 0.20/0.47 thf(fact_30_graph__homo,axiom,
% 0.20/0.47 ! [G: labele1159362096nt_a_b,F: b > b] :
% 0.20/0.47 ( ( G
% 0.20/0.47 = ( restri446606278nt_a_b @ G ) )
% 0.20/0.47 => ( graph_222606102_a_b_b @ G @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ G ) @ F ) @ G ) @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ G ) @ F ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % graph_homo
% 0.20/0.47 thf(fact_31_labeled__graph_Osel_I1_J,axiom,
% 0.20/0.47 ! [X1: set_Pr1324126435od_b_b,X22: set_b] :
% 0.20/0.47 ( ( labele1741081071nt_a_b @ ( labele1230159100nt_a_b @ X1 @ X22 ) )
% 0.20/0.47 = X1 ) ).
% 0.20/0.47
% 0.20/0.47 % labeled_graph.sel(1)
% 0.20/0.47 thf(fact_32_subgraph__def,axiom,
% 0.20/0.47 ! [G_1: labele1159362096nt_a_b,G_2: labele1159362096nt_a_b] :
% 0.20/0.47 ( ( graph_222606102_a_b_b @ G_1 @ G_2 @ ( id_on_b @ ( labele1424214014nt_a_b @ G_1 ) ) )
% 0.20/0.47 = ( ( G_1
% 0.20/0.47 = ( restri446606278nt_a_b @ G_1 ) )
% 0.20/0.47 & ( G_2
% 0.20/0.47 = ( restri446606278nt_a_b @ G_2 ) )
% 0.20/0.47 & ( ( graph_1309249505nt_a_b @ G_1 @ G_2 )
% 0.20/0.47 = G_2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % subgraph_def
% 0.20/0.47 thf(fact_33_subgraph__trans,axiom,
% 0.20/0.47 ! [G_1: labele1159362096nt_a_b,G_2: labele1159362096nt_a_b,G_3: labele1159362096nt_a_b] :
% 0.20/0.47 ( ( graph_222606102_a_b_b @ G_1 @ G_2 @ ( id_on_b @ ( labele1424214014nt_a_b @ G_1 ) ) )
% 0.20/0.47 => ( ( graph_222606102_a_b_b @ G_2 @ G_3 @ ( id_on_b @ ( labele1424214014nt_a_b @ G_2 ) ) )
% 0.20/0.47 => ( graph_222606102_a_b_b @ G_1 @ G_3 @ ( id_on_b @ ( labele1424214014nt_a_b @ G_1 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % subgraph_trans
% 0.20/0.47 thf(fact_34_map__graph__fn__eqI,axiom,
% 0.20/0.47 ! [G: labele1159362096nt_a_b,F: b > b,G2: b > b] :
% 0.20/0.47 ( ! [X4: b] :
% 0.20/0.47 ( ( member_b @ X4 @ ( labele1424214014nt_a_b @ G ) )
% 0.20/0.47 => ( ( F @ X4 )
% 0.20/0.47 = ( G2 @ X4 ) ) )
% 0.20/0.47 => ( ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ G ) @ F ) @ G )
% 0.20/0.47 = ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ G ) @ G2 ) @ G ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % map_graph_fn_eqI
% 0.20/0.47 thf(fact_35_subgraph__preserves__hom,axiom,
% 0.20/0.47 ! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,X3: labele1159362096nt_a_b,H: set_Product_prod_b_b] :
% 0.20/0.47 ( ( graph_222606102_a_b_b @ A @ B @ ( id_on_b @ ( labele1424214014nt_a_b @ A ) ) )
% 0.20/0.47 => ( ( graph_222606102_a_b_b @ X3 @ A @ H )
% 0.20/0.47 => ( graph_222606102_a_b_b @ X3 @ B @ H ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % subgraph_preserves_hom
% 0.20/0.47 thf(fact_36_labeled__graph_Oexhaust__sel,axiom,
% 0.20/0.47 ! [Labeled_graph: labele1159362096nt_a_b] :
% 0.20/0.47 ( Labeled_graph
% 0.20/0.47 = ( labele1230159100nt_a_b @ ( labele1741081071nt_a_b @ Labeled_graph ) @ ( labele1424214014nt_a_b @ Labeled_graph ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % labeled_graph.exhaust_sel
% 0.20/0.47 thf(fact_37_labeled__graph_Oexpand,axiom,
% 0.20/0.47 ! [Labeled_graph: labele1159362096nt_a_b,Labeled_graph2: labele1159362096nt_a_b] :
% 0.20/0.47 ( ( ( ( labele1741081071nt_a_b @ Labeled_graph )
% 0.20/0.47 = ( labele1741081071nt_a_b @ Labeled_graph2 ) )
% 0.20/0.47 & ( ( labele1424214014nt_a_b @ Labeled_graph )
% 0.20/0.47 = ( labele1424214014nt_a_b @ Labeled_graph2 ) ) )
% 0.20/0.47 => ( Labeled_graph = Labeled_graph2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % labeled_graph.expand
% 0.20/0.47 thf(fact_38_getRel__hom,axiom,
% 0.20/0.47 ! [Y: product_prod_b_b,Z: product_prod_b_b,L: standard_Constant_a,G: labele1835558936od_b_b,F: product_prod_b_b > b] :
% 0.20/0.47 ( ( member1652792080od_b_b @ ( produc546497367od_b_b @ Y @ Z ) @ ( getRel118493133od_b_b @ L @ G ) )
% 0.20/0.47 => ( ( member1285940496od_b_b @ Y @ ( labele442485990od_b_b @ G ) )
% 0.20/0.47 => ( ( member1285940496od_b_b @ Z @ ( labele442485990od_b_b @ G ) )
% 0.20/0.47 => ( member1285940496od_b_b @ ( product_Pair_b_b @ ( F @ Y ) @ ( F @ Z ) ) @ ( getRel904497637nt_a_b @ L @ ( map_gr1314489926tant_a @ ( bNF_Gr521784954_b_b_b @ ( labele442485990od_b_b @ G ) @ F ) @ G ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % getRel_hom
% 0.20/0.47 thf(fact_39_getRel__hom,axiom,
% 0.20/0.47 ! [Y: produc1213276845od_b_b,Z: produc1213276845od_b_b,L: standard_Constant_a,G: labele1644675410od_b_b,F: produc1213276845od_b_b > b] :
% 0.20/0.47 ( ( member1086024932od_b_b @ ( produc449289715od_b_b @ Y @ Z ) @ ( getRel59882567od_b_b @ L @ G ) )
% 0.20/0.47 => ( ( member1516365892od_b_b @ Y @ ( labele595103470od_b_b @ G ) )
% 0.20/0.47 => ( ( member1516365892od_b_b @ Z @ ( labele595103470od_b_b @ G ) )
% 0.20/0.47 => ( member1285940496od_b_b @ ( product_Pair_b_b @ ( F @ Y ) @ ( F @ Z ) ) @ ( getRel904497637nt_a_b @ L @ ( map_gr1495881666tant_a @ ( bNF_Gr492676974_b_b_b @ ( labele595103470od_b_b @ G ) @ F ) @ G ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % getRel_hom
% 0.20/0.47 thf(fact_40_getRel__hom,axiom,
% 0.20/0.47 ! [Y: b,Z: b,L: standard_Constant_a,G: labele1159362096nt_a_b,F: b > b] :
% 0.20/0.47 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ Y @ Z ) @ ( getRel904497637nt_a_b @ L @ G ) )
% 0.20/0.47 => ( ( member_b @ Y @ ( labele1424214014nt_a_b @ G ) )
% 0.20/0.47 => ( ( member_b @ Z @ ( labele1424214014nt_a_b @ G ) )
% 0.20/0.47 => ( member1285940496od_b_b @ ( product_Pair_b_b @ ( F @ Y ) @ ( F @ Z ) ) @ ( getRel904497637nt_a_b @ L @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ G ) @ F ) @ G ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % getRel_hom
% 0.20/0.47 thf(fact_41_getRel__map__fn,axiom,
% 0.20/0.47 ! [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] :
% 0.20/0.47 ( ( member1285940496od_b_b @ A22 @ ( labele442485990od_b_b @ G ) )
% 0.20/0.47 => ( ( member1285940496od_b_b @ B2 @ ( labele442485990od_b_b @ G ) )
% 0.20/0.47 => ( ( member1652792080od_b_b @ ( produc546497367od_b_b @ A22 @ B2 ) @ ( getRel118493133od_b_b @ L @ G ) )
% 0.20/0.47 => ( ( ( F @ A22 )
% 0.20/0.47 = A2 )
% 0.20/0.47 => ( ( ( F @ B2 )
% 0.20/0.47 = B3 )
% 0.20/0.47 => ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ B3 ) @ ( getRel904497637nt_a_b @ L @ ( map_gr1314489926tant_a @ ( bNF_Gr521784954_b_b_b @ ( labele442485990od_b_b @ G ) @ F ) @ G ) ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % getRel_map_fn
% 0.20/0.47 thf(fact_42_getRel__map__fn,axiom,
% 0.20/0.47 ! [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] :
% 0.20/0.47 ( ( member1516365892od_b_b @ A22 @ ( labele595103470od_b_b @ G ) )
% 0.20/0.47 => ( ( member1516365892od_b_b @ B2 @ ( labele595103470od_b_b @ G ) )
% 0.20/0.47 => ( ( member1086024932od_b_b @ ( produc449289715od_b_b @ A22 @ B2 ) @ ( getRel59882567od_b_b @ L @ G ) )
% 0.20/0.47 => ( ( ( F @ A22 )
% 0.20/0.47 = A2 )
% 0.20/0.47 => ( ( ( F @ B2 )
% 0.20/0.47 = B3 )
% 0.20/0.47 => ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ B3 ) @ ( getRel904497637nt_a_b @ L @ ( map_gr1495881666tant_a @ ( bNF_Gr492676974_b_b_b @ ( labele595103470od_b_b @ G ) @ F ) @ G ) ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % getRel_map_fn
% 0.20/0.47 thf(fact_43_getRel__map__fn,axiom,
% 0.20/0.47 ! [A22: b,G: labele1159362096nt_a_b,B2: b,L: standard_Constant_a,F: b > b,A2: b,B3: b] :
% 0.20/0.47 ( ( member_b @ A22 @ ( labele1424214014nt_a_b @ G ) )
% 0.20/0.47 => ( ( member_b @ B2 @ ( labele1424214014nt_a_b @ G ) )
% 0.20/0.47 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A22 @ B2 ) @ ( getRel904497637nt_a_b @ L @ G ) )
% 0.20/0.47 => ( ( ( F @ A22 )
% 0.20/0.47 = A2 )
% 0.20/0.47 => ( ( ( F @ B2 )
% 0.20/0.47 = B3 )
% 0.20/0.47 => ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ B3 ) @ ( getRel904497637nt_a_b @ L @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ G ) @ F ) @ G ) ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % getRel_map_fn
% 0.20/0.47 thf(fact_44_idt__eq,axiom,
% 0.20/0.47 ! [X: b,Y: b] :
% 0.20/0.47 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ standard_S_Idt_a @ ( product_Pair_b_b @ X @ Y ) ) @ ( labele1741081071nt_a_b @ g ) )
% 0.20/0.47 => ( ( hilbert_Eps_b @ ( p @ X ) )
% 0.20/0.47 = ( hilbert_Eps_b @ ( p @ Y ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % idt_eq
% 0.20/0.47 thf(fact_45_vert__P,axiom,
% 0.20/0.47 ! [X: b] :
% 0.20/0.47 ( ( member_b @ X @ ( labele1424214014nt_a_b @ g ) )
% 0.20/0.47 => ( member1285940496od_b_b @ ( product_Pair_b_b @ X @ ( hilbert_Eps_b @ ( p @ X ) ) ) @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % vert_P
% 0.20/0.47 thf(fact_46_mem__Collect__eq,axiom,
% 0.20/0.47 ! [A2: b,P: b > $o] :
% 0.20/0.47 ( ( member_b @ A2 @ ( collect_b @ P ) )
% 0.20/0.47 = ( P @ A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % mem_Collect_eq
% 0.20/0.47 thf(fact_47_mem__Collect__eq,axiom,
% 0.20/0.47 ! [A2: product_prod_b_b,P: product_prod_b_b > $o] :
% 0.20/0.47 ( ( member1285940496od_b_b @ A2 @ ( collec1481886546od_b_b @ P ) )
% 0.20/0.47 = ( P @ A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % mem_Collect_eq
% 0.20/0.47 thf(fact_48_mem__Collect__eq,axiom,
% 0.20/0.47 ! [A2: produc1213276845od_b_b,P: produc1213276845od_b_b > $o] :
% 0.20/0.47 ( ( member1516365892od_b_b @ A2 @ ( collec279084418od_b_b @ P ) )
% 0.20/0.47 = ( P @ A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % mem_Collect_eq
% 0.20/0.47 thf(fact_49_Collect__mem__eq,axiom,
% 0.20/0.47 ! [A: set_b] :
% 0.20/0.47 ( ( collect_b
% 0.20/0.47 @ ^ [X5: b] : ( member_b @ X5 @ A ) )
% 0.20/0.47 = A ) ).
% 0.20/0.47
% 0.20/0.47 % Collect_mem_eq
% 0.20/0.47 thf(fact_50_Collect__mem__eq,axiom,
% 0.20/0.47 ! [A: set_Product_prod_b_b] :
% 0.20/0.47 ( ( collec1481886546od_b_b
% 0.20/0.47 @ ^ [X5: product_prod_b_b] : ( member1285940496od_b_b @ X5 @ A ) )
% 0.20/0.47 = A ) ).
% 0.20/0.47
% 0.20/0.47 % Collect_mem_eq
% 0.20/0.47 thf(fact_51_Collect__mem__eq,axiom,
% 0.20/0.47 ! [A: set_Pr1324126435od_b_b] :
% 0.20/0.47 ( ( collec279084418od_b_b
% 0.20/0.47 @ ^ [X5: produc1213276845od_b_b] : ( member1516365892od_b_b @ X5 @ A ) )
% 0.20/0.47 = A ) ).
% 0.20/0.47
% 0.20/0.47 % Collect_mem_eq
% 0.20/0.47 thf(fact_52_getRel__subgraph,axiom,
% 0.20/0.47 ! [Y: b,Z: b,L: standard_Constant_a,G: labele1159362096nt_a_b,G3: labele1159362096nt_a_b] :
% 0.20/0.47 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ Y @ Z ) @ ( getRel904497637nt_a_b @ L @ G ) )
% 0.20/0.47 => ( ( graph_222606102_a_b_b @ G @ G3 @ ( id_on_b @ ( labele1424214014nt_a_b @ G ) ) )
% 0.20/0.47 => ( member1285940496od_b_b @ ( product_Pair_b_b @ Y @ Z ) @ ( getRel904497637nt_a_b @ L @ G3 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % getRel_subgraph
% 0.20/0.47 thf(fact_53_in__Gr,axiom,
% 0.20/0.47 ! [X: b,Y: b,A: set_b,F: b > b] :
% 0.20/0.47 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ X @ Y ) @ ( bNF_Gr_b_b @ A @ F ) )
% 0.20/0.47 = ( ( member_b @ X @ A )
% 0.20/0.47 & ( ( F @ X )
% 0.20/0.47 = Y ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % in_Gr
% 0.20/0.47 thf(fact_54_in__Gr,axiom,
% 0.20/0.47 ! [X: standard_Constant_a,Y: product_prod_b_b,A: set_St761939237tant_a,F: standard_Constant_a > product_prod_b_b] :
% 0.20/0.47 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ X @ Y ) @ ( bNF_Gr1272216980od_b_b @ A @ F ) )
% 0.20/0.47 = ( ( member1632892294tant_a @ X @ A )
% 0.20/0.47 & ( ( F @ X )
% 0.20/0.47 = Y ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % in_Gr
% 0.20/0.47 thf(fact_55_Gr__not__in,axiom,
% 0.20/0.47 ! [X: b,F2: set_b,F: b > b,Y: b] :
% 0.20/0.47 ( ( ~ ( member_b @ X @ F2 )
% 0.20/0.47 | ( ( F @ X )
% 0.20/0.47 != Y ) )
% 0.20/0.47 => ~ ( member1285940496od_b_b @ ( product_Pair_b_b @ X @ Y ) @ ( bNF_Gr_b_b @ F2 @ F ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Gr_not_in
% 0.20/0.47 thf(fact_56_Gr__not__in,axiom,
% 0.20/0.47 ! [X: standard_Constant_a,F2: set_St761939237tant_a,F: standard_Constant_a > product_prod_b_b,Y: product_prod_b_b] :
% 0.20/0.47 ( ( ~ ( member1632892294tant_a @ X @ F2 )
% 0.20/0.47 | ( ( F @ X )
% 0.20/0.47 != Y ) )
% 0.20/0.47 => ~ ( member1516365892od_b_b @ ( produc1432590431od_b_b @ X @ Y ) @ ( bNF_Gr1272216980od_b_b @ F2 @ F ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Gr_not_in
% 0.20/0.47 thf(fact_57_Id__onI,axiom,
% 0.20/0.47 ! [A2: product_prod_b_b,A: set_Product_prod_b_b] :
% 0.20/0.47 ( ( member1285940496od_b_b @ A2 @ A )
% 0.20/0.47 => ( member1652792080od_b_b @ ( produc546497367od_b_b @ A2 @ A2 ) @ ( id_on_2019020932od_b_b @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Id_onI
% 0.20/0.47 thf(fact_58_Id__onI,axiom,
% 0.20/0.47 ! [A2: produc1213276845od_b_b,A: set_Pr1324126435od_b_b] :
% 0.20/0.47 ( ( member1516365892od_b_b @ A2 @ A )
% 0.20/0.47 => ( member1086024932od_b_b @ ( produc449289715od_b_b @ A2 @ A2 ) @ ( id_on_250271696od_b_b @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Id_onI
% 0.20/0.47 thf(fact_59_Id__onI,axiom,
% 0.20/0.47 ! [A2: b,A: set_b] :
% 0.20/0.47 ( ( member_b @ A2 @ A )
% 0.20/0.47 => ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ A2 ) @ ( id_on_b @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Id_onI
% 0.20/0.47 thf(fact_60_getRel__dom_I2_J,axiom,
% 0.20/0.47 ! [G: labele1159362096nt_a_b,A2: b,B3: b,L: standard_Constant_a] :
% 0.20/0.47 ( ( G
% 0.20/0.47 = ( restri446606278nt_a_b @ G ) )
% 0.20/0.47 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ B3 ) @ ( getRel904497637nt_a_b @ L @ G ) )
% 0.20/0.47 => ( member_b @ B3 @ ( labele1424214014nt_a_b @ G ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % getRel_dom(2)
% 0.20/0.47 thf(fact_61_getRel__dom_I1_J,axiom,
% 0.20/0.47 ! [G: labele1159362096nt_a_b,A2: b,B3: b,L: standard_Constant_a] :
% 0.20/0.47 ( ( G
% 0.20/0.47 = ( restri446606278nt_a_b @ G ) )
% 0.20/0.47 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ B3 ) @ ( getRel904497637nt_a_b @ L @ G ) )
% 0.20/0.47 => ( member_b @ A2 @ ( labele1424214014nt_a_b @ G ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % getRel_dom(1)
% 0.20/0.47 thf(fact_62_Id__on__iff,axiom,
% 0.20/0.47 ! [X: product_prod_b_b,Y: product_prod_b_b,A: set_Product_prod_b_b] :
% 0.20/0.47 ( ( member1652792080od_b_b @ ( produc546497367od_b_b @ X @ Y ) @ ( id_on_2019020932od_b_b @ A ) )
% 0.20/0.47 = ( ( X = Y )
% 0.20/0.47 & ( member1285940496od_b_b @ X @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Id_on_iff
% 0.20/0.47 thf(fact_63_Id__on__iff,axiom,
% 0.20/0.47 ! [X: produc1213276845od_b_b,Y: produc1213276845od_b_b,A: set_Pr1324126435od_b_b] :
% 0.20/0.47 ( ( member1086024932od_b_b @ ( produc449289715od_b_b @ X @ Y ) @ ( id_on_250271696od_b_b @ A ) )
% 0.20/0.47 = ( ( X = Y )
% 0.20/0.47 & ( member1516365892od_b_b @ X @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Id_on_iff
% 0.20/0.47 thf(fact_64_Id__on__iff,axiom,
% 0.20/0.47 ! [X: b,Y: b,A: set_b] :
% 0.20/0.47 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ X @ Y ) @ ( id_on_b @ A ) )
% 0.20/0.47 = ( ( X = Y )
% 0.20/0.47 & ( member_b @ X @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Id_on_iff
% 0.20/0.47 thf(fact_65_Id__on__eqI,axiom,
% 0.20/0.47 ! [A2: product_prod_b_b,B3: product_prod_b_b,A: set_Product_prod_b_b] :
% 0.20/0.47 ( ( A2 = B3 )
% 0.20/0.47 => ( ( member1285940496od_b_b @ A2 @ A )
% 0.20/0.47 => ( member1652792080od_b_b @ ( produc546497367od_b_b @ A2 @ B3 ) @ ( id_on_2019020932od_b_b @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Id_on_eqI
% 0.20/0.47 thf(fact_66_Id__on__eqI,axiom,
% 0.20/0.47 ! [A2: produc1213276845od_b_b,B3: produc1213276845od_b_b,A: set_Pr1324126435od_b_b] :
% 0.20/0.47 ( ( A2 = B3 )
% 0.20/0.47 => ( ( member1516365892od_b_b @ A2 @ A )
% 0.20/0.47 => ( member1086024932od_b_b @ ( produc449289715od_b_b @ A2 @ B3 ) @ ( id_on_250271696od_b_b @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Id_on_eqI
% 0.20/0.47 thf(fact_67_Id__on__eqI,axiom,
% 0.20/0.47 ! [A2: b,B3: b,A: set_b] :
% 0.20/0.47 ( ( A2 = B3 )
% 0.20/0.47 => ( ( member_b @ A2 @ A )
% 0.20/0.47 => ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ B3 ) @ ( id_on_b @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Id_on_eqI
% 0.20/0.47 thf(fact_68_Id__onE,axiom,
% 0.20/0.47 ! [C: produc1168037607od_b_b,A: set_Product_prod_b_b] :
% 0.20/0.47 ( ( member1652792080od_b_b @ C @ ( id_on_2019020932od_b_b @ A ) )
% 0.20/0.47 => ~ ! [X4: product_prod_b_b] :
% 0.20/0.47 ( ( member1285940496od_b_b @ X4 @ A )
% 0.20/0.47 => ( C
% 0.20/0.47 != ( produc546497367od_b_b @ X4 @ X4 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Id_onE
% 0.20/0.47 thf(fact_69_Id__onE,axiom,
% 0.20/0.47 ! [C: produc970027067od_b_b,A: set_Pr1324126435od_b_b] :
% 0.20/0.47 ( ( member1086024932od_b_b @ C @ ( id_on_250271696od_b_b @ A ) )
% 0.20/0.47 => ~ ! [X4: produc1213276845od_b_b] :
% 0.20/0.47 ( ( member1516365892od_b_b @ X4 @ A )
% 0.20/0.47 => ( C
% 0.20/0.47 != ( produc449289715od_b_b @ X4 @ X4 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Id_onE
% 0.20/0.47 thf(fact_70_Id__onE,axiom,
% 0.20/0.47 ! [C: product_prod_b_b,A: set_b] :
% 0.20/0.47 ( ( member1285940496od_b_b @ C @ ( id_on_b @ A ) )
% 0.20/0.47 => ~ ! [X4: b] :
% 0.20/0.47 ( ( member_b @ X4 @ A )
% 0.20/0.47 => ( C
% 0.20/0.47 != ( product_Pair_b_b @ X4 @ X4 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Id_onE
% 0.20/0.47 thf(fact_71_refl__onD2,axiom,
% 0.20/0.47 ! [A: set_Product_prod_b_b,R: set_Pr2007082183od_b_b,X: product_prod_b_b,Y: product_prod_b_b] :
% 0.20/0.47 ( ( refl_o2134473190od_b_b @ A @ R )
% 0.20/0.47 => ( ( member1652792080od_b_b @ ( produc546497367od_b_b @ X @ Y ) @ R )
% 0.20/0.47 => ( member1285940496od_b_b @ Y @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % refl_onD2
% 0.20/0.47 thf(fact_72_refl__onD2,axiom,
% 0.20/0.47 ! [A: set_Pr1324126435od_b_b,R: set_Pr2109276827od_b_b,X: produc1213276845od_b_b,Y: produc1213276845od_b_b] :
% 0.20/0.47 ( ( refl_o1921098222od_b_b @ A @ R )
% 0.20/0.47 => ( ( member1086024932od_b_b @ ( produc449289715od_b_b @ X @ Y ) @ R )
% 0.20/0.47 => ( member1516365892od_b_b @ Y @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % refl_onD2
% 0.20/0.47 thf(fact_73_refl__onD2,axiom,
% 0.20/0.47 ! [A: set_b,R: set_Product_prod_b_b,X: b,Y: b] :
% 0.20/0.47 ( ( refl_on_b @ A @ R )
% 0.20/0.47 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ X @ Y ) @ R )
% 0.20/0.47 => ( member_b @ Y @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % refl_onD2
% 0.20/0.47 thf(fact_74_refl__onD1,axiom,
% 0.20/0.47 ! [A: set_Product_prod_b_b,R: set_Pr2007082183od_b_b,X: product_prod_b_b,Y: product_prod_b_b] :
% 0.20/0.47 ( ( refl_o2134473190od_b_b @ A @ R )
% 0.20/0.47 => ( ( member1652792080od_b_b @ ( produc546497367od_b_b @ X @ Y ) @ R )
% 0.20/0.47 => ( member1285940496od_b_b @ X @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % refl_onD1
% 0.20/0.47 thf(fact_75_refl__onD1,axiom,
% 0.20/0.47 ! [A: set_Pr1324126435od_b_b,R: set_Pr2109276827od_b_b,X: produc1213276845od_b_b,Y: produc1213276845od_b_b] :
% 0.20/0.47 ( ( refl_o1921098222od_b_b @ A @ R )
% 0.20/0.47 => ( ( member1086024932od_b_b @ ( produc449289715od_b_b @ X @ Y ) @ R )
% 0.20/0.47 => ( member1516365892od_b_b @ X @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % refl_onD1
% 0.20/0.47 thf(fact_76_refl__onD1,axiom,
% 0.20/0.47 ! [A: set_b,R: set_Product_prod_b_b,X: b,Y: b] :
% 0.20/0.47 ( ( refl_on_b @ A @ R )
% 0.20/0.47 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ X @ Y ) @ R )
% 0.20/0.47 => ( member_b @ X @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % refl_onD1
% 0.20/0.47 thf(fact_77_refl__onD,axiom,
% 0.20/0.47 ! [A: set_Product_prod_b_b,R: set_Pr2007082183od_b_b,A2: product_prod_b_b] :
% 0.20/0.47 ( ( refl_o2134473190od_b_b @ A @ R )
% 0.20/0.47 => ( ( member1285940496od_b_b @ A2 @ A )
% 0.20/0.47 => ( member1652792080od_b_b @ ( produc546497367od_b_b @ A2 @ A2 ) @ R ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % refl_onD
% 0.20/0.47 thf(fact_78_refl__onD,axiom,
% 0.20/0.47 ! [A: set_Pr1324126435od_b_b,R: set_Pr2109276827od_b_b,A2: produc1213276845od_b_b] :
% 0.20/0.47 ( ( refl_o1921098222od_b_b @ A @ R )
% 0.20/0.47 => ( ( member1516365892od_b_b @ A2 @ A )
% 0.20/0.47 => ( member1086024932od_b_b @ ( produc449289715od_b_b @ A2 @ A2 ) @ R ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % refl_onD
% 0.20/0.47 thf(fact_79_refl__onD,axiom,
% 0.20/0.47 ! [A: set_b,R: set_Product_prod_b_b,A2: b] :
% 0.20/0.47 ( ( refl_on_b @ A @ R )
% 0.20/0.47 => ( ( member_b @ A2 @ A )
% 0.20/0.47 => ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ A2 ) @ R ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % refl_onD
% 0.20/0.47 thf(fact_80_refl__on__Id__on,axiom,
% 0.20/0.47 ! [A: set_b] : ( refl_on_b @ A @ ( id_on_b @ A ) ) ).
% 0.20/0.47
% 0.20/0.47 % refl_on_Id_on
% 0.20/0.47 thf(fact_81_getRel__homR,axiom,
% 0.20/0.47 ! [Y: b,Z: b,L: standard_Constant_a,G: labele1159362096nt_a_b,U: b,F: set_Product_prod_b_b,V: b] :
% 0.20/0.47 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ Y @ Z ) @ ( getRel904497637nt_a_b @ L @ G ) )
% 0.20/0.47 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ Y @ U ) @ F )
% 0.20/0.47 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ Z @ V ) @ F )
% 0.20/0.47 => ( member1285940496od_b_b @ ( product_Pair_b_b @ U @ V ) @ ( getRel904497637nt_a_b @ L @ ( map_gr926947118tant_a @ F @ G ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % getRel_homR
% 0.20/0.47 thf(fact_82_maintained__refl,axiom,
% 0.20/0.47 ! [R2: labele935650037_a_nat,G: labele1159362096nt_a_b] : ( mainta1604381365_nat_b @ ( produc1676969687_a_nat @ R2 @ R2 ) @ G ) ).
% 0.20/0.47
% 0.20/0.47 % maintained_refl
% 0.20/0.47 thf(fact_83_edge__preserving__on__graphI,axiom,
% 0.20/0.47 ! [X3: labele1835558936od_b_b,F: product_prod_b_b > b,Y2: set_Pr1324126435od_b_b] :
% 0.20/0.47 ( ! [L2: standard_Constant_a,X4: product_prod_b_b,Y3: product_prod_b_b] :
% 0.20/0.47 ( ( member1744485444od_b_b @ ( produc618266719od_b_b @ L2 @ ( produc546497367od_b_b @ X4 @ Y3 ) ) @ ( labele372159959od_b_b @ X3 ) )
% 0.20/0.47 => ( ( member1285940496od_b_b @ X4 @ ( labele442485990od_b_b @ X3 ) )
% 0.20/0.47 => ( ( member1285940496od_b_b @ Y3 @ ( labele442485990od_b_b @ X3 ) )
% 0.20/0.47 => ( member1516365892od_b_b @ ( produc1432590431od_b_b @ L2 @ ( product_Pair_b_b @ ( F @ X4 ) @ ( F @ Y3 ) ) ) @ Y2 ) ) ) )
% 0.20/0.47 => ( edge_p1969196346tant_a @ ( bNF_Gr521784954_b_b_b @ ( labele442485990od_b_b @ X3 ) @ F ) @ ( labele372159959od_b_b @ X3 ) @ Y2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % edge_preserving_on_graphI
% 0.20/0.47 thf(fact_84_edge__preserving__on__graphI,axiom,
% 0.20/0.47 ! [X3: labele1644675410od_b_b,F: produc1213276845od_b_b > b,Y2: set_Pr1324126435od_b_b] :
% 0.20/0.47 ( ! [L2: standard_Constant_a,X4: produc1213276845od_b_b,Y3: produc1213276845od_b_b] :
% 0.20/0.47 ( ( member147868824od_b_b @ ( produc1788032435od_b_b @ L2 @ ( produc449289715od_b_b @ X4 @ Y3 ) ) @ ( labele2032816061od_b_b @ X3 ) )
% 0.20/0.47 => ( ( member1516365892od_b_b @ X4 @ ( labele595103470od_b_b @ X3 ) )
% 0.20/0.47 => ( ( member1516365892od_b_b @ Y3 @ ( labele595103470od_b_b @ X3 ) )
% 0.20/0.47 => ( member1516365892od_b_b @ ( produc1432590431od_b_b @ L2 @ ( product_Pair_b_b @ ( F @ X4 ) @ ( F @ Y3 ) ) ) @ Y2 ) ) ) )
% 0.20/0.47 => ( edge_p1817988046tant_a @ ( bNF_Gr492676974_b_b_b @ ( labele595103470od_b_b @ X3 ) @ F ) @ ( labele2032816061od_b_b @ X3 ) @ Y2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % edge_preserving_on_graphI
% 0.20/0.47 thf(fact_85_edge__preserving__on__graphI,axiom,
% 0.20/0.47 ! [X3: labele1159362096nt_a_b,F: b > b,Y2: set_Pr1324126435od_b_b] :
% 0.20/0.47 ( ! [L2: standard_Constant_a,X4: b,Y3: b] :
% 0.20/0.47 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ L2 @ ( product_Pair_b_b @ X4 @ Y3 ) ) @ ( labele1741081071nt_a_b @ X3 ) )
% 0.20/0.47 => ( ( member_b @ X4 @ ( labele1424214014nt_a_b @ X3 ) )
% 0.20/0.47 => ( ( member_b @ Y3 @ ( labele1424214014nt_a_b @ X3 ) )
% 0.20/0.47 => ( member1516365892od_b_b @ ( produc1432590431od_b_b @ L2 @ ( product_Pair_b_b @ ( F @ X4 ) @ ( F @ Y3 ) ) ) @ Y2 ) ) ) )
% 0.20/0.47 => ( edge_p1384198690tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ X3 ) @ F ) @ ( labele1741081071nt_a_b @ X3 ) @ Y2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % edge_preserving_on_graphI
% 0.20/0.47 thf(fact_86_reflexivity__rule,axiom,
% 0.20/0.47 ! [G: labele1159362096nt_a_b,L: standard_Constant_a] :
% 0.20/0.47 ( ( G
% 0.20/0.47 = ( restri446606278nt_a_b @ G ) )
% 0.20/0.47 => ( ( mainta1604381365_nat_b @ ( standa63370785tant_a @ L ) @ G )
% 0.20/0.47 => ( refl_on_b @ ( labele1424214014nt_a_b @ G ) @ ( getRel904497637nt_a_b @ L @ G ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % reflexivity_rule
% 0.20/0.47 thf(fact_87_old_Oprod_Oinject,axiom,
% 0.20/0.47 ! [A2: b,B3: b,A3: b,B4: b] :
% 0.20/0.47 ( ( ( product_Pair_b_b @ A2 @ B3 )
% 0.20/0.47 = ( product_Pair_b_b @ A3 @ B4 ) )
% 0.20/0.47 = ( ( A2 = A3 )
% 0.20/0.47 & ( B3 = B4 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % old.prod.inject
% 0.20/0.47 thf(fact_88_old_Oprod_Oinject,axiom,
% 0.20/0.47 ! [A2: standard_Constant_a,B3: product_prod_b_b,A3: standard_Constant_a,B4: product_prod_b_b] :
% 0.20/0.47 ( ( ( produc1432590431od_b_b @ A2 @ B3 )
% 0.20/0.47 = ( produc1432590431od_b_b @ A3 @ B4 ) )
% 0.20/0.47 = ( ( A2 = A3 )
% 0.20/0.47 & ( B3 = B4 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % old.prod.inject
% 0.20/0.47 thf(fact_89_prod_Oinject,axiom,
% 0.20/0.47 ! [X1: b,X22: b,Y1: b,Y22: b] :
% 0.20/0.47 ( ( ( product_Pair_b_b @ X1 @ X22 )
% 0.20/0.47 = ( product_Pair_b_b @ Y1 @ Y22 ) )
% 0.20/0.47 = ( ( X1 = Y1 )
% 0.20/0.47 & ( X22 = Y22 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.inject
% 0.20/0.47 thf(fact_90_prod_Oinject,axiom,
% 0.20/0.47 ! [X1: standard_Constant_a,X22: product_prod_b_b,Y1: standard_Constant_a,Y22: product_prod_b_b] :
% 0.20/0.47 ( ( ( produc1432590431od_b_b @ X1 @ X22 )
% 0.20/0.47 = ( produc1432590431od_b_b @ Y1 @ Y22 ) )
% 0.20/0.47 = ( ( X1 = Y1 )
% 0.20/0.47 & ( X22 = Y22 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % prod.inject
% 0.20/0.47 thf(fact_91_refl__on__domain,axiom,
% 0.20/0.47 ! [A: set_Product_prod_b_b,R: set_Pr2007082183od_b_b,A2: product_prod_b_b,B3: product_prod_b_b] :
% 0.20/0.47 ( ( refl_o2134473190od_b_b @ A @ R )
% 0.20/0.47 => ( ( member1652792080od_b_b @ ( produc546497367od_b_b @ A2 @ B3 ) @ R )
% 0.20/0.47 => ( ( member1285940496od_b_b @ A2 @ A )
% 0.20/0.47 & ( member1285940496od_b_b @ B3 @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % refl_on_domain
% 0.20/0.47 thf(fact_92_refl__on__domain,axiom,
% 0.20/0.47 ! [A: set_Pr1324126435od_b_b,R: set_Pr2109276827od_b_b,A2: produc1213276845od_b_b,B3: produc1213276845od_b_b] :
% 0.20/0.47 ( ( refl_o1921098222od_b_b @ A @ R )
% 0.20/0.47 => ( ( member1086024932od_b_b @ ( produc449289715od_b_b @ A2 @ B3 ) @ R )
% 0.20/0.47 => ( ( member1516365892od_b_b @ A2 @ A )
% 0.20/0.47 & ( member1516365892od_b_b @ B3 @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % refl_on_domain
% 0.20/0.47 thf(fact_93_refl__on__domain,axiom,
% 0.20/0.47 ! [A: set_b,R: set_Product_prod_b_b,A2: b,B3: b] :
% 0.20/0.47 ( ( refl_on_b @ A @ R )
% 0.20/0.47 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ B3 ) @ R )
% 0.20/0.47 => ( ( member_b @ A2 @ A )
% 0.20/0.47 & ( member_b @ B3 @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % refl_on_domain
% 0.20/0.47 thf(fact_94_GrD2,axiom,
% 0.20/0.47 ! [X: b,Fx: b,A: set_b,F: b > b] :
% 0.20/0.47 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ X @ Fx ) @ ( bNF_Gr_b_b @ A @ F ) )
% 0.20/0.47 => ( ( F @ X )
% 0.20/0.47 = Fx ) ) ).
% 0.20/0.47
% 0.20/0.47 % GrD2
% 0.20/0.47 thf(fact_95_GrD2,axiom,
% 0.20/0.47 ! [X: standard_Constant_a,Fx: product_prod_b_b,A: set_St761939237tant_a,F: standard_Constant_a > product_prod_b_b] :
% 0.20/0.47 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ X @ Fx ) @ ( bNF_Gr1272216980od_b_b @ A @ F ) )
% 0.20/0.47 => ( ( F @ X )
% 0.20/0.47 = Fx ) ) ).
% 0.20/0.47
% 0.20/0.47 % GrD2
% 0.20/0.47 thf(fact_96_GrD1,axiom,
% 0.20/0.47 ! [X: b,Fx: b,A: set_b,F: b > b] :
% 0.20/0.47 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ X @ Fx ) @ ( bNF_Gr_b_b @ A @ F ) )
% 0.20/0.47 => ( member_b @ X @ A ) ) ).
% 0.20/0.47
% 0.20/0.47 % GrD1
% 0.20/0.47 thf(fact_97_GrD1,axiom,
% 0.20/0.47 ! [X: standard_Constant_a,Fx: product_prod_b_b,A: set_St761939237tant_a,F: standard_Constant_a > product_prod_b_b] :
% 0.20/0.47 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ X @ Fx ) @ ( bNF_Gr1272216980od_b_b @ A @ F ) )
% 0.20/0.47 => ( member1632892294tant_a @ X @ A ) ) ).
% 0.20/0.47
% 0.20/0.47 % GrD1
% 0.20/0.47 thf(fact_98_map__graph__edge__preserving,axiom,
% 0.20/0.47 ! [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 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % map_graph_edge_preserving
% 0.20/0.47 thf(fact_99_edge__preserving__atomic,axiom,
% 0.20/0.47 ! [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] :
% 0.20/0.47 ( ( edge_p1384198690tant_a @ H1 @ E1 @ E2 )
% 0.20/0.47 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ V1 @ V12 ) @ H1 )
% 0.20/0.47 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ V2 @ V22 ) @ H1 )
% 0.20/0.47 => ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ K @ ( product_Pair_b_b @ V1 @ V2 ) ) @ E1 )
% 0.20/0.47 => ( member1516365892od_b_b @ ( produc1432590431od_b_b @ K @ ( product_Pair_b_b @ V12 @ V22 ) ) @ E2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % edge_preserving_atomic
% 0.20/0.47 thf(fact_100_surj__pair,axiom,
% 0.20/0.47 ! [P2: product_prod_b_b] :
% 0.20/0.47 ? [X4: b,Y3: b] :
% 0.20/0.47 ( P2
% 0.20/0.47 = ( product_Pair_b_b @ X4 @ Y3 ) ) ).
% 0.20/0.47
% 0.20/0.47 % surj_pair
% 0.20/0.47 thf(fact_101_surj__pair,axiom,
% 0.20/0.47 ! [P2: produc1213276845od_b_b] :
% 0.20/0.47 ? [X4: standard_Constant_a,Y3: product_prod_b_b] :
% 0.20/0.47 ( P2
% 0.20/0.47 = ( produc1432590431od_b_b @ X4 @ Y3 ) ) ).
% 0.20/0.47
% 0.20/0.47 % surj_pair
% 0.20/0.47 thf(fact_102_prod__cases,axiom,
% 0.32/0.47 ! [P: product_prod_b_b > $o,P2: product_prod_b_b] :
% 0.32/0.47 ( ! [A4: b,B5: b] : ( P @ ( product_Pair_b_b @ A4 @ B5 ) )
% 0.32/0.47 => ( P @ P2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % prod_cases
% 0.32/0.47 thf(fact_103_prod__cases,axiom,
% 0.32/0.47 ! [P: produc1213276845od_b_b > $o,P2: produc1213276845od_b_b] :
% 0.32/0.47 ( ! [A4: standard_Constant_a,B5: product_prod_b_b] : ( P @ ( produc1432590431od_b_b @ A4 @ B5 ) )
% 0.32/0.47 => ( P @ P2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % prod_cases
% 0.32/0.47 thf(fact_104_Pair__inject,axiom,
% 0.32/0.47 ! [A2: b,B3: b,A3: b,B4: b] :
% 0.32/0.47 ( ( ( product_Pair_b_b @ A2 @ B3 )
% 0.32/0.47 = ( product_Pair_b_b @ A3 @ B4 ) )
% 0.32/0.47 => ~ ( ( A2 = A3 )
% 0.32/0.47 => ( B3 != B4 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Pair_inject
% 0.32/0.47 thf(fact_105_Pair__inject,axiom,
% 0.32/0.47 ! [A2: standard_Constant_a,B3: product_prod_b_b,A3: standard_Constant_a,B4: product_prod_b_b] :
% 0.32/0.47 ( ( ( produc1432590431od_b_b @ A2 @ B3 )
% 0.32/0.47 = ( produc1432590431od_b_b @ A3 @ B4 ) )
% 0.32/0.47 => ~ ( ( A2 = A3 )
% 0.32/0.47 => ( B3 != B4 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Pair_inject
% 0.32/0.47 thf(fact_106_old_Oprod_Oexhaust,axiom,
% 0.32/0.47 ! [Y: product_prod_b_b] :
% 0.32/0.47 ~ ! [A4: b,B5: b] :
% 0.32/0.47 ( Y
% 0.32/0.47 != ( product_Pair_b_b @ A4 @ B5 ) ) ).
% 0.32/0.47
% 0.32/0.47 % old.prod.exhaust
% 0.32/0.47 thf(fact_107_old_Oprod_Oexhaust,axiom,
% 0.32/0.47 ! [Y: produc1213276845od_b_b] :
% 0.32/0.47 ~ ! [A4: standard_Constant_a,B5: product_prod_b_b] :
% 0.32/0.47 ( Y
% 0.32/0.47 != ( produc1432590431od_b_b @ A4 @ B5 ) ) ).
% 0.32/0.47
% 0.32/0.47 % old.prod.exhaust
% 0.32/0.47 thf(fact_108_old_Oprod_Oinducts,axiom,
% 0.32/0.47 ! [P: product_prod_b_b > $o,Prod: product_prod_b_b] :
% 0.32/0.47 ( ! [A4: b,B5: b] : ( P @ ( product_Pair_b_b @ A4 @ B5 ) )
% 0.32/0.47 => ( P @ Prod ) ) ).
% 0.32/0.47
% 0.32/0.47 % old.prod.inducts
% 0.32/0.47 thf(fact_109_old_Oprod_Oinducts,axiom,
% 0.32/0.47 ! [P: produc1213276845od_b_b > $o,Prod: produc1213276845od_b_b] :
% 0.32/0.47 ( ! [A4: standard_Constant_a,B5: product_prod_b_b] : ( P @ ( produc1432590431od_b_b @ A4 @ B5 ) )
% 0.32/0.47 => ( P @ Prod ) ) ).
% 0.32/0.47
% 0.32/0.47 % old.prod.inducts
% 0.32/0.47 thf(fact_110_prod__cases3,axiom,
% 0.32/0.47 ! [Y: produc1213276845od_b_b] :
% 0.32/0.47 ~ ! [A4: standard_Constant_a,B5: b,C2: b] :
% 0.32/0.47 ( Y
% 0.32/0.47 != ( produc1432590431od_b_b @ A4 @ ( product_Pair_b_b @ B5 @ C2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % prod_cases3
% 0.32/0.47 thf(fact_111_prod__induct3,axiom,
% 0.32/0.47 ! [P: produc1213276845od_b_b > $o,X: produc1213276845od_b_b] :
% 0.32/0.47 ( ! [A4: standard_Constant_a,B5: b,C2: b] : ( P @ ( produc1432590431od_b_b @ A4 @ ( product_Pair_b_b @ B5 @ C2 ) ) )
% 0.32/0.47 => ( P @ X ) ) ).
% 0.32/0.47
% 0.32/0.47 % prod_induct3
% 0.32/0.47 thf(fact_112_map__graph__in,axiom,
% 0.32/0.47 ! [G: labele1159362096nt_a_b,A2: b,B3: b,E: allego510293162tant_a,F: b > b] :
% 0.32/0.47 ( ( G
% 0.32/0.47 = ( restri446606278nt_a_b @ G ) )
% 0.32/0.47 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ B3 ) @ ( semant55076487nt_a_b @ G @ E ) )
% 0.32/0.47 => ( member1285940496od_b_b @ ( product_Pair_b_b @ ( F @ A2 ) @ ( F @ B3 ) ) @ ( semant55076487nt_a_b @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ G ) @ F ) @ G ) @ E ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % map_graph_in
% 0.32/0.47 thf(fact_113_maintainedI,axiom,
% 0.32/0.47 ! [A: labele935650037_a_nat,G: labele1159362096nt_a_b,B: labele935650037_a_nat] :
% 0.32/0.47 ( ! [F3: set_Pr2106913242_nat_b] :
% 0.32/0.47 ( ( graph_714568023_nat_b @ A @ G @ F3 )
% 0.32/0.47 => ( extens1554515172_nat_b @ ( produc1676969687_a_nat @ A @ B ) @ G @ F3 ) )
% 0.32/0.47 => ( mainta1604381365_nat_b @ ( produc1676969687_a_nat @ A @ B ) @ G ) ) ).
% 0.32/0.47
% 0.32/0.47 % maintainedI
% 0.32/0.47 thf(fact_114_maintainedI,axiom,
% 0.32/0.47 ! [A: labele1159362096nt_a_b,G: labele1159362096nt_a_b,B: labele1159362096nt_a_b] :
% 0.32/0.47 ( ! [F3: set_Product_prod_b_b] :
% 0.32/0.47 ( ( graph_222606102_a_b_b @ A @ G @ F3 )
% 0.32/0.47 => ( extens1779443913_a_b_b @ ( produc1569511545nt_a_b @ A @ B ) @ G @ F3 ) )
% 0.32/0.47 => ( mainta374363448_a_b_b @ ( produc1569511545nt_a_b @ A @ B ) @ G ) ) ).
% 0.32/0.47
% 0.32/0.47 % maintainedI
% 0.32/0.47 thf(fact_115_extensible__refl__concr,axiom,
% 0.32/0.47 ! [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] :
% 0.32/0.47 ( ( graph_222606102_a_b_b @ ( labele1230159100nt_a_b @ E_1 @ V ) @ G @ F )
% 0.32/0.47 => ( ( extens1779443913_a_b_b @ ( produc1569511545nt_a_b @ ( labele1230159100nt_a_b @ E_1 @ V ) @ ( labele1230159100nt_a_b @ E_2 @ V ) ) @ G @ F )
% 0.32/0.47 = ( graph_222606102_a_b_b @ ( labele1230159100nt_a_b @ E_2 @ V ) @ G @ F ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % extensible_refl_concr
% 0.32/0.47 thf(fact_116_extensible__refl,axiom,
% 0.32/0.47 ! [R2: labele1159362096nt_a_b,G: labele1159362096nt_a_b,F: set_Product_prod_b_b] :
% 0.32/0.47 ( ( graph_222606102_a_b_b @ R2 @ G @ F )
% 0.32/0.47 => ( extens1779443913_a_b_b @ ( produc1569511545nt_a_b @ R2 @ R2 ) @ G @ F ) ) ).
% 0.32/0.47
% 0.32/0.47 % extensible_refl
% 0.32/0.47 thf(fact_117_graph__homomorphism__semantics,axiom,
% 0.32/0.47 ! [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] :
% 0.32/0.47 ( ( graph_222606102_a_b_b @ A @ B @ F )
% 0.32/0.47 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ B3 ) @ ( semant55076487nt_a_b @ A @ E ) )
% 0.32/0.47 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ A3 ) @ F )
% 0.32/0.47 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ B3 @ B4 ) @ F )
% 0.32/0.47 => ( member1285940496od_b_b @ ( product_Pair_b_b @ A3 @ B4 ) @ ( semant55076487nt_a_b @ B @ E ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % graph_homomorphism_semantics
% 0.32/0.47 thf(fact_118_consequence__graphD_I1_J,axiom,
% 0.32/0.47 ! [Rs: set_Pr1987088711_a_nat,G: labele1159362096nt_a_b,R2: produc1871334759_a_nat] :
% 0.32/0.47 ( ( conseq956760372_nat_b @ Rs @ G )
% 0.32/0.47 => ( ( member832397200_a_nat @ R2 @ Rs )
% 0.32/0.47 => ( mainta1604381365_nat_b @ R2 @ G ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % consequence_graphD(1)
% 0.32/0.47 thf(fact_119_semantics__in__vertices_I1_J,axiom,
% 0.32/0.47 ! [A: labele1159362096nt_a_b,A2: b,B3: b,E: allego510293162tant_a] :
% 0.32/0.47 ( ( A
% 0.32/0.47 = ( restri446606278nt_a_b @ A ) )
% 0.32/0.47 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ B3 ) @ ( semant55076487nt_a_b @ A @ E ) )
% 0.32/0.47 => ( member_b @ A2 @ ( labele1424214014nt_a_b @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % semantics_in_vertices(1)
% 0.32/0.47 thf(fact_120_semantics__in__vertices_I2_J,axiom,
% 0.32/0.47 ! [A: labele1159362096nt_a_b,A2: b,B3: b,E: allego510293162tant_a] :
% 0.32/0.47 ( ( A
% 0.32/0.47 = ( restri446606278nt_a_b @ A ) )
% 0.32/0.47 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ B3 ) @ ( semant55076487nt_a_b @ A @ E ) )
% 0.32/0.47 => ( member_b @ B3 @ ( labele1424214014nt_a_b @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % semantics_in_vertices(2)
% 0.32/0.47 thf(fact_121_subgraph__semantics,axiom,
% 0.32/0.47 ! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,A2: b,B3: b,E: allego510293162tant_a] :
% 0.32/0.47 ( ( graph_222606102_a_b_b @ A @ B @ ( id_on_b @ ( labele1424214014nt_a_b @ A ) ) )
% 0.32/0.47 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ B3 ) @ ( semant55076487nt_a_b @ A @ E ) )
% 0.32/0.47 => ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ B3 ) @ ( semant55076487nt_a_b @ B @ E ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % subgraph_semantics
% 0.32/0.47 thf(fact_122_maintainedD,axiom,
% 0.32/0.47 ! [A: labele935650037_a_nat,B: labele935650037_a_nat,G: labele1159362096nt_a_b,F: set_Pr2106913242_nat_b] :
% 0.32/0.47 ( ( mainta1604381365_nat_b @ ( produc1676969687_a_nat @ A @ B ) @ G )
% 0.32/0.47 => ( ( graph_714568023_nat_b @ A @ G @ F )
% 0.32/0.47 => ( extens1554515172_nat_b @ ( produc1676969687_a_nat @ A @ B ) @ G @ F ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % maintainedD
% 0.32/0.47 thf(fact_123_maintainedD,axiom,
% 0.32/0.47 ! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,G: labele1159362096nt_a_b,F: set_Product_prod_b_b] :
% 0.32/0.47 ( ( mainta374363448_a_b_b @ ( produc1569511545nt_a_b @ A @ B ) @ G )
% 0.32/0.47 => ( ( graph_222606102_a_b_b @ A @ G @ F )
% 0.32/0.47 => ( extens1779443913_a_b_b @ ( produc1569511545nt_a_b @ A @ B ) @ G @ F ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % maintainedD
% 0.32/0.47 thf(fact_124_extensibleI,axiom,
% 0.32/0.47 ! [R22: labele1159362096nt_a_b,G: labele1159362096nt_a_b,G2: set_Product_prod_b_b,R1: labele1159362096nt_a_b,F: set_Product_prod_b_b] :
% 0.32/0.47 ( ( graph_222606102_a_b_b @ R22 @ G @ G2 )
% 0.32/0.47 => ( ( agree_221379389_a_b_b @ R1 @ F @ G2 )
% 0.32/0.47 => ( extens1779443913_a_b_b @ ( produc1569511545nt_a_b @ R1 @ R22 ) @ G @ F ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % extensibleI
% 0.32/0.47 thf(fact_125_subgraph__subset_I2_J,axiom,
% 0.32/0.47 ! [G_1: labele1159362096nt_a_b,G_2: labele1159362096nt_a_b] :
% 0.32/0.47 ( ( graph_222606102_a_b_b @ G_1 @ G_2 @ ( id_on_b @ ( labele1424214014nt_a_b @ G_1 ) ) )
% 0.32/0.47 => ( ord_le123089219od_b_b @ ( labele1741081071nt_a_b @ ( restri446606278nt_a_b @ G_1 ) ) @ ( labele1741081071nt_a_b @ G_2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % subgraph_subset(2)
% 0.32/0.47 thf(fact_126_graph__homo__union__id_I1_J,axiom,
% 0.32/0.47 ! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,G: labele1159362096nt_a_b,F: set_Product_prod_b_b] :
% 0.32/0.47 ( ( graph_222606102_a_b_b @ ( graph_1309249505nt_a_b @ A @ B ) @ G @ F )
% 0.32/0.47 => ( ( A
% 0.32/0.47 = ( restri446606278nt_a_b @ A ) )
% 0.32/0.47 => ( graph_222606102_a_b_b @ A @ G @ ( relcomp_b_b_b @ ( id_on_b @ ( labele1424214014nt_a_b @ A ) ) @ F ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % graph_homo_union_id(1)
% 0.32/0.47 thf(fact_127_graph__homo__union__id_I2_J,axiom,
% 0.32/0.47 ! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,G: labele1159362096nt_a_b,F: set_Product_prod_b_b] :
% 0.32/0.47 ( ( graph_222606102_a_b_b @ ( graph_1309249505nt_a_b @ A @ B ) @ G @ F )
% 0.32/0.47 => ( ( B
% 0.32/0.47 = ( restri446606278nt_a_b @ B ) )
% 0.32/0.47 => ( graph_222606102_a_b_b @ B @ G @ ( relcomp_b_b_b @ ( id_on_b @ ( labele1424214014nt_a_b @ B ) ) @ F ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % graph_homo_union_id(2)
% 0.32/0.47 thf(fact_128__092_060open_062f_A_092_060equiv_062_A_092_060lambda_062x_O_Aif_AgetRel_AS__Idt_AG_A_096_096_A_123x_125_A_061_A_123_125_Athen_Ax_Aelse_AEps_A_IP_Ax_J_092_060close_062,axiom,
% 0.32/0.47 ( f
% 0.32/0.47 = ( ^ [X5: b] :
% 0.32/0.47 ( if_b
% 0.32/0.47 @ ( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ X5 @ bot_bot_set_b ) )
% 0.32/0.47 = bot_bot_set_b )
% 0.32/0.47 @ X5
% 0.32/0.47 @ ( hilbert_Eps_b @ ( p @ X5 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % \<open>f \<equiv> \<lambda>x. if getRel S_Idt G `` {x} = {} then x else Eps (P x)\<close>
% 0.32/0.47 thf(fact_129_ImageI,axiom,
% 0.32/0.47 ! [A2: b,B3: product_prod_b_b,R: set_Pr621705391od_b_b,A: set_b] :
% 0.32/0.47 ( ( member641857272od_b_b @ ( produc1257047359od_b_b @ A2 @ B3 ) @ R )
% 0.32/0.47 => ( ( member_b @ A2 @ A )
% 0.32/0.47 => ( member1285940496od_b_b @ B3 @ ( image_1177096571od_b_b @ R @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ImageI
% 0.32/0.47 thf(fact_130_ImageI,axiom,
% 0.32/0.47 ! [A2: b,B3: produc1213276845od_b_b,R: set_Pr2060523537od_b_b,A: set_b] :
% 0.32/0.47 ( ( member599505522od_b_b @ ( produc800495189od_b_b @ A2 @ B3 ) @ R )
% 0.32/0.47 => ( ( member_b @ A2 @ A )
% 0.32/0.47 => ( member1516365892od_b_b @ B3 @ ( image_984343321od_b_b @ R @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ImageI
% 0.32/0.47 thf(fact_131_ImageI,axiom,
% 0.32/0.47 ! [A2: product_prod_b_b,B3: b,R: set_Pr357419743_b_b_b,A: set_Product_prod_b_b] :
% 0.32/0.47 ( ( member351494440_b_b_b @ ( produc1001682799_b_b_b @ A2 @ B3 ) @ R )
% 0.32/0.47 => ( ( member1285940496od_b_b @ A2 @ A )
% 0.32/0.47 => ( member_b @ B3 @ ( image_921732011_b_b_b @ R @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ImageI
% 0.32/0.47 thf(fact_132_ImageI,axiom,
% 0.32/0.47 ! [A2: product_prod_b_b,B3: product_prod_b_b,R: set_Pr2007082183od_b_b,A: set_Product_prod_b_b] :
% 0.32/0.47 ( ( member1652792080od_b_b @ ( produc546497367od_b_b @ A2 @ B3 ) @ R )
% 0.32/0.47 => ( ( member1285940496od_b_b @ A2 @ A )
% 0.32/0.47 => ( member1285940496od_b_b @ B3 @ ( image_1928024979od_b_b @ R @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ImageI
% 0.32/0.47 thf(fact_133_ImageI,axiom,
% 0.32/0.47 ! [A2: product_prod_b_b,B3: produc1213276845od_b_b,R: set_Pr1071216121od_b_b,A: set_Product_prod_b_b] :
% 0.32/0.47 ( ( member4694106od_b_b @ ( produc732676669od_b_b @ A2 @ B3 ) @ R )
% 0.32/0.47 => ( ( member1285940496od_b_b @ A2 @ A )
% 0.32/0.47 => ( member1516365892od_b_b @ B3 @ ( image_532916993od_b_b @ R @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ImageI
% 0.32/0.47 thf(fact_134_ImageI,axiom,
% 0.32/0.47 ! [A2: produc1213276845od_b_b,B3: b,R: set_Pr1906739389_b_b_b,A: set_Pr1324126435od_b_b] :
% 0.32/0.47 ( ( member1417789726_b_b_b @ ( produc1580777273_b_b_b @ A2 @ B3 ) @ R )
% 0.32/0.47 => ( ( member1516365892od_b_b @ A2 @ A )
% 0.32/0.47 => ( member_b @ B3 @ ( image_1764625405_b_b_b @ R @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ImageI
% 0.32/0.47 thf(fact_135_ImageI,axiom,
% 0.32/0.47 ! [A2: produc1213276845od_b_b,B3: product_prod_b_b,R: set_Pr2134561957od_b_b,A: set_Pr1324126435od_b_b] :
% 0.32/0.47 ( ( member942707974od_b_b @ ( produc1597690145od_b_b @ A2 @ B3 ) @ R )
% 0.32/0.47 => ( ( member1516365892od_b_b @ A2 @ A )
% 0.32/0.47 => ( member1285940496od_b_b @ B3 @ ( image_1397930469od_b_b @ R @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ImageI
% 0.32/0.47 thf(fact_136_ImageI,axiom,
% 0.32/0.47 ! [A2: produc1213276845od_b_b,B3: produc1213276845od_b_b,R: set_Pr2109276827od_b_b,A: set_Pr1324126435od_b_b] :
% 0.32/0.47 ( ( member1086024932od_b_b @ ( produc449289715od_b_b @ A2 @ B3 ) @ R )
% 0.32/0.47 => ( ( member1516365892od_b_b @ A2 @ A )
% 0.32/0.47 => ( member1516365892od_b_b @ B3 @ ( image_763305007od_b_b @ R @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ImageI
% 0.32/0.47 thf(fact_137_ImageI,axiom,
% 0.32/0.47 ! [A2: b,B3: b,R: set_Product_prod_b_b,A: set_b] :
% 0.32/0.47 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ B3 ) @ R )
% 0.32/0.47 => ( ( member_b @ A2 @ A )
% 0.32/0.47 => ( member_b @ B3 @ ( image_b_b @ R @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ImageI
% 0.32/0.47 thf(fact_138_ImageI,axiom,
% 0.32/0.47 ! [A2: standard_Constant_a,B3: product_prod_b_b,R: set_Pr1324126435od_b_b,A: set_St761939237tant_a] :
% 0.32/0.47 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A2 @ B3 ) @ R )
% 0.32/0.47 => ( ( member1632892294tant_a @ A2 @ A )
% 0.32/0.47 => ( member1285940496od_b_b @ B3 @ ( image_1916422435od_b_b @ R @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ImageI
% 0.32/0.47 thf(fact_139_Image__empty2,axiom,
% 0.32/0.47 ! [R2: set_Product_prod_b_b] :
% 0.32/0.47 ( ( image_b_b @ R2 @ bot_bot_set_b )
% 0.32/0.47 = bot_bot_set_b ) ).
% 0.32/0.47
% 0.32/0.47 % Image_empty2
% 0.32/0.47 thf(fact_140_Image__empty2,axiom,
% 0.32/0.47 ! [R2: set_Pr1646010159_a_nat] :
% 0.32/0.47 ( ( image_1749766139_a_nat @ R2 @ bot_bot_set_b )
% 0.32/0.47 = bot_bo1836341171_a_nat ) ).
% 0.32/0.47
% 0.32/0.47 % Image_empty2
% 0.32/0.47 thf(fact_141_Image__empty2,axiom,
% 0.32/0.47 ! [R2: set_Pr812188767_nat_b] :
% 0.32/0.47 ( ( image_924992811_nat_b @ R2 @ bot_bo1836341171_a_nat )
% 0.32/0.47 = bot_bot_set_b ) ).
% 0.32/0.47
% 0.32/0.47 % Image_empty2
% 0.32/0.47 thf(fact_142_Image__empty2,axiom,
% 0.32/0.47 ! [R2: set_Pr924198087_a_nat] :
% 0.32/0.47 ( ( image_1168831379_a_nat @ R2 @ bot_bo1836341171_a_nat )
% 0.32/0.47 = bot_bo1836341171_a_nat ) ).
% 0.32/0.47
% 0.32/0.47 % Image_empty2
% 0.32/0.47 thf(fact_143_Image__empty1,axiom,
% 0.32/0.47 ! [X3: set_b] :
% 0.32/0.47 ( ( image_b_b @ bot_bo1343651123od_b_b @ X3 )
% 0.32/0.47 = bot_bot_set_b ) ).
% 0.32/0.47
% 0.32/0.47 % Image_empty1
% 0.32/0.47 thf(fact_144_Image__empty1,axiom,
% 0.32/0.47 ! [X3: set_la1083530965_a_nat] :
% 0.32/0.47 ( ( image_1971191571_a_nat @ bot_bo1836341171_a_nat @ X3 )
% 0.32/0.47 = bot_bo2122869057_a_nat ) ).
% 0.32/0.47
% 0.32/0.47 % Image_empty1
% 0.32/0.47 thf(fact_145_Id__on__empty,axiom,
% 0.32/0.47 ( ( id_on_689842066_a_nat @ bot_bo2122869057_a_nat )
% 0.32/0.47 = bot_bo1836341171_a_nat ) ).
% 0.32/0.47
% 0.32/0.47 % Id_on_empty
% 0.32/0.47 thf(fact_146_Id__on__empty,axiom,
% 0.32/0.47 ( ( id_on_b @ bot_bot_set_b )
% 0.32/0.47 = bot_bo1343651123od_b_b ) ).
% 0.32/0.47
% 0.32/0.47 % Id_on_empty
% 0.32/0.47 thf(fact_147_Id__on__empty,axiom,
% 0.32/0.47 ( ( id_on_1651096324_a_nat @ bot_bo1836341171_a_nat )
% 0.32/0.47 = bot_bo1973379891_a_nat ) ).
% 0.32/0.47
% 0.32/0.47 % Id_on_empty
% 0.32/0.47 thf(fact_148_Gr__empty,axiom,
% 0.32/0.47 ! [F: labele935650037_a_nat > labele935650037_a_nat] :
% 0.32/0.47 ( ( bNF_Gr996500706_a_nat @ bot_bo2122869057_a_nat @ F )
% 0.32/0.47 = bot_bo1836341171_a_nat ) ).
% 0.32/0.47
% 0.32/0.47 % Gr_empty
% 0.32/0.47 thf(fact_149_Gr__empty,axiom,
% 0.32/0.47 ! [F: b > b] :
% 0.32/0.47 ( ( bNF_Gr_b_b @ bot_bot_set_b @ F )
% 0.32/0.47 = bot_bo1343651123od_b_b ) ).
% 0.32/0.47
% 0.32/0.47 % Gr_empty
% 0.32/0.47 thf(fact_150_graph__homomorphism__composes,axiom,
% 0.32/0.47 ! [A2: labele1159362096nt_a_b,B3: labele1159362096nt_a_b,X: set_Product_prod_b_b,C: labele1159362096nt_a_b,Y: set_Product_prod_b_b] :
% 0.32/0.47 ( ( graph_222606102_a_b_b @ A2 @ B3 @ X )
% 0.32/0.47 => ( ( graph_222606102_a_b_b @ B3 @ C @ Y )
% 0.32/0.47 => ( graph_222606102_a_b_b @ A2 @ C @ ( relcomp_b_b_b @ X @ Y ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % graph_homomorphism_composes
% 0.32/0.47 thf(fact_151_P__eq,axiom,
% 0.32/0.47 ! [X: b] :
% 0.32/0.47 ( ( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ X @ bot_bot_set_b ) )
% 0.32/0.47 != bot_bot_set_b )
% 0.32/0.47 => ( ( hilbert_Eps_b @ ( p @ ( hilbert_Eps_b @ ( p @ X ) ) ) )
% 0.32/0.47 = ( hilbert_Eps_b @ ( p @ X ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % P_eq
% 0.32/0.47 thf(fact_152_Gr__insert,axiom,
% 0.32/0.47 ! [X: labele935650037_a_nat,F2: set_la1083530965_a_nat,F: labele935650037_a_nat > labele935650037_a_nat] :
% 0.32/0.47 ( ( bNF_Gr996500706_a_nat @ ( insert1167839429_a_nat @ X @ F2 ) @ F )
% 0.32/0.47 = ( insert1574423351_a_nat @ ( produc1676969687_a_nat @ X @ ( F @ X ) ) @ ( bNF_Gr996500706_a_nat @ F2 @ F ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Gr_insert
% 0.32/0.47 thf(fact_153_Gr__insert,axiom,
% 0.32/0.47 ! [X: b,F2: set_b,F: b > b] :
% 0.32/0.47 ( ( bNF_Gr_b_b @ ( insert_b @ X @ F2 ) @ F )
% 0.32/0.47 = ( insert1952693431od_b_b @ ( product_Pair_b_b @ X @ ( F @ X ) ) @ ( bNF_Gr_b_b @ F2 @ F ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Gr_insert
% 0.32/0.47 thf(fact_154_Gr__insert,axiom,
% 0.32/0.47 ! [X: standard_Constant_a,F2: set_St761939237tant_a,F: standard_Constant_a > product_prod_b_b] :
% 0.32/0.47 ( ( bNF_Gr1272216980od_b_b @ ( insert1909710879tant_a @ X @ F2 ) @ F )
% 0.32/0.47 = ( insert2037698781od_b_b @ ( produc1432590431od_b_b @ X @ ( F @ X ) ) @ ( bNF_Gr1272216980od_b_b @ F2 @ F ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Gr_insert
% 0.32/0.47 thf(fact_155_map__graph__selectors_I1_J,axiom,
% 0.32/0.47 ! [F: set_Product_prod_b_b,G: labele1159362096nt_a_b] :
% 0.32/0.47 ( ( labele1424214014nt_a_b @ ( map_gr926947118tant_a @ F @ G ) )
% 0.32/0.47 = ( image_b_b @ F @ ( labele1424214014nt_a_b @ G ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % map_graph_selectors(1)
% 0.32/0.47 thf(fact_156_Image__singleton__iff,axiom,
% 0.32/0.47 ! [B3: product_prod_b_b,R: set_Pr1324126435od_b_b,A2: standard_Constant_a] :
% 0.32/0.47 ( ( member1285940496od_b_b @ B3 @ ( image_1916422435od_b_b @ R @ ( insert1909710879tant_a @ A2 @ bot_bo1160111033tant_a ) ) )
% 0.32/0.47 = ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A2 @ B3 ) @ R ) ) ).
% 0.32/0.47
% 0.32/0.47 % Image_singleton_iff
% 0.32/0.47 thf(fact_157_Image__singleton__iff,axiom,
% 0.32/0.47 ! [B3: product_prod_b_b,R: set_Pr621705391od_b_b,A2: b] :
% 0.32/0.47 ( ( member1285940496od_b_b @ B3 @ ( image_1177096571od_b_b @ R @ ( insert_b @ A2 @ bot_bot_set_b ) ) )
% 0.32/0.47 = ( member641857272od_b_b @ ( produc1257047359od_b_b @ A2 @ B3 ) @ R ) ) ).
% 0.32/0.47
% 0.32/0.47 % Image_singleton_iff
% 0.32/0.47 thf(fact_158_Image__singleton__iff,axiom,
% 0.32/0.47 ! [B3: produc1213276845od_b_b,R: set_Pr2060523537od_b_b,A2: b] :
% 0.32/0.47 ( ( member1516365892od_b_b @ B3 @ ( image_984343321od_b_b @ R @ ( insert_b @ A2 @ bot_bot_set_b ) ) )
% 0.32/0.47 = ( member599505522od_b_b @ ( produc800495189od_b_b @ A2 @ B3 ) @ R ) ) ).
% 0.32/0.47
% 0.32/0.47 % Image_singleton_iff
% 0.32/0.47 thf(fact_159_Image__singleton__iff,axiom,
% 0.32/0.47 ! [B3: b,R: set_Product_prod_b_b,A2: b] :
% 0.32/0.47 ( ( member_b @ B3 @ ( image_b_b @ R @ ( insert_b @ A2 @ bot_bot_set_b ) ) )
% 0.32/0.47 = ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ B3 ) @ R ) ) ).
% 0.32/0.47
% 0.32/0.47 % Image_singleton_iff
% 0.32/0.47 thf(fact_160_Image__singleton__iff,axiom,
% 0.32/0.47 ! [B3: b,R: set_Pr812188767_nat_b,A2: produc1871334759_a_nat] :
% 0.32/0.47 ( ( member_b @ B3 @ ( image_924992811_nat_b @ R @ ( insert1574423351_a_nat @ A2 @ bot_bo1836341171_a_nat ) ) )
% 0.32/0.47 = ( member1544800936_nat_b @ ( produc2059954415_nat_b @ A2 @ B3 ) @ R ) ) ).
% 0.32/0.47
% 0.32/0.47 % Image_singleton_iff
% 0.32/0.47 thf(fact_161_Image__singleton__iff,axiom,
% 0.32/0.47 ! [B3: product_prod_b_b,R: set_Pr667377223od_b_b,A2: produc1871334759_a_nat] :
% 0.32/0.47 ( ( member1285940496od_b_b @ B3 @ ( image_1214223635od_b_b @ R @ ( insert1574423351_a_nat @ A2 @ bot_bo1836341171_a_nat ) ) )
% 0.32/0.47 = ( member301892752od_b_b @ ( produc590959831od_b_b @ A2 @ B3 ) @ R ) ) ).
% 0.32/0.47
% 0.32/0.47 % Image_singleton_iff
% 0.32/0.47 thf(fact_162_Image__singleton__iff,axiom,
% 0.32/0.47 ! [B3: produc1213276845od_b_b,R: set_Pr1954438265od_b_b,A2: produc1871334759_a_nat] :
% 0.32/0.47 ( ( member1516365892od_b_b @ B3 @ ( image_480774529od_b_b @ R @ ( insert1574423351_a_nat @ A2 @ bot_bo1836341171_a_nat ) ) )
% 0.32/0.47 = ( member1533761242od_b_b @ ( produc401731773od_b_b @ A2 @ B3 ) @ R ) ) ).
% 0.32/0.47
% 0.32/0.47 % Image_singleton_iff
% 0.32/0.47 thf(fact_163_in__on__graph,axiom,
% 0.32/0.47 ! [X: b,G: labele1159362096nt_a_b,A2: b > b,Y: b,B3: set_Product_prod_b_b] :
% 0.32/0.47 ( ( member_b @ X @ ( labele1424214014nt_a_b @ G ) )
% 0.32/0.47 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ ( A2 @ X ) @ Y ) @ B3 )
% 0.32/0.47 => ( member1285940496od_b_b @ ( product_Pair_b_b @ X @ Y ) @ ( relcomp_b_b_b @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ G ) @ A2 ) @ B3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % in_on_graph
% 0.32/0.47 thf(fact_164_in__on__graph,axiom,
% 0.32/0.47 ! [X: b,G: labele1159362096nt_a_b,A2: b > standard_Constant_a,Y: product_prod_b_b,B3: set_Pr1324126435od_b_b] :
% 0.32/0.47 ( ( member_b @ X @ ( labele1424214014nt_a_b @ G ) )
% 0.32/0.47 => ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ ( A2 @ X ) @ Y ) @ B3 )
% 0.32/0.47 => ( member641857272od_b_b @ ( produc1257047359od_b_b @ X @ Y ) @ ( relcom112561144od_b_b @ ( bNF_Gr230160332tant_a @ ( labele1424214014nt_a_b @ G ) @ A2 ) @ B3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % in_on_graph
% 0.32/0.47 thf(fact_165_graph__homomorphism__empty,axiom,
% 0.32/0.47 ! [G: labele1159362096nt_a_b,F: set_Pr812188767_nat_b] :
% 0.32/0.47 ( ( graph_726202286_nat_b @ ( labele27098724_a_nat @ bot_bo1653310327_a_nat @ bot_bo1836341171_a_nat ) @ G @ F )
% 0.32/0.47 = ( ( F = bot_bo1113554635_nat_b )
% 0.32/0.47 & ( G
% 0.32/0.47 = ( restri446606278nt_a_b @ G ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % graph_homomorphism_empty
% 0.32/0.47 thf(fact_166_graph__homomorphism__empty,axiom,
% 0.32/0.47 ! [G: labele1159362096nt_a_b,F: set_Product_prod_b_b] :
% 0.32/0.47 ( ( graph_222606102_a_b_b @ ( labele1230159100nt_a_b @ bot_bo1664927607od_b_b @ bot_bot_set_b ) @ G @ F )
% 0.32/0.47 = ( ( F = bot_bo1343651123od_b_b )
% 0.32/0.47 & ( G
% 0.32/0.47 = ( restri446606278nt_a_b @ G ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % graph_homomorphism_empty
% 0.32/0.47 thf(fact_167_graph__unionI,axiom,
% 0.32/0.47 ! [G_1: labele1159362096nt_a_b,G_2: labele1159362096nt_a_b] :
% 0.32/0.47 ( ( ord_le123089219od_b_b @ ( labele1741081071nt_a_b @ G_1 ) @ ( labele1741081071nt_a_b @ G_2 ) )
% 0.32/0.47 => ( ( ord_less_eq_set_b @ ( labele1424214014nt_a_b @ G_1 ) @ ( labele1424214014nt_a_b @ G_2 ) )
% 0.32/0.47 => ( ( graph_1309249505nt_a_b @ G_1 @ G_2 )
% 0.32/0.47 = G_2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % graph_unionI
% 0.32/0.47 thf(fact_168_graph__single,axiom,
% 0.32/0.47 ! [A2: standard_Constant_a,B3: b,C: b] :
% 0.32/0.47 ( ( 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 ) ) )
% 0.32/0.47 = ( restri446606278nt_a_b @ ( 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 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % graph_single
% 0.32/0.47 thf(fact_169_r2,axiom,
% 0.32/0.47 ! [X: b] :
% 0.32/0.47 ( ( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ X @ bot_bot_set_b ) )
% 0.32/0.47 = bot_bot_set_b )
% 0.32/0.47 = ( ~ ( member_b @ X @ ( labele1424214014nt_a_b @ g ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % r2
% 0.32/0.47 thf(fact_170_refl__on__singleton,axiom,
% 0.32/0.47 ! [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 ) ) ).
% 0.32/0.47
% 0.32/0.47 % refl_on_singleton
% 0.32/0.47 thf(fact_171_refl__on__singleton,axiom,
% 0.32/0.47 ! [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 ) ) ).
% 0.32/0.47
% 0.32/0.47 % refl_on_singleton
% 0.32/0.47 thf(fact_172_refl__on__singleton,axiom,
% 0.32/0.47 ! [X: produc1871334759_a_nat] : ( refl_o1213627494_a_nat @ ( insert1574423351_a_nat @ X @ bot_bo1836341171_a_nat ) @ ( insert1810136247_a_nat @ ( produc1677124439_a_nat @ X @ X ) @ bot_bo1973379891_a_nat ) ) ).
% 0.32/0.47
% 0.32/0.47 % refl_on_singleton
% 0.32/0.47 thf(fact_173_rev__ImageI,axiom,
% 0.32/0.47 ! [A2: b,A: set_b,B3: product_prod_b_b,R: set_Pr621705391od_b_b] :
% 0.32/0.47 ( ( member_b @ A2 @ A )
% 0.32/0.47 => ( ( member641857272od_b_b @ ( produc1257047359od_b_b @ A2 @ B3 ) @ R )
% 0.32/0.47 => ( member1285940496od_b_b @ B3 @ ( image_1177096571od_b_b @ R @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % rev_ImageI
% 0.32/0.47 thf(fact_174_rev__ImageI,axiom,
% 0.32/0.47 ! [A2: b,A: set_b,B3: produc1213276845od_b_b,R: set_Pr2060523537od_b_b] :
% 0.32/0.47 ( ( member_b @ A2 @ A )
% 0.32/0.47 => ( ( member599505522od_b_b @ ( produc800495189od_b_b @ A2 @ B3 ) @ R )
% 0.32/0.47 => ( member1516365892od_b_b @ B3 @ ( image_984343321od_b_b @ R @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % rev_ImageI
% 0.32/0.47 thf(fact_175_rev__ImageI,axiom,
% 0.32/0.47 ! [A2: product_prod_b_b,A: set_Product_prod_b_b,B3: b,R: set_Pr357419743_b_b_b] :
% 0.32/0.47 ( ( member1285940496od_b_b @ A2 @ A )
% 0.32/0.47 => ( ( member351494440_b_b_b @ ( produc1001682799_b_b_b @ A2 @ B3 ) @ R )
% 0.32/0.47 => ( member_b @ B3 @ ( image_921732011_b_b_b @ R @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % rev_ImageI
% 0.32/0.47 thf(fact_176_rev__ImageI,axiom,
% 0.32/0.47 ! [A2: product_prod_b_b,A: set_Product_prod_b_b,B3: product_prod_b_b,R: set_Pr2007082183od_b_b] :
% 0.32/0.47 ( ( member1285940496od_b_b @ A2 @ A )
% 0.32/0.47 => ( ( member1652792080od_b_b @ ( produc546497367od_b_b @ A2 @ B3 ) @ R )
% 0.32/0.47 => ( member1285940496od_b_b @ B3 @ ( image_1928024979od_b_b @ R @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % rev_ImageI
% 0.32/0.47 thf(fact_177_rev__ImageI,axiom,
% 0.32/0.47 ! [A2: product_prod_b_b,A: set_Product_prod_b_b,B3: produc1213276845od_b_b,R: set_Pr1071216121od_b_b] :
% 0.32/0.47 ( ( member1285940496od_b_b @ A2 @ A )
% 0.32/0.47 => ( ( member4694106od_b_b @ ( produc732676669od_b_b @ A2 @ B3 ) @ R )
% 0.32/0.47 => ( member1516365892od_b_b @ B3 @ ( image_532916993od_b_b @ R @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % rev_ImageI
% 0.32/0.47 thf(fact_178_rev__ImageI,axiom,
% 0.32/0.47 ! [A2: produc1213276845od_b_b,A: set_Pr1324126435od_b_b,B3: b,R: set_Pr1906739389_b_b_b] :
% 0.32/0.47 ( ( member1516365892od_b_b @ A2 @ A )
% 0.32/0.47 => ( ( member1417789726_b_b_b @ ( produc1580777273_b_b_b @ A2 @ B3 ) @ R )
% 0.32/0.47 => ( member_b @ B3 @ ( image_1764625405_b_b_b @ R @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % rev_ImageI
% 0.32/0.47 thf(fact_179_rev__ImageI,axiom,
% 0.32/0.47 ! [A2: produc1213276845od_b_b,A: set_Pr1324126435od_b_b,B3: product_prod_b_b,R: set_Pr2134561957od_b_b] :
% 0.32/0.47 ( ( member1516365892od_b_b @ A2 @ A )
% 0.32/0.47 => ( ( member942707974od_b_b @ ( produc1597690145od_b_b @ A2 @ B3 ) @ R )
% 0.32/0.47 => ( member1285940496od_b_b @ B3 @ ( image_1397930469od_b_b @ R @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % rev_ImageI
% 0.32/0.47 thf(fact_180_rev__ImageI,axiom,
% 0.32/0.47 ! [A2: produc1213276845od_b_b,A: set_Pr1324126435od_b_b,B3: produc1213276845od_b_b,R: set_Pr2109276827od_b_b] :
% 0.32/0.47 ( ( member1516365892od_b_b @ A2 @ A )
% 0.32/0.47 => ( ( member1086024932od_b_b @ ( produc449289715od_b_b @ A2 @ B3 ) @ R )
% 0.32/0.47 => ( member1516365892od_b_b @ B3 @ ( image_763305007od_b_b @ R @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % rev_ImageI
% 0.32/0.47 thf(fact_181_rev__ImageI,axiom,
% 0.32/0.47 ! [A2: b,A: set_b,B3: b,R: set_Product_prod_b_b] :
% 0.32/0.47 ( ( member_b @ A2 @ A )
% 0.32/0.47 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ B3 ) @ R )
% 0.32/0.47 => ( member_b @ B3 @ ( image_b_b @ R @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % rev_ImageI
% 0.32/0.47 thf(fact_182_rev__ImageI,axiom,
% 0.32/0.47 ! [A2: standard_Constant_a,A: set_St761939237tant_a,B3: product_prod_b_b,R: set_Pr1324126435od_b_b] :
% 0.32/0.47 ( ( member1632892294tant_a @ A2 @ A )
% 0.32/0.47 => ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A2 @ B3 ) @ R )
% 0.32/0.47 => ( member1285940496od_b_b @ B3 @ ( image_1916422435od_b_b @ R @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % rev_ImageI
% 0.32/0.47 thf(fact_183_Image__iff,axiom,
% 0.32/0.47 ! [B3: b,R: set_Product_prod_b_b,A: set_b] :
% 0.32/0.47 ( ( member_b @ B3 @ ( image_b_b @ R @ A ) )
% 0.32/0.47 = ( ? [X5: b] :
% 0.32/0.47 ( ( member_b @ X5 @ A )
% 0.32/0.47 & ( member1285940496od_b_b @ ( product_Pair_b_b @ X5 @ B3 ) @ R ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Image_iff
% 0.32/0.47 thf(fact_184_Image__iff,axiom,
% 0.32/0.47 ! [B3: product_prod_b_b,R: set_Pr1324126435od_b_b,A: set_St761939237tant_a] :
% 0.32/0.47 ( ( member1285940496od_b_b @ B3 @ ( image_1916422435od_b_b @ R @ A ) )
% 0.32/0.47 = ( ? [X5: standard_Constant_a] :
% 0.32/0.47 ( ( member1632892294tant_a @ X5 @ A )
% 0.32/0.47 & ( member1516365892od_b_b @ ( produc1432590431od_b_b @ X5 @ B3 ) @ R ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Image_iff
% 0.32/0.47 thf(fact_185_ImageE,axiom,
% 0.32/0.47 ! [B3: b,R: set_Pr357419743_b_b_b,A: set_Product_prod_b_b] :
% 0.32/0.47 ( ( member_b @ B3 @ ( image_921732011_b_b_b @ R @ A ) )
% 0.32/0.47 => ~ ! [X4: product_prod_b_b] :
% 0.32/0.47 ( ( member351494440_b_b_b @ ( produc1001682799_b_b_b @ X4 @ B3 ) @ R )
% 0.32/0.47 => ~ ( member1285940496od_b_b @ X4 @ A ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ImageE
% 0.32/0.47 thf(fact_186_ImageE,axiom,
% 0.32/0.47 ! [B3: b,R: set_Pr1906739389_b_b_b,A: set_Pr1324126435od_b_b] :
% 0.32/0.47 ( ( member_b @ B3 @ ( image_1764625405_b_b_b @ R @ A ) )
% 0.32/0.47 => ~ ! [X4: produc1213276845od_b_b] :
% 0.32/0.47 ( ( member1417789726_b_b_b @ ( produc1580777273_b_b_b @ X4 @ B3 ) @ R )
% 0.32/0.47 => ~ ( member1516365892od_b_b @ X4 @ A ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ImageE
% 0.32/0.47 thf(fact_187_ImageE,axiom,
% 0.32/0.47 ! [B3: product_prod_b_b,R: set_Pr621705391od_b_b,A: set_b] :
% 0.32/0.47 ( ( member1285940496od_b_b @ B3 @ ( image_1177096571od_b_b @ R @ A ) )
% 0.32/0.47 => ~ ! [X4: b] :
% 0.32/0.47 ( ( member641857272od_b_b @ ( produc1257047359od_b_b @ X4 @ B3 ) @ R )
% 0.32/0.47 => ~ ( member_b @ X4 @ A ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ImageE
% 0.32/0.47 thf(fact_188_ImageE,axiom,
% 0.32/0.47 ! [B3: product_prod_b_b,R: set_Pr2007082183od_b_b,A: set_Product_prod_b_b] :
% 0.32/0.47 ( ( member1285940496od_b_b @ B3 @ ( image_1928024979od_b_b @ R @ A ) )
% 0.32/0.47 => ~ ! [X4: product_prod_b_b] :
% 0.32/0.47 ( ( member1652792080od_b_b @ ( produc546497367od_b_b @ X4 @ B3 ) @ R )
% 0.32/0.47 => ~ ( member1285940496od_b_b @ X4 @ A ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ImageE
% 0.32/0.47 thf(fact_189_ImageE,axiom,
% 0.32/0.47 ! [B3: product_prod_b_b,R: set_Pr2134561957od_b_b,A: set_Pr1324126435od_b_b] :
% 0.32/0.47 ( ( member1285940496od_b_b @ B3 @ ( image_1397930469od_b_b @ R @ A ) )
% 0.32/0.47 => ~ ! [X4: produc1213276845od_b_b] :
% 0.32/0.47 ( ( member942707974od_b_b @ ( produc1597690145od_b_b @ X4 @ B3 ) @ R )
% 0.32/0.47 => ~ ( member1516365892od_b_b @ X4 @ A ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ImageE
% 0.32/0.47 thf(fact_190_ImageE,axiom,
% 0.32/0.47 ! [B3: produc1213276845od_b_b,R: set_Pr2060523537od_b_b,A: set_b] :
% 0.32/0.47 ( ( member1516365892od_b_b @ B3 @ ( image_984343321od_b_b @ R @ A ) )
% 0.32/0.47 => ~ ! [X4: b] :
% 0.32/0.47 ( ( member599505522od_b_b @ ( produc800495189od_b_b @ X4 @ B3 ) @ R )
% 0.32/0.47 => ~ ( member_b @ X4 @ A ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ImageE
% 0.32/0.47 thf(fact_191_ImageE,axiom,
% 0.32/0.47 ! [B3: produc1213276845od_b_b,R: set_Pr1071216121od_b_b,A: set_Product_prod_b_b] :
% 0.32/0.47 ( ( member1516365892od_b_b @ B3 @ ( image_532916993od_b_b @ R @ A ) )
% 0.32/0.47 => ~ ! [X4: product_prod_b_b] :
% 0.32/0.47 ( ( member4694106od_b_b @ ( produc732676669od_b_b @ X4 @ B3 ) @ R )
% 0.32/0.47 => ~ ( member1285940496od_b_b @ X4 @ A ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ImageE
% 0.32/0.47 thf(fact_192_ImageE,axiom,
% 0.32/0.47 ! [B3: produc1213276845od_b_b,R: set_Pr2109276827od_b_b,A: set_Pr1324126435od_b_b] :
% 0.32/0.47 ( ( member1516365892od_b_b @ B3 @ ( image_763305007od_b_b @ R @ A ) )
% 0.32/0.47 => ~ ! [X4: produc1213276845od_b_b] :
% 0.32/0.47 ( ( member1086024932od_b_b @ ( produc449289715od_b_b @ X4 @ B3 ) @ R )
% 0.32/0.47 => ~ ( member1516365892od_b_b @ X4 @ A ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ImageE
% 0.32/0.47 thf(fact_193_ImageE,axiom,
% 0.32/0.47 ! [B3: b,R: set_Product_prod_b_b,A: set_b] :
% 0.32/0.47 ( ( member_b @ B3 @ ( image_b_b @ R @ A ) )
% 0.32/0.47 => ~ ! [X4: b] :
% 0.32/0.47 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ X4 @ B3 ) @ R )
% 0.32/0.47 => ~ ( member_b @ X4 @ A ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ImageE
% 0.32/0.47 thf(fact_194_ImageE,axiom,
% 0.32/0.47 ! [B3: product_prod_b_b,R: set_Pr1324126435od_b_b,A: set_St761939237tant_a] :
% 0.32/0.47 ( ( member1285940496od_b_b @ B3 @ ( image_1916422435od_b_b @ R @ A ) )
% 0.32/0.47 => ~ ! [X4: standard_Constant_a] :
% 0.32/0.47 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ X4 @ B3 ) @ R )
% 0.32/0.47 => ~ ( member1632892294tant_a @ X4 @ A ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ImageE
% 0.32/0.47 thf(fact_195_relcomp_OrelcompI,axiom,
% 0.32/0.47 ! [A2: standard_Constant_a,B3: standard_Constant_a,R: set_Pr154086431tant_a,C: product_prod_b_b,S: set_Pr1324126435od_b_b] :
% 0.32/0.47 ( ( member1214736488tant_a @ ( produc342647tant_a @ A2 @ B3 ) @ R )
% 0.32/0.47 => ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ B3 @ C ) @ S )
% 0.32/0.47 => ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A2 @ C ) @ ( relcom883816262od_b_b @ R @ S ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % relcomp.relcompI
% 0.32/0.47 thf(fact_196_relcomp_OrelcompI,axiom,
% 0.32/0.47 ! [A2: b,B3: b,R: set_Product_prod_b_b,C: b,S: set_Product_prod_b_b] :
% 0.32/0.47 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ B3 ) @ R )
% 0.32/0.47 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ B3 @ C ) @ S )
% 0.32/0.47 => ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ C ) @ ( relcomp_b_b_b @ R @ S ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % relcomp.relcompI
% 0.32/0.47 thf(fact_197_relcomp_OrelcompI,axiom,
% 0.32/0.47 ! [A2: standard_Constant_a,B3: product_prod_b_b,R: set_Pr1324126435od_b_b,C: product_prod_b_b,S: set_Pr2007082183od_b_b] :
% 0.32/0.47 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A2 @ B3 ) @ R )
% 0.32/0.47 => ( ( member1652792080od_b_b @ ( produc546497367od_b_b @ B3 @ C ) @ S )
% 0.32/0.47 => ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A2 @ C ) @ ( relcom1823941168od_b_b @ R @ S ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % relcomp.relcompI
% 0.32/0.47 thf(fact_198_relcomp_Oinducts,axiom,
% 0.32/0.47 ! [X1: b,X22: b,R: set_Product_prod_b_b,S: set_Product_prod_b_b,P: b > b > $o] :
% 0.32/0.47 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ X1 @ X22 ) @ ( relcomp_b_b_b @ R @ S ) )
% 0.32/0.47 => ( ! [A4: b,B5: b,C2: b] :
% 0.32/0.47 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A4 @ B5 ) @ R )
% 0.32/0.47 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ B5 @ C2 ) @ S )
% 0.32/0.47 => ( P @ A4 @ C2 ) ) )
% 0.32/0.47 => ( P @ X1 @ X22 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % relcomp.inducts
% 0.32/0.47 thf(fact_199_relcomp_Oinducts,axiom,
% 0.32/0.47 ! [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 > $o] :
% 0.32/0.47 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ X1 @ X22 ) @ ( relcom883816262od_b_b @ R @ S ) )
% 0.32/0.47 => ( ! [A4: standard_Constant_a,B5: standard_Constant_a,C2: product_prod_b_b] :
% 0.32/0.47 ( ( member1214736488tant_a @ ( produc342647tant_a @ A4 @ B5 ) @ R )
% 0.32/0.47 => ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ B5 @ C2 ) @ S )
% 0.32/0.47 => ( P @ A4 @ C2 ) ) )
% 0.32/0.47 => ( P @ X1 @ X22 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % relcomp.inducts
% 0.32/0.47 thf(fact_200_relcomp_Oinducts,axiom,
% 0.32/0.47 ! [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 > $o] :
% 0.32/0.47 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ X1 @ X22 ) @ ( relcom1823941168od_b_b @ R @ S ) )
% 0.32/0.47 => ( ! [A4: standard_Constant_a,B5: product_prod_b_b,C2: product_prod_b_b] :
% 0.32/0.47 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A4 @ B5 ) @ R )
% 0.32/0.47 => ( ( member1652792080od_b_b @ ( produc546497367od_b_b @ B5 @ C2 ) @ S )
% 0.32/0.47 => ( P @ A4 @ C2 ) ) )
% 0.32/0.47 => ( P @ X1 @ X22 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % relcomp.inducts
% 0.32/0.47 thf(fact_201_relcomp_Osimps,axiom,
% 0.32/0.47 ! [A1: b,A22: b,R: set_Product_prod_b_b,S: set_Product_prod_b_b] :
% 0.32/0.47 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A1 @ A22 ) @ ( relcomp_b_b_b @ R @ S ) )
% 0.32/0.47 = ( ? [A5: b,B6: b,C3: b] :
% 0.32/0.47 ( ( A1 = A5 )
% 0.32/0.47 & ( A22 = C3 )
% 0.32/0.47 & ( member1285940496od_b_b @ ( product_Pair_b_b @ A5 @ B6 ) @ R )
% 0.32/0.47 & ( member1285940496od_b_b @ ( product_Pair_b_b @ B6 @ C3 ) @ S ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % relcomp.simps
% 0.32/0.47 thf(fact_202_relcomp_Osimps,axiom,
% 0.32/0.47 ! [A1: standard_Constant_a,A22: product_prod_b_b,R: set_Pr154086431tant_a,S: set_Pr1324126435od_b_b] :
% 0.32/0.47 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A1 @ A22 ) @ ( relcom883816262od_b_b @ R @ S ) )
% 0.32/0.47 = ( ? [A5: standard_Constant_a,B6: standard_Constant_a,C3: product_prod_b_b] :
% 0.32/0.47 ( ( A1 = A5 )
% 0.32/0.47 & ( A22 = C3 )
% 0.32/0.47 & ( member1214736488tant_a @ ( produc342647tant_a @ A5 @ B6 ) @ R )
% 0.32/0.47 & ( member1516365892od_b_b @ ( produc1432590431od_b_b @ B6 @ C3 ) @ S ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % relcomp.simps
% 0.32/0.47 thf(fact_203_relcomp_Osimps,axiom,
% 0.32/0.47 ! [A1: standard_Constant_a,A22: product_prod_b_b,R: set_Pr1324126435od_b_b,S: set_Pr2007082183od_b_b] :
% 0.32/0.47 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A1 @ A22 ) @ ( relcom1823941168od_b_b @ R @ S ) )
% 0.32/0.47 = ( ? [A5: standard_Constant_a,B6: product_prod_b_b,C3: product_prod_b_b] :
% 0.32/0.47 ( ( A1 = A5 )
% 0.32/0.47 & ( A22 = C3 )
% 0.32/0.47 & ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A5 @ B6 ) @ R )
% 0.32/0.47 & ( member1652792080od_b_b @ ( produc546497367od_b_b @ B6 @ C3 ) @ S ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % relcomp.simps
% 0.32/0.47 thf(fact_204_relcomp_Ocases,axiom,
% 0.32/0.47 ! [A1: b,A22: b,R: set_Product_prod_b_b,S: set_Product_prod_b_b] :
% 0.32/0.47 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A1 @ A22 ) @ ( relcomp_b_b_b @ R @ S ) )
% 0.32/0.47 => ~ ! [B5: b] :
% 0.32/0.47 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A1 @ B5 ) @ R )
% 0.32/0.47 => ~ ( member1285940496od_b_b @ ( product_Pair_b_b @ B5 @ A22 ) @ S ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % relcomp.cases
% 0.32/0.47 thf(fact_205_relcomp_Ocases,axiom,
% 0.32/0.47 ! [A1: standard_Constant_a,A22: product_prod_b_b,R: set_Pr154086431tant_a,S: set_Pr1324126435od_b_b] :
% 0.32/0.47 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A1 @ A22 ) @ ( relcom883816262od_b_b @ R @ S ) )
% 0.32/0.47 => ~ ! [B5: standard_Constant_a] :
% 0.32/0.47 ( ( member1214736488tant_a @ ( produc342647tant_a @ A1 @ B5 ) @ R )
% 0.32/0.47 => ~ ( member1516365892od_b_b @ ( produc1432590431od_b_b @ B5 @ A22 ) @ S ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % relcomp.cases
% 0.32/0.47 thf(fact_206_relcomp_Ocases,axiom,
% 0.32/0.47 ! [A1: standard_Constant_a,A22: product_prod_b_b,R: set_Pr1324126435od_b_b,S: set_Pr2007082183od_b_b] :
% 0.32/0.47 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A1 @ A22 ) @ ( relcom1823941168od_b_b @ R @ S ) )
% 0.32/0.47 => ~ ! [B5: product_prod_b_b] :
% 0.32/0.47 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A1 @ B5 ) @ R )
% 0.32/0.47 => ~ ( member1652792080od_b_b @ ( produc546497367od_b_b @ B5 @ A22 ) @ S ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % relcomp.cases
% 0.32/0.47 thf(fact_207_relcompEpair,axiom,
% 0.32/0.47 ! [A2: b,C: b,R: set_Product_prod_b_b,S: set_Product_prod_b_b] :
% 0.32/0.47 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ C ) @ ( relcomp_b_b_b @ R @ S ) )
% 0.32/0.47 => ~ ! [B5: b] :
% 0.32/0.47 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ B5 ) @ R )
% 0.32/0.47 => ~ ( member1285940496od_b_b @ ( product_Pair_b_b @ B5 @ C ) @ S ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % relcompEpair
% 0.32/0.47 thf(fact_208_relcompEpair,axiom,
% 0.32/0.47 ! [A2: standard_Constant_a,C: product_prod_b_b,R: set_Pr154086431tant_a,S: set_Pr1324126435od_b_b] :
% 0.32/0.47 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A2 @ C ) @ ( relcom883816262od_b_b @ R @ S ) )
% 0.32/0.47 => ~ ! [B5: standard_Constant_a] :
% 0.32/0.47 ( ( member1214736488tant_a @ ( produc342647tant_a @ A2 @ B5 ) @ R )
% 0.32/0.47 => ~ ( member1516365892od_b_b @ ( produc1432590431od_b_b @ B5 @ C ) @ S ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % relcompEpair
% 0.32/0.47 thf(fact_209_relcompEpair,axiom,
% 0.32/0.47 ! [A2: standard_Constant_a,C: product_prod_b_b,R: set_Pr1324126435od_b_b,S: set_Pr2007082183od_b_b] :
% 0.32/0.47 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A2 @ C ) @ ( relcom1823941168od_b_b @ R @ S ) )
% 0.32/0.47 => ~ ! [B5: product_prod_b_b] :
% 0.32/0.47 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A2 @ B5 ) @ R )
% 0.32/0.47 => ~ ( member1652792080od_b_b @ ( produc546497367od_b_b @ B5 @ C ) @ S ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % relcompEpair
% 0.32/0.47 thf(fact_210_relcompE,axiom,
% 0.32/0.47 ! [Xz: product_prod_b_b,R: set_Product_prod_b_b,S: set_Product_prod_b_b] :
% 0.32/0.47 ( ( member1285940496od_b_b @ Xz @ ( relcomp_b_b_b @ R @ S ) )
% 0.32/0.47 => ~ ! [X4: b,Y3: b,Z2: b] :
% 0.32/0.47 ( ( Xz
% 0.32/0.47 = ( product_Pair_b_b @ X4 @ Z2 ) )
% 0.32/0.47 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ X4 @ Y3 ) @ R )
% 0.32/0.47 => ~ ( member1285940496od_b_b @ ( product_Pair_b_b @ Y3 @ Z2 ) @ S ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % relcompE
% 0.32/0.47 thf(fact_211_relcompE,axiom,
% 0.32/0.47 ! [Xz: produc1213276845od_b_b,R: set_Pr154086431tant_a,S: set_Pr1324126435od_b_b] :
% 0.32/0.47 ( ( member1516365892od_b_b @ Xz @ ( relcom883816262od_b_b @ R @ S ) )
% 0.32/0.47 => ~ ! [X4: standard_Constant_a,Y3: standard_Constant_a,Z2: product_prod_b_b] :
% 0.32/0.47 ( ( Xz
% 0.32/0.47 = ( produc1432590431od_b_b @ X4 @ Z2 ) )
% 0.32/0.47 => ( ( member1214736488tant_a @ ( produc342647tant_a @ X4 @ Y3 ) @ R )
% 0.32/0.47 => ~ ( member1516365892od_b_b @ ( produc1432590431od_b_b @ Y3 @ Z2 ) @ S ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % relcompE
% 0.32/0.47 thf(fact_212_relcompE,axiom,
% 0.32/0.47 ! [Xz: produc1213276845od_b_b,R: set_Pr1324126435od_b_b,S: set_Pr2007082183od_b_b] :
% 0.32/0.47 ( ( member1516365892od_b_b @ Xz @ ( relcom1823941168od_b_b @ R @ S ) )
% 0.32/0.47 => ~ ! [X4: standard_Constant_a,Y3: product_prod_b_b,Z2: product_prod_b_b] :
% 0.32/0.47 ( ( Xz
% 0.32/0.47 = ( produc1432590431od_b_b @ X4 @ Z2 ) )
% 0.32/0.47 => ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ X4 @ Y3 ) @ R )
% 0.32/0.47 => ~ ( member1652792080od_b_b @ ( produc546497367od_b_b @ Y3 @ Z2 ) @ S ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % relcompE
% 0.32/0.47 thf(fact_213_relcomp__Image,axiom,
% 0.32/0.47 ! [X3: set_Product_prod_b_b,Y2: set_Product_prod_b_b,Z3: set_b] :
% 0.32/0.47 ( ( image_b_b @ ( relcomp_b_b_b @ X3 @ Y2 ) @ Z3 )
% 0.32/0.47 = ( image_b_b @ Y2 @ ( image_b_b @ X3 @ Z3 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % relcomp_Image
% 0.32/0.47 thf(fact_214_Image__mono,axiom,
% 0.32/0.47 ! [R3: set_Product_prod_b_b,R: set_Product_prod_b_b,A6: set_b,A: set_b] :
% 0.32/0.47 ( ( ord_le1036320359od_b_b @ R3 @ R )
% 0.32/0.47 => ( ( ord_less_eq_set_b @ A6 @ A )
% 0.32/0.47 => ( ord_less_eq_set_b @ ( image_b_b @ R3 @ A6 ) @ ( image_b_b @ R @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Image_mono
% 0.32/0.47 thf(fact_215_agree__on__def,axiom,
% 0.32/0.47 ( agree_221379389_a_b_b
% 0.32/0.47 = ( ^ [G4: labele1159362096nt_a_b,F_1: set_Product_prod_b_b,F_2: set_Product_prod_b_b] :
% 0.32/0.47 ! [X5: b] :
% 0.32/0.47 ( ( member_b @ X5 @ ( labele1424214014nt_a_b @ G4 ) )
% 0.32/0.47 => ( ( image_b_b @ F_1 @ ( insert_b @ X5 @ bot_bot_set_b ) )
% 0.32/0.47 = ( image_b_b @ F_2 @ ( insert_b @ X5 @ bot_bot_set_b ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % agree_on_def
% 0.32/0.47 thf(fact_216_refl__on__empty,axiom,
% 0.32/0.47 refl_o1031343860_a_nat @ bot_bo2122869057_a_nat @ bot_bo1836341171_a_nat ).
% 0.32/0.47
% 0.32/0.47 % refl_on_empty
% 0.32/0.47 thf(fact_217_refl__on__empty,axiom,
% 0.32/0.47 refl_on_b @ bot_bot_set_b @ bot_bo1343651123od_b_b ).
% 0.32/0.47
% 0.32/0.47 % refl_on_empty
% 0.32/0.47 thf(fact_218_refl__on__empty,axiom,
% 0.32/0.47 refl_o1213627494_a_nat @ bot_bo1836341171_a_nat @ bot_bo1973379891_a_nat ).
% 0.32/0.47
% 0.32/0.47 % refl_on_empty
% 0.32/0.47 thf(fact_219_subrelI,axiom,
% 0.32/0.47 ! [R: set_Product_prod_b_b,S: set_Product_prod_b_b] :
% 0.32/0.47 ( ! [X4: b,Y3: b] :
% 0.32/0.47 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ X4 @ Y3 ) @ R )
% 0.32/0.47 => ( member1285940496od_b_b @ ( product_Pair_b_b @ X4 @ Y3 ) @ S ) )
% 0.32/0.47 => ( ord_le1036320359od_b_b @ R @ S ) ) ).
% 0.32/0.47
% 0.32/0.47 % subrelI
% 0.32/0.47 thf(fact_220_subrelI,axiom,
% 0.32/0.47 ! [R: set_Pr1324126435od_b_b,S: set_Pr1324126435od_b_b] :
% 0.32/0.47 ( ! [X4: standard_Constant_a,Y3: product_prod_b_b] :
% 0.32/0.47 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ X4 @ Y3 ) @ R )
% 0.32/0.47 => ( member1516365892od_b_b @ ( produc1432590431od_b_b @ X4 @ Y3 ) @ S ) )
% 0.32/0.47 => ( ord_le123089219od_b_b @ R @ S ) ) ).
% 0.32/0.47
% 0.32/0.47 % subrelI
% 0.32/0.47 thf(fact_221_graph__union__iff,axiom,
% 0.32/0.47 ! [G_1: labele1159362096nt_a_b,G_2: labele1159362096nt_a_b] :
% 0.32/0.47 ( ( ( graph_1309249505nt_a_b @ G_1 @ G_2 )
% 0.32/0.47 = G_2 )
% 0.32/0.47 = ( ( ord_le123089219od_b_b @ ( labele1741081071nt_a_b @ G_1 ) @ ( labele1741081071nt_a_b @ G_2 ) )
% 0.32/0.47 & ( ord_less_eq_set_b @ ( labele1424214014nt_a_b @ G_1 ) @ ( labele1424214014nt_a_b @ G_2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % graph_union_iff
% 0.32/0.47 thf(fact_222_restrict__subsD,axiom,
% 0.32/0.47 ! [G: labele1159362096nt_a_b] :
% 0.32/0.47 ( ( ord_le123089219od_b_b @ ( labele1741081071nt_a_b @ G ) @ ( labele1741081071nt_a_b @ ( restri446606278nt_a_b @ G ) ) )
% 0.32/0.47 => ( G
% 0.32/0.47 = ( restri446606278nt_a_b @ G ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % restrict_subsD
% 0.32/0.47 thf(fact_223_subgraph__def2,axiom,
% 0.32/0.47 ! [G_1: labele1159362096nt_a_b,G_2: labele1159362096nt_a_b] :
% 0.32/0.47 ( ( G_1
% 0.32/0.47 = ( restri446606278nt_a_b @ G_1 ) )
% 0.32/0.47 => ( ( G_2
% 0.32/0.47 = ( restri446606278nt_a_b @ G_2 ) )
% 0.32/0.47 => ( ( graph_222606102_a_b_b @ G_1 @ G_2 @ ( id_on_b @ ( labele1424214014nt_a_b @ G_1 ) ) )
% 0.32/0.47 = ( ( ord_less_eq_set_b @ ( labele1424214014nt_a_b @ G_1 ) @ ( labele1424214014nt_a_b @ G_2 ) )
% 0.32/0.47 & ( ord_le123089219od_b_b @ ( labele1741081071nt_a_b @ G_1 ) @ ( labele1741081071nt_a_b @ G_2 ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % subgraph_def2
% 0.32/0.47 thf(fact_224_subgraph__subset_I1_J,axiom,
% 0.32/0.47 ! [G_1: labele1159362096nt_a_b,G_2: labele1159362096nt_a_b] :
% 0.32/0.47 ( ( graph_222606102_a_b_b @ G_1 @ G_2 @ ( id_on_b @ ( labele1424214014nt_a_b @ G_1 ) ) )
% 0.32/0.47 => ( ord_less_eq_set_b @ ( labele1424214014nt_a_b @ G_1 ) @ ( labele1424214014nt_a_b @ G_2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % subgraph_subset(1)
% 0.32/0.47 thf(fact_225_maintainedD2,axiom,
% 0.32/0.47 ! [A: labele935650037_a_nat,B: labele935650037_a_nat,G: labele1159362096nt_a_b,F: set_Pr2106913242_nat_b] :
% 0.32/0.47 ( ( mainta1604381365_nat_b @ ( produc1676969687_a_nat @ A @ B ) @ G )
% 0.32/0.47 => ( ( graph_714568023_nat_b @ A @ G @ F )
% 0.32/0.47 => ~ ! [G5: set_Pr2106913242_nat_b] :
% 0.32/0.47 ( ( graph_714568023_nat_b @ B @ G @ G5 )
% 0.32/0.47 => ~ ( ord_le1484132922_nat_b @ F @ G5 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % maintainedD2
% 0.32/0.47 thf(fact_226_maintainedD2,axiom,
% 0.32/0.47 ! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,G: labele1159362096nt_a_b,F: set_Product_prod_b_b] :
% 0.32/0.47 ( ( mainta374363448_a_b_b @ ( produc1569511545nt_a_b @ A @ B ) @ G )
% 0.32/0.47 => ( ( graph_222606102_a_b_b @ A @ G @ F )
% 0.32/0.47 => ~ ! [G5: set_Product_prod_b_b] :
% 0.32/0.47 ( ( graph_222606102_a_b_b @ B @ G @ G5 )
% 0.32/0.47 => ~ ( ord_le1036320359od_b_b @ F @ G5 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % maintainedD2
% 0.32/0.47 thf(fact_227_Id__on__vertices__identity_I2_J,axiom,
% 0.32/0.47 ! [A2: labele1159362096nt_a_b,B3: labele1159362096nt_a_b,F: set_Product_prod_b_b,Aa: b,Ba: b] :
% 0.32/0.47 ( ( graph_222606102_a_b_b @ A2 @ B3 @ F )
% 0.32/0.47 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ Aa @ Ba ) @ F )
% 0.32/0.47 => ( member1285940496od_b_b @ ( product_Pair_b_b @ Aa @ Ba ) @ ( relcomp_b_b_b @ F @ ( id_on_b @ ( labele1424214014nt_a_b @ B3 ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Id_on_vertices_identity(2)
% 0.32/0.47 thf(fact_228_Id__on__vertices__identity_I1_J,axiom,
% 0.32/0.47 ! [A2: labele1159362096nt_a_b,B3: labele1159362096nt_a_b,F: set_Product_prod_b_b,Aa: b,Ba: b] :
% 0.32/0.47 ( ( graph_222606102_a_b_b @ A2 @ B3 @ F )
% 0.32/0.47 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ Aa @ Ba ) @ F )
% 0.32/0.47 => ( member1285940496od_b_b @ ( product_Pair_b_b @ Aa @ Ba ) @ ( relcomp_b_b_b @ ( id_on_b @ ( labele1424214014nt_a_b @ A2 ) ) @ F ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Id_on_vertices_identity(1)
% 0.32/0.47 thf(fact_229_graph__homomorphism__on__graph,axiom,
% 0.32/0.47 ! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,R2: set_Product_prod_b_b,F: b > b] :
% 0.32/0.47 ( ( graph_222606102_a_b_b @ A @ B @ R2 )
% 0.32/0.47 => ( graph_222606102_a_b_b @ A @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ B ) @ F ) @ B ) @ ( relcomp_b_b_b @ R2 @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ B ) @ F ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % graph_homomorphism_on_graph
% 0.32/0.47 thf(fact_230_singleton__insert__inj__eq,axiom,
% 0.32/0.47 ! [B3: b,A2: b,A: set_b] :
% 0.32/0.47 ( ( ( insert_b @ B3 @ bot_bot_set_b )
% 0.32/0.47 = ( insert_b @ A2 @ A ) )
% 0.32/0.47 = ( ( A2 = B3 )
% 0.32/0.47 & ( ord_less_eq_set_b @ A @ ( insert_b @ B3 @ bot_bot_set_b ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % singleton_insert_inj_eq
% 0.32/0.47 thf(fact_231_singleton__insert__inj__eq,axiom,
% 0.32/0.47 ! [B3: produc1871334759_a_nat,A2: produc1871334759_a_nat,A: set_Pr1987088711_a_nat] :
% 0.32/0.47 ( ( ( insert1574423351_a_nat @ B3 @ bot_bo1836341171_a_nat )
% 0.32/0.47 = ( insert1574423351_a_nat @ A2 @ A ) )
% 0.32/0.47 = ( ( A2 = B3 )
% 0.32/0.47 & ( ord_le1718765799_a_nat @ A @ ( insert1574423351_a_nat @ B3 @ bot_bo1836341171_a_nat ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % singleton_insert_inj_eq
% 0.32/0.47 thf(fact_232_singleton__insert__inj__eq_H,axiom,
% 0.32/0.47 ! [A2: b,A: set_b,B3: b] :
% 0.32/0.47 ( ( ( insert_b @ A2 @ A )
% 0.32/0.47 = ( insert_b @ B3 @ bot_bot_set_b ) )
% 0.32/0.47 = ( ( A2 = B3 )
% 0.32/0.47 & ( ord_less_eq_set_b @ A @ ( insert_b @ B3 @ bot_bot_set_b ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % singleton_insert_inj_eq'
% 0.32/0.47 thf(fact_233_singleton__insert__inj__eq_H,axiom,
% 0.32/0.47 ! [A2: produc1871334759_a_nat,A: set_Pr1987088711_a_nat,B3: produc1871334759_a_nat] :
% 0.32/0.47 ( ( ( insert1574423351_a_nat @ A2 @ A )
% 0.32/0.47 = ( insert1574423351_a_nat @ B3 @ bot_bo1836341171_a_nat ) )
% 0.32/0.47 = ( ( A2 = B3 )
% 0.32/0.47 & ( ord_le1718765799_a_nat @ A @ ( insert1574423351_a_nat @ B3 @ bot_bo1836341171_a_nat ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % singleton_insert_inj_eq'
% 0.32/0.47 thf(fact_234_equiv__class__subset,axiom,
% 0.32/0.47 ! [A: set_b,R: set_Product_prod_b_b,A2: b,B3: b] :
% 0.32/0.47 ( ( equiv_equiv_b @ A @ R )
% 0.32/0.47 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ B3 ) @ R )
% 0.32/0.47 => ( ord_less_eq_set_b @ ( image_b_b @ R @ ( insert_b @ A2 @ bot_bot_set_b ) ) @ ( image_b_b @ R @ ( insert_b @ B3 @ bot_bot_set_b ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % equiv_class_subset
% 0.32/0.47 thf(fact_235_equiv__class__subset,axiom,
% 0.32/0.47 ! [A: set_Pr1987088711_a_nat,R: set_Pr924198087_a_nat,A2: produc1871334759_a_nat,B3: produc1871334759_a_nat] :
% 0.32/0.47 ( ( equiv_291114781_a_nat @ A @ R )
% 0.32/0.47 => ( ( member584645392_a_nat @ ( produc1677124439_a_nat @ A2 @ B3 ) @ R )
% 0.32/0.47 => ( ord_le1718765799_a_nat @ ( image_1168831379_a_nat @ R @ ( insert1574423351_a_nat @ A2 @ bot_bo1836341171_a_nat ) ) @ ( image_1168831379_a_nat @ R @ ( insert1574423351_a_nat @ B3 @ bot_bo1836341171_a_nat ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % equiv_class_subset
% 0.32/0.47 thf(fact_236_subset__equiv__class,axiom,
% 0.32/0.47 ! [A: set_Product_prod_b_b,R: set_Pr2007082183od_b_b,B3: product_prod_b_b,A2: product_prod_b_b] :
% 0.32/0.47 ( ( equiv_1125628061od_b_b @ A @ R )
% 0.32/0.47 => ( ( ord_le1036320359od_b_b @ ( image_1928024979od_b_b @ R @ ( insert1952693431od_b_b @ B3 @ bot_bo1343651123od_b_b ) ) @ ( image_1928024979od_b_b @ R @ ( insert1952693431od_b_b @ A2 @ bot_bo1343651123od_b_b ) ) )
% 0.32/0.47 => ( ( member1285940496od_b_b @ B3 @ A )
% 0.32/0.47 => ( member1652792080od_b_b @ ( produc546497367od_b_b @ A2 @ B3 ) @ R ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % subset_equiv_class
% 0.32/0.47 thf(fact_237_subset__equiv__class,axiom,
% 0.32/0.47 ! [A: set_Pr1324126435od_b_b,R: set_Pr2109276827od_b_b,B3: produc1213276845od_b_b,A2: produc1213276845od_b_b] :
% 0.32/0.47 ( ( equiv_2048442231od_b_b @ A @ R )
% 0.32/0.47 => ( ( ord_le123089219od_b_b @ ( image_763305007od_b_b @ R @ ( insert2037698781od_b_b @ B3 @ bot_bo1664927607od_b_b ) ) @ ( image_763305007od_b_b @ R @ ( insert2037698781od_b_b @ A2 @ bot_bo1664927607od_b_b ) ) )
% 0.32/0.47 => ( ( member1516365892od_b_b @ B3 @ A )
% 0.32/0.47 => ( member1086024932od_b_b @ ( produc449289715od_b_b @ A2 @ B3 ) @ R ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % subset_equiv_class
% 0.32/0.47 thf(fact_238_subset__equiv__class,axiom,
% 0.32/0.47 ! [A: set_b,R: set_Product_prod_b_b,B3: b,A2: b] :
% 0.32/0.47 ( ( equiv_equiv_b @ A @ R )
% 0.32/0.47 => ( ( ord_less_eq_set_b @ ( image_b_b @ R @ ( insert_b @ B3 @ bot_bot_set_b ) ) @ ( image_b_b @ R @ ( insert_b @ A2 @ bot_bot_set_b ) ) )
% 0.32/0.47 => ( ( member_b @ B3 @ A )
% 0.32/0.47 => ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ B3 ) @ R ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % subset_equiv_class
% 0.32/0.47 thf(fact_239_subset__equiv__class,axiom,
% 0.32/0.47 ! [A: set_Pr1987088711_a_nat,R: set_Pr924198087_a_nat,B3: produc1871334759_a_nat,A2: produc1871334759_a_nat] :
% 0.32/0.47 ( ( equiv_291114781_a_nat @ A @ R )
% 0.32/0.47 => ( ( ord_le1718765799_a_nat @ ( image_1168831379_a_nat @ R @ ( insert1574423351_a_nat @ B3 @ bot_bo1836341171_a_nat ) ) @ ( image_1168831379_a_nat @ R @ ( insert1574423351_a_nat @ A2 @ bot_bo1836341171_a_nat ) ) )
% 0.32/0.47 => ( ( member832397200_a_nat @ B3 @ A )
% 0.32/0.47 => ( member584645392_a_nat @ ( produc1677124439_a_nat @ A2 @ B3 ) @ R ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % subset_equiv_class
% 0.32/0.47 thf(fact_240_refines__equiv__class__eq2,axiom,
% 0.32/0.47 ! [R2: set_Product_prod_b_b,S2: set_Product_prod_b_b,A: set_b,A2: b] :
% 0.32/0.47 ( ( ord_le1036320359od_b_b @ R2 @ S2 )
% 0.32/0.47 => ( ( equiv_equiv_b @ A @ R2 )
% 0.32/0.47 => ( ( equiv_equiv_b @ A @ S2 )
% 0.32/0.47 => ( ( image_b_b @ S2 @ ( image_b_b @ R2 @ ( insert_b @ A2 @ bot_bot_set_b ) ) )
% 0.32/0.47 = ( image_b_b @ S2 @ ( insert_b @ A2 @ bot_bot_set_b ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % refines_equiv_class_eq2
% 0.32/0.47 thf(fact_241_refines__equiv__class__eq2,axiom,
% 0.32/0.47 ! [R2: set_Pr924198087_a_nat,S2: set_Pr924198087_a_nat,A: set_Pr1987088711_a_nat,A2: produc1871334759_a_nat] :
% 0.32/0.47 ( ( ord_le107617383_a_nat @ R2 @ S2 )
% 0.32/0.47 => ( ( equiv_291114781_a_nat @ A @ R2 )
% 0.32/0.47 => ( ( equiv_291114781_a_nat @ A @ S2 )
% 0.32/0.47 => ( ( image_1168831379_a_nat @ S2 @ ( image_1168831379_a_nat @ R2 @ ( insert1574423351_a_nat @ A2 @ bot_bo1836341171_a_nat ) ) )
% 0.32/0.47 = ( image_1168831379_a_nat @ S2 @ ( insert1574423351_a_nat @ A2 @ bot_bo1836341171_a_nat ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % refines_equiv_class_eq2
% 0.32/0.47 thf(fact_242_empty__Collect__eq,axiom,
% 0.32/0.47 ! [P: b > $o] :
% 0.32/0.47 ( ( bot_bot_set_b
% 0.32/0.47 = ( collect_b @ P ) )
% 0.32/0.47 = ( ! [X5: b] :
% 0.32/0.47 ~ ( P @ X5 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % empty_Collect_eq
% 0.32/0.47 thf(fact_243_empty__Collect__eq,axiom,
% 0.32/0.47 ! [P: produc1871334759_a_nat > $o] :
% 0.32/0.47 ( ( bot_bo1836341171_a_nat
% 0.32/0.47 = ( collec357096914_a_nat @ P ) )
% 0.32/0.47 = ( ! [X5: produc1871334759_a_nat] :
% 0.32/0.47 ~ ( P @ X5 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % empty_Collect_eq
% 0.32/0.47 thf(fact_244_Collect__empty__eq,axiom,
% 0.32/0.47 ! [P: b > $o] :
% 0.32/0.47 ( ( ( collect_b @ P )
% 0.32/0.47 = bot_bot_set_b )
% 0.32/0.47 = ( ! [X5: b] :
% 0.32/0.47 ~ ( P @ X5 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Collect_empty_eq
% 0.32/0.47 thf(fact_245_Collect__empty__eq,axiom,
% 0.32/0.47 ! [P: produc1871334759_a_nat > $o] :
% 0.32/0.47 ( ( ( collec357096914_a_nat @ P )
% 0.32/0.47 = bot_bo1836341171_a_nat )
% 0.32/0.47 = ( ! [X5: produc1871334759_a_nat] :
% 0.32/0.47 ~ ( P @ X5 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Collect_empty_eq
% 0.32/0.47 thf(fact_246_all__not__in__conv,axiom,
% 0.32/0.47 ! [A: set_Product_prod_b_b] :
% 0.32/0.47 ( ( ! [X5: product_prod_b_b] :
% 0.32/0.47 ~ ( member1285940496od_b_b @ X5 @ A ) )
% 0.32/0.47 = ( A = bot_bo1343651123od_b_b ) ) ).
% 0.32/0.47
% 0.32/0.47 % all_not_in_conv
% 0.32/0.47 thf(fact_247_all__not__in__conv,axiom,
% 0.32/0.47 ! [A: set_Pr1324126435od_b_b] :
% 0.32/0.47 ( ( ! [X5: produc1213276845od_b_b] :
% 0.32/0.47 ~ ( member1516365892od_b_b @ X5 @ A ) )
% 0.32/0.47 = ( A = bot_bo1664927607od_b_b ) ) ).
% 0.32/0.47
% 0.32/0.47 % all_not_in_conv
% 0.32/0.47 thf(fact_248_all__not__in__conv,axiom,
% 0.32/0.47 ! [A: set_b] :
% 0.32/0.47 ( ( ! [X5: b] :
% 0.32/0.47 ~ ( member_b @ X5 @ A ) )
% 0.32/0.47 = ( A = bot_bot_set_b ) ) ).
% 0.32/0.47
% 0.32/0.47 % all_not_in_conv
% 0.32/0.47 thf(fact_249_all__not__in__conv,axiom,
% 0.32/0.47 ! [A: set_Pr1987088711_a_nat] :
% 0.32/0.47 ( ( ! [X5: produc1871334759_a_nat] :
% 0.32/0.47 ~ ( member832397200_a_nat @ X5 @ A ) )
% 0.32/0.47 = ( A = bot_bo1836341171_a_nat ) ) ).
% 0.32/0.47
% 0.32/0.47 % all_not_in_conv
% 0.32/0.47 thf(fact_250_empty__iff,axiom,
% 0.32/0.47 ! [C: product_prod_b_b] :
% 0.32/0.47 ~ ( member1285940496od_b_b @ C @ bot_bo1343651123od_b_b ) ).
% 0.32/0.47
% 0.32/0.47 % empty_iff
% 0.32/0.47 thf(fact_251_empty__iff,axiom,
% 0.32/0.47 ! [C: produc1213276845od_b_b] :
% 0.32/0.47 ~ ( member1516365892od_b_b @ C @ bot_bo1664927607od_b_b ) ).
% 0.32/0.47
% 0.32/0.47 % empty_iff
% 0.32/0.47 thf(fact_252_empty__iff,axiom,
% 0.32/0.48 ! [C: b] :
% 0.32/0.48 ~ ( member_b @ C @ bot_bot_set_b ) ).
% 0.32/0.48
% 0.32/0.48 % empty_iff
% 0.32/0.48 thf(fact_253_empty__iff,axiom,
% 0.32/0.48 ! [C: produc1871334759_a_nat] :
% 0.32/0.48 ~ ( member832397200_a_nat @ C @ bot_bo1836341171_a_nat ) ).
% 0.32/0.48
% 0.32/0.48 % empty_iff
% 0.32/0.48 thf(fact_254_subsetI,axiom,
% 0.32/0.48 ! [A: set_b,B: set_b] :
% 0.32/0.48 ( ! [X4: b] :
% 0.32/0.48 ( ( member_b @ X4 @ A )
% 0.32/0.48 => ( member_b @ X4 @ B ) )
% 0.32/0.48 => ( ord_less_eq_set_b @ A @ B ) ) ).
% 0.32/0.48
% 0.32/0.48 % subsetI
% 0.32/0.48 thf(fact_255_subsetI,axiom,
% 0.32/0.48 ! [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
% 0.32/0.48 ( ! [X4: product_prod_b_b] :
% 0.32/0.48 ( ( member1285940496od_b_b @ X4 @ A )
% 0.32/0.48 => ( member1285940496od_b_b @ X4 @ B ) )
% 0.32/0.48 => ( ord_le1036320359od_b_b @ A @ B ) ) ).
% 0.32/0.48
% 0.32/0.48 % subsetI
% 0.32/0.48 thf(fact_256_subsetI,axiom,
% 0.32/0.48 ! [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b] :
% 0.32/0.48 ( ! [X4: produc1213276845od_b_b] :
% 0.32/0.48 ( ( member1516365892od_b_b @ X4 @ A )
% 0.32/0.48 => ( member1516365892od_b_b @ X4 @ B ) )
% 0.32/0.48 => ( ord_le123089219od_b_b @ A @ B ) ) ).
% 0.32/0.48
% 0.32/0.48 % subsetI
% 0.32/0.48 thf(fact_257_insert__absorb2,axiom,
% 0.32/0.48 ! [X: b,A: set_b] :
% 0.32/0.48 ( ( insert_b @ X @ ( insert_b @ X @ A ) )
% 0.32/0.48 = ( insert_b @ X @ A ) ) ).
% 0.32/0.48
% 0.32/0.48 % insert_absorb2
% 0.32/0.48 thf(fact_258_insert__absorb2,axiom,
% 0.32/0.48 ! [X: produc1871334759_a_nat,A: set_Pr1987088711_a_nat] :
% 0.32/0.48 ( ( insert1574423351_a_nat @ X @ ( insert1574423351_a_nat @ X @ A ) )
% 0.32/0.48 = ( insert1574423351_a_nat @ X @ A ) ) ).
% 0.32/0.48
% 0.32/0.48 % insert_absorb2
% 0.32/0.48 thf(fact_259_insert__iff,axiom,
% 0.32/0.48 ! [A2: produc1871334759_a_nat,B3: produc1871334759_a_nat,A: set_Pr1987088711_a_nat] :
% 0.32/0.48 ( ( member832397200_a_nat @ A2 @ ( insert1574423351_a_nat @ B3 @ A ) )
% 0.32/0.48 = ( ( A2 = B3 )
% 0.32/0.48 | ( member832397200_a_nat @ A2 @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % insert_iff
% 0.32/0.48 thf(fact_260_insert__iff,axiom,
% 0.32/0.48 ! [A2: b,B3: b,A: set_b] :
% 0.32/0.48 ( ( member_b @ A2 @ ( insert_b @ B3 @ A ) )
% 0.32/0.48 = ( ( A2 = B3 )
% 0.32/0.48 | ( member_b @ A2 @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % insert_iff
% 0.32/0.48 thf(fact_261_insert__iff,axiom,
% 0.32/0.48 ! [A2: product_prod_b_b,B3: product_prod_b_b,A: set_Product_prod_b_b] :
% 0.32/0.48 ( ( member1285940496od_b_b @ A2 @ ( insert1952693431od_b_b @ B3 @ A ) )
% 0.32/0.48 = ( ( A2 = B3 )
% 0.32/0.48 | ( member1285940496od_b_b @ A2 @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % insert_iff
% 0.32/0.48 thf(fact_262_insert__iff,axiom,
% 0.32/0.48 ! [A2: produc1213276845od_b_b,B3: produc1213276845od_b_b,A: set_Pr1324126435od_b_b] :
% 0.32/0.48 ( ( member1516365892od_b_b @ A2 @ ( insert2037698781od_b_b @ B3 @ A ) )
% 0.32/0.48 = ( ( A2 = B3 )
% 0.32/0.48 | ( member1516365892od_b_b @ A2 @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % insert_iff
% 0.32/0.48 thf(fact_263_insertCI,axiom,
% 0.32/0.48 ! [A2: produc1871334759_a_nat,B: set_Pr1987088711_a_nat,B3: produc1871334759_a_nat] :
% 0.32/0.48 ( ( ~ ( member832397200_a_nat @ A2 @ B )
% 0.32/0.48 => ( A2 = B3 ) )
% 0.32/0.48 => ( member832397200_a_nat @ A2 @ ( insert1574423351_a_nat @ B3 @ B ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % insertCI
% 0.32/0.48 thf(fact_264_insertCI,axiom,
% 0.32/0.48 ! [A2: b,B: set_b,B3: b] :
% 0.32/0.48 ( ( ~ ( member_b @ A2 @ B )
% 0.32/0.48 => ( A2 = B3 ) )
% 0.32/0.48 => ( member_b @ A2 @ ( insert_b @ B3 @ B ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % insertCI
% 0.32/0.48 thf(fact_265_insertCI,axiom,
% 0.32/0.48 ! [A2: product_prod_b_b,B: set_Product_prod_b_b,B3: product_prod_b_b] :
% 0.32/0.48 ( ( ~ ( member1285940496od_b_b @ A2 @ B )
% 0.32/0.48 => ( A2 = B3 ) )
% 0.32/0.48 => ( member1285940496od_b_b @ A2 @ ( insert1952693431od_b_b @ B3 @ B ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % insertCI
% 0.32/0.48 thf(fact_266_insertCI,axiom,
% 0.32/0.48 ! [A2: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,B3: produc1213276845od_b_b] :
% 0.32/0.48 ( ( ~ ( member1516365892od_b_b @ A2 @ B )
% 0.32/0.48 => ( A2 = B3 ) )
% 0.32/0.48 => ( member1516365892od_b_b @ A2 @ ( insert2037698781od_b_b @ B3 @ B ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % insertCI
% 0.32/0.48 thf(fact_267_empty__subsetI,axiom,
% 0.32/0.48 ! [A: set_b] : ( ord_less_eq_set_b @ bot_bot_set_b @ A ) ).
% 0.32/0.48
% 0.32/0.48 % empty_subsetI
% 0.32/0.48 thf(fact_268_empty__subsetI,axiom,
% 0.32/0.48 ! [A: set_Pr1987088711_a_nat] : ( ord_le1718765799_a_nat @ bot_bo1836341171_a_nat @ A ) ).
% 0.32/0.48
% 0.32/0.48 % empty_subsetI
% 0.32/0.48 thf(fact_269_subset__empty,axiom,
% 0.32/0.48 ! [A: set_b] :
% 0.32/0.48 ( ( ord_less_eq_set_b @ A @ bot_bot_set_b )
% 0.32/0.48 = ( A = bot_bot_set_b ) ) ).
% 0.32/0.48
% 0.32/0.48 % subset_empty
% 0.32/0.48 thf(fact_270_subset__empty,axiom,
% 0.32/0.48 ! [A: set_Pr1987088711_a_nat] :
% 0.32/0.48 ( ( ord_le1718765799_a_nat @ A @ bot_bo1836341171_a_nat )
% 0.32/0.48 = ( A = bot_bo1836341171_a_nat ) ) ).
% 0.32/0.48
% 0.32/0.48 % subset_empty
% 0.32/0.48 thf(fact_271_singletonI,axiom,
% 0.32/0.48 ! [A2: product_prod_b_b] : ( member1285940496od_b_b @ A2 @ ( insert1952693431od_b_b @ A2 @ bot_bo1343651123od_b_b ) ) ).
% 0.32/0.48
% 0.32/0.48 % singletonI
% 0.32/0.48 thf(fact_272_singletonI,axiom,
% 0.32/0.48 ! [A2: produc1213276845od_b_b] : ( member1516365892od_b_b @ A2 @ ( insert2037698781od_b_b @ A2 @ bot_bo1664927607od_b_b ) ) ).
% 0.32/0.48
% 0.32/0.48 % singletonI
% 0.32/0.48 thf(fact_273_singletonI,axiom,
% 0.32/0.48 ! [A2: b] : ( member_b @ A2 @ ( insert_b @ A2 @ bot_bot_set_b ) ) ).
% 0.32/0.48
% 0.32/0.48 % singletonI
% 0.32/0.48 thf(fact_274_singletonI,axiom,
% 0.32/0.48 ! [A2: produc1871334759_a_nat] : ( member832397200_a_nat @ A2 @ ( insert1574423351_a_nat @ A2 @ bot_bo1836341171_a_nat ) ) ).
% 0.32/0.48
% 0.32/0.48 % singletonI
% 0.32/0.48 thf(fact_275_insert__subset,axiom,
% 0.32/0.48 ! [X: produc1871334759_a_nat,A: set_Pr1987088711_a_nat,B: set_Pr1987088711_a_nat] :
% 0.32/0.48 ( ( ord_le1718765799_a_nat @ ( insert1574423351_a_nat @ X @ A ) @ B )
% 0.32/0.48 = ( ( member832397200_a_nat @ X @ B )
% 0.32/0.48 & ( ord_le1718765799_a_nat @ A @ B ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % insert_subset
% 0.32/0.48 thf(fact_276_insert__subset,axiom,
% 0.32/0.48 ! [X: b,A: set_b,B: set_b] :
% 0.32/0.48 ( ( ord_less_eq_set_b @ ( insert_b @ X @ A ) @ B )
% 0.32/0.48 = ( ( member_b @ X @ B )
% 0.32/0.48 & ( ord_less_eq_set_b @ A @ B ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % insert_subset
% 0.32/0.48 thf(fact_277_insert__subset,axiom,
% 0.32/0.48 ! [X: product_prod_b_b,A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
% 0.32/0.48 ( ( ord_le1036320359od_b_b @ ( insert1952693431od_b_b @ X @ A ) @ B )
% 0.32/0.48 = ( ( member1285940496od_b_b @ X @ B )
% 0.32/0.48 & ( ord_le1036320359od_b_b @ A @ B ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % insert_subset
% 0.32/0.48 thf(fact_278_insert__subset,axiom,
% 0.32/0.48 ! [X: produc1213276845od_b_b,A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b] :
% 0.32/0.48 ( ( ord_le123089219od_b_b @ ( insert2037698781od_b_b @ X @ A ) @ B )
% 0.32/0.48 = ( ( member1516365892od_b_b @ X @ B )
% 0.32/0.48 & ( ord_le123089219od_b_b @ A @ B ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % insert_subset
% 0.32/0.48 thf(fact_279_relcomp__empty1,axiom,
% 0.32/0.48 ! [R2: set_Pr1987088711_a_nat] :
% 0.32/0.48 ( ( relcom1338300020_a_nat @ bot_bo1836341171_a_nat @ R2 )
% 0.32/0.48 = bot_bo1836341171_a_nat ) ).
% 0.32/0.48
% 0.32/0.48 % relcomp_empty1
% 0.32/0.48 thf(fact_280_relcomp__empty2,axiom,
% 0.32/0.48 ! [R2: set_Pr1987088711_a_nat] :
% 0.32/0.48 ( ( relcom1338300020_a_nat @ R2 @ bot_bo1836341171_a_nat )
% 0.32/0.48 = bot_bo1836341171_a_nat ) ).
% 0.32/0.48
% 0.32/0.48 % relcomp_empty2
% 0.32/0.48 thf(fact_281_graph__empty__e,axiom,
% 0.32/0.48 ! [V: set_b] :
% 0.32/0.48 ( ( labele1230159100nt_a_b @ bot_bo1664927607od_b_b @ V )
% 0.32/0.48 = ( restri446606278nt_a_b @ ( labele1230159100nt_a_b @ bot_bo1664927607od_b_b @ V ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % graph_empty_e
% 0.32/0.48 thf(fact_282_graph__homomorphism__nonempty,axiom,
% 0.32/0.48 ! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,F: set_Product_prod_b_b,E: allego510293162tant_a] :
% 0.32/0.48 ( ( graph_222606102_a_b_b @ A @ B @ F )
% 0.32/0.48 => ( ( ( semant55076487nt_a_b @ A @ E )
% 0.32/0.48 != bot_bo1343651123od_b_b )
% 0.32/0.48 => ( ( semant55076487nt_a_b @ B @ E )
% 0.32/0.48 != bot_bo1343651123od_b_b ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % graph_homomorphism_nonempty
% 0.32/0.48 thf(fact_283_ex__in__conv,axiom,
% 0.32/0.48 ! [A: set_Product_prod_b_b] :
% 0.32/0.48 ( ( ? [X5: product_prod_b_b] : ( member1285940496od_b_b @ X5 @ A ) )
% 0.32/0.48 = ( A != bot_bo1343651123od_b_b ) ) ).
% 0.32/0.48
% 0.32/0.48 % ex_in_conv
% 0.32/0.48 thf(fact_284_ex__in__conv,axiom,
% 0.32/0.48 ! [A: set_Pr1324126435od_b_b] :
% 0.32/0.48 ( ( ? [X5: produc1213276845od_b_b] : ( member1516365892od_b_b @ X5 @ A ) )
% 0.32/0.48 = ( A != bot_bo1664927607od_b_b ) ) ).
% 0.32/0.48
% 0.32/0.48 % ex_in_conv
% 0.32/0.48 thf(fact_285_ex__in__conv,axiom,
% 0.32/0.48 ! [A: set_b] :
% 0.32/0.48 ( ( ? [X5: b] : ( member_b @ X5 @ A ) )
% 0.32/0.48 = ( A != bot_bot_set_b ) ) ).
% 0.32/0.48
% 0.32/0.48 % ex_in_conv
% 0.32/0.48 thf(fact_286_ex__in__conv,axiom,
% 0.32/0.48 ! [A: set_Pr1987088711_a_nat] :
% 0.32/0.48 ( ( ? [X5: produc1871334759_a_nat] : ( member832397200_a_nat @ X5 @ A ) )
% 0.32/0.48 = ( A != bot_bo1836341171_a_nat ) ) ).
% 0.32/0.48
% 0.32/0.48 % ex_in_conv
% 0.32/0.48 thf(fact_287_equals0I,axiom,
% 0.32/0.48 ! [A: set_Product_prod_b_b] :
% 0.32/0.48 ( ! [Y3: product_prod_b_b] :
% 0.32/0.48 ~ ( member1285940496od_b_b @ Y3 @ A )
% 0.32/0.48 => ( A = bot_bo1343651123od_b_b ) ) ).
% 0.32/0.48
% 0.32/0.48 % equals0I
% 0.32/0.48 thf(fact_288_equals0I,axiom,
% 0.32/0.48 ! [A: set_Pr1324126435od_b_b] :
% 0.32/0.48 ( ! [Y3: produc1213276845od_b_b] :
% 0.32/0.48 ~ ( member1516365892od_b_b @ Y3 @ A )
% 0.32/0.48 => ( A = bot_bo1664927607od_b_b ) ) ).
% 0.32/0.48
% 0.32/0.48 % equals0I
% 0.32/0.48 thf(fact_289_equals0I,axiom,
% 0.32/0.48 ! [A: set_b] :
% 0.32/0.48 ( ! [Y3: b] :
% 0.32/0.48 ~ ( member_b @ Y3 @ A )
% 0.32/0.48 => ( A = bot_bot_set_b ) ) ).
% 0.32/0.48
% 0.32/0.48 % equals0I
% 0.32/0.48 thf(fact_290_equals0I,axiom,
% 0.32/0.48 ! [A: set_Pr1987088711_a_nat] :
% 0.32/0.48 ( ! [Y3: produc1871334759_a_nat] :
% 0.32/0.48 ~ ( member832397200_a_nat @ Y3 @ A )
% 0.32/0.48 => ( A = bot_bo1836341171_a_nat ) ) ).
% 0.32/0.48
% 0.32/0.48 % equals0I
% 0.32/0.48 thf(fact_291_equals0D,axiom,
% 0.32/0.48 ! [A: set_Product_prod_b_b,A2: product_prod_b_b] :
% 0.32/0.48 ( ( A = bot_bo1343651123od_b_b )
% 0.32/0.48 => ~ ( member1285940496od_b_b @ A2 @ A ) ) ).
% 0.32/0.48
% 0.32/0.48 % equals0D
% 0.32/0.48 thf(fact_292_equals0D,axiom,
% 0.32/0.48 ! [A: set_Pr1324126435od_b_b,A2: produc1213276845od_b_b] :
% 0.32/0.48 ( ( A = bot_bo1664927607od_b_b )
% 0.32/0.48 => ~ ( member1516365892od_b_b @ A2 @ A ) ) ).
% 0.32/0.48
% 0.32/0.48 % equals0D
% 0.32/0.48 thf(fact_293_equals0D,axiom,
% 0.32/0.48 ! [A: set_b,A2: b] :
% 0.32/0.48 ( ( A = bot_bot_set_b )
% 0.32/0.48 => ~ ( member_b @ A2 @ A ) ) ).
% 0.32/0.48
% 0.32/0.48 % equals0D
% 0.32/0.48 thf(fact_294_equals0D,axiom,
% 0.32/0.48 ! [A: set_Pr1987088711_a_nat,A2: produc1871334759_a_nat] :
% 0.32/0.48 ( ( A = bot_bo1836341171_a_nat )
% 0.32/0.48 => ~ ( member832397200_a_nat @ A2 @ A ) ) ).
% 0.32/0.48
% 0.32/0.48 % equals0D
% 0.32/0.48 thf(fact_295_emptyE,axiom,
% 0.32/0.48 ! [A2: product_prod_b_b] :
% 0.32/0.48 ~ ( member1285940496od_b_b @ A2 @ bot_bo1343651123od_b_b ) ).
% 0.32/0.48
% 0.32/0.48 % emptyE
% 0.32/0.48 thf(fact_296_emptyE,axiom,
% 0.32/0.48 ! [A2: produc1213276845od_b_b] :
% 0.32/0.48 ~ ( member1516365892od_b_b @ A2 @ bot_bo1664927607od_b_b ) ).
% 0.32/0.48
% 0.32/0.48 % emptyE
% 0.32/0.48 thf(fact_297_emptyE,axiom,
% 0.32/0.48 ! [A2: b] :
% 0.32/0.48 ~ ( member_b @ A2 @ bot_bot_set_b ) ).
% 0.32/0.48
% 0.32/0.48 % emptyE
% 0.32/0.48 thf(fact_298_emptyE,axiom,
% 0.32/0.48 ! [A2: produc1871334759_a_nat] :
% 0.32/0.48 ~ ( member832397200_a_nat @ A2 @ bot_bo1836341171_a_nat ) ).
% 0.32/0.48
% 0.32/0.48 % emptyE
% 0.32/0.48 thf(fact_299_subset__iff,axiom,
% 0.32/0.48 ( ord_less_eq_set_b
% 0.32/0.48 = ( ^ [A7: set_b,B7: set_b] :
% 0.32/0.48 ! [T: b] :
% 0.32/0.48 ( ( member_b @ T @ A7 )
% 0.32/0.48 => ( member_b @ T @ B7 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % subset_iff
% 0.32/0.48 thf(fact_300_subset__iff,axiom,
% 0.32/0.48 ( ord_le1036320359od_b_b
% 0.32/0.48 = ( ^ [A7: set_Product_prod_b_b,B7: set_Product_prod_b_b] :
% 0.32/0.48 ! [T: product_prod_b_b] :
% 0.32/0.48 ( ( member1285940496od_b_b @ T @ A7 )
% 0.32/0.48 => ( member1285940496od_b_b @ T @ B7 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % subset_iff
% 0.32/0.48 thf(fact_301_subset__iff,axiom,
% 0.32/0.48 ( ord_le123089219od_b_b
% 0.32/0.48 = ( ^ [A7: set_Pr1324126435od_b_b,B7: set_Pr1324126435od_b_b] :
% 0.32/0.48 ! [T: produc1213276845od_b_b] :
% 0.32/0.48 ( ( member1516365892od_b_b @ T @ A7 )
% 0.32/0.48 => ( member1516365892od_b_b @ T @ B7 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % subset_iff
% 0.32/0.48 thf(fact_302_subset__eq,axiom,
% 0.32/0.48 ( ord_less_eq_set_b
% 0.32/0.48 = ( ^ [A7: set_b,B7: set_b] :
% 0.32/0.48 ! [X5: b] :
% 0.32/0.48 ( ( member_b @ X5 @ A7 )
% 0.32/0.48 => ( member_b @ X5 @ B7 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % subset_eq
% 0.32/0.48 thf(fact_303_subset__eq,axiom,
% 0.32/0.48 ( ord_le1036320359od_b_b
% 0.32/0.48 = ( ^ [A7: set_Product_prod_b_b,B7: set_Product_prod_b_b] :
% 0.32/0.48 ! [X5: product_prod_b_b] :
% 0.32/0.48 ( ( member1285940496od_b_b @ X5 @ A7 )
% 0.32/0.48 => ( member1285940496od_b_b @ X5 @ B7 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % subset_eq
% 0.32/0.48 thf(fact_304_subset__eq,axiom,
% 0.32/0.48 ( ord_le123089219od_b_b
% 0.32/0.48 = ( ^ [A7: set_Pr1324126435od_b_b,B7: set_Pr1324126435od_b_b] :
% 0.32/0.48 ! [X5: produc1213276845od_b_b] :
% 0.32/0.48 ( ( member1516365892od_b_b @ X5 @ A7 )
% 0.32/0.48 => ( member1516365892od_b_b @ X5 @ B7 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % subset_eq
% 0.32/0.48 thf(fact_305_subsetD,axiom,
% 0.32/0.48 ! [A: set_b,B: set_b,C: b] :
% 0.32/0.48 ( ( ord_less_eq_set_b @ A @ B )
% 0.32/0.48 => ( ( member_b @ C @ A )
% 0.32/0.48 => ( member_b @ C @ B ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % subsetD
% 0.32/0.48 thf(fact_306_subsetD,axiom,
% 0.32/0.48 ! [A: set_Product_prod_b_b,B: set_Product_prod_b_b,C: product_prod_b_b] :
% 0.32/0.48 ( ( ord_le1036320359od_b_b @ A @ B )
% 0.32/0.48 => ( ( member1285940496od_b_b @ C @ A )
% 0.32/0.48 => ( member1285940496od_b_b @ C @ B ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % subsetD
% 0.32/0.48 thf(fact_307_subsetD,axiom,
% 0.32/0.48 ! [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b,C: produc1213276845od_b_b] :
% 0.32/0.48 ( ( ord_le123089219od_b_b @ A @ B )
% 0.32/0.48 => ( ( member1516365892od_b_b @ C @ A )
% 0.32/0.48 => ( member1516365892od_b_b @ C @ B ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % subsetD
% 0.32/0.48 thf(fact_308_in__mono,axiom,
% 0.32/0.48 ! [A: set_b,B: set_b,X: b] :
% 0.32/0.48 ( ( ord_less_eq_set_b @ A @ B )
% 0.32/0.48 => ( ( member_b @ X @ A )
% 0.32/0.48 => ( member_b @ X @ B ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % in_mono
% 0.32/0.48 thf(fact_309_in__mono,axiom,
% 0.32/0.48 ! [A: set_Product_prod_b_b,B: set_Product_prod_b_b,X: product_prod_b_b] :
% 0.32/0.48 ( ( ord_le1036320359od_b_b @ A @ B )
% 0.32/0.48 => ( ( member1285940496od_b_b @ X @ A )
% 0.32/0.48 => ( member1285940496od_b_b @ X @ B ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % in_mono
% 0.32/0.48 thf(fact_310_in__mono,axiom,
% 0.32/0.48 ! [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b,X: produc1213276845od_b_b] :
% 0.32/0.48 ( ( ord_le123089219od_b_b @ A @ B )
% 0.32/0.48 => ( ( member1516365892od_b_b @ X @ A )
% 0.32/0.48 => ( member1516365892od_b_b @ X @ B ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % in_mono
% 0.32/0.48 thf(fact_311_mk__disjoint__insert,axiom,
% 0.32/0.48 ! [A2: produc1871334759_a_nat,A: set_Pr1987088711_a_nat] :
% 0.32/0.48 ( ( member832397200_a_nat @ A2 @ A )
% 0.32/0.48 => ? [B8: set_Pr1987088711_a_nat] :
% 0.32/0.48 ( ( A
% 0.32/0.48 = ( insert1574423351_a_nat @ A2 @ B8 ) )
% 0.32/0.48 & ~ ( member832397200_a_nat @ A2 @ B8 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % mk_disjoint_insert
% 0.32/0.48 thf(fact_312_mk__disjoint__insert,axiom,
% 0.32/0.48 ! [A2: b,A: set_b] :
% 0.32/0.48 ( ( member_b @ A2 @ A )
% 0.32/0.48 => ? [B8: set_b] :
% 0.32/0.48 ( ( A
% 0.32/0.48 = ( insert_b @ A2 @ B8 ) )
% 0.32/0.48 & ~ ( member_b @ A2 @ B8 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % mk_disjoint_insert
% 0.32/0.48 thf(fact_313_mk__disjoint__insert,axiom,
% 0.32/0.48 ! [A2: product_prod_b_b,A: set_Product_prod_b_b] :
% 0.32/0.48 ( ( member1285940496od_b_b @ A2 @ A )
% 0.32/0.48 => ? [B8: set_Product_prod_b_b] :
% 0.32/0.48 ( ( A
% 0.32/0.48 = ( insert1952693431od_b_b @ A2 @ B8 ) )
% 0.32/0.48 & ~ ( member1285940496od_b_b @ A2 @ B8 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % mk_disjoint_insert
% 0.32/0.48 thf(fact_314_mk__disjoint__insert,axiom,
% 0.32/0.48 ! [A2: produc1213276845od_b_b,A: set_Pr1324126435od_b_b] :
% 0.32/0.48 ( ( member1516365892od_b_b @ A2 @ A )
% 0.32/0.48 => ? [B8: set_Pr1324126435od_b_b] :
% 0.32/0.48 ( ( A
% 0.32/0.48 = ( insert2037698781od_b_b @ A2 @ B8 ) )
% 0.32/0.48 & ~ ( member1516365892od_b_b @ A2 @ B8 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % mk_disjoint_insert
% 0.32/0.48 thf(fact_315_insert__commute,axiom,
% 0.32/0.48 ! [X: b,Y: b,A: set_b] :
% 0.32/0.48 ( ( insert_b @ X @ ( insert_b @ Y @ A ) )
% 0.32/0.48 = ( insert_b @ Y @ ( insert_b @ X @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % insert_commute
% 0.32/0.48 thf(fact_316_insert__commute,axiom,
% 0.32/0.48 ! [X: produc1871334759_a_nat,Y: produc1871334759_a_nat,A: set_Pr1987088711_a_nat] :
% 0.32/0.48 ( ( insert1574423351_a_nat @ X @ ( insert1574423351_a_nat @ Y @ A ) )
% 0.32/0.48 = ( insert1574423351_a_nat @ Y @ ( insert1574423351_a_nat @ X @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % insert_commute
% 0.32/0.48 thf(fact_317_insert__eq__iff,axiom,
% 0.32/0.48 ! [A2: produc1871334759_a_nat,A: set_Pr1987088711_a_nat,B3: produc1871334759_a_nat,B: set_Pr1987088711_a_nat] :
% 0.32/0.48 ( ~ ( member832397200_a_nat @ A2 @ A )
% 0.32/0.48 => ( ~ ( member832397200_a_nat @ B3 @ B )
% 0.32/0.48 => ( ( ( insert1574423351_a_nat @ A2 @ A )
% 0.32/0.48 = ( insert1574423351_a_nat @ B3 @ B ) )
% 0.32/0.48 = ( ( ( A2 = B3 )
% 0.32/0.48 => ( A = B ) )
% 0.32/0.48 & ( ( A2 != B3 )
% 0.32/0.48 => ? [C4: set_Pr1987088711_a_nat] :
% 0.32/0.48 ( ( A
% 0.32/0.48 = ( insert1574423351_a_nat @ B3 @ C4 ) )
% 0.32/0.48 & ~ ( member832397200_a_nat @ B3 @ C4 )
% 0.32/0.48 & ( B
% 0.32/0.48 = ( insert1574423351_a_nat @ A2 @ C4 ) )
% 0.32/0.48 & ~ ( member832397200_a_nat @ A2 @ C4 ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % insert_eq_iff
% 0.32/0.48 thf(fact_318_insert__eq__iff,axiom,
% 0.32/0.48 ! [A2: b,A: set_b,B3: b,B: set_b] :
% 0.32/0.48 ( ~ ( member_b @ A2 @ A )
% 0.32/0.48 => ( ~ ( member_b @ B3 @ B )
% 0.32/0.48 => ( ( ( insert_b @ A2 @ A )
% 0.32/0.48 = ( insert_b @ B3 @ B ) )
% 0.32/0.48 = ( ( ( A2 = B3 )
% 0.32/0.48 => ( A = B ) )
% 0.32/0.48 & ( ( A2 != B3 )
% 0.32/0.48 => ? [C4: set_b] :
% 0.32/0.48 ( ( A
% 0.32/0.48 = ( insert_b @ B3 @ C4 ) )
% 0.32/0.48 & ~ ( member_b @ B3 @ C4 )
% 0.32/0.48 & ( B
% 0.32/0.48 = ( insert_b @ A2 @ C4 ) )
% 0.32/0.48 & ~ ( member_b @ A2 @ C4 ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % insert_eq_iff
% 0.32/0.48 thf(fact_319_insert__eq__iff,axiom,
% 0.32/0.48 ! [A2: product_prod_b_b,A: set_Product_prod_b_b,B3: product_prod_b_b,B: set_Product_prod_b_b] :
% 0.32/0.48 ( ~ ( member1285940496od_b_b @ A2 @ A )
% 0.32/0.48 => ( ~ ( member1285940496od_b_b @ B3 @ B )
% 0.32/0.48 => ( ( ( insert1952693431od_b_b @ A2 @ A )
% 0.32/0.48 = ( insert1952693431od_b_b @ B3 @ B ) )
% 0.32/0.48 = ( ( ( A2 = B3 )
% 0.32/0.48 => ( A = B ) )
% 0.32/0.48 & ( ( A2 != B3 )
% 0.32/0.48 => ? [C4: set_Product_prod_b_b] :
% 0.32/0.48 ( ( A
% 0.32/0.48 = ( insert1952693431od_b_b @ B3 @ C4 ) )
% 0.32/0.48 & ~ ( member1285940496od_b_b @ B3 @ C4 )
% 0.32/0.48 & ( B
% 0.32/0.48 = ( insert1952693431od_b_b @ A2 @ C4 ) )
% 0.32/0.48 & ~ ( member1285940496od_b_b @ A2 @ C4 ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % insert_eq_iff
% 0.32/0.48 thf(fact_320_insert__eq__iff,axiom,
% 0.32/0.48 ! [A2: produc1213276845od_b_b,A: set_Pr1324126435od_b_b,B3: produc1213276845od_b_b,B: set_Pr1324126435od_b_b] :
% 0.32/0.48 ( ~ ( member1516365892od_b_b @ A2 @ A )
% 0.32/0.48 => ( ~ ( member1516365892od_b_b @ B3 @ B )
% 0.32/0.48 => ( ( ( insert2037698781od_b_b @ A2 @ A )
% 0.32/0.48 = ( insert2037698781od_b_b @ B3 @ B ) )
% 0.32/0.48 = ( ( ( A2 = B3 )
% 0.32/0.48 => ( A = B ) )
% 0.32/0.48 & ( ( A2 != B3 )
% 0.32/0.48 => ? [C4: set_Pr1324126435od_b_b] :
% 0.32/0.48 ( ( A
% 0.32/0.48 = ( insert2037698781od_b_b @ B3 @ C4 ) )
% 0.32/0.48 & ~ ( member1516365892od_b_b @ B3 @ C4 )
% 0.32/0.48 & ( B
% 0.32/0.48 = ( insert2037698781od_b_b @ A2 @ C4 ) )
% 0.32/0.48 & ~ ( member1516365892od_b_b @ A2 @ C4 ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % insert_eq_iff
% 0.32/0.48 thf(fact_321_insert__absorb,axiom,
% 0.32/0.48 ! [A2: produc1871334759_a_nat,A: set_Pr1987088711_a_nat] :
% 0.32/0.48 ( ( member832397200_a_nat @ A2 @ A )
% 0.32/0.48 => ( ( insert1574423351_a_nat @ A2 @ A )
% 0.32/0.48 = A ) ) ).
% 0.32/0.48
% 0.32/0.48 % insert_absorb
% 0.32/0.48 thf(fact_322_insert__absorb,axiom,
% 0.32/0.48 ! [A2: b,A: set_b] :
% 0.32/0.48 ( ( member_b @ A2 @ A )
% 0.32/0.48 => ( ( insert_b @ A2 @ A )
% 0.32/0.48 = A ) ) ).
% 0.32/0.48
% 0.32/0.48 % insert_absorb
% 0.32/0.48 thf(fact_323_insert__absorb,axiom,
% 0.32/0.48 ! [A2: product_prod_b_b,A: set_Product_prod_b_b] :
% 0.32/0.48 ( ( member1285940496od_b_b @ A2 @ A )
% 0.32/0.48 => ( ( insert1952693431od_b_b @ A2 @ A )
% 0.32/0.48 = A ) ) ).
% 0.32/0.48
% 0.32/0.48 % insert_absorb
% 0.32/0.48 thf(fact_324_insert__absorb,axiom,
% 0.32/0.48 ! [A2: produc1213276845od_b_b,A: set_Pr1324126435od_b_b] :
% 0.32/0.48 ( ( member1516365892od_b_b @ A2 @ A )
% 0.32/0.48 => ( ( insert2037698781od_b_b @ A2 @ A )
% 0.32/0.48 = A ) ) ).
% 0.32/0.48
% 0.32/0.48 % insert_absorb
% 0.32/0.48 thf(fact_325_insert__ident,axiom,
% 0.32/0.48 ! [X: produc1871334759_a_nat,A: set_Pr1987088711_a_nat,B: set_Pr1987088711_a_nat] :
% 0.32/0.48 ( ~ ( member832397200_a_nat @ X @ A )
% 0.32/0.48 => ( ~ ( member832397200_a_nat @ X @ B )
% 0.32/0.48 => ( ( ( insert1574423351_a_nat @ X @ A )
% 0.32/0.48 = ( insert1574423351_a_nat @ X @ B ) )
% 0.32/0.48 = ( A = B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % insert_ident
% 0.32/0.48 thf(fact_326_insert__ident,axiom,
% 0.32/0.48 ! [X: b,A: set_b,B: set_b] :
% 0.32/0.48 ( ~ ( member_b @ X @ A )
% 0.32/0.48 => ( ~ ( member_b @ X @ B )
% 0.32/0.48 => ( ( ( insert_b @ X @ A )
% 0.32/0.48 = ( insert_b @ X @ B ) )
% 0.32/0.48 = ( A = B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % insert_ident
% 0.32/0.48 thf(fact_327_insert__ident,axiom,
% 0.32/0.48 ! [X: product_prod_b_b,A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
% 0.32/0.48 ( ~ ( member1285940496od_b_b @ X @ A )
% 0.32/0.48 => ( ~ ( member1285940496od_b_b @ X @ B )
% 0.32/0.48 => ( ( ( insert1952693431od_b_b @ X @ A )
% 0.32/0.48 = ( insert1952693431od_b_b @ X @ B ) )
% 0.32/0.48 = ( A = B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % insert_ident
% 0.32/0.48 thf(fact_328_insert__ident,axiom,
% 0.32/0.48 ! [X: produc1213276845od_b_b,A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b] :
% 0.32/0.48 ( ~ ( member1516365892od_b_b @ X @ A )
% 0.32/0.48 => ( ~ ( member1516365892od_b_b @ X @ B )
% 0.32/0.48 => ( ( ( insert2037698781od_b_b @ X @ A )
% 0.32/0.48 = ( insert2037698781od_b_b @ X @ B ) )
% 0.32/0.48 = ( A = B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % insert_ident
% 0.32/0.48 thf(fact_329_Set_Oset__insert,axiom,
% 0.32/0.48 ! [X: produc1871334759_a_nat,A: set_Pr1987088711_a_nat] :
% 0.32/0.48 ( ( member832397200_a_nat @ X @ A )
% 0.32/0.48 => ~ ! [B8: set_Pr1987088711_a_nat] :
% 0.32/0.48 ( ( A
% 0.32/0.48 = ( insert1574423351_a_nat @ X @ B8 ) )
% 0.32/0.48 => ( member832397200_a_nat @ X @ B8 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Set.set_insert
% 0.32/0.48 thf(fact_330_Set_Oset__insert,axiom,
% 0.32/0.48 ! [X: b,A: set_b] :
% 0.32/0.48 ( ( member_b @ X @ A )
% 0.32/0.48 => ~ ! [B8: set_b] :
% 0.32/0.48 ( ( A
% 0.32/0.48 = ( insert_b @ X @ B8 ) )
% 0.32/0.48 => ( member_b @ X @ B8 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Set.set_insert
% 0.32/0.48 thf(fact_331_Set_Oset__insert,axiom,
% 0.32/0.48 ! [X: product_prod_b_b,A: set_Product_prod_b_b] :
% 0.32/0.48 ( ( member1285940496od_b_b @ X @ A )
% 0.32/0.48 => ~ ! [B8: set_Product_prod_b_b] :
% 0.32/0.48 ( ( A
% 0.32/0.48 = ( insert1952693431od_b_b @ X @ B8 ) )
% 0.32/0.48 => ( member1285940496od_b_b @ X @ B8 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Set.set_insert
% 0.32/0.48 thf(fact_332_Set_Oset__insert,axiom,
% 0.32/0.48 ! [X: produc1213276845od_b_b,A: set_Pr1324126435od_b_b] :
% 0.32/0.48 ( ( member1516365892od_b_b @ X @ A )
% 0.32/0.48 => ~ ! [B8: set_Pr1324126435od_b_b] :
% 0.32/0.48 ( ( A
% 0.32/0.48 = ( insert2037698781od_b_b @ X @ B8 ) )
% 0.32/0.48 => ( member1516365892od_b_b @ X @ B8 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Set.set_insert
% 0.32/0.48 thf(fact_333_insertI2,axiom,
% 0.32/0.48 ! [A2: produc1871334759_a_nat,B: set_Pr1987088711_a_nat,B3: produc1871334759_a_nat] :
% 0.32/0.48 ( ( member832397200_a_nat @ A2 @ B )
% 0.32/0.48 => ( member832397200_a_nat @ A2 @ ( insert1574423351_a_nat @ B3 @ B ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % insertI2
% 0.32/0.48 thf(fact_334_insertI2,axiom,
% 0.32/0.48 ! [A2: b,B: set_b,B3: b] :
% 0.32/0.48 ( ( member_b @ A2 @ B )
% 0.32/0.48 => ( member_b @ A2 @ ( insert_b @ B3 @ B ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % insertI2
% 0.32/0.48 thf(fact_335_insertI2,axiom,
% 0.32/0.48 ! [A2: product_prod_b_b,B: set_Product_prod_b_b,B3: product_prod_b_b] :
% 0.32/0.48 ( ( member1285940496od_b_b @ A2 @ B )
% 0.32/0.48 => ( member1285940496od_b_b @ A2 @ ( insert1952693431od_b_b @ B3 @ B ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % insertI2
% 0.32/0.48 thf(fact_336_insertI2,axiom,
% 0.32/0.48 ! [A2: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,B3: produc1213276845od_b_b] :
% 0.32/0.48 ( ( member1516365892od_b_b @ A2 @ B )
% 0.32/0.48 => ( member1516365892od_b_b @ A2 @ ( insert2037698781od_b_b @ B3 @ B ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % insertI2
% 0.32/0.48 thf(fact_337_insertI1,axiom,
% 0.32/0.48 ! [A2: produc1871334759_a_nat,B: set_Pr1987088711_a_nat] : ( member832397200_a_nat @ A2 @ ( insert1574423351_a_nat @ A2 @ B ) ) ).
% 0.32/0.48
% 0.32/0.48 % insertI1
% 0.32/0.48 thf(fact_338_insertI1,axiom,
% 0.32/0.48 ! [A2: b,B: set_b] : ( member_b @ A2 @ ( insert_b @ A2 @ B ) ) ).
% 0.32/0.48
% 0.32/0.48 % insertI1
% 0.32/0.48 thf(fact_339_insertI1,axiom,
% 0.32/0.48 ! [A2: product_prod_b_b,B: set_Product_prod_b_b] : ( member1285940496od_b_b @ A2 @ ( insert1952693431od_b_b @ A2 @ B ) ) ).
% 0.32/0.48
% 0.32/0.48 % insertI1
% 0.32/0.48 thf(fact_340_insertI1,axiom,
% 0.32/0.48 ! [A2: produc1213276845od_b_b,B: set_Pr1324126435od_b_b] : ( member1516365892od_b_b @ A2 @ ( insert2037698781od_b_b @ A2 @ B ) ) ).
% 0.32/0.48
% 0.32/0.48 % insertI1
% 0.32/0.48 thf(fact_341_insertE,axiom,
% 0.32/0.48 ! [A2: produc1871334759_a_nat,B3: produc1871334759_a_nat,A: set_Pr1987088711_a_nat] :
% 0.32/0.48 ( ( member832397200_a_nat @ A2 @ ( insert1574423351_a_nat @ B3 @ A ) )
% 0.32/0.48 => ( ( A2 != B3 )
% 0.32/0.48 => ( member832397200_a_nat @ A2 @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % insertE
% 0.32/0.48 thf(fact_342_insertE,axiom,
% 0.32/0.48 ! [A2: b,B3: b,A: set_b] :
% 0.32/0.48 ( ( member_b @ A2 @ ( insert_b @ B3 @ A ) )
% 0.32/0.48 => ( ( A2 != B3 )
% 0.32/0.48 => ( member_b @ A2 @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % insertE
% 0.32/0.48 thf(fact_343_insertE,axiom,
% 0.32/0.48 ! [A2: product_prod_b_b,B3: product_prod_b_b,A: set_Product_prod_b_b] :
% 0.32/0.48 ( ( member1285940496od_b_b @ A2 @ ( insert1952693431od_b_b @ B3 @ A ) )
% 0.32/0.48 => ( ( A2 != B3 )
% 0.32/0.48 => ( member1285940496od_b_b @ A2 @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % insertE
% 0.32/0.48 thf(fact_344_insertE,axiom,
% 0.32/0.48 ! [A2: produc1213276845od_b_b,B3: produc1213276845od_b_b,A: set_Pr1324126435od_b_b] :
% 0.32/0.48 ( ( member1516365892od_b_b @ A2 @ ( insert2037698781od_b_b @ B3 @ A ) )
% 0.32/0.48 => ( ( A2 != B3 )
% 0.32/0.48 => ( member1516365892od_b_b @ A2 @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % insertE
% 0.32/0.48 thf(fact_345_singleton__inject,axiom,
% 0.32/0.48 ! [A2: b,B3: b] :
% 0.32/0.48 ( ( ( insert_b @ A2 @ bot_bot_set_b )
% 0.32/0.48 = ( insert_b @ B3 @ bot_bot_set_b ) )
% 0.32/0.48 => ( A2 = B3 ) ) ).
% 0.32/0.48
% 0.32/0.48 % singleton_inject
% 0.32/0.48 thf(fact_346_singleton__inject,axiom,
% 0.32/0.48 ! [A2: produc1871334759_a_nat,B3: produc1871334759_a_nat] :
% 0.32/0.48 ( ( ( insert1574423351_a_nat @ A2 @ bot_bo1836341171_a_nat )
% 0.32/0.48 = ( insert1574423351_a_nat @ B3 @ bot_bo1836341171_a_nat ) )
% 0.32/0.48 => ( A2 = B3 ) ) ).
% 0.32/0.48
% 0.32/0.48 % singleton_inject
% 0.32/0.48 thf(fact_347_insert__not__empty,axiom,
% 0.32/0.48 ! [A2: b,A: set_b] :
% 0.32/0.48 ( ( insert_b @ A2 @ A )
% 0.32/0.48 != bot_bot_set_b ) ).
% 0.32/0.48
% 0.32/0.48 % insert_not_empty
% 0.32/0.48 thf(fact_348_insert__not__empty,axiom,
% 0.32/0.48 ! [A2: produc1871334759_a_nat,A: set_Pr1987088711_a_nat] :
% 0.32/0.48 ( ( insert1574423351_a_nat @ A2 @ A )
% 0.32/0.48 != bot_bo1836341171_a_nat ) ).
% 0.32/0.48
% 0.32/0.48 % insert_not_empty
% 0.32/0.48 thf(fact_349_doubleton__eq__iff,axiom,
% 0.32/0.48 ! [A2: b,B3: b,C: b,D: b] :
% 0.32/0.48 ( ( ( insert_b @ A2 @ ( insert_b @ B3 @ bot_bot_set_b ) )
% 0.32/0.48 = ( insert_b @ C @ ( insert_b @ D @ bot_bot_set_b ) ) )
% 0.32/0.48 = ( ( ( A2 = C )
% 0.32/0.48 & ( B3 = D ) )
% 0.32/0.48 | ( ( A2 = D )
% 0.32/0.48 & ( B3 = C ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % doubleton_eq_iff
% 0.32/0.48 thf(fact_350_doubleton__eq__iff,axiom,
% 0.32/0.48 ! [A2: produc1871334759_a_nat,B3: produc1871334759_a_nat,C: produc1871334759_a_nat,D: produc1871334759_a_nat] :
% 0.32/0.48 ( ( ( insert1574423351_a_nat @ A2 @ ( insert1574423351_a_nat @ B3 @ bot_bo1836341171_a_nat ) )
% 0.32/0.48 = ( insert1574423351_a_nat @ C @ ( insert1574423351_a_nat @ D @ bot_bo1836341171_a_nat ) ) )
% 0.32/0.48 = ( ( ( A2 = C )
% 0.32/0.48 & ( B3 = D ) )
% 0.32/0.48 | ( ( A2 = D )
% 0.32/0.48 & ( B3 = C ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % doubleton_eq_iff
% 0.32/0.48 thf(fact_351_ma,axiom,
% 0.32/0.48 ! [X2: produc1871334759_a_nat] :
% 0.32/0.48 ( ( member832397200_a_nat @ X2 @ ( insert1574423351_a_nat @ ( standa63370785tant_a @ standard_S_Idt_a ) @ ( insert1574423351_a_nat @ ( standa1795879409tant_a @ standard_S_Idt_a ) @ ( insert1574423351_a_nat @ ( standa997693288tant_a @ standard_S_Idt_a ) @ bot_bo1836341171_a_nat ) ) ) )
% 0.32/0.48 => ( mainta1604381365_nat_b @ X2 @ g ) ) ).
% 0.32/0.48
% 0.32/0.48 % ma
% 0.32/0.48 thf(fact_352_f,axiom,
% 0.32/0.48 ( f
% 0.32/0.48 = ( ^ [X5: b] :
% 0.32/0.48 ( if_b
% 0.32/0.48 @ ( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ X5 @ bot_bot_set_b ) )
% 0.32/0.48 = bot_bot_set_b )
% 0.32/0.48 @ X5
% 0.32/0.48 @ ( hilbert_Eps_b @ ( p @ X5 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % f
% 0.32/0.48 thf(fact_353_P,axiom,
% 0.32/0.48 ( p
% 0.32/0.48 = ( ^ [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 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % P
% 0.32/0.48 thf(fact_354_congr_I1_J,axiom,
% 0.32/0.48 ! [X: b,Y: b,L: standard_Constant_a] :
% 0.32/0.48 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ X @ Y ) @ ( getRel904497637nt_a_b @ L @ g ) )
% 0.32/0.48 => ( equiv_1821124534_set_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g )
% 0.32/0.48 @ ^ [V3: b] : ( image_b_b @ ( getRel904497637nt_a_b @ L @ g ) @ ( insert_b @ V3 @ bot_bot_set_b ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % congr(1)
% 0.32/0.48 thf(fact_355_ident,axiom,
% 0.32/0.48 ( ( getRel904497637nt_a_b @ standard_S_Idt_a @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ g ) @ f ) @ g ) )
% 0.32/0.48 = ( image_1683732397od_b_b
% 0.32/0.48 @ ^ [X5: b] : ( product_Pair_b_b @ X5 @ X5 )
% 0.32/0.48 @ ( labele1424214014nt_a_b @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ g ) @ f ) @ g ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % ident
% 0.32/0.48
% 0.32/0.48 % Helper facts (3)
% 0.32/0.48 thf(help_If_3_1_If_001tf__b_T,axiom,
% 0.32/0.48 ! [P: $o] :
% 0.32/0.48 ( ( P = $true )
% 0.32/0.48 | ( P = $false ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(help_If_2_1_If_001tf__b_T,axiom,
% 0.32/0.48 ! [X: b,Y: b] :
% 0.32/0.48 ( ( if_b @ $false @ X @ Y )
% 0.32/0.48 = Y ) ).
% 0.32/0.48
% 0.32/0.48 thf(help_If_1_1_If_001tf__b_T,axiom,
% 0.32/0.48 ! [X: b,Y: b] :
% 0.32/0.48 ( ( if_b @ $true @ X @ Y )
% 0.32/0.48 = X ) ).
% 0.32/0.48
% 0.32/0.48 % Conjectures (1)
% 0.32/0.48 thf(conj_0,conjecture,
% 0.32/0.48 member_b @ x @ ( labele1424214014nt_a_b @ g ) ).
% 0.32/0.48
% 0.32/0.48 %------------------------------------------------------------------------------
% 0.32/0.48 ------------------------
% 2.98/1.60 ---- Embedded in THF ---
% 3.32/1.60 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.32/1.60 %%% Generated on Tue Feb 24 08:28:47 EST 2026
% 3.32/1.60 %%% using '$$dhol' embedding, version 1.3.0.
% 3.32/1.60 %%% Logic specification used:
% 3.32/1.60 %%% thf(spec, logic, $$dhol).
% 3.32/1.60
% 3.32/1.60 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.XlSklPZmtK/DTF2DTF15787.p
% See solution above
% 3.32/1.60 ------------------------
% 3.32/1.65 ---- Cleaned THF ---
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% 3.32/1.65 insert1167839429_a_nat: labele935650037_a_nat > set_la1083530965_a_nat > set_la1083530965_a_nat ).
% 3.32/1.65
% 3.32/1.65 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_Itf__b_Mtf__b_J_J,type,
% 3.32/1.65 insert2037698781od_b_b: produc1213276845od_b_b > set_Pr1324126435od_b_b > set_Pr1324126435od_b_b ).
% 3.32/1.65
% 3.32/1.65 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J,type,
% 3.32/1.65 insert1574423351_a_nat: produc1871334759_a_nat > set_Pr1987088711_a_nat > set_Pr1987088711_a_nat ).
% 3.32/1.65
% 3.32/1.65 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_J,type,
% 3.32/1.65 insert1810136247_a_nat: produc398057191_a_nat > set_Pr924198087_a_nat > set_Pr924198087_a_nat ).
% 3.32/1.65
% 3.32/1.65 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_Itf__b_Mtf__b_J,type,
% 3.32/1.65 insert1952693431od_b_b: product_prod_b_b > set_Product_prod_b_b > set_Product_prod_b_b ).
% 3.32/1.65
% 3.32/1.65 thf(sy_c_Set_Oinsert_001tf__b,type,
% 3.32/1.65 insert_b: b > set_b > set_b ).
% 3.32/1.65
% 3.32/1.65 thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Oidentity__rules_001tf__a,type,
% 3.32/1.65 standa1568205540ules_a: set_St761939237tant_a > set_Pr1987088711_a_nat ).
% 3.32/1.65
% 3.32/1.65 thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Oreflexivity__rule_001t__LabeledGraphSemantics__OStandard____Constant_Itf__a_J,type,
% 3.32/1.65 standa63370785tant_a: standard_Constant_a > produc1871334759_a_nat ).
% 3.32/1.65
% 3.32/1.65 thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Osymmetry__rule_001t__LabeledGraphSemantics__OStandard____Constant_Itf__a_J,type,
% 3.32/1.65 standa997693288tant_a: standard_Constant_a > produc1871334759_a_nat ).
% 3.32/1.65
% 3.32/1.65 thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Otransitive__rule_001t__LabeledGraphSemantics__OStandard____Constant_Itf__a_J,type,
% 3.32/1.65 standa1795879409tant_a: standard_Constant_a > produc1871334759_a_nat ).
% 3.32/1.65
% 3.32/1.65 thf(sy_c_member_001t__LabeledGraphSemantics__OStandard____Constant_Itf__a_J,type,
% 3.32/1.65 member1632892294tant_a: standard_Constant_a > set_St761939237tant_a > $o ).
% 3.32/1.65
% 3.32/1.65 thf(sy_c_member_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_J,type,
% 3.32/1.65 member1214736488tant_a: produc90515391tant_a > set_Pr154086431tant_a > $o ).
% 3.32/1.65
% 3.32/1.65 thf(sy_c_member_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_Itf__b_Mtf__b_J_J_Mt__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_Itf__b_Mtf__b_J_J_J_J,type,
% 3.32/1.65 member147868824od_b_b: produc1084374401od_b_b > set_Pr1190604087od_b_b > $o ).
% 3.32/1.65
% 3.32/1.65 thf(sy_c_member_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b_Mtf__b_J_Mt__Product____Type__Oprod_Itf__b_Mtf__b_J_J_J,type,
% 3.32/1.65 member1744485444od_b_b: produc644633773od_b_b > set_Pr1021918435od_b_b > $o ).
% 3.32/1.65
% 3.32/1.65 thf(sy_c_member_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_Itf__b_Mtf__b_J_J,type,
% 3.32/1.65 member1516365892od_b_b: produc1213276845od_b_b > set_Pr1324126435od_b_b > $o ).
% 3.32/1.65
% 3.32/1.65 thf(sy_c_member_001t__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J,type,
% 3.32/1.65 member832397200_a_nat: produc1871334759_a_nat > set_Pr1987088711_a_nat > $o ).
% 3.32/1.65
% 3.32/1.65 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_Itf__b_Mtf__b_J_J_Mt__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_Itf__b_Mtf__b_J_J_J,type,
% 3.32/1.65 member1086024932od_b_b: produc970027067od_b_b > set_Pr2109276827od_b_b > $o ).
% 3.32/1.65
% 3.32/1.65 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_Itf__b_Mtf__b_J_J_Mt__Product____Type__Oprod_Itf__b_Mtf__b_J_J,type,
% 3.32/1.65 member942707974od_b_b: produc1990339951od_b_b > set_Pr2134561957od_b_b > $o ).
% 3.32/1.65
% 3.32/1.65 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_Itf__b_Mtf__b_J_J_Mtf__b_J,type,
% 3.32/1.65 member1417789726_b_b_b: produc276146823_b_b_b > set_Pr1906739389_b_b_b > $o ).
% 3.32/1.65
% 3.32/1.65 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_Itf__b_Mtf__b_J_J_J,type,
% 3.32/1.65 member1533761242od_b_b: produc1169496899od_b_b > set_Pr1954438265od_b_b > $o ).
% 3.32/1.65
% 3.32/1.65 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_J,type,
% 3.32/1.65 member584645392_a_nat: produc398057191_a_nat > set_Pr924198087_a_nat > $o ).
% 3.32/1.65
% 3.32/1.65 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_Itf__b_Mtf__b_J_J,type,
% 3.32/1.65 member301892752od_b_b: produc1485083751od_b_b > set_Pr667377223od_b_b > $o ).
% 3.32/1.65
% 3.32/1.65 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_Mtf__b_J,type,
% 3.32/1.65 member1544800936_nat_b: produc845793663_nat_b > set_Pr812188767_nat_b > $o ).
% 3.32/1.65
% 3.32/1.65 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b_Mtf__b_J_Mt__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_Itf__b_Mtf__b_J_J_J,type,
% 3.32/1.65 member4694106od_b_b: produc1052326083od_b_b > set_Pr1071216121od_b_b > $o ).
% 3.32/1.65
% 3.32/1.65 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b_Mtf__b_J_Mt__Product____Type__Oprod_Itf__b_Mtf__b_J_J,type,
% 3.32/1.65 member1652792080od_b_b: produc1168037607od_b_b > set_Pr2007082183od_b_b > $o ).
% 3.32/1.65
% 3.32/1.65 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b_Mtf__b_J_Mtf__b_J,type,
% 3.32/1.65 member351494440_b_b_b: produc2112523263_b_b_b > set_Pr357419743_b_b_b > $o ).
% 3.32/1.65
% 3.32/1.65 thf(sy_c_member_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_Itf__b_Mtf__b_J_J_J,type,
% 3.32/1.65 member599505522od_b_b: produc1605346267od_b_b > set_Pr2060523537od_b_b > $o ).
% 3.32/1.65
% 3.32/1.65 thf(sy_c_member_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_Itf__b_Mtf__b_J_J,type,
% 3.32/1.65 member641857272od_b_b: produc255402447od_b_b > set_Pr621705391od_b_b > $o ).
% 3.32/1.65
% 3.32/1.65 thf(sy_c_member_001t__Product____Type__Oprod_Itf__b_Mtf__b_J,type,
% 3.32/1.65 member1285940496od_b_b: product_prod_b_b > set_Product_prod_b_b > $o ).
% 3.32/1.65
% 3.32/1.65 thf(sy_c_member_001tf__b,type,
% 3.32/1.65 member_b: b > set_b > $o ).
% 3.32/1.65
% 3.32/1.65 thf(sy_v_G,type,
% 3.32/1.65 g: labele1159362096nt_a_b ).
% 3.32/1.65
% 3.32/1.65 thf(sy_v_L,type,
% 3.32/1.65 l: set_St761939237tant_a ).
% 3.32/1.65
% 3.32/1.65 thf(sy_v_P____,type,
% 3.32/1.65 p: b > b > $o ).
% 3.32/1.65
% 3.32/1.65 thf(sy_v_f____,type,
% 3.32/1.65 f: b > b ).
% 3.32/1.65
% 3.32/1.65 thf(sy_v_l____,type,
% 3.32/1.65 l2: standard_Constant_a ).
% 3.32/1.65
% 3.32/1.65 thf(sy_v_x____,type,
% 3.32/1.65 x: b ).
% 3.32/1.65
% 3.32/1.65 thf(sy_v_y____,type,
% 3.32/1.65 y: b ).
% 3.32/1.65
% 3.32/1.65 thf(fact_0__092_060open_062_092_060And_062xa_O_A_092_060lbrakk_062f_Axa_A_092_060in_062_Avertices_AG_059_Axa_A_092_060notin_062_Avertices_AG_092_060rbrakk_062_A_092_060Longrightarrow_062_AFalse_092_060close_062,axiom,
% 3.32/1.65 ! [Xa: b] :
% 3.32/1.65 ( ( member_b @ ( f @ Xa ) @ ( labele1424214014nt_a_b @ g ) )
% 3.32/1.65 => ( member_b @ Xa @ ( labele1424214014nt_a_b @ g ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_1_fv_I2_J,axiom,
% 3.32/1.65 member_b @ ( f @ y ) @ ( labele1424214014nt_a_b @ g ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_2_fv_I1_J,axiom,
% 3.32/1.65 member_b @ ( f @ x ) @ ( labele1424214014nt_a_b @ g ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_3_gu2,axiom,
% 3.32/1.65 ! [X: b] :
% 3.32/1.65 ( ( member_b @ X @ ( labele1424214014nt_a_b @ g ) )
% 3.32/1.65 => ( member_b @ ( f @ X ) @ ( labele1424214014nt_a_b @ g ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_4_assms_I1_J,axiom,
% 3.32/1.65 ( g
% 3.32/1.65 = ( restri446606278nt_a_b @ g ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_5_r1,axiom,
% 3.32/1.65 ! [X: b] :
% 3.32/1.65 ( ( member_b @ X @ ( labele1424214014nt_a_b @ g ) )
% 3.32/1.65 = ( p @ X @ X ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_6_assms_I2_J,axiom,
% 3.32/1.65 ! [X2: produc1871334759_a_nat] :
% 3.32/1.65 ( ( member832397200_a_nat @ X2 @ ( standa1568205540ules_a @ l ) )
% 3.32/1.65 => ( mainta1604381365_nat_b @ X2 @ g ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_7_gr,axiom,
% 3.32/1.65 member1285940496od_b_b @ ( product_Pair_b_b @ ( f @ x ) @ ( f @ y ) ) @ ( getRel904497637nt_a_b @ l2 @ g ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_8_a,axiom,
% 3.32/1.65 member1516365892od_b_b @ ( produc1432590431od_b_b @ l2 @ ( product_Pair_b_b @ ( f @ x ) @ ( f @ y ) ) ) @ ( labele1741081071nt_a_b @ g ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_9_local_Orefl,axiom,
% 3.32/1.65 refl_on_b @ ( labele1424214014nt_a_b @ g ) @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_10_equiv,axiom,
% 3.32/1.65 equiv_equiv_b @ ( labele1424214014nt_a_b @ g ) @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_11__092_060open_062graph__union_A_Imap__graph__fn_AG_Af_J_AG_A_061_AG_092_060close_062,axiom,
% 3.32/1.65 ( ( graph_1309249505nt_a_b @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ g ) @ f ) @ g ) @ g )
% 3.32/1.65 = g ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_12_gu1,axiom,
% 3.32/1.65 ! [L: standard_Constant_a,X: b,Y: b] :
% 3.32/1.65 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ L @ ( product_Pair_b_b @ X @ Y ) ) @ ( labele1741081071nt_a_b @ g ) )
% 3.32/1.65 => ( ( member_b @ X @ ( labele1424214014nt_a_b @ g ) )
% 3.32/1.65 => ( ( member_b @ Y @ ( labele1424214014nt_a_b @ g ) )
% 3.32/1.65 => ( member1516365892od_b_b @ ( produc1432590431od_b_b @ L @ ( product_Pair_b_b @ ( f @ X ) @ ( f @ Y ) ) ) @ ( labele1741081071nt_a_b @ g ) ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_13__092_060open_062_092_060And_062x_O_Ax_A_092_060in_062_Avertices_AG_A_092_060Longrightarrow_062_A_Ix_M_Ax_J_A_092_060in_062_AgetRel_AS__Idt_AG_092_060close_062,axiom,
% 3.32/1.65 ! [X: b] :
% 3.32/1.65 ( ( member_b @ X @ ( labele1424214014nt_a_b @ g ) )
% 3.32/1.65 => ( member1285940496od_b_b @ ( product_Pair_b_b @ X @ X ) @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_14_labeled__graph_Osel_I2_J,axiom,
% 3.32/1.65 ! [X1: set_Pr1324126435od_b_b,X22: set_b] :
% 3.32/1.65 ( ( labele1424214014nt_a_b @ ( labele1230159100nt_a_b @ X1 @ X22 ) )
% 3.32/1.65 = X22 ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_15_subg,axiom,
% 3.32/1.65 graph_222606102_a_b_b @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ g ) @ f ) @ g ) @ g @ ( id_on_b @ ( labele1424214014nt_a_b @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ g ) @ f ) @ g ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_16_vertices__restrict,axiom,
% 3.32/1.65 ! [G: labele1159362096nt_a_b] :
% 3.32/1.65 ( ( labele1424214014nt_a_b @ ( restri446606278nt_a_b @ G ) )
% 3.32/1.65 = ( labele1424214014nt_a_b @ G ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_17_restrict__idemp,axiom,
% 3.32/1.65 ! [X: labele1159362096nt_a_b] :
% 3.32/1.65 ( ( restri446606278nt_a_b @ ( restri446606278nt_a_b @ X ) )
% 3.32/1.65 = ( restri446606278nt_a_b @ X ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_18_graph__union__idemp_I3_J,axiom,
% 3.32/1.65 ! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b] :
% 3.32/1.65 ( ( graph_1309249505nt_a_b @ A @ ( graph_1309249505nt_a_b @ B @ A ) )
% 3.32/1.65 = ( graph_1309249505nt_a_b @ B @ A ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_19_graph__union__idemp_I2_J,axiom,
% 3.32/1.65 ! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b] :
% 3.32/1.65 ( ( graph_1309249505nt_a_b @ A @ ( graph_1309249505nt_a_b @ A @ B ) )
% 3.32/1.65 = ( graph_1309249505nt_a_b @ A @ B ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_20_graph__union__idemp_I1_J,axiom,
% 3.32/1.65 ! [A: labele1159362096nt_a_b] :
% 3.32/1.65 ( ( graph_1309249505nt_a_b @ A @ A )
% 3.32/1.65 = A ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_21_map__graph__preserves__restricted,axiom,
% 3.32/1.65 ! [G: labele1159362096nt_a_b,F: set_Product_prod_b_b] :
% 3.32/1.65 ( ( G
% 3.32/1.65 = ( restri446606278nt_a_b @ G ) )
% 3.32/1.65 => ( ( map_gr926947118tant_a @ F @ G )
% 3.32/1.65 = ( restri446606278nt_a_b @ ( map_gr926947118tant_a @ F @ G ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_22_graph__union__preserves__restrict,axiom,
% 3.32/1.65 ! [G_1: labele1159362096nt_a_b,G_2: labele1159362096nt_a_b] :
% 3.32/1.65 ( ( G_1
% 3.32/1.65 = ( restri446606278nt_a_b @ G_1 ) )
% 3.32/1.65 => ( ( G_2
% 3.32/1.65 = ( restri446606278nt_a_b @ G_2 ) )
% 3.32/1.65 => ( ( graph_1309249505nt_a_b @ G_1 @ G_2 )
% 3.32/1.65 = ( restri446606278nt_a_b @ ( graph_1309249505nt_a_b @ G_1 @ G_2 ) ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_23_labeled__graph_Ocollapse,axiom,
% 3.32/1.65 ! [Labeled_graph: labele1159362096nt_a_b] :
% 3.32/1.65 ( ( labele1230159100nt_a_b @ ( labele1741081071nt_a_b @ Labeled_graph ) @ ( labele1424214014nt_a_b @ Labeled_graph ) )
% 3.32/1.65 = Labeled_graph ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_24_subgraph__refl,axiom,
% 3.32/1.65 ! [G: labele1159362096nt_a_b] :
% 3.32/1.65 ( ( graph_222606102_a_b_b @ G @ G @ ( id_on_b @ ( labele1424214014nt_a_b @ G ) ) )
% 3.32/1.65 = ( G
% 3.32/1.65 = ( restri446606278nt_a_b @ G ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_25_subgraph__restrict,axiom,
% 3.32/1.65 ! [G: labele1159362096nt_a_b] :
% 3.32/1.65 ( ( graph_222606102_a_b_b @ G @ ( restri446606278nt_a_b @ G ) @ ( id_on_b @ ( labele1424214014nt_a_b @ G ) ) )
% 3.32/1.65 = ( G
% 3.32/1.65 = ( restri446606278nt_a_b @ G ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_26_graph__homomorphism__Id,axiom,
% 3.32/1.65 ! [A2: labele1159362096nt_a_b] : ( graph_222606102_a_b_b @ ( restri446606278nt_a_b @ A2 ) @ ( restri446606278nt_a_b @ A2 ) @ ( id_on_b @ ( labele1424214014nt_a_b @ A2 ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_27_map__graph__preserves__subgraph,axiom,
% 3.32/1.65 ! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,F: set_Product_prod_b_b] :
% 3.32/1.65 ( ( graph_222606102_a_b_b @ A @ B @ ( id_on_b @ ( labele1424214014nt_a_b @ A ) ) )
% 3.32/1.65 => ( graph_222606102_a_b_b @ ( map_gr926947118tant_a @ F @ A ) @ ( map_gr926947118tant_a @ F @ B ) @ ( id_on_b @ ( labele1424214014nt_a_b @ ( map_gr926947118tant_a @ F @ A ) ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_28_map__graph__fn__id_I2_J,axiom,
% 3.32/1.65 ! [X3: labele1159362096nt_a_b] :
% 3.32/1.65 ( ( map_gr926947118tant_a @ ( id_on_b @ ( labele1424214014nt_a_b @ X3 ) ) @ X3 )
% 3.32/1.65 = ( restri446606278nt_a_b @ X3 ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_29_map__graph__fn__graphI,axiom,
% 3.32/1.65 ! [G: labele1159362096nt_a_b,F: b > b] :
% 3.32/1.65 ( ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ G ) @ F ) @ G )
% 3.32/1.65 = ( restri446606278nt_a_b @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ G ) @ F ) @ G ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_30_graph__homo,axiom,
% 3.32/1.65 ! [G: labele1159362096nt_a_b,F: b > b] :
% 3.32/1.65 ( ( G
% 3.32/1.65 = ( restri446606278nt_a_b @ G ) )
% 3.32/1.65 => ( graph_222606102_a_b_b @ G @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ G ) @ F ) @ G ) @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ G ) @ F ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_31_labeled__graph_Osel_I1_J,axiom,
% 3.32/1.65 ! [X1: set_Pr1324126435od_b_b,X22: set_b] :
% 3.32/1.65 ( ( labele1741081071nt_a_b @ ( labele1230159100nt_a_b @ X1 @ X22 ) )
% 3.32/1.65 = X1 ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_32_subgraph__def,axiom,
% 3.32/1.65 ! [G_1: labele1159362096nt_a_b,G_2: labele1159362096nt_a_b] :
% 3.32/1.65 ( ( graph_222606102_a_b_b @ G_1 @ G_2 @ ( id_on_b @ ( labele1424214014nt_a_b @ G_1 ) ) )
% 3.32/1.65 = ( ( G_1
% 3.32/1.65 = ( restri446606278nt_a_b @ G_1 ) )
% 3.32/1.65 & ( G_2
% 3.32/1.65 = ( restri446606278nt_a_b @ G_2 ) )
% 3.32/1.65 & ( ( graph_1309249505nt_a_b @ G_1 @ G_2 )
% 3.32/1.65 = G_2 ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_33_subgraph__trans,axiom,
% 3.32/1.65 ! [G_1: labele1159362096nt_a_b,G_2: labele1159362096nt_a_b,G_3: labele1159362096nt_a_b] :
% 3.32/1.65 ( ( graph_222606102_a_b_b @ G_1 @ G_2 @ ( id_on_b @ ( labele1424214014nt_a_b @ G_1 ) ) )
% 3.32/1.65 => ( ( graph_222606102_a_b_b @ G_2 @ G_3 @ ( id_on_b @ ( labele1424214014nt_a_b @ G_2 ) ) )
% 3.32/1.65 => ( graph_222606102_a_b_b @ G_1 @ G_3 @ ( id_on_b @ ( labele1424214014nt_a_b @ G_1 ) ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_34_map__graph__fn__eqI,axiom,
% 3.32/1.65 ! [G: labele1159362096nt_a_b,F: b > b,G2: b > b] :
% 3.32/1.65 ( ! [X4: b] :
% 3.32/1.65 ( ( member_b @ X4 @ ( labele1424214014nt_a_b @ G ) )
% 3.32/1.65 => ( ( F @ X4 )
% 3.32/1.65 = ( G2 @ X4 ) ) )
% 3.32/1.65 => ( ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ G ) @ F ) @ G )
% 3.32/1.65 = ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ G ) @ G2 ) @ G ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_35_subgraph__preserves__hom,axiom,
% 3.32/1.65 ! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,X3: labele1159362096nt_a_b,H: set_Product_prod_b_b] :
% 3.32/1.65 ( ( graph_222606102_a_b_b @ A @ B @ ( id_on_b @ ( labele1424214014nt_a_b @ A ) ) )
% 3.32/1.65 => ( ( graph_222606102_a_b_b @ X3 @ A @ H )
% 3.32/1.65 => ( graph_222606102_a_b_b @ X3 @ B @ H ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_36_labeled__graph_Oexhaust__sel,axiom,
% 3.32/1.65 ! [Labeled_graph: labele1159362096nt_a_b] :
% 3.32/1.65 ( Labeled_graph
% 3.32/1.65 = ( labele1230159100nt_a_b @ ( labele1741081071nt_a_b @ Labeled_graph ) @ ( labele1424214014nt_a_b @ Labeled_graph ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_37_labeled__graph_Oexpand,axiom,
% 3.32/1.65 ! [Labeled_graph: labele1159362096nt_a_b,Labeled_graph2: labele1159362096nt_a_b] :
% 3.32/1.65 ( ( ( ( labele1741081071nt_a_b @ Labeled_graph )
% 3.32/1.65 = ( labele1741081071nt_a_b @ Labeled_graph2 ) )
% 3.32/1.65 & ( ( labele1424214014nt_a_b @ Labeled_graph )
% 3.32/1.65 = ( labele1424214014nt_a_b @ Labeled_graph2 ) ) )
% 3.32/1.65 => ( Labeled_graph = Labeled_graph2 ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_38_getRel__hom,axiom,
% 3.32/1.65 ! [Y: product_prod_b_b,Z: product_prod_b_b,L: standard_Constant_a,G: labele1835558936od_b_b,F: product_prod_b_b > b] :
% 3.32/1.65 ( ( member1652792080od_b_b @ ( produc546497367od_b_b @ Y @ Z ) @ ( getRel118493133od_b_b @ L @ G ) )
% 3.32/1.65 => ( ( member1285940496od_b_b @ Y @ ( labele442485990od_b_b @ G ) )
% 3.32/1.65 => ( ( member1285940496od_b_b @ Z @ ( labele442485990od_b_b @ G ) )
% 3.32/1.65 => ( member1285940496od_b_b @ ( product_Pair_b_b @ ( F @ Y ) @ ( F @ Z ) ) @ ( getRel904497637nt_a_b @ L @ ( map_gr1314489926tant_a @ ( bNF_Gr521784954_b_b_b @ ( labele442485990od_b_b @ G ) @ F ) @ G ) ) ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_39_getRel__hom,axiom,
% 3.32/1.65 ! [Y: produc1213276845od_b_b,Z: produc1213276845od_b_b,L: standard_Constant_a,G: labele1644675410od_b_b,F: produc1213276845od_b_b > b] :
% 3.32/1.65 ( ( member1086024932od_b_b @ ( produc449289715od_b_b @ Y @ Z ) @ ( getRel59882567od_b_b @ L @ G ) )
% 3.32/1.65 => ( ( member1516365892od_b_b @ Y @ ( labele595103470od_b_b @ G ) )
% 3.32/1.65 => ( ( member1516365892od_b_b @ Z @ ( labele595103470od_b_b @ G ) )
% 3.32/1.65 => ( member1285940496od_b_b @ ( product_Pair_b_b @ ( F @ Y ) @ ( F @ Z ) ) @ ( getRel904497637nt_a_b @ L @ ( map_gr1495881666tant_a @ ( bNF_Gr492676974_b_b_b @ ( labele595103470od_b_b @ G ) @ F ) @ G ) ) ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_40_getRel__hom,axiom,
% 3.32/1.65 ! [Y: b,Z: b,L: standard_Constant_a,G: labele1159362096nt_a_b,F: b > b] :
% 3.32/1.65 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ Y @ Z ) @ ( getRel904497637nt_a_b @ L @ G ) )
% 3.32/1.65 => ( ( member_b @ Y @ ( labele1424214014nt_a_b @ G ) )
% 3.32/1.65 => ( ( member_b @ Z @ ( labele1424214014nt_a_b @ G ) )
% 3.32/1.65 => ( member1285940496od_b_b @ ( product_Pair_b_b @ ( F @ Y ) @ ( F @ Z ) ) @ ( getRel904497637nt_a_b @ L @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ G ) @ F ) @ G ) ) ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_41_getRel__map__fn,axiom,
% 3.32/1.65 ! [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] :
% 3.32/1.65 ( ( member1285940496od_b_b @ A22 @ ( labele442485990od_b_b @ G ) )
% 3.32/1.65 => ( ( member1285940496od_b_b @ B2 @ ( labele442485990od_b_b @ G ) )
% 3.32/1.65 => ( ( member1652792080od_b_b @ ( produc546497367od_b_b @ A22 @ B2 ) @ ( getRel118493133od_b_b @ L @ G ) )
% 3.32/1.65 => ( ( ( F @ A22 )
% 3.32/1.65 = A2 )
% 3.32/1.65 => ( ( ( F @ B2 )
% 3.32/1.65 = B3 )
% 3.32/1.65 => ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ B3 ) @ ( getRel904497637nt_a_b @ L @ ( map_gr1314489926tant_a @ ( bNF_Gr521784954_b_b_b @ ( labele442485990od_b_b @ G ) @ F ) @ G ) ) ) ) ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_42_getRel__map__fn,axiom,
% 3.32/1.65 ! [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] :
% 3.32/1.65 ( ( member1516365892od_b_b @ A22 @ ( labele595103470od_b_b @ G ) )
% 3.32/1.65 => ( ( member1516365892od_b_b @ B2 @ ( labele595103470od_b_b @ G ) )
% 3.32/1.65 => ( ( member1086024932od_b_b @ ( produc449289715od_b_b @ A22 @ B2 ) @ ( getRel59882567od_b_b @ L @ G ) )
% 3.32/1.65 => ( ( ( F @ A22 )
% 3.32/1.65 = A2 )
% 3.32/1.65 => ( ( ( F @ B2 )
% 3.32/1.65 = B3 )
% 3.32/1.65 => ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ B3 ) @ ( getRel904497637nt_a_b @ L @ ( map_gr1495881666tant_a @ ( bNF_Gr492676974_b_b_b @ ( labele595103470od_b_b @ G ) @ F ) @ G ) ) ) ) ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_43_getRel__map__fn,axiom,
% 3.32/1.65 ! [A22: b,G: labele1159362096nt_a_b,B2: b,L: standard_Constant_a,F: b > b,A2: b,B3: b] :
% 3.32/1.65 ( ( member_b @ A22 @ ( labele1424214014nt_a_b @ G ) )
% 3.32/1.65 => ( ( member_b @ B2 @ ( labele1424214014nt_a_b @ G ) )
% 3.32/1.65 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A22 @ B2 ) @ ( getRel904497637nt_a_b @ L @ G ) )
% 3.32/1.65 => ( ( ( F @ A22 )
% 3.32/1.65 = A2 )
% 3.32/1.65 => ( ( ( F @ B2 )
% 3.32/1.65 = B3 )
% 3.32/1.65 => ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ B3 ) @ ( getRel904497637nt_a_b @ L @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ G ) @ F ) @ G ) ) ) ) ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_44_idt__eq,axiom,
% 3.32/1.65 ! [X: b,Y: b] :
% 3.32/1.65 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ standard_S_Idt_a @ ( product_Pair_b_b @ X @ Y ) ) @ ( labele1741081071nt_a_b @ g ) )
% 3.32/1.65 => ( ( hilbert_Eps_b @ ( p @ X ) )
% 3.32/1.65 = ( hilbert_Eps_b @ ( p @ Y ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_45_vert__P,axiom,
% 3.32/1.65 ! [X: b] :
% 3.32/1.65 ( ( member_b @ X @ ( labele1424214014nt_a_b @ g ) )
% 3.32/1.65 => ( member1285940496od_b_b @ ( product_Pair_b_b @ X @ ( hilbert_Eps_b @ ( p @ X ) ) ) @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_46_mem__Collect__eq,axiom,
% 3.32/1.65 ! [A2: b,P: b > $o] :
% 3.32/1.65 ( ( member_b @ A2 @ ( collect_b @ P ) )
% 3.32/1.65 = ( P @ A2 ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_47_mem__Collect__eq,axiom,
% 3.32/1.65 ! [A2: product_prod_b_b,P: product_prod_b_b > $o] :
% 3.32/1.65 ( ( member1285940496od_b_b @ A2 @ ( collec1481886546od_b_b @ P ) )
% 3.32/1.65 = ( P @ A2 ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_48_mem__Collect__eq,axiom,
% 3.32/1.65 ! [A2: produc1213276845od_b_b,P: produc1213276845od_b_b > $o] :
% 3.32/1.65 ( ( member1516365892od_b_b @ A2 @ ( collec279084418od_b_b @ P ) )
% 3.32/1.65 = ( P @ A2 ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_49_Collect__mem__eq,axiom,
% 3.32/1.65 ! [A: set_b] :
% 3.32/1.65 ( ( collect_b
% 3.32/1.65 @ ^ [X5: b] : ( member_b @ X5 @ A ) )
% 3.32/1.65 = A ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_50_Collect__mem__eq,axiom,
% 3.32/1.65 ! [A: set_Product_prod_b_b] :
% 3.32/1.65 ( ( collec1481886546od_b_b
% 3.32/1.65 @ ^ [X5: product_prod_b_b] : ( member1285940496od_b_b @ X5 @ A ) )
% 3.32/1.65 = A ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_51_Collect__mem__eq,axiom,
% 3.32/1.65 ! [A: set_Pr1324126435od_b_b] :
% 3.32/1.65 ( ( collec279084418od_b_b
% 3.32/1.65 @ ^ [X5: produc1213276845od_b_b] : ( member1516365892od_b_b @ X5 @ A ) )
% 3.32/1.65 = A ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_52_getRel__subgraph,axiom,
% 3.32/1.65 ! [Y: b,Z: b,L: standard_Constant_a,G: labele1159362096nt_a_b,G3: labele1159362096nt_a_b] :
% 3.32/1.65 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ Y @ Z ) @ ( getRel904497637nt_a_b @ L @ G ) )
% 3.32/1.65 => ( ( graph_222606102_a_b_b @ G @ G3 @ ( id_on_b @ ( labele1424214014nt_a_b @ G ) ) )
% 3.32/1.65 => ( member1285940496od_b_b @ ( product_Pair_b_b @ Y @ Z ) @ ( getRel904497637nt_a_b @ L @ G3 ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_53_in__Gr,axiom,
% 3.32/1.65 ! [X: b,Y: b,A: set_b,F: b > b] :
% 3.32/1.65 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ X @ Y ) @ ( bNF_Gr_b_b @ A @ F ) )
% 3.32/1.65 = ( ( member_b @ X @ A )
% 3.32/1.65 & ( ( F @ X )
% 3.32/1.65 = Y ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_54_in__Gr,axiom,
% 3.32/1.65 ! [X: standard_Constant_a,Y: product_prod_b_b,A: set_St761939237tant_a,F: standard_Constant_a > product_prod_b_b] :
% 3.32/1.65 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ X @ Y ) @ ( bNF_Gr1272216980od_b_b @ A @ F ) )
% 3.32/1.65 = ( ( member1632892294tant_a @ X @ A )
% 3.32/1.65 & ( ( F @ X )
% 3.32/1.65 = Y ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_55_Gr__not__in,axiom,
% 3.32/1.65 ! [X: b,F2: set_b,F: b > b,Y: b] :
% 3.32/1.65 ( ( ~ ( member_b @ X @ F2 )
% 3.32/1.65 | ( ( F @ X )
% 3.32/1.65 != Y ) )
% 3.32/1.65 => ~ ( member1285940496od_b_b @ ( product_Pair_b_b @ X @ Y ) @ ( bNF_Gr_b_b @ F2 @ F ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_56_Gr__not__in,axiom,
% 3.32/1.65 ! [X: standard_Constant_a,F2: set_St761939237tant_a,F: standard_Constant_a > product_prod_b_b,Y: product_prod_b_b] :
% 3.32/1.65 ( ( ~ ( member1632892294tant_a @ X @ F2 )
% 3.32/1.65 | ( ( F @ X )
% 3.32/1.65 != Y ) )
% 3.32/1.65 => ~ ( member1516365892od_b_b @ ( produc1432590431od_b_b @ X @ Y ) @ ( bNF_Gr1272216980od_b_b @ F2 @ F ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_57_Id__onI,axiom,
% 3.32/1.65 ! [A2: product_prod_b_b,A: set_Product_prod_b_b] :
% 3.32/1.65 ( ( member1285940496od_b_b @ A2 @ A )
% 3.32/1.65 => ( member1652792080od_b_b @ ( produc546497367od_b_b @ A2 @ A2 ) @ ( id_on_2019020932od_b_b @ A ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_58_Id__onI,axiom,
% 3.32/1.65 ! [A2: produc1213276845od_b_b,A: set_Pr1324126435od_b_b] :
% 3.32/1.65 ( ( member1516365892od_b_b @ A2 @ A )
% 3.32/1.65 => ( member1086024932od_b_b @ ( produc449289715od_b_b @ A2 @ A2 ) @ ( id_on_250271696od_b_b @ A ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_59_Id__onI,axiom,
% 3.32/1.65 ! [A2: b,A: set_b] :
% 3.32/1.65 ( ( member_b @ A2 @ A )
% 3.32/1.65 => ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ A2 ) @ ( id_on_b @ A ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_60_getRel__dom_I2_J,axiom,
% 3.32/1.65 ! [G: labele1159362096nt_a_b,A2: b,B3: b,L: standard_Constant_a] :
% 3.32/1.65 ( ( G
% 3.32/1.65 = ( restri446606278nt_a_b @ G ) )
% 3.32/1.65 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ B3 ) @ ( getRel904497637nt_a_b @ L @ G ) )
% 3.32/1.65 => ( member_b @ B3 @ ( labele1424214014nt_a_b @ G ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_61_getRel__dom_I1_J,axiom,
% 3.32/1.65 ! [G: labele1159362096nt_a_b,A2: b,B3: b,L: standard_Constant_a] :
% 3.32/1.65 ( ( G
% 3.32/1.65 = ( restri446606278nt_a_b @ G ) )
% 3.32/1.65 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ B3 ) @ ( getRel904497637nt_a_b @ L @ G ) )
% 3.32/1.65 => ( member_b @ A2 @ ( labele1424214014nt_a_b @ G ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_62_Id__on__iff,axiom,
% 3.32/1.65 ! [X: product_prod_b_b,Y: product_prod_b_b,A: set_Product_prod_b_b] :
% 3.32/1.65 ( ( member1652792080od_b_b @ ( produc546497367od_b_b @ X @ Y ) @ ( id_on_2019020932od_b_b @ A ) )
% 3.32/1.65 = ( ( X = Y )
% 3.32/1.65 & ( member1285940496od_b_b @ X @ A ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_63_Id__on__iff,axiom,
% 3.32/1.65 ! [X: produc1213276845od_b_b,Y: produc1213276845od_b_b,A: set_Pr1324126435od_b_b] :
% 3.32/1.65 ( ( member1086024932od_b_b @ ( produc449289715od_b_b @ X @ Y ) @ ( id_on_250271696od_b_b @ A ) )
% 3.32/1.65 = ( ( X = Y )
% 3.32/1.65 & ( member1516365892od_b_b @ X @ A ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_64_Id__on__iff,axiom,
% 3.32/1.65 ! [X: b,Y: b,A: set_b] :
% 3.32/1.65 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ X @ Y ) @ ( id_on_b @ A ) )
% 3.32/1.65 = ( ( X = Y )
% 3.32/1.65 & ( member_b @ X @ A ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_65_Id__on__eqI,axiom,
% 3.32/1.65 ! [A2: product_prod_b_b,B3: product_prod_b_b,A: set_Product_prod_b_b] :
% 3.32/1.65 ( ( A2 = B3 )
% 3.32/1.65 => ( ( member1285940496od_b_b @ A2 @ A )
% 3.32/1.65 => ( member1652792080od_b_b @ ( produc546497367od_b_b @ A2 @ B3 ) @ ( id_on_2019020932od_b_b @ A ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_66_Id__on__eqI,axiom,
% 3.32/1.65 ! [A2: produc1213276845od_b_b,B3: produc1213276845od_b_b,A: set_Pr1324126435od_b_b] :
% 3.32/1.65 ( ( A2 = B3 )
% 3.32/1.65 => ( ( member1516365892od_b_b @ A2 @ A )
% 3.32/1.65 => ( member1086024932od_b_b @ ( produc449289715od_b_b @ A2 @ B3 ) @ ( id_on_250271696od_b_b @ A ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_67_Id__on__eqI,axiom,
% 3.32/1.65 ! [A2: b,B3: b,A: set_b] :
% 3.32/1.65 ( ( A2 = B3 )
% 3.32/1.65 => ( ( member_b @ A2 @ A )
% 3.32/1.65 => ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ B3 ) @ ( id_on_b @ A ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_68_Id__onE,axiom,
% 3.32/1.65 ! [C: produc1168037607od_b_b,A: set_Product_prod_b_b] :
% 3.32/1.65 ( ( member1652792080od_b_b @ C @ ( id_on_2019020932od_b_b @ A ) )
% 3.32/1.65 => ~ ! [X4: product_prod_b_b] :
% 3.32/1.65 ( ( member1285940496od_b_b @ X4 @ A )
% 3.32/1.65 => ( C
% 3.32/1.65 != ( produc546497367od_b_b @ X4 @ X4 ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_69_Id__onE,axiom,
% 3.32/1.65 ! [C: produc970027067od_b_b,A: set_Pr1324126435od_b_b] :
% 3.32/1.65 ( ( member1086024932od_b_b @ C @ ( id_on_250271696od_b_b @ A ) )
% 3.32/1.65 => ~ ! [X4: produc1213276845od_b_b] :
% 3.32/1.65 ( ( member1516365892od_b_b @ X4 @ A )
% 3.32/1.65 => ( C
% 3.32/1.65 != ( produc449289715od_b_b @ X4 @ X4 ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_70_Id__onE,axiom,
% 3.32/1.65 ! [C: product_prod_b_b,A: set_b] :
% 3.32/1.65 ( ( member1285940496od_b_b @ C @ ( id_on_b @ A ) )
% 3.32/1.65 => ~ ! [X4: b] :
% 3.32/1.65 ( ( member_b @ X4 @ A )
% 3.32/1.65 => ( C
% 3.32/1.65 != ( product_Pair_b_b @ X4 @ X4 ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_71_refl__onD2,axiom,
% 3.32/1.65 ! [A: set_Product_prod_b_b,R: set_Pr2007082183od_b_b,X: product_prod_b_b,Y: product_prod_b_b] :
% 3.32/1.65 ( ( refl_o2134473190od_b_b @ A @ R )
% 3.32/1.65 => ( ( member1652792080od_b_b @ ( produc546497367od_b_b @ X @ Y ) @ R )
% 3.32/1.65 => ( member1285940496od_b_b @ Y @ A ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_72_refl__onD2,axiom,
% 3.32/1.65 ! [A: set_Pr1324126435od_b_b,R: set_Pr2109276827od_b_b,X: produc1213276845od_b_b,Y: produc1213276845od_b_b] :
% 3.32/1.65 ( ( refl_o1921098222od_b_b @ A @ R )
% 3.32/1.65 => ( ( member1086024932od_b_b @ ( produc449289715od_b_b @ X @ Y ) @ R )
% 3.32/1.65 => ( member1516365892od_b_b @ Y @ A ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_73_refl__onD2,axiom,
% 3.32/1.65 ! [A: set_b,R: set_Product_prod_b_b,X: b,Y: b] :
% 3.32/1.65 ( ( refl_on_b @ A @ R )
% 3.32/1.65 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ X @ Y ) @ R )
% 3.32/1.65 => ( member_b @ Y @ A ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_74_refl__onD1,axiom,
% 3.32/1.65 ! [A: set_Product_prod_b_b,R: set_Pr2007082183od_b_b,X: product_prod_b_b,Y: product_prod_b_b] :
% 3.32/1.65 ( ( refl_o2134473190od_b_b @ A @ R )
% 3.32/1.65 => ( ( member1652792080od_b_b @ ( produc546497367od_b_b @ X @ Y ) @ R )
% 3.32/1.65 => ( member1285940496od_b_b @ X @ A ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_75_refl__onD1,axiom,
% 3.32/1.65 ! [A: set_Pr1324126435od_b_b,R: set_Pr2109276827od_b_b,X: produc1213276845od_b_b,Y: produc1213276845od_b_b] :
% 3.32/1.65 ( ( refl_o1921098222od_b_b @ A @ R )
% 3.32/1.65 => ( ( member1086024932od_b_b @ ( produc449289715od_b_b @ X @ Y ) @ R )
% 3.32/1.65 => ( member1516365892od_b_b @ X @ A ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_76_refl__onD1,axiom,
% 3.32/1.65 ! [A: set_b,R: set_Product_prod_b_b,X: b,Y: b] :
% 3.32/1.65 ( ( refl_on_b @ A @ R )
% 3.32/1.65 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ X @ Y ) @ R )
% 3.32/1.65 => ( member_b @ X @ A ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_77_refl__onD,axiom,
% 3.32/1.65 ! [A: set_Product_prod_b_b,R: set_Pr2007082183od_b_b,A2: product_prod_b_b] :
% 3.32/1.65 ( ( refl_o2134473190od_b_b @ A @ R )
% 3.32/1.65 => ( ( member1285940496od_b_b @ A2 @ A )
% 3.32/1.65 => ( member1652792080od_b_b @ ( produc546497367od_b_b @ A2 @ A2 ) @ R ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_78_refl__onD,axiom,
% 3.32/1.65 ! [A: set_Pr1324126435od_b_b,R: set_Pr2109276827od_b_b,A2: produc1213276845od_b_b] :
% 3.32/1.65 ( ( refl_o1921098222od_b_b @ A @ R )
% 3.32/1.65 => ( ( member1516365892od_b_b @ A2 @ A )
% 3.32/1.65 => ( member1086024932od_b_b @ ( produc449289715od_b_b @ A2 @ A2 ) @ R ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_79_refl__onD,axiom,
% 3.32/1.65 ! [A: set_b,R: set_Product_prod_b_b,A2: b] :
% 3.32/1.65 ( ( refl_on_b @ A @ R )
% 3.32/1.65 => ( ( member_b @ A2 @ A )
% 3.32/1.65 => ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ A2 ) @ R ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_80_refl__on__Id__on,axiom,
% 3.32/1.65 ! [A: set_b] : ( refl_on_b @ A @ ( id_on_b @ A ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_81_getRel__homR,axiom,
% 3.32/1.65 ! [Y: b,Z: b,L: standard_Constant_a,G: labele1159362096nt_a_b,U: b,F: set_Product_prod_b_b,V: b] :
% 3.32/1.65 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ Y @ Z ) @ ( getRel904497637nt_a_b @ L @ G ) )
% 3.32/1.65 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ Y @ U ) @ F )
% 3.32/1.65 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ Z @ V ) @ F )
% 3.32/1.65 => ( member1285940496od_b_b @ ( product_Pair_b_b @ U @ V ) @ ( getRel904497637nt_a_b @ L @ ( map_gr926947118tant_a @ F @ G ) ) ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_82_maintained__refl,axiom,
% 3.32/1.65 ! [R2: labele935650037_a_nat,G: labele1159362096nt_a_b] : ( mainta1604381365_nat_b @ ( produc1676969687_a_nat @ R2 @ R2 ) @ G ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_83_edge__preserving__on__graphI,axiom,
% 3.32/1.65 ! [X3: labele1835558936od_b_b,F: product_prod_b_b > b,Y2: set_Pr1324126435od_b_b] :
% 3.32/1.65 ( ! [L2: standard_Constant_a,X4: product_prod_b_b,Y3: product_prod_b_b] :
% 3.32/1.65 ( ( member1744485444od_b_b @ ( produc618266719od_b_b @ L2 @ ( produc546497367od_b_b @ X4 @ Y3 ) ) @ ( labele372159959od_b_b @ X3 ) )
% 3.32/1.65 => ( ( member1285940496od_b_b @ X4 @ ( labele442485990od_b_b @ X3 ) )
% 3.32/1.65 => ( ( member1285940496od_b_b @ Y3 @ ( labele442485990od_b_b @ X3 ) )
% 3.32/1.65 => ( member1516365892od_b_b @ ( produc1432590431od_b_b @ L2 @ ( product_Pair_b_b @ ( F @ X4 ) @ ( F @ Y3 ) ) ) @ Y2 ) ) ) )
% 3.32/1.65 => ( edge_p1969196346tant_a @ ( bNF_Gr521784954_b_b_b @ ( labele442485990od_b_b @ X3 ) @ F ) @ ( labele372159959od_b_b @ X3 ) @ Y2 ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_84_edge__preserving__on__graphI,axiom,
% 3.32/1.65 ! [X3: labele1644675410od_b_b,F: produc1213276845od_b_b > b,Y2: set_Pr1324126435od_b_b] :
% 3.32/1.65 ( ! [L2: standard_Constant_a,X4: produc1213276845od_b_b,Y3: produc1213276845od_b_b] :
% 3.32/1.65 ( ( member147868824od_b_b @ ( produc1788032435od_b_b @ L2 @ ( produc449289715od_b_b @ X4 @ Y3 ) ) @ ( labele2032816061od_b_b @ X3 ) )
% 3.32/1.65 => ( ( member1516365892od_b_b @ X4 @ ( labele595103470od_b_b @ X3 ) )
% 3.32/1.65 => ( ( member1516365892od_b_b @ Y3 @ ( labele595103470od_b_b @ X3 ) )
% 3.32/1.65 => ( member1516365892od_b_b @ ( produc1432590431od_b_b @ L2 @ ( product_Pair_b_b @ ( F @ X4 ) @ ( F @ Y3 ) ) ) @ Y2 ) ) ) )
% 3.32/1.65 => ( edge_p1817988046tant_a @ ( bNF_Gr492676974_b_b_b @ ( labele595103470od_b_b @ X3 ) @ F ) @ ( labele2032816061od_b_b @ X3 ) @ Y2 ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_85_edge__preserving__on__graphI,axiom,
% 3.32/1.65 ! [X3: labele1159362096nt_a_b,F: b > b,Y2: set_Pr1324126435od_b_b] :
% 3.32/1.65 ( ! [L2: standard_Constant_a,X4: b,Y3: b] :
% 3.32/1.65 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ L2 @ ( product_Pair_b_b @ X4 @ Y3 ) ) @ ( labele1741081071nt_a_b @ X3 ) )
% 3.32/1.65 => ( ( member_b @ X4 @ ( labele1424214014nt_a_b @ X3 ) )
% 3.32/1.65 => ( ( member_b @ Y3 @ ( labele1424214014nt_a_b @ X3 ) )
% 3.32/1.65 => ( member1516365892od_b_b @ ( produc1432590431od_b_b @ L2 @ ( product_Pair_b_b @ ( F @ X4 ) @ ( F @ Y3 ) ) ) @ Y2 ) ) ) )
% 3.32/1.65 => ( edge_p1384198690tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ X3 ) @ F ) @ ( labele1741081071nt_a_b @ X3 ) @ Y2 ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_86_reflexivity__rule,axiom,
% 3.32/1.65 ! [G: labele1159362096nt_a_b,L: standard_Constant_a] :
% 3.32/1.65 ( ( G
% 3.32/1.65 = ( restri446606278nt_a_b @ G ) )
% 3.32/1.65 => ( ( mainta1604381365_nat_b @ ( standa63370785tant_a @ L ) @ G )
% 3.32/1.65 => ( refl_on_b @ ( labele1424214014nt_a_b @ G ) @ ( getRel904497637nt_a_b @ L @ G ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_87_old_Oprod_Oinject,axiom,
% 3.32/1.65 ! [A2: b,B3: b,A3: b,B4: b] :
% 3.32/1.65 ( ( ( product_Pair_b_b @ A2 @ B3 )
% 3.32/1.65 = ( product_Pair_b_b @ A3 @ B4 ) )
% 3.32/1.65 = ( ( A2 = A3 )
% 3.32/1.65 & ( B3 = B4 ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_88_old_Oprod_Oinject,axiom,
% 3.32/1.65 ! [A2: standard_Constant_a,B3: product_prod_b_b,A3: standard_Constant_a,B4: product_prod_b_b] :
% 3.32/1.65 ( ( ( produc1432590431od_b_b @ A2 @ B3 )
% 3.32/1.65 = ( produc1432590431od_b_b @ A3 @ B4 ) )
% 3.32/1.65 = ( ( A2 = A3 )
% 3.32/1.65 & ( B3 = B4 ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_89_prod_Oinject,axiom,
% 3.32/1.65 ! [X1: b,X22: b,Y1: b,Y22: b] :
% 3.32/1.65 ( ( ( product_Pair_b_b @ X1 @ X22 )
% 3.32/1.65 = ( product_Pair_b_b @ Y1 @ Y22 ) )
% 3.32/1.65 = ( ( X1 = Y1 )
% 3.32/1.65 & ( X22 = Y22 ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_90_prod_Oinject,axiom,
% 3.32/1.65 ! [X1: standard_Constant_a,X22: product_prod_b_b,Y1: standard_Constant_a,Y22: product_prod_b_b] :
% 3.32/1.65 ( ( ( produc1432590431od_b_b @ X1 @ X22 )
% 3.32/1.65 = ( produc1432590431od_b_b @ Y1 @ Y22 ) )
% 3.32/1.65 = ( ( X1 = Y1 )
% 3.32/1.65 & ( X22 = Y22 ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_91_refl__on__domain,axiom,
% 3.32/1.65 ! [A: set_Product_prod_b_b,R: set_Pr2007082183od_b_b,A2: product_prod_b_b,B3: product_prod_b_b] :
% 3.32/1.65 ( ( refl_o2134473190od_b_b @ A @ R )
% 3.32/1.65 => ( ( member1652792080od_b_b @ ( produc546497367od_b_b @ A2 @ B3 ) @ R )
% 3.32/1.65 => ( ( member1285940496od_b_b @ A2 @ A )
% 3.32/1.65 & ( member1285940496od_b_b @ B3 @ A ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_92_refl__on__domain,axiom,
% 3.32/1.65 ! [A: set_Pr1324126435od_b_b,R: set_Pr2109276827od_b_b,A2: produc1213276845od_b_b,B3: produc1213276845od_b_b] :
% 3.32/1.65 ( ( refl_o1921098222od_b_b @ A @ R )
% 3.32/1.65 => ( ( member1086024932od_b_b @ ( produc449289715od_b_b @ A2 @ B3 ) @ R )
% 3.32/1.65 => ( ( member1516365892od_b_b @ A2 @ A )
% 3.32/1.65 & ( member1516365892od_b_b @ B3 @ A ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_93_refl__on__domain,axiom,
% 3.32/1.65 ! [A: set_b,R: set_Product_prod_b_b,A2: b,B3: b] :
% 3.32/1.65 ( ( refl_on_b @ A @ R )
% 3.32/1.65 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ B3 ) @ R )
% 3.32/1.65 => ( ( member_b @ A2 @ A )
% 3.32/1.65 & ( member_b @ B3 @ A ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_94_GrD2,axiom,
% 3.32/1.65 ! [X: b,Fx: b,A: set_b,F: b > b] :
% 3.32/1.65 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ X @ Fx ) @ ( bNF_Gr_b_b @ A @ F ) )
% 3.32/1.65 => ( ( F @ X )
% 3.32/1.65 = Fx ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_95_GrD2,axiom,
% 3.32/1.65 ! [X: standard_Constant_a,Fx: product_prod_b_b,A: set_St761939237tant_a,F: standard_Constant_a > product_prod_b_b] :
% 3.32/1.65 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ X @ Fx ) @ ( bNF_Gr1272216980od_b_b @ A @ F ) )
% 3.32/1.65 => ( ( F @ X )
% 3.32/1.65 = Fx ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_96_GrD1,axiom,
% 3.32/1.65 ! [X: b,Fx: b,A: set_b,F: b > b] :
% 3.32/1.65 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ X @ Fx ) @ ( bNF_Gr_b_b @ A @ F ) )
% 3.32/1.65 => ( member_b @ X @ A ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_97_GrD1,axiom,
% 3.32/1.65 ! [X: standard_Constant_a,Fx: product_prod_b_b,A: set_St761939237tant_a,F: standard_Constant_a > product_prod_b_b] :
% 3.32/1.65 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ X @ Fx ) @ ( bNF_Gr1272216980od_b_b @ A @ F ) )
% 3.32/1.65 => ( member1632892294tant_a @ X @ A ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_98_map__graph__edge__preserving,axiom,
% 3.32/1.65 ! [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 ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_99_edge__preserving__atomic,axiom,
% 3.32/1.65 ! [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] :
% 3.32/1.65 ( ( edge_p1384198690tant_a @ H1 @ E1 @ E2 )
% 3.32/1.65 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ V1 @ V12 ) @ H1 )
% 3.32/1.65 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ V2 @ V22 ) @ H1 )
% 3.32/1.65 => ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ K @ ( product_Pair_b_b @ V1 @ V2 ) ) @ E1 )
% 3.32/1.65 => ( member1516365892od_b_b @ ( produc1432590431od_b_b @ K @ ( product_Pair_b_b @ V12 @ V22 ) ) @ E2 ) ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_100_surj__pair,axiom,
% 3.32/1.65 ! [P2: product_prod_b_b] :
% 3.32/1.65 ? [X4: b,Y3: b] :
% 3.32/1.65 ( P2
% 3.32/1.65 = ( product_Pair_b_b @ X4 @ Y3 ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_101_surj__pair,axiom,
% 3.32/1.65 ! [P2: produc1213276845od_b_b] :
% 3.32/1.65 ? [X4: standard_Constant_a,Y3: product_prod_b_b] :
% 3.32/1.65 ( P2
% 3.32/1.65 = ( produc1432590431od_b_b @ X4 @ Y3 ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_102_prod__cases,axiom,
% 3.32/1.65 ! [P: product_prod_b_b > $o,P2: product_prod_b_b] :
% 3.32/1.65 ( ! [A4: b,B5: b] : ( P @ ( product_Pair_b_b @ A4 @ B5 ) )
% 3.32/1.65 => ( P @ P2 ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_103_prod__cases,axiom,
% 3.32/1.65 ! [P: produc1213276845od_b_b > $o,P2: produc1213276845od_b_b] :
% 3.32/1.65 ( ! [A4: standard_Constant_a,B5: product_prod_b_b] : ( P @ ( produc1432590431od_b_b @ A4 @ B5 ) )
% 3.32/1.65 => ( P @ P2 ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_104_Pair__inject,axiom,
% 3.32/1.65 ! [A2: b,B3: b,A3: b,B4: b] :
% 3.32/1.65 ( ( ( product_Pair_b_b @ A2 @ B3 )
% 3.32/1.65 = ( product_Pair_b_b @ A3 @ B4 ) )
% 3.32/1.65 => ~ ( ( A2 = A3 )
% 3.32/1.65 => ( B3 != B4 ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_105_Pair__inject,axiom,
% 3.32/1.65 ! [A2: standard_Constant_a,B3: product_prod_b_b,A3: standard_Constant_a,B4: product_prod_b_b] :
% 3.32/1.65 ( ( ( produc1432590431od_b_b @ A2 @ B3 )
% 3.32/1.65 = ( produc1432590431od_b_b @ A3 @ B4 ) )
% 3.32/1.65 => ~ ( ( A2 = A3 )
% 3.32/1.65 => ( B3 != B4 ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_106_old_Oprod_Oexhaust,axiom,
% 3.32/1.65 ! [Y: product_prod_b_b] :
% 3.32/1.65 ~ ! [A4: b,B5: b] :
% 3.32/1.65 ( Y
% 3.32/1.65 != ( product_Pair_b_b @ A4 @ B5 ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_107_old_Oprod_Oexhaust,axiom,
% 3.32/1.65 ! [Y: produc1213276845od_b_b] :
% 3.32/1.65 ~ ! [A4: standard_Constant_a,B5: product_prod_b_b] :
% 3.32/1.65 ( Y
% 3.32/1.65 != ( produc1432590431od_b_b @ A4 @ B5 ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_108_old_Oprod_Oinducts,axiom,
% 3.32/1.65 ! [P: product_prod_b_b > $o,Prod: product_prod_b_b] :
% 3.32/1.65 ( ! [A4: b,B5: b] : ( P @ ( product_Pair_b_b @ A4 @ B5 ) )
% 3.32/1.65 => ( P @ Prod ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_109_old_Oprod_Oinducts,axiom,
% 3.32/1.65 ! [P: produc1213276845od_b_b > $o,Prod: produc1213276845od_b_b] :
% 3.32/1.65 ( ! [A4: standard_Constant_a,B5: product_prod_b_b] : ( P @ ( produc1432590431od_b_b @ A4 @ B5 ) )
% 3.32/1.65 => ( P @ Prod ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_110_prod__cases3,axiom,
% 3.32/1.65 ! [Y: produc1213276845od_b_b] :
% 3.32/1.65 ~ ! [A4: standard_Constant_a,B5: b,C2: b] :
% 3.32/1.65 ( Y
% 3.32/1.65 != ( produc1432590431od_b_b @ A4 @ ( product_Pair_b_b @ B5 @ C2 ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_111_prod__induct3,axiom,
% 3.32/1.65 ! [P: produc1213276845od_b_b > $o,X: produc1213276845od_b_b] :
% 3.32/1.65 ( ! [A4: standard_Constant_a,B5: b,C2: b] : ( P @ ( produc1432590431od_b_b @ A4 @ ( product_Pair_b_b @ B5 @ C2 ) ) )
% 3.32/1.65 => ( P @ X ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_112_map__graph__in,axiom,
% 3.32/1.65 ! [G: labele1159362096nt_a_b,A2: b,B3: b,E: allego510293162tant_a,F: b > b] :
% 3.32/1.65 ( ( G
% 3.32/1.65 = ( restri446606278nt_a_b @ G ) )
% 3.32/1.65 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ B3 ) @ ( semant55076487nt_a_b @ G @ E ) )
% 3.32/1.65 => ( member1285940496od_b_b @ ( product_Pair_b_b @ ( F @ A2 ) @ ( F @ B3 ) ) @ ( semant55076487nt_a_b @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ G ) @ F ) @ G ) @ E ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_113_maintainedI,axiom,
% 3.32/1.65 ! [A: labele935650037_a_nat,G: labele1159362096nt_a_b,B: labele935650037_a_nat] :
% 3.32/1.65 ( ! [F3: set_Pr2106913242_nat_b] :
% 3.32/1.65 ( ( graph_714568023_nat_b @ A @ G @ F3 )
% 3.32/1.65 => ( extens1554515172_nat_b @ ( produc1676969687_a_nat @ A @ B ) @ G @ F3 ) )
% 3.32/1.65 => ( mainta1604381365_nat_b @ ( produc1676969687_a_nat @ A @ B ) @ G ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_114_maintainedI,axiom,
% 3.32/1.65 ! [A: labele1159362096nt_a_b,G: labele1159362096nt_a_b,B: labele1159362096nt_a_b] :
% 3.32/1.65 ( ! [F3: set_Product_prod_b_b] :
% 3.32/1.65 ( ( graph_222606102_a_b_b @ A @ G @ F3 )
% 3.32/1.65 => ( extens1779443913_a_b_b @ ( produc1569511545nt_a_b @ A @ B ) @ G @ F3 ) )
% 3.32/1.65 => ( mainta374363448_a_b_b @ ( produc1569511545nt_a_b @ A @ B ) @ G ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_115_extensible__refl__concr,axiom,
% 3.32/1.65 ! [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] :
% 3.32/1.65 ( ( graph_222606102_a_b_b @ ( labele1230159100nt_a_b @ E_1 @ V ) @ G @ F )
% 3.32/1.65 => ( ( extens1779443913_a_b_b @ ( produc1569511545nt_a_b @ ( labele1230159100nt_a_b @ E_1 @ V ) @ ( labele1230159100nt_a_b @ E_2 @ V ) ) @ G @ F )
% 3.32/1.65 = ( graph_222606102_a_b_b @ ( labele1230159100nt_a_b @ E_2 @ V ) @ G @ F ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_116_extensible__refl,axiom,
% 3.32/1.65 ! [R2: labele1159362096nt_a_b,G: labele1159362096nt_a_b,F: set_Product_prod_b_b] :
% 3.32/1.65 ( ( graph_222606102_a_b_b @ R2 @ G @ F )
% 3.32/1.65 => ( extens1779443913_a_b_b @ ( produc1569511545nt_a_b @ R2 @ R2 ) @ G @ F ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_117_graph__homomorphism__semantics,axiom,
% 3.32/1.65 ! [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] :
% 3.32/1.65 ( ( graph_222606102_a_b_b @ A @ B @ F )
% 3.32/1.65 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ B3 ) @ ( semant55076487nt_a_b @ A @ E ) )
% 3.32/1.65 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ A3 ) @ F )
% 3.32/1.65 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ B3 @ B4 ) @ F )
% 3.32/1.65 => ( member1285940496od_b_b @ ( product_Pair_b_b @ A3 @ B4 ) @ ( semant55076487nt_a_b @ B @ E ) ) ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_118_consequence__graphD_I1_J,axiom,
% 3.32/1.65 ! [Rs: set_Pr1987088711_a_nat,G: labele1159362096nt_a_b,R2: produc1871334759_a_nat] :
% 3.32/1.65 ( ( conseq956760372_nat_b @ Rs @ G )
% 3.32/1.65 => ( ( member832397200_a_nat @ R2 @ Rs )
% 3.32/1.65 => ( mainta1604381365_nat_b @ R2 @ G ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_119_semantics__in__vertices_I1_J,axiom,
% 3.32/1.65 ! [A: labele1159362096nt_a_b,A2: b,B3: b,E: allego510293162tant_a] :
% 3.32/1.65 ( ( A
% 3.32/1.65 = ( restri446606278nt_a_b @ A ) )
% 3.32/1.65 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ B3 ) @ ( semant55076487nt_a_b @ A @ E ) )
% 3.32/1.65 => ( member_b @ A2 @ ( labele1424214014nt_a_b @ A ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_120_semantics__in__vertices_I2_J,axiom,
% 3.32/1.65 ! [A: labele1159362096nt_a_b,A2: b,B3: b,E: allego510293162tant_a] :
% 3.32/1.65 ( ( A
% 3.32/1.65 = ( restri446606278nt_a_b @ A ) )
% 3.32/1.65 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ B3 ) @ ( semant55076487nt_a_b @ A @ E ) )
% 3.32/1.65 => ( member_b @ B3 @ ( labele1424214014nt_a_b @ A ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_121_subgraph__semantics,axiom,
% 3.32/1.65 ! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,A2: b,B3: b,E: allego510293162tant_a] :
% 3.32/1.65 ( ( graph_222606102_a_b_b @ A @ B @ ( id_on_b @ ( labele1424214014nt_a_b @ A ) ) )
% 3.32/1.65 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ B3 ) @ ( semant55076487nt_a_b @ A @ E ) )
% 3.32/1.65 => ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ B3 ) @ ( semant55076487nt_a_b @ B @ E ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_122_maintainedD,axiom,
% 3.32/1.65 ! [A: labele935650037_a_nat,B: labele935650037_a_nat,G: labele1159362096nt_a_b,F: set_Pr2106913242_nat_b] :
% 3.32/1.65 ( ( mainta1604381365_nat_b @ ( produc1676969687_a_nat @ A @ B ) @ G )
% 3.32/1.65 => ( ( graph_714568023_nat_b @ A @ G @ F )
% 3.32/1.65 => ( extens1554515172_nat_b @ ( produc1676969687_a_nat @ A @ B ) @ G @ F ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_123_maintainedD,axiom,
% 3.32/1.65 ! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,G: labele1159362096nt_a_b,F: set_Product_prod_b_b] :
% 3.32/1.65 ( ( mainta374363448_a_b_b @ ( produc1569511545nt_a_b @ A @ B ) @ G )
% 3.32/1.65 => ( ( graph_222606102_a_b_b @ A @ G @ F )
% 3.32/1.65 => ( extens1779443913_a_b_b @ ( produc1569511545nt_a_b @ A @ B ) @ G @ F ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_124_extensibleI,axiom,
% 3.32/1.65 ! [R22: labele1159362096nt_a_b,G: labele1159362096nt_a_b,G2: set_Product_prod_b_b,R1: labele1159362096nt_a_b,F: set_Product_prod_b_b] :
% 3.32/1.65 ( ( graph_222606102_a_b_b @ R22 @ G @ G2 )
% 3.32/1.65 => ( ( agree_221379389_a_b_b @ R1 @ F @ G2 )
% 3.32/1.65 => ( extens1779443913_a_b_b @ ( produc1569511545nt_a_b @ R1 @ R22 ) @ G @ F ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_125_subgraph__subset_I2_J,axiom,
% 3.32/1.65 ! [G_1: labele1159362096nt_a_b,G_2: labele1159362096nt_a_b] :
% 3.32/1.65 ( ( graph_222606102_a_b_b @ G_1 @ G_2 @ ( id_on_b @ ( labele1424214014nt_a_b @ G_1 ) ) )
% 3.32/1.65 => ( ord_le123089219od_b_b @ ( labele1741081071nt_a_b @ ( restri446606278nt_a_b @ G_1 ) ) @ ( labele1741081071nt_a_b @ G_2 ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_126_graph__homo__union__id_I1_J,axiom,
% 3.32/1.65 ! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,G: labele1159362096nt_a_b,F: set_Product_prod_b_b] :
% 3.32/1.65 ( ( graph_222606102_a_b_b @ ( graph_1309249505nt_a_b @ A @ B ) @ G @ F )
% 3.32/1.65 => ( ( A
% 3.32/1.65 = ( restri446606278nt_a_b @ A ) )
% 3.32/1.65 => ( graph_222606102_a_b_b @ A @ G @ ( relcomp_b_b_b @ ( id_on_b @ ( labele1424214014nt_a_b @ A ) ) @ F ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_127_graph__homo__union__id_I2_J,axiom,
% 3.32/1.65 ! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,G: labele1159362096nt_a_b,F: set_Product_prod_b_b] :
% 3.32/1.65 ( ( graph_222606102_a_b_b @ ( graph_1309249505nt_a_b @ A @ B ) @ G @ F )
% 3.32/1.65 => ( ( B
% 3.32/1.65 = ( restri446606278nt_a_b @ B ) )
% 3.32/1.65 => ( graph_222606102_a_b_b @ B @ G @ ( relcomp_b_b_b @ ( id_on_b @ ( labele1424214014nt_a_b @ B ) ) @ F ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_128__092_060open_062f_A_092_060equiv_062_A_092_060lambda_062x_O_Aif_AgetRel_AS__Idt_AG_A_096_096_A_123x_125_A_061_A_123_125_Athen_Ax_Aelse_AEps_A_IP_Ax_J_092_060close_062,axiom,
% 3.32/1.65 ( f
% 3.32/1.65 = ( ^ [X5: b] :
% 3.32/1.65 ( if_b
% 3.32/1.65 @ ( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ X5 @ bot_bot_set_b ) )
% 3.32/1.65 = bot_bot_set_b )
% 3.32/1.65 @ X5
% 3.32/1.65 @ ( hilbert_Eps_b @ ( p @ X5 ) ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_129_ImageI,axiom,
% 3.32/1.65 ! [A2: b,B3: product_prod_b_b,R: set_Pr621705391od_b_b,A: set_b] :
% 3.32/1.65 ( ( member641857272od_b_b @ ( produc1257047359od_b_b @ A2 @ B3 ) @ R )
% 3.32/1.65 => ( ( member_b @ A2 @ A )
% 3.32/1.65 => ( member1285940496od_b_b @ B3 @ ( image_1177096571od_b_b @ R @ A ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_130_ImageI,axiom,
% 3.32/1.65 ! [A2: b,B3: produc1213276845od_b_b,R: set_Pr2060523537od_b_b,A: set_b] :
% 3.32/1.65 ( ( member599505522od_b_b @ ( produc800495189od_b_b @ A2 @ B3 ) @ R )
% 3.32/1.65 => ( ( member_b @ A2 @ A )
% 3.32/1.65 => ( member1516365892od_b_b @ B3 @ ( image_984343321od_b_b @ R @ A ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_131_ImageI,axiom,
% 3.32/1.65 ! [A2: product_prod_b_b,B3: b,R: set_Pr357419743_b_b_b,A: set_Product_prod_b_b] :
% 3.32/1.65 ( ( member351494440_b_b_b @ ( produc1001682799_b_b_b @ A2 @ B3 ) @ R )
% 3.32/1.65 => ( ( member1285940496od_b_b @ A2 @ A )
% 3.32/1.65 => ( member_b @ B3 @ ( image_921732011_b_b_b @ R @ A ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_132_ImageI,axiom,
% 3.32/1.65 ! [A2: product_prod_b_b,B3: product_prod_b_b,R: set_Pr2007082183od_b_b,A: set_Product_prod_b_b] :
% 3.32/1.65 ( ( member1652792080od_b_b @ ( produc546497367od_b_b @ A2 @ B3 ) @ R )
% 3.32/1.65 => ( ( member1285940496od_b_b @ A2 @ A )
% 3.32/1.65 => ( member1285940496od_b_b @ B3 @ ( image_1928024979od_b_b @ R @ A ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_133_ImageI,axiom,
% 3.32/1.65 ! [A2: product_prod_b_b,B3: produc1213276845od_b_b,R: set_Pr1071216121od_b_b,A: set_Product_prod_b_b] :
% 3.32/1.65 ( ( member4694106od_b_b @ ( produc732676669od_b_b @ A2 @ B3 ) @ R )
% 3.32/1.65 => ( ( member1285940496od_b_b @ A2 @ A )
% 3.32/1.65 => ( member1516365892od_b_b @ B3 @ ( image_532916993od_b_b @ R @ A ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_134_ImageI,axiom,
% 3.32/1.65 ! [A2: produc1213276845od_b_b,B3: b,R: set_Pr1906739389_b_b_b,A: set_Pr1324126435od_b_b] :
% 3.32/1.65 ( ( member1417789726_b_b_b @ ( produc1580777273_b_b_b @ A2 @ B3 ) @ R )
% 3.32/1.65 => ( ( member1516365892od_b_b @ A2 @ A )
% 3.32/1.65 => ( member_b @ B3 @ ( image_1764625405_b_b_b @ R @ A ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_135_ImageI,axiom,
% 3.32/1.65 ! [A2: produc1213276845od_b_b,B3: product_prod_b_b,R: set_Pr2134561957od_b_b,A: set_Pr1324126435od_b_b] :
% 3.32/1.65 ( ( member942707974od_b_b @ ( produc1597690145od_b_b @ A2 @ B3 ) @ R )
% 3.32/1.65 => ( ( member1516365892od_b_b @ A2 @ A )
% 3.32/1.65 => ( member1285940496od_b_b @ B3 @ ( image_1397930469od_b_b @ R @ A ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_136_ImageI,axiom,
% 3.32/1.65 ! [A2: produc1213276845od_b_b,B3: produc1213276845od_b_b,R: set_Pr2109276827od_b_b,A: set_Pr1324126435od_b_b] :
% 3.32/1.65 ( ( member1086024932od_b_b @ ( produc449289715od_b_b @ A2 @ B3 ) @ R )
% 3.32/1.65 => ( ( member1516365892od_b_b @ A2 @ A )
% 3.32/1.65 => ( member1516365892od_b_b @ B3 @ ( image_763305007od_b_b @ R @ A ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_137_ImageI,axiom,
% 3.32/1.65 ! [A2: b,B3: b,R: set_Product_prod_b_b,A: set_b] :
% 3.32/1.65 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ B3 ) @ R )
% 3.32/1.65 => ( ( member_b @ A2 @ A )
% 3.32/1.65 => ( member_b @ B3 @ ( image_b_b @ R @ A ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_138_ImageI,axiom,
% 3.32/1.65 ! [A2: standard_Constant_a,B3: product_prod_b_b,R: set_Pr1324126435od_b_b,A: set_St761939237tant_a] :
% 3.32/1.65 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A2 @ B3 ) @ R )
% 3.32/1.65 => ( ( member1632892294tant_a @ A2 @ A )
% 3.32/1.65 => ( member1285940496od_b_b @ B3 @ ( image_1916422435od_b_b @ R @ A ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_139_Image__empty2,axiom,
% 3.32/1.65 ! [R2: set_Product_prod_b_b] :
% 3.32/1.65 ( ( image_b_b @ R2 @ bot_bot_set_b )
% 3.32/1.65 = bot_bot_set_b ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_140_Image__empty2,axiom,
% 3.32/1.65 ! [R2: set_Pr1646010159_a_nat] :
% 3.32/1.65 ( ( image_1749766139_a_nat @ R2 @ bot_bot_set_b )
% 3.32/1.65 = bot_bo1836341171_a_nat ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_141_Image__empty2,axiom,
% 3.32/1.65 ! [R2: set_Pr812188767_nat_b] :
% 3.32/1.65 ( ( image_924992811_nat_b @ R2 @ bot_bo1836341171_a_nat )
% 3.32/1.65 = bot_bot_set_b ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_142_Image__empty2,axiom,
% 3.32/1.65 ! [R2: set_Pr924198087_a_nat] :
% 3.32/1.65 ( ( image_1168831379_a_nat @ R2 @ bot_bo1836341171_a_nat )
% 3.32/1.65 = bot_bo1836341171_a_nat ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_143_Image__empty1,axiom,
% 3.32/1.65 ! [X3: set_b] :
% 3.32/1.65 ( ( image_b_b @ bot_bo1343651123od_b_b @ X3 )
% 3.32/1.65 = bot_bot_set_b ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_144_Image__empty1,axiom,
% 3.32/1.65 ! [X3: set_la1083530965_a_nat] :
% 3.32/1.65 ( ( image_1971191571_a_nat @ bot_bo1836341171_a_nat @ X3 )
% 3.32/1.65 = bot_bo2122869057_a_nat ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_145_Id__on__empty,axiom,
% 3.32/1.65 ( ( id_on_689842066_a_nat @ bot_bo2122869057_a_nat )
% 3.32/1.65 = bot_bo1836341171_a_nat ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_146_Id__on__empty,axiom,
% 3.32/1.65 ( ( id_on_b @ bot_bot_set_b )
% 3.32/1.65 = bot_bo1343651123od_b_b ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_147_Id__on__empty,axiom,
% 3.32/1.65 ( ( id_on_1651096324_a_nat @ bot_bo1836341171_a_nat )
% 3.32/1.65 = bot_bo1973379891_a_nat ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_148_Gr__empty,axiom,
% 3.32/1.65 ! [F: labele935650037_a_nat > labele935650037_a_nat] :
% 3.32/1.65 ( ( bNF_Gr996500706_a_nat @ bot_bo2122869057_a_nat @ F )
% 3.32/1.65 = bot_bo1836341171_a_nat ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_149_Gr__empty,axiom,
% 3.32/1.65 ! [F: b > b] :
% 3.32/1.65 ( ( bNF_Gr_b_b @ bot_bot_set_b @ F )
% 3.32/1.65 = bot_bo1343651123od_b_b ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_150_graph__homomorphism__composes,axiom,
% 3.32/1.65 ! [A2: labele1159362096nt_a_b,B3: labele1159362096nt_a_b,X: set_Product_prod_b_b,C: labele1159362096nt_a_b,Y: set_Product_prod_b_b] :
% 3.32/1.65 ( ( graph_222606102_a_b_b @ A2 @ B3 @ X )
% 3.32/1.65 => ( ( graph_222606102_a_b_b @ B3 @ C @ Y )
% 3.32/1.65 => ( graph_222606102_a_b_b @ A2 @ C @ ( relcomp_b_b_b @ X @ Y ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_151_P__eq,axiom,
% 3.32/1.65 ! [X: b] :
% 3.32/1.65 ( ( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ X @ bot_bot_set_b ) )
% 3.32/1.65 != bot_bot_set_b )
% 3.32/1.65 => ( ( hilbert_Eps_b @ ( p @ ( hilbert_Eps_b @ ( p @ X ) ) ) )
% 3.32/1.65 = ( hilbert_Eps_b @ ( p @ X ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_152_Gr__insert,axiom,
% 3.32/1.65 ! [X: labele935650037_a_nat,F2: set_la1083530965_a_nat,F: labele935650037_a_nat > labele935650037_a_nat] :
% 3.32/1.65 ( ( bNF_Gr996500706_a_nat @ ( insert1167839429_a_nat @ X @ F2 ) @ F )
% 3.32/1.65 = ( insert1574423351_a_nat @ ( produc1676969687_a_nat @ X @ ( F @ X ) ) @ ( bNF_Gr996500706_a_nat @ F2 @ F ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_153_Gr__insert,axiom,
% 3.32/1.65 ! [X: b,F2: set_b,F: b > b] :
% 3.32/1.65 ( ( bNF_Gr_b_b @ ( insert_b @ X @ F2 ) @ F )
% 3.32/1.65 = ( insert1952693431od_b_b @ ( product_Pair_b_b @ X @ ( F @ X ) ) @ ( bNF_Gr_b_b @ F2 @ F ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_154_Gr__insert,axiom,
% 3.32/1.65 ! [X: standard_Constant_a,F2: set_St761939237tant_a,F: standard_Constant_a > product_prod_b_b] :
% 3.32/1.65 ( ( bNF_Gr1272216980od_b_b @ ( insert1909710879tant_a @ X @ F2 ) @ F )
% 3.32/1.65 = ( insert2037698781od_b_b @ ( produc1432590431od_b_b @ X @ ( F @ X ) ) @ ( bNF_Gr1272216980od_b_b @ F2 @ F ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_155_map__graph__selectors_I1_J,axiom,
% 3.32/1.65 ! [F: set_Product_prod_b_b,G: labele1159362096nt_a_b] :
% 3.32/1.65 ( ( labele1424214014nt_a_b @ ( map_gr926947118tant_a @ F @ G ) )
% 3.32/1.65 = ( image_b_b @ F @ ( labele1424214014nt_a_b @ G ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_156_Image__singleton__iff,axiom,
% 3.32/1.65 ! [B3: product_prod_b_b,R: set_Pr1324126435od_b_b,A2: standard_Constant_a] :
% 3.32/1.65 ( ( member1285940496od_b_b @ B3 @ ( image_1916422435od_b_b @ R @ ( insert1909710879tant_a @ A2 @ bot_bo1160111033tant_a ) ) )
% 3.32/1.65 = ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A2 @ B3 ) @ R ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_157_Image__singleton__iff,axiom,
% 3.32/1.65 ! [B3: product_prod_b_b,R: set_Pr621705391od_b_b,A2: b] :
% 3.32/1.65 ( ( member1285940496od_b_b @ B3 @ ( image_1177096571od_b_b @ R @ ( insert_b @ A2 @ bot_bot_set_b ) ) )
% 3.32/1.65 = ( member641857272od_b_b @ ( produc1257047359od_b_b @ A2 @ B3 ) @ R ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_158_Image__singleton__iff,axiom,
% 3.32/1.65 ! [B3: produc1213276845od_b_b,R: set_Pr2060523537od_b_b,A2: b] :
% 3.32/1.65 ( ( member1516365892od_b_b @ B3 @ ( image_984343321od_b_b @ R @ ( insert_b @ A2 @ bot_bot_set_b ) ) )
% 3.32/1.65 = ( member599505522od_b_b @ ( produc800495189od_b_b @ A2 @ B3 ) @ R ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_159_Image__singleton__iff,axiom,
% 3.32/1.65 ! [B3: b,R: set_Product_prod_b_b,A2: b] :
% 3.32/1.65 ( ( member_b @ B3 @ ( image_b_b @ R @ ( insert_b @ A2 @ bot_bot_set_b ) ) )
% 3.32/1.65 = ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ B3 ) @ R ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_160_Image__singleton__iff,axiom,
% 3.32/1.65 ! [B3: b,R: set_Pr812188767_nat_b,A2: produc1871334759_a_nat] :
% 3.32/1.65 ( ( member_b @ B3 @ ( image_924992811_nat_b @ R @ ( insert1574423351_a_nat @ A2 @ bot_bo1836341171_a_nat ) ) )
% 3.32/1.65 = ( member1544800936_nat_b @ ( produc2059954415_nat_b @ A2 @ B3 ) @ R ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_161_Image__singleton__iff,axiom,
% 3.32/1.65 ! [B3: product_prod_b_b,R: set_Pr667377223od_b_b,A2: produc1871334759_a_nat] :
% 3.32/1.65 ( ( member1285940496od_b_b @ B3 @ ( image_1214223635od_b_b @ R @ ( insert1574423351_a_nat @ A2 @ bot_bo1836341171_a_nat ) ) )
% 3.32/1.65 = ( member301892752od_b_b @ ( produc590959831od_b_b @ A2 @ B3 ) @ R ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_162_Image__singleton__iff,axiom,
% 3.32/1.65 ! [B3: produc1213276845od_b_b,R: set_Pr1954438265od_b_b,A2: produc1871334759_a_nat] :
% 3.32/1.65 ( ( member1516365892od_b_b @ B3 @ ( image_480774529od_b_b @ R @ ( insert1574423351_a_nat @ A2 @ bot_bo1836341171_a_nat ) ) )
% 3.32/1.65 = ( member1533761242od_b_b @ ( produc401731773od_b_b @ A2 @ B3 ) @ R ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_163_in__on__graph,axiom,
% 3.32/1.65 ! [X: b,G: labele1159362096nt_a_b,A2: b > b,Y: b,B3: set_Product_prod_b_b] :
% 3.32/1.65 ( ( member_b @ X @ ( labele1424214014nt_a_b @ G ) )
% 3.32/1.65 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ ( A2 @ X ) @ Y ) @ B3 )
% 3.32/1.65 => ( member1285940496od_b_b @ ( product_Pair_b_b @ X @ Y ) @ ( relcomp_b_b_b @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ G ) @ A2 ) @ B3 ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_164_in__on__graph,axiom,
% 3.32/1.65 ! [X: b,G: labele1159362096nt_a_b,A2: b > standard_Constant_a,Y: product_prod_b_b,B3: set_Pr1324126435od_b_b] :
% 3.32/1.65 ( ( member_b @ X @ ( labele1424214014nt_a_b @ G ) )
% 3.32/1.65 => ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ ( A2 @ X ) @ Y ) @ B3 )
% 3.32/1.65 => ( member641857272od_b_b @ ( produc1257047359od_b_b @ X @ Y ) @ ( relcom112561144od_b_b @ ( bNF_Gr230160332tant_a @ ( labele1424214014nt_a_b @ G ) @ A2 ) @ B3 ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_165_graph__homomorphism__empty,axiom,
% 3.32/1.65 ! [G: labele1159362096nt_a_b,F: set_Pr812188767_nat_b] :
% 3.32/1.65 ( ( graph_726202286_nat_b @ ( labele27098724_a_nat @ bot_bo1653310327_a_nat @ bot_bo1836341171_a_nat ) @ G @ F )
% 3.32/1.65 = ( ( F = bot_bo1113554635_nat_b )
% 3.32/1.65 & ( G
% 3.32/1.65 = ( restri446606278nt_a_b @ G ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_166_graph__homomorphism__empty,axiom,
% 3.32/1.65 ! [G: labele1159362096nt_a_b,F: set_Product_prod_b_b] :
% 3.32/1.65 ( ( graph_222606102_a_b_b @ ( labele1230159100nt_a_b @ bot_bo1664927607od_b_b @ bot_bot_set_b ) @ G @ F )
% 3.32/1.65 = ( ( F = bot_bo1343651123od_b_b )
% 3.32/1.65 & ( G
% 3.32/1.65 = ( restri446606278nt_a_b @ G ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_167_graph__unionI,axiom,
% 3.32/1.65 ! [G_1: labele1159362096nt_a_b,G_2: labele1159362096nt_a_b] :
% 3.32/1.65 ( ( ord_le123089219od_b_b @ ( labele1741081071nt_a_b @ G_1 ) @ ( labele1741081071nt_a_b @ G_2 ) )
% 3.32/1.65 => ( ( ord_less_eq_set_b @ ( labele1424214014nt_a_b @ G_1 ) @ ( labele1424214014nt_a_b @ G_2 ) )
% 3.32/1.65 => ( ( graph_1309249505nt_a_b @ G_1 @ G_2 )
% 3.32/1.65 = G_2 ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_168_graph__single,axiom,
% 3.32/1.65 ! [A2: standard_Constant_a,B3: b,C: b] :
% 3.32/1.65 ( ( 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 ) ) )
% 3.32/1.65 = ( restri446606278nt_a_b @ ( 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 ) ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_169_r2,axiom,
% 3.32/1.65 ! [X: b] :
% 3.32/1.65 ( ( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ X @ bot_bot_set_b ) )
% 3.32/1.65 = bot_bot_set_b )
% 3.32/1.65 = ( ~ ( member_b @ X @ ( labele1424214014nt_a_b @ g ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_170_refl__on__singleton,axiom,
% 3.32/1.65 ! [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 ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_171_refl__on__singleton,axiom,
% 3.32/1.65 ! [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 ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_172_refl__on__singleton,axiom,
% 3.32/1.65 ! [X: produc1871334759_a_nat] : ( refl_o1213627494_a_nat @ ( insert1574423351_a_nat @ X @ bot_bo1836341171_a_nat ) @ ( insert1810136247_a_nat @ ( produc1677124439_a_nat @ X @ X ) @ bot_bo1973379891_a_nat ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_173_rev__ImageI,axiom,
% 3.32/1.65 ! [A2: b,A: set_b,B3: product_prod_b_b,R: set_Pr621705391od_b_b] :
% 3.32/1.65 ( ( member_b @ A2 @ A )
% 3.32/1.65 => ( ( member641857272od_b_b @ ( produc1257047359od_b_b @ A2 @ B3 ) @ R )
% 3.32/1.65 => ( member1285940496od_b_b @ B3 @ ( image_1177096571od_b_b @ R @ A ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_174_rev__ImageI,axiom,
% 3.32/1.65 ! [A2: b,A: set_b,B3: produc1213276845od_b_b,R: set_Pr2060523537od_b_b] :
% 3.32/1.65 ( ( member_b @ A2 @ A )
% 3.32/1.65 => ( ( member599505522od_b_b @ ( produc800495189od_b_b @ A2 @ B3 ) @ R )
% 3.32/1.65 => ( member1516365892od_b_b @ B3 @ ( image_984343321od_b_b @ R @ A ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_175_rev__ImageI,axiom,
% 3.32/1.65 ! [A2: product_prod_b_b,A: set_Product_prod_b_b,B3: b,R: set_Pr357419743_b_b_b] :
% 3.32/1.65 ( ( member1285940496od_b_b @ A2 @ A )
% 3.32/1.65 => ( ( member351494440_b_b_b @ ( produc1001682799_b_b_b @ A2 @ B3 ) @ R )
% 3.32/1.65 => ( member_b @ B3 @ ( image_921732011_b_b_b @ R @ A ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_176_rev__ImageI,axiom,
% 3.32/1.65 ! [A2: product_prod_b_b,A: set_Product_prod_b_b,B3: product_prod_b_b,R: set_Pr2007082183od_b_b] :
% 3.32/1.65 ( ( member1285940496od_b_b @ A2 @ A )
% 3.32/1.65 => ( ( member1652792080od_b_b @ ( produc546497367od_b_b @ A2 @ B3 ) @ R )
% 3.32/1.65 => ( member1285940496od_b_b @ B3 @ ( image_1928024979od_b_b @ R @ A ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_177_rev__ImageI,axiom,
% 3.32/1.65 ! [A2: product_prod_b_b,A: set_Product_prod_b_b,B3: produc1213276845od_b_b,R: set_Pr1071216121od_b_b] :
% 3.32/1.65 ( ( member1285940496od_b_b @ A2 @ A )
% 3.32/1.65 => ( ( member4694106od_b_b @ ( produc732676669od_b_b @ A2 @ B3 ) @ R )
% 3.32/1.65 => ( member1516365892od_b_b @ B3 @ ( image_532916993od_b_b @ R @ A ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_178_rev__ImageI,axiom,
% 3.32/1.65 ! [A2: produc1213276845od_b_b,A: set_Pr1324126435od_b_b,B3: b,R: set_Pr1906739389_b_b_b] :
% 3.32/1.65 ( ( member1516365892od_b_b @ A2 @ A )
% 3.32/1.65 => ( ( member1417789726_b_b_b @ ( produc1580777273_b_b_b @ A2 @ B3 ) @ R )
% 3.32/1.65 => ( member_b @ B3 @ ( image_1764625405_b_b_b @ R @ A ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_179_rev__ImageI,axiom,
% 3.32/1.65 ! [A2: produc1213276845od_b_b,A: set_Pr1324126435od_b_b,B3: product_prod_b_b,R: set_Pr2134561957od_b_b] :
% 3.32/1.65 ( ( member1516365892od_b_b @ A2 @ A )
% 3.32/1.65 => ( ( member942707974od_b_b @ ( produc1597690145od_b_b @ A2 @ B3 ) @ R )
% 3.32/1.65 => ( member1285940496od_b_b @ B3 @ ( image_1397930469od_b_b @ R @ A ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_180_rev__ImageI,axiom,
% 3.32/1.65 ! [A2: produc1213276845od_b_b,A: set_Pr1324126435od_b_b,B3: produc1213276845od_b_b,R: set_Pr2109276827od_b_b] :
% 3.32/1.65 ( ( member1516365892od_b_b @ A2 @ A )
% 3.32/1.65 => ( ( member1086024932od_b_b @ ( produc449289715od_b_b @ A2 @ B3 ) @ R )
% 3.32/1.65 => ( member1516365892od_b_b @ B3 @ ( image_763305007od_b_b @ R @ A ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_181_rev__ImageI,axiom,
% 3.32/1.65 ! [A2: b,A: set_b,B3: b,R: set_Product_prod_b_b] :
% 3.32/1.65 ( ( member_b @ A2 @ A )
% 3.32/1.65 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ B3 ) @ R )
% 3.32/1.65 => ( member_b @ B3 @ ( image_b_b @ R @ A ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_182_rev__ImageI,axiom,
% 3.32/1.65 ! [A2: standard_Constant_a,A: set_St761939237tant_a,B3: product_prod_b_b,R: set_Pr1324126435od_b_b] :
% 3.32/1.65 ( ( member1632892294tant_a @ A2 @ A )
% 3.32/1.65 => ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A2 @ B3 ) @ R )
% 3.32/1.65 => ( member1285940496od_b_b @ B3 @ ( image_1916422435od_b_b @ R @ A ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_183_Image__iff,axiom,
% 3.32/1.65 ! [B3: b,R: set_Product_prod_b_b,A: set_b] :
% 3.32/1.65 ( ( member_b @ B3 @ ( image_b_b @ R @ A ) )
% 3.32/1.65 = ( ? [X5: b] :
% 3.32/1.65 ( ( member_b @ X5 @ A )
% 3.32/1.65 & ( member1285940496od_b_b @ ( product_Pair_b_b @ X5 @ B3 ) @ R ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_184_Image__iff,axiom,
% 3.32/1.65 ! [B3: product_prod_b_b,R: set_Pr1324126435od_b_b,A: set_St761939237tant_a] :
% 3.32/1.65 ( ( member1285940496od_b_b @ B3 @ ( image_1916422435od_b_b @ R @ A ) )
% 3.32/1.65 = ( ? [X5: standard_Constant_a] :
% 3.32/1.65 ( ( member1632892294tant_a @ X5 @ A )
% 3.32/1.65 & ( member1516365892od_b_b @ ( produc1432590431od_b_b @ X5 @ B3 ) @ R ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_185_ImageE,axiom,
% 3.32/1.65 ! [B3: b,R: set_Pr357419743_b_b_b,A: set_Product_prod_b_b] :
% 3.32/1.65 ( ( member_b @ B3 @ ( image_921732011_b_b_b @ R @ A ) )
% 3.32/1.65 => ~ ! [X4: product_prod_b_b] :
% 3.32/1.65 ( ( member351494440_b_b_b @ ( produc1001682799_b_b_b @ X4 @ B3 ) @ R )
% 3.32/1.65 => ~ ( member1285940496od_b_b @ X4 @ A ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_186_ImageE,axiom,
% 3.32/1.65 ! [B3: b,R: set_Pr1906739389_b_b_b,A: set_Pr1324126435od_b_b] :
% 3.32/1.65 ( ( member_b @ B3 @ ( image_1764625405_b_b_b @ R @ A ) )
% 3.32/1.65 => ~ ! [X4: produc1213276845od_b_b] :
% 3.32/1.65 ( ( member1417789726_b_b_b @ ( produc1580777273_b_b_b @ X4 @ B3 ) @ R )
% 3.32/1.65 => ~ ( member1516365892od_b_b @ X4 @ A ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_187_ImageE,axiom,
% 3.32/1.65 ! [B3: product_prod_b_b,R: set_Pr621705391od_b_b,A: set_b] :
% 3.32/1.65 ( ( member1285940496od_b_b @ B3 @ ( image_1177096571od_b_b @ R @ A ) )
% 3.32/1.65 => ~ ! [X4: b] :
% 3.32/1.65 ( ( member641857272od_b_b @ ( produc1257047359od_b_b @ X4 @ B3 ) @ R )
% 3.32/1.65 => ~ ( member_b @ X4 @ A ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_188_ImageE,axiom,
% 3.32/1.65 ! [B3: product_prod_b_b,R: set_Pr2007082183od_b_b,A: set_Product_prod_b_b] :
% 3.32/1.65 ( ( member1285940496od_b_b @ B3 @ ( image_1928024979od_b_b @ R @ A ) )
% 3.32/1.65 => ~ ! [X4: product_prod_b_b] :
% 3.32/1.65 ( ( member1652792080od_b_b @ ( produc546497367od_b_b @ X4 @ B3 ) @ R )
% 3.32/1.65 => ~ ( member1285940496od_b_b @ X4 @ A ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_189_ImageE,axiom,
% 3.32/1.65 ! [B3: product_prod_b_b,R: set_Pr2134561957od_b_b,A: set_Pr1324126435od_b_b] :
% 3.32/1.65 ( ( member1285940496od_b_b @ B3 @ ( image_1397930469od_b_b @ R @ A ) )
% 3.32/1.65 => ~ ! [X4: produc1213276845od_b_b] :
% 3.32/1.65 ( ( member942707974od_b_b @ ( produc1597690145od_b_b @ X4 @ B3 ) @ R )
% 3.32/1.65 => ~ ( member1516365892od_b_b @ X4 @ A ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_190_ImageE,axiom,
% 3.32/1.65 ! [B3: produc1213276845od_b_b,R: set_Pr2060523537od_b_b,A: set_b] :
% 3.32/1.65 ( ( member1516365892od_b_b @ B3 @ ( image_984343321od_b_b @ R @ A ) )
% 3.32/1.65 => ~ ! [X4: b] :
% 3.32/1.65 ( ( member599505522od_b_b @ ( produc800495189od_b_b @ X4 @ B3 ) @ R )
% 3.32/1.65 => ~ ( member_b @ X4 @ A ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_191_ImageE,axiom,
% 3.32/1.65 ! [B3: produc1213276845od_b_b,R: set_Pr1071216121od_b_b,A: set_Product_prod_b_b] :
% 3.32/1.65 ( ( member1516365892od_b_b @ B3 @ ( image_532916993od_b_b @ R @ A ) )
% 3.32/1.65 => ~ ! [X4: product_prod_b_b] :
% 3.32/1.65 ( ( member4694106od_b_b @ ( produc732676669od_b_b @ X4 @ B3 ) @ R )
% 3.32/1.65 => ~ ( member1285940496od_b_b @ X4 @ A ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_192_ImageE,axiom,
% 3.32/1.65 ! [B3: produc1213276845od_b_b,R: set_Pr2109276827od_b_b,A: set_Pr1324126435od_b_b] :
% 3.32/1.65 ( ( member1516365892od_b_b @ B3 @ ( image_763305007od_b_b @ R @ A ) )
% 3.32/1.65 => ~ ! [X4: produc1213276845od_b_b] :
% 3.32/1.65 ( ( member1086024932od_b_b @ ( produc449289715od_b_b @ X4 @ B3 ) @ R )
% 3.32/1.65 => ~ ( member1516365892od_b_b @ X4 @ A ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_193_ImageE,axiom,
% 3.32/1.65 ! [B3: b,R: set_Product_prod_b_b,A: set_b] :
% 3.32/1.65 ( ( member_b @ B3 @ ( image_b_b @ R @ A ) )
% 3.32/1.65 => ~ ! [X4: b] :
% 3.32/1.65 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ X4 @ B3 ) @ R )
% 3.32/1.65 => ~ ( member_b @ X4 @ A ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_194_ImageE,axiom,
% 3.32/1.65 ! [B3: product_prod_b_b,R: set_Pr1324126435od_b_b,A: set_St761939237tant_a] :
% 3.32/1.65 ( ( member1285940496od_b_b @ B3 @ ( image_1916422435od_b_b @ R @ A ) )
% 3.32/1.65 => ~ ! [X4: standard_Constant_a] :
% 3.32/1.65 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ X4 @ B3 ) @ R )
% 3.32/1.65 => ~ ( member1632892294tant_a @ X4 @ A ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_195_relcomp_OrelcompI,axiom,
% 3.32/1.65 ! [A2: standard_Constant_a,B3: standard_Constant_a,R: set_Pr154086431tant_a,C: product_prod_b_b,S: set_Pr1324126435od_b_b] :
% 3.32/1.65 ( ( member1214736488tant_a @ ( produc342647tant_a @ A2 @ B3 ) @ R )
% 3.32/1.65 => ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ B3 @ C ) @ S )
% 3.32/1.65 => ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A2 @ C ) @ ( relcom883816262od_b_b @ R @ S ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_196_relcomp_OrelcompI,axiom,
% 3.32/1.65 ! [A2: b,B3: b,R: set_Product_prod_b_b,C: b,S: set_Product_prod_b_b] :
% 3.32/1.65 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ B3 ) @ R )
% 3.32/1.65 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ B3 @ C ) @ S )
% 3.32/1.65 => ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ C ) @ ( relcomp_b_b_b @ R @ S ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_197_relcomp_OrelcompI,axiom,
% 3.32/1.65 ! [A2: standard_Constant_a,B3: product_prod_b_b,R: set_Pr1324126435od_b_b,C: product_prod_b_b,S: set_Pr2007082183od_b_b] :
% 3.32/1.65 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A2 @ B3 ) @ R )
% 3.32/1.65 => ( ( member1652792080od_b_b @ ( produc546497367od_b_b @ B3 @ C ) @ S )
% 3.32/1.65 => ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A2 @ C ) @ ( relcom1823941168od_b_b @ R @ S ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_198_relcomp_Oinducts,axiom,
% 3.32/1.65 ! [X1: b,X22: b,R: set_Product_prod_b_b,S: set_Product_prod_b_b,P: b > b > $o] :
% 3.32/1.65 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ X1 @ X22 ) @ ( relcomp_b_b_b @ R @ S ) )
% 3.32/1.65 => ( ! [A4: b,B5: b,C2: b] :
% 3.32/1.65 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A4 @ B5 ) @ R )
% 3.32/1.65 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ B5 @ C2 ) @ S )
% 3.32/1.65 => ( P @ A4 @ C2 ) ) )
% 3.32/1.65 => ( P @ X1 @ X22 ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_199_relcomp_Oinducts,axiom,
% 3.32/1.65 ! [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 > $o] :
% 3.32/1.65 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ X1 @ X22 ) @ ( relcom883816262od_b_b @ R @ S ) )
% 3.32/1.65 => ( ! [A4: standard_Constant_a,B5: standard_Constant_a,C2: product_prod_b_b] :
% 3.32/1.65 ( ( member1214736488tant_a @ ( produc342647tant_a @ A4 @ B5 ) @ R )
% 3.32/1.65 => ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ B5 @ C2 ) @ S )
% 3.32/1.65 => ( P @ A4 @ C2 ) ) )
% 3.32/1.65 => ( P @ X1 @ X22 ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_200_relcomp_Oinducts,axiom,
% 3.32/1.65 ! [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 > $o] :
% 3.32/1.65 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ X1 @ X22 ) @ ( relcom1823941168od_b_b @ R @ S ) )
% 3.32/1.65 => ( ! [A4: standard_Constant_a,B5: product_prod_b_b,C2: product_prod_b_b] :
% 3.32/1.65 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A4 @ B5 ) @ R )
% 3.32/1.65 => ( ( member1652792080od_b_b @ ( produc546497367od_b_b @ B5 @ C2 ) @ S )
% 3.32/1.65 => ( P @ A4 @ C2 ) ) )
% 3.32/1.65 => ( P @ X1 @ X22 ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_201_relcomp_Osimps,axiom,
% 3.32/1.65 ! [A1: b,A22: b,R: set_Product_prod_b_b,S: set_Product_prod_b_b] :
% 3.32/1.65 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A1 @ A22 ) @ ( relcomp_b_b_b @ R @ S ) )
% 3.32/1.65 = ( ? [A5: b,B6: b,C3: b] :
% 3.32/1.65 ( ( A1 = A5 )
% 3.32/1.65 & ( A22 = C3 )
% 3.32/1.65 & ( member1285940496od_b_b @ ( product_Pair_b_b @ A5 @ B6 ) @ R )
% 3.32/1.65 & ( member1285940496od_b_b @ ( product_Pair_b_b @ B6 @ C3 ) @ S ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_202_relcomp_Osimps,axiom,
% 3.32/1.65 ! [A1: standard_Constant_a,A22: product_prod_b_b,R: set_Pr154086431tant_a,S: set_Pr1324126435od_b_b] :
% 3.32/1.65 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A1 @ A22 ) @ ( relcom883816262od_b_b @ R @ S ) )
% 3.32/1.65 = ( ? [A5: standard_Constant_a,B6: standard_Constant_a,C3: product_prod_b_b] :
% 3.32/1.65 ( ( A1 = A5 )
% 3.32/1.65 & ( A22 = C3 )
% 3.32/1.65 & ( member1214736488tant_a @ ( produc342647tant_a @ A5 @ B6 ) @ R )
% 3.32/1.65 & ( member1516365892od_b_b @ ( produc1432590431od_b_b @ B6 @ C3 ) @ S ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_203_relcomp_Osimps,axiom,
% 3.32/1.65 ! [A1: standard_Constant_a,A22: product_prod_b_b,R: set_Pr1324126435od_b_b,S: set_Pr2007082183od_b_b] :
% 3.32/1.65 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A1 @ A22 ) @ ( relcom1823941168od_b_b @ R @ S ) )
% 3.32/1.65 = ( ? [A5: standard_Constant_a,B6: product_prod_b_b,C3: product_prod_b_b] :
% 3.32/1.65 ( ( A1 = A5 )
% 3.32/1.65 & ( A22 = C3 )
% 3.32/1.65 & ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A5 @ B6 ) @ R )
% 3.32/1.65 & ( member1652792080od_b_b @ ( produc546497367od_b_b @ B6 @ C3 ) @ S ) ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_204_relcomp_Ocases,axiom,
% 3.32/1.65 ! [A1: b,A22: b,R: set_Product_prod_b_b,S: set_Product_prod_b_b] :
% 3.32/1.65 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A1 @ A22 ) @ ( relcomp_b_b_b @ R @ S ) )
% 3.32/1.65 => ~ ! [B5: b] :
% 3.32/1.65 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A1 @ B5 ) @ R )
% 3.32/1.65 => ~ ( member1285940496od_b_b @ ( product_Pair_b_b @ B5 @ A22 ) @ S ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_205_relcomp_Ocases,axiom,
% 3.32/1.65 ! [A1: standard_Constant_a,A22: product_prod_b_b,R: set_Pr154086431tant_a,S: set_Pr1324126435od_b_b] :
% 3.32/1.65 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A1 @ A22 ) @ ( relcom883816262od_b_b @ R @ S ) )
% 3.32/1.65 => ~ ! [B5: standard_Constant_a] :
% 3.32/1.65 ( ( member1214736488tant_a @ ( produc342647tant_a @ A1 @ B5 ) @ R )
% 3.32/1.65 => ~ ( member1516365892od_b_b @ ( produc1432590431od_b_b @ B5 @ A22 ) @ S ) ) ) ).
% 3.32/1.65
% 3.32/1.65 thf(fact_206_relcomp_Ocases,axiom,
% 3.32/1.65 ! [A1: standard_Constant_a,A22: product_prod_b_b,R: set_Pr1324126435od_b_b,S: set_Pr2007082183od_b_b] :
% 3.32/1.65 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A1 @ A22 ) @ ( relcom1823941168od_b_b @ R @ S ) )
% 3.32/1.66 => ~ ! [B5: product_prod_b_b] :
% 3.32/1.66 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A1 @ B5 ) @ R )
% 3.32/1.66 => ~ ( member1652792080od_b_b @ ( produc546497367od_b_b @ B5 @ A22 ) @ S ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_207_relcompEpair,axiom,
% 3.32/1.66 ! [A2: b,C: b,R: set_Product_prod_b_b,S: set_Product_prod_b_b] :
% 3.32/1.66 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ C ) @ ( relcomp_b_b_b @ R @ S ) )
% 3.32/1.66 => ~ ! [B5: b] :
% 3.32/1.66 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ B5 ) @ R )
% 3.32/1.66 => ~ ( member1285940496od_b_b @ ( product_Pair_b_b @ B5 @ C ) @ S ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_208_relcompEpair,axiom,
% 3.32/1.66 ! [A2: standard_Constant_a,C: product_prod_b_b,R: set_Pr154086431tant_a,S: set_Pr1324126435od_b_b] :
% 3.32/1.66 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A2 @ C ) @ ( relcom883816262od_b_b @ R @ S ) )
% 3.32/1.66 => ~ ! [B5: standard_Constant_a] :
% 3.32/1.66 ( ( member1214736488tant_a @ ( produc342647tant_a @ A2 @ B5 ) @ R )
% 3.32/1.66 => ~ ( member1516365892od_b_b @ ( produc1432590431od_b_b @ B5 @ C ) @ S ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_209_relcompEpair,axiom,
% 3.32/1.66 ! [A2: standard_Constant_a,C: product_prod_b_b,R: set_Pr1324126435od_b_b,S: set_Pr2007082183od_b_b] :
% 3.32/1.66 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A2 @ C ) @ ( relcom1823941168od_b_b @ R @ S ) )
% 3.32/1.66 => ~ ! [B5: product_prod_b_b] :
% 3.32/1.66 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A2 @ B5 ) @ R )
% 3.32/1.66 => ~ ( member1652792080od_b_b @ ( produc546497367od_b_b @ B5 @ C ) @ S ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_210_relcompE,axiom,
% 3.32/1.66 ! [Xz: product_prod_b_b,R: set_Product_prod_b_b,S: set_Product_prod_b_b] :
% 3.32/1.66 ( ( member1285940496od_b_b @ Xz @ ( relcomp_b_b_b @ R @ S ) )
% 3.32/1.66 => ~ ! [X4: b,Y3: b,Z2: b] :
% 3.32/1.66 ( ( Xz
% 3.32/1.66 = ( product_Pair_b_b @ X4 @ Z2 ) )
% 3.32/1.66 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ X4 @ Y3 ) @ R )
% 3.32/1.66 => ~ ( member1285940496od_b_b @ ( product_Pair_b_b @ Y3 @ Z2 ) @ S ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_211_relcompE,axiom,
% 3.32/1.66 ! [Xz: produc1213276845od_b_b,R: set_Pr154086431tant_a,S: set_Pr1324126435od_b_b] :
% 3.32/1.66 ( ( member1516365892od_b_b @ Xz @ ( relcom883816262od_b_b @ R @ S ) )
% 3.32/1.66 => ~ ! [X4: standard_Constant_a,Y3: standard_Constant_a,Z2: product_prod_b_b] :
% 3.32/1.66 ( ( Xz
% 3.32/1.66 = ( produc1432590431od_b_b @ X4 @ Z2 ) )
% 3.32/1.66 => ( ( member1214736488tant_a @ ( produc342647tant_a @ X4 @ Y3 ) @ R )
% 3.32/1.66 => ~ ( member1516365892od_b_b @ ( produc1432590431od_b_b @ Y3 @ Z2 ) @ S ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_212_relcompE,axiom,
% 3.32/1.66 ! [Xz: produc1213276845od_b_b,R: set_Pr1324126435od_b_b,S: set_Pr2007082183od_b_b] :
% 3.32/1.66 ( ( member1516365892od_b_b @ Xz @ ( relcom1823941168od_b_b @ R @ S ) )
% 3.32/1.66 => ~ ! [X4: standard_Constant_a,Y3: product_prod_b_b,Z2: product_prod_b_b] :
% 3.32/1.66 ( ( Xz
% 3.32/1.66 = ( produc1432590431od_b_b @ X4 @ Z2 ) )
% 3.32/1.66 => ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ X4 @ Y3 ) @ R )
% 3.32/1.66 => ~ ( member1652792080od_b_b @ ( produc546497367od_b_b @ Y3 @ Z2 ) @ S ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_213_relcomp__Image,axiom,
% 3.32/1.66 ! [X3: set_Product_prod_b_b,Y2: set_Product_prod_b_b,Z3: set_b] :
% 3.32/1.66 ( ( image_b_b @ ( relcomp_b_b_b @ X3 @ Y2 ) @ Z3 )
% 3.32/1.66 = ( image_b_b @ Y2 @ ( image_b_b @ X3 @ Z3 ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_214_Image__mono,axiom,
% 3.32/1.66 ! [R3: set_Product_prod_b_b,R: set_Product_prod_b_b,A6: set_b,A: set_b] :
% 3.32/1.66 ( ( ord_le1036320359od_b_b @ R3 @ R )
% 3.32/1.66 => ( ( ord_less_eq_set_b @ A6 @ A )
% 3.32/1.66 => ( ord_less_eq_set_b @ ( image_b_b @ R3 @ A6 ) @ ( image_b_b @ R @ A ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_215_agree__on__def,axiom,
% 3.32/1.66 ( agree_221379389_a_b_b
% 3.32/1.66 = ( ^ [G4: labele1159362096nt_a_b,F_1: set_Product_prod_b_b,F_2: set_Product_prod_b_b] :
% 3.32/1.66 ! [X5: b] :
% 3.32/1.66 ( ( member_b @ X5 @ ( labele1424214014nt_a_b @ G4 ) )
% 3.32/1.66 => ( ( image_b_b @ F_1 @ ( insert_b @ X5 @ bot_bot_set_b ) )
% 3.32/1.66 = ( image_b_b @ F_2 @ ( insert_b @ X5 @ bot_bot_set_b ) ) ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_216_refl__on__empty,axiom,
% 3.32/1.66 refl_o1031343860_a_nat @ bot_bo2122869057_a_nat @ bot_bo1836341171_a_nat ).
% 3.32/1.66
% 3.32/1.66 thf(fact_217_refl__on__empty,axiom,
% 3.32/1.66 refl_on_b @ bot_bot_set_b @ bot_bo1343651123od_b_b ).
% 3.32/1.66
% 3.32/1.66 thf(fact_218_refl__on__empty,axiom,
% 3.32/1.66 refl_o1213627494_a_nat @ bot_bo1836341171_a_nat @ bot_bo1973379891_a_nat ).
% 3.32/1.66
% 3.32/1.66 thf(fact_219_subrelI,axiom,
% 3.32/1.66 ! [R: set_Product_prod_b_b,S: set_Product_prod_b_b] :
% 3.32/1.66 ( ! [X4: b,Y3: b] :
% 3.32/1.66 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ X4 @ Y3 ) @ R )
% 3.32/1.66 => ( member1285940496od_b_b @ ( product_Pair_b_b @ X4 @ Y3 ) @ S ) )
% 3.32/1.66 => ( ord_le1036320359od_b_b @ R @ S ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_220_subrelI,axiom,
% 3.32/1.66 ! [R: set_Pr1324126435od_b_b,S: set_Pr1324126435od_b_b] :
% 3.32/1.66 ( ! [X4: standard_Constant_a,Y3: product_prod_b_b] :
% 3.32/1.66 ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ X4 @ Y3 ) @ R )
% 3.32/1.66 => ( member1516365892od_b_b @ ( produc1432590431od_b_b @ X4 @ Y3 ) @ S ) )
% 3.32/1.66 => ( ord_le123089219od_b_b @ R @ S ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_221_graph__union__iff,axiom,
% 3.32/1.66 ! [G_1: labele1159362096nt_a_b,G_2: labele1159362096nt_a_b] :
% 3.32/1.66 ( ( ( graph_1309249505nt_a_b @ G_1 @ G_2 )
% 3.32/1.66 = G_2 )
% 3.32/1.66 = ( ( ord_le123089219od_b_b @ ( labele1741081071nt_a_b @ G_1 ) @ ( labele1741081071nt_a_b @ G_2 ) )
% 3.32/1.66 & ( ord_less_eq_set_b @ ( labele1424214014nt_a_b @ G_1 ) @ ( labele1424214014nt_a_b @ G_2 ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_222_restrict__subsD,axiom,
% 3.32/1.66 ! [G: labele1159362096nt_a_b] :
% 3.32/1.66 ( ( ord_le123089219od_b_b @ ( labele1741081071nt_a_b @ G ) @ ( labele1741081071nt_a_b @ ( restri446606278nt_a_b @ G ) ) )
% 3.32/1.66 => ( G
% 3.32/1.66 = ( restri446606278nt_a_b @ G ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_223_subgraph__def2,axiom,
% 3.32/1.66 ! [G_1: labele1159362096nt_a_b,G_2: labele1159362096nt_a_b] :
% 3.32/1.66 ( ( G_1
% 3.32/1.66 = ( restri446606278nt_a_b @ G_1 ) )
% 3.32/1.66 => ( ( G_2
% 3.32/1.66 = ( restri446606278nt_a_b @ G_2 ) )
% 3.32/1.66 => ( ( graph_222606102_a_b_b @ G_1 @ G_2 @ ( id_on_b @ ( labele1424214014nt_a_b @ G_1 ) ) )
% 3.32/1.66 = ( ( ord_less_eq_set_b @ ( labele1424214014nt_a_b @ G_1 ) @ ( labele1424214014nt_a_b @ G_2 ) )
% 3.32/1.66 & ( ord_le123089219od_b_b @ ( labele1741081071nt_a_b @ G_1 ) @ ( labele1741081071nt_a_b @ G_2 ) ) ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_224_subgraph__subset_I1_J,axiom,
% 3.32/1.66 ! [G_1: labele1159362096nt_a_b,G_2: labele1159362096nt_a_b] :
% 3.32/1.66 ( ( graph_222606102_a_b_b @ G_1 @ G_2 @ ( id_on_b @ ( labele1424214014nt_a_b @ G_1 ) ) )
% 3.32/1.66 => ( ord_less_eq_set_b @ ( labele1424214014nt_a_b @ G_1 ) @ ( labele1424214014nt_a_b @ G_2 ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_225_maintainedD2,axiom,
% 3.32/1.66 ! [A: labele935650037_a_nat,B: labele935650037_a_nat,G: labele1159362096nt_a_b,F: set_Pr2106913242_nat_b] :
% 3.32/1.66 ( ( mainta1604381365_nat_b @ ( produc1676969687_a_nat @ A @ B ) @ G )
% 3.32/1.66 => ( ( graph_714568023_nat_b @ A @ G @ F )
% 3.32/1.66 => ~ ! [G5: set_Pr2106913242_nat_b] :
% 3.32/1.66 ( ( graph_714568023_nat_b @ B @ G @ G5 )
% 3.32/1.66 => ~ ( ord_le1484132922_nat_b @ F @ G5 ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_226_maintainedD2,axiom,
% 3.32/1.66 ! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,G: labele1159362096nt_a_b,F: set_Product_prod_b_b] :
% 3.32/1.66 ( ( mainta374363448_a_b_b @ ( produc1569511545nt_a_b @ A @ B ) @ G )
% 3.32/1.66 => ( ( graph_222606102_a_b_b @ A @ G @ F )
% 3.32/1.66 => ~ ! [G5: set_Product_prod_b_b] :
% 3.32/1.66 ( ( graph_222606102_a_b_b @ B @ G @ G5 )
% 3.32/1.66 => ~ ( ord_le1036320359od_b_b @ F @ G5 ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_227_Id__on__vertices__identity_I2_J,axiom,
% 3.32/1.66 ! [A2: labele1159362096nt_a_b,B3: labele1159362096nt_a_b,F: set_Product_prod_b_b,Aa: b,Ba: b] :
% 3.32/1.66 ( ( graph_222606102_a_b_b @ A2 @ B3 @ F )
% 3.32/1.66 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ Aa @ Ba ) @ F )
% 3.32/1.66 => ( member1285940496od_b_b @ ( product_Pair_b_b @ Aa @ Ba ) @ ( relcomp_b_b_b @ F @ ( id_on_b @ ( labele1424214014nt_a_b @ B3 ) ) ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_228_Id__on__vertices__identity_I1_J,axiom,
% 3.32/1.66 ! [A2: labele1159362096nt_a_b,B3: labele1159362096nt_a_b,F: set_Product_prod_b_b,Aa: b,Ba: b] :
% 3.32/1.66 ( ( graph_222606102_a_b_b @ A2 @ B3 @ F )
% 3.32/1.66 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ Aa @ Ba ) @ F )
% 3.32/1.66 => ( member1285940496od_b_b @ ( product_Pair_b_b @ Aa @ Ba ) @ ( relcomp_b_b_b @ ( id_on_b @ ( labele1424214014nt_a_b @ A2 ) ) @ F ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_229_graph__homomorphism__on__graph,axiom,
% 3.32/1.66 ! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,R2: set_Product_prod_b_b,F: b > b] :
% 3.32/1.66 ( ( graph_222606102_a_b_b @ A @ B @ R2 )
% 3.32/1.66 => ( graph_222606102_a_b_b @ A @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ B ) @ F ) @ B ) @ ( relcomp_b_b_b @ R2 @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ B ) @ F ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_230_singleton__insert__inj__eq,axiom,
% 3.32/1.66 ! [B3: b,A2: b,A: set_b] :
% 3.32/1.66 ( ( ( insert_b @ B3 @ bot_bot_set_b )
% 3.32/1.66 = ( insert_b @ A2 @ A ) )
% 3.32/1.66 = ( ( A2 = B3 )
% 3.32/1.66 & ( ord_less_eq_set_b @ A @ ( insert_b @ B3 @ bot_bot_set_b ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_231_singleton__insert__inj__eq,axiom,
% 3.32/1.66 ! [B3: produc1871334759_a_nat,A2: produc1871334759_a_nat,A: set_Pr1987088711_a_nat] :
% 3.32/1.66 ( ( ( insert1574423351_a_nat @ B3 @ bot_bo1836341171_a_nat )
% 3.32/1.66 = ( insert1574423351_a_nat @ A2 @ A ) )
% 3.32/1.66 = ( ( A2 = B3 )
% 3.32/1.66 & ( ord_le1718765799_a_nat @ A @ ( insert1574423351_a_nat @ B3 @ bot_bo1836341171_a_nat ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_232_singleton__insert__inj__eq_H,axiom,
% 3.32/1.66 ! [A2: b,A: set_b,B3: b] :
% 3.32/1.66 ( ( ( insert_b @ A2 @ A )
% 3.32/1.66 = ( insert_b @ B3 @ bot_bot_set_b ) )
% 3.32/1.66 = ( ( A2 = B3 )
% 3.32/1.66 & ( ord_less_eq_set_b @ A @ ( insert_b @ B3 @ bot_bot_set_b ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_233_singleton__insert__inj__eq_H,axiom,
% 3.32/1.66 ! [A2: produc1871334759_a_nat,A: set_Pr1987088711_a_nat,B3: produc1871334759_a_nat] :
% 3.32/1.66 ( ( ( insert1574423351_a_nat @ A2 @ A )
% 3.32/1.66 = ( insert1574423351_a_nat @ B3 @ bot_bo1836341171_a_nat ) )
% 3.32/1.66 = ( ( A2 = B3 )
% 3.32/1.66 & ( ord_le1718765799_a_nat @ A @ ( insert1574423351_a_nat @ B3 @ bot_bo1836341171_a_nat ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_234_equiv__class__subset,axiom,
% 3.32/1.66 ! [A: set_b,R: set_Product_prod_b_b,A2: b,B3: b] :
% 3.32/1.66 ( ( equiv_equiv_b @ A @ R )
% 3.32/1.66 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ B3 ) @ R )
% 3.32/1.66 => ( ord_less_eq_set_b @ ( image_b_b @ R @ ( insert_b @ A2 @ bot_bot_set_b ) ) @ ( image_b_b @ R @ ( insert_b @ B3 @ bot_bot_set_b ) ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_235_equiv__class__subset,axiom,
% 3.32/1.66 ! [A: set_Pr1987088711_a_nat,R: set_Pr924198087_a_nat,A2: produc1871334759_a_nat,B3: produc1871334759_a_nat] :
% 3.32/1.66 ( ( equiv_291114781_a_nat @ A @ R )
% 3.32/1.66 => ( ( member584645392_a_nat @ ( produc1677124439_a_nat @ A2 @ B3 ) @ R )
% 3.32/1.66 => ( ord_le1718765799_a_nat @ ( image_1168831379_a_nat @ R @ ( insert1574423351_a_nat @ A2 @ bot_bo1836341171_a_nat ) ) @ ( image_1168831379_a_nat @ R @ ( insert1574423351_a_nat @ B3 @ bot_bo1836341171_a_nat ) ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_236_subset__equiv__class,axiom,
% 3.32/1.66 ! [A: set_Product_prod_b_b,R: set_Pr2007082183od_b_b,B3: product_prod_b_b,A2: product_prod_b_b] :
% 3.32/1.66 ( ( equiv_1125628061od_b_b @ A @ R )
% 3.32/1.66 => ( ( ord_le1036320359od_b_b @ ( image_1928024979od_b_b @ R @ ( insert1952693431od_b_b @ B3 @ bot_bo1343651123od_b_b ) ) @ ( image_1928024979od_b_b @ R @ ( insert1952693431od_b_b @ A2 @ bot_bo1343651123od_b_b ) ) )
% 3.32/1.66 => ( ( member1285940496od_b_b @ B3 @ A )
% 3.32/1.66 => ( member1652792080od_b_b @ ( produc546497367od_b_b @ A2 @ B3 ) @ R ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_237_subset__equiv__class,axiom,
% 3.32/1.66 ! [A: set_Pr1324126435od_b_b,R: set_Pr2109276827od_b_b,B3: produc1213276845od_b_b,A2: produc1213276845od_b_b] :
% 3.32/1.66 ( ( equiv_2048442231od_b_b @ A @ R )
% 3.32/1.66 => ( ( ord_le123089219od_b_b @ ( image_763305007od_b_b @ R @ ( insert2037698781od_b_b @ B3 @ bot_bo1664927607od_b_b ) ) @ ( image_763305007od_b_b @ R @ ( insert2037698781od_b_b @ A2 @ bot_bo1664927607od_b_b ) ) )
% 3.32/1.66 => ( ( member1516365892od_b_b @ B3 @ A )
% 3.32/1.66 => ( member1086024932od_b_b @ ( produc449289715od_b_b @ A2 @ B3 ) @ R ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_238_subset__equiv__class,axiom,
% 3.32/1.66 ! [A: set_b,R: set_Product_prod_b_b,B3: b,A2: b] :
% 3.32/1.66 ( ( equiv_equiv_b @ A @ R )
% 3.32/1.66 => ( ( ord_less_eq_set_b @ ( image_b_b @ R @ ( insert_b @ B3 @ bot_bot_set_b ) ) @ ( image_b_b @ R @ ( insert_b @ A2 @ bot_bot_set_b ) ) )
% 3.32/1.66 => ( ( member_b @ B3 @ A )
% 3.32/1.66 => ( member1285940496od_b_b @ ( product_Pair_b_b @ A2 @ B3 ) @ R ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_239_subset__equiv__class,axiom,
% 3.32/1.66 ! [A: set_Pr1987088711_a_nat,R: set_Pr924198087_a_nat,B3: produc1871334759_a_nat,A2: produc1871334759_a_nat] :
% 3.32/1.66 ( ( equiv_291114781_a_nat @ A @ R )
% 3.32/1.66 => ( ( ord_le1718765799_a_nat @ ( image_1168831379_a_nat @ R @ ( insert1574423351_a_nat @ B3 @ bot_bo1836341171_a_nat ) ) @ ( image_1168831379_a_nat @ R @ ( insert1574423351_a_nat @ A2 @ bot_bo1836341171_a_nat ) ) )
% 3.32/1.66 => ( ( member832397200_a_nat @ B3 @ A )
% 3.32/1.66 => ( member584645392_a_nat @ ( produc1677124439_a_nat @ A2 @ B3 ) @ R ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_240_refines__equiv__class__eq2,axiom,
% 3.32/1.66 ! [R2: set_Product_prod_b_b,S2: set_Product_prod_b_b,A: set_b,A2: b] :
% 3.32/1.66 ( ( ord_le1036320359od_b_b @ R2 @ S2 )
% 3.32/1.66 => ( ( equiv_equiv_b @ A @ R2 )
% 3.32/1.66 => ( ( equiv_equiv_b @ A @ S2 )
% 3.32/1.66 => ( ( image_b_b @ S2 @ ( image_b_b @ R2 @ ( insert_b @ A2 @ bot_bot_set_b ) ) )
% 3.32/1.66 = ( image_b_b @ S2 @ ( insert_b @ A2 @ bot_bot_set_b ) ) ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_241_refines__equiv__class__eq2,axiom,
% 3.32/1.66 ! [R2: set_Pr924198087_a_nat,S2: set_Pr924198087_a_nat,A: set_Pr1987088711_a_nat,A2: produc1871334759_a_nat] :
% 3.32/1.66 ( ( ord_le107617383_a_nat @ R2 @ S2 )
% 3.32/1.66 => ( ( equiv_291114781_a_nat @ A @ R2 )
% 3.32/1.66 => ( ( equiv_291114781_a_nat @ A @ S2 )
% 3.32/1.66 => ( ( image_1168831379_a_nat @ S2 @ ( image_1168831379_a_nat @ R2 @ ( insert1574423351_a_nat @ A2 @ bot_bo1836341171_a_nat ) ) )
% 3.32/1.66 = ( image_1168831379_a_nat @ S2 @ ( insert1574423351_a_nat @ A2 @ bot_bo1836341171_a_nat ) ) ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_242_empty__Collect__eq,axiom,
% 3.32/1.66 ! [P: b > $o] :
% 3.32/1.66 ( ( bot_bot_set_b
% 3.32/1.66 = ( collect_b @ P ) )
% 3.32/1.66 = ( ! [X5: b] :
% 3.32/1.66 ~ ( P @ X5 ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_243_empty__Collect__eq,axiom,
% 3.32/1.66 ! [P: produc1871334759_a_nat > $o] :
% 3.32/1.66 ( ( bot_bo1836341171_a_nat
% 3.32/1.66 = ( collec357096914_a_nat @ P ) )
% 3.32/1.66 = ( ! [X5: produc1871334759_a_nat] :
% 3.32/1.66 ~ ( P @ X5 ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_244_Collect__empty__eq,axiom,
% 3.32/1.66 ! [P: b > $o] :
% 3.32/1.66 ( ( ( collect_b @ P )
% 3.32/1.66 = bot_bot_set_b )
% 3.32/1.66 = ( ! [X5: b] :
% 3.32/1.66 ~ ( P @ X5 ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_245_Collect__empty__eq,axiom,
% 3.32/1.66 ! [P: produc1871334759_a_nat > $o] :
% 3.32/1.66 ( ( ( collec357096914_a_nat @ P )
% 3.32/1.66 = bot_bo1836341171_a_nat )
% 3.32/1.66 = ( ! [X5: produc1871334759_a_nat] :
% 3.32/1.66 ~ ( P @ X5 ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_246_all__not__in__conv,axiom,
% 3.32/1.66 ! [A: set_Product_prod_b_b] :
% 3.32/1.66 ( ( ! [X5: product_prod_b_b] :
% 3.32/1.66 ~ ( member1285940496od_b_b @ X5 @ A ) )
% 3.32/1.66 = ( A = bot_bo1343651123od_b_b ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_247_all__not__in__conv,axiom,
% 3.32/1.66 ! [A: set_Pr1324126435od_b_b] :
% 3.32/1.66 ( ( ! [X5: produc1213276845od_b_b] :
% 3.32/1.66 ~ ( member1516365892od_b_b @ X5 @ A ) )
% 3.32/1.66 = ( A = bot_bo1664927607od_b_b ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_248_all__not__in__conv,axiom,
% 3.32/1.66 ! [A: set_b] :
% 3.32/1.66 ( ( ! [X5: b] :
% 3.32/1.66 ~ ( member_b @ X5 @ A ) )
% 3.32/1.66 = ( A = bot_bot_set_b ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_249_all__not__in__conv,axiom,
% 3.32/1.66 ! [A: set_Pr1987088711_a_nat] :
% 3.32/1.66 ( ( ! [X5: produc1871334759_a_nat] :
% 3.32/1.66 ~ ( member832397200_a_nat @ X5 @ A ) )
% 3.32/1.66 = ( A = bot_bo1836341171_a_nat ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_250_empty__iff,axiom,
% 3.32/1.66 ! [C: product_prod_b_b] :
% 3.32/1.66 ~ ( member1285940496od_b_b @ C @ bot_bo1343651123od_b_b ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_251_empty__iff,axiom,
% 3.32/1.66 ! [C: produc1213276845od_b_b] :
% 3.32/1.66 ~ ( member1516365892od_b_b @ C @ bot_bo1664927607od_b_b ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_252_empty__iff,axiom,
% 3.32/1.66 ! [C: b] :
% 3.32/1.66 ~ ( member_b @ C @ bot_bot_set_b ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_253_empty__iff,axiom,
% 3.32/1.66 ! [C: produc1871334759_a_nat] :
% 3.32/1.66 ~ ( member832397200_a_nat @ C @ bot_bo1836341171_a_nat ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_254_subsetI,axiom,
% 3.32/1.66 ! [A: set_b,B: set_b] :
% 3.32/1.66 ( ! [X4: b] :
% 3.32/1.66 ( ( member_b @ X4 @ A )
% 3.32/1.66 => ( member_b @ X4 @ B ) )
% 3.32/1.66 => ( ord_less_eq_set_b @ A @ B ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_255_subsetI,axiom,
% 3.32/1.66 ! [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
% 3.32/1.66 ( ! [X4: product_prod_b_b] :
% 3.32/1.66 ( ( member1285940496od_b_b @ X4 @ A )
% 3.32/1.66 => ( member1285940496od_b_b @ X4 @ B ) )
% 3.32/1.66 => ( ord_le1036320359od_b_b @ A @ B ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_256_subsetI,axiom,
% 3.32/1.66 ! [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b] :
% 3.32/1.66 ( ! [X4: produc1213276845od_b_b] :
% 3.32/1.66 ( ( member1516365892od_b_b @ X4 @ A )
% 3.32/1.66 => ( member1516365892od_b_b @ X4 @ B ) )
% 3.32/1.66 => ( ord_le123089219od_b_b @ A @ B ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_257_insert__absorb2,axiom,
% 3.32/1.66 ! [X: b,A: set_b] :
% 3.32/1.66 ( ( insert_b @ X @ ( insert_b @ X @ A ) )
% 3.32/1.66 = ( insert_b @ X @ A ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_258_insert__absorb2,axiom,
% 3.32/1.66 ! [X: produc1871334759_a_nat,A: set_Pr1987088711_a_nat] :
% 3.32/1.66 ( ( insert1574423351_a_nat @ X @ ( insert1574423351_a_nat @ X @ A ) )
% 3.32/1.66 = ( insert1574423351_a_nat @ X @ A ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_259_insert__iff,axiom,
% 3.32/1.66 ! [A2: produc1871334759_a_nat,B3: produc1871334759_a_nat,A: set_Pr1987088711_a_nat] :
% 3.32/1.66 ( ( member832397200_a_nat @ A2 @ ( insert1574423351_a_nat @ B3 @ A ) )
% 3.32/1.66 = ( ( A2 = B3 )
% 3.32/1.66 | ( member832397200_a_nat @ A2 @ A ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_260_insert__iff,axiom,
% 3.32/1.66 ! [A2: b,B3: b,A: set_b] :
% 3.32/1.66 ( ( member_b @ A2 @ ( insert_b @ B3 @ A ) )
% 3.32/1.66 = ( ( A2 = B3 )
% 3.32/1.66 | ( member_b @ A2 @ A ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_261_insert__iff,axiom,
% 3.32/1.66 ! [A2: product_prod_b_b,B3: product_prod_b_b,A: set_Product_prod_b_b] :
% 3.32/1.66 ( ( member1285940496od_b_b @ A2 @ ( insert1952693431od_b_b @ B3 @ A ) )
% 3.32/1.66 = ( ( A2 = B3 )
% 3.32/1.66 | ( member1285940496od_b_b @ A2 @ A ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_262_insert__iff,axiom,
% 3.32/1.66 ! [A2: produc1213276845od_b_b,B3: produc1213276845od_b_b,A: set_Pr1324126435od_b_b] :
% 3.32/1.66 ( ( member1516365892od_b_b @ A2 @ ( insert2037698781od_b_b @ B3 @ A ) )
% 3.32/1.66 = ( ( A2 = B3 )
% 3.32/1.66 | ( member1516365892od_b_b @ A2 @ A ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_263_insertCI,axiom,
% 3.32/1.66 ! [A2: produc1871334759_a_nat,B: set_Pr1987088711_a_nat,B3: produc1871334759_a_nat] :
% 3.32/1.66 ( ( ~ ( member832397200_a_nat @ A2 @ B )
% 3.32/1.66 => ( A2 = B3 ) )
% 3.32/1.66 => ( member832397200_a_nat @ A2 @ ( insert1574423351_a_nat @ B3 @ B ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_264_insertCI,axiom,
% 3.32/1.66 ! [A2: b,B: set_b,B3: b] :
% 3.32/1.66 ( ( ~ ( member_b @ A2 @ B )
% 3.32/1.66 => ( A2 = B3 ) )
% 3.32/1.66 => ( member_b @ A2 @ ( insert_b @ B3 @ B ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_265_insertCI,axiom,
% 3.32/1.66 ! [A2: product_prod_b_b,B: set_Product_prod_b_b,B3: product_prod_b_b] :
% 3.32/1.66 ( ( ~ ( member1285940496od_b_b @ A2 @ B )
% 3.32/1.66 => ( A2 = B3 ) )
% 3.32/1.66 => ( member1285940496od_b_b @ A2 @ ( insert1952693431od_b_b @ B3 @ B ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_266_insertCI,axiom,
% 3.32/1.66 ! [A2: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,B3: produc1213276845od_b_b] :
% 3.32/1.66 ( ( ~ ( member1516365892od_b_b @ A2 @ B )
% 3.32/1.66 => ( A2 = B3 ) )
% 3.32/1.66 => ( member1516365892od_b_b @ A2 @ ( insert2037698781od_b_b @ B3 @ B ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_267_empty__subsetI,axiom,
% 3.32/1.66 ! [A: set_b] : ( ord_less_eq_set_b @ bot_bot_set_b @ A ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_268_empty__subsetI,axiom,
% 3.32/1.66 ! [A: set_Pr1987088711_a_nat] : ( ord_le1718765799_a_nat @ bot_bo1836341171_a_nat @ A ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_269_subset__empty,axiom,
% 3.32/1.66 ! [A: set_b] :
% 3.32/1.66 ( ( ord_less_eq_set_b @ A @ bot_bot_set_b )
% 3.32/1.66 = ( A = bot_bot_set_b ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_270_subset__empty,axiom,
% 3.32/1.66 ! [A: set_Pr1987088711_a_nat] :
% 3.32/1.66 ( ( ord_le1718765799_a_nat @ A @ bot_bo1836341171_a_nat )
% 3.32/1.66 = ( A = bot_bo1836341171_a_nat ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_271_singletonI,axiom,
% 3.32/1.66 ! [A2: product_prod_b_b] : ( member1285940496od_b_b @ A2 @ ( insert1952693431od_b_b @ A2 @ bot_bo1343651123od_b_b ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_272_singletonI,axiom,
% 3.32/1.66 ! [A2: produc1213276845od_b_b] : ( member1516365892od_b_b @ A2 @ ( insert2037698781od_b_b @ A2 @ bot_bo1664927607od_b_b ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_273_singletonI,axiom,
% 3.32/1.66 ! [A2: b] : ( member_b @ A2 @ ( insert_b @ A2 @ bot_bot_set_b ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_274_singletonI,axiom,
% 3.32/1.66 ! [A2: produc1871334759_a_nat] : ( member832397200_a_nat @ A2 @ ( insert1574423351_a_nat @ A2 @ bot_bo1836341171_a_nat ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_275_insert__subset,axiom,
% 3.32/1.66 ! [X: produc1871334759_a_nat,A: set_Pr1987088711_a_nat,B: set_Pr1987088711_a_nat] :
% 3.32/1.66 ( ( ord_le1718765799_a_nat @ ( insert1574423351_a_nat @ X @ A ) @ B )
% 3.32/1.66 = ( ( member832397200_a_nat @ X @ B )
% 3.32/1.66 & ( ord_le1718765799_a_nat @ A @ B ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_276_insert__subset,axiom,
% 3.32/1.66 ! [X: b,A: set_b,B: set_b] :
% 3.32/1.66 ( ( ord_less_eq_set_b @ ( insert_b @ X @ A ) @ B )
% 3.32/1.66 = ( ( member_b @ X @ B )
% 3.32/1.66 & ( ord_less_eq_set_b @ A @ B ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_277_insert__subset,axiom,
% 3.32/1.66 ! [X: product_prod_b_b,A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
% 3.32/1.66 ( ( ord_le1036320359od_b_b @ ( insert1952693431od_b_b @ X @ A ) @ B )
% 3.32/1.66 = ( ( member1285940496od_b_b @ X @ B )
% 3.32/1.66 & ( ord_le1036320359od_b_b @ A @ B ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_278_insert__subset,axiom,
% 3.32/1.66 ! [X: produc1213276845od_b_b,A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b] :
% 3.32/1.66 ( ( ord_le123089219od_b_b @ ( insert2037698781od_b_b @ X @ A ) @ B )
% 3.32/1.66 = ( ( member1516365892od_b_b @ X @ B )
% 3.32/1.66 & ( ord_le123089219od_b_b @ A @ B ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_279_relcomp__empty1,axiom,
% 3.32/1.66 ! [R2: set_Pr1987088711_a_nat] :
% 3.32/1.66 ( ( relcom1338300020_a_nat @ bot_bo1836341171_a_nat @ R2 )
% 3.32/1.66 = bot_bo1836341171_a_nat ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_280_relcomp__empty2,axiom,
% 3.32/1.66 ! [R2: set_Pr1987088711_a_nat] :
% 3.32/1.66 ( ( relcom1338300020_a_nat @ R2 @ bot_bo1836341171_a_nat )
% 3.32/1.66 = bot_bo1836341171_a_nat ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_281_graph__empty__e,axiom,
% 3.32/1.66 ! [V: set_b] :
% 3.32/1.66 ( ( labele1230159100nt_a_b @ bot_bo1664927607od_b_b @ V )
% 3.32/1.66 = ( restri446606278nt_a_b @ ( labele1230159100nt_a_b @ bot_bo1664927607od_b_b @ V ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_282_graph__homomorphism__nonempty,axiom,
% 3.32/1.66 ! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b,F: set_Product_prod_b_b,E: allego510293162tant_a] :
% 3.32/1.66 ( ( graph_222606102_a_b_b @ A @ B @ F )
% 3.32/1.66 => ( ( ( semant55076487nt_a_b @ A @ E )
% 3.32/1.66 != bot_bo1343651123od_b_b )
% 3.32/1.66 => ( ( semant55076487nt_a_b @ B @ E )
% 3.32/1.66 != bot_bo1343651123od_b_b ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_283_ex__in__conv,axiom,
% 3.32/1.66 ! [A: set_Product_prod_b_b] :
% 3.32/1.66 ( ( ? [X5: product_prod_b_b] : ( member1285940496od_b_b @ X5 @ A ) )
% 3.32/1.66 = ( A != bot_bo1343651123od_b_b ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_284_ex__in__conv,axiom,
% 3.32/1.66 ! [A: set_Pr1324126435od_b_b] :
% 3.32/1.66 ( ( ? [X5: produc1213276845od_b_b] : ( member1516365892od_b_b @ X5 @ A ) )
% 3.32/1.66 = ( A != bot_bo1664927607od_b_b ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_285_ex__in__conv,axiom,
% 3.32/1.66 ! [A: set_b] :
% 3.32/1.66 ( ( ? [X5: b] : ( member_b @ X5 @ A ) )
% 3.32/1.66 = ( A != bot_bot_set_b ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_286_ex__in__conv,axiom,
% 3.32/1.66 ! [A: set_Pr1987088711_a_nat] :
% 3.32/1.66 ( ( ? [X5: produc1871334759_a_nat] : ( member832397200_a_nat @ X5 @ A ) )
% 3.32/1.66 = ( A != bot_bo1836341171_a_nat ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_287_equals0I,axiom,
% 3.32/1.66 ! [A: set_Product_prod_b_b] :
% 3.32/1.66 ( ! [Y3: product_prod_b_b] :
% 3.32/1.66 ~ ( member1285940496od_b_b @ Y3 @ A )
% 3.32/1.66 => ( A = bot_bo1343651123od_b_b ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_288_equals0I,axiom,
% 3.32/1.66 ! [A: set_Pr1324126435od_b_b] :
% 3.32/1.66 ( ! [Y3: produc1213276845od_b_b] :
% 3.32/1.66 ~ ( member1516365892od_b_b @ Y3 @ A )
% 3.32/1.66 => ( A = bot_bo1664927607od_b_b ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_289_equals0I,axiom,
% 3.32/1.66 ! [A: set_b] :
% 3.32/1.66 ( ! [Y3: b] :
% 3.32/1.66 ~ ( member_b @ Y3 @ A )
% 3.32/1.66 => ( A = bot_bot_set_b ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_290_equals0I,axiom,
% 3.32/1.66 ! [A: set_Pr1987088711_a_nat] :
% 3.32/1.66 ( ! [Y3: produc1871334759_a_nat] :
% 3.32/1.66 ~ ( member832397200_a_nat @ Y3 @ A )
% 3.32/1.66 => ( A = bot_bo1836341171_a_nat ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_291_equals0D,axiom,
% 3.32/1.66 ! [A: set_Product_prod_b_b,A2: product_prod_b_b] :
% 3.32/1.66 ( ( A = bot_bo1343651123od_b_b )
% 3.32/1.66 => ~ ( member1285940496od_b_b @ A2 @ A ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_292_equals0D,axiom,
% 3.32/1.66 ! [A: set_Pr1324126435od_b_b,A2: produc1213276845od_b_b] :
% 3.32/1.66 ( ( A = bot_bo1664927607od_b_b )
% 3.32/1.66 => ~ ( member1516365892od_b_b @ A2 @ A ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_293_equals0D,axiom,
% 3.32/1.66 ! [A: set_b,A2: b] :
% 3.32/1.66 ( ( A = bot_bot_set_b )
% 3.32/1.66 => ~ ( member_b @ A2 @ A ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_294_equals0D,axiom,
% 3.32/1.66 ! [A: set_Pr1987088711_a_nat,A2: produc1871334759_a_nat] :
% 3.32/1.66 ( ( A = bot_bo1836341171_a_nat )
% 3.32/1.66 => ~ ( member832397200_a_nat @ A2 @ A ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_295_emptyE,axiom,
% 3.32/1.66 ! [A2: product_prod_b_b] :
% 3.32/1.66 ~ ( member1285940496od_b_b @ A2 @ bot_bo1343651123od_b_b ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_296_emptyE,axiom,
% 3.32/1.66 ! [A2: produc1213276845od_b_b] :
% 3.32/1.66 ~ ( member1516365892od_b_b @ A2 @ bot_bo1664927607od_b_b ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_297_emptyE,axiom,
% 3.32/1.66 ! [A2: b] :
% 3.32/1.66 ~ ( member_b @ A2 @ bot_bot_set_b ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_298_emptyE,axiom,
% 3.32/1.66 ! [A2: produc1871334759_a_nat] :
% 3.32/1.66 ~ ( member832397200_a_nat @ A2 @ bot_bo1836341171_a_nat ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_299_subset__iff,axiom,
% 3.32/1.66 ( ord_less_eq_set_b
% 3.32/1.66 = ( ^ [A7: set_b,B7: set_b] :
% 3.32/1.66 ! [T: b] :
% 3.32/1.66 ( ( member_b @ T @ A7 )
% 3.32/1.66 => ( member_b @ T @ B7 ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_300_subset__iff,axiom,
% 3.32/1.66 ( ord_le1036320359od_b_b
% 3.32/1.66 = ( ^ [A7: set_Product_prod_b_b,B7: set_Product_prod_b_b] :
% 3.32/1.66 ! [T: product_prod_b_b] :
% 3.32/1.66 ( ( member1285940496od_b_b @ T @ A7 )
% 3.32/1.66 => ( member1285940496od_b_b @ T @ B7 ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_301_subset__iff,axiom,
% 3.32/1.66 ( ord_le123089219od_b_b
% 3.32/1.66 = ( ^ [A7: set_Pr1324126435od_b_b,B7: set_Pr1324126435od_b_b] :
% 3.32/1.66 ! [T: produc1213276845od_b_b] :
% 3.32/1.66 ( ( member1516365892od_b_b @ T @ A7 )
% 3.32/1.66 => ( member1516365892od_b_b @ T @ B7 ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_302_subset__eq,axiom,
% 3.32/1.66 ( ord_less_eq_set_b
% 3.32/1.66 = ( ^ [A7: set_b,B7: set_b] :
% 3.32/1.66 ! [X5: b] :
% 3.32/1.66 ( ( member_b @ X5 @ A7 )
% 3.32/1.66 => ( member_b @ X5 @ B7 ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_303_subset__eq,axiom,
% 3.32/1.66 ( ord_le1036320359od_b_b
% 3.32/1.66 = ( ^ [A7: set_Product_prod_b_b,B7: set_Product_prod_b_b] :
% 3.32/1.66 ! [X5: product_prod_b_b] :
% 3.32/1.66 ( ( member1285940496od_b_b @ X5 @ A7 )
% 3.32/1.66 => ( member1285940496od_b_b @ X5 @ B7 ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_304_subset__eq,axiom,
% 3.32/1.66 ( ord_le123089219od_b_b
% 3.32/1.66 = ( ^ [A7: set_Pr1324126435od_b_b,B7: set_Pr1324126435od_b_b] :
% 3.32/1.66 ! [X5: produc1213276845od_b_b] :
% 3.32/1.66 ( ( member1516365892od_b_b @ X5 @ A7 )
% 3.32/1.66 => ( member1516365892od_b_b @ X5 @ B7 ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_305_subsetD,axiom,
% 3.32/1.66 ! [A: set_b,B: set_b,C: b] :
% 3.32/1.66 ( ( ord_less_eq_set_b @ A @ B )
% 3.32/1.66 => ( ( member_b @ C @ A )
% 3.32/1.66 => ( member_b @ C @ B ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_306_subsetD,axiom,
% 3.32/1.66 ! [A: set_Product_prod_b_b,B: set_Product_prod_b_b,C: product_prod_b_b] :
% 3.32/1.66 ( ( ord_le1036320359od_b_b @ A @ B )
% 3.32/1.66 => ( ( member1285940496od_b_b @ C @ A )
% 3.32/1.66 => ( member1285940496od_b_b @ C @ B ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_307_subsetD,axiom,
% 3.32/1.66 ! [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b,C: produc1213276845od_b_b] :
% 3.32/1.66 ( ( ord_le123089219od_b_b @ A @ B )
% 3.32/1.66 => ( ( member1516365892od_b_b @ C @ A )
% 3.32/1.66 => ( member1516365892od_b_b @ C @ B ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_308_in__mono,axiom,
% 3.32/1.66 ! [A: set_b,B: set_b,X: b] :
% 3.32/1.66 ( ( ord_less_eq_set_b @ A @ B )
% 3.32/1.66 => ( ( member_b @ X @ A )
% 3.32/1.66 => ( member_b @ X @ B ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_309_in__mono,axiom,
% 3.32/1.66 ! [A: set_Product_prod_b_b,B: set_Product_prod_b_b,X: product_prod_b_b] :
% 3.32/1.66 ( ( ord_le1036320359od_b_b @ A @ B )
% 3.32/1.66 => ( ( member1285940496od_b_b @ X @ A )
% 3.32/1.66 => ( member1285940496od_b_b @ X @ B ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_310_in__mono,axiom,
% 3.32/1.66 ! [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b,X: produc1213276845od_b_b] :
% 3.32/1.66 ( ( ord_le123089219od_b_b @ A @ B )
% 3.32/1.66 => ( ( member1516365892od_b_b @ X @ A )
% 3.32/1.66 => ( member1516365892od_b_b @ X @ B ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_311_mk__disjoint__insert,axiom,
% 3.32/1.66 ! [A2: produc1871334759_a_nat,A: set_Pr1987088711_a_nat] :
% 3.32/1.66 ( ( member832397200_a_nat @ A2 @ A )
% 3.32/1.66 => ? [B8: set_Pr1987088711_a_nat] :
% 3.32/1.66 ( ( A
% 3.32/1.66 = ( insert1574423351_a_nat @ A2 @ B8 ) )
% 3.32/1.66 & ~ ( member832397200_a_nat @ A2 @ B8 ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_312_mk__disjoint__insert,axiom,
% 3.32/1.66 ! [A2: b,A: set_b] :
% 3.32/1.66 ( ( member_b @ A2 @ A )
% 3.32/1.66 => ? [B8: set_b] :
% 3.32/1.66 ( ( A
% 3.32/1.66 = ( insert_b @ A2 @ B8 ) )
% 3.32/1.66 & ~ ( member_b @ A2 @ B8 ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_313_mk__disjoint__insert,axiom,
% 3.32/1.66 ! [A2: product_prod_b_b,A: set_Product_prod_b_b] :
% 3.32/1.66 ( ( member1285940496od_b_b @ A2 @ A )
% 3.32/1.66 => ? [B8: set_Product_prod_b_b] :
% 3.32/1.66 ( ( A
% 3.32/1.66 = ( insert1952693431od_b_b @ A2 @ B8 ) )
% 3.32/1.66 & ~ ( member1285940496od_b_b @ A2 @ B8 ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_314_mk__disjoint__insert,axiom,
% 3.32/1.66 ! [A2: produc1213276845od_b_b,A: set_Pr1324126435od_b_b] :
% 3.32/1.66 ( ( member1516365892od_b_b @ A2 @ A )
% 3.32/1.66 => ? [B8: set_Pr1324126435od_b_b] :
% 3.32/1.66 ( ( A
% 3.32/1.66 = ( insert2037698781od_b_b @ A2 @ B8 ) )
% 3.32/1.66 & ~ ( member1516365892od_b_b @ A2 @ B8 ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_315_insert__commute,axiom,
% 3.32/1.66 ! [X: b,Y: b,A: set_b] :
% 3.32/1.66 ( ( insert_b @ X @ ( insert_b @ Y @ A ) )
% 3.32/1.66 = ( insert_b @ Y @ ( insert_b @ X @ A ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_316_insert__commute,axiom,
% 3.32/1.66 ! [X: produc1871334759_a_nat,Y: produc1871334759_a_nat,A: set_Pr1987088711_a_nat] :
% 3.32/1.66 ( ( insert1574423351_a_nat @ X @ ( insert1574423351_a_nat @ Y @ A ) )
% 3.32/1.66 = ( insert1574423351_a_nat @ Y @ ( insert1574423351_a_nat @ X @ A ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_317_insert__eq__iff,axiom,
% 3.32/1.66 ! [A2: produc1871334759_a_nat,A: set_Pr1987088711_a_nat,B3: produc1871334759_a_nat,B: set_Pr1987088711_a_nat] :
% 3.32/1.66 ( ~ ( member832397200_a_nat @ A2 @ A )
% 3.32/1.66 => ( ~ ( member832397200_a_nat @ B3 @ B )
% 3.32/1.66 => ( ( ( insert1574423351_a_nat @ A2 @ A )
% 3.32/1.66 = ( insert1574423351_a_nat @ B3 @ B ) )
% 3.32/1.66 = ( ( ( A2 = B3 )
% 3.32/1.66 => ( A = B ) )
% 3.32/1.66 & ( ( A2 != B3 )
% 3.32/1.66 => ? [C4: set_Pr1987088711_a_nat] :
% 3.32/1.66 ( ( A
% 3.32/1.66 = ( insert1574423351_a_nat @ B3 @ C4 ) )
% 3.32/1.66 & ~ ( member832397200_a_nat @ B3 @ C4 )
% 3.32/1.66 & ( B
% 3.32/1.66 = ( insert1574423351_a_nat @ A2 @ C4 ) )
% 3.32/1.66 & ~ ( member832397200_a_nat @ A2 @ C4 ) ) ) ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_318_insert__eq__iff,axiom,
% 3.32/1.66 ! [A2: b,A: set_b,B3: b,B: set_b] :
% 3.32/1.66 ( ~ ( member_b @ A2 @ A )
% 3.32/1.66 => ( ~ ( member_b @ B3 @ B )
% 3.32/1.66 => ( ( ( insert_b @ A2 @ A )
% 3.32/1.66 = ( insert_b @ B3 @ B ) )
% 3.32/1.66 = ( ( ( A2 = B3 )
% 3.32/1.66 => ( A = B ) )
% 3.32/1.66 & ( ( A2 != B3 )
% 3.32/1.66 => ? [C4: set_b] :
% 3.32/1.66 ( ( A
% 3.32/1.66 = ( insert_b @ B3 @ C4 ) )
% 3.32/1.66 & ~ ( member_b @ B3 @ C4 )
% 3.32/1.66 & ( B
% 3.32/1.66 = ( insert_b @ A2 @ C4 ) )
% 3.32/1.66 & ~ ( member_b @ A2 @ C4 ) ) ) ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_319_insert__eq__iff,axiom,
% 3.32/1.66 ! [A2: product_prod_b_b,A: set_Product_prod_b_b,B3: product_prod_b_b,B: set_Product_prod_b_b] :
% 3.32/1.66 ( ~ ( member1285940496od_b_b @ A2 @ A )
% 3.32/1.66 => ( ~ ( member1285940496od_b_b @ B3 @ B )
% 3.32/1.66 => ( ( ( insert1952693431od_b_b @ A2 @ A )
% 3.32/1.66 = ( insert1952693431od_b_b @ B3 @ B ) )
% 3.32/1.66 = ( ( ( A2 = B3 )
% 3.32/1.66 => ( A = B ) )
% 3.32/1.66 & ( ( A2 != B3 )
% 3.32/1.66 => ? [C4: set_Product_prod_b_b] :
% 3.32/1.66 ( ( A
% 3.32/1.66 = ( insert1952693431od_b_b @ B3 @ C4 ) )
% 3.32/1.66 & ~ ( member1285940496od_b_b @ B3 @ C4 )
% 3.32/1.66 & ( B
% 3.32/1.66 = ( insert1952693431od_b_b @ A2 @ C4 ) )
% 3.32/1.66 & ~ ( member1285940496od_b_b @ A2 @ C4 ) ) ) ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_320_insert__eq__iff,axiom,
% 3.32/1.66 ! [A2: produc1213276845od_b_b,A: set_Pr1324126435od_b_b,B3: produc1213276845od_b_b,B: set_Pr1324126435od_b_b] :
% 3.32/1.66 ( ~ ( member1516365892od_b_b @ A2 @ A )
% 3.32/1.66 => ( ~ ( member1516365892od_b_b @ B3 @ B )
% 3.32/1.66 => ( ( ( insert2037698781od_b_b @ A2 @ A )
% 3.32/1.66 = ( insert2037698781od_b_b @ B3 @ B ) )
% 3.32/1.66 = ( ( ( A2 = B3 )
% 3.32/1.66 => ( A = B ) )
% 3.32/1.66 & ( ( A2 != B3 )
% 3.32/1.66 => ? [C4: set_Pr1324126435od_b_b] :
% 3.32/1.66 ( ( A
% 3.32/1.66 = ( insert2037698781od_b_b @ B3 @ C4 ) )
% 3.32/1.66 & ~ ( member1516365892od_b_b @ B3 @ C4 )
% 3.32/1.66 & ( B
% 3.32/1.66 = ( insert2037698781od_b_b @ A2 @ C4 ) )
% 3.32/1.66 & ~ ( member1516365892od_b_b @ A2 @ C4 ) ) ) ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_321_insert__absorb,axiom,
% 3.32/1.66 ! [A2: produc1871334759_a_nat,A: set_Pr1987088711_a_nat] :
% 3.32/1.66 ( ( member832397200_a_nat @ A2 @ A )
% 3.32/1.66 => ( ( insert1574423351_a_nat @ A2 @ A )
% 3.32/1.66 = A ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_322_insert__absorb,axiom,
% 3.32/1.66 ! [A2: b,A: set_b] :
% 3.32/1.66 ( ( member_b @ A2 @ A )
% 3.32/1.66 => ( ( insert_b @ A2 @ A )
% 3.32/1.66 = A ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_323_insert__absorb,axiom,
% 3.32/1.66 ! [A2: product_prod_b_b,A: set_Product_prod_b_b] :
% 3.32/1.66 ( ( member1285940496od_b_b @ A2 @ A )
% 3.32/1.66 => ( ( insert1952693431od_b_b @ A2 @ A )
% 3.32/1.66 = A ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_324_insert__absorb,axiom,
% 3.32/1.66 ! [A2: produc1213276845od_b_b,A: set_Pr1324126435od_b_b] :
% 3.32/1.66 ( ( member1516365892od_b_b @ A2 @ A )
% 3.32/1.66 => ( ( insert2037698781od_b_b @ A2 @ A )
% 3.32/1.66 = A ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_325_insert__ident,axiom,
% 3.32/1.66 ! [X: produc1871334759_a_nat,A: set_Pr1987088711_a_nat,B: set_Pr1987088711_a_nat] :
% 3.32/1.66 ( ~ ( member832397200_a_nat @ X @ A )
% 3.32/1.66 => ( ~ ( member832397200_a_nat @ X @ B )
% 3.32/1.66 => ( ( ( insert1574423351_a_nat @ X @ A )
% 3.32/1.66 = ( insert1574423351_a_nat @ X @ B ) )
% 3.32/1.66 = ( A = B ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_326_insert__ident,axiom,
% 3.32/1.66 ! [X: b,A: set_b,B: set_b] :
% 3.32/1.66 ( ~ ( member_b @ X @ A )
% 3.32/1.66 => ( ~ ( member_b @ X @ B )
% 3.32/1.66 => ( ( ( insert_b @ X @ A )
% 3.32/1.66 = ( insert_b @ X @ B ) )
% 3.32/1.66 = ( A = B ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_327_insert__ident,axiom,
% 3.32/1.66 ! [X: product_prod_b_b,A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
% 3.32/1.66 ( ~ ( member1285940496od_b_b @ X @ A )
% 3.32/1.66 => ( ~ ( member1285940496od_b_b @ X @ B )
% 3.32/1.66 => ( ( ( insert1952693431od_b_b @ X @ A )
% 3.32/1.66 = ( insert1952693431od_b_b @ X @ B ) )
% 3.32/1.66 = ( A = B ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_328_insert__ident,axiom,
% 3.32/1.66 ! [X: produc1213276845od_b_b,A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b] :
% 3.32/1.66 ( ~ ( member1516365892od_b_b @ X @ A )
% 3.32/1.66 => ( ~ ( member1516365892od_b_b @ X @ B )
% 3.32/1.66 => ( ( ( insert2037698781od_b_b @ X @ A )
% 3.32/1.66 = ( insert2037698781od_b_b @ X @ B ) )
% 3.32/1.66 = ( A = B ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_329_Set_Oset__insert,axiom,
% 3.32/1.66 ! [X: produc1871334759_a_nat,A: set_Pr1987088711_a_nat] :
% 3.32/1.66 ( ( member832397200_a_nat @ X @ A )
% 3.32/1.66 => ~ ! [B8: set_Pr1987088711_a_nat] :
% 3.32/1.66 ( ( A
% 3.32/1.66 = ( insert1574423351_a_nat @ X @ B8 ) )
% 3.32/1.66 => ( member832397200_a_nat @ X @ B8 ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_330_Set_Oset__insert,axiom,
% 3.32/1.66 ! [X: b,A: set_b] :
% 3.32/1.66 ( ( member_b @ X @ A )
% 3.32/1.66 => ~ ! [B8: set_b] :
% 3.32/1.66 ( ( A
% 3.32/1.66 = ( insert_b @ X @ B8 ) )
% 3.32/1.66 => ( member_b @ X @ B8 ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_331_Set_Oset__insert,axiom,
% 3.32/1.66 ! [X: product_prod_b_b,A: set_Product_prod_b_b] :
% 3.32/1.66 ( ( member1285940496od_b_b @ X @ A )
% 3.32/1.66 => ~ ! [B8: set_Product_prod_b_b] :
% 3.32/1.66 ( ( A
% 3.32/1.66 = ( insert1952693431od_b_b @ X @ B8 ) )
% 3.32/1.66 => ( member1285940496od_b_b @ X @ B8 ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_332_Set_Oset__insert,axiom,
% 3.32/1.66 ! [X: produc1213276845od_b_b,A: set_Pr1324126435od_b_b] :
% 3.32/1.66 ( ( member1516365892od_b_b @ X @ A )
% 3.32/1.66 => ~ ! [B8: set_Pr1324126435od_b_b] :
% 3.32/1.66 ( ( A
% 3.32/1.66 = ( insert2037698781od_b_b @ X @ B8 ) )
% 3.32/1.66 => ( member1516365892od_b_b @ X @ B8 ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_333_insertI2,axiom,
% 3.32/1.66 ! [A2: produc1871334759_a_nat,B: set_Pr1987088711_a_nat,B3: produc1871334759_a_nat] :
% 3.32/1.66 ( ( member832397200_a_nat @ A2 @ B )
% 3.32/1.66 => ( member832397200_a_nat @ A2 @ ( insert1574423351_a_nat @ B3 @ B ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_334_insertI2,axiom,
% 3.32/1.66 ! [A2: b,B: set_b,B3: b] :
% 3.32/1.66 ( ( member_b @ A2 @ B )
% 3.32/1.66 => ( member_b @ A2 @ ( insert_b @ B3 @ B ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_335_insertI2,axiom,
% 3.32/1.66 ! [A2: product_prod_b_b,B: set_Product_prod_b_b,B3: product_prod_b_b] :
% 3.32/1.66 ( ( member1285940496od_b_b @ A2 @ B )
% 3.32/1.66 => ( member1285940496od_b_b @ A2 @ ( insert1952693431od_b_b @ B3 @ B ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_336_insertI2,axiom,
% 3.32/1.66 ! [A2: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,B3: produc1213276845od_b_b] :
% 3.32/1.66 ( ( member1516365892od_b_b @ A2 @ B )
% 3.32/1.66 => ( member1516365892od_b_b @ A2 @ ( insert2037698781od_b_b @ B3 @ B ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_337_insertI1,axiom,
% 3.32/1.66 ! [A2: produc1871334759_a_nat,B: set_Pr1987088711_a_nat] : ( member832397200_a_nat @ A2 @ ( insert1574423351_a_nat @ A2 @ B ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_338_insertI1,axiom,
% 3.32/1.66 ! [A2: b,B: set_b] : ( member_b @ A2 @ ( insert_b @ A2 @ B ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_339_insertI1,axiom,
% 3.32/1.66 ! [A2: product_prod_b_b,B: set_Product_prod_b_b] : ( member1285940496od_b_b @ A2 @ ( insert1952693431od_b_b @ A2 @ B ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_340_insertI1,axiom,
% 3.32/1.66 ! [A2: produc1213276845od_b_b,B: set_Pr1324126435od_b_b] : ( member1516365892od_b_b @ A2 @ ( insert2037698781od_b_b @ A2 @ B ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_341_insertE,axiom,
% 3.32/1.66 ! [A2: produc1871334759_a_nat,B3: produc1871334759_a_nat,A: set_Pr1987088711_a_nat] :
% 3.32/1.66 ( ( member832397200_a_nat @ A2 @ ( insert1574423351_a_nat @ B3 @ A ) )
% 3.32/1.66 => ( ( A2 != B3 )
% 3.32/1.66 => ( member832397200_a_nat @ A2 @ A ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_342_insertE,axiom,
% 3.32/1.66 ! [A2: b,B3: b,A: set_b] :
% 3.32/1.66 ( ( member_b @ A2 @ ( insert_b @ B3 @ A ) )
% 3.32/1.66 => ( ( A2 != B3 )
% 3.32/1.66 => ( member_b @ A2 @ A ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_343_insertE,axiom,
% 3.32/1.66 ! [A2: product_prod_b_b,B3: product_prod_b_b,A: set_Product_prod_b_b] :
% 3.32/1.66 ( ( member1285940496od_b_b @ A2 @ ( insert1952693431od_b_b @ B3 @ A ) )
% 3.32/1.66 => ( ( A2 != B3 )
% 3.32/1.66 => ( member1285940496od_b_b @ A2 @ A ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_344_insertE,axiom,
% 3.32/1.66 ! [A2: produc1213276845od_b_b,B3: produc1213276845od_b_b,A: set_Pr1324126435od_b_b] :
% 3.32/1.66 ( ( member1516365892od_b_b @ A2 @ ( insert2037698781od_b_b @ B3 @ A ) )
% 3.32/1.66 => ( ( A2 != B3 )
% 3.32/1.66 => ( member1516365892od_b_b @ A2 @ A ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_345_singleton__inject,axiom,
% 3.32/1.66 ! [A2: b,B3: b] :
% 3.32/1.66 ( ( ( insert_b @ A2 @ bot_bot_set_b )
% 3.32/1.66 = ( insert_b @ B3 @ bot_bot_set_b ) )
% 3.32/1.66 => ( A2 = B3 ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_346_singleton__inject,axiom,
% 3.32/1.66 ! [A2: produc1871334759_a_nat,B3: produc1871334759_a_nat] :
% 3.32/1.66 ( ( ( insert1574423351_a_nat @ A2 @ bot_bo1836341171_a_nat )
% 3.32/1.66 = ( insert1574423351_a_nat @ B3 @ bot_bo1836341171_a_nat ) )
% 3.32/1.66 => ( A2 = B3 ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_347_insert__not__empty,axiom,
% 3.32/1.66 ! [A2: b,A: set_b] :
% 3.32/1.66 ( ( insert_b @ A2 @ A )
% 3.32/1.66 != bot_bot_set_b ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_348_insert__not__empty,axiom,
% 3.32/1.66 ! [A2: produc1871334759_a_nat,A: set_Pr1987088711_a_nat] :
% 3.32/1.66 ( ( insert1574423351_a_nat @ A2 @ A )
% 3.32/1.66 != bot_bo1836341171_a_nat ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_349_doubleton__eq__iff,axiom,
% 3.32/1.66 ! [A2: b,B3: b,C: b,D: b] :
% 3.32/1.66 ( ( ( insert_b @ A2 @ ( insert_b @ B3 @ bot_bot_set_b ) )
% 3.32/1.66 = ( insert_b @ C @ ( insert_b @ D @ bot_bot_set_b ) ) )
% 3.32/1.66 = ( ( ( A2 = C )
% 3.32/1.66 & ( B3 = D ) )
% 3.32/1.66 | ( ( A2 = D )
% 3.32/1.66 & ( B3 = C ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_350_doubleton__eq__iff,axiom,
% 3.32/1.66 ! [A2: produc1871334759_a_nat,B3: produc1871334759_a_nat,C: produc1871334759_a_nat,D: produc1871334759_a_nat] :
% 3.32/1.66 ( ( ( insert1574423351_a_nat @ A2 @ ( insert1574423351_a_nat @ B3 @ bot_bo1836341171_a_nat ) )
% 3.32/1.66 = ( insert1574423351_a_nat @ C @ ( insert1574423351_a_nat @ D @ bot_bo1836341171_a_nat ) ) )
% 3.32/1.66 = ( ( ( A2 = C )
% 3.32/1.66 & ( B3 = D ) )
% 3.32/1.66 | ( ( A2 = D )
% 3.32/1.66 & ( B3 = C ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_351_ma,axiom,
% 3.32/1.66 ! [X2: produc1871334759_a_nat] :
% 3.32/1.66 ( ( member832397200_a_nat @ X2 @ ( insert1574423351_a_nat @ ( standa63370785tant_a @ standard_S_Idt_a ) @ ( insert1574423351_a_nat @ ( standa1795879409tant_a @ standard_S_Idt_a ) @ ( insert1574423351_a_nat @ ( standa997693288tant_a @ standard_S_Idt_a ) @ bot_bo1836341171_a_nat ) ) ) )
% 3.32/1.66 => ( mainta1604381365_nat_b @ X2 @ g ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_352_f,axiom,
% 3.32/1.66 ( f
% 3.32/1.66 = ( ^ [X5: b] :
% 3.32/1.66 ( if_b
% 3.32/1.66 @ ( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ X5 @ bot_bot_set_b ) )
% 3.32/1.66 = bot_bot_set_b )
% 3.32/1.66 @ X5
% 3.32/1.66 @ ( hilbert_Eps_b @ ( p @ X5 ) ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_353_P,axiom,
% 3.32/1.66 ( p
% 3.32/1.66 = ( ^ [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 ) ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_354_congr_I1_J,axiom,
% 3.32/1.66 ! [X: b,Y: b,L: standard_Constant_a] :
% 3.32/1.66 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ X @ Y ) @ ( getRel904497637nt_a_b @ L @ g ) )
% 3.32/1.66 => ( equiv_1821124534_set_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g )
% 3.32/1.66 @ ^ [V3: b] : ( image_b_b @ ( getRel904497637nt_a_b @ L @ g ) @ ( insert_b @ V3 @ bot_bot_set_b ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(fact_355_ident,axiom,
% 3.32/1.66 ( ( getRel904497637nt_a_b @ standard_S_Idt_a @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ g ) @ f ) @ g ) )
% 3.32/1.66 = ( image_1683732397od_b_b
% 3.32/1.66 @ ^ [X5: b] : ( product_Pair_b_b @ X5 @ X5 )
% 3.32/1.66 @ ( labele1424214014nt_a_b @ ( map_gr926947118tant_a @ ( bNF_Gr_b_b @ ( labele1424214014nt_a_b @ g ) @ f ) @ g ) ) ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(help_If_3_1_If_001tf__b_T,axiom,
% 3.32/1.66 ! [P: $o] :
% 3.32/1.66 ( ( P = $true )
% 3.32/1.66 | ( P = $false ) ) ).
% 3.32/1.66
% 3.32/1.66 thf(help_If_2_1_If_001tf__b_T,axiom,
% 3.32/1.66 ! [X: b,Y: b] :
% 3.32/1.66 ( ( if_b @ $false @ X @ Y )
% 3.32/1.66 = Y ) ).
% 3.32/1.66
% 3.32/1.66 thf(help_If_1_1_If_001tf__b_T,axiom,
% 3.32/1.66 ! [X: b,Y: b] :
% 3.32/1.66 ( ( if_b @ $true @ X @ Y )
% 3.32/1.66 = X ) ).
% 3.32/1.66
% 3.32/1.66 thf(conj_0,conjecture,
% 3.32/1.66 member_b @ x @ ( labele1424214014nt_a_b @ g ) ).
% 3.32/1.66 ------------------------
% 3.32/1.68 % (15986)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_15787 for (2999ds/18Mi)
% 3.32/1.68 % (15984)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_15787 for (2999ds/2Mi)
% 3.32/1.68 % (15983)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_15787 for (2999ds/2Mi)
% 3.32/1.68 % (15985)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_15787 for (2999ds/275Mi)
% 3.32/1.68 % (15981)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_15787 for (2999ds/4Mi)
% 3.32/1.68 % (15983)Instruction limit reached!
% 3.32/1.68 % (15983)------------------------------
% 3.32/1.68 % (15983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.32/1.68 % (15983)Termination reason: Unknown
% 3.32/1.68 % (15983)Termination phase: shuffling
% 3.32/1.68
% 3.32/1.68 % (15983)Memory used [KB]: 1535
% 3.32/1.68 % (15984)Instruction limit reached!
% 3.32/1.68 % (15984)------------------------------
% 3.32/1.68 % (15984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.32/1.68 % (15984)Termination reason: Unknown
% 3.32/1.68 % (15984)Termination phase: shuffling
% 3.32/1.68
% 3.32/1.68 % (15984)Memory used [KB]: 1663
% 3.32/1.68 % (15984)Time elapsed: 0.002 s
% 3.32/1.68 % (15984)Instructions burned: 2 (million)
% 3.32/1.68 % (15984)------------------------------
% 3.32/1.68 % (15984)------------------------------
% 3.32/1.68 % (15983)Time elapsed: 0.002 s
% 3.32/1.68 % (15983)Instructions burned: 2 (million)
% 3.32/1.68 % (15983)------------------------------
% 3.32/1.68 % (15983)------------------------------
% 3.32/1.69 % (15981)Instruction limit reached!
% 3.32/1.69 % (15981)------------------------------
% 3.32/1.69 % (15981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.32/1.69 % (15981)Termination reason: Unknown
% 3.32/1.69 % (15981)Termination phase: shuffling
% 3.32/1.69
% 3.32/1.69 % (15981)Memory used [KB]: 1791
% 3.32/1.69 % (15981)Time elapsed: 0.004 s
% 3.32/1.69 % (15981)Instructions burned: 7 (million)
% 3.32/1.69 % (15981)------------------------------
% 3.32/1.69 % (15981)------------------------------
% 3.32/1.69 % (15982)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_15787 for (2999ds/27Mi)
% 3.32/1.69 % (15986)Instruction limit reached!
% 3.32/1.69 % (15986)------------------------------
% 3.32/1.69 % (15986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.32/1.69 % (15986)Termination reason: Unknown
% 3.32/1.69 % (15986)Termination phase: shuffling
% 3.32/1.69
% 3.32/1.69 % (15986)Memory used [KB]: 1918
% 3.32/1.69 % (15986)Time elapsed: 0.008 s
% 3.32/1.69 % (15986)Instructions burned: 20 (million)
% 3.32/1.69 % (15986)------------------------------
% 3.32/1.69 % (15986)------------------------------
% 3.32/1.69 % (15980)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_15787 for (2999ds/183Mi)
% 3.37/1.70 % (15988)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_15787 for (2999ds/37Mi)
% 3.37/1.70 % (15989)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_15787 for (2999ds/15Mi)
% 3.37/1.70 % (15990)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_15787 for (2999ds/3Mi)
% 3.37/1.70 % (15987)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_15787 for (2999ds/3Mi)
% 3.37/1.70 % (15990)Instruction limit reached!
% 3.37/1.70 % (15990)------------------------------
% 3.37/1.70 % (15990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.70 % (15990)Termination reason: Unknown
% 3.37/1.70 % (15990)Termination phase: shuffling
% 3.37/1.70
% 3.37/1.70 % (15990)Memory used [KB]: 1663
% 3.37/1.70 % (15990)Time elapsed: 0.003 s
% 3.37/1.70 % (15990)Instructions burned: 5 (million)
% 3.37/1.70 % (15990)------------------------------
% 3.37/1.70 % (15990)------------------------------
% 3.37/1.70 % (15987)Instruction limit reached!
% 3.37/1.70 % (15987)------------------------------
% 3.37/1.70 % (15987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.70 % (15987)Termination reason: Unknown
% 3.37/1.70 % (15987)Termination phase: shuffling
% 3.37/1.70
% 3.37/1.70 % (15987)Memory used [KB]: 1663
% 3.37/1.70 % (15987)Time elapsed: 0.004 s
% 3.37/1.70 % (15987)Instructions burned: 4 (million)
% 3.37/1.70 % (15987)------------------------------
% 3.37/1.70 % (15987)------------------------------
% 3.37/1.70 % (15985)Refutation not found, incomplete strategy
% 3.37/1.70 % (15985)------------------------------
% 3.37/1.70 % (15985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.70 % (15985)Termination reason: Refutation not found, incomplete strategy
% 3.37/1.70
% 3.37/1.70
% 3.37/1.70 % (15985)Memory used [KB]: 6652
% 3.37/1.70 % (15985)Time elapsed: 0.021 s
% 3.37/1.70 % (15985)Instructions burned: 57 (million)
% 3.37/1.70 % (15985)------------------------------
% 3.37/1.70 % (15985)------------------------------
% 3.37/1.71 % (15982)Instruction limit reached!
% 3.37/1.71 % (15982)------------------------------
% 3.37/1.71 % (15982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.71 % (15982)Termination reason: Unknown
% 3.37/1.71 % (15982)Termination phase: shuffling
% 3.37/1.71
% 3.37/1.71 % (15982)Memory used [KB]: 2046
% 3.37/1.71 % (15982)Time elapsed: 0.017 s
% 3.37/1.71 % (15982)Instructions burned: 28 (million)
% 3.37/1.71 % (15982)------------------------------
% 3.37/1.71 % (15982)------------------------------
% 3.37/1.71 % (15989)Instruction limit reached!
% 3.37/1.71 % (15989)------------------------------
% 3.37/1.71 % (15989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.71 % (15989)Termination reason: Unknown
% 3.37/1.71 % (15989)Termination phase: shuffling
% 3.37/1.71
% 3.37/1.71 % (15989)Memory used [KB]: 1918
% 3.37/1.71 % (15989)Time elapsed: 0.008 s
% 3.37/1.71 % (15989)Instructions burned: 15 (million)
% 3.37/1.71 % (15989)------------------------------
% 3.37/1.71 % (15989)------------------------------
% 3.37/1.71 % (15988)Instruction limit reached!
% 3.37/1.71 % (15988)------------------------------
% 3.37/1.71 % (15988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.71 % (15988)Termination reason: Unknown
% 3.37/1.71 % (15988)Termination phase: shuffling
% 3.37/1.71
% 3.37/1.71 % (15988)Memory used [KB]: 2430
% 3.37/1.71 % (15988)Time elapsed: 0.013 s
% 3.37/1.71 % (15988)Instructions burned: 39 (million)
% 3.37/1.71 % (15988)------------------------------
% 3.37/1.71 % (15988)------------------------------
% 3.37/1.71 % (15991)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_15787 for (2999ds/1041Mi)
% 3.37/1.72 % (15993)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_15787 for (2999ds/16Mi)
% 3.37/1.72 % (15992)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_15787 for (2999ds/7Mi)
% 3.37/1.72 % (15994)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_15787 for (2999ds/3Mi)
% 3.37/1.72 % (15996)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_15787 for (2999ds/7Mi)
% 3.37/1.72 % (15994)Instruction limit reached!
% 3.37/1.72 % (15994)------------------------------
% 3.37/1.72 % (15994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.72 % (15994)Termination reason: Unknown
% 3.37/1.72 % (15992)Instruction limit reached!
% 3.37/1.72 % (15992)------------------------------
% 3.37/1.72 % (15992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.72 % (15994)Termination phase: shuffling
% 3.37/1.72
% 3.37/1.72 % (15994)Memory used [KB]: 1663
% 3.37/1.72 % (15994)Time elapsed: 0.003 s
% 3.37/1.72 % (15994)Instructions burned: 3 (million)
% 3.37/1.72 % (15994)------------------------------
% 3.37/1.72 % (15994)------------------------------
% 3.37/1.72 % (15992)Termination reason: Unknown
% 3.37/1.72 % (15992)Termination phase: shuffling
% 3.37/1.72
% 3.37/1.72 % (15992)Memory used [KB]: 1791
% 3.37/1.72 % (15992)Time elapsed: 0.005 s
% 3.37/1.72 % (15992)Instructions burned: 9 (million)
% 3.37/1.72 % (15992)------------------------------
% 3.37/1.72 % (15992)------------------------------
% 3.37/1.72 % (15996)Instruction limit reached!
% 3.37/1.72 % (15996)------------------------------
% 3.37/1.72 % (15996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.72 % (15996)Termination reason: Unknown
% 3.37/1.72 % (15996)Termination phase: shuffling
% 3.37/1.72
% 3.37/1.72 % (15996)Memory used [KB]: 1791
% 3.37/1.72 % (15996)Time elapsed: 0.004 s
% 3.37/1.72 % (15996)Instructions burned: 8 (million)
% 3.37/1.72 % (15996)------------------------------
% 3.37/1.72 % (15996)------------------------------
% 3.37/1.73 % (15995)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_15787 for (2999ds/3Mi)
% 3.37/1.73 % (15993)Instruction limit reached!
% 3.37/1.73 % (15993)------------------------------
% 3.37/1.73 % (15993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.73 % (15993)Termination reason: Unknown
% 3.37/1.73 % (15993)Termination phase: shuffling
% 3.37/1.73
% 3.37/1.73 % (15993)Memory used [KB]: 1918
% 3.37/1.73 % (15993)Time elapsed: 0.008 s
% 3.37/1.73 % (15993)Instructions burned: 17 (million)
% 3.37/1.73 % (15993)------------------------------
% 3.37/1.73 % (15993)------------------------------
% 3.37/1.73 % (15995)Instruction limit reached!
% 3.37/1.73 % (15995)------------------------------
% 3.37/1.73 % (15995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.73 % (15995)Termination reason: Unknown
% 3.37/1.73 % (15995)Termination phase: shuffling
% 3.37/1.73
% 3.37/1.73 % (15995)Memory used [KB]: 1663
% 3.37/1.73 % (15995)Time elapsed: 0.004 s
% 3.37/1.73 % (15995)Instructions burned: 3 (million)
% 3.37/1.73 % (15995)------------------------------
% 3.37/1.73 % (15995)------------------------------
% 3.37/1.73 % (15997)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_15787 for (2999ds/3Mi)
% 3.37/1.73 % (15997)Instruction limit reached!
% 3.37/1.73 % (15997)------------------------------
% 3.37/1.73 % (15997)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.73 % (15997)Termination reason: Unknown
% 3.37/1.73 % (15997)Termination phase: shuffling
% 3.37/1.73
% 3.37/1.73 % (15997)Memory used [KB]: 1791
% 3.37/1.73 % (15997)Time elapsed: 0.003 s
% 3.37/1.73 % (15997)Instructions burned: 5 (million)
% 3.37/1.73 % (15999)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_15787 for (2999ds/18Mi)
% 3.37/1.73 % (15997)------------------------------
% 3.37/1.73 % (15997)------------------------------
% 3.37/1.74 % (16000)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_15787 for (2999ds/710Mi)
% 3.37/1.74 % (15998)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_15787 for (2999ds/4Mi)
% 3.37/1.74 % (15998)Instruction limit reached!
% 3.37/1.74 % (15998)------------------------------
% 3.37/1.74 % (15998)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.74 % (15998)Termination reason: Unknown
% 3.37/1.74 % (15998)Termination phase: shuffling
% 3.37/1.74
% 3.37/1.74 % (15998)Memory used [KB]: 1663
% 3.37/1.74 % (15998)Time elapsed: 0.004 s
% 3.37/1.74 % (15998)Instructions burned: 5 (million)
% 3.37/1.74 % (15998)------------------------------
% 3.37/1.74 % (15998)------------------------------
% 3.37/1.74 % (15999)Instruction limit reached!
% 3.37/1.74 % (15999)------------------------------
% 3.37/1.74 % (15999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.74 % (15999)Termination reason: Unknown
% 3.37/1.74 % (15999)Termination phase: shuffling
% 3.37/1.74
% 3.37/1.74 % (15999)Memory used [KB]: 1918
% 3.37/1.74 % (15999)Time elapsed: 0.009 s
% 3.37/1.74 % (15999)Instructions burned: 20 (million)
% 3.37/1.74 % (15999)------------------------------
% 3.37/1.74 % (15999)------------------------------
% 3.37/1.74 % (16002)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_15787 for (2999ds/902Mi)
% 3.37/1.75 % (16001)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_15787 for (2999ds/6Mi)
% 3.37/1.75 % (15980)Instruction limit reached!
% 3.37/1.75 % (15980)------------------------------
% 3.37/1.75 % (15980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.75 % (15980)Termination reason: Unknown
% 3.37/1.75 % (15980)Termination phase: Saturation
% 3.37/1.75
% 3.37/1.75 % (15980)Memory used [KB]: 7547
% 3.37/1.75 % (15980)Time elapsed: 0.054 s
% 3.37/1.75 % (15980)Instructions burned: 185 (million)
% 3.37/1.75 % (15980)------------------------------
% 3.37/1.75 % (15980)------------------------------
% 3.37/1.75 % (16001)Instruction limit reached!
% 3.37/1.75 % (16001)------------------------------
% 3.37/1.75 % (16001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.75 % (16001)Termination reason: Unknown
% 3.37/1.75 % (16001)Termination phase: shuffling
% 3.37/1.75
% 3.37/1.75 % (16001)Memory used [KB]: 1791
% 3.37/1.75 % (16001)Time elapsed: 0.005 s
% 3.37/1.75 % (16001)Instructions burned: 6 (million)
% 3.37/1.75 % (16001)------------------------------
% 3.37/1.75 % (16001)------------------------------
% 3.37/1.75 % (16004)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_15787 for (2999ds/5Mi)
% 3.37/1.75 % (16000)Refutation not found, incomplete strategy
% 3.37/1.75 % (16000)------------------------------
% 3.37/1.75 % (16000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.75 % (16000)Termination reason: Refutation not found, incomplete strategy
% 3.37/1.75
% 3.37/1.75
% 3.37/1.75 % (16000)Memory used [KB]: 6652
% 3.37/1.75 % (16000)Time elapsed: 0.040 s
% 3.37/1.75 % (16000)Instructions burned: 57 (million)
% 3.37/1.75 % (16000)------------------------------
% 3.37/1.75 % (16000)------------------------------
% 3.37/1.75 % (16003)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_15787 for (2999ds/21Mi)
% 3.37/1.75 % (16004)Instruction limit reached!
% 3.37/1.75 % (16004)------------------------------
% 3.37/1.75 % (16004)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.75 % (16004)Termination reason: Unknown
% 3.37/1.75 % (16004)Termination phase: shuffling
% 3.37/1.75
% 3.37/1.75 % (16004)Memory used [KB]: 1791
% 3.37/1.75 % (16004)Time elapsed: 0.003 s
% 3.37/1.75 % (16004)Instructions burned: 6 (million)
% 3.37/1.75 % (16004)------------------------------
% 3.37/1.75 % (16004)------------------------------
% 3.37/1.76 % (16005)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_15787 for (2999ds/6Mi)
% 3.37/1.76 % (16005)Instruction limit reached!
% 3.37/1.76 % (16005)------------------------------
% 3.37/1.76 % (16005)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.76 % (16005)Termination reason: Unknown
% 3.37/1.76 % (16005)Termination phase: shuffling
% 3.37/1.76
% 3.37/1.76 % (16005)Memory used [KB]: 1791
% 3.37/1.76 % (16005)Time elapsed: 0.003 s
% 3.37/1.76 % (16005)Instructions burned: 6 (million)
% 3.37/1.76 % (16005)------------------------------
% 3.37/1.76 % (16005)------------------------------
% 3.37/1.76 % (16003)Instruction limit reached!
% 3.37/1.76 % (16003)------------------------------
% 3.37/1.76 % (16003)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.76 % (16003)Termination reason: Unknown
% 3.37/1.76 % (16003)Termination phase: shuffling
% 3.37/1.76
% 3.37/1.76 % (16003)Memory used [KB]: 1918
% 3.37/1.76 % (16003)Time elapsed: 0.009 s
% 3.37/1.76 % (16003)Instructions burned: 22 (million)
% 3.37/1.76 % (16003)------------------------------
% 3.37/1.76 % (16003)------------------------------
% 3.37/1.76 % (16006)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_15787 for (2999ds/377Mi)
% 3.37/1.76 % (16008)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_15787 for (2999ds/19Mi)
% 3.37/1.76 % (16007)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_15787 for (2999ds/779Mi)
% 3.37/1.77 % (16009)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_15787 for (2998ds/879Mi)
% 3.37/1.77 % (16008)Instruction limit reached!
% 3.37/1.77 % (16008)------------------------------
% 3.37/1.77 % (16008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.77 % (16008)Termination reason: Unknown
% 3.37/1.77 % (16008)Termination phase: shuffling
% 3.37/1.77
% 3.37/1.77 % (16008)Memory used [KB]: 2046
% 3.37/1.77 % (16008)Time elapsed: 0.007 s
% 3.37/1.77 % (16008)Instructions burned: 21 (million)
% 3.37/1.77 % (16008)------------------------------
% 3.37/1.77 % (16008)------------------------------
% 3.37/1.77 % (16010)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_15787 for (2998ds/17Mi)
% 3.37/1.78 % (16010)Instruction limit reached!
% 3.37/1.78 % (16010)------------------------------
% 3.37/1.78 % (16010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.78 % (16010)Termination reason: Unknown
% 3.37/1.78 % (16010)Termination phase: shuffling
% 3.37/1.78
% 3.37/1.78 % (16010)Memory used [KB]: 1918
% 3.37/1.78 % (16010)Time elapsed: 0.007 s
% 3.37/1.78 % (16010)Instructions burned: 19 (million)
% 3.37/1.78 % (16010)------------------------------
% 3.37/1.78 % (16010)------------------------------
% 3.37/1.78 % (16011)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_15787 for (2998ds/3Mi)
% 3.37/1.78 % (16011)Instruction limit reached!
% 3.37/1.78 % (16011)------------------------------
% 3.37/1.78 % (16011)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.78 % (16011)Termination reason: Unknown
% 3.37/1.78 % (16011)Termination phase: shuffling
% 3.37/1.78
% 3.37/1.78 % (16011)Memory used [KB]: 1791
% 3.37/1.78 % (16011)Time elapsed: 0.003 s
% 3.37/1.78 % (16011)Instructions burned: 6 (million)
% 3.37/1.78 % (16011)------------------------------
% 3.37/1.78 % (16011)------------------------------
% 3.37/1.79 % (16012)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_15787 for (2998ds/30Mi)
% 3.37/1.79 % (16009)First to succeed.
% 3.37/1.79 % (16013)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_15787 for (2998ds/127Mi)
% 3.37/1.80 % (16009)Refutation found. Thanks to Tanya!
% 3.37/1.80 % SZS status Theorem for DTF2THF_15787
% 3.37/1.80 % SZS output start Proof for DTF2THF_15787
% 3.37/1.80 thf(type_def_5, type, set_St761939237tant_a: $tType).
% 3.37/1.80 thf(type_def_6, type, standard_Constant_a: $tType).
% 3.37/1.80 thf(type_def_7, type, product_prod_b_b: $tType).
% 3.37/1.80 thf(type_def_9, type, set_Pr1324126435od_b_b: $tType).
% 3.37/1.80 thf(type_def_10, type, set_la1083530965_a_nat: $tType).
% 3.37/1.80 thf(type_def_11, type, labele935650037_a_nat: $tType).
% 3.37/1.80 thf(type_def_12, type, set_Pr1987088711_a_nat: $tType).
% 3.37/1.80 thf(type_def_13, type, produc1213276845od_b_b: $tType).
% 3.37/1.80 thf(type_def_14, type, b: $tType).
% 3.37/1.80 thf(type_def_15, type, set_Pr1906739389_b_b_b: $tType).
% 3.37/1.80 thf(type_def_16, type, set_Product_prod_b_b: $tType).
% 3.37/1.80 thf(type_def_17, type, set_Pr357419743_b_b_b: $tType).
% 3.37/1.80 thf(type_def_18, type, set_b: $tType).
% 3.37/1.80 thf(type_def_19, type, set_Pr1649131859tant_a: $tType).
% 3.37/1.80 thf(type_def_20, type, set_Pr2109276827od_b_b: $tType).
% 3.37/1.80 thf(type_def_21, type, set_Pr924198087_a_nat: $tType).
% 3.37/1.80 thf(type_def_22, type, set_Pr2007082183od_b_b: $tType).
% 3.37/1.80 thf(type_def_23, type, labele1644675410od_b_b: $tType).
% 3.37/1.80 thf(type_def_24, type, labele1835558936od_b_b: $tType).
% 3.37/1.80 thf(type_def_25, type, labele1159362096nt_a_b: $tType).
% 3.37/1.80 thf(type_def_26, type, allego510293162tant_a: $tType).
% 3.37/1.80 thf(type_def_27, type, set_Pr1190604087od_b_b: $tType).
% 3.37/1.80 thf(type_def_28, type, set_Pr1021918435od_b_b: $tType).
% 3.37/1.80 thf(type_def_29, type, set_Pr2106913242_nat_b: $tType).
% 3.37/1.80 thf(type_def_30, type, labele1322729112_a_nat: $tType).
% 3.37/1.80 thf(type_def_31, type, set_Pr812188767_nat_b: $tType).
% 3.37/1.80 thf(type_def_32, type, set_Pr197580003_a_nat: $tType).
% 3.37/1.80 thf(type_def_33, type, produc90515391tant_a: $tType).
% 3.37/1.80 thf(type_def_34, type, produc970027067od_b_b: $tType).
% 3.37/1.80 thf(type_def_35, type, produc1084374401od_b_b: $tType).
% 3.37/1.80 thf(type_def_36, type, produc1168037607od_b_b: $tType).
% 3.37/1.80 thf(type_def_37, type, produc644633773od_b_b: $tType).
% 3.37/1.80 thf(type_def_38, type, produc1871334759_a_nat: $tType).
% 3.37/1.80 thf(type_def_39, type, produc1398946881nt_a_b: $tType).
% 3.37/1.80 thf(type_def_40, type, produc1990339951od_b_b: $tType).
% 3.37/1.80 thf(type_def_41, type, produc276146823_b_b_b: $tType).
% 3.37/1.80 thf(type_def_42, type, produc1169496899od_b_b: $tType).
% 3.37/1.80 thf(type_def_43, type, produc398057191_a_nat: $tType).
% 3.37/1.80 thf(type_def_44, type, produc1485083751od_b_b: $tType).
% 3.37/1.80 thf(type_def_45, type, produc845793663_nat_b: $tType).
% 3.37/1.80 thf(type_def_46, type, produc1052326083od_b_b: $tType).
% 3.37/1.80 thf(type_def_47, type, produc2112523263_b_b_b: $tType).
% 3.37/1.80 thf(type_def_48, type, produc1605346267od_b_b: $tType).
% 3.37/1.80 thf(type_def_49, type, produc255402447od_b_b: $tType).
% 3.37/1.80 thf(type_def_50, type, set_Pr2134561957od_b_b: $tType).
% 3.37/1.80 thf(type_def_51, type, set_Pr1954438265od_b_b: $tType).
% 3.37/1.80 thf(type_def_52, type, set_Pr667377223od_b_b: $tType).
% 3.37/1.80 thf(type_def_53, type, set_Pr1071216121od_b_b: $tType).
% 3.37/1.80 thf(type_def_54, type, set_Pr2060523537od_b_b: $tType).
% 3.37/1.80 thf(type_def_55, type, set_Pr1646010159_a_nat: $tType).
% 3.37/1.80 thf(type_def_56, type, set_Pr621705391od_b_b: $tType).
% 3.37/1.80 thf(type_def_57, type, set_Pr154086431tant_a: $tType).
% 3.37/1.80 thf(func_def_0, type, set_Pr197580003_a_nat: $tType).
% 3.37/1.80 thf(func_def_1, type, set_Pr924198087_a_nat: $tType).
% 3.37/1.80 thf(func_def_2, type, produc398057191_a_nat: $tType).
% 3.37/1.80 thf(func_def_3, type, set_Pr1954438265od_b_b: $tType).
% 3.37/1.80 thf(func_def_4, type, produc1169496899od_b_b: $tType).
% 3.37/1.80 thf(func_def_5, type, set_Pr1190604087od_b_b: $tType).
% 3.37/1.80 thf(func_def_6, type, produc1084374401od_b_b: $tType).
% 3.37/1.80 thf(func_def_7, type, labele1322729112_a_nat: $tType).
% 3.37/1.80 thf(func_def_8, type, set_Pr667377223od_b_b: $tType).
% 3.37/1.80 thf(func_def_9, type, produc1485083751od_b_b: $tType).
% 3.37/1.80 thf(func_def_10, type, set_Pr2109276827od_b_b: $tType).
% 3.37/1.80 thf(func_def_11, type, set_Pr1646010159_a_nat: $tType).
% 3.37/1.80 thf(func_def_12, type, set_Pr812188767_nat_b: $tType).
% 3.37/1.80 thf(func_def_13, type, produc970027067od_b_b: $tType).
% 3.37/1.80 thf(func_def_14, type, produc845793663_nat_b: $tType).
% 3.37/1.80 thf(func_def_15, type, set_Pr1987088711_a_nat: $tType).
% 3.37/1.80 thf(func_def_16, type, produc1871334759_a_nat: $tType).
% 3.37/1.80 thf(func_def_17, type, produc1398946881nt_a_b: $tType).
% 3.37/1.80 thf(func_def_18, type, labele1644675410od_b_b: $tType).
% 3.37/1.80 thf(func_def_19, type, set_Pr1071216121od_b_b: $tType).
% 3.37/1.80 thf(func_def_20, type, set_Pr2134561957od_b_b: $tType).
% 3.37/1.80 thf(func_def_21, type, set_Pr1021918435od_b_b: $tType).
% 3.37/1.80 thf(func_def_22, type, produc1052326083od_b_b: $tType).
% 3.37/1.80 thf(func_def_23, type, produc1990339951od_b_b: $tType).
% 3.37/1.80 thf(func_def_24, type, produc644633773od_b_b: $tType).
% 3.37/1.80 thf(func_def_25, type, set_Pr2060523537od_b_b: $tType).
% 3.37/1.80 thf(func_def_26, type, set_Pr1906739389_b_b_b: $tType).
% 3.37/1.80 thf(func_def_27, type, produc1605346267od_b_b: $tType).
% 3.37/1.80 thf(func_def_28, type, produc276146823_b_b_b: $tType).
% 3.37/1.80 thf(func_def_29, type, set_Pr154086431tant_a: $tType).
% 3.37/1.80 thf(func_def_30, type, set_Pr1324126435od_b_b: $tType).
% 3.37/1.80 thf(func_def_31, type, produc90515391tant_a: $tType).
% 3.37/1.80 thf(func_def_32, type, labele1835558936od_b_b: $tType).
% 3.37/1.80 thf(func_def_33, type, set_Pr2007082183od_b_b: $tType).
% 3.37/1.80 thf(func_def_34, type, produc1213276845od_b_b: $tType).
% 3.37/1.80 thf(func_def_35, type, set_la1083530965_a_nat: $tType).
% 3.37/1.80 thf(func_def_36, type, produc1168037607od_b_b: $tType).
% 3.37/1.80 thf(func_def_37, type, labele935650037_a_nat: $tType).
% 3.37/1.80 thf(func_def_38, type, set_Pr1649131859tant_a: $tType).
% 3.37/1.80 thf(func_def_39, type, allego510293162tant_a: $tType).
% 3.37/1.80 thf(func_def_40, type, labele1159362096nt_a_b: $tType).
% 3.37/1.80 thf(func_def_41, type, set_Pr621705391od_b_b: $tType).
% 3.37/1.80 thf(func_def_42, type, set_Pr357419743_b_b_b: $tType).
% 3.37/1.80 thf(func_def_43, type, produc255402447od_b_b: $tType).
% 3.37/1.80 thf(func_def_44, type, produc2112523263_b_b_b: $tType).
% 3.37/1.80 thf(func_def_45, type, set_St761939237tant_a: $tType).
% 3.37/1.80 thf(func_def_46, type, set_Pr2106913242_nat_b: $tType).
% 3.37/1.80 thf(func_def_47, type, set_Product_prod_b_b: $tType).
% 3.37/1.80 thf(func_def_48, type, standard_Constant_a: $tType).
% 3.37/1.80 thf(func_def_49, type, product_prod_b_b: $tType).
% 3.37/1.80 thf(func_def_50, type, set_b: $tType).
% 3.37/1.80 thf(func_def_51, type, b: $tType).
% 3.37/1.80 thf(func_def_52, type, bNF_Gr1272216980od_b_b: set_St761939237tant_a > (standard_Constant_a > product_prod_b_b) > set_Pr1324126435od_b_b).
% 3.37/1.80 thf(func_def_53, type, bNF_Gr996500706_a_nat: set_la1083530965_a_nat > (labele935650037_a_nat > labele935650037_a_nat) > set_Pr1987088711_a_nat).
% 3.37/1.80 thf(func_def_54, type, bNF_Gr492676974_b_b_b: set_Pr1324126435od_b_b > (produc1213276845od_b_b > b) > set_Pr1906739389_b_b_b).
% 3.37/1.80 thf(func_def_55, type, bNF_Gr521784954_b_b_b: set_Product_prod_b_b > (product_prod_b_b > b) > set_Pr357419743_b_b_b).
% 3.37/1.80 thf(func_def_56, type, bNF_Gr230160332tant_a: set_b > (b > standard_Constant_a) > set_Pr1649131859tant_a).
% 3.37/1.80 thf(func_def_57, type, bNF_Gr_b_b: set_b > (b > b) > set_Product_prod_b_b).
% 3.37/1.80 thf(func_def_58, type, equiv_1821124534_set_b: set_Product_prod_b_b > (b > set_b) > $o).
% 3.37/1.80 thf(func_def_59, type, equiv_2048442231od_b_b: set_Pr1324126435od_b_b > set_Pr2109276827od_b_b > $o).
% 3.37/1.80 thf(func_def_60, type, equiv_291114781_a_nat: set_Pr1987088711_a_nat > set_Pr924198087_a_nat > $o).
% 3.37/1.80 thf(func_def_61, type, equiv_1125628061od_b_b: set_Product_prod_b_b > set_Pr2007082183od_b_b > $o).
% 3.37/1.80 thf(func_def_62, type, equiv_equiv_b: set_b > set_Product_prod_b_b > $o).
% 3.37/1.80 thf(func_def_63, type, hilbert_Eps_b: (b > $o) > b).
% 3.37/1.80 thf(func_def_64, type, if_b: $o > b > b > b).
% 3.37/1.80 thf(func_def_65, type, standard_S_Idt_a: standard_Constant_a).
% 3.37/1.80 thf(func_def_66, type, getRel59882567od_b_b: standard_Constant_a > labele1644675410od_b_b > set_Pr2109276827od_b_b).
% 3.37/1.80 thf(func_def_67, type, getRel118493133od_b_b: standard_Constant_a > labele1835558936od_b_b > set_Pr2007082183od_b_b).
% 3.37/1.80 thf(func_def_68, type, getRel904497637nt_a_b: standard_Constant_a > labele1159362096nt_a_b > set_Product_prod_b_b).
% 3.37/1.80 thf(func_def_69, type, semant55076487nt_a_b: labele1159362096nt_a_b > allego510293162tant_a > set_Product_prod_b_b).
% 3.37/1.80 thf(func_def_70, type, edge_p1817988046tant_a: set_Pr1906739389_b_b_b > set_Pr1190604087od_b_b > set_Pr1324126435od_b_b > $o).
% 3.37/1.80 thf(func_def_71, type, edge_p1969196346tant_a: set_Pr357419743_b_b_b > set_Pr1021918435od_b_b > set_Pr1324126435od_b_b > $o).
% 3.37/1.80 thf(func_def_72, type, edge_p1384198690tant_a: set_Product_prod_b_b > set_Pr1324126435od_b_b > set_Pr1324126435od_b_b > $o).
% 3.37/1.80 thf(func_def_73, type, graph_714568023_nat_b: labele935650037_a_nat > labele1159362096nt_a_b > set_Pr2106913242_nat_b > $o).
% 3.37/1.80 thf(func_def_74, type, graph_726202286_nat_b: labele1322729112_a_nat > labele1159362096nt_a_b > set_Pr812188767_nat_b > $o).
% 3.37/1.80 thf(func_def_75, type, graph_222606102_a_b_b: labele1159362096nt_a_b > labele1159362096nt_a_b > set_Product_prod_b_b > $o).
% 3.37/1.80 thf(func_def_76, type, graph_1309249505nt_a_b: labele1159362096nt_a_b > labele1159362096nt_a_b > labele1159362096nt_a_b).
% 3.37/1.80 thf(func_def_77, type, labele27098724_a_nat: set_Pr197580003_a_nat > set_Pr1987088711_a_nat > labele1322729112_a_nat).
% 3.37/1.80 thf(func_def_78, type, labele1230159100nt_a_b: set_Pr1324126435od_b_b > set_b > labele1159362096nt_a_b).
% 3.37/1.80 thf(func_def_79, type, labele2032816061od_b_b: labele1644675410od_b_b > set_Pr1190604087od_b_b).
% 3.37/1.80 thf(func_def_80, type, labele372159959od_b_b: labele1835558936od_b_b > set_Pr1021918435od_b_b).
% 3.37/1.80 thf(func_def_81, type, labele1741081071nt_a_b: labele1159362096nt_a_b > set_Pr1324126435od_b_b).
% 3.37/1.80 thf(func_def_82, type, labele595103470od_b_b: labele1644675410od_b_b > set_Pr1324126435od_b_b).
% 3.37/1.80 thf(func_def_83, type, labele442485990od_b_b: labele1835558936od_b_b > set_Product_prod_b_b).
% 3.37/1.80 thf(func_def_84, type, labele1424214014nt_a_b: labele1159362096nt_a_b > set_b).
% 3.37/1.80 thf(func_def_85, type, map_gr1495881666tant_a: set_Pr1906739389_b_b_b > labele1644675410od_b_b > labele1159362096nt_a_b).
% 3.37/1.80 thf(func_def_86, type, map_gr1314489926tant_a: set_Pr357419743_b_b_b > labele1835558936od_b_b > labele1159362096nt_a_b).
% 3.37/1.80 thf(func_def_87, type, map_gr926947118tant_a: set_Product_prod_b_b > labele1159362096nt_a_b > labele1159362096nt_a_b).
% 3.37/1.80 thf(func_def_88, type, restri446606278nt_a_b: labele1159362096nt_a_b > labele1159362096nt_a_b).
% 3.37/1.80 thf(func_def_89, type, bot_bo1160111033tant_a: set_St761939237tant_a).
% 3.37/1.80 thf(func_def_90, type, bot_bo2122869057_a_nat: set_la1083530965_a_nat).
% 3.37/1.80 thf(func_def_91, type, bot_bo1653310327_a_nat: set_Pr197580003_a_nat).
% 3.37/1.80 thf(func_def_92, type, bot_bo1664927607od_b_b: set_Pr1324126435od_b_b).
% 3.37/1.80 thf(func_def_93, type, bot_bo1836341171_a_nat: set_Pr1987088711_a_nat).
% 3.37/1.80 thf(func_def_94, type, bot_bo1973379891_a_nat: set_Pr924198087_a_nat).
% 3.37/1.80 thf(func_def_95, type, bot_bo1113554635_nat_b: set_Pr812188767_nat_b).
% 3.37/1.80 thf(func_def_96, type, bot_bo1343651123od_b_b: set_Product_prod_b_b).
% 3.37/1.80 thf(func_def_97, type, bot_bot_set_b: set_b).
% 3.37/1.80 thf(func_def_98, type, ord_le123089219od_b_b: set_Pr1324126435od_b_b > set_Pr1324126435od_b_b > $o).
% 3.37/1.80 thf(func_def_99, type, ord_le1718765799_a_nat: set_Pr1987088711_a_nat > set_Pr1987088711_a_nat > $o).
% 3.37/1.80 thf(func_def_100, type, ord_le1484132922_nat_b: set_Pr2106913242_nat_b > set_Pr2106913242_nat_b > $o).
% 3.37/1.80 thf(func_def_101, type, ord_le107617383_a_nat: set_Pr924198087_a_nat > set_Pr924198087_a_nat > $o).
% 3.37/1.80 thf(func_def_102, type, ord_le1036320359od_b_b: set_Product_prod_b_b > set_Product_prod_b_b > $o).
% 3.37/1.80 thf(func_def_103, type, ord_less_eq_set_b: set_b > set_b > $o).
% 3.37/1.80 thf(func_def_104, type, produc342647tant_a: standard_Constant_a > standard_Constant_a > produc90515391tant_a).
% 3.37/1.80 thf(func_def_105, type, produc1788032435od_b_b: standard_Constant_a > produc970027067od_b_b > produc1084374401od_b_b).
% 3.37/1.80 thf(func_def_106, type, produc618266719od_b_b: standard_Constant_a > produc1168037607od_b_b > produc644633773od_b_b).
% 3.37/1.80 thf(func_def_107, type, produc1432590431od_b_b: standard_Constant_a > product_prod_b_b > produc1213276845od_b_b).
% 3.37/1.80 thf(func_def_108, type, produc1676969687_a_nat: labele935650037_a_nat > labele935650037_a_nat > produc1871334759_a_nat).
% 3.37/1.80 thf(func_def_109, type, produc1569511545nt_a_b: labele1159362096nt_a_b > labele1159362096nt_a_b > produc1398946881nt_a_b).
% 3.37/1.80 thf(func_def_110, type, produc449289715od_b_b: produc1213276845od_b_b > produc1213276845od_b_b > produc970027067od_b_b).
% 3.37/1.80 thf(func_def_111, type, produc1597690145od_b_b: produc1213276845od_b_b > product_prod_b_b > produc1990339951od_b_b).
% 3.37/1.80 thf(func_def_112, type, produc1580777273_b_b_b: produc1213276845od_b_b > b > produc276146823_b_b_b).
% 3.37/1.80 thf(func_def_113, type, produc401731773od_b_b: produc1871334759_a_nat > produc1213276845od_b_b > produc1169496899od_b_b).
% 3.37/1.80 thf(func_def_114, type, produc1677124439_a_nat: produc1871334759_a_nat > produc1871334759_a_nat > produc398057191_a_nat).
% 3.37/1.80 thf(func_def_115, type, produc590959831od_b_b: produc1871334759_a_nat > product_prod_b_b > produc1485083751od_b_b).
% 3.37/1.80 thf(func_def_116, type, produc2059954415_nat_b: produc1871334759_a_nat > b > produc845793663_nat_b).
% 3.37/1.80 thf(func_def_117, type, produc732676669od_b_b: product_prod_b_b > produc1213276845od_b_b > produc1052326083od_b_b).
% 3.37/1.80 thf(func_def_118, type, produc546497367od_b_b: product_prod_b_b > product_prod_b_b > produc1168037607od_b_b).
% 3.37/1.80 thf(func_def_119, type, produc1001682799_b_b_b: product_prod_b_b > b > produc2112523263_b_b_b).
% 3.37/1.80 thf(func_def_120, type, produc800495189od_b_b: b > produc1213276845od_b_b > produc1605346267od_b_b).
% 3.37/1.80 thf(func_def_121, type, produc1257047359od_b_b: b > product_prod_b_b > produc255402447od_b_b).
% 3.37/1.80 thf(func_def_122, type, product_Pair_b_b: b > b > product_prod_b_b).
% 3.37/1.80 thf(func_def_123, type, id_on_689842066_a_nat: set_la1083530965_a_nat > set_Pr1987088711_a_nat).
% 3.37/1.80 thf(func_def_124, type, id_on_250271696od_b_b: set_Pr1324126435od_b_b > set_Pr2109276827od_b_b).
% 3.37/1.80 thf(func_def_125, type, id_on_1651096324_a_nat: set_Pr1987088711_a_nat > set_Pr924198087_a_nat).
% 3.37/1.80 thf(func_def_126, type, id_on_2019020932od_b_b: set_Product_prod_b_b > set_Pr2007082183od_b_b).
% 3.37/1.80 thf(func_def_127, type, id_on_b: set_b > set_Product_prod_b_b).
% 3.37/1.80 thf(func_def_128, type, image_1916422435od_b_b: set_Pr1324126435od_b_b > set_St761939237tant_a > set_Product_prod_b_b).
% 3.37/1.80 thf(func_def_129, type, image_1971191571_a_nat: set_Pr1987088711_a_nat > set_la1083530965_a_nat > set_la1083530965_a_nat).
% 3.37/1.80 thf(func_def_130, type, image_763305007od_b_b: set_Pr2109276827od_b_b > set_Pr1324126435od_b_b > set_Pr1324126435od_b_b).
% 3.37/1.80 thf(func_def_131, type, image_1397930469od_b_b: set_Pr2134561957od_b_b > set_Pr1324126435od_b_b > set_Product_prod_b_b).
% 3.37/1.80 thf(func_def_132, type, image_1764625405_b_b_b: set_Pr1906739389_b_b_b > set_Pr1324126435od_b_b > set_b).
% 3.37/1.80 thf(func_def_133, type, image_480774529od_b_b: set_Pr1954438265od_b_b > set_Pr1987088711_a_nat > set_Pr1324126435od_b_b).
% 3.37/1.80 thf(func_def_134, type, image_1168831379_a_nat: set_Pr924198087_a_nat > set_Pr1987088711_a_nat > set_Pr1987088711_a_nat).
% 3.37/1.80 thf(func_def_135, type, image_1214223635od_b_b: set_Pr667377223od_b_b > set_Pr1987088711_a_nat > set_Product_prod_b_b).
% 3.37/1.80 thf(func_def_136, type, image_924992811_nat_b: set_Pr812188767_nat_b > set_Pr1987088711_a_nat > set_b).
% 3.37/1.80 thf(func_def_137, type, image_532916993od_b_b: set_Pr1071216121od_b_b > set_Product_prod_b_b > set_Pr1324126435od_b_b).
% 3.37/1.80 thf(func_def_138, type, image_1928024979od_b_b: set_Pr2007082183od_b_b > set_Product_prod_b_b > set_Product_prod_b_b).
% 3.37/1.80 thf(func_def_139, type, image_921732011_b_b_b: set_Pr357419743_b_b_b > set_Product_prod_b_b > set_b).
% 3.37/1.80 thf(func_def_140, type, image_984343321od_b_b: set_Pr2060523537od_b_b > set_b > set_Pr1324126435od_b_b).
% 3.37/1.80 thf(func_def_141, type, image_1749766139_a_nat: set_Pr1646010159_a_nat > set_b > set_Pr1987088711_a_nat).
% 3.37/1.80 thf(func_def_142, type, image_1177096571od_b_b: set_Pr621705391od_b_b > set_b > set_Product_prod_b_b).
% 3.37/1.80 thf(func_def_143, type, image_b_b: set_Product_prod_b_b > set_b > set_b).
% 3.37/1.80 thf(func_def_144, type, refl_o1031343860_a_nat: set_la1083530965_a_nat > set_Pr1987088711_a_nat > $o).
% 3.37/1.80 thf(func_def_145, type, refl_o1921098222od_b_b: set_Pr1324126435od_b_b > set_Pr2109276827od_b_b > $o).
% 3.37/1.80 thf(func_def_146, type, refl_o1213627494_a_nat: set_Pr1987088711_a_nat > set_Pr924198087_a_nat > $o).
% 3.37/1.80 thf(func_def_147, type, refl_o2134473190od_b_b: set_Product_prod_b_b > set_Pr2007082183od_b_b > $o).
% 3.37/1.80 thf(func_def_148, type, refl_on_b: set_b > set_Product_prod_b_b > $o).
% 3.37/1.80 thf(func_def_149, type, relcom883816262od_b_b: set_Pr154086431tant_a > set_Pr1324126435od_b_b > set_Pr1324126435od_b_b).
% 3.37/1.80 thf(func_def_150, type, relcom1823941168od_b_b: set_Pr1324126435od_b_b > set_Pr2007082183od_b_b > set_Pr1324126435od_b_b).
% 3.37/1.80 thf(func_def_151, type, relcom1338300020_a_nat: set_Pr1987088711_a_nat > set_Pr1987088711_a_nat > set_Pr1987088711_a_nat).
% 3.37/1.80 thf(func_def_152, type, relcom112561144od_b_b: set_Pr1649131859tant_a > set_Pr1324126435od_b_b > set_Pr621705391od_b_b).
% 3.37/1.80 thf(func_def_153, type, relcomp_b_b_b: set_Product_prod_b_b > set_Product_prod_b_b > set_Product_prod_b_b).
% 3.37/1.80 thf(func_def_154, type, agree_221379389_a_b_b: labele1159362096nt_a_b > set_Product_prod_b_b > set_Product_prod_b_b > $o).
% 3.37/1.80 thf(func_def_155, type, conseq956760372_nat_b: set_Pr1987088711_a_nat > labele1159362096nt_a_b > $o).
% 3.37/1.80 thf(func_def_156, type, extens1554515172_nat_b: produc1871334759_a_nat > labele1159362096nt_a_b > set_Pr2106913242_nat_b > $o).
% 3.37/1.80 thf(func_def_157, type, extens1779443913_a_b_b: produc1398946881nt_a_b > labele1159362096nt_a_b > set_Product_prod_b_b > $o).
% 3.37/1.80 thf(func_def_158, type, mainta1604381365_nat_b: produc1871334759_a_nat > labele1159362096nt_a_b > $o).
% 3.37/1.80 thf(func_def_159, type, mainta374363448_a_b_b: produc1398946881nt_a_b > labele1159362096nt_a_b > $o).
% 3.37/1.80 thf(func_def_160, type, collec279084418od_b_b: (produc1213276845od_b_b > $o) > set_Pr1324126435od_b_b).
% 3.37/1.80 thf(func_def_161, type, collec357096914_a_nat: (produc1871334759_a_nat > $o) > set_Pr1987088711_a_nat).
% 3.37/1.80 thf(func_def_162, type, collec1481886546od_b_b: (product_prod_b_b > $o) > set_Product_prod_b_b).
% 3.37/1.80 thf(func_def_163, type, collect_b: (b > $o) > set_b).
% 3.37/1.80 thf(func_def_164, type, image_1683732397od_b_b: (b > product_prod_b_b) > set_b > set_Product_prod_b_b).
% 3.37/1.80 thf(func_def_165, type, insert1909710879tant_a: standard_Constant_a > set_St761939237tant_a > set_St761939237tant_a).
% 3.37/1.80 thf(func_def_166, type, insert1167839429_a_nat: labele935650037_a_nat > set_la1083530965_a_nat > set_la1083530965_a_nat).
% 3.37/1.80 thf(func_def_167, type, insert2037698781od_b_b: produc1213276845od_b_b > set_Pr1324126435od_b_b > set_Pr1324126435od_b_b).
% 3.37/1.80 thf(func_def_168, type, insert1574423351_a_nat: produc1871334759_a_nat > set_Pr1987088711_a_nat > set_Pr1987088711_a_nat).
% 3.37/1.80 thf(func_def_169, type, insert1810136247_a_nat: produc398057191_a_nat > set_Pr924198087_a_nat > set_Pr924198087_a_nat).
% 3.37/1.80 thf(func_def_170, type, insert1952693431od_b_b: product_prod_b_b > set_Product_prod_b_b > set_Product_prod_b_b).
% 3.37/1.80 thf(func_def_171, type, insert_b: b > set_b > set_b).
% 3.37/1.80 thf(func_def_172, type, standa1568205540ules_a: set_St761939237tant_a > set_Pr1987088711_a_nat).
% 3.37/1.80 thf(func_def_173, type, standa63370785tant_a: standard_Constant_a > produc1871334759_a_nat).
% 3.37/1.80 thf(func_def_174, type, standa997693288tant_a: standard_Constant_a > produc1871334759_a_nat).
% 3.37/1.80 thf(func_def_175, type, standa1795879409tant_a: standard_Constant_a > produc1871334759_a_nat).
% 3.37/1.80 thf(func_def_176, type, member1632892294tant_a: standard_Constant_a > set_St761939237tant_a > $o).
% 3.37/1.80 thf(func_def_177, type, member1214736488tant_a: produc90515391tant_a > set_Pr154086431tant_a > $o).
% 3.37/1.80 thf(func_def_178, type, member147868824od_b_b: produc1084374401od_b_b > set_Pr1190604087od_b_b > $o).
% 3.37/1.80 thf(func_def_179, type, member1744485444od_b_b: produc644633773od_b_b > set_Pr1021918435od_b_b > $o).
% 3.37/1.80 thf(func_def_180, type, member1516365892od_b_b: produc1213276845od_b_b > set_Pr1324126435od_b_b > $o).
% 3.37/1.80 thf(func_def_181, type, member832397200_a_nat: produc1871334759_a_nat > set_Pr1987088711_a_nat > $o).
% 3.37/1.80 thf(func_def_182, type, member1086024932od_b_b: produc970027067od_b_b > set_Pr2109276827od_b_b > $o).
% 3.37/1.80 thf(func_def_183, type, member942707974od_b_b: produc1990339951od_b_b > set_Pr2134561957od_b_b > $o).
% 3.37/1.80 thf(func_def_184, type, member1417789726_b_b_b: produc276146823_b_b_b > set_Pr1906739389_b_b_b > $o).
% 3.37/1.80 thf(func_def_185, type, member1533761242od_b_b: produc1169496899od_b_b > set_Pr1954438265od_b_b > $o).
% 3.37/1.80 thf(func_def_186, type, member584645392_a_nat: produc398057191_a_nat > set_Pr924198087_a_nat > $o).
% 3.37/1.80 thf(func_def_187, type, member301892752od_b_b: produc1485083751od_b_b > set_Pr667377223od_b_b > $o).
% 3.37/1.80 thf(func_def_188, type, member1544800936_nat_b: produc845793663_nat_b > set_Pr812188767_nat_b > $o).
% 3.37/1.80 thf(func_def_189, type, member4694106od_b_b: produc1052326083od_b_b > set_Pr1071216121od_b_b > $o).
% 3.37/1.80 thf(func_def_190, type, member1652792080od_b_b: produc1168037607od_b_b > set_Pr2007082183od_b_b > $o).
% 3.37/1.80 thf(func_def_191, type, member351494440_b_b_b: produc2112523263_b_b_b > set_Pr357419743_b_b_b > $o).
% 3.37/1.80 thf(func_def_192, type, member599505522od_b_b: produc1605346267od_b_b > set_Pr2060523537od_b_b > $o).
% 3.37/1.80 thf(func_def_193, type, member641857272od_b_b: produc255402447od_b_b > set_Pr621705391od_b_b > $o).
% 3.37/1.80 thf(func_def_194, type, member1285940496od_b_b: product_prod_b_b > set_Product_prod_b_b > $o).
% 3.37/1.80 thf(func_def_195, type, member_b: b > set_b > $o).
% 3.37/1.80 thf(func_def_196, type, g: labele1159362096nt_a_b).
% 3.37/1.80 thf(func_def_197, type, l: set_St761939237tant_a).
% 3.37/1.80 thf(func_def_198, type, p: b > b > $o).
% 3.37/1.80 thf(func_def_199, type, f: b > b).
% 3.37/1.80 thf(func_def_200, type, l2: standard_Constant_a).
% 3.37/1.80 thf(func_def_201, type, x: b).
% 3.37/1.80 thf(func_def_202, type, y: b).
% 3.37/1.80 thf(func_def_219, type, ph1: !>[X0: $tType]:(X0)).
% 3.37/1.80 thf(f1039,plain,(
% 3.37/1.80 $false),
% 3.37/1.80 inference(subsumption_resolution,[status(thm)],[f1038,f973])).
% 3.37/1.80 thf(f973,plain,(
% 3.37/1.80 ((member_b @ x @ (labele1424214014nt_a_b @ g)) != $true)),
% 3.37/1.80 inference(cnf_transformation,[status(thm)],[f957])).
% 3.37/1.80 thf(f957,plain,(
% 3.37/1.80 ((member_b @ x @ (labele1424214014nt_a_b @ g)) != $true)),
% 3.37/1.80 inference(flattening,[status(thm)],[f884])).
% 3.37/1.80 thf(f884,plain,(
% 3.37/1.80 ~((member_b @ x @ (labele1424214014nt_a_b @ g)) = $true)),
% 3.37/1.80 inference(fool_elimination,[status(thm)],[f883])).
% 3.37/1.80 thf(f883,plain,(
% 3.37/1.80 ~(member_b @ x @ (labele1424214014nt_a_b @ g))),
% 3.37/1.80 inference(rectify,[status(thm)],[f361])).
% 3.37/1.80 thf(f361,negated_conjecture,(
% 3.37/1.80 ~(member_b @ x @ (labele1424214014nt_a_b @ g))),
% 3.37/1.80 inference(negated_conjecture,[status(cth)],[f360])).
% 3.37/1.80 thf(f360,conjecture,(
% 3.37/1.80 (member_b @ x @ (labele1424214014nt_a_b @ g))),
% 3.37/1.80 file('/export/starexec/sandbox/tmp/tmp.XlSklPZmtK/DTF2THF_15787.p',conj_0)).
% 3.37/1.80 thf(f1038,plain,(
% 3.37/1.80 ((member_b @ x @ (labele1424214014nt_a_b @ g)) = $true)),
% 3.37/1.80 inference(trivial_inequality_removal,[status(thm)],[f1037])).
% 3.37/1.80 thf(f1037,plain,(
% 3.37/1.80 ($true != $true) | ((member_b @ x @ (labele1424214014nt_a_b @ g)) = $true)),
% 3.37/1.80 inference(superposition,[status(thm)],[f1026,f1031])).
% 3.37/1.80 thf(f1031,plain,(
% 3.37/1.80 ((member_b @ (if_b @ (bot_bot_set_b = (image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ x @ bot_bot_set_b))) @ x @ (hilbert_Eps_b @ (^[Y0 : b]: (member_b @ Y0 @ (image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ x @ bot_bot_set_b)))))) @ (labele1424214014nt_a_b @ g)) = $true)),
% 3.37/1.80 inference(beta_eta_normalization,[status(thm)],[f1004])).
% 3.37/1.80 thf(f1004,plain,(
% 3.37/1.80 ((member_b @ ((^[Y0 : b]: (if_b @ (bot_bot_set_b = (image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ Y0 @ bot_bot_set_b))) @ Y0 @ (hilbert_Eps_b @ ((^[Y1 : b]: ((^[Y2 : b]: (member_b @ Y2 @ (image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ Y1 @ bot_bot_set_b)))))) @ Y0)))) @ x) @ (labele1424214014nt_a_b @ g)) = $true)),
% 3.37/1.80 inference(definition_unfolding,[status(thm)],[f983,f997])).
% 3.37/1.80 thf(f997,plain,(
% 3.37/1.80 (f = (^[Y0 : b]: (if_b @ (bot_bot_set_b = (image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ Y0 @ bot_bot_set_b))) @ Y0 @ (hilbert_Eps_b @ ((^[Y1 : b]: ((^[Y2 : b]: (member_b @ Y2 @ (image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ Y1 @ bot_bot_set_b)))))) @ Y0)))))),
% 3.37/1.80 inference(definition_unfolding,[status(thm)],[f982,f981])).
% 3.37/1.80 thf(f981,plain,(
% 3.37/1.80 (p = (^[Y0 : b]: ((^[Y1 : b]: (member_b @ Y1 @ (image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ Y0 @ bot_bot_set_b)))))))),
% 3.37/1.80 inference(cnf_transformation,[status(thm)],[f550])).
% 3.37/1.80 thf(f550,plain,(
% 3.37/1.80 (p = (^[Y0 : b]: ((^[Y1 : b]: (member_b @ Y1 @ (image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ Y0 @ bot_bot_set_b)))))))),
% 3.37/1.80 inference(fool_elimination,[status(thm)],[f549])).
% 3.37/1.80 thf(f549,plain,(
% 3.37/1.80 (p = (^[X0 : b, X1 : b] : (member_b @ X1 @ (image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ X0 @ bot_bot_set_b)))))),
% 3.37/1.80 inference(rectify,[status(thm)],[f354])).
% 3.37/1.80 thf(f354,axiom,(
% 3.37/1.80 (p = (^[X26 : b, X85 : b] : (member_b @ X85 @ (image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ X26 @ bot_bot_set_b)))))),
% 3.37/1.80 file('/export/starexec/sandbox/tmp/tmp.XlSklPZmtK/DTF2THF_15787.p',fact_353_P)).
% 3.37/1.80 thf(f982,plain,(
% 3.37/1.80 (f = (^[Y0 : b]: (if_b @ (bot_bot_set_b = (image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ Y0 @ bot_bot_set_b))) @ Y0 @ (hilbert_Eps_b @ (p @ Y0)))))),
% 3.37/1.80 inference(cnf_transformation,[status(thm)],[f534])).
% 3.37/1.80 thf(f534,plain,(
% 3.37/1.80 (f = (^[Y0 : b]: (if_b @ (bot_bot_set_b = (image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ Y0 @ bot_bot_set_b))) @ Y0 @ (hilbert_Eps_b @ (p @ Y0)))))),
% 3.37/1.80 inference(fool_elimination,[status(thm)],[f533])).
% 3.37/1.80 thf(f533,plain,(
% 3.37/1.80 ((^[X0 : b] : (if_b @ (bot_bot_set_b = (image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ X0 @ bot_bot_set_b))) @ X0 @ (hilbert_Eps_b @ (p @ X0)))) = f)),
% 3.37/1.80 inference(rectify,[status(thm)],[f353])).
% 3.37/1.80 thf(f353,axiom,(
% 3.37/1.80 ((^[X26 : b] : (if_b @ (bot_bot_set_b = (image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ X26 @ bot_bot_set_b))) @ X26 @ (hilbert_Eps_b @ (p @ X26)))) = f)),
% 3.37/1.80 file('/export/starexec/sandbox/tmp/tmp.XlSklPZmtK/DTF2THF_15787.p',fact_352_f)).
% 3.37/1.80 thf(f983,plain,(
% 3.37/1.80 ((member_b @ (f @ x) @ (labele1424214014nt_a_b @ g)) = $true)),
% 3.37/1.80 inference(cnf_transformation,[status(thm)],[f442])).
% 3.37/1.80 thf(f442,plain,(
% 3.37/1.80 ((member_b @ (f @ x) @ (labele1424214014nt_a_b @ g)) = $true)),
% 3.37/1.80 inference(fool_elimination,[status(thm)],[f441])).
% 3.37/1.80 thf(f441,plain,(
% 3.37/1.80 (member_b @ (f @ x) @ (labele1424214014nt_a_b @ g))),
% 3.37/1.80 inference(rectify,[status(thm)],[f3])).
% 3.37/1.80 thf(f3,axiom,(
% 3.37/1.80 (member_b @ (f @ x) @ (labele1424214014nt_a_b @ g))),
% 3.37/1.80 file('/export/starexec/sandbox/tmp/tmp.XlSklPZmtK/DTF2THF_15787.p',fact_2_fv_I1_J)).
% 3.37/1.80 thf(f1026,plain,(
% 3.37/1.80 ( ! [X0 : b] : (((member_b @ (if_b @ (bot_bot_set_b = (image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ X0 @ bot_bot_set_b))) @ X0 @ (hilbert_Eps_b @ (^[Y0 : b]: (member_b @ Y0 @ (image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ X0 @ bot_bot_set_b)))))) @ (labele1424214014nt_a_b @ g)) != $true) | ((member_b @ X0 @ (labele1424214014nt_a_b @ g)) = $true)) )),
% 3.37/1.80 inference(beta_eta_normalization,[status(thm)],[f1008])).
% 3.37/1.80 thf(f1008,plain,(
% 3.37/1.80 ( ! [X0 : b] : (((member_b @ ((^[Y0 : b]: (if_b @ (bot_bot_set_b = (image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ Y0 @ bot_bot_set_b))) @ Y0 @ (hilbert_Eps_b @ ((^[Y1 : b]: ((^[Y2 : b]: (member_b @ Y2 @ (image_b_b @ (getRel904497637nt_a_b @ standard_S_Idt_a @ g) @ (insert_b @ Y1 @ bot_bot_set_b)))))) @ Y0)))) @ X0) @ (labele1424214014nt_a_b @ g)) != $true) | ((member_b @ X0 @ (labele1424214014nt_a_b @ g)) = $true)) )),
% 3.37/1.80 inference(definition_unfolding,[status(thm)],[f989,f997])).
% 3.37/1.80 thf(f989,plain,(
% 3.37/1.80 ( ! [X0 : b] : (((member_b @ (f @ X0) @ (labele1424214014nt_a_b @ g)) != $true) | ((member_b @ X0 @ (labele1424214014nt_a_b @ g)) = $true)) )),
% 3.37/1.80 inference(cnf_transformation,[status(thm)],[f970])).
% 3.37/1.80 thf(f970,plain,(
% 3.37/1.80 ! [X0 : b] : (((member_b @ (f @ X0) @ (labele1424214014nt_a_b @ g)) != $true) | ((member_b @ X0 @ (labele1424214014nt_a_b @ g)) = $true))),
% 3.37/1.80 inference(ennf_transformation,[status(thm)],[f822])).
% 3.37/1.80 thf(f822,plain,(
% 3.37/1.80 ! [X0 : b] : (((member_b @ (f @ X0) @ (labele1424214014nt_a_b @ g)) = $true) => ((member_b @ X0 @ (labele1424214014nt_a_b @ g)) = $true))),
% 3.37/1.80 inference(fool_elimination,[status(thm)],[f821])).
% 3.37/1.80 thf(f821,plain,(
% 3.37/1.80 ! [X0 : b] : ((member_b @ (f @ X0) @ (labele1424214014nt_a_b @ g)) => (member_b @ X0 @ (labele1424214014nt_a_b @ g)))),
% 3.37/1.80 inference(rectify,[status(thm)],[f1])).
% 3.37/1.80 thf(f1,axiom,(
% 3.37/1.80 ! [X0 : b] : ((member_b @ (f @ X0) @ (labele1424214014nt_a_b @ g)) => (member_b @ X0 @ (labele1424214014nt_a_b @ g)))),
% 3.37/1.80 file('/export/starexec/sandbox/tmp/tmp.XlSklPZmtK/DTF2THF_15787.p',fact_0__092_060open_062_092_060And_062xa_O_A_092_060lbrakk_062f_Axa_A_092_060in_062_Avertices_AG_059_Axa_A_092_060notin_062_Avertices_AG_092_060rbrakk_062_A_092_060Longrightarrow_062_AFalse_092_060close_062)).
% 3.37/1.80 % SZS output end Proof for DTF2THF_15787
% 3.37/1.80 % (16009)------------------------------
% 3.37/1.80 % (16009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.37/1.80 % (16009)Termination reason: Refutation
% 3.37/1.80
% 3.37/1.80 % (16009)Memory used [KB]: 7036
% 3.37/1.80 % (16009)Time elapsed: 0.028 s
% 3.37/1.80 % (16009)Instructions burned: 84 (million)
% 3.37/1.80 % (16009)------------------------------
% 3.37/1.80 % (16009)------------------------------
% 3.37/1.80 % (15979)Success in time 0.137 s
%------------------------------------------------------------------------------