%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP180^1 : 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 : n008.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 08:56:12 AM UTC 2026
% Result : Theorem 4.93s 2.13s
% Output : Refutation 4.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 98 ( 28 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 366 ( 20 ~; 10 |; 0 &; 330 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 44 ( 43 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 251 ( 248 usr; 27 con; 0-4 aty)
% Number of variables : 32 ( 0 ^; 32 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
set_St1111633946tant_V: $tType ).
thf(type_def_6,type,
standard_Constant_V: $tType ).
thf(type_def_7,type,
product_prod_V_V: $tType ).
thf(type_def_9,type,
set_Pr744279122od_V_V: $tType ).
thf(type_def_10,type,
set_la14611914_V_nat: $tType ).
thf(type_def_11,type,
labele2128733290_V_nat: $tType ).
thf(type_def_12,type,
set_Pr1058435079_V_nat: $tType ).
thf(type_def_13,type,
produc1699571228od_V_V: $tType ).
thf(type_def_14,type,
v: $tType ).
thf(type_def_15,type,
set_Pr257494450_V_V_V: $tType ).
thf(type_def_16,type,
set_Product_prod_V_V: $tType ).
thf(type_def_17,type,
set_Pr1228022213_V_V_V: $tType ).
thf(type_def_18,type,
set_V2: $tType ).
thf(type_def_19,type,
v2: $tType ).
thf(type_def_20,type,
set_Product_prod_V_V2: $tType ).
thf(type_def_21,type,
set_V: $tType ).
thf(type_def_22,type,
labele201426742od_V_V: $tType ).
thf(type_def_23,type,
set_Pr2015814777od_V_V: $tType ).
thf(type_def_24,type,
labele236903175od_V_V: $tType ).
thf(type_def_25,type,
set_Pr2022779335od_V_V: $tType ).
thf(type_def_26,type,
labele788688367nt_V_V: $tType ).
thf(type_def_27,type,
set_Product_prod_V_V3: $tType ).
thf(type_def_28,type,
labele2115946735nt_V_V: $tType ).
thf(type_def_29,type,
allego859987871tant_V: $tType ).
thf(type_def_30,type,
set_Pr872354016od_V_V: $tType ).
thf(type_def_31,type,
set_Pr951255342od_V_V: $tType ).
thf(type_def_32,type,
set_Pr1498723630od_V_V: $tType ).
thf(type_def_33,type,
set_Pr53436518_nat_V: $tType ).
thf(type_def_34,type,
labele506073123_V_nat: $tType ).
thf(type_def_35,type,
set_Pr1056235617_nat_V: $tType ).
thf(type_def_36,type,
set_Pr1326571566_V_nat: $tType ).
thf(type_def_37,type,
produc778275879_V_nat: $tType ).
thf(type_def_38,type,
set_Pr361461255at_nat: $tType ).
thf(type_def_39,type,
set_Pr597600647_V_nat: $tType ).
thf(type_def_40,type,
set_Pr473545225_V_nat: $tType ).
thf(type_def_41,type,
set_Pr1007924423_V_nat: $tType ).
thf(type_def_42,type,
produc1082089497od_V_V: $tType ).
thf(type_def_43,type,
produc1269720746od_V_V: $tType ).
thf(type_def_44,type,
produc522115815od_V_V: $tType ).
thf(type_def_45,type,
produc1443401592od_V_V: $tType ).
thf(type_def_46,type,
product_prod_V_V2: $tType ).
thf(type_def_47,type,
produc1113554040od_V_V: $tType ).
thf(type_def_48,type,
produc651414759nt_V_V: $tType ).
thf(func_def_0,type,
set_Pr361461255at_nat: $tType ).
thf(func_def_1,type,
set_Pr1326571566_V_nat: $tType ).
thf(func_def_2,type,
set_Pr1007924423_V_nat: $tType ).
thf(func_def_3,type,
set_Pr872354016od_V_V: $tType ).
thf(func_def_4,type,
produc1269720746od_V_V: $tType ).
thf(func_def_5,type,
set_Pr597600647_V_nat: $tType ).
thf(func_def_6,type,
labele506073123_V_nat: $tType ).
thf(func_def_7,type,
set_Pr2015814777od_V_V: $tType ).
thf(func_def_8,type,
set_Pr1056235617_nat_V: $tType ).
thf(func_def_9,type,
produc1082089497od_V_V: $tType ).
thf(func_def_10,type,
set_Pr473545225_V_nat: $tType ).
thf(func_def_11,type,
set_Pr1058435079_V_nat: $tType ).
thf(func_def_12,type,
produc778275879_V_nat: $tType ).
thf(func_def_13,type,
produc651414759nt_V_V: $tType ).
thf(func_def_14,type,
labele201426742od_V_V: $tType ).
thf(func_def_15,type,
set_Pr951255342od_V_V: $tType ).
thf(func_def_16,type,
produc1443401592od_V_V: $tType ).
thf(func_def_17,type,
set_Pr257494450_V_V_V: $tType ).
thf(func_def_18,type,
set_Pr744279122od_V_V: $tType ).
thf(func_def_19,type,
set_Pr1498723630od_V_V: $tType ).
thf(func_def_20,type,
labele236903175od_V_V: $tType ).
thf(func_def_21,type,
set_Pr2022779335od_V_V: $tType ).
thf(func_def_22,type,
produc1699571228od_V_V: $tType ).
thf(func_def_23,type,
produc1113554040od_V_V: $tType ).
thf(func_def_24,type,
set_la14611914_V_nat: $tType ).
thf(func_def_25,type,
produc522115815od_V_V: $tType ).
thf(func_def_26,type,
labele2128733290_V_nat: $tType ).
thf(func_def_27,type,
allego859987871tant_V: $tType ).
thf(func_def_28,type,
labele2115946735nt_V_V: $tType ).
thf(func_def_29,type,
set_Pr1228022213_V_V_V: $tType ).
thf(func_def_30,type,
labele788688367nt_V_V: $tType ).
thf(func_def_31,type,
set_St1111633946tant_V: $tType ).
thf(func_def_32,type,
set_Pr53436518_nat_V: $tType ).
thf(func_def_33,type,
set_Product_prod_V_V: $tType ).
thf(func_def_34,type,
set_Product_prod_V_V2: $tType ).
thf(func_def_35,type,
set_Product_prod_V_V3: $tType ).
thf(func_def_36,type,
standard_Constant_V: $tType ).
thf(func_def_37,type,
product_prod_V_V: $tType ).
thf(func_def_38,type,
product_prod_V_V2: $tType ).
thf(func_def_39,type,
set_V: $tType ).
thf(func_def_40,type,
set_V2: $tType ).
thf(func_def_41,type,
v: $tType ).
thf(func_def_42,type,
v2: $tType ).
thf(func_def_43,type,
bNF_Gr320641027od_V_V: set_St1111633946tant_V > ( standard_Constant_V > product_prod_V_V ) > set_Pr744279122od_V_V ).
thf(func_def_44,type,
bNF_Gr17960482_V_nat: set_la14611914_V_nat > ( labele2128733290_V_nat > labele2128733290_V_nat ) > set_Pr1058435079_V_nat ).
thf(func_def_45,type,
bNF_Gr480427157_V_V_V: set_Pr744279122od_V_V > ( produc1699571228od_V_V > v ) > set_Pr257494450_V_V_V ).
thf(func_def_46,type,
bNF_Gr1069958334_V_V_V: set_Product_prod_V_V > ( product_prod_V_V > v ) > set_Pr1228022213_V_V_V ).
thf(func_def_47,type,
bNF_Gr_V_V: set_V2 > ( v2 > v ) > set_Product_prod_V_V2 ).
thf(func_def_48,type,
bNF_Gr_V_V2: set_V > ( v > v ) > set_Product_prod_V_V ).
thf(func_def_49,type,
comp_V1480932210od_V_V: ( v > produc1699571228od_V_V ) > ( produc1699571228od_V_V > v ) > produc1699571228od_V_V > produc1699571228od_V_V ).
thf(func_def_50,type,
comp_V772749048od_V_V: ( v > product_prod_V_V ) > ( product_prod_V_V > v ) > product_prod_V_V > product_prod_V_V ).
thf(func_def_51,type,
comp_V_V_V: ( v > v2 ) > ( v2 > v ) > v2 > v2 ).
thf(func_def_52,type,
comp_V_V_V2: ( v > v ) > ( v > v ) > v > v ).
thf(func_def_53,type,
standard_S_Bot_V: standard_Constant_V ).
thf(func_def_54,type,
standard_S_Const_V: v2 > standard_Constant_V ).
thf(func_def_55,type,
standard_S_Top_V: standard_Constant_V ).
thf(func_def_56,type,
getRel2057312683od_V_V: standard_Constant_V > labele201426742od_V_V > set_Pr2015814777od_V_V ).
thf(func_def_57,type,
getRel1902920892od_V_V: standard_Constant_V > labele236903175od_V_V > set_Pr2022779335od_V_V ).
thf(func_def_58,type,
getRel632961956nt_V_V: standard_Constant_V > labele788688367nt_V_V > set_Product_prod_V_V3 ).
thf(func_def_59,type,
getRel1432786916nt_V_V: standard_Constant_V > labele2115946735nt_V_V > set_Product_prod_V_V ).
thf(func_def_60,type,
semant993842370nt_V_V: labele2115946735nt_V_V > allego859987871tant_V > set_Product_prod_V_V ).
thf(func_def_61,type,
edge_p669293514tant_V: set_Pr257494450_V_V_V > set_Pr872354016od_V_V > set_Pr744279122od_V_V > $o ).
thf(func_def_62,type,
edge_p1776314003tant_V: set_Pr1228022213_V_V_V > set_Pr951255342od_V_V > set_Pr744279122od_V_V > $o ).
thf(func_def_63,type,
edge_p1322161019tant_V: set_Product_prod_V_V2 > set_Pr1498723630od_V_V > set_Pr744279122od_V_V > $o ).
thf(func_def_64,type,
edge_p1560004099tant_V: set_Product_prod_V_V > set_Pr744279122od_V_V > set_Pr744279122od_V_V > $o ).
thf(func_def_65,type,
graph_1541575154_nat_V: labele2128733290_V_nat > labele2115946735nt_V_V > set_Pr53436518_nat_V > $o ).
thf(func_def_66,type,
graph_227683057_nat_V: labele506073123_V_nat > labele2115946735nt_V_V > set_Pr1056235617_nat_V > $o ).
thf(func_def_67,type,
graph_840721237_V_V_V: labele236903175od_V_V > labele2115946735nt_V_V > set_Pr1228022213_V_V_V > $o ).
thf(func_def_68,type,
graph_1808119_V_V_V: labele2115946735nt_V_V > labele2115946735nt_V_V > set_Product_prod_V_V > $o ).
thf(func_def_69,type,
graph_1141886696nt_V_V: labele2115946735nt_V_V > labele2115946735nt_V_V > labele2115946735nt_V_V ).
thf(func_def_70,type,
labele1193521135_V_nat: set_Pr1326571566_V_nat > set_Pr1058435079_V_nat > labele506073123_V_nat ).
thf(func_def_71,type,
labele94156371od_V_V: set_Pr951255342od_V_V > set_Product_prod_V_V > labele236903175od_V_V ).
thf(func_def_72,type,
labele712009229nt_V_V: set_Pr744279122od_V_V > set_V > labele2115946735nt_V_V ).
thf(func_def_73,type,
labele1794513953od_V_V: labele201426742od_V_V > set_Pr872354016od_V_V ).
thf(func_def_74,type,
labele668941254od_V_V: labele236903175od_V_V > set_Pr951255342od_V_V ).
thf(func_def_75,type,
labele1469545390nt_V_V: labele788688367nt_V_V > set_Pr1498723630od_V_V ).
thf(func_def_76,type,
labele515735386nt_V_V: labele2115946735nt_V_V > set_Pr744279122od_V_V ).
thf(func_def_77,type,
labele1328382418od_V_V: labele201426742od_V_V > set_Pr744279122od_V_V ).
thf(func_def_78,type,
labele1822884081_V_nat: labele506073123_V_nat > set_Pr1058435079_V_nat ).
thf(func_def_79,type,
labele981584981od_V_V: labele236903175od_V_V > set_Product_prod_V_V ).
thf(func_def_80,type,
labele1152678333nt_V_V: labele788688367nt_V_V > set_V2 ).
thf(func_def_81,type,
labele1134902411nt_V_V: labele2115946735nt_V_V > set_V ).
thf(func_def_82,type,
map_gr157381846tant_V: set_Pr257494450_V_V_V > labele201426742od_V_V > labele2115946735nt_V_V ).
thf(func_def_83,type,
map_gr875022471tant_V: set_Pr1228022213_V_V_V > labele236903175od_V_V > labele2115946735nt_V_V ).
thf(func_def_84,type,
map_gr530397039tant_V: set_Product_prod_V_V2 > labele788688367nt_V_V > labele2115946735nt_V_V ).
thf(func_def_85,type,
map_gr907434255tant_V: set_Product_prod_V_V > labele2115946735nt_V_V > labele2115946735nt_V_V ).
thf(func_def_86,type,
restri1699516426od_V_V: labele201426742od_V_V > labele201426742od_V_V ).
thf(func_def_87,type,
restri1932147897_V_nat: labele506073123_V_nat > labele506073123_V_nat ).
thf(func_def_88,type,
restri1502575645od_V_V: labele236903175od_V_V > labele236903175od_V_V ).
thf(func_def_89,type,
restri175070597nt_V_V: labele788688367nt_V_V > labele788688367nt_V_V ).
thf(func_def_90,type,
restri1305980611nt_V_V: labele2115946735nt_V_V > labele2115946735nt_V_V ).
thf(func_def_91,type,
sup_su693515134od_V_V: set_Pr744279122od_V_V > set_Pr744279122od_V_V > set_Pr744279122od_V_V ).
thf(func_def_92,type,
sup_su1043134939_V_nat: set_Pr1058435079_V_nat > set_Pr1058435079_V_nat > set_Pr1058435079_V_nat ).
thf(func_def_93,type,
sup_su551882943od_V_V: set_Product_prod_V_V > set_Product_prod_V_V > set_Product_prod_V_V ).
thf(func_def_94,type,
sup_sup_set_V: set_V2 > set_V2 > set_V2 ).
thf(func_def_95,type,
sup_sup_set_V2: set_V > set_V > set_V ).
thf(func_def_96,type,
bot_bo2024487199_V_V_o: produc1699571228od_V_V > $o ).
thf(func_def_97,type,
bot_bo1078500394_nat_o: produc778275879_V_nat > $o ).
thf(func_def_98,type,
bot_bo1168561222_V_V_o: product_prod_V_V > $o ).
thf(func_def_99,type,
bot_bot_V_o: v2 > $o ).
thf(func_def_100,type,
bot_bot_V_o2: v > $o ).
thf(func_def_101,type,
bot_bo1053950006_V_nat: set_la14611914_V_nat ).
thf(func_def_102,type,
bot_bo634818242_V_nat: set_Pr1326571566_V_nat ).
thf(func_def_103,type,
bot_bo451843010od_V_V: set_Pr951255342od_V_V ).
thf(func_def_104,type,
bot_bo667804902od_V_V: set_Pr744279122od_V_V ).
thf(func_def_105,type,
bot_bo323535987at_nat: set_Pr361461255at_nat ).
thf(func_def_106,type,
bot_bo1196823539_V_nat: set_Pr597600647_V_nat ).
thf(func_def_107,type,
bot_bo907687539_V_nat: set_Pr1058435079_V_nat ).
thf(func_def_108,type,
bot_bo1834032757_V_nat: set_Pr473545225_V_nat ).
thf(func_def_109,type,
bot_bo2057106227_V_nat: set_Pr1007924423_V_nat ).
thf(func_def_110,type,
bot_bo1708783349_nat_V: set_Pr1056235617_nat_V ).
thf(func_def_111,type,
bot_bo12878899od_V_V: set_Pr2022779335od_V_V ).
thf(func_def_112,type,
bot_bo688400985_V_V_V: set_Pr1228022213_V_V_V ).
thf(func_def_113,type,
bot_bo1389414743od_V_V: set_Product_prod_V_V ).
thf(func_def_114,type,
bot_bot_set_V: set_V2 ).
thf(func_def_115,type,
bot_bot_set_V2: set_V ).
thf(func_def_116,type,
produc2132932316od_V_V: standard_Constant_V > produc1082089497od_V_V > produc1269720746od_V_V ).
thf(func_def_117,type,
produc1482441770od_V_V: standard_Constant_V > produc522115815od_V_V > produc1443401592od_V_V ).
thf(func_def_118,type,
produc1171747370od_V_V: standard_Constant_V > product_prod_V_V2 > produc1113554040od_V_V ).
thf(func_def_119,type,
produc107991630od_V_V: standard_Constant_V > product_prod_V_V > produc1699571228od_V_V ).
thf(func_def_120,type,
produc698429463_V_nat: labele2128733290_V_nat > labele2128733290_V_nat > produc778275879_V_nat ).
thf(func_def_121,type,
produc533118295nt_V_V: labele2115946735nt_V_V > labele2115946735nt_V_V > produc651414759nt_V_V ).
thf(func_def_122,type,
produc1736057425od_V_V: produc1699571228od_V_V > produc1699571228od_V_V > produc1082089497od_V_V ).
thf(func_def_123,type,
produc1905750615od_V_V: product_prod_V_V > product_prod_V_V > produc522115815od_V_V ).
thf(func_def_124,type,
product_Pair_V_V: v2 > v2 > product_prod_V_V2 ).
thf(func_def_125,type,
product_Pair_V_V2: v > v > product_prod_V_V ).
thf(func_def_126,type,
id_on_1882925319_V_nat: set_la14611914_V_nat > set_Pr1058435079_V_nat ).
thf(func_def_127,type,
id_on_1491482303od_V_V: set_Pr744279122od_V_V > set_Pr2015814777od_V_V ).
thf(func_def_128,type,
id_on_558037444_V_nat: set_Pr1058435079_V_nat > set_Pr1007924423_V_nat ).
thf(func_def_129,type,
id_on_2125509800od_V_V: set_Product_prod_V_V > set_Pr2022779335od_V_V ).
thf(func_def_130,type,
id_on_V: set_V2 > set_Product_prod_V_V3 ).
thf(func_def_131,type,
id_on_V2: set_V > set_Product_prod_V_V ).
thf(func_def_132,type,
conseq1236301781_nat_V: set_Pr1058435079_V_nat > labele2115946735nt_V_V > $o ).
thf(func_def_133,type,
extens1072773157_nat_V: produc778275879_V_nat > labele2115946735nt_V_V > set_Pr53436518_nat_V > $o ).
thf(func_def_134,type,
extens1533825066_V_V_V: produc651414759nt_V_V > labele2115946735nt_V_V > set_Product_prod_V_V > $o ).
thf(func_def_135,type,
mainta1342478555od_V_V: produc778275879_V_nat > labele201426742od_V_V > $o ).
thf(func_def_136,type,
mainta922614952_V_nat: produc778275879_V_nat > labele506073123_V_nat > $o ).
thf(func_def_137,type,
mainta1984786828od_V_V: produc778275879_V_nat > labele236903175od_V_V > $o ).
thf(func_def_138,type,
mainta1026355316_nat_V: produc778275879_V_nat > labele788688367nt_V_V > $o ).
thf(func_def_139,type,
mainta197426964_nat_V: produc778275879_V_nat > labele2115946735nt_V_V > $o ).
thf(func_def_140,type,
mainta1699210777_V_V_V: produc651414759nt_V_V > labele2115946735nt_V_V > $o ).
thf(func_def_141,type,
collec1840263537od_V_V: ( produc1699571228od_V_V > $o ) > set_Pr744279122od_V_V ).
thf(func_def_142,type,
collec1411521682_V_nat: ( produc778275879_V_nat > $o ) > set_Pr1058435079_V_nat ).
thf(func_def_143,type,
collec2040633974od_V_V: ( product_prod_V_V > $o ) > set_Product_prod_V_V ).
thf(func_def_144,type,
collect_V: ( v2 > $o ) > set_V2 ).
thf(func_def_145,type,
collect_V2: ( v > $o ) > set_V ).
thf(func_def_146,type,
insert1818834324tant_V: standard_Constant_V > set_St1111633946tant_V > set_St1111633946tant_V ).
thf(func_def_147,type,
insert213439034_V_nat: labele2128733290_V_nat > set_la14611914_V_nat > set_la14611914_V_nat ).
thf(func_def_148,type,
insert135842892od_V_V: produc1699571228od_V_V > set_Pr744279122od_V_V > set_Pr744279122od_V_V ).
thf(func_def_149,type,
insert481364471_V_nat: produc778275879_V_nat > set_Pr1058435079_V_nat > set_Pr1058435079_V_nat ).
thf(func_def_150,type,
insert2024285275od_V_V: product_prod_V_V > set_Product_prod_V_V > set_Product_prod_V_V ).
thf(func_def_151,type,
insert_V: v2 > set_V2 > set_V2 ).
thf(func_def_152,type,
insert_V2: v > set_V > set_V ).
thf(func_def_153,type,
standa434642387_V_nat: set_Pr1058435079_V_nat > set_Pr361461255at_nat ).
thf(func_def_154,type,
standa1571708471od_V_V: set_Product_prod_V_V > set_Pr597600647_V_nat ).
thf(func_def_155,type,
standa1897115807ules_V: set_V2 > set_Pr1058435079_V_nat ).
thf(func_def_156,type,
standa294833961ules_V: set_V > set_Pr473545225_V_nat ).
thf(func_def_157,type,
standa1568205529ules_V: set_St1111633946tant_V > set_Pr1058435079_V_nat ).
thf(func_def_158,type,
standa1319953089tant_V: produc778275879_V_nat ).
thf(func_def_159,type,
standa157301464ules_V: set_V2 > set_St1111633946tant_V > set_Pr1058435079_V_nat ).
thf(func_def_160,type,
standa214871990tant_V: standard_Constant_V > produc778275879_V_nat ).
thf(func_def_161,type,
member1542015739tant_V: standard_Constant_V > set_St1111633946tant_V > $o ).
thf(func_def_162,type,
member600445121od_V_V: produc1269720746od_V_V > set_Pr872354016od_V_V > $o ).
thf(func_def_163,type,
member361435663od_V_V: produc1443401592od_V_V > set_Pr951255342od_V_V > $o ).
thf(func_def_164,type,
member1416643087od_V_V: produc1113554040od_V_V > set_Pr1498723630od_V_V > $o ).
thf(func_def_165,type,
member1010391347od_V_V: produc1699571228od_V_V > set_Pr744279122od_V_V > $o ).
thf(func_def_166,type,
member1886821968_V_nat: produc778275879_V_nat > set_Pr1058435079_V_nat > $o ).
thf(func_def_167,type,
member785416642od_V_V: produc1082089497od_V_V > set_Pr2015814777od_V_V > $o ).
thf(func_def_168,type,
member134497296od_V_V: produc522115815od_V_V > set_Pr2022779335od_V_V > $o ).
thf(func_def_169,type,
member1990987792od_V_V: product_prod_V_V2 > set_Product_prod_V_V3 > $o ).
thf(func_def_170,type,
member2015049524od_V_V: product_prod_V_V > set_Product_prod_V_V > $o ).
thf(func_def_171,type,
member_V: v2 > set_V2 > $o ).
thf(func_def_172,type,
member_V2: v > set_V > $o ).
thf(func_def_173,type,
c: set_V2 ).
thf(func_def_174,type,
g: labele2115946735nt_V_V ).
thf(func_def_175,type,
l: set_St1111633946tant_V ).
thf(func_def_176,type,
h: v > v ).
thf(func_def_177,type,
m: v2 > v ).
thf(func_def_178,type,
x: v ).
thf(func_def_179,type,
xa: v2 ).
thf(func_def_180,type,
y: v2 ).
thf(func_def_188,type,
sP0: set_Pr1058435079_V_nat > produc778275879_V_nat > set_Pr1058435079_V_nat > $o ).
thf(func_def_189,type,
sP1: produc1699571228od_V_V > set_Pr744279122od_V_V > set_Pr744279122od_V_V > produc1699571228od_V_V > $o ).
thf(func_def_190,type,
sP2: produc1699571228od_V_V > set_Pr744279122od_V_V > produc1699571228od_V_V > set_Pr744279122od_V_V > $o ).
thf(func_def_191,type,
sP3: set_Pr1058435079_V_nat > produc778275879_V_nat > produc778275879_V_nat > set_Pr1058435079_V_nat > $o ).
thf(func_def_192,type,
sP4: set_Pr1058435079_V_nat > produc778275879_V_nat > produc778275879_V_nat > set_Pr1058435079_V_nat > $o ).
thf(func_def_193,type,
sP5: set_Product_prod_V_V > product_prod_V_V > set_Product_prod_V_V > product_prod_V_V > $o ).
thf(func_def_194,type,
sP6: product_prod_V_V > set_Product_prod_V_V > product_prod_V_V > set_Product_prod_V_V > $o ).
thf(func_def_195,type,
sP7: set_V > set_V > v > v > $o ).
thf(func_def_196,type,
sP8: set_V > set_V > v > v > $o ).
thf(func_def_197,type,
sP9: v > set_V > set_V > $o ).
thf(func_def_198,type,
sP10: set_V2 > v2 > v2 > set_V2 > $o ).
thf(func_def_199,type,
sP11: set_V2 > v2 > v2 > set_V2 > $o ).
thf(func_def_200,type,
sP12: set_Pr1058435079_V_nat > produc778275879_V_nat > set_Pr1058435079_V_nat > $o ).
thf(func_def_201,type,
sP13: v > set_V > set_V > $o ).
thf(func_def_202,type,
sP14: product_prod_V_V > set_Product_prod_V_V > set_Product_prod_V_V > $o ).
thf(func_def_203,type,
sP15: set_Product_prod_V_V > product_prod_V_V > set_Product_prod_V_V > $o ).
thf(func_def_204,type,
sK16: produc778275879_V_nat > set_Pr1058435079_V_nat > set_Pr1058435079_V_nat ).
thf(func_def_205,type,
sK17: produc1699571228od_V_V > v ).
thf(func_def_206,type,
sK18: produc1699571228od_V_V > v ).
thf(func_def_207,type,
sK19: produc1699571228od_V_V > standard_Constant_V ).
thf(func_def_208,type,
sK20: ( produc1699571228od_V_V > $o ) > product_prod_V_V ).
thf(func_def_209,type,
sK21: ( produc1699571228od_V_V > $o ) > standard_Constant_V ).
thf(func_def_210,type,
sK22: labele236903175od_V_V > ( product_prod_V_V > v ) > set_Pr744279122od_V_V > standard_Constant_V ).
thf(func_def_211,type,
sK23: labele236903175od_V_V > ( product_prod_V_V > v ) > set_Pr744279122od_V_V > product_prod_V_V ).
thf(func_def_212,type,
sK24: labele236903175od_V_V > ( product_prod_V_V > v ) > set_Pr744279122od_V_V > product_prod_V_V ).
thf(func_def_213,type,
sK25: set_Product_prod_V_V > product_prod_V_V > set_Product_prod_V_V ).
thf(func_def_214,type,
sK26: ( product_prod_V_V > $o ) > product_prod_V_V ).
thf(func_def_215,type,
sK27: set_V2 > v2 ).
thf(func_def_216,type,
sK28: v ).
thf(func_def_217,type,
sK29: set_V > v ).
thf(func_def_218,type,
sK30: set_Pr1058435079_V_nat > produc778275879_V_nat ).
thf(func_def_219,type,
sK31: produc778275879_V_nat > set_Pr1058435079_V_nat > set_Pr1058435079_V_nat ).
thf(func_def_220,type,
sK32: labele788688367nt_V_V > ( v2 > v ) > ( v > v2 ) > v2 ).
thf(func_def_221,type,
sK33: labele2128733290_V_nat > labele2128733290_V_nat > labele2115946735nt_V_V > set_Pr53436518_nat_V ).
thf(func_def_222,type,
sK34: ( produc1699571228od_V_V > $o ) > product_prod_V_V ).
thf(func_def_223,type,
sK35: ( produc1699571228od_V_V > $o ) > standard_Constant_V ).
thf(func_def_224,type,
sK36: product_prod_V_V > v ).
thf(func_def_225,type,
sK37: product_prod_V_V > v ).
thf(func_def_226,type,
sK38: produc1699571228od_V_V > set_Pr744279122od_V_V > set_Pr744279122od_V_V > produc1699571228od_V_V > set_Pr744279122od_V_V ).
thf(func_def_227,type,
sK39: set_Pr744279122od_V_V > ( produc1699571228od_V_V > v ) > labele201426742od_V_V > produc1699571228od_V_V ).
thf(func_def_228,type,
sK40: set_Pr744279122od_V_V > ( produc1699571228od_V_V > v ) > labele201426742od_V_V > standard_Constant_V ).
thf(func_def_229,type,
sK41: set_Pr744279122od_V_V > ( produc1699571228od_V_V > v ) > labele201426742od_V_V > produc1699571228od_V_V ).
thf(func_def_230,type,
sK42: set_Pr744279122od_V_V > produc1699571228od_V_V ).
thf(func_def_231,type,
sK43: set_Pr744279122od_V_V > produc1699571228od_V_V ).
thf(func_def_232,type,
sK44: v2 > v ).
thf(func_def_233,type,
sK45: ( v > $o ) > v ).
thf(func_def_234,type,
sK46: set_Pr1058435079_V_nat > produc778275879_V_nat ).
thf(func_def_235,type,
sK47: set_Pr1058435079_V_nat > produc778275879_V_nat > produc778275879_V_nat > set_Pr1058435079_V_nat > set_Pr1058435079_V_nat ).
thf(func_def_236,type,
sK48: set_Product_prod_V_V > product_prod_V_V ).
thf(func_def_237,type,
sK49: set_Pr744279122od_V_V > produc1699571228od_V_V > set_Pr744279122od_V_V ).
thf(func_def_238,type,
sK50: ( v > produc1699571228od_V_V ) > ( produc1699571228od_V_V > v ) > labele201426742od_V_V > produc1699571228od_V_V ).
thf(func_def_239,type,
sK51: set_Product_prod_V_V > product_prod_V_V > set_Product_prod_V_V > product_prod_V_V > set_Product_prod_V_V ).
thf(func_def_240,type,
sK52: set_V2 > v2 ).
thf(func_def_241,type,
sK53: set_V > set_V > v > v > set_V ).
thf(func_def_242,type,
sK54: ( produc1699571228od_V_V > $o ) > v ).
thf(func_def_243,type,
sK55: ( produc1699571228od_V_V > $o ) > v ).
thf(func_def_244,type,
sK56: ( produc1699571228od_V_V > $o ) > standard_Constant_V ).
thf(func_def_245,type,
sK57: set_Pr744279122od_V_V > produc1082089497od_V_V > produc1699571228od_V_V ).
thf(func_def_246,type,
sK58: ( product_prod_V_V > $o ) > v ).
thf(func_def_247,type,
sK59: ( product_prod_V_V > $o ) > v ).
thf(func_def_248,type,
sK60: set_Pr744279122od_V_V > ( v > v ) > labele2115946735nt_V_V > v ).
thf(func_def_249,type,
sK61: set_Pr744279122od_V_V > ( v > v ) > labele2115946735nt_V_V > v ).
thf(func_def_250,type,
sK62: set_Pr744279122od_V_V > ( v > v ) > labele2115946735nt_V_V > standard_Constant_V ).
thf(func_def_251,type,
sK63: ( v > v ) > labele2115946735nt_V_V > ( v > v ) > v ).
thf(func_def_252,type,
sK64: produc1699571228od_V_V > set_Pr744279122od_V_V > set_Pr744279122od_V_V ).
thf(func_def_253,type,
sK65: product_prod_V_V > v ).
thf(func_def_254,type,
sK66: product_prod_V_V > v ).
thf(func_def_255,type,
sK67: labele236903175od_V_V > ( product_prod_V_V > v ) > ( v > product_prod_V_V ) > product_prod_V_V ).
thf(func_def_256,type,
sK68: ( v > v ) > labele2115946735nt_V_V > ( v > v ) > v ).
thf(func_def_257,type,
sK69: set_V2 > v2 > set_V2 ).
thf(func_def_258,type,
sK70: ( produc778275879_V_nat > $o ) > produc778275879_V_nat ).
thf(func_def_259,type,
sK71: v2 > v ).
thf(func_def_260,type,
sK72: set_V > v > set_V ).
thf(func_def_261,type,
sK73: set_Product_prod_V_V > product_prod_V_V ).
thf(func_def_262,type,
sK74: set_Product_prod_V_V > product_prod_V_V ).
thf(func_def_263,type,
sK75: set_V2 > v2 > v2 > set_V2 > set_V2 ).
thf(func_def_264,type,
sK76: set_V2 > v2 ).
thf(func_def_265,type,
sK77: ( product_prod_V_V > $o ) > v ).
thf(func_def_266,type,
sK78: ( product_prod_V_V > $o ) > v ).
thf(func_def_267,type,
sK79: ( produc778275879_V_nat > $o ) > produc778275879_V_nat ).
thf(func_def_268,type,
sK80: ( v > $o ) > v ).
thf(func_def_269,type,
sK81: produc1699571228od_V_V > product_prod_V_V ).
thf(func_def_270,type,
sK82: produc1699571228od_V_V > standard_Constant_V ).
thf(func_def_271,type,
sK83: set_V2 > product_prod_V_V2 > v2 ).
thf(func_def_272,type,
sK84: labele788688367nt_V_V > ( v2 > v ) > set_Pr744279122od_V_V > standard_Constant_V ).
thf(func_def_273,type,
sK85: labele788688367nt_V_V > ( v2 > v ) > set_Pr744279122od_V_V > v2 ).
thf(func_def_274,type,
sK86: labele788688367nt_V_V > ( v2 > v ) > set_Pr744279122od_V_V > v2 ).
thf(func_def_275,type,
sK87: ( v > v ) > labele2115946735nt_V_V > v ).
thf(func_def_276,type,
sK88: labele2115946735nt_V_V > labele2115946735nt_V_V > labele2115946735nt_V_V > set_Product_prod_V_V ).
thf(func_def_277,type,
sK89: ( product_prod_V_V > $o ) > product_prod_V_V ).
thf(func_def_278,type,
sK90: set_Pr1058435079_V_nat > set_Pr1058435079_V_nat > ( produc778275879_V_nat > $o ) > produc778275879_V_nat ).
thf(func_def_279,type,
sK91: set_Pr1058435079_V_nat > ( produc778275879_V_nat > $o ) > produc778275879_V_nat ).
thf(func_def_280,type,
sK92: set_Pr1058435079_V_nat > ( produc778275879_V_nat > $o ) > produc778275879_V_nat ).
thf(func_def_281,type,
sK93: set_Pr1058435079_V_nat > produc778275879_V_nat ).
thf(func_def_282,type,
sK94: set_V > product_prod_V_V > v ).
thf(func_def_283,type,
sK95: set_V2 > v2 > set_V2 ).
thf(func_def_284,type,
sK96: set_V > v ).
thf(func_def_285,type,
sK97: v2 > v ).
thf(func_def_286,type,
sK98: set_Pr744279122od_V_V > produc1699571228od_V_V ).
thf(func_def_287,type,
sK99: set_V > v > set_V ).
thf(func_def_288,type,
sK100: v2 > v ).
thf(func_def_289,type,
sK101: produc522115815od_V_V > set_Product_prod_V_V > product_prod_V_V ).
thf(func_def_290,type,
sK102: set_Product_prod_V_V > product_prod_V_V > set_Product_prod_V_V ).
thf(func_def_291,type,
sK103: set_V > v ).
thf(func_def_292,type,
sK104: set_Pr1058435079_V_nat > ( produc778275879_V_nat > $o ) > set_Pr1058435079_V_nat > produc778275879_V_nat ).
thf(func_def_293,type,
sK105: set_Pr1058435079_V_nat > ( produc778275879_V_nat > $o ) > produc778275879_V_nat ).
thf(func_def_294,type,
sK106: ( produc778275879_V_nat > $o ) > set_Pr1058435079_V_nat > produc778275879_V_nat ).
thf(func_def_295,type,
sK107: produc1699571228od_V_V > product_prod_V_V ).
thf(func_def_296,type,
sK108: produc1699571228od_V_V > standard_Constant_V ).
thf(func_def_298,type,
ph110:
!>[X0: $tType] : X0 ).
thf(f2484,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f2479]) ).
thf(f2479,plain,
$true != $true,
inference(superposition,[status(thm)],[f2468,f2002]) ).
thf(f2002,plain,
( ( graph_1808119_V_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) @ g @ ( id_on_V2 @ ( labele1134902411nt_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f641]) ).
thf(f641,plain,
( ( graph_1808119_V_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) @ g @ ( id_on_V2 @ ( labele1134902411nt_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f640]) ).
thf(f640,plain,
graph_1808119_V_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) @ g @ ( id_on_V2 @ ( labele1134902411nt_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,axiom,
graph_1808119_V_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) @ g @ ( id_on_V2 @ ( labele1134902411nt_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ),
file('/export/starexec/sandbox/tmp/tmp.OGMuvyH1wq/DTF2THF_13384.p',fact_8_h_I3_J) ).
thf(f2468,plain,
( ( graph_1808119_V_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) @ g @ ( id_on_V2 @ ( labele1134902411nt_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ) )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f2464]) ).
thf(f2464,plain,
( ( ( graph_1808119_V_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) @ g @ ( id_on_V2 @ ( labele1134902411nt_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f2462,f2201]) ).
thf(f2201,plain,
( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ y ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f637]) ).
thf(f637,plain,
( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ y ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f636]) ).
thf(f636,plain,
member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ y ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ y ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ),
file('/export/starexec/sandbox/tmp/tmp.OGMuvyH1wq/DTF2THF_13384.p',fact_6__092_060open_062_Im_Ax_M_Am_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ay_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062) ).
thf(f2462,plain,
! [X0: labele2115946735nt_V_V] :
( ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ y ) @ X0 ) )
!= $true )
| ( ( graph_1808119_V_V_V @ X0 @ g @ ( id_on_V2 @ ( labele1134902411nt_V_V @ X0 ) ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f2461]) ).
thf(f2461,plain,
! [X0: labele2115946735nt_V_V] :
( ( ( graph_1808119_V_V_V @ X0 @ g @ ( id_on_V2 @ ( labele1134902411nt_V_V @ X0 ) ) )
!= $true )
| ( $true != $true )
| ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ y ) @ X0 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f1916,f1995]) ).
thf(f1995,plain,
! [X2: standard_Constant_V,X3: labele2115946735nt_V_V,X0: labele2115946735nt_V_V,X1: v,X4: v] :
( ( $true
= ( member2015049524od_V_V @ ( product_Pair_V_V2 @ X4 @ X1 ) @ ( getRel1432786916nt_V_V @ X2 @ X0 ) ) )
| ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ X4 @ X1 ) @ ( getRel1432786916nt_V_V @ X2 @ X3 ) )
!= $true )
| ( ( graph_1808119_V_V_V @ X3 @ X0 @ ( id_on_V2 @ ( labele1134902411nt_V_V @ X3 ) ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f1166]) ).
thf(f1166,plain,
! [X0: labele2115946735nt_V_V,X1: v,X2: standard_Constant_V,X3: labele2115946735nt_V_V,X4: v] :
( ( ( graph_1808119_V_V_V @ X3 @ X0 @ ( id_on_V2 @ ( labele1134902411nt_V_V @ X3 ) ) )
!= $true )
| ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ X4 @ X1 ) @ ( getRel1432786916nt_V_V @ X2 @ X3 ) )
!= $true )
| ( $true
= ( member2015049524od_V_V @ ( product_Pair_V_V2 @ X4 @ X1 ) @ ( getRel1432786916nt_V_V @ X2 @ X0 ) ) ) ),
inference(flattening,[status(thm)],[f1165]) ).
thf(f1165,plain,
! [X0: labele2115946735nt_V_V,X1: v,X2: standard_Constant_V,X3: labele2115946735nt_V_V,X4: v] :
( ( $true
= ( member2015049524od_V_V @ ( product_Pair_V_V2 @ X4 @ X1 ) @ ( getRel1432786916nt_V_V @ X2 @ X0 ) ) )
| ( ( graph_1808119_V_V_V @ X3 @ X0 @ ( id_on_V2 @ ( labele1134902411nt_V_V @ X3 ) ) )
!= $true )
| ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ X4 @ X1 ) @ ( getRel1432786916nt_V_V @ X2 @ X3 ) )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f503]) ).
thf(f503,plain,
! [X0: labele2115946735nt_V_V,X1: v,X2: standard_Constant_V,X3: labele2115946735nt_V_V,X4: v] :
( ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ X4 @ X1 ) @ ( getRel1432786916nt_V_V @ X2 @ X3 ) )
= $true )
=> ( ( ( graph_1808119_V_V_V @ X3 @ X0 @ ( id_on_V2 @ ( labele1134902411nt_V_V @ X3 ) ) )
= $true )
=> ( $true
= ( member2015049524od_V_V @ ( product_Pair_V_V2 @ X4 @ X1 ) @ ( getRel1432786916nt_V_V @ X2 @ X0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f502]) ).
thf(f502,plain,
! [X0: labele2115946735nt_V_V,X1: v,X2: standard_Constant_V,X3: labele2115946735nt_V_V,X4: v] :
( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ X4 @ X1 ) @ ( getRel1432786916nt_V_V @ X2 @ X3 ) )
=> ( ( graph_1808119_V_V_V @ X3 @ X0 @ ( id_on_V2 @ ( labele1134902411nt_V_V @ X3 ) ) )
=> ( member2015049524od_V_V @ ( product_Pair_V_V2 @ X4 @ X1 ) @ ( getRel1432786916nt_V_V @ X2 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f39]) ).
thf(f39,axiom,
! [X29: labele2115946735nt_V_V,X19: v,X20: standard_Constant_V,X21: labele2115946735nt_V_V,X18: v] :
( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ X18 @ X19 ) @ ( getRel1432786916nt_V_V @ X20 @ X21 ) )
=> ( ( graph_1808119_V_V_V @ X21 @ X29 @ ( id_on_V2 @ ( labele1134902411nt_V_V @ X21 ) ) )
=> ( member2015049524od_V_V @ ( product_Pair_V_V2 @ X18 @ X19 ) @ ( getRel1432786916nt_V_V @ X20 @ X29 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.OGMuvyH1wq/DTF2THF_13384.p',fact_38_getRel__subgraph) ).
thf(f1916,plain,
( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ y ) @ g ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f1001]) ).
thf(f1001,plain,
( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ y ) @ g ) )
!= $true ),
inference(flattening,[status(thm)],[f779]) ).
thf(f779,plain,
( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ y ) @ g ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f778]) ).
thf(f778,plain,
~ ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ y ) @ g ) ),
inference(rectify,[status(thm)],[f357]) ).
thf(f357,negated_conjecture,
~ ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ y ) @ g ) ),
inference(negated_conjecture,[status(cth)],[f356]) ).
thf(f356,conjecture,
member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ y ) @ g ),
file('/export/starexec/sandbox/tmp/tmp.OGMuvyH1wq/DTF2THF_13384.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP180^1 : 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
% 0.16/0.34 % Computer : n008.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 08:29:09 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : ITP180^1 : TPTP v9.2.1. Released v7.5.0.
% 0.20/0.46 % Domain : Interactive Theorem Proving
% 0.20/0.46 % Problem : Sledgehammer StandardRules problem prob_651__5393624_1
% 0.20/0.46 % Version : Especial.
% 0.20/0.46 % English :
% 0.20/0.46
% 0.20/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.20/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.20/0.46 % Source : [Des21]
% 0.20/0.46 % Names : StandardRules/prob_651__5393624_1 [Des21]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.23 v8.1.0, 0.27 v7.5.0
% 0.20/0.46 % Syntax : Number of formulae : 537 ( 195 unt; 181 typ; 0 def)
% 0.20/0.46 % Number of atoms : 924 ( 468 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 6 ( 2 avg)
% 0.20/0.46 % Number of connectives : 2959 ( 141 ~; 28 |; 78 &;2417 @)
% 0.20/0.46 % ( 0 <=>; 295 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 20 ( 6 avg)
% 0.20/0.46 % Number of types : 44 ( 43 usr)
% 0.20/0.46 % Number of type conns : 300 ( 300 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 139 ( 138 usr; 24 con; 0-3 aty)
% 0.20/0.46 % Number of variables : 888 ( 24 ^; 839 !; 25 ?; 888 :)
% 0.20/0.46 % SPC : TH0_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 15:39:26.524
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % Could-be-implicit typings (43)
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J_J_Mt__Nat__Onat_J_J_J,type,
% 0.20/0.46 set_Pr361461255at_nat: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J_J_J_J,type,
% 0.20/0.46 set_Pr1326571566_V_nat: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J_J_J,type,
% 0.20/0.46 set_Pr1007924423_V_nat: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_Mt__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_J_J_J,type,
% 0.20/0.46 set_Pr872354016od_V_V: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_Mt__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_J_J,type,
% 0.20/0.46 produc1269720746od_V_V: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_It__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_It__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_Mt__Nat__Onat_J_J_J,type,
% 0.20/0.46 set_Pr597600647_V_nat: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J_J,type,
% 0.20/0.46 labele506073123_V_nat: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_Mt__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_J_J,type,
% 0.20/0.46 set_Pr2015814777od_V_V: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J_Mtf__V__H_J_J,type,
% 0.20/0.46 set_Pr1056235617_nat_V: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_Mt__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_J,type,
% 0.20/0.46 produc1082089497od_V_V: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V__H_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V__H_J_Mt__Nat__Onat_J_J_J,type,
% 0.20/0.46 set_Pr473545225_V_nat: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J_J,type,
% 0.20/0.46 set_Pr1058435079_V_nat: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J,type,
% 0.20/0.46 produc778275879_V_nat: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mtf__V__H_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mtf__V__H_J_J,type,
% 0.20/0.46 produc651414759nt_V_V: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_J,type,
% 0.20/0.46 labele201426742od_V_V: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_J_J,type,
% 0.20/0.46 set_Pr951255342od_V_V: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_J,type,
% 0.20/0.46 produc1443401592od_V_V: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_Mtf__V__H_J_J,type,
% 0.20/0.46 set_Pr257494450_V_V_V: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_J,type,
% 0.20/0.46 set_Pr744279122od_V_V: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V_Mtf__V_J_J_J,type,
% 0.20/0.46 set_Pr1498723630od_V_V: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J,type,
% 0.20/0.46 labele236903175od_V_V: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_J,type,
% 0.20/0.46 set_Pr2022779335od_V_V: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J,type,
% 0.20/0.46 produc1699571228od_V_V: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V_Mtf__V_J_J,type,
% 0.20/0.46 produc1113554040od_V_V: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J,type,
% 0.20/0.46 set_la14611914_V_nat: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J,type,
% 0.20/0.46 produc522115815od_V_V: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J,type,
% 0.20/0.46 labele2128733290_V_nat: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__LabeledGraphSemantics__Oallegorical____term_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_J,type,
% 0.20/0.46 allego859987871tant_V: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mtf__V__H_J,type,
% 0.20/0.46 labele2115946735nt_V_V: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_Mtf__V__H_J_J,type,
% 0.20/0.46 set_Pr1228022213_V_V_V: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mtf__V_J,type,
% 0.20/0.46 labele788688367nt_V_V: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_J,type,
% 0.20/0.46 set_St1111633946tant_V: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mtf__V__H_J_J,type,
% 0.20/0.46 set_Pr53436518_nat_V: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J,type,
% 0.20/0.46 set_Product_prod_V_V: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__V_Mtf__V__H_J_J,type,
% 0.20/0.46 set_Product_prod_V_V2: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__V_Mtf__V_J_J,type,
% 0.20/0.46 set_Product_prod_V_V3: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J,type,
% 0.20/0.46 standard_Constant_V: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J,type,
% 0.20/0.46 product_prod_V_V: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Product____Type__Oprod_Itf__V_Mtf__V_J,type,
% 0.20/0.46 product_prod_V_V2: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_Itf__V__H_J,type,
% 0.20/0.46 set_V: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_t__Set__Oset_Itf__V_J,type,
% 0.20/0.46 set_V2: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_tf__V__H,type,
% 0.20/0.46 v: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_n_tf__V,type,
% 0.20/0.46 v2: $tType ).
% 0.20/0.46
% 0.20/0.46 % Explicit typings (138)
% 0.20/0.46 thf(sy_c_BNF__Def_OGr_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J,type,
% 0.20/0.46 bNF_Gr320641027od_V_V: set_St1111633946tant_V > ( standard_Constant_V > product_prod_V_V ) > set_Pr744279122od_V_V ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_BNF__Def_OGr_001t__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_001t__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J,type,
% 0.20/0.46 bNF_Gr17960482_V_nat: set_la14611914_V_nat > ( labele2128733290_V_nat > labele2128733290_V_nat ) > set_Pr1058435079_V_nat ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_BNF__Def_OGr_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_001tf__V__H,type,
% 0.20/0.46 bNF_Gr480427157_V_V_V: set_Pr744279122od_V_V > ( produc1699571228od_V_V > v ) > set_Pr257494450_V_V_V ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_BNF__Def_OGr_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_001tf__V__H,type,
% 0.20/0.46 bNF_Gr1069958334_V_V_V: set_Product_prod_V_V > ( product_prod_V_V > v ) > set_Pr1228022213_V_V_V ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_BNF__Def_OGr_001tf__V_001tf__V__H,type,
% 0.20/0.46 bNF_Gr_V_V: set_V2 > ( v2 > v ) > set_Product_prod_V_V2 ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_BNF__Def_OGr_001tf__V__H_001tf__V__H,type,
% 0.20/0.46 bNF_Gr_V_V2: set_V > ( v > v ) > set_Product_prod_V_V ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Fun_Ocomp_001tf__V__H_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J,type,
% 0.20/0.46 comp_V1480932210od_V_V: ( v > produc1699571228od_V_V ) > ( produc1699571228od_V_V > v ) > produc1699571228od_V_V > produc1699571228od_V_V ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Fun_Ocomp_001tf__V__H_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J,type,
% 0.20/0.46 comp_V772749048od_V_V: ( v > product_prod_V_V ) > ( product_prod_V_V > v ) > product_prod_V_V > product_prod_V_V ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Fun_Ocomp_001tf__V__H_001tf__V_001tf__V,type,
% 0.20/0.46 comp_V_V_V: ( v > v2 ) > ( v2 > v ) > v2 > v2 ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Fun_Ocomp_001tf__V__H_001tf__V__H_001tf__V__H,type,
% 0.20/0.46 comp_V_V_V2: ( v > v ) > ( v > v ) > v > v ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_LabeledGraphSemantics_OStandard__Constant_OS__Bot_001tf__V,type,
% 0.20/0.46 standard_S_Bot_V: standard_Constant_V ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_LabeledGraphSemantics_OStandard__Constant_OS__Const_001tf__V,type,
% 0.20/0.46 standard_S_Const_V: v2 > standard_Constant_V ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_LabeledGraphSemantics_OStandard__Constant_OS__Top_001tf__V,type,
% 0.20/0.46 standard_S_Top_V: standard_Constant_V ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_LabeledGraphSemantics_OgetRel_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J,type,
% 0.20/0.46 getRel2057312683od_V_V: standard_Constant_V > labele201426742od_V_V > set_Pr2015814777od_V_V ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_LabeledGraphSemantics_OgetRel_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J,type,
% 0.20/0.46 getRel1902920892od_V_V: standard_Constant_V > labele236903175od_V_V > set_Pr2022779335od_V_V ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_LabeledGraphSemantics_OgetRel_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001tf__V,type,
% 0.20/0.46 getRel632961956nt_V_V: standard_Constant_V > labele788688367nt_V_V > set_Product_prod_V_V3 ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_LabeledGraphSemantics_OgetRel_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001tf__V__H,type,
% 0.20/0.46 getRel1432786916nt_V_V: standard_Constant_V > labele2115946735nt_V_V > set_Product_prod_V_V ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_LabeledGraphSemantics_Osemantics_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001tf__V__H,type,
% 0.20/0.46 semant993842370nt_V_V: labele2115946735nt_V_V > allego859987871tant_V > set_Product_prod_V_V ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_LabeledGraphs_Oedge__preserving_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_001tf__V__H_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J,type,
% 0.20/0.46 edge_p669293514tant_V: set_Pr257494450_V_V_V > set_Pr872354016od_V_V > set_Pr744279122od_V_V > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_LabeledGraphs_Oedge__preserving_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_001tf__V__H_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J,type,
% 0.20/0.46 edge_p1776314003tant_V: set_Pr1228022213_V_V_V > set_Pr951255342od_V_V > set_Pr744279122od_V_V > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_LabeledGraphs_Oedge__preserving_001tf__V_001tf__V__H_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J,type,
% 0.20/0.46 edge_p1322161019tant_V: set_Product_prod_V_V2 > set_Pr1498723630od_V_V > set_Pr744279122od_V_V > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_LabeledGraphs_Oedge__preserving_001tf__V__H_001tf__V__H_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J,type,
% 0.20/0.46 edge_p1560004099tant_V: set_Product_prod_V_V > set_Pr744279122od_V_V > set_Pr744279122od_V_V > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_LabeledGraphs_Ograph__homomorphism_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Nat__Onat_001tf__V__H,type,
% 0.20/0.46 graph_1541575154_nat_V: labele2128733290_V_nat > labele2115946735nt_V_V > set_Pr53436518_nat_V > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_LabeledGraphs_Ograph__homomorphism_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J_001tf__V__H,type,
% 0.20/0.46 graph_227683057_nat_V: labele506073123_V_nat > labele2115946735nt_V_V > set_Pr1056235617_nat_V > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_LabeledGraphs_Ograph__homomorphism_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_001tf__V__H,type,
% 0.20/0.46 graph_840721237_V_V_V: labele236903175od_V_V > labele2115946735nt_V_V > set_Pr1228022213_V_V_V > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_LabeledGraphs_Ograph__homomorphism_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001tf__V__H_001tf__V__H,type,
% 0.20/0.46 graph_1808119_V_V_V: labele2115946735nt_V_V > labele2115946735nt_V_V > set_Product_prod_V_V > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_LabeledGraphs_Ograph__union_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001tf__V__H,type,
% 0.20/0.46 graph_1141886696nt_V_V: labele2115946735nt_V_V > labele2115946735nt_V_V > labele2115946735nt_V_V ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_LabeledGraphs_Olabeled__graph_OLG_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J,type,
% 0.20/0.46 labele1193521135_V_nat: set_Pr1326571566_V_nat > set_Pr1058435079_V_nat > labele506073123_V_nat ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_LabeledGraphs_Olabeled__graph_OLG_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J,type,
% 0.20/0.46 labele94156371od_V_V: set_Pr951255342od_V_V > set_Product_prod_V_V > labele236903175od_V_V ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_LabeledGraphs_Olabeled__graph_OLG_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001tf__V__H,type,
% 0.20/0.46 labele712009229nt_V_V: set_Pr744279122od_V_V > set_V > labele2115946735nt_V_V ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_LabeledGraphs_Olabeled__graph_Oedges_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J,type,
% 0.20/0.46 labele1794513953od_V_V: labele201426742od_V_V > set_Pr872354016od_V_V ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_LabeledGraphs_Olabeled__graph_Oedges_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J,type,
% 0.20/0.46 labele668941254od_V_V: labele236903175od_V_V > set_Pr951255342od_V_V ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_LabeledGraphs_Olabeled__graph_Oedges_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001tf__V,type,
% 0.20/0.46 labele1469545390nt_V_V: labele788688367nt_V_V > set_Pr1498723630od_V_V ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_LabeledGraphs_Olabeled__graph_Oedges_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001tf__V__H,type,
% 0.20/0.46 labele515735386nt_V_V: labele2115946735nt_V_V > set_Pr744279122od_V_V ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_LabeledGraphs_Olabeled__graph_Overtices_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J,type,
% 0.20/0.46 labele1328382418od_V_V: labele201426742od_V_V > set_Pr744279122od_V_V ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_LabeledGraphs_Olabeled__graph_Overtices_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J,type,
% 0.20/0.46 labele1822884081_V_nat: labele506073123_V_nat > set_Pr1058435079_V_nat ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_LabeledGraphs_Olabeled__graph_Overtices_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J,type,
% 0.20/0.46 labele981584981od_V_V: labele236903175od_V_V > set_Product_prod_V_V ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_LabeledGraphs_Olabeled__graph_Overtices_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001tf__V,type,
% 0.20/0.46 labele1152678333nt_V_V: labele788688367nt_V_V > set_V2 ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_LabeledGraphs_Olabeled__graph_Overtices_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001tf__V__H,type,
% 0.20/0.46 labele1134902411nt_V_V: labele2115946735nt_V_V > set_V ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_LabeledGraphs_Omap__graph_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_001tf__V__H_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J,type,
% 0.20/0.46 map_gr157381846tant_V: set_Pr257494450_V_V_V > labele201426742od_V_V > labele2115946735nt_V_V ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_LabeledGraphs_Omap__graph_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_001tf__V__H_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J,type,
% 0.20/0.46 map_gr875022471tant_V: set_Pr1228022213_V_V_V > labele236903175od_V_V > labele2115946735nt_V_V ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_LabeledGraphs_Omap__graph_001tf__V_001tf__V__H_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J,type,
% 0.20/0.46 map_gr530397039tant_V: set_Product_prod_V_V2 > labele788688367nt_V_V > labele2115946735nt_V_V ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_LabeledGraphs_Omap__graph_001tf__V__H_001tf__V__H_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J,type,
% 0.20/0.46 map_gr907434255tant_V: set_Product_prod_V_V > labele2115946735nt_V_V > labele2115946735nt_V_V ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_LabeledGraphs_Orestrict_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J,type,
% 0.20/0.46 restri1699516426od_V_V: labele201426742od_V_V > labele201426742od_V_V ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_LabeledGraphs_Orestrict_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J,type,
% 0.20/0.46 restri1932147897_V_nat: labele506073123_V_nat > labele506073123_V_nat ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_LabeledGraphs_Orestrict_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J,type,
% 0.20/0.46 restri1502575645od_V_V: labele236903175od_V_V > labele236903175od_V_V ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_LabeledGraphs_Orestrict_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001tf__V,type,
% 0.20/0.46 restri175070597nt_V_V: labele788688367nt_V_V > labele788688367nt_V_V ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_LabeledGraphs_Orestrict_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001tf__V__H,type,
% 0.20/0.46 restri1305980611nt_V_V: labele2115946735nt_V_V > labele2115946735nt_V_V ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_J,type,
% 0.20/0.46 sup_su693515134od_V_V: set_Pr744279122od_V_V > set_Pr744279122od_V_V > set_Pr744279122od_V_V ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J_J,type,
% 0.20/0.46 sup_su1043134939_V_nat: set_Pr1058435079_V_nat > set_Pr1058435079_V_nat > set_Pr1058435079_V_nat ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J,type,
% 0.20/0.46 sup_su551882943od_V_V: set_Product_prod_V_V > set_Product_prod_V_V > set_Product_prod_V_V ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_Itf__V_J,type,
% 0.20/0.46 sup_sup_set_V: set_V2 > set_V2 > set_V2 ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_Itf__V__H_J,type,
% 0.20/0.46 sup_sup_set_V2: set_V > set_V > set_V ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_M_Eo_J,type,
% 0.20/0.46 bot_bo2024487199_V_V_o: produc1699571228od_V_V > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J_M_Eo_J,type,
% 0.20/0.46 bot_bo1078500394_nat_o: produc778275879_V_nat > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_M_Eo_J,type,
% 0.20/0.46 bot_bo1168561222_V_V_o: product_prod_V_V > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Orderings_Obot__class_Obot_001_062_Itf__V_M_Eo_J,type,
% 0.20/0.46 bot_bot_V_o: v2 > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Orderings_Obot__class_Obot_001_062_Itf__V__H_M_Eo_J,type,
% 0.20/0.46 bot_bot_V_o2: v > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J,type,
% 0.20/0.46 bot_bo1053950006_V_nat: set_la14611914_V_nat ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J_J_J_J,type,
% 0.20/0.46 bot_bo634818242_V_nat: set_Pr1326571566_V_nat ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_J_J,type,
% 0.20/0.46 bot_bo451843010od_V_V: set_Pr951255342od_V_V ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_J,type,
% 0.20/0.46 bot_bo667804902od_V_V: set_Pr744279122od_V_V ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J_J_Mt__Nat__Onat_J_J_J,type,
% 0.20/0.46 bot_bo323535987at_nat: set_Pr361461255at_nat ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_It__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_It__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_Mt__Nat__Onat_J_J_J,type,
% 0.20/0.46 bot_bo1196823539_V_nat: set_Pr597600647_V_nat ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J_J,type,
% 0.20/0.46 bot_bo907687539_V_nat: set_Pr1058435079_V_nat ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V__H_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V__H_J_Mt__Nat__Onat_J_J_J,type,
% 0.20/0.47 bot_bo1834032757_V_nat: set_Pr473545225_V_nat ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J_J_J,type,
% 0.20/0.47 bot_bo2057106227_V_nat: set_Pr1007924423_V_nat ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J_Mtf__V__H_J_J,type,
% 0.20/0.47 bot_bo1708783349_nat_V: set_Pr1056235617_nat_V ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_J,type,
% 0.20/0.47 bot_bo12878899od_V_V: set_Pr2022779335od_V_V ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_Mtf__V__H_J_J,type,
% 0.20/0.47 bot_bo688400985_V_V_V: set_Pr1228022213_V_V_V ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J,type,
% 0.20/0.47 bot_bo1389414743od_V_V: set_Product_prod_V_V ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__V_J,type,
% 0.20/0.47 bot_bot_set_V: set_V2 ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__V__H_J,type,
% 0.20/0.47 bot_bot_set_V2: set_V ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_OPair_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_Mt__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_J,type,
% 0.20/0.47 produc2132932316od_V_V: standard_Constant_V > produc1082089497od_V_V > produc1269720746od_V_V ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_OPair_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J,type,
% 0.20/0.47 produc1482441770od_V_V: standard_Constant_V > produc522115815od_V_V > produc1443401592od_V_V ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_OPair_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Product____Type__Oprod_Itf__V_Mtf__V_J,type,
% 0.20/0.47 produc1171747370od_V_V: standard_Constant_V > product_prod_V_V2 > produc1113554040od_V_V ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_OPair_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J,type,
% 0.20/0.47 produc107991630od_V_V: standard_Constant_V > product_prod_V_V > produc1699571228od_V_V ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_OPair_001t__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_001t__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J,type,
% 0.20/0.47 produc698429463_V_nat: labele2128733290_V_nat > labele2128733290_V_nat > produc778275879_V_nat ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_OPair_001t__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mtf__V__H_J_001t__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mtf__V__H_J,type,
% 0.20/0.47 produc533118295nt_V_V: labele2115946735nt_V_V > labele2115946735nt_V_V > produc651414759nt_V_V ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J,type,
% 0.20/0.47 produc1736057425od_V_V: produc1699571228od_V_V > produc1699571228od_V_V > produc1082089497od_V_V ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J,type,
% 0.20/0.47 produc1905750615od_V_V: product_prod_V_V > product_prod_V_V > produc522115815od_V_V ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_OPair_001tf__V_001tf__V,type,
% 0.20/0.47 product_Pair_V_V: v2 > v2 > product_prod_V_V2 ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Product__Type_OPair_001tf__V__H_001tf__V__H,type,
% 0.20/0.47 product_Pair_V_V2: v > v > product_prod_V_V ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Relation_OId__on_001t__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J,type,
% 0.20/0.47 id_on_1882925319_V_nat: set_la14611914_V_nat > set_Pr1058435079_V_nat ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Relation_OId__on_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J,type,
% 0.20/0.47 id_on_1491482303od_V_V: set_Pr744279122od_V_V > set_Pr2015814777od_V_V ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Relation_OId__on_001t__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J,type,
% 0.20/0.47 id_on_558037444_V_nat: set_Pr1058435079_V_nat > set_Pr1007924423_V_nat ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Relation_OId__on_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J,type,
% 0.20/0.47 id_on_2125509800od_V_V: set_Product_prod_V_V > set_Pr2022779335od_V_V ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Relation_OId__on_001tf__V,type,
% 0.20/0.47 id_on_V: set_V2 > set_Product_prod_V_V3 ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Relation_OId__on_001tf__V__H,type,
% 0.20/0.47 id_on_V2: set_V > set_Product_prod_V_V ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_RulesAndChains_Oconsequence__graph_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Nat__Onat_001tf__V__H,type,
% 0.20/0.47 conseq1236301781_nat_V: set_Pr1058435079_V_nat > labele2115946735nt_V_V > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_RulesAndChains_Oextensible_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Nat__Onat_001tf__V__H,type,
% 0.20/0.47 extens1072773157_nat_V: produc778275879_V_nat > labele2115946735nt_V_V > set_Pr53436518_nat_V > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_RulesAndChains_Oextensible_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001tf__V__H_001tf__V__H,type,
% 0.20/0.47 extens1533825066_V_V_V: produc651414759nt_V_V > labele2115946735nt_V_V > set_Product_prod_V_V > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_RulesAndChains_Omaintained_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Nat__Onat_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J,type,
% 0.20/0.47 mainta1342478555od_V_V: produc778275879_V_nat > labele201426742od_V_V > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_RulesAndChains_Omaintained_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Nat__Onat_001t__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J,type,
% 0.20/0.47 mainta922614952_V_nat: produc778275879_V_nat > labele506073123_V_nat > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_RulesAndChains_Omaintained_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Nat__Onat_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J,type,
% 0.20/0.47 mainta1984786828od_V_V: produc778275879_V_nat > labele236903175od_V_V > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_RulesAndChains_Omaintained_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Nat__Onat_001tf__V,type,
% 0.20/0.47 mainta1026355316_nat_V: produc778275879_V_nat > labele788688367nt_V_V > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_RulesAndChains_Omaintained_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Nat__Onat_001tf__V__H,type,
% 0.20/0.47 mainta197426964_nat_V: produc778275879_V_nat > labele2115946735nt_V_V > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_RulesAndChains_Omaintained_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001tf__V__H_001tf__V__H,type,
% 0.20/0.47 mainta1699210777_V_V_V: produc651414759nt_V_V > labele2115946735nt_V_V > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J,type,
% 0.20/0.47 collec1840263537od_V_V: ( produc1699571228od_V_V > $o ) > set_Pr744279122od_V_V ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J,type,
% 0.20/0.47 collec1411521682_V_nat: ( produc778275879_V_nat > $o ) > set_Pr1058435079_V_nat ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J,type,
% 0.20/0.47 collec2040633974od_V_V: ( product_prod_V_V > $o ) > set_Product_prod_V_V ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Set_OCollect_001tf__V,type,
% 0.20/0.47 collect_V: ( v2 > $o ) > set_V2 ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Set_OCollect_001tf__V__H,type,
% 0.20/0.47 collect_V2: ( v > $o ) > set_V ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Set_Oinsert_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J,type,
% 0.20/0.47 insert1818834324tant_V: standard_Constant_V > set_St1111633946tant_V > set_St1111633946tant_V ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Set_Oinsert_001t__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J,type,
% 0.20/0.47 insert213439034_V_nat: labele2128733290_V_nat > set_la14611914_V_nat > set_la14611914_V_nat ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J,type,
% 0.20/0.47 insert135842892od_V_V: produc1699571228od_V_V > set_Pr744279122od_V_V > set_Pr744279122od_V_V ).
% 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__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J,type,
% 0.20/0.47 insert481364471_V_nat: produc778275879_V_nat > set_Pr1058435079_V_nat > set_Pr1058435079_V_nat ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J,type,
% 0.20/0.47 insert2024285275od_V_V: product_prod_V_V > set_Product_prod_V_V > set_Product_prod_V_V ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Set_Oinsert_001tf__V,type,
% 0.20/0.47 insert_V: v2 > set_V2 > set_V2 ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_Set_Oinsert_001tf__V__H,type,
% 0.20/0.47 insert_V2: v > set_V > set_V ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Oconstant__rules_001t__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J,type,
% 0.20/0.47 standa434642387_V_nat: set_Pr1058435079_V_nat > set_Pr361461255at_nat ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Oconstant__rules_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J,type,
% 0.20/0.47 standa1571708471od_V_V: set_Product_prod_V_V > set_Pr597600647_V_nat ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Oconstant__rules_001tf__V,type,
% 0.20/0.47 standa1897115807ules_V: set_V2 > set_Pr1058435079_V_nat ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Oconstant__rules_001tf__V__H,type,
% 0.20/0.47 standa294833961ules_V: set_V > set_Pr473545225_V_nat ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Oidentity__rules_001tf__V,type,
% 0.20/0.47 standa1568205529ules_V: set_St1111633946tant_V > set_Pr1058435079_V_nat ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Ononempty__rule_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J,type,
% 0.20/0.47 standa1319953089tant_V: produc778275879_V_nat ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Ostandard__rules_001tf__V,type,
% 0.20/0.47 standa157301464ules_V: set_V2 > set_St1111633946tant_V > set_Pr1058435079_V_nat ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Otop__rule_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J,type,
% 0.20/0.47 standa214871990tant_V: standard_Constant_V > produc778275879_V_nat ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_member_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J,type,
% 0.20/0.47 member1542015739tant_V: standard_Constant_V > set_St1111633946tant_V > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_Mt__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_J_J,type,
% 0.20/0.47 member600445121od_V_V: produc1269720746od_V_V > set_Pr872354016od_V_V > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_J,type,
% 0.20/0.47 member361435663od_V_V: produc1443401592od_V_V > set_Pr951255342od_V_V > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V_Mtf__V_J_J,type,
% 0.20/0.47 member1416643087od_V_V: produc1113554040od_V_V > set_Pr1498723630od_V_V > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J,type,
% 0.20/0.47 member1010391347od_V_V: produc1699571228od_V_V > set_Pr744279122od_V_V > $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__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J,type,
% 0.20/0.47 member1886821968_V_nat: produc778275879_V_nat > set_Pr1058435079_V_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__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_Mt__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_J,type,
% 0.20/0.47 member785416642od_V_V: produc1082089497od_V_V > set_Pr2015814777od_V_V > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J,type,
% 0.20/0.47 member134497296od_V_V: produc522115815od_V_V > set_Pr2022779335od_V_V > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_member_001t__Product____Type__Oprod_Itf__V_Mtf__V_J,type,
% 0.20/0.47 member1990987792od_V_V: product_prod_V_V2 > set_Product_prod_V_V3 > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_member_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J,type,
% 0.20/0.47 member2015049524od_V_V: product_prod_V_V > set_Product_prod_V_V > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_member_001tf__V,type,
% 0.20/0.47 member_V: v2 > set_V2 > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_c_member_001tf__V__H,type,
% 0.20/0.47 member_V2: v > set_V > $o ).
% 0.20/0.47
% 0.20/0.47 thf(sy_v_C,type,
% 0.20/0.47 c: set_V2 ).
% 0.20/0.47
% 0.20/0.47 thf(sy_v_G_H,type,
% 0.20/0.47 g: labele2115946735nt_V_V ).
% 0.20/0.47
% 0.20/0.47 thf(sy_v_L,type,
% 0.20/0.47 l: set_St1111633946tant_V ).
% 0.20/0.47
% 0.20/0.47 thf(sy_v_h____,type,
% 0.20/0.47 h: v > v ).
% 0.20/0.47
% 0.20/0.47 thf(sy_v_m____,type,
% 0.20/0.47 m: v2 > v ).
% 0.20/0.47
% 0.20/0.47 thf(sy_v_x____,type,
% 0.20/0.47 x: v ).
% 0.20/0.47
% 0.20/0.47 thf(sy_v_xa____,type,
% 0.20/0.47 xa: v2 ).
% 0.20/0.47
% 0.20/0.47 thf(sy_v_y____,type,
% 0.20/0.47 y: v2 ).
% 0.20/0.47
% 0.20/0.47 % Relevant facts (355)
% 0.20/0.47 thf(fact_0_x,axiom,
% 0.20/0.47 member_V2 @ x @ ( labele1134902411nt_V_V @ g ) ).
% 0.20/0.47
% 0.20/0.47 % x
% 0.20/0.47 thf(fact_1__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062x_O_Ax_A_092_060in_062_Avertices_AG_H_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.20/0.47 ~ ! [X: v] :
% 0.20/0.47 ~ ( member_V2 @ X @ ( labele1134902411nt_V_V @ g ) ) ).
% 0.20/0.47
% 0.20/0.47 % \<open>\<And>thesis. (\<And>x. x \<in> vertices G' \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.20/0.47 thf(fact_2__C1_C_I3_J,axiom,
% 0.20/0.47 ( ( m @ xa )
% 0.20/0.47 = ( m @ y ) ) ).
% 0.20/0.47
% 0.20/0.47 % "1"(3)
% 0.20/0.47 thf(fact_3__C1_C_I1_J,axiom,
% 0.31/0.47 member_V @ xa @ c ).
% 0.31/0.47
% 0.31/0.47 % "1"(1)
% 0.31/0.47 thf(fact_4__C1_C_I2_J,axiom,
% 0.31/0.47 member_V @ y @ c ).
% 0.31/0.47
% 0.31/0.47 % "1"(2)
% 0.31/0.47 thf(fact_5__092_060open_062_Im_Ax_M_Am_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ax_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062,axiom,
% 0.31/0.47 member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ xa ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ).
% 0.31/0.47
% 0.31/0.47 % \<open>(m x, m x) \<in> getRel (S_Const x) (map_graph_fn G' h)\<close>
% 0.31/0.47 thf(fact_6__092_060open_062_Im_Ax_M_Am_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ay_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062,axiom,
% 0.31/0.47 member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ y ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ).
% 0.31/0.47
% 0.31/0.47 % \<open>(m x, m x) \<in> getRel (S_Const y) (map_graph_fn G' h)\<close>
% 0.31/0.47 thf(fact_7_gr_I1_J,axiom,
% 0.31/0.47 ( g
% 0.31/0.47 = ( restri1305980611nt_V_V @ g ) ) ).
% 0.31/0.47
% 0.31/0.47 % gr(1)
% 0.31/0.47 thf(fact_8_h_I3_J,axiom,
% 0.31/0.47 graph_1808119_V_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) @ g @ ( id_on_V2 @ ( labele1134902411nt_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % h(3)
% 0.31/0.47 thf(fact_9_Standard__Constant_Oinject,axiom,
% 0.31/0.47 ! [X4: v2,Y4: v2] :
% 0.31/0.47 ( ( ( standard_S_Const_V @ X4 )
% 0.31/0.47 = ( standard_S_Const_V @ Y4 ) )
% 0.31/0.47 = ( X4 = Y4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % Standard_Constant.inject
% 0.31/0.47 thf(fact_10_prod_Oinject,axiom,
% 0.31/0.47 ! [X1: v,X2: v,Y1: v,Y2: v] :
% 0.31/0.47 ( ( ( product_Pair_V_V2 @ X1 @ X2 )
% 0.31/0.47 = ( product_Pair_V_V2 @ Y1 @ Y2 ) )
% 0.31/0.47 = ( ( X1 = Y1 )
% 0.31/0.47 & ( X2 = Y2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod.inject
% 0.31/0.47 thf(fact_11_prod_Oinject,axiom,
% 0.31/0.47 ! [X1: standard_Constant_V,X2: product_prod_V_V,Y1: standard_Constant_V,Y2: product_prod_V_V] :
% 0.31/0.47 ( ( ( produc107991630od_V_V @ X1 @ X2 )
% 0.31/0.47 = ( produc107991630od_V_V @ Y1 @ Y2 ) )
% 0.31/0.47 = ( ( X1 = Y1 )
% 0.31/0.47 & ( X2 = Y2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod.inject
% 0.31/0.47 thf(fact_12_old_Oprod_Oinject,axiom,
% 0.31/0.47 ! [A: v,B: v,A2: v,B2: v] :
% 0.31/0.47 ( ( ( product_Pair_V_V2 @ A @ B )
% 0.31/0.47 = ( product_Pair_V_V2 @ A2 @ B2 ) )
% 0.31/0.47 = ( ( A = A2 )
% 0.31/0.47 & ( B = B2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.inject
% 0.31/0.47 thf(fact_13_old_Oprod_Oinject,axiom,
% 0.31/0.47 ! [A: standard_Constant_V,B: product_prod_V_V,A2: standard_Constant_V,B2: product_prod_V_V] :
% 0.31/0.47 ( ( ( produc107991630od_V_V @ A @ B )
% 0.31/0.47 = ( produc107991630od_V_V @ A2 @ B2 ) )
% 0.31/0.47 = ( ( A = A2 )
% 0.31/0.47 & ( B = B2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.inject
% 0.31/0.47 thf(fact_14_m,axiom,
% 0.31/0.47 ! [X3: v2] :
% 0.31/0.47 ( ( member_V @ X3 @ c )
% 0.31/0.47 => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ X3 ) @ ( m @ X3 ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ X3 ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % m
% 0.31/0.47 thf(fact_15_top__nonempty,axiom,
% 0.31/0.47 member2015049524od_V_V @ ( product_Pair_V_V2 @ x @ x ) @ ( getRel1432786916nt_V_V @ standard_S_Top_V @ g ) ).
% 0.31/0.47
% 0.31/0.47 % top_nonempty
% 0.31/0.47 thf(fact_16_cf,axiom,
% 0.31/0.47 ( ( getRel1432786916nt_V_V @ standard_S_Bot_V @ g )
% 0.31/0.47 = bot_bo1389414743od_V_V ) ).
% 0.31/0.47
% 0.31/0.47 % cf
% 0.31/0.47 thf(fact_17__092_060open_062_092_060And_062c_O_Ac_A_092_060in_062_AC_A_092_060Longrightarrow_062_A_092_060exists_062v_O_A_Iv_M_Av_J_A_092_060in_062_AgetRel_A_IS__Const_Ac_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062,axiom,
% 0.31/0.47 ! [C: v2] :
% 0.31/0.47 ( ( member_V @ C @ c )
% 0.31/0.47 => ? [V: v] : ( member2015049524od_V_V @ ( product_Pair_V_V2 @ V @ V ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ C ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % \<open>\<And>c. c \<in> C \<Longrightarrow> \<exists>v. (v, v) \<in> getRel (S_Const c) (map_graph_fn G' h)\<close>
% 0.31/0.47 thf(fact_18__092_060open_062_092_060forall_062c_O_A_092_060exists_062v_O_Ac_A_092_060in_062_AC_A_092_060longrightarrow_062_A_Iv_M_Av_J_A_092_060in_062_AgetRel_A_IS__Const_Ac_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062,axiom,
% 0.31/0.47 ! [C2: v2] :
% 0.31/0.47 ? [V: v] :
% 0.31/0.47 ( ( member_V @ C2 @ c )
% 0.31/0.47 => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ V @ V ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ C2 ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % \<open>\<forall>c. \<exists>v. c \<in> C \<longrightarrow> (v, v) \<in> getRel (S_Const c) (map_graph_fn G' h)\<close>
% 0.31/0.47 thf(fact_19__092_060open_062_092_060exists_062f_O_A_092_060forall_062x_O_Ax_A_092_060in_062_AC_A_092_060longrightarrow_062_A_If_Ax_M_Af_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ax_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062,axiom,
% 0.31/0.47 ? [F: v2 > v] :
% 0.31/0.47 ! [X5: v2] :
% 0.31/0.47 ( ( member_V @ X5 @ c )
% 0.31/0.47 => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( F @ X5 ) @ ( F @ X5 ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ X5 ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % \<open>\<exists>f. \<forall>x. x \<in> C \<longrightarrow> (f x, f x) \<in> getRel (S_Const x) (map_graph_fn G' h)\<close>
% 0.31/0.47 thf(fact_20__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062m_O_A_I_092_060And_062x_O_Ax_A_092_060in_062_AC_A_092_060Longrightarrow_062_A_Im_Ax_M_Am_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ax_J_A_Imap__graph__fn_AG_H_Ah_J_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.31/0.47 ~ ! [M: v2 > v] :
% 0.31/0.47 ~ ! [X5: v2] :
% 0.31/0.47 ( ( member_V @ X5 @ c )
% 0.31/0.47 => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( M @ X5 ) @ ( M @ X5 ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ X5 ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % \<open>\<And>thesis. (\<And>m. (\<And>x. x \<in> C \<Longrightarrow> (m x, m x) \<in> getRel (S_Const x) (map_graph_fn G' h)) \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.31/0.47 thf(fact_21_getRel__homR,axiom,
% 0.31/0.47 ! [Y: v,Z: v,L: standard_Constant_V,G: labele2115946735nt_V_V,U: v,F2: set_Product_prod_V_V,V2: v] :
% 0.31/0.47 ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ Y @ Z ) @ ( getRel1432786916nt_V_V @ L @ G ) )
% 0.31/0.47 => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ Y @ U ) @ F2 )
% 0.31/0.47 => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ Z @ V2 ) @ F2 )
% 0.31/0.47 => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ U @ V2 ) @ ( getRel1432786916nt_V_V @ L @ ( map_gr907434255tant_V @ F2 @ G ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % getRel_homR
% 0.31/0.47 thf(fact_22_surj__pair,axiom,
% 0.31/0.47 ! [P: product_prod_V_V] :
% 0.31/0.47 ? [X: v,Y3: v] :
% 0.31/0.47 ( P
% 0.31/0.47 = ( product_Pair_V_V2 @ X @ Y3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % surj_pair
% 0.31/0.47 thf(fact_23_surj__pair,axiom,
% 0.31/0.47 ! [P: produc1699571228od_V_V] :
% 0.31/0.47 ? [X: standard_Constant_V,Y3: product_prod_V_V] :
% 0.31/0.47 ( P
% 0.31/0.47 = ( produc107991630od_V_V @ X @ Y3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % surj_pair
% 0.31/0.47 thf(fact_24_h_I1_J,axiom,
% 0.31/0.47 ( ( comp_V_V_V2 @ h @ h )
% 0.31/0.47 = h ) ).
% 0.31/0.47
% 0.31/0.47 % h(1)
% 0.31/0.47 thf(fact_25_getRel__map__fn,axiom,
% 0.31/0.47 ! [A22: product_prod_V_V,G: labele236903175od_V_V,B22: product_prod_V_V,L: standard_Constant_V,F2: product_prod_V_V > v,A: v,B: v] :
% 0.31/0.47 ( ( member2015049524od_V_V @ A22 @ ( labele981584981od_V_V @ G ) )
% 0.31/0.47 => ( ( member2015049524od_V_V @ B22 @ ( labele981584981od_V_V @ G ) )
% 0.31/0.47 => ( ( member134497296od_V_V @ ( produc1905750615od_V_V @ A22 @ B22 ) @ ( getRel1902920892od_V_V @ L @ G ) )
% 0.31/0.47 => ( ( ( F2 @ A22 )
% 0.31/0.47 = A )
% 0.31/0.47 => ( ( ( F2 @ B22 )
% 0.31/0.47 = B )
% 0.31/0.47 => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( getRel1432786916nt_V_V @ L @ ( map_gr875022471tant_V @ ( bNF_Gr1069958334_V_V_V @ ( labele981584981od_V_V @ G ) @ F2 ) @ G ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % getRel_map_fn
% 0.31/0.47 thf(fact_26_getRel__map__fn,axiom,
% 0.31/0.47 ! [A22: v2,G: labele788688367nt_V_V,B22: v2,L: standard_Constant_V,F2: v2 > v,A: v,B: v] :
% 0.31/0.47 ( ( member_V @ A22 @ ( labele1152678333nt_V_V @ G ) )
% 0.31/0.47 => ( ( member_V @ B22 @ ( labele1152678333nt_V_V @ G ) )
% 0.31/0.47 => ( ( member1990987792od_V_V @ ( product_Pair_V_V @ A22 @ B22 ) @ ( getRel632961956nt_V_V @ L @ G ) )
% 0.31/0.47 => ( ( ( F2 @ A22 )
% 0.31/0.47 = A )
% 0.31/0.47 => ( ( ( F2 @ B22 )
% 0.31/0.47 = B )
% 0.31/0.47 => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( getRel1432786916nt_V_V @ L @ ( map_gr530397039tant_V @ ( bNF_Gr_V_V @ ( labele1152678333nt_V_V @ G ) @ F2 ) @ G ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % getRel_map_fn
% 0.31/0.47 thf(fact_27_getRel__map__fn,axiom,
% 0.31/0.47 ! [A22: produc1699571228od_V_V,G: labele201426742od_V_V,B22: produc1699571228od_V_V,L: standard_Constant_V,F2: produc1699571228od_V_V > v,A: v,B: v] :
% 0.31/0.47 ( ( member1010391347od_V_V @ A22 @ ( labele1328382418od_V_V @ G ) )
% 0.31/0.47 => ( ( member1010391347od_V_V @ B22 @ ( labele1328382418od_V_V @ G ) )
% 0.31/0.47 => ( ( member785416642od_V_V @ ( produc1736057425od_V_V @ A22 @ B22 ) @ ( getRel2057312683od_V_V @ L @ G ) )
% 0.31/0.47 => ( ( ( F2 @ A22 )
% 0.31/0.47 = A )
% 0.31/0.47 => ( ( ( F2 @ B22 )
% 0.31/0.47 = B )
% 0.31/0.47 => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( getRel1432786916nt_V_V @ L @ ( map_gr157381846tant_V @ ( bNF_Gr480427157_V_V_V @ ( labele1328382418od_V_V @ G ) @ F2 ) @ G ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % getRel_map_fn
% 0.31/0.47 thf(fact_28_getRel__map__fn,axiom,
% 0.31/0.47 ! [A22: v,G: labele2115946735nt_V_V,B22: v,L: standard_Constant_V,F2: v > v,A: v,B: v] :
% 0.31/0.47 ( ( member_V2 @ A22 @ ( labele1134902411nt_V_V @ G ) )
% 0.31/0.47 => ( ( member_V2 @ B22 @ ( labele1134902411nt_V_V @ G ) )
% 0.31/0.47 => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A22 @ B22 ) @ ( getRel1432786916nt_V_V @ L @ G ) )
% 0.31/0.47 => ( ( ( F2 @ A22 )
% 0.31/0.47 = A )
% 0.31/0.47 => ( ( ( F2 @ B22 )
% 0.31/0.47 = B )
% 0.31/0.47 => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( getRel1432786916nt_V_V @ L @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ G ) @ F2 ) @ G ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % getRel_map_fn
% 0.31/0.47 thf(fact_29_getRel__hom,axiom,
% 0.31/0.47 ! [Y: product_prod_V_V,Z: product_prod_V_V,L: standard_Constant_V,G: labele236903175od_V_V,F2: product_prod_V_V > v] :
% 0.31/0.47 ( ( member134497296od_V_V @ ( produc1905750615od_V_V @ Y @ Z ) @ ( getRel1902920892od_V_V @ L @ G ) )
% 0.31/0.47 => ( ( member2015049524od_V_V @ Y @ ( labele981584981od_V_V @ G ) )
% 0.31/0.47 => ( ( member2015049524od_V_V @ Z @ ( labele981584981od_V_V @ G ) )
% 0.31/0.47 => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( F2 @ Y ) @ ( F2 @ Z ) ) @ ( getRel1432786916nt_V_V @ L @ ( map_gr875022471tant_V @ ( bNF_Gr1069958334_V_V_V @ ( labele981584981od_V_V @ G ) @ F2 ) @ G ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % getRel_hom
% 0.31/0.47 thf(fact_30_getRel__hom,axiom,
% 0.31/0.47 ! [Y: v2,Z: v2,L: standard_Constant_V,G: labele788688367nt_V_V,F2: v2 > v] :
% 0.31/0.47 ( ( member1990987792od_V_V @ ( product_Pair_V_V @ Y @ Z ) @ ( getRel632961956nt_V_V @ L @ G ) )
% 0.31/0.47 => ( ( member_V @ Y @ ( labele1152678333nt_V_V @ G ) )
% 0.31/0.47 => ( ( member_V @ Z @ ( labele1152678333nt_V_V @ G ) )
% 0.31/0.47 => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( F2 @ Y ) @ ( F2 @ Z ) ) @ ( getRel1432786916nt_V_V @ L @ ( map_gr530397039tant_V @ ( bNF_Gr_V_V @ ( labele1152678333nt_V_V @ G ) @ F2 ) @ G ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % getRel_hom
% 0.31/0.47 thf(fact_31_getRel__hom,axiom,
% 0.31/0.47 ! [Y: produc1699571228od_V_V,Z: produc1699571228od_V_V,L: standard_Constant_V,G: labele201426742od_V_V,F2: produc1699571228od_V_V > v] :
% 0.31/0.47 ( ( member785416642od_V_V @ ( produc1736057425od_V_V @ Y @ Z ) @ ( getRel2057312683od_V_V @ L @ G ) )
% 0.31/0.47 => ( ( member1010391347od_V_V @ Y @ ( labele1328382418od_V_V @ G ) )
% 0.31/0.47 => ( ( member1010391347od_V_V @ Z @ ( labele1328382418od_V_V @ G ) )
% 0.31/0.47 => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( F2 @ Y ) @ ( F2 @ Z ) ) @ ( getRel1432786916nt_V_V @ L @ ( map_gr157381846tant_V @ ( bNF_Gr480427157_V_V_V @ ( labele1328382418od_V_V @ G ) @ F2 ) @ G ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % getRel_hom
% 0.31/0.47 thf(fact_32_getRel__hom,axiom,
% 0.31/0.47 ! [Y: v,Z: v,L: standard_Constant_V,G: labele2115946735nt_V_V,F2: v > v] :
% 0.31/0.47 ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ Y @ Z ) @ ( getRel1432786916nt_V_V @ L @ G ) )
% 0.31/0.47 => ( ( member_V2 @ Y @ ( labele1134902411nt_V_V @ G ) )
% 0.31/0.47 => ( ( member_V2 @ Z @ ( labele1134902411nt_V_V @ G ) )
% 0.31/0.47 => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( F2 @ Y ) @ ( F2 @ Z ) ) @ ( getRel1432786916nt_V_V @ L @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ G ) @ F2 ) @ G ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % getRel_hom
% 0.31/0.47 thf(fact_33_Standard__Constant_Odistinct_I1_J,axiom,
% 0.31/0.47 standard_S_Top_V != standard_S_Bot_V ).
% 0.31/0.47
% 0.31/0.47 % Standard_Constant.distinct(1)
% 0.31/0.47 thf(fact_34_Standard__Constant_Odistinct_I5_J,axiom,
% 0.31/0.47 ! [X4: v2] :
% 0.31/0.47 ( standard_S_Top_V
% 0.31/0.47 != ( standard_S_Const_V @ X4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % Standard_Constant.distinct(5)
% 0.31/0.47 thf(fact_35_Standard__Constant_Odistinct_I9_J,axiom,
% 0.31/0.47 ! [X4: v2] :
% 0.31/0.47 ( standard_S_Bot_V
% 0.31/0.47 != ( standard_S_Const_V @ X4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % Standard_Constant.distinct(9)
% 0.31/0.47 thf(fact_36_getRel__dom_I1_J,axiom,
% 0.31/0.47 ! [G: labele2115946735nt_V_V,A: v,B: v,L: standard_Constant_V] :
% 0.31/0.47 ( ( G
% 0.31/0.47 = ( restri1305980611nt_V_V @ G ) )
% 0.31/0.47 => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( getRel1432786916nt_V_V @ L @ G ) )
% 0.31/0.47 => ( member_V2 @ A @ ( labele1134902411nt_V_V @ G ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % getRel_dom(1)
% 0.31/0.47 thf(fact_37_getRel__dom_I2_J,axiom,
% 0.31/0.47 ! [G: labele2115946735nt_V_V,A: v,B: v,L: standard_Constant_V] :
% 0.31/0.47 ( ( G
% 0.31/0.47 = ( restri1305980611nt_V_V @ G ) )
% 0.31/0.47 => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( getRel1432786916nt_V_V @ L @ G ) )
% 0.31/0.47 => ( member_V2 @ B @ ( labele1134902411nt_V_V @ G ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % getRel_dom(2)
% 0.31/0.47 thf(fact_38_getRel__subgraph,axiom,
% 0.31/0.47 ! [Y: v,Z: v,L: standard_Constant_V,G: labele2115946735nt_V_V,G2: labele2115946735nt_V_V] :
% 0.31/0.47 ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ Y @ Z ) @ ( getRel1432786916nt_V_V @ L @ G ) )
% 0.31/0.47 => ( ( graph_1808119_V_V_V @ G @ G2 @ ( id_on_V2 @ ( labele1134902411nt_V_V @ G ) ) )
% 0.31/0.47 => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ Y @ Z ) @ ( getRel1432786916nt_V_V @ L @ G2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % getRel_subgraph
% 0.31/0.47 thf(fact_39_old_Oprod_Oinducts,axiom,
% 0.31/0.47 ! [P2: product_prod_V_V > $o,Prod: product_prod_V_V] :
% 0.31/0.47 ( ! [A3: v,B3: v] : ( P2 @ ( product_Pair_V_V2 @ A3 @ B3 ) )
% 0.31/0.47 => ( P2 @ Prod ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.inducts
% 0.31/0.47 thf(fact_40_old_Oprod_Oinducts,axiom,
% 0.31/0.47 ! [P2: produc1699571228od_V_V > $o,Prod: produc1699571228od_V_V] :
% 0.31/0.47 ( ! [A3: standard_Constant_V,B3: product_prod_V_V] : ( P2 @ ( produc107991630od_V_V @ A3 @ B3 ) )
% 0.31/0.47 => ( P2 @ Prod ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.inducts
% 0.31/0.47 thf(fact_41_old_Oprod_Oexhaust,axiom,
% 0.31/0.47 ! [Y: product_prod_V_V] :
% 0.31/0.47 ~ ! [A3: v,B3: v] :
% 0.31/0.47 ( Y
% 0.31/0.47 != ( product_Pair_V_V2 @ A3 @ B3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.exhaust
% 0.31/0.47 thf(fact_42_old_Oprod_Oexhaust,axiom,
% 0.31/0.47 ! [Y: produc1699571228od_V_V] :
% 0.31/0.47 ~ ! [A3: standard_Constant_V,B3: product_prod_V_V] :
% 0.31/0.47 ( Y
% 0.31/0.47 != ( produc107991630od_V_V @ A3 @ B3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.prod.exhaust
% 0.31/0.47 thf(fact_43_prod__induct3,axiom,
% 0.31/0.47 ! [P2: produc1699571228od_V_V > $o,X3: produc1699571228od_V_V] :
% 0.31/0.47 ( ! [A3: standard_Constant_V,B3: v,C3: v] : ( P2 @ ( produc107991630od_V_V @ A3 @ ( product_Pair_V_V2 @ B3 @ C3 ) ) )
% 0.31/0.47 => ( P2 @ X3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod_induct3
% 0.31/0.47 thf(fact_44_prod__cases3,axiom,
% 0.31/0.47 ! [Y: produc1699571228od_V_V] :
% 0.31/0.47 ~ ! [A3: standard_Constant_V,B3: v,C3: v] :
% 0.31/0.47 ( Y
% 0.31/0.47 != ( produc107991630od_V_V @ A3 @ ( product_Pair_V_V2 @ B3 @ C3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod_cases3
% 0.31/0.47 thf(fact_45_Pair__inject,axiom,
% 0.31/0.47 ! [A: v,B: v,A2: v,B2: v] :
% 0.31/0.47 ( ( ( product_Pair_V_V2 @ A @ B )
% 0.31/0.47 = ( product_Pair_V_V2 @ A2 @ B2 ) )
% 0.31/0.47 => ~ ( ( A = A2 )
% 0.31/0.47 => ( B != B2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Pair_inject
% 0.31/0.47 thf(fact_46_Pair__inject,axiom,
% 0.31/0.47 ! [A: standard_Constant_V,B: product_prod_V_V,A2: standard_Constant_V,B2: product_prod_V_V] :
% 0.31/0.47 ( ( ( produc107991630od_V_V @ A @ B )
% 0.31/0.47 = ( produc107991630od_V_V @ A2 @ B2 ) )
% 0.31/0.47 => ~ ( ( A = A2 )
% 0.31/0.47 => ( B != B2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Pair_inject
% 0.31/0.47 thf(fact_47_prod__cases,axiom,
% 0.31/0.47 ! [P2: product_prod_V_V > $o,P: product_prod_V_V] :
% 0.31/0.47 ( ! [A3: v,B3: v] : ( P2 @ ( product_Pair_V_V2 @ A3 @ B3 ) )
% 0.31/0.47 => ( P2 @ P ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod_cases
% 0.31/0.47 thf(fact_48_prod__cases,axiom,
% 0.31/0.47 ! [P2: produc1699571228od_V_V > $o,P: produc1699571228od_V_V] :
% 0.31/0.47 ( ! [A3: standard_Constant_V,B3: product_prod_V_V] : ( P2 @ ( produc107991630od_V_V @ A3 @ B3 ) )
% 0.31/0.47 => ( P2 @ P ) ) ).
% 0.31/0.47
% 0.31/0.47 % prod_cases
% 0.31/0.47 thf(fact_49_mg,axiom,
% 0.31/0.47 ! [R: produc778275879_V_nat] :
% 0.31/0.47 ( ( mainta197426964_nat_V @ R @ g )
% 0.31/0.47 => ( mainta197426964_nat_V @ R @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % mg
% 0.31/0.47 thf(fact_50_mem__Collect__eq,axiom,
% 0.31/0.47 ! [A: product_prod_V_V,P2: product_prod_V_V > $o] :
% 0.31/0.47 ( ( member2015049524od_V_V @ A @ ( collec2040633974od_V_V @ P2 ) )
% 0.31/0.47 = ( P2 @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 % mem_Collect_eq
% 0.31/0.47 thf(fact_51_mem__Collect__eq,axiom,
% 0.31/0.47 ! [A: v,P2: v > $o] :
% 0.31/0.47 ( ( member_V2 @ A @ ( collect_V2 @ P2 ) )
% 0.31/0.47 = ( P2 @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 % mem_Collect_eq
% 0.31/0.47 thf(fact_52_mem__Collect__eq,axiom,
% 0.31/0.47 ! [A: v2,P2: v2 > $o] :
% 0.31/0.47 ( ( member_V @ A @ ( collect_V @ P2 ) )
% 0.31/0.47 = ( P2 @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 % mem_Collect_eq
% 0.31/0.47 thf(fact_53_mem__Collect__eq,axiom,
% 0.31/0.47 ! [A: produc1699571228od_V_V,P2: produc1699571228od_V_V > $o] :
% 0.31/0.47 ( ( member1010391347od_V_V @ A @ ( collec1840263537od_V_V @ P2 ) )
% 0.31/0.47 = ( P2 @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 % mem_Collect_eq
% 0.31/0.47 thf(fact_54_Collect__mem__eq,axiom,
% 0.31/0.47 ! [A4: set_Product_prod_V_V] :
% 0.31/0.47 ( ( collec2040633974od_V_V
% 0.31/0.47 @ ^ [X6: product_prod_V_V] : ( member2015049524od_V_V @ X6 @ A4 ) )
% 0.31/0.47 = A4 ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_mem_eq
% 0.31/0.47 thf(fact_55_Collect__mem__eq,axiom,
% 0.31/0.47 ! [A4: set_V] :
% 0.31/0.47 ( ( collect_V2
% 0.31/0.47 @ ^ [X6: v] : ( member_V2 @ X6 @ A4 ) )
% 0.31/0.47 = A4 ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_mem_eq
% 0.31/0.47 thf(fact_56_Collect__mem__eq,axiom,
% 0.31/0.47 ! [A4: set_V2] :
% 0.31/0.47 ( ( collect_V
% 0.31/0.47 @ ^ [X6: v2] : ( member_V @ X6 @ A4 ) )
% 0.31/0.47 = A4 ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_mem_eq
% 0.31/0.47 thf(fact_57_Collect__mem__eq,axiom,
% 0.31/0.47 ! [A4: set_Pr744279122od_V_V] :
% 0.31/0.47 ( ( collec1840263537od_V_V
% 0.31/0.47 @ ^ [X6: produc1699571228od_V_V] : ( member1010391347od_V_V @ X6 @ A4 ) )
% 0.31/0.47 = A4 ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_mem_eq
% 0.31/0.47 thf(fact_58_graph__homo,axiom,
% 0.31/0.47 ! [G: labele2115946735nt_V_V,F2: v > v] :
% 0.31/0.47 ( ( G
% 0.31/0.47 = ( restri1305980611nt_V_V @ G ) )
% 0.31/0.47 => ( graph_1808119_V_V_V @ G @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ G ) @ F2 ) @ G ) @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ G ) @ F2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % graph_homo
% 0.31/0.47 thf(fact_59_map__graph__fn__id_I2_J,axiom,
% 0.31/0.47 ! [X7: labele2115946735nt_V_V] :
% 0.31/0.47 ( ( map_gr907434255tant_V @ ( id_on_V2 @ ( labele1134902411nt_V_V @ X7 ) ) @ X7 )
% 0.31/0.47 = ( restri1305980611nt_V_V @ X7 ) ) ).
% 0.31/0.47
% 0.31/0.47 % map_graph_fn_id(2)
% 0.31/0.47 thf(fact_60_map__graph__fn__graphI,axiom,
% 0.31/0.47 ! [G: labele2115946735nt_V_V,F2: v > v] :
% 0.31/0.47 ( ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ G ) @ F2 ) @ G )
% 0.31/0.47 = ( restri1305980611nt_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ G ) @ F2 ) @ G ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % map_graph_fn_graphI
% 0.31/0.47 thf(fact_61_map__graph__preserves__subgraph,axiom,
% 0.31/0.47 ! [A4: labele2115946735nt_V_V,B4: labele2115946735nt_V_V,F2: set_Product_prod_V_V] :
% 0.31/0.47 ( ( graph_1808119_V_V_V @ A4 @ B4 @ ( id_on_V2 @ ( labele1134902411nt_V_V @ A4 ) ) )
% 0.31/0.47 => ( graph_1808119_V_V_V @ ( map_gr907434255tant_V @ F2 @ A4 ) @ ( map_gr907434255tant_V @ F2 @ B4 ) @ ( id_on_V2 @ ( labele1134902411nt_V_V @ ( map_gr907434255tant_V @ F2 @ A4 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % map_graph_preserves_subgraph
% 0.31/0.47 thf(fact_62_subgraph__refl,axiom,
% 0.31/0.47 ! [G: labele2115946735nt_V_V] :
% 0.31/0.47 ( ( graph_1808119_V_V_V @ G @ G @ ( id_on_V2 @ ( labele1134902411nt_V_V @ G ) ) )
% 0.31/0.47 = ( G
% 0.31/0.47 = ( restri1305980611nt_V_V @ G ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % subgraph_refl
% 0.31/0.47 thf(fact_63_subgraph__restrict,axiom,
% 0.31/0.47 ! [G: labele2115946735nt_V_V] :
% 0.31/0.47 ( ( graph_1808119_V_V_V @ G @ ( restri1305980611nt_V_V @ G ) @ ( id_on_V2 @ ( labele1134902411nt_V_V @ G ) ) )
% 0.31/0.47 = ( G
% 0.31/0.47 = ( restri1305980611nt_V_V @ G ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % subgraph_restrict
% 0.31/0.47 thf(fact_64_graph__homomorphism__Id,axiom,
% 0.31/0.47 ! [A: labele2115946735nt_V_V] : ( graph_1808119_V_V_V @ ( restri1305980611nt_V_V @ A ) @ ( restri1305980611nt_V_V @ A ) @ ( id_on_V2 @ ( labele1134902411nt_V_V @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % graph_homomorphism_Id
% 0.31/0.47 thf(fact_65_Id__on__empty,axiom,
% 0.31/0.47 ( ( id_on_1882925319_V_nat @ bot_bo1053950006_V_nat )
% 0.31/0.47 = bot_bo907687539_V_nat ) ).
% 0.31/0.47
% 0.31/0.47 % Id_on_empty
% 0.31/0.47 thf(fact_66_Id__on__empty,axiom,
% 0.31/0.47 ( ( id_on_2125509800od_V_V @ bot_bo1389414743od_V_V )
% 0.31/0.47 = bot_bo12878899od_V_V ) ).
% 0.31/0.47
% 0.31/0.47 % Id_on_empty
% 0.31/0.47 thf(fact_67_Id__on__empty,axiom,
% 0.31/0.47 ( ( id_on_V2 @ bot_bot_set_V2 )
% 0.31/0.47 = bot_bo1389414743od_V_V ) ).
% 0.31/0.47
% 0.31/0.47 % Id_on_empty
% 0.31/0.47 thf(fact_68_Id__on__empty,axiom,
% 0.31/0.47 ( ( id_on_558037444_V_nat @ bot_bo907687539_V_nat )
% 0.31/0.47 = bot_bo2057106227_V_nat ) ).
% 0.31/0.47
% 0.31/0.47 % Id_on_empty
% 0.31/0.47 thf(fact_69_Gr__empty,axiom,
% 0.31/0.47 ! [F2: labele2128733290_V_nat > labele2128733290_V_nat] :
% 0.31/0.47 ( ( bNF_Gr17960482_V_nat @ bot_bo1053950006_V_nat @ F2 )
% 0.31/0.47 = bot_bo907687539_V_nat ) ).
% 0.31/0.47
% 0.31/0.47 % Gr_empty
% 0.31/0.47 thf(fact_70_Gr__empty,axiom,
% 0.31/0.47 ! [F2: v > v] :
% 0.31/0.47 ( ( bNF_Gr_V_V2 @ bot_bot_set_V2 @ F2 )
% 0.31/0.47 = bot_bo1389414743od_V_V ) ).
% 0.31/0.47
% 0.31/0.47 % Gr_empty
% 0.31/0.47 thf(fact_71_restrict__idemp,axiom,
% 0.31/0.47 ! [X3: labele2115946735nt_V_V] :
% 0.31/0.47 ( ( restri1305980611nt_V_V @ ( restri1305980611nt_V_V @ X3 ) )
% 0.31/0.47 = ( restri1305980611nt_V_V @ X3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % restrict_idemp
% 0.31/0.47 thf(fact_72_in__Gr,axiom,
% 0.31/0.47 ! [X3: v,Y: v,A4: set_V,F2: v > v] :
% 0.31/0.47 ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ X3 @ Y ) @ ( bNF_Gr_V_V2 @ A4 @ F2 ) )
% 0.31/0.47 = ( ( member_V2 @ X3 @ A4 )
% 0.31/0.47 & ( ( F2 @ X3 )
% 0.31/0.47 = Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % in_Gr
% 0.31/0.47 thf(fact_73_in__Gr,axiom,
% 0.31/0.47 ! [X3: standard_Constant_V,Y: product_prod_V_V,A4: set_St1111633946tant_V,F2: standard_Constant_V > product_prod_V_V] :
% 0.31/0.47 ( ( member1010391347od_V_V @ ( produc107991630od_V_V @ X3 @ Y ) @ ( bNF_Gr320641027od_V_V @ A4 @ F2 ) )
% 0.31/0.47 = ( ( member1542015739tant_V @ X3 @ A4 )
% 0.31/0.47 & ( ( F2 @ X3 )
% 0.31/0.47 = Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % in_Gr
% 0.31/0.47 thf(fact_74_Gr__not__in,axiom,
% 0.31/0.47 ! [X3: v,F3: set_V,F2: v > v,Y: v] :
% 0.31/0.47 ( ( ~ ( member_V2 @ X3 @ F3 )
% 0.31/0.47 | ( ( F2 @ X3 )
% 0.31/0.47 != Y ) )
% 0.31/0.47 => ~ ( member2015049524od_V_V @ ( product_Pair_V_V2 @ X3 @ Y ) @ ( bNF_Gr_V_V2 @ F3 @ F2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Gr_not_in
% 0.31/0.47 thf(fact_75_Gr__not__in,axiom,
% 0.31/0.47 ! [X3: standard_Constant_V,F3: set_St1111633946tant_V,F2: standard_Constant_V > product_prod_V_V,Y: product_prod_V_V] :
% 0.31/0.47 ( ( ~ ( member1542015739tant_V @ X3 @ F3 )
% 0.31/0.47 | ( ( F2 @ X3 )
% 0.31/0.47 != Y ) )
% 0.31/0.47 => ~ ( member1010391347od_V_V @ ( produc107991630od_V_V @ X3 @ Y ) @ ( bNF_Gr320641027od_V_V @ F3 @ F2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Gr_not_in
% 0.31/0.47 thf(fact_76_Id__onI,axiom,
% 0.31/0.47 ! [A: product_prod_V_V,A4: set_Product_prod_V_V] :
% 0.31/0.47 ( ( member2015049524od_V_V @ A @ A4 )
% 0.31/0.47 => ( member134497296od_V_V @ ( produc1905750615od_V_V @ A @ A ) @ ( id_on_2125509800od_V_V @ A4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Id_onI
% 0.31/0.47 thf(fact_77_Id__onI,axiom,
% 0.31/0.47 ! [A: v2,A4: set_V2] :
% 0.31/0.47 ( ( member_V @ A @ A4 )
% 0.31/0.47 => ( member1990987792od_V_V @ ( product_Pair_V_V @ A @ A ) @ ( id_on_V @ A4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Id_onI
% 0.31/0.47 thf(fact_78_Id__onI,axiom,
% 0.31/0.47 ! [A: produc1699571228od_V_V,A4: set_Pr744279122od_V_V] :
% 0.31/0.47 ( ( member1010391347od_V_V @ A @ A4 )
% 0.31/0.47 => ( member785416642od_V_V @ ( produc1736057425od_V_V @ A @ A ) @ ( id_on_1491482303od_V_V @ A4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Id_onI
% 0.31/0.47 thf(fact_79_Id__onI,axiom,
% 0.31/0.47 ! [A: v,A4: set_V] :
% 0.31/0.47 ( ( member_V2 @ A @ A4 )
% 0.31/0.47 => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ A ) @ ( id_on_V2 @ A4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Id_onI
% 0.31/0.47 thf(fact_80_vertices__restrict,axiom,
% 0.31/0.47 ! [G: labele2115946735nt_V_V] :
% 0.31/0.47 ( ( labele1134902411nt_V_V @ ( restri1305980611nt_V_V @ G ) )
% 0.31/0.47 = ( labele1134902411nt_V_V @ G ) ) ).
% 0.31/0.47
% 0.31/0.47 % vertices_restrict
% 0.31/0.47 thf(fact_81_map__graph__preserves__restricted,axiom,
% 0.31/0.47 ! [G: labele2115946735nt_V_V,F2: set_Product_prod_V_V] :
% 0.31/0.47 ( ( G
% 0.31/0.47 = ( restri1305980611nt_V_V @ G ) )
% 0.31/0.47 => ( ( map_gr907434255tant_V @ F2 @ G )
% 0.31/0.47 = ( restri1305980611nt_V_V @ ( map_gr907434255tant_V @ F2 @ G ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % map_graph_preserves_restricted
% 0.31/0.47 thf(fact_82_map__graph__fn__comp,axiom,
% 0.31/0.47 ! [G: labele2115946735nt_V_V,F2: v > v,G3: v > v] :
% 0.31/0.47 ( ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ G ) @ ( comp_V_V_V2 @ F2 @ G3 ) ) @ G )
% 0.31/0.47 = ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ G ) @ G3 ) @ G ) ) @ F2 ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ G ) @ G3 ) @ G ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % map_graph_fn_comp
% 0.31/0.47 thf(fact_83_assms_I1_J,axiom,
% 0.31/0.47 ! [X5: produc778275879_V_nat] :
% 0.31/0.47 ( ( member1886821968_V_nat @ X5 @ ( standa157301464ules_V @ c @ l ) )
% 0.31/0.47 => ( mainta197426964_nat_V @ X5 @ g ) ) ).
% 0.31/0.47
% 0.31/0.47 % assms(1)
% 0.31/0.47 thf(fact_84_ne,axiom,
% 0.31/0.47 mainta197426964_nat_V @ standa1319953089tant_V @ g ).
% 0.31/0.47
% 0.31/0.47 % ne
% 0.31/0.47 thf(fact_85__092_060open_062maintained_Anonempty__rule_AG_H_A_061_A_Ivertices_AG_H_A_092_060noteq_062_A_123_125_J_092_060close_062,axiom,
% 0.31/0.47 ( ( mainta197426964_nat_V @ standa1319953089tant_V @ g )
% 0.31/0.47 = ( ( labele1134902411nt_V_V @ g )
% 0.31/0.47 != bot_bot_set_V2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % \<open>maintained nonempty_rule G' = (vertices G' \<noteq> {})\<close>
% 0.31/0.47 thf(fact_86_maintained__preserved__by__isomorphism,axiom,
% 0.31/0.47 ! [G: labele236903175od_V_V,F2: v > product_prod_V_V,G3: product_prod_V_V > v,R: produc778275879_V_nat] :
% 0.31/0.47 ( ! [X: product_prod_V_V] :
% 0.31/0.47 ( ( member2015049524od_V_V @ X @ ( labele981584981od_V_V @ G ) )
% 0.31/0.47 => ( ( comp_V772749048od_V_V @ F2 @ G3 @ X )
% 0.31/0.47 = X ) )
% 0.31/0.47 => ( ( G
% 0.31/0.47 = ( restri1502575645od_V_V @ G ) )
% 0.31/0.47 => ( ( mainta197426964_nat_V @ R @ ( map_gr875022471tant_V @ ( bNF_Gr1069958334_V_V_V @ ( labele981584981od_V_V @ G ) @ G3 ) @ G ) )
% 0.31/0.47 => ( mainta1984786828od_V_V @ R @ G ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % maintained_preserved_by_isomorphism
% 0.31/0.47 thf(fact_87_maintained__preserved__by__isomorphism,axiom,
% 0.31/0.47 ! [G: labele788688367nt_V_V,F2: v > v2,G3: v2 > v,R: produc778275879_V_nat] :
% 0.31/0.47 ( ! [X: v2] :
% 0.31/0.47 ( ( member_V @ X @ ( labele1152678333nt_V_V @ G ) )
% 0.31/0.47 => ( ( comp_V_V_V @ F2 @ G3 @ X )
% 0.31/0.47 = X ) )
% 0.31/0.47 => ( ( G
% 0.31/0.47 = ( restri175070597nt_V_V @ G ) )
% 0.31/0.47 => ( ( mainta197426964_nat_V @ R @ ( map_gr530397039tant_V @ ( bNF_Gr_V_V @ ( labele1152678333nt_V_V @ G ) @ G3 ) @ G ) )
% 0.31/0.47 => ( mainta1026355316_nat_V @ R @ G ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % maintained_preserved_by_isomorphism
% 0.31/0.47 thf(fact_88_maintained__preserved__by__isomorphism,axiom,
% 0.31/0.47 ! [G: labele201426742od_V_V,F2: v > produc1699571228od_V_V,G3: produc1699571228od_V_V > v,R: produc778275879_V_nat] :
% 0.31/0.47 ( ! [X: produc1699571228od_V_V] :
% 0.31/0.47 ( ( member1010391347od_V_V @ X @ ( labele1328382418od_V_V @ G ) )
% 0.31/0.47 => ( ( comp_V1480932210od_V_V @ F2 @ G3 @ X )
% 0.31/0.47 = X ) )
% 0.31/0.47 => ( ( G
% 0.31/0.47 = ( restri1699516426od_V_V @ G ) )
% 0.31/0.47 => ( ( mainta197426964_nat_V @ R @ ( map_gr157381846tant_V @ ( bNF_Gr480427157_V_V_V @ ( labele1328382418od_V_V @ G ) @ G3 ) @ G ) )
% 0.31/0.47 => ( mainta1342478555od_V_V @ R @ G ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % maintained_preserved_by_isomorphism
% 0.31/0.47 thf(fact_89_maintained__preserved__by__isomorphism,axiom,
% 0.31/0.47 ! [G: labele2115946735nt_V_V,F2: v > v,G3: v > v,R: produc778275879_V_nat] :
% 0.31/0.47 ( ! [X: v] :
% 0.31/0.47 ( ( member_V2 @ X @ ( labele1134902411nt_V_V @ G ) )
% 0.31/0.47 => ( ( comp_V_V_V2 @ F2 @ G3 @ X )
% 0.31/0.47 = X ) )
% 0.31/0.47 => ( ( G
% 0.31/0.47 = ( restri1305980611nt_V_V @ G ) )
% 0.31/0.47 => ( ( mainta197426964_nat_V @ R @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ G ) @ G3 ) @ G ) )
% 0.31/0.47 => ( mainta197426964_nat_V @ R @ G ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % maintained_preserved_by_isomorphism
% 0.31/0.47 thf(fact_90_idemp__embedding__maintained__preserved,axiom,
% 0.31/0.47 ! [G: labele2115946735nt_V_V,F2: v > v,R: produc778275879_V_nat] :
% 0.31/0.47 ( ( graph_1808119_V_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ G ) @ F2 ) @ G ) @ G @ ( id_on_V2 @ ( labele1134902411nt_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ G ) @ F2 ) @ G ) ) ) )
% 0.31/0.47 => ( ! [X: v] :
% 0.31/0.47 ( ( member_V2 @ X @ ( labele1134902411nt_V_V @ G ) )
% 0.31/0.47 => ( ( comp_V_V_V2 @ F2 @ F2 @ X )
% 0.31/0.47 = ( F2 @ X ) ) )
% 0.31/0.47 => ( ( mainta197426964_nat_V @ R @ G )
% 0.31/0.47 => ( mainta197426964_nat_V @ R @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ G ) @ F2 ) @ G ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % idemp_embedding_maintained_preserved
% 0.31/0.47 thf(fact_91_Id__onE,axiom,
% 0.31/0.47 ! [C: produc522115815od_V_V,A4: set_Product_prod_V_V] :
% 0.31/0.47 ( ( member134497296od_V_V @ C @ ( id_on_2125509800od_V_V @ A4 ) )
% 0.31/0.47 => ~ ! [X: product_prod_V_V] :
% 0.31/0.47 ( ( member2015049524od_V_V @ X @ A4 )
% 0.31/0.47 => ( C
% 0.31/0.47 != ( produc1905750615od_V_V @ X @ X ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Id_onE
% 0.31/0.47 thf(fact_92_Id__onE,axiom,
% 0.31/0.47 ! [C: product_prod_V_V2,A4: set_V2] :
% 0.31/0.47 ( ( member1990987792od_V_V @ C @ ( id_on_V @ A4 ) )
% 0.31/0.47 => ~ ! [X: v2] :
% 0.31/0.47 ( ( member_V @ X @ A4 )
% 0.31/0.47 => ( C
% 0.31/0.47 != ( product_Pair_V_V @ X @ X ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Id_onE
% 0.31/0.47 thf(fact_93_Id__onE,axiom,
% 0.31/0.47 ! [C: produc1082089497od_V_V,A4: set_Pr744279122od_V_V] :
% 0.31/0.47 ( ( member785416642od_V_V @ C @ ( id_on_1491482303od_V_V @ A4 ) )
% 0.31/0.47 => ~ ! [X: produc1699571228od_V_V] :
% 0.31/0.47 ( ( member1010391347od_V_V @ X @ A4 )
% 0.31/0.47 => ( C
% 0.31/0.47 != ( produc1736057425od_V_V @ X @ X ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Id_onE
% 0.31/0.47 thf(fact_94_Id__onE,axiom,
% 0.31/0.47 ! [C: product_prod_V_V,A4: set_V] :
% 0.31/0.47 ( ( member2015049524od_V_V @ C @ ( id_on_V2 @ A4 ) )
% 0.31/0.47 => ~ ! [X: v] :
% 0.31/0.47 ( ( member_V2 @ X @ A4 )
% 0.31/0.47 => ( C
% 0.31/0.47 != ( product_Pair_V_V2 @ X @ X ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Id_onE
% 0.31/0.47 thf(fact_95_Id__on__eqI,axiom,
% 0.31/0.47 ! [A: product_prod_V_V,B: product_prod_V_V,A4: set_Product_prod_V_V] :
% 0.31/0.47 ( ( A = B )
% 0.31/0.47 => ( ( member2015049524od_V_V @ A @ A4 )
% 0.31/0.47 => ( member134497296od_V_V @ ( produc1905750615od_V_V @ A @ B ) @ ( id_on_2125509800od_V_V @ A4 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Id_on_eqI
% 0.31/0.47 thf(fact_96_Id__on__eqI,axiom,
% 0.31/0.47 ! [A: v2,B: v2,A4: set_V2] :
% 0.31/0.47 ( ( A = B )
% 0.31/0.47 => ( ( member_V @ A @ A4 )
% 0.31/0.47 => ( member1990987792od_V_V @ ( product_Pair_V_V @ A @ B ) @ ( id_on_V @ A4 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Id_on_eqI
% 0.31/0.47 thf(fact_97_Id__on__eqI,axiom,
% 0.31/0.47 ! [A: produc1699571228od_V_V,B: produc1699571228od_V_V,A4: set_Pr744279122od_V_V] :
% 0.31/0.47 ( ( A = B )
% 0.31/0.47 => ( ( member1010391347od_V_V @ A @ A4 )
% 0.31/0.47 => ( member785416642od_V_V @ ( produc1736057425od_V_V @ A @ B ) @ ( id_on_1491482303od_V_V @ A4 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Id_on_eqI
% 0.31/0.47 thf(fact_98_Id__on__eqI,axiom,
% 0.31/0.47 ! [A: v,B: v,A4: set_V] :
% 0.31/0.47 ( ( A = B )
% 0.31/0.47 => ( ( member_V2 @ A @ A4 )
% 0.31/0.47 => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( id_on_V2 @ A4 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Id_on_eqI
% 0.31/0.47 thf(fact_99_Id__on__iff,axiom,
% 0.31/0.47 ! [X3: product_prod_V_V,Y: product_prod_V_V,A4: set_Product_prod_V_V] :
% 0.31/0.47 ( ( member134497296od_V_V @ ( produc1905750615od_V_V @ X3 @ Y ) @ ( id_on_2125509800od_V_V @ A4 ) )
% 0.31/0.47 = ( ( X3 = Y )
% 0.31/0.47 & ( member2015049524od_V_V @ X3 @ A4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Id_on_iff
% 0.31/0.47 thf(fact_100_Id__on__iff,axiom,
% 0.31/0.47 ! [X3: v2,Y: v2,A4: set_V2] :
% 0.31/0.47 ( ( member1990987792od_V_V @ ( product_Pair_V_V @ X3 @ Y ) @ ( id_on_V @ A4 ) )
% 0.31/0.47 = ( ( X3 = Y )
% 0.31/0.47 & ( member_V @ X3 @ A4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Id_on_iff
% 0.31/0.47 thf(fact_101_Id__on__iff,axiom,
% 0.31/0.47 ! [X3: produc1699571228od_V_V,Y: produc1699571228od_V_V,A4: set_Pr744279122od_V_V] :
% 0.31/0.47 ( ( member785416642od_V_V @ ( produc1736057425od_V_V @ X3 @ Y ) @ ( id_on_1491482303od_V_V @ A4 ) )
% 0.31/0.47 = ( ( X3 = Y )
% 0.31/0.47 & ( member1010391347od_V_V @ X3 @ A4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Id_on_iff
% 0.31/0.47 thf(fact_102_Id__on__iff,axiom,
% 0.31/0.47 ! [X3: v,Y: v,A4: set_V] :
% 0.31/0.47 ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ X3 @ Y ) @ ( id_on_V2 @ A4 ) )
% 0.31/0.47 = ( ( X3 = Y )
% 0.31/0.47 & ( member_V2 @ X3 @ A4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Id_on_iff
% 0.31/0.47 thf(fact_103_subgraph__preserves__hom,axiom,
% 0.31/0.47 ! [A4: labele2115946735nt_V_V,B4: labele2115946735nt_V_V,X7: labele2115946735nt_V_V,H: set_Product_prod_V_V] :
% 0.31/0.47 ( ( graph_1808119_V_V_V @ A4 @ B4 @ ( id_on_V2 @ ( labele1134902411nt_V_V @ A4 ) ) )
% 0.31/0.47 => ( ( graph_1808119_V_V_V @ X7 @ A4 @ H )
% 0.31/0.47 => ( graph_1808119_V_V_V @ X7 @ B4 @ H ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % subgraph_preserves_hom
% 0.31/0.47 thf(fact_104_subgraph__trans,axiom,
% 0.31/0.47 ! [G_1: labele2115946735nt_V_V,G_2: labele2115946735nt_V_V,G_3: labele2115946735nt_V_V] :
% 0.31/0.47 ( ( graph_1808119_V_V_V @ G_1 @ G_2 @ ( id_on_V2 @ ( labele1134902411nt_V_V @ G_1 ) ) )
% 0.31/0.47 => ( ( graph_1808119_V_V_V @ G_2 @ G_3 @ ( id_on_V2 @ ( labele1134902411nt_V_V @ G_2 ) ) )
% 0.31/0.47 => ( graph_1808119_V_V_V @ G_1 @ G_3 @ ( id_on_V2 @ ( labele1134902411nt_V_V @ G_1 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % subgraph_trans
% 0.31/0.47 thf(fact_105_map__graph__fn__eqI,axiom,
% 0.31/0.47 ! [G: labele2115946735nt_V_V,F2: v > v,G3: v > v] :
% 0.31/0.47 ( ! [X: v] :
% 0.31/0.47 ( ( member_V2 @ X @ ( labele1134902411nt_V_V @ G ) )
% 0.31/0.47 => ( ( F2 @ X )
% 0.31/0.47 = ( G3 @ X ) ) )
% 0.31/0.47 => ( ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ G ) @ F2 ) @ G )
% 0.31/0.47 = ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ G ) @ G3 ) @ G ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % map_graph_fn_eqI
% 0.31/0.47 thf(fact_106_tr,axiom,
% 0.31/0.47 mainta197426964_nat_V @ ( standa214871990tant_V @ standard_S_Top_V ) @ g ).
% 0.31/0.47
% 0.31/0.47 % tr
% 0.31/0.47 thf(fact_107_h_I4_J,axiom,
% 0.31/0.47 ! [L: standard_Constant_V,X3: v,Y: v] :
% 0.31/0.47 ( ( member1010391347od_V_V @ ( produc107991630od_V_V @ L @ ( product_Pair_V_V2 @ X3 @ Y ) ) @ ( labele515735386nt_V_V @ g ) )
% 0.31/0.47 = ( member1010391347od_V_V @ ( produc107991630od_V_V @ L @ ( product_Pair_V_V2 @ ( h @ X3 ) @ ( h @ Y ) ) ) @ ( labele515735386nt_V_V @ g ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % h(4)
% 0.31/0.47 thf(fact_108_maintained__refl,axiom,
% 0.31/0.47 ! [R2: labele2128733290_V_nat,G: labele2115946735nt_V_V] : ( mainta197426964_nat_V @ ( produc698429463_V_nat @ R2 @ R2 ) @ G ) ).
% 0.31/0.47
% 0.31/0.47 % maintained_refl
% 0.31/0.47 thf(fact_109_comp__apply,axiom,
% 0.31/0.47 ( comp_V_V_V2
% 0.31/0.47 = ( ^ [F4: v > v,G4: v > v,X6: v] : ( F4 @ ( G4 @ X6 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % comp_apply
% 0.31/0.47 thf(fact_110_empty__Collect__eq,axiom,
% 0.31/0.47 ! [P2: product_prod_V_V > $o] :
% 0.31/0.47 ( ( bot_bo1389414743od_V_V
% 0.31/0.47 = ( collec2040633974od_V_V @ P2 ) )
% 0.31/0.47 = ( ! [X6: product_prod_V_V] :
% 0.31/0.47 ~ ( P2 @ X6 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % empty_Collect_eq
% 0.31/0.47 thf(fact_111_empty__Collect__eq,axiom,
% 0.31/0.47 ! [P2: v > $o] :
% 0.31/0.47 ( ( bot_bot_set_V2
% 0.31/0.47 = ( collect_V2 @ P2 ) )
% 0.31/0.47 = ( ! [X6: v] :
% 0.31/0.47 ~ ( P2 @ X6 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % empty_Collect_eq
% 0.31/0.47 thf(fact_112_empty__Collect__eq,axiom,
% 0.31/0.47 ! [P2: produc778275879_V_nat > $o] :
% 0.31/0.47 ( ( bot_bo907687539_V_nat
% 0.31/0.47 = ( collec1411521682_V_nat @ P2 ) )
% 0.31/0.47 = ( ! [X6: produc778275879_V_nat] :
% 0.31/0.47 ~ ( P2 @ X6 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % empty_Collect_eq
% 0.31/0.47 thf(fact_113_Collect__empty__eq,axiom,
% 0.31/0.47 ! [P2: product_prod_V_V > $o] :
% 0.31/0.47 ( ( ( collec2040633974od_V_V @ P2 )
% 0.31/0.47 = bot_bo1389414743od_V_V )
% 0.31/0.47 = ( ! [X6: product_prod_V_V] :
% 0.31/0.47 ~ ( P2 @ X6 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_empty_eq
% 0.31/0.47 thf(fact_114_Collect__empty__eq,axiom,
% 0.31/0.47 ! [P2: v > $o] :
% 0.31/0.47 ( ( ( collect_V2 @ P2 )
% 0.31/0.47 = bot_bot_set_V2 )
% 0.31/0.47 = ( ! [X6: v] :
% 0.31/0.47 ~ ( P2 @ X6 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_empty_eq
% 0.31/0.47 thf(fact_115_Collect__empty__eq,axiom,
% 0.31/0.47 ! [P2: produc778275879_V_nat > $o] :
% 0.31/0.47 ( ( ( collec1411521682_V_nat @ P2 )
% 0.31/0.47 = bot_bo907687539_V_nat )
% 0.31/0.47 = ( ! [X6: produc778275879_V_nat] :
% 0.31/0.47 ~ ( P2 @ X6 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_empty_eq
% 0.31/0.47 thf(fact_116_empty__iff,axiom,
% 0.31/0.47 ! [C: v2] :
% 0.31/0.47 ~ ( member_V @ C @ bot_bot_set_V ) ).
% 0.31/0.47
% 0.31/0.47 % empty_iff
% 0.31/0.47 thf(fact_117_empty__iff,axiom,
% 0.31/0.47 ! [C: produc1699571228od_V_V] :
% 0.31/0.47 ~ ( member1010391347od_V_V @ C @ bot_bo667804902od_V_V ) ).
% 0.31/0.47
% 0.31/0.47 % empty_iff
% 0.31/0.47 thf(fact_118_empty__iff,axiom,
% 0.31/0.47 ! [C: product_prod_V_V] :
% 0.31/0.47 ~ ( member2015049524od_V_V @ C @ bot_bo1389414743od_V_V ) ).
% 0.31/0.47
% 0.31/0.47 % empty_iff
% 0.31/0.47 thf(fact_119_empty__iff,axiom,
% 0.31/0.47 ! [C: v] :
% 0.31/0.47 ~ ( member_V2 @ C @ bot_bot_set_V2 ) ).
% 0.31/0.47
% 0.31/0.47 % empty_iff
% 0.31/0.47 thf(fact_120_empty__iff,axiom,
% 0.31/0.47 ! [C: produc778275879_V_nat] :
% 0.31/0.47 ~ ( member1886821968_V_nat @ C @ bot_bo907687539_V_nat ) ).
% 0.31/0.47
% 0.31/0.47 % empty_iff
% 0.31/0.47 thf(fact_121_all__not__in__conv,axiom,
% 0.31/0.47 ! [A4: set_V2] :
% 0.31/0.47 ( ( ! [X6: v2] :
% 0.31/0.47 ~ ( member_V @ X6 @ A4 ) )
% 0.31/0.47 = ( A4 = bot_bot_set_V ) ) ).
% 0.31/0.47
% 0.31/0.47 % all_not_in_conv
% 0.31/0.47 thf(fact_122_all__not__in__conv,axiom,
% 0.31/0.47 ! [A4: set_Pr744279122od_V_V] :
% 0.31/0.47 ( ( ! [X6: produc1699571228od_V_V] :
% 0.31/0.47 ~ ( member1010391347od_V_V @ X6 @ A4 ) )
% 0.31/0.47 = ( A4 = bot_bo667804902od_V_V ) ) ).
% 0.31/0.47
% 0.31/0.47 % all_not_in_conv
% 0.31/0.47 thf(fact_123_all__not__in__conv,axiom,
% 0.31/0.47 ! [A4: set_Product_prod_V_V] :
% 0.31/0.47 ( ( ! [X6: product_prod_V_V] :
% 0.31/0.47 ~ ( member2015049524od_V_V @ X6 @ A4 ) )
% 0.31/0.47 = ( A4 = bot_bo1389414743od_V_V ) ) ).
% 0.31/0.47
% 0.31/0.47 % all_not_in_conv
% 0.31/0.47 thf(fact_124_all__not__in__conv,axiom,
% 0.31/0.47 ! [A4: set_V] :
% 0.31/0.47 ( ( ! [X6: v] :
% 0.31/0.47 ~ ( member_V2 @ X6 @ A4 ) )
% 0.31/0.47 = ( A4 = bot_bot_set_V2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % all_not_in_conv
% 0.31/0.47 thf(fact_125_all__not__in__conv,axiom,
% 0.31/0.47 ! [A4: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ( ! [X6: produc778275879_V_nat] :
% 0.31/0.47 ~ ( member1886821968_V_nat @ X6 @ A4 ) )
% 0.31/0.47 = ( A4 = bot_bo907687539_V_nat ) ) ).
% 0.31/0.47
% 0.31/0.47 % all_not_in_conv
% 0.31/0.47 thf(fact_126_nonempty__rule,axiom,
% 0.31/0.47 ! [G: labele236903175od_V_V] :
% 0.31/0.47 ( ( G
% 0.31/0.47 = ( restri1502575645od_V_V @ G ) )
% 0.31/0.47 => ( ( mainta1984786828od_V_V @ standa1319953089tant_V @ G )
% 0.31/0.47 = ( ( labele981584981od_V_V @ G )
% 0.31/0.47 != bot_bo1389414743od_V_V ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % nonempty_rule
% 0.31/0.47 thf(fact_127_nonempty__rule,axiom,
% 0.31/0.47 ! [G: labele506073123_V_nat] :
% 0.31/0.47 ( ( G
% 0.31/0.47 = ( restri1932147897_V_nat @ G ) )
% 0.31/0.47 => ( ( mainta922614952_V_nat @ standa1319953089tant_V @ G )
% 0.31/0.47 = ( ( labele1822884081_V_nat @ G )
% 0.31/0.47 != bot_bo907687539_V_nat ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % nonempty_rule
% 0.31/0.47 thf(fact_128_nonempty__rule,axiom,
% 0.31/0.47 ! [G: labele2115946735nt_V_V] :
% 0.31/0.47 ( ( G
% 0.31/0.47 = ( restri1305980611nt_V_V @ G ) )
% 0.31/0.47 => ( ( mainta197426964_nat_V @ standa1319953089tant_V @ G )
% 0.31/0.47 = ( ( labele1134902411nt_V_V @ G )
% 0.31/0.47 != bot_bot_set_V2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % nonempty_rule
% 0.31/0.47 thf(fact_129__092_060open_062maintainedA_A_Iidentity__rules_AL_J_AG_H_092_060close_062,axiom,
% 0.31/0.47 ! [X5: produc778275879_V_nat] :
% 0.31/0.47 ( ( member1886821968_V_nat @ X5 @ ( standa1568205529ules_V @ l ) )
% 0.31/0.47 => ( mainta197426964_nat_V @ X5 @ g ) ) ).
% 0.31/0.47
% 0.31/0.47 % \<open>maintainedA (identity_rules L) G'\<close>
% 0.31/0.47 thf(fact_130_labeled__graph_Oexpand,axiom,
% 0.31/0.47 ! [Labeled_graph: labele2115946735nt_V_V,Labeled_graph2: labele2115946735nt_V_V] :
% 0.31/0.47 ( ( ( ( labele515735386nt_V_V @ Labeled_graph )
% 0.31/0.47 = ( labele515735386nt_V_V @ Labeled_graph2 ) )
% 0.31/0.47 & ( ( labele1134902411nt_V_V @ Labeled_graph )
% 0.31/0.47 = ( labele1134902411nt_V_V @ Labeled_graph2 ) ) )
% 0.31/0.47 => ( Labeled_graph = Labeled_graph2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % labeled_graph.expand
% 0.31/0.47 thf(fact_131_emptyE,axiom,
% 0.31/0.47 ! [A: v2] :
% 0.31/0.47 ~ ( member_V @ A @ bot_bot_set_V ) ).
% 0.31/0.47
% 0.31/0.47 % emptyE
% 0.31/0.47 thf(fact_132_emptyE,axiom,
% 0.31/0.47 ! [A: produc1699571228od_V_V] :
% 0.31/0.47 ~ ( member1010391347od_V_V @ A @ bot_bo667804902od_V_V ) ).
% 0.31/0.47
% 0.31/0.47 % emptyE
% 0.31/0.47 thf(fact_133_emptyE,axiom,
% 0.31/0.47 ! [A: product_prod_V_V] :
% 0.31/0.47 ~ ( member2015049524od_V_V @ A @ bot_bo1389414743od_V_V ) ).
% 0.31/0.47
% 0.31/0.47 % emptyE
% 0.31/0.47 thf(fact_134_emptyE,axiom,
% 0.31/0.47 ! [A: v] :
% 0.31/0.47 ~ ( member_V2 @ A @ bot_bot_set_V2 ) ).
% 0.31/0.47
% 0.31/0.47 % emptyE
% 0.31/0.47 thf(fact_135_emptyE,axiom,
% 0.31/0.47 ! [A: produc778275879_V_nat] :
% 0.31/0.47 ~ ( member1886821968_V_nat @ A @ bot_bo907687539_V_nat ) ).
% 0.31/0.47
% 0.31/0.47 % emptyE
% 0.31/0.47 thf(fact_136_equals0D,axiom,
% 0.31/0.47 ! [A4: set_V2,A: v2] :
% 0.31/0.47 ( ( A4 = bot_bot_set_V )
% 0.31/0.47 => ~ ( member_V @ A @ A4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % equals0D
% 0.31/0.47 thf(fact_137_equals0D,axiom,
% 0.31/0.47 ! [A4: set_Pr744279122od_V_V,A: produc1699571228od_V_V] :
% 0.31/0.47 ( ( A4 = bot_bo667804902od_V_V )
% 0.31/0.47 => ~ ( member1010391347od_V_V @ A @ A4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % equals0D
% 0.31/0.47 thf(fact_138_equals0D,axiom,
% 0.31/0.47 ! [A4: set_Product_prod_V_V,A: product_prod_V_V] :
% 0.31/0.47 ( ( A4 = bot_bo1389414743od_V_V )
% 0.31/0.47 => ~ ( member2015049524od_V_V @ A @ A4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % equals0D
% 0.31/0.47 thf(fact_139_equals0D,axiom,
% 0.31/0.47 ! [A4: set_V,A: v] :
% 0.31/0.47 ( ( A4 = bot_bot_set_V2 )
% 0.31/0.47 => ~ ( member_V2 @ A @ A4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % equals0D
% 0.31/0.47 thf(fact_140_equals0D,axiom,
% 0.31/0.47 ! [A4: set_Pr1058435079_V_nat,A: produc778275879_V_nat] :
% 0.31/0.47 ( ( A4 = bot_bo907687539_V_nat )
% 0.31/0.47 => ~ ( member1886821968_V_nat @ A @ A4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % equals0D
% 0.31/0.47 thf(fact_141_equals0I,axiom,
% 0.31/0.47 ! [A4: set_V2] :
% 0.31/0.47 ( ! [Y3: v2] :
% 0.31/0.47 ~ ( member_V @ Y3 @ A4 )
% 0.31/0.47 => ( A4 = bot_bot_set_V ) ) ).
% 0.31/0.47
% 0.31/0.47 % equals0I
% 0.31/0.47 thf(fact_142_equals0I,axiom,
% 0.31/0.47 ! [A4: set_Pr744279122od_V_V] :
% 0.31/0.47 ( ! [Y3: produc1699571228od_V_V] :
% 0.31/0.47 ~ ( member1010391347od_V_V @ Y3 @ A4 )
% 0.31/0.47 => ( A4 = bot_bo667804902od_V_V ) ) ).
% 0.31/0.47
% 0.31/0.47 % equals0I
% 0.31/0.47 thf(fact_143_equals0I,axiom,
% 0.31/0.47 ! [A4: set_Product_prod_V_V] :
% 0.31/0.47 ( ! [Y3: product_prod_V_V] :
% 0.31/0.47 ~ ( member2015049524od_V_V @ Y3 @ A4 )
% 0.31/0.47 => ( A4 = bot_bo1389414743od_V_V ) ) ).
% 0.31/0.47
% 0.31/0.47 % equals0I
% 0.31/0.47 thf(fact_144_equals0I,axiom,
% 0.31/0.47 ! [A4: set_V] :
% 0.31/0.47 ( ! [Y3: v] :
% 0.31/0.47 ~ ( member_V2 @ Y3 @ A4 )
% 0.31/0.47 => ( A4 = bot_bot_set_V2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % equals0I
% 0.31/0.47 thf(fact_145_equals0I,axiom,
% 0.31/0.47 ! [A4: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ! [Y3: produc778275879_V_nat] :
% 0.31/0.47 ~ ( member1886821968_V_nat @ Y3 @ A4 )
% 0.31/0.47 => ( A4 = bot_bo907687539_V_nat ) ) ).
% 0.31/0.47
% 0.31/0.47 % equals0I
% 0.31/0.47 thf(fact_146_ex__in__conv,axiom,
% 0.31/0.47 ! [A4: set_V2] :
% 0.31/0.47 ( ( ? [X6: v2] : ( member_V @ X6 @ A4 ) )
% 0.31/0.47 = ( A4 != bot_bot_set_V ) ) ).
% 0.31/0.47
% 0.31/0.47 % ex_in_conv
% 0.31/0.47 thf(fact_147_ex__in__conv,axiom,
% 0.31/0.47 ! [A4: set_Pr744279122od_V_V] :
% 0.31/0.47 ( ( ? [X6: produc1699571228od_V_V] : ( member1010391347od_V_V @ X6 @ A4 ) )
% 0.31/0.47 = ( A4 != bot_bo667804902od_V_V ) ) ).
% 0.31/0.47
% 0.31/0.47 % ex_in_conv
% 0.31/0.47 thf(fact_148_ex__in__conv,axiom,
% 0.31/0.47 ! [A4: set_Product_prod_V_V] :
% 0.31/0.47 ( ( ? [X6: product_prod_V_V] : ( member2015049524od_V_V @ X6 @ A4 ) )
% 0.31/0.47 = ( A4 != bot_bo1389414743od_V_V ) ) ).
% 0.31/0.47
% 0.31/0.47 % ex_in_conv
% 0.31/0.47 thf(fact_149_ex__in__conv,axiom,
% 0.31/0.47 ! [A4: set_V] :
% 0.31/0.47 ( ( ? [X6: v] : ( member_V2 @ X6 @ A4 ) )
% 0.31/0.47 = ( A4 != bot_bot_set_V2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % ex_in_conv
% 0.31/0.47 thf(fact_150_ex__in__conv,axiom,
% 0.31/0.47 ! [A4: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ( ? [X6: produc778275879_V_nat] : ( member1886821968_V_nat @ X6 @ A4 ) )
% 0.31/0.47 = ( A4 != bot_bo907687539_V_nat ) ) ).
% 0.31/0.47
% 0.31/0.47 % ex_in_conv
% 0.31/0.47 thf(fact_151_comp__def,axiom,
% 0.31/0.47 ( comp_V_V_V2
% 0.31/0.47 = ( ^ [F4: v > v,G4: v > v,X6: v] : ( F4 @ ( G4 @ X6 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % comp_def
% 0.31/0.47 thf(fact_152_comp__assoc,axiom,
% 0.31/0.47 ! [F2: v > v,G3: v > v,H: v > v] :
% 0.31/0.47 ( ( comp_V_V_V2 @ ( comp_V_V_V2 @ F2 @ G3 ) @ H )
% 0.31/0.47 = ( comp_V_V_V2 @ F2 @ ( comp_V_V_V2 @ G3 @ H ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % comp_assoc
% 0.31/0.47 thf(fact_153_comp__eq__dest,axiom,
% 0.31/0.47 ! [A: v > v,B: v > v,C: v > v,D: v > v,V2: v] :
% 0.31/0.47 ( ( ( comp_V_V_V2 @ A @ B )
% 0.31/0.47 = ( comp_V_V_V2 @ C @ D ) )
% 0.31/0.47 => ( ( A @ ( B @ V2 ) )
% 0.31/0.47 = ( C @ ( D @ V2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % comp_eq_dest
% 0.31/0.47 thf(fact_154_comp__eq__elim,axiom,
% 0.31/0.47 ! [A: v > v,B: v > v,C: v > v,D: v > v] :
% 0.31/0.47 ( ( ( comp_V_V_V2 @ A @ B )
% 0.31/0.47 = ( comp_V_V_V2 @ C @ D ) )
% 0.31/0.47 => ! [V3: v] :
% 0.31/0.47 ( ( A @ ( B @ V3 ) )
% 0.31/0.47 = ( C @ ( D @ V3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % comp_eq_elim
% 0.31/0.47 thf(fact_155_comp__eq__dest__lhs,axiom,
% 0.31/0.47 ! [A: v > v,B: v > v,C: v > v,V2: v] :
% 0.31/0.47 ( ( ( comp_V_V_V2 @ A @ B )
% 0.31/0.47 = C )
% 0.31/0.47 => ( ( A @ ( B @ V2 ) )
% 0.31/0.47 = ( C @ V2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % comp_eq_dest_lhs
% 0.31/0.47 thf(fact_156_edge__preserving__on__graphI,axiom,
% 0.31/0.47 ! [X7: labele236903175od_V_V,F2: product_prod_V_V > v,Y5: set_Pr744279122od_V_V] :
% 0.31/0.47 ( ! [L2: standard_Constant_V,X: product_prod_V_V,Y3: product_prod_V_V] :
% 0.31/0.47 ( ( member361435663od_V_V @ ( produc1482441770od_V_V @ L2 @ ( produc1905750615od_V_V @ X @ Y3 ) ) @ ( labele668941254od_V_V @ X7 ) )
% 0.31/0.47 => ( ( member2015049524od_V_V @ X @ ( labele981584981od_V_V @ X7 ) )
% 0.31/0.47 => ( ( member2015049524od_V_V @ Y3 @ ( labele981584981od_V_V @ X7 ) )
% 0.31/0.47 => ( member1010391347od_V_V @ ( produc107991630od_V_V @ L2 @ ( product_Pair_V_V2 @ ( F2 @ X ) @ ( F2 @ Y3 ) ) ) @ Y5 ) ) ) )
% 0.31/0.47 => ( edge_p1776314003tant_V @ ( bNF_Gr1069958334_V_V_V @ ( labele981584981od_V_V @ X7 ) @ F2 ) @ ( labele668941254od_V_V @ X7 ) @ Y5 ) ) ).
% 0.31/0.47
% 0.31/0.47 % edge_preserving_on_graphI
% 0.31/0.47 thf(fact_157_edge__preserving__on__graphI,axiom,
% 0.31/0.47 ! [X7: labele788688367nt_V_V,F2: v2 > v,Y5: set_Pr744279122od_V_V] :
% 0.31/0.47 ( ! [L2: standard_Constant_V,X: v2,Y3: v2] :
% 0.31/0.47 ( ( member1416643087od_V_V @ ( produc1171747370od_V_V @ L2 @ ( product_Pair_V_V @ X @ Y3 ) ) @ ( labele1469545390nt_V_V @ X7 ) )
% 0.31/0.47 => ( ( member_V @ X @ ( labele1152678333nt_V_V @ X7 ) )
% 0.31/0.47 => ( ( member_V @ Y3 @ ( labele1152678333nt_V_V @ X7 ) )
% 0.31/0.47 => ( member1010391347od_V_V @ ( produc107991630od_V_V @ L2 @ ( product_Pair_V_V2 @ ( F2 @ X ) @ ( F2 @ Y3 ) ) ) @ Y5 ) ) ) )
% 0.31/0.47 => ( edge_p1322161019tant_V @ ( bNF_Gr_V_V @ ( labele1152678333nt_V_V @ X7 ) @ F2 ) @ ( labele1469545390nt_V_V @ X7 ) @ Y5 ) ) ).
% 0.31/0.47
% 0.31/0.47 % edge_preserving_on_graphI
% 0.31/0.47 thf(fact_158_edge__preserving__on__graphI,axiom,
% 0.31/0.47 ! [X7: labele201426742od_V_V,F2: produc1699571228od_V_V > v,Y5: set_Pr744279122od_V_V] :
% 0.31/0.47 ( ! [L2: standard_Constant_V,X: produc1699571228od_V_V,Y3: produc1699571228od_V_V] :
% 0.31/0.47 ( ( member600445121od_V_V @ ( produc2132932316od_V_V @ L2 @ ( produc1736057425od_V_V @ X @ Y3 ) ) @ ( labele1794513953od_V_V @ X7 ) )
% 0.31/0.47 => ( ( member1010391347od_V_V @ X @ ( labele1328382418od_V_V @ X7 ) )
% 0.31/0.47 => ( ( member1010391347od_V_V @ Y3 @ ( labele1328382418od_V_V @ X7 ) )
% 0.31/0.47 => ( member1010391347od_V_V @ ( produc107991630od_V_V @ L2 @ ( product_Pair_V_V2 @ ( F2 @ X ) @ ( F2 @ Y3 ) ) ) @ Y5 ) ) ) )
% 0.31/0.47 => ( edge_p669293514tant_V @ ( bNF_Gr480427157_V_V_V @ ( labele1328382418od_V_V @ X7 ) @ F2 ) @ ( labele1794513953od_V_V @ X7 ) @ Y5 ) ) ).
% 0.31/0.47
% 0.31/0.47 % edge_preserving_on_graphI
% 0.31/0.47 thf(fact_159_edge__preserving__on__graphI,axiom,
% 0.31/0.47 ! [X7: labele2115946735nt_V_V,F2: v > v,Y5: set_Pr744279122od_V_V] :
% 0.31/0.47 ( ! [L2: standard_Constant_V,X: v,Y3: v] :
% 0.31/0.47 ( ( member1010391347od_V_V @ ( produc107991630od_V_V @ L2 @ ( product_Pair_V_V2 @ X @ Y3 ) ) @ ( labele515735386nt_V_V @ X7 ) )
% 0.31/0.47 => ( ( member_V2 @ X @ ( labele1134902411nt_V_V @ X7 ) )
% 0.31/0.47 => ( ( member_V2 @ Y3 @ ( labele1134902411nt_V_V @ X7 ) )
% 0.31/0.47 => ( member1010391347od_V_V @ ( produc107991630od_V_V @ L2 @ ( product_Pair_V_V2 @ ( F2 @ X ) @ ( F2 @ Y3 ) ) ) @ Y5 ) ) ) )
% 0.31/0.47 => ( edge_p1560004099tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ X7 ) @ F2 ) @ ( labele515735386nt_V_V @ X7 ) @ Y5 ) ) ).
% 0.31/0.47
% 0.31/0.47 % edge_preserving_on_graphI
% 0.31/0.47 thf(fact_160_GrD2,axiom,
% 0.31/0.47 ! [X3: v,Fx: v,A4: set_V,F2: v > v] :
% 0.31/0.47 ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ X3 @ Fx ) @ ( bNF_Gr_V_V2 @ A4 @ F2 ) )
% 0.31/0.47 => ( ( F2 @ X3 )
% 0.31/0.47 = Fx ) ) ).
% 0.31/0.47
% 0.31/0.47 % GrD2
% 0.31/0.47 thf(fact_161_GrD2,axiom,
% 0.31/0.47 ! [X3: standard_Constant_V,Fx: product_prod_V_V,A4: set_St1111633946tant_V,F2: standard_Constant_V > product_prod_V_V] :
% 0.31/0.47 ( ( member1010391347od_V_V @ ( produc107991630od_V_V @ X3 @ Fx ) @ ( bNF_Gr320641027od_V_V @ A4 @ F2 ) )
% 0.31/0.47 => ( ( F2 @ X3 )
% 0.31/0.47 = Fx ) ) ).
% 0.31/0.47
% 0.31/0.47 % GrD2
% 0.31/0.47 thf(fact_162_GrD1,axiom,
% 0.31/0.47 ! [X3: v,Fx: v,A4: set_V,F2: v > v] :
% 0.31/0.47 ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ X3 @ Fx ) @ ( bNF_Gr_V_V2 @ A4 @ F2 ) )
% 0.31/0.47 => ( member_V2 @ X3 @ A4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % GrD1
% 0.31/0.47 thf(fact_163_GrD1,axiom,
% 0.31/0.47 ! [X3: standard_Constant_V,Fx: product_prod_V_V,A4: set_St1111633946tant_V,F2: standard_Constant_V > product_prod_V_V] :
% 0.31/0.47 ( ( member1010391347od_V_V @ ( produc107991630od_V_V @ X3 @ Fx ) @ ( bNF_Gr320641027od_V_V @ A4 @ F2 ) )
% 0.31/0.47 => ( member1542015739tant_V @ X3 @ A4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % GrD1
% 0.31/0.47 thf(fact_164_map__graph__edge__preserving,axiom,
% 0.31/0.47 ! [F2: set_Product_prod_V_V,G: labele2115946735nt_V_V] : ( edge_p1560004099tant_V @ F2 @ ( labele515735386nt_V_V @ G ) @ ( labele515735386nt_V_V @ ( map_gr907434255tant_V @ F2 @ G ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % map_graph_edge_preserving
% 0.31/0.47 thf(fact_165_bot__empty__eq,axiom,
% 0.31/0.47 ( bot_bot_V_o
% 0.31/0.47 = ( ^ [X6: v2] : ( member_V @ X6 @ bot_bot_set_V ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % bot_empty_eq
% 0.31/0.47 thf(fact_166_bot__empty__eq,axiom,
% 0.31/0.47 ( bot_bo2024487199_V_V_o
% 0.31/0.47 = ( ^ [X6: produc1699571228od_V_V] : ( member1010391347od_V_V @ X6 @ bot_bo667804902od_V_V ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % bot_empty_eq
% 0.31/0.47 thf(fact_167_bot__empty__eq,axiom,
% 0.31/0.47 ( bot_bo1168561222_V_V_o
% 0.31/0.47 = ( ^ [X6: product_prod_V_V] : ( member2015049524od_V_V @ X6 @ bot_bo1389414743od_V_V ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % bot_empty_eq
% 0.31/0.47 thf(fact_168_bot__empty__eq,axiom,
% 0.31/0.47 ( bot_bot_V_o2
% 0.31/0.47 = ( ^ [X6: v] : ( member_V2 @ X6 @ bot_bot_set_V2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % bot_empty_eq
% 0.31/0.47 thf(fact_169_bot__empty__eq,axiom,
% 0.31/0.47 ( bot_bo1078500394_nat_o
% 0.31/0.47 = ( ^ [X6: produc778275879_V_nat] : ( member1886821968_V_nat @ X6 @ bot_bo907687539_V_nat ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % bot_empty_eq
% 0.31/0.47 thf(fact_170_bot__set__def,axiom,
% 0.31/0.47 ( bot_bo1389414743od_V_V
% 0.31/0.47 = ( collec2040633974od_V_V @ bot_bo1168561222_V_V_o ) ) ).
% 0.31/0.47
% 0.31/0.47 % bot_set_def
% 0.31/0.47 thf(fact_171_bot__set__def,axiom,
% 0.31/0.47 ( bot_bot_set_V2
% 0.31/0.47 = ( collect_V2 @ bot_bot_V_o2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % bot_set_def
% 0.31/0.47 thf(fact_172_bot__set__def,axiom,
% 0.31/0.47 ( bot_bo907687539_V_nat
% 0.31/0.47 = ( collec1411521682_V_nat @ bot_bo1078500394_nat_o ) ) ).
% 0.31/0.47
% 0.31/0.47 % bot_set_def
% 0.31/0.47 thf(fact_173_consequence__graphD_I1_J,axiom,
% 0.31/0.47 ! [Rs: set_Pr1058435079_V_nat,G: labele2115946735nt_V_V,R2: produc778275879_V_nat] :
% 0.31/0.47 ( ( conseq1236301781_nat_V @ Rs @ G )
% 0.31/0.47 => ( ( member1886821968_V_nat @ R2 @ Rs )
% 0.31/0.47 => ( mainta197426964_nat_V @ R2 @ G ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % consequence_graphD(1)
% 0.31/0.47 thf(fact_174_edge__preserving__atomic,axiom,
% 0.31/0.47 ! [H1: set_Product_prod_V_V,E1: set_Pr744279122od_V_V,E2: set_Pr744279122od_V_V,V1: v,V12: v,V22: v,V23: v,K: standard_Constant_V] :
% 0.31/0.47 ( ( edge_p1560004099tant_V @ H1 @ E1 @ E2 )
% 0.31/0.47 => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ V1 @ V12 ) @ H1 )
% 0.31/0.47 => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ V22 @ V23 ) @ H1 )
% 0.31/0.47 => ( ( member1010391347od_V_V @ ( produc107991630od_V_V @ K @ ( product_Pair_V_V2 @ V1 @ V22 ) ) @ E1 )
% 0.31/0.47 => ( member1010391347od_V_V @ ( produc107991630od_V_V @ K @ ( product_Pair_V_V2 @ V12 @ V23 ) ) @ E2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % edge_preserving_atomic
% 0.31/0.47 thf(fact_175_mnt,axiom,
% 0.31/0.47 ! [X5: produc778275879_V_nat] :
% 0.31/0.47 ( ( member1886821968_V_nat @ X5 @ ( sup_su1043134939_V_nat @ ( sup_su1043134939_V_nat @ ( standa1897115807ules_V @ c ) @ ( standa1568205529ules_V @ l ) ) @ ( insert481364471_V_nat @ ( standa214871990tant_V @ standard_S_Top_V ) @ ( insert481364471_V_nat @ standa1319953089tant_V @ bot_bo907687539_V_nat ) ) ) )
% 0.31/0.47 => ( mainta197426964_nat_V @ X5 @ g ) ) ).
% 0.31/0.47
% 0.31/0.47 % mnt
% 0.31/0.47 thf(fact_176_map__graph__in,axiom,
% 0.31/0.47 ! [G: labele2115946735nt_V_V,A: v,B: v,E: allego859987871tant_V,F2: v > v] :
% 0.31/0.47 ( ( G
% 0.31/0.47 = ( restri1305980611nt_V_V @ G ) )
% 0.31/0.47 => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( semant993842370nt_V_V @ G @ E ) )
% 0.31/0.47 => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( F2 @ A ) @ ( F2 @ B ) ) @ ( semant993842370nt_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ G ) @ F2 ) @ G ) @ E ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % map_graph_in
% 0.31/0.47 thf(fact_177_maintainedI,axiom,
% 0.31/0.47 ! [A4: labele2128733290_V_nat,G: labele2115946735nt_V_V,B4: labele2128733290_V_nat] :
% 0.31/0.47 ( ! [F: set_Pr53436518_nat_V] :
% 0.31/0.47 ( ( graph_1541575154_nat_V @ A4 @ G @ F )
% 0.31/0.47 => ( extens1072773157_nat_V @ ( produc698429463_V_nat @ A4 @ B4 ) @ G @ F ) )
% 0.31/0.47 => ( mainta197426964_nat_V @ ( produc698429463_V_nat @ A4 @ B4 ) @ G ) ) ).
% 0.31/0.47
% 0.31/0.47 % maintainedI
% 0.31/0.47 thf(fact_178_maintainedI,axiom,
% 0.31/0.47 ! [A4: labele2115946735nt_V_V,G: labele2115946735nt_V_V,B4: labele2115946735nt_V_V] :
% 0.31/0.47 ( ! [F: set_Product_prod_V_V] :
% 0.31/0.47 ( ( graph_1808119_V_V_V @ A4 @ G @ F )
% 0.31/0.47 => ( extens1533825066_V_V_V @ ( produc533118295nt_V_V @ A4 @ B4 ) @ G @ F ) )
% 0.31/0.47 => ( mainta1699210777_V_V_V @ ( produc533118295nt_V_V @ A4 @ B4 ) @ G ) ) ).
% 0.31/0.47
% 0.31/0.47 % maintainedI
% 0.31/0.47 thf(fact_179_graph__homomorphism__empty,axiom,
% 0.31/0.47 ! [G: labele2115946735nt_V_V,F2: set_Pr1228022213_V_V_V] :
% 0.31/0.47 ( ( graph_840721237_V_V_V @ ( labele94156371od_V_V @ bot_bo451843010od_V_V @ bot_bo1389414743od_V_V ) @ G @ F2 )
% 0.31/0.47 = ( ( F2 = bot_bo688400985_V_V_V )
% 0.31/0.47 & ( G
% 0.31/0.47 = ( restri1305980611nt_V_V @ G ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % graph_homomorphism_empty
% 0.31/0.47 thf(fact_180_graph__homomorphism__empty,axiom,
% 0.31/0.47 ! [G: labele2115946735nt_V_V,F2: set_Pr1056235617_nat_V] :
% 0.31/0.47 ( ( graph_227683057_nat_V @ ( labele1193521135_V_nat @ bot_bo634818242_V_nat @ bot_bo907687539_V_nat ) @ G @ F2 )
% 0.31/0.47 = ( ( F2 = bot_bo1708783349_nat_V )
% 0.31/0.47 & ( G
% 0.31/0.47 = ( restri1305980611nt_V_V @ G ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % graph_homomorphism_empty
% 0.31/0.47 thf(fact_181_graph__homomorphism__empty,axiom,
% 0.31/0.47 ! [G: labele2115946735nt_V_V,F2: set_Product_prod_V_V] :
% 0.31/0.47 ( ( graph_1808119_V_V_V @ ( labele712009229nt_V_V @ bot_bo667804902od_V_V @ bot_bot_set_V2 ) @ G @ F2 )
% 0.31/0.47 = ( ( F2 = bot_bo1389414743od_V_V )
% 0.31/0.47 & ( G
% 0.31/0.47 = ( restri1305980611nt_V_V @ G ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % graph_homomorphism_empty
% 0.31/0.47 thf(fact_182_subgraph__def,axiom,
% 0.31/0.47 ! [G_1: labele2115946735nt_V_V,G_2: labele2115946735nt_V_V] :
% 0.31/0.47 ( ( graph_1808119_V_V_V @ G_1 @ G_2 @ ( id_on_V2 @ ( labele1134902411nt_V_V @ G_1 ) ) )
% 0.31/0.47 = ( ( G_1
% 0.31/0.47 = ( restri1305980611nt_V_V @ G_1 ) )
% 0.31/0.47 & ( G_2
% 0.31/0.47 = ( restri1305980611nt_V_V @ G_2 ) )
% 0.31/0.47 & ( ( graph_1141886696nt_V_V @ G_1 @ G_2 )
% 0.31/0.47 = G_2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % subgraph_def
% 0.31/0.47 thf(fact_183_insert__absorb2,axiom,
% 0.31/0.47 ! [X3: produc778275879_V_nat,A4: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ( insert481364471_V_nat @ X3 @ ( insert481364471_V_nat @ X3 @ A4 ) )
% 0.31/0.47 = ( insert481364471_V_nat @ X3 @ A4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_absorb2
% 0.31/0.47 thf(fact_184_insert__iff,axiom,
% 0.31/0.47 ! [A: produc778275879_V_nat,B: produc778275879_V_nat,A4: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ( member1886821968_V_nat @ A @ ( insert481364471_V_nat @ B @ A4 ) )
% 0.31/0.47 = ( ( A = B )
% 0.31/0.47 | ( member1886821968_V_nat @ A @ A4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_iff
% 0.31/0.47 thf(fact_185_insert__iff,axiom,
% 0.31/0.47 ! [A: product_prod_V_V,B: product_prod_V_V,A4: set_Product_prod_V_V] :
% 0.31/0.47 ( ( member2015049524od_V_V @ A @ ( insert2024285275od_V_V @ B @ A4 ) )
% 0.31/0.47 = ( ( A = B )
% 0.31/0.47 | ( member2015049524od_V_V @ A @ A4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_iff
% 0.31/0.47 thf(fact_186_insert__iff,axiom,
% 0.31/0.47 ! [A: v,B: v,A4: set_V] :
% 0.31/0.47 ( ( member_V2 @ A @ ( insert_V2 @ B @ A4 ) )
% 0.31/0.47 = ( ( A = B )
% 0.31/0.47 | ( member_V2 @ A @ A4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_iff
% 0.31/0.47 thf(fact_187_insert__iff,axiom,
% 0.31/0.47 ! [A: v2,B: v2,A4: set_V2] :
% 0.31/0.47 ( ( member_V @ A @ ( insert_V @ B @ A4 ) )
% 0.31/0.47 = ( ( A = B )
% 0.31/0.47 | ( member_V @ A @ A4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_iff
% 0.31/0.47 thf(fact_188_insert__iff,axiom,
% 0.31/0.47 ! [A: produc1699571228od_V_V,B: produc1699571228od_V_V,A4: set_Pr744279122od_V_V] :
% 0.31/0.47 ( ( member1010391347od_V_V @ A @ ( insert135842892od_V_V @ B @ A4 ) )
% 0.31/0.47 = ( ( A = B )
% 0.31/0.47 | ( member1010391347od_V_V @ A @ A4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_iff
% 0.31/0.47 thf(fact_189_insertCI,axiom,
% 0.31/0.47 ! [A: produc778275879_V_nat,B4: set_Pr1058435079_V_nat,B: produc778275879_V_nat] :
% 0.31/0.47 ( ( ~ ( member1886821968_V_nat @ A @ B4 )
% 0.31/0.47 => ( A = B ) )
% 0.31/0.47 => ( member1886821968_V_nat @ A @ ( insert481364471_V_nat @ B @ B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertCI
% 0.31/0.47 thf(fact_190_insertCI,axiom,
% 0.31/0.47 ! [A: product_prod_V_V,B4: set_Product_prod_V_V,B: product_prod_V_V] :
% 0.31/0.47 ( ( ~ ( member2015049524od_V_V @ A @ B4 )
% 0.31/0.47 => ( A = B ) )
% 0.31/0.47 => ( member2015049524od_V_V @ A @ ( insert2024285275od_V_V @ B @ B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertCI
% 0.31/0.47 thf(fact_191_insertCI,axiom,
% 0.31/0.47 ! [A: v,B4: set_V,B: v] :
% 0.31/0.47 ( ( ~ ( member_V2 @ A @ B4 )
% 0.31/0.47 => ( A = B ) )
% 0.31/0.47 => ( member_V2 @ A @ ( insert_V2 @ B @ B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertCI
% 0.31/0.47 thf(fact_192_insertCI,axiom,
% 0.31/0.47 ! [A: v2,B4: set_V2,B: v2] :
% 0.31/0.47 ( ( ~ ( member_V @ A @ B4 )
% 0.31/0.47 => ( A = B ) )
% 0.31/0.47 => ( member_V @ A @ ( insert_V @ B @ B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertCI
% 0.31/0.47 thf(fact_193_insertCI,axiom,
% 0.31/0.47 ! [A: produc1699571228od_V_V,B4: set_Pr744279122od_V_V,B: produc1699571228od_V_V] :
% 0.31/0.47 ( ( ~ ( member1010391347od_V_V @ A @ B4 )
% 0.31/0.47 => ( A = B ) )
% 0.31/0.47 => ( member1010391347od_V_V @ A @ ( insert135842892od_V_V @ B @ B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertCI
% 0.31/0.47 thf(fact_194_Un__iff,axiom,
% 0.31/0.47 ! [C: product_prod_V_V,A4: set_Product_prod_V_V,B4: set_Product_prod_V_V] :
% 0.31/0.47 ( ( member2015049524od_V_V @ C @ ( sup_su551882943od_V_V @ A4 @ B4 ) )
% 0.31/0.47 = ( ( member2015049524od_V_V @ C @ A4 )
% 0.31/0.47 | ( member2015049524od_V_V @ C @ B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_iff
% 0.31/0.47 thf(fact_195_Un__iff,axiom,
% 0.31/0.47 ! [C: v,A4: set_V,B4: set_V] :
% 0.31/0.47 ( ( member_V2 @ C @ ( sup_sup_set_V2 @ A4 @ B4 ) )
% 0.31/0.47 = ( ( member_V2 @ C @ A4 )
% 0.31/0.47 | ( member_V2 @ C @ B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_iff
% 0.31/0.47 thf(fact_196_Un__iff,axiom,
% 0.31/0.47 ! [C: v2,A4: set_V2,B4: set_V2] :
% 0.31/0.47 ( ( member_V @ C @ ( sup_sup_set_V @ A4 @ B4 ) )
% 0.31/0.47 = ( ( member_V @ C @ A4 )
% 0.31/0.47 | ( member_V @ C @ B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_iff
% 0.31/0.47 thf(fact_197_Un__iff,axiom,
% 0.31/0.47 ! [C: produc1699571228od_V_V,A4: set_Pr744279122od_V_V,B4: set_Pr744279122od_V_V] :
% 0.31/0.47 ( ( member1010391347od_V_V @ C @ ( sup_su693515134od_V_V @ A4 @ B4 ) )
% 0.31/0.47 = ( ( member1010391347od_V_V @ C @ A4 )
% 0.31/0.47 | ( member1010391347od_V_V @ C @ B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_iff
% 0.31/0.47 thf(fact_198_Un__iff,axiom,
% 0.31/0.47 ! [C: produc778275879_V_nat,A4: set_Pr1058435079_V_nat,B4: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ( member1886821968_V_nat @ C @ ( sup_su1043134939_V_nat @ A4 @ B4 ) )
% 0.31/0.47 = ( ( member1886821968_V_nat @ C @ A4 )
% 0.31/0.47 | ( member1886821968_V_nat @ C @ B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_iff
% 0.31/0.47 thf(fact_199_UnCI,axiom,
% 0.31/0.47 ! [C: product_prod_V_V,B4: set_Product_prod_V_V,A4: set_Product_prod_V_V] :
% 0.31/0.47 ( ( ~ ( member2015049524od_V_V @ C @ B4 )
% 0.31/0.47 => ( member2015049524od_V_V @ C @ A4 ) )
% 0.31/0.47 => ( member2015049524od_V_V @ C @ ( sup_su551882943od_V_V @ A4 @ B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnCI
% 0.31/0.47 thf(fact_200_UnCI,axiom,
% 0.31/0.47 ! [C: v,B4: set_V,A4: set_V] :
% 0.31/0.47 ( ( ~ ( member_V2 @ C @ B4 )
% 0.31/0.47 => ( member_V2 @ C @ A4 ) )
% 0.31/0.47 => ( member_V2 @ C @ ( sup_sup_set_V2 @ A4 @ B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnCI
% 0.31/0.47 thf(fact_201_UnCI,axiom,
% 0.31/0.47 ! [C: v2,B4: set_V2,A4: set_V2] :
% 0.31/0.47 ( ( ~ ( member_V @ C @ B4 )
% 0.31/0.47 => ( member_V @ C @ A4 ) )
% 0.31/0.47 => ( member_V @ C @ ( sup_sup_set_V @ A4 @ B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnCI
% 0.31/0.47 thf(fact_202_UnCI,axiom,
% 0.31/0.47 ! [C: produc1699571228od_V_V,B4: set_Pr744279122od_V_V,A4: set_Pr744279122od_V_V] :
% 0.31/0.47 ( ( ~ ( member1010391347od_V_V @ C @ B4 )
% 0.31/0.47 => ( member1010391347od_V_V @ C @ A4 ) )
% 0.31/0.47 => ( member1010391347od_V_V @ C @ ( sup_su693515134od_V_V @ A4 @ B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnCI
% 0.31/0.47 thf(fact_203_UnCI,axiom,
% 0.31/0.47 ! [C: produc778275879_V_nat,B4: set_Pr1058435079_V_nat,A4: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ( ~ ( member1886821968_V_nat @ C @ B4 )
% 0.31/0.47 => ( member1886821968_V_nat @ C @ A4 ) )
% 0.31/0.47 => ( member1886821968_V_nat @ C @ ( sup_su1043134939_V_nat @ A4 @ B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnCI
% 0.31/0.47 thf(fact_204_singletonI,axiom,
% 0.31/0.47 ! [A: v2] : ( member_V @ A @ ( insert_V @ A @ bot_bot_set_V ) ) ).
% 0.31/0.47
% 0.31/0.47 % singletonI
% 0.31/0.47 thf(fact_205_singletonI,axiom,
% 0.31/0.47 ! [A: produc1699571228od_V_V] : ( member1010391347od_V_V @ A @ ( insert135842892od_V_V @ A @ bot_bo667804902od_V_V ) ) ).
% 0.31/0.47
% 0.31/0.47 % singletonI
% 0.31/0.47 thf(fact_206_singletonI,axiom,
% 0.31/0.47 ! [A: product_prod_V_V] : ( member2015049524od_V_V @ A @ ( insert2024285275od_V_V @ A @ bot_bo1389414743od_V_V ) ) ).
% 0.31/0.47
% 0.31/0.47 % singletonI
% 0.31/0.47 thf(fact_207_singletonI,axiom,
% 0.31/0.47 ! [A: v] : ( member_V2 @ A @ ( insert_V2 @ A @ bot_bot_set_V2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % singletonI
% 0.31/0.47 thf(fact_208_singletonI,axiom,
% 0.31/0.47 ! [A: produc778275879_V_nat] : ( member1886821968_V_nat @ A @ ( insert481364471_V_nat @ A @ bot_bo907687539_V_nat ) ) ).
% 0.31/0.47
% 0.31/0.47 % singletonI
% 0.31/0.47 thf(fact_209_Un__empty,axiom,
% 0.31/0.47 ! [A4: set_Product_prod_V_V,B4: set_Product_prod_V_V] :
% 0.31/0.47 ( ( ( sup_su551882943od_V_V @ A4 @ B4 )
% 0.31/0.47 = bot_bo1389414743od_V_V )
% 0.31/0.47 = ( ( A4 = bot_bo1389414743od_V_V )
% 0.31/0.47 & ( B4 = bot_bo1389414743od_V_V ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_empty
% 0.31/0.47 thf(fact_210_Un__empty,axiom,
% 0.31/0.47 ! [A4: set_V,B4: set_V] :
% 0.31/0.47 ( ( ( sup_sup_set_V2 @ A4 @ B4 )
% 0.31/0.47 = bot_bot_set_V2 )
% 0.31/0.47 = ( ( A4 = bot_bot_set_V2 )
% 0.31/0.47 & ( B4 = bot_bot_set_V2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_empty
% 0.31/0.47 thf(fact_211_Un__empty,axiom,
% 0.31/0.47 ! [A4: set_Pr1058435079_V_nat,B4: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ( ( sup_su1043134939_V_nat @ A4 @ B4 )
% 0.31/0.47 = bot_bo907687539_V_nat )
% 0.31/0.47 = ( ( A4 = bot_bo907687539_V_nat )
% 0.31/0.47 & ( B4 = bot_bo907687539_V_nat ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_empty
% 0.31/0.47 thf(fact_212_Un__insert__right,axiom,
% 0.31/0.47 ! [A4: set_Pr1058435079_V_nat,A: produc778275879_V_nat,B4: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ( sup_su1043134939_V_nat @ A4 @ ( insert481364471_V_nat @ A @ B4 ) )
% 0.31/0.47 = ( insert481364471_V_nat @ A @ ( sup_su1043134939_V_nat @ A4 @ B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_insert_right
% 0.31/0.47 thf(fact_213_Un__insert__left,axiom,
% 0.31/0.47 ! [A: produc778275879_V_nat,B4: set_Pr1058435079_V_nat,C4: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ( sup_su1043134939_V_nat @ ( insert481364471_V_nat @ A @ B4 ) @ C4 )
% 0.31/0.47 = ( insert481364471_V_nat @ A @ ( sup_su1043134939_V_nat @ B4 @ C4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_insert_left
% 0.31/0.47 thf(fact_214_graph__union__preserves__restrict,axiom,
% 0.31/0.47 ! [G_1: labele2115946735nt_V_V,G_2: labele2115946735nt_V_V] :
% 0.31/0.47 ( ( G_1
% 0.31/0.47 = ( restri1305980611nt_V_V @ G_1 ) )
% 0.31/0.47 => ( ( G_2
% 0.31/0.47 = ( restri1305980611nt_V_V @ G_2 ) )
% 0.31/0.47 => ( ( graph_1141886696nt_V_V @ G_1 @ G_2 )
% 0.31/0.47 = ( restri1305980611nt_V_V @ ( graph_1141886696nt_V_V @ G_1 @ G_2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % graph_union_preserves_restrict
% 0.31/0.47 thf(fact_215_graph__union__vertices,axiom,
% 0.31/0.47 ! [G_1: labele2115946735nt_V_V,G_2: labele2115946735nt_V_V] :
% 0.31/0.47 ( ( labele1134902411nt_V_V @ ( graph_1141886696nt_V_V @ G_1 @ G_2 ) )
% 0.31/0.47 = ( sup_sup_set_V2 @ ( labele1134902411nt_V_V @ G_1 ) @ ( labele1134902411nt_V_V @ G_2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % graph_union_vertices
% 0.31/0.47 thf(fact_216_labeled__graph_Ocollapse,axiom,
% 0.31/0.47 ! [Labeled_graph: labele2115946735nt_V_V] :
% 0.31/0.47 ( ( labele712009229nt_V_V @ ( labele515735386nt_V_V @ Labeled_graph ) @ ( labele1134902411nt_V_V @ Labeled_graph ) )
% 0.31/0.47 = Labeled_graph ) ).
% 0.31/0.47
% 0.31/0.47 % labeled_graph.collapse
% 0.31/0.47 thf(fact_217_extensible__refl,axiom,
% 0.31/0.47 ! [R2: labele2115946735nt_V_V,G: labele2115946735nt_V_V,F2: set_Product_prod_V_V] :
% 0.31/0.47 ( ( graph_1808119_V_V_V @ R2 @ G @ F2 )
% 0.31/0.47 => ( extens1533825066_V_V_V @ ( produc533118295nt_V_V @ R2 @ R2 ) @ G @ F2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % extensible_refl
% 0.31/0.47 thf(fact_218_graph__empty__e,axiom,
% 0.31/0.47 ! [V2: set_V] :
% 0.31/0.47 ( ( labele712009229nt_V_V @ bot_bo667804902od_V_V @ V2 )
% 0.31/0.47 = ( restri1305980611nt_V_V @ ( labele712009229nt_V_V @ bot_bo667804902od_V_V @ V2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % graph_empty_e
% 0.31/0.47 thf(fact_219_constant__rules__empty,axiom,
% 0.31/0.47 ( ( standa1571708471od_V_V @ bot_bo1389414743od_V_V )
% 0.31/0.47 = bot_bo1196823539_V_nat ) ).
% 0.31/0.47
% 0.31/0.47 % constant_rules_empty
% 0.31/0.47 thf(fact_220_constant__rules__empty,axiom,
% 0.31/0.47 ( ( standa294833961ules_V @ bot_bot_set_V2 )
% 0.31/0.47 = bot_bo1834032757_V_nat ) ).
% 0.31/0.47
% 0.31/0.47 % constant_rules_empty
% 0.31/0.47 thf(fact_221_constant__rules__empty,axiom,
% 0.31/0.47 ( ( standa434642387_V_nat @ bot_bo907687539_V_nat )
% 0.31/0.47 = bot_bo323535987at_nat ) ).
% 0.31/0.47
% 0.31/0.47 % constant_rules_empty
% 0.31/0.47 thf(fact_222_constant__rules__empty,axiom,
% 0.31/0.47 ( ( standa1897115807ules_V @ bot_bot_set_V )
% 0.31/0.47 = bot_bo907687539_V_nat ) ).
% 0.31/0.47
% 0.31/0.47 % constant_rules_empty
% 0.31/0.47 thf(fact_223_Gr__insert,axiom,
% 0.31/0.47 ! [X3: labele2128733290_V_nat,F3: set_la14611914_V_nat,F2: labele2128733290_V_nat > labele2128733290_V_nat] :
% 0.31/0.47 ( ( bNF_Gr17960482_V_nat @ ( insert213439034_V_nat @ X3 @ F3 ) @ F2 )
% 0.31/0.47 = ( insert481364471_V_nat @ ( produc698429463_V_nat @ X3 @ ( F2 @ X3 ) ) @ ( bNF_Gr17960482_V_nat @ F3 @ F2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Gr_insert
% 0.31/0.47 thf(fact_224_Gr__insert,axiom,
% 0.31/0.47 ! [X3: v,F3: set_V,F2: v > v] :
% 0.31/0.47 ( ( bNF_Gr_V_V2 @ ( insert_V2 @ X3 @ F3 ) @ F2 )
% 0.31/0.47 = ( insert2024285275od_V_V @ ( product_Pair_V_V2 @ X3 @ ( F2 @ X3 ) ) @ ( bNF_Gr_V_V2 @ F3 @ F2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Gr_insert
% 0.31/0.47 thf(fact_225_Gr__insert,axiom,
% 0.31/0.47 ! [X3: standard_Constant_V,F3: set_St1111633946tant_V,F2: standard_Constant_V > product_prod_V_V] :
% 0.31/0.47 ( ( bNF_Gr320641027od_V_V @ ( insert1818834324tant_V @ X3 @ F3 ) @ F2 )
% 0.31/0.47 = ( insert135842892od_V_V @ ( produc107991630od_V_V @ X3 @ ( F2 @ X3 ) ) @ ( bNF_Gr320641027od_V_V @ F3 @ F2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Gr_insert
% 0.31/0.47 thf(fact_226_extensible__refl__concr,axiom,
% 0.31/0.47 ! [E_1: set_Pr744279122od_V_V,V2: set_V,G: labele2115946735nt_V_V,F2: set_Product_prod_V_V,E_2: set_Pr744279122od_V_V] :
% 0.31/0.47 ( ( graph_1808119_V_V_V @ ( labele712009229nt_V_V @ E_1 @ V2 ) @ G @ F2 )
% 0.31/0.47 => ( ( extens1533825066_V_V_V @ ( produc533118295nt_V_V @ ( labele712009229nt_V_V @ E_1 @ V2 ) @ ( labele712009229nt_V_V @ E_2 @ V2 ) ) @ G @ F2 )
% 0.31/0.47 = ( graph_1808119_V_V_V @ ( labele712009229nt_V_V @ E_2 @ V2 ) @ G @ F2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % extensible_refl_concr
% 0.31/0.47 thf(fact_227_graph__single,axiom,
% 0.31/0.47 ! [A: standard_Constant_V,B: v,C: v] :
% 0.31/0.47 ( ( labele712009229nt_V_V @ ( insert135842892od_V_V @ ( produc107991630od_V_V @ A @ ( product_Pair_V_V2 @ B @ C ) ) @ bot_bo667804902od_V_V ) @ ( insert_V2 @ B @ ( insert_V2 @ C @ bot_bot_set_V2 ) ) )
% 0.31/0.47 = ( restri1305980611nt_V_V @ ( labele712009229nt_V_V @ ( insert135842892od_V_V @ ( produc107991630od_V_V @ A @ ( product_Pair_V_V2 @ B @ C ) ) @ bot_bo667804902od_V_V ) @ ( insert_V2 @ B @ ( insert_V2 @ C @ bot_bot_set_V2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % graph_single
% 0.31/0.47 thf(fact_228_insert__is__Un,axiom,
% 0.31/0.47 ( insert2024285275od_V_V
% 0.31/0.47 = ( ^ [A5: product_prod_V_V] : ( sup_su551882943od_V_V @ ( insert2024285275od_V_V @ A5 @ bot_bo1389414743od_V_V ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_is_Un
% 0.31/0.47 thf(fact_229_insert__is__Un,axiom,
% 0.31/0.47 ( insert_V2
% 0.31/0.47 = ( ^ [A5: v] : ( sup_sup_set_V2 @ ( insert_V2 @ A5 @ bot_bot_set_V2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_is_Un
% 0.31/0.47 thf(fact_230_insert__is__Un,axiom,
% 0.31/0.47 ( insert481364471_V_nat
% 0.31/0.47 = ( ^ [A5: produc778275879_V_nat] : ( sup_su1043134939_V_nat @ ( insert481364471_V_nat @ A5 @ bot_bo907687539_V_nat ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_is_Un
% 0.31/0.47 thf(fact_231_Un__singleton__iff,axiom,
% 0.31/0.47 ! [A4: set_Product_prod_V_V,B4: set_Product_prod_V_V,X3: product_prod_V_V] :
% 0.31/0.47 ( ( ( sup_su551882943od_V_V @ A4 @ B4 )
% 0.31/0.47 = ( insert2024285275od_V_V @ X3 @ bot_bo1389414743od_V_V ) )
% 0.31/0.47 = ( ( ( A4 = bot_bo1389414743od_V_V )
% 0.31/0.47 & ( B4
% 0.31/0.47 = ( insert2024285275od_V_V @ X3 @ bot_bo1389414743od_V_V ) ) )
% 0.31/0.47 | ( ( A4
% 0.31/0.47 = ( insert2024285275od_V_V @ X3 @ bot_bo1389414743od_V_V ) )
% 0.31/0.47 & ( B4 = bot_bo1389414743od_V_V ) )
% 0.31/0.47 | ( ( A4
% 0.31/0.47 = ( insert2024285275od_V_V @ X3 @ bot_bo1389414743od_V_V ) )
% 0.31/0.47 & ( B4
% 0.31/0.47 = ( insert2024285275od_V_V @ X3 @ bot_bo1389414743od_V_V ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_singleton_iff
% 0.31/0.47 thf(fact_232_Un__singleton__iff,axiom,
% 0.31/0.47 ! [A4: set_V,B4: set_V,X3: v] :
% 0.31/0.47 ( ( ( sup_sup_set_V2 @ A4 @ B4 )
% 0.31/0.47 = ( insert_V2 @ X3 @ bot_bot_set_V2 ) )
% 0.31/0.47 = ( ( ( A4 = bot_bot_set_V2 )
% 0.31/0.47 & ( B4
% 0.31/0.47 = ( insert_V2 @ X3 @ bot_bot_set_V2 ) ) )
% 0.31/0.47 | ( ( A4
% 0.31/0.47 = ( insert_V2 @ X3 @ bot_bot_set_V2 ) )
% 0.31/0.47 & ( B4 = bot_bot_set_V2 ) )
% 0.31/0.47 | ( ( A4
% 0.31/0.47 = ( insert_V2 @ X3 @ bot_bot_set_V2 ) )
% 0.31/0.47 & ( B4
% 0.31/0.47 = ( insert_V2 @ X3 @ bot_bot_set_V2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_singleton_iff
% 0.31/0.47 thf(fact_233_Un__singleton__iff,axiom,
% 0.31/0.47 ! [A4: set_Pr1058435079_V_nat,B4: set_Pr1058435079_V_nat,X3: produc778275879_V_nat] :
% 0.31/0.47 ( ( ( sup_su1043134939_V_nat @ A4 @ B4 )
% 0.31/0.47 = ( insert481364471_V_nat @ X3 @ bot_bo907687539_V_nat ) )
% 0.31/0.47 = ( ( ( A4 = bot_bo907687539_V_nat )
% 0.31/0.47 & ( B4
% 0.31/0.47 = ( insert481364471_V_nat @ X3 @ bot_bo907687539_V_nat ) ) )
% 0.31/0.47 | ( ( A4
% 0.31/0.47 = ( insert481364471_V_nat @ X3 @ bot_bo907687539_V_nat ) )
% 0.31/0.47 & ( B4 = bot_bo907687539_V_nat ) )
% 0.31/0.47 | ( ( A4
% 0.31/0.47 = ( insert481364471_V_nat @ X3 @ bot_bo907687539_V_nat ) )
% 0.31/0.47 & ( B4
% 0.31/0.47 = ( insert481364471_V_nat @ X3 @ bot_bo907687539_V_nat ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_singleton_iff
% 0.31/0.47 thf(fact_234_singleton__Un__iff,axiom,
% 0.31/0.47 ! [X3: product_prod_V_V,A4: set_Product_prod_V_V,B4: set_Product_prod_V_V] :
% 0.31/0.47 ( ( ( insert2024285275od_V_V @ X3 @ bot_bo1389414743od_V_V )
% 0.31/0.47 = ( sup_su551882943od_V_V @ A4 @ B4 ) )
% 0.31/0.47 = ( ( ( A4 = bot_bo1389414743od_V_V )
% 0.31/0.47 & ( B4
% 0.31/0.47 = ( insert2024285275od_V_V @ X3 @ bot_bo1389414743od_V_V ) ) )
% 0.31/0.47 | ( ( A4
% 0.31/0.47 = ( insert2024285275od_V_V @ X3 @ bot_bo1389414743od_V_V ) )
% 0.31/0.47 & ( B4 = bot_bo1389414743od_V_V ) )
% 0.31/0.47 | ( ( A4
% 0.31/0.47 = ( insert2024285275od_V_V @ X3 @ bot_bo1389414743od_V_V ) )
% 0.31/0.47 & ( B4
% 0.31/0.47 = ( insert2024285275od_V_V @ X3 @ bot_bo1389414743od_V_V ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % singleton_Un_iff
% 0.31/0.47 thf(fact_235_singleton__Un__iff,axiom,
% 0.31/0.47 ! [X3: v,A4: set_V,B4: set_V] :
% 0.31/0.47 ( ( ( insert_V2 @ X3 @ bot_bot_set_V2 )
% 0.31/0.47 = ( sup_sup_set_V2 @ A4 @ B4 ) )
% 0.31/0.47 = ( ( ( A4 = bot_bot_set_V2 )
% 0.31/0.47 & ( B4
% 0.31/0.47 = ( insert_V2 @ X3 @ bot_bot_set_V2 ) ) )
% 0.31/0.47 | ( ( A4
% 0.31/0.47 = ( insert_V2 @ X3 @ bot_bot_set_V2 ) )
% 0.31/0.47 & ( B4 = bot_bot_set_V2 ) )
% 0.31/0.47 | ( ( A4
% 0.31/0.47 = ( insert_V2 @ X3 @ bot_bot_set_V2 ) )
% 0.31/0.47 & ( B4
% 0.31/0.47 = ( insert_V2 @ X3 @ bot_bot_set_V2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % singleton_Un_iff
% 0.31/0.47 thf(fact_236_singleton__Un__iff,axiom,
% 0.31/0.47 ! [X3: produc778275879_V_nat,A4: set_Pr1058435079_V_nat,B4: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ( ( insert481364471_V_nat @ X3 @ bot_bo907687539_V_nat )
% 0.31/0.47 = ( sup_su1043134939_V_nat @ A4 @ B4 ) )
% 0.31/0.47 = ( ( ( A4 = bot_bo907687539_V_nat )
% 0.31/0.47 & ( B4
% 0.31/0.47 = ( insert481364471_V_nat @ X3 @ bot_bo907687539_V_nat ) ) )
% 0.31/0.47 | ( ( A4
% 0.31/0.47 = ( insert481364471_V_nat @ X3 @ bot_bo907687539_V_nat ) )
% 0.31/0.47 & ( B4 = bot_bo907687539_V_nat ) )
% 0.31/0.47 | ( ( A4
% 0.31/0.47 = ( insert481364471_V_nat @ X3 @ bot_bo907687539_V_nat ) )
% 0.31/0.47 & ( B4
% 0.31/0.47 = ( insert481364471_V_nat @ X3 @ bot_bo907687539_V_nat ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % singleton_Un_iff
% 0.31/0.47 thf(fact_237_graph__union__def,axiom,
% 0.31/0.47 ( graph_1141886696nt_V_V
% 0.31/0.47 = ( ^ [G_12: labele2115946735nt_V_V,G_22: labele2115946735nt_V_V] : ( labele712009229nt_V_V @ ( sup_su693515134od_V_V @ ( labele515735386nt_V_V @ G_12 ) @ ( labele515735386nt_V_V @ G_22 ) ) @ ( sup_sup_set_V2 @ ( labele1134902411nt_V_V @ G_12 ) @ ( labele1134902411nt_V_V @ G_22 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % graph_union_def
% 0.31/0.47 thf(fact_238_Un__empty__left,axiom,
% 0.31/0.47 ! [B4: set_Product_prod_V_V] :
% 0.31/0.47 ( ( sup_su551882943od_V_V @ bot_bo1389414743od_V_V @ B4 )
% 0.31/0.47 = B4 ) ).
% 0.31/0.47
% 0.31/0.47 % Un_empty_left
% 0.31/0.47 thf(fact_239_Un__empty__left,axiom,
% 0.31/0.47 ! [B4: set_V] :
% 0.31/0.47 ( ( sup_sup_set_V2 @ bot_bot_set_V2 @ B4 )
% 0.31/0.47 = B4 ) ).
% 0.31/0.47
% 0.31/0.47 % Un_empty_left
% 0.31/0.47 thf(fact_240_Un__empty__left,axiom,
% 0.31/0.47 ! [B4: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ( sup_su1043134939_V_nat @ bot_bo907687539_V_nat @ B4 )
% 0.31/0.47 = B4 ) ).
% 0.31/0.47
% 0.31/0.47 % Un_empty_left
% 0.31/0.47 thf(fact_241_Un__empty__right,axiom,
% 0.31/0.47 ! [A4: set_Product_prod_V_V] :
% 0.31/0.47 ( ( sup_su551882943od_V_V @ A4 @ bot_bo1389414743od_V_V )
% 0.31/0.47 = A4 ) ).
% 0.31/0.47
% 0.31/0.47 % Un_empty_right
% 0.31/0.47 thf(fact_242_Un__empty__right,axiom,
% 0.31/0.47 ! [A4: set_V] :
% 0.31/0.47 ( ( sup_sup_set_V2 @ A4 @ bot_bot_set_V2 )
% 0.31/0.47 = A4 ) ).
% 0.31/0.47
% 0.31/0.47 % Un_empty_right
% 0.31/0.47 thf(fact_243_Un__empty__right,axiom,
% 0.31/0.47 ! [A4: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ( sup_su1043134939_V_nat @ A4 @ bot_bo907687539_V_nat )
% 0.31/0.47 = A4 ) ).
% 0.31/0.47
% 0.31/0.47 % Un_empty_right
% 0.31/0.47 thf(fact_244_singletonD,axiom,
% 0.31/0.47 ! [B: v2,A: v2] :
% 0.31/0.47 ( ( member_V @ B @ ( insert_V @ A @ bot_bot_set_V ) )
% 0.31/0.47 => ( B = A ) ) ).
% 0.31/0.47
% 0.31/0.47 % singletonD
% 0.31/0.47 thf(fact_245_singletonD,axiom,
% 0.31/0.47 ! [B: produc1699571228od_V_V,A: produc1699571228od_V_V] :
% 0.31/0.47 ( ( member1010391347od_V_V @ B @ ( insert135842892od_V_V @ A @ bot_bo667804902od_V_V ) )
% 0.31/0.47 => ( B = A ) ) ).
% 0.31/0.47
% 0.31/0.47 % singletonD
% 0.31/0.47 thf(fact_246_singletonD,axiom,
% 0.31/0.47 ! [B: product_prod_V_V,A: product_prod_V_V] :
% 0.31/0.47 ( ( member2015049524od_V_V @ B @ ( insert2024285275od_V_V @ A @ bot_bo1389414743od_V_V ) )
% 0.31/0.47 => ( B = A ) ) ).
% 0.31/0.47
% 0.31/0.47 % singletonD
% 0.31/0.47 thf(fact_247_singletonD,axiom,
% 0.31/0.47 ! [B: v,A: v] :
% 0.31/0.47 ( ( member_V2 @ B @ ( insert_V2 @ A @ bot_bot_set_V2 ) )
% 0.31/0.47 => ( B = A ) ) ).
% 0.31/0.47
% 0.31/0.47 % singletonD
% 0.31/0.47 thf(fact_248_singletonD,axiom,
% 0.31/0.47 ! [B: produc778275879_V_nat,A: produc778275879_V_nat] :
% 0.31/0.47 ( ( member1886821968_V_nat @ B @ ( insert481364471_V_nat @ A @ bot_bo907687539_V_nat ) )
% 0.31/0.47 => ( B = A ) ) ).
% 0.31/0.47
% 0.31/0.47 % singletonD
% 0.31/0.47 thf(fact_249_singleton__iff,axiom,
% 0.31/0.47 ! [B: v2,A: v2] :
% 0.31/0.47 ( ( member_V @ B @ ( insert_V @ A @ bot_bot_set_V ) )
% 0.31/0.47 = ( B = A ) ) ).
% 0.31/0.47
% 0.31/0.47 % singleton_iff
% 0.31/0.47 thf(fact_250_singleton__iff,axiom,
% 0.31/0.47 ! [B: produc1699571228od_V_V,A: produc1699571228od_V_V] :
% 0.31/0.47 ( ( member1010391347od_V_V @ B @ ( insert135842892od_V_V @ A @ bot_bo667804902od_V_V ) )
% 0.31/0.47 = ( B = A ) ) ).
% 0.31/0.47
% 0.31/0.47 % singleton_iff
% 0.31/0.47 thf(fact_251_singleton__iff,axiom,
% 0.31/0.47 ! [B: product_prod_V_V,A: product_prod_V_V] :
% 0.31/0.47 ( ( member2015049524od_V_V @ B @ ( insert2024285275od_V_V @ A @ bot_bo1389414743od_V_V ) )
% 0.31/0.47 = ( B = A ) ) ).
% 0.31/0.47
% 0.31/0.47 % singleton_iff
% 0.31/0.47 thf(fact_252_singleton__iff,axiom,
% 0.31/0.47 ! [B: v,A: v] :
% 0.31/0.47 ( ( member_V2 @ B @ ( insert_V2 @ A @ bot_bot_set_V2 ) )
% 0.31/0.47 = ( B = A ) ) ).
% 0.31/0.47
% 0.31/0.47 % singleton_iff
% 0.31/0.47 thf(fact_253_singleton__iff,axiom,
% 0.31/0.47 ! [B: produc778275879_V_nat,A: produc778275879_V_nat] :
% 0.31/0.47 ( ( member1886821968_V_nat @ B @ ( insert481364471_V_nat @ A @ bot_bo907687539_V_nat ) )
% 0.31/0.47 = ( B = A ) ) ).
% 0.31/0.47
% 0.31/0.47 % singleton_iff
% 0.31/0.47 thf(fact_254_doubleton__eq__iff,axiom,
% 0.31/0.47 ! [A: product_prod_V_V,B: product_prod_V_V,C: product_prod_V_V,D: product_prod_V_V] :
% 0.31/0.47 ( ( ( insert2024285275od_V_V @ A @ ( insert2024285275od_V_V @ B @ bot_bo1389414743od_V_V ) )
% 0.31/0.47 = ( insert2024285275od_V_V @ C @ ( insert2024285275od_V_V @ D @ bot_bo1389414743od_V_V ) ) )
% 0.31/0.47 = ( ( ( A = C )
% 0.31/0.47 & ( B = D ) )
% 0.31/0.47 | ( ( A = D )
% 0.31/0.47 & ( B = C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % doubleton_eq_iff
% 0.31/0.47 thf(fact_255_doubleton__eq__iff,axiom,
% 0.31/0.47 ! [A: v,B: v,C: v,D: v] :
% 0.31/0.47 ( ( ( insert_V2 @ A @ ( insert_V2 @ B @ bot_bot_set_V2 ) )
% 0.31/0.47 = ( insert_V2 @ C @ ( insert_V2 @ D @ bot_bot_set_V2 ) ) )
% 0.31/0.47 = ( ( ( A = C )
% 0.31/0.47 & ( B = D ) )
% 0.31/0.47 | ( ( A = D )
% 0.31/0.47 & ( B = C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % doubleton_eq_iff
% 0.31/0.47 thf(fact_256_doubleton__eq__iff,axiom,
% 0.31/0.47 ! [A: produc778275879_V_nat,B: produc778275879_V_nat,C: produc778275879_V_nat,D: produc778275879_V_nat] :
% 0.31/0.47 ( ( ( insert481364471_V_nat @ A @ ( insert481364471_V_nat @ B @ bot_bo907687539_V_nat ) )
% 0.31/0.47 = ( insert481364471_V_nat @ C @ ( insert481364471_V_nat @ D @ bot_bo907687539_V_nat ) ) )
% 0.31/0.47 = ( ( ( A = C )
% 0.31/0.47 & ( B = D ) )
% 0.31/0.47 | ( ( A = D )
% 0.31/0.47 & ( B = C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % doubleton_eq_iff
% 0.31/0.47 thf(fact_257_insert__not__empty,axiom,
% 0.31/0.47 ! [A: product_prod_V_V,A4: set_Product_prod_V_V] :
% 0.31/0.47 ( ( insert2024285275od_V_V @ A @ A4 )
% 0.31/0.47 != bot_bo1389414743od_V_V ) ).
% 0.31/0.47
% 0.31/0.47 % insert_not_empty
% 0.31/0.47 thf(fact_258_insert__not__empty,axiom,
% 0.31/0.47 ! [A: v,A4: set_V] :
% 0.31/0.47 ( ( insert_V2 @ A @ A4 )
% 0.31/0.47 != bot_bot_set_V2 ) ).
% 0.31/0.47
% 0.31/0.47 % insert_not_empty
% 0.31/0.47 thf(fact_259_insert__not__empty,axiom,
% 0.31/0.47 ! [A: produc778275879_V_nat,A4: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ( insert481364471_V_nat @ A @ A4 )
% 0.31/0.47 != bot_bo907687539_V_nat ) ).
% 0.31/0.47
% 0.31/0.47 % insert_not_empty
% 0.31/0.47 thf(fact_260_singleton__inject,axiom,
% 0.31/0.47 ! [A: product_prod_V_V,B: product_prod_V_V] :
% 0.31/0.47 ( ( ( insert2024285275od_V_V @ A @ bot_bo1389414743od_V_V )
% 0.31/0.47 = ( insert2024285275od_V_V @ B @ bot_bo1389414743od_V_V ) )
% 0.31/0.47 => ( A = B ) ) ).
% 0.31/0.47
% 0.31/0.47 % singleton_inject
% 0.31/0.47 thf(fact_261_singleton__inject,axiom,
% 0.31/0.47 ! [A: v,B: v] :
% 0.31/0.47 ( ( ( insert_V2 @ A @ bot_bot_set_V2 )
% 0.31/0.47 = ( insert_V2 @ B @ bot_bot_set_V2 ) )
% 0.31/0.47 => ( A = B ) ) ).
% 0.31/0.47
% 0.31/0.47 % singleton_inject
% 0.31/0.47 thf(fact_262_singleton__inject,axiom,
% 0.31/0.47 ! [A: produc778275879_V_nat,B: produc778275879_V_nat] :
% 0.31/0.47 ( ( ( insert481364471_V_nat @ A @ bot_bo907687539_V_nat )
% 0.31/0.47 = ( insert481364471_V_nat @ B @ bot_bo907687539_V_nat ) )
% 0.31/0.47 => ( A = B ) ) ).
% 0.31/0.47
% 0.31/0.47 % singleton_inject
% 0.31/0.47 thf(fact_263_mk__disjoint__insert,axiom,
% 0.31/0.47 ! [A: produc778275879_V_nat,A4: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ( member1886821968_V_nat @ A @ A4 )
% 0.31/0.47 => ? [B5: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ( A4
% 0.31/0.47 = ( insert481364471_V_nat @ A @ B5 ) )
% 0.31/0.47 & ~ ( member1886821968_V_nat @ A @ B5 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % mk_disjoint_insert
% 0.31/0.47 thf(fact_264_mk__disjoint__insert,axiom,
% 0.31/0.47 ! [A: product_prod_V_V,A4: set_Product_prod_V_V] :
% 0.31/0.47 ( ( member2015049524od_V_V @ A @ A4 )
% 0.31/0.47 => ? [B5: set_Product_prod_V_V] :
% 0.31/0.47 ( ( A4
% 0.31/0.47 = ( insert2024285275od_V_V @ A @ B5 ) )
% 0.31/0.47 & ~ ( member2015049524od_V_V @ A @ B5 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % mk_disjoint_insert
% 0.31/0.47 thf(fact_265_mk__disjoint__insert,axiom,
% 0.31/0.47 ! [A: v,A4: set_V] :
% 0.31/0.47 ( ( member_V2 @ A @ A4 )
% 0.31/0.47 => ? [B5: set_V] :
% 0.31/0.47 ( ( A4
% 0.31/0.47 = ( insert_V2 @ A @ B5 ) )
% 0.31/0.47 & ~ ( member_V2 @ A @ B5 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % mk_disjoint_insert
% 0.31/0.47 thf(fact_266_mk__disjoint__insert,axiom,
% 0.31/0.47 ! [A: v2,A4: set_V2] :
% 0.31/0.47 ( ( member_V @ A @ A4 )
% 0.31/0.47 => ? [B5: set_V2] :
% 0.31/0.47 ( ( A4
% 0.31/0.47 = ( insert_V @ A @ B5 ) )
% 0.31/0.47 & ~ ( member_V @ A @ B5 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % mk_disjoint_insert
% 0.31/0.47 thf(fact_267_mk__disjoint__insert,axiom,
% 0.31/0.47 ! [A: produc1699571228od_V_V,A4: set_Pr744279122od_V_V] :
% 0.31/0.47 ( ( member1010391347od_V_V @ A @ A4 )
% 0.31/0.47 => ? [B5: set_Pr744279122od_V_V] :
% 0.31/0.47 ( ( A4
% 0.31/0.47 = ( insert135842892od_V_V @ A @ B5 ) )
% 0.31/0.47 & ~ ( member1010391347od_V_V @ A @ B5 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % mk_disjoint_insert
% 0.31/0.47 thf(fact_268_Un__left__commute,axiom,
% 0.31/0.47 ! [A4: set_Pr1058435079_V_nat,B4: set_Pr1058435079_V_nat,C4: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ( sup_su1043134939_V_nat @ A4 @ ( sup_su1043134939_V_nat @ B4 @ C4 ) )
% 0.31/0.47 = ( sup_su1043134939_V_nat @ B4 @ ( sup_su1043134939_V_nat @ A4 @ C4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_left_commute
% 0.31/0.47 thf(fact_269_insert__commute,axiom,
% 0.31/0.47 ! [X3: produc778275879_V_nat,Y: produc778275879_V_nat,A4: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ( insert481364471_V_nat @ X3 @ ( insert481364471_V_nat @ Y @ A4 ) )
% 0.31/0.47 = ( insert481364471_V_nat @ Y @ ( insert481364471_V_nat @ X3 @ A4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_commute
% 0.31/0.47 thf(fact_270_Un__left__absorb,axiom,
% 0.31/0.47 ! [A4: set_Pr1058435079_V_nat,B4: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ( sup_su1043134939_V_nat @ A4 @ ( sup_su1043134939_V_nat @ A4 @ B4 ) )
% 0.31/0.47 = ( sup_su1043134939_V_nat @ A4 @ B4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_left_absorb
% 0.31/0.47 thf(fact_271_insert__eq__iff,axiom,
% 0.31/0.47 ! [A: produc778275879_V_nat,A4: set_Pr1058435079_V_nat,B: produc778275879_V_nat,B4: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ~ ( member1886821968_V_nat @ A @ A4 )
% 0.31/0.47 => ( ~ ( member1886821968_V_nat @ B @ B4 )
% 0.31/0.47 => ( ( ( insert481364471_V_nat @ A @ A4 )
% 0.31/0.47 = ( insert481364471_V_nat @ B @ B4 ) )
% 0.31/0.47 = ( ( ( A = B )
% 0.31/0.47 => ( A4 = B4 ) )
% 0.31/0.47 & ( ( A != B )
% 0.31/0.47 => ? [C5: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ( A4
% 0.31/0.47 = ( insert481364471_V_nat @ B @ C5 ) )
% 0.31/0.47 & ~ ( member1886821968_V_nat @ B @ C5 )
% 0.31/0.47 & ( B4
% 0.31/0.47 = ( insert481364471_V_nat @ A @ C5 ) )
% 0.31/0.47 & ~ ( member1886821968_V_nat @ A @ C5 ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_eq_iff
% 0.31/0.47 thf(fact_272_insert__eq__iff,axiom,
% 0.31/0.47 ! [A: product_prod_V_V,A4: set_Product_prod_V_V,B: product_prod_V_V,B4: set_Product_prod_V_V] :
% 0.31/0.47 ( ~ ( member2015049524od_V_V @ A @ A4 )
% 0.31/0.47 => ( ~ ( member2015049524od_V_V @ B @ B4 )
% 0.31/0.47 => ( ( ( insert2024285275od_V_V @ A @ A4 )
% 0.31/0.47 = ( insert2024285275od_V_V @ B @ B4 ) )
% 0.31/0.47 = ( ( ( A = B )
% 0.31/0.47 => ( A4 = B4 ) )
% 0.31/0.47 & ( ( A != B )
% 0.31/0.47 => ? [C5: set_Product_prod_V_V] :
% 0.31/0.47 ( ( A4
% 0.31/0.47 = ( insert2024285275od_V_V @ B @ C5 ) )
% 0.31/0.47 & ~ ( member2015049524od_V_V @ B @ C5 )
% 0.31/0.47 & ( B4
% 0.31/0.47 = ( insert2024285275od_V_V @ A @ C5 ) )
% 0.31/0.47 & ~ ( member2015049524od_V_V @ A @ C5 ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_eq_iff
% 0.31/0.47 thf(fact_273_insert__eq__iff,axiom,
% 0.31/0.47 ! [A: v,A4: set_V,B: v,B4: set_V] :
% 0.31/0.47 ( ~ ( member_V2 @ A @ A4 )
% 0.31/0.47 => ( ~ ( member_V2 @ B @ B4 )
% 0.31/0.47 => ( ( ( insert_V2 @ A @ A4 )
% 0.31/0.47 = ( insert_V2 @ B @ B4 ) )
% 0.31/0.47 = ( ( ( A = B )
% 0.31/0.47 => ( A4 = B4 ) )
% 0.31/0.47 & ( ( A != B )
% 0.31/0.47 => ? [C5: set_V] :
% 0.31/0.47 ( ( A4
% 0.31/0.47 = ( insert_V2 @ B @ C5 ) )
% 0.31/0.47 & ~ ( member_V2 @ B @ C5 )
% 0.31/0.47 & ( B4
% 0.31/0.47 = ( insert_V2 @ A @ C5 ) )
% 0.31/0.47 & ~ ( member_V2 @ A @ C5 ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_eq_iff
% 0.31/0.47 thf(fact_274_insert__eq__iff,axiom,
% 0.31/0.47 ! [A: v2,A4: set_V2,B: v2,B4: set_V2] :
% 0.31/0.47 ( ~ ( member_V @ A @ A4 )
% 0.31/0.47 => ( ~ ( member_V @ B @ B4 )
% 0.31/0.47 => ( ( ( insert_V @ A @ A4 )
% 0.31/0.47 = ( insert_V @ B @ B4 ) )
% 0.31/0.47 = ( ( ( A = B )
% 0.31/0.47 => ( A4 = B4 ) )
% 0.31/0.47 & ( ( A != B )
% 0.31/0.47 => ? [C5: set_V2] :
% 0.31/0.47 ( ( A4
% 0.31/0.47 = ( insert_V @ B @ C5 ) )
% 0.31/0.47 & ~ ( member_V @ B @ C5 )
% 0.31/0.47 & ( B4
% 0.31/0.47 = ( insert_V @ A @ C5 ) )
% 0.31/0.47 & ~ ( member_V @ A @ C5 ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_eq_iff
% 0.31/0.47 thf(fact_275_insert__eq__iff,axiom,
% 0.31/0.47 ! [A: produc1699571228od_V_V,A4: set_Pr744279122od_V_V,B: produc1699571228od_V_V,B4: set_Pr744279122od_V_V] :
% 0.31/0.47 ( ~ ( member1010391347od_V_V @ A @ A4 )
% 0.31/0.47 => ( ~ ( member1010391347od_V_V @ B @ B4 )
% 0.31/0.47 => ( ( ( insert135842892od_V_V @ A @ A4 )
% 0.31/0.47 = ( insert135842892od_V_V @ B @ B4 ) )
% 0.31/0.47 = ( ( ( A = B )
% 0.31/0.47 => ( A4 = B4 ) )
% 0.31/0.47 & ( ( A != B )
% 0.31/0.47 => ? [C5: set_Pr744279122od_V_V] :
% 0.31/0.47 ( ( A4
% 0.31/0.47 = ( insert135842892od_V_V @ B @ C5 ) )
% 0.31/0.47 & ~ ( member1010391347od_V_V @ B @ C5 )
% 0.31/0.47 & ( B4
% 0.31/0.47 = ( insert135842892od_V_V @ A @ C5 ) )
% 0.31/0.47 & ~ ( member1010391347od_V_V @ A @ C5 ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_eq_iff
% 0.31/0.47 thf(fact_276_insert__absorb,axiom,
% 0.31/0.47 ! [A: produc778275879_V_nat,A4: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ( member1886821968_V_nat @ A @ A4 )
% 0.31/0.47 => ( ( insert481364471_V_nat @ A @ A4 )
% 0.31/0.47 = A4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_absorb
% 0.31/0.47 thf(fact_277_insert__absorb,axiom,
% 0.31/0.47 ! [A: product_prod_V_V,A4: set_Product_prod_V_V] :
% 0.31/0.47 ( ( member2015049524od_V_V @ A @ A4 )
% 0.31/0.47 => ( ( insert2024285275od_V_V @ A @ A4 )
% 0.31/0.47 = A4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_absorb
% 0.31/0.47 thf(fact_278_insert__absorb,axiom,
% 0.31/0.47 ! [A: v,A4: set_V] :
% 0.31/0.47 ( ( member_V2 @ A @ A4 )
% 0.31/0.47 => ( ( insert_V2 @ A @ A4 )
% 0.31/0.47 = A4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_absorb
% 0.31/0.47 thf(fact_279_insert__absorb,axiom,
% 0.31/0.47 ! [A: v2,A4: set_V2] :
% 0.31/0.47 ( ( member_V @ A @ A4 )
% 0.31/0.47 => ( ( insert_V @ A @ A4 )
% 0.31/0.47 = A4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_absorb
% 0.31/0.47 thf(fact_280_insert__absorb,axiom,
% 0.31/0.47 ! [A: produc1699571228od_V_V,A4: set_Pr744279122od_V_V] :
% 0.31/0.47 ( ( member1010391347od_V_V @ A @ A4 )
% 0.31/0.47 => ( ( insert135842892od_V_V @ A @ A4 )
% 0.31/0.47 = A4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_absorb
% 0.31/0.47 thf(fact_281_insert__ident,axiom,
% 0.31/0.47 ! [X3: produc778275879_V_nat,A4: set_Pr1058435079_V_nat,B4: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ~ ( member1886821968_V_nat @ X3 @ A4 )
% 0.31/0.47 => ( ~ ( member1886821968_V_nat @ X3 @ B4 )
% 0.31/0.47 => ( ( ( insert481364471_V_nat @ X3 @ A4 )
% 0.31/0.47 = ( insert481364471_V_nat @ X3 @ B4 ) )
% 0.31/0.47 = ( A4 = B4 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_ident
% 0.31/0.47 thf(fact_282_insert__ident,axiom,
% 0.31/0.47 ! [X3: product_prod_V_V,A4: set_Product_prod_V_V,B4: set_Product_prod_V_V] :
% 0.31/0.47 ( ~ ( member2015049524od_V_V @ X3 @ A4 )
% 0.31/0.47 => ( ~ ( member2015049524od_V_V @ X3 @ B4 )
% 0.31/0.47 => ( ( ( insert2024285275od_V_V @ X3 @ A4 )
% 0.31/0.47 = ( insert2024285275od_V_V @ X3 @ B4 ) )
% 0.31/0.47 = ( A4 = B4 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_ident
% 0.31/0.47 thf(fact_283_insert__ident,axiom,
% 0.31/0.47 ! [X3: v,A4: set_V,B4: set_V] :
% 0.31/0.47 ( ~ ( member_V2 @ X3 @ A4 )
% 0.31/0.47 => ( ~ ( member_V2 @ X3 @ B4 )
% 0.31/0.47 => ( ( ( insert_V2 @ X3 @ A4 )
% 0.31/0.47 = ( insert_V2 @ X3 @ B4 ) )
% 0.31/0.47 = ( A4 = B4 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_ident
% 0.31/0.47 thf(fact_284_insert__ident,axiom,
% 0.31/0.47 ! [X3: v2,A4: set_V2,B4: set_V2] :
% 0.31/0.47 ( ~ ( member_V @ X3 @ A4 )
% 0.31/0.47 => ( ~ ( member_V @ X3 @ B4 )
% 0.31/0.47 => ( ( ( insert_V @ X3 @ A4 )
% 0.31/0.47 = ( insert_V @ X3 @ B4 ) )
% 0.31/0.47 = ( A4 = B4 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_ident
% 0.31/0.47 thf(fact_285_insert__ident,axiom,
% 0.31/0.47 ! [X3: produc1699571228od_V_V,A4: set_Pr744279122od_V_V,B4: set_Pr744279122od_V_V] :
% 0.31/0.47 ( ~ ( member1010391347od_V_V @ X3 @ A4 )
% 0.31/0.47 => ( ~ ( member1010391347od_V_V @ X3 @ B4 )
% 0.31/0.47 => ( ( ( insert135842892od_V_V @ X3 @ A4 )
% 0.31/0.47 = ( insert135842892od_V_V @ X3 @ B4 ) )
% 0.31/0.47 = ( A4 = B4 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_ident
% 0.31/0.47 thf(fact_286_Set_Oset__insert,axiom,
% 0.31/0.47 ! [X3: produc778275879_V_nat,A4: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ( member1886821968_V_nat @ X3 @ A4 )
% 0.31/0.47 => ~ ! [B5: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ( A4
% 0.31/0.47 = ( insert481364471_V_nat @ X3 @ B5 ) )
% 0.31/0.47 => ( member1886821968_V_nat @ X3 @ B5 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Set.set_insert
% 0.31/0.47 thf(fact_287_Set_Oset__insert,axiom,
% 0.31/0.47 ! [X3: product_prod_V_V,A4: set_Product_prod_V_V] :
% 0.31/0.47 ( ( member2015049524od_V_V @ X3 @ A4 )
% 0.31/0.47 => ~ ! [B5: set_Product_prod_V_V] :
% 0.31/0.47 ( ( A4
% 0.31/0.47 = ( insert2024285275od_V_V @ X3 @ B5 ) )
% 0.31/0.47 => ( member2015049524od_V_V @ X3 @ B5 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Set.set_insert
% 0.31/0.47 thf(fact_288_Set_Oset__insert,axiom,
% 0.31/0.47 ! [X3: v,A4: set_V] :
% 0.31/0.47 ( ( member_V2 @ X3 @ A4 )
% 0.31/0.47 => ~ ! [B5: set_V] :
% 0.31/0.47 ( ( A4
% 0.31/0.47 = ( insert_V2 @ X3 @ B5 ) )
% 0.31/0.47 => ( member_V2 @ X3 @ B5 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Set.set_insert
% 0.31/0.47 thf(fact_289_Set_Oset__insert,axiom,
% 0.31/0.47 ! [X3: v2,A4: set_V2] :
% 0.31/0.47 ( ( member_V @ X3 @ A4 )
% 0.31/0.47 => ~ ! [B5: set_V2] :
% 0.31/0.47 ( ( A4
% 0.31/0.47 = ( insert_V @ X3 @ B5 ) )
% 0.31/0.47 => ( member_V @ X3 @ B5 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Set.set_insert
% 0.31/0.47 thf(fact_290_Set_Oset__insert,axiom,
% 0.31/0.47 ! [X3: produc1699571228od_V_V,A4: set_Pr744279122od_V_V] :
% 0.31/0.47 ( ( member1010391347od_V_V @ X3 @ A4 )
% 0.31/0.47 => ~ ! [B5: set_Pr744279122od_V_V] :
% 0.31/0.47 ( ( A4
% 0.31/0.47 = ( insert135842892od_V_V @ X3 @ B5 ) )
% 0.31/0.47 => ( member1010391347od_V_V @ X3 @ B5 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Set.set_insert
% 0.31/0.47 thf(fact_291_Un__commute,axiom,
% 0.31/0.47 ( sup_su1043134939_V_nat
% 0.31/0.47 = ( ^ [A6: set_Pr1058435079_V_nat,B6: set_Pr1058435079_V_nat] : ( sup_su1043134939_V_nat @ B6 @ A6 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_commute
% 0.31/0.47 thf(fact_292_Un__absorb,axiom,
% 0.31/0.47 ! [A4: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ( sup_su1043134939_V_nat @ A4 @ A4 )
% 0.31/0.47 = A4 ) ).
% 0.31/0.47
% 0.31/0.47 % Un_absorb
% 0.31/0.47 thf(fact_293_insertI2,axiom,
% 0.31/0.47 ! [A: produc778275879_V_nat,B4: set_Pr1058435079_V_nat,B: produc778275879_V_nat] :
% 0.31/0.47 ( ( member1886821968_V_nat @ A @ B4 )
% 0.31/0.47 => ( member1886821968_V_nat @ A @ ( insert481364471_V_nat @ B @ B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertI2
% 0.31/0.47 thf(fact_294_insertI2,axiom,
% 0.31/0.47 ! [A: product_prod_V_V,B4: set_Product_prod_V_V,B: product_prod_V_V] :
% 0.31/0.47 ( ( member2015049524od_V_V @ A @ B4 )
% 0.31/0.47 => ( member2015049524od_V_V @ A @ ( insert2024285275od_V_V @ B @ B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertI2
% 0.31/0.47 thf(fact_295_insertI2,axiom,
% 0.31/0.47 ! [A: v,B4: set_V,B: v] :
% 0.31/0.47 ( ( member_V2 @ A @ B4 )
% 0.31/0.47 => ( member_V2 @ A @ ( insert_V2 @ B @ B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertI2
% 0.31/0.47 thf(fact_296_insertI2,axiom,
% 0.31/0.47 ! [A: v2,B4: set_V2,B: v2] :
% 0.31/0.47 ( ( member_V @ A @ B4 )
% 0.31/0.47 => ( member_V @ A @ ( insert_V @ B @ B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertI2
% 0.31/0.47 thf(fact_297_insertI2,axiom,
% 0.31/0.47 ! [A: produc1699571228od_V_V,B4: set_Pr744279122od_V_V,B: produc1699571228od_V_V] :
% 0.31/0.47 ( ( member1010391347od_V_V @ A @ B4 )
% 0.31/0.47 => ( member1010391347od_V_V @ A @ ( insert135842892od_V_V @ B @ B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertI2
% 0.31/0.47 thf(fact_298_insertI1,axiom,
% 0.31/0.47 ! [A: produc778275879_V_nat,B4: set_Pr1058435079_V_nat] : ( member1886821968_V_nat @ A @ ( insert481364471_V_nat @ A @ B4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertI1
% 0.31/0.47 thf(fact_299_insertI1,axiom,
% 0.31/0.47 ! [A: product_prod_V_V,B4: set_Product_prod_V_V] : ( member2015049524od_V_V @ A @ ( insert2024285275od_V_V @ A @ B4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertI1
% 0.31/0.47 thf(fact_300_insertI1,axiom,
% 0.31/0.47 ! [A: v,B4: set_V] : ( member_V2 @ A @ ( insert_V2 @ A @ B4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertI1
% 0.31/0.47 thf(fact_301_insertI1,axiom,
% 0.31/0.47 ! [A: v2,B4: set_V2] : ( member_V @ A @ ( insert_V @ A @ B4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertI1
% 0.31/0.47 thf(fact_302_insertI1,axiom,
% 0.31/0.47 ! [A: produc1699571228od_V_V,B4: set_Pr744279122od_V_V] : ( member1010391347od_V_V @ A @ ( insert135842892od_V_V @ A @ B4 ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertI1
% 0.31/0.47 thf(fact_303_Un__assoc,axiom,
% 0.31/0.47 ! [A4: set_Pr1058435079_V_nat,B4: set_Pr1058435079_V_nat,C4: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ( sup_su1043134939_V_nat @ ( sup_su1043134939_V_nat @ A4 @ B4 ) @ C4 )
% 0.31/0.47 = ( sup_su1043134939_V_nat @ A4 @ ( sup_su1043134939_V_nat @ B4 @ C4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_assoc
% 0.31/0.47 thf(fact_304_insertE,axiom,
% 0.31/0.47 ! [A: produc778275879_V_nat,B: produc778275879_V_nat,A4: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ( member1886821968_V_nat @ A @ ( insert481364471_V_nat @ B @ A4 ) )
% 0.31/0.47 => ( ( A != B )
% 0.31/0.47 => ( member1886821968_V_nat @ A @ A4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertE
% 0.31/0.47 thf(fact_305_insertE,axiom,
% 0.31/0.47 ! [A: product_prod_V_V,B: product_prod_V_V,A4: set_Product_prod_V_V] :
% 0.31/0.47 ( ( member2015049524od_V_V @ A @ ( insert2024285275od_V_V @ B @ A4 ) )
% 0.31/0.47 => ( ( A != B )
% 0.31/0.47 => ( member2015049524od_V_V @ A @ A4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertE
% 0.31/0.47 thf(fact_306_insertE,axiom,
% 0.31/0.47 ! [A: v,B: v,A4: set_V] :
% 0.31/0.47 ( ( member_V2 @ A @ ( insert_V2 @ B @ A4 ) )
% 0.31/0.47 => ( ( A != B )
% 0.31/0.47 => ( member_V2 @ A @ A4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertE
% 0.31/0.47 thf(fact_307_insertE,axiom,
% 0.31/0.47 ! [A: v2,B: v2,A4: set_V2] :
% 0.31/0.47 ( ( member_V @ A @ ( insert_V @ B @ A4 ) )
% 0.31/0.47 => ( ( A != B )
% 0.31/0.47 => ( member_V @ A @ A4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertE
% 0.31/0.47 thf(fact_308_insertE,axiom,
% 0.31/0.47 ! [A: produc1699571228od_V_V,B: produc1699571228od_V_V,A4: set_Pr744279122od_V_V] :
% 0.31/0.47 ( ( member1010391347od_V_V @ A @ ( insert135842892od_V_V @ B @ A4 ) )
% 0.31/0.47 => ( ( A != B )
% 0.31/0.47 => ( member1010391347od_V_V @ A @ A4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insertE
% 0.31/0.47 thf(fact_309_ball__Un,axiom,
% 0.31/0.47 ! [A4: set_Pr1058435079_V_nat,B4: set_Pr1058435079_V_nat,P2: produc778275879_V_nat > $o] :
% 0.31/0.47 ( ( ! [X6: produc778275879_V_nat] :
% 0.31/0.47 ( ( member1886821968_V_nat @ X6 @ ( sup_su1043134939_V_nat @ A4 @ B4 ) )
% 0.31/0.47 => ( P2 @ X6 ) ) )
% 0.31/0.47 = ( ! [X6: produc778275879_V_nat] :
% 0.31/0.47 ( ( member1886821968_V_nat @ X6 @ A4 )
% 0.31/0.47 => ( P2 @ X6 ) )
% 0.31/0.47 & ! [X6: produc778275879_V_nat] :
% 0.31/0.47 ( ( member1886821968_V_nat @ X6 @ B4 )
% 0.31/0.47 => ( P2 @ X6 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ball_Un
% 0.31/0.47 thf(fact_310_bex__Un,axiom,
% 0.31/0.47 ! [A4: set_Pr1058435079_V_nat,B4: set_Pr1058435079_V_nat,P2: produc778275879_V_nat > $o] :
% 0.31/0.47 ( ( ? [X6: produc778275879_V_nat] :
% 0.31/0.47 ( ( member1886821968_V_nat @ X6 @ ( sup_su1043134939_V_nat @ A4 @ B4 ) )
% 0.31/0.47 & ( P2 @ X6 ) ) )
% 0.31/0.47 = ( ? [X6: produc778275879_V_nat] :
% 0.31/0.47 ( ( member1886821968_V_nat @ X6 @ A4 )
% 0.31/0.47 & ( P2 @ X6 ) )
% 0.31/0.47 | ? [X6: produc778275879_V_nat] :
% 0.31/0.47 ( ( member1886821968_V_nat @ X6 @ B4 )
% 0.31/0.47 & ( P2 @ X6 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % bex_Un
% 0.31/0.47 thf(fact_311_UnI2,axiom,
% 0.31/0.47 ! [C: product_prod_V_V,B4: set_Product_prod_V_V,A4: set_Product_prod_V_V] :
% 0.31/0.47 ( ( member2015049524od_V_V @ C @ B4 )
% 0.31/0.47 => ( member2015049524od_V_V @ C @ ( sup_su551882943od_V_V @ A4 @ B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnI2
% 0.31/0.47 thf(fact_312_UnI2,axiom,
% 0.31/0.47 ! [C: v,B4: set_V,A4: set_V] :
% 0.31/0.47 ( ( member_V2 @ C @ B4 )
% 0.31/0.47 => ( member_V2 @ C @ ( sup_sup_set_V2 @ A4 @ B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnI2
% 0.31/0.47 thf(fact_313_UnI2,axiom,
% 0.31/0.47 ! [C: v2,B4: set_V2,A4: set_V2] :
% 0.31/0.47 ( ( member_V @ C @ B4 )
% 0.31/0.47 => ( member_V @ C @ ( sup_sup_set_V @ A4 @ B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnI2
% 0.31/0.47 thf(fact_314_UnI2,axiom,
% 0.31/0.47 ! [C: produc1699571228od_V_V,B4: set_Pr744279122od_V_V,A4: set_Pr744279122od_V_V] :
% 0.31/0.47 ( ( member1010391347od_V_V @ C @ B4 )
% 0.31/0.47 => ( member1010391347od_V_V @ C @ ( sup_su693515134od_V_V @ A4 @ B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnI2
% 0.31/0.47 thf(fact_315_UnI2,axiom,
% 0.31/0.47 ! [C: produc778275879_V_nat,B4: set_Pr1058435079_V_nat,A4: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ( member1886821968_V_nat @ C @ B4 )
% 0.31/0.47 => ( member1886821968_V_nat @ C @ ( sup_su1043134939_V_nat @ A4 @ B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnI2
% 0.31/0.47 thf(fact_316_UnI1,axiom,
% 0.31/0.47 ! [C: product_prod_V_V,A4: set_Product_prod_V_V,B4: set_Product_prod_V_V] :
% 0.31/0.47 ( ( member2015049524od_V_V @ C @ A4 )
% 0.31/0.47 => ( member2015049524od_V_V @ C @ ( sup_su551882943od_V_V @ A4 @ B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnI1
% 0.31/0.47 thf(fact_317_UnI1,axiom,
% 0.31/0.47 ! [C: v,A4: set_V,B4: set_V] :
% 0.31/0.47 ( ( member_V2 @ C @ A4 )
% 0.31/0.47 => ( member_V2 @ C @ ( sup_sup_set_V2 @ A4 @ B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnI1
% 0.31/0.47 thf(fact_318_UnI1,axiom,
% 0.31/0.47 ! [C: v2,A4: set_V2,B4: set_V2] :
% 0.31/0.47 ( ( member_V @ C @ A4 )
% 0.31/0.47 => ( member_V @ C @ ( sup_sup_set_V @ A4 @ B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnI1
% 0.31/0.47 thf(fact_319_UnI1,axiom,
% 0.31/0.47 ! [C: produc1699571228od_V_V,A4: set_Pr744279122od_V_V,B4: set_Pr744279122od_V_V] :
% 0.31/0.47 ( ( member1010391347od_V_V @ C @ A4 )
% 0.31/0.47 => ( member1010391347od_V_V @ C @ ( sup_su693515134od_V_V @ A4 @ B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnI1
% 0.31/0.47 thf(fact_320_UnI1,axiom,
% 0.31/0.47 ! [C: produc778275879_V_nat,A4: set_Pr1058435079_V_nat,B4: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ( member1886821968_V_nat @ C @ A4 )
% 0.31/0.47 => ( member1886821968_V_nat @ C @ ( sup_su1043134939_V_nat @ A4 @ B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnI1
% 0.31/0.47 thf(fact_321_UnE,axiom,
% 0.31/0.47 ! [C: product_prod_V_V,A4: set_Product_prod_V_V,B4: set_Product_prod_V_V] :
% 0.31/0.47 ( ( member2015049524od_V_V @ C @ ( sup_su551882943od_V_V @ A4 @ B4 ) )
% 0.31/0.47 => ( ~ ( member2015049524od_V_V @ C @ A4 )
% 0.31/0.47 => ( member2015049524od_V_V @ C @ B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnE
% 0.31/0.47 thf(fact_322_UnE,axiom,
% 0.31/0.47 ! [C: v,A4: set_V,B4: set_V] :
% 0.31/0.47 ( ( member_V2 @ C @ ( sup_sup_set_V2 @ A4 @ B4 ) )
% 0.31/0.47 => ( ~ ( member_V2 @ C @ A4 )
% 0.31/0.47 => ( member_V2 @ C @ B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnE
% 0.31/0.47 thf(fact_323_UnE,axiom,
% 0.31/0.47 ! [C: v2,A4: set_V2,B4: set_V2] :
% 0.31/0.47 ( ( member_V @ C @ ( sup_sup_set_V @ A4 @ B4 ) )
% 0.31/0.47 => ( ~ ( member_V @ C @ A4 )
% 0.31/0.47 => ( member_V @ C @ B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnE
% 0.31/0.47 thf(fact_324_UnE,axiom,
% 0.31/0.47 ! [C: produc1699571228od_V_V,A4: set_Pr744279122od_V_V,B4: set_Pr744279122od_V_V] :
% 0.31/0.47 ( ( member1010391347od_V_V @ C @ ( sup_su693515134od_V_V @ A4 @ B4 ) )
% 0.31/0.47 => ( ~ ( member1010391347od_V_V @ C @ A4 )
% 0.31/0.47 => ( member1010391347od_V_V @ C @ B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnE
% 0.31/0.47 thf(fact_325_UnE,axiom,
% 0.31/0.47 ! [C: produc778275879_V_nat,A4: set_Pr1058435079_V_nat,B4: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ( member1886821968_V_nat @ C @ ( sup_su1043134939_V_nat @ A4 @ B4 ) )
% 0.31/0.47 => ( ~ ( member1886821968_V_nat @ C @ A4 )
% 0.31/0.47 => ( member1886821968_V_nat @ C @ B4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnE
% 0.31/0.47 thf(fact_326_labeled__graph_Osel_I2_J,axiom,
% 0.31/0.47 ! [X1: set_Pr744279122od_V_V,X2: set_V] :
% 0.31/0.47 ( ( labele1134902411nt_V_V @ ( labele712009229nt_V_V @ X1 @ X2 ) )
% 0.31/0.47 = X2 ) ).
% 0.31/0.47
% 0.31/0.47 % labeled_graph.sel(2)
% 0.31/0.47 thf(fact_327_labeled__graph_Osel_I1_J,axiom,
% 0.31/0.47 ! [X1: set_Pr744279122od_V_V,X2: set_V] :
% 0.31/0.47 ( ( labele515735386nt_V_V @ ( labele712009229nt_V_V @ X1 @ X2 ) )
% 0.31/0.47 = X1 ) ).
% 0.31/0.47
% 0.31/0.47 % labeled_graph.sel(1)
% 0.31/0.47 thf(fact_328_graph__homomorphism__semantics,axiom,
% 0.31/0.47 ! [A4: labele2115946735nt_V_V,B4: labele2115946735nt_V_V,F2: set_Product_prod_V_V,A: v,B: v,E: allego859987871tant_V,A2: v,B2: v] :
% 0.31/0.47 ( ( graph_1808119_V_V_V @ A4 @ B4 @ F2 )
% 0.31/0.47 => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( semant993842370nt_V_V @ A4 @ E ) )
% 0.31/0.47 => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ A2 ) @ F2 )
% 0.31/0.47 => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ B @ B2 ) @ F2 )
% 0.31/0.47 => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A2 @ B2 ) @ ( semant993842370nt_V_V @ B4 @ E ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % graph_homomorphism_semantics
% 0.31/0.47 thf(fact_329_graph__homomorphism__nonempty,axiom,
% 0.31/0.47 ! [A4: labele2115946735nt_V_V,B4: labele2115946735nt_V_V,F2: set_Product_prod_V_V,E: allego859987871tant_V] :
% 0.31/0.47 ( ( graph_1808119_V_V_V @ A4 @ B4 @ F2 )
% 0.31/0.47 => ( ( ( semant993842370nt_V_V @ A4 @ E )
% 0.31/0.47 != bot_bo1389414743od_V_V )
% 0.31/0.47 => ( ( semant993842370nt_V_V @ B4 @ E )
% 0.31/0.47 != bot_bo1389414743od_V_V ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % graph_homomorphism_nonempty
% 0.31/0.47 thf(fact_330_labeled__graph_Oexhaust__sel,axiom,
% 0.31/0.47 ! [Labeled_graph: labele2115946735nt_V_V] :
% 0.31/0.47 ( Labeled_graph
% 0.31/0.47 = ( labele712009229nt_V_V @ ( labele515735386nt_V_V @ Labeled_graph ) @ ( labele1134902411nt_V_V @ Labeled_graph ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % labeled_graph.exhaust_sel
% 0.31/0.47 thf(fact_331_standard__rules__def,axiom,
% 0.31/0.47 ( standa157301464ules_V
% 0.31/0.47 = ( ^ [C5: set_V2,L3: set_St1111633946tant_V] : ( sup_su1043134939_V_nat @ ( sup_su1043134939_V_nat @ ( standa1897115807ules_V @ C5 ) @ ( standa1568205529ules_V @ L3 ) ) @ ( insert481364471_V_nat @ ( standa214871990tant_V @ standard_S_Top_V ) @ ( insert481364471_V_nat @ standa1319953089tant_V @ bot_bo907687539_V_nat ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % standard_rules_def
% 0.31/0.47 thf(fact_332_semantics__in__vertices_I2_J,axiom,
% 0.31/0.47 ! [A4: labele2115946735nt_V_V,A: v,B: v,E: allego859987871tant_V] :
% 0.31/0.47 ( ( A4
% 0.31/0.47 = ( restri1305980611nt_V_V @ A4 ) )
% 0.31/0.47 => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( semant993842370nt_V_V @ A4 @ E ) )
% 0.31/0.47 => ( member_V2 @ B @ ( labele1134902411nt_V_V @ A4 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % semantics_in_vertices(2)
% 0.31/0.47 thf(fact_333_semantics__in__vertices_I1_J,axiom,
% 0.31/0.47 ! [A4: labele2115946735nt_V_V,A: v,B: v,E: allego859987871tant_V] :
% 0.31/0.47 ( ( A4
% 0.31/0.47 = ( restri1305980611nt_V_V @ A4 ) )
% 0.31/0.47 => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( semant993842370nt_V_V @ A4 @ E ) )
% 0.31/0.47 => ( member_V2 @ A @ ( labele1134902411nt_V_V @ A4 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % semantics_in_vertices(1)
% 0.31/0.47 thf(fact_334_subgraph__semantics,axiom,
% 0.31/0.47 ! [A4: labele2115946735nt_V_V,B4: labele2115946735nt_V_V,A: v,B: v,E: allego859987871tant_V] :
% 0.31/0.47 ( ( graph_1808119_V_V_V @ A4 @ B4 @ ( id_on_V2 @ ( labele1134902411nt_V_V @ A4 ) ) )
% 0.31/0.47 => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( semant993842370nt_V_V @ A4 @ E ) )
% 0.31/0.47 => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( semant993842370nt_V_V @ B4 @ E ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % subgraph_semantics
% 0.31/0.47 thf(fact_335_maintainedD,axiom,
% 0.31/0.47 ! [A4: labele2128733290_V_nat,B4: labele2128733290_V_nat,G: labele2115946735nt_V_V,F2: set_Pr53436518_nat_V] :
% 0.31/0.47 ( ( mainta197426964_nat_V @ ( produc698429463_V_nat @ A4 @ B4 ) @ G )
% 0.31/0.47 => ( ( graph_1541575154_nat_V @ A4 @ G @ F2 )
% 0.31/0.47 => ( extens1072773157_nat_V @ ( produc698429463_V_nat @ A4 @ B4 ) @ G @ F2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % maintainedD
% 0.31/0.47 thf(fact_336_maintainedD,axiom,
% 0.31/0.47 ! [A4: labele2115946735nt_V_V,B4: labele2115946735nt_V_V,G: labele2115946735nt_V_V,F2: set_Product_prod_V_V] :
% 0.31/0.47 ( ( mainta1699210777_V_V_V @ ( produc533118295nt_V_V @ A4 @ B4 ) @ G )
% 0.31/0.47 => ( ( graph_1808119_V_V_V @ A4 @ G @ F2 )
% 0.31/0.47 => ( extens1533825066_V_V_V @ ( produc533118295nt_V_V @ A4 @ B4 ) @ G @ F2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % maintainedD
% 0.31/0.47 thf(fact_337_sup__bot_Oright__neutral,axiom,
% 0.31/0.47 ! [A: set_Product_prod_V_V] :
% 0.31/0.47 ( ( sup_su551882943od_V_V @ A @ bot_bo1389414743od_V_V )
% 0.31/0.47 = A ) ).
% 0.31/0.47
% 0.31/0.47 % sup_bot.right_neutral
% 0.31/0.47 thf(fact_338_sup__bot_Oright__neutral,axiom,
% 0.31/0.47 ! [A: set_V] :
% 0.31/0.47 ( ( sup_sup_set_V2 @ A @ bot_bot_set_V2 )
% 0.31/0.47 = A ) ).
% 0.31/0.47
% 0.31/0.47 % sup_bot.right_neutral
% 0.31/0.47 thf(fact_339_sup__bot_Oright__neutral,axiom,
% 0.31/0.47 ! [A: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ( sup_su1043134939_V_nat @ A @ bot_bo907687539_V_nat )
% 0.31/0.47 = A ) ).
% 0.31/0.47
% 0.31/0.47 % sup_bot.right_neutral
% 0.31/0.47 thf(fact_340_sup__bot_Oneutr__eq__iff,axiom,
% 0.31/0.47 ! [A: set_Product_prod_V_V,B: set_Product_prod_V_V] :
% 0.31/0.47 ( ( bot_bo1389414743od_V_V
% 0.31/0.47 = ( sup_su551882943od_V_V @ A @ B ) )
% 0.31/0.47 = ( ( A = bot_bo1389414743od_V_V )
% 0.31/0.47 & ( B = bot_bo1389414743od_V_V ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % sup_bot.neutr_eq_iff
% 0.31/0.47 thf(fact_341_sup__bot_Oneutr__eq__iff,axiom,
% 0.31/0.47 ! [A: set_V,B: set_V] :
% 0.31/0.47 ( ( bot_bot_set_V2
% 0.31/0.47 = ( sup_sup_set_V2 @ A @ B ) )
% 0.31/0.47 = ( ( A = bot_bot_set_V2 )
% 0.31/0.47 & ( B = bot_bot_set_V2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % sup_bot.neutr_eq_iff
% 0.31/0.47 thf(fact_342_sup__bot_Oneutr__eq__iff,axiom,
% 0.31/0.47 ! [A: set_Pr1058435079_V_nat,B: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ( bot_bo907687539_V_nat
% 0.31/0.47 = ( sup_su1043134939_V_nat @ A @ B ) )
% 0.31/0.47 = ( ( A = bot_bo907687539_V_nat )
% 0.31/0.47 & ( B = bot_bo907687539_V_nat ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % sup_bot.neutr_eq_iff
% 0.31/0.47 thf(fact_343_sup__bot_Oleft__neutral,axiom,
% 0.31/0.47 ! [A: set_Product_prod_V_V] :
% 0.31/0.47 ( ( sup_su551882943od_V_V @ bot_bo1389414743od_V_V @ A )
% 0.31/0.47 = A ) ).
% 0.31/0.47
% 0.31/0.47 % sup_bot.left_neutral
% 0.31/0.47 thf(fact_344_sup__bot_Oleft__neutral,axiom,
% 0.31/0.47 ! [A: set_V] :
% 0.31/0.47 ( ( sup_sup_set_V2 @ bot_bot_set_V2 @ A )
% 0.31/0.47 = A ) ).
% 0.31/0.47
% 0.31/0.47 % sup_bot.left_neutral
% 0.31/0.47 thf(fact_345_sup__bot_Oleft__neutral,axiom,
% 0.31/0.47 ! [A: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ( sup_su1043134939_V_nat @ bot_bo907687539_V_nat @ A )
% 0.31/0.47 = A ) ).
% 0.31/0.47
% 0.31/0.47 % sup_bot.left_neutral
% 0.31/0.47 thf(fact_346_sup__bot_Oeq__neutr__iff,axiom,
% 0.31/0.47 ! [A: set_Product_prod_V_V,B: set_Product_prod_V_V] :
% 0.31/0.47 ( ( ( sup_su551882943od_V_V @ A @ B )
% 0.31/0.47 = bot_bo1389414743od_V_V )
% 0.31/0.47 = ( ( A = bot_bo1389414743od_V_V )
% 0.31/0.47 & ( B = bot_bo1389414743od_V_V ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % sup_bot.eq_neutr_iff
% 0.31/0.47 thf(fact_347_sup__bot_Oeq__neutr__iff,axiom,
% 0.31/0.47 ! [A: set_V,B: set_V] :
% 0.31/0.47 ( ( ( sup_sup_set_V2 @ A @ B )
% 0.31/0.47 = bot_bot_set_V2 )
% 0.31/0.47 = ( ( A = bot_bot_set_V2 )
% 0.31/0.47 & ( B = bot_bot_set_V2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % sup_bot.eq_neutr_iff
% 0.31/0.47 thf(fact_348_sup__bot_Oeq__neutr__iff,axiom,
% 0.31/0.47 ! [A: set_Pr1058435079_V_nat,B: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ( ( sup_su1043134939_V_nat @ A @ B )
% 0.31/0.47 = bot_bo907687539_V_nat )
% 0.31/0.47 = ( ( A = bot_bo907687539_V_nat )
% 0.31/0.47 & ( B = bot_bo907687539_V_nat ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % sup_bot.eq_neutr_iff
% 0.31/0.47 thf(fact_349_sup_Oright__idem,axiom,
% 0.31/0.47 ! [A: set_Pr1058435079_V_nat,B: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ( sup_su1043134939_V_nat @ ( sup_su1043134939_V_nat @ A @ B ) @ B )
% 0.31/0.47 = ( sup_su1043134939_V_nat @ A @ B ) ) ).
% 0.31/0.47
% 0.31/0.47 % sup.right_idem
% 0.31/0.47 thf(fact_350_sup__left__idem,axiom,
% 0.31/0.47 ! [X3: set_Pr1058435079_V_nat,Y: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ( sup_su1043134939_V_nat @ X3 @ ( sup_su1043134939_V_nat @ X3 @ Y ) )
% 0.31/0.47 = ( sup_su1043134939_V_nat @ X3 @ Y ) ) ).
% 0.31/0.47
% 0.31/0.47 % sup_left_idem
% 0.31/0.47 thf(fact_351_sup_Oleft__idem,axiom,
% 0.31/0.47 ! [A: set_Pr1058435079_V_nat,B: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ( sup_su1043134939_V_nat @ A @ ( sup_su1043134939_V_nat @ A @ B ) )
% 0.31/0.47 = ( sup_su1043134939_V_nat @ A @ B ) ) ).
% 0.31/0.47
% 0.31/0.47 % sup.left_idem
% 0.31/0.47 thf(fact_352_sup__idem,axiom,
% 0.31/0.47 ! [X3: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ( sup_su1043134939_V_nat @ X3 @ X3 )
% 0.31/0.47 = X3 ) ).
% 0.31/0.47
% 0.31/0.47 % sup_idem
% 0.31/0.47 thf(fact_353_sup_Oidem,axiom,
% 0.31/0.47 ! [A: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ( sup_su1043134939_V_nat @ A @ A )
% 0.31/0.47 = A ) ).
% 0.31/0.47
% 0.31/0.47 % sup.idem
% 0.31/0.47 thf(fact_354_sup__bot__left,axiom,
% 0.31/0.47 ! [X3: set_Pr1058435079_V_nat] :
% 0.31/0.47 ( ( sup_su1043134939_V_nat @ bot_bo907687539_V_nat @ X3 )
% 0.31/0.47 = X3 ) ).
% 0.31/0.47
% 0.31/0.47 % sup_bot_left
% 0.31/0.47
% 0.31/0.47 % Conjectures (1)
% 0.31/0.47 thf(conj_0,conjecture,
% 0.31/0.47 member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ y ) @ g ) ).
% 0.31/0.47
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 ------------------------
% 3.93/1.83 ---- Embedded in THF ---
% 3.93/1.83 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.93/1.83 %%% Generated on Tue Feb 24 08:29:11 EST 2026
% 3.93/1.83 %%% using '$$dhol' embedding, version 1.3.0.
% 3.93/1.83 %%% Logic specification used:
% 3.93/1.83 %%% thf(spec, logic, $$dhol).
% 3.93/1.83
% 3.93/1.83 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.OGMuvyH1wq/DTF2DTF13384.p
% See solution above
% 3.93/1.83 ------------------------
% 3.98/1.90 ---- Cleaned THF ---
% 3.98/1.90 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J_J_Mt__Nat__Onat_J_J_J,type,
% 3.98/1.90 set_Pr361461255at_nat: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J_J_J_J,type,
% 3.98/1.90 set_Pr1326571566_V_nat: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J_J_J,type,
% 3.98/1.90 set_Pr1007924423_V_nat: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_Mt__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_J_J_J,type,
% 3.98/1.90 set_Pr872354016od_V_V: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_Mt__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_J_J,type,
% 3.98/1.90 produc1269720746od_V_V: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_It__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_It__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_Mt__Nat__Onat_J_J_J,type,
% 3.98/1.90 set_Pr597600647_V_nat: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_t__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J_J,type,
% 3.98/1.90 labele506073123_V_nat: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_Mt__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_J_J,type,
% 3.98/1.90 set_Pr2015814777od_V_V: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J_Mtf__V__H_J_J,type,
% 3.98/1.90 set_Pr1056235617_nat_V: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_Mt__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_J,type,
% 3.98/1.90 produc1082089497od_V_V: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V__H_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V__H_J_Mt__Nat__Onat_J_J_J,type,
% 3.98/1.90 set_Pr473545225_V_nat: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J_J,type,
% 3.98/1.90 set_Pr1058435079_V_nat: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_t__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J,type,
% 3.98/1.90 produc778275879_V_nat: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_t__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mtf__V__H_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mtf__V__H_J_J,type,
% 3.98/1.90 produc651414759nt_V_V: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_t__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_J,type,
% 3.98/1.90 labele201426742od_V_V: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_J_J,type,
% 3.98/1.90 set_Pr951255342od_V_V: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_J,type,
% 3.98/1.90 produc1443401592od_V_V: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_Mtf__V__H_J_J,type,
% 3.98/1.90 set_Pr257494450_V_V_V: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_J,type,
% 3.98/1.90 set_Pr744279122od_V_V: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V_Mtf__V_J_J_J,type,
% 3.98/1.90 set_Pr1498723630od_V_V: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_t__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J,type,
% 3.98/1.90 labele236903175od_V_V: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_J,type,
% 3.98/1.90 set_Pr2022779335od_V_V: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J,type,
% 3.98/1.90 produc1699571228od_V_V: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V_Mtf__V_J_J,type,
% 3.98/1.90 produc1113554040od_V_V: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_t__Set__Oset_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J,type,
% 3.98/1.90 set_la14611914_V_nat: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J,type,
% 3.98/1.90 produc522115815od_V_V: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_t__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J,type,
% 3.98/1.90 labele2128733290_V_nat: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_t__LabeledGraphSemantics__Oallegorical____term_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_J,type,
% 3.98/1.90 allego859987871tant_V: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_t__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mtf__V__H_J,type,
% 3.98/1.90 labele2115946735nt_V_V: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_Mtf__V__H_J_J,type,
% 3.98/1.90 set_Pr1228022213_V_V_V: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_t__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mtf__V_J,type,
% 3.98/1.90 labele788688367nt_V_V: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_t__Set__Oset_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_J,type,
% 3.98/1.90 set_St1111633946tant_V: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mtf__V__H_J_J,type,
% 3.98/1.90 set_Pr53436518_nat_V: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J,type,
% 3.98/1.90 set_Product_prod_V_V: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__V_Mtf__V__H_J_J,type,
% 3.98/1.90 set_Product_prod_V_V2: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__V_Mtf__V_J_J,type,
% 3.98/1.90 set_Product_prod_V_V3: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J,type,
% 3.98/1.90 standard_Constant_V: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J,type,
% 3.98/1.90 product_prod_V_V: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_t__Product____Type__Oprod_Itf__V_Mtf__V_J,type,
% 3.98/1.90 product_prod_V_V2: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_t__Set__Oset_Itf__V__H_J,type,
% 3.98/1.90 set_V: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_t__Set__Oset_Itf__V_J,type,
% 3.98/1.90 set_V2: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_tf__V__H,type,
% 3.98/1.90 v: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(ty_n_tf__V,type,
% 3.98/1.90 v2: $tType ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_BNF__Def_OGr_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J,type,
% 3.98/1.90 bNF_Gr320641027od_V_V: set_St1111633946tant_V > ( standard_Constant_V > product_prod_V_V ) > set_Pr744279122od_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_BNF__Def_OGr_001t__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_001t__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J,type,
% 3.98/1.90 bNF_Gr17960482_V_nat: set_la14611914_V_nat > ( labele2128733290_V_nat > labele2128733290_V_nat ) > set_Pr1058435079_V_nat ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_BNF__Def_OGr_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_001tf__V__H,type,
% 3.98/1.90 bNF_Gr480427157_V_V_V: set_Pr744279122od_V_V > ( produc1699571228od_V_V > v ) > set_Pr257494450_V_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_BNF__Def_OGr_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_001tf__V__H,type,
% 3.98/1.90 bNF_Gr1069958334_V_V_V: set_Product_prod_V_V > ( product_prod_V_V > v ) > set_Pr1228022213_V_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_BNF__Def_OGr_001tf__V_001tf__V__H,type,
% 3.98/1.90 bNF_Gr_V_V: set_V2 > ( v2 > v ) > set_Product_prod_V_V2 ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_BNF__Def_OGr_001tf__V__H_001tf__V__H,type,
% 3.98/1.90 bNF_Gr_V_V2: set_V > ( v > v ) > set_Product_prod_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Fun_Ocomp_001tf__V__H_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J,type,
% 3.98/1.90 comp_V1480932210od_V_V: ( v > produc1699571228od_V_V ) > ( produc1699571228od_V_V > v ) > produc1699571228od_V_V > produc1699571228od_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Fun_Ocomp_001tf__V__H_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J,type,
% 3.98/1.90 comp_V772749048od_V_V: ( v > product_prod_V_V ) > ( product_prod_V_V > v ) > product_prod_V_V > product_prod_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Fun_Ocomp_001tf__V__H_001tf__V_001tf__V,type,
% 3.98/1.90 comp_V_V_V: ( v > v2 ) > ( v2 > v ) > v2 > v2 ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Fun_Ocomp_001tf__V__H_001tf__V__H_001tf__V__H,type,
% 3.98/1.90 comp_V_V_V2: ( v > v ) > ( v > v ) > v > v ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_LabeledGraphSemantics_OStandard__Constant_OS__Bot_001tf__V,type,
% 3.98/1.90 standard_S_Bot_V: standard_Constant_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_LabeledGraphSemantics_OStandard__Constant_OS__Const_001tf__V,type,
% 3.98/1.90 standard_S_Const_V: v2 > standard_Constant_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_LabeledGraphSemantics_OStandard__Constant_OS__Top_001tf__V,type,
% 3.98/1.90 standard_S_Top_V: standard_Constant_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_LabeledGraphSemantics_OgetRel_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J,type,
% 3.98/1.90 getRel2057312683od_V_V: standard_Constant_V > labele201426742od_V_V > set_Pr2015814777od_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_LabeledGraphSemantics_OgetRel_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J,type,
% 3.98/1.90 getRel1902920892od_V_V: standard_Constant_V > labele236903175od_V_V > set_Pr2022779335od_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_LabeledGraphSemantics_OgetRel_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001tf__V,type,
% 3.98/1.90 getRel632961956nt_V_V: standard_Constant_V > labele788688367nt_V_V > set_Product_prod_V_V3 ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_LabeledGraphSemantics_OgetRel_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001tf__V__H,type,
% 3.98/1.90 getRel1432786916nt_V_V: standard_Constant_V > labele2115946735nt_V_V > set_Product_prod_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_LabeledGraphSemantics_Osemantics_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001tf__V__H,type,
% 3.98/1.90 semant993842370nt_V_V: labele2115946735nt_V_V > allego859987871tant_V > set_Product_prod_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_LabeledGraphs_Oedge__preserving_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_001tf__V__H_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J,type,
% 3.98/1.90 edge_p669293514tant_V: set_Pr257494450_V_V_V > set_Pr872354016od_V_V > set_Pr744279122od_V_V > $o ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_LabeledGraphs_Oedge__preserving_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_001tf__V__H_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J,type,
% 3.98/1.90 edge_p1776314003tant_V: set_Pr1228022213_V_V_V > set_Pr951255342od_V_V > set_Pr744279122od_V_V > $o ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_LabeledGraphs_Oedge__preserving_001tf__V_001tf__V__H_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J,type,
% 3.98/1.90 edge_p1322161019tant_V: set_Product_prod_V_V2 > set_Pr1498723630od_V_V > set_Pr744279122od_V_V > $o ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_LabeledGraphs_Oedge__preserving_001tf__V__H_001tf__V__H_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J,type,
% 3.98/1.90 edge_p1560004099tant_V: set_Product_prod_V_V > set_Pr744279122od_V_V > set_Pr744279122od_V_V > $o ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_LabeledGraphs_Ograph__homomorphism_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Nat__Onat_001tf__V__H,type,
% 3.98/1.90 graph_1541575154_nat_V: labele2128733290_V_nat > labele2115946735nt_V_V > set_Pr53436518_nat_V > $o ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_LabeledGraphs_Ograph__homomorphism_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J_001tf__V__H,type,
% 3.98/1.90 graph_227683057_nat_V: labele506073123_V_nat > labele2115946735nt_V_V > set_Pr1056235617_nat_V > $o ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_LabeledGraphs_Ograph__homomorphism_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_001tf__V__H,type,
% 3.98/1.90 graph_840721237_V_V_V: labele236903175od_V_V > labele2115946735nt_V_V > set_Pr1228022213_V_V_V > $o ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_LabeledGraphs_Ograph__homomorphism_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001tf__V__H_001tf__V__H,type,
% 3.98/1.90 graph_1808119_V_V_V: labele2115946735nt_V_V > labele2115946735nt_V_V > set_Product_prod_V_V > $o ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_LabeledGraphs_Ograph__union_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001tf__V__H,type,
% 3.98/1.90 graph_1141886696nt_V_V: labele2115946735nt_V_V > labele2115946735nt_V_V > labele2115946735nt_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_LabeledGraphs_Olabeled__graph_OLG_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J,type,
% 3.98/1.90 labele1193521135_V_nat: set_Pr1326571566_V_nat > set_Pr1058435079_V_nat > labele506073123_V_nat ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_LabeledGraphs_Olabeled__graph_OLG_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J,type,
% 3.98/1.90 labele94156371od_V_V: set_Pr951255342od_V_V > set_Product_prod_V_V > labele236903175od_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_LabeledGraphs_Olabeled__graph_OLG_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001tf__V__H,type,
% 3.98/1.90 labele712009229nt_V_V: set_Pr744279122od_V_V > set_V > labele2115946735nt_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_LabeledGraphs_Olabeled__graph_Oedges_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J,type,
% 3.98/1.90 labele1794513953od_V_V: labele201426742od_V_V > set_Pr872354016od_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_LabeledGraphs_Olabeled__graph_Oedges_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J,type,
% 3.98/1.90 labele668941254od_V_V: labele236903175od_V_V > set_Pr951255342od_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_LabeledGraphs_Olabeled__graph_Oedges_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001tf__V,type,
% 3.98/1.90 labele1469545390nt_V_V: labele788688367nt_V_V > set_Pr1498723630od_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_LabeledGraphs_Olabeled__graph_Oedges_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001tf__V__H,type,
% 3.98/1.90 labele515735386nt_V_V: labele2115946735nt_V_V > set_Pr744279122od_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_LabeledGraphs_Olabeled__graph_Overtices_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J,type,
% 3.98/1.90 labele1328382418od_V_V: labele201426742od_V_V > set_Pr744279122od_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_LabeledGraphs_Olabeled__graph_Overtices_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J,type,
% 3.98/1.90 labele1822884081_V_nat: labele506073123_V_nat > set_Pr1058435079_V_nat ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_LabeledGraphs_Olabeled__graph_Overtices_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J,type,
% 3.98/1.90 labele981584981od_V_V: labele236903175od_V_V > set_Product_prod_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_LabeledGraphs_Olabeled__graph_Overtices_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001tf__V,type,
% 3.98/1.90 labele1152678333nt_V_V: labele788688367nt_V_V > set_V2 ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_LabeledGraphs_Olabeled__graph_Overtices_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001tf__V__H,type,
% 3.98/1.90 labele1134902411nt_V_V: labele2115946735nt_V_V > set_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_LabeledGraphs_Omap__graph_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_001tf__V__H_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J,type,
% 3.98/1.90 map_gr157381846tant_V: set_Pr257494450_V_V_V > labele201426742od_V_V > labele2115946735nt_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_LabeledGraphs_Omap__graph_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_001tf__V__H_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J,type,
% 3.98/1.90 map_gr875022471tant_V: set_Pr1228022213_V_V_V > labele236903175od_V_V > labele2115946735nt_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_LabeledGraphs_Omap__graph_001tf__V_001tf__V__H_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J,type,
% 3.98/1.90 map_gr530397039tant_V: set_Product_prod_V_V2 > labele788688367nt_V_V > labele2115946735nt_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_LabeledGraphs_Omap__graph_001tf__V__H_001tf__V__H_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J,type,
% 3.98/1.90 map_gr907434255tant_V: set_Product_prod_V_V > labele2115946735nt_V_V > labele2115946735nt_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_LabeledGraphs_Orestrict_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J,type,
% 3.98/1.90 restri1699516426od_V_V: labele201426742od_V_V > labele201426742od_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_LabeledGraphs_Orestrict_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J,type,
% 3.98/1.90 restri1932147897_V_nat: labele506073123_V_nat > labele506073123_V_nat ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_LabeledGraphs_Orestrict_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J,type,
% 3.98/1.90 restri1502575645od_V_V: labele236903175od_V_V > labele236903175od_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_LabeledGraphs_Orestrict_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001tf__V,type,
% 3.98/1.90 restri175070597nt_V_V: labele788688367nt_V_V > labele788688367nt_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_LabeledGraphs_Orestrict_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001tf__V__H,type,
% 3.98/1.90 restri1305980611nt_V_V: labele2115946735nt_V_V > labele2115946735nt_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_J,type,
% 3.98/1.90 sup_su693515134od_V_V: set_Pr744279122od_V_V > set_Pr744279122od_V_V > set_Pr744279122od_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J_J,type,
% 3.98/1.90 sup_su1043134939_V_nat: set_Pr1058435079_V_nat > set_Pr1058435079_V_nat > set_Pr1058435079_V_nat ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J,type,
% 3.98/1.90 sup_su551882943od_V_V: set_Product_prod_V_V > set_Product_prod_V_V > set_Product_prod_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_Itf__V_J,type,
% 3.98/1.90 sup_sup_set_V: set_V2 > set_V2 > set_V2 ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_Itf__V__H_J,type,
% 3.98/1.90 sup_sup_set_V2: set_V > set_V > set_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_M_Eo_J,type,
% 3.98/1.90 bot_bo2024487199_V_V_o: produc1699571228od_V_V > $o ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J_M_Eo_J,type,
% 3.98/1.90 bot_bo1078500394_nat_o: produc778275879_V_nat > $o ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_M_Eo_J,type,
% 3.98/1.90 bot_bo1168561222_V_V_o: product_prod_V_V > $o ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Orderings_Obot__class_Obot_001_062_Itf__V_M_Eo_J,type,
% 3.98/1.90 bot_bot_V_o: v2 > $o ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Orderings_Obot__class_Obot_001_062_Itf__V__H_M_Eo_J,type,
% 3.98/1.90 bot_bot_V_o2: v > $o ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J,type,
% 3.98/1.90 bot_bo1053950006_V_nat: set_la14611914_V_nat ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J_J_J_J,type,
% 3.98/1.90 bot_bo634818242_V_nat: set_Pr1326571566_V_nat ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_J_J,type,
% 3.98/1.90 bot_bo451843010od_V_V: set_Pr951255342od_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_J,type,
% 3.98/1.90 bot_bo667804902od_V_V: set_Pr744279122od_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J_J_Mt__Nat__Onat_J_J_J,type,
% 3.98/1.90 bot_bo323535987at_nat: set_Pr361461255at_nat ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_It__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_It__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_Mt__Nat__Onat_J_J_J,type,
% 3.98/1.90 bot_bo1196823539_V_nat: set_Pr597600647_V_nat ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J_J,type,
% 3.98/1.90 bot_bo907687539_V_nat: set_Pr1058435079_V_nat ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V__H_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V__H_J_Mt__Nat__Onat_J_J_J,type,
% 3.98/1.90 bot_bo1834032757_V_nat: set_Pr473545225_V_nat ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J_J_J,type,
% 3.98/1.90 bot_bo2057106227_V_nat: set_Pr1007924423_V_nat ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J_Mtf__V__H_J_J,type,
% 3.98/1.90 bot_bo1708783349_nat_V: set_Pr1056235617_nat_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_J,type,
% 3.98/1.90 bot_bo12878899od_V_V: set_Pr2022779335od_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_Mtf__V__H_J_J,type,
% 3.98/1.90 bot_bo688400985_V_V_V: set_Pr1228022213_V_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J,type,
% 3.98/1.90 bot_bo1389414743od_V_V: set_Product_prod_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__V_J,type,
% 3.98/1.90 bot_bot_set_V: set_V2 ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__V__H_J,type,
% 3.98/1.90 bot_bot_set_V2: set_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Product__Type_OPair_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_Mt__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_J,type,
% 3.98/1.90 produc2132932316od_V_V: standard_Constant_V > produc1082089497od_V_V > produc1269720746od_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Product__Type_OPair_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J,type,
% 3.98/1.90 produc1482441770od_V_V: standard_Constant_V > produc522115815od_V_V > produc1443401592od_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Product__Type_OPair_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Product____Type__Oprod_Itf__V_Mtf__V_J,type,
% 3.98/1.90 produc1171747370od_V_V: standard_Constant_V > product_prod_V_V2 > produc1113554040od_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Product__Type_OPair_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J,type,
% 3.98/1.90 produc107991630od_V_V: standard_Constant_V > product_prod_V_V > produc1699571228od_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Product__Type_OPair_001t__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_001t__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J,type,
% 3.98/1.90 produc698429463_V_nat: labele2128733290_V_nat > labele2128733290_V_nat > produc778275879_V_nat ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Product__Type_OPair_001t__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mtf__V__H_J_001t__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mtf__V__H_J,type,
% 3.98/1.90 produc533118295nt_V_V: labele2115946735nt_V_V > labele2115946735nt_V_V > produc651414759nt_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J,type,
% 3.98/1.90 produc1736057425od_V_V: produc1699571228od_V_V > produc1699571228od_V_V > produc1082089497od_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J,type,
% 3.98/1.90 produc1905750615od_V_V: product_prod_V_V > product_prod_V_V > produc522115815od_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Product__Type_OPair_001tf__V_001tf__V,type,
% 3.98/1.90 product_Pair_V_V: v2 > v2 > product_prod_V_V2 ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Product__Type_OPair_001tf__V__H_001tf__V__H,type,
% 3.98/1.90 product_Pair_V_V2: v > v > product_prod_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Relation_OId__on_001t__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J,type,
% 3.98/1.90 id_on_1882925319_V_nat: set_la14611914_V_nat > set_Pr1058435079_V_nat ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Relation_OId__on_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J,type,
% 3.98/1.90 id_on_1491482303od_V_V: set_Pr744279122od_V_V > set_Pr2015814777od_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Relation_OId__on_001t__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J,type,
% 3.98/1.90 id_on_558037444_V_nat: set_Pr1058435079_V_nat > set_Pr1007924423_V_nat ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Relation_OId__on_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J,type,
% 3.98/1.90 id_on_2125509800od_V_V: set_Product_prod_V_V > set_Pr2022779335od_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Relation_OId__on_001tf__V,type,
% 3.98/1.90 id_on_V: set_V2 > set_Product_prod_V_V3 ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Relation_OId__on_001tf__V__H,type,
% 3.98/1.90 id_on_V2: set_V > set_Product_prod_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_RulesAndChains_Oconsequence__graph_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Nat__Onat_001tf__V__H,type,
% 3.98/1.90 conseq1236301781_nat_V: set_Pr1058435079_V_nat > labele2115946735nt_V_V > $o ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_RulesAndChains_Oextensible_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Nat__Onat_001tf__V__H,type,
% 3.98/1.90 extens1072773157_nat_V: produc778275879_V_nat > labele2115946735nt_V_V > set_Pr53436518_nat_V > $o ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_RulesAndChains_Oextensible_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001tf__V__H_001tf__V__H,type,
% 3.98/1.90 extens1533825066_V_V_V: produc651414759nt_V_V > labele2115946735nt_V_V > set_Product_prod_V_V > $o ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_RulesAndChains_Omaintained_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Nat__Onat_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J,type,
% 3.98/1.90 mainta1342478555od_V_V: produc778275879_V_nat > labele201426742od_V_V > $o ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_RulesAndChains_Omaintained_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Nat__Onat_001t__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J,type,
% 3.98/1.90 mainta922614952_V_nat: produc778275879_V_nat > labele506073123_V_nat > $o ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_RulesAndChains_Omaintained_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Nat__Onat_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J,type,
% 3.98/1.90 mainta1984786828od_V_V: produc778275879_V_nat > labele236903175od_V_V > $o ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_RulesAndChains_Omaintained_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Nat__Onat_001tf__V,type,
% 3.98/1.90 mainta1026355316_nat_V: produc778275879_V_nat > labele788688367nt_V_V > $o ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_RulesAndChains_Omaintained_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001t__Nat__Onat_001tf__V__H,type,
% 3.98/1.90 mainta197426964_nat_V: produc778275879_V_nat > labele2115946735nt_V_V > $o ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_RulesAndChains_Omaintained_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_001tf__V__H_001tf__V__H,type,
% 3.98/1.90 mainta1699210777_V_V_V: produc651414759nt_V_V > labele2115946735nt_V_V > $o ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J,type,
% 3.98/1.90 collec1840263537od_V_V: ( produc1699571228od_V_V > $o ) > set_Pr744279122od_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J,type,
% 3.98/1.90 collec1411521682_V_nat: ( produc778275879_V_nat > $o ) > set_Pr1058435079_V_nat ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J,type,
% 3.98/1.90 collec2040633974od_V_V: ( product_prod_V_V > $o ) > set_Product_prod_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Set_OCollect_001tf__V,type,
% 3.98/1.90 collect_V: ( v2 > $o ) > set_V2 ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Set_OCollect_001tf__V__H,type,
% 3.98/1.90 collect_V2: ( v > $o ) > set_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Set_Oinsert_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J,type,
% 3.98/1.90 insert1818834324tant_V: standard_Constant_V > set_St1111633946tant_V > set_St1111633946tant_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Set_Oinsert_001t__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J,type,
% 3.98/1.90 insert213439034_V_nat: labele2128733290_V_nat > set_la14611914_V_nat > set_la14611914_V_nat ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J,type,
% 3.98/1.90 insert135842892od_V_V: produc1699571228od_V_V > set_Pr744279122od_V_V > set_Pr744279122od_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J,type,
% 3.98/1.90 insert481364471_V_nat: produc778275879_V_nat > set_Pr1058435079_V_nat > set_Pr1058435079_V_nat ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J,type,
% 3.98/1.90 insert2024285275od_V_V: product_prod_V_V > set_Product_prod_V_V > set_Product_prod_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Set_Oinsert_001tf__V,type,
% 3.98/1.90 insert_V: v2 > set_V2 > set_V2 ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_Set_Oinsert_001tf__V__H,type,
% 3.98/1.90 insert_V2: v > set_V > set_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Oconstant__rules_001t__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J,type,
% 3.98/1.90 standa434642387_V_nat: set_Pr1058435079_V_nat > set_Pr361461255at_nat ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Oconstant__rules_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J,type,
% 3.98/1.90 standa1571708471od_V_V: set_Product_prod_V_V > set_Pr597600647_V_nat ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Oconstant__rules_001tf__V,type,
% 3.98/1.90 standa1897115807ules_V: set_V2 > set_Pr1058435079_V_nat ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Oconstant__rules_001tf__V__H,type,
% 3.98/1.90 standa294833961ules_V: set_V > set_Pr473545225_V_nat ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Oidentity__rules_001tf__V,type,
% 3.98/1.90 standa1568205529ules_V: set_St1111633946tant_V > set_Pr1058435079_V_nat ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Ononempty__rule_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J,type,
% 3.98/1.90 standa1319953089tant_V: produc778275879_V_nat ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Ostandard__rules_001tf__V,type,
% 3.98/1.90 standa157301464ules_V: set_V2 > set_St1111633946tant_V > set_Pr1058435079_V_nat ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Otop__rule_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J,type,
% 3.98/1.90 standa214871990tant_V: standard_Constant_V > produc778275879_V_nat ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_member_001t__LabeledGraphSemantics__OStandard____Constant_Itf__V_J,type,
% 3.98/1.90 member1542015739tant_V: standard_Constant_V > set_St1111633946tant_V > $o ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_member_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_Mt__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_J_J,type,
% 3.98/1.90 member600445121od_V_V: produc1269720746od_V_V > set_Pr872354016od_V_V > $o ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_member_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_J,type,
% 3.98/1.90 member361435663od_V_V: produc1443401592od_V_V > set_Pr951255342od_V_V > $o ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_member_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V_Mtf__V_J_J,type,
% 3.98/1.90 member1416643087od_V_V: produc1113554040od_V_V > set_Pr1498723630od_V_V > $o ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_member_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J,type,
% 3.98/1.90 member1010391347od_V_V: produc1699571228od_V_V > set_Pr744279122od_V_V > $o ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_member_001t__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Nat__Onat_J_J,type,
% 3.98/1.90 member1886821968_V_nat: produc778275879_V_nat > set_Pr1058435079_V_nat > $o ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_Mt__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__V_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J_J,type,
% 3.98/1.90 member785416642od_V_V: produc1082089497od_V_V > set_Pr2015814777od_V_V > $o ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_Mt__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J_J,type,
% 3.98/1.90 member134497296od_V_V: produc522115815od_V_V > set_Pr2022779335od_V_V > $o ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_member_001t__Product____Type__Oprod_Itf__V_Mtf__V_J,type,
% 3.98/1.90 member1990987792od_V_V: product_prod_V_V2 > set_Product_prod_V_V3 > $o ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_member_001t__Product____Type__Oprod_Itf__V__H_Mtf__V__H_J,type,
% 3.98/1.90 member2015049524od_V_V: product_prod_V_V > set_Product_prod_V_V > $o ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_member_001tf__V,type,
% 3.98/1.90 member_V: v2 > set_V2 > $o ).
% 3.98/1.90
% 3.98/1.90 thf(sy_c_member_001tf__V__H,type,
% 3.98/1.90 member_V2: v > set_V > $o ).
% 3.98/1.90
% 3.98/1.90 thf(sy_v_C,type,
% 3.98/1.90 c: set_V2 ).
% 3.98/1.90
% 3.98/1.90 thf(sy_v_G_H,type,
% 3.98/1.90 g: labele2115946735nt_V_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_v_L,type,
% 3.98/1.90 l: set_St1111633946tant_V ).
% 3.98/1.90
% 3.98/1.90 thf(sy_v_h____,type,
% 3.98/1.90 h: v > v ).
% 3.98/1.90
% 3.98/1.90 thf(sy_v_m____,type,
% 3.98/1.90 m: v2 > v ).
% 3.98/1.90
% 3.98/1.90 thf(sy_v_x____,type,
% 3.98/1.90 x: v ).
% 3.98/1.90
% 3.98/1.90 thf(sy_v_xa____,type,
% 3.98/1.90 xa: v2 ).
% 3.98/1.90
% 3.98/1.90 thf(sy_v_y____,type,
% 3.98/1.90 y: v2 ).
% 3.98/1.90
% 3.98/1.90 thf(fact_0_x,axiom,
% 3.98/1.90 member_V2 @ x @ ( labele1134902411nt_V_V @ g ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_1__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062x_O_Ax_A_092_060in_062_Avertices_AG_H_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 3.98/1.90 ~ ! [X: v] :
% 3.98/1.90 ~ ( member_V2 @ X @ ( labele1134902411nt_V_V @ g ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_2__C1_C_I3_J,axiom,
% 3.98/1.90 ( ( m @ xa )
% 3.98/1.90 = ( m @ y ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_3__C1_C_I1_J,axiom,
% 3.98/1.90 member_V @ xa @ c ).
% 3.98/1.90
% 3.98/1.90 thf(fact_4__C1_C_I2_J,axiom,
% 3.98/1.90 member_V @ y @ c ).
% 3.98/1.90
% 3.98/1.90 thf(fact_5__092_060open_062_Im_Ax_M_Am_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ax_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062,axiom,
% 3.98/1.90 member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ xa ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_6__092_060open_062_Im_Ax_M_Am_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ay_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062,axiom,
% 3.98/1.90 member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ y ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_7_gr_I1_J,axiom,
% 3.98/1.90 ( g
% 3.98/1.90 = ( restri1305980611nt_V_V @ g ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_8_h_I3_J,axiom,
% 3.98/1.90 graph_1808119_V_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) @ g @ ( id_on_V2 @ ( labele1134902411nt_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_9_Standard__Constant_Oinject,axiom,
% 3.98/1.90 ! [X4: v2,Y4: v2] :
% 3.98/1.90 ( ( ( standard_S_Const_V @ X4 )
% 3.98/1.90 = ( standard_S_Const_V @ Y4 ) )
% 3.98/1.90 = ( X4 = Y4 ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_10_prod_Oinject,axiom,
% 3.98/1.90 ! [X1: v,X2: v,Y1: v,Y2: v] :
% 3.98/1.90 ( ( ( product_Pair_V_V2 @ X1 @ X2 )
% 3.98/1.90 = ( product_Pair_V_V2 @ Y1 @ Y2 ) )
% 3.98/1.90 = ( ( X1 = Y1 )
% 3.98/1.90 & ( X2 = Y2 ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_11_prod_Oinject,axiom,
% 3.98/1.90 ! [X1: standard_Constant_V,X2: product_prod_V_V,Y1: standard_Constant_V,Y2: product_prod_V_V] :
% 3.98/1.90 ( ( ( produc107991630od_V_V @ X1 @ X2 )
% 3.98/1.90 = ( produc107991630od_V_V @ Y1 @ Y2 ) )
% 3.98/1.90 = ( ( X1 = Y1 )
% 3.98/1.90 & ( X2 = Y2 ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_12_old_Oprod_Oinject,axiom,
% 3.98/1.90 ! [A: v,B: v,A2: v,B2: v] :
% 3.98/1.90 ( ( ( product_Pair_V_V2 @ A @ B )
% 3.98/1.90 = ( product_Pair_V_V2 @ A2 @ B2 ) )
% 3.98/1.90 = ( ( A = A2 )
% 3.98/1.90 & ( B = B2 ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_13_old_Oprod_Oinject,axiom,
% 3.98/1.90 ! [A: standard_Constant_V,B: product_prod_V_V,A2: standard_Constant_V,B2: product_prod_V_V] :
% 3.98/1.90 ( ( ( produc107991630od_V_V @ A @ B )
% 3.98/1.90 = ( produc107991630od_V_V @ A2 @ B2 ) )
% 3.98/1.90 = ( ( A = A2 )
% 3.98/1.90 & ( B = B2 ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_14_m,axiom,
% 3.98/1.90 ! [X3: v2] :
% 3.98/1.90 ( ( member_V @ X3 @ c )
% 3.98/1.90 => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ X3 ) @ ( m @ X3 ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ X3 ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_15_top__nonempty,axiom,
% 3.98/1.90 member2015049524od_V_V @ ( product_Pair_V_V2 @ x @ x ) @ ( getRel1432786916nt_V_V @ standard_S_Top_V @ g ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_16_cf,axiom,
% 3.98/1.90 ( ( getRel1432786916nt_V_V @ standard_S_Bot_V @ g )
% 3.98/1.90 = bot_bo1389414743od_V_V ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_17__092_060open_062_092_060And_062c_O_Ac_A_092_060in_062_AC_A_092_060Longrightarrow_062_A_092_060exists_062v_O_A_Iv_M_Av_J_A_092_060in_062_AgetRel_A_IS__Const_Ac_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062,axiom,
% 3.98/1.90 ! [C: v2] :
% 3.98/1.90 ( ( member_V @ C @ c )
% 3.98/1.90 => ? [V: v] : ( member2015049524od_V_V @ ( product_Pair_V_V2 @ V @ V ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ C ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_18__092_060open_062_092_060forall_062c_O_A_092_060exists_062v_O_Ac_A_092_060in_062_AC_A_092_060longrightarrow_062_A_Iv_M_Av_J_A_092_060in_062_AgetRel_A_IS__Const_Ac_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062,axiom,
% 3.98/1.90 ! [C2: v2] :
% 3.98/1.90 ? [V: v] :
% 3.98/1.90 ( ( member_V @ C2 @ c )
% 3.98/1.90 => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ V @ V ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ C2 ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_19__092_060open_062_092_060exists_062f_O_A_092_060forall_062x_O_Ax_A_092_060in_062_AC_A_092_060longrightarrow_062_A_If_Ax_M_Af_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ax_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062,axiom,
% 3.98/1.90 ? [F: v2 > v] :
% 3.98/1.90 ! [X5: v2] :
% 3.98/1.90 ( ( member_V @ X5 @ c )
% 3.98/1.90 => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( F @ X5 ) @ ( F @ X5 ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ X5 ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_20__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062m_O_A_I_092_060And_062x_O_Ax_A_092_060in_062_AC_A_092_060Longrightarrow_062_A_Im_Ax_M_Am_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ax_J_A_Imap__graph__fn_AG_H_Ah_J_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 3.98/1.90 ~ ! [M: v2 > v] :
% 3.98/1.90 ~ ! [X5: v2] :
% 3.98/1.90 ( ( member_V @ X5 @ c )
% 3.98/1.90 => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( M @ X5 ) @ ( M @ X5 ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ X5 ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_21_getRel__homR,axiom,
% 3.98/1.90 ! [Y: v,Z: v,L: standard_Constant_V,G: labele2115946735nt_V_V,U: v,F2: set_Product_prod_V_V,V2: v] :
% 3.98/1.90 ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ Y @ Z ) @ ( getRel1432786916nt_V_V @ L @ G ) )
% 3.98/1.90 => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ Y @ U ) @ F2 )
% 3.98/1.90 => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ Z @ V2 ) @ F2 )
% 3.98/1.90 => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ U @ V2 ) @ ( getRel1432786916nt_V_V @ L @ ( map_gr907434255tant_V @ F2 @ G ) ) ) ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_22_surj__pair,axiom,
% 3.98/1.90 ! [P: product_prod_V_V] :
% 3.98/1.90 ? [X: v,Y3: v] :
% 3.98/1.90 ( P
% 3.98/1.90 = ( product_Pair_V_V2 @ X @ Y3 ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_23_surj__pair,axiom,
% 3.98/1.90 ! [P: produc1699571228od_V_V] :
% 3.98/1.90 ? [X: standard_Constant_V,Y3: product_prod_V_V] :
% 3.98/1.90 ( P
% 3.98/1.90 = ( produc107991630od_V_V @ X @ Y3 ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_24_h_I1_J,axiom,
% 3.98/1.90 ( ( comp_V_V_V2 @ h @ h )
% 3.98/1.90 = h ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_25_getRel__map__fn,axiom,
% 3.98/1.90 ! [A22: product_prod_V_V,G: labele236903175od_V_V,B22: product_prod_V_V,L: standard_Constant_V,F2: product_prod_V_V > v,A: v,B: v] :
% 3.98/1.90 ( ( member2015049524od_V_V @ A22 @ ( labele981584981od_V_V @ G ) )
% 3.98/1.90 => ( ( member2015049524od_V_V @ B22 @ ( labele981584981od_V_V @ G ) )
% 3.98/1.90 => ( ( member134497296od_V_V @ ( produc1905750615od_V_V @ A22 @ B22 ) @ ( getRel1902920892od_V_V @ L @ G ) )
% 3.98/1.90 => ( ( ( F2 @ A22 )
% 3.98/1.90 = A )
% 3.98/1.90 => ( ( ( F2 @ B22 )
% 3.98/1.90 = B )
% 3.98/1.90 => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( getRel1432786916nt_V_V @ L @ ( map_gr875022471tant_V @ ( bNF_Gr1069958334_V_V_V @ ( labele981584981od_V_V @ G ) @ F2 ) @ G ) ) ) ) ) ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_26_getRel__map__fn,axiom,
% 3.98/1.90 ! [A22: v2,G: labele788688367nt_V_V,B22: v2,L: standard_Constant_V,F2: v2 > v,A: v,B: v] :
% 3.98/1.90 ( ( member_V @ A22 @ ( labele1152678333nt_V_V @ G ) )
% 3.98/1.90 => ( ( member_V @ B22 @ ( labele1152678333nt_V_V @ G ) )
% 3.98/1.90 => ( ( member1990987792od_V_V @ ( product_Pair_V_V @ A22 @ B22 ) @ ( getRel632961956nt_V_V @ L @ G ) )
% 3.98/1.90 => ( ( ( F2 @ A22 )
% 3.98/1.90 = A )
% 3.98/1.90 => ( ( ( F2 @ B22 )
% 3.98/1.90 = B )
% 3.98/1.90 => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( getRel1432786916nt_V_V @ L @ ( map_gr530397039tant_V @ ( bNF_Gr_V_V @ ( labele1152678333nt_V_V @ G ) @ F2 ) @ G ) ) ) ) ) ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_27_getRel__map__fn,axiom,
% 3.98/1.90 ! [A22: produc1699571228od_V_V,G: labele201426742od_V_V,B22: produc1699571228od_V_V,L: standard_Constant_V,F2: produc1699571228od_V_V > v,A: v,B: v] :
% 3.98/1.90 ( ( member1010391347od_V_V @ A22 @ ( labele1328382418od_V_V @ G ) )
% 3.98/1.90 => ( ( member1010391347od_V_V @ B22 @ ( labele1328382418od_V_V @ G ) )
% 3.98/1.90 => ( ( member785416642od_V_V @ ( produc1736057425od_V_V @ A22 @ B22 ) @ ( getRel2057312683od_V_V @ L @ G ) )
% 3.98/1.90 => ( ( ( F2 @ A22 )
% 3.98/1.90 = A )
% 3.98/1.90 => ( ( ( F2 @ B22 )
% 3.98/1.90 = B )
% 3.98/1.90 => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( getRel1432786916nt_V_V @ L @ ( map_gr157381846tant_V @ ( bNF_Gr480427157_V_V_V @ ( labele1328382418od_V_V @ G ) @ F2 ) @ G ) ) ) ) ) ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_28_getRel__map__fn,axiom,
% 3.98/1.90 ! [A22: v,G: labele2115946735nt_V_V,B22: v,L: standard_Constant_V,F2: v > v,A: v,B: v] :
% 3.98/1.90 ( ( member_V2 @ A22 @ ( labele1134902411nt_V_V @ G ) )
% 3.98/1.90 => ( ( member_V2 @ B22 @ ( labele1134902411nt_V_V @ G ) )
% 3.98/1.90 => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A22 @ B22 ) @ ( getRel1432786916nt_V_V @ L @ G ) )
% 3.98/1.90 => ( ( ( F2 @ A22 )
% 3.98/1.90 = A )
% 3.98/1.90 => ( ( ( F2 @ B22 )
% 3.98/1.90 = B )
% 3.98/1.90 => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( getRel1432786916nt_V_V @ L @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ G ) @ F2 ) @ G ) ) ) ) ) ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_29_getRel__hom,axiom,
% 3.98/1.90 ! [Y: product_prod_V_V,Z: product_prod_V_V,L: standard_Constant_V,G: labele236903175od_V_V,F2: product_prod_V_V > v] :
% 3.98/1.90 ( ( member134497296od_V_V @ ( produc1905750615od_V_V @ Y @ Z ) @ ( getRel1902920892od_V_V @ L @ G ) )
% 3.98/1.90 => ( ( member2015049524od_V_V @ Y @ ( labele981584981od_V_V @ G ) )
% 3.98/1.90 => ( ( member2015049524od_V_V @ Z @ ( labele981584981od_V_V @ G ) )
% 3.98/1.90 => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( F2 @ Y ) @ ( F2 @ Z ) ) @ ( getRel1432786916nt_V_V @ L @ ( map_gr875022471tant_V @ ( bNF_Gr1069958334_V_V_V @ ( labele981584981od_V_V @ G ) @ F2 ) @ G ) ) ) ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_30_getRel__hom,axiom,
% 3.98/1.90 ! [Y: v2,Z: v2,L: standard_Constant_V,G: labele788688367nt_V_V,F2: v2 > v] :
% 3.98/1.90 ( ( member1990987792od_V_V @ ( product_Pair_V_V @ Y @ Z ) @ ( getRel632961956nt_V_V @ L @ G ) )
% 3.98/1.90 => ( ( member_V @ Y @ ( labele1152678333nt_V_V @ G ) )
% 3.98/1.90 => ( ( member_V @ Z @ ( labele1152678333nt_V_V @ G ) )
% 3.98/1.90 => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( F2 @ Y ) @ ( F2 @ Z ) ) @ ( getRel1432786916nt_V_V @ L @ ( map_gr530397039tant_V @ ( bNF_Gr_V_V @ ( labele1152678333nt_V_V @ G ) @ F2 ) @ G ) ) ) ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_31_getRel__hom,axiom,
% 3.98/1.90 ! [Y: produc1699571228od_V_V,Z: produc1699571228od_V_V,L: standard_Constant_V,G: labele201426742od_V_V,F2: produc1699571228od_V_V > v] :
% 3.98/1.90 ( ( member785416642od_V_V @ ( produc1736057425od_V_V @ Y @ Z ) @ ( getRel2057312683od_V_V @ L @ G ) )
% 3.98/1.90 => ( ( member1010391347od_V_V @ Y @ ( labele1328382418od_V_V @ G ) )
% 3.98/1.90 => ( ( member1010391347od_V_V @ Z @ ( labele1328382418od_V_V @ G ) )
% 3.98/1.90 => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( F2 @ Y ) @ ( F2 @ Z ) ) @ ( getRel1432786916nt_V_V @ L @ ( map_gr157381846tant_V @ ( bNF_Gr480427157_V_V_V @ ( labele1328382418od_V_V @ G ) @ F2 ) @ G ) ) ) ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_32_getRel__hom,axiom,
% 3.98/1.90 ! [Y: v,Z: v,L: standard_Constant_V,G: labele2115946735nt_V_V,F2: v > v] :
% 3.98/1.90 ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ Y @ Z ) @ ( getRel1432786916nt_V_V @ L @ G ) )
% 3.98/1.90 => ( ( member_V2 @ Y @ ( labele1134902411nt_V_V @ G ) )
% 3.98/1.90 => ( ( member_V2 @ Z @ ( labele1134902411nt_V_V @ G ) )
% 3.98/1.90 => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( F2 @ Y ) @ ( F2 @ Z ) ) @ ( getRel1432786916nt_V_V @ L @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ G ) @ F2 ) @ G ) ) ) ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_33_Standard__Constant_Odistinct_I1_J,axiom,
% 3.98/1.90 standard_S_Top_V != standard_S_Bot_V ).
% 3.98/1.90
% 3.98/1.90 thf(fact_34_Standard__Constant_Odistinct_I5_J,axiom,
% 3.98/1.90 ! [X4: v2] :
% 3.98/1.90 ( standard_S_Top_V
% 3.98/1.90 != ( standard_S_Const_V @ X4 ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_35_Standard__Constant_Odistinct_I9_J,axiom,
% 3.98/1.90 ! [X4: v2] :
% 3.98/1.90 ( standard_S_Bot_V
% 3.98/1.90 != ( standard_S_Const_V @ X4 ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_36_getRel__dom_I1_J,axiom,
% 3.98/1.90 ! [G: labele2115946735nt_V_V,A: v,B: v,L: standard_Constant_V] :
% 3.98/1.90 ( ( G
% 3.98/1.90 = ( restri1305980611nt_V_V @ G ) )
% 3.98/1.90 => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( getRel1432786916nt_V_V @ L @ G ) )
% 3.98/1.90 => ( member_V2 @ A @ ( labele1134902411nt_V_V @ G ) ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_37_getRel__dom_I2_J,axiom,
% 3.98/1.90 ! [G: labele2115946735nt_V_V,A: v,B: v,L: standard_Constant_V] :
% 3.98/1.90 ( ( G
% 3.98/1.90 = ( restri1305980611nt_V_V @ G ) )
% 3.98/1.90 => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( getRel1432786916nt_V_V @ L @ G ) )
% 3.98/1.90 => ( member_V2 @ B @ ( labele1134902411nt_V_V @ G ) ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_38_getRel__subgraph,axiom,
% 3.98/1.90 ! [Y: v,Z: v,L: standard_Constant_V,G: labele2115946735nt_V_V,G2: labele2115946735nt_V_V] :
% 3.98/1.90 ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ Y @ Z ) @ ( getRel1432786916nt_V_V @ L @ G ) )
% 3.98/1.90 => ( ( graph_1808119_V_V_V @ G @ G2 @ ( id_on_V2 @ ( labele1134902411nt_V_V @ G ) ) )
% 3.98/1.90 => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ Y @ Z ) @ ( getRel1432786916nt_V_V @ L @ G2 ) ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_39_old_Oprod_Oinducts,axiom,
% 3.98/1.90 ! [P2: product_prod_V_V > $o,Prod: product_prod_V_V] :
% 3.98/1.90 ( ! [A3: v,B3: v] : ( P2 @ ( product_Pair_V_V2 @ A3 @ B3 ) )
% 3.98/1.90 => ( P2 @ Prod ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_40_old_Oprod_Oinducts,axiom,
% 3.98/1.90 ! [P2: produc1699571228od_V_V > $o,Prod: produc1699571228od_V_V] :
% 3.98/1.90 ( ! [A3: standard_Constant_V,B3: product_prod_V_V] : ( P2 @ ( produc107991630od_V_V @ A3 @ B3 ) )
% 3.98/1.90 => ( P2 @ Prod ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_41_old_Oprod_Oexhaust,axiom,
% 3.98/1.90 ! [Y: product_prod_V_V] :
% 3.98/1.90 ~ ! [A3: v,B3: v] :
% 3.98/1.90 ( Y
% 3.98/1.90 != ( product_Pair_V_V2 @ A3 @ B3 ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_42_old_Oprod_Oexhaust,axiom,
% 3.98/1.90 ! [Y: produc1699571228od_V_V] :
% 3.98/1.90 ~ ! [A3: standard_Constant_V,B3: product_prod_V_V] :
% 3.98/1.90 ( Y
% 3.98/1.90 != ( produc107991630od_V_V @ A3 @ B3 ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_43_prod__induct3,axiom,
% 3.98/1.90 ! [P2: produc1699571228od_V_V > $o,X3: produc1699571228od_V_V] :
% 3.98/1.90 ( ! [A3: standard_Constant_V,B3: v,C3: v] : ( P2 @ ( produc107991630od_V_V @ A3 @ ( product_Pair_V_V2 @ B3 @ C3 ) ) )
% 3.98/1.90 => ( P2 @ X3 ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_44_prod__cases3,axiom,
% 3.98/1.90 ! [Y: produc1699571228od_V_V] :
% 3.98/1.90 ~ ! [A3: standard_Constant_V,B3: v,C3: v] :
% 3.98/1.90 ( Y
% 3.98/1.90 != ( produc107991630od_V_V @ A3 @ ( product_Pair_V_V2 @ B3 @ C3 ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_45_Pair__inject,axiom,
% 3.98/1.90 ! [A: v,B: v,A2: v,B2: v] :
% 3.98/1.90 ( ( ( product_Pair_V_V2 @ A @ B )
% 3.98/1.90 = ( product_Pair_V_V2 @ A2 @ B2 ) )
% 3.98/1.90 => ~ ( ( A = A2 )
% 3.98/1.90 => ( B != B2 ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_46_Pair__inject,axiom,
% 3.98/1.90 ! [A: standard_Constant_V,B: product_prod_V_V,A2: standard_Constant_V,B2: product_prod_V_V] :
% 3.98/1.90 ( ( ( produc107991630od_V_V @ A @ B )
% 3.98/1.90 = ( produc107991630od_V_V @ A2 @ B2 ) )
% 3.98/1.90 => ~ ( ( A = A2 )
% 3.98/1.90 => ( B != B2 ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_47_prod__cases,axiom,
% 3.98/1.90 ! [P2: product_prod_V_V > $o,P: product_prod_V_V] :
% 3.98/1.90 ( ! [A3: v,B3: v] : ( P2 @ ( product_Pair_V_V2 @ A3 @ B3 ) )
% 3.98/1.90 => ( P2 @ P ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_48_prod__cases,axiom,
% 3.98/1.90 ! [P2: produc1699571228od_V_V > $o,P: produc1699571228od_V_V] :
% 3.98/1.90 ( ! [A3: standard_Constant_V,B3: product_prod_V_V] : ( P2 @ ( produc107991630od_V_V @ A3 @ B3 ) )
% 3.98/1.90 => ( P2 @ P ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_49_mg,axiom,
% 3.98/1.90 ! [R: produc778275879_V_nat] :
% 3.98/1.90 ( ( mainta197426964_nat_V @ R @ g )
% 3.98/1.90 => ( mainta197426964_nat_V @ R @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_50_mem__Collect__eq,axiom,
% 3.98/1.90 ! [A: product_prod_V_V,P2: product_prod_V_V > $o] :
% 3.98/1.90 ( ( member2015049524od_V_V @ A @ ( collec2040633974od_V_V @ P2 ) )
% 3.98/1.90 = ( P2 @ A ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_51_mem__Collect__eq,axiom,
% 3.98/1.90 ! [A: v,P2: v > $o] :
% 3.98/1.90 ( ( member_V2 @ A @ ( collect_V2 @ P2 ) )
% 3.98/1.90 = ( P2 @ A ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_52_mem__Collect__eq,axiom,
% 3.98/1.90 ! [A: v2,P2: v2 > $o] :
% 3.98/1.90 ( ( member_V @ A @ ( collect_V @ P2 ) )
% 3.98/1.90 = ( P2 @ A ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_53_mem__Collect__eq,axiom,
% 3.98/1.90 ! [A: produc1699571228od_V_V,P2: produc1699571228od_V_V > $o] :
% 3.98/1.90 ( ( member1010391347od_V_V @ A @ ( collec1840263537od_V_V @ P2 ) )
% 3.98/1.90 = ( P2 @ A ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_54_Collect__mem__eq,axiom,
% 3.98/1.90 ! [A4: set_Product_prod_V_V] :
% 3.98/1.90 ( ( collec2040633974od_V_V
% 3.98/1.90 @ ^ [X6: product_prod_V_V] : ( member2015049524od_V_V @ X6 @ A4 ) )
% 3.98/1.90 = A4 ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_55_Collect__mem__eq,axiom,
% 3.98/1.90 ! [A4: set_V] :
% 3.98/1.90 ( ( collect_V2
% 3.98/1.90 @ ^ [X6: v] : ( member_V2 @ X6 @ A4 ) )
% 3.98/1.90 = A4 ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_56_Collect__mem__eq,axiom,
% 3.98/1.90 ! [A4: set_V2] :
% 3.98/1.90 ( ( collect_V
% 3.98/1.90 @ ^ [X6: v2] : ( member_V @ X6 @ A4 ) )
% 3.98/1.90 = A4 ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_57_Collect__mem__eq,axiom,
% 3.98/1.90 ! [A4: set_Pr744279122od_V_V] :
% 3.98/1.90 ( ( collec1840263537od_V_V
% 3.98/1.90 @ ^ [X6: produc1699571228od_V_V] : ( member1010391347od_V_V @ X6 @ A4 ) )
% 3.98/1.90 = A4 ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_58_graph__homo,axiom,
% 3.98/1.90 ! [G: labele2115946735nt_V_V,F2: v > v] :
% 3.98/1.90 ( ( G
% 3.98/1.90 = ( restri1305980611nt_V_V @ G ) )
% 3.98/1.90 => ( graph_1808119_V_V_V @ G @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ G ) @ F2 ) @ G ) @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ G ) @ F2 ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_59_map__graph__fn__id_I2_J,axiom,
% 3.98/1.90 ! [X7: labele2115946735nt_V_V] :
% 3.98/1.90 ( ( map_gr907434255tant_V @ ( id_on_V2 @ ( labele1134902411nt_V_V @ X7 ) ) @ X7 )
% 3.98/1.90 = ( restri1305980611nt_V_V @ X7 ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_60_map__graph__fn__graphI,axiom,
% 3.98/1.90 ! [G: labele2115946735nt_V_V,F2: v > v] :
% 3.98/1.90 ( ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ G ) @ F2 ) @ G )
% 3.98/1.90 = ( restri1305980611nt_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ G ) @ F2 ) @ G ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_61_map__graph__preserves__subgraph,axiom,
% 3.98/1.90 ! [A4: labele2115946735nt_V_V,B4: labele2115946735nt_V_V,F2: set_Product_prod_V_V] :
% 3.98/1.90 ( ( graph_1808119_V_V_V @ A4 @ B4 @ ( id_on_V2 @ ( labele1134902411nt_V_V @ A4 ) ) )
% 3.98/1.90 => ( graph_1808119_V_V_V @ ( map_gr907434255tant_V @ F2 @ A4 ) @ ( map_gr907434255tant_V @ F2 @ B4 ) @ ( id_on_V2 @ ( labele1134902411nt_V_V @ ( map_gr907434255tant_V @ F2 @ A4 ) ) ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_62_subgraph__refl,axiom,
% 3.98/1.90 ! [G: labele2115946735nt_V_V] :
% 3.98/1.90 ( ( graph_1808119_V_V_V @ G @ G @ ( id_on_V2 @ ( labele1134902411nt_V_V @ G ) ) )
% 3.98/1.90 = ( G
% 3.98/1.90 = ( restri1305980611nt_V_V @ G ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_63_subgraph__restrict,axiom,
% 3.98/1.90 ! [G: labele2115946735nt_V_V] :
% 3.98/1.90 ( ( graph_1808119_V_V_V @ G @ ( restri1305980611nt_V_V @ G ) @ ( id_on_V2 @ ( labele1134902411nt_V_V @ G ) ) )
% 3.98/1.90 = ( G
% 3.98/1.90 = ( restri1305980611nt_V_V @ G ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_64_graph__homomorphism__Id,axiom,
% 3.98/1.90 ! [A: labele2115946735nt_V_V] : ( graph_1808119_V_V_V @ ( restri1305980611nt_V_V @ A ) @ ( restri1305980611nt_V_V @ A ) @ ( id_on_V2 @ ( labele1134902411nt_V_V @ A ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_65_Id__on__empty,axiom,
% 3.98/1.90 ( ( id_on_1882925319_V_nat @ bot_bo1053950006_V_nat )
% 3.98/1.90 = bot_bo907687539_V_nat ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_66_Id__on__empty,axiom,
% 3.98/1.90 ( ( id_on_2125509800od_V_V @ bot_bo1389414743od_V_V )
% 3.98/1.90 = bot_bo12878899od_V_V ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_67_Id__on__empty,axiom,
% 3.98/1.90 ( ( id_on_V2 @ bot_bot_set_V2 )
% 3.98/1.90 = bot_bo1389414743od_V_V ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_68_Id__on__empty,axiom,
% 3.98/1.90 ( ( id_on_558037444_V_nat @ bot_bo907687539_V_nat )
% 3.98/1.90 = bot_bo2057106227_V_nat ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_69_Gr__empty,axiom,
% 3.98/1.90 ! [F2: labele2128733290_V_nat > labele2128733290_V_nat] :
% 3.98/1.90 ( ( bNF_Gr17960482_V_nat @ bot_bo1053950006_V_nat @ F2 )
% 3.98/1.90 = bot_bo907687539_V_nat ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_70_Gr__empty,axiom,
% 3.98/1.90 ! [F2: v > v] :
% 3.98/1.90 ( ( bNF_Gr_V_V2 @ bot_bot_set_V2 @ F2 )
% 3.98/1.90 = bot_bo1389414743od_V_V ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_71_restrict__idemp,axiom,
% 3.98/1.90 ! [X3: labele2115946735nt_V_V] :
% 3.98/1.90 ( ( restri1305980611nt_V_V @ ( restri1305980611nt_V_V @ X3 ) )
% 3.98/1.90 = ( restri1305980611nt_V_V @ X3 ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_72_in__Gr,axiom,
% 3.98/1.90 ! [X3: v,Y: v,A4: set_V,F2: v > v] :
% 3.98/1.90 ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ X3 @ Y ) @ ( bNF_Gr_V_V2 @ A4 @ F2 ) )
% 3.98/1.90 = ( ( member_V2 @ X3 @ A4 )
% 3.98/1.90 & ( ( F2 @ X3 )
% 3.98/1.90 = Y ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_73_in__Gr,axiom,
% 3.98/1.90 ! [X3: standard_Constant_V,Y: product_prod_V_V,A4: set_St1111633946tant_V,F2: standard_Constant_V > product_prod_V_V] :
% 3.98/1.90 ( ( member1010391347od_V_V @ ( produc107991630od_V_V @ X3 @ Y ) @ ( bNF_Gr320641027od_V_V @ A4 @ F2 ) )
% 3.98/1.90 = ( ( member1542015739tant_V @ X3 @ A4 )
% 3.98/1.90 & ( ( F2 @ X3 )
% 3.98/1.90 = Y ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_74_Gr__not__in,axiom,
% 3.98/1.90 ! [X3: v,F3: set_V,F2: v > v,Y: v] :
% 3.98/1.90 ( ( ~ ( member_V2 @ X3 @ F3 )
% 3.98/1.90 | ( ( F2 @ X3 )
% 3.98/1.90 != Y ) )
% 3.98/1.90 => ~ ( member2015049524od_V_V @ ( product_Pair_V_V2 @ X3 @ Y ) @ ( bNF_Gr_V_V2 @ F3 @ F2 ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_75_Gr__not__in,axiom,
% 3.98/1.90 ! [X3: standard_Constant_V,F3: set_St1111633946tant_V,F2: standard_Constant_V > product_prod_V_V,Y: product_prod_V_V] :
% 3.98/1.90 ( ( ~ ( member1542015739tant_V @ X3 @ F3 )
% 3.98/1.90 | ( ( F2 @ X3 )
% 3.98/1.90 != Y ) )
% 3.98/1.90 => ~ ( member1010391347od_V_V @ ( produc107991630od_V_V @ X3 @ Y ) @ ( bNF_Gr320641027od_V_V @ F3 @ F2 ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_76_Id__onI,axiom,
% 3.98/1.90 ! [A: product_prod_V_V,A4: set_Product_prod_V_V] :
% 3.98/1.90 ( ( member2015049524od_V_V @ A @ A4 )
% 3.98/1.90 => ( member134497296od_V_V @ ( produc1905750615od_V_V @ A @ A ) @ ( id_on_2125509800od_V_V @ A4 ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_77_Id__onI,axiom,
% 3.98/1.90 ! [A: v2,A4: set_V2] :
% 3.98/1.90 ( ( member_V @ A @ A4 )
% 3.98/1.90 => ( member1990987792od_V_V @ ( product_Pair_V_V @ A @ A ) @ ( id_on_V @ A4 ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_78_Id__onI,axiom,
% 3.98/1.90 ! [A: produc1699571228od_V_V,A4: set_Pr744279122od_V_V] :
% 3.98/1.90 ( ( member1010391347od_V_V @ A @ A4 )
% 3.98/1.90 => ( member785416642od_V_V @ ( produc1736057425od_V_V @ A @ A ) @ ( id_on_1491482303od_V_V @ A4 ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_79_Id__onI,axiom,
% 3.98/1.90 ! [A: v,A4: set_V] :
% 3.98/1.90 ( ( member_V2 @ A @ A4 )
% 3.98/1.90 => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ A ) @ ( id_on_V2 @ A4 ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_80_vertices__restrict,axiom,
% 3.98/1.90 ! [G: labele2115946735nt_V_V] :
% 3.98/1.90 ( ( labele1134902411nt_V_V @ ( restri1305980611nt_V_V @ G ) )
% 3.98/1.90 = ( labele1134902411nt_V_V @ G ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_81_map__graph__preserves__restricted,axiom,
% 3.98/1.90 ! [G: labele2115946735nt_V_V,F2: set_Product_prod_V_V] :
% 3.98/1.90 ( ( G
% 3.98/1.90 = ( restri1305980611nt_V_V @ G ) )
% 3.98/1.90 => ( ( map_gr907434255tant_V @ F2 @ G )
% 3.98/1.90 = ( restri1305980611nt_V_V @ ( map_gr907434255tant_V @ F2 @ G ) ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_82_map__graph__fn__comp,axiom,
% 3.98/1.90 ! [G: labele2115946735nt_V_V,F2: v > v,G3: v > v] :
% 3.98/1.90 ( ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ G ) @ ( comp_V_V_V2 @ F2 @ G3 ) ) @ G )
% 3.98/1.90 = ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ G ) @ G3 ) @ G ) ) @ F2 ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ G ) @ G3 ) @ G ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_83_assms_I1_J,axiom,
% 3.98/1.90 ! [X5: produc778275879_V_nat] :
% 3.98/1.90 ( ( member1886821968_V_nat @ X5 @ ( standa157301464ules_V @ c @ l ) )
% 3.98/1.90 => ( mainta197426964_nat_V @ X5 @ g ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_84_ne,axiom,
% 3.98/1.90 mainta197426964_nat_V @ standa1319953089tant_V @ g ).
% 3.98/1.90
% 3.98/1.90 thf(fact_85__092_060open_062maintained_Anonempty__rule_AG_H_A_061_A_Ivertices_AG_H_A_092_060noteq_062_A_123_125_J_092_060close_062,axiom,
% 3.98/1.90 ( ( mainta197426964_nat_V @ standa1319953089tant_V @ g )
% 3.98/1.90 = ( ( labele1134902411nt_V_V @ g )
% 3.98/1.90 != bot_bot_set_V2 ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_86_maintained__preserved__by__isomorphism,axiom,
% 3.98/1.90 ! [G: labele236903175od_V_V,F2: v > product_prod_V_V,G3: product_prod_V_V > v,R: produc778275879_V_nat] :
% 3.98/1.90 ( ! [X: product_prod_V_V] :
% 3.98/1.90 ( ( member2015049524od_V_V @ X @ ( labele981584981od_V_V @ G ) )
% 3.98/1.90 => ( ( comp_V772749048od_V_V @ F2 @ G3 @ X )
% 3.98/1.90 = X ) )
% 3.98/1.90 => ( ( G
% 3.98/1.90 = ( restri1502575645od_V_V @ G ) )
% 3.98/1.90 => ( ( mainta197426964_nat_V @ R @ ( map_gr875022471tant_V @ ( bNF_Gr1069958334_V_V_V @ ( labele981584981od_V_V @ G ) @ G3 ) @ G ) )
% 3.98/1.90 => ( mainta1984786828od_V_V @ R @ G ) ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_87_maintained__preserved__by__isomorphism,axiom,
% 3.98/1.90 ! [G: labele788688367nt_V_V,F2: v > v2,G3: v2 > v,R: produc778275879_V_nat] :
% 3.98/1.90 ( ! [X: v2] :
% 3.98/1.90 ( ( member_V @ X @ ( labele1152678333nt_V_V @ G ) )
% 3.98/1.90 => ( ( comp_V_V_V @ F2 @ G3 @ X )
% 3.98/1.90 = X ) )
% 3.98/1.90 => ( ( G
% 3.98/1.90 = ( restri175070597nt_V_V @ G ) )
% 3.98/1.90 => ( ( mainta197426964_nat_V @ R @ ( map_gr530397039tant_V @ ( bNF_Gr_V_V @ ( labele1152678333nt_V_V @ G ) @ G3 ) @ G ) )
% 3.98/1.90 => ( mainta1026355316_nat_V @ R @ G ) ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_88_maintained__preserved__by__isomorphism,axiom,
% 3.98/1.90 ! [G: labele201426742od_V_V,F2: v > produc1699571228od_V_V,G3: produc1699571228od_V_V > v,R: produc778275879_V_nat] :
% 3.98/1.90 ( ! [X: produc1699571228od_V_V] :
% 3.98/1.90 ( ( member1010391347od_V_V @ X @ ( labele1328382418od_V_V @ G ) )
% 3.98/1.90 => ( ( comp_V1480932210od_V_V @ F2 @ G3 @ X )
% 3.98/1.90 = X ) )
% 3.98/1.90 => ( ( G
% 3.98/1.90 = ( restri1699516426od_V_V @ G ) )
% 3.98/1.90 => ( ( mainta197426964_nat_V @ R @ ( map_gr157381846tant_V @ ( bNF_Gr480427157_V_V_V @ ( labele1328382418od_V_V @ G ) @ G3 ) @ G ) )
% 3.98/1.90 => ( mainta1342478555od_V_V @ R @ G ) ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_89_maintained__preserved__by__isomorphism,axiom,
% 3.98/1.90 ! [G: labele2115946735nt_V_V,F2: v > v,G3: v > v,R: produc778275879_V_nat] :
% 3.98/1.90 ( ! [X: v] :
% 3.98/1.90 ( ( member_V2 @ X @ ( labele1134902411nt_V_V @ G ) )
% 3.98/1.90 => ( ( comp_V_V_V2 @ F2 @ G3 @ X )
% 3.98/1.90 = X ) )
% 3.98/1.90 => ( ( G
% 3.98/1.90 = ( restri1305980611nt_V_V @ G ) )
% 3.98/1.90 => ( ( mainta197426964_nat_V @ R @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ G ) @ G3 ) @ G ) )
% 3.98/1.90 => ( mainta197426964_nat_V @ R @ G ) ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_90_idemp__embedding__maintained__preserved,axiom,
% 3.98/1.90 ! [G: labele2115946735nt_V_V,F2: v > v,R: produc778275879_V_nat] :
% 3.98/1.90 ( ( graph_1808119_V_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ G ) @ F2 ) @ G ) @ G @ ( id_on_V2 @ ( labele1134902411nt_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ G ) @ F2 ) @ G ) ) ) )
% 3.98/1.90 => ( ! [X: v] :
% 3.98/1.90 ( ( member_V2 @ X @ ( labele1134902411nt_V_V @ G ) )
% 3.98/1.90 => ( ( comp_V_V_V2 @ F2 @ F2 @ X )
% 3.98/1.90 = ( F2 @ X ) ) )
% 3.98/1.90 => ( ( mainta197426964_nat_V @ R @ G )
% 3.98/1.90 => ( mainta197426964_nat_V @ R @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ G ) @ F2 ) @ G ) ) ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_91_Id__onE,axiom,
% 3.98/1.90 ! [C: produc522115815od_V_V,A4: set_Product_prod_V_V] :
% 3.98/1.90 ( ( member134497296od_V_V @ C @ ( id_on_2125509800od_V_V @ A4 ) )
% 3.98/1.90 => ~ ! [X: product_prod_V_V] :
% 3.98/1.90 ( ( member2015049524od_V_V @ X @ A4 )
% 3.98/1.90 => ( C
% 3.98/1.90 != ( produc1905750615od_V_V @ X @ X ) ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_92_Id__onE,axiom,
% 3.98/1.90 ! [C: product_prod_V_V2,A4: set_V2] :
% 3.98/1.90 ( ( member1990987792od_V_V @ C @ ( id_on_V @ A4 ) )
% 3.98/1.90 => ~ ! [X: v2] :
% 3.98/1.90 ( ( member_V @ X @ A4 )
% 3.98/1.90 => ( C
% 3.98/1.90 != ( product_Pair_V_V @ X @ X ) ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_93_Id__onE,axiom,
% 3.98/1.90 ! [C: produc1082089497od_V_V,A4: set_Pr744279122od_V_V] :
% 3.98/1.90 ( ( member785416642od_V_V @ C @ ( id_on_1491482303od_V_V @ A4 ) )
% 3.98/1.90 => ~ ! [X: produc1699571228od_V_V] :
% 3.98/1.90 ( ( member1010391347od_V_V @ X @ A4 )
% 3.98/1.90 => ( C
% 3.98/1.90 != ( produc1736057425od_V_V @ X @ X ) ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_94_Id__onE,axiom,
% 3.98/1.90 ! [C: product_prod_V_V,A4: set_V] :
% 3.98/1.90 ( ( member2015049524od_V_V @ C @ ( id_on_V2 @ A4 ) )
% 3.98/1.90 => ~ ! [X: v] :
% 3.98/1.90 ( ( member_V2 @ X @ A4 )
% 3.98/1.90 => ( C
% 3.98/1.90 != ( product_Pair_V_V2 @ X @ X ) ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_95_Id__on__eqI,axiom,
% 3.98/1.90 ! [A: product_prod_V_V,B: product_prod_V_V,A4: set_Product_prod_V_V] :
% 3.98/1.90 ( ( A = B )
% 3.98/1.90 => ( ( member2015049524od_V_V @ A @ A4 )
% 3.98/1.90 => ( member134497296od_V_V @ ( produc1905750615od_V_V @ A @ B ) @ ( id_on_2125509800od_V_V @ A4 ) ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_96_Id__on__eqI,axiom,
% 3.98/1.90 ! [A: v2,B: v2,A4: set_V2] :
% 3.98/1.90 ( ( A = B )
% 3.98/1.90 => ( ( member_V @ A @ A4 )
% 3.98/1.90 => ( member1990987792od_V_V @ ( product_Pair_V_V @ A @ B ) @ ( id_on_V @ A4 ) ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_97_Id__on__eqI,axiom,
% 3.98/1.90 ! [A: produc1699571228od_V_V,B: produc1699571228od_V_V,A4: set_Pr744279122od_V_V] :
% 3.98/1.90 ( ( A = B )
% 3.98/1.90 => ( ( member1010391347od_V_V @ A @ A4 )
% 3.98/1.90 => ( member785416642od_V_V @ ( produc1736057425od_V_V @ A @ B ) @ ( id_on_1491482303od_V_V @ A4 ) ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_98_Id__on__eqI,axiom,
% 3.98/1.90 ! [A: v,B: v,A4: set_V] :
% 3.98/1.90 ( ( A = B )
% 3.98/1.90 => ( ( member_V2 @ A @ A4 )
% 3.98/1.90 => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( id_on_V2 @ A4 ) ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_99_Id__on__iff,axiom,
% 3.98/1.90 ! [X3: product_prod_V_V,Y: product_prod_V_V,A4: set_Product_prod_V_V] :
% 3.98/1.90 ( ( member134497296od_V_V @ ( produc1905750615od_V_V @ X3 @ Y ) @ ( id_on_2125509800od_V_V @ A4 ) )
% 3.98/1.90 = ( ( X3 = Y )
% 3.98/1.90 & ( member2015049524od_V_V @ X3 @ A4 ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_100_Id__on__iff,axiom,
% 3.98/1.90 ! [X3: v2,Y: v2,A4: set_V2] :
% 3.98/1.90 ( ( member1990987792od_V_V @ ( product_Pair_V_V @ X3 @ Y ) @ ( id_on_V @ A4 ) )
% 3.98/1.90 = ( ( X3 = Y )
% 3.98/1.90 & ( member_V @ X3 @ A4 ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_101_Id__on__iff,axiom,
% 3.98/1.90 ! [X3: produc1699571228od_V_V,Y: produc1699571228od_V_V,A4: set_Pr744279122od_V_V] :
% 3.98/1.90 ( ( member785416642od_V_V @ ( produc1736057425od_V_V @ X3 @ Y ) @ ( id_on_1491482303od_V_V @ A4 ) )
% 3.98/1.90 = ( ( X3 = Y )
% 3.98/1.90 & ( member1010391347od_V_V @ X3 @ A4 ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_102_Id__on__iff,axiom,
% 3.98/1.90 ! [X3: v,Y: v,A4: set_V] :
% 3.98/1.90 ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ X3 @ Y ) @ ( id_on_V2 @ A4 ) )
% 3.98/1.90 = ( ( X3 = Y )
% 3.98/1.90 & ( member_V2 @ X3 @ A4 ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_103_subgraph__preserves__hom,axiom,
% 3.98/1.90 ! [A4: labele2115946735nt_V_V,B4: labele2115946735nt_V_V,X7: labele2115946735nt_V_V,H: set_Product_prod_V_V] :
% 3.98/1.90 ( ( graph_1808119_V_V_V @ A4 @ B4 @ ( id_on_V2 @ ( labele1134902411nt_V_V @ A4 ) ) )
% 3.98/1.90 => ( ( graph_1808119_V_V_V @ X7 @ A4 @ H )
% 3.98/1.90 => ( graph_1808119_V_V_V @ X7 @ B4 @ H ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_104_subgraph__trans,axiom,
% 3.98/1.90 ! [G_1: labele2115946735nt_V_V,G_2: labele2115946735nt_V_V,G_3: labele2115946735nt_V_V] :
% 3.98/1.90 ( ( graph_1808119_V_V_V @ G_1 @ G_2 @ ( id_on_V2 @ ( labele1134902411nt_V_V @ G_1 ) ) )
% 3.98/1.90 => ( ( graph_1808119_V_V_V @ G_2 @ G_3 @ ( id_on_V2 @ ( labele1134902411nt_V_V @ G_2 ) ) )
% 3.98/1.90 => ( graph_1808119_V_V_V @ G_1 @ G_3 @ ( id_on_V2 @ ( labele1134902411nt_V_V @ G_1 ) ) ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_105_map__graph__fn__eqI,axiom,
% 3.98/1.90 ! [G: labele2115946735nt_V_V,F2: v > v,G3: v > v] :
% 3.98/1.90 ( ! [X: v] :
% 3.98/1.90 ( ( member_V2 @ X @ ( labele1134902411nt_V_V @ G ) )
% 3.98/1.90 => ( ( F2 @ X )
% 3.98/1.90 = ( G3 @ X ) ) )
% 3.98/1.90 => ( ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ G ) @ F2 ) @ G )
% 3.98/1.90 = ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ G ) @ G3 ) @ G ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_106_tr,axiom,
% 3.98/1.90 mainta197426964_nat_V @ ( standa214871990tant_V @ standard_S_Top_V ) @ g ).
% 3.98/1.90
% 3.98/1.90 thf(fact_107_h_I4_J,axiom,
% 3.98/1.90 ! [L: standard_Constant_V,X3: v,Y: v] :
% 3.98/1.90 ( ( member1010391347od_V_V @ ( produc107991630od_V_V @ L @ ( product_Pair_V_V2 @ X3 @ Y ) ) @ ( labele515735386nt_V_V @ g ) )
% 3.98/1.90 = ( member1010391347od_V_V @ ( produc107991630od_V_V @ L @ ( product_Pair_V_V2 @ ( h @ X3 ) @ ( h @ Y ) ) ) @ ( labele515735386nt_V_V @ g ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_108_maintained__refl,axiom,
% 3.98/1.90 ! [R2: labele2128733290_V_nat,G: labele2115946735nt_V_V] : ( mainta197426964_nat_V @ ( produc698429463_V_nat @ R2 @ R2 ) @ G ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_109_comp__apply,axiom,
% 3.98/1.90 ( comp_V_V_V2
% 3.98/1.90 = ( ^ [F4: v > v,G4: v > v,X6: v] : ( F4 @ ( G4 @ X6 ) ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_110_empty__Collect__eq,axiom,
% 3.98/1.90 ! [P2: product_prod_V_V > $o] :
% 3.98/1.90 ( ( bot_bo1389414743od_V_V
% 3.98/1.90 = ( collec2040633974od_V_V @ P2 ) )
% 3.98/1.90 = ( ! [X6: product_prod_V_V] :
% 3.98/1.90 ~ ( P2 @ X6 ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_111_empty__Collect__eq,axiom,
% 3.98/1.90 ! [P2: v > $o] :
% 3.98/1.90 ( ( bot_bot_set_V2
% 3.98/1.90 = ( collect_V2 @ P2 ) )
% 3.98/1.90 = ( ! [X6: v] :
% 3.98/1.90 ~ ( P2 @ X6 ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_112_empty__Collect__eq,axiom,
% 3.98/1.90 ! [P2: produc778275879_V_nat > $o] :
% 3.98/1.90 ( ( bot_bo907687539_V_nat
% 3.98/1.90 = ( collec1411521682_V_nat @ P2 ) )
% 3.98/1.90 = ( ! [X6: produc778275879_V_nat] :
% 3.98/1.90 ~ ( P2 @ X6 ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_113_Collect__empty__eq,axiom,
% 3.98/1.90 ! [P2: product_prod_V_V > $o] :
% 3.98/1.90 ( ( ( collec2040633974od_V_V @ P2 )
% 3.98/1.90 = bot_bo1389414743od_V_V )
% 3.98/1.90 = ( ! [X6: product_prod_V_V] :
% 3.98/1.90 ~ ( P2 @ X6 ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_114_Collect__empty__eq,axiom,
% 3.98/1.90 ! [P2: v > $o] :
% 3.98/1.90 ( ( ( collect_V2 @ P2 )
% 3.98/1.90 = bot_bot_set_V2 )
% 3.98/1.90 = ( ! [X6: v] :
% 3.98/1.90 ~ ( P2 @ X6 ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_115_Collect__empty__eq,axiom,
% 3.98/1.90 ! [P2: produc778275879_V_nat > $o] :
% 3.98/1.90 ( ( ( collec1411521682_V_nat @ P2 )
% 3.98/1.90 = bot_bo907687539_V_nat )
% 3.98/1.90 = ( ! [X6: produc778275879_V_nat] :
% 3.98/1.90 ~ ( P2 @ X6 ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_116_empty__iff,axiom,
% 3.98/1.90 ! [C: v2] :
% 3.98/1.90 ~ ( member_V @ C @ bot_bot_set_V ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_117_empty__iff,axiom,
% 3.98/1.90 ! [C: produc1699571228od_V_V] :
% 3.98/1.90 ~ ( member1010391347od_V_V @ C @ bot_bo667804902od_V_V ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_118_empty__iff,axiom,
% 3.98/1.90 ! [C: product_prod_V_V] :
% 3.98/1.90 ~ ( member2015049524od_V_V @ C @ bot_bo1389414743od_V_V ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_119_empty__iff,axiom,
% 3.98/1.90 ! [C: v] :
% 3.98/1.90 ~ ( member_V2 @ C @ bot_bot_set_V2 ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_120_empty__iff,axiom,
% 3.98/1.90 ! [C: produc778275879_V_nat] :
% 3.98/1.90 ~ ( member1886821968_V_nat @ C @ bot_bo907687539_V_nat ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_121_all__not__in__conv,axiom,
% 3.98/1.90 ! [A4: set_V2] :
% 3.98/1.90 ( ( ! [X6: v2] :
% 3.98/1.90 ~ ( member_V @ X6 @ A4 ) )
% 3.98/1.90 = ( A4 = bot_bot_set_V ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_122_all__not__in__conv,axiom,
% 3.98/1.90 ! [A4: set_Pr744279122od_V_V] :
% 3.98/1.90 ( ( ! [X6: produc1699571228od_V_V] :
% 3.98/1.90 ~ ( member1010391347od_V_V @ X6 @ A4 ) )
% 3.98/1.90 = ( A4 = bot_bo667804902od_V_V ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_123_all__not__in__conv,axiom,
% 3.98/1.90 ! [A4: set_Product_prod_V_V] :
% 3.98/1.90 ( ( ! [X6: product_prod_V_V] :
% 3.98/1.90 ~ ( member2015049524od_V_V @ X6 @ A4 ) )
% 3.98/1.90 = ( A4 = bot_bo1389414743od_V_V ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_124_all__not__in__conv,axiom,
% 3.98/1.90 ! [A4: set_V] :
% 3.98/1.90 ( ( ! [X6: v] :
% 3.98/1.90 ~ ( member_V2 @ X6 @ A4 ) )
% 3.98/1.90 = ( A4 = bot_bot_set_V2 ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_125_all__not__in__conv,axiom,
% 3.98/1.90 ! [A4: set_Pr1058435079_V_nat] :
% 3.98/1.90 ( ( ! [X6: produc778275879_V_nat] :
% 3.98/1.90 ~ ( member1886821968_V_nat @ X6 @ A4 ) )
% 3.98/1.90 = ( A4 = bot_bo907687539_V_nat ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_126_nonempty__rule,axiom,
% 3.98/1.90 ! [G: labele236903175od_V_V] :
% 3.98/1.90 ( ( G
% 3.98/1.90 = ( restri1502575645od_V_V @ G ) )
% 3.98/1.90 => ( ( mainta1984786828od_V_V @ standa1319953089tant_V @ G )
% 3.98/1.90 = ( ( labele981584981od_V_V @ G )
% 3.98/1.90 != bot_bo1389414743od_V_V ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_127_nonempty__rule,axiom,
% 3.98/1.90 ! [G: labele506073123_V_nat] :
% 3.98/1.90 ( ( G
% 3.98/1.90 = ( restri1932147897_V_nat @ G ) )
% 3.98/1.90 => ( ( mainta922614952_V_nat @ standa1319953089tant_V @ G )
% 3.98/1.90 = ( ( labele1822884081_V_nat @ G )
% 3.98/1.90 != bot_bo907687539_V_nat ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_128_nonempty__rule,axiom,
% 3.98/1.90 ! [G: labele2115946735nt_V_V] :
% 3.98/1.90 ( ( G
% 3.98/1.90 = ( restri1305980611nt_V_V @ G ) )
% 3.98/1.90 => ( ( mainta197426964_nat_V @ standa1319953089tant_V @ G )
% 3.98/1.90 = ( ( labele1134902411nt_V_V @ G )
% 3.98/1.90 != bot_bot_set_V2 ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_129__092_060open_062maintainedA_A_Iidentity__rules_AL_J_AG_H_092_060close_062,axiom,
% 3.98/1.90 ! [X5: produc778275879_V_nat] :
% 3.98/1.90 ( ( member1886821968_V_nat @ X5 @ ( standa1568205529ules_V @ l ) )
% 3.98/1.90 => ( mainta197426964_nat_V @ X5 @ g ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_130_labeled__graph_Oexpand,axiom,
% 3.98/1.90 ! [Labeled_graph: labele2115946735nt_V_V,Labeled_graph2: labele2115946735nt_V_V] :
% 3.98/1.90 ( ( ( ( labele515735386nt_V_V @ Labeled_graph )
% 3.98/1.90 = ( labele515735386nt_V_V @ Labeled_graph2 ) )
% 3.98/1.90 & ( ( labele1134902411nt_V_V @ Labeled_graph )
% 3.98/1.90 = ( labele1134902411nt_V_V @ Labeled_graph2 ) ) )
% 3.98/1.90 => ( Labeled_graph = Labeled_graph2 ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_131_emptyE,axiom,
% 3.98/1.90 ! [A: v2] :
% 3.98/1.90 ~ ( member_V @ A @ bot_bot_set_V ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_132_emptyE,axiom,
% 3.98/1.90 ! [A: produc1699571228od_V_V] :
% 3.98/1.90 ~ ( member1010391347od_V_V @ A @ bot_bo667804902od_V_V ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_133_emptyE,axiom,
% 3.98/1.90 ! [A: product_prod_V_V] :
% 3.98/1.90 ~ ( member2015049524od_V_V @ A @ bot_bo1389414743od_V_V ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_134_emptyE,axiom,
% 3.98/1.90 ! [A: v] :
% 3.98/1.90 ~ ( member_V2 @ A @ bot_bot_set_V2 ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_135_emptyE,axiom,
% 3.98/1.90 ! [A: produc778275879_V_nat] :
% 3.98/1.90 ~ ( member1886821968_V_nat @ A @ bot_bo907687539_V_nat ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_136_equals0D,axiom,
% 3.98/1.90 ! [A4: set_V2,A: v2] :
% 3.98/1.90 ( ( A4 = bot_bot_set_V )
% 3.98/1.90 => ~ ( member_V @ A @ A4 ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_137_equals0D,axiom,
% 3.98/1.90 ! [A4: set_Pr744279122od_V_V,A: produc1699571228od_V_V] :
% 3.98/1.90 ( ( A4 = bot_bo667804902od_V_V )
% 3.98/1.90 => ~ ( member1010391347od_V_V @ A @ A4 ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_138_equals0D,axiom,
% 3.98/1.90 ! [A4: set_Product_prod_V_V,A: product_prod_V_V] :
% 3.98/1.90 ( ( A4 = bot_bo1389414743od_V_V )
% 3.98/1.90 => ~ ( member2015049524od_V_V @ A @ A4 ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_139_equals0D,axiom,
% 3.98/1.90 ! [A4: set_V,A: v] :
% 3.98/1.90 ( ( A4 = bot_bot_set_V2 )
% 3.98/1.90 => ~ ( member_V2 @ A @ A4 ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_140_equals0D,axiom,
% 3.98/1.90 ! [A4: set_Pr1058435079_V_nat,A: produc778275879_V_nat] :
% 3.98/1.90 ( ( A4 = bot_bo907687539_V_nat )
% 3.98/1.90 => ~ ( member1886821968_V_nat @ A @ A4 ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_141_equals0I,axiom,
% 3.98/1.90 ! [A4: set_V2] :
% 3.98/1.90 ( ! [Y3: v2] :
% 3.98/1.90 ~ ( member_V @ Y3 @ A4 )
% 3.98/1.90 => ( A4 = bot_bot_set_V ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_142_equals0I,axiom,
% 3.98/1.90 ! [A4: set_Pr744279122od_V_V] :
% 3.98/1.90 ( ! [Y3: produc1699571228od_V_V] :
% 3.98/1.90 ~ ( member1010391347od_V_V @ Y3 @ A4 )
% 3.98/1.90 => ( A4 = bot_bo667804902od_V_V ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_143_equals0I,axiom,
% 3.98/1.90 ! [A4: set_Product_prod_V_V] :
% 3.98/1.90 ( ! [Y3: product_prod_V_V] :
% 3.98/1.90 ~ ( member2015049524od_V_V @ Y3 @ A4 )
% 3.98/1.90 => ( A4 = bot_bo1389414743od_V_V ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_144_equals0I,axiom,
% 3.98/1.90 ! [A4: set_V] :
% 3.98/1.90 ( ! [Y3: v] :
% 3.98/1.90 ~ ( member_V2 @ Y3 @ A4 )
% 3.98/1.90 => ( A4 = bot_bot_set_V2 ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_145_equals0I,axiom,
% 3.98/1.90 ! [A4: set_Pr1058435079_V_nat] :
% 3.98/1.90 ( ! [Y3: produc778275879_V_nat] :
% 3.98/1.90 ~ ( member1886821968_V_nat @ Y3 @ A4 )
% 3.98/1.90 => ( A4 = bot_bo907687539_V_nat ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_146_ex__in__conv,axiom,
% 3.98/1.90 ! [A4: set_V2] :
% 3.98/1.90 ( ( ? [X6: v2] : ( member_V @ X6 @ A4 ) )
% 3.98/1.90 = ( A4 != bot_bot_set_V ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_147_ex__in__conv,axiom,
% 3.98/1.90 ! [A4: set_Pr744279122od_V_V] :
% 3.98/1.90 ( ( ? [X6: produc1699571228od_V_V] : ( member1010391347od_V_V @ X6 @ A4 ) )
% 3.98/1.90 = ( A4 != bot_bo667804902od_V_V ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_148_ex__in__conv,axiom,
% 3.98/1.90 ! [A4: set_Product_prod_V_V] :
% 3.98/1.90 ( ( ? [X6: product_prod_V_V] : ( member2015049524od_V_V @ X6 @ A4 ) )
% 3.98/1.90 = ( A4 != bot_bo1389414743od_V_V ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_149_ex__in__conv,axiom,
% 3.98/1.90 ! [A4: set_V] :
% 3.98/1.90 ( ( ? [X6: v] : ( member_V2 @ X6 @ A4 ) )
% 3.98/1.90 = ( A4 != bot_bot_set_V2 ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_150_ex__in__conv,axiom,
% 3.98/1.90 ! [A4: set_Pr1058435079_V_nat] :
% 3.98/1.90 ( ( ? [X6: produc778275879_V_nat] : ( member1886821968_V_nat @ X6 @ A4 ) )
% 3.98/1.90 = ( A4 != bot_bo907687539_V_nat ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_151_comp__def,axiom,
% 3.98/1.90 ( comp_V_V_V2
% 3.98/1.90 = ( ^ [F4: v > v,G4: v > v,X6: v] : ( F4 @ ( G4 @ X6 ) ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_152_comp__assoc,axiom,
% 3.98/1.90 ! [F2: v > v,G3: v > v,H: v > v] :
% 3.98/1.90 ( ( comp_V_V_V2 @ ( comp_V_V_V2 @ F2 @ G3 ) @ H )
% 3.98/1.90 = ( comp_V_V_V2 @ F2 @ ( comp_V_V_V2 @ G3 @ H ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_153_comp__eq__dest,axiom,
% 3.98/1.90 ! [A: v > v,B: v > v,C: v > v,D: v > v,V2: v] :
% 3.98/1.90 ( ( ( comp_V_V_V2 @ A @ B )
% 3.98/1.90 = ( comp_V_V_V2 @ C @ D ) )
% 3.98/1.90 => ( ( A @ ( B @ V2 ) )
% 3.98/1.90 = ( C @ ( D @ V2 ) ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_154_comp__eq__elim,axiom,
% 3.98/1.90 ! [A: v > v,B: v > v,C: v > v,D: v > v] :
% 3.98/1.90 ( ( ( comp_V_V_V2 @ A @ B )
% 3.98/1.90 = ( comp_V_V_V2 @ C @ D ) )
% 3.98/1.90 => ! [V3: v] :
% 3.98/1.90 ( ( A @ ( B @ V3 ) )
% 3.98/1.90 = ( C @ ( D @ V3 ) ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_155_comp__eq__dest__lhs,axiom,
% 3.98/1.90 ! [A: v > v,B: v > v,C: v > v,V2: v] :
% 3.98/1.90 ( ( ( comp_V_V_V2 @ A @ B )
% 3.98/1.90 = C )
% 3.98/1.90 => ( ( A @ ( B @ V2 ) )
% 3.98/1.90 = ( C @ V2 ) ) ) ).
% 3.98/1.90
% 3.98/1.90 thf(fact_156_edge__preserving__on__graphI,axiom,
% 3.98/1.90 ! [X7: labele236903175od_V_V,F2: product_prod_V_V > v,Y5: set_Pr744279122od_V_V] :
% 3.98/1.91 ( ! [L2: standard_Constant_V,X: product_prod_V_V,Y3: product_prod_V_V] :
% 3.98/1.91 ( ( member361435663od_V_V @ ( produc1482441770od_V_V @ L2 @ ( produc1905750615od_V_V @ X @ Y3 ) ) @ ( labele668941254od_V_V @ X7 ) )
% 3.98/1.91 => ( ( member2015049524od_V_V @ X @ ( labele981584981od_V_V @ X7 ) )
% 3.98/1.91 => ( ( member2015049524od_V_V @ Y3 @ ( labele981584981od_V_V @ X7 ) )
% 3.98/1.91 => ( member1010391347od_V_V @ ( produc107991630od_V_V @ L2 @ ( product_Pair_V_V2 @ ( F2 @ X ) @ ( F2 @ Y3 ) ) ) @ Y5 ) ) ) )
% 3.98/1.91 => ( edge_p1776314003tant_V @ ( bNF_Gr1069958334_V_V_V @ ( labele981584981od_V_V @ X7 ) @ F2 ) @ ( labele668941254od_V_V @ X7 ) @ Y5 ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_157_edge__preserving__on__graphI,axiom,
% 3.98/1.91 ! [X7: labele788688367nt_V_V,F2: v2 > v,Y5: set_Pr744279122od_V_V] :
% 3.98/1.91 ( ! [L2: standard_Constant_V,X: v2,Y3: v2] :
% 3.98/1.91 ( ( member1416643087od_V_V @ ( produc1171747370od_V_V @ L2 @ ( product_Pair_V_V @ X @ Y3 ) ) @ ( labele1469545390nt_V_V @ X7 ) )
% 3.98/1.91 => ( ( member_V @ X @ ( labele1152678333nt_V_V @ X7 ) )
% 3.98/1.91 => ( ( member_V @ Y3 @ ( labele1152678333nt_V_V @ X7 ) )
% 3.98/1.91 => ( member1010391347od_V_V @ ( produc107991630od_V_V @ L2 @ ( product_Pair_V_V2 @ ( F2 @ X ) @ ( F2 @ Y3 ) ) ) @ Y5 ) ) ) )
% 3.98/1.91 => ( edge_p1322161019tant_V @ ( bNF_Gr_V_V @ ( labele1152678333nt_V_V @ X7 ) @ F2 ) @ ( labele1469545390nt_V_V @ X7 ) @ Y5 ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_158_edge__preserving__on__graphI,axiom,
% 3.98/1.91 ! [X7: labele201426742od_V_V,F2: produc1699571228od_V_V > v,Y5: set_Pr744279122od_V_V] :
% 3.98/1.91 ( ! [L2: standard_Constant_V,X: produc1699571228od_V_V,Y3: produc1699571228od_V_V] :
% 3.98/1.91 ( ( member600445121od_V_V @ ( produc2132932316od_V_V @ L2 @ ( produc1736057425od_V_V @ X @ Y3 ) ) @ ( labele1794513953od_V_V @ X7 ) )
% 3.98/1.91 => ( ( member1010391347od_V_V @ X @ ( labele1328382418od_V_V @ X7 ) )
% 3.98/1.91 => ( ( member1010391347od_V_V @ Y3 @ ( labele1328382418od_V_V @ X7 ) )
% 3.98/1.91 => ( member1010391347od_V_V @ ( produc107991630od_V_V @ L2 @ ( product_Pair_V_V2 @ ( F2 @ X ) @ ( F2 @ Y3 ) ) ) @ Y5 ) ) ) )
% 3.98/1.91 => ( edge_p669293514tant_V @ ( bNF_Gr480427157_V_V_V @ ( labele1328382418od_V_V @ X7 ) @ F2 ) @ ( labele1794513953od_V_V @ X7 ) @ Y5 ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_159_edge__preserving__on__graphI,axiom,
% 3.98/1.91 ! [X7: labele2115946735nt_V_V,F2: v > v,Y5: set_Pr744279122od_V_V] :
% 3.98/1.91 ( ! [L2: standard_Constant_V,X: v,Y3: v] :
% 3.98/1.91 ( ( member1010391347od_V_V @ ( produc107991630od_V_V @ L2 @ ( product_Pair_V_V2 @ X @ Y3 ) ) @ ( labele515735386nt_V_V @ X7 ) )
% 3.98/1.91 => ( ( member_V2 @ X @ ( labele1134902411nt_V_V @ X7 ) )
% 3.98/1.91 => ( ( member_V2 @ Y3 @ ( labele1134902411nt_V_V @ X7 ) )
% 3.98/1.91 => ( member1010391347od_V_V @ ( produc107991630od_V_V @ L2 @ ( product_Pair_V_V2 @ ( F2 @ X ) @ ( F2 @ Y3 ) ) ) @ Y5 ) ) ) )
% 3.98/1.91 => ( edge_p1560004099tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ X7 ) @ F2 ) @ ( labele515735386nt_V_V @ X7 ) @ Y5 ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_160_GrD2,axiom,
% 3.98/1.91 ! [X3: v,Fx: v,A4: set_V,F2: v > v] :
% 3.98/1.91 ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ X3 @ Fx ) @ ( bNF_Gr_V_V2 @ A4 @ F2 ) )
% 3.98/1.91 => ( ( F2 @ X3 )
% 3.98/1.91 = Fx ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_161_GrD2,axiom,
% 3.98/1.91 ! [X3: standard_Constant_V,Fx: product_prod_V_V,A4: set_St1111633946tant_V,F2: standard_Constant_V > product_prod_V_V] :
% 3.98/1.91 ( ( member1010391347od_V_V @ ( produc107991630od_V_V @ X3 @ Fx ) @ ( bNF_Gr320641027od_V_V @ A4 @ F2 ) )
% 3.98/1.91 => ( ( F2 @ X3 )
% 3.98/1.91 = Fx ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_162_GrD1,axiom,
% 3.98/1.91 ! [X3: v,Fx: v,A4: set_V,F2: v > v] :
% 3.98/1.91 ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ X3 @ Fx ) @ ( bNF_Gr_V_V2 @ A4 @ F2 ) )
% 3.98/1.91 => ( member_V2 @ X3 @ A4 ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_163_GrD1,axiom,
% 3.98/1.91 ! [X3: standard_Constant_V,Fx: product_prod_V_V,A4: set_St1111633946tant_V,F2: standard_Constant_V > product_prod_V_V] :
% 3.98/1.91 ( ( member1010391347od_V_V @ ( produc107991630od_V_V @ X3 @ Fx ) @ ( bNF_Gr320641027od_V_V @ A4 @ F2 ) )
% 3.98/1.91 => ( member1542015739tant_V @ X3 @ A4 ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_164_map__graph__edge__preserving,axiom,
% 3.98/1.91 ! [F2: set_Product_prod_V_V,G: labele2115946735nt_V_V] : ( edge_p1560004099tant_V @ F2 @ ( labele515735386nt_V_V @ G ) @ ( labele515735386nt_V_V @ ( map_gr907434255tant_V @ F2 @ G ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_165_bot__empty__eq,axiom,
% 3.98/1.91 ( bot_bot_V_o
% 3.98/1.91 = ( ^ [X6: v2] : ( member_V @ X6 @ bot_bot_set_V ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_166_bot__empty__eq,axiom,
% 3.98/1.91 ( bot_bo2024487199_V_V_o
% 3.98/1.91 = ( ^ [X6: produc1699571228od_V_V] : ( member1010391347od_V_V @ X6 @ bot_bo667804902od_V_V ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_167_bot__empty__eq,axiom,
% 3.98/1.91 ( bot_bo1168561222_V_V_o
% 3.98/1.91 = ( ^ [X6: product_prod_V_V] : ( member2015049524od_V_V @ X6 @ bot_bo1389414743od_V_V ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_168_bot__empty__eq,axiom,
% 3.98/1.91 ( bot_bot_V_o2
% 3.98/1.91 = ( ^ [X6: v] : ( member_V2 @ X6 @ bot_bot_set_V2 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_169_bot__empty__eq,axiom,
% 3.98/1.91 ( bot_bo1078500394_nat_o
% 3.98/1.91 = ( ^ [X6: produc778275879_V_nat] : ( member1886821968_V_nat @ X6 @ bot_bo907687539_V_nat ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_170_bot__set__def,axiom,
% 3.98/1.91 ( bot_bo1389414743od_V_V
% 3.98/1.91 = ( collec2040633974od_V_V @ bot_bo1168561222_V_V_o ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_171_bot__set__def,axiom,
% 3.98/1.91 ( bot_bot_set_V2
% 3.98/1.91 = ( collect_V2 @ bot_bot_V_o2 ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_172_bot__set__def,axiom,
% 3.98/1.91 ( bot_bo907687539_V_nat
% 3.98/1.91 = ( collec1411521682_V_nat @ bot_bo1078500394_nat_o ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_173_consequence__graphD_I1_J,axiom,
% 3.98/1.91 ! [Rs: set_Pr1058435079_V_nat,G: labele2115946735nt_V_V,R2: produc778275879_V_nat] :
% 3.98/1.91 ( ( conseq1236301781_nat_V @ Rs @ G )
% 3.98/1.91 => ( ( member1886821968_V_nat @ R2 @ Rs )
% 3.98/1.91 => ( mainta197426964_nat_V @ R2 @ G ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_174_edge__preserving__atomic,axiom,
% 3.98/1.91 ! [H1: set_Product_prod_V_V,E1: set_Pr744279122od_V_V,E2: set_Pr744279122od_V_V,V1: v,V12: v,V22: v,V23: v,K: standard_Constant_V] :
% 3.98/1.91 ( ( edge_p1560004099tant_V @ H1 @ E1 @ E2 )
% 3.98/1.91 => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ V1 @ V12 ) @ H1 )
% 3.98/1.91 => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ V22 @ V23 ) @ H1 )
% 3.98/1.91 => ( ( member1010391347od_V_V @ ( produc107991630od_V_V @ K @ ( product_Pair_V_V2 @ V1 @ V22 ) ) @ E1 )
% 3.98/1.91 => ( member1010391347od_V_V @ ( produc107991630od_V_V @ K @ ( product_Pair_V_V2 @ V12 @ V23 ) ) @ E2 ) ) ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_175_mnt,axiom,
% 3.98/1.91 ! [X5: produc778275879_V_nat] :
% 3.98/1.91 ( ( member1886821968_V_nat @ X5 @ ( sup_su1043134939_V_nat @ ( sup_su1043134939_V_nat @ ( standa1897115807ules_V @ c ) @ ( standa1568205529ules_V @ l ) ) @ ( insert481364471_V_nat @ ( standa214871990tant_V @ standard_S_Top_V ) @ ( insert481364471_V_nat @ standa1319953089tant_V @ bot_bo907687539_V_nat ) ) ) )
% 3.98/1.91 => ( mainta197426964_nat_V @ X5 @ g ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_176_map__graph__in,axiom,
% 3.98/1.91 ! [G: labele2115946735nt_V_V,A: v,B: v,E: allego859987871tant_V,F2: v > v] :
% 3.98/1.91 ( ( G
% 3.98/1.91 = ( restri1305980611nt_V_V @ G ) )
% 3.98/1.91 => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( semant993842370nt_V_V @ G @ E ) )
% 3.98/1.91 => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( F2 @ A ) @ ( F2 @ B ) ) @ ( semant993842370nt_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ G ) @ F2 ) @ G ) @ E ) ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_177_maintainedI,axiom,
% 3.98/1.91 ! [A4: labele2128733290_V_nat,G: labele2115946735nt_V_V,B4: labele2128733290_V_nat] :
% 3.98/1.91 ( ! [F: set_Pr53436518_nat_V] :
% 3.98/1.91 ( ( graph_1541575154_nat_V @ A4 @ G @ F )
% 3.98/1.91 => ( extens1072773157_nat_V @ ( produc698429463_V_nat @ A4 @ B4 ) @ G @ F ) )
% 3.98/1.91 => ( mainta197426964_nat_V @ ( produc698429463_V_nat @ A4 @ B4 ) @ G ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_178_maintainedI,axiom,
% 3.98/1.91 ! [A4: labele2115946735nt_V_V,G: labele2115946735nt_V_V,B4: labele2115946735nt_V_V] :
% 3.98/1.91 ( ! [F: set_Product_prod_V_V] :
% 3.98/1.91 ( ( graph_1808119_V_V_V @ A4 @ G @ F )
% 3.98/1.91 => ( extens1533825066_V_V_V @ ( produc533118295nt_V_V @ A4 @ B4 ) @ G @ F ) )
% 3.98/1.91 => ( mainta1699210777_V_V_V @ ( produc533118295nt_V_V @ A4 @ B4 ) @ G ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_179_graph__homomorphism__empty,axiom,
% 3.98/1.91 ! [G: labele2115946735nt_V_V,F2: set_Pr1228022213_V_V_V] :
% 3.98/1.91 ( ( graph_840721237_V_V_V @ ( labele94156371od_V_V @ bot_bo451843010od_V_V @ bot_bo1389414743od_V_V ) @ G @ F2 )
% 3.98/1.91 = ( ( F2 = bot_bo688400985_V_V_V )
% 3.98/1.91 & ( G
% 3.98/1.91 = ( restri1305980611nt_V_V @ G ) ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_180_graph__homomorphism__empty,axiom,
% 3.98/1.91 ! [G: labele2115946735nt_V_V,F2: set_Pr1056235617_nat_V] :
% 3.98/1.91 ( ( graph_227683057_nat_V @ ( labele1193521135_V_nat @ bot_bo634818242_V_nat @ bot_bo907687539_V_nat ) @ G @ F2 )
% 3.98/1.91 = ( ( F2 = bot_bo1708783349_nat_V )
% 3.98/1.91 & ( G
% 3.98/1.91 = ( restri1305980611nt_V_V @ G ) ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_181_graph__homomorphism__empty,axiom,
% 3.98/1.91 ! [G: labele2115946735nt_V_V,F2: set_Product_prod_V_V] :
% 3.98/1.91 ( ( graph_1808119_V_V_V @ ( labele712009229nt_V_V @ bot_bo667804902od_V_V @ bot_bot_set_V2 ) @ G @ F2 )
% 3.98/1.91 = ( ( F2 = bot_bo1389414743od_V_V )
% 3.98/1.91 & ( G
% 3.98/1.91 = ( restri1305980611nt_V_V @ G ) ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_182_subgraph__def,axiom,
% 3.98/1.91 ! [G_1: labele2115946735nt_V_V,G_2: labele2115946735nt_V_V] :
% 3.98/1.91 ( ( graph_1808119_V_V_V @ G_1 @ G_2 @ ( id_on_V2 @ ( labele1134902411nt_V_V @ G_1 ) ) )
% 3.98/1.91 = ( ( G_1
% 3.98/1.91 = ( restri1305980611nt_V_V @ G_1 ) )
% 3.98/1.91 & ( G_2
% 3.98/1.91 = ( restri1305980611nt_V_V @ G_2 ) )
% 3.98/1.91 & ( ( graph_1141886696nt_V_V @ G_1 @ G_2 )
% 3.98/1.91 = G_2 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_183_insert__absorb2,axiom,
% 3.98/1.91 ! [X3: produc778275879_V_nat,A4: set_Pr1058435079_V_nat] :
% 3.98/1.91 ( ( insert481364471_V_nat @ X3 @ ( insert481364471_V_nat @ X3 @ A4 ) )
% 3.98/1.91 = ( insert481364471_V_nat @ X3 @ A4 ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_184_insert__iff,axiom,
% 3.98/1.91 ! [A: produc778275879_V_nat,B: produc778275879_V_nat,A4: set_Pr1058435079_V_nat] :
% 3.98/1.91 ( ( member1886821968_V_nat @ A @ ( insert481364471_V_nat @ B @ A4 ) )
% 3.98/1.91 = ( ( A = B )
% 3.98/1.91 | ( member1886821968_V_nat @ A @ A4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_185_insert__iff,axiom,
% 3.98/1.91 ! [A: product_prod_V_V,B: product_prod_V_V,A4: set_Product_prod_V_V] :
% 3.98/1.91 ( ( member2015049524od_V_V @ A @ ( insert2024285275od_V_V @ B @ A4 ) )
% 3.98/1.91 = ( ( A = B )
% 3.98/1.91 | ( member2015049524od_V_V @ A @ A4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_186_insert__iff,axiom,
% 3.98/1.91 ! [A: v,B: v,A4: set_V] :
% 3.98/1.91 ( ( member_V2 @ A @ ( insert_V2 @ B @ A4 ) )
% 3.98/1.91 = ( ( A = B )
% 3.98/1.91 | ( member_V2 @ A @ A4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_187_insert__iff,axiom,
% 3.98/1.91 ! [A: v2,B: v2,A4: set_V2] :
% 3.98/1.91 ( ( member_V @ A @ ( insert_V @ B @ A4 ) )
% 3.98/1.91 = ( ( A = B )
% 3.98/1.91 | ( member_V @ A @ A4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_188_insert__iff,axiom,
% 3.98/1.91 ! [A: produc1699571228od_V_V,B: produc1699571228od_V_V,A4: set_Pr744279122od_V_V] :
% 3.98/1.91 ( ( member1010391347od_V_V @ A @ ( insert135842892od_V_V @ B @ A4 ) )
% 3.98/1.91 = ( ( A = B )
% 3.98/1.91 | ( member1010391347od_V_V @ A @ A4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_189_insertCI,axiom,
% 3.98/1.91 ! [A: produc778275879_V_nat,B4: set_Pr1058435079_V_nat,B: produc778275879_V_nat] :
% 3.98/1.91 ( ( ~ ( member1886821968_V_nat @ A @ B4 )
% 3.98/1.91 => ( A = B ) )
% 3.98/1.91 => ( member1886821968_V_nat @ A @ ( insert481364471_V_nat @ B @ B4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_190_insertCI,axiom,
% 3.98/1.91 ! [A: product_prod_V_V,B4: set_Product_prod_V_V,B: product_prod_V_V] :
% 3.98/1.91 ( ( ~ ( member2015049524od_V_V @ A @ B4 )
% 3.98/1.91 => ( A = B ) )
% 3.98/1.91 => ( member2015049524od_V_V @ A @ ( insert2024285275od_V_V @ B @ B4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_191_insertCI,axiom,
% 3.98/1.91 ! [A: v,B4: set_V,B: v] :
% 3.98/1.91 ( ( ~ ( member_V2 @ A @ B4 )
% 3.98/1.91 => ( A = B ) )
% 3.98/1.91 => ( member_V2 @ A @ ( insert_V2 @ B @ B4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_192_insertCI,axiom,
% 3.98/1.91 ! [A: v2,B4: set_V2,B: v2] :
% 3.98/1.91 ( ( ~ ( member_V @ A @ B4 )
% 3.98/1.91 => ( A = B ) )
% 3.98/1.91 => ( member_V @ A @ ( insert_V @ B @ B4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_193_insertCI,axiom,
% 3.98/1.91 ! [A: produc1699571228od_V_V,B4: set_Pr744279122od_V_V,B: produc1699571228od_V_V] :
% 3.98/1.91 ( ( ~ ( member1010391347od_V_V @ A @ B4 )
% 3.98/1.91 => ( A = B ) )
% 3.98/1.91 => ( member1010391347od_V_V @ A @ ( insert135842892od_V_V @ B @ B4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_194_Un__iff,axiom,
% 3.98/1.91 ! [C: product_prod_V_V,A4: set_Product_prod_V_V,B4: set_Product_prod_V_V] :
% 3.98/1.91 ( ( member2015049524od_V_V @ C @ ( sup_su551882943od_V_V @ A4 @ B4 ) )
% 3.98/1.91 = ( ( member2015049524od_V_V @ C @ A4 )
% 3.98/1.91 | ( member2015049524od_V_V @ C @ B4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_195_Un__iff,axiom,
% 3.98/1.91 ! [C: v,A4: set_V,B4: set_V] :
% 3.98/1.91 ( ( member_V2 @ C @ ( sup_sup_set_V2 @ A4 @ B4 ) )
% 3.98/1.91 = ( ( member_V2 @ C @ A4 )
% 3.98/1.91 | ( member_V2 @ C @ B4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_196_Un__iff,axiom,
% 3.98/1.91 ! [C: v2,A4: set_V2,B4: set_V2] :
% 3.98/1.91 ( ( member_V @ C @ ( sup_sup_set_V @ A4 @ B4 ) )
% 3.98/1.91 = ( ( member_V @ C @ A4 )
% 3.98/1.91 | ( member_V @ C @ B4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_197_Un__iff,axiom,
% 3.98/1.91 ! [C: produc1699571228od_V_V,A4: set_Pr744279122od_V_V,B4: set_Pr744279122od_V_V] :
% 3.98/1.91 ( ( member1010391347od_V_V @ C @ ( sup_su693515134od_V_V @ A4 @ B4 ) )
% 3.98/1.91 = ( ( member1010391347od_V_V @ C @ A4 )
% 3.98/1.91 | ( member1010391347od_V_V @ C @ B4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_198_Un__iff,axiom,
% 3.98/1.91 ! [C: produc778275879_V_nat,A4: set_Pr1058435079_V_nat,B4: set_Pr1058435079_V_nat] :
% 3.98/1.91 ( ( member1886821968_V_nat @ C @ ( sup_su1043134939_V_nat @ A4 @ B4 ) )
% 3.98/1.91 = ( ( member1886821968_V_nat @ C @ A4 )
% 3.98/1.91 | ( member1886821968_V_nat @ C @ B4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_199_UnCI,axiom,
% 3.98/1.91 ! [C: product_prod_V_V,B4: set_Product_prod_V_V,A4: set_Product_prod_V_V] :
% 3.98/1.91 ( ( ~ ( member2015049524od_V_V @ C @ B4 )
% 3.98/1.91 => ( member2015049524od_V_V @ C @ A4 ) )
% 3.98/1.91 => ( member2015049524od_V_V @ C @ ( sup_su551882943od_V_V @ A4 @ B4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_200_UnCI,axiom,
% 3.98/1.91 ! [C: v,B4: set_V,A4: set_V] :
% 3.98/1.91 ( ( ~ ( member_V2 @ C @ B4 )
% 3.98/1.91 => ( member_V2 @ C @ A4 ) )
% 3.98/1.91 => ( member_V2 @ C @ ( sup_sup_set_V2 @ A4 @ B4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_201_UnCI,axiom,
% 3.98/1.91 ! [C: v2,B4: set_V2,A4: set_V2] :
% 3.98/1.91 ( ( ~ ( member_V @ C @ B4 )
% 3.98/1.91 => ( member_V @ C @ A4 ) )
% 3.98/1.91 => ( member_V @ C @ ( sup_sup_set_V @ A4 @ B4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_202_UnCI,axiom,
% 3.98/1.91 ! [C: produc1699571228od_V_V,B4: set_Pr744279122od_V_V,A4: set_Pr744279122od_V_V] :
% 3.98/1.91 ( ( ~ ( member1010391347od_V_V @ C @ B4 )
% 3.98/1.91 => ( member1010391347od_V_V @ C @ A4 ) )
% 3.98/1.91 => ( member1010391347od_V_V @ C @ ( sup_su693515134od_V_V @ A4 @ B4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_203_UnCI,axiom,
% 3.98/1.91 ! [C: produc778275879_V_nat,B4: set_Pr1058435079_V_nat,A4: set_Pr1058435079_V_nat] :
% 3.98/1.91 ( ( ~ ( member1886821968_V_nat @ C @ B4 )
% 3.98/1.91 => ( member1886821968_V_nat @ C @ A4 ) )
% 3.98/1.91 => ( member1886821968_V_nat @ C @ ( sup_su1043134939_V_nat @ A4 @ B4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_204_singletonI,axiom,
% 3.98/1.91 ! [A: v2] : ( member_V @ A @ ( insert_V @ A @ bot_bot_set_V ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_205_singletonI,axiom,
% 3.98/1.91 ! [A: produc1699571228od_V_V] : ( member1010391347od_V_V @ A @ ( insert135842892od_V_V @ A @ bot_bo667804902od_V_V ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_206_singletonI,axiom,
% 3.98/1.91 ! [A: product_prod_V_V] : ( member2015049524od_V_V @ A @ ( insert2024285275od_V_V @ A @ bot_bo1389414743od_V_V ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_207_singletonI,axiom,
% 3.98/1.91 ! [A: v] : ( member_V2 @ A @ ( insert_V2 @ A @ bot_bot_set_V2 ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_208_singletonI,axiom,
% 3.98/1.91 ! [A: produc778275879_V_nat] : ( member1886821968_V_nat @ A @ ( insert481364471_V_nat @ A @ bot_bo907687539_V_nat ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_209_Un__empty,axiom,
% 3.98/1.91 ! [A4: set_Product_prod_V_V,B4: set_Product_prod_V_V] :
% 3.98/1.91 ( ( ( sup_su551882943od_V_V @ A4 @ B4 )
% 3.98/1.91 = bot_bo1389414743od_V_V )
% 3.98/1.91 = ( ( A4 = bot_bo1389414743od_V_V )
% 3.98/1.91 & ( B4 = bot_bo1389414743od_V_V ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_210_Un__empty,axiom,
% 3.98/1.91 ! [A4: set_V,B4: set_V] :
% 3.98/1.91 ( ( ( sup_sup_set_V2 @ A4 @ B4 )
% 3.98/1.91 = bot_bot_set_V2 )
% 3.98/1.91 = ( ( A4 = bot_bot_set_V2 )
% 3.98/1.91 & ( B4 = bot_bot_set_V2 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_211_Un__empty,axiom,
% 3.98/1.91 ! [A4: set_Pr1058435079_V_nat,B4: set_Pr1058435079_V_nat] :
% 3.98/1.91 ( ( ( sup_su1043134939_V_nat @ A4 @ B4 )
% 3.98/1.91 = bot_bo907687539_V_nat )
% 3.98/1.91 = ( ( A4 = bot_bo907687539_V_nat )
% 3.98/1.91 & ( B4 = bot_bo907687539_V_nat ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_212_Un__insert__right,axiom,
% 3.98/1.91 ! [A4: set_Pr1058435079_V_nat,A: produc778275879_V_nat,B4: set_Pr1058435079_V_nat] :
% 3.98/1.91 ( ( sup_su1043134939_V_nat @ A4 @ ( insert481364471_V_nat @ A @ B4 ) )
% 3.98/1.91 = ( insert481364471_V_nat @ A @ ( sup_su1043134939_V_nat @ A4 @ B4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_213_Un__insert__left,axiom,
% 3.98/1.91 ! [A: produc778275879_V_nat,B4: set_Pr1058435079_V_nat,C4: set_Pr1058435079_V_nat] :
% 3.98/1.91 ( ( sup_su1043134939_V_nat @ ( insert481364471_V_nat @ A @ B4 ) @ C4 )
% 3.98/1.91 = ( insert481364471_V_nat @ A @ ( sup_su1043134939_V_nat @ B4 @ C4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_214_graph__union__preserves__restrict,axiom,
% 3.98/1.91 ! [G_1: labele2115946735nt_V_V,G_2: labele2115946735nt_V_V] :
% 3.98/1.91 ( ( G_1
% 3.98/1.91 = ( restri1305980611nt_V_V @ G_1 ) )
% 3.98/1.91 => ( ( G_2
% 3.98/1.91 = ( restri1305980611nt_V_V @ G_2 ) )
% 3.98/1.91 => ( ( graph_1141886696nt_V_V @ G_1 @ G_2 )
% 3.98/1.91 = ( restri1305980611nt_V_V @ ( graph_1141886696nt_V_V @ G_1 @ G_2 ) ) ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_215_graph__union__vertices,axiom,
% 3.98/1.91 ! [G_1: labele2115946735nt_V_V,G_2: labele2115946735nt_V_V] :
% 3.98/1.91 ( ( labele1134902411nt_V_V @ ( graph_1141886696nt_V_V @ G_1 @ G_2 ) )
% 3.98/1.91 = ( sup_sup_set_V2 @ ( labele1134902411nt_V_V @ G_1 ) @ ( labele1134902411nt_V_V @ G_2 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_216_labeled__graph_Ocollapse,axiom,
% 3.98/1.91 ! [Labeled_graph: labele2115946735nt_V_V] :
% 3.98/1.91 ( ( labele712009229nt_V_V @ ( labele515735386nt_V_V @ Labeled_graph ) @ ( labele1134902411nt_V_V @ Labeled_graph ) )
% 3.98/1.91 = Labeled_graph ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_217_extensible__refl,axiom,
% 3.98/1.91 ! [R2: labele2115946735nt_V_V,G: labele2115946735nt_V_V,F2: set_Product_prod_V_V] :
% 3.98/1.91 ( ( graph_1808119_V_V_V @ R2 @ G @ F2 )
% 3.98/1.91 => ( extens1533825066_V_V_V @ ( produc533118295nt_V_V @ R2 @ R2 ) @ G @ F2 ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_218_graph__empty__e,axiom,
% 3.98/1.91 ! [V2: set_V] :
% 3.98/1.91 ( ( labele712009229nt_V_V @ bot_bo667804902od_V_V @ V2 )
% 3.98/1.91 = ( restri1305980611nt_V_V @ ( labele712009229nt_V_V @ bot_bo667804902od_V_V @ V2 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_219_constant__rules__empty,axiom,
% 3.98/1.91 ( ( standa1571708471od_V_V @ bot_bo1389414743od_V_V )
% 3.98/1.91 = bot_bo1196823539_V_nat ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_220_constant__rules__empty,axiom,
% 3.98/1.91 ( ( standa294833961ules_V @ bot_bot_set_V2 )
% 3.98/1.91 = bot_bo1834032757_V_nat ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_221_constant__rules__empty,axiom,
% 3.98/1.91 ( ( standa434642387_V_nat @ bot_bo907687539_V_nat )
% 3.98/1.91 = bot_bo323535987at_nat ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_222_constant__rules__empty,axiom,
% 3.98/1.91 ( ( standa1897115807ules_V @ bot_bot_set_V )
% 3.98/1.91 = bot_bo907687539_V_nat ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_223_Gr__insert,axiom,
% 3.98/1.91 ! [X3: labele2128733290_V_nat,F3: set_la14611914_V_nat,F2: labele2128733290_V_nat > labele2128733290_V_nat] :
% 3.98/1.91 ( ( bNF_Gr17960482_V_nat @ ( insert213439034_V_nat @ X3 @ F3 ) @ F2 )
% 3.98/1.91 = ( insert481364471_V_nat @ ( produc698429463_V_nat @ X3 @ ( F2 @ X3 ) ) @ ( bNF_Gr17960482_V_nat @ F3 @ F2 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_224_Gr__insert,axiom,
% 3.98/1.91 ! [X3: v,F3: set_V,F2: v > v] :
% 3.98/1.91 ( ( bNF_Gr_V_V2 @ ( insert_V2 @ X3 @ F3 ) @ F2 )
% 3.98/1.91 = ( insert2024285275od_V_V @ ( product_Pair_V_V2 @ X3 @ ( F2 @ X3 ) ) @ ( bNF_Gr_V_V2 @ F3 @ F2 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_225_Gr__insert,axiom,
% 3.98/1.91 ! [X3: standard_Constant_V,F3: set_St1111633946tant_V,F2: standard_Constant_V > product_prod_V_V] :
% 3.98/1.91 ( ( bNF_Gr320641027od_V_V @ ( insert1818834324tant_V @ X3 @ F3 ) @ F2 )
% 3.98/1.91 = ( insert135842892od_V_V @ ( produc107991630od_V_V @ X3 @ ( F2 @ X3 ) ) @ ( bNF_Gr320641027od_V_V @ F3 @ F2 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_226_extensible__refl__concr,axiom,
% 3.98/1.91 ! [E_1: set_Pr744279122od_V_V,V2: set_V,G: labele2115946735nt_V_V,F2: set_Product_prod_V_V,E_2: set_Pr744279122od_V_V] :
% 3.98/1.91 ( ( graph_1808119_V_V_V @ ( labele712009229nt_V_V @ E_1 @ V2 ) @ G @ F2 )
% 3.98/1.91 => ( ( extens1533825066_V_V_V @ ( produc533118295nt_V_V @ ( labele712009229nt_V_V @ E_1 @ V2 ) @ ( labele712009229nt_V_V @ E_2 @ V2 ) ) @ G @ F2 )
% 3.98/1.91 = ( graph_1808119_V_V_V @ ( labele712009229nt_V_V @ E_2 @ V2 ) @ G @ F2 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_227_graph__single,axiom,
% 3.98/1.91 ! [A: standard_Constant_V,B: v,C: v] :
% 3.98/1.91 ( ( labele712009229nt_V_V @ ( insert135842892od_V_V @ ( produc107991630od_V_V @ A @ ( product_Pair_V_V2 @ B @ C ) ) @ bot_bo667804902od_V_V ) @ ( insert_V2 @ B @ ( insert_V2 @ C @ bot_bot_set_V2 ) ) )
% 3.98/1.91 = ( restri1305980611nt_V_V @ ( labele712009229nt_V_V @ ( insert135842892od_V_V @ ( produc107991630od_V_V @ A @ ( product_Pair_V_V2 @ B @ C ) ) @ bot_bo667804902od_V_V ) @ ( insert_V2 @ B @ ( insert_V2 @ C @ bot_bot_set_V2 ) ) ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_228_insert__is__Un,axiom,
% 3.98/1.91 ( insert2024285275od_V_V
% 3.98/1.91 = ( ^ [A5: product_prod_V_V] : ( sup_su551882943od_V_V @ ( insert2024285275od_V_V @ A5 @ bot_bo1389414743od_V_V ) ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_229_insert__is__Un,axiom,
% 3.98/1.91 ( insert_V2
% 3.98/1.91 = ( ^ [A5: v] : ( sup_sup_set_V2 @ ( insert_V2 @ A5 @ bot_bot_set_V2 ) ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_230_insert__is__Un,axiom,
% 3.98/1.91 ( insert481364471_V_nat
% 3.98/1.91 = ( ^ [A5: produc778275879_V_nat] : ( sup_su1043134939_V_nat @ ( insert481364471_V_nat @ A5 @ bot_bo907687539_V_nat ) ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_231_Un__singleton__iff,axiom,
% 3.98/1.91 ! [A4: set_Product_prod_V_V,B4: set_Product_prod_V_V,X3: product_prod_V_V] :
% 3.98/1.91 ( ( ( sup_su551882943od_V_V @ A4 @ B4 )
% 3.98/1.91 = ( insert2024285275od_V_V @ X3 @ bot_bo1389414743od_V_V ) )
% 3.98/1.91 = ( ( ( A4 = bot_bo1389414743od_V_V )
% 3.98/1.91 & ( B4
% 3.98/1.91 = ( insert2024285275od_V_V @ X3 @ bot_bo1389414743od_V_V ) ) )
% 3.98/1.91 | ( ( A4
% 3.98/1.91 = ( insert2024285275od_V_V @ X3 @ bot_bo1389414743od_V_V ) )
% 3.98/1.91 & ( B4 = bot_bo1389414743od_V_V ) )
% 3.98/1.91 | ( ( A4
% 3.98/1.91 = ( insert2024285275od_V_V @ X3 @ bot_bo1389414743od_V_V ) )
% 3.98/1.91 & ( B4
% 3.98/1.91 = ( insert2024285275od_V_V @ X3 @ bot_bo1389414743od_V_V ) ) ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_232_Un__singleton__iff,axiom,
% 3.98/1.91 ! [A4: set_V,B4: set_V,X3: v] :
% 3.98/1.91 ( ( ( sup_sup_set_V2 @ A4 @ B4 )
% 3.98/1.91 = ( insert_V2 @ X3 @ bot_bot_set_V2 ) )
% 3.98/1.91 = ( ( ( A4 = bot_bot_set_V2 )
% 3.98/1.91 & ( B4
% 3.98/1.91 = ( insert_V2 @ X3 @ bot_bot_set_V2 ) ) )
% 3.98/1.91 | ( ( A4
% 3.98/1.91 = ( insert_V2 @ X3 @ bot_bot_set_V2 ) )
% 3.98/1.91 & ( B4 = bot_bot_set_V2 ) )
% 3.98/1.91 | ( ( A4
% 3.98/1.91 = ( insert_V2 @ X3 @ bot_bot_set_V2 ) )
% 3.98/1.91 & ( B4
% 3.98/1.91 = ( insert_V2 @ X3 @ bot_bot_set_V2 ) ) ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_233_Un__singleton__iff,axiom,
% 3.98/1.91 ! [A4: set_Pr1058435079_V_nat,B4: set_Pr1058435079_V_nat,X3: produc778275879_V_nat] :
% 3.98/1.91 ( ( ( sup_su1043134939_V_nat @ A4 @ B4 )
% 3.98/1.91 = ( insert481364471_V_nat @ X3 @ bot_bo907687539_V_nat ) )
% 3.98/1.91 = ( ( ( A4 = bot_bo907687539_V_nat )
% 3.98/1.91 & ( B4
% 3.98/1.91 = ( insert481364471_V_nat @ X3 @ bot_bo907687539_V_nat ) ) )
% 3.98/1.91 | ( ( A4
% 3.98/1.91 = ( insert481364471_V_nat @ X3 @ bot_bo907687539_V_nat ) )
% 3.98/1.91 & ( B4 = bot_bo907687539_V_nat ) )
% 3.98/1.91 | ( ( A4
% 3.98/1.91 = ( insert481364471_V_nat @ X3 @ bot_bo907687539_V_nat ) )
% 3.98/1.91 & ( B4
% 3.98/1.91 = ( insert481364471_V_nat @ X3 @ bot_bo907687539_V_nat ) ) ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_234_singleton__Un__iff,axiom,
% 3.98/1.91 ! [X3: product_prod_V_V,A4: set_Product_prod_V_V,B4: set_Product_prod_V_V] :
% 3.98/1.91 ( ( ( insert2024285275od_V_V @ X3 @ bot_bo1389414743od_V_V )
% 3.98/1.91 = ( sup_su551882943od_V_V @ A4 @ B4 ) )
% 3.98/1.91 = ( ( ( A4 = bot_bo1389414743od_V_V )
% 3.98/1.91 & ( B4
% 3.98/1.91 = ( insert2024285275od_V_V @ X3 @ bot_bo1389414743od_V_V ) ) )
% 3.98/1.91 | ( ( A4
% 3.98/1.91 = ( insert2024285275od_V_V @ X3 @ bot_bo1389414743od_V_V ) )
% 3.98/1.91 & ( B4 = bot_bo1389414743od_V_V ) )
% 3.98/1.91 | ( ( A4
% 3.98/1.91 = ( insert2024285275od_V_V @ X3 @ bot_bo1389414743od_V_V ) )
% 3.98/1.91 & ( B4
% 3.98/1.91 = ( insert2024285275od_V_V @ X3 @ bot_bo1389414743od_V_V ) ) ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_235_singleton__Un__iff,axiom,
% 3.98/1.91 ! [X3: v,A4: set_V,B4: set_V] :
% 3.98/1.91 ( ( ( insert_V2 @ X3 @ bot_bot_set_V2 )
% 3.98/1.91 = ( sup_sup_set_V2 @ A4 @ B4 ) )
% 3.98/1.91 = ( ( ( A4 = bot_bot_set_V2 )
% 3.98/1.91 & ( B4
% 3.98/1.91 = ( insert_V2 @ X3 @ bot_bot_set_V2 ) ) )
% 3.98/1.91 | ( ( A4
% 3.98/1.91 = ( insert_V2 @ X3 @ bot_bot_set_V2 ) )
% 3.98/1.91 & ( B4 = bot_bot_set_V2 ) )
% 3.98/1.91 | ( ( A4
% 3.98/1.91 = ( insert_V2 @ X3 @ bot_bot_set_V2 ) )
% 3.98/1.91 & ( B4
% 3.98/1.91 = ( insert_V2 @ X3 @ bot_bot_set_V2 ) ) ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_236_singleton__Un__iff,axiom,
% 3.98/1.91 ! [X3: produc778275879_V_nat,A4: set_Pr1058435079_V_nat,B4: set_Pr1058435079_V_nat] :
% 3.98/1.91 ( ( ( insert481364471_V_nat @ X3 @ bot_bo907687539_V_nat )
% 3.98/1.91 = ( sup_su1043134939_V_nat @ A4 @ B4 ) )
% 3.98/1.91 = ( ( ( A4 = bot_bo907687539_V_nat )
% 3.98/1.91 & ( B4
% 3.98/1.91 = ( insert481364471_V_nat @ X3 @ bot_bo907687539_V_nat ) ) )
% 3.98/1.91 | ( ( A4
% 3.98/1.91 = ( insert481364471_V_nat @ X3 @ bot_bo907687539_V_nat ) )
% 3.98/1.91 & ( B4 = bot_bo907687539_V_nat ) )
% 3.98/1.91 | ( ( A4
% 3.98/1.91 = ( insert481364471_V_nat @ X3 @ bot_bo907687539_V_nat ) )
% 3.98/1.91 & ( B4
% 3.98/1.91 = ( insert481364471_V_nat @ X3 @ bot_bo907687539_V_nat ) ) ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_237_graph__union__def,axiom,
% 3.98/1.91 ( graph_1141886696nt_V_V
% 3.98/1.91 = ( ^ [G_12: labele2115946735nt_V_V,G_22: labele2115946735nt_V_V] : ( labele712009229nt_V_V @ ( sup_su693515134od_V_V @ ( labele515735386nt_V_V @ G_12 ) @ ( labele515735386nt_V_V @ G_22 ) ) @ ( sup_sup_set_V2 @ ( labele1134902411nt_V_V @ G_12 ) @ ( labele1134902411nt_V_V @ G_22 ) ) ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_238_Un__empty__left,axiom,
% 3.98/1.91 ! [B4: set_Product_prod_V_V] :
% 3.98/1.91 ( ( sup_su551882943od_V_V @ bot_bo1389414743od_V_V @ B4 )
% 3.98/1.91 = B4 ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_239_Un__empty__left,axiom,
% 3.98/1.91 ! [B4: set_V] :
% 3.98/1.91 ( ( sup_sup_set_V2 @ bot_bot_set_V2 @ B4 )
% 3.98/1.91 = B4 ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_240_Un__empty__left,axiom,
% 3.98/1.91 ! [B4: set_Pr1058435079_V_nat] :
% 3.98/1.91 ( ( sup_su1043134939_V_nat @ bot_bo907687539_V_nat @ B4 )
% 3.98/1.91 = B4 ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_241_Un__empty__right,axiom,
% 3.98/1.91 ! [A4: set_Product_prod_V_V] :
% 3.98/1.91 ( ( sup_su551882943od_V_V @ A4 @ bot_bo1389414743od_V_V )
% 3.98/1.91 = A4 ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_242_Un__empty__right,axiom,
% 3.98/1.91 ! [A4: set_V] :
% 3.98/1.91 ( ( sup_sup_set_V2 @ A4 @ bot_bot_set_V2 )
% 3.98/1.91 = A4 ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_243_Un__empty__right,axiom,
% 3.98/1.91 ! [A4: set_Pr1058435079_V_nat] :
% 3.98/1.91 ( ( sup_su1043134939_V_nat @ A4 @ bot_bo907687539_V_nat )
% 3.98/1.91 = A4 ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_244_singletonD,axiom,
% 3.98/1.91 ! [B: v2,A: v2] :
% 3.98/1.91 ( ( member_V @ B @ ( insert_V @ A @ bot_bot_set_V ) )
% 3.98/1.91 => ( B = A ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_245_singletonD,axiom,
% 3.98/1.91 ! [B: produc1699571228od_V_V,A: produc1699571228od_V_V] :
% 3.98/1.91 ( ( member1010391347od_V_V @ B @ ( insert135842892od_V_V @ A @ bot_bo667804902od_V_V ) )
% 3.98/1.91 => ( B = A ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_246_singletonD,axiom,
% 3.98/1.91 ! [B: product_prod_V_V,A: product_prod_V_V] :
% 3.98/1.91 ( ( member2015049524od_V_V @ B @ ( insert2024285275od_V_V @ A @ bot_bo1389414743od_V_V ) )
% 3.98/1.91 => ( B = A ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_247_singletonD,axiom,
% 3.98/1.91 ! [B: v,A: v] :
% 3.98/1.91 ( ( member_V2 @ B @ ( insert_V2 @ A @ bot_bot_set_V2 ) )
% 3.98/1.91 => ( B = A ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_248_singletonD,axiom,
% 3.98/1.91 ! [B: produc778275879_V_nat,A: produc778275879_V_nat] :
% 3.98/1.91 ( ( member1886821968_V_nat @ B @ ( insert481364471_V_nat @ A @ bot_bo907687539_V_nat ) )
% 3.98/1.91 => ( B = A ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_249_singleton__iff,axiom,
% 3.98/1.91 ! [B: v2,A: v2] :
% 3.98/1.91 ( ( member_V @ B @ ( insert_V @ A @ bot_bot_set_V ) )
% 3.98/1.91 = ( B = A ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_250_singleton__iff,axiom,
% 3.98/1.91 ! [B: produc1699571228od_V_V,A: produc1699571228od_V_V] :
% 3.98/1.91 ( ( member1010391347od_V_V @ B @ ( insert135842892od_V_V @ A @ bot_bo667804902od_V_V ) )
% 3.98/1.91 = ( B = A ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_251_singleton__iff,axiom,
% 3.98/1.91 ! [B: product_prod_V_V,A: product_prod_V_V] :
% 3.98/1.91 ( ( member2015049524od_V_V @ B @ ( insert2024285275od_V_V @ A @ bot_bo1389414743od_V_V ) )
% 3.98/1.91 = ( B = A ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_252_singleton__iff,axiom,
% 3.98/1.91 ! [B: v,A: v] :
% 3.98/1.91 ( ( member_V2 @ B @ ( insert_V2 @ A @ bot_bot_set_V2 ) )
% 3.98/1.91 = ( B = A ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_253_singleton__iff,axiom,
% 3.98/1.91 ! [B: produc778275879_V_nat,A: produc778275879_V_nat] :
% 3.98/1.91 ( ( member1886821968_V_nat @ B @ ( insert481364471_V_nat @ A @ bot_bo907687539_V_nat ) )
% 3.98/1.91 = ( B = A ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_254_doubleton__eq__iff,axiom,
% 3.98/1.91 ! [A: product_prod_V_V,B: product_prod_V_V,C: product_prod_V_V,D: product_prod_V_V] :
% 3.98/1.91 ( ( ( insert2024285275od_V_V @ A @ ( insert2024285275od_V_V @ B @ bot_bo1389414743od_V_V ) )
% 3.98/1.91 = ( insert2024285275od_V_V @ C @ ( insert2024285275od_V_V @ D @ bot_bo1389414743od_V_V ) ) )
% 3.98/1.91 = ( ( ( A = C )
% 3.98/1.91 & ( B = D ) )
% 3.98/1.91 | ( ( A = D )
% 3.98/1.91 & ( B = C ) ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_255_doubleton__eq__iff,axiom,
% 3.98/1.91 ! [A: v,B: v,C: v,D: v] :
% 3.98/1.91 ( ( ( insert_V2 @ A @ ( insert_V2 @ B @ bot_bot_set_V2 ) )
% 3.98/1.91 = ( insert_V2 @ C @ ( insert_V2 @ D @ bot_bot_set_V2 ) ) )
% 3.98/1.91 = ( ( ( A = C )
% 3.98/1.91 & ( B = D ) )
% 3.98/1.91 | ( ( A = D )
% 3.98/1.91 & ( B = C ) ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_256_doubleton__eq__iff,axiom,
% 3.98/1.91 ! [A: produc778275879_V_nat,B: produc778275879_V_nat,C: produc778275879_V_nat,D: produc778275879_V_nat] :
% 3.98/1.91 ( ( ( insert481364471_V_nat @ A @ ( insert481364471_V_nat @ B @ bot_bo907687539_V_nat ) )
% 3.98/1.91 = ( insert481364471_V_nat @ C @ ( insert481364471_V_nat @ D @ bot_bo907687539_V_nat ) ) )
% 3.98/1.91 = ( ( ( A = C )
% 3.98/1.91 & ( B = D ) )
% 3.98/1.91 | ( ( A = D )
% 3.98/1.91 & ( B = C ) ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_257_insert__not__empty,axiom,
% 3.98/1.91 ! [A: product_prod_V_V,A4: set_Product_prod_V_V] :
% 3.98/1.91 ( ( insert2024285275od_V_V @ A @ A4 )
% 3.98/1.91 != bot_bo1389414743od_V_V ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_258_insert__not__empty,axiom,
% 3.98/1.91 ! [A: v,A4: set_V] :
% 3.98/1.91 ( ( insert_V2 @ A @ A4 )
% 3.98/1.91 != bot_bot_set_V2 ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_259_insert__not__empty,axiom,
% 3.98/1.91 ! [A: produc778275879_V_nat,A4: set_Pr1058435079_V_nat] :
% 3.98/1.91 ( ( insert481364471_V_nat @ A @ A4 )
% 3.98/1.91 != bot_bo907687539_V_nat ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_260_singleton__inject,axiom,
% 3.98/1.91 ! [A: product_prod_V_V,B: product_prod_V_V] :
% 3.98/1.91 ( ( ( insert2024285275od_V_V @ A @ bot_bo1389414743od_V_V )
% 3.98/1.91 = ( insert2024285275od_V_V @ B @ bot_bo1389414743od_V_V ) )
% 3.98/1.91 => ( A = B ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_261_singleton__inject,axiom,
% 3.98/1.91 ! [A: v,B: v] :
% 3.98/1.91 ( ( ( insert_V2 @ A @ bot_bot_set_V2 )
% 3.98/1.91 = ( insert_V2 @ B @ bot_bot_set_V2 ) )
% 3.98/1.91 => ( A = B ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_262_singleton__inject,axiom,
% 3.98/1.91 ! [A: produc778275879_V_nat,B: produc778275879_V_nat] :
% 3.98/1.91 ( ( ( insert481364471_V_nat @ A @ bot_bo907687539_V_nat )
% 3.98/1.91 = ( insert481364471_V_nat @ B @ bot_bo907687539_V_nat ) )
% 3.98/1.91 => ( A = B ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_263_mk__disjoint__insert,axiom,
% 3.98/1.91 ! [A: produc778275879_V_nat,A4: set_Pr1058435079_V_nat] :
% 3.98/1.91 ( ( member1886821968_V_nat @ A @ A4 )
% 3.98/1.91 => ? [B5: set_Pr1058435079_V_nat] :
% 3.98/1.91 ( ( A4
% 3.98/1.91 = ( insert481364471_V_nat @ A @ B5 ) )
% 3.98/1.91 & ~ ( member1886821968_V_nat @ A @ B5 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_264_mk__disjoint__insert,axiom,
% 3.98/1.91 ! [A: product_prod_V_V,A4: set_Product_prod_V_V] :
% 3.98/1.91 ( ( member2015049524od_V_V @ A @ A4 )
% 3.98/1.91 => ? [B5: set_Product_prod_V_V] :
% 3.98/1.91 ( ( A4
% 3.98/1.91 = ( insert2024285275od_V_V @ A @ B5 ) )
% 3.98/1.91 & ~ ( member2015049524od_V_V @ A @ B5 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_265_mk__disjoint__insert,axiom,
% 3.98/1.91 ! [A: v,A4: set_V] :
% 3.98/1.91 ( ( member_V2 @ A @ A4 )
% 3.98/1.91 => ? [B5: set_V] :
% 3.98/1.91 ( ( A4
% 3.98/1.91 = ( insert_V2 @ A @ B5 ) )
% 3.98/1.91 & ~ ( member_V2 @ A @ B5 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_266_mk__disjoint__insert,axiom,
% 3.98/1.91 ! [A: v2,A4: set_V2] :
% 3.98/1.91 ( ( member_V @ A @ A4 )
% 3.98/1.91 => ? [B5: set_V2] :
% 3.98/1.91 ( ( A4
% 3.98/1.91 = ( insert_V @ A @ B5 ) )
% 3.98/1.91 & ~ ( member_V @ A @ B5 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_267_mk__disjoint__insert,axiom,
% 3.98/1.91 ! [A: produc1699571228od_V_V,A4: set_Pr744279122od_V_V] :
% 3.98/1.91 ( ( member1010391347od_V_V @ A @ A4 )
% 3.98/1.91 => ? [B5: set_Pr744279122od_V_V] :
% 3.98/1.91 ( ( A4
% 3.98/1.91 = ( insert135842892od_V_V @ A @ B5 ) )
% 3.98/1.91 & ~ ( member1010391347od_V_V @ A @ B5 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_268_Un__left__commute,axiom,
% 3.98/1.91 ! [A4: set_Pr1058435079_V_nat,B4: set_Pr1058435079_V_nat,C4: set_Pr1058435079_V_nat] :
% 3.98/1.91 ( ( sup_su1043134939_V_nat @ A4 @ ( sup_su1043134939_V_nat @ B4 @ C4 ) )
% 3.98/1.91 = ( sup_su1043134939_V_nat @ B4 @ ( sup_su1043134939_V_nat @ A4 @ C4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_269_insert__commute,axiom,
% 3.98/1.91 ! [X3: produc778275879_V_nat,Y: produc778275879_V_nat,A4: set_Pr1058435079_V_nat] :
% 3.98/1.91 ( ( insert481364471_V_nat @ X3 @ ( insert481364471_V_nat @ Y @ A4 ) )
% 3.98/1.91 = ( insert481364471_V_nat @ Y @ ( insert481364471_V_nat @ X3 @ A4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_270_Un__left__absorb,axiom,
% 3.98/1.91 ! [A4: set_Pr1058435079_V_nat,B4: set_Pr1058435079_V_nat] :
% 3.98/1.91 ( ( sup_su1043134939_V_nat @ A4 @ ( sup_su1043134939_V_nat @ A4 @ B4 ) )
% 3.98/1.91 = ( sup_su1043134939_V_nat @ A4 @ B4 ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_271_insert__eq__iff,axiom,
% 3.98/1.91 ! [A: produc778275879_V_nat,A4: set_Pr1058435079_V_nat,B: produc778275879_V_nat,B4: set_Pr1058435079_V_nat] :
% 3.98/1.91 ( ~ ( member1886821968_V_nat @ A @ A4 )
% 3.98/1.91 => ( ~ ( member1886821968_V_nat @ B @ B4 )
% 3.98/1.91 => ( ( ( insert481364471_V_nat @ A @ A4 )
% 3.98/1.91 = ( insert481364471_V_nat @ B @ B4 ) )
% 3.98/1.91 = ( ( ( A = B )
% 3.98/1.91 => ( A4 = B4 ) )
% 3.98/1.91 & ( ( A != B )
% 3.98/1.91 => ? [C5: set_Pr1058435079_V_nat] :
% 3.98/1.91 ( ( A4
% 3.98/1.91 = ( insert481364471_V_nat @ B @ C5 ) )
% 3.98/1.91 & ~ ( member1886821968_V_nat @ B @ C5 )
% 3.98/1.91 & ( B4
% 3.98/1.91 = ( insert481364471_V_nat @ A @ C5 ) )
% 3.98/1.91 & ~ ( member1886821968_V_nat @ A @ C5 ) ) ) ) ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_272_insert__eq__iff,axiom,
% 3.98/1.91 ! [A: product_prod_V_V,A4: set_Product_prod_V_V,B: product_prod_V_V,B4: set_Product_prod_V_V] :
% 3.98/1.91 ( ~ ( member2015049524od_V_V @ A @ A4 )
% 3.98/1.91 => ( ~ ( member2015049524od_V_V @ B @ B4 )
% 3.98/1.91 => ( ( ( insert2024285275od_V_V @ A @ A4 )
% 3.98/1.91 = ( insert2024285275od_V_V @ B @ B4 ) )
% 3.98/1.91 = ( ( ( A = B )
% 3.98/1.91 => ( A4 = B4 ) )
% 3.98/1.91 & ( ( A != B )
% 3.98/1.91 => ? [C5: set_Product_prod_V_V] :
% 3.98/1.91 ( ( A4
% 3.98/1.91 = ( insert2024285275od_V_V @ B @ C5 ) )
% 3.98/1.91 & ~ ( member2015049524od_V_V @ B @ C5 )
% 3.98/1.91 & ( B4
% 3.98/1.91 = ( insert2024285275od_V_V @ A @ C5 ) )
% 3.98/1.91 & ~ ( member2015049524od_V_V @ A @ C5 ) ) ) ) ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_273_insert__eq__iff,axiom,
% 3.98/1.91 ! [A: v,A4: set_V,B: v,B4: set_V] :
% 3.98/1.91 ( ~ ( member_V2 @ A @ A4 )
% 3.98/1.91 => ( ~ ( member_V2 @ B @ B4 )
% 3.98/1.91 => ( ( ( insert_V2 @ A @ A4 )
% 3.98/1.91 = ( insert_V2 @ B @ B4 ) )
% 3.98/1.91 = ( ( ( A = B )
% 3.98/1.91 => ( A4 = B4 ) )
% 3.98/1.91 & ( ( A != B )
% 3.98/1.91 => ? [C5: set_V] :
% 3.98/1.91 ( ( A4
% 3.98/1.91 = ( insert_V2 @ B @ C5 ) )
% 3.98/1.91 & ~ ( member_V2 @ B @ C5 )
% 3.98/1.91 & ( B4
% 3.98/1.91 = ( insert_V2 @ A @ C5 ) )
% 3.98/1.91 & ~ ( member_V2 @ A @ C5 ) ) ) ) ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_274_insert__eq__iff,axiom,
% 3.98/1.91 ! [A: v2,A4: set_V2,B: v2,B4: set_V2] :
% 3.98/1.91 ( ~ ( member_V @ A @ A4 )
% 3.98/1.91 => ( ~ ( member_V @ B @ B4 )
% 3.98/1.91 => ( ( ( insert_V @ A @ A4 )
% 3.98/1.91 = ( insert_V @ B @ B4 ) )
% 3.98/1.91 = ( ( ( A = B )
% 3.98/1.91 => ( A4 = B4 ) )
% 3.98/1.91 & ( ( A != B )
% 3.98/1.91 => ? [C5: set_V2] :
% 3.98/1.91 ( ( A4
% 3.98/1.91 = ( insert_V @ B @ C5 ) )
% 3.98/1.91 & ~ ( member_V @ B @ C5 )
% 3.98/1.91 & ( B4
% 3.98/1.91 = ( insert_V @ A @ C5 ) )
% 3.98/1.91 & ~ ( member_V @ A @ C5 ) ) ) ) ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_275_insert__eq__iff,axiom,
% 3.98/1.91 ! [A: produc1699571228od_V_V,A4: set_Pr744279122od_V_V,B: produc1699571228od_V_V,B4: set_Pr744279122od_V_V] :
% 3.98/1.91 ( ~ ( member1010391347od_V_V @ A @ A4 )
% 3.98/1.91 => ( ~ ( member1010391347od_V_V @ B @ B4 )
% 3.98/1.91 => ( ( ( insert135842892od_V_V @ A @ A4 )
% 3.98/1.91 = ( insert135842892od_V_V @ B @ B4 ) )
% 3.98/1.91 = ( ( ( A = B )
% 3.98/1.91 => ( A4 = B4 ) )
% 3.98/1.91 & ( ( A != B )
% 3.98/1.91 => ? [C5: set_Pr744279122od_V_V] :
% 3.98/1.91 ( ( A4
% 3.98/1.91 = ( insert135842892od_V_V @ B @ C5 ) )
% 3.98/1.91 & ~ ( member1010391347od_V_V @ B @ C5 )
% 3.98/1.91 & ( B4
% 3.98/1.91 = ( insert135842892od_V_V @ A @ C5 ) )
% 3.98/1.91 & ~ ( member1010391347od_V_V @ A @ C5 ) ) ) ) ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_276_insert__absorb,axiom,
% 3.98/1.91 ! [A: produc778275879_V_nat,A4: set_Pr1058435079_V_nat] :
% 3.98/1.91 ( ( member1886821968_V_nat @ A @ A4 )
% 3.98/1.91 => ( ( insert481364471_V_nat @ A @ A4 )
% 3.98/1.91 = A4 ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_277_insert__absorb,axiom,
% 3.98/1.91 ! [A: product_prod_V_V,A4: set_Product_prod_V_V] :
% 3.98/1.91 ( ( member2015049524od_V_V @ A @ A4 )
% 3.98/1.91 => ( ( insert2024285275od_V_V @ A @ A4 )
% 3.98/1.91 = A4 ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_278_insert__absorb,axiom,
% 3.98/1.91 ! [A: v,A4: set_V] :
% 3.98/1.91 ( ( member_V2 @ A @ A4 )
% 3.98/1.91 => ( ( insert_V2 @ A @ A4 )
% 3.98/1.91 = A4 ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_279_insert__absorb,axiom,
% 3.98/1.91 ! [A: v2,A4: set_V2] :
% 3.98/1.91 ( ( member_V @ A @ A4 )
% 3.98/1.91 => ( ( insert_V @ A @ A4 )
% 3.98/1.91 = A4 ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_280_insert__absorb,axiom,
% 3.98/1.91 ! [A: produc1699571228od_V_V,A4: set_Pr744279122od_V_V] :
% 3.98/1.91 ( ( member1010391347od_V_V @ A @ A4 )
% 3.98/1.91 => ( ( insert135842892od_V_V @ A @ A4 )
% 3.98/1.91 = A4 ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_281_insert__ident,axiom,
% 3.98/1.91 ! [X3: produc778275879_V_nat,A4: set_Pr1058435079_V_nat,B4: set_Pr1058435079_V_nat] :
% 3.98/1.91 ( ~ ( member1886821968_V_nat @ X3 @ A4 )
% 3.98/1.91 => ( ~ ( member1886821968_V_nat @ X3 @ B4 )
% 3.98/1.91 => ( ( ( insert481364471_V_nat @ X3 @ A4 )
% 3.98/1.91 = ( insert481364471_V_nat @ X3 @ B4 ) )
% 3.98/1.91 = ( A4 = B4 ) ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_282_insert__ident,axiom,
% 3.98/1.91 ! [X3: product_prod_V_V,A4: set_Product_prod_V_V,B4: set_Product_prod_V_V] :
% 3.98/1.91 ( ~ ( member2015049524od_V_V @ X3 @ A4 )
% 3.98/1.91 => ( ~ ( member2015049524od_V_V @ X3 @ B4 )
% 3.98/1.91 => ( ( ( insert2024285275od_V_V @ X3 @ A4 )
% 3.98/1.91 = ( insert2024285275od_V_V @ X3 @ B4 ) )
% 3.98/1.91 = ( A4 = B4 ) ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_283_insert__ident,axiom,
% 3.98/1.91 ! [X3: v,A4: set_V,B4: set_V] :
% 3.98/1.91 ( ~ ( member_V2 @ X3 @ A4 )
% 3.98/1.91 => ( ~ ( member_V2 @ X3 @ B4 )
% 3.98/1.91 => ( ( ( insert_V2 @ X3 @ A4 )
% 3.98/1.91 = ( insert_V2 @ X3 @ B4 ) )
% 3.98/1.91 = ( A4 = B4 ) ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_284_insert__ident,axiom,
% 3.98/1.91 ! [X3: v2,A4: set_V2,B4: set_V2] :
% 3.98/1.91 ( ~ ( member_V @ X3 @ A4 )
% 3.98/1.91 => ( ~ ( member_V @ X3 @ B4 )
% 3.98/1.91 => ( ( ( insert_V @ X3 @ A4 )
% 3.98/1.91 = ( insert_V @ X3 @ B4 ) )
% 3.98/1.91 = ( A4 = B4 ) ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_285_insert__ident,axiom,
% 3.98/1.91 ! [X3: produc1699571228od_V_V,A4: set_Pr744279122od_V_V,B4: set_Pr744279122od_V_V] :
% 3.98/1.91 ( ~ ( member1010391347od_V_V @ X3 @ A4 )
% 3.98/1.91 => ( ~ ( member1010391347od_V_V @ X3 @ B4 )
% 3.98/1.91 => ( ( ( insert135842892od_V_V @ X3 @ A4 )
% 3.98/1.91 = ( insert135842892od_V_V @ X3 @ B4 ) )
% 3.98/1.91 = ( A4 = B4 ) ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_286_Set_Oset__insert,axiom,
% 3.98/1.91 ! [X3: produc778275879_V_nat,A4: set_Pr1058435079_V_nat] :
% 3.98/1.91 ( ( member1886821968_V_nat @ X3 @ A4 )
% 3.98/1.91 => ~ ! [B5: set_Pr1058435079_V_nat] :
% 3.98/1.91 ( ( A4
% 3.98/1.91 = ( insert481364471_V_nat @ X3 @ B5 ) )
% 3.98/1.91 => ( member1886821968_V_nat @ X3 @ B5 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_287_Set_Oset__insert,axiom,
% 3.98/1.91 ! [X3: product_prod_V_V,A4: set_Product_prod_V_V] :
% 3.98/1.91 ( ( member2015049524od_V_V @ X3 @ A4 )
% 3.98/1.91 => ~ ! [B5: set_Product_prod_V_V] :
% 3.98/1.91 ( ( A4
% 3.98/1.91 = ( insert2024285275od_V_V @ X3 @ B5 ) )
% 3.98/1.91 => ( member2015049524od_V_V @ X3 @ B5 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_288_Set_Oset__insert,axiom,
% 3.98/1.91 ! [X3: v,A4: set_V] :
% 3.98/1.91 ( ( member_V2 @ X3 @ A4 )
% 3.98/1.91 => ~ ! [B5: set_V] :
% 3.98/1.91 ( ( A4
% 3.98/1.91 = ( insert_V2 @ X3 @ B5 ) )
% 3.98/1.91 => ( member_V2 @ X3 @ B5 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_289_Set_Oset__insert,axiom,
% 3.98/1.91 ! [X3: v2,A4: set_V2] :
% 3.98/1.91 ( ( member_V @ X3 @ A4 )
% 3.98/1.91 => ~ ! [B5: set_V2] :
% 3.98/1.91 ( ( A4
% 3.98/1.91 = ( insert_V @ X3 @ B5 ) )
% 3.98/1.91 => ( member_V @ X3 @ B5 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_290_Set_Oset__insert,axiom,
% 3.98/1.91 ! [X3: produc1699571228od_V_V,A4: set_Pr744279122od_V_V] :
% 3.98/1.91 ( ( member1010391347od_V_V @ X3 @ A4 )
% 3.98/1.91 => ~ ! [B5: set_Pr744279122od_V_V] :
% 3.98/1.91 ( ( A4
% 3.98/1.91 = ( insert135842892od_V_V @ X3 @ B5 ) )
% 3.98/1.91 => ( member1010391347od_V_V @ X3 @ B5 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_291_Un__commute,axiom,
% 3.98/1.91 ( sup_su1043134939_V_nat
% 3.98/1.91 = ( ^ [A6: set_Pr1058435079_V_nat,B6: set_Pr1058435079_V_nat] : ( sup_su1043134939_V_nat @ B6 @ A6 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_292_Un__absorb,axiom,
% 3.98/1.91 ! [A4: set_Pr1058435079_V_nat] :
% 3.98/1.91 ( ( sup_su1043134939_V_nat @ A4 @ A4 )
% 3.98/1.91 = A4 ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_293_insertI2,axiom,
% 3.98/1.91 ! [A: produc778275879_V_nat,B4: set_Pr1058435079_V_nat,B: produc778275879_V_nat] :
% 3.98/1.91 ( ( member1886821968_V_nat @ A @ B4 )
% 3.98/1.91 => ( member1886821968_V_nat @ A @ ( insert481364471_V_nat @ B @ B4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_294_insertI2,axiom,
% 3.98/1.91 ! [A: product_prod_V_V,B4: set_Product_prod_V_V,B: product_prod_V_V] :
% 3.98/1.91 ( ( member2015049524od_V_V @ A @ B4 )
% 3.98/1.91 => ( member2015049524od_V_V @ A @ ( insert2024285275od_V_V @ B @ B4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_295_insertI2,axiom,
% 3.98/1.91 ! [A: v,B4: set_V,B: v] :
% 3.98/1.91 ( ( member_V2 @ A @ B4 )
% 3.98/1.91 => ( member_V2 @ A @ ( insert_V2 @ B @ B4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_296_insertI2,axiom,
% 3.98/1.91 ! [A: v2,B4: set_V2,B: v2] :
% 3.98/1.91 ( ( member_V @ A @ B4 )
% 3.98/1.91 => ( member_V @ A @ ( insert_V @ B @ B4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_297_insertI2,axiom,
% 3.98/1.91 ! [A: produc1699571228od_V_V,B4: set_Pr744279122od_V_V,B: produc1699571228od_V_V] :
% 3.98/1.91 ( ( member1010391347od_V_V @ A @ B4 )
% 3.98/1.91 => ( member1010391347od_V_V @ A @ ( insert135842892od_V_V @ B @ B4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_298_insertI1,axiom,
% 3.98/1.91 ! [A: produc778275879_V_nat,B4: set_Pr1058435079_V_nat] : ( member1886821968_V_nat @ A @ ( insert481364471_V_nat @ A @ B4 ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_299_insertI1,axiom,
% 3.98/1.91 ! [A: product_prod_V_V,B4: set_Product_prod_V_V] : ( member2015049524od_V_V @ A @ ( insert2024285275od_V_V @ A @ B4 ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_300_insertI1,axiom,
% 3.98/1.91 ! [A: v,B4: set_V] : ( member_V2 @ A @ ( insert_V2 @ A @ B4 ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_301_insertI1,axiom,
% 3.98/1.91 ! [A: v2,B4: set_V2] : ( member_V @ A @ ( insert_V @ A @ B4 ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_302_insertI1,axiom,
% 3.98/1.91 ! [A: produc1699571228od_V_V,B4: set_Pr744279122od_V_V] : ( member1010391347od_V_V @ A @ ( insert135842892od_V_V @ A @ B4 ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_303_Un__assoc,axiom,
% 3.98/1.91 ! [A4: set_Pr1058435079_V_nat,B4: set_Pr1058435079_V_nat,C4: set_Pr1058435079_V_nat] :
% 3.98/1.91 ( ( sup_su1043134939_V_nat @ ( sup_su1043134939_V_nat @ A4 @ B4 ) @ C4 )
% 3.98/1.91 = ( sup_su1043134939_V_nat @ A4 @ ( sup_su1043134939_V_nat @ B4 @ C4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_304_insertE,axiom,
% 3.98/1.91 ! [A: produc778275879_V_nat,B: produc778275879_V_nat,A4: set_Pr1058435079_V_nat] :
% 3.98/1.91 ( ( member1886821968_V_nat @ A @ ( insert481364471_V_nat @ B @ A4 ) )
% 3.98/1.91 => ( ( A != B )
% 3.98/1.91 => ( member1886821968_V_nat @ A @ A4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_305_insertE,axiom,
% 3.98/1.91 ! [A: product_prod_V_V,B: product_prod_V_V,A4: set_Product_prod_V_V] :
% 3.98/1.91 ( ( member2015049524od_V_V @ A @ ( insert2024285275od_V_V @ B @ A4 ) )
% 3.98/1.91 => ( ( A != B )
% 3.98/1.91 => ( member2015049524od_V_V @ A @ A4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_306_insertE,axiom,
% 3.98/1.91 ! [A: v,B: v,A4: set_V] :
% 3.98/1.91 ( ( member_V2 @ A @ ( insert_V2 @ B @ A4 ) )
% 3.98/1.91 => ( ( A != B )
% 3.98/1.91 => ( member_V2 @ A @ A4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_307_insertE,axiom,
% 3.98/1.91 ! [A: v2,B: v2,A4: set_V2] :
% 3.98/1.91 ( ( member_V @ A @ ( insert_V @ B @ A4 ) )
% 3.98/1.91 => ( ( A != B )
% 3.98/1.91 => ( member_V @ A @ A4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_308_insertE,axiom,
% 3.98/1.91 ! [A: produc1699571228od_V_V,B: produc1699571228od_V_V,A4: set_Pr744279122od_V_V] :
% 3.98/1.91 ( ( member1010391347od_V_V @ A @ ( insert135842892od_V_V @ B @ A4 ) )
% 3.98/1.91 => ( ( A != B )
% 3.98/1.91 => ( member1010391347od_V_V @ A @ A4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_309_ball__Un,axiom,
% 3.98/1.91 ! [A4: set_Pr1058435079_V_nat,B4: set_Pr1058435079_V_nat,P2: produc778275879_V_nat > $o] :
% 3.98/1.91 ( ( ! [X6: produc778275879_V_nat] :
% 3.98/1.91 ( ( member1886821968_V_nat @ X6 @ ( sup_su1043134939_V_nat @ A4 @ B4 ) )
% 3.98/1.91 => ( P2 @ X6 ) ) )
% 3.98/1.91 = ( ! [X6: produc778275879_V_nat] :
% 3.98/1.91 ( ( member1886821968_V_nat @ X6 @ A4 )
% 3.98/1.91 => ( P2 @ X6 ) )
% 3.98/1.91 & ! [X6: produc778275879_V_nat] :
% 3.98/1.91 ( ( member1886821968_V_nat @ X6 @ B4 )
% 3.98/1.91 => ( P2 @ X6 ) ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_310_bex__Un,axiom,
% 3.98/1.91 ! [A4: set_Pr1058435079_V_nat,B4: set_Pr1058435079_V_nat,P2: produc778275879_V_nat > $o] :
% 3.98/1.91 ( ( ? [X6: produc778275879_V_nat] :
% 3.98/1.91 ( ( member1886821968_V_nat @ X6 @ ( sup_su1043134939_V_nat @ A4 @ B4 ) )
% 3.98/1.91 & ( P2 @ X6 ) ) )
% 3.98/1.91 = ( ? [X6: produc778275879_V_nat] :
% 3.98/1.91 ( ( member1886821968_V_nat @ X6 @ A4 )
% 3.98/1.91 & ( P2 @ X6 ) )
% 3.98/1.91 | ? [X6: produc778275879_V_nat] :
% 3.98/1.91 ( ( member1886821968_V_nat @ X6 @ B4 )
% 3.98/1.91 & ( P2 @ X6 ) ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_311_UnI2,axiom,
% 3.98/1.91 ! [C: product_prod_V_V,B4: set_Product_prod_V_V,A4: set_Product_prod_V_V] :
% 3.98/1.91 ( ( member2015049524od_V_V @ C @ B4 )
% 3.98/1.91 => ( member2015049524od_V_V @ C @ ( sup_su551882943od_V_V @ A4 @ B4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_312_UnI2,axiom,
% 3.98/1.91 ! [C: v,B4: set_V,A4: set_V] :
% 3.98/1.91 ( ( member_V2 @ C @ B4 )
% 3.98/1.91 => ( member_V2 @ C @ ( sup_sup_set_V2 @ A4 @ B4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_313_UnI2,axiom,
% 3.98/1.91 ! [C: v2,B4: set_V2,A4: set_V2] :
% 3.98/1.91 ( ( member_V @ C @ B4 )
% 3.98/1.91 => ( member_V @ C @ ( sup_sup_set_V @ A4 @ B4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_314_UnI2,axiom,
% 3.98/1.91 ! [C: produc1699571228od_V_V,B4: set_Pr744279122od_V_V,A4: set_Pr744279122od_V_V] :
% 3.98/1.91 ( ( member1010391347od_V_V @ C @ B4 )
% 3.98/1.91 => ( member1010391347od_V_V @ C @ ( sup_su693515134od_V_V @ A4 @ B4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_315_UnI2,axiom,
% 3.98/1.91 ! [C: produc778275879_V_nat,B4: set_Pr1058435079_V_nat,A4: set_Pr1058435079_V_nat] :
% 3.98/1.91 ( ( member1886821968_V_nat @ C @ B4 )
% 3.98/1.91 => ( member1886821968_V_nat @ C @ ( sup_su1043134939_V_nat @ A4 @ B4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_316_UnI1,axiom,
% 3.98/1.91 ! [C: product_prod_V_V,A4: set_Product_prod_V_V,B4: set_Product_prod_V_V] :
% 3.98/1.91 ( ( member2015049524od_V_V @ C @ A4 )
% 3.98/1.91 => ( member2015049524od_V_V @ C @ ( sup_su551882943od_V_V @ A4 @ B4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_317_UnI1,axiom,
% 3.98/1.91 ! [C: v,A4: set_V,B4: set_V] :
% 3.98/1.91 ( ( member_V2 @ C @ A4 )
% 3.98/1.91 => ( member_V2 @ C @ ( sup_sup_set_V2 @ A4 @ B4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_318_UnI1,axiom,
% 3.98/1.91 ! [C: v2,A4: set_V2,B4: set_V2] :
% 3.98/1.91 ( ( member_V @ C @ A4 )
% 3.98/1.91 => ( member_V @ C @ ( sup_sup_set_V @ A4 @ B4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_319_UnI1,axiom,
% 3.98/1.91 ! [C: produc1699571228od_V_V,A4: set_Pr744279122od_V_V,B4: set_Pr744279122od_V_V] :
% 3.98/1.91 ( ( member1010391347od_V_V @ C @ A4 )
% 3.98/1.91 => ( member1010391347od_V_V @ C @ ( sup_su693515134od_V_V @ A4 @ B4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_320_UnI1,axiom,
% 3.98/1.91 ! [C: produc778275879_V_nat,A4: set_Pr1058435079_V_nat,B4: set_Pr1058435079_V_nat] :
% 3.98/1.91 ( ( member1886821968_V_nat @ C @ A4 )
% 3.98/1.91 => ( member1886821968_V_nat @ C @ ( sup_su1043134939_V_nat @ A4 @ B4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_321_UnE,axiom,
% 3.98/1.91 ! [C: product_prod_V_V,A4: set_Product_prod_V_V,B4: set_Product_prod_V_V] :
% 3.98/1.91 ( ( member2015049524od_V_V @ C @ ( sup_su551882943od_V_V @ A4 @ B4 ) )
% 3.98/1.91 => ( ~ ( member2015049524od_V_V @ C @ A4 )
% 3.98/1.91 => ( member2015049524od_V_V @ C @ B4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_322_UnE,axiom,
% 3.98/1.91 ! [C: v,A4: set_V,B4: set_V] :
% 3.98/1.91 ( ( member_V2 @ C @ ( sup_sup_set_V2 @ A4 @ B4 ) )
% 3.98/1.91 => ( ~ ( member_V2 @ C @ A4 )
% 3.98/1.91 => ( member_V2 @ C @ B4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_323_UnE,axiom,
% 3.98/1.91 ! [C: v2,A4: set_V2,B4: set_V2] :
% 3.98/1.91 ( ( member_V @ C @ ( sup_sup_set_V @ A4 @ B4 ) )
% 3.98/1.91 => ( ~ ( member_V @ C @ A4 )
% 3.98/1.91 => ( member_V @ C @ B4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_324_UnE,axiom,
% 3.98/1.91 ! [C: produc1699571228od_V_V,A4: set_Pr744279122od_V_V,B4: set_Pr744279122od_V_V] :
% 3.98/1.91 ( ( member1010391347od_V_V @ C @ ( sup_su693515134od_V_V @ A4 @ B4 ) )
% 3.98/1.91 => ( ~ ( member1010391347od_V_V @ C @ A4 )
% 3.98/1.91 => ( member1010391347od_V_V @ C @ B4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_325_UnE,axiom,
% 3.98/1.91 ! [C: produc778275879_V_nat,A4: set_Pr1058435079_V_nat,B4: set_Pr1058435079_V_nat] :
% 3.98/1.91 ( ( member1886821968_V_nat @ C @ ( sup_su1043134939_V_nat @ A4 @ B4 ) )
% 3.98/1.91 => ( ~ ( member1886821968_V_nat @ C @ A4 )
% 3.98/1.91 => ( member1886821968_V_nat @ C @ B4 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_326_labeled__graph_Osel_I2_J,axiom,
% 3.98/1.91 ! [X1: set_Pr744279122od_V_V,X2: set_V] :
% 3.98/1.91 ( ( labele1134902411nt_V_V @ ( labele712009229nt_V_V @ X1 @ X2 ) )
% 3.98/1.91 = X2 ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_327_labeled__graph_Osel_I1_J,axiom,
% 3.98/1.91 ! [X1: set_Pr744279122od_V_V,X2: set_V] :
% 3.98/1.91 ( ( labele515735386nt_V_V @ ( labele712009229nt_V_V @ X1 @ X2 ) )
% 3.98/1.91 = X1 ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_328_graph__homomorphism__semantics,axiom,
% 3.98/1.91 ! [A4: labele2115946735nt_V_V,B4: labele2115946735nt_V_V,F2: set_Product_prod_V_V,A: v,B: v,E: allego859987871tant_V,A2: v,B2: v] :
% 3.98/1.91 ( ( graph_1808119_V_V_V @ A4 @ B4 @ F2 )
% 3.98/1.91 => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( semant993842370nt_V_V @ A4 @ E ) )
% 3.98/1.91 => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ A2 ) @ F2 )
% 3.98/1.91 => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ B @ B2 ) @ F2 )
% 3.98/1.91 => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A2 @ B2 ) @ ( semant993842370nt_V_V @ B4 @ E ) ) ) ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_329_graph__homomorphism__nonempty,axiom,
% 3.98/1.91 ! [A4: labele2115946735nt_V_V,B4: labele2115946735nt_V_V,F2: set_Product_prod_V_V,E: allego859987871tant_V] :
% 3.98/1.91 ( ( graph_1808119_V_V_V @ A4 @ B4 @ F2 )
% 3.98/1.91 => ( ( ( semant993842370nt_V_V @ A4 @ E )
% 3.98/1.91 != bot_bo1389414743od_V_V )
% 3.98/1.91 => ( ( semant993842370nt_V_V @ B4 @ E )
% 3.98/1.91 != bot_bo1389414743od_V_V ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_330_labeled__graph_Oexhaust__sel,axiom,
% 3.98/1.91 ! [Labeled_graph: labele2115946735nt_V_V] :
% 3.98/1.91 ( Labeled_graph
% 3.98/1.91 = ( labele712009229nt_V_V @ ( labele515735386nt_V_V @ Labeled_graph ) @ ( labele1134902411nt_V_V @ Labeled_graph ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_331_standard__rules__def,axiom,
% 3.98/1.91 ( standa157301464ules_V
% 3.98/1.91 = ( ^ [C5: set_V2,L3: set_St1111633946tant_V] : ( sup_su1043134939_V_nat @ ( sup_su1043134939_V_nat @ ( standa1897115807ules_V @ C5 ) @ ( standa1568205529ules_V @ L3 ) ) @ ( insert481364471_V_nat @ ( standa214871990tant_V @ standard_S_Top_V ) @ ( insert481364471_V_nat @ standa1319953089tant_V @ bot_bo907687539_V_nat ) ) ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_332_semantics__in__vertices_I2_J,axiom,
% 3.98/1.91 ! [A4: labele2115946735nt_V_V,A: v,B: v,E: allego859987871tant_V] :
% 3.98/1.91 ( ( A4
% 3.98/1.91 = ( restri1305980611nt_V_V @ A4 ) )
% 3.98/1.91 => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( semant993842370nt_V_V @ A4 @ E ) )
% 3.98/1.91 => ( member_V2 @ B @ ( labele1134902411nt_V_V @ A4 ) ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_333_semantics__in__vertices_I1_J,axiom,
% 3.98/1.91 ! [A4: labele2115946735nt_V_V,A: v,B: v,E: allego859987871tant_V] :
% 3.98/1.91 ( ( A4
% 3.98/1.91 = ( restri1305980611nt_V_V @ A4 ) )
% 3.98/1.91 => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( semant993842370nt_V_V @ A4 @ E ) )
% 3.98/1.91 => ( member_V2 @ A @ ( labele1134902411nt_V_V @ A4 ) ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_334_subgraph__semantics,axiom,
% 3.98/1.91 ! [A4: labele2115946735nt_V_V,B4: labele2115946735nt_V_V,A: v,B: v,E: allego859987871tant_V] :
% 3.98/1.91 ( ( graph_1808119_V_V_V @ A4 @ B4 @ ( id_on_V2 @ ( labele1134902411nt_V_V @ A4 ) ) )
% 3.98/1.91 => ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( semant993842370nt_V_V @ A4 @ E ) )
% 3.98/1.91 => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ A @ B ) @ ( semant993842370nt_V_V @ B4 @ E ) ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_335_maintainedD,axiom,
% 3.98/1.91 ! [A4: labele2128733290_V_nat,B4: labele2128733290_V_nat,G: labele2115946735nt_V_V,F2: set_Pr53436518_nat_V] :
% 3.98/1.91 ( ( mainta197426964_nat_V @ ( produc698429463_V_nat @ A4 @ B4 ) @ G )
% 3.98/1.91 => ( ( graph_1541575154_nat_V @ A4 @ G @ F2 )
% 3.98/1.91 => ( extens1072773157_nat_V @ ( produc698429463_V_nat @ A4 @ B4 ) @ G @ F2 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_336_maintainedD,axiom,
% 3.98/1.91 ! [A4: labele2115946735nt_V_V,B4: labele2115946735nt_V_V,G: labele2115946735nt_V_V,F2: set_Product_prod_V_V] :
% 3.98/1.91 ( ( mainta1699210777_V_V_V @ ( produc533118295nt_V_V @ A4 @ B4 ) @ G )
% 3.98/1.91 => ( ( graph_1808119_V_V_V @ A4 @ G @ F2 )
% 3.98/1.91 => ( extens1533825066_V_V_V @ ( produc533118295nt_V_V @ A4 @ B4 ) @ G @ F2 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_337_sup__bot_Oright__neutral,axiom,
% 3.98/1.91 ! [A: set_Product_prod_V_V] :
% 3.98/1.91 ( ( sup_su551882943od_V_V @ A @ bot_bo1389414743od_V_V )
% 3.98/1.91 = A ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_338_sup__bot_Oright__neutral,axiom,
% 3.98/1.91 ! [A: set_V] :
% 3.98/1.91 ( ( sup_sup_set_V2 @ A @ bot_bot_set_V2 )
% 3.98/1.91 = A ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_339_sup__bot_Oright__neutral,axiom,
% 3.98/1.91 ! [A: set_Pr1058435079_V_nat] :
% 3.98/1.91 ( ( sup_su1043134939_V_nat @ A @ bot_bo907687539_V_nat )
% 3.98/1.91 = A ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_340_sup__bot_Oneutr__eq__iff,axiom,
% 3.98/1.91 ! [A: set_Product_prod_V_V,B: set_Product_prod_V_V] :
% 3.98/1.91 ( ( bot_bo1389414743od_V_V
% 3.98/1.91 = ( sup_su551882943od_V_V @ A @ B ) )
% 3.98/1.91 = ( ( A = bot_bo1389414743od_V_V )
% 3.98/1.91 & ( B = bot_bo1389414743od_V_V ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_341_sup__bot_Oneutr__eq__iff,axiom,
% 3.98/1.91 ! [A: set_V,B: set_V] :
% 3.98/1.91 ( ( bot_bot_set_V2
% 3.98/1.91 = ( sup_sup_set_V2 @ A @ B ) )
% 3.98/1.91 = ( ( A = bot_bot_set_V2 )
% 3.98/1.91 & ( B = bot_bot_set_V2 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_342_sup__bot_Oneutr__eq__iff,axiom,
% 3.98/1.91 ! [A: set_Pr1058435079_V_nat,B: set_Pr1058435079_V_nat] :
% 3.98/1.91 ( ( bot_bo907687539_V_nat
% 3.98/1.91 = ( sup_su1043134939_V_nat @ A @ B ) )
% 3.98/1.91 = ( ( A = bot_bo907687539_V_nat )
% 3.98/1.91 & ( B = bot_bo907687539_V_nat ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_343_sup__bot_Oleft__neutral,axiom,
% 3.98/1.91 ! [A: set_Product_prod_V_V] :
% 3.98/1.91 ( ( sup_su551882943od_V_V @ bot_bo1389414743od_V_V @ A )
% 3.98/1.91 = A ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_344_sup__bot_Oleft__neutral,axiom,
% 3.98/1.91 ! [A: set_V] :
% 3.98/1.91 ( ( sup_sup_set_V2 @ bot_bot_set_V2 @ A )
% 3.98/1.91 = A ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_345_sup__bot_Oleft__neutral,axiom,
% 3.98/1.91 ! [A: set_Pr1058435079_V_nat] :
% 3.98/1.91 ( ( sup_su1043134939_V_nat @ bot_bo907687539_V_nat @ A )
% 3.98/1.91 = A ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_346_sup__bot_Oeq__neutr__iff,axiom,
% 3.98/1.91 ! [A: set_Product_prod_V_V,B: set_Product_prod_V_V] :
% 3.98/1.91 ( ( ( sup_su551882943od_V_V @ A @ B )
% 3.98/1.91 = bot_bo1389414743od_V_V )
% 3.98/1.91 = ( ( A = bot_bo1389414743od_V_V )
% 3.98/1.91 & ( B = bot_bo1389414743od_V_V ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_347_sup__bot_Oeq__neutr__iff,axiom,
% 3.98/1.91 ! [A: set_V,B: set_V] :
% 3.98/1.91 ( ( ( sup_sup_set_V2 @ A @ B )
% 3.98/1.91 = bot_bot_set_V2 )
% 3.98/1.91 = ( ( A = bot_bot_set_V2 )
% 3.98/1.91 & ( B = bot_bot_set_V2 ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_348_sup__bot_Oeq__neutr__iff,axiom,
% 3.98/1.91 ! [A: set_Pr1058435079_V_nat,B: set_Pr1058435079_V_nat] :
% 3.98/1.91 ( ( ( sup_su1043134939_V_nat @ A @ B )
% 3.98/1.91 = bot_bo907687539_V_nat )
% 3.98/1.91 = ( ( A = bot_bo907687539_V_nat )
% 3.98/1.91 & ( B = bot_bo907687539_V_nat ) ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_349_sup_Oright__idem,axiom,
% 3.98/1.91 ! [A: set_Pr1058435079_V_nat,B: set_Pr1058435079_V_nat] :
% 3.98/1.91 ( ( sup_su1043134939_V_nat @ ( sup_su1043134939_V_nat @ A @ B ) @ B )
% 3.98/1.91 = ( sup_su1043134939_V_nat @ A @ B ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_350_sup__left__idem,axiom,
% 3.98/1.91 ! [X3: set_Pr1058435079_V_nat,Y: set_Pr1058435079_V_nat] :
% 3.98/1.91 ( ( sup_su1043134939_V_nat @ X3 @ ( sup_su1043134939_V_nat @ X3 @ Y ) )
% 3.98/1.91 = ( sup_su1043134939_V_nat @ X3 @ Y ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_351_sup_Oleft__idem,axiom,
% 3.98/1.91 ! [A: set_Pr1058435079_V_nat,B: set_Pr1058435079_V_nat] :
% 3.98/1.91 ( ( sup_su1043134939_V_nat @ A @ ( sup_su1043134939_V_nat @ A @ B ) )
% 3.98/1.91 = ( sup_su1043134939_V_nat @ A @ B ) ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_352_sup__idem,axiom,
% 3.98/1.91 ! [X3: set_Pr1058435079_V_nat] :
% 3.98/1.91 ( ( sup_su1043134939_V_nat @ X3 @ X3 )
% 3.98/1.91 = X3 ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_353_sup_Oidem,axiom,
% 3.98/1.91 ! [A: set_Pr1058435079_V_nat] :
% 3.98/1.91 ( ( sup_su1043134939_V_nat @ A @ A )
% 3.98/1.91 = A ) ).
% 3.98/1.91
% 3.98/1.91 thf(fact_354_sup__bot__left,axiom,
% 3.98/1.91 ! [X3: set_Pr1058435079_V_nat] :
% 3.98/1.91 ( ( sup_su1043134939_V_nat @ bot_bo907687539_V_nat @ X3 )
% 3.98/1.91 = X3 ) ).
% 3.98/1.91
% 3.98/1.91 thf(conj_0,conjecture,
% 3.98/1.91 member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ y ) @ g ) ).
% 3.98/1.91 ------------------------
% 3.98/1.96 % (13491)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13384 for (2999ds/183Mi)
% 3.98/1.96 % (13496)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_13384 for (2999ds/275Mi)
% 3.98/1.96 % (13497)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13384 for (2999ds/18Mi)
% 3.98/1.96 % (13495)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_13384 for (2999ds/2Mi)
% 3.98/1.96 % (13493)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_13384 for (2999ds/27Mi)
% 3.98/1.96 % (13492)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_13384 for (2999ds/4Mi)
% 3.98/1.96 % (13494)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_13384 for (2999ds/2Mi)
% 3.98/1.96 % (13495)Instruction limit reached!
% 3.98/1.96 % (13495)------------------------------
% 3.98/1.96 % (13495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.98/1.96 % (13495)Termination reason: Unknown
% 3.98/1.96 % (13495)Termination phase: shuffling
% 3.98/1.96
% 3.98/1.96 % (13495)Memory used [KB]: 1535
% 3.98/1.96 % (13495)Time elapsed: 0.003 s
% 3.98/1.96 % (13495)Instructions burned: 2 (million)
% 3.98/1.96 % (13495)------------------------------
% 3.98/1.96 % (13495)------------------------------
% 3.98/1.96 % (13494)Instruction limit reached!
% 3.98/1.96 % (13494)------------------------------
% 3.98/1.96 % (13494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.98/1.96 % (13494)Termination reason: Unknown
% 3.98/1.96 % (13494)Termination phase: shuffling
% 3.98/1.96
% 3.98/1.96 % (13494)Memory used [KB]: 1535
% 3.98/1.96 % (13494)Time elapsed: 0.004 s
% 3.98/1.96 % (13494)Instructions burned: 3 (million)
% 3.98/1.96 % (13494)------------------------------
% 3.98/1.96 % (13494)------------------------------
% 3.98/1.96 % (13492)Instruction limit reached!
% 3.98/1.96 % (13492)------------------------------
% 3.98/1.96 % (13492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.98/1.96 % (13492)Termination reason: Unknown
% 3.98/1.96 % (13492)Termination phase: shuffling
% 3.98/1.96
% 3.98/1.96 % (13492)Memory used [KB]: 1663
% 3.98/1.96 % (13492)Time elapsed: 0.005 s
% 3.98/1.96 % (13492)Instructions burned: 5 (million)
% 3.98/1.96 % (13492)------------------------------
% 3.98/1.96 % (13492)------------------------------
% 3.98/1.97 % (13497)Instruction limit reached!
% 3.98/1.97 % (13497)------------------------------
% 3.98/1.97 % (13497)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.98/1.97 % (13497)Termination reason: Unknown
% 3.98/1.97 % (13497)Termination phase: shuffling
% 3.98/1.97
% 3.98/1.97 % (13497)Memory used [KB]: 1918
% 3.98/1.97 % (13497)Time elapsed: 0.011 s
% 3.98/1.97 % (13497)Instructions burned: 18 (million)
% 3.98/1.97 % (13497)------------------------------
% 3.98/1.97 % (13497)------------------------------
% 3.98/1.97 % (13493)Instruction limit reached!
% 3.98/1.97 % (13493)------------------------------
% 3.98/1.97 % (13493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.98/1.97 % (13493)Termination reason: Unknown
% 3.98/1.97 % (13493)Termination phase: shuffling
% 3.98/1.97
% 3.98/1.97 % (13493)Memory used [KB]: 2046
% 3.98/1.97 % (13493)Time elapsed: 0.017 s
% 3.98/1.97 % (13493)Instructions burned: 28 (million)
% 3.98/1.97 % (13493)------------------------------
% 3.98/1.97 % (13493)------------------------------
% 3.98/1.98 % (13500)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_13384 for (2999ds/15Mi)
% 3.98/1.98 % (13498)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_13384 for (2999ds/3Mi)
% 3.98/1.98 % (13499)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_13384 for (2999ds/37Mi)
% 3.98/1.98 % (13498)Instruction limit reached!
% 3.98/1.98 % (13498)------------------------------
% 3.98/1.98 % (13498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.98/1.98 % (13498)Termination reason: Unknown
% 3.98/1.98 % (13498)Termination phase: shuffling
% 3.98/1.98
% 3.98/1.98 % (13498)Memory used [KB]: 1535
% 3.98/1.98 % (13498)Time elapsed: 0.004 s
% 3.98/1.98 % (13498)Instructions burned: 4 (million)
% 3.98/1.98 % (13498)------------------------------
% 3.98/1.98 % (13498)------------------------------
% 3.98/1.98 % (13501)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_13384 for (2999ds/3Mi)
% 3.98/1.98 % (13500)Instruction limit reached!
% 3.98/1.98 % (13500)------------------------------
% 3.98/1.98 % (13500)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.98/1.98 % (13500)Termination reason: Unknown
% 3.98/1.98 % (13500)Termination phase: shuffling
% 3.98/1.98
% 3.98/1.98 % (13500)Memory used [KB]: 1791
% 3.98/1.98 % (13500)Time elapsed: 0.010 s
% 3.98/1.98 % (13500)Instructions burned: 15 (million)
% 3.98/1.98 % (13500)------------------------------
% 3.98/1.98 % (13500)------------------------------
% 3.98/1.99 % (13501)Instruction limit reached!
% 3.98/1.99 % (13501)------------------------------
% 3.98/1.99 % (13501)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.98/1.99 % (13501)Termination reason: Unknown
% 3.98/1.99 % (13501)Termination phase: shuffling
% 3.98/1.99
% 3.98/1.99 % (13501)Memory used [KB]: 1535
% 3.98/1.99 % (13501)Time elapsed: 0.004 s
% 3.98/1.99 % (13501)Instructions burned: 3 (million)
% 3.98/1.99 % (13501)------------------------------
% 3.98/1.99 % (13501)------------------------------
% 3.98/1.99 % (13496)Refutation not found, incomplete strategy
% 3.98/1.99 % (13496)------------------------------
% 3.98/1.99 % (13496)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.98/1.99 % (13496)Termination reason: Refutation not found, incomplete strategy
% 3.98/1.99
% 3.98/1.99
% 3.98/1.99 % (13496)Memory used [KB]: 6652
% 3.98/1.99 % (13496)Time elapsed: 0.031 s
% 3.98/1.99 % (13496)Instructions burned: 56 (million)
% 3.98/1.99 % (13496)------------------------------
% 3.98/1.99 % (13496)------------------------------
% 3.98/1.99 % (13502)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_13384 for (2999ds/1041Mi)
% 3.98/1.99 % (13499)Instruction limit reached!
% 3.98/1.99 % (13499)------------------------------
% 3.98/1.99 % (13499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.98/1.99 % (13499)Termination reason: Unknown
% 3.98/1.99 % (13499)Termination phase: shuffling
% 3.98/1.99
% 3.98/1.99 % (13499)Memory used [KB]: 2174
% 3.98/1.99 % (13499)Time elapsed: 0.021 s
% 3.98/1.99 % (13499)Instructions burned: 38 (million)
% 3.98/1.99 % (13499)------------------------------
% 3.98/1.99 % (13499)------------------------------
% 3.98/2.00 % (13503)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_13384 for (2999ds/7Mi)
% 3.98/2.00 % (13504)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_13384 for (2999ds/16Mi)
% 3.98/2.00 % (13505)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_13384 for (2999ds/3Mi)
% 3.98/2.00 % (13506)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_13384 for (2999ds/3Mi)
% 3.98/2.00 % (13505)Instruction limit reached!
% 3.98/2.00 % (13505)------------------------------
% 3.98/2.00 % (13505)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.98/2.00 % (13505)Termination reason: Unknown
% 3.98/2.00 % (13505)Termination phase: shuffling
% 3.98/2.00
% 3.98/2.00 % (13505)Memory used [KB]: 1535
% 3.98/2.00 % (13505)Time elapsed: 0.004 s
% 3.98/2.00 % (13505)Instructions burned: 3 (million)
% 3.98/2.00 % (13505)------------------------------
% 3.98/2.00 % (13505)------------------------------
% 3.98/2.01 % (13506)Instruction limit reached!
% 3.98/2.01 % (13506)------------------------------
% 3.98/2.01 % (13506)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.98/2.01 % (13506)Termination reason: Unknown
% 3.98/2.01 % (13506)Termination phase: shuffling
% 3.98/2.01
% 3.98/2.01 % (13506)Memory used [KB]: 1535
% 3.98/2.01 % (13506)Time elapsed: 0.003 s
% 3.98/2.01 % (13506)Instructions burned: 3 (million)
% 3.98/2.01 % (13506)------------------------------
% 3.98/2.01 % (13506)------------------------------
% 3.98/2.01 % (13504)Instruction limit reached!
% 3.98/2.01 % (13504)------------------------------
% 3.98/2.01 % (13504)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.98/2.01 % (13504)Termination reason: Unknown
% 3.98/2.01 % (13504)Termination phase: shuffling
% 3.98/2.01
% 3.98/2.01 % (13504)Memory used [KB]: 1791
% 3.98/2.01 % (13504)Time elapsed: 0.010 s
% 3.98/2.01 % (13504)Instructions burned: 16 (million)
% 3.98/2.01 % (13504)------------------------------
% 3.98/2.01 % (13504)------------------------------
% 3.98/2.01 % (13503)Instruction limit reached!
% 3.98/2.01 % (13503)------------------------------
% 3.98/2.01 % (13503)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.98/2.01 % (13503)Termination reason: Unknown
% 3.98/2.01 % (13503)Termination phase: shuffling
% 3.98/2.01
% 3.98/2.01 % (13503)Memory used [KB]: 1663
% 3.98/2.01 % (13503)Time elapsed: 0.008 s
% 3.98/2.01 % (13503)Instructions burned: 8 (million)
% 3.98/2.01 % (13503)------------------------------
% 3.98/2.01 % (13503)------------------------------
% 3.98/2.01 % (13507)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_13384 for (2999ds/7Mi)
% 3.98/2.02 % (13507)Instruction limit reached!
% 3.98/2.02 % (13507)------------------------------
% 3.98/2.02 % (13507)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.98/2.02 % (13507)Termination reason: Unknown
% 3.98/2.02 % (13507)Termination phase: shuffling
% 3.98/2.02
% 3.98/2.02 % (13507)Memory used [KB]: 1663
% 3.98/2.02 % (13507)Time elapsed: 0.005 s
% 3.98/2.02 % (13507)Instructions burned: 7 (million)
% 3.98/2.02 % (13507)------------------------------
% 3.98/2.02 % (13507)------------------------------
% 3.98/2.02 % (13508)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_13384 for (2999ds/3Mi)
% 3.98/2.02 % (13509)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_13384 for (2999ds/4Mi)
% 3.98/2.02 % (13508)Instruction limit reached!
% 3.98/2.02 % (13508)------------------------------
% 3.98/2.02 % (13508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.98/2.02 % (13508)Termination reason: Unknown
% 3.98/2.02 % (13508)Termination phase: shuffling
% 3.98/2.02
% 3.98/2.02 % (13508)Memory used [KB]: 1535
% 3.98/2.02 % (13508)Time elapsed: 0.004 s
% 3.98/2.02 % (13508)Instructions burned: 3 (million)
% 3.98/2.02 % (13508)------------------------------
% 3.98/2.02 % (13508)------------------------------
% 3.98/2.03 % (13509)Instruction limit reached!
% 3.98/2.03 % (13509)------------------------------
% 3.98/2.03 % (13509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.98/2.03 % (13509)Termination reason: Unknown
% 3.98/2.03 % (13509)Termination phase: shuffling
% 3.98/2.03
% 3.98/2.03 % (13509)Memory used [KB]: 1535
% 3.98/2.03 % (13509)Time elapsed: 0.004 s
% 3.98/2.03 % (13509)Instructions burned: 5 (million)
% 3.98/2.03 % (13509)------------------------------
% 3.98/2.03 % (13509)------------------------------
% 4.57/2.03 % (13510)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_13384 for (2999ds/18Mi)
% 4.57/2.03 % (13511)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_13384 for (2999ds/710Mi)
% 4.57/2.04 % (13512)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_13384 for (2999ds/6Mi)
% 4.57/2.04 % (13510)Instruction limit reached!
% 4.57/2.04 % (13510)------------------------------
% 4.57/2.04 % (13510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.57/2.04 % (13510)Termination reason: Unknown
% 4.57/2.04 % (13510)Termination phase: shuffling
% 4.57/2.04
% 4.57/2.04 % (13510)Memory used [KB]: 1791
% 4.57/2.04 % (13510)Time elapsed: 0.012 s
% 4.57/2.04 % (13510)Instructions burned: 18 (million)
% 4.57/2.04 % (13510)------------------------------
% 4.57/2.04 % (13510)------------------------------
% 4.57/2.04 % (13512)Instruction limit reached!
% 4.57/2.04 % (13512)------------------------------
% 4.57/2.04 % (13512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.57/2.04 % (13512)Termination reason: Unknown
% 4.57/2.04 % (13512)Termination phase: shuffling
% 4.57/2.04
% 4.57/2.04 % (13512)Memory used [KB]: 1663
% 4.57/2.04 % (13512)Time elapsed: 0.006 s
% 4.57/2.04 % (13512)Instructions burned: 7 (million)
% 4.57/2.04 % (13512)------------------------------
% 4.57/2.04 % (13512)------------------------------
% 4.57/2.04 % (13513)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_13384 for (2998ds/902Mi)
% 4.57/2.04 % (13514)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_13384 for (2998ds/21Mi)
% 4.57/2.05 % (13491)Instruction limit reached!
% 4.57/2.05 % (13491)------------------------------
% 4.57/2.05 % (13491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.57/2.05 % (13491)Termination reason: Unknown
% 4.57/2.05 % (13491)Termination phase: Saturation
% 4.57/2.05
% 4.57/2.05 % (13491)Memory used [KB]: 7419
% 4.57/2.05 % (13491)Time elapsed: 0.096 s
% 4.57/2.05 % (13491)Instructions burned: 183 (million)
% 4.57/2.05 % (13491)------------------------------
% 4.57/2.05 % (13491)------------------------------
% 4.57/2.06 % (13514)Instruction limit reached!
% 4.57/2.06 % (13514)------------------------------
% 4.57/2.06 % (13514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.57/2.06 % (13514)Termination reason: Unknown
% 4.57/2.06 % (13514)Termination phase: shuffling
% 4.57/2.06
% 4.57/2.06 % (13514)Memory used [KB]: 1918
% 4.57/2.06 % (13514)Time elapsed: 0.013 s
% 4.57/2.06 % (13514)Instructions burned: 22 (million)
% 4.57/2.06 % (13514)------------------------------
% 4.57/2.06 % (13514)------------------------------
% 4.57/2.06 % (13516)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_13384 for (2998ds/6Mi)
% 4.57/2.06 % (13515)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_13384 for (2998ds/5Mi)
% 4.57/2.06 % (13515)Instruction limit reached!
% 4.57/2.06 % (13515)------------------------------
% 4.57/2.06 % (13515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.57/2.06 % (13515)Termination reason: Unknown
% 4.57/2.06 % (13515)Termination phase: shuffling
% 4.57/2.06
% 4.57/2.06 % (13515)Memory used [KB]: 1663
% 4.57/2.06 % (13515)Time elapsed: 0.005 s
% 4.57/2.06 % (13515)Instructions burned: 5 (million)
% 4.57/2.06 % (13515)------------------------------
% 4.57/2.06 % (13515)------------------------------
% 4.57/2.06 % (13516)Instruction limit reached!
% 4.57/2.06 % (13516)------------------------------
% 4.57/2.06 % (13516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.57/2.06 % (13516)Termination reason: Unknown
% 4.57/2.06 % (13516)Termination phase: shuffling
% 4.57/2.06
% 4.57/2.06 % (13516)Memory used [KB]: 1663
% 4.57/2.06 % (13516)Time elapsed: 0.006 s
% 4.57/2.06 % (13516)Instructions burned: 7 (million)
% 4.57/2.06 % (13516)------------------------------
% 4.57/2.06 % (13516)------------------------------
% 4.57/2.07 % (13517)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_13384 for (2998ds/377Mi)
% 4.57/2.07 % (13518)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_13384 for (2998ds/779Mi)
% 4.57/2.08 % (13519)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_13384 for (2998ds/19Mi)
% 4.57/2.08 % (13520)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_13384 for (2998ds/879Mi)
% 4.57/2.09 % (13519)Instruction limit reached!
% 4.57/2.09 % (13519)------------------------------
% 4.57/2.09 % (13519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.57/2.09 % (13519)Termination reason: Unknown
% 4.57/2.09 % (13519)Termination phase: shuffling
% 4.57/2.09
% 4.57/2.09 % (13519)Memory used [KB]: 1918
% 4.57/2.09 % (13519)Time elapsed: 0.012 s
% 4.57/2.09 % (13519)Instructions burned: 20 (million)
% 4.57/2.09 % (13519)------------------------------
% 4.57/2.09 % (13519)------------------------------
% 4.57/2.11 % (13521)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_13384 for (2998ds/17Mi)
% 4.57/2.12 % (13521)Instruction limit reached!
% 4.57/2.12 % (13521)------------------------------
% 4.57/2.12 % (13521)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.57/2.12 % (13521)Termination reason: Unknown
% 4.57/2.12 % (13521)Termination phase: shuffling
% 4.57/2.12
% 4.57/2.12 % (13521)Memory used [KB]: 1791
% 4.57/2.12 % (13521)Time elapsed: 0.011 s
% 4.57/2.12 % (13521)Instructions burned: 18 (million)
% 4.57/2.12 % (13521)------------------------------
% 4.57/2.12 % (13521)------------------------------
% 4.93/2.13 % (13513)First to succeed.
% 4.93/2.13 % (13513)Refutation found. Thanks to Tanya!
% 4.93/2.13 % SZS status Theorem for DTF2THF_13384
% 4.93/2.13 % SZS output start Proof for DTF2THF_13384
% 4.93/2.13 thf(type_def_5, type, set_St1111633946tant_V: $tType).
% 4.93/2.13 thf(type_def_6, type, standard_Constant_V: $tType).
% 4.93/2.13 thf(type_def_7, type, product_prod_V_V: $tType).
% 4.93/2.13 thf(type_def_9, type, set_Pr744279122od_V_V: $tType).
% 4.93/2.13 thf(type_def_10, type, set_la14611914_V_nat: $tType).
% 4.93/2.13 thf(type_def_11, type, labele2128733290_V_nat: $tType).
% 4.93/2.13 thf(type_def_12, type, set_Pr1058435079_V_nat: $tType).
% 4.93/2.13 thf(type_def_13, type, produc1699571228od_V_V: $tType).
% 4.93/2.13 thf(type_def_14, type, v: $tType).
% 4.93/2.13 thf(type_def_15, type, set_Pr257494450_V_V_V: $tType).
% 4.93/2.13 thf(type_def_16, type, set_Product_prod_V_V: $tType).
% 4.93/2.13 thf(type_def_17, type, set_Pr1228022213_V_V_V: $tType).
% 4.93/2.13 thf(type_def_18, type, set_V2: $tType).
% 4.93/2.13 thf(type_def_19, type, v2: $tType).
% 4.93/2.13 thf(type_def_20, type, set_Product_prod_V_V2: $tType).
% 4.93/2.13 thf(type_def_21, type, set_V: $tType).
% 4.93/2.13 thf(type_def_22, type, labele201426742od_V_V: $tType).
% 4.93/2.13 thf(type_def_23, type, set_Pr2015814777od_V_V: $tType).
% 4.93/2.13 thf(type_def_24, type, labele236903175od_V_V: $tType).
% 4.93/2.13 thf(type_def_25, type, set_Pr2022779335od_V_V: $tType).
% 4.93/2.13 thf(type_def_26, type, labele788688367nt_V_V: $tType).
% 4.93/2.13 thf(type_def_27, type, set_Product_prod_V_V3: $tType).
% 4.93/2.13 thf(type_def_28, type, labele2115946735nt_V_V: $tType).
% 4.93/2.13 thf(type_def_29, type, allego859987871tant_V: $tType).
% 4.93/2.13 thf(type_def_30, type, set_Pr872354016od_V_V: $tType).
% 4.93/2.13 thf(type_def_31, type, set_Pr951255342od_V_V: $tType).
% 4.93/2.13 thf(type_def_32, type, set_Pr1498723630od_V_V: $tType).
% 4.93/2.13 thf(type_def_33, type, set_Pr53436518_nat_V: $tType).
% 4.93/2.13 thf(type_def_34, type, labele506073123_V_nat: $tType).
% 4.93/2.13 thf(type_def_35, type, set_Pr1056235617_nat_V: $tType).
% 4.93/2.13 thf(type_def_36, type, set_Pr1326571566_V_nat: $tType).
% 4.93/2.13 thf(type_def_37, type, produc778275879_V_nat: $tType).
% 4.93/2.13 thf(type_def_38, type, set_Pr361461255at_nat: $tType).
% 4.93/2.13 thf(type_def_39, type, set_Pr597600647_V_nat: $tType).
% 4.93/2.13 thf(type_def_40, type, set_Pr473545225_V_nat: $tType).
% 4.93/2.13 thf(type_def_41, type, set_Pr1007924423_V_nat: $tType).
% 4.93/2.13 thf(type_def_42, type, produc1082089497od_V_V: $tType).
% 4.93/2.13 thf(type_def_43, type, produc1269720746od_V_V: $tType).
% 4.93/2.13 thf(type_def_44, type, produc522115815od_V_V: $tType).
% 4.93/2.13 thf(type_def_45, type, produc1443401592od_V_V: $tType).
% 4.93/2.13 thf(type_def_46, type, product_prod_V_V2: $tType).
% 4.93/2.13 thf(type_def_47, type, produc1113554040od_V_V: $tType).
% 4.93/2.13 thf(type_def_48, type, produc651414759nt_V_V: $tType).
% 4.93/2.13 thf(func_def_0, type, set_Pr361461255at_nat: $tType).
% 4.93/2.13 thf(func_def_1, type, set_Pr1326571566_V_nat: $tType).
% 4.93/2.13 thf(func_def_2, type, set_Pr1007924423_V_nat: $tType).
% 4.93/2.13 thf(func_def_3, type, set_Pr872354016od_V_V: $tType).
% 4.93/2.13 thf(func_def_4, type, produc1269720746od_V_V: $tType).
% 4.93/2.13 thf(func_def_5, type, set_Pr597600647_V_nat: $tType).
% 4.93/2.13 thf(func_def_6, type, labele506073123_V_nat: $tType).
% 4.93/2.13 thf(func_def_7, type, set_Pr2015814777od_V_V: $tType).
% 4.93/2.13 thf(func_def_8, type, set_Pr1056235617_nat_V: $tType).
% 4.93/2.13 thf(func_def_9, type, produc1082089497od_V_V: $tType).
% 4.93/2.13 thf(func_def_10, type, set_Pr473545225_V_nat: $tType).
% 4.93/2.13 thf(func_def_11, type, set_Pr1058435079_V_nat: $tType).
% 4.93/2.13 thf(func_def_12, type, produc778275879_V_nat: $tType).
% 4.93/2.13 thf(func_def_13, type, produc651414759nt_V_V: $tType).
% 4.93/2.13 thf(func_def_14, type, labele201426742od_V_V: $tType).
% 4.93/2.13 thf(func_def_15, type, set_Pr951255342od_V_V: $tType).
% 4.93/2.13 thf(func_def_16, type, produc1443401592od_V_V: $tType).
% 4.93/2.13 thf(func_def_17, type, set_Pr257494450_V_V_V: $tType).
% 4.93/2.13 thf(func_def_18, type, set_Pr744279122od_V_V: $tType).
% 4.93/2.13 thf(func_def_19, type, set_Pr1498723630od_V_V: $tType).
% 4.93/2.13 thf(func_def_20, type, labele236903175od_V_V: $tType).
% 4.93/2.13 thf(func_def_21, type, set_Pr2022779335od_V_V: $tType).
% 4.93/2.13 thf(func_def_22, type, produc1699571228od_V_V: $tType).
% 4.93/2.13 thf(func_def_23, type, produc1113554040od_V_V: $tType).
% 4.93/2.13 thf(func_def_24, type, set_la14611914_V_nat: $tType).
% 4.93/2.13 thf(func_def_25, type, produc522115815od_V_V: $tType).
% 4.93/2.13 thf(func_def_26, type, labele2128733290_V_nat: $tType).
% 4.93/2.13 thf(func_def_27, type, allego859987871tant_V: $tType).
% 4.93/2.13 thf(func_def_28, type, labele2115946735nt_V_V: $tType).
% 4.93/2.13 thf(func_def_29, type, set_Pr1228022213_V_V_V: $tType).
% 4.93/2.13 thf(func_def_30, type, labele788688367nt_V_V: $tType).
% 4.93/2.13 thf(func_def_31, type, set_St1111633946tant_V: $tType).
% 4.93/2.13 thf(func_def_32, type, set_Pr53436518_nat_V: $tType).
% 4.93/2.13 thf(func_def_33, type, set_Product_prod_V_V: $tType).
% 4.93/2.13 thf(func_def_34, type, set_Product_prod_V_V2: $tType).
% 4.93/2.13 thf(func_def_35, type, set_Product_prod_V_V3: $tType).
% 4.93/2.13 thf(func_def_36, type, standard_Constant_V: $tType).
% 4.93/2.13 thf(func_def_37, type, product_prod_V_V: $tType).
% 4.93/2.13 thf(func_def_38, type, product_prod_V_V2: $tType).
% 4.93/2.13 thf(func_def_39, type, set_V: $tType).
% 4.93/2.13 thf(func_def_40, type, set_V2: $tType).
% 4.93/2.13 thf(func_def_41, type, v: $tType).
% 4.93/2.13 thf(func_def_42, type, v2: $tType).
% 4.93/2.13 thf(func_def_43, type, bNF_Gr320641027od_V_V: set_St1111633946tant_V > (standard_Constant_V > product_prod_V_V) > set_Pr744279122od_V_V).
% 4.93/2.13 thf(func_def_44, type, bNF_Gr17960482_V_nat: set_la14611914_V_nat > (labele2128733290_V_nat > labele2128733290_V_nat) > set_Pr1058435079_V_nat).
% 4.93/2.13 thf(func_def_45, type, bNF_Gr480427157_V_V_V: set_Pr744279122od_V_V > (produc1699571228od_V_V > v) > set_Pr257494450_V_V_V).
% 4.93/2.13 thf(func_def_46, type, bNF_Gr1069958334_V_V_V: set_Product_prod_V_V > (product_prod_V_V > v) > set_Pr1228022213_V_V_V).
% 4.93/2.13 thf(func_def_47, type, bNF_Gr_V_V: set_V2 > (v2 > v) > set_Product_prod_V_V2).
% 4.93/2.13 thf(func_def_48, type, bNF_Gr_V_V2: set_V > (v > v) > set_Product_prod_V_V).
% 4.93/2.13 thf(func_def_49, type, comp_V1480932210od_V_V: (v > produc1699571228od_V_V) > (produc1699571228od_V_V > v) > produc1699571228od_V_V > produc1699571228od_V_V).
% 4.93/2.13 thf(func_def_50, type, comp_V772749048od_V_V: (v > product_prod_V_V) > (product_prod_V_V > v) > product_prod_V_V > product_prod_V_V).
% 4.93/2.13 thf(func_def_51, type, comp_V_V_V: (v > v2) > (v2 > v) > v2 > v2).
% 4.93/2.13 thf(func_def_52, type, comp_V_V_V2: (v > v) > (v > v) > v > v).
% 4.93/2.13 thf(func_def_53, type, standard_S_Bot_V: standard_Constant_V).
% 4.93/2.13 thf(func_def_54, type, standard_S_Const_V: v2 > standard_Constant_V).
% 4.93/2.13 thf(func_def_55, type, standard_S_Top_V: standard_Constant_V).
% 4.93/2.13 thf(func_def_56, type, getRel2057312683od_V_V: standard_Constant_V > labele201426742od_V_V > set_Pr2015814777od_V_V).
% 4.93/2.13 thf(func_def_57, type, getRel1902920892od_V_V: standard_Constant_V > labele236903175od_V_V > set_Pr2022779335od_V_V).
% 4.93/2.13 thf(func_def_58, type, getRel632961956nt_V_V: standard_Constant_V > labele788688367nt_V_V > set_Product_prod_V_V3).
% 4.93/2.13 thf(func_def_59, type, getRel1432786916nt_V_V: standard_Constant_V > labele2115946735nt_V_V > set_Product_prod_V_V).
% 4.93/2.13 thf(func_def_60, type, semant993842370nt_V_V: labele2115946735nt_V_V > allego859987871tant_V > set_Product_prod_V_V).
% 4.93/2.13 thf(func_def_61, type, edge_p669293514tant_V: set_Pr257494450_V_V_V > set_Pr872354016od_V_V > set_Pr744279122od_V_V > $o).
% 4.93/2.13 thf(func_def_62, type, edge_p1776314003tant_V: set_Pr1228022213_V_V_V > set_Pr951255342od_V_V > set_Pr744279122od_V_V > $o).
% 4.93/2.13 thf(func_def_63, type, edge_p1322161019tant_V: set_Product_prod_V_V2 > set_Pr1498723630od_V_V > set_Pr744279122od_V_V > $o).
% 4.93/2.13 thf(func_def_64, type, edge_p1560004099tant_V: set_Product_prod_V_V > set_Pr744279122od_V_V > set_Pr744279122od_V_V > $o).
% 4.93/2.13 thf(func_def_65, type, graph_1541575154_nat_V: labele2128733290_V_nat > labele2115946735nt_V_V > set_Pr53436518_nat_V > $o).
% 4.93/2.13 thf(func_def_66, type, graph_227683057_nat_V: labele506073123_V_nat > labele2115946735nt_V_V > set_Pr1056235617_nat_V > $o).
% 4.93/2.13 thf(func_def_67, type, graph_840721237_V_V_V: labele236903175od_V_V > labele2115946735nt_V_V > set_Pr1228022213_V_V_V > $o).
% 4.93/2.13 thf(func_def_68, type, graph_1808119_V_V_V: labele2115946735nt_V_V > labele2115946735nt_V_V > set_Product_prod_V_V > $o).
% 4.93/2.13 thf(func_def_69, type, graph_1141886696nt_V_V: labele2115946735nt_V_V > labele2115946735nt_V_V > labele2115946735nt_V_V).
% 4.93/2.13 thf(func_def_70, type, labele1193521135_V_nat: set_Pr1326571566_V_nat > set_Pr1058435079_V_nat > labele506073123_V_nat).
% 4.93/2.13 thf(func_def_71, type, labele94156371od_V_V: set_Pr951255342od_V_V > set_Product_prod_V_V > labele236903175od_V_V).
% 4.93/2.13 thf(func_def_72, type, labele712009229nt_V_V: set_Pr744279122od_V_V > set_V > labele2115946735nt_V_V).
% 4.93/2.13 thf(func_def_73, type, labele1794513953od_V_V: labele201426742od_V_V > set_Pr872354016od_V_V).
% 4.93/2.13 thf(func_def_74, type, labele668941254od_V_V: labele236903175od_V_V > set_Pr951255342od_V_V).
% 4.93/2.13 thf(func_def_75, type, labele1469545390nt_V_V: labele788688367nt_V_V > set_Pr1498723630od_V_V).
% 4.93/2.13 thf(func_def_76, type, labele515735386nt_V_V: labele2115946735nt_V_V > set_Pr744279122od_V_V).
% 4.93/2.13 thf(func_def_77, type, labele1328382418od_V_V: labele201426742od_V_V > set_Pr744279122od_V_V).
% 4.93/2.13 thf(func_def_78, type, labele1822884081_V_nat: labele506073123_V_nat > set_Pr1058435079_V_nat).
% 4.93/2.13 thf(func_def_79, type, labele981584981od_V_V: labele236903175od_V_V > set_Product_prod_V_V).
% 4.93/2.13 thf(func_def_80, type, labele1152678333nt_V_V: labele788688367nt_V_V > set_V2).
% 4.93/2.13 thf(func_def_81, type, labele1134902411nt_V_V: labele2115946735nt_V_V > set_V).
% 4.93/2.13 thf(func_def_82, type, map_gr157381846tant_V: set_Pr257494450_V_V_V > labele201426742od_V_V > labele2115946735nt_V_V).
% 4.93/2.13 thf(func_def_83, type, map_gr875022471tant_V: set_Pr1228022213_V_V_V > labele236903175od_V_V > labele2115946735nt_V_V).
% 4.93/2.13 thf(func_def_84, type, map_gr530397039tant_V: set_Product_prod_V_V2 > labele788688367nt_V_V > labele2115946735nt_V_V).
% 4.93/2.13 thf(func_def_85, type, map_gr907434255tant_V: set_Product_prod_V_V > labele2115946735nt_V_V > labele2115946735nt_V_V).
% 4.93/2.13 thf(func_def_86, type, restri1699516426od_V_V: labele201426742od_V_V > labele201426742od_V_V).
% 4.93/2.13 thf(func_def_87, type, restri1932147897_V_nat: labele506073123_V_nat > labele506073123_V_nat).
% 4.93/2.13 thf(func_def_88, type, restri1502575645od_V_V: labele236903175od_V_V > labele236903175od_V_V).
% 4.93/2.13 thf(func_def_89, type, restri175070597nt_V_V: labele788688367nt_V_V > labele788688367nt_V_V).
% 4.93/2.13 thf(func_def_90, type, restri1305980611nt_V_V: labele2115946735nt_V_V > labele2115946735nt_V_V).
% 4.93/2.13 thf(func_def_91, type, sup_su693515134od_V_V: set_Pr744279122od_V_V > set_Pr744279122od_V_V > set_Pr744279122od_V_V).
% 4.93/2.13 thf(func_def_92, type, sup_su1043134939_V_nat: set_Pr1058435079_V_nat > set_Pr1058435079_V_nat > set_Pr1058435079_V_nat).
% 4.93/2.13 thf(func_def_93, type, sup_su551882943od_V_V: set_Product_prod_V_V > set_Product_prod_V_V > set_Product_prod_V_V).
% 4.93/2.13 thf(func_def_94, type, sup_sup_set_V: set_V2 > set_V2 > set_V2).
% 4.93/2.13 thf(func_def_95, type, sup_sup_set_V2: set_V > set_V > set_V).
% 4.93/2.13 thf(func_def_96, type, bot_bo2024487199_V_V_o: produc1699571228od_V_V > $o).
% 4.93/2.13 thf(func_def_97, type, bot_bo1078500394_nat_o: produc778275879_V_nat > $o).
% 4.93/2.13 thf(func_def_98, type, bot_bo1168561222_V_V_o: product_prod_V_V > $o).
% 4.93/2.13 thf(func_def_99, type, bot_bot_V_o: v2 > $o).
% 4.93/2.13 thf(func_def_100, type, bot_bot_V_o2: v > $o).
% 4.93/2.13 thf(func_def_101, type, bot_bo1053950006_V_nat: set_la14611914_V_nat).
% 4.93/2.13 thf(func_def_102, type, bot_bo634818242_V_nat: set_Pr1326571566_V_nat).
% 4.93/2.13 thf(func_def_103, type, bot_bo451843010od_V_V: set_Pr951255342od_V_V).
% 4.93/2.13 thf(func_def_104, type, bot_bo667804902od_V_V: set_Pr744279122od_V_V).
% 4.93/2.13 thf(func_def_105, type, bot_bo323535987at_nat: set_Pr361461255at_nat).
% 4.93/2.13 thf(func_def_106, type, bot_bo1196823539_V_nat: set_Pr597600647_V_nat).
% 4.93/2.13 thf(func_def_107, type, bot_bo907687539_V_nat: set_Pr1058435079_V_nat).
% 4.93/2.13 thf(func_def_108, type, bot_bo1834032757_V_nat: set_Pr473545225_V_nat).
% 4.93/2.13 thf(func_def_109, type, bot_bo2057106227_V_nat: set_Pr1007924423_V_nat).
% 4.93/2.13 thf(func_def_110, type, bot_bo1708783349_nat_V: set_Pr1056235617_nat_V).
% 4.93/2.13 thf(func_def_111, type, bot_bo12878899od_V_V: set_Pr2022779335od_V_V).
% 4.93/2.13 thf(func_def_112, type, bot_bo688400985_V_V_V: set_Pr1228022213_V_V_V).
% 4.93/2.13 thf(func_def_113, type, bot_bo1389414743od_V_V: set_Product_prod_V_V).
% 4.93/2.13 thf(func_def_114, type, bot_bot_set_V: set_V2).
% 4.93/2.13 thf(func_def_115, type, bot_bot_set_V2: set_V).
% 4.93/2.13 thf(func_def_116, type, produc2132932316od_V_V: standard_Constant_V > produc1082089497od_V_V > produc1269720746od_V_V).
% 4.93/2.13 thf(func_def_117, type, produc1482441770od_V_V: standard_Constant_V > produc522115815od_V_V > produc1443401592od_V_V).
% 4.93/2.13 thf(func_def_118, type, produc1171747370od_V_V: standard_Constant_V > product_prod_V_V2 > produc1113554040od_V_V).
% 4.93/2.13 thf(func_def_119, type, produc107991630od_V_V: standard_Constant_V > product_prod_V_V > produc1699571228od_V_V).
% 4.93/2.13 thf(func_def_120, type, produc698429463_V_nat: labele2128733290_V_nat > labele2128733290_V_nat > produc778275879_V_nat).
% 4.93/2.13 thf(func_def_121, type, produc533118295nt_V_V: labele2115946735nt_V_V > labele2115946735nt_V_V > produc651414759nt_V_V).
% 4.93/2.13 thf(func_def_122, type, produc1736057425od_V_V: produc1699571228od_V_V > produc1699571228od_V_V > produc1082089497od_V_V).
% 4.93/2.13 thf(func_def_123, type, produc1905750615od_V_V: product_prod_V_V > product_prod_V_V > produc522115815od_V_V).
% 4.93/2.13 thf(func_def_124, type, product_Pair_V_V: v2 > v2 > product_prod_V_V2).
% 4.93/2.13 thf(func_def_125, type, product_Pair_V_V2: v > v > product_prod_V_V).
% 4.93/2.13 thf(func_def_126, type, id_on_1882925319_V_nat: set_la14611914_V_nat > set_Pr1058435079_V_nat).
% 4.93/2.13 thf(func_def_127, type, id_on_1491482303od_V_V: set_Pr744279122od_V_V > set_Pr2015814777od_V_V).
% 4.93/2.13 thf(func_def_128, type, id_on_558037444_V_nat: set_Pr1058435079_V_nat > set_Pr1007924423_V_nat).
% 4.93/2.13 thf(func_def_129, type, id_on_2125509800od_V_V: set_Product_prod_V_V > set_Pr2022779335od_V_V).
% 4.93/2.13 thf(func_def_130, type, id_on_V: set_V2 > set_Product_prod_V_V3).
% 4.93/2.13 thf(func_def_131, type, id_on_V2: set_V > set_Product_prod_V_V).
% 4.93/2.13 thf(func_def_132, type, conseq1236301781_nat_V: set_Pr1058435079_V_nat > labele2115946735nt_V_V > $o).
% 4.93/2.13 thf(func_def_133, type, extens1072773157_nat_V: produc778275879_V_nat > labele2115946735nt_V_V > set_Pr53436518_nat_V > $o).
% 4.93/2.13 thf(func_def_134, type, extens1533825066_V_V_V: produc651414759nt_V_V > labele2115946735nt_V_V > set_Product_prod_V_V > $o).
% 4.93/2.13 thf(func_def_135, type, mainta1342478555od_V_V: produc778275879_V_nat > labele201426742od_V_V > $o).
% 4.93/2.13 thf(func_def_136, type, mainta922614952_V_nat: produc778275879_V_nat > labele506073123_V_nat > $o).
% 4.93/2.13 thf(func_def_137, type, mainta1984786828od_V_V: produc778275879_V_nat > labele236903175od_V_V > $o).
% 4.93/2.13 thf(func_def_138, type, mainta1026355316_nat_V: produc778275879_V_nat > labele788688367nt_V_V > $o).
% 4.93/2.13 thf(func_def_139, type, mainta197426964_nat_V: produc778275879_V_nat > labele2115946735nt_V_V > $o).
% 4.93/2.13 thf(func_def_140, type, mainta1699210777_V_V_V: produc651414759nt_V_V > labele2115946735nt_V_V > $o).
% 4.93/2.13 thf(func_def_141, type, collec1840263537od_V_V: (produc1699571228od_V_V > $o) > set_Pr744279122od_V_V).
% 4.93/2.13 thf(func_def_142, type, collec1411521682_V_nat: (produc778275879_V_nat > $o) > set_Pr1058435079_V_nat).
% 4.93/2.13 thf(func_def_143, type, collec2040633974od_V_V: (product_prod_V_V > $o) > set_Product_prod_V_V).
% 4.93/2.13 thf(func_def_144, type, collect_V: (v2 > $o) > set_V2).
% 4.93/2.13 thf(func_def_145, type, collect_V2: (v > $o) > set_V).
% 4.93/2.13 thf(func_def_146, type, insert1818834324tant_V: standard_Constant_V > set_St1111633946tant_V > set_St1111633946tant_V).
% 4.93/2.13 thf(func_def_147, type, insert213439034_V_nat: labele2128733290_V_nat > set_la14611914_V_nat > set_la14611914_V_nat).
% 4.93/2.13 thf(func_def_148, type, insert135842892od_V_V: produc1699571228od_V_V > set_Pr744279122od_V_V > set_Pr744279122od_V_V).
% 4.93/2.13 thf(func_def_149, type, insert481364471_V_nat: produc778275879_V_nat > set_Pr1058435079_V_nat > set_Pr1058435079_V_nat).
% 4.93/2.13 thf(func_def_150, type, insert2024285275od_V_V: product_prod_V_V > set_Product_prod_V_V > set_Product_prod_V_V).
% 4.93/2.13 thf(func_def_151, type, insert_V: v2 > set_V2 > set_V2).
% 4.93/2.13 thf(func_def_152, type, insert_V2: v > set_V > set_V).
% 4.93/2.13 thf(func_def_153, type, standa434642387_V_nat: set_Pr1058435079_V_nat > set_Pr361461255at_nat).
% 4.93/2.13 thf(func_def_154, type, standa1571708471od_V_V: set_Product_prod_V_V > set_Pr597600647_V_nat).
% 4.93/2.13 thf(func_def_155, type, standa1897115807ules_V: set_V2 > set_Pr1058435079_V_nat).
% 4.93/2.13 thf(func_def_156, type, standa294833961ules_V: set_V > set_Pr473545225_V_nat).
% 4.93/2.13 thf(func_def_157, type, standa1568205529ules_V: set_St1111633946tant_V > set_Pr1058435079_V_nat).
% 4.93/2.13 thf(func_def_158, type, standa1319953089tant_V: produc778275879_V_nat).
% 4.93/2.13 thf(func_def_159, type, standa157301464ules_V: set_V2 > set_St1111633946tant_V > set_Pr1058435079_V_nat).
% 4.93/2.13 thf(func_def_160, type, standa214871990tant_V: standard_Constant_V > produc778275879_V_nat).
% 4.93/2.13 thf(func_def_161, type, member1542015739tant_V: standard_Constant_V > set_St1111633946tant_V > $o).
% 4.93/2.13 thf(func_def_162, type, member600445121od_V_V: produc1269720746od_V_V > set_Pr872354016od_V_V > $o).
% 4.93/2.13 thf(func_def_163, type, member361435663od_V_V: produc1443401592od_V_V > set_Pr951255342od_V_V > $o).
% 4.93/2.13 thf(func_def_164, type, member1416643087od_V_V: produc1113554040od_V_V > set_Pr1498723630od_V_V > $o).
% 4.93/2.13 thf(func_def_165, type, member1010391347od_V_V: produc1699571228od_V_V > set_Pr744279122od_V_V > $o).
% 4.93/2.13 thf(func_def_166, type, member1886821968_V_nat: produc778275879_V_nat > set_Pr1058435079_V_nat > $o).
% 4.93/2.13 thf(func_def_167, type, member785416642od_V_V: produc1082089497od_V_V > set_Pr2015814777od_V_V > $o).
% 4.93/2.13 thf(func_def_168, type, member134497296od_V_V: produc522115815od_V_V > set_Pr2022779335od_V_V > $o).
% 4.93/2.13 thf(func_def_169, type, member1990987792od_V_V: product_prod_V_V2 > set_Product_prod_V_V3 > $o).
% 4.93/2.13 thf(func_def_170, type, member2015049524od_V_V: product_prod_V_V > set_Product_prod_V_V > $o).
% 4.93/2.13 thf(func_def_171, type, member_V: v2 > set_V2 > $o).
% 4.93/2.13 thf(func_def_172, type, member_V2: v > set_V > $o).
% 4.93/2.13 thf(func_def_173, type, c: set_V2).
% 4.93/2.13 thf(func_def_174, type, g: labele2115946735nt_V_V).
% 4.93/2.13 thf(func_def_175, type, l: set_St1111633946tant_V).
% 4.93/2.13 thf(func_def_176, type, h: v > v).
% 4.93/2.13 thf(func_def_177, type, m: v2 > v).
% 4.93/2.13 thf(func_def_178, type, x: v).
% 4.93/2.13 thf(func_def_179, type, xa: v2).
% 4.93/2.13 thf(func_def_180, type, y: v2).
% 4.93/2.13 thf(func_def_188, type, sP0: set_Pr1058435079_V_nat > produc778275879_V_nat > set_Pr1058435079_V_nat > $o).
% 4.93/2.13 thf(func_def_189, type, sP1: produc1699571228od_V_V > set_Pr744279122od_V_V > set_Pr744279122od_V_V > produc1699571228od_V_V > $o).
% 4.93/2.13 thf(func_def_190, type, sP2: produc1699571228od_V_V > set_Pr744279122od_V_V > produc1699571228od_V_V > set_Pr744279122od_V_V > $o).
% 4.93/2.13 thf(func_def_191, type, sP3: set_Pr1058435079_V_nat > produc778275879_V_nat > produc778275879_V_nat > set_Pr1058435079_V_nat > $o).
% 4.93/2.13 thf(func_def_192, type, sP4: set_Pr1058435079_V_nat > produc778275879_V_nat > produc778275879_V_nat > set_Pr1058435079_V_nat > $o).
% 4.93/2.13 thf(func_def_193, type, sP5: set_Product_prod_V_V > product_prod_V_V > set_Product_prod_V_V > product_prod_V_V > $o).
% 4.93/2.13 thf(func_def_194, type, sP6: product_prod_V_V > set_Product_prod_V_V > product_prod_V_V > set_Product_prod_V_V > $o).
% 4.93/2.13 thf(func_def_195, type, sP7: set_V > set_V > v > v > $o).
% 4.93/2.13 thf(func_def_196, type, sP8: set_V > set_V > v > v > $o).
% 4.93/2.13 thf(func_def_197, type, sP9: v > set_V > set_V > $o).
% 4.93/2.13 thf(func_def_198, type, sP10: set_V2 > v2 > v2 > set_V2 > $o).
% 4.93/2.13 thf(func_def_199, type, sP11: set_V2 > v2 > v2 > set_V2 > $o).
% 4.93/2.13 thf(func_def_200, type, sP12: set_Pr1058435079_V_nat > produc778275879_V_nat > set_Pr1058435079_V_nat > $o).
% 4.93/2.13 thf(func_def_201, type, sP13: v > set_V > set_V > $o).
% 4.93/2.13 thf(func_def_202, type, sP14: product_prod_V_V > set_Product_prod_V_V > set_Product_prod_V_V > $o).
% 4.93/2.13 thf(func_def_203, type, sP15: set_Product_prod_V_V > product_prod_V_V > set_Product_prod_V_V > $o).
% 4.93/2.13 thf(func_def_204, type, sK16: produc778275879_V_nat > set_Pr1058435079_V_nat > set_Pr1058435079_V_nat).
% 4.93/2.13 thf(func_def_205, type, sK17: produc1699571228od_V_V > v).
% 4.93/2.13 thf(func_def_206, type, sK18: produc1699571228od_V_V > v).
% 4.93/2.13 thf(func_def_207, type, sK19: produc1699571228od_V_V > standard_Constant_V).
% 4.93/2.13 thf(func_def_208, type, sK20: (produc1699571228od_V_V > $o) > product_prod_V_V).
% 4.93/2.13 thf(func_def_209, type, sK21: (produc1699571228od_V_V > $o) > standard_Constant_V).
% 4.93/2.13 thf(func_def_210, type, sK22: labele236903175od_V_V > (product_prod_V_V > v) > set_Pr744279122od_V_V > standard_Constant_V).
% 4.93/2.13 thf(func_def_211, type, sK23: labele236903175od_V_V > (product_prod_V_V > v) > set_Pr744279122od_V_V > product_prod_V_V).
% 4.93/2.13 thf(func_def_212, type, sK24: labele236903175od_V_V > (product_prod_V_V > v) > set_Pr744279122od_V_V > product_prod_V_V).
% 4.93/2.13 thf(func_def_213, type, sK25: set_Product_prod_V_V > product_prod_V_V > set_Product_prod_V_V).
% 4.93/2.13 thf(func_def_214, type, sK26: (product_prod_V_V > $o) > product_prod_V_V).
% 4.93/2.13 thf(func_def_215, type, sK27: set_V2 > v2).
% 4.93/2.13 thf(func_def_216, type, sK28: v).
% 4.93/2.13 thf(func_def_217, type, sK29: set_V > v).
% 4.93/2.13 thf(func_def_218, type, sK30: set_Pr1058435079_V_nat > produc778275879_V_nat).
% 4.93/2.13 thf(func_def_219, type, sK31: produc778275879_V_nat > set_Pr1058435079_V_nat > set_Pr1058435079_V_nat).
% 4.93/2.13 thf(func_def_220, type, sK32: labele788688367nt_V_V > (v2 > v) > (v > v2) > v2).
% 4.93/2.13 thf(func_def_221, type, sK33: labele2128733290_V_nat > labele2128733290_V_nat > labele2115946735nt_V_V > set_Pr53436518_nat_V).
% 4.93/2.13 thf(func_def_222, type, sK34: (produc1699571228od_V_V > $o) > product_prod_V_V).
% 4.93/2.13 thf(func_def_223, type, sK35: (produc1699571228od_V_V > $o) > standard_Constant_V).
% 4.93/2.13 thf(func_def_224, type, sK36: product_prod_V_V > v).
% 4.93/2.13 thf(func_def_225, type, sK37: product_prod_V_V > v).
% 4.93/2.13 thf(func_def_226, type, sK38: produc1699571228od_V_V > set_Pr744279122od_V_V > set_Pr744279122od_V_V > produc1699571228od_V_V > set_Pr744279122od_V_V).
% 4.93/2.13 thf(func_def_227, type, sK39: set_Pr744279122od_V_V > (produc1699571228od_V_V > v) > labele201426742od_V_V > produc1699571228od_V_V).
% 4.93/2.13 thf(func_def_228, type, sK40: set_Pr744279122od_V_V > (produc1699571228od_V_V > v) > labele201426742od_V_V > standard_Constant_V).
% 4.93/2.13 thf(func_def_229, type, sK41: set_Pr744279122od_V_V > (produc1699571228od_V_V > v) > labele201426742od_V_V > produc1699571228od_V_V).
% 4.93/2.13 thf(func_def_230, type, sK42: set_Pr744279122od_V_V > produc1699571228od_V_V).
% 4.93/2.13 thf(func_def_231, type, sK43: set_Pr744279122od_V_V > produc1699571228od_V_V).
% 4.93/2.13 thf(func_def_232, type, sK44: v2 > v).
% 4.93/2.13 thf(func_def_233, type, sK45: (v > $o) > v).
% 4.93/2.13 thf(func_def_234, type, sK46: set_Pr1058435079_V_nat > produc778275879_V_nat).
% 4.93/2.13 thf(func_def_235, type, sK47: set_Pr1058435079_V_nat > produc778275879_V_nat > produc778275879_V_nat > set_Pr1058435079_V_nat > set_Pr1058435079_V_nat).
% 4.93/2.13 thf(func_def_236, type, sK48: set_Product_prod_V_V > product_prod_V_V).
% 4.93/2.13 thf(func_def_237, type, sK49: set_Pr744279122od_V_V > produc1699571228od_V_V > set_Pr744279122od_V_V).
% 4.93/2.13 thf(func_def_238, type, sK50: (v > produc1699571228od_V_V) > (produc1699571228od_V_V > v) > labele201426742od_V_V > produc1699571228od_V_V).
% 4.93/2.13 thf(func_def_239, type, sK51: set_Product_prod_V_V > product_prod_V_V > set_Product_prod_V_V > product_prod_V_V > set_Product_prod_V_V).
% 4.93/2.13 thf(func_def_240, type, sK52: set_V2 > v2).
% 4.93/2.13 thf(func_def_241, type, sK53: set_V > set_V > v > v > set_V).
% 4.93/2.13 thf(func_def_242, type, sK54: (produc1699571228od_V_V > $o) > v).
% 4.93/2.13 thf(func_def_243, type, sK55: (produc1699571228od_V_V > $o) > v).
% 4.93/2.13 thf(func_def_244, type, sK56: (produc1699571228od_V_V > $o) > standard_Constant_V).
% 4.93/2.13 thf(func_def_245, type, sK57: set_Pr744279122od_V_V > produc1082089497od_V_V > produc1699571228od_V_V).
% 4.93/2.13 thf(func_def_246, type, sK58: (product_prod_V_V > $o) > v).
% 4.93/2.13 thf(func_def_247, type, sK59: (product_prod_V_V > $o) > v).
% 4.93/2.13 thf(func_def_248, type, sK60: set_Pr744279122od_V_V > (v > v) > labele2115946735nt_V_V > v).
% 4.93/2.13 thf(func_def_249, type, sK61: set_Pr744279122od_V_V > (v > v) > labele2115946735nt_V_V > v).
% 4.93/2.13 thf(func_def_250, type, sK62: set_Pr744279122od_V_V > (v > v) > labele2115946735nt_V_V > standard_Constant_V).
% 4.93/2.13 thf(func_def_251, type, sK63: (v > v) > labele2115946735nt_V_V > (v > v) > v).
% 4.93/2.13 thf(func_def_252, type, sK64: produc1699571228od_V_V > set_Pr744279122od_V_V > set_Pr744279122od_V_V).
% 4.93/2.13 thf(func_def_253, type, sK65: product_prod_V_V > v).
% 4.93/2.13 thf(func_def_254, type, sK66: product_prod_V_V > v).
% 4.93/2.13 thf(func_def_255, type, sK67: labele236903175od_V_V > (product_prod_V_V > v) > (v > product_prod_V_V) > product_prod_V_V).
% 4.93/2.13 thf(func_def_256, type, sK68: (v > v) > labele2115946735nt_V_V > (v > v) > v).
% 4.93/2.13 thf(func_def_257, type, sK69: set_V2 > v2 > set_V2).
% 4.93/2.13 thf(func_def_258, type, sK70: (produc778275879_V_nat > $o) > produc778275879_V_nat).
% 4.93/2.13 thf(func_def_259, type, sK71: v2 > v).
% 4.93/2.13 thf(func_def_260, type, sK72: set_V > v > set_V).
% 4.93/2.13 thf(func_def_261, type, sK73: set_Product_prod_V_V > product_prod_V_V).
% 4.93/2.13 thf(func_def_262, type, sK74: set_Product_prod_V_V > product_prod_V_V).
% 4.93/2.13 thf(func_def_263, type, sK75: set_V2 > v2 > v2 > set_V2 > set_V2).
% 4.93/2.13 thf(func_def_264, type, sK76: set_V2 > v2).
% 4.93/2.13 thf(func_def_265, type, sK77: (product_prod_V_V > $o) > v).
% 4.93/2.13 thf(func_def_266, type, sK78: (product_prod_V_V > $o) > v).
% 4.93/2.13 thf(func_def_267, type, sK79: (produc778275879_V_nat > $o) > produc778275879_V_nat).
% 4.93/2.13 thf(func_def_268, type, sK80: (v > $o) > v).
% 4.93/2.13 thf(func_def_269, type, sK81: produc1699571228od_V_V > product_prod_V_V).
% 4.93/2.13 thf(func_def_270, type, sK82: produc1699571228od_V_V > standard_Constant_V).
% 4.93/2.13 thf(func_def_271, type, sK83: set_V2 > product_prod_V_V2 > v2).
% 4.93/2.13 thf(func_def_272, type, sK84: labele788688367nt_V_V > (v2 > v) > set_Pr744279122od_V_V > standard_Constant_V).
% 4.93/2.13 thf(func_def_273, type, sK85: labele788688367nt_V_V > (v2 > v) > set_Pr744279122od_V_V > v2).
% 4.93/2.13 thf(func_def_274, type, sK86: labele788688367nt_V_V > (v2 > v) > set_Pr744279122od_V_V > v2).
% 4.93/2.13 thf(func_def_275, type, sK87: (v > v) > labele2115946735nt_V_V > v).
% 4.93/2.13 thf(func_def_276, type, sK88: labele2115946735nt_V_V > labele2115946735nt_V_V > labele2115946735nt_V_V > set_Product_prod_V_V).
% 4.93/2.13 thf(func_def_277, type, sK89: (product_prod_V_V > $o) > product_prod_V_V).
% 4.93/2.13 thf(func_def_278, type, sK90: set_Pr1058435079_V_nat > set_Pr1058435079_V_nat > (produc778275879_V_nat > $o) > produc778275879_V_nat).
% 4.93/2.13 thf(func_def_279, type, sK91: set_Pr1058435079_V_nat > (produc778275879_V_nat > $o) > produc778275879_V_nat).
% 4.93/2.13 thf(func_def_280, type, sK92: set_Pr1058435079_V_nat > (produc778275879_V_nat > $o) > produc778275879_V_nat).
% 4.93/2.13 thf(func_def_281, type, sK93: set_Pr1058435079_V_nat > produc778275879_V_nat).
% 4.93/2.13 thf(func_def_282, type, sK94: set_V > product_prod_V_V > v).
% 4.93/2.13 thf(func_def_283, type, sK95: set_V2 > v2 > set_V2).
% 4.93/2.13 thf(func_def_284, type, sK96: set_V > v).
% 4.93/2.13 thf(func_def_285, type, sK97: v2 > v).
% 4.93/2.13 thf(func_def_286, type, sK98: set_Pr744279122od_V_V > produc1699571228od_V_V).
% 4.93/2.13 thf(func_def_287, type, sK99: set_V > v > set_V).
% 4.93/2.13 thf(func_def_288, type, sK100: v2 > v).
% 4.93/2.13 thf(func_def_289, type, sK101: produc522115815od_V_V > set_Product_prod_V_V > product_prod_V_V).
% 4.93/2.13 thf(func_def_290, type, sK102: set_Product_prod_V_V > product_prod_V_V > set_Product_prod_V_V).
% 4.93/2.13 thf(func_def_291, type, sK103: set_V > v).
% 4.93/2.13 thf(func_def_292, type, sK104: set_Pr1058435079_V_nat > (produc778275879_V_nat > $o) > set_Pr1058435079_V_nat > produc778275879_V_nat).
% 4.93/2.13 thf(func_def_293, type, sK105: set_Pr1058435079_V_nat > (produc778275879_V_nat > $o) > produc778275879_V_nat).
% 4.93/2.13 thf(func_def_294, type, sK106: (produc778275879_V_nat > $o) > set_Pr1058435079_V_nat > produc778275879_V_nat).
% 4.93/2.13 thf(func_def_295, type, sK107: produc1699571228od_V_V > product_prod_V_V).
% 4.93/2.13 thf(func_def_296, type, sK108: produc1699571228od_V_V > standard_Constant_V).
% 4.93/2.13 thf(func_def_298, type, ph110: !>[X0: $tType]:(X0)).
% 4.93/2.13 thf(f2484,plain,(
% 4.93/2.13 $false),
% 4.93/2.13 inference(trivial_inequality_removal,[status(thm)],[f2479])).
% 4.93/2.13 thf(f2479,plain,(
% 4.93/2.13 ($true != $true)),
% 4.93/2.13 inference(superposition,[status(thm)],[f2468,f2002])).
% 4.93/2.13 thf(f2002,plain,(
% 4.93/2.13 ((graph_1808119_V_V_V @ (map_gr907434255tant_V @ (bNF_Gr_V_V2 @ (labele1134902411nt_V_V @ g) @ h) @ g) @ g @ (id_on_V2 @ (labele1134902411nt_V_V @ (map_gr907434255tant_V @ (bNF_Gr_V_V2 @ (labele1134902411nt_V_V @ g) @ h) @ g)))) = $true)),
% 4.93/2.13 inference(cnf_transformation,[status(thm)],[f641])).
% 4.93/2.13 thf(f641,plain,(
% 4.93/2.13 ((graph_1808119_V_V_V @ (map_gr907434255tant_V @ (bNF_Gr_V_V2 @ (labele1134902411nt_V_V @ g) @ h) @ g) @ g @ (id_on_V2 @ (labele1134902411nt_V_V @ (map_gr907434255tant_V @ (bNF_Gr_V_V2 @ (labele1134902411nt_V_V @ g) @ h) @ g)))) = $true)),
% 4.93/2.13 inference(fool_elimination,[status(thm)],[f640])).
% 4.93/2.13 thf(f640,plain,(
% 4.93/2.13 (graph_1808119_V_V_V @ (map_gr907434255tant_V @ (bNF_Gr_V_V2 @ (labele1134902411nt_V_V @ g) @ h) @ g) @ g @ (id_on_V2 @ (labele1134902411nt_V_V @ (map_gr907434255tant_V @ (bNF_Gr_V_V2 @ (labele1134902411nt_V_V @ g) @ h) @ g))))),
% 4.93/2.13 inference(rectify,[status(thm)],[f9])).
% 4.93/2.13 thf(f9,axiom,(
% 4.93/2.13 (graph_1808119_V_V_V @ (map_gr907434255tant_V @ (bNF_Gr_V_V2 @ (labele1134902411nt_V_V @ g) @ h) @ g) @ g @ (id_on_V2 @ (labele1134902411nt_V_V @ (map_gr907434255tant_V @ (bNF_Gr_V_V2 @ (labele1134902411nt_V_V @ g) @ h) @ g))))),
% 4.93/2.13 file('/export/starexec/sandbox/tmp/tmp.OGMuvyH1wq/DTF2THF_13384.p',fact_8_h_I3_J)).
% 4.93/2.13 thf(f2468,plain,(
% 4.93/2.13 ((graph_1808119_V_V_V @ (map_gr907434255tant_V @ (bNF_Gr_V_V2 @ (labele1134902411nt_V_V @ g) @ h) @ g) @ g @ (id_on_V2 @ (labele1134902411nt_V_V @ (map_gr907434255tant_V @ (bNF_Gr_V_V2 @ (labele1134902411nt_V_V @ g) @ h) @ g)))) != $true)),
% 4.93/2.13 inference(trivial_inequality_removal,[status(thm)],[f2464])).
% 4.93/2.13 thf(f2464,plain,(
% 4.93/2.13 ((graph_1808119_V_V_V @ (map_gr907434255tant_V @ (bNF_Gr_V_V2 @ (labele1134902411nt_V_V @ g) @ h) @ g) @ g @ (id_on_V2 @ (labele1134902411nt_V_V @ (map_gr907434255tant_V @ (bNF_Gr_V_V2 @ (labele1134902411nt_V_V @ g) @ h) @ g)))) != $true) | ($true != $true)),
% 4.93/2.13 inference(superposition,[status(thm)],[f2462,f2201])).
% 4.93/2.13 thf(f2201,plain,(
% 4.93/2.13 ((member2015049524od_V_V @ (product_Pair_V_V2 @ (m @ xa) @ (m @ xa)) @ (getRel1432786916nt_V_V @ (standard_S_Const_V @ y) @ (map_gr907434255tant_V @ (bNF_Gr_V_V2 @ (labele1134902411nt_V_V @ g) @ h) @ g))) = $true)),
% 4.93/2.13 inference(cnf_transformation,[status(thm)],[f637])).
% 4.93/2.13 thf(f637,plain,(
% 4.93/2.13 ((member2015049524od_V_V @ (product_Pair_V_V2 @ (m @ xa) @ (m @ xa)) @ (getRel1432786916nt_V_V @ (standard_S_Const_V @ y) @ (map_gr907434255tant_V @ (bNF_Gr_V_V2 @ (labele1134902411nt_V_V @ g) @ h) @ g))) = $true)),
% 4.93/2.13 inference(fool_elimination,[status(thm)],[f636])).
% 4.93/2.13 thf(f636,plain,(
% 4.93/2.13 (member2015049524od_V_V @ (product_Pair_V_V2 @ (m @ xa) @ (m @ xa)) @ (getRel1432786916nt_V_V @ (standard_S_Const_V @ y) @ (map_gr907434255tant_V @ (bNF_Gr_V_V2 @ (labele1134902411nt_V_V @ g) @ h) @ g)))),
% 4.93/2.13 inference(rectify,[status(thm)],[f7])).
% 4.93/2.13 thf(f7,axiom,(
% 4.93/2.13 (member2015049524od_V_V @ (product_Pair_V_V2 @ (m @ xa) @ (m @ xa)) @ (getRel1432786916nt_V_V @ (standard_S_Const_V @ y) @ (map_gr907434255tant_V @ (bNF_Gr_V_V2 @ (labele1134902411nt_V_V @ g) @ h) @ g)))),
% 4.93/2.13 file('/export/starexec/sandbox/tmp/tmp.OGMuvyH1wq/DTF2THF_13384.p',fact_6__092_060open_062_Im_Ax_M_Am_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ay_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062)).
% 4.93/2.13 thf(f2462,plain,(
% 4.93/2.13 ( ! [X0 : labele2115946735nt_V_V] : (((member2015049524od_V_V @ (product_Pair_V_V2 @ (m @ xa) @ (m @ xa)) @ (getRel1432786916nt_V_V @ (standard_S_Const_V @ y) @ X0)) != $true) | ((graph_1808119_V_V_V @ X0 @ g @ (id_on_V2 @ (labele1134902411nt_V_V @ X0))) != $true)) )),
% 4.93/2.13 inference(trivial_inequality_removal,[status(thm)],[f2461])).
% 4.93/2.13 thf(f2461,plain,(
% 4.93/2.13 ( ! [X0 : labele2115946735nt_V_V] : (((graph_1808119_V_V_V @ X0 @ g @ (id_on_V2 @ (labele1134902411nt_V_V @ X0))) != $true) | ($true != $true) | ((member2015049524od_V_V @ (product_Pair_V_V2 @ (m @ xa) @ (m @ xa)) @ (getRel1432786916nt_V_V @ (standard_S_Const_V @ y) @ X0)) != $true)) )),
% 4.93/2.13 inference(superposition,[status(thm)],[f1916,f1995])).
% 4.93/2.13 thf(f1995,plain,(
% 4.93/2.13 ( ! [X2 : standard_Constant_V,X3 : labele2115946735nt_V_V,X0 : labele2115946735nt_V_V,X1 : v,X4 : v] : (($true = (member2015049524od_V_V @ (product_Pair_V_V2 @ X4 @ X1) @ (getRel1432786916nt_V_V @ X2 @ X0))) | ((member2015049524od_V_V @ (product_Pair_V_V2 @ X4 @ X1) @ (getRel1432786916nt_V_V @ X2 @ X3)) != $true) | ((graph_1808119_V_V_V @ X3 @ X0 @ (id_on_V2 @ (labele1134902411nt_V_V @ X3))) != $true)) )),
% 4.93/2.13 inference(cnf_transformation,[status(thm)],[f1166])).
% 4.93/2.13 thf(f1166,plain,(
% 4.93/2.13 ! [X0 : labele2115946735nt_V_V,X1 : v,X2 : standard_Constant_V,X3 : labele2115946735nt_V_V,X4 : v] : (((graph_1808119_V_V_V @ X3 @ X0 @ (id_on_V2 @ (labele1134902411nt_V_V @ X3))) != $true) | ((member2015049524od_V_V @ (product_Pair_V_V2 @ X4 @ X1) @ (getRel1432786916nt_V_V @ X2 @ X3)) != $true) | ($true = (member2015049524od_V_V @ (product_Pair_V_V2 @ X4 @ X1) @ (getRel1432786916nt_V_V @ X2 @ X0))))),
% 4.93/2.13 inference(flattening,[status(thm)],[f1165])).
% 4.93/2.13 thf(f1165,plain,(
% 4.93/2.13 ! [X0 : labele2115946735nt_V_V,X1 : v,X2 : standard_Constant_V,X3 : labele2115946735nt_V_V,X4 : v] : ((($true = (member2015049524od_V_V @ (product_Pair_V_V2 @ X4 @ X1) @ (getRel1432786916nt_V_V @ X2 @ X0))) | ((graph_1808119_V_V_V @ X3 @ X0 @ (id_on_V2 @ (labele1134902411nt_V_V @ X3))) != $true)) | ((member2015049524od_V_V @ (product_Pair_V_V2 @ X4 @ X1) @ (getRel1432786916nt_V_V @ X2 @ X3)) != $true))),
% 4.93/2.13 inference(ennf_transformation,[status(thm)],[f503])).
% 4.93/2.13 thf(f503,plain,(
% 4.93/2.13 ! [X0 : labele2115946735nt_V_V,X1 : v,X2 : standard_Constant_V,X3 : labele2115946735nt_V_V,X4 : v] : (((member2015049524od_V_V @ (product_Pair_V_V2 @ X4 @ X1) @ (getRel1432786916nt_V_V @ X2 @ X3)) = $true) => (((graph_1808119_V_V_V @ X3 @ X0 @ (id_on_V2 @ (labele1134902411nt_V_V @ X3))) = $true) => ($true = (member2015049524od_V_V @ (product_Pair_V_V2 @ X4 @ X1) @ (getRel1432786916nt_V_V @ X2 @ X0)))))),
% 4.93/2.13 inference(fool_elimination,[status(thm)],[f502])).
% 4.93/2.13 thf(f502,plain,(
% 4.93/2.13 ! [X0 : labele2115946735nt_V_V,X1 : v,X2 : standard_Constant_V,X3 : labele2115946735nt_V_V,X4 : v] : ((member2015049524od_V_V @ (product_Pair_V_V2 @ X4 @ X1) @ (getRel1432786916nt_V_V @ X2 @ X3)) => ((graph_1808119_V_V_V @ X3 @ X0 @ (id_on_V2 @ (labele1134902411nt_V_V @ X3))) => (member2015049524od_V_V @ (product_Pair_V_V2 @ X4 @ X1) @ (getRel1432786916nt_V_V @ X2 @ X0))))),
% 4.93/2.13 inference(rectify,[status(thm)],[f39])).
% 4.93/2.13 thf(f39,axiom,(
% 4.93/2.13 ! [X29 : labele2115946735nt_V_V,X19 : v,X20 : standard_Constant_V,X21 : labele2115946735nt_V_V,X18 : v] : ((member2015049524od_V_V @ (product_Pair_V_V2 @ X18 @ X19) @ (getRel1432786916nt_V_V @ X20 @ X21)) => ((graph_1808119_V_V_V @ X21 @ X29 @ (id_on_V2 @ (labele1134902411nt_V_V @ X21))) => (member2015049524od_V_V @ (product_Pair_V_V2 @ X18 @ X19) @ (getRel1432786916nt_V_V @ X20 @ X29))))),
% 4.93/2.13 file('/export/starexec/sandbox/tmp/tmp.OGMuvyH1wq/DTF2THF_13384.p',fact_38_getRel__subgraph)).
% 4.93/2.13 thf(f1916,plain,(
% 4.93/2.13 ((member2015049524od_V_V @ (product_Pair_V_V2 @ (m @ xa) @ (m @ xa)) @ (getRel1432786916nt_V_V @ (standard_S_Const_V @ y) @ g)) != $true)),
% 4.93/2.13 inference(cnf_transformation,[status(thm)],[f1001])).
% 4.93/2.13 thf(f1001,plain,(
% 4.93/2.13 ((member2015049524od_V_V @ (product_Pair_V_V2 @ (m @ xa) @ (m @ xa)) @ (getRel1432786916nt_V_V @ (standard_S_Const_V @ y) @ g)) != $true)),
% 4.93/2.13 inference(flattening,[status(thm)],[f779])).
% 4.93/2.13 thf(f779,plain,(
% 4.93/2.13 ~((member2015049524od_V_V @ (product_Pair_V_V2 @ (m @ xa) @ (m @ xa)) @ (getRel1432786916nt_V_V @ (standard_S_Const_V @ y) @ g)) = $true)),
% 4.93/2.13 inference(fool_elimination,[status(thm)],[f778])).
% 4.93/2.13 thf(f778,plain,(
% 4.93/2.13 ~(member2015049524od_V_V @ (product_Pair_V_V2 @ (m @ xa) @ (m @ xa)) @ (getRel1432786916nt_V_V @ (standard_S_Const_V @ y) @ g))),
% 4.93/2.13 inference(rectify,[status(thm)],[f357])).
% 4.93/2.13 thf(f357,negated_conjecture,(
% 4.93/2.13 ~(member2015049524od_V_V @ (product_Pair_V_V2 @ (m @ xa) @ (m @ xa)) @ (getRel1432786916nt_V_V @ (standard_S_Const_V @ y) @ g))),
% 4.93/2.13 inference(negated_conjecture,[status(cth)],[f356])).
% 4.93/2.13 thf(f356,conjecture,(
% 4.93/2.13 (member2015049524od_V_V @ (product_Pair_V_V2 @ (m @ xa) @ (m @ xa)) @ (getRel1432786916nt_V_V @ (standard_S_Const_V @ y) @ g))),
% 4.93/2.13 file('/export/starexec/sandbox/tmp/tmp.OGMuvyH1wq/DTF2THF_13384.p',conj_0)).
% 4.93/2.13 % SZS output end Proof for DTF2THF_13384
% 4.93/2.13 % (13513)------------------------------
% 4.93/2.13 % (13513)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.93/2.13 % (13513)Termination reason: Refutation
% 4.93/2.13
% 4.93/2.13 % (13513)Memory used [KB]: 7931
% 4.93/2.13 % (13513)Time elapsed: 0.089 s
% 4.93/2.13 % (13513)Instructions burned: 161 (million)
% 4.93/2.13 % (13513)------------------------------
% 4.93/2.13 % (13513)------------------------------
% 4.93/2.13 % (13490)Success in time 0.206 s
%------------------------------------------------------------------------------