%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP178^1 : 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 : n006.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 08:56:11 AM UTC 2026
% Result : Theorem 3.07s 1.78s
% Output : Refutation 3.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 56 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 199 ( 99 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 1749 ( 45 ~; 29 |; 24 &;1645 @)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 42 ( 41 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 171 ( 168 usr; 14 con; 0-6 aty)
% Number of variables : 86 ( 0 ^; 80 !; 6 ?; 86 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
set_nat: $tType ).
thf(type_def_7,type,
set_Pr1647387645at_nat: $tType ).
thf(type_def_8,type,
set_Pr1986765409at_nat: $tType ).
thf(type_def_9,type,
set_Pr1490359111at_nat: $tType ).
thf(type_def_10,type,
set_Pr9961929at_nat: $tType ).
thf(type_def_11,type,
set_Product_prod_b_b: $tType ).
thf(type_def_12,type,
set_b: $tType ).
thf(type_def_13,type,
allego510293162tant_a: $tType ).
thf(type_def_14,type,
allego1565409692at_nat: $tType ).
thf(type_def_15,type,
allegorical_term_b: $tType ).
thf(type_def_16,type,
labeled_graph_b_nat: $tType ).
thf(type_def_17,type,
labele935650037_a_nat: $tType ).
thf(type_def_18,type,
labele1835409643at_nat: $tType ).
thf(type_def_19,type,
set_Pr1163220871term_b: $tType ).
thf(type_def_20,type,
set_Pr1987088711_a_nat: $tType ).
thf(type_def_21,type,
set_Pr551076371_b_nat: $tType ).
thf(type_def_22,type,
set_Pr2041158302at_nat: $tType ).
thf(type_def_23,type,
produc1871334759_a_nat: $tType ).
thf(type_def_24,type,
nat: $tType ).
thf(type_def_25,type,
produc1478835367term_b: $tType ).
thf(type_def_26,type,
produc1391440311at_nat: $tType ).
thf(type_def_27,type,
produc1235635379_b_nat: $tType ).
thf(type_def_28,type,
product_prod_nat_nat: $tType ).
thf(type_def_29,type,
produc1116408039term_b: $tType ).
thf(type_def_30,type,
produc398057191_a_nat: $tType ).
thf(type_def_31,type,
produc446386919_b_nat: $tType ).
thf(type_def_32,type,
produc842455143at_nat: $tType ).
thf(type_def_33,type,
produc116665063_a_nat: $tType ).
thf(type_def_34,type,
set_al1193902458term_b: $tType ).
thf(type_def_35,type,
set_la1083530965_a_nat: $tType ).
thf(type_def_36,type,
set_la1976028319_b_nat: $tType ).
thf(type_def_37,type,
set_Pr1839611079term_b: $tType ).
thf(type_def_38,type,
set_Pr924198087_a_nat: $tType ).
thf(type_def_39,type,
set_Pr1173424071_b_nat: $tType ).
thf(type_def_40,type,
set_Pr2123625671_a_nat: $tType ).
thf(type_def_41,type,
set_Pr665622551at_nat: $tType ).
thf(type_def_42,type,
itself_nat: $tType ).
thf(type_def_43,type,
set_a: $tType ).
thf(type_def_44,type,
set_St761939237tant_a: $tType ).
thf(type_def_45,type,
standard_Constant_a: $tType ).
thf(type_def_46,type,
b: $tType ).
thf(func_def_0,type,
set_Pr2123625671_a_nat: $tType ).
thf(func_def_1,type,
produc116665063_a_nat: $tType ).
thf(func_def_2,type,
set_Pr924198087_a_nat: $tType ).
thf(func_def_3,type,
produc398057191_a_nat: $tType ).
thf(func_def_4,type,
set_Pr1173424071_b_nat: $tType ).
thf(func_def_5,type,
set_Pr1839611079term_b: $tType ).
thf(func_def_6,type,
produc446386919_b_nat: $tType ).
thf(func_def_7,type,
produc1116408039term_b: $tType ).
thf(func_def_8,type,
set_Pr1987088711_a_nat: $tType ).
thf(func_def_9,type,
set_Pr665622551at_nat: $tType ).
thf(func_def_10,type,
produc1871334759_a_nat: $tType ).
thf(func_def_11,type,
produc1391440311at_nat: $tType ).
thf(func_def_12,type,
set_Pr551076371_b_nat: $tType ).
thf(func_def_13,type,
set_Pr1647387645at_nat: $tType ).
thf(func_def_14,type,
set_Pr1490359111at_nat: $tType ).
thf(func_def_15,type,
set_Pr1163220871term_b: $tType ).
thf(func_def_16,type,
set_Pr2041158302at_nat: $tType ).
thf(func_def_17,type,
produc1235635379_b_nat: $tType ).
thf(func_def_18,type,
produc842455143at_nat: $tType ).
thf(func_def_19,type,
produc1478835367term_b: $tType ).
thf(func_def_20,type,
set_la1083530965_a_nat: $tType ).
thf(func_def_21,type,
labele935650037_a_nat: $tType ).
thf(func_def_22,type,
labele1835409643at_nat: $tType ).
thf(func_def_23,type,
set_Pr9961929at_nat: $tType ).
thf(func_def_24,type,
allego510293162tant_a: $tType ).
thf(func_def_25,type,
allego1565409692at_nat: $tType ).
thf(func_def_26,type,
set_la1976028319_b_nat: $tType ).
thf(func_def_27,type,
set_St761939237tant_a: $tType ).
thf(func_def_28,type,
set_Pr1986765409at_nat: $tType ).
thf(func_def_29,type,
set_al1193902458term_b: $tType ).
thf(func_def_30,type,
labeled_graph_b_nat: $tType ).
thf(func_def_31,type,
set_Product_prod_b_b: $tType ).
thf(func_def_32,type,
standard_Constant_a: $tType ).
thf(func_def_33,type,
product_prod_nat_nat: $tType ).
thf(func_def_34,type,
allegorical_term_b: $tType ).
thf(func_def_35,type,
set_nat: $tType ).
thf(func_def_36,type,
itself_nat: $tType ).
thf(func_def_37,type,
set_b: $tType ).
thf(func_def_38,type,
set_a: $tType ).
thf(func_def_39,type,
nat: $tType ).
thf(func_def_40,type,
b: $tType ).
thf(func_def_41,type,
finite_finite_nat: set_nat > $o ).
thf(func_def_42,type,
finite1242387294at_nat: set_Pr1647387645at_nat > $o ).
thf(func_def_43,type,
finite772653738at_nat: set_Pr1986765409at_nat > $o ).
thf(func_def_44,type,
finite48957584at_nat: set_Pr1490359111at_nat > $o ).
thf(func_def_45,type,
finite1987068434at_nat: set_Pr9961929at_nat > $o ).
thf(func_def_46,type,
finite1015599120od_b_b: set_Product_prod_b_b > $o ).
thf(func_def_47,type,
finite_finite_b: set_b > $o ).
thf(func_def_48,type,
allego745587551tant_a: allego510293162tant_a > allego510293162tant_a > allego510293162tant_a ).
thf(func_def_49,type,
allego266765201at_nat: allego1565409692at_nat > allego1565409692at_nat > allego1565409692at_nat ).
thf(func_def_50,type,
allegorical_A_Int_b: allegorical_term_b > allegorical_term_b > allegorical_term_b ).
thf(func_def_51,type,
semantics_b_nat: labeled_graph_b_nat > allegorical_term_b > set_Pr1986765409at_nat ).
thf(func_def_52,type,
graph_2130075512at_nat: labele935650037_a_nat > labele935650037_a_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_53,type,
graph_2111906684at_nat: labele1835409643at_nat > labele1835409643at_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_54,type,
graph_529870330at_nat: labeled_graph_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_55,type,
graph_union_b_nat: labeled_graph_b_nat > labeled_graph_b_nat > labeled_graph_b_nat ).
thf(func_def_56,type,
labeled_LG_b_nat: set_Pr9961929at_nat > set_nat > labeled_graph_b_nat ).
thf(func_def_57,type,
labele195203296_a_nat: labele935650037_a_nat > set_Pr1647387645at_nat ).
thf(func_def_58,type,
labele2032268018at_nat: labele1835409643at_nat > set_Pr1490359111at_nat ).
thf(func_def_59,type,
labeled_edges_b_nat: labeled_graph_b_nat > set_Pr9961929at_nat ).
thf(func_def_60,type,
labele1810595089_a_nat: labele935650037_a_nat > set_nat ).
thf(func_def_61,type,
labele560327297at_nat: labele1835409643at_nat > set_nat ).
thf(func_def_62,type,
labele460410879_b_nat: labeled_graph_b_nat > set_nat ).
thf(func_def_63,type,
restri572569417_a_nat: labele935650037_a_nat > labele935650037_a_nat ).
thf(func_def_64,type,
restri321299017at_nat: labele1835409643at_nat > labele1835409643at_nat ).
thf(func_def_65,type,
restrict_b_nat: labeled_graph_b_nat > labeled_graph_b_nat ).
thf(func_def_66,type,
unival1191217828term_b: set_Pr1163220871term_b > $o ).
thf(func_def_67,type,
unival1637751524_a_nat: set_Pr1987088711_a_nat > $o ).
thf(func_def_68,type,
unival857119480_b_nat: set_Pr551076371_b_nat > $o ).
thf(func_def_69,type,
univalent_nat_nat: set_Pr1986765409at_nat > $o ).
thf(func_def_70,type,
unival633212949at_nat: set_Pr2041158302at_nat > $o ).
thf(func_def_71,type,
unival989235430at_nat: set_Pr9961929at_nat > $o ).
thf(func_def_72,type,
bot_bo1024461546_nat_o: produc1871334759_a_nat > $o ).
thf(func_def_73,type,
bot_bot_nat: nat ).
thf(func_def_74,type,
bot_bot_set_nat: set_nat ).
thf(func_def_75,type,
bot_bo1836341171_a_nat: set_Pr1987088711_a_nat ).
thf(func_def_76,type,
bot_bo2130386637at_nat: set_Pr1986765409at_nat ).
thf(func_def_77,type,
bot_bo1626616373at_nat: set_Pr9961929at_nat ).
thf(func_def_78,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_79,type,
ord_less_eq_set_nat: set_nat > set_nat > $o ).
thf(func_def_80,type,
ord_le138473255term_b: set_Pr1163220871term_b > set_Pr1163220871term_b > $o ).
thf(func_def_81,type,
ord_le1718765799_a_nat: set_Pr1987088711_a_nat > set_Pr1987088711_a_nat > $o ).
thf(func_def_82,type,
ord_le13035955_b_nat: set_Pr551076371_b_nat > set_Pr551076371_b_nat > $o ).
thf(func_def_83,type,
ord_le841296385at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_84,type,
ord_le910748009at_nat: set_Pr9961929at_nat > set_Pr9961929at_nat > $o ).
thf(func_def_85,type,
produc1990145943term_b: allegorical_term_b > allegorical_term_b > produc1478835367term_b ).
thf(func_def_86,type,
produc1676969687_a_nat: labele935650037_a_nat > labele935650037_a_nat > produc1871334759_a_nat ).
thf(func_def_87,type,
produc590202991at_nat: labele1835409643at_nat > labele1835409643at_nat > produc1391440311at_nat ).
thf(func_def_88,type,
produc951298923_b_nat: labeled_graph_b_nat > labeled_graph_b_nat > produc1235635379_b_nat ).
thf(func_def_89,type,
product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
thf(func_def_90,type,
produc859843415term_b: produc1478835367term_b > produc1478835367term_b > produc1116408039term_b ).
thf(func_def_91,type,
produc1677124439_a_nat: produc1871334759_a_nat > produc1871334759_a_nat > produc398057191_a_nat ).
thf(func_def_92,type,
produc1754969175_b_nat: produc1235635379_b_nat > produc1235635379_b_nat > produc446386919_b_nat ).
thf(func_def_93,type,
produc1168807639at_nat: product_prod_nat_nat > product_prod_nat_nat > produc842455143at_nat ).
thf(func_def_94,type,
produc170611543_a_nat: produc398057191_a_nat > produc398057191_a_nat > produc116665063_a_nat ).
thf(func_def_95,type,
produc854192515term_b: produc1478835367term_b > allegorical_term_b ).
thf(func_def_96,type,
produc719117507_a_nat: produc1871334759_a_nat > labele935650037_a_nat ).
thf(func_def_97,type,
produc1995789403at_nat: produc1391440311at_nat > labele1835409643at_nat ).
thf(func_def_98,type,
produc1542243159_b_nat: produc1235635379_b_nat > labeled_graph_b_nat ).
thf(func_def_99,type,
product_fst_nat_nat: product_prod_nat_nat > nat ).
thf(func_def_100,type,
produc1049080131_a_nat: produc398057191_a_nat > produc1871334759_a_nat ).
thf(func_def_101,type,
produc1223098053term_b: produc1478835367term_b > allegorical_term_b ).
thf(func_def_102,type,
produc880161797_a_nat: produc1871334759_a_nat > labele935650037_a_nat ).
thf(func_def_103,type,
produc1564126365at_nat: produc1391440311at_nat > labele1835409643at_nat ).
thf(func_def_104,type,
produc194497945_b_nat: produc1235635379_b_nat > labeled_graph_b_nat ).
thf(func_def_105,type,
product_snd_nat_nat: product_prod_nat_nat > nat ).
thf(func_def_106,type,
produc1022852229_a_nat: produc398057191_a_nat > produc1871334759_a_nat ).
thf(func_def_107,type,
domain859272460term_b: set_Pr1163220871term_b > set_al1193902458term_b ).
thf(func_def_108,type,
domain1068567884_a_nat: set_Pr1987088711_a_nat > set_la1083530965_a_nat ).
thf(func_def_109,type,
domain767519072_b_nat: set_Pr551076371_b_nat > set_la1976028319_b_nat ).
thf(func_def_110,type,
domain_nat_nat: set_Pr1986765409at_nat > set_nat ).
thf(func_def_111,type,
domain1101989710at_nat: set_Pr9961929at_nat > set_b ).
thf(func_def_112,type,
id_on_1536886967term_b: set_al1193902458term_b > set_Pr1163220871term_b ).
thf(func_def_113,type,
id_on_689842066_a_nat: set_la1083530965_a_nat > set_Pr1987088711_a_nat ).
thf(func_def_114,type,
id_on_583275916_b_nat: set_la1976028319_b_nat > set_Pr551076371_b_nat ).
thf(func_def_115,type,
id_on_nat: set_nat > set_Pr1986765409at_nat ).
thf(func_def_116,type,
id_on_1664915780term_b: set_Pr1163220871term_b > set_Pr1839611079term_b ).
thf(func_def_117,type,
id_on_1651096324_a_nat: set_Pr1987088711_a_nat > set_Pr924198087_a_nat ).
thf(func_def_118,type,
id_on_138931664_b_nat: set_Pr551076371_b_nat > set_Pr1173424071_b_nat ).
thf(func_def_119,type,
id_on_2144791838at_nat: set_Pr1986765409at_nat > set_Pr1490359111at_nat ).
thf(func_def_120,type,
id_on_1395957380_a_nat: set_Pr924198087_a_nat > set_Pr2123625671_a_nat ).
thf(func_def_121,type,
image_329221075term_b: set_Pr1163220871term_b > set_al1193902458term_b > set_al1193902458term_b ).
thf(func_def_122,type,
image_1971191571_a_nat: set_Pr1987088711_a_nat > set_la1083530965_a_nat > set_la1083530965_a_nat ).
thf(func_def_123,type,
image_1183964583_b_nat: set_Pr551076371_b_nat > set_la1976028319_b_nat > set_la1976028319_b_nat ).
thf(func_def_124,type,
image_nat_nat: set_Pr1986765409at_nat > set_nat > set_nat ).
thf(func_def_125,type,
image_1168831379_a_nat: set_Pr924198087_a_nat > set_Pr1987088711_a_nat > set_Pr1987088711_a_nat ).
thf(func_def_126,type,
image_1356842150at_nat: set_Pr2041158302at_nat > set_Pr9961929at_nat > set_nat ).
thf(func_def_127,type,
image_2112855445at_nat: set_Pr9961929at_nat > set_b > set_Pr1986765409at_nat ).
thf(func_def_128,type,
relcom1955155673term_b: set_Pr1163220871term_b > set_Pr1163220871term_b > set_Pr1163220871term_b ).
thf(func_def_129,type,
relcom1338300020_a_nat: set_Pr1987088711_a_nat > set_Pr1987088711_a_nat > set_Pr1987088711_a_nat ).
thf(func_def_130,type,
relcom1426860350_b_nat: set_Pr551076371_b_nat > set_Pr551076371_b_nat > set_Pr551076371_b_nat ).
thf(func_def_131,type,
relcomp_nat_nat_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(func_def_132,type,
relcom195261566at_nat: set_Pr9961929at_nat > set_Pr1490359111at_nat > set_Pr9961929at_nat ).
thf(func_def_133,type,
relcom14055552at_nat: set_Product_prod_b_b > set_Pr9961929at_nat > set_Pr9961929at_nat ).
thf(func_def_134,type,
inv_translation: set_nat > $o ).
thf(func_def_135,type,
transl1275713022tant_a: allego510293162tant_a > labele935650037_a_nat ).
thf(func_def_136,type,
transl490985778at_nat: allego1565409692at_nat > labele1835409643at_nat ).
thf(func_def_137,type,
translation_b: allegorical_term_b > labeled_graph_b_nat ).
thf(func_def_138,type,
agree_on_b_nat_nat: labeled_graph_b_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_139,type,
chain_b_nat: ( nat > labeled_graph_b_nat ) > $o ).
thf(func_def_140,type,
chain_sup_b_nat: ( nat > labeled_graph_b_nat ) > labeled_graph_b_nat ).
thf(func_def_141,type,
conseq1730780375at_nat: set_Pr551076371_b_nat > labeled_graph_b_nat > $o ).
thf(func_def_142,type,
extensible_b_nat_nat: produc1235635379_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_143,type,
fair_chain_b_nat_nat: set_Pr551076371_b_nat > ( nat > labeled_graph_b_nat ) > $o ).
thf(func_def_144,type,
fin_ma971967913at_nat: produc1235635379_b_nat > labeled_graph_b_nat > $o ).
thf(func_def_145,type,
maintained_b_nat_nat: produc1235635379_b_nat > labeled_graph_b_nat > $o ).
thf(func_def_146,type,
set_of1384085797_a_nat: set_Pr1987088711_a_nat > $o ).
thf(func_def_147,type,
set_of195930477at_nat: set_Pr665622551at_nat > $o ).
thf(func_def_148,type,
set_of41538795_b_nat: set_Pr551076371_b_nat > $o ).
thf(func_def_149,type,
weak_u2026406106at_nat: itself_nat > produc1235635379_b_nat > labeled_graph_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_150,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(func_def_151,type,
collec135640594term_b: ( produc1478835367term_b > $o ) > set_Pr1163220871term_b ).
thf(func_def_152,type,
collec357096914_a_nat: ( produc1871334759_a_nat > $o ) > set_Pr1987088711_a_nat ).
thf(func_def_153,type,
collec1615000990_b_nat: ( produc1235635379_b_nat > $o ) > set_Pr551076371_b_nat ).
thf(func_def_154,type,
collec7649004at_nat: ( product_prod_nat_nat > $o ) > set_Pr1986765409at_nat ).
thf(func_def_155,type,
collec1701899602_a_nat: ( produc398057191_a_nat > $o ) > set_Pr924198087_a_nat ).
thf(func_def_156,type,
standa1897115818ules_a: set_a > set_Pr1987088711_a_nat ).
thf(func_def_157,type,
standa1568205540ules_a: set_St761939237tant_a > set_Pr1987088711_a_nat ).
thf(func_def_158,type,
standa1410829644tant_a: produc1871334759_a_nat ).
thf(func_def_159,type,
standa214789732at_nat: produc1391440311at_nat ).
thf(func_def_160,type,
standa879863266rule_b: produc1235635379_b_nat ).
thf(func_def_161,type,
standa63370785tant_a: standard_Constant_a > produc1871334759_a_nat ).
thf(func_def_162,type,
standa2131591247at_nat: product_prod_nat_nat > produc1391440311at_nat ).
thf(func_def_163,type,
standa1329480013rule_b: b > produc1235635379_b_nat ).
thf(func_def_164,type,
standa305748545tant_a: standard_Constant_a > produc1871334759_a_nat ).
thf(func_def_165,type,
standa153097263at_nat: product_prod_nat_nat > produc1391440311at_nat ).
thf(func_def_166,type,
standa1360217389rule_b: b > produc1235635379_b_nat ).
thf(func_def_167,type,
member93680451term_b: allegorical_term_b > set_al1193902458term_b > $o ).
thf(func_def_168,type,
member964390942_a_nat: labele935650037_a_nat > set_la1083530965_a_nat > $o ).
thf(func_def_169,type,
member1483953152_b_nat: labeled_graph_b_nat > set_la1976028319_b_nat > $o ).
thf(func_def_170,type,
member_nat: nat > set_nat > $o ).
thf(func_def_171,type,
member516522448term_b: produc1478835367term_b > set_Pr1163220871term_b > $o ).
thf(func_def_172,type,
member832397200_a_nat: produc1871334759_a_nat > set_Pr1987088711_a_nat > $o ).
thf(func_def_173,type,
member1129678944at_nat: produc1391440311at_nat > set_Pr665622551at_nat > $o ).
thf(func_def_174,type,
member963855452_b_nat: produc1235635379_b_nat > set_Pr551076371_b_nat > $o ).
thf(func_def_175,type,
member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
thf(func_def_176,type,
member1449757456term_b: produc1116408039term_b > set_Pr1839611079term_b > $o ).
thf(func_def_177,type,
member584645392_a_nat: produc398057191_a_nat > set_Pr924198087_a_nat > $o ).
thf(func_def_178,type,
member889223696_b_nat: produc446386919_b_nat > set_Pr1173424071_b_nat > $o ).
thf(func_def_179,type,
member2027625872at_nat: produc842455143at_nat > set_Pr1490359111at_nat > $o ).
thf(func_def_180,type,
member829905680_a_nat: produc116665063_a_nat > set_Pr2123625671_a_nat > $o ).
thf(func_def_181,type,
c: set_a ).
thf(func_def_182,type,
u: allegorical_term_b ).
thf(func_def_183,type,
v: allegorical_term_b ).
thf(func_def_184,type,
x: produc1871334759_a_nat ).
thf(func_def_201,type,
sK0: allegorical_term_b > produc1478835367term_b > allegorical_term_b ).
thf(func_def_202,type,
sK1: labeled_graph_b_nat > produc1235635379_b_nat > labeled_graph_b_nat ).
thf(func_def_203,type,
sK2: produc1235635379_b_nat > labeled_graph_b_nat ).
thf(func_def_204,type,
sK3: produc1235635379_b_nat > labeled_graph_b_nat ).
thf(func_def_205,type,
sK4: allegorical_term_b > produc1478835367term_b > allegorical_term_b ).
thf(func_def_206,type,
sK5: ( produc1478835367term_b > $o ) > allegorical_term_b ).
thf(func_def_207,type,
sK6: ( produc1478835367term_b > $o ) > allegorical_term_b ).
thf(func_def_208,type,
sK7: ( produc1478835367term_b > $o ) > allegorical_term_b ).
thf(func_def_209,type,
sK8: ( produc1478835367term_b > $o ) > allegorical_term_b ).
thf(func_def_210,type,
sK9: ( produc1235635379_b_nat > $o ) > labeled_graph_b_nat ).
thf(func_def_211,type,
sK10: ( produc1235635379_b_nat > $o ) > labeled_graph_b_nat ).
thf(func_def_212,type,
sK11: produc1235635379_b_nat > labeled_graph_b_nat > labeled_graph_b_nat ).
thf(func_def_213,type,
sK12: produc1478835367term_b > allegorical_term_b ).
thf(func_def_214,type,
sK13: produc1478835367term_b > allegorical_term_b ).
thf(func_def_215,type,
sK14: ( labeled_graph_b_nat > labeled_graph_b_nat > $o ) > labeled_graph_b_nat ).
thf(func_def_216,type,
sK15: ( labeled_graph_b_nat > labeled_graph_b_nat > $o ) > labeled_graph_b_nat ).
thf(func_def_217,type,
sK16: produc1478835367term_b > allegorical_term_b ).
thf(func_def_218,type,
sK17: produc1478835367term_b > allegorical_term_b ).
thf(func_def_219,type,
sK18: ( produc1235635379_b_nat > $o ) > labeled_graph_b_nat ).
thf(func_def_220,type,
sK19: ( produc1235635379_b_nat > $o ) > labeled_graph_b_nat ).
thf(func_def_221,type,
sK20: ( allegorical_term_b > allegorical_term_b > $o ) > allegorical_term_b ).
thf(func_def_222,type,
sK21: ( allegorical_term_b > allegorical_term_b > $o ) > allegorical_term_b ).
thf(func_def_223,type,
sK22: produc1235635379_b_nat > labeled_graph_b_nat ).
thf(func_def_224,type,
sK23: produc1235635379_b_nat > labeled_graph_b_nat ).
thf(f1186,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f1185,f1152]) ).
thf(f1152,plain,
! [X0: allegorical_term_b,X1: allegorical_term_b] :
( $true
= ( graph_529870330at_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( translation_b @ X1 ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f1151,f1148]) ).
thf(f1148,plain,
! [X2: labeled_graph_b_nat,X0: labeled_graph_b_nat] :
( ( produc1542243159_b_nat @ ( produc951298923_b_nat @ X2 @ X0 ) )
= X2 ),
inference(equality_resolution,[status(thm)],[f1118]) ).
thf(f1118,plain,
! [X2: labeled_graph_b_nat,X0: labeled_graph_b_nat,X1: produc1235635379_b_nat] :
( ( ( produc951298923_b_nat @ X2 @ X0 )
!= X1 )
| ( ( produc1542243159_b_nat @ X1 )
= X2 ) ),
inference(cnf_transformation,[status(thm)],[f939]) ).
thf(f939,plain,
! [X0: labeled_graph_b_nat,X1: produc1235635379_b_nat,X2: labeled_graph_b_nat] :
( ( ( produc951298923_b_nat @ X2 @ X0 )
!= X1 )
| ( ( produc1542243159_b_nat @ X1 )
= X2 ) ),
inference(ennf_transformation,[status(thm)],[f926]) ).
thf(f926,plain,
! [X0: labeled_graph_b_nat,X1: produc1235635379_b_nat,X2: labeled_graph_b_nat] :
( ( ( produc951298923_b_nat @ X2 @ X0 )
= X1 )
=> ( ( produc1542243159_b_nat @ X1 )
= X2 ) ),
inference(rectify,[status(thm)],[f187]) ).
thf(f187,axiom,
! [X58: labeled_graph_b_nat,X15: produc1235635379_b_nat,X19: labeled_graph_b_nat] :
( ( ( produc951298923_b_nat @ X19 @ X58 )
= X15 )
=> ( ( produc1542243159_b_nat @ X15 )
= X19 ) ),
file('/export/starexec/sandbox/tmp/tmp.bgqouCdkA9/DTF2THF_15711.p',fact_186_fstI) ).
thf(f1151,plain,
! [X0: allegorical_term_b,X1: allegorical_term_b] :
( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) ) ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f1063,f1036]) ).
thf(f1036,plain,
! [X0: labeled_graph_b_nat,X1: labeled_graph_b_nat] :
( ( produc194497945_b_nat @ ( produc951298923_b_nat @ X0 @ X1 ) )
= X1 ),
inference(cnf_transformation,[status(thm)],[f937]) ).
thf(f937,plain,
! [X0: labeled_graph_b_nat,X1: labeled_graph_b_nat] :
( ( produc194497945_b_nat @ ( produc951298923_b_nat @ X0 @ X1 ) )
= X1 ),
inference(rectify,[status(thm)],[f87]) ).
thf(f87,axiom,
! [X11: labeled_graph_b_nat,X12: labeled_graph_b_nat] :
( ( produc194497945_b_nat @ ( produc951298923_b_nat @ X11 @ X12 ) )
= X12 ),
file('/export/starexec/sandbox/tmp/tmp.bgqouCdkA9/DTF2THF_15711.p',fact_86_snd__conv) ).
thf(f1063,plain,
! [X0: allegorical_term_b,X1: allegorical_term_b] :
( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f694]) ).
thf(f694,plain,
! [X0: allegorical_term_b,X1: allegorical_term_b] :
( ( $true
= ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) ) ) ) ) )
& ( $true
= ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) ) ) ) ) )
& ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) ) )
= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) ) ) ) )
& ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) ) ) ) ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f693]) ).
thf(f693,plain,
! [X0: allegorical_term_b,X1: allegorical_term_b] :
( ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) ) )
= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) ) ) ) )
& ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) ) ) ) )
& ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) ) ) ) )
& ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X1: allegorical_term_b,X0: allegorical_term_b] :
( ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X0 ) @ ( translation_b @ ( allegorical_A_Int_b @ X0 @ X1 ) ) ) )
= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X0 ) @ ( translation_b @ ( allegorical_A_Int_b @ X0 @ X1 ) ) ) ) ) )
& ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X0 ) @ ( translation_b @ ( allegorical_A_Int_b @ X0 @ X1 ) ) ) ) ) )
& ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X0 ) @ ( translation_b @ ( allegorical_A_Int_b @ X0 @ X1 ) ) ) ) ) )
& ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X0 ) @ ( translation_b @ ( allegorical_A_Int_b @ X0 @ X1 ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X0 ) @ ( translation_b @ ( allegorical_A_Int_b @ X0 @ X1 ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X0 ) @ ( translation_b @ ( allegorical_A_Int_b @ X0 @ X1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bgqouCdkA9/DTF2THF_15711.p',fact_3_graph__rule__translation) ).
thf(f1185,plain,
( $true
!= ( graph_529870330at_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( translation_b @ u ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1184,f1127]) ).
thf(f1127,plain,
! [X2: allegorical_term_b,X0: allegorical_term_b] :
( ( produc1223098053term_b @ ( produc1990145943term_b @ X0 @ X2 ) )
= X2 ),
inference(equality_resolution,[status(thm)],[f1053]) ).
thf(f1053,plain,
! [X2: allegorical_term_b,X0: allegorical_term_b,X1: produc1478835367term_b] :
( ( ( produc1223098053term_b @ X1 )
= X2 )
| ( ( produc1990145943term_b @ X0 @ X2 )
!= X1 ) ),
inference(cnf_transformation,[status(thm)],[f947]) ).
thf(f947,plain,
! [X0: allegorical_term_b,X1: produc1478835367term_b,X2: allegorical_term_b] :
( ( ( produc1223098053term_b @ X1 )
= X2 )
| ( ( produc1990145943term_b @ X0 @ X2 )
!= X1 ) ),
inference(ennf_transformation,[status(thm)],[f928]) ).
thf(f928,plain,
! [X0: allegorical_term_b,X1: produc1478835367term_b,X2: allegorical_term_b] :
( ( ( produc1990145943term_b @ X0 @ X2 )
= X1 )
=> ( ( produc1223098053term_b @ X1 )
= X2 ) ),
inference(rectify,[status(thm)],[f181]) ).
thf(f181,axiom,
! [X19: allegorical_term_b,X15: produc1478835367term_b,X58: allegorical_term_b] :
( ( ( produc1990145943term_b @ X19 @ X58 )
= X15 )
=> ( ( produc1223098053term_b @ X15 )
= X58 ) ),
file('/export/starexec/sandbox/tmp/tmp.bgqouCdkA9/DTF2THF_15711.p',fact_180_sndI) ).
thf(f1184,plain,
( ( graph_529870330at_nat @ ( translation_b @ u ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( translation_b @ u ) ) ) )
!= $true ),
inference(forward_demodulation,[status(thm)],[f1183,f1036]) ).
thf(f1183,plain,
( ( graph_529870330at_nat @ ( translation_b @ u ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( translation_b @ u ) ) ) )
!= $true ),
inference(forward_demodulation,[status(thm)],[f1182,f1129]) ).
thf(f1129,plain,
! [X2: allegorical_term_b,X1: allegorical_term_b] :
( ( produc854192515term_b @ ( produc1990145943term_b @ X1 @ X2 ) )
= X1 ),
inference(equality_resolution,[status(thm)],[f1057]) ).
thf(f1057,plain,
! [X2: allegorical_term_b,X0: produc1478835367term_b,X1: allegorical_term_b] :
( ( ( produc854192515term_b @ X0 )
= X1 )
| ( ( produc1990145943term_b @ X1 @ X2 )
!= X0 ) ),
inference(cnf_transformation,[status(thm)],[f999]) ).
thf(f999,plain,
! [X0: produc1478835367term_b,X1: allegorical_term_b] :
( ( ( ( produc854192515term_b @ X0 )
= X1 )
| ! [X2: allegorical_term_b] :
( ( produc1990145943term_b @ X1 @ X2 )
!= X0 ) )
& ( ( ( produc1990145943term_b @ X1 @ ( sK4 @ X1 @ X0 ) )
= X0 )
| ( ( produc854192515term_b @ X0 )
!= X1 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f997,f998]) ).
thf(f998,plain,
! [X0: produc1478835367term_b,X1: allegorical_term_b] :
( ? [X3: allegorical_term_b] :
( ( produc1990145943term_b @ X1 @ X3 )
= X0 )
=> ( ( produc1990145943term_b @ X1 @ ( sK4 @ X1 @ X0 ) )
= X0 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f997,plain,
! [X0: produc1478835367term_b,X1: allegorical_term_b] :
( ( ( ( produc854192515term_b @ X0 )
= X1 )
| ! [X2: allegorical_term_b] :
( ( produc1990145943term_b @ X1 @ X2 )
!= X0 ) )
& ( ? [X3: allegorical_term_b] :
( ( produc1990145943term_b @ X1 @ X3 )
= X0 )
| ( ( produc854192515term_b @ X0 )
!= X1 ) ) ),
inference(rectify,[status(thm)],[f996]) ).
thf(f996,plain,
! [X0: produc1478835367term_b,X1: allegorical_term_b] :
( ( ( ( produc854192515term_b @ X0 )
= X1 )
| ! [X2: allegorical_term_b] :
( ( produc1990145943term_b @ X1 @ X2 )
!= X0 ) )
& ( ? [X2: allegorical_term_b] :
( ( produc1990145943term_b @ X1 @ X2 )
= X0 )
| ( ( produc854192515term_b @ X0 )
!= X1 ) ) ),
inference(nnf_transformation,[status(thm)],[f778]) ).
thf(f778,plain,
! [X0: produc1478835367term_b,X1: allegorical_term_b] :
( ( ( produc854192515term_b @ X0 )
= X1 )
<=> ? [X2: allegorical_term_b] :
( ( produc1990145943term_b @ X1 @ X2 )
= X0 ) ),
inference(fool_elimination,[status(thm)],[f777]) ).
thf(f777,plain,
! [X0: produc1478835367term_b,X1: allegorical_term_b] :
? [X2: allegorical_term_b] :
( ( ( produc1990145943term_b @ X1 @ X2 )
= X0 )
= ( ( produc854192515term_b @ X0 )
= X1 ) ),
inference(rectify,[status(thm)],[f204]) ).
thf(f204,axiom,
! [X21: produc1478835367term_b,X3: allegorical_term_b] :
? [X72: allegorical_term_b] :
( ( ( produc1990145943term_b @ X3 @ X72 )
= X21 )
= ( ( produc854192515term_b @ X21 )
= X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.bgqouCdkA9/DTF2THF_15711.p',fact_203_eq__fst__iff) ).
thf(f1182,plain,
( $true
!= ( graph_529870330at_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1181,f1148]) ).
thf(f1181,plain,
( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f1180,f1120]) ).
thf(f1120,plain,
! [X0: allegorical_term_b] :
( ( finite_finite_nat @ ( labele460410879_b_nat @ ( translation_b @ X0 ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f698]) ).
thf(f698,plain,
! [X0: allegorical_term_b] :
( ( finite_finite_nat @ ( labele460410879_b_nat @ ( translation_b @ X0 ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f697]) ).
thf(f697,plain,
! [X0: allegorical_term_b] : ( finite_finite_nat @ ( labele460410879_b_nat @ ( translation_b @ X0 ) ) ),
inference(rectify,[status(thm)],[f21]) ).
thf(f21,axiom,
! [X0: allegorical_term_b] : ( finite_finite_nat @ ( labele460410879_b_nat @ ( translation_b @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bgqouCdkA9/DTF2THF_15711.p',fact_20_verts__in__translation__finite_I1_J) ).
thf(f1180,plain,
( ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
!= $true )
| ( $true
!= ( finite_finite_nat @ ( labele460410879_b_nat @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1179,f1036]) ).
thf(f1179,plain,
( ( ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
!= $true )
| ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f1178,f1085]) ).
thf(f1085,plain,
! [X0: allegorical_term_b] :
( ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( translation_b @ X0 ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f756]) ).
thf(f756,plain,
! [X0: allegorical_term_b] :
( ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( translation_b @ X0 ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f755]) ).
thf(f755,plain,
! [X0: allegorical_term_b] : ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( translation_b @ X0 ) ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,axiom,
! [X0: allegorical_term_b] : ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( translation_b @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bgqouCdkA9/DTF2THF_15711.p',fact_12_verts__in__translation__finite_I2_J) ).
thf(f1178,plain,
( ( ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
!= $true )
| ( ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
!= $true )
| ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
!= $true ) ),
inference(forward_demodulation,[status(thm)],[f1177,f1036]) ).
thf(f1177,plain,
( ( ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
!= $true )
| ( ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
!= $true )
| ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f1176,f1159]) ).
thf(f1159,plain,
! [X0: allegorical_term_b,X1: allegorical_term_b] :
( ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) )
= ( restrict_b_nat @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1064,f1036]) ).
thf(f1064,plain,
! [X0: allegorical_term_b,X1: allegorical_term_b] :
( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) ) )
= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f694]) ).
thf(f1176,plain,
( ( ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
!= $true )
| ( ( translation_b @ ( allegorical_A_Int_b @ u @ v ) )
!= ( restrict_b_nat @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) )
| ( ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
!= $true )
| ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
!= $true ) ),
inference(forward_demodulation,[status(thm)],[f1175,f1127]) ).
thf(f1175,plain,
( ( ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) )
!= ( restrict_b_nat @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
| ( ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
!= $true )
| ( ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
!= $true )
| ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
!= $true ) ),
inference(forward_demodulation,[status(thm)],[f1093,f1036]) ).
thf(f1093,plain,
( ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
!= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
| ( ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
!= $true )
| ( ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
!= $true )
| ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f946]) ).
thf(f946,plain,
( ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
!= $true )
| ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
!= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
| ( ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
!= $true )
| ( ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f712]) ).
thf(f712,plain,
~ ( ( ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
= $true )
& ( ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
= $true )
& ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
& ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f711]) ).
thf(f711,plain,
~ ( ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
& ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
& ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
& ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f357]) ).
thf(f357,negated_conjecture,
~ ( ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
& ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
& ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
& ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f356]) ).
thf(f356,conjecture,
( ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
& ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
& ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
& ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bgqouCdkA9/DTF2THF_15711.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP178^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.34 % Computer : n006.cluster.edu
% 0.19/0.34 % Model : x86_64 x86_64
% 0.19/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.34 % Memory : 8042.1875MB
% 0.19/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.34 % CPULimit : 300
% 0.19/0.34 % WCLimit : 300
% 0.19/0.34 % DateTime : Tue Feb 24 08:28:45 EST 2026
% 0.19/0.35 % CPUTime :
% 0.19/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.27/0.47 ---- Original DTF file ---
% 0.27/0.47 thf(spec,logic,$$dhol).
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 % File : ITP178^1 : TPTP v9.2.1. Released v7.5.0.
% 0.27/0.47 % Domain : Interactive Theorem Proving
% 0.27/0.47 % Problem : Sledgehammer StandardRules problem prob_429__5391446_1
% 0.27/0.47 % Version : Especial.
% 0.27/0.47 % English :
% 0.27/0.47
% 0.27/0.47 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.27/0.47 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.27/0.47 % Source : [Des21]
% 0.27/0.47 % Names : StandardRules/prob_429__5391446_1 [Des21]
% 0.27/0.47
% 0.27/0.47 % Status : Theorem
% 0.27/0.47 % Rating : 0.33 v9.1.0, 0.12 v9.0.0, 0.40 v8.2.0, 0.31 v8.1.0, 0.36 v7.5.0
% 0.27/0.47 % Syntax : Number of formulae : 541 ( 143 unt; 185 typ; 0 def)
% 0.27/0.47 % Number of atoms : 993 ( 367 equ; 0 cnn)
% 0.27/0.47 % Maximal formula atoms : 12 ( 2 avg)
% 0.27/0.47 % Number of connectives : 3581 ( 95 ~; 1 |; 131 &;2941 @)
% 0.27/0.47 % ( 0 <=>; 413 =>; 0 <=; 0 <~>)
% 0.27/0.47 % Maximal formula depth : 19 ( 7 avg)
% 0.27/0.47 % Number of types : 42 ( 41 usr)
% 0.27/0.47 % Number of type conns : 272 ( 272 >; 0 *; 0 +; 0 <<)
% 0.27/0.47 % Number of symbols : 145 ( 144 usr; 12 con; 0-6 aty)
% 0.27/0.47 % Number of variables : 1063 ( 62 ^; 951 !; 50 ?;1063 :)
% 0.27/0.47 % SPC : TH0_THM_EQU_NAR
% 0.27/0.47
% 0.27/0.47 % Comments : This file was generated by Sledgehammer 2021-02-23 15:38:28.807
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 % Could-be-implicit typings (41)
% 0.27/0.47 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_J_J_J,type,
% 0.27/0.47 set_Pr2123625671_a_nat: $tType ).
% 0.27/0.47
% 0.27/0.47 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_J_J,type,
% 0.27/0.47 produc116665063_a_nat: $tType ).
% 0.27/0.47
% 0.27/0.47 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_J_J,type,
% 0.27/0.47 set_Pr924198087_a_nat: $tType ).
% 0.27/0.47
% 0.27/0.47 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_J,type,
% 0.27/0.47 produc398057191_a_nat: $tType ).
% 0.27/0.47
% 0.27/0.47 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_J_J_J,type,
% 0.27/0.47 set_Pr1173424071_b_nat: $tType ).
% 0.27/0.47
% 0.27/0.47 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphSemantics__Oallegorical____term_Itf__b_J_Mt__LabeledGraphSemantics__Oallegorical____term_Itf__b_J_J_Mt__Product____Type__Oprod_It__LabeledGraphSemantics__Oallegorical____term_Itf__b_J_Mt__LabeledGraphSemantics__Oallegorical____term_Itf__b_J_J_J_J,type,
% 0.27/0.47 set_Pr1839611079term_b: $tType ).
% 0.27/0.47
% 0.27/0.47 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_J_J,type,
% 0.27/0.47 produc446386919_b_nat: $tType ).
% 0.27/0.47
% 0.27/0.47 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphSemantics__Oallegorical____term_Itf__b_J_Mt__LabeledGraphSemantics__Oallegorical____term_Itf__b_J_J_Mt__Product____Type__Oprod_It__LabeledGraphSemantics__Oallegorical____term_Itf__b_J_Mt__LabeledGraphSemantics__Oallegorical____term_Itf__b_J_J_J,type,
% 0.27/0.47 produc1116408039term_b: $tType ).
% 0.27/0.47
% 0.27/0.47 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_J,type,
% 0.27/0.47 set_Pr1987088711_a_nat: $tType ).
% 0.27/0.47
% 0.27/0.47 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Nat__Onat_J_J_J,type,
% 0.27/0.47 set_Pr665622551at_nat: $tType ).
% 0.27/0.47
% 0.27/0.47 thf(ty_n_t__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J,type,
% 0.27/0.47 produc1871334759_a_nat: $tType ).
% 0.27/0.47
% 0.27/0.47 thf(ty_n_t__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Nat__Onat_J_J,type,
% 0.27/0.47 produc1391440311at_nat: $tType ).
% 0.27/0.47
% 0.27/0.47 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_J_J,type,
% 0.27/0.47 set_Pr551076371_b_nat: $tType ).
% 0.27/0.47
% 0.27/0.47 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 0.27/0.47 set_Pr1647387645at_nat: $tType ).
% 0.27/0.47
% 0.27/0.47 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
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% 0.27/0.47 fin_ma971967913at_nat: produc1235635379_b_nat > labeled_graph_b_nat > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_RulesAndChains_Omaintained_001tf__b_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.27/0.47 maintained_b_nat_nat: produc1235635379_b_nat > labeled_graph_b_nat > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_RulesAndChains_Oset__of__graph__rules_001t__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_001t__Nat__Onat,type,
% 0.27/0.47 set_of1384085797_a_nat: set_Pr1987088711_a_nat > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_RulesAndChains_Oset__of__graph__rules_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
% 0.27/0.47 set_of195930477at_nat: set_Pr665622551at_nat > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_RulesAndChains_Oset__of__graph__rules_001tf__b_001t__Nat__Onat,type,
% 0.27/0.47 set_of41538795_b_nat: set_Pr551076371_b_nat > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_RulesAndChains_Oweak__universal_001t__Nat__Onat_001tf__b_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.27/0.47 weak_u2026406106at_nat: itself_nat > produc1235635379_b_nat > labeled_graph_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 0.27/0.47 collect_nat: ( nat > $o ) > set_nat ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__LabeledGraphSemantics__Oallegorical____term_Itf__b_J_Mt__LabeledGraphSemantics__Oallegorical____term_Itf__b_J_J,type,
% 0.27/0.47 collec135640594term_b: ( produc1478835367term_b > $o ) > set_Pr1163220871term_b ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J,type,
% 0.27/0.47 collec357096914_a_nat: ( produc1871334759_a_nat > $o ) > set_Pr1987088711_a_nat ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_J,type,
% 0.27/0.47 collec1615000990_b_nat: ( produc1235635379_b_nat > $o ) > set_Pr551076371_b_nat ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.27/0.47 collec7649004at_nat: ( product_prod_nat_nat > $o ) > set_Pr1986765409at_nat ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_J,type,
% 0.27/0.47 collec1701899602_a_nat: ( produc398057191_a_nat > $o ) > set_Pr924198087_a_nat ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Oconstant__rules_001tf__a,type,
% 0.27/0.47 standa1897115818ules_a: set_a > set_Pr1987088711_a_nat ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Oidentity__rules_001tf__a,type,
% 0.27/0.47 standa1568205540ules_a: set_St761939237tant_a > set_Pr1987088711_a_nat ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Ononempty__rule_001t__LabeledGraphSemantics__OStandard____Constant_Itf__a_J,type,
% 0.27/0.47 standa1410829644tant_a: produc1871334759_a_nat ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Ononempty__rule_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.27/0.47 standa214789732at_nat: produc1391440311at_nat ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Ononempty__rule_001tf__b,type,
% 0.27/0.47 standa879863266rule_b: produc1235635379_b_nat ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Oreflexivity__rule_001t__LabeledGraphSemantics__OStandard____Constant_Itf__a_J,type,
% 0.27/0.47 standa63370785tant_a: standard_Constant_a > produc1871334759_a_nat ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Oreflexivity__rule_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.27/0.47 standa2131591247at_nat: product_prod_nat_nat > produc1391440311at_nat ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Oreflexivity__rule_001tf__b,type,
% 0.27/0.47 standa1329480013rule_b: b > produc1235635379_b_nat ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Otop__rule_001t__LabeledGraphSemantics__OStandard____Constant_Itf__a_J,type,
% 0.27/0.47 standa305748545tant_a: standard_Constant_a > produc1871334759_a_nat ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Otop__rule_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.27/0.47 standa153097263at_nat: product_prod_nat_nat > produc1391440311at_nat ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Otop__rule_001tf__b,type,
% 0.27/0.47 standa1360217389rule_b: b > produc1235635379_b_nat ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_member_001t__LabeledGraphSemantics__Oallegorical____term_Itf__b_J,type,
% 0.27/0.47 member93680451term_b: allegorical_term_b > set_al1193902458term_b > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_member_001t__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J,type,
% 0.27/0.47 member964390942_a_nat: labele935650037_a_nat > set_la1083530965_a_nat > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_member_001t__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J,type,
% 0.27/0.47 member1483953152_b_nat: labeled_graph_b_nat > set_la1976028319_b_nat > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_member_001t__Nat__Onat,type,
% 0.27/0.47 member_nat: nat > set_nat > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__LabeledGraphSemantics__Oallegorical____term_Itf__b_J_Mt__LabeledGraphSemantics__Oallegorical____term_Itf__b_J_J,type,
% 0.27/0.47 member516522448term_b: produc1478835367term_b > set_Pr1163220871term_b > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J,type,
% 0.27/0.47 member832397200_a_nat: produc1871334759_a_nat > set_Pr1987088711_a_nat > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Nat__Onat_J_J,type,
% 0.27/0.47 member1129678944at_nat: produc1391440311at_nat > set_Pr665622551at_nat > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_J,type,
% 0.27/0.47 member963855452_b_nat: produc1235635379_b_nat > set_Pr551076371_b_nat > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.27/0.47 member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphSemantics__Oallegorical____term_Itf__b_J_Mt__LabeledGraphSemantics__Oallegorical____term_Itf__b_J_J_Mt__Product____Type__Oprod_It__LabeledGraphSemantics__Oallegorical____term_Itf__b_J_Mt__LabeledGraphSemantics__Oallegorical____term_Itf__b_J_J_J,type,
% 0.27/0.47 member1449757456term_b: produc1116408039term_b > set_Pr1839611079term_b > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_J,type,
% 0.27/0.47 member584645392_a_nat: produc398057191_a_nat > set_Pr924198087_a_nat > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_J_J,type,
% 0.27/0.47 member889223696_b_nat: produc446386919_b_nat > set_Pr1173424071_b_nat > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.27/0.47 member2027625872at_nat: produc842455143at_nat > set_Pr1490359111at_nat > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_J_J,type,
% 0.27/0.47 member829905680_a_nat: produc116665063_a_nat > set_Pr2123625671_a_nat > $o ).
% 0.27/0.47
% 0.27/0.47 thf(sy_v_C,type,
% 0.27/0.47 c: set_a ).
% 0.27/0.47
% 0.27/0.47 thf(sy_v_u,type,
% 0.27/0.47 u: allegorical_term_b ).
% 0.27/0.47
% 0.27/0.47 thf(sy_v_v,type,
% 0.27/0.47 v: allegorical_term_b ).
% 0.27/0.47
% 0.27/0.47 thf(sy_v_x,type,
% 0.27/0.47 x: produc1871334759_a_nat ).
% 0.27/0.47
% 0.27/0.47 % Relevant facts (355)
% 0.27/0.47 thf(fact_0_assms,axiom,
% 0.27/0.47 member832397200_a_nat @ x @ ( standa1897115818ules_a @ c ) ).
% 0.27/0.47
% 0.27/0.47 % assms
% 0.27/0.47 thf(fact_1_graph__rule__translation,axiom,
% 0.27/0.47 ! [X: allego1565409692at_nat,Y: allego1565409692at_nat] :
% 0.27/0.47 ( ( graph_2111906684at_nat @ ( produc1995789403at_nat @ ( produc590202991at_nat @ ( transl490985778at_nat @ X ) @ ( transl490985778at_nat @ ( allego266765201at_nat @ X @ Y ) ) ) ) @ ( produc1564126365at_nat @ ( produc590202991at_nat @ ( transl490985778at_nat @ X ) @ ( transl490985778at_nat @ ( allego266765201at_nat @ X @ Y ) ) ) ) @ ( id_on_nat @ ( labele560327297at_nat @ ( produc1995789403at_nat @ ( produc590202991at_nat @ ( transl490985778at_nat @ X ) @ ( transl490985778at_nat @ ( allego266765201at_nat @ X @ Y ) ) ) ) ) ) )
% 0.27/0.47 & ( ( produc1564126365at_nat @ ( produc590202991at_nat @ ( transl490985778at_nat @ X ) @ ( transl490985778at_nat @ ( allego266765201at_nat @ X @ Y ) ) ) )
% 0.27/0.47 = ( restri321299017at_nat @ ( produc1564126365at_nat @ ( produc590202991at_nat @ ( transl490985778at_nat @ X ) @ ( transl490985778at_nat @ ( allego266765201at_nat @ X @ Y ) ) ) ) ) )
% 0.27/0.47 & ( finite_finite_nat @ ( labele560327297at_nat @ ( produc1564126365at_nat @ ( produc590202991at_nat @ ( transl490985778at_nat @ X ) @ ( transl490985778at_nat @ ( allego266765201at_nat @ X @ Y ) ) ) ) ) )
% 0.27/0.47 & ( finite48957584at_nat @ ( labele2032268018at_nat @ ( produc1564126365at_nat @ ( produc590202991at_nat @ ( transl490985778at_nat @ X ) @ ( transl490985778at_nat @ ( allego266765201at_nat @ X @ Y ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % graph_rule_translation
% 0.27/0.47 thf(fact_2_graph__rule__translation,axiom,
% 0.27/0.47 ! [X: allego510293162tant_a,Y: allego510293162tant_a] :
% 0.27/0.47 ( ( graph_2130075512at_nat @ ( produc719117507_a_nat @ ( produc1676969687_a_nat @ ( transl1275713022tant_a @ X ) @ ( transl1275713022tant_a @ ( allego745587551tant_a @ X @ Y ) ) ) ) @ ( produc880161797_a_nat @ ( produc1676969687_a_nat @ ( transl1275713022tant_a @ X ) @ ( transl1275713022tant_a @ ( allego745587551tant_a @ X @ Y ) ) ) ) @ ( id_on_nat @ ( labele1810595089_a_nat @ ( produc719117507_a_nat @ ( produc1676969687_a_nat @ ( transl1275713022tant_a @ X ) @ ( transl1275713022tant_a @ ( allego745587551tant_a @ X @ Y ) ) ) ) ) ) )
% 0.27/0.47 & ( ( produc880161797_a_nat @ ( produc1676969687_a_nat @ ( transl1275713022tant_a @ X ) @ ( transl1275713022tant_a @ ( allego745587551tant_a @ X @ Y ) ) ) )
% 0.27/0.47 = ( restri572569417_a_nat @ ( produc880161797_a_nat @ ( produc1676969687_a_nat @ ( transl1275713022tant_a @ X ) @ ( transl1275713022tant_a @ ( allego745587551tant_a @ X @ Y ) ) ) ) ) )
% 0.27/0.47 & ( finite_finite_nat @ ( labele1810595089_a_nat @ ( produc880161797_a_nat @ ( produc1676969687_a_nat @ ( transl1275713022tant_a @ X ) @ ( transl1275713022tant_a @ ( allego745587551tant_a @ X @ Y ) ) ) ) ) )
% 0.27/0.47 & ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( produc880161797_a_nat @ ( produc1676969687_a_nat @ ( transl1275713022tant_a @ X ) @ ( transl1275713022tant_a @ ( allego745587551tant_a @ X @ Y ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % graph_rule_translation
% 0.27/0.47 thf(fact_3_graph__rule__translation,axiom,
% 0.27/0.47 ! [X: allegorical_term_b,Y: allegorical_term_b] :
% 0.27/0.47 ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X ) @ ( translation_b @ ( allegorical_A_Int_b @ X @ Y ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X ) @ ( translation_b @ ( allegorical_A_Int_b @ X @ Y ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X ) @ ( translation_b @ ( allegorical_A_Int_b @ X @ Y ) ) ) ) ) ) )
% 0.27/0.47 & ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X ) @ ( translation_b @ ( allegorical_A_Int_b @ X @ Y ) ) ) )
% 0.27/0.47 = ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X ) @ ( translation_b @ ( allegorical_A_Int_b @ X @ Y ) ) ) ) ) )
% 0.27/0.47 & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X ) @ ( translation_b @ ( allegorical_A_Int_b @ X @ Y ) ) ) ) ) )
% 0.27/0.47 & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X ) @ ( translation_b @ ( allegorical_A_Int_b @ X @ Y ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % graph_rule_translation
% 0.27/0.47 thf(fact_4_subgraph__refl,axiom,
% 0.27/0.47 ! [G: labele935650037_a_nat] :
% 0.27/0.47 ( ( graph_2130075512at_nat @ G @ G @ ( id_on_nat @ ( labele1810595089_a_nat @ G ) ) )
% 0.27/0.47 = ( G
% 0.27/0.47 = ( restri572569417_a_nat @ G ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % subgraph_refl
% 0.27/0.47 thf(fact_5_subgraph__refl,axiom,
% 0.27/0.47 ! [G: labeled_graph_b_nat] :
% 0.27/0.47 ( ( graph_529870330at_nat @ G @ G @ ( id_on_nat @ ( labele460410879_b_nat @ G ) ) )
% 0.27/0.47 = ( G
% 0.27/0.47 = ( restrict_b_nat @ G ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % subgraph_refl
% 0.27/0.47 thf(fact_6_subgraph__restrict,axiom,
% 0.27/0.47 ! [G: labele935650037_a_nat] :
% 0.27/0.47 ( ( graph_2130075512at_nat @ G @ ( restri572569417_a_nat @ G ) @ ( id_on_nat @ ( labele1810595089_a_nat @ G ) ) )
% 0.27/0.47 = ( G
% 0.27/0.47 = ( restri572569417_a_nat @ G ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % subgraph_restrict
% 0.27/0.47 thf(fact_7_subgraph__restrict,axiom,
% 0.27/0.47 ! [G: labeled_graph_b_nat] :
% 0.27/0.47 ( ( graph_529870330at_nat @ G @ ( restrict_b_nat @ G ) @ ( id_on_nat @ ( labele460410879_b_nat @ G ) ) )
% 0.27/0.47 = ( G
% 0.27/0.47 = ( restrict_b_nat @ G ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % subgraph_restrict
% 0.27/0.47 thf(fact_8_graph__homomorphism__Id,axiom,
% 0.27/0.47 ! [A: labele935650037_a_nat] : ( graph_2130075512at_nat @ ( restri572569417_a_nat @ A ) @ ( restri572569417_a_nat @ A ) @ ( id_on_nat @ ( labele1810595089_a_nat @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % graph_homomorphism_Id
% 0.27/0.47 thf(fact_9_graph__homomorphism__Id,axiom,
% 0.27/0.47 ! [A: labeled_graph_b_nat] : ( graph_529870330at_nat @ ( restrict_b_nat @ A ) @ ( restrict_b_nat @ A ) @ ( id_on_nat @ ( labele460410879_b_nat @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % graph_homomorphism_Id
% 0.27/0.47 thf(fact_10_verts__in__translation__finite_I2_J,axiom,
% 0.27/0.47 ! [X: allego1565409692at_nat] : ( finite48957584at_nat @ ( labele2032268018at_nat @ ( transl490985778at_nat @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % verts_in_translation_finite(2)
% 0.27/0.47 thf(fact_11_verts__in__translation__finite_I2_J,axiom,
% 0.27/0.47 ! [X: allego510293162tant_a] : ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( transl1275713022tant_a @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % verts_in_translation_finite(2)
% 0.27/0.47 thf(fact_12_verts__in__translation__finite_I2_J,axiom,
% 0.27/0.47 ! [X: allegorical_term_b] : ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( translation_b @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % verts_in_translation_finite(2)
% 0.27/0.47 thf(fact_13_are__rules_I1_J,axiom,
% 0.27/0.47 ( ( graph_2111906684at_nat @ ( produc1995789403at_nat @ standa214789732at_nat ) @ ( produc1564126365at_nat @ standa214789732at_nat ) @ ( id_on_nat @ ( labele560327297at_nat @ ( produc1995789403at_nat @ standa214789732at_nat ) ) ) )
% 0.27/0.47 & ( ( produc1564126365at_nat @ standa214789732at_nat )
% 0.27/0.47 = ( restri321299017at_nat @ ( produc1564126365at_nat @ standa214789732at_nat ) ) )
% 0.27/0.47 & ( finite_finite_nat @ ( labele560327297at_nat @ ( produc1564126365at_nat @ standa214789732at_nat ) ) )
% 0.27/0.47 & ( finite48957584at_nat @ ( labele2032268018at_nat @ ( produc1564126365at_nat @ standa214789732at_nat ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % are_rules(1)
% 0.27/0.47 thf(fact_14_are__rules_I1_J,axiom,
% 0.27/0.47 ( ( graph_2130075512at_nat @ ( produc719117507_a_nat @ standa1410829644tant_a ) @ ( produc880161797_a_nat @ standa1410829644tant_a ) @ ( id_on_nat @ ( labele1810595089_a_nat @ ( produc719117507_a_nat @ standa1410829644tant_a ) ) ) )
% 0.27/0.47 & ( ( produc880161797_a_nat @ standa1410829644tant_a )
% 0.27/0.47 = ( restri572569417_a_nat @ ( produc880161797_a_nat @ standa1410829644tant_a ) ) )
% 0.27/0.47 & ( finite_finite_nat @ ( labele1810595089_a_nat @ ( produc880161797_a_nat @ standa1410829644tant_a ) ) )
% 0.27/0.47 & ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( produc880161797_a_nat @ standa1410829644tant_a ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % are_rules(1)
% 0.27/0.47 thf(fact_15_are__rules_I1_J,axiom,
% 0.27/0.47 ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ standa879863266rule_b ) @ ( produc194497945_b_nat @ standa879863266rule_b ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ standa879863266rule_b ) ) ) )
% 0.27/0.47 & ( ( produc194497945_b_nat @ standa879863266rule_b )
% 0.27/0.47 = ( restrict_b_nat @ ( produc194497945_b_nat @ standa879863266rule_b ) ) )
% 0.27/0.47 & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ standa879863266rule_b ) ) )
% 0.27/0.47 & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ standa879863266rule_b ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % are_rules(1)
% 0.27/0.47 thf(fact_16_are__rules_I2_J,axiom,
% 0.27/0.47 ! [T: product_prod_nat_nat] :
% 0.27/0.47 ( ( graph_2111906684at_nat @ ( produc1995789403at_nat @ ( standa153097263at_nat @ T ) ) @ ( produc1564126365at_nat @ ( standa153097263at_nat @ T ) ) @ ( id_on_nat @ ( labele560327297at_nat @ ( produc1995789403at_nat @ ( standa153097263at_nat @ T ) ) ) ) )
% 0.27/0.47 & ( ( produc1564126365at_nat @ ( standa153097263at_nat @ T ) )
% 0.27/0.47 = ( restri321299017at_nat @ ( produc1564126365at_nat @ ( standa153097263at_nat @ T ) ) ) )
% 0.27/0.47 & ( finite_finite_nat @ ( labele560327297at_nat @ ( produc1564126365at_nat @ ( standa153097263at_nat @ T ) ) ) )
% 0.27/0.47 & ( finite48957584at_nat @ ( labele2032268018at_nat @ ( produc1564126365at_nat @ ( standa153097263at_nat @ T ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % are_rules(2)
% 0.27/0.47 thf(fact_17_are__rules_I2_J,axiom,
% 0.27/0.47 ! [T: standard_Constant_a] :
% 0.27/0.47 ( ( graph_2130075512at_nat @ ( produc719117507_a_nat @ ( standa305748545tant_a @ T ) ) @ ( produc880161797_a_nat @ ( standa305748545tant_a @ T ) ) @ ( id_on_nat @ ( labele1810595089_a_nat @ ( produc719117507_a_nat @ ( standa305748545tant_a @ T ) ) ) ) )
% 0.27/0.47 & ( ( produc880161797_a_nat @ ( standa305748545tant_a @ T ) )
% 0.27/0.47 = ( restri572569417_a_nat @ ( produc880161797_a_nat @ ( standa305748545tant_a @ T ) ) ) )
% 0.27/0.47 & ( finite_finite_nat @ ( labele1810595089_a_nat @ ( produc880161797_a_nat @ ( standa305748545tant_a @ T ) ) ) )
% 0.27/0.47 & ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( produc880161797_a_nat @ ( standa305748545tant_a @ T ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % are_rules(2)
% 0.27/0.47 thf(fact_18_are__rules_I2_J,axiom,
% 0.27/0.47 ! [T: b] :
% 0.27/0.47 ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( standa1360217389rule_b @ T ) ) @ ( produc194497945_b_nat @ ( standa1360217389rule_b @ T ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( standa1360217389rule_b @ T ) ) ) ) )
% 0.27/0.47 & ( ( produc194497945_b_nat @ ( standa1360217389rule_b @ T ) )
% 0.27/0.47 = ( restrict_b_nat @ ( produc194497945_b_nat @ ( standa1360217389rule_b @ T ) ) ) )
% 0.27/0.47 & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( standa1360217389rule_b @ T ) ) ) )
% 0.27/0.47 & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( standa1360217389rule_b @ T ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % are_rules(2)
% 0.27/0.47 thf(fact_19_verts__in__translation__finite_I1_J,axiom,
% 0.27/0.47 ! [X: allego510293162tant_a] : ( finite_finite_nat @ ( labele1810595089_a_nat @ ( transl1275713022tant_a @ X ) ) ) ).
% 0.27/0.47
% 0.27/0.47 % verts_in_translation_finite(1)
% 0.27/0.48 thf(fact_20_verts__in__translation__finite_I1_J,axiom,
% 0.27/0.48 ! [X: allegorical_term_b] : ( finite_finite_nat @ ( labele460410879_b_nat @ ( translation_b @ X ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % verts_in_translation_finite(1)
% 0.27/0.48 thf(fact_21_are__rules_I3_J,axiom,
% 0.27/0.48 ! [I: product_prod_nat_nat] :
% 0.27/0.48 ( ( graph_2111906684at_nat @ ( produc1995789403at_nat @ ( standa2131591247at_nat @ I ) ) @ ( produc1564126365at_nat @ ( standa2131591247at_nat @ I ) ) @ ( id_on_nat @ ( labele560327297at_nat @ ( produc1995789403at_nat @ ( standa2131591247at_nat @ I ) ) ) ) )
% 0.27/0.48 & ( ( produc1564126365at_nat @ ( standa2131591247at_nat @ I ) )
% 0.27/0.48 = ( restri321299017at_nat @ ( produc1564126365at_nat @ ( standa2131591247at_nat @ I ) ) ) )
% 0.27/0.48 & ( finite_finite_nat @ ( labele560327297at_nat @ ( produc1564126365at_nat @ ( standa2131591247at_nat @ I ) ) ) )
% 0.27/0.48 & ( finite48957584at_nat @ ( labele2032268018at_nat @ ( produc1564126365at_nat @ ( standa2131591247at_nat @ I ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % are_rules(3)
% 0.27/0.48 thf(fact_22_are__rules_I3_J,axiom,
% 0.27/0.48 ! [I: standard_Constant_a] :
% 0.27/0.48 ( ( graph_2130075512at_nat @ ( produc719117507_a_nat @ ( standa63370785tant_a @ I ) ) @ ( produc880161797_a_nat @ ( standa63370785tant_a @ I ) ) @ ( id_on_nat @ ( labele1810595089_a_nat @ ( produc719117507_a_nat @ ( standa63370785tant_a @ I ) ) ) ) )
% 0.27/0.48 & ( ( produc880161797_a_nat @ ( standa63370785tant_a @ I ) )
% 0.27/0.48 = ( restri572569417_a_nat @ ( produc880161797_a_nat @ ( standa63370785tant_a @ I ) ) ) )
% 0.27/0.48 & ( finite_finite_nat @ ( labele1810595089_a_nat @ ( produc880161797_a_nat @ ( standa63370785tant_a @ I ) ) ) )
% 0.27/0.48 & ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( produc880161797_a_nat @ ( standa63370785tant_a @ I ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % are_rules(3)
% 0.27/0.48 thf(fact_23_are__rules_I3_J,axiom,
% 0.27/0.48 ! [I: b] :
% 0.27/0.48 ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( standa1329480013rule_b @ I ) ) @ ( produc194497945_b_nat @ ( standa1329480013rule_b @ I ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( standa1329480013rule_b @ I ) ) ) ) )
% 0.27/0.48 & ( ( produc194497945_b_nat @ ( standa1329480013rule_b @ I ) )
% 0.27/0.48 = ( restrict_b_nat @ ( produc194497945_b_nat @ ( standa1329480013rule_b @ I ) ) ) )
% 0.27/0.48 & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( standa1329480013rule_b @ I ) ) ) )
% 0.27/0.48 & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( standa1329480013rule_b @ I ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % are_rules(3)
% 0.27/0.48 thf(fact_24_prod_Ocollapse,axiom,
% 0.27/0.48 ! [Prod: product_prod_nat_nat] :
% 0.27/0.48 ( ( product_Pair_nat_nat @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) )
% 0.27/0.48 = Prod ) ).
% 0.27/0.48
% 0.27/0.48 % prod.collapse
% 0.27/0.48 thf(fact_25_prod_Ocollapse,axiom,
% 0.27/0.48 ! [Prod: produc398057191_a_nat] :
% 0.27/0.48 ( ( produc1677124439_a_nat @ ( produc1049080131_a_nat @ Prod ) @ ( produc1022852229_a_nat @ Prod ) )
% 0.27/0.48 = Prod ) ).
% 0.27/0.48
% 0.27/0.48 % prod.collapse
% 0.27/0.48 thf(fact_26_prod_Ocollapse,axiom,
% 0.27/0.48 ! [Prod: produc1871334759_a_nat] :
% 0.27/0.48 ( ( produc1676969687_a_nat @ ( produc719117507_a_nat @ Prod ) @ ( produc880161797_a_nat @ Prod ) )
% 0.27/0.48 = Prod ) ).
% 0.27/0.48
% 0.27/0.48 % prod.collapse
% 0.27/0.48 thf(fact_27_prod_Ocollapse,axiom,
% 0.27/0.48 ! [Prod: produc1478835367term_b] :
% 0.27/0.48 ( ( produc1990145943term_b @ ( produc854192515term_b @ Prod ) @ ( produc1223098053term_b @ Prod ) )
% 0.27/0.48 = Prod ) ).
% 0.27/0.48
% 0.27/0.48 % prod.collapse
% 0.27/0.48 thf(fact_28_prod_Ocollapse,axiom,
% 0.27/0.48 ! [Prod: produc1235635379_b_nat] :
% 0.27/0.48 ( ( produc951298923_b_nat @ ( produc1542243159_b_nat @ Prod ) @ ( produc194497945_b_nat @ Prod ) )
% 0.27/0.48 = Prod ) ).
% 0.27/0.48
% 0.27/0.48 % prod.collapse
% 0.27/0.48 thf(fact_29_translation__graph,axiom,
% 0.27/0.48 ( transl1275713022tant_a
% 0.27/0.48 = ( ^ [X2: allego510293162tant_a] : ( restri572569417_a_nat @ ( transl1275713022tant_a @ X2 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % translation_graph
% 0.27/0.48 thf(fact_30_translation__graph,axiom,
% 0.27/0.48 ( translation_b
% 0.27/0.48 = ( ^ [X2: allegorical_term_b] : ( restrict_b_nat @ ( translation_b @ X2 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % translation_graph
% 0.27/0.48 thf(fact_31_vertices__restrict,axiom,
% 0.27/0.48 ! [G: labele935650037_a_nat] :
% 0.27/0.48 ( ( labele1810595089_a_nat @ ( restri572569417_a_nat @ G ) )
% 0.27/0.48 = ( labele1810595089_a_nat @ G ) ) ).
% 0.27/0.48
% 0.27/0.48 % vertices_restrict
% 0.27/0.48 thf(fact_32_vertices__restrict,axiom,
% 0.27/0.48 ! [G: labeled_graph_b_nat] :
% 0.27/0.48 ( ( labele460410879_b_nat @ ( restrict_b_nat @ G ) )
% 0.27/0.48 = ( labele460410879_b_nat @ G ) ) ).
% 0.27/0.48
% 0.27/0.48 % vertices_restrict
% 0.27/0.48 thf(fact_33_old_Oprod_Oinject,axiom,
% 0.27/0.48 ! [A: nat,B: nat,A2: nat,B2: nat] :
% 0.27/0.48 ( ( ( product_Pair_nat_nat @ A @ B )
% 0.27/0.48 = ( product_Pair_nat_nat @ A2 @ B2 ) )
% 0.27/0.48 = ( ( A = A2 )
% 0.27/0.48 & ( B = B2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % old.prod.inject
% 0.27/0.48 thf(fact_34_old_Oprod_Oinject,axiom,
% 0.27/0.48 ! [A: produc1871334759_a_nat,B: produc1871334759_a_nat,A2: produc1871334759_a_nat,B2: produc1871334759_a_nat] :
% 0.27/0.48 ( ( ( produc1677124439_a_nat @ A @ B )
% 0.27/0.48 = ( produc1677124439_a_nat @ A2 @ B2 ) )
% 0.27/0.48 = ( ( A = A2 )
% 0.27/0.48 & ( B = B2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % old.prod.inject
% 0.27/0.48 thf(fact_35_old_Oprod_Oinject,axiom,
% 0.27/0.48 ! [A: labele935650037_a_nat,B: labele935650037_a_nat,A2: labele935650037_a_nat,B2: labele935650037_a_nat] :
% 0.27/0.48 ( ( ( produc1676969687_a_nat @ A @ B )
% 0.27/0.48 = ( produc1676969687_a_nat @ A2 @ B2 ) )
% 0.27/0.48 = ( ( A = A2 )
% 0.27/0.48 & ( B = B2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % old.prod.inject
% 0.27/0.48 thf(fact_36_old_Oprod_Oinject,axiom,
% 0.27/0.48 ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,A2: labeled_graph_b_nat,B2: labeled_graph_b_nat] :
% 0.27/0.48 ( ( ( produc951298923_b_nat @ A @ B )
% 0.27/0.48 = ( produc951298923_b_nat @ A2 @ B2 ) )
% 0.27/0.48 = ( ( A = A2 )
% 0.27/0.48 & ( B = B2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % old.prod.inject
% 0.27/0.48 thf(fact_37_old_Oprod_Oinject,axiom,
% 0.27/0.48 ! [A: allegorical_term_b,B: allegorical_term_b,A2: allegorical_term_b,B2: allegorical_term_b] :
% 0.27/0.48 ( ( ( produc1990145943term_b @ A @ B )
% 0.27/0.48 = ( produc1990145943term_b @ A2 @ B2 ) )
% 0.27/0.48 = ( ( A = A2 )
% 0.27/0.48 & ( B = B2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % old.prod.inject
% 0.27/0.48 thf(fact_38_prod_Oinject,axiom,
% 0.27/0.48 ! [X1: nat,X22: nat,Y1: nat,Y2: nat] :
% 0.27/0.48 ( ( ( product_Pair_nat_nat @ X1 @ X22 )
% 0.27/0.48 = ( product_Pair_nat_nat @ Y1 @ Y2 ) )
% 0.27/0.48 = ( ( X1 = Y1 )
% 0.27/0.48 & ( X22 = Y2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % prod.inject
% 0.27/0.48 thf(fact_39_prod_Oinject,axiom,
% 0.27/0.48 ! [X1: produc1871334759_a_nat,X22: produc1871334759_a_nat,Y1: produc1871334759_a_nat,Y2: produc1871334759_a_nat] :
% 0.27/0.48 ( ( ( produc1677124439_a_nat @ X1 @ X22 )
% 0.27/0.48 = ( produc1677124439_a_nat @ Y1 @ Y2 ) )
% 0.27/0.48 = ( ( X1 = Y1 )
% 0.27/0.48 & ( X22 = Y2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % prod.inject
% 0.27/0.48 thf(fact_40_prod_Oinject,axiom,
% 0.27/0.48 ! [X1: labele935650037_a_nat,X22: labele935650037_a_nat,Y1: labele935650037_a_nat,Y2: labele935650037_a_nat] :
% 0.27/0.48 ( ( ( produc1676969687_a_nat @ X1 @ X22 )
% 0.27/0.48 = ( produc1676969687_a_nat @ Y1 @ Y2 ) )
% 0.27/0.48 = ( ( X1 = Y1 )
% 0.27/0.48 & ( X22 = Y2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % prod.inject
% 0.27/0.48 thf(fact_41_prod_Oinject,axiom,
% 0.27/0.48 ! [X1: labeled_graph_b_nat,X22: labeled_graph_b_nat,Y1: labeled_graph_b_nat,Y2: labeled_graph_b_nat] :
% 0.27/0.48 ( ( ( produc951298923_b_nat @ X1 @ X22 )
% 0.27/0.48 = ( produc951298923_b_nat @ Y1 @ Y2 ) )
% 0.27/0.48 = ( ( X1 = Y1 )
% 0.27/0.48 & ( X22 = Y2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % prod.inject
% 0.27/0.48 thf(fact_42_prod_Oinject,axiom,
% 0.27/0.48 ! [X1: allegorical_term_b,X22: allegorical_term_b,Y1: allegorical_term_b,Y2: allegorical_term_b] :
% 0.27/0.48 ( ( ( produc1990145943term_b @ X1 @ X22 )
% 0.27/0.48 = ( produc1990145943term_b @ Y1 @ Y2 ) )
% 0.27/0.48 = ( ( X1 = Y1 )
% 0.27/0.48 & ( X22 = Y2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % prod.inject
% 0.27/0.48 thf(fact_43_restrict__idemp,axiom,
% 0.27/0.48 ! [X3: labele935650037_a_nat] :
% 0.27/0.48 ( ( restri572569417_a_nat @ ( restri572569417_a_nat @ X3 ) )
% 0.27/0.48 = ( restri572569417_a_nat @ X3 ) ) ).
% 0.27/0.48
% 0.27/0.48 % restrict_idemp
% 0.27/0.48 thf(fact_44_restrict__idemp,axiom,
% 0.27/0.48 ! [X3: labeled_graph_b_nat] :
% 0.27/0.48 ( ( restrict_b_nat @ ( restrict_b_nat @ X3 ) )
% 0.27/0.48 = ( restrict_b_nat @ X3 ) ) ).
% 0.27/0.48
% 0.27/0.48 % restrict_idemp
% 0.27/0.48 thf(fact_45_old_Oprod_Oinducts,axiom,
% 0.27/0.48 ! [P: product_prod_nat_nat > $o,Prod: product_prod_nat_nat] :
% 0.27/0.48 ( ! [A3: nat,B3: nat] : ( P @ ( product_Pair_nat_nat @ A3 @ B3 ) )
% 0.27/0.48 => ( P @ Prod ) ) ).
% 0.27/0.48
% 0.27/0.48 % old.prod.inducts
% 0.27/0.48 thf(fact_46_old_Oprod_Oinducts,axiom,
% 0.27/0.48 ! [P: produc398057191_a_nat > $o,Prod: produc398057191_a_nat] :
% 0.27/0.48 ( ! [A3: produc1871334759_a_nat,B3: produc1871334759_a_nat] : ( P @ ( produc1677124439_a_nat @ A3 @ B3 ) )
% 0.27/0.48 => ( P @ Prod ) ) ).
% 0.27/0.48
% 0.27/0.48 % old.prod.inducts
% 0.27/0.48 thf(fact_47_old_Oprod_Oinducts,axiom,
% 0.27/0.48 ! [P: produc1871334759_a_nat > $o,Prod: produc1871334759_a_nat] :
% 0.27/0.48 ( ! [A3: labele935650037_a_nat,B3: labele935650037_a_nat] : ( P @ ( produc1676969687_a_nat @ A3 @ B3 ) )
% 0.27/0.48 => ( P @ Prod ) ) ).
% 0.27/0.48
% 0.27/0.48 % old.prod.inducts
% 0.27/0.48 thf(fact_48_old_Oprod_Oinducts,axiom,
% 0.27/0.48 ! [P: produc1235635379_b_nat > $o,Prod: produc1235635379_b_nat] :
% 0.27/0.48 ( ! [A3: labeled_graph_b_nat,B3: labeled_graph_b_nat] : ( P @ ( produc951298923_b_nat @ A3 @ B3 ) )
% 0.27/0.48 => ( P @ Prod ) ) ).
% 0.27/0.48
% 0.27/0.48 % old.prod.inducts
% 0.27/0.48 thf(fact_49_old_Oprod_Oinducts,axiom,
% 0.27/0.48 ! [P: produc1478835367term_b > $o,Prod: produc1478835367term_b] :
% 0.27/0.48 ( ! [A3: allegorical_term_b,B3: allegorical_term_b] : ( P @ ( produc1990145943term_b @ A3 @ B3 ) )
% 0.27/0.48 => ( P @ Prod ) ) ).
% 0.27/0.48
% 0.27/0.48 % old.prod.inducts
% 0.27/0.48 thf(fact_50_old_Oprod_Oexhaust,axiom,
% 0.27/0.48 ! [Y3: product_prod_nat_nat] :
% 0.27/0.48 ~ ! [A3: nat,B3: nat] :
% 0.27/0.48 ( Y3
% 0.27/0.48 != ( product_Pair_nat_nat @ A3 @ B3 ) ) ).
% 0.27/0.48
% 0.27/0.48 % old.prod.exhaust
% 0.27/0.48 thf(fact_51_old_Oprod_Oexhaust,axiom,
% 0.27/0.48 ! [Y3: produc398057191_a_nat] :
% 0.27/0.48 ~ ! [A3: produc1871334759_a_nat,B3: produc1871334759_a_nat] :
% 0.27/0.48 ( Y3
% 0.27/0.48 != ( produc1677124439_a_nat @ A3 @ B3 ) ) ).
% 0.27/0.48
% 0.27/0.48 % old.prod.exhaust
% 0.27/0.48 thf(fact_52_old_Oprod_Oexhaust,axiom,
% 0.27/0.48 ! [Y3: produc1871334759_a_nat] :
% 0.27/0.48 ~ ! [A3: labele935650037_a_nat,B3: labele935650037_a_nat] :
% 0.27/0.48 ( Y3
% 0.27/0.48 != ( produc1676969687_a_nat @ A3 @ B3 ) ) ).
% 0.27/0.48
% 0.27/0.48 % old.prod.exhaust
% 0.27/0.48 thf(fact_53_old_Oprod_Oexhaust,axiom,
% 0.27/0.48 ! [Y3: produc1235635379_b_nat] :
% 0.27/0.48 ~ ! [A3: labeled_graph_b_nat,B3: labeled_graph_b_nat] :
% 0.27/0.48 ( Y3
% 0.27/0.48 != ( produc951298923_b_nat @ A3 @ B3 ) ) ).
% 0.27/0.48
% 0.27/0.48 % old.prod.exhaust
% 0.27/0.48 thf(fact_54_old_Oprod_Oexhaust,axiom,
% 0.27/0.48 ! [Y3: produc1478835367term_b] :
% 0.27/0.48 ~ ! [A3: allegorical_term_b,B3: allegorical_term_b] :
% 0.27/0.48 ( Y3
% 0.27/0.48 != ( produc1990145943term_b @ A3 @ B3 ) ) ).
% 0.27/0.48
% 0.27/0.48 % old.prod.exhaust
% 0.27/0.48 thf(fact_55_prod__induct3,axiom,
% 0.27/0.48 ! [P: produc398057191_a_nat > $o,X3: produc398057191_a_nat] :
% 0.27/0.48 ( ! [A3: produc1871334759_a_nat,B3: labele935650037_a_nat,C: labele935650037_a_nat] : ( P @ ( produc1677124439_a_nat @ A3 @ ( produc1676969687_a_nat @ B3 @ C ) ) )
% 0.27/0.48 => ( P @ X3 ) ) ).
% 0.27/0.48
% 0.27/0.48 % prod_induct3
% 0.27/0.48 thf(fact_56_prod__cases3,axiom,
% 0.27/0.48 ! [Y3: produc398057191_a_nat] :
% 0.27/0.48 ~ ! [A3: produc1871334759_a_nat,B3: labele935650037_a_nat,C: labele935650037_a_nat] :
% 0.27/0.48 ( Y3
% 0.27/0.48 != ( produc1677124439_a_nat @ A3 @ ( produc1676969687_a_nat @ B3 @ C ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % prod_cases3
% 0.27/0.48 thf(fact_57_Pair__inject,axiom,
% 0.27/0.48 ! [A: nat,B: nat,A2: nat,B2: nat] :
% 0.27/0.48 ( ( ( product_Pair_nat_nat @ A @ B )
% 0.27/0.48 = ( product_Pair_nat_nat @ A2 @ B2 ) )
% 0.27/0.48 => ~ ( ( A = A2 )
% 0.27/0.48 => ( B != B2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Pair_inject
% 0.27/0.48 thf(fact_58_Pair__inject,axiom,
% 0.27/0.48 ! [A: produc1871334759_a_nat,B: produc1871334759_a_nat,A2: produc1871334759_a_nat,B2: produc1871334759_a_nat] :
% 0.27/0.48 ( ( ( produc1677124439_a_nat @ A @ B )
% 0.27/0.48 = ( produc1677124439_a_nat @ A2 @ B2 ) )
% 0.27/0.48 => ~ ( ( A = A2 )
% 0.27/0.48 => ( B != B2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Pair_inject
% 0.27/0.48 thf(fact_59_Pair__inject,axiom,
% 0.27/0.48 ! [A: labele935650037_a_nat,B: labele935650037_a_nat,A2: labele935650037_a_nat,B2: labele935650037_a_nat] :
% 0.27/0.48 ( ( ( produc1676969687_a_nat @ A @ B )
% 0.27/0.48 = ( produc1676969687_a_nat @ A2 @ B2 ) )
% 0.27/0.48 => ~ ( ( A = A2 )
% 0.27/0.48 => ( B != B2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Pair_inject
% 0.27/0.48 thf(fact_60_Pair__inject,axiom,
% 0.27/0.48 ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,A2: labeled_graph_b_nat,B2: labeled_graph_b_nat] :
% 0.27/0.48 ( ( ( produc951298923_b_nat @ A @ B )
% 0.27/0.48 = ( produc951298923_b_nat @ A2 @ B2 ) )
% 0.27/0.48 => ~ ( ( A = A2 )
% 0.27/0.48 => ( B != B2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Pair_inject
% 0.27/0.48 thf(fact_61_Pair__inject,axiom,
% 0.27/0.48 ! [A: allegorical_term_b,B: allegorical_term_b,A2: allegorical_term_b,B2: allegorical_term_b] :
% 0.27/0.48 ( ( ( produc1990145943term_b @ A @ B )
% 0.27/0.48 = ( produc1990145943term_b @ A2 @ B2 ) )
% 0.27/0.48 => ~ ( ( A = A2 )
% 0.27/0.48 => ( B != B2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Pair_inject
% 0.27/0.48 thf(fact_62_prod__cases,axiom,
% 0.27/0.48 ! [P: product_prod_nat_nat > $o,P2: product_prod_nat_nat] :
% 0.27/0.48 ( ! [A3: nat,B3: nat] : ( P @ ( product_Pair_nat_nat @ A3 @ B3 ) )
% 0.27/0.48 => ( P @ P2 ) ) ).
% 0.27/0.48
% 0.27/0.48 % prod_cases
% 0.27/0.48 thf(fact_63_prod__cases,axiom,
% 0.27/0.48 ! [P: produc398057191_a_nat > $o,P2: produc398057191_a_nat] :
% 0.27/0.48 ( ! [A3: produc1871334759_a_nat,B3: produc1871334759_a_nat] : ( P @ ( produc1677124439_a_nat @ A3 @ B3 ) )
% 0.27/0.48 => ( P @ P2 ) ) ).
% 0.27/0.48
% 0.27/0.48 % prod_cases
% 0.27/0.48 thf(fact_64_prod__cases,axiom,
% 0.27/0.48 ! [P: produc1871334759_a_nat > $o,P2: produc1871334759_a_nat] :
% 0.27/0.48 ( ! [A3: labele935650037_a_nat,B3: labele935650037_a_nat] : ( P @ ( produc1676969687_a_nat @ A3 @ B3 ) )
% 0.27/0.48 => ( P @ P2 ) ) ).
% 0.27/0.48
% 0.27/0.48 % prod_cases
% 0.27/0.48 thf(fact_65_prod__cases,axiom,
% 0.27/0.48 ! [P: produc1235635379_b_nat > $o,P2: produc1235635379_b_nat] :
% 0.27/0.48 ( ! [A3: labeled_graph_b_nat,B3: labeled_graph_b_nat] : ( P @ ( produc951298923_b_nat @ A3 @ B3 ) )
% 0.27/0.48 => ( P @ P2 ) ) ).
% 0.27/0.48
% 0.27/0.48 % prod_cases
% 0.27/0.48 thf(fact_66_prod__cases,axiom,
% 0.27/0.48 ! [P: produc1478835367term_b > $o,P2: produc1478835367term_b] :
% 0.27/0.48 ( ! [A3: allegorical_term_b,B3: allegorical_term_b] : ( P @ ( produc1990145943term_b @ A3 @ B3 ) )
% 0.27/0.48 => ( P @ P2 ) ) ).
% 0.27/0.48
% 0.27/0.48 % prod_cases
% 0.27/0.48 thf(fact_67_surj__pair,axiom,
% 0.27/0.48 ! [P2: product_prod_nat_nat] :
% 0.27/0.48 ? [X4: nat,Y4: nat] :
% 0.27/0.48 ( P2
% 0.27/0.48 = ( product_Pair_nat_nat @ X4 @ Y4 ) ) ).
% 0.27/0.48
% 0.27/0.48 % surj_pair
% 0.27/0.48 thf(fact_68_surj__pair,axiom,
% 0.27/0.48 ! [P2: produc398057191_a_nat] :
% 0.27/0.48 ? [X4: produc1871334759_a_nat,Y4: produc1871334759_a_nat] :
% 0.27/0.48 ( P2
% 0.27/0.48 = ( produc1677124439_a_nat @ X4 @ Y4 ) ) ).
% 0.27/0.48
% 0.27/0.48 % surj_pair
% 0.27/0.48 thf(fact_69_surj__pair,axiom,
% 0.27/0.48 ! [P2: produc1871334759_a_nat] :
% 0.27/0.48 ? [X4: labele935650037_a_nat,Y4: labele935650037_a_nat] :
% 0.27/0.48 ( P2
% 0.27/0.48 = ( produc1676969687_a_nat @ X4 @ Y4 ) ) ).
% 0.27/0.48
% 0.27/0.48 % surj_pair
% 0.27/0.48 thf(fact_70_surj__pair,axiom,
% 0.27/0.48 ! [P2: produc1235635379_b_nat] :
% 0.27/0.48 ? [X4: labeled_graph_b_nat,Y4: labeled_graph_b_nat] :
% 0.27/0.48 ( P2
% 0.27/0.48 = ( produc951298923_b_nat @ X4 @ Y4 ) ) ).
% 0.27/0.48
% 0.27/0.48 % surj_pair
% 0.27/0.48 thf(fact_71_surj__pair,axiom,
% 0.27/0.48 ! [P2: produc1478835367term_b] :
% 0.27/0.48 ? [X4: allegorical_term_b,Y4: allegorical_term_b] :
% 0.27/0.48 ( P2
% 0.27/0.48 = ( produc1990145943term_b @ X4 @ Y4 ) ) ).
% 0.27/0.48
% 0.27/0.48 % surj_pair
% 0.27/0.48 thf(fact_72_fst__conv,axiom,
% 0.27/0.48 ! [X1: nat,X22: nat] :
% 0.27/0.48 ( ( product_fst_nat_nat @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 0.27/0.48 = X1 ) ).
% 0.27/0.48
% 0.27/0.48 % fst_conv
% 0.27/0.48 thf(fact_73_fst__conv,axiom,
% 0.27/0.48 ! [X1: produc1871334759_a_nat,X22: produc1871334759_a_nat] :
% 0.27/0.48 ( ( produc1049080131_a_nat @ ( produc1677124439_a_nat @ X1 @ X22 ) )
% 0.27/0.48 = X1 ) ).
% 0.27/0.48
% 0.27/0.48 % fst_conv
% 0.27/0.48 thf(fact_74_fst__conv,axiom,
% 0.27/0.48 ! [X1: labele935650037_a_nat,X22: labele935650037_a_nat] :
% 0.27/0.48 ( ( produc719117507_a_nat @ ( produc1676969687_a_nat @ X1 @ X22 ) )
% 0.27/0.48 = X1 ) ).
% 0.27/0.48
% 0.27/0.48 % fst_conv
% 0.27/0.48 thf(fact_75_fst__conv,axiom,
% 0.27/0.48 ! [X1: labeled_graph_b_nat,X22: labeled_graph_b_nat] :
% 0.27/0.48 ( ( produc1542243159_b_nat @ ( produc951298923_b_nat @ X1 @ X22 ) )
% 0.27/0.48 = X1 ) ).
% 0.27/0.48
% 0.27/0.48 % fst_conv
% 0.27/0.48 thf(fact_76_fst__conv,axiom,
% 0.27/0.48 ! [X1: allegorical_term_b,X22: allegorical_term_b] :
% 0.27/0.48 ( ( produc854192515term_b @ ( produc1990145943term_b @ X1 @ X22 ) )
% 0.27/0.48 = X1 ) ).
% 0.27/0.48
% 0.27/0.48 % fst_conv
% 0.27/0.48 thf(fact_77_fst__eqD,axiom,
% 0.27/0.48 ! [X3: nat,Y3: nat,A: nat] :
% 0.27/0.48 ( ( ( product_fst_nat_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 0.27/0.48 = A )
% 0.27/0.48 => ( X3 = A ) ) ).
% 0.27/0.48
% 0.27/0.48 % fst_eqD
% 0.27/0.48 thf(fact_78_fst__eqD,axiom,
% 0.27/0.48 ! [X3: produc1871334759_a_nat,Y3: produc1871334759_a_nat,A: produc1871334759_a_nat] :
% 0.27/0.48 ( ( ( produc1049080131_a_nat @ ( produc1677124439_a_nat @ X3 @ Y3 ) )
% 0.27/0.48 = A )
% 0.27/0.48 => ( X3 = A ) ) ).
% 0.27/0.48
% 0.27/0.48 % fst_eqD
% 0.27/0.48 thf(fact_79_fst__eqD,axiom,
% 0.27/0.48 ! [X3: labele935650037_a_nat,Y3: labele935650037_a_nat,A: labele935650037_a_nat] :
% 0.27/0.48 ( ( ( produc719117507_a_nat @ ( produc1676969687_a_nat @ X3 @ Y3 ) )
% 0.27/0.48 = A )
% 0.27/0.48 => ( X3 = A ) ) ).
% 0.27/0.48
% 0.27/0.48 % fst_eqD
% 0.27/0.48 thf(fact_80_fst__eqD,axiom,
% 0.27/0.48 ! [X3: labeled_graph_b_nat,Y3: labeled_graph_b_nat,A: labeled_graph_b_nat] :
% 0.27/0.48 ( ( ( produc1542243159_b_nat @ ( produc951298923_b_nat @ X3 @ Y3 ) )
% 0.27/0.48 = A )
% 0.27/0.48 => ( X3 = A ) ) ).
% 0.27/0.48
% 0.27/0.48 % fst_eqD
% 0.27/0.48 thf(fact_81_fst__eqD,axiom,
% 0.27/0.48 ! [X3: allegorical_term_b,Y3: allegorical_term_b,A: allegorical_term_b] :
% 0.27/0.48 ( ( ( produc854192515term_b @ ( produc1990145943term_b @ X3 @ Y3 ) )
% 0.27/0.48 = A )
% 0.27/0.48 => ( X3 = A ) ) ).
% 0.27/0.48
% 0.27/0.48 % fst_eqD
% 0.27/0.48 thf(fact_82_snd__conv,axiom,
% 0.27/0.48 ! [X1: nat,X22: nat] :
% 0.27/0.48 ( ( product_snd_nat_nat @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 0.27/0.48 = X22 ) ).
% 0.27/0.48
% 0.27/0.48 % snd_conv
% 0.27/0.48 thf(fact_83_snd__conv,axiom,
% 0.27/0.48 ! [X1: produc1871334759_a_nat,X22: produc1871334759_a_nat] :
% 0.27/0.48 ( ( produc1022852229_a_nat @ ( produc1677124439_a_nat @ X1 @ X22 ) )
% 0.27/0.48 = X22 ) ).
% 0.27/0.48
% 0.27/0.48 % snd_conv
% 0.27/0.48 thf(fact_84_snd__conv,axiom,
% 0.27/0.48 ! [X1: labele935650037_a_nat,X22: labele935650037_a_nat] :
% 0.27/0.48 ( ( produc880161797_a_nat @ ( produc1676969687_a_nat @ X1 @ X22 ) )
% 0.27/0.48 = X22 ) ).
% 0.27/0.48
% 0.27/0.48 % snd_conv
% 0.27/0.48 thf(fact_85_snd__conv,axiom,
% 0.27/0.48 ! [X1: allegorical_term_b,X22: allegorical_term_b] :
% 0.27/0.48 ( ( produc1223098053term_b @ ( produc1990145943term_b @ X1 @ X22 ) )
% 0.27/0.48 = X22 ) ).
% 0.27/0.48
% 0.27/0.48 % snd_conv
% 0.27/0.48 thf(fact_86_snd__conv,axiom,
% 0.27/0.48 ! [X1: labeled_graph_b_nat,X22: labeled_graph_b_nat] :
% 0.27/0.48 ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ X1 @ X22 ) )
% 0.27/0.48 = X22 ) ).
% 0.27/0.48
% 0.27/0.48 % snd_conv
% 0.27/0.48 thf(fact_87_snd__eqD,axiom,
% 0.27/0.48 ! [X3: nat,Y3: nat,A: nat] :
% 0.27/0.48 ( ( ( product_snd_nat_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 0.27/0.48 = A )
% 0.27/0.48 => ( Y3 = A ) ) ).
% 0.27/0.48
% 0.27/0.48 % snd_eqD
% 0.27/0.48 thf(fact_88_snd__eqD,axiom,
% 0.27/0.48 ! [X3: produc1871334759_a_nat,Y3: produc1871334759_a_nat,A: produc1871334759_a_nat] :
% 0.27/0.48 ( ( ( produc1022852229_a_nat @ ( produc1677124439_a_nat @ X3 @ Y3 ) )
% 0.27/0.48 = A )
% 0.27/0.48 => ( Y3 = A ) ) ).
% 0.27/0.48
% 0.27/0.48 % snd_eqD
% 0.27/0.48 thf(fact_89_snd__eqD,axiom,
% 0.27/0.48 ! [X3: labele935650037_a_nat,Y3: labele935650037_a_nat,A: labele935650037_a_nat] :
% 0.27/0.48 ( ( ( produc880161797_a_nat @ ( produc1676969687_a_nat @ X3 @ Y3 ) )
% 0.27/0.48 = A )
% 0.27/0.48 => ( Y3 = A ) ) ).
% 0.27/0.48
% 0.27/0.48 % snd_eqD
% 0.27/0.48 thf(fact_90_snd__eqD,axiom,
% 0.27/0.48 ! [X3: allegorical_term_b,Y3: allegorical_term_b,A: allegorical_term_b] :
% 0.27/0.48 ( ( ( produc1223098053term_b @ ( produc1990145943term_b @ X3 @ Y3 ) )
% 0.27/0.48 = A )
% 0.27/0.48 => ( Y3 = A ) ) ).
% 0.27/0.48
% 0.27/0.48 % snd_eqD
% 0.27/0.48 thf(fact_91_snd__eqD,axiom,
% 0.27/0.48 ! [X3: labeled_graph_b_nat,Y3: labeled_graph_b_nat,A: labeled_graph_b_nat] :
% 0.27/0.48 ( ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ X3 @ Y3 ) )
% 0.27/0.48 = A )
% 0.27/0.48 => ( Y3 = A ) ) ).
% 0.27/0.48
% 0.27/0.48 % snd_eqD
% 0.27/0.48 thf(fact_92_prod__eq__iff,axiom,
% 0.27/0.48 ( ( ^ [Y5: produc1871334759_a_nat,Z: produc1871334759_a_nat] : ( Y5 = Z ) )
% 0.27/0.48 = ( ^ [S: produc1871334759_a_nat,T2: produc1871334759_a_nat] :
% 0.27/0.48 ( ( ( produc719117507_a_nat @ S )
% 0.27/0.48 = ( produc719117507_a_nat @ T2 ) )
% 0.27/0.48 & ( ( produc880161797_a_nat @ S )
% 0.27/0.48 = ( produc880161797_a_nat @ T2 ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % prod_eq_iff
% 0.27/0.48 thf(fact_93_prod__eq__iff,axiom,
% 0.27/0.48 ( ( ^ [Y5: produc1478835367term_b,Z: produc1478835367term_b] : ( Y5 = Z ) )
% 0.27/0.48 = ( ^ [S: produc1478835367term_b,T2: produc1478835367term_b] :
% 0.27/0.48 ( ( ( produc854192515term_b @ S )
% 0.27/0.48 = ( produc854192515term_b @ T2 ) )
% 0.27/0.48 & ( ( produc1223098053term_b @ S )
% 0.27/0.48 = ( produc1223098053term_b @ T2 ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % prod_eq_iff
% 0.27/0.48 thf(fact_94_prod__eq__iff,axiom,
% 0.27/0.48 ( ( ^ [Y5: produc1235635379_b_nat,Z: produc1235635379_b_nat] : ( Y5 = Z ) )
% 0.27/0.48 = ( ^ [S: produc1235635379_b_nat,T2: produc1235635379_b_nat] :
% 0.27/0.48 ( ( ( produc1542243159_b_nat @ S )
% 0.27/0.48 = ( produc1542243159_b_nat @ T2 ) )
% 0.27/0.48 & ( ( produc194497945_b_nat @ S )
% 0.27/0.48 = ( produc194497945_b_nat @ T2 ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % prod_eq_iff
% 0.27/0.48 thf(fact_95_prod_Oexpand,axiom,
% 0.27/0.48 ! [Prod: produc1871334759_a_nat,Prod2: produc1871334759_a_nat] :
% 0.27/0.48 ( ( ( ( produc719117507_a_nat @ Prod )
% 0.27/0.48 = ( produc719117507_a_nat @ Prod2 ) )
% 0.27/0.48 & ( ( produc880161797_a_nat @ Prod )
% 0.27/0.48 = ( produc880161797_a_nat @ Prod2 ) ) )
% 0.27/0.48 => ( Prod = Prod2 ) ) ).
% 0.27/0.48
% 0.27/0.48 % prod.expand
% 0.27/0.48 thf(fact_96_prod_Oexpand,axiom,
% 0.27/0.48 ! [Prod: produc1478835367term_b,Prod2: produc1478835367term_b] :
% 0.27/0.48 ( ( ( ( produc854192515term_b @ Prod )
% 0.27/0.48 = ( produc854192515term_b @ Prod2 ) )
% 0.27/0.48 & ( ( produc1223098053term_b @ Prod )
% 0.27/0.48 = ( produc1223098053term_b @ Prod2 ) ) )
% 0.27/0.48 => ( Prod = Prod2 ) ) ).
% 0.27/0.48
% 0.27/0.48 % prod.expand
% 0.27/0.48 thf(fact_97_prod_Oexpand,axiom,
% 0.27/0.48 ! [Prod: produc1235635379_b_nat,Prod2: produc1235635379_b_nat] :
% 0.27/0.48 ( ( ( ( produc1542243159_b_nat @ Prod )
% 0.27/0.48 = ( produc1542243159_b_nat @ Prod2 ) )
% 0.27/0.48 & ( ( produc194497945_b_nat @ Prod )
% 0.27/0.48 = ( produc194497945_b_nat @ Prod2 ) ) )
% 0.27/0.48 => ( Prod = Prod2 ) ) ).
% 0.27/0.48
% 0.27/0.48 % prod.expand
% 0.27/0.48 thf(fact_98_prod__eqI,axiom,
% 0.27/0.48 ! [P2: produc1871334759_a_nat,Q: produc1871334759_a_nat] :
% 0.27/0.48 ( ( ( produc719117507_a_nat @ P2 )
% 0.27/0.48 = ( produc719117507_a_nat @ Q ) )
% 0.27/0.48 => ( ( ( produc880161797_a_nat @ P2 )
% 0.27/0.48 = ( produc880161797_a_nat @ Q ) )
% 0.27/0.48 => ( P2 = Q ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % prod_eqI
% 0.27/0.48 thf(fact_99_prod__eqI,axiom,
% 0.27/0.48 ! [P2: produc1478835367term_b,Q: produc1478835367term_b] :
% 0.27/0.48 ( ( ( produc854192515term_b @ P2 )
% 0.27/0.48 = ( produc854192515term_b @ Q ) )
% 0.27/0.48 => ( ( ( produc1223098053term_b @ P2 )
% 0.27/0.48 = ( produc1223098053term_b @ Q ) )
% 0.27/0.48 => ( P2 = Q ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % prod_eqI
% 0.27/0.48 thf(fact_100_prod__eqI,axiom,
% 0.27/0.48 ! [P2: produc1235635379_b_nat,Q: produc1235635379_b_nat] :
% 0.27/0.48 ( ( ( produc1542243159_b_nat @ P2 )
% 0.27/0.48 = ( produc1542243159_b_nat @ Q ) )
% 0.27/0.48 => ( ( ( produc194497945_b_nat @ P2 )
% 0.27/0.48 = ( produc194497945_b_nat @ Q ) )
% 0.27/0.48 => ( P2 = Q ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % prod_eqI
% 0.27/0.48 thf(fact_101_labeled__graph_Oexpand,axiom,
% 0.27/0.48 ! [Labeled_graph: labele935650037_a_nat,Labeled_graph2: labele935650037_a_nat] :
% 0.27/0.48 ( ( ( ( labele195203296_a_nat @ Labeled_graph )
% 0.27/0.48 = ( labele195203296_a_nat @ Labeled_graph2 ) )
% 0.27/0.48 & ( ( labele1810595089_a_nat @ Labeled_graph )
% 0.27/0.48 = ( labele1810595089_a_nat @ Labeled_graph2 ) ) )
% 0.27/0.48 => ( Labeled_graph = Labeled_graph2 ) ) ).
% 0.27/0.48
% 0.27/0.48 % labeled_graph.expand
% 0.27/0.48 thf(fact_102_labeled__graph_Oexpand,axiom,
% 0.27/0.48 ! [Labeled_graph: labeled_graph_b_nat,Labeled_graph2: labeled_graph_b_nat] :
% 0.27/0.48 ( ( ( ( labeled_edges_b_nat @ Labeled_graph )
% 0.27/0.48 = ( labeled_edges_b_nat @ Labeled_graph2 ) )
% 0.27/0.48 & ( ( labele460410879_b_nat @ Labeled_graph )
% 0.27/0.48 = ( labele460410879_b_nat @ Labeled_graph2 ) ) )
% 0.27/0.48 => ( Labeled_graph = Labeled_graph2 ) ) ).
% 0.27/0.48
% 0.27/0.48 % labeled_graph.expand
% 0.27/0.48 thf(fact_103_surjective__pairing,axiom,
% 0.27/0.48 ! [T: product_prod_nat_nat] :
% 0.27/0.48 ( T
% 0.27/0.48 = ( product_Pair_nat_nat @ ( product_fst_nat_nat @ T ) @ ( product_snd_nat_nat @ T ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % surjective_pairing
% 0.27/0.48 thf(fact_104_surjective__pairing,axiom,
% 0.27/0.48 ! [T: produc398057191_a_nat] :
% 0.27/0.48 ( T
% 0.27/0.48 = ( produc1677124439_a_nat @ ( produc1049080131_a_nat @ T ) @ ( produc1022852229_a_nat @ T ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % surjective_pairing
% 0.27/0.48 thf(fact_105_surjective__pairing,axiom,
% 0.27/0.48 ! [T: produc1871334759_a_nat] :
% 0.27/0.48 ( T
% 0.27/0.48 = ( produc1676969687_a_nat @ ( produc719117507_a_nat @ T ) @ ( produc880161797_a_nat @ T ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % surjective_pairing
% 0.27/0.48 thf(fact_106_surjective__pairing,axiom,
% 0.27/0.48 ! [T: produc1478835367term_b] :
% 0.27/0.48 ( T
% 0.27/0.48 = ( produc1990145943term_b @ ( produc854192515term_b @ T ) @ ( produc1223098053term_b @ T ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % surjective_pairing
% 0.27/0.48 thf(fact_107_surjective__pairing,axiom,
% 0.27/0.48 ! [T: produc1235635379_b_nat] :
% 0.27/0.48 ( T
% 0.27/0.48 = ( produc951298923_b_nat @ ( produc1542243159_b_nat @ T ) @ ( produc194497945_b_nat @ T ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % surjective_pairing
% 0.27/0.48 thf(fact_108_prod_Oexhaust__sel,axiom,
% 0.27/0.48 ! [Prod: product_prod_nat_nat] :
% 0.27/0.48 ( Prod
% 0.27/0.48 = ( product_Pair_nat_nat @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % prod.exhaust_sel
% 0.27/0.48 thf(fact_109_prod_Oexhaust__sel,axiom,
% 0.27/0.48 ! [Prod: produc398057191_a_nat] :
% 0.27/0.48 ( Prod
% 0.27/0.48 = ( produc1677124439_a_nat @ ( produc1049080131_a_nat @ Prod ) @ ( produc1022852229_a_nat @ Prod ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % prod.exhaust_sel
% 0.27/0.48 thf(fact_110_prod_Oexhaust__sel,axiom,
% 0.27/0.48 ! [Prod: produc1871334759_a_nat] :
% 0.27/0.48 ( Prod
% 0.27/0.48 = ( produc1676969687_a_nat @ ( produc719117507_a_nat @ Prod ) @ ( produc880161797_a_nat @ Prod ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % prod.exhaust_sel
% 0.27/0.48 thf(fact_111_prod_Oexhaust__sel,axiom,
% 0.27/0.48 ! [Prod: produc1478835367term_b] :
% 0.27/0.48 ( Prod
% 0.27/0.48 = ( produc1990145943term_b @ ( produc854192515term_b @ Prod ) @ ( produc1223098053term_b @ Prod ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % prod.exhaust_sel
% 0.27/0.48 thf(fact_112_prod_Oexhaust__sel,axiom,
% 0.27/0.48 ! [Prod: produc1235635379_b_nat] :
% 0.27/0.48 ( Prod
% 0.27/0.48 = ( produc951298923_b_nat @ ( produc1542243159_b_nat @ Prod ) @ ( produc194497945_b_nat @ Prod ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % prod.exhaust_sel
% 0.27/0.48 thf(fact_113_subgraph__preserves__hom,axiom,
% 0.27/0.48 ! [A4: labele935650037_a_nat,B4: labele935650037_a_nat,X: labele935650037_a_nat,H: set_Pr1986765409at_nat] :
% 0.27/0.48 ( ( graph_2130075512at_nat @ A4 @ B4 @ ( id_on_nat @ ( labele1810595089_a_nat @ A4 ) ) )
% 0.27/0.48 => ( ( graph_2130075512at_nat @ X @ A4 @ H )
% 0.27/0.48 => ( graph_2130075512at_nat @ X @ B4 @ H ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % subgraph_preserves_hom
% 0.27/0.48 thf(fact_114_subgraph__preserves__hom,axiom,
% 0.27/0.48 ! [A4: labeled_graph_b_nat,B4: labeled_graph_b_nat,X: labeled_graph_b_nat,H: set_Pr1986765409at_nat] :
% 0.27/0.48 ( ( graph_529870330at_nat @ A4 @ B4 @ ( id_on_nat @ ( labele460410879_b_nat @ A4 ) ) )
% 0.27/0.48 => ( ( graph_529870330at_nat @ X @ A4 @ H )
% 0.27/0.48 => ( graph_529870330at_nat @ X @ B4 @ H ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % subgraph_preserves_hom
% 0.27/0.48 thf(fact_115_subgraph__trans,axiom,
% 0.27/0.48 ! [G_1: labele935650037_a_nat,G_2: labele935650037_a_nat,G_3: labele935650037_a_nat] :
% 0.27/0.48 ( ( graph_2130075512at_nat @ G_1 @ G_2 @ ( id_on_nat @ ( labele1810595089_a_nat @ G_1 ) ) )
% 0.27/0.48 => ( ( graph_2130075512at_nat @ G_2 @ G_3 @ ( id_on_nat @ ( labele1810595089_a_nat @ G_2 ) ) )
% 0.27/0.48 => ( graph_2130075512at_nat @ G_1 @ G_3 @ ( id_on_nat @ ( labele1810595089_a_nat @ G_1 ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % subgraph_trans
% 0.27/0.48 thf(fact_116_subgraph__trans,axiom,
% 0.27/0.48 ! [G_1: labeled_graph_b_nat,G_2: labeled_graph_b_nat,G_3: labeled_graph_b_nat] :
% 0.27/0.48 ( ( graph_529870330at_nat @ G_1 @ G_2 @ ( id_on_nat @ ( labele460410879_b_nat @ G_1 ) ) )
% 0.27/0.48 => ( ( graph_529870330at_nat @ G_2 @ G_3 @ ( id_on_nat @ ( labele460410879_b_nat @ G_2 ) ) )
% 0.27/0.48 => ( graph_529870330at_nat @ G_1 @ G_3 @ ( id_on_nat @ ( labele460410879_b_nat @ G_1 ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % subgraph_trans
% 0.27/0.48 thf(fact_117_Id__onI,axiom,
% 0.27/0.48 ! [A: produc1478835367term_b,A4: set_Pr1163220871term_b] :
% 0.27/0.48 ( ( member516522448term_b @ A @ A4 )
% 0.27/0.48 => ( member1449757456term_b @ ( produc859843415term_b @ A @ A ) @ ( id_on_1664915780term_b @ A4 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Id_onI
% 0.27/0.48 thf(fact_118_Id__onI,axiom,
% 0.27/0.48 ! [A: produc1235635379_b_nat,A4: set_Pr551076371_b_nat] :
% 0.27/0.48 ( ( member963855452_b_nat @ A @ A4 )
% 0.27/0.48 => ( member889223696_b_nat @ ( produc1754969175_b_nat @ A @ A ) @ ( id_on_138931664_b_nat @ A4 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Id_onI
% 0.27/0.48 thf(fact_119_Id__onI,axiom,
% 0.27/0.48 ! [A: produc398057191_a_nat,A4: set_Pr924198087_a_nat] :
% 0.27/0.48 ( ( member584645392_a_nat @ A @ A4 )
% 0.27/0.48 => ( member829905680_a_nat @ ( produc170611543_a_nat @ A @ A ) @ ( id_on_1395957380_a_nat @ A4 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Id_onI
% 0.27/0.48 thf(fact_120_Id__onI,axiom,
% 0.27/0.48 ! [A: product_prod_nat_nat,A4: set_Pr1986765409at_nat] :
% 0.27/0.48 ( ( member701585322at_nat @ A @ A4 )
% 0.27/0.48 => ( member2027625872at_nat @ ( produc1168807639at_nat @ A @ A ) @ ( id_on_2144791838at_nat @ A4 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Id_onI
% 0.27/0.48 thf(fact_121_Id__onI,axiom,
% 0.27/0.48 ! [A: labele935650037_a_nat,A4: set_la1083530965_a_nat] :
% 0.27/0.48 ( ( member964390942_a_nat @ A @ A4 )
% 0.27/0.48 => ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ A ) @ ( id_on_689842066_a_nat @ A4 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Id_onI
% 0.27/0.48 thf(fact_122_Id__onI,axiom,
% 0.27/0.48 ! [A: produc1871334759_a_nat,A4: set_Pr1987088711_a_nat] :
% 0.27/0.48 ( ( member832397200_a_nat @ A @ A4 )
% 0.27/0.48 => ( member584645392_a_nat @ ( produc1677124439_a_nat @ A @ A ) @ ( id_on_1651096324_a_nat @ A4 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Id_onI
% 0.27/0.48 thf(fact_123_Id__onI,axiom,
% 0.27/0.48 ! [A: nat,A4: set_nat] :
% 0.27/0.48 ( ( member_nat @ A @ A4 )
% 0.27/0.48 => ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ A ) @ ( id_on_nat @ A4 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Id_onI
% 0.27/0.48 thf(fact_124_Id__onI,axiom,
% 0.27/0.48 ! [A: labeled_graph_b_nat,A4: set_la1976028319_b_nat] :
% 0.27/0.48 ( ( member1483953152_b_nat @ A @ A4 )
% 0.27/0.48 => ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ A ) @ ( id_on_583275916_b_nat @ A4 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Id_onI
% 0.27/0.48 thf(fact_125_Id__onI,axiom,
% 0.27/0.48 ! [A: allegorical_term_b,A4: set_al1193902458term_b] :
% 0.27/0.48 ( ( member93680451term_b @ A @ A4 )
% 0.27/0.48 => ( member516522448term_b @ ( produc1990145943term_b @ A @ A ) @ ( id_on_1536886967term_b @ A4 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Id_onI
% 0.27/0.48 thf(fact_126_set__of__graph__rules__def,axiom,
% 0.27/0.48 ( set_of195930477at_nat
% 0.27/0.48 = ( ^ [Rs: set_Pr665622551at_nat] :
% 0.27/0.48 ! [X5: produc1391440311at_nat] :
% 0.27/0.48 ( ( member1129678944at_nat @ X5 @ Rs )
% 0.27/0.48 => ( ( graph_2111906684at_nat @ ( produc1995789403at_nat @ X5 ) @ ( produc1564126365at_nat @ X5 ) @ ( id_on_nat @ ( labele560327297at_nat @ ( produc1995789403at_nat @ X5 ) ) ) )
% 0.27/0.48 & ( ( produc1564126365at_nat @ X5 )
% 0.27/0.48 = ( restri321299017at_nat @ ( produc1564126365at_nat @ X5 ) ) )
% 0.27/0.48 & ( finite_finite_nat @ ( labele560327297at_nat @ ( produc1564126365at_nat @ X5 ) ) )
% 0.27/0.48 & ( finite48957584at_nat @ ( labele2032268018at_nat @ ( produc1564126365at_nat @ X5 ) ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % set_of_graph_rules_def
% 0.27/0.48 thf(fact_127_set__of__graph__rules__def,axiom,
% 0.27/0.48 ( set_of1384085797_a_nat
% 0.27/0.48 = ( ^ [Rs: set_Pr1987088711_a_nat] :
% 0.27/0.48 ! [X5: produc1871334759_a_nat] :
% 0.27/0.48 ( ( member832397200_a_nat @ X5 @ Rs )
% 0.27/0.48 => ( ( graph_2130075512at_nat @ ( produc719117507_a_nat @ X5 ) @ ( produc880161797_a_nat @ X5 ) @ ( id_on_nat @ ( labele1810595089_a_nat @ ( produc719117507_a_nat @ X5 ) ) ) )
% 0.27/0.48 & ( ( produc880161797_a_nat @ X5 )
% 0.27/0.48 = ( restri572569417_a_nat @ ( produc880161797_a_nat @ X5 ) ) )
% 0.27/0.48 & ( finite_finite_nat @ ( labele1810595089_a_nat @ ( produc880161797_a_nat @ X5 ) ) )
% 0.27/0.48 & ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( produc880161797_a_nat @ X5 ) ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % set_of_graph_rules_def
% 0.27/0.48 thf(fact_128_set__of__graph__rules__def,axiom,
% 0.27/0.48 ( set_of41538795_b_nat
% 0.27/0.48 = ( ^ [Rs: set_Pr551076371_b_nat] :
% 0.27/0.48 ! [X5: produc1235635379_b_nat] :
% 0.27/0.48 ( ( member963855452_b_nat @ X5 @ Rs )
% 0.27/0.48 => ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ X5 ) @ ( produc194497945_b_nat @ X5 ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ X5 ) ) ) )
% 0.27/0.48 & ( ( produc194497945_b_nat @ X5 )
% 0.27/0.48 = ( restrict_b_nat @ ( produc194497945_b_nat @ X5 ) ) )
% 0.27/0.48 & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ X5 ) ) )
% 0.27/0.48 & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ X5 ) ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % set_of_graph_rules_def
% 0.27/0.48 thf(fact_129_mem__Collect__eq,axiom,
% 0.27/0.48 ! [A: produc1478835367term_b,P: produc1478835367term_b > $o] :
% 0.27/0.48 ( ( member516522448term_b @ A @ ( collec135640594term_b @ P ) )
% 0.27/0.48 = ( P @ A ) ) ).
% 0.27/0.48
% 0.27/0.48 % mem_Collect_eq
% 0.27/0.48 thf(fact_130_mem__Collect__eq,axiom,
% 0.27/0.48 ! [A: produc1235635379_b_nat,P: produc1235635379_b_nat > $o] :
% 0.27/0.48 ( ( member963855452_b_nat @ A @ ( collec1615000990_b_nat @ P ) )
% 0.27/0.48 = ( P @ A ) ) ).
% 0.27/0.48
% 0.27/0.48 % mem_Collect_eq
% 0.27/0.48 thf(fact_131_mem__Collect__eq,axiom,
% 0.27/0.48 ! [A: produc398057191_a_nat,P: produc398057191_a_nat > $o] :
% 0.27/0.48 ( ( member584645392_a_nat @ A @ ( collec1701899602_a_nat @ P ) )
% 0.27/0.48 = ( P @ A ) ) ).
% 0.27/0.48
% 0.27/0.48 % mem_Collect_eq
% 0.27/0.48 thf(fact_132_mem__Collect__eq,axiom,
% 0.27/0.48 ! [A: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 0.27/0.48 ( ( member701585322at_nat @ A @ ( collec7649004at_nat @ P ) )
% 0.27/0.48 = ( P @ A ) ) ).
% 0.27/0.48
% 0.27/0.48 % mem_Collect_eq
% 0.27/0.48 thf(fact_133_mem__Collect__eq,axiom,
% 0.27/0.48 ! [A: nat,P: nat > $o] :
% 0.27/0.48 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 0.27/0.48 = ( P @ A ) ) ).
% 0.27/0.48
% 0.27/0.48 % mem_Collect_eq
% 0.27/0.48 thf(fact_134_mem__Collect__eq,axiom,
% 0.27/0.48 ! [A: produc1871334759_a_nat,P: produc1871334759_a_nat > $o] :
% 0.27/0.48 ( ( member832397200_a_nat @ A @ ( collec357096914_a_nat @ P ) )
% 0.27/0.48 = ( P @ A ) ) ).
% 0.27/0.48
% 0.27/0.48 % mem_Collect_eq
% 0.27/0.48 thf(fact_135_Collect__mem__eq,axiom,
% 0.27/0.48 ! [A4: set_Pr1163220871term_b] :
% 0.27/0.48 ( ( collec135640594term_b
% 0.27/0.48 @ ^ [X5: produc1478835367term_b] : ( member516522448term_b @ X5 @ A4 ) )
% 0.27/0.48 = A4 ) ).
% 0.27/0.48
% 0.27/0.48 % Collect_mem_eq
% 0.27/0.48 thf(fact_136_Collect__mem__eq,axiom,
% 0.27/0.48 ! [A4: set_Pr551076371_b_nat] :
% 0.27/0.48 ( ( collec1615000990_b_nat
% 0.27/0.48 @ ^ [X5: produc1235635379_b_nat] : ( member963855452_b_nat @ X5 @ A4 ) )
% 0.27/0.48 = A4 ) ).
% 0.27/0.48
% 0.27/0.48 % Collect_mem_eq
% 0.27/0.48 thf(fact_137_Collect__mem__eq,axiom,
% 0.27/0.48 ! [A4: set_Pr924198087_a_nat] :
% 0.27/0.48 ( ( collec1701899602_a_nat
% 0.27/0.48 @ ^ [X5: produc398057191_a_nat] : ( member584645392_a_nat @ X5 @ A4 ) )
% 0.27/0.48 = A4 ) ).
% 0.27/0.48
% 0.27/0.48 % Collect_mem_eq
% 0.27/0.48 thf(fact_138_Collect__mem__eq,axiom,
% 0.27/0.48 ! [A4: set_Pr1986765409at_nat] :
% 0.27/0.48 ( ( collec7649004at_nat
% 0.27/0.48 @ ^ [X5: product_prod_nat_nat] : ( member701585322at_nat @ X5 @ A4 ) )
% 0.27/0.48 = A4 ) ).
% 0.27/0.48
% 0.27/0.48 % Collect_mem_eq
% 0.27/0.48 thf(fact_139_Collect__mem__eq,axiom,
% 0.27/0.48 ! [A4: set_nat] :
% 0.27/0.48 ( ( collect_nat
% 0.27/0.48 @ ^ [X5: nat] : ( member_nat @ X5 @ A4 ) )
% 0.27/0.48 = A4 ) ).
% 0.27/0.48
% 0.27/0.48 % Collect_mem_eq
% 0.27/0.48 thf(fact_140_Collect__mem__eq,axiom,
% 0.27/0.48 ! [A4: set_Pr1987088711_a_nat] :
% 0.27/0.48 ( ( collec357096914_a_nat
% 0.27/0.48 @ ^ [X5: produc1871334759_a_nat] : ( member832397200_a_nat @ X5 @ A4 ) )
% 0.27/0.48 = A4 ) ).
% 0.27/0.48
% 0.27/0.48 % Collect_mem_eq
% 0.27/0.48 thf(fact_141_Collect__cong,axiom,
% 0.27/0.48 ! [P: produc1871334759_a_nat > $o,Q2: produc1871334759_a_nat > $o] :
% 0.27/0.48 ( ! [X4: produc1871334759_a_nat] :
% 0.27/0.48 ( ( P @ X4 )
% 0.27/0.48 = ( Q2 @ X4 ) )
% 0.27/0.48 => ( ( collec357096914_a_nat @ P )
% 0.27/0.48 = ( collec357096914_a_nat @ Q2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Collect_cong
% 0.27/0.48 thf(fact_142_verts__in__translation,axiom,
% 0.27/0.48 ! [X: allego510293162tant_a] : ( inv_translation @ ( labele1810595089_a_nat @ ( transl1275713022tant_a @ X ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % verts_in_translation
% 0.27/0.48 thf(fact_143_verts__in__translation,axiom,
% 0.27/0.48 ! [X: allegorical_term_b] : ( inv_translation @ ( labele460410879_b_nat @ ( translation_b @ X ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % verts_in_translation
% 0.27/0.48 thf(fact_144_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.27/0.48 ! [P: allegorical_term_b > allegorical_term_b > $o,X3: allegorical_term_b,Y3: allegorical_term_b,A: produc1478835367term_b] :
% 0.27/0.48 ( ( P @ X3 @ Y3 )
% 0.27/0.48 => ( ( A
% 0.27/0.48 = ( produc1990145943term_b @ X3 @ Y3 ) )
% 0.27/0.48 => ( P @ ( produc854192515term_b @ A ) @ ( produc1223098053term_b @ A ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % BNF_Greatest_Fixpoint.subst_Pair
% 0.27/0.48 thf(fact_145_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.27/0.48 ! [P: labeled_graph_b_nat > labeled_graph_b_nat > $o,X3: labeled_graph_b_nat,Y3: labeled_graph_b_nat,A: produc1235635379_b_nat] :
% 0.27/0.48 ( ( P @ X3 @ Y3 )
% 0.27/0.48 => ( ( A
% 0.27/0.48 = ( produc951298923_b_nat @ X3 @ Y3 ) )
% 0.27/0.48 => ( P @ ( produc1542243159_b_nat @ A ) @ ( produc194497945_b_nat @ A ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % BNF_Greatest_Fixpoint.subst_Pair
% 0.27/0.48 thf(fact_146_conjI__realizer,axiom,
% 0.27/0.48 ! [P: allegorical_term_b > $o,P2: allegorical_term_b,Q2: allegorical_term_b > $o,Q: allegorical_term_b] :
% 0.27/0.48 ( ( P @ P2 )
% 0.27/0.48 => ( ( Q2 @ Q )
% 0.27/0.48 => ( ( P @ ( produc854192515term_b @ ( produc1990145943term_b @ P2 @ Q ) ) )
% 0.27/0.48 & ( Q2 @ ( produc1223098053term_b @ ( produc1990145943term_b @ P2 @ Q ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % conjI_realizer
% 0.27/0.48 thf(fact_147_conjI__realizer,axiom,
% 0.27/0.48 ! [P: labeled_graph_b_nat > $o,P2: labeled_graph_b_nat,Q2: labeled_graph_b_nat > $o,Q: labeled_graph_b_nat] :
% 0.27/0.48 ( ( P @ P2 )
% 0.27/0.48 => ( ( Q2 @ Q )
% 0.27/0.48 => ( ( P @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ P2 @ Q ) ) )
% 0.27/0.48 & ( Q2 @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ P2 @ Q ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % conjI_realizer
% 0.27/0.48 thf(fact_148_exI__realizer,axiom,
% 0.27/0.48 ! [P: allegorical_term_b > allegorical_term_b > $o,Y3: allegorical_term_b,X3: allegorical_term_b] :
% 0.27/0.48 ( ( P @ Y3 @ X3 )
% 0.27/0.48 => ( P @ ( produc1223098053term_b @ ( produc1990145943term_b @ X3 @ Y3 ) ) @ ( produc854192515term_b @ ( produc1990145943term_b @ X3 @ Y3 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % exI_realizer
% 0.27/0.48 thf(fact_149_exI__realizer,axiom,
% 0.27/0.48 ! [P: labeled_graph_b_nat > labeled_graph_b_nat > $o,Y3: labeled_graph_b_nat,X3: labeled_graph_b_nat] :
% 0.27/0.48 ( ( P @ Y3 @ X3 )
% 0.27/0.48 => ( P @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ X3 @ Y3 ) ) @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ X3 @ Y3 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % exI_realizer
% 0.27/0.48 thf(fact_150_allegorical__term_Oinject_I1_J,axiom,
% 0.27/0.48 ! [X11: allegorical_term_b,X12: allegorical_term_b,Y11: allegorical_term_b,Y12: allegorical_term_b] :
% 0.27/0.48 ( ( ( allegorical_A_Int_b @ X11 @ X12 )
% 0.27/0.48 = ( allegorical_A_Int_b @ Y11 @ Y12 ) )
% 0.27/0.48 = ( ( X11 = Y11 )
% 0.27/0.48 & ( X12 = Y12 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % allegorical_term.inject(1)
% 0.27/0.48 thf(fact_151_fin__maintainedI,axiom,
% 0.27/0.48 ! [R: produc1235635379_b_nat,G: labeled_graph_b_nat] :
% 0.27/0.48 ( ! [F: labeled_graph_b_nat,F2: set_Pr1986765409at_nat] :
% 0.27/0.48 ( ( ( F
% 0.27/0.48 = ( restrict_b_nat @ F ) )
% 0.27/0.48 & ( finite_finite_nat @ ( labele460410879_b_nat @ F ) )
% 0.27/0.48 & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ F ) ) )
% 0.27/0.48 => ( ( graph_529870330at_nat @ F @ ( produc1542243159_b_nat @ R ) @ ( id_on_nat @ ( labele460410879_b_nat @ F ) ) )
% 0.27/0.48 => ( ( extensible_b_nat_nat @ ( produc951298923_b_nat @ F @ ( produc1542243159_b_nat @ R ) ) @ G @ F2 )
% 0.27/0.48 => ( ( graph_529870330at_nat @ F @ G @ F2 )
% 0.27/0.48 => ( extensible_b_nat_nat @ ( produc951298923_b_nat @ F @ ( produc194497945_b_nat @ R ) ) @ G @ F2 ) ) ) ) )
% 0.27/0.48 => ( fin_ma971967913at_nat @ R @ G ) ) ).
% 0.27/0.48
% 0.27/0.48 % fin_maintainedI
% 0.27/0.48 thf(fact_152_set__of__graph__rulesD_I1_J,axiom,
% 0.27/0.48 ! [Rs2: set_Pr1987088711_a_nat,R: produc1871334759_a_nat] :
% 0.27/0.48 ( ( set_of1384085797_a_nat @ Rs2 )
% 0.27/0.48 => ( ( member832397200_a_nat @ R @ Rs2 )
% 0.27/0.48 => ( ( ( produc719117507_a_nat @ R )
% 0.27/0.48 = ( restri572569417_a_nat @ ( produc719117507_a_nat @ R ) ) )
% 0.27/0.48 & ( finite_finite_nat @ ( labele1810595089_a_nat @ ( produc719117507_a_nat @ R ) ) )
% 0.27/0.48 & ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( produc719117507_a_nat @ R ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % set_of_graph_rulesD(1)
% 0.27/0.48 thf(fact_153_set__of__graph__rulesD_I1_J,axiom,
% 0.27/0.48 ! [Rs2: set_Pr551076371_b_nat,R: produc1235635379_b_nat] :
% 0.27/0.48 ( ( set_of41538795_b_nat @ Rs2 )
% 0.27/0.48 => ( ( member963855452_b_nat @ R @ Rs2 )
% 0.27/0.48 => ( ( ( produc1542243159_b_nat @ R )
% 0.27/0.48 = ( restrict_b_nat @ ( produc1542243159_b_nat @ R ) ) )
% 0.27/0.48 & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ R ) ) )
% 0.27/0.48 & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc1542243159_b_nat @ R ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % set_of_graph_rulesD(1)
% 0.27/0.48 thf(fact_154_set__of__graph__rulesD_I2_J,axiom,
% 0.27/0.48 ! [Rs2: set_Pr1987088711_a_nat,R: produc1871334759_a_nat] :
% 0.27/0.48 ( ( set_of1384085797_a_nat @ Rs2 )
% 0.27/0.48 => ( ( member832397200_a_nat @ R @ Rs2 )
% 0.27/0.48 => ( ( ( produc880161797_a_nat @ R )
% 0.27/0.48 = ( restri572569417_a_nat @ ( produc880161797_a_nat @ R ) ) )
% 0.27/0.48 & ( finite_finite_nat @ ( labele1810595089_a_nat @ ( produc880161797_a_nat @ R ) ) )
% 0.27/0.48 & ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( produc880161797_a_nat @ R ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % set_of_graph_rulesD(2)
% 0.27/0.48 thf(fact_155_set__of__graph__rulesD_I2_J,axiom,
% 0.27/0.48 ! [Rs2: set_Pr551076371_b_nat,R: produc1235635379_b_nat] :
% 0.27/0.48 ( ( set_of41538795_b_nat @ Rs2 )
% 0.27/0.48 => ( ( member963855452_b_nat @ R @ Rs2 )
% 0.27/0.48 => ( ( ( produc194497945_b_nat @ R )
% 0.27/0.48 = ( restrict_b_nat @ ( produc194497945_b_nat @ R ) ) )
% 0.27/0.48 & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ R ) ) )
% 0.27/0.48 & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ R ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % set_of_graph_rulesD(2)
% 0.27/0.48 thf(fact_156_extensible__refl,axiom,
% 0.27/0.48 ! [R: labeled_graph_b_nat,G: labeled_graph_b_nat,F3: set_Pr1986765409at_nat] :
% 0.27/0.48 ( ( graph_529870330at_nat @ R @ G @ F3 )
% 0.27/0.48 => ( extensible_b_nat_nat @ ( produc951298923_b_nat @ R @ R ) @ G @ F3 ) ) ).
% 0.27/0.48
% 0.27/0.48 % extensible_refl
% 0.27/0.48 thf(fact_157_set__of__graph__rulesD_I3_J,axiom,
% 0.27/0.48 ! [Rs2: set_Pr1987088711_a_nat,R: produc1871334759_a_nat] :
% 0.27/0.48 ( ( set_of1384085797_a_nat @ Rs2 )
% 0.27/0.48 => ( ( member832397200_a_nat @ R @ Rs2 )
% 0.27/0.48 => ( graph_2130075512at_nat @ ( produc719117507_a_nat @ R ) @ ( produc880161797_a_nat @ R ) @ ( id_on_nat @ ( labele1810595089_a_nat @ ( produc719117507_a_nat @ R ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % set_of_graph_rulesD(3)
% 0.27/0.48 thf(fact_158_set__of__graph__rulesD_I3_J,axiom,
% 0.27/0.48 ! [Rs2: set_Pr551076371_b_nat,R: produc1235635379_b_nat] :
% 0.27/0.48 ( ( set_of41538795_b_nat @ Rs2 )
% 0.27/0.48 => ( ( member963855452_b_nat @ R @ Rs2 )
% 0.27/0.48 => ( graph_529870330at_nat @ ( produc1542243159_b_nat @ R ) @ ( produc194497945_b_nat @ R ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ R ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % set_of_graph_rulesD(3)
% 0.27/0.48 thf(fact_159_exE__realizer_H,axiom,
% 0.27/0.48 ! [P: allegorical_term_b > allegorical_term_b > $o,P2: produc1478835367term_b] :
% 0.27/0.48 ( ( P @ ( produc1223098053term_b @ P2 ) @ ( produc854192515term_b @ P2 ) )
% 0.27/0.48 => ~ ! [X4: allegorical_term_b,Y4: allegorical_term_b] :
% 0.27/0.48 ~ ( P @ Y4 @ X4 ) ) ).
% 0.27/0.48
% 0.27/0.48 % exE_realizer'
% 0.27/0.48 thf(fact_160_exE__realizer_H,axiom,
% 0.27/0.48 ! [P: labeled_graph_b_nat > labeled_graph_b_nat > $o,P2: produc1235635379_b_nat] :
% 0.27/0.48 ( ( P @ ( produc194497945_b_nat @ P2 ) @ ( produc1542243159_b_nat @ P2 ) )
% 0.27/0.48 => ~ ! [X4: labeled_graph_b_nat,Y4: labeled_graph_b_nat] :
% 0.27/0.48 ~ ( P @ Y4 @ X4 ) ) ).
% 0.27/0.48
% 0.27/0.48 % exE_realizer'
% 0.27/0.48 thf(fact_161_Id__onE,axiom,
% 0.27/0.48 ! [C2: produc398057191_a_nat,A4: set_Pr1987088711_a_nat] :
% 0.27/0.48 ( ( member584645392_a_nat @ C2 @ ( id_on_1651096324_a_nat @ A4 ) )
% 0.27/0.48 => ~ ! [X4: produc1871334759_a_nat] :
% 0.27/0.48 ( ( member832397200_a_nat @ X4 @ A4 )
% 0.27/0.48 => ( C2
% 0.27/0.48 != ( produc1677124439_a_nat @ X4 @ X4 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Id_onE
% 0.27/0.48 thf(fact_162_Id__onE,axiom,
% 0.27/0.48 ! [C2: produc1871334759_a_nat,A4: set_la1083530965_a_nat] :
% 0.27/0.48 ( ( member832397200_a_nat @ C2 @ ( id_on_689842066_a_nat @ A4 ) )
% 0.27/0.48 => ~ ! [X4: labele935650037_a_nat] :
% 0.27/0.48 ( ( member964390942_a_nat @ X4 @ A4 )
% 0.27/0.48 => ( C2
% 0.27/0.48 != ( produc1676969687_a_nat @ X4 @ X4 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Id_onE
% 0.27/0.48 thf(fact_163_Id__onE,axiom,
% 0.27/0.48 ! [C2: product_prod_nat_nat,A4: set_nat] :
% 0.27/0.48 ( ( member701585322at_nat @ C2 @ ( id_on_nat @ A4 ) )
% 0.27/0.48 => ~ ! [X4: nat] :
% 0.27/0.48 ( ( member_nat @ X4 @ A4 )
% 0.27/0.48 => ( C2
% 0.27/0.48 != ( product_Pair_nat_nat @ X4 @ X4 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Id_onE
% 0.27/0.48 thf(fact_164_Id__onE,axiom,
% 0.27/0.48 ! [C2: produc1235635379_b_nat,A4: set_la1976028319_b_nat] :
% 0.27/0.48 ( ( member963855452_b_nat @ C2 @ ( id_on_583275916_b_nat @ A4 ) )
% 0.27/0.48 => ~ ! [X4: labeled_graph_b_nat] :
% 0.27/0.48 ( ( member1483953152_b_nat @ X4 @ A4 )
% 0.27/0.48 => ( C2
% 0.27/0.48 != ( produc951298923_b_nat @ X4 @ X4 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Id_onE
% 0.27/0.48 thf(fact_165_Id__onE,axiom,
% 0.27/0.48 ! [C2: produc1478835367term_b,A4: set_al1193902458term_b] :
% 0.27/0.48 ( ( member516522448term_b @ C2 @ ( id_on_1536886967term_b @ A4 ) )
% 0.27/0.48 => ~ ! [X4: allegorical_term_b] :
% 0.27/0.48 ( ( member93680451term_b @ X4 @ A4 )
% 0.27/0.48 => ( C2
% 0.27/0.48 != ( produc1990145943term_b @ X4 @ X4 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Id_onE
% 0.27/0.48 thf(fact_166_Id__on__eqI,axiom,
% 0.27/0.48 ! [A: labele935650037_a_nat,B: labele935650037_a_nat,A4: set_la1083530965_a_nat] :
% 0.27/0.48 ( ( A = B )
% 0.27/0.48 => ( ( member964390942_a_nat @ A @ A4 )
% 0.27/0.48 => ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B ) @ ( id_on_689842066_a_nat @ A4 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Id_on_eqI
% 0.27/0.48 thf(fact_167_Id__on__eqI,axiom,
% 0.27/0.48 ! [A: produc1871334759_a_nat,B: produc1871334759_a_nat,A4: set_Pr1987088711_a_nat] :
% 0.27/0.48 ( ( A = B )
% 0.27/0.48 => ( ( member832397200_a_nat @ A @ A4 )
% 0.27/0.48 => ( member584645392_a_nat @ ( produc1677124439_a_nat @ A @ B ) @ ( id_on_1651096324_a_nat @ A4 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Id_on_eqI
% 0.27/0.48 thf(fact_168_Id__on__eqI,axiom,
% 0.27/0.48 ! [A: nat,B: nat,A4: set_nat] :
% 0.27/0.48 ( ( A = B )
% 0.27/0.48 => ( ( member_nat @ A @ A4 )
% 0.27/0.48 => ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( id_on_nat @ A4 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Id_on_eqI
% 0.27/0.48 thf(fact_169_Id__on__eqI,axiom,
% 0.27/0.48 ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,A4: set_la1976028319_b_nat] :
% 0.27/0.48 ( ( A = B )
% 0.27/0.48 => ( ( member1483953152_b_nat @ A @ A4 )
% 0.27/0.48 => ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B ) @ ( id_on_583275916_b_nat @ A4 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Id_on_eqI
% 0.27/0.48 thf(fact_170_Id__on__eqI,axiom,
% 0.27/0.48 ! [A: allegorical_term_b,B: allegorical_term_b,A4: set_al1193902458term_b] :
% 0.27/0.48 ( ( A = B )
% 0.27/0.48 => ( ( member93680451term_b @ A @ A4 )
% 0.27/0.48 => ( member516522448term_b @ ( produc1990145943term_b @ A @ B ) @ ( id_on_1536886967term_b @ A4 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Id_on_eqI
% 0.27/0.48 thf(fact_171_Id__on__iff,axiom,
% 0.27/0.48 ! [X3: produc1871334759_a_nat,Y3: produc1871334759_a_nat,A4: set_Pr1987088711_a_nat] :
% 0.27/0.48 ( ( member584645392_a_nat @ ( produc1677124439_a_nat @ X3 @ Y3 ) @ ( id_on_1651096324_a_nat @ A4 ) )
% 0.27/0.48 = ( ( X3 = Y3 )
% 0.27/0.48 & ( member832397200_a_nat @ X3 @ A4 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Id_on_iff
% 0.27/0.48 thf(fact_172_Id__on__iff,axiom,
% 0.27/0.48 ! [X3: labele935650037_a_nat,Y3: labele935650037_a_nat,A4: set_la1083530965_a_nat] :
% 0.27/0.48 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ X3 @ Y3 ) @ ( id_on_689842066_a_nat @ A4 ) )
% 0.27/0.48 = ( ( X3 = Y3 )
% 0.27/0.48 & ( member964390942_a_nat @ X3 @ A4 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Id_on_iff
% 0.27/0.48 thf(fact_173_Id__on__iff,axiom,
% 0.27/0.48 ! [X3: nat,Y3: nat,A4: set_nat] :
% 0.27/0.48 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ ( id_on_nat @ A4 ) )
% 0.27/0.48 = ( ( X3 = Y3 )
% 0.27/0.48 & ( member_nat @ X3 @ A4 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Id_on_iff
% 0.27/0.48 thf(fact_174_Id__on__iff,axiom,
% 0.27/0.48 ! [X3: labeled_graph_b_nat,Y3: labeled_graph_b_nat,A4: set_la1976028319_b_nat] :
% 0.27/0.48 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ X3 @ Y3 ) @ ( id_on_583275916_b_nat @ A4 ) )
% 0.27/0.48 = ( ( X3 = Y3 )
% 0.27/0.48 & ( member1483953152_b_nat @ X3 @ A4 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Id_on_iff
% 0.27/0.48 thf(fact_175_Id__on__iff,axiom,
% 0.27/0.48 ! [X3: allegorical_term_b,Y3: allegorical_term_b,A4: set_al1193902458term_b] :
% 0.27/0.48 ( ( member516522448term_b @ ( produc1990145943term_b @ X3 @ Y3 ) @ ( id_on_1536886967term_b @ A4 ) )
% 0.27/0.48 = ( ( X3 = Y3 )
% 0.27/0.48 & ( member93680451term_b @ X3 @ A4 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Id_on_iff
% 0.27/0.48 thf(fact_176_fin__maintained__def,axiom,
% 0.27/0.48 ( fin_ma971967913at_nat
% 0.27/0.48 = ( ^ [R2: produc1235635379_b_nat,G2: labeled_graph_b_nat] :
% 0.27/0.48 ! [F4: labeled_graph_b_nat,F5: set_Pr1986765409at_nat] :
% 0.27/0.48 ( ( ( F4
% 0.27/0.48 = ( restrict_b_nat @ F4 ) )
% 0.27/0.48 & ( finite_finite_nat @ ( labele460410879_b_nat @ F4 ) )
% 0.27/0.48 & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ F4 ) ) )
% 0.27/0.48 => ( ( graph_529870330at_nat @ F4 @ ( produc1542243159_b_nat @ R2 ) @ ( id_on_nat @ ( labele460410879_b_nat @ F4 ) ) )
% 0.27/0.48 => ( ( extensible_b_nat_nat @ ( produc951298923_b_nat @ F4 @ ( produc1542243159_b_nat @ R2 ) ) @ G2 @ F5 )
% 0.27/0.48 => ( ( graph_529870330at_nat @ F4 @ G2 @ F5 )
% 0.27/0.48 => ( extensible_b_nat_nat @ ( produc951298923_b_nat @ F4 @ ( produc194497945_b_nat @ R2 ) ) @ G2 @ F5 ) ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % fin_maintained_def
% 0.27/0.48 thf(fact_177_fair__chainD_I2_J,axiom,
% 0.27/0.48 ! [Rs2: set_Pr551076371_b_nat,S2: nat > labeled_graph_b_nat,R: produc1235635379_b_nat,I: nat,F3: set_Pr1986765409at_nat] :
% 0.27/0.48 ( ( fair_chain_b_nat_nat @ Rs2 @ S2 )
% 0.27/0.48 => ( ( member963855452_b_nat @ R @ Rs2 )
% 0.27/0.48 => ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ R ) @ ( S2 @ I ) @ F3 )
% 0.27/0.48 => ? [J: nat] : ( extensible_b_nat_nat @ R @ ( S2 @ J ) @ F3 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % fair_chainD(2)
% 0.27/0.48 thf(fact_178_identity__rules__graph__rule,axiom,
% 0.27/0.48 ! [X3: produc1871334759_a_nat,L: set_St761939237tant_a] :
% 0.27/0.48 ( ( member832397200_a_nat @ X3 @ ( standa1568205540ules_a @ L ) )
% 0.27/0.48 => ( ( graph_2130075512at_nat @ ( produc719117507_a_nat @ X3 ) @ ( produc880161797_a_nat @ X3 ) @ ( id_on_nat @ ( labele1810595089_a_nat @ ( produc719117507_a_nat @ X3 ) ) ) )
% 0.27/0.48 & ( ( produc880161797_a_nat @ X3 )
% 0.27/0.48 = ( restri572569417_a_nat @ ( produc880161797_a_nat @ X3 ) ) )
% 0.27/0.48 & ( finite_finite_nat @ ( labele1810595089_a_nat @ ( produc880161797_a_nat @ X3 ) ) )
% 0.27/0.48 & ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( produc880161797_a_nat @ X3 ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % identity_rules_graph_rule
% 0.27/0.48 thf(fact_179_maintainedI,axiom,
% 0.27/0.48 ! [A4: labeled_graph_b_nat,G: labeled_graph_b_nat,B4: labeled_graph_b_nat] :
% 0.27/0.48 ( ! [F2: set_Pr1986765409at_nat] :
% 0.27/0.48 ( ( graph_529870330at_nat @ A4 @ G @ F2 )
% 0.27/0.48 => ( extensible_b_nat_nat @ ( produc951298923_b_nat @ A4 @ B4 ) @ G @ F2 ) )
% 0.27/0.48 => ( maintained_b_nat_nat @ ( produc951298923_b_nat @ A4 @ B4 ) @ G ) ) ).
% 0.27/0.48
% 0.27/0.48 % maintainedI
% 0.27/0.48 thf(fact_180_sndI,axiom,
% 0.27/0.48 ! [X3: produc1478835367term_b,Y3: allegorical_term_b,Z2: allegorical_term_b] :
% 0.27/0.48 ( ( X3
% 0.27/0.48 = ( produc1990145943term_b @ Y3 @ Z2 ) )
% 0.27/0.48 => ( ( produc1223098053term_b @ X3 )
% 0.27/0.48 = Z2 ) ) ).
% 0.27/0.48
% 0.27/0.48 % sndI
% 0.27/0.48 thf(fact_181_sndI,axiom,
% 0.27/0.48 ! [X3: produc1235635379_b_nat,Y3: labeled_graph_b_nat,Z2: labeled_graph_b_nat] :
% 0.27/0.48 ( ( X3
% 0.27/0.48 = ( produc951298923_b_nat @ Y3 @ Z2 ) )
% 0.27/0.48 => ( ( produc194497945_b_nat @ X3 )
% 0.27/0.48 = Z2 ) ) ).
% 0.27/0.48
% 0.27/0.48 % sndI
% 0.27/0.48 thf(fact_182_consequence__graphI,axiom,
% 0.27/0.48 ! [Rs2: set_Pr551076371_b_nat,G: labeled_graph_b_nat] :
% 0.27/0.48 ( ! [R3: produc1235635379_b_nat] :
% 0.27/0.48 ( ( member963855452_b_nat @ R3 @ Rs2 )
% 0.27/0.48 => ( maintained_b_nat_nat @ R3 @ G ) )
% 0.27/0.48 => ( ! [R3: produc1235635379_b_nat] :
% 0.27/0.48 ( ( member963855452_b_nat @ R3 @ Rs2 )
% 0.27/0.48 => ( graph_529870330at_nat @ ( produc1542243159_b_nat @ R3 ) @ ( produc194497945_b_nat @ R3 ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ R3 ) ) ) ) )
% 0.27/0.48 => ( ( G
% 0.27/0.48 = ( restrict_b_nat @ G ) )
% 0.27/0.48 => ( conseq1730780375at_nat @ Rs2 @ G ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % consequence_graphI
% 0.27/0.48 thf(fact_183_consequence__graph__def,axiom,
% 0.27/0.48 ( conseq1730780375at_nat
% 0.27/0.48 = ( ^ [Rs: set_Pr551076371_b_nat,G2: labeled_graph_b_nat] :
% 0.27/0.48 ( ( G2
% 0.27/0.48 = ( restrict_b_nat @ G2 ) )
% 0.27/0.48 & ! [X5: produc1235635379_b_nat] :
% 0.27/0.48 ( ( member963855452_b_nat @ X5 @ Rs )
% 0.27/0.48 => ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ X5 ) @ ( produc194497945_b_nat @ X5 ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ X5 ) ) ) )
% 0.27/0.48 & ( maintained_b_nat_nat @ X5 @ G2 ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % consequence_graph_def
% 0.27/0.48 thf(fact_184_maintained__def,axiom,
% 0.27/0.48 ( maintained_b_nat_nat
% 0.27/0.48 = ( ^ [R2: produc1235635379_b_nat,G2: labeled_graph_b_nat] :
% 0.27/0.48 ! [F5: set_Pr1986765409at_nat] :
% 0.27/0.48 ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ R2 ) @ G2 @ F5 )
% 0.27/0.48 => ( extensible_b_nat_nat @ R2 @ G2 @ F5 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % maintained_def
% 0.27/0.48 thf(fact_185_maintainedD,axiom,
% 0.27/0.48 ! [A4: labeled_graph_b_nat,B4: labeled_graph_b_nat,G: labeled_graph_b_nat,F3: set_Pr1986765409at_nat] :
% 0.27/0.48 ( ( maintained_b_nat_nat @ ( produc951298923_b_nat @ A4 @ B4 ) @ G )
% 0.27/0.48 => ( ( graph_529870330at_nat @ A4 @ G @ F3 )
% 0.27/0.48 => ( extensible_b_nat_nat @ ( produc951298923_b_nat @ A4 @ B4 ) @ G @ F3 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % maintainedD
% 0.27/0.48 thf(fact_186_fstI,axiom,
% 0.27/0.48 ! [X3: produc1235635379_b_nat,Y3: labeled_graph_b_nat,Z2: labeled_graph_b_nat] :
% 0.27/0.48 ( ( X3
% 0.27/0.48 = ( produc951298923_b_nat @ Y3 @ Z2 ) )
% 0.27/0.48 => ( ( produc1542243159_b_nat @ X3 )
% 0.27/0.48 = Y3 ) ) ).
% 0.27/0.48
% 0.27/0.48 % fstI
% 0.27/0.48 thf(fact_187_fstI,axiom,
% 0.27/0.48 ! [X3: produc1478835367term_b,Y3: allegorical_term_b,Z2: allegorical_term_b] :
% 0.27/0.48 ( ( X3
% 0.27/0.48 = ( produc1990145943term_b @ Y3 @ Z2 ) )
% 0.27/0.48 => ( ( produc854192515term_b @ X3 )
% 0.27/0.48 = Y3 ) ) ).
% 0.27/0.48
% 0.27/0.48 % fstI
% 0.27/0.48 thf(fact_188_fair__chainI,axiom,
% 0.27/0.48 ! [S2: nat > labeled_graph_b_nat,Rs2: set_Pr551076371_b_nat] :
% 0.27/0.48 ( ( chain_b_nat @ S2 )
% 0.27/0.48 => ( ! [R3: produc1235635379_b_nat,F2: set_Pr1986765409at_nat,I2: nat] :
% 0.27/0.48 ( ( member963855452_b_nat @ R3 @ Rs2 )
% 0.27/0.48 => ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ R3 ) @ ( S2 @ I2 ) @ F2 )
% 0.27/0.48 => ? [J2: nat] : ( extensible_b_nat_nat @ R3 @ ( S2 @ J2 ) @ F2 ) ) )
% 0.27/0.48 => ( fair_chain_b_nat_nat @ Rs2 @ S2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % fair_chainI
% 0.27/0.48 thf(fact_189_maintained__holds__iff,axiom,
% 0.27/0.48 ! [G: labeled_graph_b_nat,E_L: allegorical_term_b,E_R: allegorical_term_b] :
% 0.27/0.48 ( ( G
% 0.27/0.48 = ( restrict_b_nat @ G ) )
% 0.27/0.48 => ( ( maintained_b_nat_nat @ ( produc951298923_b_nat @ ( translation_b @ E_L ) @ ( translation_b @ ( allegorical_A_Int_b @ E_L @ E_R ) ) ) @ G )
% 0.27/0.48 = ( ( semantics_b_nat @ G @ ( produc854192515term_b @ ( produc1990145943term_b @ E_L @ ( allegorical_A_Int_b @ E_L @ E_R ) ) ) )
% 0.27/0.48 = ( semantics_b_nat @ G @ ( produc1223098053term_b @ ( produc1990145943term_b @ E_L @ ( allegorical_A_Int_b @ E_L @ E_R ) ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % maintained_holds_iff
% 0.27/0.48 thf(fact_190_fair__chain__def,axiom,
% 0.27/0.48 ( fair_chain_b_nat_nat
% 0.27/0.48 = ( ^ [Rs: set_Pr551076371_b_nat,S3: nat > labeled_graph_b_nat] :
% 0.27/0.48 ( ( chain_b_nat @ S3 )
% 0.27/0.48 & ! [R2: produc1235635379_b_nat,F5: set_Pr1986765409at_nat,I3: nat] :
% 0.27/0.48 ( ( ( member963855452_b_nat @ R2 @ Rs )
% 0.27/0.48 & ( graph_529870330at_nat @ ( produc1542243159_b_nat @ R2 ) @ ( S3 @ I3 ) @ F5 ) )
% 0.27/0.48 => ? [J3: nat] : ( extensible_b_nat_nat @ R2 @ ( S3 @ J3 ) @ F5 ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % fair_chain_def
% 0.27/0.48 thf(fact_191_chain__sup__graph,axiom,
% 0.27/0.48 ! [S2: nat > labeled_graph_b_nat] :
% 0.27/0.48 ( ( chain_b_nat @ S2 )
% 0.27/0.48 => ( ( chain_sup_b_nat @ S2 )
% 0.27/0.48 = ( restrict_b_nat @ ( chain_sup_b_nat @ S2 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % chain_sup_graph
% 0.27/0.48 thf(fact_192_chain__sup__subgraph,axiom,
% 0.27/0.48 ! [S2: nat > labeled_graph_b_nat,J4: nat] :
% 0.27/0.48 ( ( chain_b_nat @ S2 )
% 0.27/0.48 => ( graph_529870330at_nat @ ( S2 @ J4 ) @ ( chain_sup_b_nat @ S2 ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( S2 @ J4 ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % chain_sup_subgraph
% 0.27/0.48 thf(fact_193_chain__then__restrict,axiom,
% 0.27/0.48 ! [S2: nat > labeled_graph_b_nat,I: nat] :
% 0.27/0.48 ( ( chain_b_nat @ S2 )
% 0.27/0.48 => ( ( S2 @ I )
% 0.27/0.48 = ( restrict_b_nat @ ( S2 @ I ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % chain_then_restrict
% 0.27/0.48 thf(fact_194_graph__homomorphism__semantics,axiom,
% 0.27/0.48 ! [A4: labeled_graph_b_nat,B4: labeled_graph_b_nat,F3: set_Pr1986765409at_nat,A: nat,B: nat,E: allegorical_term_b,A2: nat,B2: nat] :
% 0.27/0.48 ( ( graph_529870330at_nat @ A4 @ B4 @ F3 )
% 0.27/0.48 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( semantics_b_nat @ A4 @ E ) )
% 0.27/0.48 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ A2 ) @ F3 )
% 0.27/0.48 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ B @ B2 ) @ F3 )
% 0.27/0.48 => ( member701585322at_nat @ ( product_Pair_nat_nat @ A2 @ B2 ) @ ( semantics_b_nat @ B4 @ E ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % graph_homomorphism_semantics
% 0.27/0.48 thf(fact_195_semantics__in__vertices_I2_J,axiom,
% 0.27/0.48 ! [A4: labeled_graph_b_nat,A: nat,B: nat,E: allegorical_term_b] :
% 0.27/0.48 ( ( A4
% 0.27/0.48 = ( restrict_b_nat @ A4 ) )
% 0.27/0.48 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( semantics_b_nat @ A4 @ E ) )
% 0.27/0.48 => ( member_nat @ B @ ( labele460410879_b_nat @ A4 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % semantics_in_vertices(2)
% 0.27/0.48 thf(fact_196_semantics__in__vertices_I1_J,axiom,
% 0.27/0.48 ! [A4: labeled_graph_b_nat,A: nat,B: nat,E: allegorical_term_b] :
% 0.27/0.48 ( ( A4
% 0.27/0.48 = ( restrict_b_nat @ A4 ) )
% 0.27/0.48 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( semantics_b_nat @ A4 @ E ) )
% 0.27/0.48 => ( member_nat @ A @ ( labele460410879_b_nat @ A4 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % semantics_in_vertices(1)
% 0.27/0.48 thf(fact_197_subgraph__semantics,axiom,
% 0.27/0.48 ! [A4: labeled_graph_b_nat,B4: labeled_graph_b_nat,A: nat,B: nat,E: allegorical_term_b] :
% 0.27/0.48 ( ( graph_529870330at_nat @ A4 @ B4 @ ( id_on_nat @ ( labele460410879_b_nat @ A4 ) ) )
% 0.27/0.48 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( semantics_b_nat @ A4 @ E ) )
% 0.27/0.48 => ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( semantics_b_nat @ B4 @ E ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % subgraph_semantics
% 0.27/0.48 thf(fact_198_maintained__holds__subset__iff,axiom,
% 0.27/0.48 ! [G: labeled_graph_b_nat,E_L: allegorical_term_b,E_R: allegorical_term_b] :
% 0.27/0.48 ( ( G
% 0.27/0.48 = ( restrict_b_nat @ G ) )
% 0.27/0.48 => ( ( maintained_b_nat_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ E_L @ ( allegorical_A_Int_b @ E_L @ E_R ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ E_L @ ( allegorical_A_Int_b @ E_L @ E_R ) ) ) ) ) @ G )
% 0.27/0.48 = ( ord_le841296385at_nat @ ( semantics_b_nat @ G @ E_L ) @ ( semantics_b_nat @ G @ E_R ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % maintained_holds_subset_iff
% 0.27/0.48 thf(fact_199_find__graph__occurence,axiom,
% 0.27/0.48 ! [S2: nat > labeled_graph_b_nat,E2: set_Pr9961929at_nat,V: set_nat,F3: set_Pr1986765409at_nat] :
% 0.27/0.48 ( ( chain_b_nat @ S2 )
% 0.27/0.48 => ( ( finite1987068434at_nat @ E2 )
% 0.27/0.48 => ( ( finite_finite_nat @ V )
% 0.27/0.48 => ( ( graph_529870330at_nat @ ( labeled_LG_b_nat @ E2 @ V ) @ ( chain_sup_b_nat @ S2 ) @ F3 )
% 0.27/0.48 => ? [I2: nat] : ( graph_529870330at_nat @ ( labeled_LG_b_nat @ E2 @ V ) @ ( S2 @ I2 ) @ F3 ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % find_graph_occurence
% 0.27/0.48 thf(fact_200_eq__snd__iff,axiom,
% 0.27/0.48 ! [B: allegorical_term_b,P2: produc1478835367term_b] :
% 0.27/0.48 ( ( B
% 0.27/0.48 = ( produc1223098053term_b @ P2 ) )
% 0.27/0.48 = ( ? [A5: allegorical_term_b] :
% 0.27/0.48 ( P2
% 0.27/0.48 = ( produc1990145943term_b @ A5 @ B ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % eq_snd_iff
% 0.27/0.48 thf(fact_201_eq__snd__iff,axiom,
% 0.27/0.48 ! [B: labeled_graph_b_nat,P2: produc1235635379_b_nat] :
% 0.27/0.48 ( ( B
% 0.27/0.48 = ( produc194497945_b_nat @ P2 ) )
% 0.27/0.48 = ( ? [A5: labeled_graph_b_nat] :
% 0.27/0.48 ( P2
% 0.27/0.48 = ( produc951298923_b_nat @ A5 @ B ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % eq_snd_iff
% 0.27/0.48 thf(fact_202_eq__fst__iff,axiom,
% 0.27/0.48 ! [A: labeled_graph_b_nat,P2: produc1235635379_b_nat] :
% 0.27/0.48 ( ( A
% 0.27/0.48 = ( produc1542243159_b_nat @ P2 ) )
% 0.27/0.48 = ( ? [B5: labeled_graph_b_nat] :
% 0.27/0.48 ( P2
% 0.27/0.48 = ( produc951298923_b_nat @ A @ B5 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % eq_fst_iff
% 0.27/0.48 thf(fact_203_eq__fst__iff,axiom,
% 0.27/0.48 ! [A: allegorical_term_b,P2: produc1478835367term_b] :
% 0.27/0.48 ( ( A
% 0.27/0.48 = ( produc854192515term_b @ P2 ) )
% 0.27/0.48 = ( ? [B5: allegorical_term_b] :
% 0.27/0.48 ( P2
% 0.27/0.48 = ( produc1990145943term_b @ A @ B5 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % eq_fst_iff
% 0.27/0.48 thf(fact_204_labeled__graph_Ocollapse,axiom,
% 0.27/0.48 ! [Labeled_graph: labeled_graph_b_nat] :
% 0.27/0.48 ( ( labeled_LG_b_nat @ ( labeled_edges_b_nat @ Labeled_graph ) @ ( labele460410879_b_nat @ Labeled_graph ) )
% 0.27/0.48 = Labeled_graph ) ).
% 0.27/0.48
% 0.27/0.48 % labeled_graph.collapse
% 0.27/0.48 thf(fact_205_extensible__refl__concr,axiom,
% 0.27/0.48 ! [E_1: set_Pr9961929at_nat,V2: set_nat,G: labeled_graph_b_nat,F3: set_Pr1986765409at_nat,E_2: set_Pr9961929at_nat] :
% 0.27/0.48 ( ( graph_529870330at_nat @ ( labeled_LG_b_nat @ E_1 @ V2 ) @ G @ F3 )
% 0.27/0.48 => ( ( extensible_b_nat_nat @ ( produc951298923_b_nat @ ( labeled_LG_b_nat @ E_1 @ V2 ) @ ( labeled_LG_b_nat @ E_2 @ V2 ) ) @ G @ F3 )
% 0.27/0.48 = ( graph_529870330at_nat @ ( labeled_LG_b_nat @ E_2 @ V2 ) @ G @ F3 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % extensible_refl_concr
% 0.27/0.48 thf(fact_206_subrelI,axiom,
% 0.27/0.48 ! [R4: set_Pr1987088711_a_nat,S4: set_Pr1987088711_a_nat] :
% 0.27/0.48 ( ! [X4: labele935650037_a_nat,Y4: labele935650037_a_nat] :
% 0.27/0.48 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ X4 @ Y4 ) @ R4 )
% 0.27/0.48 => ( member832397200_a_nat @ ( produc1676969687_a_nat @ X4 @ Y4 ) @ S4 ) )
% 0.27/0.48 => ( ord_le1718765799_a_nat @ R4 @ S4 ) ) ).
% 0.27/0.48
% 0.27/0.48 % subrelI
% 0.27/0.48 thf(fact_207_subrelI,axiom,
% 0.27/0.48 ! [R4: set_Pr551076371_b_nat,S4: set_Pr551076371_b_nat] :
% 0.27/0.48 ( ! [X4: labeled_graph_b_nat,Y4: labeled_graph_b_nat] :
% 0.27/0.48 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ X4 @ Y4 ) @ R4 )
% 0.27/0.48 => ( member963855452_b_nat @ ( produc951298923_b_nat @ X4 @ Y4 ) @ S4 ) )
% 0.27/0.48 => ( ord_le13035955_b_nat @ R4 @ S4 ) ) ).
% 0.27/0.48
% 0.27/0.48 % subrelI
% 0.27/0.48 thf(fact_208_subrelI,axiom,
% 0.27/0.48 ! [R4: set_Pr1163220871term_b,S4: set_Pr1163220871term_b] :
% 0.27/0.48 ( ! [X4: allegorical_term_b,Y4: allegorical_term_b] :
% 0.27/0.48 ( ( member516522448term_b @ ( produc1990145943term_b @ X4 @ Y4 ) @ R4 )
% 0.27/0.48 => ( member516522448term_b @ ( produc1990145943term_b @ X4 @ Y4 ) @ S4 ) )
% 0.27/0.48 => ( ord_le138473255term_b @ R4 @ S4 ) ) ).
% 0.27/0.48
% 0.27/0.48 % subrelI
% 0.27/0.48 thf(fact_209_finite__has__maximal2,axiom,
% 0.27/0.48 ! [A4: set_nat,A: nat] :
% 0.27/0.48 ( ( finite_finite_nat @ A4 )
% 0.27/0.48 => ( ( member_nat @ A @ A4 )
% 0.27/0.48 => ? [X4: nat] :
% 0.27/0.48 ( ( member_nat @ X4 @ A4 )
% 0.27/0.48 & ( ord_less_eq_nat @ A @ X4 )
% 0.27/0.48 & ! [Xa: nat] :
% 0.27/0.48 ( ( member_nat @ Xa @ A4 )
% 0.27/0.48 => ( ( ord_less_eq_nat @ X4 @ Xa )
% 0.27/0.48 => ( X4 = Xa ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % finite_has_maximal2
% 0.27/0.48 thf(fact_210_finite__has__minimal2,axiom,
% 0.27/0.48 ! [A4: set_nat,A: nat] :
% 0.27/0.48 ( ( finite_finite_nat @ A4 )
% 0.27/0.48 => ( ( member_nat @ A @ A4 )
% 0.27/0.48 => ? [X4: nat] :
% 0.27/0.48 ( ( member_nat @ X4 @ A4 )
% 0.27/0.48 & ( ord_less_eq_nat @ X4 @ A )
% 0.27/0.48 & ! [Xa: nat] :
% 0.27/0.48 ( ( member_nat @ Xa @ A4 )
% 0.27/0.48 => ( ( ord_less_eq_nat @ Xa @ X4 )
% 0.27/0.48 => ( X4 = Xa ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % finite_has_minimal2
% 0.27/0.48 thf(fact_211_finite__subset,axiom,
% 0.27/0.48 ! [A4: set_nat,B4: set_nat] :
% 0.27/0.48 ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 0.27/0.48 => ( ( finite_finite_nat @ B4 )
% 0.27/0.48 => ( finite_finite_nat @ A4 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % finite_subset
% 0.27/0.48 thf(fact_212_finite__subset,axiom,
% 0.27/0.48 ! [A4: set_Pr9961929at_nat,B4: set_Pr9961929at_nat] :
% 0.27/0.48 ( ( ord_le910748009at_nat @ A4 @ B4 )
% 0.27/0.48 => ( ( finite1987068434at_nat @ B4 )
% 0.27/0.48 => ( finite1987068434at_nat @ A4 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % finite_subset
% 0.27/0.48 thf(fact_213_infinite__super,axiom,
% 0.27/0.48 ! [S2: set_nat,T3: set_nat] :
% 0.27/0.48 ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 0.27/0.48 => ( ~ ( finite_finite_nat @ S2 )
% 0.27/0.48 => ~ ( finite_finite_nat @ T3 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % infinite_super
% 0.27/0.48 thf(fact_214_infinite__super,axiom,
% 0.27/0.48 ! [S2: set_Pr9961929at_nat,T3: set_Pr9961929at_nat] :
% 0.27/0.48 ( ( ord_le910748009at_nat @ S2 @ T3 )
% 0.27/0.48 => ( ~ ( finite1987068434at_nat @ S2 )
% 0.27/0.48 => ~ ( finite1987068434at_nat @ T3 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % infinite_super
% 0.27/0.48 thf(fact_215_rev__finite__subset,axiom,
% 0.27/0.48 ! [B4: set_nat,A4: set_nat] :
% 0.27/0.48 ( ( finite_finite_nat @ B4 )
% 0.27/0.48 => ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 0.27/0.48 => ( finite_finite_nat @ A4 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % rev_finite_subset
% 0.27/0.48 thf(fact_216_rev__finite__subset,axiom,
% 0.27/0.48 ! [B4: set_Pr9961929at_nat,A4: set_Pr9961929at_nat] :
% 0.27/0.48 ( ( finite1987068434at_nat @ B4 )
% 0.27/0.48 => ( ( ord_le910748009at_nat @ A4 @ B4 )
% 0.27/0.48 => ( finite1987068434at_nat @ A4 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % rev_finite_subset
% 0.27/0.48 thf(fact_217_labeled__graph_Osel_I2_J,axiom,
% 0.27/0.48 ! [X1: set_Pr9961929at_nat,X22: set_nat] :
% 0.27/0.48 ( ( labele460410879_b_nat @ ( labeled_LG_b_nat @ X1 @ X22 ) )
% 0.27/0.48 = X22 ) ).
% 0.27/0.48
% 0.27/0.48 % labeled_graph.sel(2)
% 0.27/0.48 thf(fact_218_labeled__graph_Osel_I1_J,axiom,
% 0.27/0.48 ! [X1: set_Pr9961929at_nat,X22: set_nat] :
% 0.27/0.48 ( ( labeled_edges_b_nat @ ( labeled_LG_b_nat @ X1 @ X22 ) )
% 0.27/0.48 = X1 ) ).
% 0.27/0.48
% 0.27/0.48 % labeled_graph.sel(1)
% 0.27/0.48 thf(fact_219_restrict__subsD,axiom,
% 0.27/0.48 ! [G: labeled_graph_b_nat] :
% 0.27/0.48 ( ( ord_le910748009at_nat @ ( labeled_edges_b_nat @ G ) @ ( labeled_edges_b_nat @ ( restrict_b_nat @ G ) ) )
% 0.27/0.48 => ( G
% 0.27/0.48 = ( restrict_b_nat @ G ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % restrict_subsD
% 0.27/0.48 thf(fact_220_subgraph__def2,axiom,
% 0.27/0.48 ! [G_1: labeled_graph_b_nat,G_2: labeled_graph_b_nat] :
% 0.27/0.48 ( ( G_1
% 0.27/0.48 = ( restrict_b_nat @ G_1 ) )
% 0.27/0.48 => ( ( G_2
% 0.27/0.48 = ( restrict_b_nat @ G_2 ) )
% 0.27/0.48 => ( ( graph_529870330at_nat @ G_1 @ G_2 @ ( id_on_nat @ ( labele460410879_b_nat @ G_1 ) ) )
% 0.27/0.48 = ( ( ord_less_eq_set_nat @ ( labele460410879_b_nat @ G_1 ) @ ( labele460410879_b_nat @ G_2 ) )
% 0.27/0.48 & ( ord_le910748009at_nat @ ( labeled_edges_b_nat @ G_1 ) @ ( labeled_edges_b_nat @ G_2 ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % subgraph_def2
% 0.27/0.48 thf(fact_221_labeled__graph_Oexhaust__sel,axiom,
% 0.27/0.48 ! [Labeled_graph: labeled_graph_b_nat] :
% 0.27/0.48 ( Labeled_graph
% 0.27/0.48 = ( labeled_LG_b_nat @ ( labeled_edges_b_nat @ Labeled_graph ) @ ( labele460410879_b_nat @ Labeled_graph ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % labeled_graph.exhaust_sel
% 0.27/0.48 thf(fact_222_subgraph__subset_I1_J,axiom,
% 0.27/0.48 ! [G_1: labeled_graph_b_nat,G_2: labeled_graph_b_nat] :
% 0.27/0.48 ( ( graph_529870330at_nat @ G_1 @ G_2 @ ( id_on_nat @ ( labele460410879_b_nat @ G_1 ) ) )
% 0.27/0.48 => ( ord_less_eq_set_nat @ ( labele460410879_b_nat @ G_1 ) @ ( labele460410879_b_nat @ G_2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % subgraph_subset(1)
% 0.27/0.48 thf(fact_223_maintainedD2,axiom,
% 0.27/0.48 ! [A4: labeled_graph_b_nat,B4: labeled_graph_b_nat,G: labeled_graph_b_nat,F3: set_Pr1986765409at_nat] :
% 0.27/0.48 ( ( maintained_b_nat_nat @ ( produc951298923_b_nat @ A4 @ B4 ) @ G )
% 0.27/0.48 => ( ( graph_529870330at_nat @ A4 @ G @ F3 )
% 0.27/0.48 => ~ ! [G3: set_Pr1986765409at_nat] :
% 0.27/0.48 ( ( graph_529870330at_nat @ B4 @ G @ G3 )
% 0.27/0.48 => ~ ( ord_le841296385at_nat @ F3 @ G3 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % maintainedD2
% 0.27/0.48 thf(fact_224_subgraph__subset_I2_J,axiom,
% 0.27/0.48 ! [G_1: labeled_graph_b_nat,G_2: labeled_graph_b_nat] :
% 0.27/0.48 ( ( graph_529870330at_nat @ G_1 @ G_2 @ ( id_on_nat @ ( labele460410879_b_nat @ G_1 ) ) )
% 0.27/0.48 => ( ord_le910748009at_nat @ ( labeled_edges_b_nat @ ( restrict_b_nat @ G_1 ) ) @ ( labeled_edges_b_nat @ G_2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % subgraph_subset(2)
% 0.27/0.48 thf(fact_225_subsetI,axiom,
% 0.27/0.48 ! [A4: set_Pr1987088711_a_nat,B4: set_Pr1987088711_a_nat] :
% 0.27/0.48 ( ! [X4: produc1871334759_a_nat] :
% 0.27/0.48 ( ( member832397200_a_nat @ X4 @ A4 )
% 0.27/0.48 => ( member832397200_a_nat @ X4 @ B4 ) )
% 0.27/0.48 => ( ord_le1718765799_a_nat @ A4 @ B4 ) ) ).
% 0.27/0.48
% 0.27/0.48 % subsetI
% 0.27/0.48 thf(fact_226_order__refl,axiom,
% 0.27/0.48 ! [X3: nat] : ( ord_less_eq_nat @ X3 @ X3 ) ).
% 0.27/0.48
% 0.27/0.48 % order_refl
% 0.27/0.48 thf(fact_227_dual__order_Oantisym,axiom,
% 0.27/0.48 ! [B: nat,A: nat] :
% 0.27/0.48 ( ( ord_less_eq_nat @ B @ A )
% 0.27/0.48 => ( ( ord_less_eq_nat @ A @ B )
% 0.27/0.48 => ( A = B ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % dual_order.antisym
% 0.27/0.48 thf(fact_228_dual__order_Oeq__iff,axiom,
% 0.27/0.48 ( ( ^ [Y5: nat,Z: nat] : ( Y5 = Z ) )
% 0.27/0.48 = ( ^ [A5: nat,B5: nat] :
% 0.27/0.48 ( ( ord_less_eq_nat @ B5 @ A5 )
% 0.27/0.48 & ( ord_less_eq_nat @ A5 @ B5 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % dual_order.eq_iff
% 0.27/0.48 thf(fact_229_dual__order_Otrans,axiom,
% 0.27/0.48 ! [B: nat,A: nat,C2: nat] :
% 0.27/0.48 ( ( ord_less_eq_nat @ B @ A )
% 0.27/0.48 => ( ( ord_less_eq_nat @ C2 @ B )
% 0.27/0.48 => ( ord_less_eq_nat @ C2 @ A ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % dual_order.trans
% 0.27/0.48 thf(fact_230_linorder__wlog,axiom,
% 0.27/0.48 ! [P: nat > nat > $o,A: nat,B: nat] :
% 0.27/0.48 ( ! [A3: nat,B3: nat] :
% 0.27/0.48 ( ( ord_less_eq_nat @ A3 @ B3 )
% 0.27/0.48 => ( P @ A3 @ B3 ) )
% 0.27/0.48 => ( ! [A3: nat,B3: nat] :
% 0.27/0.48 ( ( P @ B3 @ A3 )
% 0.27/0.48 => ( P @ A3 @ B3 ) )
% 0.27/0.48 => ( P @ A @ B ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % linorder_wlog
% 0.27/0.48 thf(fact_231_dual__order_Orefl,axiom,
% 0.27/0.48 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 0.27/0.48
% 0.27/0.48 % dual_order.refl
% 0.27/0.48 thf(fact_232_order__trans,axiom,
% 0.27/0.48 ! [X3: nat,Y3: nat,Z2: nat] :
% 0.27/0.48 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.27/0.48 => ( ( ord_less_eq_nat @ Y3 @ Z2 )
% 0.27/0.48 => ( ord_less_eq_nat @ X3 @ Z2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % order_trans
% 0.27/0.48 thf(fact_233_order__class_Oorder_Oantisym,axiom,
% 0.27/0.48 ! [A: nat,B: nat] :
% 0.27/0.48 ( ( ord_less_eq_nat @ A @ B )
% 0.27/0.48 => ( ( ord_less_eq_nat @ B @ A )
% 0.27/0.48 => ( A = B ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % order_class.order.antisym
% 0.27/0.48 thf(fact_234_ord__le__eq__trans,axiom,
% 0.27/0.48 ! [A: nat,B: nat,C2: nat] :
% 0.27/0.48 ( ( ord_less_eq_nat @ A @ B )
% 0.27/0.48 => ( ( B = C2 )
% 0.27/0.48 => ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % ord_le_eq_trans
% 0.27/0.48 thf(fact_235_ord__eq__le__trans,axiom,
% 0.27/0.48 ! [A: nat,B: nat,C2: nat] :
% 0.27/0.48 ( ( A = B )
% 0.27/0.48 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.27/0.48 => ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % ord_eq_le_trans
% 0.27/0.48 thf(fact_236_order__class_Oorder_Oeq__iff,axiom,
% 0.27/0.48 ( ( ^ [Y5: nat,Z: nat] : ( Y5 = Z ) )
% 0.27/0.48 = ( ^ [A5: nat,B5: nat] :
% 0.27/0.48 ( ( ord_less_eq_nat @ A5 @ B5 )
% 0.27/0.48 & ( ord_less_eq_nat @ B5 @ A5 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % order_class.order.eq_iff
% 0.27/0.48 thf(fact_237_antisym__conv,axiom,
% 0.27/0.48 ! [Y3: nat,X3: nat] :
% 0.27/0.48 ( ( ord_less_eq_nat @ Y3 @ X3 )
% 0.27/0.48 => ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.27/0.48 = ( X3 = Y3 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % antisym_conv
% 0.27/0.48 thf(fact_238_le__cases3,axiom,
% 0.27/0.48 ! [X3: nat,Y3: nat,Z2: nat] :
% 0.27/0.48 ( ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.27/0.48 => ~ ( ord_less_eq_nat @ Y3 @ Z2 ) )
% 0.27/0.48 => ( ( ( ord_less_eq_nat @ Y3 @ X3 )
% 0.27/0.48 => ~ ( ord_less_eq_nat @ X3 @ Z2 ) )
% 0.27/0.48 => ( ( ( ord_less_eq_nat @ X3 @ Z2 )
% 0.27/0.48 => ~ ( ord_less_eq_nat @ Z2 @ Y3 ) )
% 0.27/0.48 => ( ( ( ord_less_eq_nat @ Z2 @ Y3 )
% 0.27/0.48 => ~ ( ord_less_eq_nat @ Y3 @ X3 ) )
% 0.27/0.48 => ( ( ( ord_less_eq_nat @ Y3 @ Z2 )
% 0.27/0.48 => ~ ( ord_less_eq_nat @ Z2 @ X3 ) )
% 0.27/0.48 => ~ ( ( ord_less_eq_nat @ Z2 @ X3 )
% 0.27/0.48 => ~ ( ord_less_eq_nat @ X3 @ Y3 ) ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % le_cases3
% 0.27/0.48 thf(fact_239_order_Otrans,axiom,
% 0.27/0.48 ! [A: nat,B: nat,C2: nat] :
% 0.27/0.48 ( ( ord_less_eq_nat @ A @ B )
% 0.27/0.48 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.27/0.48 => ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % order.trans
% 0.27/0.48 thf(fact_240_le__cases,axiom,
% 0.27/0.48 ! [X3: nat,Y3: nat] :
% 0.27/0.48 ( ~ ( ord_less_eq_nat @ X3 @ Y3 )
% 0.27/0.48 => ( ord_less_eq_nat @ Y3 @ X3 ) ) ).
% 0.27/0.48
% 0.27/0.48 % le_cases
% 0.27/0.48 thf(fact_241_eq__refl,axiom,
% 0.27/0.48 ! [X3: nat,Y3: nat] :
% 0.27/0.48 ( ( X3 = Y3 )
% 0.27/0.48 => ( ord_less_eq_nat @ X3 @ Y3 ) ) ).
% 0.27/0.48
% 0.27/0.48 % eq_refl
% 0.27/0.48 thf(fact_242_linear,axiom,
% 0.27/0.48 ! [X3: nat,Y3: nat] :
% 0.27/0.48 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.27/0.48 | ( ord_less_eq_nat @ Y3 @ X3 ) ) ).
% 0.27/0.48
% 0.27/0.48 % linear
% 0.27/0.48 thf(fact_243_antisym,axiom,
% 0.27/0.48 ! [X3: nat,Y3: nat] :
% 0.27/0.48 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.27/0.48 => ( ( ord_less_eq_nat @ Y3 @ X3 )
% 0.27/0.48 => ( X3 = Y3 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % antisym
% 0.27/0.48 thf(fact_244_eq__iff,axiom,
% 0.27/0.48 ( ( ^ [Y5: nat,Z: nat] : ( Y5 = Z ) )
% 0.27/0.48 = ( ^ [X5: nat,Y6: nat] :
% 0.27/0.48 ( ( ord_less_eq_nat @ X5 @ Y6 )
% 0.27/0.48 & ( ord_less_eq_nat @ Y6 @ X5 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % eq_iff
% 0.27/0.48 thf(fact_245_ord__le__eq__subst,axiom,
% 0.27/0.48 ! [A: nat,B: nat,F3: nat > nat,C2: nat] :
% 0.27/0.48 ( ( ord_less_eq_nat @ A @ B )
% 0.27/0.48 => ( ( ( F3 @ B )
% 0.27/0.48 = C2 )
% 0.27/0.48 => ( ! [X4: nat,Y4: nat] :
% 0.27/0.48 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 0.27/0.48 => ( ord_less_eq_nat @ ( F3 @ X4 ) @ ( F3 @ Y4 ) ) )
% 0.27/0.48 => ( ord_less_eq_nat @ ( F3 @ A ) @ C2 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % ord_le_eq_subst
% 0.27/0.48 thf(fact_246_ord__eq__le__subst,axiom,
% 0.27/0.48 ! [A: nat,F3: nat > nat,B: nat,C2: nat] :
% 0.27/0.48 ( ( A
% 0.27/0.48 = ( F3 @ B ) )
% 0.27/0.48 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.27/0.48 => ( ! [X4: nat,Y4: nat] :
% 0.27/0.48 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 0.27/0.48 => ( ord_less_eq_nat @ ( F3 @ X4 ) @ ( F3 @ Y4 ) ) )
% 0.27/0.48 => ( ord_less_eq_nat @ A @ ( F3 @ C2 ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % ord_eq_le_subst
% 0.27/0.48 thf(fact_247_order__subst2,axiom,
% 0.27/0.48 ! [A: nat,B: nat,F3: nat > nat,C2: nat] :
% 0.27/0.48 ( ( ord_less_eq_nat @ A @ B )
% 0.27/0.48 => ( ( ord_less_eq_nat @ ( F3 @ B ) @ C2 )
% 0.27/0.48 => ( ! [X4: nat,Y4: nat] :
% 0.27/0.48 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 0.27/0.48 => ( ord_less_eq_nat @ ( F3 @ X4 ) @ ( F3 @ Y4 ) ) )
% 0.27/0.48 => ( ord_less_eq_nat @ ( F3 @ A ) @ C2 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % order_subst2
% 0.27/0.48 thf(fact_248_order__subst1,axiom,
% 0.27/0.48 ! [A: nat,F3: nat > nat,B: nat,C2: nat] :
% 0.27/0.48 ( ( ord_less_eq_nat @ A @ ( F3 @ B ) )
% 0.27/0.48 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.27/0.48 => ( ! [X4: nat,Y4: nat] :
% 0.27/0.48 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 0.27/0.48 => ( ord_less_eq_nat @ ( F3 @ X4 ) @ ( F3 @ Y4 ) ) )
% 0.27/0.48 => ( ord_less_eq_nat @ A @ ( F3 @ C2 ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % order_subst1
% 0.27/0.48 thf(fact_249_subset__iff,axiom,
% 0.27/0.48 ( ord_le1718765799_a_nat
% 0.27/0.48 = ( ^ [A6: set_Pr1987088711_a_nat,B6: set_Pr1987088711_a_nat] :
% 0.27/0.48 ! [T2: produc1871334759_a_nat] :
% 0.27/0.48 ( ( member832397200_a_nat @ T2 @ A6 )
% 0.27/0.48 => ( member832397200_a_nat @ T2 @ B6 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % subset_iff
% 0.27/0.48 thf(fact_250_subset__eq,axiom,
% 0.27/0.48 ( ord_le1718765799_a_nat
% 0.27/0.48 = ( ^ [A6: set_Pr1987088711_a_nat,B6: set_Pr1987088711_a_nat] :
% 0.27/0.48 ! [X5: produc1871334759_a_nat] :
% 0.27/0.48 ( ( member832397200_a_nat @ X5 @ A6 )
% 0.27/0.48 => ( member832397200_a_nat @ X5 @ B6 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % subset_eq
% 0.27/0.48 thf(fact_251_subsetD,axiom,
% 0.27/0.48 ! [A4: set_Pr1987088711_a_nat,B4: set_Pr1987088711_a_nat,C2: produc1871334759_a_nat] :
% 0.27/0.48 ( ( ord_le1718765799_a_nat @ A4 @ B4 )
% 0.27/0.48 => ( ( member832397200_a_nat @ C2 @ A4 )
% 0.27/0.48 => ( member832397200_a_nat @ C2 @ B4 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % subsetD
% 0.27/0.48 thf(fact_252_in__mono,axiom,
% 0.27/0.48 ! [A4: set_Pr1987088711_a_nat,B4: set_Pr1987088711_a_nat,X3: produc1871334759_a_nat] :
% 0.27/0.48 ( ( ord_le1718765799_a_nat @ A4 @ B4 )
% 0.27/0.48 => ( ( member832397200_a_nat @ X3 @ A4 )
% 0.27/0.48 => ( member832397200_a_nat @ X3 @ B4 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % in_mono
% 0.27/0.48 thf(fact_253_chain,axiom,
% 0.27/0.48 ! [S2: nat > labeled_graph_b_nat,I: nat,J4: nat] :
% 0.27/0.48 ( ( chain_b_nat @ S2 )
% 0.27/0.48 => ( ( ord_less_eq_nat @ I @ J4 )
% 0.27/0.48 => ( graph_529870330at_nat @ ( S2 @ I ) @ ( S2 @ J4 ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( S2 @ I ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % chain
% 0.27/0.48 thf(fact_254_chain__def2,axiom,
% 0.27/0.48 ( chain_b_nat
% 0.27/0.48 = ( ^ [S3: nat > labeled_graph_b_nat] :
% 0.27/0.48 ! [I3: nat,J3: nat] :
% 0.27/0.48 ( ( ord_less_eq_nat @ I3 @ J3 )
% 0.27/0.48 => ( graph_529870330at_nat @ ( S3 @ I3 ) @ ( S3 @ J3 ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( S3 @ I3 ) ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % chain_def2
% 0.27/0.48 thf(fact_255_graph__unionI,axiom,
% 0.27/0.48 ! [G_1: labeled_graph_b_nat,G_2: labeled_graph_b_nat] :
% 0.27/0.48 ( ( ord_le910748009at_nat @ ( labeled_edges_b_nat @ G_1 ) @ ( labeled_edges_b_nat @ G_2 ) )
% 0.27/0.48 => ( ( ord_less_eq_set_nat @ ( labele460410879_b_nat @ G_1 ) @ ( labele460410879_b_nat @ G_2 ) )
% 0.27/0.48 => ( ( graph_union_b_nat @ G_1 @ G_2 )
% 0.27/0.48 = G_2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % graph_unionI
% 0.27/0.48 thf(fact_256_extensibleD,axiom,
% 0.27/0.48 ! [R: produc1235635379_b_nat,G: labeled_graph_b_nat,F3: set_Pr1986765409at_nat] :
% 0.27/0.48 ( ( extensible_b_nat_nat @ R @ G @ F3 )
% 0.27/0.48 => ~ ! [G3: set_Pr1986765409at_nat] :
% 0.27/0.48 ( ( graph_529870330at_nat @ ( produc194497945_b_nat @ R ) @ G @ G3 )
% 0.27/0.48 => ~ ( agree_on_b_nat_nat @ ( produc1542243159_b_nat @ R ) @ F3 @ G3 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % extensibleD
% 0.27/0.48 thf(fact_257_extensible__def,axiom,
% 0.27/0.48 ( extensible_b_nat_nat
% 0.27/0.48 = ( ^ [R2: produc1235635379_b_nat,G2: labeled_graph_b_nat,F5: set_Pr1986765409at_nat] :
% 0.27/0.48 ? [G4: set_Pr1986765409at_nat] :
% 0.27/0.48 ( ( graph_529870330at_nat @ ( produc194497945_b_nat @ R2 ) @ G2 @ G4 )
% 0.27/0.48 & ( agree_on_b_nat_nat @ ( produc1542243159_b_nat @ R2 ) @ F5 @ G4 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % extensible_def
% 0.27/0.48 thf(fact_258_extensibleI,axiom,
% 0.27/0.48 ! [R22: labeled_graph_b_nat,G: labeled_graph_b_nat,G5: set_Pr1986765409at_nat,R1: labeled_graph_b_nat,F3: set_Pr1986765409at_nat] :
% 0.27/0.48 ( ( graph_529870330at_nat @ R22 @ G @ G5 )
% 0.27/0.48 => ( ( agree_on_b_nat_nat @ R1 @ F3 @ G5 )
% 0.27/0.48 => ( extensible_b_nat_nat @ ( produc951298923_b_nat @ R1 @ R22 ) @ G @ F3 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % extensibleI
% 0.27/0.48 thf(fact_259_graph__union__preserves__restrict,axiom,
% 0.27/0.48 ! [G_1: labeled_graph_b_nat,G_2: labeled_graph_b_nat] :
% 0.27/0.48 ( ( G_1
% 0.27/0.48 = ( restrict_b_nat @ G_1 ) )
% 0.27/0.48 => ( ( G_2
% 0.27/0.48 = ( restrict_b_nat @ G_2 ) )
% 0.27/0.48 => ( ( graph_union_b_nat @ G_1 @ G_2 )
% 0.27/0.48 = ( restrict_b_nat @ ( graph_union_b_nat @ G_1 @ G_2 ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % graph_union_preserves_restrict
% 0.27/0.48 thf(fact_260_subgraph__def,axiom,
% 0.27/0.48 ! [G_1: labeled_graph_b_nat,G_2: labeled_graph_b_nat] :
% 0.27/0.48 ( ( graph_529870330at_nat @ G_1 @ G_2 @ ( id_on_nat @ ( labele460410879_b_nat @ G_1 ) ) )
% 0.27/0.48 = ( ( G_1
% 0.27/0.48 = ( restrict_b_nat @ G_1 ) )
% 0.27/0.48 & ( G_2
% 0.27/0.48 = ( restrict_b_nat @ G_2 ) )
% 0.27/0.48 & ( ( graph_union_b_nat @ G_1 @ G_2 )
% 0.27/0.48 = G_2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % subgraph_def
% 0.27/0.48 thf(fact_261_graph__union__iff,axiom,
% 0.27/0.48 ! [G_1: labeled_graph_b_nat,G_2: labeled_graph_b_nat] :
% 0.27/0.48 ( ( ( graph_union_b_nat @ G_1 @ G_2 )
% 0.27/0.48 = G_2 )
% 0.27/0.48 = ( ( ord_le910748009at_nat @ ( labeled_edges_b_nat @ G_1 ) @ ( labeled_edges_b_nat @ G_2 ) )
% 0.27/0.48 & ( ord_less_eq_set_nat @ ( labele460410879_b_nat @ G_1 ) @ ( labele460410879_b_nat @ G_2 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % graph_union_iff
% 0.27/0.48 thf(fact_262_finite__nat__set__iff__bounded__le,axiom,
% 0.27/0.48 ( finite_finite_nat
% 0.27/0.48 = ( ^ [N: set_nat] :
% 0.27/0.48 ? [M: nat] :
% 0.27/0.48 ! [X5: nat] :
% 0.27/0.48 ( ( member_nat @ X5 @ N )
% 0.27/0.48 => ( ord_less_eq_nat @ X5 @ M ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % finite_nat_set_iff_bounded_le
% 0.27/0.48 thf(fact_263_nonempty__rule,axiom,
% 0.27/0.48 ! [G: labeled_graph_b_nat] :
% 0.27/0.48 ( ( G
% 0.27/0.48 = ( restrict_b_nat @ G ) )
% 0.27/0.48 => ( ( maintained_b_nat_nat @ standa879863266rule_b @ G )
% 0.27/0.48 = ( ( labele460410879_b_nat @ G )
% 0.27/0.48 != bot_bot_set_nat ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % nonempty_rule
% 0.27/0.48 thf(fact_264_weak__universalI,axiom,
% 0.27/0.48 ! [R: produc1235635379_b_nat,G_1: labeled_graph_b_nat,F_1: set_Pr1986765409at_nat,G_2: labeled_graph_b_nat,T: itself_nat,F_2: set_Pr1986765409at_nat] :
% 0.27/0.48 ( ! [H_1: set_Pr1986765409at_nat,H_2: set_Pr1986765409at_nat,G6: labeled_graph_b_nat] :
% 0.27/0.48 ( ( graph_529870330at_nat @ ( produc194497945_b_nat @ R ) @ G6 @ H_1 )
% 0.27/0.48 => ( ( graph_529870330at_nat @ G_1 @ G6 @ H_2 )
% 0.27/0.48 => ( ( ord_le841296385at_nat @ ( relcomp_nat_nat_nat @ F_1 @ H_2 ) @ H_1 )
% 0.27/0.48 => ? [H2: set_Pr1986765409at_nat] :
% 0.27/0.48 ( ( graph_529870330at_nat @ G_2 @ G6 @ H2 )
% 0.27/0.48 & ( ord_le841296385at_nat @ H_2 @ H2 ) ) ) ) )
% 0.27/0.48 => ( weak_u2026406106at_nat @ T @ R @ G_1 @ G_2 @ F_1 @ F_2 ) ) ).
% 0.27/0.48
% 0.27/0.48 % weak_universalI
% 0.27/0.48 thf(fact_265_Id__on__empty,axiom,
% 0.27/0.48 ( ( id_on_nat @ bot_bot_set_nat )
% 0.27/0.48 = bot_bo2130386637at_nat ) ).
% 0.27/0.48
% 0.27/0.48 % Id_on_empty
% 0.27/0.48 thf(fact_266_graph__homomorphism__composes,axiom,
% 0.27/0.48 ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,X3: set_Pr1986765409at_nat,C2: labeled_graph_b_nat,Y3: set_Pr1986765409at_nat] :
% 0.27/0.48 ( ( graph_529870330at_nat @ A @ B @ X3 )
% 0.27/0.48 => ( ( graph_529870330at_nat @ B @ C2 @ Y3 )
% 0.27/0.48 => ( graph_529870330at_nat @ A @ C2 @ ( relcomp_nat_nat_nat @ X3 @ Y3 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % graph_homomorphism_composes
% 0.27/0.48 thf(fact_267_graph__empty__e,axiom,
% 0.27/0.48 ! [V2: set_nat] :
% 0.27/0.48 ( ( labeled_LG_b_nat @ bot_bo1626616373at_nat @ V2 )
% 0.27/0.48 = ( restrict_b_nat @ ( labeled_LG_b_nat @ bot_bo1626616373at_nat @ V2 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % graph_empty_e
% 0.27/0.48 thf(fact_268_graph__homomorphism__empty,axiom,
% 0.27/0.48 ! [G: labeled_graph_b_nat,F3: set_Pr1986765409at_nat] :
% 0.27/0.48 ( ( graph_529870330at_nat @ ( labeled_LG_b_nat @ bot_bo1626616373at_nat @ bot_bot_set_nat ) @ G @ F3 )
% 0.27/0.48 = ( ( F3 = bot_bo2130386637at_nat )
% 0.27/0.48 & ( G
% 0.27/0.48 = ( restrict_b_nat @ G ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % graph_homomorphism_empty
% 0.27/0.48 thf(fact_269_bot_Oextremum,axiom,
% 0.27/0.48 ! [A: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A ) ).
% 0.27/0.48
% 0.27/0.48 % bot.extremum
% 0.27/0.48 thf(fact_270_bot_Oextremum__unique,axiom,
% 0.27/0.48 ! [A: nat] :
% 0.27/0.48 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 0.27/0.48 = ( A = bot_bot_nat ) ) ).
% 0.27/0.48
% 0.27/0.48 % bot.extremum_unique
% 0.27/0.48 thf(fact_271_bot_Oextremum__uniqueI,axiom,
% 0.27/0.48 ! [A: nat] :
% 0.27/0.48 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 0.27/0.48 => ( A = bot_bot_nat ) ) ).
% 0.27/0.48
% 0.27/0.48 % bot.extremum_uniqueI
% 0.27/0.48 thf(fact_272_relcomp_OrelcompI,axiom,
% 0.27/0.48 ! [A: labele935650037_a_nat,B: labele935650037_a_nat,R4: set_Pr1987088711_a_nat,C2: labele935650037_a_nat,S4: set_Pr1987088711_a_nat] :
% 0.27/0.48 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B ) @ R4 )
% 0.27/0.48 => ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ B @ C2 ) @ S4 )
% 0.27/0.48 => ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ C2 ) @ ( relcom1338300020_a_nat @ R4 @ S4 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % relcomp.relcompI
% 0.27/0.48 thf(fact_273_relcomp_OrelcompI,axiom,
% 0.27/0.48 ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,R4: set_Pr551076371_b_nat,C2: labeled_graph_b_nat,S4: set_Pr551076371_b_nat] :
% 0.27/0.48 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B ) @ R4 )
% 0.27/0.48 => ( ( member963855452_b_nat @ ( produc951298923_b_nat @ B @ C2 ) @ S4 )
% 0.27/0.48 => ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ C2 ) @ ( relcom1426860350_b_nat @ R4 @ S4 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % relcomp.relcompI
% 0.27/0.48 thf(fact_274_relcomp_OrelcompI,axiom,
% 0.27/0.48 ! [A: allegorical_term_b,B: allegorical_term_b,R4: set_Pr1163220871term_b,C2: allegorical_term_b,S4: set_Pr1163220871term_b] :
% 0.27/0.48 ( ( member516522448term_b @ ( produc1990145943term_b @ A @ B ) @ R4 )
% 0.27/0.48 => ( ( member516522448term_b @ ( produc1990145943term_b @ B @ C2 ) @ S4 )
% 0.27/0.48 => ( member516522448term_b @ ( produc1990145943term_b @ A @ C2 ) @ ( relcom1955155673term_b @ R4 @ S4 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % relcomp.relcompI
% 0.27/0.48 thf(fact_275_relcomp_Oinducts,axiom,
% 0.27/0.48 ! [X1: labele935650037_a_nat,X22: labele935650037_a_nat,R4: set_Pr1987088711_a_nat,S4: set_Pr1987088711_a_nat,P: labele935650037_a_nat > labele935650037_a_nat > $o] :
% 0.27/0.48 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ X1 @ X22 ) @ ( relcom1338300020_a_nat @ R4 @ S4 ) )
% 0.27/0.48 => ( ! [A3: labele935650037_a_nat,B3: labele935650037_a_nat,C: labele935650037_a_nat] :
% 0.27/0.48 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A3 @ B3 ) @ R4 )
% 0.27/0.48 => ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ B3 @ C ) @ S4 )
% 0.27/0.48 => ( P @ A3 @ C ) ) )
% 0.27/0.48 => ( P @ X1 @ X22 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % relcomp.inducts
% 0.27/0.48 thf(fact_276_relcomp_Oinducts,axiom,
% 0.27/0.48 ! [X1: labeled_graph_b_nat,X22: labeled_graph_b_nat,R4: set_Pr551076371_b_nat,S4: set_Pr551076371_b_nat,P: labeled_graph_b_nat > labeled_graph_b_nat > $o] :
% 0.27/0.48 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ X1 @ X22 ) @ ( relcom1426860350_b_nat @ R4 @ S4 ) )
% 0.27/0.48 => ( ! [A3: labeled_graph_b_nat,B3: labeled_graph_b_nat,C: labeled_graph_b_nat] :
% 0.27/0.48 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A3 @ B3 ) @ R4 )
% 0.27/0.48 => ( ( member963855452_b_nat @ ( produc951298923_b_nat @ B3 @ C ) @ S4 )
% 0.27/0.48 => ( P @ A3 @ C ) ) )
% 0.27/0.48 => ( P @ X1 @ X22 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % relcomp.inducts
% 0.27/0.48 thf(fact_277_relcomp_Oinducts,axiom,
% 0.27/0.48 ! [X1: allegorical_term_b,X22: allegorical_term_b,R4: set_Pr1163220871term_b,S4: set_Pr1163220871term_b,P: allegorical_term_b > allegorical_term_b > $o] :
% 0.27/0.48 ( ( member516522448term_b @ ( produc1990145943term_b @ X1 @ X22 ) @ ( relcom1955155673term_b @ R4 @ S4 ) )
% 0.27/0.48 => ( ! [A3: allegorical_term_b,B3: allegorical_term_b,C: allegorical_term_b] :
% 0.27/0.48 ( ( member516522448term_b @ ( produc1990145943term_b @ A3 @ B3 ) @ R4 )
% 0.27/0.48 => ( ( member516522448term_b @ ( produc1990145943term_b @ B3 @ C ) @ S4 )
% 0.27/0.48 => ( P @ A3 @ C ) ) )
% 0.27/0.48 => ( P @ X1 @ X22 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % relcomp.inducts
% 0.27/0.48 thf(fact_278_relcomp_Osimps,axiom,
% 0.27/0.48 ! [A1: labele935650037_a_nat,A22: labele935650037_a_nat,R4: set_Pr1987088711_a_nat,S4: set_Pr1987088711_a_nat] :
% 0.27/0.48 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A1 @ A22 ) @ ( relcom1338300020_a_nat @ R4 @ S4 ) )
% 0.27/0.48 = ( ? [A5: labele935650037_a_nat,B5: labele935650037_a_nat,C3: labele935650037_a_nat] :
% 0.27/0.48 ( ( A1 = A5 )
% 0.27/0.48 & ( A22 = C3 )
% 0.27/0.48 & ( member832397200_a_nat @ ( produc1676969687_a_nat @ A5 @ B5 ) @ R4 )
% 0.27/0.48 & ( member832397200_a_nat @ ( produc1676969687_a_nat @ B5 @ C3 ) @ S4 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % relcomp.simps
% 0.27/0.48 thf(fact_279_relcomp_Osimps,axiom,
% 0.27/0.48 ! [A1: labeled_graph_b_nat,A22: labeled_graph_b_nat,R4: set_Pr551076371_b_nat,S4: set_Pr551076371_b_nat] :
% 0.27/0.48 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A1 @ A22 ) @ ( relcom1426860350_b_nat @ R4 @ S4 ) )
% 0.27/0.48 = ( ? [A5: labeled_graph_b_nat,B5: labeled_graph_b_nat,C3: labeled_graph_b_nat] :
% 0.27/0.48 ( ( A1 = A5 )
% 0.27/0.48 & ( A22 = C3 )
% 0.27/0.48 & ( member963855452_b_nat @ ( produc951298923_b_nat @ A5 @ B5 ) @ R4 )
% 0.27/0.48 & ( member963855452_b_nat @ ( produc951298923_b_nat @ B5 @ C3 ) @ S4 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % relcomp.simps
% 0.27/0.48 thf(fact_280_relcomp_Osimps,axiom,
% 0.27/0.48 ! [A1: allegorical_term_b,A22: allegorical_term_b,R4: set_Pr1163220871term_b,S4: set_Pr1163220871term_b] :
% 0.27/0.48 ( ( member516522448term_b @ ( produc1990145943term_b @ A1 @ A22 ) @ ( relcom1955155673term_b @ R4 @ S4 ) )
% 0.27/0.48 = ( ? [A5: allegorical_term_b,B5: allegorical_term_b,C3: allegorical_term_b] :
% 0.27/0.48 ( ( A1 = A5 )
% 0.27/0.48 & ( A22 = C3 )
% 0.27/0.48 & ( member516522448term_b @ ( produc1990145943term_b @ A5 @ B5 ) @ R4 )
% 0.27/0.48 & ( member516522448term_b @ ( produc1990145943term_b @ B5 @ C3 ) @ S4 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % relcomp.simps
% 0.27/0.48 thf(fact_281_relcomp_Ocases,axiom,
% 0.27/0.48 ! [A1: labele935650037_a_nat,A22: labele935650037_a_nat,R4: set_Pr1987088711_a_nat,S4: set_Pr1987088711_a_nat] :
% 0.27/0.48 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A1 @ A22 ) @ ( relcom1338300020_a_nat @ R4 @ S4 ) )
% 0.27/0.48 => ~ ! [B3: labele935650037_a_nat] :
% 0.27/0.48 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A1 @ B3 ) @ R4 )
% 0.27/0.48 => ~ ( member832397200_a_nat @ ( produc1676969687_a_nat @ B3 @ A22 ) @ S4 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % relcomp.cases
% 0.27/0.48 thf(fact_282_relcomp_Ocases,axiom,
% 0.27/0.48 ! [A1: labeled_graph_b_nat,A22: labeled_graph_b_nat,R4: set_Pr551076371_b_nat,S4: set_Pr551076371_b_nat] :
% 0.27/0.48 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A1 @ A22 ) @ ( relcom1426860350_b_nat @ R4 @ S4 ) )
% 0.27/0.48 => ~ ! [B3: labeled_graph_b_nat] :
% 0.27/0.48 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A1 @ B3 ) @ R4 )
% 0.27/0.48 => ~ ( member963855452_b_nat @ ( produc951298923_b_nat @ B3 @ A22 ) @ S4 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % relcomp.cases
% 0.27/0.48 thf(fact_283_relcomp_Ocases,axiom,
% 0.27/0.48 ! [A1: allegorical_term_b,A22: allegorical_term_b,R4: set_Pr1163220871term_b,S4: set_Pr1163220871term_b] :
% 0.27/0.48 ( ( member516522448term_b @ ( produc1990145943term_b @ A1 @ A22 ) @ ( relcom1955155673term_b @ R4 @ S4 ) )
% 0.27/0.48 => ~ ! [B3: allegorical_term_b] :
% 0.27/0.48 ( ( member516522448term_b @ ( produc1990145943term_b @ A1 @ B3 ) @ R4 )
% 0.27/0.48 => ~ ( member516522448term_b @ ( produc1990145943term_b @ B3 @ A22 ) @ S4 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % relcomp.cases
% 0.27/0.48 thf(fact_284_relcompEpair,axiom,
% 0.27/0.48 ! [A: labele935650037_a_nat,C2: labele935650037_a_nat,R4: set_Pr1987088711_a_nat,S4: set_Pr1987088711_a_nat] :
% 0.27/0.48 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ C2 ) @ ( relcom1338300020_a_nat @ R4 @ S4 ) )
% 0.27/0.48 => ~ ! [B3: labele935650037_a_nat] :
% 0.27/0.48 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B3 ) @ R4 )
% 0.27/0.48 => ~ ( member832397200_a_nat @ ( produc1676969687_a_nat @ B3 @ C2 ) @ S4 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % relcompEpair
% 0.27/0.48 thf(fact_285_relcompEpair,axiom,
% 0.27/0.48 ! [A: labeled_graph_b_nat,C2: labeled_graph_b_nat,R4: set_Pr551076371_b_nat,S4: set_Pr551076371_b_nat] :
% 0.27/0.48 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ C2 ) @ ( relcom1426860350_b_nat @ R4 @ S4 ) )
% 0.27/0.48 => ~ ! [B3: labeled_graph_b_nat] :
% 0.27/0.48 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B3 ) @ R4 )
% 0.27/0.48 => ~ ( member963855452_b_nat @ ( produc951298923_b_nat @ B3 @ C2 ) @ S4 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % relcompEpair
% 0.27/0.48 thf(fact_286_relcompEpair,axiom,
% 0.27/0.48 ! [A: allegorical_term_b,C2: allegorical_term_b,R4: set_Pr1163220871term_b,S4: set_Pr1163220871term_b] :
% 0.27/0.48 ( ( member516522448term_b @ ( produc1990145943term_b @ A @ C2 ) @ ( relcom1955155673term_b @ R4 @ S4 ) )
% 0.27/0.48 => ~ ! [B3: allegorical_term_b] :
% 0.27/0.48 ( ( member516522448term_b @ ( produc1990145943term_b @ A @ B3 ) @ R4 )
% 0.27/0.48 => ~ ( member516522448term_b @ ( produc1990145943term_b @ B3 @ C2 ) @ S4 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % relcompEpair
% 0.27/0.48 thf(fact_287_relcompE,axiom,
% 0.27/0.48 ! [Xz: produc1871334759_a_nat,R4: set_Pr1987088711_a_nat,S4: set_Pr1987088711_a_nat] :
% 0.27/0.48 ( ( member832397200_a_nat @ Xz @ ( relcom1338300020_a_nat @ R4 @ S4 ) )
% 0.27/0.48 => ~ ! [X4: labele935650037_a_nat,Y4: labele935650037_a_nat,Z3: labele935650037_a_nat] :
% 0.27/0.48 ( ( Xz
% 0.27/0.48 = ( produc1676969687_a_nat @ X4 @ Z3 ) )
% 0.27/0.48 => ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ X4 @ Y4 ) @ R4 )
% 0.27/0.48 => ~ ( member832397200_a_nat @ ( produc1676969687_a_nat @ Y4 @ Z3 ) @ S4 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % relcompE
% 0.27/0.48 thf(fact_288_relcompE,axiom,
% 0.27/0.48 ! [Xz: produc1235635379_b_nat,R4: set_Pr551076371_b_nat,S4: set_Pr551076371_b_nat] :
% 0.27/0.48 ( ( member963855452_b_nat @ Xz @ ( relcom1426860350_b_nat @ R4 @ S4 ) )
% 0.27/0.48 => ~ ! [X4: labeled_graph_b_nat,Y4: labeled_graph_b_nat,Z3: labeled_graph_b_nat] :
% 0.27/0.48 ( ( Xz
% 0.27/0.48 = ( produc951298923_b_nat @ X4 @ Z3 ) )
% 0.27/0.48 => ( ( member963855452_b_nat @ ( produc951298923_b_nat @ X4 @ Y4 ) @ R4 )
% 0.27/0.48 => ~ ( member963855452_b_nat @ ( produc951298923_b_nat @ Y4 @ Z3 ) @ S4 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % relcompE
% 0.27/0.48 thf(fact_289_relcompE,axiom,
% 0.27/0.48 ! [Xz: produc1478835367term_b,R4: set_Pr1163220871term_b,S4: set_Pr1163220871term_b] :
% 0.27/0.48 ( ( member516522448term_b @ Xz @ ( relcom1955155673term_b @ R4 @ S4 ) )
% 0.27/0.48 => ~ ! [X4: allegorical_term_b,Y4: allegorical_term_b,Z3: allegorical_term_b] :
% 0.27/0.48 ( ( Xz
% 0.27/0.48 = ( produc1990145943term_b @ X4 @ Z3 ) )
% 0.27/0.48 => ( ( member516522448term_b @ ( produc1990145943term_b @ X4 @ Y4 ) @ R4 )
% 0.27/0.48 => ~ ( member516522448term_b @ ( produc1990145943term_b @ Y4 @ Z3 ) @ S4 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % relcompE
% 0.27/0.48 thf(fact_290_finite_OemptyI,axiom,
% 0.27/0.48 finite_finite_nat @ bot_bot_set_nat ).
% 0.27/0.48
% 0.27/0.48 % finite.emptyI
% 0.27/0.48 thf(fact_291_finite_OemptyI,axiom,
% 0.27/0.48 finite1987068434at_nat @ bot_bo1626616373at_nat ).
% 0.27/0.48
% 0.27/0.48 % finite.emptyI
% 0.27/0.48 thf(fact_292_infinite__imp__nonempty,axiom,
% 0.27/0.48 ! [S2: set_nat] :
% 0.27/0.48 ( ~ ( finite_finite_nat @ S2 )
% 0.27/0.48 => ( S2 != bot_bot_set_nat ) ) ).
% 0.27/0.48
% 0.27/0.48 % infinite_imp_nonempty
% 0.27/0.48 thf(fact_293_infinite__imp__nonempty,axiom,
% 0.27/0.48 ! [S2: set_Pr9961929at_nat] :
% 0.27/0.48 ( ~ ( finite1987068434at_nat @ S2 )
% 0.27/0.48 => ( S2 != bot_bo1626616373at_nat ) ) ).
% 0.27/0.48
% 0.27/0.48 % infinite_imp_nonempty
% 0.27/0.48 thf(fact_294_finite__has__minimal,axiom,
% 0.27/0.48 ! [A4: set_nat] :
% 0.27/0.48 ( ( finite_finite_nat @ A4 )
% 0.27/0.48 => ( ( A4 != bot_bot_set_nat )
% 0.27/0.48 => ? [X4: nat] :
% 0.27/0.48 ( ( member_nat @ X4 @ A4 )
% 0.27/0.48 & ! [Xa: nat] :
% 0.27/0.48 ( ( member_nat @ Xa @ A4 )
% 0.27/0.48 => ( ( ord_less_eq_nat @ Xa @ X4 )
% 0.27/0.48 => ( X4 = Xa ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % finite_has_minimal
% 0.27/0.48 thf(fact_295_finite__has__maximal,axiom,
% 0.27/0.48 ! [A4: set_nat] :
% 0.27/0.48 ( ( finite_finite_nat @ A4 )
% 0.27/0.48 => ( ( A4 != bot_bot_set_nat )
% 0.27/0.48 => ? [X4: nat] :
% 0.27/0.48 ( ( member_nat @ X4 @ A4 )
% 0.27/0.48 & ! [Xa: nat] :
% 0.27/0.48 ( ( member_nat @ Xa @ A4 )
% 0.27/0.48 => ( ( ord_less_eq_nat @ X4 @ Xa )
% 0.27/0.48 => ( X4 = Xa ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % finite_has_maximal
% 0.27/0.48 thf(fact_296_graph__homomorphism__nonempty,axiom,
% 0.27/0.48 ! [A4: labeled_graph_b_nat,B4: labeled_graph_b_nat,F3: set_Pr1986765409at_nat,E: allegorical_term_b] :
% 0.27/0.48 ( ( graph_529870330at_nat @ A4 @ B4 @ F3 )
% 0.27/0.48 => ( ( ( semantics_b_nat @ A4 @ E )
% 0.27/0.48 != bot_bo2130386637at_nat )
% 0.27/0.48 => ( ( semantics_b_nat @ B4 @ E )
% 0.27/0.48 != bot_bo2130386637at_nat ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % graph_homomorphism_nonempty
% 0.27/0.48 thf(fact_297_bounded__Max__nat,axiom,
% 0.27/0.48 ! [P: nat > $o,X3: nat,M2: nat] :
% 0.27/0.48 ( ( P @ X3 )
% 0.27/0.48 => ( ! [X4: nat] :
% 0.27/0.48 ( ( P @ X4 )
% 0.27/0.48 => ( ord_less_eq_nat @ X4 @ M2 ) )
% 0.27/0.48 => ~ ! [M3: nat] :
% 0.27/0.48 ( ( P @ M3 )
% 0.27/0.48 => ~ ! [X6: nat] :
% 0.27/0.48 ( ( P @ X6 )
% 0.27/0.48 => ( ord_less_eq_nat @ X6 @ M3 ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % bounded_Max_nat
% 0.27/0.48 thf(fact_298_Id__on__vertices__identity_I2_J,axiom,
% 0.27/0.48 ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,F3: set_Pr1986765409at_nat,Aa: nat,Ba: nat] :
% 0.27/0.48 ( ( graph_529870330at_nat @ A @ B @ F3 )
% 0.27/0.48 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ Aa @ Ba ) @ F3 )
% 0.27/0.48 => ( member701585322at_nat @ ( product_Pair_nat_nat @ Aa @ Ba ) @ ( relcomp_nat_nat_nat @ F3 @ ( id_on_nat @ ( labele460410879_b_nat @ B ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Id_on_vertices_identity(2)
% 0.27/0.48 thf(fact_299_Id__on__vertices__identity_I1_J,axiom,
% 0.27/0.48 ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,F3: set_Pr1986765409at_nat,Aa: nat,Ba: nat] :
% 0.27/0.48 ( ( graph_529870330at_nat @ A @ B @ F3 )
% 0.27/0.48 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ Aa @ Ba ) @ F3 )
% 0.27/0.48 => ( member701585322at_nat @ ( product_Pair_nat_nat @ Aa @ Ba ) @ ( relcomp_nat_nat_nat @ ( id_on_nat @ ( labele460410879_b_nat @ A ) ) @ F3 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Id_on_vertices_identity(1)
% 0.27/0.48 thf(fact_300_translation__homomorphism_I2_J,axiom,
% 0.27/0.48 ! [E: allegorical_term_b,G: labeled_graph_b_nat,F3: set_Pr1986765409at_nat] :
% 0.27/0.48 ( ( graph_529870330at_nat @ ( translation_b @ E ) @ G @ F3 )
% 0.27/0.48 => ( ( semantics_b_nat @ G @ E )
% 0.27/0.48 != bot_bo2130386637at_nat ) ) ).
% 0.27/0.48
% 0.27/0.48 % translation_homomorphism(2)
% 0.27/0.48 thf(fact_301_weak__universalD,axiom,
% 0.27/0.48 ! [T: itself_nat,R: produc1235635379_b_nat,G_1: labeled_graph_b_nat,G_2: labeled_graph_b_nat,F_1: set_Pr1986765409at_nat,F_2: set_Pr1986765409at_nat,G: labeled_graph_b_nat,H_12: set_Pr1986765409at_nat,H_22: set_Pr1986765409at_nat] :
% 0.27/0.48 ( ( weak_u2026406106at_nat @ T @ R @ G_1 @ G_2 @ F_1 @ F_2 )
% 0.27/0.48 => ( ( graph_529870330at_nat @ ( produc194497945_b_nat @ R ) @ G @ H_12 )
% 0.27/0.48 => ( ( graph_529870330at_nat @ G_1 @ G @ H_22 )
% 0.27/0.48 => ( ( ord_le841296385at_nat @ ( relcomp_nat_nat_nat @ F_1 @ H_22 ) @ H_12 )
% 0.27/0.48 => ? [H3: set_Pr1986765409at_nat] :
% 0.27/0.48 ( ( graph_529870330at_nat @ G_2 @ G @ H3 )
% 0.27/0.48 & ( ord_le841296385at_nat @ H_22 @ H3 ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % weak_universalD
% 0.27/0.48 thf(fact_302_weak__universal__def,axiom,
% 0.27/0.48 ( weak_u2026406106at_nat
% 0.27/0.48 = ( ^ [Uu: itself_nat,R2: produc1235635379_b_nat,G_12: labeled_graph_b_nat,G_22: labeled_graph_b_nat,F_12: set_Pr1986765409at_nat,F_22: set_Pr1986765409at_nat] :
% 0.27/0.48 ! [H_13: set_Pr1986765409at_nat,H_23: set_Pr1986765409at_nat,G2: labeled_graph_b_nat] :
% 0.27/0.48 ( ( ( graph_529870330at_nat @ ( produc194497945_b_nat @ R2 ) @ G2 @ H_13 )
% 0.27/0.48 & ( graph_529870330at_nat @ G_12 @ G2 @ H_23 )
% 0.27/0.48 & ( ord_le841296385at_nat @ ( relcomp_nat_nat_nat @ F_12 @ H_23 ) @ H_13 ) )
% 0.27/0.48 => ? [H4: set_Pr1986765409at_nat] :
% 0.27/0.48 ( ( graph_529870330at_nat @ G_22 @ G2 @ H4 )
% 0.27/0.48 & ( ord_le841296385at_nat @ H_23 @ H4 ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % weak_universal_def
% 0.27/0.48 thf(fact_303_graph__homo__union__id_I2_J,axiom,
% 0.27/0.48 ! [A4: labeled_graph_b_nat,B4: labeled_graph_b_nat,G: labeled_graph_b_nat,F3: set_Pr1986765409at_nat] :
% 0.27/0.48 ( ( graph_529870330at_nat @ ( graph_union_b_nat @ A4 @ B4 ) @ G @ F3 )
% 0.27/0.48 => ( ( B4
% 0.27/0.48 = ( restrict_b_nat @ B4 ) )
% 0.27/0.48 => ( graph_529870330at_nat @ B4 @ G @ ( relcomp_nat_nat_nat @ ( id_on_nat @ ( labele460410879_b_nat @ B4 ) ) @ F3 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % graph_homo_union_id(2)
% 0.27/0.48 thf(fact_304_graph__homo__union__id_I1_J,axiom,
% 0.27/0.48 ! [A4: labeled_graph_b_nat,B4: labeled_graph_b_nat,G: labeled_graph_b_nat,F3: set_Pr1986765409at_nat] :
% 0.27/0.48 ( ( graph_529870330at_nat @ ( graph_union_b_nat @ A4 @ B4 ) @ G @ F3 )
% 0.27/0.48 => ( ( A4
% 0.27/0.48 = ( restrict_b_nat @ A4 ) )
% 0.27/0.48 => ( graph_529870330at_nat @ A4 @ G @ ( relcomp_nat_nat_nat @ ( id_on_nat @ ( labele460410879_b_nat @ A4 ) ) @ F3 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % graph_homo_union_id(1)
% 0.27/0.48 thf(fact_305_finite__relcomp,axiom,
% 0.27/0.48 ! [R: set_Product_prod_b_b,S2: set_Pr9961929at_nat] :
% 0.27/0.48 ( ( finite1015599120od_b_b @ R )
% 0.27/0.48 => ( ( finite1987068434at_nat @ S2 )
% 0.27/0.48 => ( finite1987068434at_nat @ ( relcom14055552at_nat @ R @ S2 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % finite_relcomp
% 0.27/0.48 thf(fact_306_finite__relcomp,axiom,
% 0.27/0.48 ! [R: set_Pr9961929at_nat,S2: set_Pr1490359111at_nat] :
% 0.27/0.48 ( ( finite1987068434at_nat @ R )
% 0.27/0.48 => ( ( finite48957584at_nat @ S2 )
% 0.27/0.48 => ( finite1987068434at_nat @ ( relcom195261566at_nat @ R @ S2 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % finite_relcomp
% 0.27/0.48 thf(fact_307_subset__emptyI,axiom,
% 0.27/0.48 ! [A4: set_Pr1987088711_a_nat] :
% 0.27/0.48 ( ! [X4: produc1871334759_a_nat] :
% 0.27/0.48 ~ ( member832397200_a_nat @ X4 @ A4 )
% 0.27/0.48 => ( ord_le1718765799_a_nat @ A4 @ bot_bo1836341171_a_nat ) ) ).
% 0.27/0.48
% 0.27/0.48 % subset_emptyI
% 0.27/0.48 thf(fact_308_bot__empty__eq,axiom,
% 0.27/0.48 ( bot_bo1024461546_nat_o
% 0.27/0.48 = ( ^ [X5: produc1871334759_a_nat] : ( member832397200_a_nat @ X5 @ bot_bo1836341171_a_nat ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % bot_empty_eq
% 0.27/0.48 thf(fact_309_ssubst__Pair__rhs,axiom,
% 0.27/0.48 ! [R4: labele935650037_a_nat,S4: labele935650037_a_nat,R: set_Pr1987088711_a_nat,S5: labele935650037_a_nat] :
% 0.27/0.48 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ R4 @ S4 ) @ R )
% 0.27/0.48 => ( ( S5 = S4 )
% 0.27/0.48 => ( member832397200_a_nat @ ( produc1676969687_a_nat @ R4 @ S5 ) @ R ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % ssubst_Pair_rhs
% 0.27/0.48 thf(fact_310_ssubst__Pair__rhs,axiom,
% 0.27/0.48 ! [R4: labeled_graph_b_nat,S4: labeled_graph_b_nat,R: set_Pr551076371_b_nat,S5: labeled_graph_b_nat] :
% 0.27/0.48 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ R4 @ S4 ) @ R )
% 0.27/0.48 => ( ( S5 = S4 )
% 0.27/0.48 => ( member963855452_b_nat @ ( produc951298923_b_nat @ R4 @ S5 ) @ R ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % ssubst_Pair_rhs
% 0.27/0.48 thf(fact_311_ssubst__Pair__rhs,axiom,
% 0.27/0.48 ! [R4: allegorical_term_b,S4: allegorical_term_b,R: set_Pr1163220871term_b,S5: allegorical_term_b] :
% 0.27/0.48 ( ( member516522448term_b @ ( produc1990145943term_b @ R4 @ S4 ) @ R )
% 0.27/0.48 => ( ( S5 = S4 )
% 0.27/0.48 => ( member516522448term_b @ ( produc1990145943term_b @ R4 @ S5 ) @ R ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % ssubst_Pair_rhs
% 0.27/0.48 thf(fact_312_agree__iff__subset,axiom,
% 0.27/0.48 ! [G: labeled_graph_b_nat,X: labeled_graph_b_nat,F3: set_Pr1986765409at_nat,G5: set_Pr1986765409at_nat] :
% 0.27/0.48 ( ( graph_529870330at_nat @ G @ X @ F3 )
% 0.27/0.48 => ( ( univalent_nat_nat @ G5 )
% 0.27/0.48 => ( ( agree_on_b_nat_nat @ G @ F3 @ G5 )
% 0.27/0.48 = ( ord_le841296385at_nat @ F3 @ G5 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % agree_iff_subset
% 0.27/0.48 thf(fact_313_id__univalent,axiom,
% 0.27/0.48 ! [X3: set_nat] : ( univalent_nat_nat @ ( id_on_nat @ X3 ) ) ).
% 0.27/0.48
% 0.27/0.48 % id_univalent
% 0.27/0.48 thf(fact_314_univalentD,axiom,
% 0.27/0.48 ! [R: set_Pr1987088711_a_nat,X3: labele935650037_a_nat,Y3: labele935650037_a_nat,Z2: labele935650037_a_nat] :
% 0.27/0.48 ( ( unival1637751524_a_nat @ R )
% 0.27/0.48 => ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ X3 @ Y3 ) @ R )
% 0.27/0.48 => ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ X3 @ Z2 ) @ R )
% 0.27/0.48 => ( Z2 = Y3 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % univalentD
% 0.27/0.48 thf(fact_315_univalentD,axiom,
% 0.27/0.48 ! [R: set_Pr551076371_b_nat,X3: labeled_graph_b_nat,Y3: labeled_graph_b_nat,Z2: labeled_graph_b_nat] :
% 0.27/0.48 ( ( unival857119480_b_nat @ R )
% 0.27/0.48 => ( ( member963855452_b_nat @ ( produc951298923_b_nat @ X3 @ Y3 ) @ R )
% 0.27/0.48 => ( ( member963855452_b_nat @ ( produc951298923_b_nat @ X3 @ Z2 ) @ R )
% 0.27/0.48 => ( Z2 = Y3 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % univalentD
% 0.27/0.48 thf(fact_316_univalentD,axiom,
% 0.27/0.48 ! [R: set_Pr1163220871term_b,X3: allegorical_term_b,Y3: allegorical_term_b,Z2: allegorical_term_b] :
% 0.27/0.48 ( ( unival1191217828term_b @ R )
% 0.27/0.48 => ( ( member516522448term_b @ ( produc1990145943term_b @ X3 @ Y3 ) @ R )
% 0.27/0.48 => ( ( member516522448term_b @ ( produc1990145943term_b @ X3 @ Z2 ) @ R )
% 0.27/0.48 => ( Z2 = Y3 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % univalentD
% 0.27/0.48 thf(fact_317_univalent__def,axiom,
% 0.27/0.48 ( unival1637751524_a_nat
% 0.27/0.48 = ( ^ [R2: set_Pr1987088711_a_nat] :
% 0.27/0.48 ! [X5: labele935650037_a_nat,Y6: labele935650037_a_nat,Z4: labele935650037_a_nat] :
% 0.27/0.48 ( ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ X5 @ Y6 ) @ R2 )
% 0.27/0.48 & ( member832397200_a_nat @ ( produc1676969687_a_nat @ X5 @ Z4 ) @ R2 ) )
% 0.27/0.48 => ( Z4 = Y6 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % univalent_def
% 0.27/0.48 thf(fact_318_univalent__def,axiom,
% 0.27/0.48 ( unival857119480_b_nat
% 0.27/0.48 = ( ^ [R2: set_Pr551076371_b_nat] :
% 0.27/0.48 ! [X5: labeled_graph_b_nat,Y6: labeled_graph_b_nat,Z4: labeled_graph_b_nat] :
% 0.27/0.48 ( ( ( member963855452_b_nat @ ( produc951298923_b_nat @ X5 @ Y6 ) @ R2 )
% 0.27/0.48 & ( member963855452_b_nat @ ( produc951298923_b_nat @ X5 @ Z4 ) @ R2 ) )
% 0.27/0.48 => ( Z4 = Y6 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % univalent_def
% 0.27/0.48 thf(fact_319_univalent__def,axiom,
% 0.27/0.48 ( unival1191217828term_b
% 0.27/0.48 = ( ^ [R2: set_Pr1163220871term_b] :
% 0.27/0.48 ! [X5: allegorical_term_b,Y6: allegorical_term_b,Z4: allegorical_term_b] :
% 0.27/0.48 ( ( ( member516522448term_b @ ( produc1990145943term_b @ X5 @ Y6 ) @ R2 )
% 0.27/0.48 & ( member516522448term_b @ ( produc1990145943term_b @ X5 @ Z4 ) @ R2 ) )
% 0.27/0.48 => ( Z4 = Y6 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % univalent_def
% 0.27/0.48 thf(fact_320_find__graph__occurence__vertices,axiom,
% 0.27/0.48 ! [S2: nat > labeled_graph_b_nat,V: set_nat,F3: set_Pr1986765409at_nat] :
% 0.27/0.48 ( ( chain_b_nat @ S2 )
% 0.27/0.48 => ( ( finite_finite_nat @ V )
% 0.27/0.48 => ( ( univalent_nat_nat @ F3 )
% 0.27/0.48 => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F3 @ V ) @ ( labele460410879_b_nat @ ( chain_sup_b_nat @ S2 ) ) )
% 0.27/0.48 => ? [I2: nat] : ( ord_less_eq_set_nat @ ( image_nat_nat @ F3 @ V ) @ ( labele460410879_b_nat @ ( S2 @ I2 ) ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % find_graph_occurence_vertices
% 0.27/0.48 thf(fact_321_find__graph__occurence__vertices,axiom,
% 0.27/0.48 ! [S2: nat > labeled_graph_b_nat,V: set_Pr9961929at_nat,F3: set_Pr2041158302at_nat] :
% 0.27/0.48 ( ( chain_b_nat @ S2 )
% 0.27/0.48 => ( ( finite1987068434at_nat @ V )
% 0.27/0.48 => ( ( unival633212949at_nat @ F3 )
% 0.27/0.48 => ( ( ord_less_eq_set_nat @ ( image_1356842150at_nat @ F3 @ V ) @ ( labele460410879_b_nat @ ( chain_sup_b_nat @ S2 ) ) )
% 0.27/0.48 => ? [I2: nat] : ( ord_less_eq_set_nat @ ( image_1356842150at_nat @ F3 @ V ) @ ( labele460410879_b_nat @ ( S2 @ I2 ) ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % find_graph_occurence_vertices
% 0.27/0.48 thf(fact_322_ImageI,axiom,
% 0.27/0.48 ! [A: produc1871334759_a_nat,B: produc1871334759_a_nat,R4: set_Pr924198087_a_nat,A4: set_Pr1987088711_a_nat] :
% 0.27/0.48 ( ( member584645392_a_nat @ ( produc1677124439_a_nat @ A @ B ) @ R4 )
% 0.27/0.48 => ( ( member832397200_a_nat @ A @ A4 )
% 0.27/0.48 => ( member832397200_a_nat @ B @ ( image_1168831379_a_nat @ R4 @ A4 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % ImageI
% 0.27/0.48 thf(fact_323_ImageI,axiom,
% 0.27/0.48 ! [A: labele935650037_a_nat,B: labele935650037_a_nat,R4: set_Pr1987088711_a_nat,A4: set_la1083530965_a_nat] :
% 0.27/0.48 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B ) @ R4 )
% 0.27/0.48 => ( ( member964390942_a_nat @ A @ A4 )
% 0.27/0.48 => ( member964390942_a_nat @ B @ ( image_1971191571_a_nat @ R4 @ A4 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % ImageI
% 0.27/0.48 thf(fact_324_ImageI,axiom,
% 0.27/0.48 ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,R4: set_Pr551076371_b_nat,A4: set_la1976028319_b_nat] :
% 0.27/0.48 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B ) @ R4 )
% 0.27/0.48 => ( ( member1483953152_b_nat @ A @ A4 )
% 0.27/0.48 => ( member1483953152_b_nat @ B @ ( image_1183964583_b_nat @ R4 @ A4 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % ImageI
% 0.27/0.48 thf(fact_325_ImageI,axiom,
% 0.27/0.48 ! [A: allegorical_term_b,B: allegorical_term_b,R4: set_Pr1163220871term_b,A4: set_al1193902458term_b] :
% 0.27/0.48 ( ( member516522448term_b @ ( produc1990145943term_b @ A @ B ) @ R4 )
% 0.27/0.48 => ( ( member93680451term_b @ A @ A4 )
% 0.27/0.48 => ( member93680451term_b @ B @ ( image_329221075term_b @ R4 @ A4 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % ImageI
% 0.27/0.48 thf(fact_326_Domain__Id__on,axiom,
% 0.27/0.48 ! [A4: set_nat] :
% 0.27/0.48 ( ( domain_nat_nat @ ( id_on_nat @ A4 ) )
% 0.27/0.48 = A4 ) ).
% 0.27/0.48
% 0.27/0.48 % Domain_Id_on
% 0.27/0.48 thf(fact_327_univalent__finite_I2_J,axiom,
% 0.27/0.48 ! [R: set_Pr9961929at_nat] :
% 0.27/0.48 ( ( unival989235430at_nat @ R )
% 0.27/0.48 => ( ( finite_finite_b @ ( domain1101989710at_nat @ R ) )
% 0.27/0.48 = ( finite1987068434at_nat @ R ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % univalent_finite(2)
% 0.27/0.48 thf(fact_328_finite__Domain,axiom,
% 0.27/0.48 ! [R4: set_Pr9961929at_nat] :
% 0.27/0.48 ( ( finite1987068434at_nat @ R4 )
% 0.27/0.48 => ( finite_finite_b @ ( domain1101989710at_nat @ R4 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % finite_Domain
% 0.27/0.48 thf(fact_329_finite__Image,axiom,
% 0.27/0.48 ! [R: set_Pr9961929at_nat,A4: set_b] :
% 0.27/0.48 ( ( finite1987068434at_nat @ R )
% 0.27/0.48 => ( finite772653738at_nat @ ( image_2112855445at_nat @ R @ A4 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % finite_Image
% 0.27/0.48 thf(fact_330_Domain_Oinducts,axiom,
% 0.27/0.48 ! [X3: labele935650037_a_nat,R4: set_Pr1987088711_a_nat,P: labele935650037_a_nat > $o] :
% 0.27/0.48 ( ( member964390942_a_nat @ X3 @ ( domain1068567884_a_nat @ R4 ) )
% 0.27/0.48 => ( ! [A3: labele935650037_a_nat,B3: labele935650037_a_nat] :
% 0.27/0.48 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A3 @ B3 ) @ R4 )
% 0.27/0.48 => ( P @ A3 ) )
% 0.27/0.48 => ( P @ X3 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Domain.inducts
% 0.27/0.48 thf(fact_331_Domain_Oinducts,axiom,
% 0.27/0.48 ! [X3: labeled_graph_b_nat,R4: set_Pr551076371_b_nat,P: labeled_graph_b_nat > $o] :
% 0.27/0.48 ( ( member1483953152_b_nat @ X3 @ ( domain767519072_b_nat @ R4 ) )
% 0.27/0.48 => ( ! [A3: labeled_graph_b_nat,B3: labeled_graph_b_nat] :
% 0.27/0.48 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A3 @ B3 ) @ R4 )
% 0.27/0.48 => ( P @ A3 ) )
% 0.27/0.48 => ( P @ X3 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Domain.inducts
% 0.27/0.48 thf(fact_332_Domain_Oinducts,axiom,
% 0.27/0.48 ! [X3: allegorical_term_b,R4: set_Pr1163220871term_b,P: allegorical_term_b > $o] :
% 0.27/0.48 ( ( member93680451term_b @ X3 @ ( domain859272460term_b @ R4 ) )
% 0.27/0.48 => ( ! [A3: allegorical_term_b,B3: allegorical_term_b] :
% 0.27/0.48 ( ( member516522448term_b @ ( produc1990145943term_b @ A3 @ B3 ) @ R4 )
% 0.27/0.48 => ( P @ A3 ) )
% 0.27/0.48 => ( P @ X3 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Domain.inducts
% 0.27/0.48 thf(fact_333_Domain_ODomainI,axiom,
% 0.27/0.48 ! [A: labele935650037_a_nat,B: labele935650037_a_nat,R4: set_Pr1987088711_a_nat] :
% 0.27/0.48 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B ) @ R4 )
% 0.27/0.48 => ( member964390942_a_nat @ A @ ( domain1068567884_a_nat @ R4 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Domain.DomainI
% 0.27/0.48 thf(fact_334_Domain_ODomainI,axiom,
% 0.27/0.48 ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,R4: set_Pr551076371_b_nat] :
% 0.27/0.48 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B ) @ R4 )
% 0.27/0.48 => ( member1483953152_b_nat @ A @ ( domain767519072_b_nat @ R4 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Domain.DomainI
% 0.27/0.48 thf(fact_335_Domain_ODomainI,axiom,
% 0.27/0.48 ! [A: allegorical_term_b,B: allegorical_term_b,R4: set_Pr1163220871term_b] :
% 0.27/0.48 ( ( member516522448term_b @ ( produc1990145943term_b @ A @ B ) @ R4 )
% 0.27/0.48 => ( member93680451term_b @ A @ ( domain859272460term_b @ R4 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Domain.DomainI
% 0.27/0.48 thf(fact_336_Domain_Osimps,axiom,
% 0.27/0.48 ! [A: labele935650037_a_nat,R4: set_Pr1987088711_a_nat] :
% 0.27/0.48 ( ( member964390942_a_nat @ A @ ( domain1068567884_a_nat @ R4 ) )
% 0.27/0.48 = ( ? [A5: labele935650037_a_nat,B5: labele935650037_a_nat] :
% 0.27/0.48 ( ( A = A5 )
% 0.27/0.48 & ( member832397200_a_nat @ ( produc1676969687_a_nat @ A5 @ B5 ) @ R4 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Domain.simps
% 0.27/0.48 thf(fact_337_Domain_Osimps,axiom,
% 0.27/0.48 ! [A: labeled_graph_b_nat,R4: set_Pr551076371_b_nat] :
% 0.27/0.48 ( ( member1483953152_b_nat @ A @ ( domain767519072_b_nat @ R4 ) )
% 0.27/0.48 = ( ? [A5: labeled_graph_b_nat,B5: labeled_graph_b_nat] :
% 0.27/0.48 ( ( A = A5 )
% 0.27/0.48 & ( member963855452_b_nat @ ( produc951298923_b_nat @ A5 @ B5 ) @ R4 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Domain.simps
% 0.27/0.48 thf(fact_338_Domain_Osimps,axiom,
% 0.27/0.48 ! [A: allegorical_term_b,R4: set_Pr1163220871term_b] :
% 0.27/0.48 ( ( member93680451term_b @ A @ ( domain859272460term_b @ R4 ) )
% 0.27/0.48 = ( ? [A5: allegorical_term_b,B5: allegorical_term_b] :
% 0.27/0.48 ( ( A = A5 )
% 0.27/0.48 & ( member516522448term_b @ ( produc1990145943term_b @ A5 @ B5 ) @ R4 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Domain.simps
% 0.27/0.48 thf(fact_339_Domain_Ocases,axiom,
% 0.27/0.48 ! [A: labele935650037_a_nat,R4: set_Pr1987088711_a_nat] :
% 0.27/0.48 ( ( member964390942_a_nat @ A @ ( domain1068567884_a_nat @ R4 ) )
% 0.27/0.48 => ~ ! [B3: labele935650037_a_nat] :
% 0.27/0.48 ~ ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B3 ) @ R4 ) ) ).
% 0.27/0.48
% 0.27/0.48 % Domain.cases
% 0.27/0.48 thf(fact_340_Domain_Ocases,axiom,
% 0.27/0.48 ! [A: labeled_graph_b_nat,R4: set_Pr551076371_b_nat] :
% 0.27/0.48 ( ( member1483953152_b_nat @ A @ ( domain767519072_b_nat @ R4 ) )
% 0.27/0.48 => ~ ! [B3: labeled_graph_b_nat] :
% 0.27/0.48 ~ ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B3 ) @ R4 ) ) ).
% 0.27/0.48
% 0.27/0.48 % Domain.cases
% 0.27/0.48 thf(fact_341_Domain_Ocases,axiom,
% 0.27/0.48 ! [A: allegorical_term_b,R4: set_Pr1163220871term_b] :
% 0.27/0.48 ( ( member93680451term_b @ A @ ( domain859272460term_b @ R4 ) )
% 0.27/0.48 => ~ ! [B3: allegorical_term_b] :
% 0.27/0.48 ~ ( member516522448term_b @ ( produc1990145943term_b @ A @ B3 ) @ R4 ) ) ).
% 0.27/0.48
% 0.27/0.48 % Domain.cases
% 0.27/0.48 thf(fact_342_Domain__iff,axiom,
% 0.27/0.48 ! [A: labele935650037_a_nat,R4: set_Pr1987088711_a_nat] :
% 0.27/0.48 ( ( member964390942_a_nat @ A @ ( domain1068567884_a_nat @ R4 ) )
% 0.27/0.48 = ( ? [Y6: labele935650037_a_nat] : ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ Y6 ) @ R4 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Domain_iff
% 0.27/0.48 thf(fact_343_Domain__iff,axiom,
% 0.27/0.48 ! [A: labeled_graph_b_nat,R4: set_Pr551076371_b_nat] :
% 0.27/0.48 ( ( member1483953152_b_nat @ A @ ( domain767519072_b_nat @ R4 ) )
% 0.27/0.48 = ( ? [Y6: labeled_graph_b_nat] : ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ Y6 ) @ R4 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Domain_iff
% 0.27/0.48 thf(fact_344_Domain__iff,axiom,
% 0.27/0.48 ! [A: allegorical_term_b,R4: set_Pr1163220871term_b] :
% 0.27/0.48 ( ( member93680451term_b @ A @ ( domain859272460term_b @ R4 ) )
% 0.27/0.48 = ( ? [Y6: allegorical_term_b] : ( member516522448term_b @ ( produc1990145943term_b @ A @ Y6 ) @ R4 ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Domain_iff
% 0.27/0.48 thf(fact_345_DomainE,axiom,
% 0.27/0.48 ! [A: labele935650037_a_nat,R4: set_Pr1987088711_a_nat] :
% 0.27/0.48 ( ( member964390942_a_nat @ A @ ( domain1068567884_a_nat @ R4 ) )
% 0.27/0.48 => ~ ! [B3: labele935650037_a_nat] :
% 0.27/0.48 ~ ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B3 ) @ R4 ) ) ).
% 0.27/0.48
% 0.27/0.48 % DomainE
% 0.27/0.48 thf(fact_346_DomainE,axiom,
% 0.27/0.48 ! [A: labeled_graph_b_nat,R4: set_Pr551076371_b_nat] :
% 0.27/0.48 ( ( member1483953152_b_nat @ A @ ( domain767519072_b_nat @ R4 ) )
% 0.27/0.48 => ~ ! [B3: labeled_graph_b_nat] :
% 0.27/0.48 ~ ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B3 ) @ R4 ) ) ).
% 0.27/0.48
% 0.27/0.48 % DomainE
% 0.27/0.48 thf(fact_347_DomainE,axiom,
% 0.27/0.48 ! [A: allegorical_term_b,R4: set_Pr1163220871term_b] :
% 0.27/0.48 ( ( member93680451term_b @ A @ ( domain859272460term_b @ R4 ) )
% 0.27/0.48 => ~ ! [B3: allegorical_term_b] :
% 0.27/0.48 ~ ( member516522448term_b @ ( produc1990145943term_b @ A @ B3 ) @ R4 ) ) ).
% 0.27/0.48
% 0.27/0.48 % DomainE
% 0.27/0.48 thf(fact_348_rev__ImageI,axiom,
% 0.27/0.48 ! [A: labele935650037_a_nat,A4: set_la1083530965_a_nat,B: labele935650037_a_nat,R4: set_Pr1987088711_a_nat] :
% 0.27/0.48 ( ( member964390942_a_nat @ A @ A4 )
% 0.27/0.48 => ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B ) @ R4 )
% 0.27/0.48 => ( member964390942_a_nat @ B @ ( image_1971191571_a_nat @ R4 @ A4 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % rev_ImageI
% 0.27/0.48 thf(fact_349_rev__ImageI,axiom,
% 0.27/0.48 ! [A: produc1871334759_a_nat,A4: set_Pr1987088711_a_nat,B: produc1871334759_a_nat,R4: set_Pr924198087_a_nat] :
% 0.27/0.48 ( ( member832397200_a_nat @ A @ A4 )
% 0.27/0.48 => ( ( member584645392_a_nat @ ( produc1677124439_a_nat @ A @ B ) @ R4 )
% 0.27/0.48 => ( member832397200_a_nat @ B @ ( image_1168831379_a_nat @ R4 @ A4 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % rev_ImageI
% 0.27/0.48 thf(fact_350_rev__ImageI,axiom,
% 0.27/0.48 ! [A: labeled_graph_b_nat,A4: set_la1976028319_b_nat,B: labeled_graph_b_nat,R4: set_Pr551076371_b_nat] :
% 0.27/0.48 ( ( member1483953152_b_nat @ A @ A4 )
% 0.27/0.48 => ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B ) @ R4 )
% 0.27/0.48 => ( member1483953152_b_nat @ B @ ( image_1183964583_b_nat @ R4 @ A4 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % rev_ImageI
% 0.27/0.48 thf(fact_351_rev__ImageI,axiom,
% 0.27/0.48 ! [A: allegorical_term_b,A4: set_al1193902458term_b,B: allegorical_term_b,R4: set_Pr1163220871term_b] :
% 0.27/0.48 ( ( member93680451term_b @ A @ A4 )
% 0.27/0.48 => ( ( member516522448term_b @ ( produc1990145943term_b @ A @ B ) @ R4 )
% 0.27/0.48 => ( member93680451term_b @ B @ ( image_329221075term_b @ R4 @ A4 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % rev_ImageI
% 0.27/0.48 thf(fact_352_Image__iff,axiom,
% 0.27/0.48 ! [B: labele935650037_a_nat,R4: set_Pr1987088711_a_nat,A4: set_la1083530965_a_nat] :
% 0.27/0.48 ( ( member964390942_a_nat @ B @ ( image_1971191571_a_nat @ R4 @ A4 ) )
% 0.27/0.48 = ( ? [X5: labele935650037_a_nat] :
% 0.27/0.48 ( ( member964390942_a_nat @ X5 @ A4 )
% 0.27/0.48 & ( member832397200_a_nat @ ( produc1676969687_a_nat @ X5 @ B ) @ R4 ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 % Image_iff
% 0.27/0.48 thf(fact_353_Image__iff,axiom,
% 0.27/0.49 ! [B: labeled_graph_b_nat,R4: set_Pr551076371_b_nat,A4: set_la1976028319_b_nat] :
% 0.27/0.49 ( ( member1483953152_b_nat @ B @ ( image_1183964583_b_nat @ R4 @ A4 ) )
% 0.27/0.49 = ( ? [X5: labeled_graph_b_nat] :
% 0.27/0.49 ( ( member1483953152_b_nat @ X5 @ A4 )
% 0.27/0.49 & ( member963855452_b_nat @ ( produc951298923_b_nat @ X5 @ B ) @ R4 ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % Image_iff
% 0.27/0.49 thf(fact_354_Image__iff,axiom,
% 0.27/0.49 ! [B: allegorical_term_b,R4: set_Pr1163220871term_b,A4: set_al1193902458term_b] :
% 0.27/0.49 ( ( member93680451term_b @ B @ ( image_329221075term_b @ R4 @ A4 ) )
% 0.27/0.49 = ( ? [X5: allegorical_term_b] :
% 0.27/0.49 ( ( member93680451term_b @ X5 @ A4 )
% 0.27/0.49 & ( member516522448term_b @ ( produc1990145943term_b @ X5 @ B ) @ R4 ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 % Image_iff
% 0.27/0.49
% 0.27/0.49 % Conjectures (1)
% 0.27/0.49 thf(conj_0,conjecture,
% 0.27/0.49 ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
% 0.27/0.49 & ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
% 0.27/0.49 = ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
% 0.27/0.49 & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
% 0.27/0.49 & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) ) ).
% 0.27/0.49
% 0.27/0.49 %------------------------------------------------------------------------------
% 0.27/0.49 ------------------------
% 2.85/1.56 ---- Embedded in THF ---
% 2.85/1.56 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.85/1.56 %%% Generated on Tue Feb 24 08:28:46 EST 2026
% 2.85/1.56 %%% using '$$dhol' embedding, version 1.3.0.
% 2.85/1.56 %%% Logic specification used:
% 2.85/1.56 %%% thf(spec, logic, $$dhol).
% 2.85/1.56
% 2.85/1.56 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.bgqouCdkA9/DTF2DTF15711.p
% See solution above
% 2.85/1.57 ------------------------
% 3.03/1.61 ---- Cleaned THF ---
% 3.03/1.61 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_J_J_J,type,
% 3.03/1.61 set_Pr2123625671_a_nat: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_J_J,type,
% 3.03/1.61 produc116665063_a_nat: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_J_J,type,
% 3.03/1.61 set_Pr924198087_a_nat: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_J,type,
% 3.03/1.61 produc398057191_a_nat: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_J_J_J,type,
% 3.03/1.61 set_Pr1173424071_b_nat: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphSemantics__Oallegorical____term_Itf__b_J_Mt__LabeledGraphSemantics__Oallegorical____term_Itf__b_J_J_Mt__Product____Type__Oprod_It__LabeledGraphSemantics__Oallegorical____term_Itf__b_J_Mt__LabeledGraphSemantics__Oallegorical____term_Itf__b_J_J_J_J,type,
% 3.03/1.61 set_Pr1839611079term_b: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_J_J,type,
% 3.03/1.61 produc446386919_b_nat: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphSemantics__Oallegorical____term_Itf__b_J_Mt__LabeledGraphSemantics__Oallegorical____term_Itf__b_J_J_Mt__Product____Type__Oprod_It__LabeledGraphSemantics__Oallegorical____term_Itf__b_J_Mt__LabeledGraphSemantics__Oallegorical____term_Itf__b_J_J_J,type,
% 3.03/1.61 produc1116408039term_b: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_J,type,
% 3.03/1.61 set_Pr1987088711_a_nat: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Nat__Onat_J_J_J,type,
% 3.03/1.61 set_Pr665622551at_nat: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(ty_n_t__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J,type,
% 3.03/1.61 produc1871334759_a_nat: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(ty_n_t__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Nat__Onat_J_J,type,
% 3.03/1.61 produc1391440311at_nat: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_J_J,type,
% 3.03/1.61 set_Pr551076371_b_nat: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 3.03/1.61 set_Pr1647387645at_nat: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 3.03/1.61 set_Pr1490359111at_nat: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphSemantics__Oallegorical____term_Itf__b_J_Mt__LabeledGraphSemantics__Oallegorical____term_Itf__b_J_J_J,type,
% 3.03/1.61 set_Pr1163220871term_b: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Nat__Onat_J_J,type,
% 3.03/1.61 set_Pr2041158302at_nat: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(ty_n_t__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_J,type,
% 3.03/1.61 produc1235635379_b_nat: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 3.03/1.61 produc842455143at_nat: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(ty_n_t__Product____Type__Oprod_It__LabeledGraphSemantics__Oallegorical____term_Itf__b_J_Mt__LabeledGraphSemantics__Oallegorical____term_Itf__b_J_J,type,
% 3.03/1.61 produc1478835367term_b: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(ty_n_t__Set__Oset_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J,type,
% 3.03/1.61 set_la1083530965_a_nat: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(ty_n_t__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J,type,
% 3.03/1.61 labele935650037_a_nat: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(ty_n_t__LabeledGraphs__Olabeled____graph_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Nat__Onat_J,type,
% 3.03/1.61 labele1835409643at_nat: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 3.03/1.61 set_Pr9961929at_nat: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(ty_n_t__LabeledGraphSemantics__Oallegorical____term_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_J,type,
% 3.03/1.61 allego510293162tant_a: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(ty_n_t__LabeledGraphSemantics__Oallegorical____term_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 3.03/1.61 allego1565409692at_nat: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(ty_n_t__Set__Oset_It__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_J,type,
% 3.03/1.61 set_la1976028319_b_nat: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(ty_n_t__Set__Oset_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_J,type,
% 3.03/1.61 set_St761939237tant_a: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 3.03/1.61 set_Pr1986765409at_nat: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(ty_n_t__Set__Oset_It__LabeledGraphSemantics__Oallegorical____term_Itf__b_J_J,type,
% 3.03/1.61 set_al1193902458term_b: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(ty_n_t__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J,type,
% 3.03/1.61 labeled_graph_b_nat: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__b_Mtf__b_J_J,type,
% 3.03/1.61 set_Product_prod_b_b: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(ty_n_t__LabeledGraphSemantics__OStandard____Constant_Itf__a_J,type,
% 3.03/1.61 standard_Constant_a: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 3.03/1.61 product_prod_nat_nat: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(ty_n_t__LabeledGraphSemantics__Oallegorical____term_Itf__b_J,type,
% 3.03/1.61 allegorical_term_b: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 3.03/1.61 set_nat: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(ty_n_t__itself_It__Nat__Onat_J,type,
% 3.03/1.61 itself_nat: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(ty_n_t__Set__Oset_Itf__b_J,type,
% 3.03/1.61 set_b: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 3.03/1.61 set_a: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(ty_n_t__Nat__Onat,type,
% 3.03/1.61 nat: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(ty_n_tf__b,type,
% 3.03/1.61 b: $tType ).
% 3.03/1.61
% 3.03/1.61 thf(sy_c_Finite__Set_Ofinite_001t__Nat__Onat,type,
% 3.03/1.61 finite_finite_nat: set_nat > $o ).
% 3.03/1.61
% 3.03/1.61 thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 3.03/1.61 finite1242387294at_nat: set_Pr1647387645at_nat > $o ).
% 3.03/1.61
% 3.03/1.61 thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 3.03/1.61 finite772653738at_nat: set_Pr1986765409at_nat > $o ).
% 3.03/1.61
% 3.03/1.61 thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 3.03/1.61 finite48957584at_nat: set_Pr1490359111at_nat > $o ).
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% 3.03/1.61
% 3.03/1.61 thf(sy_c_member_001t__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J,type,
% 3.03/1.61 member964390942_a_nat: labele935650037_a_nat > set_la1083530965_a_nat > $o ).
% 3.03/1.61
% 3.03/1.61 thf(sy_c_member_001t__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J,type,
% 3.03/1.61 member1483953152_b_nat: labeled_graph_b_nat > set_la1976028319_b_nat > $o ).
% 3.03/1.61
% 3.03/1.61 thf(sy_c_member_001t__Nat__Onat,type,
% 3.03/1.61 member_nat: nat > set_nat > $o ).
% 3.03/1.61
% 3.03/1.61 thf(sy_c_member_001t__Product____Type__Oprod_It__LabeledGraphSemantics__Oallegorical____term_Itf__b_J_Mt__LabeledGraphSemantics__Oallegorical____term_Itf__b_J_J,type,
% 3.03/1.61 member516522448term_b: produc1478835367term_b > set_Pr1163220871term_b > $o ).
% 3.03/1.61
% 3.03/1.61 thf(sy_c_member_001t__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J,type,
% 3.03/1.61 member832397200_a_nat: produc1871334759_a_nat > set_Pr1987088711_a_nat > $o ).
% 3.03/1.61
% 3.03/1.61 thf(sy_c_member_001t__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Nat__Onat_J_J,type,
% 3.03/1.61 member1129678944at_nat: produc1391440311at_nat > set_Pr665622551at_nat > $o ).
% 3.03/1.61
% 3.03/1.61 thf(sy_c_member_001t__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_J,type,
% 3.03/1.61 member963855452_b_nat: produc1235635379_b_nat > set_Pr551076371_b_nat > $o ).
% 3.03/1.61
% 3.03/1.61 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 3.03/1.61 member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
% 3.03/1.61
% 3.03/1.61 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphSemantics__Oallegorical____term_Itf__b_J_Mt__LabeledGraphSemantics__Oallegorical____term_Itf__b_J_J_Mt__Product____Type__Oprod_It__LabeledGraphSemantics__Oallegorical____term_Itf__b_J_Mt__LabeledGraphSemantics__Oallegorical____term_Itf__b_J_J_J,type,
% 3.03/1.61 member1449757456term_b: produc1116408039term_b > set_Pr1839611079term_b > $o ).
% 3.03/1.61
% 3.03/1.61 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_J,type,
% 3.03/1.61 member584645392_a_nat: produc398057191_a_nat > set_Pr924198087_a_nat > $o ).
% 3.03/1.61
% 3.03/1.61 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_Itf__b_Mt__Nat__Onat_J_J_J,type,
% 3.03/1.61 member889223696_b_nat: produc446386919_b_nat > set_Pr1173424071_b_nat > $o ).
% 3.03/1.61
% 3.03/1.61 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 3.03/1.61 member2027625872at_nat: produc842455143at_nat > set_Pr1490359111at_nat > $o ).
% 3.03/1.61
% 3.03/1.61 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_Mt__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Nat__Onat_J_J_J_J,type,
% 3.03/1.61 member829905680_a_nat: produc116665063_a_nat > set_Pr2123625671_a_nat > $o ).
% 3.03/1.61
% 3.03/1.61 thf(sy_v_C,type,
% 3.03/1.61 c: set_a ).
% 3.03/1.61
% 3.03/1.61 thf(sy_v_u,type,
% 3.03/1.61 u: allegorical_term_b ).
% 3.03/1.61
% 3.03/1.61 thf(sy_v_v,type,
% 3.03/1.61 v: allegorical_term_b ).
% 3.03/1.61
% 3.03/1.61 thf(sy_v_x,type,
% 3.03/1.61 x: produc1871334759_a_nat ).
% 3.03/1.61
% 3.03/1.61 thf(fact_0_assms,axiom,
% 3.03/1.61 member832397200_a_nat @ x @ ( standa1897115818ules_a @ c ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_1_graph__rule__translation,axiom,
% 3.03/1.61 ! [X: allego1565409692at_nat,Y: allego1565409692at_nat] :
% 3.03/1.61 ( ( graph_2111906684at_nat @ ( produc1995789403at_nat @ ( produc590202991at_nat @ ( transl490985778at_nat @ X ) @ ( transl490985778at_nat @ ( allego266765201at_nat @ X @ Y ) ) ) ) @ ( produc1564126365at_nat @ ( produc590202991at_nat @ ( transl490985778at_nat @ X ) @ ( transl490985778at_nat @ ( allego266765201at_nat @ X @ Y ) ) ) ) @ ( id_on_nat @ ( labele560327297at_nat @ ( produc1995789403at_nat @ ( produc590202991at_nat @ ( transl490985778at_nat @ X ) @ ( transl490985778at_nat @ ( allego266765201at_nat @ X @ Y ) ) ) ) ) ) )
% 3.03/1.61 & ( ( produc1564126365at_nat @ ( produc590202991at_nat @ ( transl490985778at_nat @ X ) @ ( transl490985778at_nat @ ( allego266765201at_nat @ X @ Y ) ) ) )
% 3.03/1.61 = ( restri321299017at_nat @ ( produc1564126365at_nat @ ( produc590202991at_nat @ ( transl490985778at_nat @ X ) @ ( transl490985778at_nat @ ( allego266765201at_nat @ X @ Y ) ) ) ) ) )
% 3.03/1.61 & ( finite_finite_nat @ ( labele560327297at_nat @ ( produc1564126365at_nat @ ( produc590202991at_nat @ ( transl490985778at_nat @ X ) @ ( transl490985778at_nat @ ( allego266765201at_nat @ X @ Y ) ) ) ) ) )
% 3.03/1.61 & ( finite48957584at_nat @ ( labele2032268018at_nat @ ( produc1564126365at_nat @ ( produc590202991at_nat @ ( transl490985778at_nat @ X ) @ ( transl490985778at_nat @ ( allego266765201at_nat @ X @ Y ) ) ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_2_graph__rule__translation,axiom,
% 3.03/1.61 ! [X: allego510293162tant_a,Y: allego510293162tant_a] :
% 3.03/1.61 ( ( graph_2130075512at_nat @ ( produc719117507_a_nat @ ( produc1676969687_a_nat @ ( transl1275713022tant_a @ X ) @ ( transl1275713022tant_a @ ( allego745587551tant_a @ X @ Y ) ) ) ) @ ( produc880161797_a_nat @ ( produc1676969687_a_nat @ ( transl1275713022tant_a @ X ) @ ( transl1275713022tant_a @ ( allego745587551tant_a @ X @ Y ) ) ) ) @ ( id_on_nat @ ( labele1810595089_a_nat @ ( produc719117507_a_nat @ ( produc1676969687_a_nat @ ( transl1275713022tant_a @ X ) @ ( transl1275713022tant_a @ ( allego745587551tant_a @ X @ Y ) ) ) ) ) ) )
% 3.03/1.61 & ( ( produc880161797_a_nat @ ( produc1676969687_a_nat @ ( transl1275713022tant_a @ X ) @ ( transl1275713022tant_a @ ( allego745587551tant_a @ X @ Y ) ) ) )
% 3.03/1.61 = ( restri572569417_a_nat @ ( produc880161797_a_nat @ ( produc1676969687_a_nat @ ( transl1275713022tant_a @ X ) @ ( transl1275713022tant_a @ ( allego745587551tant_a @ X @ Y ) ) ) ) ) )
% 3.03/1.61 & ( finite_finite_nat @ ( labele1810595089_a_nat @ ( produc880161797_a_nat @ ( produc1676969687_a_nat @ ( transl1275713022tant_a @ X ) @ ( transl1275713022tant_a @ ( allego745587551tant_a @ X @ Y ) ) ) ) ) )
% 3.03/1.61 & ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( produc880161797_a_nat @ ( produc1676969687_a_nat @ ( transl1275713022tant_a @ X ) @ ( transl1275713022tant_a @ ( allego745587551tant_a @ X @ Y ) ) ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_3_graph__rule__translation,axiom,
% 3.03/1.61 ! [X: allegorical_term_b,Y: allegorical_term_b] :
% 3.03/1.61 ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X ) @ ( translation_b @ ( allegorical_A_Int_b @ X @ Y ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X ) @ ( translation_b @ ( allegorical_A_Int_b @ X @ Y ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X ) @ ( translation_b @ ( allegorical_A_Int_b @ X @ Y ) ) ) ) ) ) )
% 3.03/1.61 & ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X ) @ ( translation_b @ ( allegorical_A_Int_b @ X @ Y ) ) ) )
% 3.03/1.61 = ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X ) @ ( translation_b @ ( allegorical_A_Int_b @ X @ Y ) ) ) ) ) )
% 3.03/1.61 & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X ) @ ( translation_b @ ( allegorical_A_Int_b @ X @ Y ) ) ) ) ) )
% 3.03/1.61 & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X ) @ ( translation_b @ ( allegorical_A_Int_b @ X @ Y ) ) ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_4_subgraph__refl,axiom,
% 3.03/1.61 ! [G: labele935650037_a_nat] :
% 3.03/1.61 ( ( graph_2130075512at_nat @ G @ G @ ( id_on_nat @ ( labele1810595089_a_nat @ G ) ) )
% 3.03/1.61 = ( G
% 3.03/1.61 = ( restri572569417_a_nat @ G ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_5_subgraph__refl,axiom,
% 3.03/1.61 ! [G: labeled_graph_b_nat] :
% 3.03/1.61 ( ( graph_529870330at_nat @ G @ G @ ( id_on_nat @ ( labele460410879_b_nat @ G ) ) )
% 3.03/1.61 = ( G
% 3.03/1.61 = ( restrict_b_nat @ G ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_6_subgraph__restrict,axiom,
% 3.03/1.61 ! [G: labele935650037_a_nat] :
% 3.03/1.61 ( ( graph_2130075512at_nat @ G @ ( restri572569417_a_nat @ G ) @ ( id_on_nat @ ( labele1810595089_a_nat @ G ) ) )
% 3.03/1.61 = ( G
% 3.03/1.61 = ( restri572569417_a_nat @ G ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_7_subgraph__restrict,axiom,
% 3.03/1.61 ! [G: labeled_graph_b_nat] :
% 3.03/1.61 ( ( graph_529870330at_nat @ G @ ( restrict_b_nat @ G ) @ ( id_on_nat @ ( labele460410879_b_nat @ G ) ) )
% 3.03/1.61 = ( G
% 3.03/1.61 = ( restrict_b_nat @ G ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_8_graph__homomorphism__Id,axiom,
% 3.03/1.61 ! [A: labele935650037_a_nat] : ( graph_2130075512at_nat @ ( restri572569417_a_nat @ A ) @ ( restri572569417_a_nat @ A ) @ ( id_on_nat @ ( labele1810595089_a_nat @ A ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_9_graph__homomorphism__Id,axiom,
% 3.03/1.61 ! [A: labeled_graph_b_nat] : ( graph_529870330at_nat @ ( restrict_b_nat @ A ) @ ( restrict_b_nat @ A ) @ ( id_on_nat @ ( labele460410879_b_nat @ A ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_10_verts__in__translation__finite_I2_J,axiom,
% 3.03/1.61 ! [X: allego1565409692at_nat] : ( finite48957584at_nat @ ( labele2032268018at_nat @ ( transl490985778at_nat @ X ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_11_verts__in__translation__finite_I2_J,axiom,
% 3.03/1.61 ! [X: allego510293162tant_a] : ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( transl1275713022tant_a @ X ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_12_verts__in__translation__finite_I2_J,axiom,
% 3.03/1.61 ! [X: allegorical_term_b] : ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( translation_b @ X ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_13_are__rules_I1_J,axiom,
% 3.03/1.61 ( ( graph_2111906684at_nat @ ( produc1995789403at_nat @ standa214789732at_nat ) @ ( produc1564126365at_nat @ standa214789732at_nat ) @ ( id_on_nat @ ( labele560327297at_nat @ ( produc1995789403at_nat @ standa214789732at_nat ) ) ) )
% 3.03/1.61 & ( ( produc1564126365at_nat @ standa214789732at_nat )
% 3.03/1.61 = ( restri321299017at_nat @ ( produc1564126365at_nat @ standa214789732at_nat ) ) )
% 3.03/1.61 & ( finite_finite_nat @ ( labele560327297at_nat @ ( produc1564126365at_nat @ standa214789732at_nat ) ) )
% 3.03/1.61 & ( finite48957584at_nat @ ( labele2032268018at_nat @ ( produc1564126365at_nat @ standa214789732at_nat ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_14_are__rules_I1_J,axiom,
% 3.03/1.61 ( ( graph_2130075512at_nat @ ( produc719117507_a_nat @ standa1410829644tant_a ) @ ( produc880161797_a_nat @ standa1410829644tant_a ) @ ( id_on_nat @ ( labele1810595089_a_nat @ ( produc719117507_a_nat @ standa1410829644tant_a ) ) ) )
% 3.03/1.61 & ( ( produc880161797_a_nat @ standa1410829644tant_a )
% 3.03/1.61 = ( restri572569417_a_nat @ ( produc880161797_a_nat @ standa1410829644tant_a ) ) )
% 3.03/1.61 & ( finite_finite_nat @ ( labele1810595089_a_nat @ ( produc880161797_a_nat @ standa1410829644tant_a ) ) )
% 3.03/1.61 & ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( produc880161797_a_nat @ standa1410829644tant_a ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_15_are__rules_I1_J,axiom,
% 3.03/1.61 ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ standa879863266rule_b ) @ ( produc194497945_b_nat @ standa879863266rule_b ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ standa879863266rule_b ) ) ) )
% 3.03/1.61 & ( ( produc194497945_b_nat @ standa879863266rule_b )
% 3.03/1.61 = ( restrict_b_nat @ ( produc194497945_b_nat @ standa879863266rule_b ) ) )
% 3.03/1.61 & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ standa879863266rule_b ) ) )
% 3.03/1.61 & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ standa879863266rule_b ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_16_are__rules_I2_J,axiom,
% 3.03/1.61 ! [T: product_prod_nat_nat] :
% 3.03/1.61 ( ( graph_2111906684at_nat @ ( produc1995789403at_nat @ ( standa153097263at_nat @ T ) ) @ ( produc1564126365at_nat @ ( standa153097263at_nat @ T ) ) @ ( id_on_nat @ ( labele560327297at_nat @ ( produc1995789403at_nat @ ( standa153097263at_nat @ T ) ) ) ) )
% 3.03/1.61 & ( ( produc1564126365at_nat @ ( standa153097263at_nat @ T ) )
% 3.03/1.61 = ( restri321299017at_nat @ ( produc1564126365at_nat @ ( standa153097263at_nat @ T ) ) ) )
% 3.03/1.61 & ( finite_finite_nat @ ( labele560327297at_nat @ ( produc1564126365at_nat @ ( standa153097263at_nat @ T ) ) ) )
% 3.03/1.61 & ( finite48957584at_nat @ ( labele2032268018at_nat @ ( produc1564126365at_nat @ ( standa153097263at_nat @ T ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_17_are__rules_I2_J,axiom,
% 3.03/1.61 ! [T: standard_Constant_a] :
% 3.03/1.61 ( ( graph_2130075512at_nat @ ( produc719117507_a_nat @ ( standa305748545tant_a @ T ) ) @ ( produc880161797_a_nat @ ( standa305748545tant_a @ T ) ) @ ( id_on_nat @ ( labele1810595089_a_nat @ ( produc719117507_a_nat @ ( standa305748545tant_a @ T ) ) ) ) )
% 3.03/1.61 & ( ( produc880161797_a_nat @ ( standa305748545tant_a @ T ) )
% 3.03/1.61 = ( restri572569417_a_nat @ ( produc880161797_a_nat @ ( standa305748545tant_a @ T ) ) ) )
% 3.03/1.61 & ( finite_finite_nat @ ( labele1810595089_a_nat @ ( produc880161797_a_nat @ ( standa305748545tant_a @ T ) ) ) )
% 3.03/1.61 & ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( produc880161797_a_nat @ ( standa305748545tant_a @ T ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_18_are__rules_I2_J,axiom,
% 3.03/1.61 ! [T: b] :
% 3.03/1.61 ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( standa1360217389rule_b @ T ) ) @ ( produc194497945_b_nat @ ( standa1360217389rule_b @ T ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( standa1360217389rule_b @ T ) ) ) ) )
% 3.03/1.61 & ( ( produc194497945_b_nat @ ( standa1360217389rule_b @ T ) )
% 3.03/1.61 = ( restrict_b_nat @ ( produc194497945_b_nat @ ( standa1360217389rule_b @ T ) ) ) )
% 3.03/1.61 & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( standa1360217389rule_b @ T ) ) ) )
% 3.03/1.61 & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( standa1360217389rule_b @ T ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_19_verts__in__translation__finite_I1_J,axiom,
% 3.03/1.61 ! [X: allego510293162tant_a] : ( finite_finite_nat @ ( labele1810595089_a_nat @ ( transl1275713022tant_a @ X ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_20_verts__in__translation__finite_I1_J,axiom,
% 3.03/1.61 ! [X: allegorical_term_b] : ( finite_finite_nat @ ( labele460410879_b_nat @ ( translation_b @ X ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_21_are__rules_I3_J,axiom,
% 3.03/1.61 ! [I: product_prod_nat_nat] :
% 3.03/1.61 ( ( graph_2111906684at_nat @ ( produc1995789403at_nat @ ( standa2131591247at_nat @ I ) ) @ ( produc1564126365at_nat @ ( standa2131591247at_nat @ I ) ) @ ( id_on_nat @ ( labele560327297at_nat @ ( produc1995789403at_nat @ ( standa2131591247at_nat @ I ) ) ) ) )
% 3.03/1.61 & ( ( produc1564126365at_nat @ ( standa2131591247at_nat @ I ) )
% 3.03/1.61 = ( restri321299017at_nat @ ( produc1564126365at_nat @ ( standa2131591247at_nat @ I ) ) ) )
% 3.03/1.61 & ( finite_finite_nat @ ( labele560327297at_nat @ ( produc1564126365at_nat @ ( standa2131591247at_nat @ I ) ) ) )
% 3.03/1.61 & ( finite48957584at_nat @ ( labele2032268018at_nat @ ( produc1564126365at_nat @ ( standa2131591247at_nat @ I ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_22_are__rules_I3_J,axiom,
% 3.03/1.61 ! [I: standard_Constant_a] :
% 3.03/1.61 ( ( graph_2130075512at_nat @ ( produc719117507_a_nat @ ( standa63370785tant_a @ I ) ) @ ( produc880161797_a_nat @ ( standa63370785tant_a @ I ) ) @ ( id_on_nat @ ( labele1810595089_a_nat @ ( produc719117507_a_nat @ ( standa63370785tant_a @ I ) ) ) ) )
% 3.03/1.61 & ( ( produc880161797_a_nat @ ( standa63370785tant_a @ I ) )
% 3.03/1.61 = ( restri572569417_a_nat @ ( produc880161797_a_nat @ ( standa63370785tant_a @ I ) ) ) )
% 3.03/1.61 & ( finite_finite_nat @ ( labele1810595089_a_nat @ ( produc880161797_a_nat @ ( standa63370785tant_a @ I ) ) ) )
% 3.03/1.61 & ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( produc880161797_a_nat @ ( standa63370785tant_a @ I ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_23_are__rules_I3_J,axiom,
% 3.03/1.61 ! [I: b] :
% 3.03/1.61 ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( standa1329480013rule_b @ I ) ) @ ( produc194497945_b_nat @ ( standa1329480013rule_b @ I ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( standa1329480013rule_b @ I ) ) ) ) )
% 3.03/1.61 & ( ( produc194497945_b_nat @ ( standa1329480013rule_b @ I ) )
% 3.03/1.61 = ( restrict_b_nat @ ( produc194497945_b_nat @ ( standa1329480013rule_b @ I ) ) ) )
% 3.03/1.61 & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( standa1329480013rule_b @ I ) ) ) )
% 3.03/1.61 & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( standa1329480013rule_b @ I ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_24_prod_Ocollapse,axiom,
% 3.03/1.61 ! [Prod: product_prod_nat_nat] :
% 3.03/1.61 ( ( product_Pair_nat_nat @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) )
% 3.03/1.61 = Prod ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_25_prod_Ocollapse,axiom,
% 3.03/1.61 ! [Prod: produc398057191_a_nat] :
% 3.03/1.61 ( ( produc1677124439_a_nat @ ( produc1049080131_a_nat @ Prod ) @ ( produc1022852229_a_nat @ Prod ) )
% 3.03/1.61 = Prod ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_26_prod_Ocollapse,axiom,
% 3.03/1.61 ! [Prod: produc1871334759_a_nat] :
% 3.03/1.61 ( ( produc1676969687_a_nat @ ( produc719117507_a_nat @ Prod ) @ ( produc880161797_a_nat @ Prod ) )
% 3.03/1.61 = Prod ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_27_prod_Ocollapse,axiom,
% 3.03/1.61 ! [Prod: produc1478835367term_b] :
% 3.03/1.61 ( ( produc1990145943term_b @ ( produc854192515term_b @ Prod ) @ ( produc1223098053term_b @ Prod ) )
% 3.03/1.61 = Prod ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_28_prod_Ocollapse,axiom,
% 3.03/1.61 ! [Prod: produc1235635379_b_nat] :
% 3.03/1.61 ( ( produc951298923_b_nat @ ( produc1542243159_b_nat @ Prod ) @ ( produc194497945_b_nat @ Prod ) )
% 3.03/1.61 = Prod ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_29_translation__graph,axiom,
% 3.03/1.61 ( transl1275713022tant_a
% 3.03/1.61 = ( ^ [X2: allego510293162tant_a] : ( restri572569417_a_nat @ ( transl1275713022tant_a @ X2 ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_30_translation__graph,axiom,
% 3.03/1.61 ( translation_b
% 3.03/1.61 = ( ^ [X2: allegorical_term_b] : ( restrict_b_nat @ ( translation_b @ X2 ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_31_vertices__restrict,axiom,
% 3.03/1.61 ! [G: labele935650037_a_nat] :
% 3.03/1.61 ( ( labele1810595089_a_nat @ ( restri572569417_a_nat @ G ) )
% 3.03/1.61 = ( labele1810595089_a_nat @ G ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_32_vertices__restrict,axiom,
% 3.03/1.61 ! [G: labeled_graph_b_nat] :
% 3.03/1.61 ( ( labele460410879_b_nat @ ( restrict_b_nat @ G ) )
% 3.03/1.61 = ( labele460410879_b_nat @ G ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_33_old_Oprod_Oinject,axiom,
% 3.03/1.61 ! [A: nat,B: nat,A2: nat,B2: nat] :
% 3.03/1.61 ( ( ( product_Pair_nat_nat @ A @ B )
% 3.03/1.61 = ( product_Pair_nat_nat @ A2 @ B2 ) )
% 3.03/1.61 = ( ( A = A2 )
% 3.03/1.61 & ( B = B2 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_34_old_Oprod_Oinject,axiom,
% 3.03/1.61 ! [A: produc1871334759_a_nat,B: produc1871334759_a_nat,A2: produc1871334759_a_nat,B2: produc1871334759_a_nat] :
% 3.03/1.61 ( ( ( produc1677124439_a_nat @ A @ B )
% 3.03/1.61 = ( produc1677124439_a_nat @ A2 @ B2 ) )
% 3.03/1.61 = ( ( A = A2 )
% 3.03/1.61 & ( B = B2 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_35_old_Oprod_Oinject,axiom,
% 3.03/1.61 ! [A: labele935650037_a_nat,B: labele935650037_a_nat,A2: labele935650037_a_nat,B2: labele935650037_a_nat] :
% 3.03/1.61 ( ( ( produc1676969687_a_nat @ A @ B )
% 3.03/1.61 = ( produc1676969687_a_nat @ A2 @ B2 ) )
% 3.03/1.61 = ( ( A = A2 )
% 3.03/1.61 & ( B = B2 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_36_old_Oprod_Oinject,axiom,
% 3.03/1.61 ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,A2: labeled_graph_b_nat,B2: labeled_graph_b_nat] :
% 3.03/1.61 ( ( ( produc951298923_b_nat @ A @ B )
% 3.03/1.61 = ( produc951298923_b_nat @ A2 @ B2 ) )
% 3.03/1.61 = ( ( A = A2 )
% 3.03/1.61 & ( B = B2 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_37_old_Oprod_Oinject,axiom,
% 3.03/1.61 ! [A: allegorical_term_b,B: allegorical_term_b,A2: allegorical_term_b,B2: allegorical_term_b] :
% 3.03/1.61 ( ( ( produc1990145943term_b @ A @ B )
% 3.03/1.61 = ( produc1990145943term_b @ A2 @ B2 ) )
% 3.03/1.61 = ( ( A = A2 )
% 3.03/1.61 & ( B = B2 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_38_prod_Oinject,axiom,
% 3.03/1.61 ! [X1: nat,X22: nat,Y1: nat,Y2: nat] :
% 3.03/1.61 ( ( ( product_Pair_nat_nat @ X1 @ X22 )
% 3.03/1.61 = ( product_Pair_nat_nat @ Y1 @ Y2 ) )
% 3.03/1.61 = ( ( X1 = Y1 )
% 3.03/1.61 & ( X22 = Y2 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_39_prod_Oinject,axiom,
% 3.03/1.61 ! [X1: produc1871334759_a_nat,X22: produc1871334759_a_nat,Y1: produc1871334759_a_nat,Y2: produc1871334759_a_nat] :
% 3.03/1.61 ( ( ( produc1677124439_a_nat @ X1 @ X22 )
% 3.03/1.61 = ( produc1677124439_a_nat @ Y1 @ Y2 ) )
% 3.03/1.61 = ( ( X1 = Y1 )
% 3.03/1.61 & ( X22 = Y2 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_40_prod_Oinject,axiom,
% 3.03/1.61 ! [X1: labele935650037_a_nat,X22: labele935650037_a_nat,Y1: labele935650037_a_nat,Y2: labele935650037_a_nat] :
% 3.03/1.61 ( ( ( produc1676969687_a_nat @ X1 @ X22 )
% 3.03/1.61 = ( produc1676969687_a_nat @ Y1 @ Y2 ) )
% 3.03/1.61 = ( ( X1 = Y1 )
% 3.03/1.61 & ( X22 = Y2 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_41_prod_Oinject,axiom,
% 3.03/1.61 ! [X1: labeled_graph_b_nat,X22: labeled_graph_b_nat,Y1: labeled_graph_b_nat,Y2: labeled_graph_b_nat] :
% 3.03/1.61 ( ( ( produc951298923_b_nat @ X1 @ X22 )
% 3.03/1.61 = ( produc951298923_b_nat @ Y1 @ Y2 ) )
% 3.03/1.61 = ( ( X1 = Y1 )
% 3.03/1.61 & ( X22 = Y2 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_42_prod_Oinject,axiom,
% 3.03/1.61 ! [X1: allegorical_term_b,X22: allegorical_term_b,Y1: allegorical_term_b,Y2: allegorical_term_b] :
% 3.03/1.61 ( ( ( produc1990145943term_b @ X1 @ X22 )
% 3.03/1.61 = ( produc1990145943term_b @ Y1 @ Y2 ) )
% 3.03/1.61 = ( ( X1 = Y1 )
% 3.03/1.61 & ( X22 = Y2 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_43_restrict__idemp,axiom,
% 3.03/1.61 ! [X3: labele935650037_a_nat] :
% 3.03/1.61 ( ( restri572569417_a_nat @ ( restri572569417_a_nat @ X3 ) )
% 3.03/1.61 = ( restri572569417_a_nat @ X3 ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_44_restrict__idemp,axiom,
% 3.03/1.61 ! [X3: labeled_graph_b_nat] :
% 3.03/1.61 ( ( restrict_b_nat @ ( restrict_b_nat @ X3 ) )
% 3.03/1.61 = ( restrict_b_nat @ X3 ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_45_old_Oprod_Oinducts,axiom,
% 3.03/1.61 ! [P: product_prod_nat_nat > $o,Prod: product_prod_nat_nat] :
% 3.03/1.61 ( ! [A3: nat,B3: nat] : ( P @ ( product_Pair_nat_nat @ A3 @ B3 ) )
% 3.03/1.61 => ( P @ Prod ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_46_old_Oprod_Oinducts,axiom,
% 3.03/1.61 ! [P: produc398057191_a_nat > $o,Prod: produc398057191_a_nat] :
% 3.03/1.61 ( ! [A3: produc1871334759_a_nat,B3: produc1871334759_a_nat] : ( P @ ( produc1677124439_a_nat @ A3 @ B3 ) )
% 3.03/1.61 => ( P @ Prod ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_47_old_Oprod_Oinducts,axiom,
% 3.03/1.61 ! [P: produc1871334759_a_nat > $o,Prod: produc1871334759_a_nat] :
% 3.03/1.61 ( ! [A3: labele935650037_a_nat,B3: labele935650037_a_nat] : ( P @ ( produc1676969687_a_nat @ A3 @ B3 ) )
% 3.03/1.61 => ( P @ Prod ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_48_old_Oprod_Oinducts,axiom,
% 3.03/1.61 ! [P: produc1235635379_b_nat > $o,Prod: produc1235635379_b_nat] :
% 3.03/1.61 ( ! [A3: labeled_graph_b_nat,B3: labeled_graph_b_nat] : ( P @ ( produc951298923_b_nat @ A3 @ B3 ) )
% 3.03/1.61 => ( P @ Prod ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_49_old_Oprod_Oinducts,axiom,
% 3.03/1.61 ! [P: produc1478835367term_b > $o,Prod: produc1478835367term_b] :
% 3.03/1.61 ( ! [A3: allegorical_term_b,B3: allegorical_term_b] : ( P @ ( produc1990145943term_b @ A3 @ B3 ) )
% 3.03/1.61 => ( P @ Prod ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_50_old_Oprod_Oexhaust,axiom,
% 3.03/1.61 ! [Y3: product_prod_nat_nat] :
% 3.03/1.61 ~ ! [A3: nat,B3: nat] :
% 3.03/1.61 ( Y3
% 3.03/1.61 != ( product_Pair_nat_nat @ A3 @ B3 ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_51_old_Oprod_Oexhaust,axiom,
% 3.03/1.61 ! [Y3: produc398057191_a_nat] :
% 3.03/1.61 ~ ! [A3: produc1871334759_a_nat,B3: produc1871334759_a_nat] :
% 3.03/1.61 ( Y3
% 3.03/1.61 != ( produc1677124439_a_nat @ A3 @ B3 ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_52_old_Oprod_Oexhaust,axiom,
% 3.03/1.61 ! [Y3: produc1871334759_a_nat] :
% 3.03/1.61 ~ ! [A3: labele935650037_a_nat,B3: labele935650037_a_nat] :
% 3.03/1.61 ( Y3
% 3.03/1.61 != ( produc1676969687_a_nat @ A3 @ B3 ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_53_old_Oprod_Oexhaust,axiom,
% 3.03/1.61 ! [Y3: produc1235635379_b_nat] :
% 3.03/1.61 ~ ! [A3: labeled_graph_b_nat,B3: labeled_graph_b_nat] :
% 3.03/1.61 ( Y3
% 3.03/1.61 != ( produc951298923_b_nat @ A3 @ B3 ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_54_old_Oprod_Oexhaust,axiom,
% 3.03/1.61 ! [Y3: produc1478835367term_b] :
% 3.03/1.61 ~ ! [A3: allegorical_term_b,B3: allegorical_term_b] :
% 3.03/1.61 ( Y3
% 3.03/1.61 != ( produc1990145943term_b @ A3 @ B3 ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_55_prod__induct3,axiom,
% 3.03/1.61 ! [P: produc398057191_a_nat > $o,X3: produc398057191_a_nat] :
% 3.03/1.61 ( ! [A3: produc1871334759_a_nat,B3: labele935650037_a_nat,C: labele935650037_a_nat] : ( P @ ( produc1677124439_a_nat @ A3 @ ( produc1676969687_a_nat @ B3 @ C ) ) )
% 3.03/1.61 => ( P @ X3 ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_56_prod__cases3,axiom,
% 3.03/1.61 ! [Y3: produc398057191_a_nat] :
% 3.03/1.61 ~ ! [A3: produc1871334759_a_nat,B3: labele935650037_a_nat,C: labele935650037_a_nat] :
% 3.03/1.61 ( Y3
% 3.03/1.61 != ( produc1677124439_a_nat @ A3 @ ( produc1676969687_a_nat @ B3 @ C ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_57_Pair__inject,axiom,
% 3.03/1.61 ! [A: nat,B: nat,A2: nat,B2: nat] :
% 3.03/1.61 ( ( ( product_Pair_nat_nat @ A @ B )
% 3.03/1.61 = ( product_Pair_nat_nat @ A2 @ B2 ) )
% 3.03/1.61 => ~ ( ( A = A2 )
% 3.03/1.61 => ( B != B2 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_58_Pair__inject,axiom,
% 3.03/1.61 ! [A: produc1871334759_a_nat,B: produc1871334759_a_nat,A2: produc1871334759_a_nat,B2: produc1871334759_a_nat] :
% 3.03/1.61 ( ( ( produc1677124439_a_nat @ A @ B )
% 3.03/1.61 = ( produc1677124439_a_nat @ A2 @ B2 ) )
% 3.03/1.61 => ~ ( ( A = A2 )
% 3.03/1.61 => ( B != B2 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_59_Pair__inject,axiom,
% 3.03/1.61 ! [A: labele935650037_a_nat,B: labele935650037_a_nat,A2: labele935650037_a_nat,B2: labele935650037_a_nat] :
% 3.03/1.61 ( ( ( produc1676969687_a_nat @ A @ B )
% 3.03/1.61 = ( produc1676969687_a_nat @ A2 @ B2 ) )
% 3.03/1.61 => ~ ( ( A = A2 )
% 3.03/1.61 => ( B != B2 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_60_Pair__inject,axiom,
% 3.03/1.61 ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,A2: labeled_graph_b_nat,B2: labeled_graph_b_nat] :
% 3.03/1.61 ( ( ( produc951298923_b_nat @ A @ B )
% 3.03/1.61 = ( produc951298923_b_nat @ A2 @ B2 ) )
% 3.03/1.61 => ~ ( ( A = A2 )
% 3.03/1.61 => ( B != B2 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_61_Pair__inject,axiom,
% 3.03/1.61 ! [A: allegorical_term_b,B: allegorical_term_b,A2: allegorical_term_b,B2: allegorical_term_b] :
% 3.03/1.61 ( ( ( produc1990145943term_b @ A @ B )
% 3.03/1.61 = ( produc1990145943term_b @ A2 @ B2 ) )
% 3.03/1.61 => ~ ( ( A = A2 )
% 3.03/1.61 => ( B != B2 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_62_prod__cases,axiom,
% 3.03/1.61 ! [P: product_prod_nat_nat > $o,P2: product_prod_nat_nat] :
% 3.03/1.61 ( ! [A3: nat,B3: nat] : ( P @ ( product_Pair_nat_nat @ A3 @ B3 ) )
% 3.03/1.61 => ( P @ P2 ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_63_prod__cases,axiom,
% 3.03/1.61 ! [P: produc398057191_a_nat > $o,P2: produc398057191_a_nat] :
% 3.03/1.61 ( ! [A3: produc1871334759_a_nat,B3: produc1871334759_a_nat] : ( P @ ( produc1677124439_a_nat @ A3 @ B3 ) )
% 3.03/1.61 => ( P @ P2 ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_64_prod__cases,axiom,
% 3.03/1.61 ! [P: produc1871334759_a_nat > $o,P2: produc1871334759_a_nat] :
% 3.03/1.61 ( ! [A3: labele935650037_a_nat,B3: labele935650037_a_nat] : ( P @ ( produc1676969687_a_nat @ A3 @ B3 ) )
% 3.03/1.61 => ( P @ P2 ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_65_prod__cases,axiom,
% 3.03/1.61 ! [P: produc1235635379_b_nat > $o,P2: produc1235635379_b_nat] :
% 3.03/1.61 ( ! [A3: labeled_graph_b_nat,B3: labeled_graph_b_nat] : ( P @ ( produc951298923_b_nat @ A3 @ B3 ) )
% 3.03/1.61 => ( P @ P2 ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_66_prod__cases,axiom,
% 3.03/1.61 ! [P: produc1478835367term_b > $o,P2: produc1478835367term_b] :
% 3.03/1.61 ( ! [A3: allegorical_term_b,B3: allegorical_term_b] : ( P @ ( produc1990145943term_b @ A3 @ B3 ) )
% 3.03/1.61 => ( P @ P2 ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_67_surj__pair,axiom,
% 3.03/1.61 ! [P2: product_prod_nat_nat] :
% 3.03/1.61 ? [X4: nat,Y4: nat] :
% 3.03/1.61 ( P2
% 3.03/1.61 = ( product_Pair_nat_nat @ X4 @ Y4 ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_68_surj__pair,axiom,
% 3.03/1.61 ! [P2: produc398057191_a_nat] :
% 3.03/1.61 ? [X4: produc1871334759_a_nat,Y4: produc1871334759_a_nat] :
% 3.03/1.61 ( P2
% 3.03/1.61 = ( produc1677124439_a_nat @ X4 @ Y4 ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_69_surj__pair,axiom,
% 3.03/1.61 ! [P2: produc1871334759_a_nat] :
% 3.03/1.61 ? [X4: labele935650037_a_nat,Y4: labele935650037_a_nat] :
% 3.03/1.61 ( P2
% 3.03/1.61 = ( produc1676969687_a_nat @ X4 @ Y4 ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_70_surj__pair,axiom,
% 3.03/1.61 ! [P2: produc1235635379_b_nat] :
% 3.03/1.61 ? [X4: labeled_graph_b_nat,Y4: labeled_graph_b_nat] :
% 3.03/1.61 ( P2
% 3.03/1.61 = ( produc951298923_b_nat @ X4 @ Y4 ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_71_surj__pair,axiom,
% 3.03/1.61 ! [P2: produc1478835367term_b] :
% 3.03/1.61 ? [X4: allegorical_term_b,Y4: allegorical_term_b] :
% 3.03/1.61 ( P2
% 3.03/1.61 = ( produc1990145943term_b @ X4 @ Y4 ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_72_fst__conv,axiom,
% 3.03/1.61 ! [X1: nat,X22: nat] :
% 3.03/1.61 ( ( product_fst_nat_nat @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 3.03/1.61 = X1 ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_73_fst__conv,axiom,
% 3.03/1.61 ! [X1: produc1871334759_a_nat,X22: produc1871334759_a_nat] :
% 3.03/1.61 ( ( produc1049080131_a_nat @ ( produc1677124439_a_nat @ X1 @ X22 ) )
% 3.03/1.61 = X1 ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_74_fst__conv,axiom,
% 3.03/1.61 ! [X1: labele935650037_a_nat,X22: labele935650037_a_nat] :
% 3.03/1.61 ( ( produc719117507_a_nat @ ( produc1676969687_a_nat @ X1 @ X22 ) )
% 3.03/1.61 = X1 ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_75_fst__conv,axiom,
% 3.03/1.61 ! [X1: labeled_graph_b_nat,X22: labeled_graph_b_nat] :
% 3.03/1.61 ( ( produc1542243159_b_nat @ ( produc951298923_b_nat @ X1 @ X22 ) )
% 3.03/1.61 = X1 ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_76_fst__conv,axiom,
% 3.03/1.61 ! [X1: allegorical_term_b,X22: allegorical_term_b] :
% 3.03/1.61 ( ( produc854192515term_b @ ( produc1990145943term_b @ X1 @ X22 ) )
% 3.03/1.61 = X1 ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_77_fst__eqD,axiom,
% 3.03/1.61 ! [X3: nat,Y3: nat,A: nat] :
% 3.03/1.61 ( ( ( product_fst_nat_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 3.03/1.61 = A )
% 3.03/1.61 => ( X3 = A ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_78_fst__eqD,axiom,
% 3.03/1.61 ! [X3: produc1871334759_a_nat,Y3: produc1871334759_a_nat,A: produc1871334759_a_nat] :
% 3.03/1.61 ( ( ( produc1049080131_a_nat @ ( produc1677124439_a_nat @ X3 @ Y3 ) )
% 3.03/1.61 = A )
% 3.03/1.61 => ( X3 = A ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_79_fst__eqD,axiom,
% 3.03/1.61 ! [X3: labele935650037_a_nat,Y3: labele935650037_a_nat,A: labele935650037_a_nat] :
% 3.03/1.61 ( ( ( produc719117507_a_nat @ ( produc1676969687_a_nat @ X3 @ Y3 ) )
% 3.03/1.61 = A )
% 3.03/1.61 => ( X3 = A ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_80_fst__eqD,axiom,
% 3.03/1.61 ! [X3: labeled_graph_b_nat,Y3: labeled_graph_b_nat,A: labeled_graph_b_nat] :
% 3.03/1.61 ( ( ( produc1542243159_b_nat @ ( produc951298923_b_nat @ X3 @ Y3 ) )
% 3.03/1.61 = A )
% 3.03/1.61 => ( X3 = A ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_81_fst__eqD,axiom,
% 3.03/1.61 ! [X3: allegorical_term_b,Y3: allegorical_term_b,A: allegorical_term_b] :
% 3.03/1.61 ( ( ( produc854192515term_b @ ( produc1990145943term_b @ X3 @ Y3 ) )
% 3.03/1.61 = A )
% 3.03/1.61 => ( X3 = A ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_82_snd__conv,axiom,
% 3.03/1.61 ! [X1: nat,X22: nat] :
% 3.03/1.61 ( ( product_snd_nat_nat @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 3.03/1.61 = X22 ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_83_snd__conv,axiom,
% 3.03/1.61 ! [X1: produc1871334759_a_nat,X22: produc1871334759_a_nat] :
% 3.03/1.61 ( ( produc1022852229_a_nat @ ( produc1677124439_a_nat @ X1 @ X22 ) )
% 3.03/1.61 = X22 ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_84_snd__conv,axiom,
% 3.03/1.61 ! [X1: labele935650037_a_nat,X22: labele935650037_a_nat] :
% 3.03/1.61 ( ( produc880161797_a_nat @ ( produc1676969687_a_nat @ X1 @ X22 ) )
% 3.03/1.61 = X22 ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_85_snd__conv,axiom,
% 3.03/1.61 ! [X1: allegorical_term_b,X22: allegorical_term_b] :
% 3.03/1.61 ( ( produc1223098053term_b @ ( produc1990145943term_b @ X1 @ X22 ) )
% 3.03/1.61 = X22 ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_86_snd__conv,axiom,
% 3.03/1.61 ! [X1: labeled_graph_b_nat,X22: labeled_graph_b_nat] :
% 3.03/1.61 ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ X1 @ X22 ) )
% 3.03/1.61 = X22 ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_87_snd__eqD,axiom,
% 3.03/1.61 ! [X3: nat,Y3: nat,A: nat] :
% 3.03/1.61 ( ( ( product_snd_nat_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 3.03/1.61 = A )
% 3.03/1.61 => ( Y3 = A ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_88_snd__eqD,axiom,
% 3.03/1.61 ! [X3: produc1871334759_a_nat,Y3: produc1871334759_a_nat,A: produc1871334759_a_nat] :
% 3.03/1.61 ( ( ( produc1022852229_a_nat @ ( produc1677124439_a_nat @ X3 @ Y3 ) )
% 3.03/1.61 = A )
% 3.03/1.61 => ( Y3 = A ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_89_snd__eqD,axiom,
% 3.03/1.61 ! [X3: labele935650037_a_nat,Y3: labele935650037_a_nat,A: labele935650037_a_nat] :
% 3.03/1.61 ( ( ( produc880161797_a_nat @ ( produc1676969687_a_nat @ X3 @ Y3 ) )
% 3.03/1.61 = A )
% 3.03/1.61 => ( Y3 = A ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_90_snd__eqD,axiom,
% 3.03/1.61 ! [X3: allegorical_term_b,Y3: allegorical_term_b,A: allegorical_term_b] :
% 3.03/1.61 ( ( ( produc1223098053term_b @ ( produc1990145943term_b @ X3 @ Y3 ) )
% 3.03/1.61 = A )
% 3.03/1.61 => ( Y3 = A ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_91_snd__eqD,axiom,
% 3.03/1.61 ! [X3: labeled_graph_b_nat,Y3: labeled_graph_b_nat,A: labeled_graph_b_nat] :
% 3.03/1.61 ( ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ X3 @ Y3 ) )
% 3.03/1.61 = A )
% 3.03/1.61 => ( Y3 = A ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_92_prod__eq__iff,axiom,
% 3.03/1.61 ( ( ^ [Y5: produc1871334759_a_nat,Z: produc1871334759_a_nat] : ( Y5 = Z ) )
% 3.03/1.61 = ( ^ [S: produc1871334759_a_nat,T2: produc1871334759_a_nat] :
% 3.03/1.61 ( ( ( produc719117507_a_nat @ S )
% 3.03/1.61 = ( produc719117507_a_nat @ T2 ) )
% 3.03/1.61 & ( ( produc880161797_a_nat @ S )
% 3.03/1.61 = ( produc880161797_a_nat @ T2 ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_93_prod__eq__iff,axiom,
% 3.03/1.61 ( ( ^ [Y5: produc1478835367term_b,Z: produc1478835367term_b] : ( Y5 = Z ) )
% 3.03/1.61 = ( ^ [S: produc1478835367term_b,T2: produc1478835367term_b] :
% 3.03/1.61 ( ( ( produc854192515term_b @ S )
% 3.03/1.61 = ( produc854192515term_b @ T2 ) )
% 3.03/1.61 & ( ( produc1223098053term_b @ S )
% 3.03/1.61 = ( produc1223098053term_b @ T2 ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_94_prod__eq__iff,axiom,
% 3.03/1.61 ( ( ^ [Y5: produc1235635379_b_nat,Z: produc1235635379_b_nat] : ( Y5 = Z ) )
% 3.03/1.61 = ( ^ [S: produc1235635379_b_nat,T2: produc1235635379_b_nat] :
% 3.03/1.61 ( ( ( produc1542243159_b_nat @ S )
% 3.03/1.61 = ( produc1542243159_b_nat @ T2 ) )
% 3.03/1.61 & ( ( produc194497945_b_nat @ S )
% 3.03/1.61 = ( produc194497945_b_nat @ T2 ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_95_prod_Oexpand,axiom,
% 3.03/1.61 ! [Prod: produc1871334759_a_nat,Prod2: produc1871334759_a_nat] :
% 3.03/1.61 ( ( ( ( produc719117507_a_nat @ Prod )
% 3.03/1.61 = ( produc719117507_a_nat @ Prod2 ) )
% 3.03/1.61 & ( ( produc880161797_a_nat @ Prod )
% 3.03/1.61 = ( produc880161797_a_nat @ Prod2 ) ) )
% 3.03/1.61 => ( Prod = Prod2 ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_96_prod_Oexpand,axiom,
% 3.03/1.61 ! [Prod: produc1478835367term_b,Prod2: produc1478835367term_b] :
% 3.03/1.61 ( ( ( ( produc854192515term_b @ Prod )
% 3.03/1.61 = ( produc854192515term_b @ Prod2 ) )
% 3.03/1.61 & ( ( produc1223098053term_b @ Prod )
% 3.03/1.61 = ( produc1223098053term_b @ Prod2 ) ) )
% 3.03/1.61 => ( Prod = Prod2 ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_97_prod_Oexpand,axiom,
% 3.03/1.61 ! [Prod: produc1235635379_b_nat,Prod2: produc1235635379_b_nat] :
% 3.03/1.61 ( ( ( ( produc1542243159_b_nat @ Prod )
% 3.03/1.61 = ( produc1542243159_b_nat @ Prod2 ) )
% 3.03/1.61 & ( ( produc194497945_b_nat @ Prod )
% 3.03/1.61 = ( produc194497945_b_nat @ Prod2 ) ) )
% 3.03/1.61 => ( Prod = Prod2 ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_98_prod__eqI,axiom,
% 3.03/1.61 ! [P2: produc1871334759_a_nat,Q: produc1871334759_a_nat] :
% 3.03/1.61 ( ( ( produc719117507_a_nat @ P2 )
% 3.03/1.61 = ( produc719117507_a_nat @ Q ) )
% 3.03/1.61 => ( ( ( produc880161797_a_nat @ P2 )
% 3.03/1.61 = ( produc880161797_a_nat @ Q ) )
% 3.03/1.61 => ( P2 = Q ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_99_prod__eqI,axiom,
% 3.03/1.61 ! [P2: produc1478835367term_b,Q: produc1478835367term_b] :
% 3.03/1.61 ( ( ( produc854192515term_b @ P2 )
% 3.03/1.61 = ( produc854192515term_b @ Q ) )
% 3.03/1.61 => ( ( ( produc1223098053term_b @ P2 )
% 3.03/1.61 = ( produc1223098053term_b @ Q ) )
% 3.03/1.61 => ( P2 = Q ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_100_prod__eqI,axiom,
% 3.03/1.61 ! [P2: produc1235635379_b_nat,Q: produc1235635379_b_nat] :
% 3.03/1.61 ( ( ( produc1542243159_b_nat @ P2 )
% 3.03/1.61 = ( produc1542243159_b_nat @ Q ) )
% 3.03/1.61 => ( ( ( produc194497945_b_nat @ P2 )
% 3.03/1.61 = ( produc194497945_b_nat @ Q ) )
% 3.03/1.61 => ( P2 = Q ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_101_labeled__graph_Oexpand,axiom,
% 3.03/1.61 ! [Labeled_graph: labele935650037_a_nat,Labeled_graph2: labele935650037_a_nat] :
% 3.03/1.61 ( ( ( ( labele195203296_a_nat @ Labeled_graph )
% 3.03/1.61 = ( labele195203296_a_nat @ Labeled_graph2 ) )
% 3.03/1.61 & ( ( labele1810595089_a_nat @ Labeled_graph )
% 3.03/1.61 = ( labele1810595089_a_nat @ Labeled_graph2 ) ) )
% 3.03/1.61 => ( Labeled_graph = Labeled_graph2 ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_102_labeled__graph_Oexpand,axiom,
% 3.03/1.61 ! [Labeled_graph: labeled_graph_b_nat,Labeled_graph2: labeled_graph_b_nat] :
% 3.03/1.61 ( ( ( ( labeled_edges_b_nat @ Labeled_graph )
% 3.03/1.61 = ( labeled_edges_b_nat @ Labeled_graph2 ) )
% 3.03/1.61 & ( ( labele460410879_b_nat @ Labeled_graph )
% 3.03/1.61 = ( labele460410879_b_nat @ Labeled_graph2 ) ) )
% 3.03/1.61 => ( Labeled_graph = Labeled_graph2 ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_103_surjective__pairing,axiom,
% 3.03/1.61 ! [T: product_prod_nat_nat] :
% 3.03/1.61 ( T
% 3.03/1.61 = ( product_Pair_nat_nat @ ( product_fst_nat_nat @ T ) @ ( product_snd_nat_nat @ T ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_104_surjective__pairing,axiom,
% 3.03/1.61 ! [T: produc398057191_a_nat] :
% 3.03/1.61 ( T
% 3.03/1.61 = ( produc1677124439_a_nat @ ( produc1049080131_a_nat @ T ) @ ( produc1022852229_a_nat @ T ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_105_surjective__pairing,axiom,
% 3.03/1.61 ! [T: produc1871334759_a_nat] :
% 3.03/1.61 ( T
% 3.03/1.61 = ( produc1676969687_a_nat @ ( produc719117507_a_nat @ T ) @ ( produc880161797_a_nat @ T ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_106_surjective__pairing,axiom,
% 3.03/1.61 ! [T: produc1478835367term_b] :
% 3.03/1.61 ( T
% 3.03/1.61 = ( produc1990145943term_b @ ( produc854192515term_b @ T ) @ ( produc1223098053term_b @ T ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_107_surjective__pairing,axiom,
% 3.03/1.61 ! [T: produc1235635379_b_nat] :
% 3.03/1.61 ( T
% 3.03/1.61 = ( produc951298923_b_nat @ ( produc1542243159_b_nat @ T ) @ ( produc194497945_b_nat @ T ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_108_prod_Oexhaust__sel,axiom,
% 3.03/1.61 ! [Prod: product_prod_nat_nat] :
% 3.03/1.61 ( Prod
% 3.03/1.61 = ( product_Pair_nat_nat @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_109_prod_Oexhaust__sel,axiom,
% 3.03/1.61 ! [Prod: produc398057191_a_nat] :
% 3.03/1.61 ( Prod
% 3.03/1.61 = ( produc1677124439_a_nat @ ( produc1049080131_a_nat @ Prod ) @ ( produc1022852229_a_nat @ Prod ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_110_prod_Oexhaust__sel,axiom,
% 3.03/1.61 ! [Prod: produc1871334759_a_nat] :
% 3.03/1.61 ( Prod
% 3.03/1.61 = ( produc1676969687_a_nat @ ( produc719117507_a_nat @ Prod ) @ ( produc880161797_a_nat @ Prod ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_111_prod_Oexhaust__sel,axiom,
% 3.03/1.61 ! [Prod: produc1478835367term_b] :
% 3.03/1.61 ( Prod
% 3.03/1.61 = ( produc1990145943term_b @ ( produc854192515term_b @ Prod ) @ ( produc1223098053term_b @ Prod ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_112_prod_Oexhaust__sel,axiom,
% 3.03/1.61 ! [Prod: produc1235635379_b_nat] :
% 3.03/1.61 ( Prod
% 3.03/1.61 = ( produc951298923_b_nat @ ( produc1542243159_b_nat @ Prod ) @ ( produc194497945_b_nat @ Prod ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_113_subgraph__preserves__hom,axiom,
% 3.03/1.61 ! [A4: labele935650037_a_nat,B4: labele935650037_a_nat,X: labele935650037_a_nat,H: set_Pr1986765409at_nat] :
% 3.03/1.61 ( ( graph_2130075512at_nat @ A4 @ B4 @ ( id_on_nat @ ( labele1810595089_a_nat @ A4 ) ) )
% 3.03/1.61 => ( ( graph_2130075512at_nat @ X @ A4 @ H )
% 3.03/1.61 => ( graph_2130075512at_nat @ X @ B4 @ H ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_114_subgraph__preserves__hom,axiom,
% 3.03/1.61 ! [A4: labeled_graph_b_nat,B4: labeled_graph_b_nat,X: labeled_graph_b_nat,H: set_Pr1986765409at_nat] :
% 3.03/1.61 ( ( graph_529870330at_nat @ A4 @ B4 @ ( id_on_nat @ ( labele460410879_b_nat @ A4 ) ) )
% 3.03/1.61 => ( ( graph_529870330at_nat @ X @ A4 @ H )
% 3.03/1.61 => ( graph_529870330at_nat @ X @ B4 @ H ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_115_subgraph__trans,axiom,
% 3.03/1.61 ! [G_1: labele935650037_a_nat,G_2: labele935650037_a_nat,G_3: labele935650037_a_nat] :
% 3.03/1.61 ( ( graph_2130075512at_nat @ G_1 @ G_2 @ ( id_on_nat @ ( labele1810595089_a_nat @ G_1 ) ) )
% 3.03/1.61 => ( ( graph_2130075512at_nat @ G_2 @ G_3 @ ( id_on_nat @ ( labele1810595089_a_nat @ G_2 ) ) )
% 3.03/1.61 => ( graph_2130075512at_nat @ G_1 @ G_3 @ ( id_on_nat @ ( labele1810595089_a_nat @ G_1 ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_116_subgraph__trans,axiom,
% 3.03/1.61 ! [G_1: labeled_graph_b_nat,G_2: labeled_graph_b_nat,G_3: labeled_graph_b_nat] :
% 3.03/1.61 ( ( graph_529870330at_nat @ G_1 @ G_2 @ ( id_on_nat @ ( labele460410879_b_nat @ G_1 ) ) )
% 3.03/1.61 => ( ( graph_529870330at_nat @ G_2 @ G_3 @ ( id_on_nat @ ( labele460410879_b_nat @ G_2 ) ) )
% 3.03/1.61 => ( graph_529870330at_nat @ G_1 @ G_3 @ ( id_on_nat @ ( labele460410879_b_nat @ G_1 ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_117_Id__onI,axiom,
% 3.03/1.61 ! [A: produc1478835367term_b,A4: set_Pr1163220871term_b] :
% 3.03/1.61 ( ( member516522448term_b @ A @ A4 )
% 3.03/1.61 => ( member1449757456term_b @ ( produc859843415term_b @ A @ A ) @ ( id_on_1664915780term_b @ A4 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_118_Id__onI,axiom,
% 3.03/1.61 ! [A: produc1235635379_b_nat,A4: set_Pr551076371_b_nat] :
% 3.03/1.61 ( ( member963855452_b_nat @ A @ A4 )
% 3.03/1.61 => ( member889223696_b_nat @ ( produc1754969175_b_nat @ A @ A ) @ ( id_on_138931664_b_nat @ A4 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_119_Id__onI,axiom,
% 3.03/1.61 ! [A: produc398057191_a_nat,A4: set_Pr924198087_a_nat] :
% 3.03/1.61 ( ( member584645392_a_nat @ A @ A4 )
% 3.03/1.61 => ( member829905680_a_nat @ ( produc170611543_a_nat @ A @ A ) @ ( id_on_1395957380_a_nat @ A4 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_120_Id__onI,axiom,
% 3.03/1.61 ! [A: product_prod_nat_nat,A4: set_Pr1986765409at_nat] :
% 3.03/1.61 ( ( member701585322at_nat @ A @ A4 )
% 3.03/1.61 => ( member2027625872at_nat @ ( produc1168807639at_nat @ A @ A ) @ ( id_on_2144791838at_nat @ A4 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_121_Id__onI,axiom,
% 3.03/1.61 ! [A: labele935650037_a_nat,A4: set_la1083530965_a_nat] :
% 3.03/1.61 ( ( member964390942_a_nat @ A @ A4 )
% 3.03/1.61 => ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ A ) @ ( id_on_689842066_a_nat @ A4 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_122_Id__onI,axiom,
% 3.03/1.61 ! [A: produc1871334759_a_nat,A4: set_Pr1987088711_a_nat] :
% 3.03/1.61 ( ( member832397200_a_nat @ A @ A4 )
% 3.03/1.61 => ( member584645392_a_nat @ ( produc1677124439_a_nat @ A @ A ) @ ( id_on_1651096324_a_nat @ A4 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_123_Id__onI,axiom,
% 3.03/1.61 ! [A: nat,A4: set_nat] :
% 3.03/1.61 ( ( member_nat @ A @ A4 )
% 3.03/1.61 => ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ A ) @ ( id_on_nat @ A4 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_124_Id__onI,axiom,
% 3.03/1.61 ! [A: labeled_graph_b_nat,A4: set_la1976028319_b_nat] :
% 3.03/1.61 ( ( member1483953152_b_nat @ A @ A4 )
% 3.03/1.61 => ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ A ) @ ( id_on_583275916_b_nat @ A4 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_125_Id__onI,axiom,
% 3.03/1.61 ! [A: allegorical_term_b,A4: set_al1193902458term_b] :
% 3.03/1.61 ( ( member93680451term_b @ A @ A4 )
% 3.03/1.61 => ( member516522448term_b @ ( produc1990145943term_b @ A @ A ) @ ( id_on_1536886967term_b @ A4 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_126_set__of__graph__rules__def,axiom,
% 3.03/1.61 ( set_of195930477at_nat
% 3.03/1.61 = ( ^ [Rs: set_Pr665622551at_nat] :
% 3.03/1.61 ! [X5: produc1391440311at_nat] :
% 3.03/1.61 ( ( member1129678944at_nat @ X5 @ Rs )
% 3.03/1.61 => ( ( graph_2111906684at_nat @ ( produc1995789403at_nat @ X5 ) @ ( produc1564126365at_nat @ X5 ) @ ( id_on_nat @ ( labele560327297at_nat @ ( produc1995789403at_nat @ X5 ) ) ) )
% 3.03/1.61 & ( ( produc1564126365at_nat @ X5 )
% 3.03/1.61 = ( restri321299017at_nat @ ( produc1564126365at_nat @ X5 ) ) )
% 3.03/1.61 & ( finite_finite_nat @ ( labele560327297at_nat @ ( produc1564126365at_nat @ X5 ) ) )
% 3.03/1.61 & ( finite48957584at_nat @ ( labele2032268018at_nat @ ( produc1564126365at_nat @ X5 ) ) ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_127_set__of__graph__rules__def,axiom,
% 3.03/1.61 ( set_of1384085797_a_nat
% 3.03/1.61 = ( ^ [Rs: set_Pr1987088711_a_nat] :
% 3.03/1.61 ! [X5: produc1871334759_a_nat] :
% 3.03/1.61 ( ( member832397200_a_nat @ X5 @ Rs )
% 3.03/1.61 => ( ( graph_2130075512at_nat @ ( produc719117507_a_nat @ X5 ) @ ( produc880161797_a_nat @ X5 ) @ ( id_on_nat @ ( labele1810595089_a_nat @ ( produc719117507_a_nat @ X5 ) ) ) )
% 3.03/1.61 & ( ( produc880161797_a_nat @ X5 )
% 3.03/1.61 = ( restri572569417_a_nat @ ( produc880161797_a_nat @ X5 ) ) )
% 3.03/1.61 & ( finite_finite_nat @ ( labele1810595089_a_nat @ ( produc880161797_a_nat @ X5 ) ) )
% 3.03/1.61 & ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( produc880161797_a_nat @ X5 ) ) ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_128_set__of__graph__rules__def,axiom,
% 3.03/1.61 ( set_of41538795_b_nat
% 3.03/1.61 = ( ^ [Rs: set_Pr551076371_b_nat] :
% 3.03/1.61 ! [X5: produc1235635379_b_nat] :
% 3.03/1.61 ( ( member963855452_b_nat @ X5 @ Rs )
% 3.03/1.61 => ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ X5 ) @ ( produc194497945_b_nat @ X5 ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ X5 ) ) ) )
% 3.03/1.61 & ( ( produc194497945_b_nat @ X5 )
% 3.03/1.61 = ( restrict_b_nat @ ( produc194497945_b_nat @ X5 ) ) )
% 3.03/1.61 & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ X5 ) ) )
% 3.03/1.61 & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ X5 ) ) ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_129_mem__Collect__eq,axiom,
% 3.03/1.61 ! [A: produc1478835367term_b,P: produc1478835367term_b > $o] :
% 3.03/1.61 ( ( member516522448term_b @ A @ ( collec135640594term_b @ P ) )
% 3.03/1.61 = ( P @ A ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_130_mem__Collect__eq,axiom,
% 3.03/1.61 ! [A: produc1235635379_b_nat,P: produc1235635379_b_nat > $o] :
% 3.03/1.61 ( ( member963855452_b_nat @ A @ ( collec1615000990_b_nat @ P ) )
% 3.03/1.61 = ( P @ A ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_131_mem__Collect__eq,axiom,
% 3.03/1.61 ! [A: produc398057191_a_nat,P: produc398057191_a_nat > $o] :
% 3.03/1.61 ( ( member584645392_a_nat @ A @ ( collec1701899602_a_nat @ P ) )
% 3.03/1.61 = ( P @ A ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_132_mem__Collect__eq,axiom,
% 3.03/1.61 ! [A: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 3.03/1.61 ( ( member701585322at_nat @ A @ ( collec7649004at_nat @ P ) )
% 3.03/1.61 = ( P @ A ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_133_mem__Collect__eq,axiom,
% 3.03/1.61 ! [A: nat,P: nat > $o] :
% 3.03/1.61 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 3.03/1.61 = ( P @ A ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_134_mem__Collect__eq,axiom,
% 3.03/1.61 ! [A: produc1871334759_a_nat,P: produc1871334759_a_nat > $o] :
% 3.03/1.61 ( ( member832397200_a_nat @ A @ ( collec357096914_a_nat @ P ) )
% 3.03/1.61 = ( P @ A ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_135_Collect__mem__eq,axiom,
% 3.03/1.61 ! [A4: set_Pr1163220871term_b] :
% 3.03/1.61 ( ( collec135640594term_b
% 3.03/1.61 @ ^ [X5: produc1478835367term_b] : ( member516522448term_b @ X5 @ A4 ) )
% 3.03/1.61 = A4 ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_136_Collect__mem__eq,axiom,
% 3.03/1.61 ! [A4: set_Pr551076371_b_nat] :
% 3.03/1.61 ( ( collec1615000990_b_nat
% 3.03/1.61 @ ^ [X5: produc1235635379_b_nat] : ( member963855452_b_nat @ X5 @ A4 ) )
% 3.03/1.61 = A4 ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_137_Collect__mem__eq,axiom,
% 3.03/1.61 ! [A4: set_Pr924198087_a_nat] :
% 3.03/1.61 ( ( collec1701899602_a_nat
% 3.03/1.61 @ ^ [X5: produc398057191_a_nat] : ( member584645392_a_nat @ X5 @ A4 ) )
% 3.03/1.61 = A4 ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_138_Collect__mem__eq,axiom,
% 3.03/1.61 ! [A4: set_Pr1986765409at_nat] :
% 3.03/1.61 ( ( collec7649004at_nat
% 3.03/1.61 @ ^ [X5: product_prod_nat_nat] : ( member701585322at_nat @ X5 @ A4 ) )
% 3.03/1.61 = A4 ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_139_Collect__mem__eq,axiom,
% 3.03/1.61 ! [A4: set_nat] :
% 3.03/1.61 ( ( collect_nat
% 3.03/1.61 @ ^ [X5: nat] : ( member_nat @ X5 @ A4 ) )
% 3.03/1.61 = A4 ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_140_Collect__mem__eq,axiom,
% 3.03/1.61 ! [A4: set_Pr1987088711_a_nat] :
% 3.03/1.61 ( ( collec357096914_a_nat
% 3.03/1.61 @ ^ [X5: produc1871334759_a_nat] : ( member832397200_a_nat @ X5 @ A4 ) )
% 3.03/1.61 = A4 ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_141_Collect__cong,axiom,
% 3.03/1.61 ! [P: produc1871334759_a_nat > $o,Q2: produc1871334759_a_nat > $o] :
% 3.03/1.61 ( ! [X4: produc1871334759_a_nat] :
% 3.03/1.61 ( ( P @ X4 )
% 3.03/1.61 = ( Q2 @ X4 ) )
% 3.03/1.61 => ( ( collec357096914_a_nat @ P )
% 3.03/1.61 = ( collec357096914_a_nat @ Q2 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_142_verts__in__translation,axiom,
% 3.03/1.61 ! [X: allego510293162tant_a] : ( inv_translation @ ( labele1810595089_a_nat @ ( transl1275713022tant_a @ X ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_143_verts__in__translation,axiom,
% 3.03/1.61 ! [X: allegorical_term_b] : ( inv_translation @ ( labele460410879_b_nat @ ( translation_b @ X ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_144_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 3.03/1.61 ! [P: allegorical_term_b > allegorical_term_b > $o,X3: allegorical_term_b,Y3: allegorical_term_b,A: produc1478835367term_b] :
% 3.03/1.61 ( ( P @ X3 @ Y3 )
% 3.03/1.61 => ( ( A
% 3.03/1.61 = ( produc1990145943term_b @ X3 @ Y3 ) )
% 3.03/1.61 => ( P @ ( produc854192515term_b @ A ) @ ( produc1223098053term_b @ A ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_145_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 3.03/1.61 ! [P: labeled_graph_b_nat > labeled_graph_b_nat > $o,X3: labeled_graph_b_nat,Y3: labeled_graph_b_nat,A: produc1235635379_b_nat] :
% 3.03/1.61 ( ( P @ X3 @ Y3 )
% 3.03/1.61 => ( ( A
% 3.03/1.61 = ( produc951298923_b_nat @ X3 @ Y3 ) )
% 3.03/1.61 => ( P @ ( produc1542243159_b_nat @ A ) @ ( produc194497945_b_nat @ A ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_146_conjI__realizer,axiom,
% 3.03/1.61 ! [P: allegorical_term_b > $o,P2: allegorical_term_b,Q2: allegorical_term_b > $o,Q: allegorical_term_b] :
% 3.03/1.61 ( ( P @ P2 )
% 3.03/1.61 => ( ( Q2 @ Q )
% 3.03/1.61 => ( ( P @ ( produc854192515term_b @ ( produc1990145943term_b @ P2 @ Q ) ) )
% 3.03/1.61 & ( Q2 @ ( produc1223098053term_b @ ( produc1990145943term_b @ P2 @ Q ) ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_147_conjI__realizer,axiom,
% 3.03/1.61 ! [P: labeled_graph_b_nat > $o,P2: labeled_graph_b_nat,Q2: labeled_graph_b_nat > $o,Q: labeled_graph_b_nat] :
% 3.03/1.61 ( ( P @ P2 )
% 3.03/1.61 => ( ( Q2 @ Q )
% 3.03/1.61 => ( ( P @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ P2 @ Q ) ) )
% 3.03/1.61 & ( Q2 @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ P2 @ Q ) ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_148_exI__realizer,axiom,
% 3.03/1.61 ! [P: allegorical_term_b > allegorical_term_b > $o,Y3: allegorical_term_b,X3: allegorical_term_b] :
% 3.03/1.61 ( ( P @ Y3 @ X3 )
% 3.03/1.61 => ( P @ ( produc1223098053term_b @ ( produc1990145943term_b @ X3 @ Y3 ) ) @ ( produc854192515term_b @ ( produc1990145943term_b @ X3 @ Y3 ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_149_exI__realizer,axiom,
% 3.03/1.61 ! [P: labeled_graph_b_nat > labeled_graph_b_nat > $o,Y3: labeled_graph_b_nat,X3: labeled_graph_b_nat] :
% 3.03/1.61 ( ( P @ Y3 @ X3 )
% 3.03/1.61 => ( P @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ X3 @ Y3 ) ) @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ X3 @ Y3 ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_150_allegorical__term_Oinject_I1_J,axiom,
% 3.03/1.61 ! [X11: allegorical_term_b,X12: allegorical_term_b,Y11: allegorical_term_b,Y12: allegorical_term_b] :
% 3.03/1.61 ( ( ( allegorical_A_Int_b @ X11 @ X12 )
% 3.03/1.61 = ( allegorical_A_Int_b @ Y11 @ Y12 ) )
% 3.03/1.61 = ( ( X11 = Y11 )
% 3.03/1.61 & ( X12 = Y12 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_151_fin__maintainedI,axiom,
% 3.03/1.61 ! [R: produc1235635379_b_nat,G: labeled_graph_b_nat] :
% 3.03/1.61 ( ! [F: labeled_graph_b_nat,F2: set_Pr1986765409at_nat] :
% 3.03/1.61 ( ( ( F
% 3.03/1.61 = ( restrict_b_nat @ F ) )
% 3.03/1.61 & ( finite_finite_nat @ ( labele460410879_b_nat @ F ) )
% 3.03/1.61 & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ F ) ) )
% 3.03/1.61 => ( ( graph_529870330at_nat @ F @ ( produc1542243159_b_nat @ R ) @ ( id_on_nat @ ( labele460410879_b_nat @ F ) ) )
% 3.03/1.61 => ( ( extensible_b_nat_nat @ ( produc951298923_b_nat @ F @ ( produc1542243159_b_nat @ R ) ) @ G @ F2 )
% 3.03/1.61 => ( ( graph_529870330at_nat @ F @ G @ F2 )
% 3.03/1.61 => ( extensible_b_nat_nat @ ( produc951298923_b_nat @ F @ ( produc194497945_b_nat @ R ) ) @ G @ F2 ) ) ) ) )
% 3.03/1.61 => ( fin_ma971967913at_nat @ R @ G ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_152_set__of__graph__rulesD_I1_J,axiom,
% 3.03/1.61 ! [Rs2: set_Pr1987088711_a_nat,R: produc1871334759_a_nat] :
% 3.03/1.61 ( ( set_of1384085797_a_nat @ Rs2 )
% 3.03/1.61 => ( ( member832397200_a_nat @ R @ Rs2 )
% 3.03/1.61 => ( ( ( produc719117507_a_nat @ R )
% 3.03/1.61 = ( restri572569417_a_nat @ ( produc719117507_a_nat @ R ) ) )
% 3.03/1.61 & ( finite_finite_nat @ ( labele1810595089_a_nat @ ( produc719117507_a_nat @ R ) ) )
% 3.03/1.61 & ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( produc719117507_a_nat @ R ) ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_153_set__of__graph__rulesD_I1_J,axiom,
% 3.03/1.61 ! [Rs2: set_Pr551076371_b_nat,R: produc1235635379_b_nat] :
% 3.03/1.61 ( ( set_of41538795_b_nat @ Rs2 )
% 3.03/1.61 => ( ( member963855452_b_nat @ R @ Rs2 )
% 3.03/1.61 => ( ( ( produc1542243159_b_nat @ R )
% 3.03/1.61 = ( restrict_b_nat @ ( produc1542243159_b_nat @ R ) ) )
% 3.03/1.61 & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ R ) ) )
% 3.03/1.61 & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc1542243159_b_nat @ R ) ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_154_set__of__graph__rulesD_I2_J,axiom,
% 3.03/1.61 ! [Rs2: set_Pr1987088711_a_nat,R: produc1871334759_a_nat] :
% 3.03/1.61 ( ( set_of1384085797_a_nat @ Rs2 )
% 3.03/1.61 => ( ( member832397200_a_nat @ R @ Rs2 )
% 3.03/1.61 => ( ( ( produc880161797_a_nat @ R )
% 3.03/1.61 = ( restri572569417_a_nat @ ( produc880161797_a_nat @ R ) ) )
% 3.03/1.61 & ( finite_finite_nat @ ( labele1810595089_a_nat @ ( produc880161797_a_nat @ R ) ) )
% 3.03/1.61 & ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( produc880161797_a_nat @ R ) ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_155_set__of__graph__rulesD_I2_J,axiom,
% 3.03/1.61 ! [Rs2: set_Pr551076371_b_nat,R: produc1235635379_b_nat] :
% 3.03/1.61 ( ( set_of41538795_b_nat @ Rs2 )
% 3.03/1.61 => ( ( member963855452_b_nat @ R @ Rs2 )
% 3.03/1.61 => ( ( ( produc194497945_b_nat @ R )
% 3.03/1.61 = ( restrict_b_nat @ ( produc194497945_b_nat @ R ) ) )
% 3.03/1.61 & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ R ) ) )
% 3.03/1.61 & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ R ) ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_156_extensible__refl,axiom,
% 3.03/1.61 ! [R: labeled_graph_b_nat,G: labeled_graph_b_nat,F3: set_Pr1986765409at_nat] :
% 3.03/1.61 ( ( graph_529870330at_nat @ R @ G @ F3 )
% 3.03/1.61 => ( extensible_b_nat_nat @ ( produc951298923_b_nat @ R @ R ) @ G @ F3 ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_157_set__of__graph__rulesD_I3_J,axiom,
% 3.03/1.61 ! [Rs2: set_Pr1987088711_a_nat,R: produc1871334759_a_nat] :
% 3.03/1.61 ( ( set_of1384085797_a_nat @ Rs2 )
% 3.03/1.61 => ( ( member832397200_a_nat @ R @ Rs2 )
% 3.03/1.61 => ( graph_2130075512at_nat @ ( produc719117507_a_nat @ R ) @ ( produc880161797_a_nat @ R ) @ ( id_on_nat @ ( labele1810595089_a_nat @ ( produc719117507_a_nat @ R ) ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_158_set__of__graph__rulesD_I3_J,axiom,
% 3.03/1.61 ! [Rs2: set_Pr551076371_b_nat,R: produc1235635379_b_nat] :
% 3.03/1.61 ( ( set_of41538795_b_nat @ Rs2 )
% 3.03/1.61 => ( ( member963855452_b_nat @ R @ Rs2 )
% 3.03/1.61 => ( graph_529870330at_nat @ ( produc1542243159_b_nat @ R ) @ ( produc194497945_b_nat @ R ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ R ) ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_159_exE__realizer_H,axiom,
% 3.03/1.61 ! [P: allegorical_term_b > allegorical_term_b > $o,P2: produc1478835367term_b] :
% 3.03/1.61 ( ( P @ ( produc1223098053term_b @ P2 ) @ ( produc854192515term_b @ P2 ) )
% 3.03/1.61 => ~ ! [X4: allegorical_term_b,Y4: allegorical_term_b] :
% 3.03/1.61 ~ ( P @ Y4 @ X4 ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_160_exE__realizer_H,axiom,
% 3.03/1.61 ! [P: labeled_graph_b_nat > labeled_graph_b_nat > $o,P2: produc1235635379_b_nat] :
% 3.03/1.61 ( ( P @ ( produc194497945_b_nat @ P2 ) @ ( produc1542243159_b_nat @ P2 ) )
% 3.03/1.61 => ~ ! [X4: labeled_graph_b_nat,Y4: labeled_graph_b_nat] :
% 3.03/1.61 ~ ( P @ Y4 @ X4 ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_161_Id__onE,axiom,
% 3.03/1.61 ! [C2: produc398057191_a_nat,A4: set_Pr1987088711_a_nat] :
% 3.03/1.61 ( ( member584645392_a_nat @ C2 @ ( id_on_1651096324_a_nat @ A4 ) )
% 3.03/1.61 => ~ ! [X4: produc1871334759_a_nat] :
% 3.03/1.61 ( ( member832397200_a_nat @ X4 @ A4 )
% 3.03/1.61 => ( C2
% 3.03/1.61 != ( produc1677124439_a_nat @ X4 @ X4 ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_162_Id__onE,axiom,
% 3.03/1.61 ! [C2: produc1871334759_a_nat,A4: set_la1083530965_a_nat] :
% 3.03/1.61 ( ( member832397200_a_nat @ C2 @ ( id_on_689842066_a_nat @ A4 ) )
% 3.03/1.61 => ~ ! [X4: labele935650037_a_nat] :
% 3.03/1.61 ( ( member964390942_a_nat @ X4 @ A4 )
% 3.03/1.61 => ( C2
% 3.03/1.61 != ( produc1676969687_a_nat @ X4 @ X4 ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_163_Id__onE,axiom,
% 3.03/1.61 ! [C2: product_prod_nat_nat,A4: set_nat] :
% 3.03/1.61 ( ( member701585322at_nat @ C2 @ ( id_on_nat @ A4 ) )
% 3.03/1.61 => ~ ! [X4: nat] :
% 3.03/1.61 ( ( member_nat @ X4 @ A4 )
% 3.03/1.61 => ( C2
% 3.03/1.61 != ( product_Pair_nat_nat @ X4 @ X4 ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_164_Id__onE,axiom,
% 3.03/1.61 ! [C2: produc1235635379_b_nat,A4: set_la1976028319_b_nat] :
% 3.03/1.61 ( ( member963855452_b_nat @ C2 @ ( id_on_583275916_b_nat @ A4 ) )
% 3.03/1.61 => ~ ! [X4: labeled_graph_b_nat] :
% 3.03/1.61 ( ( member1483953152_b_nat @ X4 @ A4 )
% 3.03/1.61 => ( C2
% 3.03/1.61 != ( produc951298923_b_nat @ X4 @ X4 ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_165_Id__onE,axiom,
% 3.03/1.61 ! [C2: produc1478835367term_b,A4: set_al1193902458term_b] :
% 3.03/1.61 ( ( member516522448term_b @ C2 @ ( id_on_1536886967term_b @ A4 ) )
% 3.03/1.61 => ~ ! [X4: allegorical_term_b] :
% 3.03/1.61 ( ( member93680451term_b @ X4 @ A4 )
% 3.03/1.61 => ( C2
% 3.03/1.61 != ( produc1990145943term_b @ X4 @ X4 ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_166_Id__on__eqI,axiom,
% 3.03/1.61 ! [A: labele935650037_a_nat,B: labele935650037_a_nat,A4: set_la1083530965_a_nat] :
% 3.03/1.61 ( ( A = B )
% 3.03/1.61 => ( ( member964390942_a_nat @ A @ A4 )
% 3.03/1.61 => ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B ) @ ( id_on_689842066_a_nat @ A4 ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_167_Id__on__eqI,axiom,
% 3.03/1.61 ! [A: produc1871334759_a_nat,B: produc1871334759_a_nat,A4: set_Pr1987088711_a_nat] :
% 3.03/1.61 ( ( A = B )
% 3.03/1.61 => ( ( member832397200_a_nat @ A @ A4 )
% 3.03/1.61 => ( member584645392_a_nat @ ( produc1677124439_a_nat @ A @ B ) @ ( id_on_1651096324_a_nat @ A4 ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_168_Id__on__eqI,axiom,
% 3.03/1.61 ! [A: nat,B: nat,A4: set_nat] :
% 3.03/1.61 ( ( A = B )
% 3.03/1.61 => ( ( member_nat @ A @ A4 )
% 3.03/1.61 => ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( id_on_nat @ A4 ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_169_Id__on__eqI,axiom,
% 3.03/1.61 ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,A4: set_la1976028319_b_nat] :
% 3.03/1.61 ( ( A = B )
% 3.03/1.61 => ( ( member1483953152_b_nat @ A @ A4 )
% 3.03/1.61 => ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B ) @ ( id_on_583275916_b_nat @ A4 ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_170_Id__on__eqI,axiom,
% 3.03/1.61 ! [A: allegorical_term_b,B: allegorical_term_b,A4: set_al1193902458term_b] :
% 3.03/1.61 ( ( A = B )
% 3.03/1.61 => ( ( member93680451term_b @ A @ A4 )
% 3.03/1.61 => ( member516522448term_b @ ( produc1990145943term_b @ A @ B ) @ ( id_on_1536886967term_b @ A4 ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_171_Id__on__iff,axiom,
% 3.03/1.61 ! [X3: produc1871334759_a_nat,Y3: produc1871334759_a_nat,A4: set_Pr1987088711_a_nat] :
% 3.03/1.61 ( ( member584645392_a_nat @ ( produc1677124439_a_nat @ X3 @ Y3 ) @ ( id_on_1651096324_a_nat @ A4 ) )
% 3.03/1.61 = ( ( X3 = Y3 )
% 3.03/1.61 & ( member832397200_a_nat @ X3 @ A4 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_172_Id__on__iff,axiom,
% 3.03/1.61 ! [X3: labele935650037_a_nat,Y3: labele935650037_a_nat,A4: set_la1083530965_a_nat] :
% 3.03/1.61 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ X3 @ Y3 ) @ ( id_on_689842066_a_nat @ A4 ) )
% 3.03/1.61 = ( ( X3 = Y3 )
% 3.03/1.61 & ( member964390942_a_nat @ X3 @ A4 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_173_Id__on__iff,axiom,
% 3.03/1.61 ! [X3: nat,Y3: nat,A4: set_nat] :
% 3.03/1.61 ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ ( id_on_nat @ A4 ) )
% 3.03/1.61 = ( ( X3 = Y3 )
% 3.03/1.61 & ( member_nat @ X3 @ A4 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_174_Id__on__iff,axiom,
% 3.03/1.61 ! [X3: labeled_graph_b_nat,Y3: labeled_graph_b_nat,A4: set_la1976028319_b_nat] :
% 3.03/1.61 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ X3 @ Y3 ) @ ( id_on_583275916_b_nat @ A4 ) )
% 3.03/1.61 = ( ( X3 = Y3 )
% 3.03/1.61 & ( member1483953152_b_nat @ X3 @ A4 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_175_Id__on__iff,axiom,
% 3.03/1.61 ! [X3: allegorical_term_b,Y3: allegorical_term_b,A4: set_al1193902458term_b] :
% 3.03/1.61 ( ( member516522448term_b @ ( produc1990145943term_b @ X3 @ Y3 ) @ ( id_on_1536886967term_b @ A4 ) )
% 3.03/1.61 = ( ( X3 = Y3 )
% 3.03/1.61 & ( member93680451term_b @ X3 @ A4 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_176_fin__maintained__def,axiom,
% 3.03/1.61 ( fin_ma971967913at_nat
% 3.03/1.61 = ( ^ [R2: produc1235635379_b_nat,G2: labeled_graph_b_nat] :
% 3.03/1.61 ! [F4: labeled_graph_b_nat,F5: set_Pr1986765409at_nat] :
% 3.03/1.61 ( ( ( F4
% 3.03/1.61 = ( restrict_b_nat @ F4 ) )
% 3.03/1.61 & ( finite_finite_nat @ ( labele460410879_b_nat @ F4 ) )
% 3.03/1.61 & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ F4 ) ) )
% 3.03/1.61 => ( ( graph_529870330at_nat @ F4 @ ( produc1542243159_b_nat @ R2 ) @ ( id_on_nat @ ( labele460410879_b_nat @ F4 ) ) )
% 3.03/1.61 => ( ( extensible_b_nat_nat @ ( produc951298923_b_nat @ F4 @ ( produc1542243159_b_nat @ R2 ) ) @ G2 @ F5 )
% 3.03/1.61 => ( ( graph_529870330at_nat @ F4 @ G2 @ F5 )
% 3.03/1.61 => ( extensible_b_nat_nat @ ( produc951298923_b_nat @ F4 @ ( produc194497945_b_nat @ R2 ) ) @ G2 @ F5 ) ) ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_177_fair__chainD_I2_J,axiom,
% 3.03/1.61 ! [Rs2: set_Pr551076371_b_nat,S2: nat > labeled_graph_b_nat,R: produc1235635379_b_nat,I: nat,F3: set_Pr1986765409at_nat] :
% 3.03/1.61 ( ( fair_chain_b_nat_nat @ Rs2 @ S2 )
% 3.03/1.61 => ( ( member963855452_b_nat @ R @ Rs2 )
% 3.03/1.61 => ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ R ) @ ( S2 @ I ) @ F3 )
% 3.03/1.61 => ? [J: nat] : ( extensible_b_nat_nat @ R @ ( S2 @ J ) @ F3 ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_178_identity__rules__graph__rule,axiom,
% 3.03/1.61 ! [X3: produc1871334759_a_nat,L: set_St761939237tant_a] :
% 3.03/1.61 ( ( member832397200_a_nat @ X3 @ ( standa1568205540ules_a @ L ) )
% 3.03/1.61 => ( ( graph_2130075512at_nat @ ( produc719117507_a_nat @ X3 ) @ ( produc880161797_a_nat @ X3 ) @ ( id_on_nat @ ( labele1810595089_a_nat @ ( produc719117507_a_nat @ X3 ) ) ) )
% 3.03/1.61 & ( ( produc880161797_a_nat @ X3 )
% 3.03/1.61 = ( restri572569417_a_nat @ ( produc880161797_a_nat @ X3 ) ) )
% 3.03/1.61 & ( finite_finite_nat @ ( labele1810595089_a_nat @ ( produc880161797_a_nat @ X3 ) ) )
% 3.03/1.61 & ( finite1242387294at_nat @ ( labele195203296_a_nat @ ( produc880161797_a_nat @ X3 ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_179_maintainedI,axiom,
% 3.03/1.61 ! [A4: labeled_graph_b_nat,G: labeled_graph_b_nat,B4: labeled_graph_b_nat] :
% 3.03/1.61 ( ! [F2: set_Pr1986765409at_nat] :
% 3.03/1.61 ( ( graph_529870330at_nat @ A4 @ G @ F2 )
% 3.03/1.61 => ( extensible_b_nat_nat @ ( produc951298923_b_nat @ A4 @ B4 ) @ G @ F2 ) )
% 3.03/1.61 => ( maintained_b_nat_nat @ ( produc951298923_b_nat @ A4 @ B4 ) @ G ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_180_sndI,axiom,
% 3.03/1.61 ! [X3: produc1478835367term_b,Y3: allegorical_term_b,Z2: allegorical_term_b] :
% 3.03/1.61 ( ( X3
% 3.03/1.61 = ( produc1990145943term_b @ Y3 @ Z2 ) )
% 3.03/1.61 => ( ( produc1223098053term_b @ X3 )
% 3.03/1.61 = Z2 ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_181_sndI,axiom,
% 3.03/1.61 ! [X3: produc1235635379_b_nat,Y3: labeled_graph_b_nat,Z2: labeled_graph_b_nat] :
% 3.03/1.61 ( ( X3
% 3.03/1.61 = ( produc951298923_b_nat @ Y3 @ Z2 ) )
% 3.03/1.61 => ( ( produc194497945_b_nat @ X3 )
% 3.03/1.61 = Z2 ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_182_consequence__graphI,axiom,
% 3.03/1.61 ! [Rs2: set_Pr551076371_b_nat,G: labeled_graph_b_nat] :
% 3.03/1.61 ( ! [R3: produc1235635379_b_nat] :
% 3.03/1.61 ( ( member963855452_b_nat @ R3 @ Rs2 )
% 3.03/1.61 => ( maintained_b_nat_nat @ R3 @ G ) )
% 3.03/1.61 => ( ! [R3: produc1235635379_b_nat] :
% 3.03/1.61 ( ( member963855452_b_nat @ R3 @ Rs2 )
% 3.03/1.61 => ( graph_529870330at_nat @ ( produc1542243159_b_nat @ R3 ) @ ( produc194497945_b_nat @ R3 ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ R3 ) ) ) ) )
% 3.03/1.61 => ( ( G
% 3.03/1.61 = ( restrict_b_nat @ G ) )
% 3.03/1.61 => ( conseq1730780375at_nat @ Rs2 @ G ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_183_consequence__graph__def,axiom,
% 3.03/1.61 ( conseq1730780375at_nat
% 3.03/1.61 = ( ^ [Rs: set_Pr551076371_b_nat,G2: labeled_graph_b_nat] :
% 3.03/1.61 ( ( G2
% 3.03/1.61 = ( restrict_b_nat @ G2 ) )
% 3.03/1.61 & ! [X5: produc1235635379_b_nat] :
% 3.03/1.61 ( ( member963855452_b_nat @ X5 @ Rs )
% 3.03/1.61 => ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ X5 ) @ ( produc194497945_b_nat @ X5 ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ X5 ) ) ) )
% 3.03/1.61 & ( maintained_b_nat_nat @ X5 @ G2 ) ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_184_maintained__def,axiom,
% 3.03/1.61 ( maintained_b_nat_nat
% 3.03/1.61 = ( ^ [R2: produc1235635379_b_nat,G2: labeled_graph_b_nat] :
% 3.03/1.61 ! [F5: set_Pr1986765409at_nat] :
% 3.03/1.61 ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ R2 ) @ G2 @ F5 )
% 3.03/1.61 => ( extensible_b_nat_nat @ R2 @ G2 @ F5 ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_185_maintainedD,axiom,
% 3.03/1.61 ! [A4: labeled_graph_b_nat,B4: labeled_graph_b_nat,G: labeled_graph_b_nat,F3: set_Pr1986765409at_nat] :
% 3.03/1.61 ( ( maintained_b_nat_nat @ ( produc951298923_b_nat @ A4 @ B4 ) @ G )
% 3.03/1.61 => ( ( graph_529870330at_nat @ A4 @ G @ F3 )
% 3.03/1.61 => ( extensible_b_nat_nat @ ( produc951298923_b_nat @ A4 @ B4 ) @ G @ F3 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_186_fstI,axiom,
% 3.03/1.61 ! [X3: produc1235635379_b_nat,Y3: labeled_graph_b_nat,Z2: labeled_graph_b_nat] :
% 3.03/1.61 ( ( X3
% 3.03/1.61 = ( produc951298923_b_nat @ Y3 @ Z2 ) )
% 3.03/1.61 => ( ( produc1542243159_b_nat @ X3 )
% 3.03/1.61 = Y3 ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_187_fstI,axiom,
% 3.03/1.61 ! [X3: produc1478835367term_b,Y3: allegorical_term_b,Z2: allegorical_term_b] :
% 3.03/1.61 ( ( X3
% 3.03/1.61 = ( produc1990145943term_b @ Y3 @ Z2 ) )
% 3.03/1.61 => ( ( produc854192515term_b @ X3 )
% 3.03/1.61 = Y3 ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_188_fair__chainI,axiom,
% 3.03/1.61 ! [S2: nat > labeled_graph_b_nat,Rs2: set_Pr551076371_b_nat] :
% 3.03/1.61 ( ( chain_b_nat @ S2 )
% 3.03/1.61 => ( ! [R3: produc1235635379_b_nat,F2: set_Pr1986765409at_nat,I2: nat] :
% 3.03/1.61 ( ( member963855452_b_nat @ R3 @ Rs2 )
% 3.03/1.61 => ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ R3 ) @ ( S2 @ I2 ) @ F2 )
% 3.03/1.61 => ? [J2: nat] : ( extensible_b_nat_nat @ R3 @ ( S2 @ J2 ) @ F2 ) ) )
% 3.03/1.61 => ( fair_chain_b_nat_nat @ Rs2 @ S2 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_189_maintained__holds__iff,axiom,
% 3.03/1.61 ! [G: labeled_graph_b_nat,E_L: allegorical_term_b,E_R: allegorical_term_b] :
% 3.03/1.61 ( ( G
% 3.03/1.61 = ( restrict_b_nat @ G ) )
% 3.03/1.61 => ( ( maintained_b_nat_nat @ ( produc951298923_b_nat @ ( translation_b @ E_L ) @ ( translation_b @ ( allegorical_A_Int_b @ E_L @ E_R ) ) ) @ G )
% 3.03/1.61 = ( ( semantics_b_nat @ G @ ( produc854192515term_b @ ( produc1990145943term_b @ E_L @ ( allegorical_A_Int_b @ E_L @ E_R ) ) ) )
% 3.03/1.61 = ( semantics_b_nat @ G @ ( produc1223098053term_b @ ( produc1990145943term_b @ E_L @ ( allegorical_A_Int_b @ E_L @ E_R ) ) ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_190_fair__chain__def,axiom,
% 3.03/1.61 ( fair_chain_b_nat_nat
% 3.03/1.61 = ( ^ [Rs: set_Pr551076371_b_nat,S3: nat > labeled_graph_b_nat] :
% 3.03/1.61 ( ( chain_b_nat @ S3 )
% 3.03/1.61 & ! [R2: produc1235635379_b_nat,F5: set_Pr1986765409at_nat,I3: nat] :
% 3.03/1.61 ( ( ( member963855452_b_nat @ R2 @ Rs )
% 3.03/1.61 & ( graph_529870330at_nat @ ( produc1542243159_b_nat @ R2 ) @ ( S3 @ I3 ) @ F5 ) )
% 3.03/1.61 => ? [J3: nat] : ( extensible_b_nat_nat @ R2 @ ( S3 @ J3 ) @ F5 ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_191_chain__sup__graph,axiom,
% 3.03/1.61 ! [S2: nat > labeled_graph_b_nat] :
% 3.03/1.61 ( ( chain_b_nat @ S2 )
% 3.03/1.61 => ( ( chain_sup_b_nat @ S2 )
% 3.03/1.61 = ( restrict_b_nat @ ( chain_sup_b_nat @ S2 ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_192_chain__sup__subgraph,axiom,
% 3.03/1.61 ! [S2: nat > labeled_graph_b_nat,J4: nat] :
% 3.03/1.61 ( ( chain_b_nat @ S2 )
% 3.03/1.61 => ( graph_529870330at_nat @ ( S2 @ J4 ) @ ( chain_sup_b_nat @ S2 ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( S2 @ J4 ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_193_chain__then__restrict,axiom,
% 3.03/1.61 ! [S2: nat > labeled_graph_b_nat,I: nat] :
% 3.03/1.61 ( ( chain_b_nat @ S2 )
% 3.03/1.61 => ( ( S2 @ I )
% 3.03/1.61 = ( restrict_b_nat @ ( S2 @ I ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_194_graph__homomorphism__semantics,axiom,
% 3.03/1.61 ! [A4: labeled_graph_b_nat,B4: labeled_graph_b_nat,F3: set_Pr1986765409at_nat,A: nat,B: nat,E: allegorical_term_b,A2: nat,B2: nat] :
% 3.03/1.61 ( ( graph_529870330at_nat @ A4 @ B4 @ F3 )
% 3.03/1.61 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( semantics_b_nat @ A4 @ E ) )
% 3.03/1.61 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ A2 ) @ F3 )
% 3.03/1.61 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ B @ B2 ) @ F3 )
% 3.03/1.61 => ( member701585322at_nat @ ( product_Pair_nat_nat @ A2 @ B2 ) @ ( semantics_b_nat @ B4 @ E ) ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_195_semantics__in__vertices_I2_J,axiom,
% 3.03/1.61 ! [A4: labeled_graph_b_nat,A: nat,B: nat,E: allegorical_term_b] :
% 3.03/1.61 ( ( A4
% 3.03/1.61 = ( restrict_b_nat @ A4 ) )
% 3.03/1.61 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( semantics_b_nat @ A4 @ E ) )
% 3.03/1.61 => ( member_nat @ B @ ( labele460410879_b_nat @ A4 ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_196_semantics__in__vertices_I1_J,axiom,
% 3.03/1.61 ! [A4: labeled_graph_b_nat,A: nat,B: nat,E: allegorical_term_b] :
% 3.03/1.61 ( ( A4
% 3.03/1.61 = ( restrict_b_nat @ A4 ) )
% 3.03/1.61 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( semantics_b_nat @ A4 @ E ) )
% 3.03/1.61 => ( member_nat @ A @ ( labele460410879_b_nat @ A4 ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_197_subgraph__semantics,axiom,
% 3.03/1.61 ! [A4: labeled_graph_b_nat,B4: labeled_graph_b_nat,A: nat,B: nat,E: allegorical_term_b] :
% 3.03/1.61 ( ( graph_529870330at_nat @ A4 @ B4 @ ( id_on_nat @ ( labele460410879_b_nat @ A4 ) ) )
% 3.03/1.61 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( semantics_b_nat @ A4 @ E ) )
% 3.03/1.61 => ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( semantics_b_nat @ B4 @ E ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_198_maintained__holds__subset__iff,axiom,
% 3.03/1.61 ! [G: labeled_graph_b_nat,E_L: allegorical_term_b,E_R: allegorical_term_b] :
% 3.03/1.61 ( ( G
% 3.03/1.61 = ( restrict_b_nat @ G ) )
% 3.03/1.61 => ( ( maintained_b_nat_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ E_L @ ( allegorical_A_Int_b @ E_L @ E_R ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ E_L @ ( allegorical_A_Int_b @ E_L @ E_R ) ) ) ) ) @ G )
% 3.03/1.61 = ( ord_le841296385at_nat @ ( semantics_b_nat @ G @ E_L ) @ ( semantics_b_nat @ G @ E_R ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_199_find__graph__occurence,axiom,
% 3.03/1.61 ! [S2: nat > labeled_graph_b_nat,E2: set_Pr9961929at_nat,V: set_nat,F3: set_Pr1986765409at_nat] :
% 3.03/1.61 ( ( chain_b_nat @ S2 )
% 3.03/1.61 => ( ( finite1987068434at_nat @ E2 )
% 3.03/1.61 => ( ( finite_finite_nat @ V )
% 3.03/1.61 => ( ( graph_529870330at_nat @ ( labeled_LG_b_nat @ E2 @ V ) @ ( chain_sup_b_nat @ S2 ) @ F3 )
% 3.03/1.61 => ? [I2: nat] : ( graph_529870330at_nat @ ( labeled_LG_b_nat @ E2 @ V ) @ ( S2 @ I2 ) @ F3 ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_200_eq__snd__iff,axiom,
% 3.03/1.61 ! [B: allegorical_term_b,P2: produc1478835367term_b] :
% 3.03/1.61 ( ( B
% 3.03/1.61 = ( produc1223098053term_b @ P2 ) )
% 3.03/1.61 = ( ? [A5: allegorical_term_b] :
% 3.03/1.61 ( P2
% 3.03/1.61 = ( produc1990145943term_b @ A5 @ B ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_201_eq__snd__iff,axiom,
% 3.03/1.61 ! [B: labeled_graph_b_nat,P2: produc1235635379_b_nat] :
% 3.03/1.61 ( ( B
% 3.03/1.61 = ( produc194497945_b_nat @ P2 ) )
% 3.03/1.61 = ( ? [A5: labeled_graph_b_nat] :
% 3.03/1.61 ( P2
% 3.03/1.61 = ( produc951298923_b_nat @ A5 @ B ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_202_eq__fst__iff,axiom,
% 3.03/1.61 ! [A: labeled_graph_b_nat,P2: produc1235635379_b_nat] :
% 3.03/1.61 ( ( A
% 3.03/1.61 = ( produc1542243159_b_nat @ P2 ) )
% 3.03/1.61 = ( ? [B5: labeled_graph_b_nat] :
% 3.03/1.61 ( P2
% 3.03/1.61 = ( produc951298923_b_nat @ A @ B5 ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_203_eq__fst__iff,axiom,
% 3.03/1.61 ! [A: allegorical_term_b,P2: produc1478835367term_b] :
% 3.03/1.61 ( ( A
% 3.03/1.61 = ( produc854192515term_b @ P2 ) )
% 3.03/1.61 = ( ? [B5: allegorical_term_b] :
% 3.03/1.61 ( P2
% 3.03/1.61 = ( produc1990145943term_b @ A @ B5 ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_204_labeled__graph_Ocollapse,axiom,
% 3.03/1.61 ! [Labeled_graph: labeled_graph_b_nat] :
% 3.03/1.61 ( ( labeled_LG_b_nat @ ( labeled_edges_b_nat @ Labeled_graph ) @ ( labele460410879_b_nat @ Labeled_graph ) )
% 3.03/1.61 = Labeled_graph ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_205_extensible__refl__concr,axiom,
% 3.03/1.61 ! [E_1: set_Pr9961929at_nat,V2: set_nat,G: labeled_graph_b_nat,F3: set_Pr1986765409at_nat,E_2: set_Pr9961929at_nat] :
% 3.03/1.61 ( ( graph_529870330at_nat @ ( labeled_LG_b_nat @ E_1 @ V2 ) @ G @ F3 )
% 3.03/1.61 => ( ( extensible_b_nat_nat @ ( produc951298923_b_nat @ ( labeled_LG_b_nat @ E_1 @ V2 ) @ ( labeled_LG_b_nat @ E_2 @ V2 ) ) @ G @ F3 )
% 3.03/1.61 = ( graph_529870330at_nat @ ( labeled_LG_b_nat @ E_2 @ V2 ) @ G @ F3 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_206_subrelI,axiom,
% 3.03/1.61 ! [R4: set_Pr1987088711_a_nat,S4: set_Pr1987088711_a_nat] :
% 3.03/1.61 ( ! [X4: labele935650037_a_nat,Y4: labele935650037_a_nat] :
% 3.03/1.61 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ X4 @ Y4 ) @ R4 )
% 3.03/1.61 => ( member832397200_a_nat @ ( produc1676969687_a_nat @ X4 @ Y4 ) @ S4 ) )
% 3.03/1.61 => ( ord_le1718765799_a_nat @ R4 @ S4 ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_207_subrelI,axiom,
% 3.03/1.61 ! [R4: set_Pr551076371_b_nat,S4: set_Pr551076371_b_nat] :
% 3.03/1.61 ( ! [X4: labeled_graph_b_nat,Y4: labeled_graph_b_nat] :
% 3.03/1.61 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ X4 @ Y4 ) @ R4 )
% 3.03/1.61 => ( member963855452_b_nat @ ( produc951298923_b_nat @ X4 @ Y4 ) @ S4 ) )
% 3.03/1.61 => ( ord_le13035955_b_nat @ R4 @ S4 ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_208_subrelI,axiom,
% 3.03/1.61 ! [R4: set_Pr1163220871term_b,S4: set_Pr1163220871term_b] :
% 3.03/1.61 ( ! [X4: allegorical_term_b,Y4: allegorical_term_b] :
% 3.03/1.61 ( ( member516522448term_b @ ( produc1990145943term_b @ X4 @ Y4 ) @ R4 )
% 3.03/1.61 => ( member516522448term_b @ ( produc1990145943term_b @ X4 @ Y4 ) @ S4 ) )
% 3.03/1.61 => ( ord_le138473255term_b @ R4 @ S4 ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_209_finite__has__maximal2,axiom,
% 3.03/1.61 ! [A4: set_nat,A: nat] :
% 3.03/1.61 ( ( finite_finite_nat @ A4 )
% 3.03/1.61 => ( ( member_nat @ A @ A4 )
% 3.03/1.61 => ? [X4: nat] :
% 3.03/1.61 ( ( member_nat @ X4 @ A4 )
% 3.03/1.61 & ( ord_less_eq_nat @ A @ X4 )
% 3.03/1.61 & ! [Xa: nat] :
% 3.03/1.61 ( ( member_nat @ Xa @ A4 )
% 3.03/1.61 => ( ( ord_less_eq_nat @ X4 @ Xa )
% 3.03/1.61 => ( X4 = Xa ) ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_210_finite__has__minimal2,axiom,
% 3.03/1.61 ! [A4: set_nat,A: nat] :
% 3.03/1.61 ( ( finite_finite_nat @ A4 )
% 3.03/1.61 => ( ( member_nat @ A @ A4 )
% 3.03/1.61 => ? [X4: nat] :
% 3.03/1.61 ( ( member_nat @ X4 @ A4 )
% 3.03/1.61 & ( ord_less_eq_nat @ X4 @ A )
% 3.03/1.61 & ! [Xa: nat] :
% 3.03/1.61 ( ( member_nat @ Xa @ A4 )
% 3.03/1.61 => ( ( ord_less_eq_nat @ Xa @ X4 )
% 3.03/1.61 => ( X4 = Xa ) ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_211_finite__subset,axiom,
% 3.03/1.61 ! [A4: set_nat,B4: set_nat] :
% 3.03/1.61 ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 3.03/1.61 => ( ( finite_finite_nat @ B4 )
% 3.03/1.61 => ( finite_finite_nat @ A4 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_212_finite__subset,axiom,
% 3.03/1.61 ! [A4: set_Pr9961929at_nat,B4: set_Pr9961929at_nat] :
% 3.03/1.61 ( ( ord_le910748009at_nat @ A4 @ B4 )
% 3.03/1.61 => ( ( finite1987068434at_nat @ B4 )
% 3.03/1.61 => ( finite1987068434at_nat @ A4 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_213_infinite__super,axiom,
% 3.03/1.61 ! [S2: set_nat,T3: set_nat] :
% 3.03/1.61 ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 3.03/1.61 => ( ~ ( finite_finite_nat @ S2 )
% 3.03/1.61 => ~ ( finite_finite_nat @ T3 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_214_infinite__super,axiom,
% 3.03/1.61 ! [S2: set_Pr9961929at_nat,T3: set_Pr9961929at_nat] :
% 3.03/1.61 ( ( ord_le910748009at_nat @ S2 @ T3 )
% 3.03/1.61 => ( ~ ( finite1987068434at_nat @ S2 )
% 3.03/1.61 => ~ ( finite1987068434at_nat @ T3 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_215_rev__finite__subset,axiom,
% 3.03/1.61 ! [B4: set_nat,A4: set_nat] :
% 3.03/1.61 ( ( finite_finite_nat @ B4 )
% 3.03/1.61 => ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 3.03/1.61 => ( finite_finite_nat @ A4 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_216_rev__finite__subset,axiom,
% 3.03/1.61 ! [B4: set_Pr9961929at_nat,A4: set_Pr9961929at_nat] :
% 3.03/1.61 ( ( finite1987068434at_nat @ B4 )
% 3.03/1.61 => ( ( ord_le910748009at_nat @ A4 @ B4 )
% 3.03/1.61 => ( finite1987068434at_nat @ A4 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_217_labeled__graph_Osel_I2_J,axiom,
% 3.03/1.61 ! [X1: set_Pr9961929at_nat,X22: set_nat] :
% 3.03/1.61 ( ( labele460410879_b_nat @ ( labeled_LG_b_nat @ X1 @ X22 ) )
% 3.03/1.61 = X22 ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_218_labeled__graph_Osel_I1_J,axiom,
% 3.03/1.61 ! [X1: set_Pr9961929at_nat,X22: set_nat] :
% 3.03/1.61 ( ( labeled_edges_b_nat @ ( labeled_LG_b_nat @ X1 @ X22 ) )
% 3.03/1.61 = X1 ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_219_restrict__subsD,axiom,
% 3.03/1.61 ! [G: labeled_graph_b_nat] :
% 3.03/1.61 ( ( ord_le910748009at_nat @ ( labeled_edges_b_nat @ G ) @ ( labeled_edges_b_nat @ ( restrict_b_nat @ G ) ) )
% 3.03/1.61 => ( G
% 3.03/1.61 = ( restrict_b_nat @ G ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_220_subgraph__def2,axiom,
% 3.03/1.61 ! [G_1: labeled_graph_b_nat,G_2: labeled_graph_b_nat] :
% 3.03/1.61 ( ( G_1
% 3.03/1.61 = ( restrict_b_nat @ G_1 ) )
% 3.03/1.61 => ( ( G_2
% 3.03/1.61 = ( restrict_b_nat @ G_2 ) )
% 3.03/1.61 => ( ( graph_529870330at_nat @ G_1 @ G_2 @ ( id_on_nat @ ( labele460410879_b_nat @ G_1 ) ) )
% 3.03/1.61 = ( ( ord_less_eq_set_nat @ ( labele460410879_b_nat @ G_1 ) @ ( labele460410879_b_nat @ G_2 ) )
% 3.03/1.61 & ( ord_le910748009at_nat @ ( labeled_edges_b_nat @ G_1 ) @ ( labeled_edges_b_nat @ G_2 ) ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_221_labeled__graph_Oexhaust__sel,axiom,
% 3.03/1.61 ! [Labeled_graph: labeled_graph_b_nat] :
% 3.03/1.61 ( Labeled_graph
% 3.03/1.61 = ( labeled_LG_b_nat @ ( labeled_edges_b_nat @ Labeled_graph ) @ ( labele460410879_b_nat @ Labeled_graph ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_222_subgraph__subset_I1_J,axiom,
% 3.03/1.61 ! [G_1: labeled_graph_b_nat,G_2: labeled_graph_b_nat] :
% 3.03/1.61 ( ( graph_529870330at_nat @ G_1 @ G_2 @ ( id_on_nat @ ( labele460410879_b_nat @ G_1 ) ) )
% 3.03/1.61 => ( ord_less_eq_set_nat @ ( labele460410879_b_nat @ G_1 ) @ ( labele460410879_b_nat @ G_2 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_223_maintainedD2,axiom,
% 3.03/1.61 ! [A4: labeled_graph_b_nat,B4: labeled_graph_b_nat,G: labeled_graph_b_nat,F3: set_Pr1986765409at_nat] :
% 3.03/1.61 ( ( maintained_b_nat_nat @ ( produc951298923_b_nat @ A4 @ B4 ) @ G )
% 3.03/1.61 => ( ( graph_529870330at_nat @ A4 @ G @ F3 )
% 3.03/1.61 => ~ ! [G3: set_Pr1986765409at_nat] :
% 3.03/1.61 ( ( graph_529870330at_nat @ B4 @ G @ G3 )
% 3.03/1.61 => ~ ( ord_le841296385at_nat @ F3 @ G3 ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_224_subgraph__subset_I2_J,axiom,
% 3.03/1.61 ! [G_1: labeled_graph_b_nat,G_2: labeled_graph_b_nat] :
% 3.03/1.61 ( ( graph_529870330at_nat @ G_1 @ G_2 @ ( id_on_nat @ ( labele460410879_b_nat @ G_1 ) ) )
% 3.03/1.61 => ( ord_le910748009at_nat @ ( labeled_edges_b_nat @ ( restrict_b_nat @ G_1 ) ) @ ( labeled_edges_b_nat @ G_2 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_225_subsetI,axiom,
% 3.03/1.61 ! [A4: set_Pr1987088711_a_nat,B4: set_Pr1987088711_a_nat] :
% 3.03/1.61 ( ! [X4: produc1871334759_a_nat] :
% 3.03/1.61 ( ( member832397200_a_nat @ X4 @ A4 )
% 3.03/1.61 => ( member832397200_a_nat @ X4 @ B4 ) )
% 3.03/1.61 => ( ord_le1718765799_a_nat @ A4 @ B4 ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_226_order__refl,axiom,
% 3.03/1.61 ! [X3: nat] : ( ord_less_eq_nat @ X3 @ X3 ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_227_dual__order_Oantisym,axiom,
% 3.03/1.61 ! [B: nat,A: nat] :
% 3.03/1.61 ( ( ord_less_eq_nat @ B @ A )
% 3.03/1.61 => ( ( ord_less_eq_nat @ A @ B )
% 3.03/1.61 => ( A = B ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_228_dual__order_Oeq__iff,axiom,
% 3.03/1.61 ( ( ^ [Y5: nat,Z: nat] : ( Y5 = Z ) )
% 3.03/1.61 = ( ^ [A5: nat,B5: nat] :
% 3.03/1.61 ( ( ord_less_eq_nat @ B5 @ A5 )
% 3.03/1.61 & ( ord_less_eq_nat @ A5 @ B5 ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_229_dual__order_Otrans,axiom,
% 3.03/1.61 ! [B: nat,A: nat,C2: nat] :
% 3.03/1.61 ( ( ord_less_eq_nat @ B @ A )
% 3.03/1.61 => ( ( ord_less_eq_nat @ C2 @ B )
% 3.03/1.61 => ( ord_less_eq_nat @ C2 @ A ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_230_linorder__wlog,axiom,
% 3.03/1.61 ! [P: nat > nat > $o,A: nat,B: nat] :
% 3.03/1.61 ( ! [A3: nat,B3: nat] :
% 3.03/1.61 ( ( ord_less_eq_nat @ A3 @ B3 )
% 3.03/1.61 => ( P @ A3 @ B3 ) )
% 3.03/1.61 => ( ! [A3: nat,B3: nat] :
% 3.03/1.61 ( ( P @ B3 @ A3 )
% 3.03/1.61 => ( P @ A3 @ B3 ) )
% 3.03/1.61 => ( P @ A @ B ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_231_dual__order_Orefl,axiom,
% 3.03/1.61 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_232_order__trans,axiom,
% 3.03/1.61 ! [X3: nat,Y3: nat,Z2: nat] :
% 3.03/1.61 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 3.03/1.61 => ( ( ord_less_eq_nat @ Y3 @ Z2 )
% 3.03/1.61 => ( ord_less_eq_nat @ X3 @ Z2 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_233_order__class_Oorder_Oantisym,axiom,
% 3.03/1.61 ! [A: nat,B: nat] :
% 3.03/1.61 ( ( ord_less_eq_nat @ A @ B )
% 3.03/1.61 => ( ( ord_less_eq_nat @ B @ A )
% 3.03/1.61 => ( A = B ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_234_ord__le__eq__trans,axiom,
% 3.03/1.61 ! [A: nat,B: nat,C2: nat] :
% 3.03/1.61 ( ( ord_less_eq_nat @ A @ B )
% 3.03/1.61 => ( ( B = C2 )
% 3.03/1.61 => ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_235_ord__eq__le__trans,axiom,
% 3.03/1.61 ! [A: nat,B: nat,C2: nat] :
% 3.03/1.61 ( ( A = B )
% 3.03/1.61 => ( ( ord_less_eq_nat @ B @ C2 )
% 3.03/1.61 => ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_236_order__class_Oorder_Oeq__iff,axiom,
% 3.03/1.61 ( ( ^ [Y5: nat,Z: nat] : ( Y5 = Z ) )
% 3.03/1.61 = ( ^ [A5: nat,B5: nat] :
% 3.03/1.61 ( ( ord_less_eq_nat @ A5 @ B5 )
% 3.03/1.61 & ( ord_less_eq_nat @ B5 @ A5 ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_237_antisym__conv,axiom,
% 3.03/1.61 ! [Y3: nat,X3: nat] :
% 3.03/1.61 ( ( ord_less_eq_nat @ Y3 @ X3 )
% 3.03/1.61 => ( ( ord_less_eq_nat @ X3 @ Y3 )
% 3.03/1.61 = ( X3 = Y3 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_238_le__cases3,axiom,
% 3.03/1.61 ! [X3: nat,Y3: nat,Z2: nat] :
% 3.03/1.61 ( ( ( ord_less_eq_nat @ X3 @ Y3 )
% 3.03/1.61 => ~ ( ord_less_eq_nat @ Y3 @ Z2 ) )
% 3.03/1.61 => ( ( ( ord_less_eq_nat @ Y3 @ X3 )
% 3.03/1.61 => ~ ( ord_less_eq_nat @ X3 @ Z2 ) )
% 3.03/1.61 => ( ( ( ord_less_eq_nat @ X3 @ Z2 )
% 3.03/1.61 => ~ ( ord_less_eq_nat @ Z2 @ Y3 ) )
% 3.03/1.61 => ( ( ( ord_less_eq_nat @ Z2 @ Y3 )
% 3.03/1.61 => ~ ( ord_less_eq_nat @ Y3 @ X3 ) )
% 3.03/1.61 => ( ( ( ord_less_eq_nat @ Y3 @ Z2 )
% 3.03/1.61 => ~ ( ord_less_eq_nat @ Z2 @ X3 ) )
% 3.03/1.61 => ~ ( ( ord_less_eq_nat @ Z2 @ X3 )
% 3.03/1.61 => ~ ( ord_less_eq_nat @ X3 @ Y3 ) ) ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_239_order_Otrans,axiom,
% 3.03/1.61 ! [A: nat,B: nat,C2: nat] :
% 3.03/1.61 ( ( ord_less_eq_nat @ A @ B )
% 3.03/1.61 => ( ( ord_less_eq_nat @ B @ C2 )
% 3.03/1.61 => ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_240_le__cases,axiom,
% 3.03/1.61 ! [X3: nat,Y3: nat] :
% 3.03/1.61 ( ~ ( ord_less_eq_nat @ X3 @ Y3 )
% 3.03/1.61 => ( ord_less_eq_nat @ Y3 @ X3 ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_241_eq__refl,axiom,
% 3.03/1.61 ! [X3: nat,Y3: nat] :
% 3.03/1.61 ( ( X3 = Y3 )
% 3.03/1.61 => ( ord_less_eq_nat @ X3 @ Y3 ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_242_linear,axiom,
% 3.03/1.61 ! [X3: nat,Y3: nat] :
% 3.03/1.61 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 3.03/1.61 | ( ord_less_eq_nat @ Y3 @ X3 ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_243_antisym,axiom,
% 3.03/1.61 ! [X3: nat,Y3: nat] :
% 3.03/1.61 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 3.03/1.61 => ( ( ord_less_eq_nat @ Y3 @ X3 )
% 3.03/1.61 => ( X3 = Y3 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_244_eq__iff,axiom,
% 3.03/1.61 ( ( ^ [Y5: nat,Z: nat] : ( Y5 = Z ) )
% 3.03/1.61 = ( ^ [X5: nat,Y6: nat] :
% 3.03/1.61 ( ( ord_less_eq_nat @ X5 @ Y6 )
% 3.03/1.61 & ( ord_less_eq_nat @ Y6 @ X5 ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_245_ord__le__eq__subst,axiom,
% 3.03/1.61 ! [A: nat,B: nat,F3: nat > nat,C2: nat] :
% 3.03/1.61 ( ( ord_less_eq_nat @ A @ B )
% 3.03/1.61 => ( ( ( F3 @ B )
% 3.03/1.61 = C2 )
% 3.03/1.61 => ( ! [X4: nat,Y4: nat] :
% 3.03/1.61 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 3.03/1.61 => ( ord_less_eq_nat @ ( F3 @ X4 ) @ ( F3 @ Y4 ) ) )
% 3.03/1.61 => ( ord_less_eq_nat @ ( F3 @ A ) @ C2 ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_246_ord__eq__le__subst,axiom,
% 3.03/1.61 ! [A: nat,F3: nat > nat,B: nat,C2: nat] :
% 3.03/1.61 ( ( A
% 3.03/1.61 = ( F3 @ B ) )
% 3.03/1.61 => ( ( ord_less_eq_nat @ B @ C2 )
% 3.03/1.61 => ( ! [X4: nat,Y4: nat] :
% 3.03/1.61 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 3.03/1.61 => ( ord_less_eq_nat @ ( F3 @ X4 ) @ ( F3 @ Y4 ) ) )
% 3.03/1.61 => ( ord_less_eq_nat @ A @ ( F3 @ C2 ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_247_order__subst2,axiom,
% 3.03/1.61 ! [A: nat,B: nat,F3: nat > nat,C2: nat] :
% 3.03/1.61 ( ( ord_less_eq_nat @ A @ B )
% 3.03/1.61 => ( ( ord_less_eq_nat @ ( F3 @ B ) @ C2 )
% 3.03/1.61 => ( ! [X4: nat,Y4: nat] :
% 3.03/1.61 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 3.03/1.61 => ( ord_less_eq_nat @ ( F3 @ X4 ) @ ( F3 @ Y4 ) ) )
% 3.03/1.61 => ( ord_less_eq_nat @ ( F3 @ A ) @ C2 ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_248_order__subst1,axiom,
% 3.03/1.61 ! [A: nat,F3: nat > nat,B: nat,C2: nat] :
% 3.03/1.61 ( ( ord_less_eq_nat @ A @ ( F3 @ B ) )
% 3.03/1.61 => ( ( ord_less_eq_nat @ B @ C2 )
% 3.03/1.61 => ( ! [X4: nat,Y4: nat] :
% 3.03/1.61 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 3.03/1.61 => ( ord_less_eq_nat @ ( F3 @ X4 ) @ ( F3 @ Y4 ) ) )
% 3.03/1.61 => ( ord_less_eq_nat @ A @ ( F3 @ C2 ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_249_subset__iff,axiom,
% 3.03/1.61 ( ord_le1718765799_a_nat
% 3.03/1.61 = ( ^ [A6: set_Pr1987088711_a_nat,B6: set_Pr1987088711_a_nat] :
% 3.03/1.61 ! [T2: produc1871334759_a_nat] :
% 3.03/1.61 ( ( member832397200_a_nat @ T2 @ A6 )
% 3.03/1.61 => ( member832397200_a_nat @ T2 @ B6 ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_250_subset__eq,axiom,
% 3.03/1.61 ( ord_le1718765799_a_nat
% 3.03/1.61 = ( ^ [A6: set_Pr1987088711_a_nat,B6: set_Pr1987088711_a_nat] :
% 3.03/1.61 ! [X5: produc1871334759_a_nat] :
% 3.03/1.61 ( ( member832397200_a_nat @ X5 @ A6 )
% 3.03/1.61 => ( member832397200_a_nat @ X5 @ B6 ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_251_subsetD,axiom,
% 3.03/1.61 ! [A4: set_Pr1987088711_a_nat,B4: set_Pr1987088711_a_nat,C2: produc1871334759_a_nat] :
% 3.03/1.61 ( ( ord_le1718765799_a_nat @ A4 @ B4 )
% 3.03/1.61 => ( ( member832397200_a_nat @ C2 @ A4 )
% 3.03/1.61 => ( member832397200_a_nat @ C2 @ B4 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_252_in__mono,axiom,
% 3.03/1.61 ! [A4: set_Pr1987088711_a_nat,B4: set_Pr1987088711_a_nat,X3: produc1871334759_a_nat] :
% 3.03/1.61 ( ( ord_le1718765799_a_nat @ A4 @ B4 )
% 3.03/1.61 => ( ( member832397200_a_nat @ X3 @ A4 )
% 3.03/1.61 => ( member832397200_a_nat @ X3 @ B4 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_253_chain,axiom,
% 3.03/1.61 ! [S2: nat > labeled_graph_b_nat,I: nat,J4: nat] :
% 3.03/1.61 ( ( chain_b_nat @ S2 )
% 3.03/1.61 => ( ( ord_less_eq_nat @ I @ J4 )
% 3.03/1.61 => ( graph_529870330at_nat @ ( S2 @ I ) @ ( S2 @ J4 ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( S2 @ I ) ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_254_chain__def2,axiom,
% 3.03/1.61 ( chain_b_nat
% 3.03/1.61 = ( ^ [S3: nat > labeled_graph_b_nat] :
% 3.03/1.61 ! [I3: nat,J3: nat] :
% 3.03/1.61 ( ( ord_less_eq_nat @ I3 @ J3 )
% 3.03/1.61 => ( graph_529870330at_nat @ ( S3 @ I3 ) @ ( S3 @ J3 ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( S3 @ I3 ) ) ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_255_graph__unionI,axiom,
% 3.03/1.61 ! [G_1: labeled_graph_b_nat,G_2: labeled_graph_b_nat] :
% 3.03/1.61 ( ( ord_le910748009at_nat @ ( labeled_edges_b_nat @ G_1 ) @ ( labeled_edges_b_nat @ G_2 ) )
% 3.03/1.61 => ( ( ord_less_eq_set_nat @ ( labele460410879_b_nat @ G_1 ) @ ( labele460410879_b_nat @ G_2 ) )
% 3.03/1.61 => ( ( graph_union_b_nat @ G_1 @ G_2 )
% 3.03/1.61 = G_2 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_256_extensibleD,axiom,
% 3.03/1.61 ! [R: produc1235635379_b_nat,G: labeled_graph_b_nat,F3: set_Pr1986765409at_nat] :
% 3.03/1.61 ( ( extensible_b_nat_nat @ R @ G @ F3 )
% 3.03/1.61 => ~ ! [G3: set_Pr1986765409at_nat] :
% 3.03/1.61 ( ( graph_529870330at_nat @ ( produc194497945_b_nat @ R ) @ G @ G3 )
% 3.03/1.61 => ~ ( agree_on_b_nat_nat @ ( produc1542243159_b_nat @ R ) @ F3 @ G3 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_257_extensible__def,axiom,
% 3.03/1.61 ( extensible_b_nat_nat
% 3.03/1.61 = ( ^ [R2: produc1235635379_b_nat,G2: labeled_graph_b_nat,F5: set_Pr1986765409at_nat] :
% 3.03/1.61 ? [G4: set_Pr1986765409at_nat] :
% 3.03/1.61 ( ( graph_529870330at_nat @ ( produc194497945_b_nat @ R2 ) @ G2 @ G4 )
% 3.03/1.61 & ( agree_on_b_nat_nat @ ( produc1542243159_b_nat @ R2 ) @ F5 @ G4 ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_258_extensibleI,axiom,
% 3.03/1.61 ! [R22: labeled_graph_b_nat,G: labeled_graph_b_nat,G5: set_Pr1986765409at_nat,R1: labeled_graph_b_nat,F3: set_Pr1986765409at_nat] :
% 3.03/1.61 ( ( graph_529870330at_nat @ R22 @ G @ G5 )
% 3.03/1.61 => ( ( agree_on_b_nat_nat @ R1 @ F3 @ G5 )
% 3.03/1.61 => ( extensible_b_nat_nat @ ( produc951298923_b_nat @ R1 @ R22 ) @ G @ F3 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_259_graph__union__preserves__restrict,axiom,
% 3.03/1.61 ! [G_1: labeled_graph_b_nat,G_2: labeled_graph_b_nat] :
% 3.03/1.61 ( ( G_1
% 3.03/1.61 = ( restrict_b_nat @ G_1 ) )
% 3.03/1.61 => ( ( G_2
% 3.03/1.61 = ( restrict_b_nat @ G_2 ) )
% 3.03/1.61 => ( ( graph_union_b_nat @ G_1 @ G_2 )
% 3.03/1.61 = ( restrict_b_nat @ ( graph_union_b_nat @ G_1 @ G_2 ) ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_260_subgraph__def,axiom,
% 3.03/1.61 ! [G_1: labeled_graph_b_nat,G_2: labeled_graph_b_nat] :
% 3.03/1.61 ( ( graph_529870330at_nat @ G_1 @ G_2 @ ( id_on_nat @ ( labele460410879_b_nat @ G_1 ) ) )
% 3.03/1.61 = ( ( G_1
% 3.03/1.61 = ( restrict_b_nat @ G_1 ) )
% 3.03/1.61 & ( G_2
% 3.03/1.61 = ( restrict_b_nat @ G_2 ) )
% 3.03/1.61 & ( ( graph_union_b_nat @ G_1 @ G_2 )
% 3.03/1.61 = G_2 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_261_graph__union__iff,axiom,
% 3.03/1.61 ! [G_1: labeled_graph_b_nat,G_2: labeled_graph_b_nat] :
% 3.03/1.61 ( ( ( graph_union_b_nat @ G_1 @ G_2 )
% 3.03/1.61 = G_2 )
% 3.03/1.61 = ( ( ord_le910748009at_nat @ ( labeled_edges_b_nat @ G_1 ) @ ( labeled_edges_b_nat @ G_2 ) )
% 3.03/1.61 & ( ord_less_eq_set_nat @ ( labele460410879_b_nat @ G_1 ) @ ( labele460410879_b_nat @ G_2 ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_262_finite__nat__set__iff__bounded__le,axiom,
% 3.03/1.61 ( finite_finite_nat
% 3.03/1.61 = ( ^ [N: set_nat] :
% 3.03/1.61 ? [M: nat] :
% 3.03/1.61 ! [X5: nat] :
% 3.03/1.61 ( ( member_nat @ X5 @ N )
% 3.03/1.61 => ( ord_less_eq_nat @ X5 @ M ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_263_nonempty__rule,axiom,
% 3.03/1.61 ! [G: labeled_graph_b_nat] :
% 3.03/1.61 ( ( G
% 3.03/1.61 = ( restrict_b_nat @ G ) )
% 3.03/1.61 => ( ( maintained_b_nat_nat @ standa879863266rule_b @ G )
% 3.03/1.61 = ( ( labele460410879_b_nat @ G )
% 3.03/1.61 != bot_bot_set_nat ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_264_weak__universalI,axiom,
% 3.03/1.61 ! [R: produc1235635379_b_nat,G_1: labeled_graph_b_nat,F_1: set_Pr1986765409at_nat,G_2: labeled_graph_b_nat,T: itself_nat,F_2: set_Pr1986765409at_nat] :
% 3.03/1.61 ( ! [H_1: set_Pr1986765409at_nat,H_2: set_Pr1986765409at_nat,G6: labeled_graph_b_nat] :
% 3.03/1.61 ( ( graph_529870330at_nat @ ( produc194497945_b_nat @ R ) @ G6 @ H_1 )
% 3.03/1.61 => ( ( graph_529870330at_nat @ G_1 @ G6 @ H_2 )
% 3.03/1.61 => ( ( ord_le841296385at_nat @ ( relcomp_nat_nat_nat @ F_1 @ H_2 ) @ H_1 )
% 3.03/1.61 => ? [H2: set_Pr1986765409at_nat] :
% 3.03/1.61 ( ( graph_529870330at_nat @ G_2 @ G6 @ H2 )
% 3.03/1.61 & ( ord_le841296385at_nat @ H_2 @ H2 ) ) ) ) )
% 3.03/1.61 => ( weak_u2026406106at_nat @ T @ R @ G_1 @ G_2 @ F_1 @ F_2 ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_265_Id__on__empty,axiom,
% 3.03/1.61 ( ( id_on_nat @ bot_bot_set_nat )
% 3.03/1.61 = bot_bo2130386637at_nat ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_266_graph__homomorphism__composes,axiom,
% 3.03/1.61 ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,X3: set_Pr1986765409at_nat,C2: labeled_graph_b_nat,Y3: set_Pr1986765409at_nat] :
% 3.03/1.61 ( ( graph_529870330at_nat @ A @ B @ X3 )
% 3.03/1.61 => ( ( graph_529870330at_nat @ B @ C2 @ Y3 )
% 3.03/1.61 => ( graph_529870330at_nat @ A @ C2 @ ( relcomp_nat_nat_nat @ X3 @ Y3 ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_267_graph__empty__e,axiom,
% 3.03/1.61 ! [V2: set_nat] :
% 3.03/1.61 ( ( labeled_LG_b_nat @ bot_bo1626616373at_nat @ V2 )
% 3.03/1.61 = ( restrict_b_nat @ ( labeled_LG_b_nat @ bot_bo1626616373at_nat @ V2 ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_268_graph__homomorphism__empty,axiom,
% 3.03/1.61 ! [G: labeled_graph_b_nat,F3: set_Pr1986765409at_nat] :
% 3.03/1.61 ( ( graph_529870330at_nat @ ( labeled_LG_b_nat @ bot_bo1626616373at_nat @ bot_bot_set_nat ) @ G @ F3 )
% 3.03/1.61 = ( ( F3 = bot_bo2130386637at_nat )
% 3.03/1.61 & ( G
% 3.03/1.61 = ( restrict_b_nat @ G ) ) ) ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_269_bot_Oextremum,axiom,
% 3.03/1.61 ! [A: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A ) ).
% 3.03/1.61
% 3.03/1.61 thf(fact_270_bot_Oextremum__unique,axiom,
% 3.03/1.61 ! [A: nat] :
% 3.03/1.62 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 3.03/1.62 = ( A = bot_bot_nat ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_271_bot_Oextremum__uniqueI,axiom,
% 3.03/1.62 ! [A: nat] :
% 3.03/1.62 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 3.03/1.62 => ( A = bot_bot_nat ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_272_relcomp_OrelcompI,axiom,
% 3.03/1.62 ! [A: labele935650037_a_nat,B: labele935650037_a_nat,R4: set_Pr1987088711_a_nat,C2: labele935650037_a_nat,S4: set_Pr1987088711_a_nat] :
% 3.03/1.62 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B ) @ R4 )
% 3.03/1.62 => ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ B @ C2 ) @ S4 )
% 3.03/1.62 => ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ C2 ) @ ( relcom1338300020_a_nat @ R4 @ S4 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_273_relcomp_OrelcompI,axiom,
% 3.03/1.62 ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,R4: set_Pr551076371_b_nat,C2: labeled_graph_b_nat,S4: set_Pr551076371_b_nat] :
% 3.03/1.62 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B ) @ R4 )
% 3.03/1.62 => ( ( member963855452_b_nat @ ( produc951298923_b_nat @ B @ C2 ) @ S4 )
% 3.03/1.62 => ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ C2 ) @ ( relcom1426860350_b_nat @ R4 @ S4 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_274_relcomp_OrelcompI,axiom,
% 3.03/1.62 ! [A: allegorical_term_b,B: allegorical_term_b,R4: set_Pr1163220871term_b,C2: allegorical_term_b,S4: set_Pr1163220871term_b] :
% 3.03/1.62 ( ( member516522448term_b @ ( produc1990145943term_b @ A @ B ) @ R4 )
% 3.03/1.62 => ( ( member516522448term_b @ ( produc1990145943term_b @ B @ C2 ) @ S4 )
% 3.03/1.62 => ( member516522448term_b @ ( produc1990145943term_b @ A @ C2 ) @ ( relcom1955155673term_b @ R4 @ S4 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_275_relcomp_Oinducts,axiom,
% 3.03/1.62 ! [X1: labele935650037_a_nat,X22: labele935650037_a_nat,R4: set_Pr1987088711_a_nat,S4: set_Pr1987088711_a_nat,P: labele935650037_a_nat > labele935650037_a_nat > $o] :
% 3.03/1.62 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ X1 @ X22 ) @ ( relcom1338300020_a_nat @ R4 @ S4 ) )
% 3.03/1.62 => ( ! [A3: labele935650037_a_nat,B3: labele935650037_a_nat,C: labele935650037_a_nat] :
% 3.03/1.62 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A3 @ B3 ) @ R4 )
% 3.03/1.62 => ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ B3 @ C ) @ S4 )
% 3.03/1.62 => ( P @ A3 @ C ) ) )
% 3.03/1.62 => ( P @ X1 @ X22 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_276_relcomp_Oinducts,axiom,
% 3.03/1.62 ! [X1: labeled_graph_b_nat,X22: labeled_graph_b_nat,R4: set_Pr551076371_b_nat,S4: set_Pr551076371_b_nat,P: labeled_graph_b_nat > labeled_graph_b_nat > $o] :
% 3.03/1.62 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ X1 @ X22 ) @ ( relcom1426860350_b_nat @ R4 @ S4 ) )
% 3.03/1.62 => ( ! [A3: labeled_graph_b_nat,B3: labeled_graph_b_nat,C: labeled_graph_b_nat] :
% 3.03/1.62 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A3 @ B3 ) @ R4 )
% 3.03/1.62 => ( ( member963855452_b_nat @ ( produc951298923_b_nat @ B3 @ C ) @ S4 )
% 3.03/1.62 => ( P @ A3 @ C ) ) )
% 3.03/1.62 => ( P @ X1 @ X22 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_277_relcomp_Oinducts,axiom,
% 3.03/1.62 ! [X1: allegorical_term_b,X22: allegorical_term_b,R4: set_Pr1163220871term_b,S4: set_Pr1163220871term_b,P: allegorical_term_b > allegorical_term_b > $o] :
% 3.03/1.62 ( ( member516522448term_b @ ( produc1990145943term_b @ X1 @ X22 ) @ ( relcom1955155673term_b @ R4 @ S4 ) )
% 3.03/1.62 => ( ! [A3: allegorical_term_b,B3: allegorical_term_b,C: allegorical_term_b] :
% 3.03/1.62 ( ( member516522448term_b @ ( produc1990145943term_b @ A3 @ B3 ) @ R4 )
% 3.03/1.62 => ( ( member516522448term_b @ ( produc1990145943term_b @ B3 @ C ) @ S4 )
% 3.03/1.62 => ( P @ A3 @ C ) ) )
% 3.03/1.62 => ( P @ X1 @ X22 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_278_relcomp_Osimps,axiom,
% 3.03/1.62 ! [A1: labele935650037_a_nat,A22: labele935650037_a_nat,R4: set_Pr1987088711_a_nat,S4: set_Pr1987088711_a_nat] :
% 3.03/1.62 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A1 @ A22 ) @ ( relcom1338300020_a_nat @ R4 @ S4 ) )
% 3.03/1.62 = ( ? [A5: labele935650037_a_nat,B5: labele935650037_a_nat,C3: labele935650037_a_nat] :
% 3.03/1.62 ( ( A1 = A5 )
% 3.03/1.62 & ( A22 = C3 )
% 3.03/1.62 & ( member832397200_a_nat @ ( produc1676969687_a_nat @ A5 @ B5 ) @ R4 )
% 3.03/1.62 & ( member832397200_a_nat @ ( produc1676969687_a_nat @ B5 @ C3 ) @ S4 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_279_relcomp_Osimps,axiom,
% 3.03/1.62 ! [A1: labeled_graph_b_nat,A22: labeled_graph_b_nat,R4: set_Pr551076371_b_nat,S4: set_Pr551076371_b_nat] :
% 3.03/1.62 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A1 @ A22 ) @ ( relcom1426860350_b_nat @ R4 @ S4 ) )
% 3.03/1.62 = ( ? [A5: labeled_graph_b_nat,B5: labeled_graph_b_nat,C3: labeled_graph_b_nat] :
% 3.03/1.62 ( ( A1 = A5 )
% 3.03/1.62 & ( A22 = C3 )
% 3.03/1.62 & ( member963855452_b_nat @ ( produc951298923_b_nat @ A5 @ B5 ) @ R4 )
% 3.03/1.62 & ( member963855452_b_nat @ ( produc951298923_b_nat @ B5 @ C3 ) @ S4 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_280_relcomp_Osimps,axiom,
% 3.03/1.62 ! [A1: allegorical_term_b,A22: allegorical_term_b,R4: set_Pr1163220871term_b,S4: set_Pr1163220871term_b] :
% 3.03/1.62 ( ( member516522448term_b @ ( produc1990145943term_b @ A1 @ A22 ) @ ( relcom1955155673term_b @ R4 @ S4 ) )
% 3.03/1.62 = ( ? [A5: allegorical_term_b,B5: allegorical_term_b,C3: allegorical_term_b] :
% 3.03/1.62 ( ( A1 = A5 )
% 3.03/1.62 & ( A22 = C3 )
% 3.03/1.62 & ( member516522448term_b @ ( produc1990145943term_b @ A5 @ B5 ) @ R4 )
% 3.03/1.62 & ( member516522448term_b @ ( produc1990145943term_b @ B5 @ C3 ) @ S4 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_281_relcomp_Ocases,axiom,
% 3.03/1.62 ! [A1: labele935650037_a_nat,A22: labele935650037_a_nat,R4: set_Pr1987088711_a_nat,S4: set_Pr1987088711_a_nat] :
% 3.03/1.62 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A1 @ A22 ) @ ( relcom1338300020_a_nat @ R4 @ S4 ) )
% 3.03/1.62 => ~ ! [B3: labele935650037_a_nat] :
% 3.03/1.62 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A1 @ B3 ) @ R4 )
% 3.03/1.62 => ~ ( member832397200_a_nat @ ( produc1676969687_a_nat @ B3 @ A22 ) @ S4 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_282_relcomp_Ocases,axiom,
% 3.03/1.62 ! [A1: labeled_graph_b_nat,A22: labeled_graph_b_nat,R4: set_Pr551076371_b_nat,S4: set_Pr551076371_b_nat] :
% 3.03/1.62 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A1 @ A22 ) @ ( relcom1426860350_b_nat @ R4 @ S4 ) )
% 3.03/1.62 => ~ ! [B3: labeled_graph_b_nat] :
% 3.03/1.62 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A1 @ B3 ) @ R4 )
% 3.03/1.62 => ~ ( member963855452_b_nat @ ( produc951298923_b_nat @ B3 @ A22 ) @ S4 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_283_relcomp_Ocases,axiom,
% 3.03/1.62 ! [A1: allegorical_term_b,A22: allegorical_term_b,R4: set_Pr1163220871term_b,S4: set_Pr1163220871term_b] :
% 3.03/1.62 ( ( member516522448term_b @ ( produc1990145943term_b @ A1 @ A22 ) @ ( relcom1955155673term_b @ R4 @ S4 ) )
% 3.03/1.62 => ~ ! [B3: allegorical_term_b] :
% 3.03/1.62 ( ( member516522448term_b @ ( produc1990145943term_b @ A1 @ B3 ) @ R4 )
% 3.03/1.62 => ~ ( member516522448term_b @ ( produc1990145943term_b @ B3 @ A22 ) @ S4 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_284_relcompEpair,axiom,
% 3.03/1.62 ! [A: labele935650037_a_nat,C2: labele935650037_a_nat,R4: set_Pr1987088711_a_nat,S4: set_Pr1987088711_a_nat] :
% 3.03/1.62 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ C2 ) @ ( relcom1338300020_a_nat @ R4 @ S4 ) )
% 3.03/1.62 => ~ ! [B3: labele935650037_a_nat] :
% 3.03/1.62 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B3 ) @ R4 )
% 3.03/1.62 => ~ ( member832397200_a_nat @ ( produc1676969687_a_nat @ B3 @ C2 ) @ S4 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_285_relcompEpair,axiom,
% 3.03/1.62 ! [A: labeled_graph_b_nat,C2: labeled_graph_b_nat,R4: set_Pr551076371_b_nat,S4: set_Pr551076371_b_nat] :
% 3.03/1.62 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ C2 ) @ ( relcom1426860350_b_nat @ R4 @ S4 ) )
% 3.03/1.62 => ~ ! [B3: labeled_graph_b_nat] :
% 3.03/1.62 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B3 ) @ R4 )
% 3.03/1.62 => ~ ( member963855452_b_nat @ ( produc951298923_b_nat @ B3 @ C2 ) @ S4 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_286_relcompEpair,axiom,
% 3.03/1.62 ! [A: allegorical_term_b,C2: allegorical_term_b,R4: set_Pr1163220871term_b,S4: set_Pr1163220871term_b] :
% 3.03/1.62 ( ( member516522448term_b @ ( produc1990145943term_b @ A @ C2 ) @ ( relcom1955155673term_b @ R4 @ S4 ) )
% 3.03/1.62 => ~ ! [B3: allegorical_term_b] :
% 3.03/1.62 ( ( member516522448term_b @ ( produc1990145943term_b @ A @ B3 ) @ R4 )
% 3.03/1.62 => ~ ( member516522448term_b @ ( produc1990145943term_b @ B3 @ C2 ) @ S4 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_287_relcompE,axiom,
% 3.03/1.62 ! [Xz: produc1871334759_a_nat,R4: set_Pr1987088711_a_nat,S4: set_Pr1987088711_a_nat] :
% 3.03/1.62 ( ( member832397200_a_nat @ Xz @ ( relcom1338300020_a_nat @ R4 @ S4 ) )
% 3.03/1.62 => ~ ! [X4: labele935650037_a_nat,Y4: labele935650037_a_nat,Z3: labele935650037_a_nat] :
% 3.03/1.62 ( ( Xz
% 3.03/1.62 = ( produc1676969687_a_nat @ X4 @ Z3 ) )
% 3.03/1.62 => ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ X4 @ Y4 ) @ R4 )
% 3.03/1.62 => ~ ( member832397200_a_nat @ ( produc1676969687_a_nat @ Y4 @ Z3 ) @ S4 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_288_relcompE,axiom,
% 3.03/1.62 ! [Xz: produc1235635379_b_nat,R4: set_Pr551076371_b_nat,S4: set_Pr551076371_b_nat] :
% 3.03/1.62 ( ( member963855452_b_nat @ Xz @ ( relcom1426860350_b_nat @ R4 @ S4 ) )
% 3.03/1.62 => ~ ! [X4: labeled_graph_b_nat,Y4: labeled_graph_b_nat,Z3: labeled_graph_b_nat] :
% 3.03/1.62 ( ( Xz
% 3.03/1.62 = ( produc951298923_b_nat @ X4 @ Z3 ) )
% 3.03/1.62 => ( ( member963855452_b_nat @ ( produc951298923_b_nat @ X4 @ Y4 ) @ R4 )
% 3.03/1.62 => ~ ( member963855452_b_nat @ ( produc951298923_b_nat @ Y4 @ Z3 ) @ S4 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_289_relcompE,axiom,
% 3.03/1.62 ! [Xz: produc1478835367term_b,R4: set_Pr1163220871term_b,S4: set_Pr1163220871term_b] :
% 3.03/1.62 ( ( member516522448term_b @ Xz @ ( relcom1955155673term_b @ R4 @ S4 ) )
% 3.03/1.62 => ~ ! [X4: allegorical_term_b,Y4: allegorical_term_b,Z3: allegorical_term_b] :
% 3.03/1.62 ( ( Xz
% 3.03/1.62 = ( produc1990145943term_b @ X4 @ Z3 ) )
% 3.03/1.62 => ( ( member516522448term_b @ ( produc1990145943term_b @ X4 @ Y4 ) @ R4 )
% 3.03/1.62 => ~ ( member516522448term_b @ ( produc1990145943term_b @ Y4 @ Z3 ) @ S4 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_290_finite_OemptyI,axiom,
% 3.03/1.62 finite_finite_nat @ bot_bot_set_nat ).
% 3.03/1.62
% 3.03/1.62 thf(fact_291_finite_OemptyI,axiom,
% 3.03/1.62 finite1987068434at_nat @ bot_bo1626616373at_nat ).
% 3.03/1.62
% 3.03/1.62 thf(fact_292_infinite__imp__nonempty,axiom,
% 3.03/1.62 ! [S2: set_nat] :
% 3.03/1.62 ( ~ ( finite_finite_nat @ S2 )
% 3.03/1.62 => ( S2 != bot_bot_set_nat ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_293_infinite__imp__nonempty,axiom,
% 3.03/1.62 ! [S2: set_Pr9961929at_nat] :
% 3.03/1.62 ( ~ ( finite1987068434at_nat @ S2 )
% 3.03/1.62 => ( S2 != bot_bo1626616373at_nat ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_294_finite__has__minimal,axiom,
% 3.03/1.62 ! [A4: set_nat] :
% 3.03/1.62 ( ( finite_finite_nat @ A4 )
% 3.03/1.62 => ( ( A4 != bot_bot_set_nat )
% 3.03/1.62 => ? [X4: nat] :
% 3.03/1.62 ( ( member_nat @ X4 @ A4 )
% 3.03/1.62 & ! [Xa: nat] :
% 3.03/1.62 ( ( member_nat @ Xa @ A4 )
% 3.03/1.62 => ( ( ord_less_eq_nat @ Xa @ X4 )
% 3.03/1.62 => ( X4 = Xa ) ) ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_295_finite__has__maximal,axiom,
% 3.03/1.62 ! [A4: set_nat] :
% 3.03/1.62 ( ( finite_finite_nat @ A4 )
% 3.03/1.62 => ( ( A4 != bot_bot_set_nat )
% 3.03/1.62 => ? [X4: nat] :
% 3.03/1.62 ( ( member_nat @ X4 @ A4 )
% 3.03/1.62 & ! [Xa: nat] :
% 3.03/1.62 ( ( member_nat @ Xa @ A4 )
% 3.03/1.62 => ( ( ord_less_eq_nat @ X4 @ Xa )
% 3.03/1.62 => ( X4 = Xa ) ) ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_296_graph__homomorphism__nonempty,axiom,
% 3.03/1.62 ! [A4: labeled_graph_b_nat,B4: labeled_graph_b_nat,F3: set_Pr1986765409at_nat,E: allegorical_term_b] :
% 3.03/1.62 ( ( graph_529870330at_nat @ A4 @ B4 @ F3 )
% 3.03/1.62 => ( ( ( semantics_b_nat @ A4 @ E )
% 3.03/1.62 != bot_bo2130386637at_nat )
% 3.03/1.62 => ( ( semantics_b_nat @ B4 @ E )
% 3.03/1.62 != bot_bo2130386637at_nat ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_297_bounded__Max__nat,axiom,
% 3.03/1.62 ! [P: nat > $o,X3: nat,M2: nat] :
% 3.03/1.62 ( ( P @ X3 )
% 3.03/1.62 => ( ! [X4: nat] :
% 3.03/1.62 ( ( P @ X4 )
% 3.03/1.62 => ( ord_less_eq_nat @ X4 @ M2 ) )
% 3.03/1.62 => ~ ! [M3: nat] :
% 3.03/1.62 ( ( P @ M3 )
% 3.03/1.62 => ~ ! [X6: nat] :
% 3.03/1.62 ( ( P @ X6 )
% 3.03/1.62 => ( ord_less_eq_nat @ X6 @ M3 ) ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_298_Id__on__vertices__identity_I2_J,axiom,
% 3.03/1.62 ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,F3: set_Pr1986765409at_nat,Aa: nat,Ba: nat] :
% 3.03/1.62 ( ( graph_529870330at_nat @ A @ B @ F3 )
% 3.03/1.62 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ Aa @ Ba ) @ F3 )
% 3.03/1.62 => ( member701585322at_nat @ ( product_Pair_nat_nat @ Aa @ Ba ) @ ( relcomp_nat_nat_nat @ F3 @ ( id_on_nat @ ( labele460410879_b_nat @ B ) ) ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_299_Id__on__vertices__identity_I1_J,axiom,
% 3.03/1.62 ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,F3: set_Pr1986765409at_nat,Aa: nat,Ba: nat] :
% 3.03/1.62 ( ( graph_529870330at_nat @ A @ B @ F3 )
% 3.03/1.62 => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ Aa @ Ba ) @ F3 )
% 3.03/1.62 => ( member701585322at_nat @ ( product_Pair_nat_nat @ Aa @ Ba ) @ ( relcomp_nat_nat_nat @ ( id_on_nat @ ( labele460410879_b_nat @ A ) ) @ F3 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_300_translation__homomorphism_I2_J,axiom,
% 3.03/1.62 ! [E: allegorical_term_b,G: labeled_graph_b_nat,F3: set_Pr1986765409at_nat] :
% 3.03/1.62 ( ( graph_529870330at_nat @ ( translation_b @ E ) @ G @ F3 )
% 3.03/1.62 => ( ( semantics_b_nat @ G @ E )
% 3.03/1.62 != bot_bo2130386637at_nat ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_301_weak__universalD,axiom,
% 3.03/1.62 ! [T: itself_nat,R: produc1235635379_b_nat,G_1: labeled_graph_b_nat,G_2: labeled_graph_b_nat,F_1: set_Pr1986765409at_nat,F_2: set_Pr1986765409at_nat,G: labeled_graph_b_nat,H_12: set_Pr1986765409at_nat,H_22: set_Pr1986765409at_nat] :
% 3.03/1.62 ( ( weak_u2026406106at_nat @ T @ R @ G_1 @ G_2 @ F_1 @ F_2 )
% 3.03/1.62 => ( ( graph_529870330at_nat @ ( produc194497945_b_nat @ R ) @ G @ H_12 )
% 3.03/1.62 => ( ( graph_529870330at_nat @ G_1 @ G @ H_22 )
% 3.03/1.62 => ( ( ord_le841296385at_nat @ ( relcomp_nat_nat_nat @ F_1 @ H_22 ) @ H_12 )
% 3.03/1.62 => ? [H3: set_Pr1986765409at_nat] :
% 3.03/1.62 ( ( graph_529870330at_nat @ G_2 @ G @ H3 )
% 3.03/1.62 & ( ord_le841296385at_nat @ H_22 @ H3 ) ) ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_302_weak__universal__def,axiom,
% 3.03/1.62 ( weak_u2026406106at_nat
% 3.03/1.62 = ( ^ [Uu: itself_nat,R2: produc1235635379_b_nat,G_12: labeled_graph_b_nat,G_22: labeled_graph_b_nat,F_12: set_Pr1986765409at_nat,F_22: set_Pr1986765409at_nat] :
% 3.03/1.62 ! [H_13: set_Pr1986765409at_nat,H_23: set_Pr1986765409at_nat,G2: labeled_graph_b_nat] :
% 3.03/1.62 ( ( ( graph_529870330at_nat @ ( produc194497945_b_nat @ R2 ) @ G2 @ H_13 )
% 3.03/1.62 & ( graph_529870330at_nat @ G_12 @ G2 @ H_23 )
% 3.03/1.62 & ( ord_le841296385at_nat @ ( relcomp_nat_nat_nat @ F_12 @ H_23 ) @ H_13 ) )
% 3.03/1.62 => ? [H4: set_Pr1986765409at_nat] :
% 3.03/1.62 ( ( graph_529870330at_nat @ G_22 @ G2 @ H4 )
% 3.03/1.62 & ( ord_le841296385at_nat @ H_23 @ H4 ) ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_303_graph__homo__union__id_I2_J,axiom,
% 3.03/1.62 ! [A4: labeled_graph_b_nat,B4: labeled_graph_b_nat,G: labeled_graph_b_nat,F3: set_Pr1986765409at_nat] :
% 3.03/1.62 ( ( graph_529870330at_nat @ ( graph_union_b_nat @ A4 @ B4 ) @ G @ F3 )
% 3.03/1.62 => ( ( B4
% 3.03/1.62 = ( restrict_b_nat @ B4 ) )
% 3.03/1.62 => ( graph_529870330at_nat @ B4 @ G @ ( relcomp_nat_nat_nat @ ( id_on_nat @ ( labele460410879_b_nat @ B4 ) ) @ F3 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_304_graph__homo__union__id_I1_J,axiom,
% 3.03/1.62 ! [A4: labeled_graph_b_nat,B4: labeled_graph_b_nat,G: labeled_graph_b_nat,F3: set_Pr1986765409at_nat] :
% 3.03/1.62 ( ( graph_529870330at_nat @ ( graph_union_b_nat @ A4 @ B4 ) @ G @ F3 )
% 3.03/1.62 => ( ( A4
% 3.03/1.62 = ( restrict_b_nat @ A4 ) )
% 3.03/1.62 => ( graph_529870330at_nat @ A4 @ G @ ( relcomp_nat_nat_nat @ ( id_on_nat @ ( labele460410879_b_nat @ A4 ) ) @ F3 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_305_finite__relcomp,axiom,
% 3.03/1.62 ! [R: set_Product_prod_b_b,S2: set_Pr9961929at_nat] :
% 3.03/1.62 ( ( finite1015599120od_b_b @ R )
% 3.03/1.62 => ( ( finite1987068434at_nat @ S2 )
% 3.03/1.62 => ( finite1987068434at_nat @ ( relcom14055552at_nat @ R @ S2 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_306_finite__relcomp,axiom,
% 3.03/1.62 ! [R: set_Pr9961929at_nat,S2: set_Pr1490359111at_nat] :
% 3.03/1.62 ( ( finite1987068434at_nat @ R )
% 3.03/1.62 => ( ( finite48957584at_nat @ S2 )
% 3.03/1.62 => ( finite1987068434at_nat @ ( relcom195261566at_nat @ R @ S2 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_307_subset__emptyI,axiom,
% 3.03/1.62 ! [A4: set_Pr1987088711_a_nat] :
% 3.03/1.62 ( ! [X4: produc1871334759_a_nat] :
% 3.03/1.62 ~ ( member832397200_a_nat @ X4 @ A4 )
% 3.03/1.62 => ( ord_le1718765799_a_nat @ A4 @ bot_bo1836341171_a_nat ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_308_bot__empty__eq,axiom,
% 3.03/1.62 ( bot_bo1024461546_nat_o
% 3.03/1.62 = ( ^ [X5: produc1871334759_a_nat] : ( member832397200_a_nat @ X5 @ bot_bo1836341171_a_nat ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_309_ssubst__Pair__rhs,axiom,
% 3.03/1.62 ! [R4: labele935650037_a_nat,S4: labele935650037_a_nat,R: set_Pr1987088711_a_nat,S5: labele935650037_a_nat] :
% 3.03/1.62 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ R4 @ S4 ) @ R )
% 3.03/1.62 => ( ( S5 = S4 )
% 3.03/1.62 => ( member832397200_a_nat @ ( produc1676969687_a_nat @ R4 @ S5 ) @ R ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_310_ssubst__Pair__rhs,axiom,
% 3.03/1.62 ! [R4: labeled_graph_b_nat,S4: labeled_graph_b_nat,R: set_Pr551076371_b_nat,S5: labeled_graph_b_nat] :
% 3.03/1.62 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ R4 @ S4 ) @ R )
% 3.03/1.62 => ( ( S5 = S4 )
% 3.03/1.62 => ( member963855452_b_nat @ ( produc951298923_b_nat @ R4 @ S5 ) @ R ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_311_ssubst__Pair__rhs,axiom,
% 3.03/1.62 ! [R4: allegorical_term_b,S4: allegorical_term_b,R: set_Pr1163220871term_b,S5: allegorical_term_b] :
% 3.03/1.62 ( ( member516522448term_b @ ( produc1990145943term_b @ R4 @ S4 ) @ R )
% 3.03/1.62 => ( ( S5 = S4 )
% 3.03/1.62 => ( member516522448term_b @ ( produc1990145943term_b @ R4 @ S5 ) @ R ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_312_agree__iff__subset,axiom,
% 3.03/1.62 ! [G: labeled_graph_b_nat,X: labeled_graph_b_nat,F3: set_Pr1986765409at_nat,G5: set_Pr1986765409at_nat] :
% 3.03/1.62 ( ( graph_529870330at_nat @ G @ X @ F3 )
% 3.03/1.62 => ( ( univalent_nat_nat @ G5 )
% 3.03/1.62 => ( ( agree_on_b_nat_nat @ G @ F3 @ G5 )
% 3.03/1.62 = ( ord_le841296385at_nat @ F3 @ G5 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_313_id__univalent,axiom,
% 3.03/1.62 ! [X3: set_nat] : ( univalent_nat_nat @ ( id_on_nat @ X3 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_314_univalentD,axiom,
% 3.03/1.62 ! [R: set_Pr1987088711_a_nat,X3: labele935650037_a_nat,Y3: labele935650037_a_nat,Z2: labele935650037_a_nat] :
% 3.03/1.62 ( ( unival1637751524_a_nat @ R )
% 3.03/1.62 => ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ X3 @ Y3 ) @ R )
% 3.03/1.62 => ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ X3 @ Z2 ) @ R )
% 3.03/1.62 => ( Z2 = Y3 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_315_univalentD,axiom,
% 3.03/1.62 ! [R: set_Pr551076371_b_nat,X3: labeled_graph_b_nat,Y3: labeled_graph_b_nat,Z2: labeled_graph_b_nat] :
% 3.03/1.62 ( ( unival857119480_b_nat @ R )
% 3.03/1.62 => ( ( member963855452_b_nat @ ( produc951298923_b_nat @ X3 @ Y3 ) @ R )
% 3.03/1.62 => ( ( member963855452_b_nat @ ( produc951298923_b_nat @ X3 @ Z2 ) @ R )
% 3.03/1.62 => ( Z2 = Y3 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_316_univalentD,axiom,
% 3.03/1.62 ! [R: set_Pr1163220871term_b,X3: allegorical_term_b,Y3: allegorical_term_b,Z2: allegorical_term_b] :
% 3.03/1.62 ( ( unival1191217828term_b @ R )
% 3.03/1.62 => ( ( member516522448term_b @ ( produc1990145943term_b @ X3 @ Y3 ) @ R )
% 3.03/1.62 => ( ( member516522448term_b @ ( produc1990145943term_b @ X3 @ Z2 ) @ R )
% 3.03/1.62 => ( Z2 = Y3 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_317_univalent__def,axiom,
% 3.03/1.62 ( unival1637751524_a_nat
% 3.03/1.62 = ( ^ [R2: set_Pr1987088711_a_nat] :
% 3.03/1.62 ! [X5: labele935650037_a_nat,Y6: labele935650037_a_nat,Z4: labele935650037_a_nat] :
% 3.03/1.62 ( ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ X5 @ Y6 ) @ R2 )
% 3.03/1.62 & ( member832397200_a_nat @ ( produc1676969687_a_nat @ X5 @ Z4 ) @ R2 ) )
% 3.03/1.62 => ( Z4 = Y6 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_318_univalent__def,axiom,
% 3.03/1.62 ( unival857119480_b_nat
% 3.03/1.62 = ( ^ [R2: set_Pr551076371_b_nat] :
% 3.03/1.62 ! [X5: labeled_graph_b_nat,Y6: labeled_graph_b_nat,Z4: labeled_graph_b_nat] :
% 3.03/1.62 ( ( ( member963855452_b_nat @ ( produc951298923_b_nat @ X5 @ Y6 ) @ R2 )
% 3.03/1.62 & ( member963855452_b_nat @ ( produc951298923_b_nat @ X5 @ Z4 ) @ R2 ) )
% 3.03/1.62 => ( Z4 = Y6 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_319_univalent__def,axiom,
% 3.03/1.62 ( unival1191217828term_b
% 3.03/1.62 = ( ^ [R2: set_Pr1163220871term_b] :
% 3.03/1.62 ! [X5: allegorical_term_b,Y6: allegorical_term_b,Z4: allegorical_term_b] :
% 3.03/1.62 ( ( ( member516522448term_b @ ( produc1990145943term_b @ X5 @ Y6 ) @ R2 )
% 3.03/1.62 & ( member516522448term_b @ ( produc1990145943term_b @ X5 @ Z4 ) @ R2 ) )
% 3.03/1.62 => ( Z4 = Y6 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_320_find__graph__occurence__vertices,axiom,
% 3.03/1.62 ! [S2: nat > labeled_graph_b_nat,V: set_nat,F3: set_Pr1986765409at_nat] :
% 3.03/1.62 ( ( chain_b_nat @ S2 )
% 3.03/1.62 => ( ( finite_finite_nat @ V )
% 3.03/1.62 => ( ( univalent_nat_nat @ F3 )
% 3.03/1.62 => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F3 @ V ) @ ( labele460410879_b_nat @ ( chain_sup_b_nat @ S2 ) ) )
% 3.03/1.62 => ? [I2: nat] : ( ord_less_eq_set_nat @ ( image_nat_nat @ F3 @ V ) @ ( labele460410879_b_nat @ ( S2 @ I2 ) ) ) ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_321_find__graph__occurence__vertices,axiom,
% 3.03/1.62 ! [S2: nat > labeled_graph_b_nat,V: set_Pr9961929at_nat,F3: set_Pr2041158302at_nat] :
% 3.03/1.62 ( ( chain_b_nat @ S2 )
% 3.03/1.62 => ( ( finite1987068434at_nat @ V )
% 3.03/1.62 => ( ( unival633212949at_nat @ F3 )
% 3.03/1.62 => ( ( ord_less_eq_set_nat @ ( image_1356842150at_nat @ F3 @ V ) @ ( labele460410879_b_nat @ ( chain_sup_b_nat @ S2 ) ) )
% 3.03/1.62 => ? [I2: nat] : ( ord_less_eq_set_nat @ ( image_1356842150at_nat @ F3 @ V ) @ ( labele460410879_b_nat @ ( S2 @ I2 ) ) ) ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_322_ImageI,axiom,
% 3.03/1.62 ! [A: produc1871334759_a_nat,B: produc1871334759_a_nat,R4: set_Pr924198087_a_nat,A4: set_Pr1987088711_a_nat] :
% 3.03/1.62 ( ( member584645392_a_nat @ ( produc1677124439_a_nat @ A @ B ) @ R4 )
% 3.03/1.62 => ( ( member832397200_a_nat @ A @ A4 )
% 3.03/1.62 => ( member832397200_a_nat @ B @ ( image_1168831379_a_nat @ R4 @ A4 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_323_ImageI,axiom,
% 3.03/1.62 ! [A: labele935650037_a_nat,B: labele935650037_a_nat,R4: set_Pr1987088711_a_nat,A4: set_la1083530965_a_nat] :
% 3.03/1.62 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B ) @ R4 )
% 3.03/1.62 => ( ( member964390942_a_nat @ A @ A4 )
% 3.03/1.62 => ( member964390942_a_nat @ B @ ( image_1971191571_a_nat @ R4 @ A4 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_324_ImageI,axiom,
% 3.03/1.62 ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,R4: set_Pr551076371_b_nat,A4: set_la1976028319_b_nat] :
% 3.03/1.62 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B ) @ R4 )
% 3.03/1.62 => ( ( member1483953152_b_nat @ A @ A4 )
% 3.03/1.62 => ( member1483953152_b_nat @ B @ ( image_1183964583_b_nat @ R4 @ A4 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_325_ImageI,axiom,
% 3.03/1.62 ! [A: allegorical_term_b,B: allegorical_term_b,R4: set_Pr1163220871term_b,A4: set_al1193902458term_b] :
% 3.03/1.62 ( ( member516522448term_b @ ( produc1990145943term_b @ A @ B ) @ R4 )
% 3.03/1.62 => ( ( member93680451term_b @ A @ A4 )
% 3.03/1.62 => ( member93680451term_b @ B @ ( image_329221075term_b @ R4 @ A4 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_326_Domain__Id__on,axiom,
% 3.03/1.62 ! [A4: set_nat] :
% 3.03/1.62 ( ( domain_nat_nat @ ( id_on_nat @ A4 ) )
% 3.03/1.62 = A4 ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_327_univalent__finite_I2_J,axiom,
% 3.03/1.62 ! [R: set_Pr9961929at_nat] :
% 3.03/1.62 ( ( unival989235430at_nat @ R )
% 3.03/1.62 => ( ( finite_finite_b @ ( domain1101989710at_nat @ R ) )
% 3.03/1.62 = ( finite1987068434at_nat @ R ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_328_finite__Domain,axiom,
% 3.03/1.62 ! [R4: set_Pr9961929at_nat] :
% 3.03/1.62 ( ( finite1987068434at_nat @ R4 )
% 3.03/1.62 => ( finite_finite_b @ ( domain1101989710at_nat @ R4 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_329_finite__Image,axiom,
% 3.03/1.62 ! [R: set_Pr9961929at_nat,A4: set_b] :
% 3.03/1.62 ( ( finite1987068434at_nat @ R )
% 3.03/1.62 => ( finite772653738at_nat @ ( image_2112855445at_nat @ R @ A4 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_330_Domain_Oinducts,axiom,
% 3.03/1.62 ! [X3: labele935650037_a_nat,R4: set_Pr1987088711_a_nat,P: labele935650037_a_nat > $o] :
% 3.03/1.62 ( ( member964390942_a_nat @ X3 @ ( domain1068567884_a_nat @ R4 ) )
% 3.03/1.62 => ( ! [A3: labele935650037_a_nat,B3: labele935650037_a_nat] :
% 3.03/1.62 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A3 @ B3 ) @ R4 )
% 3.03/1.62 => ( P @ A3 ) )
% 3.03/1.62 => ( P @ X3 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_331_Domain_Oinducts,axiom,
% 3.03/1.62 ! [X3: labeled_graph_b_nat,R4: set_Pr551076371_b_nat,P: labeled_graph_b_nat > $o] :
% 3.03/1.62 ( ( member1483953152_b_nat @ X3 @ ( domain767519072_b_nat @ R4 ) )
% 3.03/1.62 => ( ! [A3: labeled_graph_b_nat,B3: labeled_graph_b_nat] :
% 3.03/1.62 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A3 @ B3 ) @ R4 )
% 3.03/1.62 => ( P @ A3 ) )
% 3.03/1.62 => ( P @ X3 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_332_Domain_Oinducts,axiom,
% 3.03/1.62 ! [X3: allegorical_term_b,R4: set_Pr1163220871term_b,P: allegorical_term_b > $o] :
% 3.03/1.62 ( ( member93680451term_b @ X3 @ ( domain859272460term_b @ R4 ) )
% 3.03/1.62 => ( ! [A3: allegorical_term_b,B3: allegorical_term_b] :
% 3.03/1.62 ( ( member516522448term_b @ ( produc1990145943term_b @ A3 @ B3 ) @ R4 )
% 3.03/1.62 => ( P @ A3 ) )
% 3.03/1.62 => ( P @ X3 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_333_Domain_ODomainI,axiom,
% 3.03/1.62 ! [A: labele935650037_a_nat,B: labele935650037_a_nat,R4: set_Pr1987088711_a_nat] :
% 3.03/1.62 ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B ) @ R4 )
% 3.03/1.62 => ( member964390942_a_nat @ A @ ( domain1068567884_a_nat @ R4 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_334_Domain_ODomainI,axiom,
% 3.03/1.62 ! [A: labeled_graph_b_nat,B: labeled_graph_b_nat,R4: set_Pr551076371_b_nat] :
% 3.03/1.62 ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B ) @ R4 )
% 3.03/1.62 => ( member1483953152_b_nat @ A @ ( domain767519072_b_nat @ R4 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_335_Domain_ODomainI,axiom,
% 3.03/1.62 ! [A: allegorical_term_b,B: allegorical_term_b,R4: set_Pr1163220871term_b] :
% 3.03/1.62 ( ( member516522448term_b @ ( produc1990145943term_b @ A @ B ) @ R4 )
% 3.03/1.62 => ( member93680451term_b @ A @ ( domain859272460term_b @ R4 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_336_Domain_Osimps,axiom,
% 3.03/1.62 ! [A: labele935650037_a_nat,R4: set_Pr1987088711_a_nat] :
% 3.03/1.62 ( ( member964390942_a_nat @ A @ ( domain1068567884_a_nat @ R4 ) )
% 3.03/1.62 = ( ? [A5: labele935650037_a_nat,B5: labele935650037_a_nat] :
% 3.03/1.62 ( ( A = A5 )
% 3.03/1.62 & ( member832397200_a_nat @ ( produc1676969687_a_nat @ A5 @ B5 ) @ R4 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_337_Domain_Osimps,axiom,
% 3.03/1.62 ! [A: labeled_graph_b_nat,R4: set_Pr551076371_b_nat] :
% 3.03/1.62 ( ( member1483953152_b_nat @ A @ ( domain767519072_b_nat @ R4 ) )
% 3.03/1.62 = ( ? [A5: labeled_graph_b_nat,B5: labeled_graph_b_nat] :
% 3.03/1.62 ( ( A = A5 )
% 3.03/1.62 & ( member963855452_b_nat @ ( produc951298923_b_nat @ A5 @ B5 ) @ R4 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_338_Domain_Osimps,axiom,
% 3.03/1.62 ! [A: allegorical_term_b,R4: set_Pr1163220871term_b] :
% 3.03/1.62 ( ( member93680451term_b @ A @ ( domain859272460term_b @ R4 ) )
% 3.03/1.62 = ( ? [A5: allegorical_term_b,B5: allegorical_term_b] :
% 3.03/1.62 ( ( A = A5 )
% 3.03/1.62 & ( member516522448term_b @ ( produc1990145943term_b @ A5 @ B5 ) @ R4 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_339_Domain_Ocases,axiom,
% 3.03/1.62 ! [A: labele935650037_a_nat,R4: set_Pr1987088711_a_nat] :
% 3.03/1.62 ( ( member964390942_a_nat @ A @ ( domain1068567884_a_nat @ R4 ) )
% 3.03/1.62 => ~ ! [B3: labele935650037_a_nat] :
% 3.03/1.62 ~ ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B3 ) @ R4 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_340_Domain_Ocases,axiom,
% 3.03/1.62 ! [A: labeled_graph_b_nat,R4: set_Pr551076371_b_nat] :
% 3.03/1.62 ( ( member1483953152_b_nat @ A @ ( domain767519072_b_nat @ R4 ) )
% 3.03/1.62 => ~ ! [B3: labeled_graph_b_nat] :
% 3.03/1.62 ~ ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B3 ) @ R4 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_341_Domain_Ocases,axiom,
% 3.03/1.62 ! [A: allegorical_term_b,R4: set_Pr1163220871term_b] :
% 3.03/1.62 ( ( member93680451term_b @ A @ ( domain859272460term_b @ R4 ) )
% 3.03/1.62 => ~ ! [B3: allegorical_term_b] :
% 3.03/1.62 ~ ( member516522448term_b @ ( produc1990145943term_b @ A @ B3 ) @ R4 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_342_Domain__iff,axiom,
% 3.03/1.62 ! [A: labele935650037_a_nat,R4: set_Pr1987088711_a_nat] :
% 3.03/1.62 ( ( member964390942_a_nat @ A @ ( domain1068567884_a_nat @ R4 ) )
% 3.03/1.62 = ( ? [Y6: labele935650037_a_nat] : ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ Y6 ) @ R4 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_343_Domain__iff,axiom,
% 3.03/1.62 ! [A: labeled_graph_b_nat,R4: set_Pr551076371_b_nat] :
% 3.03/1.62 ( ( member1483953152_b_nat @ A @ ( domain767519072_b_nat @ R4 ) )
% 3.03/1.62 = ( ? [Y6: labeled_graph_b_nat] : ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ Y6 ) @ R4 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_344_Domain__iff,axiom,
% 3.03/1.62 ! [A: allegorical_term_b,R4: set_Pr1163220871term_b] :
% 3.03/1.62 ( ( member93680451term_b @ A @ ( domain859272460term_b @ R4 ) )
% 3.03/1.62 = ( ? [Y6: allegorical_term_b] : ( member516522448term_b @ ( produc1990145943term_b @ A @ Y6 ) @ R4 ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_345_DomainE,axiom,
% 3.03/1.62 ! [A: labele935650037_a_nat,R4: set_Pr1987088711_a_nat] :
% 3.03/1.62 ( ( member964390942_a_nat @ A @ ( domain1068567884_a_nat @ R4 ) )
% 3.03/1.62 => ~ ! [B3: labele935650037_a_nat] :
% 3.03/1.62 ~ ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B3 ) @ R4 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_346_DomainE,axiom,
% 3.03/1.62 ! [A: labeled_graph_b_nat,R4: set_Pr551076371_b_nat] :
% 3.03/1.62 ( ( member1483953152_b_nat @ A @ ( domain767519072_b_nat @ R4 ) )
% 3.03/1.62 => ~ ! [B3: labeled_graph_b_nat] :
% 3.03/1.62 ~ ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B3 ) @ R4 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_347_DomainE,axiom,
% 3.03/1.62 ! [A: allegorical_term_b,R4: set_Pr1163220871term_b] :
% 3.03/1.62 ( ( member93680451term_b @ A @ ( domain859272460term_b @ R4 ) )
% 3.03/1.62 => ~ ! [B3: allegorical_term_b] :
% 3.03/1.62 ~ ( member516522448term_b @ ( produc1990145943term_b @ A @ B3 ) @ R4 ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_348_rev__ImageI,axiom,
% 3.03/1.62 ! [A: labele935650037_a_nat,A4: set_la1083530965_a_nat,B: labele935650037_a_nat,R4: set_Pr1987088711_a_nat] :
% 3.03/1.62 ( ( member964390942_a_nat @ A @ A4 )
% 3.03/1.62 => ( ( member832397200_a_nat @ ( produc1676969687_a_nat @ A @ B ) @ R4 )
% 3.03/1.62 => ( member964390942_a_nat @ B @ ( image_1971191571_a_nat @ R4 @ A4 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_349_rev__ImageI,axiom,
% 3.03/1.62 ! [A: produc1871334759_a_nat,A4: set_Pr1987088711_a_nat,B: produc1871334759_a_nat,R4: set_Pr924198087_a_nat] :
% 3.03/1.62 ( ( member832397200_a_nat @ A @ A4 )
% 3.03/1.62 => ( ( member584645392_a_nat @ ( produc1677124439_a_nat @ A @ B ) @ R4 )
% 3.03/1.62 => ( member832397200_a_nat @ B @ ( image_1168831379_a_nat @ R4 @ A4 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_350_rev__ImageI,axiom,
% 3.03/1.62 ! [A: labeled_graph_b_nat,A4: set_la1976028319_b_nat,B: labeled_graph_b_nat,R4: set_Pr551076371_b_nat] :
% 3.03/1.62 ( ( member1483953152_b_nat @ A @ A4 )
% 3.03/1.62 => ( ( member963855452_b_nat @ ( produc951298923_b_nat @ A @ B ) @ R4 )
% 3.03/1.62 => ( member1483953152_b_nat @ B @ ( image_1183964583_b_nat @ R4 @ A4 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_351_rev__ImageI,axiom,
% 3.03/1.62 ! [A: allegorical_term_b,A4: set_al1193902458term_b,B: allegorical_term_b,R4: set_Pr1163220871term_b] :
% 3.03/1.62 ( ( member93680451term_b @ A @ A4 )
% 3.03/1.62 => ( ( member516522448term_b @ ( produc1990145943term_b @ A @ B ) @ R4 )
% 3.03/1.62 => ( member93680451term_b @ B @ ( image_329221075term_b @ R4 @ A4 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_352_Image__iff,axiom,
% 3.03/1.62 ! [B: labele935650037_a_nat,R4: set_Pr1987088711_a_nat,A4: set_la1083530965_a_nat] :
% 3.03/1.62 ( ( member964390942_a_nat @ B @ ( image_1971191571_a_nat @ R4 @ A4 ) )
% 3.03/1.62 = ( ? [X5: labele935650037_a_nat] :
% 3.03/1.62 ( ( member964390942_a_nat @ X5 @ A4 )
% 3.03/1.62 & ( member832397200_a_nat @ ( produc1676969687_a_nat @ X5 @ B ) @ R4 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_353_Image__iff,axiom,
% 3.03/1.62 ! [B: labeled_graph_b_nat,R4: set_Pr551076371_b_nat,A4: set_la1976028319_b_nat] :
% 3.03/1.62 ( ( member1483953152_b_nat @ B @ ( image_1183964583_b_nat @ R4 @ A4 ) )
% 3.03/1.62 = ( ? [X5: labeled_graph_b_nat] :
% 3.03/1.62 ( ( member1483953152_b_nat @ X5 @ A4 )
% 3.03/1.62 & ( member963855452_b_nat @ ( produc951298923_b_nat @ X5 @ B ) @ R4 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(fact_354_Image__iff,axiom,
% 3.03/1.62 ! [B: allegorical_term_b,R4: set_Pr1163220871term_b,A4: set_al1193902458term_b] :
% 3.03/1.62 ( ( member93680451term_b @ B @ ( image_329221075term_b @ R4 @ A4 ) )
% 3.03/1.62 = ( ? [X5: allegorical_term_b] :
% 3.03/1.62 ( ( member93680451term_b @ X5 @ A4 )
% 3.03/1.62 & ( member516522448term_b @ ( produc1990145943term_b @ X5 @ B ) @ R4 ) ) ) ) ).
% 3.03/1.62
% 3.03/1.62 thf(conj_0,conjecture,
% 3.03/1.62 ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
% 3.03/1.62 & ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
% 3.03/1.62 = ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
% 3.03/1.62 & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
% 3.03/1.62 & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) ) ).
% 3.03/1.62 ------------------------
% 3.03/1.64 % (16037)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_15711 for (2999ds/2Mi)
% 3.03/1.64 % (16040)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_15711 for (2999ds/18Mi)
% 3.03/1.64 % (16034)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_15711 for (2999ds/183Mi)
% 3.03/1.64 % (16037)Instruction limit reached!
% 3.03/1.64 % (16037)------------------------------
% 3.03/1.64 % (16037)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.64 % (16037)Termination reason: Unknown
% 3.03/1.64 % (16037)Termination phase: shuffling
% 3.03/1.64
% 3.03/1.64 % (16037)Memory used [KB]: 1663
% 3.03/1.64 % (16037)Time elapsed: 0.002 s
% 3.03/1.64 % (16037)Instructions burned: 2 (million)
% 3.03/1.64 % (16037)------------------------------
% 3.03/1.64 % (16037)------------------------------
% 3.03/1.65 % (16040)Instruction limit reached!
% 3.03/1.65 % (16040)------------------------------
% 3.03/1.65 % (16040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.65 % (16040)Termination reason: Unknown
% 3.03/1.65 % (16040)Termination phase: shuffling
% 3.03/1.65
% 3.03/1.65 % (16040)Memory used [KB]: 1918
% 3.03/1.65 % (16040)Time elapsed: 0.007 s
% 3.03/1.65 % (16040)Instructions burned: 18 (million)
% 3.03/1.65 % (16040)------------------------------
% 3.03/1.65 % (16040)------------------------------
% 3.03/1.65 % (16035)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_15711 for (2999ds/4Mi)
% 3.03/1.65 % (16036)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_15711 for (2999ds/27Mi)
% 3.03/1.65 % (16038)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_15711 for (2999ds/2Mi)
% 3.03/1.65 % (16039)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_15711 for (2999ds/275Mi)
% 3.03/1.65 % (16038)Instruction limit reached!
% 3.03/1.65 % (16038)------------------------------
% 3.03/1.65 % (16038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.65 % (16038)Termination reason: Unknown
% 3.03/1.65 % (16038)Termination phase: shuffling
% 3.03/1.65
% 3.03/1.65 % (16038)Memory used [KB]: 1663
% 3.03/1.65 % (16038)Time elapsed: 0.004 s
% 3.03/1.65 % (16038)Instructions burned: 3 (million)
% 3.03/1.65 % (16038)------------------------------
% 3.03/1.65 % (16038)------------------------------
% 3.03/1.65 % (16041)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_15711 for (2999ds/3Mi)
% 3.03/1.65 % (16035)Instruction limit reached!
% 3.03/1.65 % (16035)------------------------------
% 3.03/1.65 % (16035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.65 % (16035)Termination reason: Unknown
% 3.03/1.65 % (16035)Termination phase: shuffling
% 3.03/1.65
% 3.03/1.65 % (16035)Memory used [KB]: 1663
% 3.03/1.65 % (16035)Time elapsed: 0.005 s
% 3.03/1.65 % (16035)Instructions burned: 4 (million)
% 3.03/1.65 % (16035)------------------------------
% 3.03/1.65 % (16035)------------------------------
% 3.03/1.65 % (16041)Instruction limit reached!
% 3.03/1.65 % (16041)------------------------------
% 3.03/1.65 % (16041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.65 % (16041)Termination reason: Unknown
% 3.03/1.65 % (16041)Termination phase: shuffling
% 3.03/1.65
% 3.03/1.65 % (16041)Memory used [KB]: 1663
% 3.03/1.65 % (16041)Time elapsed: 0.003 s
% 3.03/1.65 % (16041)Instructions burned: 5 (million)
% 3.03/1.65 % (16041)------------------------------
% 3.03/1.65 % (16041)------------------------------
% 3.03/1.66 % (16042)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_15711 for (2999ds/37Mi)
% 3.03/1.66 % (16045)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_15711 for (2999ds/1041Mi)
% 3.03/1.67 % (16036)Instruction limit reached!
% 3.03/1.67 % (16036)------------------------------
% 3.03/1.67 % (16036)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.67 % (16036)Termination reason: Unknown
% 3.03/1.67 % (16036)Termination phase: shuffling
% 3.03/1.67
% 3.03/1.67 % (16036)Memory used [KB]: 2174
% 3.03/1.67 % (16036)Time elapsed: 0.019 s
% 3.03/1.67 % (16036)Instructions burned: 28 (million)
% 3.03/1.67 % (16036)------------------------------
% 3.03/1.67 % (16036)------------------------------
% 3.03/1.67 % (16042)Instruction limit reached!
% 3.03/1.67 % (16042)------------------------------
% 3.03/1.67 % (16042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.67 % (16042)Termination reason: Unknown
% 3.03/1.67 % (16042)Termination phase: shuffling
% 3.03/1.67
% 3.03/1.67 % (16042)Memory used [KB]: 2302
% 3.03/1.67 % (16042)Time elapsed: 0.012 s
% 3.03/1.67 % (16042)Instructions burned: 39 (million)
% 3.03/1.67 % (16042)------------------------------
% 3.03/1.67 % (16042)------------------------------
% 3.03/1.67 % (16043)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_15711 for (2999ds/15Mi)
% 3.03/1.67 % (16044)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_15711 for (2999ds/3Mi)
% 3.03/1.67 % (16044)Instruction limit reached!
% 3.03/1.67 % (16044)------------------------------
% 3.03/1.67 % (16044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.67 % (16044)Termination reason: Unknown
% 3.03/1.67 % (16044)Termination phase: shuffling
% 3.03/1.67
% 3.03/1.67 % (16044)Memory used [KB]: 1663
% 3.03/1.67 % (16044)Time elapsed: 0.004 s
% 3.03/1.67 % (16044)Instructions burned: 3 (million)
% 3.03/1.67 % (16044)------------------------------
% 3.03/1.67 % (16044)------------------------------
% 3.03/1.68 % (16047)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_15711 for (2999ds/16Mi)
% 3.03/1.68 % (16043)Instruction limit reached!
% 3.03/1.68 % (16043)------------------------------
% 3.03/1.68 % (16043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.68 % (16043)Termination reason: Unknown
% 3.03/1.68 % (16043)Termination phase: shuffling
% 3.03/1.68
% 3.03/1.68 % (16043)Memory used [KB]: 1791
% 3.03/1.68 % (16043)Time elapsed: 0.011 s
% 3.03/1.68 % (16043)Instructions burned: 15 (million)
% 3.03/1.68 % (16043)------------------------------
% 3.03/1.68 % (16043)------------------------------
% 3.03/1.68 % (16047)Instruction limit reached!
% 3.03/1.68 % (16047)------------------------------
% 3.03/1.68 % (16047)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.68 % (16047)Termination reason: Unknown
% 3.03/1.68 % (16047)Termination phase: shuffling
% 3.03/1.68
% 3.03/1.68 % (16047)Memory used [KB]: 1918
% 3.03/1.68 % (16047)Time elapsed: 0.006 s
% 3.03/1.68 % (16047)Instructions burned: 16 (million)
% 3.03/1.68 % (16047)------------------------------
% 3.03/1.68 % (16047)------------------------------
% 3.03/1.68 % (16046)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_15711 for (2999ds/7Mi)
% 3.03/1.69 % (16046)Instruction limit reached!
% 3.03/1.69 % (16046)------------------------------
% 3.03/1.69 % (16046)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.69 % (16046)Termination reason: Unknown
% 3.03/1.69 % (16046)Termination phase: shuffling
% 3.03/1.69
% 3.03/1.69 % (16046)Memory used [KB]: 1663
% 3.03/1.69 % (16046)Time elapsed: 0.006 s
% 3.03/1.69 % (16046)Instructions burned: 8 (million)
% 3.03/1.69 % (16046)------------------------------
% 3.03/1.69 % (16046)------------------------------
% 3.03/1.69 % (16048)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_15711 for (2999ds/3Mi)
% 3.03/1.69 % (16048)Instruction limit reached!
% 3.03/1.69 % (16048)------------------------------
% 3.03/1.69 % (16048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.69 % (16048)Termination reason: Unknown
% 3.03/1.69 % (16048)Termination phase: shuffling
% 3.03/1.69
% 3.03/1.69 % (16048)Memory used [KB]: 1663
% 3.03/1.69 % (16048)Time elapsed: 0.004 s
% 3.03/1.69 % (16048)Instructions burned: 3 (million)
% 3.03/1.69 % (16048)------------------------------
% 3.03/1.69 % (16048)------------------------------
% 3.03/1.69 % (16050)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_15711 for (2999ds/7Mi)
% 3.03/1.70 % (16050)Instruction limit reached!
% 3.03/1.70 % (16050)------------------------------
% 3.03/1.70 % (16050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.03/1.70 % (16050)Termination reason: Unknown
% 3.03/1.70 % (16050)Termination phase: shuffling
% 3.03/1.70
% 3.03/1.70 % (16050)Memory used [KB]: 1791
% 3.03/1.70 % (16050)Time elapsed: 0.004 s
% 3.03/1.70 % (16050)Instructions burned: 9 (million)
% 3.03/1.70 % (16050)------------------------------
% 3.03/1.70 % (16050)------------------------------
% 3.07/1.70 % (16049)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_15711 for (2999ds/3Mi)
% 3.07/1.70 % (16049)Instruction limit reached!
% 3.07/1.70 % (16049)------------------------------
% 3.07/1.70 % (16049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.70 % (16049)Termination reason: Unknown
% 3.07/1.70 % (16049)Termination phase: shuffling
% 3.07/1.70
% 3.07/1.70 % (16049)Memory used [KB]: 1663
% 3.07/1.70 % (16049)Time elapsed: 0.004 s
% 3.07/1.70 % (16049)Instructions burned: 3 (million)
% 3.07/1.70 % (16049)------------------------------
% 3.07/1.70 % (16049)------------------------------
% 3.07/1.70 % (16034)Instruction limit reached!
% 3.07/1.70 % (16034)------------------------------
% 3.07/1.70 % (16034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.70 % (16039)Refutation not found, incomplete strategy
% 3.07/1.70 % (16039)------------------------------
% 3.07/1.70 % (16039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.70 % (16034)Termination reason: Unknown
% 3.07/1.70 % (16039)Termination reason: Refutation not found, incomplete strategy
% 3.07/1.70
% 3.07/1.70 % (16034)Termination phase: Saturation
% 3.07/1.70
% 3.07/1.70
% 3.07/1.70 % (16034)Memory used [KB]: 7675
% 3.07/1.70 % (16034)Time elapsed: 0.057 s
% 3.07/1.70 % (16039)Memory used [KB]: 7036
% 3.07/1.70 % (16034)Instructions burned: 185 (million)
% 3.07/1.70 % (16034)------------------------------
% 3.07/1.70 % (16034)------------------------------
% 3.07/1.70 % (16039)Time elapsed: 0.050 s
% 3.07/1.70 % (16039)Instructions burned: 84 (million)
% 3.07/1.70 % (16039)------------------------------
% 3.07/1.70 % (16039)------------------------------
% 3.07/1.70 % (16051)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_15711 for (2999ds/3Mi)
% 3.07/1.70 % (16051)Instruction limit reached!
% 3.07/1.70 % (16051)------------------------------
% 3.07/1.70 % (16051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.70 % (16051)Termination reason: Unknown
% 3.07/1.70 % (16051)Termination phase: shuffling
% 3.07/1.70
% 3.07/1.70 % (16051)Memory used [KB]: 1663
% 3.07/1.70 % (16051)Time elapsed: 0.003 s
% 3.07/1.70 % (16051)Instructions burned: 4 (million)
% 3.07/1.70 % (16051)------------------------------
% 3.07/1.70 % (16051)------------------------------
% 3.07/1.71 % (16053)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_15711 for (2999ds/18Mi)
% 3.07/1.71 % (16055)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_15711 for (2999ds/6Mi)
% 3.07/1.71 % (16052)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_15711 for (2999ds/4Mi)
% 3.07/1.71 % (16053)Instruction limit reached!
% 3.07/1.71 % (16053)------------------------------
% 3.07/1.71 % (16053)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.71 % (16053)Termination reason: Unknown
% 3.07/1.71 % (16053)Termination phase: shuffling
% 3.07/1.71
% 3.07/1.71 % (16053)Memory used [KB]: 1918
% 3.07/1.71 % (16053)Time elapsed: 0.007 s
% 3.07/1.71 % (16053)Instructions burned: 18 (million)
% 3.07/1.71 % (16053)------------------------------
% 3.07/1.71 % (16053)------------------------------
% 3.07/1.71 % (16055)Instruction limit reached!
% 3.07/1.71 % (16055)------------------------------
% 3.07/1.71 % (16055)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.71 % (16055)Termination reason: Unknown
% 3.07/1.71 % (16055)Termination phase: shuffling
% 3.07/1.71
% 3.07/1.71 % (16055)Memory used [KB]: 1663
% 3.07/1.71 % (16055)Time elapsed: 0.003 s
% 3.07/1.71 % (16055)Instructions burned: 6 (million)
% 3.07/1.71 % (16055)------------------------------
% 3.07/1.71 % (16055)------------------------------
% 3.07/1.71 % (16052)Instruction limit reached!
% 3.07/1.71 % (16052)------------------------------
% 3.07/1.71 % (16052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.71 % (16052)Termination reason: Unknown
% 3.07/1.71 % (16052)Termination phase: shuffling
% 3.07/1.71
% 3.07/1.71 % (16052)Memory used [KB]: 1663
% 3.07/1.71 % (16052)Time elapsed: 0.005 s
% 3.07/1.71 % (16052)Instructions burned: 5 (million)
% 3.07/1.71 % (16052)------------------------------
% 3.07/1.71 % (16052)------------------------------
% 3.07/1.71 % (16057)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_15711 for (2999ds/21Mi)
% 3.07/1.72 % (16054)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_15711 for (2999ds/710Mi)
% 3.07/1.72 % (16056)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_15711 for (2999ds/902Mi)
% 3.07/1.72 % (16058)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_15711 for (2999ds/5Mi)
% 3.07/1.72 % (16057)Instruction limit reached!
% 3.07/1.72 % (16057)------------------------------
% 3.07/1.72 % (16057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.72 % (16057)Termination reason: Unknown
% 3.07/1.72 % (16057)Termination phase: shuffling
% 3.07/1.72
% 3.07/1.72 % (16057)Memory used [KB]: 1918
% 3.07/1.72 % (16057)Time elapsed: 0.009 s
% 3.07/1.72 % (16057)Instructions burned: 21 (million)
% 3.07/1.72 % (16057)------------------------------
% 3.07/1.72 % (16057)------------------------------
% 3.07/1.72 % (16059)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_15711 for (2999ds/6Mi)
% 3.07/1.72 % (16058)Instruction limit reached!
% 3.07/1.72 % (16058)------------------------------
% 3.07/1.72 % (16058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.72 % (16058)Termination reason: Unknown
% 3.07/1.72 % (16058)Termination phase: shuffling
% 3.07/1.72
% 3.07/1.72 % (16058)Memory used [KB]: 1663
% 3.07/1.72 % (16058)Time elapsed: 0.003 s
% 3.07/1.72 % (16058)Instructions burned: 7 (million)
% 3.07/1.72 % (16058)------------------------------
% 3.07/1.72 % (16058)------------------------------
% 3.07/1.72 % (16059)Instruction limit reached!
% 3.07/1.72 % (16059)------------------------------
% 3.07/1.72 % (16059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.72 % (16059)Termination reason: Unknown
% 3.07/1.72 % (16059)Termination phase: shuffling
% 3.07/1.72
% 3.07/1.72 % (16059)Memory used [KB]: 1663
% 3.07/1.72 % (16059)Time elapsed: 0.004 s
% 3.07/1.72 % (16059)Instructions burned: 7 (million)
% 3.07/1.72 % (16059)------------------------------
% 3.07/1.72 % (16059)------------------------------
% 3.07/1.73 % (16060)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_15711 for (2999ds/377Mi)
% 3.07/1.73 % (16061)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_15711 for (2999ds/779Mi)
% 3.07/1.73 % (16062)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_15711 for (2999ds/19Mi)
% 3.07/1.73 % (16063)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_15711 for (2999ds/879Mi)
% 3.07/1.74 % (16062)Instruction limit reached!
% 3.07/1.74 % (16062)------------------------------
% 3.07/1.74 % (16062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.74 % (16062)Termination reason: Unknown
% 3.07/1.74 % (16062)Termination phase: shuffling
% 3.07/1.74
% 3.07/1.74 % (16062)Memory used [KB]: 2046
% 3.07/1.74 % (16062)Time elapsed: 0.007 s
% 3.07/1.74 % (16062)Instructions burned: 22 (million)
% 3.07/1.74 % (16062)------------------------------
% 3.07/1.74 % (16062)------------------------------
% 3.07/1.75 % (16064)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_15711 for (2998ds/17Mi)
% 3.07/1.75 % (16064)Instruction limit reached!
% 3.07/1.75 % (16064)------------------------------
% 3.07/1.75 % (16064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.75 % (16064)Termination reason: Unknown
% 3.07/1.75 % (16064)Termination phase: shuffling
% 3.07/1.75
% 3.07/1.75 % (16064)Memory used [KB]: 1918
% 3.07/1.75 % (16064)Time elapsed: 0.007 s
% 3.07/1.75 % (16064)Instructions burned: 17 (million)
% 3.07/1.75 % (16064)------------------------------
% 3.07/1.75 % (16064)------------------------------
% 3.07/1.76 % (16065)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_15711 for (2998ds/3Mi)
% 3.07/1.76 % (16065)Instruction limit reached!
% 3.07/1.76 % (16065)------------------------------
% 3.07/1.76 % (16065)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.76 % (16065)Termination reason: Unknown
% 3.07/1.76 % (16065)Termination phase: shuffling
% 3.07/1.76
% 3.07/1.76 % (16065)Memory used [KB]: 1663
% 3.07/1.76 % (16065)Time elapsed: 0.002 s
% 3.07/1.76 % (16065)Instructions burned: 3 (million)
% 3.07/1.76 % (16065)------------------------------
% 3.07/1.76 % (16065)------------------------------
% 3.07/1.77 % (16054)First to succeed.
% 3.07/1.77 % (16056)Refutation not found, incomplete strategy
% 3.07/1.77 % (16056)------------------------------
% 3.07/1.77 % (16056)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.77 % (16056)Termination reason: Refutation not found, incomplete strategy
% 3.07/1.77
% 3.07/1.77
% 3.07/1.77 % (16056)Memory used [KB]: 8059
% 3.07/1.77 % (16056)Time elapsed: 0.054 s
% 3.07/1.77 % (16056)Instructions burned: 168 (million)
% 3.07/1.77 % (16056)------------------------------
% 3.07/1.77 % (16056)------------------------------
% 3.07/1.77 % (16066)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_15711 for (2998ds/30Mi)
% 3.07/1.78 % (16054)Refutation found. Thanks to Tanya!
% 3.07/1.78 % SZS status Theorem for DTF2THF_15711
% 3.07/1.78 % SZS output start Proof for DTF2THF_15711
% 3.07/1.78 thf(type_def_5, type, set_nat: $tType).
% 3.07/1.78 thf(type_def_7, type, set_Pr1647387645at_nat: $tType).
% 3.07/1.78 thf(type_def_8, type, set_Pr1986765409at_nat: $tType).
% 3.07/1.78 thf(type_def_9, type, set_Pr1490359111at_nat: $tType).
% 3.07/1.78 thf(type_def_10, type, set_Pr9961929at_nat: $tType).
% 3.07/1.78 thf(type_def_11, type, set_Product_prod_b_b: $tType).
% 3.07/1.78 thf(type_def_12, type, set_b: $tType).
% 3.07/1.78 thf(type_def_13, type, allego510293162tant_a: $tType).
% 3.07/1.78 thf(type_def_14, type, allego1565409692at_nat: $tType).
% 3.07/1.78 thf(type_def_15, type, allegorical_term_b: $tType).
% 3.07/1.78 thf(type_def_16, type, labeled_graph_b_nat: $tType).
% 3.07/1.78 thf(type_def_17, type, labele935650037_a_nat: $tType).
% 3.07/1.78 thf(type_def_18, type, labele1835409643at_nat: $tType).
% 3.07/1.78 thf(type_def_19, type, set_Pr1163220871term_b: $tType).
% 3.07/1.78 thf(type_def_20, type, set_Pr1987088711_a_nat: $tType).
% 3.07/1.78 thf(type_def_21, type, set_Pr551076371_b_nat: $tType).
% 3.07/1.78 thf(type_def_22, type, set_Pr2041158302at_nat: $tType).
% 3.07/1.78 thf(type_def_23, type, produc1871334759_a_nat: $tType).
% 3.07/1.78 thf(type_def_24, type, nat: $tType).
% 3.07/1.78 thf(type_def_25, type, produc1478835367term_b: $tType).
% 3.07/1.78 thf(type_def_26, type, produc1391440311at_nat: $tType).
% 3.07/1.78 thf(type_def_27, type, produc1235635379_b_nat: $tType).
% 3.07/1.78 thf(type_def_28, type, product_prod_nat_nat: $tType).
% 3.07/1.78 thf(type_def_29, type, produc1116408039term_b: $tType).
% 3.07/1.78 thf(type_def_30, type, produc398057191_a_nat: $tType).
% 3.07/1.78 thf(type_def_31, type, produc446386919_b_nat: $tType).
% 3.07/1.78 thf(type_def_32, type, produc842455143at_nat: $tType).
% 3.07/1.78 thf(type_def_33, type, produc116665063_a_nat: $tType).
% 3.07/1.78 thf(type_def_34, type, set_al1193902458term_b: $tType).
% 3.07/1.78 thf(type_def_35, type, set_la1083530965_a_nat: $tType).
% 3.07/1.78 thf(type_def_36, type, set_la1976028319_b_nat: $tType).
% 3.07/1.78 thf(type_def_37, type, set_Pr1839611079term_b: $tType).
% 3.07/1.78 thf(type_def_38, type, set_Pr924198087_a_nat: $tType).
% 3.07/1.78 thf(type_def_39, type, set_Pr1173424071_b_nat: $tType).
% 3.07/1.78 thf(type_def_40, type, set_Pr2123625671_a_nat: $tType).
% 3.07/1.78 thf(type_def_41, type, set_Pr665622551at_nat: $tType).
% 3.07/1.78 thf(type_def_42, type, itself_nat: $tType).
% 3.07/1.78 thf(type_def_43, type, set_a: $tType).
% 3.07/1.78 thf(type_def_44, type, set_St761939237tant_a: $tType).
% 3.07/1.78 thf(type_def_45, type, standard_Constant_a: $tType).
% 3.07/1.78 thf(type_def_46, type, b: $tType).
% 3.07/1.78 thf(func_def_0, type, set_Pr2123625671_a_nat: $tType).
% 3.07/1.78 thf(func_def_1, type, produc116665063_a_nat: $tType).
% 3.07/1.78 thf(func_def_2, type, set_Pr924198087_a_nat: $tType).
% 3.07/1.78 thf(func_def_3, type, produc398057191_a_nat: $tType).
% 3.07/1.78 thf(func_def_4, type, set_Pr1173424071_b_nat: $tType).
% 3.07/1.78 thf(func_def_5, type, set_Pr1839611079term_b: $tType).
% 3.07/1.78 thf(func_def_6, type, produc446386919_b_nat: $tType).
% 3.07/1.78 thf(func_def_7, type, produc1116408039term_b: $tType).
% 3.07/1.78 thf(func_def_8, type, set_Pr1987088711_a_nat: $tType).
% 3.07/1.78 thf(func_def_9, type, set_Pr665622551at_nat: $tType).
% 3.07/1.78 thf(func_def_10, type, produc1871334759_a_nat: $tType).
% 3.07/1.78 thf(func_def_11, type, produc1391440311at_nat: $tType).
% 3.07/1.78 thf(func_def_12, type, set_Pr551076371_b_nat: $tType).
% 3.07/1.78 thf(func_def_13, type, set_Pr1647387645at_nat: $tType).
% 3.07/1.78 thf(func_def_14, type, set_Pr1490359111at_nat: $tType).
% 3.07/1.78 thf(func_def_15, type, set_Pr1163220871term_b: $tType).
% 3.07/1.78 thf(func_def_16, type, set_Pr2041158302at_nat: $tType).
% 3.07/1.78 thf(func_def_17, type, produc1235635379_b_nat: $tType).
% 3.07/1.78 thf(func_def_18, type, produc842455143at_nat: $tType).
% 3.07/1.78 thf(func_def_19, type, produc1478835367term_b: $tType).
% 3.07/1.78 thf(func_def_20, type, set_la1083530965_a_nat: $tType).
% 3.07/1.78 thf(func_def_21, type, labele935650037_a_nat: $tType).
% 3.07/1.78 thf(func_def_22, type, labele1835409643at_nat: $tType).
% 3.07/1.78 thf(func_def_23, type, set_Pr9961929at_nat: $tType).
% 3.07/1.78 thf(func_def_24, type, allego510293162tant_a: $tType).
% 3.07/1.78 thf(func_def_25, type, allego1565409692at_nat: $tType).
% 3.07/1.78 thf(func_def_26, type, set_la1976028319_b_nat: $tType).
% 3.07/1.78 thf(func_def_27, type, set_St761939237tant_a: $tType).
% 3.07/1.78 thf(func_def_28, type, set_Pr1986765409at_nat: $tType).
% 3.07/1.78 thf(func_def_29, type, set_al1193902458term_b: $tType).
% 3.07/1.78 thf(func_def_30, type, labeled_graph_b_nat: $tType).
% 3.07/1.78 thf(func_def_31, type, set_Product_prod_b_b: $tType).
% 3.07/1.78 thf(func_def_32, type, standard_Constant_a: $tType).
% 3.07/1.78 thf(func_def_33, type, product_prod_nat_nat: $tType).
% 3.07/1.78 thf(func_def_34, type, allegorical_term_b: $tType).
% 3.07/1.78 thf(func_def_35, type, set_nat: $tType).
% 3.07/1.78 thf(func_def_36, type, itself_nat: $tType).
% 3.07/1.78 thf(func_def_37, type, set_b: $tType).
% 3.07/1.78 thf(func_def_38, type, set_a: $tType).
% 3.07/1.78 thf(func_def_39, type, nat: $tType).
% 3.07/1.78 thf(func_def_40, type, b: $tType).
% 3.07/1.78 thf(func_def_41, type, finite_finite_nat: set_nat > $o).
% 3.07/1.78 thf(func_def_42, type, finite1242387294at_nat: set_Pr1647387645at_nat > $o).
% 3.07/1.78 thf(func_def_43, type, finite772653738at_nat: set_Pr1986765409at_nat > $o).
% 3.07/1.78 thf(func_def_44, type, finite48957584at_nat: set_Pr1490359111at_nat > $o).
% 3.07/1.78 thf(func_def_45, type, finite1987068434at_nat: set_Pr9961929at_nat > $o).
% 3.07/1.78 thf(func_def_46, type, finite1015599120od_b_b: set_Product_prod_b_b > $o).
% 3.07/1.78 thf(func_def_47, type, finite_finite_b: set_b > $o).
% 3.07/1.78 thf(func_def_48, type, allego745587551tant_a: allego510293162tant_a > allego510293162tant_a > allego510293162tant_a).
% 3.07/1.78 thf(func_def_49, type, allego266765201at_nat: allego1565409692at_nat > allego1565409692at_nat > allego1565409692at_nat).
% 3.07/1.78 thf(func_def_50, type, allegorical_A_Int_b: allegorical_term_b > allegorical_term_b > allegorical_term_b).
% 3.07/1.78 thf(func_def_51, type, semantics_b_nat: labeled_graph_b_nat > allegorical_term_b > set_Pr1986765409at_nat).
% 3.07/1.78 thf(func_def_52, type, graph_2130075512at_nat: labele935650037_a_nat > labele935650037_a_nat > set_Pr1986765409at_nat > $o).
% 3.07/1.78 thf(func_def_53, type, graph_2111906684at_nat: labele1835409643at_nat > labele1835409643at_nat > set_Pr1986765409at_nat > $o).
% 3.07/1.78 thf(func_def_54, type, graph_529870330at_nat: labeled_graph_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat > $o).
% 3.07/1.78 thf(func_def_55, type, graph_union_b_nat: labeled_graph_b_nat > labeled_graph_b_nat > labeled_graph_b_nat).
% 3.07/1.78 thf(func_def_56, type, labeled_LG_b_nat: set_Pr9961929at_nat > set_nat > labeled_graph_b_nat).
% 3.07/1.78 thf(func_def_57, type, labele195203296_a_nat: labele935650037_a_nat > set_Pr1647387645at_nat).
% 3.07/1.78 thf(func_def_58, type, labele2032268018at_nat: labele1835409643at_nat > set_Pr1490359111at_nat).
% 3.07/1.78 thf(func_def_59, type, labeled_edges_b_nat: labeled_graph_b_nat > set_Pr9961929at_nat).
% 3.07/1.78 thf(func_def_60, type, labele1810595089_a_nat: labele935650037_a_nat > set_nat).
% 3.07/1.78 thf(func_def_61, type, labele560327297at_nat: labele1835409643at_nat > set_nat).
% 3.07/1.78 thf(func_def_62, type, labele460410879_b_nat: labeled_graph_b_nat > set_nat).
% 3.07/1.78 thf(func_def_63, type, restri572569417_a_nat: labele935650037_a_nat > labele935650037_a_nat).
% 3.07/1.78 thf(func_def_64, type, restri321299017at_nat: labele1835409643at_nat > labele1835409643at_nat).
% 3.07/1.78 thf(func_def_65, type, restrict_b_nat: labeled_graph_b_nat > labeled_graph_b_nat).
% 3.07/1.78 thf(func_def_66, type, unival1191217828term_b: set_Pr1163220871term_b > $o).
% 3.07/1.78 thf(func_def_67, type, unival1637751524_a_nat: set_Pr1987088711_a_nat > $o).
% 3.07/1.78 thf(func_def_68, type, unival857119480_b_nat: set_Pr551076371_b_nat > $o).
% 3.07/1.78 thf(func_def_69, type, univalent_nat_nat: set_Pr1986765409at_nat > $o).
% 3.07/1.78 thf(func_def_70, type, unival633212949at_nat: set_Pr2041158302at_nat > $o).
% 3.07/1.78 thf(func_def_71, type, unival989235430at_nat: set_Pr9961929at_nat > $o).
% 3.07/1.78 thf(func_def_72, type, bot_bo1024461546_nat_o: produc1871334759_a_nat > $o).
% 3.07/1.78 thf(func_def_73, type, bot_bot_nat: nat).
% 3.07/1.78 thf(func_def_74, type, bot_bot_set_nat: set_nat).
% 3.07/1.78 thf(func_def_75, type, bot_bo1836341171_a_nat: set_Pr1987088711_a_nat).
% 3.07/1.78 thf(func_def_76, type, bot_bo2130386637at_nat: set_Pr1986765409at_nat).
% 3.07/1.78 thf(func_def_77, type, bot_bo1626616373at_nat: set_Pr9961929at_nat).
% 3.07/1.78 thf(func_def_78, type, ord_less_eq_nat: nat > nat > $o).
% 3.07/1.78 thf(func_def_79, type, ord_less_eq_set_nat: set_nat > set_nat > $o).
% 3.07/1.78 thf(func_def_80, type, ord_le138473255term_b: set_Pr1163220871term_b > set_Pr1163220871term_b > $o).
% 3.07/1.78 thf(func_def_81, type, ord_le1718765799_a_nat: set_Pr1987088711_a_nat > set_Pr1987088711_a_nat > $o).
% 3.07/1.78 thf(func_def_82, type, ord_le13035955_b_nat: set_Pr551076371_b_nat > set_Pr551076371_b_nat > $o).
% 3.07/1.78 thf(func_def_83, type, ord_le841296385at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o).
% 3.07/1.78 thf(func_def_84, type, ord_le910748009at_nat: set_Pr9961929at_nat > set_Pr9961929at_nat > $o).
% 3.07/1.78 thf(func_def_85, type, produc1990145943term_b: allegorical_term_b > allegorical_term_b > produc1478835367term_b).
% 3.07/1.78 thf(func_def_86, type, produc1676969687_a_nat: labele935650037_a_nat > labele935650037_a_nat > produc1871334759_a_nat).
% 3.07/1.78 thf(func_def_87, type, produc590202991at_nat: labele1835409643at_nat > labele1835409643at_nat > produc1391440311at_nat).
% 3.07/1.78 thf(func_def_88, type, produc951298923_b_nat: labeled_graph_b_nat > labeled_graph_b_nat > produc1235635379_b_nat).
% 3.07/1.78 thf(func_def_89, type, product_Pair_nat_nat: nat > nat > product_prod_nat_nat).
% 3.07/1.78 thf(func_def_90, type, produc859843415term_b: produc1478835367term_b > produc1478835367term_b > produc1116408039term_b).
% 3.07/1.78 thf(func_def_91, type, produc1677124439_a_nat: produc1871334759_a_nat > produc1871334759_a_nat > produc398057191_a_nat).
% 3.07/1.78 thf(func_def_92, type, produc1754969175_b_nat: produc1235635379_b_nat > produc1235635379_b_nat > produc446386919_b_nat).
% 3.07/1.78 thf(func_def_93, type, produc1168807639at_nat: product_prod_nat_nat > product_prod_nat_nat > produc842455143at_nat).
% 3.07/1.78 thf(func_def_94, type, produc170611543_a_nat: produc398057191_a_nat > produc398057191_a_nat > produc116665063_a_nat).
% 3.07/1.78 thf(func_def_95, type, produc854192515term_b: produc1478835367term_b > allegorical_term_b).
% 3.07/1.78 thf(func_def_96, type, produc719117507_a_nat: produc1871334759_a_nat > labele935650037_a_nat).
% 3.07/1.78 thf(func_def_97, type, produc1995789403at_nat: produc1391440311at_nat > labele1835409643at_nat).
% 3.07/1.78 thf(func_def_98, type, produc1542243159_b_nat: produc1235635379_b_nat > labeled_graph_b_nat).
% 3.07/1.78 thf(func_def_99, type, product_fst_nat_nat: product_prod_nat_nat > nat).
% 3.07/1.78 thf(func_def_100, type, produc1049080131_a_nat: produc398057191_a_nat > produc1871334759_a_nat).
% 3.07/1.78 thf(func_def_101, type, produc1223098053term_b: produc1478835367term_b > allegorical_term_b).
% 3.07/1.78 thf(func_def_102, type, produc880161797_a_nat: produc1871334759_a_nat > labele935650037_a_nat).
% 3.07/1.78 thf(func_def_103, type, produc1564126365at_nat: produc1391440311at_nat > labele1835409643at_nat).
% 3.07/1.78 thf(func_def_104, type, produc194497945_b_nat: produc1235635379_b_nat > labeled_graph_b_nat).
% 3.07/1.78 thf(func_def_105, type, product_snd_nat_nat: product_prod_nat_nat > nat).
% 3.07/1.78 thf(func_def_106, type, produc1022852229_a_nat: produc398057191_a_nat > produc1871334759_a_nat).
% 3.07/1.78 thf(func_def_107, type, domain859272460term_b: set_Pr1163220871term_b > set_al1193902458term_b).
% 3.07/1.78 thf(func_def_108, type, domain1068567884_a_nat: set_Pr1987088711_a_nat > set_la1083530965_a_nat).
% 3.07/1.78 thf(func_def_109, type, domain767519072_b_nat: set_Pr551076371_b_nat > set_la1976028319_b_nat).
% 3.07/1.78 thf(func_def_110, type, domain_nat_nat: set_Pr1986765409at_nat > set_nat).
% 3.07/1.78 thf(func_def_111, type, domain1101989710at_nat: set_Pr9961929at_nat > set_b).
% 3.07/1.78 thf(func_def_112, type, id_on_1536886967term_b: set_al1193902458term_b > set_Pr1163220871term_b).
% 3.07/1.78 thf(func_def_113, type, id_on_689842066_a_nat: set_la1083530965_a_nat > set_Pr1987088711_a_nat).
% 3.07/1.78 thf(func_def_114, type, id_on_583275916_b_nat: set_la1976028319_b_nat > set_Pr551076371_b_nat).
% 3.07/1.78 thf(func_def_115, type, id_on_nat: set_nat > set_Pr1986765409at_nat).
% 3.07/1.78 thf(func_def_116, type, id_on_1664915780term_b: set_Pr1163220871term_b > set_Pr1839611079term_b).
% 3.07/1.78 thf(func_def_117, type, id_on_1651096324_a_nat: set_Pr1987088711_a_nat > set_Pr924198087_a_nat).
% 3.07/1.78 thf(func_def_118, type, id_on_138931664_b_nat: set_Pr551076371_b_nat > set_Pr1173424071_b_nat).
% 3.07/1.78 thf(func_def_119, type, id_on_2144791838at_nat: set_Pr1986765409at_nat > set_Pr1490359111at_nat).
% 3.07/1.78 thf(func_def_120, type, id_on_1395957380_a_nat: set_Pr924198087_a_nat > set_Pr2123625671_a_nat).
% 3.07/1.78 thf(func_def_121, type, image_329221075term_b: set_Pr1163220871term_b > set_al1193902458term_b > set_al1193902458term_b).
% 3.07/1.78 thf(func_def_122, type, image_1971191571_a_nat: set_Pr1987088711_a_nat > set_la1083530965_a_nat > set_la1083530965_a_nat).
% 3.07/1.78 thf(func_def_123, type, image_1183964583_b_nat: set_Pr551076371_b_nat > set_la1976028319_b_nat > set_la1976028319_b_nat).
% 3.07/1.78 thf(func_def_124, type, image_nat_nat: set_Pr1986765409at_nat > set_nat > set_nat).
% 3.07/1.78 thf(func_def_125, type, image_1168831379_a_nat: set_Pr924198087_a_nat > set_Pr1987088711_a_nat > set_Pr1987088711_a_nat).
% 3.07/1.78 thf(func_def_126, type, image_1356842150at_nat: set_Pr2041158302at_nat > set_Pr9961929at_nat > set_nat).
% 3.07/1.78 thf(func_def_127, type, image_2112855445at_nat: set_Pr9961929at_nat > set_b > set_Pr1986765409at_nat).
% 3.07/1.78 thf(func_def_128, type, relcom1955155673term_b: set_Pr1163220871term_b > set_Pr1163220871term_b > set_Pr1163220871term_b).
% 3.07/1.78 thf(func_def_129, type, relcom1338300020_a_nat: set_Pr1987088711_a_nat > set_Pr1987088711_a_nat > set_Pr1987088711_a_nat).
% 3.07/1.78 thf(func_def_130, type, relcom1426860350_b_nat: set_Pr551076371_b_nat > set_Pr551076371_b_nat > set_Pr551076371_b_nat).
% 3.07/1.78 thf(func_def_131, type, relcomp_nat_nat_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat).
% 3.07/1.78 thf(func_def_132, type, relcom195261566at_nat: set_Pr9961929at_nat > set_Pr1490359111at_nat > set_Pr9961929at_nat).
% 3.07/1.78 thf(func_def_133, type, relcom14055552at_nat: set_Product_prod_b_b > set_Pr9961929at_nat > set_Pr9961929at_nat).
% 3.07/1.78 thf(func_def_134, type, inv_translation: set_nat > $o).
% 3.07/1.78 thf(func_def_135, type, transl1275713022tant_a: allego510293162tant_a > labele935650037_a_nat).
% 3.07/1.78 thf(func_def_136, type, transl490985778at_nat: allego1565409692at_nat > labele1835409643at_nat).
% 3.07/1.78 thf(func_def_137, type, translation_b: allegorical_term_b > labeled_graph_b_nat).
% 3.07/1.78 thf(func_def_138, type, agree_on_b_nat_nat: labeled_graph_b_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o).
% 3.07/1.78 thf(func_def_139, type, chain_b_nat: (nat > labeled_graph_b_nat) > $o).
% 3.07/1.78 thf(func_def_140, type, chain_sup_b_nat: (nat > labeled_graph_b_nat) > labeled_graph_b_nat).
% 3.07/1.78 thf(func_def_141, type, conseq1730780375at_nat: set_Pr551076371_b_nat > labeled_graph_b_nat > $o).
% 3.07/1.78 thf(func_def_142, type, extensible_b_nat_nat: produc1235635379_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat > $o).
% 3.07/1.78 thf(func_def_143, type, fair_chain_b_nat_nat: set_Pr551076371_b_nat > (nat > labeled_graph_b_nat) > $o).
% 3.07/1.78 thf(func_def_144, type, fin_ma971967913at_nat: produc1235635379_b_nat > labeled_graph_b_nat > $o).
% 3.07/1.78 thf(func_def_145, type, maintained_b_nat_nat: produc1235635379_b_nat > labeled_graph_b_nat > $o).
% 3.07/1.78 thf(func_def_146, type, set_of1384085797_a_nat: set_Pr1987088711_a_nat > $o).
% 3.07/1.78 thf(func_def_147, type, set_of195930477at_nat: set_Pr665622551at_nat > $o).
% 3.07/1.78 thf(func_def_148, type, set_of41538795_b_nat: set_Pr551076371_b_nat > $o).
% 3.07/1.78 thf(func_def_149, type, weak_u2026406106at_nat: itself_nat > produc1235635379_b_nat > labeled_graph_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o).
% 3.07/1.78 thf(func_def_150, type, collect_nat: (nat > $o) > set_nat).
% 3.07/1.78 thf(func_def_151, type, collec135640594term_b: (produc1478835367term_b > $o) > set_Pr1163220871term_b).
% 3.07/1.78 thf(func_def_152, type, collec357096914_a_nat: (produc1871334759_a_nat > $o) > set_Pr1987088711_a_nat).
% 3.07/1.78 thf(func_def_153, type, collec1615000990_b_nat: (produc1235635379_b_nat > $o) > set_Pr551076371_b_nat).
% 3.07/1.78 thf(func_def_154, type, collec7649004at_nat: (product_prod_nat_nat > $o) > set_Pr1986765409at_nat).
% 3.07/1.78 thf(func_def_155, type, collec1701899602_a_nat: (produc398057191_a_nat > $o) > set_Pr924198087_a_nat).
% 3.07/1.78 thf(func_def_156, type, standa1897115818ules_a: set_a > set_Pr1987088711_a_nat).
% 3.07/1.78 thf(func_def_157, type, standa1568205540ules_a: set_St761939237tant_a > set_Pr1987088711_a_nat).
% 3.07/1.78 thf(func_def_158, type, standa1410829644tant_a: produc1871334759_a_nat).
% 3.07/1.78 thf(func_def_159, type, standa214789732at_nat: produc1391440311at_nat).
% 3.07/1.78 thf(func_def_160, type, standa879863266rule_b: produc1235635379_b_nat).
% 3.07/1.78 thf(func_def_161, type, standa63370785tant_a: standard_Constant_a > produc1871334759_a_nat).
% 3.07/1.78 thf(func_def_162, type, standa2131591247at_nat: product_prod_nat_nat > produc1391440311at_nat).
% 3.07/1.78 thf(func_def_163, type, standa1329480013rule_b: b > produc1235635379_b_nat).
% 3.07/1.78 thf(func_def_164, type, standa305748545tant_a: standard_Constant_a > produc1871334759_a_nat).
% 3.07/1.78 thf(func_def_165, type, standa153097263at_nat: product_prod_nat_nat > produc1391440311at_nat).
% 3.07/1.78 thf(func_def_166, type, standa1360217389rule_b: b > produc1235635379_b_nat).
% 3.07/1.78 thf(func_def_167, type, member93680451term_b: allegorical_term_b > set_al1193902458term_b > $o).
% 3.07/1.78 thf(func_def_168, type, member964390942_a_nat: labele935650037_a_nat > set_la1083530965_a_nat > $o).
% 3.07/1.78 thf(func_def_169, type, member1483953152_b_nat: labeled_graph_b_nat > set_la1976028319_b_nat > $o).
% 3.07/1.78 thf(func_def_170, type, member_nat: nat > set_nat > $o).
% 3.07/1.78 thf(func_def_171, type, member516522448term_b: produc1478835367term_b > set_Pr1163220871term_b > $o).
% 3.07/1.78 thf(func_def_172, type, member832397200_a_nat: produc1871334759_a_nat > set_Pr1987088711_a_nat > $o).
% 3.07/1.78 thf(func_def_173, type, member1129678944at_nat: produc1391440311at_nat > set_Pr665622551at_nat > $o).
% 3.07/1.78 thf(func_def_174, type, member963855452_b_nat: produc1235635379_b_nat > set_Pr551076371_b_nat > $o).
% 3.07/1.78 thf(func_def_175, type, member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o).
% 3.07/1.78 thf(func_def_176, type, member1449757456term_b: produc1116408039term_b > set_Pr1839611079term_b > $o).
% 3.07/1.78 thf(func_def_177, type, member584645392_a_nat: produc398057191_a_nat > set_Pr924198087_a_nat > $o).
% 3.07/1.78 thf(func_def_178, type, member889223696_b_nat: produc446386919_b_nat > set_Pr1173424071_b_nat > $o).
% 3.07/1.78 thf(func_def_179, type, member2027625872at_nat: produc842455143at_nat > set_Pr1490359111at_nat > $o).
% 3.07/1.78 thf(func_def_180, type, member829905680_a_nat: produc116665063_a_nat > set_Pr2123625671_a_nat > $o).
% 3.07/1.78 thf(func_def_181, type, c: set_a).
% 3.07/1.78 thf(func_def_182, type, u: allegorical_term_b).
% 3.07/1.78 thf(func_def_183, type, v: allegorical_term_b).
% 3.07/1.78 thf(func_def_184, type, x: produc1871334759_a_nat).
% 3.07/1.78 thf(func_def_201, type, sK0: allegorical_term_b > produc1478835367term_b > allegorical_term_b).
% 3.07/1.78 thf(func_def_202, type, sK1: labeled_graph_b_nat > produc1235635379_b_nat > labeled_graph_b_nat).
% 3.07/1.78 thf(func_def_203, type, sK2: produc1235635379_b_nat > labeled_graph_b_nat).
% 3.07/1.78 thf(func_def_204, type, sK3: produc1235635379_b_nat > labeled_graph_b_nat).
% 3.07/1.78 thf(func_def_205, type, sK4: allegorical_term_b > produc1478835367term_b > allegorical_term_b).
% 3.07/1.78 thf(func_def_206, type, sK5: (produc1478835367term_b > $o) > allegorical_term_b).
% 3.07/1.78 thf(func_def_207, type, sK6: (produc1478835367term_b > $o) > allegorical_term_b).
% 3.07/1.78 thf(func_def_208, type, sK7: (produc1478835367term_b > $o) > allegorical_term_b).
% 3.07/1.78 thf(func_def_209, type, sK8: (produc1478835367term_b > $o) > allegorical_term_b).
% 3.07/1.78 thf(func_def_210, type, sK9: (produc1235635379_b_nat > $o) > labeled_graph_b_nat).
% 3.07/1.78 thf(func_def_211, type, sK10: (produc1235635379_b_nat > $o) > labeled_graph_b_nat).
% 3.07/1.78 thf(func_def_212, type, sK11: produc1235635379_b_nat > labeled_graph_b_nat > labeled_graph_b_nat).
% 3.07/1.78 thf(func_def_213, type, sK12: produc1478835367term_b > allegorical_term_b).
% 3.07/1.78 thf(func_def_214, type, sK13: produc1478835367term_b > allegorical_term_b).
% 3.07/1.78 thf(func_def_215, type, sK14: (labeled_graph_b_nat > labeled_graph_b_nat > $o) > labeled_graph_b_nat).
% 3.07/1.78 thf(func_def_216, type, sK15: (labeled_graph_b_nat > labeled_graph_b_nat > $o) > labeled_graph_b_nat).
% 3.07/1.78 thf(func_def_217, type, sK16: produc1478835367term_b > allegorical_term_b).
% 3.07/1.78 thf(func_def_218, type, sK17: produc1478835367term_b > allegorical_term_b).
% 3.07/1.78 thf(func_def_219, type, sK18: (produc1235635379_b_nat > $o) > labeled_graph_b_nat).
% 3.07/1.78 thf(func_def_220, type, sK19: (produc1235635379_b_nat > $o) > labeled_graph_b_nat).
% 3.07/1.78 thf(func_def_221, type, sK20: (allegorical_term_b > allegorical_term_b > $o) > allegorical_term_b).
% 3.07/1.78 thf(func_def_222, type, sK21: (allegorical_term_b > allegorical_term_b > $o) > allegorical_term_b).
% 3.07/1.78 thf(func_def_223, type, sK22: produc1235635379_b_nat > labeled_graph_b_nat).
% 3.07/1.78 thf(func_def_224, type, sK23: produc1235635379_b_nat > labeled_graph_b_nat).
% 3.07/1.78 thf(f1186,plain,(
% 3.07/1.78 $false),
% 3.07/1.78 inference(subsumption_resolution,[status(thm)],[f1185,f1152])).
% 3.07/1.78 thf(f1152,plain,(
% 3.07/1.78 ( ! [X0 : allegorical_term_b,X1 : allegorical_term_b] : (($true = (graph_529870330at_nat @ (translation_b @ X1) @ (translation_b @ (allegorical_A_Int_b @ X1 @ X0)) @ (id_on_nat @ (labele460410879_b_nat @ (translation_b @ X1)))))) )),
% 3.07/1.78 inference(backward_demodulation,[status(thm)],[f1151,f1148])).
% 3.07/1.78 thf(f1148,plain,(
% 3.07/1.78 ( ! [X2 : labeled_graph_b_nat,X0 : labeled_graph_b_nat] : (((produc1542243159_b_nat @ (produc951298923_b_nat @ X2 @ X0)) = X2)) )),
% 3.07/1.78 inference(equality_resolution,[status(thm)],[f1118])).
% 3.07/1.78 thf(f1118,plain,(
% 3.07/1.78 ( ! [X2 : labeled_graph_b_nat,X0 : labeled_graph_b_nat,X1 : produc1235635379_b_nat] : (((produc951298923_b_nat @ X2 @ X0) != X1) | ((produc1542243159_b_nat @ X1) = X2)) )),
% 3.07/1.78 inference(cnf_transformation,[status(thm)],[f939])).
% 3.07/1.78 thf(f939,plain,(
% 3.07/1.78 ! [X0 : labeled_graph_b_nat,X1 : produc1235635379_b_nat,X2 : labeled_graph_b_nat] : (((produc951298923_b_nat @ X2 @ X0) != X1) | ((produc1542243159_b_nat @ X1) = X2))),
% 3.07/1.78 inference(ennf_transformation,[status(thm)],[f926])).
% 3.07/1.78 thf(f926,plain,(
% 3.07/1.78 ! [X0 : labeled_graph_b_nat,X1 : produc1235635379_b_nat,X2 : labeled_graph_b_nat] : (((produc951298923_b_nat @ X2 @ X0) = X1) => ((produc1542243159_b_nat @ X1) = X2))),
% 3.07/1.78 inference(rectify,[status(thm)],[f187])).
% 3.07/1.78 thf(f187,axiom,(
% 3.07/1.78 ! [X58 : labeled_graph_b_nat,X15 : produc1235635379_b_nat,X19 : labeled_graph_b_nat] : (((produc951298923_b_nat @ X19 @ X58) = X15) => ((produc1542243159_b_nat @ X15) = X19))),
% 3.07/1.78 file('/export/starexec/sandbox/tmp/tmp.bgqouCdkA9/DTF2THF_15711.p',fact_186_fstI)).
% 3.07/1.78 thf(f1151,plain,(
% 3.07/1.78 ( ! [X0 : allegorical_term_b,X1 : allegorical_term_b] : (((graph_529870330at_nat @ (produc1542243159_b_nat @ (produc951298923_b_nat @ (translation_b @ X1) @ (translation_b @ (allegorical_A_Int_b @ X1 @ X0)))) @ (translation_b @ (allegorical_A_Int_b @ X1 @ X0)) @ (id_on_nat @ (labele460410879_b_nat @ (produc1542243159_b_nat @ (produc951298923_b_nat @ (translation_b @ X1) @ (translation_b @ (allegorical_A_Int_b @ X1 @ X0))))))) = $true)) )),
% 3.07/1.78 inference(forward_demodulation,[status(thm)],[f1063,f1036])).
% 3.07/1.78 thf(f1036,plain,(
% 3.07/1.78 ( ! [X0 : labeled_graph_b_nat,X1 : labeled_graph_b_nat] : (((produc194497945_b_nat @ (produc951298923_b_nat @ X0 @ X1)) = X1)) )),
% 3.07/1.78 inference(cnf_transformation,[status(thm)],[f937])).
% 3.07/1.78 thf(f937,plain,(
% 3.07/1.78 ! [X0 : labeled_graph_b_nat,X1 : labeled_graph_b_nat] : ((produc194497945_b_nat @ (produc951298923_b_nat @ X0 @ X1)) = X1)),
% 3.07/1.78 inference(rectify,[status(thm)],[f87])).
% 3.07/1.78 thf(f87,axiom,(
% 3.07/1.78 ! [X11 : labeled_graph_b_nat,X12 : labeled_graph_b_nat] : ((produc194497945_b_nat @ (produc951298923_b_nat @ X11 @ X12)) = X12)),
% 3.07/1.78 file('/export/starexec/sandbox/tmp/tmp.bgqouCdkA9/DTF2THF_15711.p',fact_86_snd__conv)).
% 3.07/1.78 thf(f1063,plain,(
% 3.07/1.78 ( ! [X0 : allegorical_term_b,X1 : allegorical_term_b] : (((graph_529870330at_nat @ (produc1542243159_b_nat @ (produc951298923_b_nat @ (translation_b @ X1) @ (translation_b @ (allegorical_A_Int_b @ X1 @ X0)))) @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ X1) @ (translation_b @ (allegorical_A_Int_b @ X1 @ X0)))) @ (id_on_nat @ (labele460410879_b_nat @ (produc1542243159_b_nat @ (produc951298923_b_nat @ (translation_b @ X1) @ (translation_b @ (allegorical_A_Int_b @ X1 @ X0))))))) = $true)) )),
% 3.07/1.78 inference(cnf_transformation,[status(thm)],[f694])).
% 3.07/1.78 thf(f694,plain,(
% 3.07/1.78 ! [X0 : allegorical_term_b,X1 : allegorical_term_b] : (($true = (finite_finite_nat @ (labele460410879_b_nat @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ X1) @ (translation_b @ (allegorical_A_Int_b @ X1 @ X0))))))) & ($true = (finite1987068434at_nat @ (labeled_edges_b_nat @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ X1) @ (translation_b @ (allegorical_A_Int_b @ X1 @ X0))))))) & ((produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ X1) @ (translation_b @ (allegorical_A_Int_b @ X1 @ X0)))) = (restrict_b_nat @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ X1) @ (translation_b @ (allegorical_A_Int_b @ X1 @ X0)))))) & ((graph_529870330at_nat @ (produc1542243159_b_nat @ (produc951298923_b_nat @ (translation_b @ X1) @ (translation_b @ (allegorical_A_Int_b @ X1 @ X0)))) @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ X1) @ (translation_b @ (allegorical_A_Int_b @ X1 @ X0)))) @ (id_on_nat @ (labele460410879_b_nat @ (produc1542243159_b_nat @ (produc951298923_b_nat @ (translation_b @ X1) @ (translation_b @ (allegorical_A_Int_b @ X1 @ X0))))))) = $true))),
% 3.07/1.78 inference(fool_elimination,[status(thm)],[f693])).
% 3.07/1.78 thf(f693,plain,(
% 3.07/1.78 ! [X0 : allegorical_term_b,X1 : allegorical_term_b] : (((produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ X1) @ (translation_b @ (allegorical_A_Int_b @ X1 @ X0)))) = (restrict_b_nat @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ X1) @ (translation_b @ (allegorical_A_Int_b @ X1 @ X0)))))) & (finite1987068434at_nat @ (labeled_edges_b_nat @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ X1) @ (translation_b @ (allegorical_A_Int_b @ X1 @ X0)))))) & (finite_finite_nat @ (labele460410879_b_nat @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ X1) @ (translation_b @ (allegorical_A_Int_b @ X1 @ X0)))))) & (graph_529870330at_nat @ (produc1542243159_b_nat @ (produc951298923_b_nat @ (translation_b @ X1) @ (translation_b @ (allegorical_A_Int_b @ X1 @ X0)))) @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ X1) @ (translation_b @ (allegorical_A_Int_b @ X1 @ X0)))) @ (id_on_nat @ (labele460410879_b_nat @ (produc1542243159_b_nat @ (produc951298923_b_nat @ (translation_b @ X1) @ (translation_b @ (allegorical_A_Int_b @ X1 @ X0))))))))),
% 3.07/1.78 inference(rectify,[status(thm)],[f4])).
% 3.07/1.78 thf(f4,axiom,(
% 3.07/1.78 ! [X1 : allegorical_term_b,X0 : allegorical_term_b] : (((produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ X0) @ (translation_b @ (allegorical_A_Int_b @ X0 @ X1)))) = (restrict_b_nat @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ X0) @ (translation_b @ (allegorical_A_Int_b @ X0 @ X1)))))) & (finite1987068434at_nat @ (labeled_edges_b_nat @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ X0) @ (translation_b @ (allegorical_A_Int_b @ X0 @ X1)))))) & (finite_finite_nat @ (labele460410879_b_nat @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ X0) @ (translation_b @ (allegorical_A_Int_b @ X0 @ X1)))))) & (graph_529870330at_nat @ (produc1542243159_b_nat @ (produc951298923_b_nat @ (translation_b @ X0) @ (translation_b @ (allegorical_A_Int_b @ X0 @ X1)))) @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ X0) @ (translation_b @ (allegorical_A_Int_b @ X0 @ X1)))) @ (id_on_nat @ (labele460410879_b_nat @ (produc1542243159_b_nat @ (produc951298923_b_nat @ (translation_b @ X0) @ (translation_b @ (allegorical_A_Int_b @ X0 @ X1))))))))),
% 3.07/1.78 file('/export/starexec/sandbox/tmp/tmp.bgqouCdkA9/DTF2THF_15711.p',fact_3_graph__rule__translation)).
% 3.07/1.78 thf(f1185,plain,(
% 3.07/1.78 ($true != (graph_529870330at_nat @ (translation_b @ u) @ (translation_b @ (allegorical_A_Int_b @ u @ v)) @ (id_on_nat @ (labele460410879_b_nat @ (translation_b @ u)))))),
% 3.07/1.78 inference(forward_demodulation,[status(thm)],[f1184,f1127])).
% 3.07/1.78 thf(f1127,plain,(
% 3.07/1.78 ( ! [X2 : allegorical_term_b,X0 : allegorical_term_b] : (((produc1223098053term_b @ (produc1990145943term_b @ X0 @ X2)) = X2)) )),
% 3.07/1.78 inference(equality_resolution,[status(thm)],[f1053])).
% 3.07/1.78 thf(f1053,plain,(
% 3.07/1.78 ( ! [X2 : allegorical_term_b,X0 : allegorical_term_b,X1 : produc1478835367term_b] : (((produc1223098053term_b @ X1) = X2) | ((produc1990145943term_b @ X0 @ X2) != X1)) )),
% 3.07/1.78 inference(cnf_transformation,[status(thm)],[f947])).
% 3.07/1.78 thf(f947,plain,(
% 3.07/1.78 ! [X0 : allegorical_term_b,X1 : produc1478835367term_b,X2 : allegorical_term_b] : (((produc1223098053term_b @ X1) = X2) | ((produc1990145943term_b @ X0 @ X2) != X1))),
% 3.07/1.78 inference(ennf_transformation,[status(thm)],[f928])).
% 3.07/1.78 thf(f928,plain,(
% 3.07/1.78 ! [X0 : allegorical_term_b,X1 : produc1478835367term_b,X2 : allegorical_term_b] : (((produc1990145943term_b @ X0 @ X2) = X1) => ((produc1223098053term_b @ X1) = X2))),
% 3.07/1.78 inference(rectify,[status(thm)],[f181])).
% 3.07/1.78 thf(f181,axiom,(
% 3.07/1.78 ! [X19 : allegorical_term_b,X15 : produc1478835367term_b,X58 : allegorical_term_b] : (((produc1990145943term_b @ X19 @ X58) = X15) => ((produc1223098053term_b @ X15) = X58))),
% 3.07/1.78 file('/export/starexec/sandbox/tmp/tmp.bgqouCdkA9/DTF2THF_15711.p',fact_180_sndI)).
% 3.07/1.78 thf(f1184,plain,(
% 3.07/1.78 ((graph_529870330at_nat @ (translation_b @ u) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (id_on_nat @ (labele460410879_b_nat @ (translation_b @ u)))) != $true)),
% 3.07/1.78 inference(forward_demodulation,[status(thm)],[f1183,f1036])).
% 3.07/1.78 thf(f1183,plain,(
% 3.07/1.78 ((graph_529870330at_nat @ (translation_b @ u) @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ u) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))) @ (id_on_nat @ (labele460410879_b_nat @ (translation_b @ u)))) != $true)),
% 3.07/1.78 inference(forward_demodulation,[status(thm)],[f1182,f1129])).
% 3.07/1.78 thf(f1129,plain,(
% 3.07/1.78 ( ! [X2 : allegorical_term_b,X1 : allegorical_term_b] : (((produc854192515term_b @ (produc1990145943term_b @ X1 @ X2)) = X1)) )),
% 3.07/1.78 inference(equality_resolution,[status(thm)],[f1057])).
% 3.07/1.78 thf(f1057,plain,(
% 3.07/1.78 ( ! [X2 : allegorical_term_b,X0 : produc1478835367term_b,X1 : allegorical_term_b] : (((produc854192515term_b @ X0) = X1) | ((produc1990145943term_b @ X1 @ X2) != X0)) )),
% 3.07/1.78 inference(cnf_transformation,[status(thm)],[f999])).
% 3.07/1.78 thf(f999,plain,(
% 3.07/1.78 ! [X0 : produc1478835367term_b,X1 : allegorical_term_b] : ((((produc854192515term_b @ X0) = X1) | ! [X2 : allegorical_term_b] : ((produc1990145943term_b @ X1 @ X2) != X0)) & (((produc1990145943term_b @ X1 @ (sK4 @ X1 @ X0)) = X0) | ((produc854192515term_b @ X0) != X1)))),
% 3.07/1.78 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f997,f998])).
% 3.07/1.78 thf(f998,plain,(
% 3.07/1.78 ! [X0 : produc1478835367term_b,X1 : allegorical_term_b] : (? [X3 : allegorical_term_b] : ((produc1990145943term_b @ X1 @ X3) = X0) => ((produc1990145943term_b @ X1 @ (sK4 @ X1 @ X0)) = X0))),
% 3.07/1.78 introduced(definition,[],[choice_axiom])).
% 3.07/1.78 thf(f997,plain,(
% 3.07/1.78 ! [X0 : produc1478835367term_b,X1 : allegorical_term_b] : ((((produc854192515term_b @ X0) = X1) | ! [X2 : allegorical_term_b] : ((produc1990145943term_b @ X1 @ X2) != X0)) & (? [X3 : allegorical_term_b] : ((produc1990145943term_b @ X1 @ X3) = X0) | ((produc854192515term_b @ X0) != X1)))),
% 3.07/1.78 inference(rectify,[status(thm)],[f996])).
% 3.07/1.78 thf(f996,plain,(
% 3.07/1.78 ! [X0 : produc1478835367term_b,X1 : allegorical_term_b] : ((((produc854192515term_b @ X0) = X1) | ! [X2 : allegorical_term_b] : ((produc1990145943term_b @ X1 @ X2) != X0)) & (? [X2 : allegorical_term_b] : ((produc1990145943term_b @ X1 @ X2) = X0) | ((produc854192515term_b @ X0) != X1)))),
% 3.07/1.78 inference(nnf_transformation,[status(thm)],[f778])).
% 3.07/1.78 thf(f778,plain,(
% 3.07/1.78 ! [X0 : produc1478835367term_b,X1 : allegorical_term_b] : (((produc854192515term_b @ X0) = X1) <=> ? [X2 : allegorical_term_b] : ((produc1990145943term_b @ X1 @ X2) = X0))),
% 3.07/1.78 inference(fool_elimination,[status(thm)],[f777])).
% 3.07/1.78 thf(f777,plain,(
% 3.07/1.78 ! [X0 : produc1478835367term_b,X1 : allegorical_term_b] : (? [X2 : allegorical_term_b] : ((produc1990145943term_b @ X1 @ X2) = X0) = ((produc854192515term_b @ X0) = X1))),
% 3.07/1.78 inference(rectify,[status(thm)],[f204])).
% 3.07/1.78 thf(f204,axiom,(
% 3.07/1.78 ! [X21 : produc1478835367term_b,X3 : allegorical_term_b] : (? [X72 : allegorical_term_b] : ((produc1990145943term_b @ X3 @ X72) = X21) = ((produc854192515term_b @ X21) = X3))),
% 3.07/1.78 file('/export/starexec/sandbox/tmp/tmp.bgqouCdkA9/DTF2THF_15711.p',fact_203_eq__fst__iff)).
% 3.07/1.78 thf(f1182,plain,(
% 3.07/1.78 ($true != (graph_529870330at_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))) @ (id_on_nat @ (labele460410879_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v))))))))),
% 3.07/1.78 inference(forward_demodulation,[status(thm)],[f1181,f1148])).
% 3.07/1.78 thf(f1181,plain,(
% 3.07/1.78 ((graph_529870330at_nat @ (produc1542243159_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))) @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))) @ (id_on_nat @ (labele460410879_b_nat @ (produc1542243159_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v))))))))) != $true)),
% 3.07/1.78 inference(subsumption_resolution,[status(thm)],[f1180,f1120])).
% 3.07/1.78 thf(f1120,plain,(
% 3.07/1.78 ( ! [X0 : allegorical_term_b] : (((finite_finite_nat @ (labele460410879_b_nat @ (translation_b @ X0))) = $true)) )),
% 3.07/1.78 inference(cnf_transformation,[status(thm)],[f698])).
% 3.07/1.78 thf(f698,plain,(
% 3.07/1.78 ! [X0 : allegorical_term_b] : ((finite_finite_nat @ (labele460410879_b_nat @ (translation_b @ X0))) = $true)),
% 3.07/1.78 inference(fool_elimination,[status(thm)],[f697])).
% 3.07/1.78 thf(f697,plain,(
% 3.07/1.78 ! [X0 : allegorical_term_b] : (finite_finite_nat @ (labele460410879_b_nat @ (translation_b @ X0)))),
% 3.07/1.78 inference(rectify,[status(thm)],[f21])).
% 3.07/1.78 thf(f21,axiom,(
% 3.07/1.78 ! [X0 : allegorical_term_b] : (finite_finite_nat @ (labele460410879_b_nat @ (translation_b @ X0)))),
% 3.07/1.78 file('/export/starexec/sandbox/tmp/tmp.bgqouCdkA9/DTF2THF_15711.p',fact_20_verts__in__translation__finite_I1_J)).
% 3.07/1.78 thf(f1180,plain,(
% 3.07/1.78 ((graph_529870330at_nat @ (produc1542243159_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))) @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))) @ (id_on_nat @ (labele460410879_b_nat @ (produc1542243159_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v))))))))) != $true) | ($true != (finite_finite_nat @ (labele460410879_b_nat @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))))),
% 3.07/1.78 inference(forward_demodulation,[status(thm)],[f1179,f1036])).
% 3.07/1.78 thf(f1179,plain,(
% 3.07/1.78 ((finite_finite_nat @ (labele460410879_b_nat @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))))) != $true) | ((graph_529870330at_nat @ (produc1542243159_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))) @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))) @ (id_on_nat @ (labele460410879_b_nat @ (produc1542243159_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v))))))))) != $true)),
% 3.07/1.78 inference(subsumption_resolution,[status(thm)],[f1178,f1085])).
% 3.07/1.78 thf(f1085,plain,(
% 3.07/1.78 ( ! [X0 : allegorical_term_b] : (((finite1987068434at_nat @ (labeled_edges_b_nat @ (translation_b @ X0))) = $true)) )),
% 3.07/1.78 inference(cnf_transformation,[status(thm)],[f756])).
% 3.07/1.78 thf(f756,plain,(
% 3.07/1.78 ! [X0 : allegorical_term_b] : ((finite1987068434at_nat @ (labeled_edges_b_nat @ (translation_b @ X0))) = $true)),
% 3.07/1.78 inference(fool_elimination,[status(thm)],[f755])).
% 3.07/1.78 thf(f755,plain,(
% 3.07/1.78 ! [X0 : allegorical_term_b] : (finite1987068434at_nat @ (labeled_edges_b_nat @ (translation_b @ X0)))),
% 3.07/1.78 inference(rectify,[status(thm)],[f13])).
% 3.07/1.78 thf(f13,axiom,(
% 3.07/1.78 ! [X0 : allegorical_term_b] : (finite1987068434at_nat @ (labeled_edges_b_nat @ (translation_b @ X0)))),
% 3.07/1.78 file('/export/starexec/sandbox/tmp/tmp.bgqouCdkA9/DTF2THF_15711.p',fact_12_verts__in__translation__finite_I2_J)).
% 3.07/1.78 thf(f1178,plain,(
% 3.07/1.78 ((finite1987068434at_nat @ (labeled_edges_b_nat @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))) != $true) | ((finite_finite_nat @ (labele460410879_b_nat @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))))) != $true) | ((graph_529870330at_nat @ (produc1542243159_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))) @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))) @ (id_on_nat @ (labele460410879_b_nat @ (produc1542243159_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v))))))))) != $true)),
% 3.07/1.78 inference(forward_demodulation,[status(thm)],[f1177,f1036])).
% 3.07/1.78 thf(f1177,plain,(
% 3.07/1.78 ((finite1987068434at_nat @ (labeled_edges_b_nat @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))))) != $true) | ((finite_finite_nat @ (labele460410879_b_nat @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))))) != $true) | ((graph_529870330at_nat @ (produc1542243159_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))) @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))) @ (id_on_nat @ (labele460410879_b_nat @ (produc1542243159_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v))))))))) != $true)),
% 3.07/1.78 inference(subsumption_resolution,[status(thm)],[f1176,f1159])).
% 3.07/1.78 thf(f1159,plain,(
% 3.07/1.78 ( ! [X0 : allegorical_term_b,X1 : allegorical_term_b] : (((translation_b @ (allegorical_A_Int_b @ X1 @ X0)) = (restrict_b_nat @ (translation_b @ (allegorical_A_Int_b @ X1 @ X0))))) )),
% 3.07/1.78 inference(forward_demodulation,[status(thm)],[f1064,f1036])).
% 3.07/1.78 thf(f1064,plain,(
% 3.07/1.78 ( ! [X0 : allegorical_term_b,X1 : allegorical_term_b] : (((produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ X1) @ (translation_b @ (allegorical_A_Int_b @ X1 @ X0)))) = (restrict_b_nat @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ X1) @ (translation_b @ (allegorical_A_Int_b @ X1 @ X0))))))) )),
% 3.07/1.78 inference(cnf_transformation,[status(thm)],[f694])).
% 3.07/1.78 thf(f1176,plain,(
% 3.07/1.78 ((finite1987068434at_nat @ (labeled_edges_b_nat @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))))) != $true) | ((translation_b @ (allegorical_A_Int_b @ u @ v)) != (restrict_b_nat @ (translation_b @ (allegorical_A_Int_b @ u @ v)))) | ((finite_finite_nat @ (labele460410879_b_nat @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))))) != $true) | ((graph_529870330at_nat @ (produc1542243159_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))) @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))) @ (id_on_nat @ (labele460410879_b_nat @ (produc1542243159_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v))))))))) != $true)),
% 3.07/1.78 inference(forward_demodulation,[status(thm)],[f1175,f1127])).
% 3.07/1.78 thf(f1175,plain,(
% 3.07/1.78 ((translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) != (restrict_b_nat @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))) | ((finite1987068434at_nat @ (labeled_edges_b_nat @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))))) != $true) | ((finite_finite_nat @ (labele460410879_b_nat @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))))) != $true) | ((graph_529870330at_nat @ (produc1542243159_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))) @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))) @ (id_on_nat @ (labele460410879_b_nat @ (produc1542243159_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v))))))))) != $true)),
% 3.07/1.78 inference(forward_demodulation,[status(thm)],[f1093,f1036])).
% 3.07/1.78 thf(f1093,plain,(
% 3.07/1.78 ((produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))) != (restrict_b_nat @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))))) | ((finite_finite_nat @ (labele460410879_b_nat @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))))) != $true) | ((finite1987068434at_nat @ (labeled_edges_b_nat @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))))) != $true) | ((graph_529870330at_nat @ (produc1542243159_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))) @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))) @ (id_on_nat @ (labele460410879_b_nat @ (produc1542243159_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v))))))))) != $true)),
% 3.07/1.78 inference(cnf_transformation,[status(thm)],[f946])).
% 3.07/1.78 thf(f946,plain,(
% 3.07/1.78 ((graph_529870330at_nat @ (produc1542243159_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))) @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))) @ (id_on_nat @ (labele460410879_b_nat @ (produc1542243159_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v))))))))) != $true) | ((produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))) != (restrict_b_nat @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))))) | ((finite1987068434at_nat @ (labeled_edges_b_nat @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))))) != $true) | ((finite_finite_nat @ (labele460410879_b_nat @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))))) != $true)),
% 3.07/1.78 inference(ennf_transformation,[status(thm)],[f712])).
% 3.07/1.78 thf(f712,plain,(
% 3.07/1.78 ~(((finite1987068434at_nat @ (labeled_edges_b_nat @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))))) = $true) & ((finite_finite_nat @ (labele460410879_b_nat @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))))) = $true) & ((produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))) = (restrict_b_nat @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))))) & ((graph_529870330at_nat @ (produc1542243159_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))) @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))) @ (id_on_nat @ (labele460410879_b_nat @ (produc1542243159_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v))))))))) = $true))),
% 3.07/1.78 inference(fool_elimination,[status(thm)],[f711])).
% 3.07/1.78 thf(f711,plain,(
% 3.07/1.78 ~((finite1987068434at_nat @ (labeled_edges_b_nat @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))))) & (finite_finite_nat @ (labele460410879_b_nat @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))))) & (graph_529870330at_nat @ (produc1542243159_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))) @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))) @ (id_on_nat @ (labele460410879_b_nat @ (produc1542243159_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v))))))))) & ((produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))) = (restrict_b_nat @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))))))),
% 3.07/1.78 inference(rectify,[status(thm)],[f357])).
% 3.07/1.78 thf(f357,negated_conjecture,(
% 3.07/1.78 ~((finite1987068434at_nat @ (labeled_edges_b_nat @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))))) & (finite_finite_nat @ (labele460410879_b_nat @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))))) & (graph_529870330at_nat @ (produc1542243159_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))) @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))) @ (id_on_nat @ (labele460410879_b_nat @ (produc1542243159_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v))))))))) & ((produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))) = (restrict_b_nat @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))))))),
% 3.07/1.78 inference(negated_conjecture,[status(cth)],[f356])).
% 3.07/1.78 thf(f356,conjecture,(
% 3.07/1.78 (finite1987068434at_nat @ (labeled_edges_b_nat @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))))) & (finite_finite_nat @ (labele460410879_b_nat @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))))) & (graph_529870330at_nat @ (produc1542243159_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))) @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))) @ (id_on_nat @ (labele460410879_b_nat @ (produc1542243159_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v))))))))) & ((produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))))) = (restrict_b_nat @ (produc194497945_b_nat @ (produc951298923_b_nat @ (translation_b @ (produc854192515term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v)))) @ (translation_b @ (produc1223098053term_b @ (produc1990145943term_b @ u @ (allegorical_A_Int_b @ u @ v))))))))),
% 3.07/1.78 file('/export/starexec/sandbox/tmp/tmp.bgqouCdkA9/DTF2THF_15711.p',conj_0)).
% 3.07/1.78 % SZS output end Proof for DTF2THF_15711
% 3.07/1.78 % (16054)------------------------------
% 3.07/1.78 % (16054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.07/1.78 % (16054)Termination reason: Refutation
% 3.07/1.78
% 3.07/1.78 % (16054)Memory used [KB]: 7164
% 3.07/1.78 % (16054)Time elapsed: 0.060 s
% 3.07/1.78 % (16054)Instructions burned: 90 (million)
% 3.07/1.78 % (16054)------------------------------
% 3.07/1.78 % (16054)------------------------------
% 3.07/1.78 % (16033)Success in time 0.147 s
%------------------------------------------------------------------------------