DT2H2X---1.9.5.THM-Ref.s

%------------------------------------------------------------------------------
% File     : DT2H2X---1.9.5
% Problem  : ITP179^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300

% Computer : n029.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 7.63s 2.30s
% Output   : Refutation 7.63s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   20
% Syntax   : Number of formulae    :  100 (  41 unt;   0 typ;   6 def)
%            Number of atoms       :  395 ( 164 equ;   0 cnn)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives : 1577 (  78   ~;  80   |;  38   &;1372   @)
%                                         (   9 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   4 avg)
%            Number of types       :   55 (  54 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  203 ( 200 usr;  36 con; 0-3 aty)
%            Number of variables   :  103 (   0   ^; 103   !;   0   ?; 103   :)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_5,type,
    nat: $tType ).

thf(type_def_6,type,
    standard_Constant_a: $tType ).

thf(type_def_7,type,
    labele431970251um_a_b: $tType ).

thf(type_def_8,type,
    set_Pr1916610317um_a_b: $tType ).

thf(type_def_10,type,
    set_Pr1986765409at_nat: $tType ).

thf(type_def_11,type,
    set_Pr1647387645at_nat: $tType ).

thf(type_def_12,type,
    set_Pr1174980151um_a_b: $tType ).

thf(type_def_13,type,
    set_Pr409224873um_a_b: $tType ).

thf(type_def_14,type,
    set_Pr375490359_b_nat: $tType ).

thf(type_def_15,type,
    labele935650037_a_nat: $tType ).

thf(type_def_16,type,
    labele498606060at_nat: $tType ).

thf(type_def_17,type,
    set_Pr689416536at_nat: $tType ).

thf(type_def_18,type,
    set_Pr304595758um_a_b: $tType ).

thf(type_def_19,type,
    labele261019144um_a_b: $tType ).

thf(type_def_20,type,
    set_Pr1902304780_b_nat: $tType ).

thf(type_def_21,type,
    set_Pr653770722um_a_b: $tType ).

thf(type_def_22,type,
    labele1191284958um_a_b: $tType ).

thf(type_def_23,type,
    set_Pr507214050_b_nat: $tType ).

thf(type_def_24,type,
    set_Pr55236280um_a_b: $tType ).

thf(type_def_25,type,
    set_nat: $tType ).

thf(type_def_26,type,
    set_Pr1355257963at_nat: $tType ).

thf(type_def_27,type,
    set_Pr2065572323um_a_b: $tType ).

thf(type_def_28,type,
    set_Pr1429673827um_a_b: $tType ).

thf(type_def_29,type,
    set_Sum_sum_a_b: $tType ).

thf(type_def_30,type,
    set_St761939237tant_a: $tType ).

thf(type_def_31,type,
    product_prod_nat_nat: $tType ).

thf(type_def_32,type,
    produc1032616263at_nat: $tType ).

thf(type_def_33,type,
    produc1124793815um_a_b: $tType ).

thf(type_def_34,type,
    produc1003469085um_a_b: $tType ).

thf(type_def_35,type,
    produc1548871597um_a_b: $tType ).

thf(type_def_36,type,
    produc1963079155um_a_b: $tType ).

thf(type_def_37,type,
    sum_sum_a_b: $tType ).

thf(type_def_38,type,
    produc1394389750um_a_b: $tType ).

thf(type_def_39,type,
    produc1871334759_a_nat: $tType ).

thf(type_def_40,type,
    produc204140796um_a_b: $tType ).

thf(type_def_41,type,
    produc1681803642um_a_b: $tType ).

thf(type_def_42,type,
    produc1546082365um_a_b: $tType ).

thf(type_def_43,type,
    produc1798470614um_a_b: $tType ).

thf(type_def_44,type,
    produc1918750183um_a_b: $tType ).

thf(type_def_45,type,
    produc585753260um_a_b: $tType ).

thf(type_def_46,type,
    produc1978941143_b_nat: $tType ).

thf(type_def_47,type,
    produc1733247354um_a_b: $tType ).

thf(type_def_48,type,
    produc323101606um_a_b: $tType ).

thf(type_def_49,type,
    set_Pr326391507um_a_b: $tType ).

thf(type_def_50,type,
    set_Pr1994339542um_a_b: $tType ).

thf(type_def_51,type,
    set_Pr1134469976at_nat: $tType ).

thf(type_def_52,type,
    set_Pr1618094130um_a_b: $tType ).

thf(type_def_53,type,
    set_Pr1155046920um_a_b: $tType ).

thf(type_def_54,type,
    set_Pr1121389018um_a_b: $tType ).

thf(type_def_55,type,
    set_Pr386468381um_a_b: $tType ).

thf(type_def_56,type,
    set_Pr195945996um_a_b: $tType ).

thf(type_def_57,type,
    set_Pr45173959um_a_b: $tType ).

thf(type_def_58,type,
    set_Pr1558970842um_a_b: $tType ).

thf(type_def_59,type,
    set_Pr1783309276um_a_b: $tType ).

thf(func_def_0,type,
    set_Pr1355257963at_nat: $tType ).

thf(func_def_1,type,
    set_Pr1429673827um_a_b: $tType ).

thf(func_def_2,type,
    set_Pr2065572323um_a_b: $tType ).

thf(func_def_3,type,
    set_Pr1558970842um_a_b: $tType ).

thf(func_def_4,type,
    set_Pr1121389018um_a_b: $tType ).

thf(func_def_5,type,
    produc1733247354um_a_b: $tType ).

thf(func_def_6,type,
    produc1681803642um_a_b: $tType ).

thf(func_def_7,type,
    produc1871334759_a_nat: $tType ).

thf(func_def_8,type,
    labele498606060at_nat: $tType ).

thf(func_def_9,type,
    set_Pr304595758um_a_b: $tType ).

thf(func_def_10,type,
    set_Pr409224873um_a_b: $tType ).

thf(func_def_11,type,
    set_Pr45173959um_a_b: $tType ).

thf(func_def_12,type,
    set_Pr689416536at_nat: $tType ).

thf(func_def_13,type,
    set_Pr1134469976at_nat: $tType ).

thf(func_def_14,type,
    labele1191284958um_a_b: $tType ).

thf(func_def_15,type,
    produc1963079155um_a_b: $tType ).

thf(func_def_16,type,
    produc1918750183um_a_b: $tType ).

thf(func_def_17,type,
    set_Pr55236280um_a_b: $tType ).

thf(func_def_18,type,
    set_Pr326391507um_a_b: $tType ).

thf(func_def_19,type,
    set_Pr386468381um_a_b: $tType ).

thf(func_def_20,type,
    labele261019144um_a_b: $tType ).

thf(func_def_21,type,
    produc1003469085um_a_b: $tType ).

thf(func_def_22,type,
    produc1546082365um_a_b: $tType ).

thf(func_def_23,type,
    set_Pr1783309276um_a_b: $tType ).

thf(func_def_24,type,
    set_Pr507214050_b_nat: $tType ).

thf(func_def_25,type,
    set_Pr653770722um_a_b: $tType ).

thf(func_def_26,type,
    set_Pr1155046920um_a_b: $tType ).

thf(func_def_27,type,
    set_Pr1647387645at_nat: $tType ).

thf(func_def_28,type,
    produc323101606um_a_b: $tType ).

thf(func_def_29,type,
    produc585753260um_a_b: $tType ).

thf(func_def_30,type,
    produc1032616263at_nat: $tType ).

thf(func_def_31,type,
    set_Pr1994339542um_a_b: $tType ).

thf(func_def_32,type,
    set_Pr1902304780_b_nat: $tType ).

thf(func_def_33,type,
    set_Pr195945996um_a_b: $tType ).

thf(func_def_34,type,
    set_Pr1618094130um_a_b: $tType ).

thf(func_def_35,type,
    labele431970251um_a_b: $tType ).

thf(func_def_36,type,
    produc1394389750um_a_b: $tType ).

thf(func_def_37,type,
    produc1798470614um_a_b: $tType ).

thf(func_def_38,type,
    produc204140796um_a_b: $tType ).

thf(func_def_39,type,
    set_Pr1916610317um_a_b: $tType ).

thf(func_def_40,type,
    labele935650037_a_nat: $tType ).

thf(func_def_41,type,
    produc1548871597um_a_b: $tType ).

thf(func_def_42,type,
    set_Pr375490359_b_nat: $tType ).

thf(func_def_43,type,
    set_Pr1174980151um_a_b: $tType ).

thf(func_def_44,type,
    produc1978941143_b_nat: $tType ).

thf(func_def_45,type,
    produc1124793815um_a_b: $tType ).

thf(func_def_46,type,
    set_St761939237tant_a: $tType ).

thf(func_def_47,type,
    set_Pr1986765409at_nat: $tType ).

thf(func_def_48,type,
    standard_Constant_a: $tType ).

thf(func_def_49,type,
    product_prod_nat_nat: $tType ).

thf(func_def_50,type,
    set_Sum_sum_a_b: $tType ).

thf(func_def_51,type,
    sum_sum_a_b: $tType ).

thf(func_def_52,type,
    set_nat: $tType ).

thf(func_def_53,type,
    nat: $tType ).

thf(func_def_54,type,
    zero_zero_nat: nat ).

thf(func_def_55,type,
    standard_S_Bot_a: standard_Constant_a ).

thf(func_def_56,type,
    standard_S_Idt_a: standard_Constant_a ).

thf(func_def_57,type,
    getRel1465196352um_a_b: standard_Constant_a > labele431970251um_a_b > set_Pr1916610317um_a_b ).

thf(func_def_58,type,
    edge_p170421892tant_a: set_Pr1986765409at_nat > set_Pr1647387645at_nat > set_Pr1647387645at_nat > $o ).

thf(func_def_59,type,
    edge_p1382426714tant_a: set_Pr1174980151um_a_b > set_Pr1647387645at_nat > set_Pr409224873um_a_b > $o ).

thf(func_def_60,type,
    edge_p749155930tant_a: set_Pr375490359_b_nat > set_Pr409224873um_a_b > set_Pr1647387645at_nat > $o ).

thf(func_def_61,type,
    edge_p1871801392tant_a: set_Pr1916610317um_a_b > set_Pr409224873um_a_b > set_Pr409224873um_a_b > $o ).

thf(func_def_62,type,
    graph_2130075512at_nat: labele935650037_a_nat > labele935650037_a_nat > set_Pr1986765409at_nat > $o ).

thf(func_def_63,type,
    graph_1452133198um_a_b: labele935650037_a_nat > labele431970251um_a_b > set_Pr1174980151um_a_b > $o ).

thf(func_def_64,type,
    graph_149544303at_nat: labele498606060at_nat > labele935650037_a_nat > set_Pr689416536at_nat > $o ).

thf(func_def_65,type,
    graph_166346565um_a_b: labele498606060at_nat > labele431970251um_a_b > set_Pr304595758um_a_b > $o ).

thf(func_def_66,type,
    graph_1203757137_b_nat: labele261019144um_a_b > labele935650037_a_nat > set_Pr1902304780_b_nat > $o ).

thf(func_def_67,type,
    graph_502887975um_a_b: labele261019144um_a_b > labele431970251um_a_b > set_Pr653770722um_a_b > $o ).

thf(func_def_68,type,
    graph_1815313447_b_nat: labele1191284958um_a_b > labele935650037_a_nat > set_Pr507214050_b_nat > $o ).

thf(func_def_69,type,
    graph_1763806717um_a_b: labele1191284958um_a_b > labele431970251um_a_b > set_Pr55236280um_a_b > $o ).

thf(func_def_70,type,
    graph_165730638_b_nat: labele431970251um_a_b > labele935650037_a_nat > set_Pr375490359_b_nat > $o ).

thf(func_def_71,type,
    graph_611893540um_a_b: labele431970251um_a_b > labele431970251um_a_b > set_Pr1916610317um_a_b > $o ).

thf(func_def_72,type,
    labele16114835_a_nat: set_Pr1647387645at_nat > set_nat > labele935650037_a_nat ).

thf(func_def_73,type,
    labele1813985418at_nat: set_Pr1355257963at_nat > set_Pr1647387645at_nat > labele498606060at_nat ).

thf(func_def_74,type,
    labele2034032468um_a_b: set_Pr2065572323um_a_b > set_Pr1174980151um_a_b > labele261019144um_a_b ).

thf(func_def_75,type,
    labele989994um_a_b: set_Pr1429673827um_a_b > set_Pr1916610317um_a_b > labele1191284958um_a_b ).

thf(func_def_76,type,
    labele1729654377um_a_b: set_Pr409224873um_a_b > set_Sum_sum_a_b > labele431970251um_a_b ).

thf(func_def_77,type,
    labele195203296_a_nat: labele935650037_a_nat > set_Pr1647387645at_nat ).

thf(func_def_78,type,
    labele1939049654um_a_b: labele431970251um_a_b > set_Pr409224873um_a_b ).

thf(func_def_79,type,
    labele1810595089_a_nat: labele935650037_a_nat > set_nat ).

thf(func_def_80,type,
    labele577278695um_a_b: labele431970251um_a_b > set_Sum_sum_a_b ).

thf(func_def_81,type,
    restri572569417_a_nat: labele935650037_a_nat > labele935650037_a_nat ).

thf(func_def_82,type,
    restri1162247455um_a_b: labele431970251um_a_b > labele431970251um_a_b ).

thf(func_def_83,type,
    unival860567212at_nat: set_Pr1647387645at_nat > $o ).

thf(func_def_84,type,
    unival1487587672um_a_b: set_Pr409224873um_a_b > $o ).

thf(func_def_85,type,
    unival2092813468um_a_b: set_Pr1174980151um_a_b > $o ).

thf(func_def_86,type,
    unival118648434um_a_b: set_Pr1916610317um_a_b > $o ).

thf(func_def_87,type,
    bot_bot_nat: nat ).

thf(func_def_88,type,
    bot_bo1160111033tant_a: set_St761939237tant_a ).

thf(func_def_89,type,
    bot_bot_set_nat: set_nat ).

thf(func_def_90,type,
    bot_bo810816657at_nat: set_Pr1647387645at_nat ).

thf(func_def_91,type,
    bot_bo1524397311at_nat: set_Pr1355257963at_nat ).

thf(func_def_92,type,
    bot_bo1208513655um_a_b: set_Pr2065572323um_a_b ).

thf(func_def_93,type,
    bot_bo1262778871um_a_b: set_Pr1429673827um_a_b ).

thf(func_def_94,type,
    bot_bo1262634813um_a_b: set_Pr409224873um_a_b ).

thf(func_def_95,type,
    bot_bo2130386637at_nat: set_Pr1986765409at_nat ).

thf(func_def_96,type,
    bot_bo575978147um_a_b: set_Pr1174980151um_a_b ).

thf(func_def_97,type,
    bot_bo1582968772at_nat: set_Pr689416536at_nat ).

thf(func_def_98,type,
    bot_bo627753370um_a_b: set_Pr304595758um_a_b ).

thf(func_def_99,type,
    bot_bo949957280_b_nat: set_Pr1902304780_b_nat ).

thf(func_def_100,type,
    bot_bo1892785270um_a_b: set_Pr653770722um_a_b ).

thf(func_def_101,type,
    bot_bo1746228598_b_nat: set_Pr507214050_b_nat ).

thf(func_def_102,type,
    bot_bo1217542988um_a_b: set_Pr55236280um_a_b ).

thf(func_def_103,type,
    bot_bo1923972003_b_nat: set_Pr375490359_b_nat ).

thf(func_def_104,type,
    bot_bo225809273um_a_b: set_Pr1916610317um_a_b ).

thf(func_def_105,type,
    bot_bo1491243248um_a_b: set_Sum_sum_a_b ).

thf(func_def_106,type,
    ord_less_eq_nat: nat > nat > $o ).

thf(func_def_107,type,
    ord_le1739761029tant_a: set_St761939237tant_a > set_St761939237tant_a > $o ).

thf(func_def_108,type,
    ord_less_eq_set_nat: set_nat > set_nat > $o ).

thf(func_def_109,type,
    ord_le1909159005at_nat: set_Pr1647387645at_nat > set_Pr1647387645at_nat > $o ).

thf(func_def_110,type,
    ord_le615126793um_a_b: set_Pr409224873um_a_b > set_Pr409224873um_a_b > $o ).

thf(func_def_111,type,
    ord_le841296385at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o ).

thf(func_def_112,type,
    ord_le823954903um_a_b: set_Pr1174980151um_a_b > set_Pr1174980151um_a_b > $o ).

thf(func_def_113,type,
    ord_le1059794605um_a_b: set_Pr1916610317um_a_b > set_Pr1916610317um_a_b > $o ).

thf(func_def_114,type,
    ord_le192794300um_a_b: set_Sum_sum_a_b > set_Sum_sum_a_b > $o ).

thf(func_def_115,type,
    produc407553657at_nat: standard_Constant_a > product_prod_nat_nat > produc1032616263at_nat ).

thf(func_def_116,type,
    produc414524239um_a_b: standard_Constant_a > produc1124793815um_a_b > produc1003469085um_a_b ).

thf(func_def_117,type,
    produc1697725733um_a_b: standard_Constant_a > produc1548871597um_a_b > produc1963079155um_a_b ).

thf(func_def_118,type,
    produc584843310um_a_b: standard_Constant_a > sum_sum_a_b > produc1394389750um_a_b ).

thf(func_def_119,type,
    produc1676969687_a_nat: labele935650037_a_nat > labele935650037_a_nat > produc1871334759_a_nat ).

thf(func_def_120,type,
    product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).

thf(func_def_121,type,
    produc1346373166um_a_b: nat > produc1124793815um_a_b > produc204140796um_a_b ).

thf(func_def_122,type,
    produc1808556047um_a_b: nat > sum_sum_a_b > produc1124793815um_a_b ).

thf(func_def_123,type,
    produc522766386um_a_b: produc1963079155um_a_b > sum_sum_a_b > produc1681803642um_a_b ).

thf(func_def_124,type,
    produc335036333um_a_b: product_prod_nat_nat > produc1124793815um_a_b > produc1546082365um_a_b ).

thf(func_def_125,type,
    produc1872245072um_a_b: product_prod_nat_nat > sum_sum_a_b > produc1798470614um_a_b ).

thf(func_def_126,type,
    produc27163479um_a_b: produc1124793815um_a_b > produc1124793815um_a_b > produc1918750183um_a_b ).

thf(func_def_127,type,
    produc831476262um_a_b: produc1124793815um_a_b > sum_sum_a_b > produc585753260um_a_b ).

thf(func_def_128,type,
    produc522153487_b_nat: sum_sum_a_b > nat > produc1978941143_b_nat ).

thf(func_def_129,type,
    produc230853810um_a_b: sum_sum_a_b > produc1963079155um_a_b > produc1733247354um_a_b ).

thf(func_def_130,type,
    produc1637282520um_a_b: sum_sum_a_b > produc1124793815um_a_b > produc323101606um_a_b ).

thf(func_def_131,type,
    produc176426981um_a_b: sum_sum_a_b > sum_sum_a_b > produc1548871597um_a_b ).

thf(func_def_132,type,
    domain1060562500at_nat: set_Pr1647387645at_nat > set_St761939237tant_a ).

thf(func_def_133,type,
    domain1362581744um_a_b: set_Pr409224873um_a_b > set_St761939237tant_a ).

thf(func_def_134,type,
    domain_nat_nat: set_Pr1986765409at_nat > set_nat ).

thf(func_def_135,type,
    domain1368163076um_a_b: set_Pr1174980151um_a_b > set_nat ).

thf(func_def_136,type,
    domain2069673178um_a_b: set_Pr1916610317um_a_b > set_Sum_sum_a_b ).

thf(func_def_137,type,
    id_on_Sum_sum_a_b: set_Sum_sum_a_b > set_Pr1916610317um_a_b ).

thf(func_def_138,type,
    image_127502653at_nat: set_Pr1647387645at_nat > set_St761939237tant_a > set_Pr1986765409at_nat ).

thf(func_def_139,type,
    image_1179143699um_a_b: set_Pr326391507um_a_b > set_St761939237tant_a > set_Pr1174980151um_a_b ).

thf(func_def_140,type,
    image_2023280617um_a_b: set_Pr409224873um_a_b > set_St761939237tant_a > set_Pr1916610317um_a_b ).

thf(func_def_141,type,
    image_2129435242um_a_b: set_Pr1994339542um_a_b > set_St761939237tant_a > set_Sum_sum_a_b ).

thf(func_def_142,type,
    image_nat_nat: set_Pr1986765409at_nat > set_nat > set_nat ).

thf(func_def_143,type,
    image_489788268at_nat: set_Pr1134469976at_nat > set_nat > set_Pr1647387645at_nat ).

thf(func_def_144,type,
    image_1228479730um_a_b: set_Pr1618094130um_a_b > set_nat > set_Pr1174980151um_a_b ).

thf(func_def_145,type,
    image_166667464um_a_b: set_Pr1155046920um_a_b > set_nat > set_Pr1916610317um_a_b ).

thf(func_def_146,type,
    image_256773707um_a_b: set_Pr1174980151um_a_b > set_nat > set_Sum_sum_a_b ).

thf(func_def_147,type,
    image_452296684at_nat: set_Pr689416536at_nat > set_Pr1647387645at_nat > set_nat ).

thf(func_def_148,type,
    image_1774897262um_a_b: set_Pr1121389018um_a_b > set_Pr409224873um_a_b > set_Sum_sum_a_b ).

thf(func_def_149,type,
    image_320480233um_a_b: set_Pr386468381um_a_b > set_Pr1986765409at_nat > set_Pr1174980151um_a_b ).

thf(func_def_150,type,
    image_1754351636um_a_b: set_Pr195945996um_a_b > set_Pr1986765409at_nat > set_Sum_sum_a_b ).

thf(func_def_151,type,
    image_128716052_b_nat: set_Pr1902304780_b_nat > set_Pr1174980151um_a_b > set_nat ).

thf(func_def_152,type,
    image_1464989587um_a_b: set_Pr45173959um_a_b > set_Pr1174980151um_a_b > set_Pr1174980151um_a_b ).

thf(func_def_153,type,
    image_869585130um_a_b: set_Pr653770722um_a_b > set_Pr1174980151um_a_b > set_Sum_sum_a_b ).

thf(func_def_154,type,
    image_1117854795_b_nat: set_Pr375490359_b_nat > set_Sum_sum_a_b > set_nat ).

thf(func_def_155,type,
    image_1482984686um_a_b: set_Pr1558970842um_a_b > set_Sum_sum_a_b > set_Pr409224873um_a_b ).

thf(func_def_156,type,
    image_1675391388um_a_b: set_Pr1783309276um_a_b > set_Sum_sum_a_b > set_Pr1174980151um_a_b ).

thf(func_def_157,type,
    image_1918588449um_a_b: set_Pr1916610317um_a_b > set_Sum_sum_a_b > set_Sum_sum_a_b ).

thf(func_def_158,type,
    mainta522127984um_a_b: produc1871334759_a_nat > labele431970251um_a_b > $o ).

thf(func_def_159,type,
    collect_nat: ( nat > $o ) > set_nat ).

thf(func_def_160,type,
    collec52779676at_nat: ( produc1032616263at_nat > $o ) > set_Pr1647387645at_nat ).

thf(func_def_161,type,
    collec1254333256um_a_b: ( produc1963079155um_a_b > $o ) > set_Pr409224873um_a_b ).

thf(func_def_162,type,
    collec492052930um_a_b: ( produc1124793815um_a_b > $o ) > set_Pr1174980151um_a_b ).

thf(func_def_163,type,
    collec1769032088um_a_b: ( produc1548871597um_a_b > $o ) > set_Pr1916610317um_a_b ).

thf(func_def_164,type,
    collect_Sum_sum_a_b: ( sum_sum_a_b > $o ) > set_Sum_sum_a_b ).

thf(func_def_165,type,
    insert1909710879tant_a: standard_Constant_a > set_St761939237tant_a > set_St761939237tant_a ).

thf(func_def_166,type,
    insert_nat: nat > set_nat > set_nat ).

thf(func_def_167,type,
    insert1625259895at_nat: produc1032616263at_nat > set_Pr1647387645at_nat > set_Pr1647387645at_nat ).

thf(func_def_168,type,
    insert323157027um_a_b: produc1963079155um_a_b > set_Pr409224873um_a_b > set_Pr409224873um_a_b ).

thf(func_def_169,type,
    insert271595217at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).

thf(func_def_170,type,
    insert983991207um_a_b: produc1124793815um_a_b > set_Pr1174980151um_a_b > set_Pr1174980151um_a_b ).

thf(func_def_171,type,
    insert1435405693um_a_b: produc1548871597um_a_b > set_Pr1916610317um_a_b > set_Pr1916610317um_a_b ).

thf(func_def_172,type,
    insert_Sum_sum_a_b: sum_sum_a_b > set_Sum_sum_a_b > set_Sum_sum_a_b ).

thf(func_def_173,type,
    standa1343274079tant_a: standard_Constant_a > standard_Constant_a > produc1871334759_a_nat ).

thf(func_def_174,type,
    standa1410829644tant_a: produc1871334759_a_nat ).

thf(func_def_175,type,
    standa63370785tant_a: standard_Constant_a > produc1871334759_a_nat ).

thf(func_def_176,type,
    standa997693288tant_a: standard_Constant_a > produc1871334759_a_nat ).

thf(func_def_177,type,
    standa1795879409tant_a: standard_Constant_a > produc1871334759_a_nat ).

thf(func_def_178,type,
    member1632892294tant_a: standard_Constant_a > set_St761939237tant_a > $o ).

thf(func_def_179,type,
    member_nat: nat > set_nat > $o ).

thf(func_def_180,type,
    member1696759390at_nat: produc1032616263at_nat > set_Pr1647387645at_nat > $o ).

thf(func_def_181,type,
    member1502344244um_a_b: produc1003469085um_a_b > set_Pr326391507um_a_b > $o ).

thf(func_def_182,type,
    member1998628618um_a_b: produc1963079155um_a_b > set_Pr409224873um_a_b > $o ).

thf(func_def_183,type,
    member1641046175um_a_b: produc1394389750um_a_b > set_Pr1994339542um_a_b > $o ).

thf(func_def_184,type,
    member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).

thf(func_def_185,type,
    member1139034387um_a_b: produc204140796um_a_b > set_Pr1618094130um_a_b > $o ).

thf(func_def_186,type,
    member1294585472um_a_b: produc1124793815um_a_b > set_Pr1174980151um_a_b > $o ).

thf(func_def_187,type,
    member1590479267um_a_b: produc1681803642um_a_b > set_Pr1121389018um_a_b > $o ).

thf(func_def_188,type,
    member834135910um_a_b: produc1546082365um_a_b > set_Pr386468381um_a_b > $o ).

thf(func_def_189,type,
    member585880557um_a_b: produc1798470614um_a_b > set_Pr195945996um_a_b > $o ).

thf(func_def_190,type,
    member429827856um_a_b: produc1918750183um_a_b > set_Pr45173959um_a_b > $o ).

thf(func_def_191,type,
    member748122307um_a_b: produc585753260um_a_b > set_Pr653770722um_a_b > $o ).

thf(func_def_192,type,
    member1249152_b_nat: produc1978941143_b_nat > set_Pr375490359_b_nat > $o ).

thf(func_def_193,type,
    member1641922979um_a_b: produc1733247354um_a_b > set_Pr1558970842um_a_b > $o ).

thf(func_def_194,type,
    member485470653um_a_b: produc323101606um_a_b > set_Pr1783309276um_a_b > $o ).

thf(func_def_195,type,
    member947389014um_a_b: produc1548871597um_a_b > set_Pr1916610317um_a_b > $o ).

thf(func_def_196,type,
    member_Sum_sum_a_b: sum_sum_a_b > set_Sum_sum_a_b > $o ).

thf(func_def_197,type,
    g: labele431970251um_a_b ).

thf(func_def_198,type,
    f: set_Pr1174980151um_a_b ).

thf(func_def_199,type,
    l: standard_Constant_a ).

thf(func_def_200,type,
    v: sum_sum_a_b ).

thf(func_def_212,type,
    sK0: standard_Constant_a > set_Pr1647387645at_nat > product_prod_nat_nat ).

thf(func_def_213,type,
    sK1: set_nat > nat ).

thf(func_def_214,type,
    sK2: nat > set_Pr1174980151um_a_b > sum_sum_a_b ).

thf(func_def_215,type,
    sK3: nat > set_Pr1174980151um_a_b > nat ).

thf(func_def_216,type,
    sK4: nat > set_Pr1986765409at_nat > nat ).

thf(func_def_217,type,
    sK5: labele431970251um_a_b > set_Pr409224873um_a_b ).

thf(func_def_218,type,
    sK6: labele431970251um_a_b > set_Sum_sum_a_b ).

thf(func_def_219,type,
    sK7: set_Pr1647387645at_nat > produc1032616263at_nat ).

thf(func_def_220,type,
    sK8: nat > set_Pr1174980151um_a_b > sum_sum_a_b ).

thf(func_def_221,type,
    sK9: set_Pr1174980151um_a_b > produc1124793815um_a_b ).

thf(func_def_222,type,
    sK10: ( labele935650037_a_nat > $o ) > set_nat ).

thf(func_def_223,type,
    sK11: ( labele935650037_a_nat > $o ) > set_Pr1647387645at_nat ).

thf(func_def_224,type,
    sK12: set_Pr1174980151um_a_b > nat > sum_sum_a_b ).

thf(func_def_225,type,
    sK13: set_Pr1174980151um_a_b > produc1124793815um_a_b ).

thf(func_def_226,type,
    sK14: set_Pr1174980151um_a_b > produc1124793815um_a_b ).

thf(func_def_227,type,
    sK15: set_Pr1174980151um_a_b > set_Pr1174980151um_a_b > nat ).

thf(func_def_228,type,
    sK16: set_Pr1174980151um_a_b > set_Pr1174980151um_a_b > sum_sum_a_b ).

thf(func_def_229,type,
    sK17: ( labele431970251um_a_b > $o ) > set_Sum_sum_a_b ).

thf(func_def_230,type,
    sK18: ( labele431970251um_a_b > $o ) > set_Pr409224873um_a_b ).

thf(func_def_231,type,
    sK19: ( standard_Constant_a > $o ) > set_Pr1647387645at_nat > standard_Constant_a ).

thf(func_def_232,type,
    sK20: ( standard_Constant_a > $o ) > set_Pr1647387645at_nat > product_prod_nat_nat ).

thf(func_def_233,type,
    sK21: set_Pr1647387645at_nat > standard_Constant_a > product_prod_nat_nat ).

thf(func_def_234,type,
    sK22: set_Pr1986765409at_nat > ( nat > $o ) > nat ).

thf(func_def_235,type,
    sK23: set_Pr1986765409at_nat > ( nat > $o ) > nat ).

thf(func_def_236,type,
    sK24: set_Pr1986765409at_nat > nat > nat ).

thf(func_def_237,type,
    sK25: set_Pr1647387645at_nat > produc1032616263at_nat ).

thf(func_def_238,type,
    sK26: set_Pr1986765409at_nat > nat > nat ).

thf(func_def_239,type,
    sK27: sum_sum_a_b > set_Pr1174980151um_a_b > set_nat > nat ).

thf(func_def_240,type,
    sK28: set_Pr1174980151um_a_b > ( nat > $o ) > sum_sum_a_b ).

thf(func_def_241,type,
    sK29: set_Pr1174980151um_a_b > ( nat > $o ) > nat ).

thf(func_def_242,type,
    sK30: sum_sum_a_b ).

thf(func_def_243,type,
    sK31: nat > set_Pr1174980151um_a_b > sum_sum_a_b ).

thf(func_def_244,type,
    sK32: set_Pr1647387645at_nat > produc1032616263at_nat ).

thf(func_def_245,type,
    sK33: set_Sum_sum_a_b > set_Sum_sum_a_b > sum_sum_a_b ).

thf(func_def_246,type,
    sK34: set_Pr1986765409at_nat > nat > nat ).

thf(func_def_247,type,
    sK35: set_Pr1986765409at_nat > nat > nat ).

thf(func_def_248,type,
    sK36: set_nat > nat ).

thf(func_def_249,type,
    sK37: standard_Constant_a > set_Pr1647387645at_nat > standard_Constant_a ).

thf(func_def_250,type,
    sK38: standard_Constant_a > set_Pr1647387645at_nat > product_prod_nat_nat ).

thf(func_def_251,type,
    sK39: sum_sum_a_b > set_Pr1174980151um_a_b > set_nat > nat ).

thf(func_def_252,type,
    sK40: set_nat > nat ).

thf(func_def_253,type,
    sK41: labele935650037_a_nat > set_Pr1647387645at_nat ).

thf(func_def_254,type,
    sK42: labele935650037_a_nat > set_nat ).

thf(func_def_255,type,
    sK43: standard_Constant_a > set_Pr1647387645at_nat > product_prod_nat_nat ).

thf(func_def_256,type,
    sK44: set_Pr1647387645at_nat > set_Pr1647387645at_nat > product_prod_nat_nat ).

thf(func_def_257,type,
    sK45: set_Pr1647387645at_nat > set_Pr1647387645at_nat > standard_Constant_a ).

thf(func_def_260,type,
    ph47: 
      !>[X0: $tType] : X0 ).

thf(f3283,plain,
    $false,
    inference(avatar_sat_refutation,[status(thm)],[f1491,f3269,f3271,f3274,f3277,f3279,f3282]) ).

thf(f3282,plain,
    spl46_6,
    inference(avatar_contradiction_clause,[status(thm)],[f3281]) ).

thf(f3281,plain,
    ( $false
    | spl46_6 ),
    inference(subsumption_resolution,[status(thm)],[f3280,f1358]) ).

thf(f1358,plain,
    ( ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( labele1939049654um_a_b @ g ) )
    = $true ),
    inference(cnf_transformation,[status(thm)],[f610]) ).

thf(f610,plain,
    ( ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( labele1939049654um_a_b @ g ) )
    = $true ),
    inference(fool_elimination,[status(thm)],[f609]) ).

thf(f609,plain,
    edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( labele1939049654um_a_b @ g ),
    inference(rectify,[status(thm)],[f3]) ).

thf(f3,axiom,
    edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( labele1939049654um_a_b @ g ),
    file('/export/starexec/sandbox2/tmp/tmp.XpaU65CC0V/DTF2THF_20438.p',fact_2__092_060open_062edge__preserving_A_123_I0_058_058_063_Hc1_M_Av_J_125_A_123_IS__Idt_M_A0_058_058_063_Hc1_M_A0_058_058_063_Hc1_J_125_A_Iedges_AG_J_092_060close_062) ).

thf(f3280,plain,
    ( ( ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( labele1939049654um_a_b @ g ) )
     != $true )
    | spl46_6 ),
    inference(forward_demodulation,[status(thm)],[f1490,f1313]) ).

thf(f1313,plain,
    ! [X0: set_nat,X1: set_Pr1647387645at_nat] :
      ( ( labele195203296_a_nat @ ( labele16114835_a_nat @ X1 @ X0 ) )
      = X1 ),
    inference(cnf_transformation,[status(thm)],[f943]) ).

thf(f943,plain,
    ! [X0: set_nat,X1: set_Pr1647387645at_nat] :
      ( ( labele195203296_a_nat @ ( labele16114835_a_nat @ X1 @ X0 ) )
      = X1 ),
    inference(rectify,[status(thm)],[f138]) ).

thf(f138,axiom,
    ! [X10: set_nat,X9: set_Pr1647387645at_nat] :
      ( ( labele195203296_a_nat @ ( labele16114835_a_nat @ X9 @ X10 ) )
      = X9 ),
    file('/export/starexec/sandbox2/tmp/tmp.XpaU65CC0V/DTF2THF_20438.p',fact_137_labeled__graph_Osel_I1_J) ).

thf(f1490,plain,
    ( ( ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ) ) ) @ ( labele1939049654um_a_b @ g ) )
     != $true )
    | spl46_6 ),
    inference(avatar_component_clause,[status(thm)],[f1489]) ).

thf(f1489,definition,
    ( spl46_6
  <=> ( ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ) ) ) @ ( labele1939049654um_a_b @ g ) )
      = $true ) ),
    introduced(definition,[new_symbols(naming,[spl46_6])],[avatar_definition]) ).

thf(f3279,plain,
    spl46_5,
    inference(avatar_contradiction_clause,[status(thm)],[f3278]) ).

thf(f3278,plain,
    ( $false
    | spl46_5 ),
    inference(subsumption_resolution,[status(thm)],[f1487,f1417]) ).

thf(f1417,plain,
    ( ( unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) )
    = $true ),
    inference(definition_unfolding,[status(thm)],[f1295,f1375]) ).

thf(f1375,plain,
    ( ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b )
    = f ),
    inference(cnf_transformation,[status(thm)],[f5]) ).

thf(f5,axiom,
    ( ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b )
    = f ),
    file('/export/starexec/sandbox2/tmp/tmp.XpaU65CC0V/DTF2THF_20438.p',fact_4_f) ).

thf(f1295,plain,
    ( ( unival2092813468um_a_b @ f )
    = $true ),
    inference(cnf_transformation,[status(thm)],[f862]) ).

thf(f862,plain,
    ( ( unival2092813468um_a_b @ f )
    = $true ),
    inference(fool_elimination,[status(thm)],[f861]) ).

thf(f861,plain,
    unival2092813468um_a_b @ f,
    inference(rectify,[status(thm)],[f10]) ).

thf(f10,axiom,
    unival2092813468um_a_b @ f,
    file('/export/starexec/sandbox2/tmp/tmp.XpaU65CC0V/DTF2THF_20438.p',fact_9_u) ).

thf(f1487,plain,
    ( ( ( unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) )
     != $true )
    | spl46_5 ),
    inference(avatar_component_clause,[status(thm)],[f1486]) ).

thf(f1486,definition,
    ( spl46_5
  <=> ( ( unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) )
      = $true ) ),
    introduced(definition,[new_symbols(naming,[spl46_5])],[avatar_definition]) ).

thf(f3277,plain,
    spl46_4,
    inference(avatar_contradiction_clause,[status(thm)],[f3276]) ).

thf(f3276,plain,
    ( $false
    | spl46_4 ),
    inference(subsumption_resolution,[status(thm)],[f3275,f1411]) ).

thf(f1411,plain,
    ( $true
    = ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( insert_nat @ zero_zero_nat @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ) ) @ ( labele577278695um_a_b @ g ) ) ),
    inference(definition_unfolding,[status(thm)],[f1279,f1375,f1232]) ).

thf(f1232,plain,
    ( bot_bot_set_nat
    = ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ),
    inference(cnf_transformation,[status(thm)],[f32]) ).

thf(f32,axiom,
    ( bot_bot_set_nat
    = ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ),
    file('/export/starexec/sandbox2/tmp/tmp.XpaU65CC0V/DTF2THF_20438.p',fact_31_Domain__empty) ).

thf(f1279,plain,
    ( ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ f @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) @ ( labele577278695um_a_b @ g ) )
    = $true ),
    inference(cnf_transformation,[status(thm)],[f526]) ).

thf(f526,plain,
    ( ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ f @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) @ ( labele577278695um_a_b @ g ) )
    = $true ),
    inference(fool_elimination,[status(thm)],[f525]) ).

thf(f525,plain,
    ord_le192794300um_a_b @ ( image_256773707um_a_b @ f @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) @ ( labele577278695um_a_b @ g ),
    inference(rectify,[status(thm)],[f4]) ).

thf(f4,axiom,
    ord_le192794300um_a_b @ ( image_256773707um_a_b @ f @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) @ ( labele577278695um_a_b @ g ),
    file('/export/starexec/sandbox2/tmp/tmp.XpaU65CC0V/DTF2THF_20438.p',fact_3_r) ).

thf(f3275,plain,
    ( ( $true
     != ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( insert_nat @ zero_zero_nat @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ) ) @ ( labele577278695um_a_b @ g ) ) )
    | spl46_4 ),
    inference(forward_demodulation,[status(thm)],[f1484,f1398]) ).

thf(f1398,plain,
    ! [X0: set_nat,X1: set_Pr1647387645at_nat] :
      ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ X1 @ X0 ) )
      = X0 ),
    inference(cnf_transformation,[status(thm)],[f944]) ).

thf(f944,plain,
    ! [X0: set_nat,X1: set_Pr1647387645at_nat] :
      ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ X1 @ X0 ) )
      = X0 ),
    inference(rectify,[status(thm)],[f136]) ).

thf(f136,axiom,
    ! [X10: set_nat,X9: set_Pr1647387645at_nat] :
      ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ X9 @ X10 ) )
      = X10 ),
    file('/export/starexec/sandbox2/tmp/tmp.XpaU65CC0V/DTF2THF_20438.p',fact_135_labeled__graph_Osel_I2_J) ).

thf(f1484,plain,
    ( ( ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ) ) ) ) @ ( labele577278695um_a_b @ g ) )
     != $true )
    | spl46_4 ),
    inference(avatar_component_clause,[status(thm)],[f1483]) ).

thf(f1483,definition,
    ( spl46_4
  <=> ( ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ) ) ) ) @ ( labele577278695um_a_b @ g ) )
      = $true ) ),
    introduced(definition,[new_symbols(naming,[spl46_4])],[avatar_definition]) ).

thf(f3274,plain,
    spl46_3,
    inference(avatar_contradiction_clause,[status(thm)],[f3273]) ).

thf(f3273,plain,
    ( $false
    | spl46_3 ),
    inference(subsumption_resolution,[status(thm)],[f3272,f1343]) ).

thf(f1343,plain,
    ! [X2: sum_sum_a_b,X0: set_Pr1174980151um_a_b,X1: nat] :
      ( ( insert_nat @ X1 @ ( domain1368163076um_a_b @ X0 ) )
      = ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ X1 @ X2 ) @ X0 ) ) ),
    inference(cnf_transformation,[status(thm)],[f964]) ).

thf(f964,plain,
    ! [X0: set_Pr1174980151um_a_b,X1: nat,X2: sum_sum_a_b] :
      ( ( insert_nat @ X1 @ ( domain1368163076um_a_b @ X0 ) )
      = ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ X1 @ X2 ) @ X0 ) ) ),
    inference(rectify,[status(thm)],[f13]) ).

thf(f13,axiom,
    ! [X4: set_Pr1174980151um_a_b,X0: nat,X1: sum_sum_a_b] :
      ( ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ X0 @ X1 ) @ X4 ) )
      = ( insert_nat @ X0 @ ( domain1368163076um_a_b @ X4 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.XpaU65CC0V/DTF2THF_20438.p',fact_12_Domain__insert) ).

thf(f3272,plain,
    ( ( ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) )
     != ( insert_nat @ zero_zero_nat @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ) )
    | spl46_3 ),
    inference(forward_demodulation,[status(thm)],[f1481,f1398]) ).

thf(f1481,plain,
    ( ( ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) )
     != ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ) ) ) )
    | spl46_3 ),
    inference(avatar_component_clause,[status(thm)],[f1480]) ).

thf(f1480,definition,
    ( spl46_3
  <=> ( ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) )
      = ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ) ) ) ) ),
    introduced(definition,[new_symbols(naming,[spl46_3])],[avatar_definition]) ).

thf(f3271,plain,
    spl46_2,
    inference(avatar_contradiction_clause,[status(thm)],[f3270]) ).

thf(f3270,plain,
    ( $false
    | spl46_2 ),
    inference(subsumption_resolution,[status(thm)],[f1478,f1208]) ).

thf(f1208,plain,
    ( g
    = ( restri1162247455um_a_b @ g ) ),
    inference(cnf_transformation,[status(thm)],[f1]) ).

thf(f1,axiom,
    ( g
    = ( restri1162247455um_a_b @ g ) ),
    file('/export/starexec/sandbox2/tmp/tmp.XpaU65CC0V/DTF2THF_20438.p',fact_0_g) ).

thf(f1478,plain,
    ( ( g
     != ( restri1162247455um_a_b @ g ) )
    | spl46_2 ),
    inference(avatar_component_clause,[status(thm)],[f1477]) ).

thf(f1477,definition,
    ( spl46_2
  <=> ( g
      = ( restri1162247455um_a_b @ g ) ) ),
    introduced(definition,[new_symbols(naming,[spl46_2])],[avatar_definition]) ).

thf(f3269,plain,
    spl46_1,
    inference(avatar_contradiction_clause,[status(thm)],[f3268]) ).

thf(f3268,plain,
    ( $false
    | spl46_1 ),
    inference(equality_resolution,[status(thm)],[f3228]) ).

thf(f3228,plain,
    ( ! [X0: nat] :
        ( ( insert_nat @ X0 @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) )
       != ( insert_nat @ zero_zero_nat @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ) )
    | spl46_1 ),
    inference(trivial_inequality_removal,[status(thm)],[f3227]) ).

thf(f3227,plain,
    ( ! [X0: nat] :
        ( ( $true != $true )
        | ( ( insert_nat @ X0 @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) )
         != ( insert_nat @ zero_zero_nat @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ) ) )
    | spl46_1 ),
    inference(superposition,[status(thm)],[f3184,f1402]) ).

thf(f1402,plain,
    ! [X2: nat,X0: nat,X1: set_nat] :
      ( ( $true
        = ( ord_less_eq_set_nat @ X1 @ ( insert_nat @ X2 @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ) ) )
      | ( ( insert_nat @ X0 @ X1 )
       != ( insert_nat @ X2 @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ) ) ),
    inference(definition_unfolding,[status(thm)],[f1195,f1232,f1232]) ).

thf(f1195,plain,
    ! [X2: nat,X0: nat,X1: set_nat] :
      ( ( $true
        = ( ord_less_eq_set_nat @ X1 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) )
      | ( ( insert_nat @ X2 @ bot_bot_set_nat )
       != ( insert_nat @ X0 @ X1 ) ) ),
    inference(cnf_transformation,[status(thm)],[f1052]) ).

thf(f1052,plain,
    ! [X0: nat,X1: set_nat,X2: nat] :
      ( ( ( ( insert_nat @ X2 @ bot_bot_set_nat )
          = ( insert_nat @ X0 @ X1 ) )
        | ( X0 != X2 )
        | ( $true
         != ( ord_less_eq_set_nat @ X1 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) )
      & ( ( ( X0 = X2 )
          & ( $true
            = ( ord_less_eq_set_nat @ X1 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) )
        | ( ( insert_nat @ X2 @ bot_bot_set_nat )
         != ( insert_nat @ X0 @ X1 ) ) ) ),
    inference(flattening,[status(thm)],[f1051]) ).

thf(f1051,plain,
    ! [X0: nat,X1: set_nat,X2: nat] :
      ( ( ( ( insert_nat @ X2 @ bot_bot_set_nat )
          = ( insert_nat @ X0 @ X1 ) )
        | ( X0 != X2 )
        | ( $true
         != ( ord_less_eq_set_nat @ X1 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) )
      & ( ( ( X0 = X2 )
          & ( $true
            = ( ord_less_eq_set_nat @ X1 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) )
        | ( ( insert_nat @ X2 @ bot_bot_set_nat )
         != ( insert_nat @ X0 @ X1 ) ) ) ),
    inference(nnf_transformation,[status(thm)],[f357]) ).

thf(f357,plain,
    ! [X0: nat,X1: set_nat,X2: nat] :
      ( ( ( insert_nat @ X2 @ bot_bot_set_nat )
        = ( insert_nat @ X0 @ X1 ) )
    <=> ( ( X0 = X2 )
        & ( $true
          = ( ord_less_eq_set_nat @ X1 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ) ),
    inference(fool_elimination,[status(thm)],[f356]) ).

thf(f356,plain,
    ! [X0: nat,X1: set_nat,X2: nat] :
      ( ( ( ( insert_nat @ X2 @ bot_bot_set_nat )
          = ( insert_nat @ X0 @ X1 ) )
        = ( ord_less_eq_set_nat @ X1 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) )
      & ( X0 = X2 ) ),
    inference(rectify,[status(thm)],[f154]) ).

thf(f154,axiom,
    ! [X0: nat,X15: set_nat,X1: nat] :
      ( ( ( ( insert_nat @ X0 @ X15 )
          = ( insert_nat @ X1 @ bot_bot_set_nat ) )
        = ( ord_less_eq_set_nat @ X15 @ ( insert_nat @ X1 @ bot_bot_set_nat ) ) )
      & ( X0 = X1 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.XpaU65CC0V/DTF2THF_20438.p',fact_153_singleton__insert__inj__eq_H) ).

thf(f3184,plain,
    ( ( ( ord_less_eq_set_nat @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) @ ( insert_nat @ zero_zero_nat @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ) )
     != $true )
    | spl46_1 ),
    inference(subsumption_resolution,[status(thm)],[f3182,f1448]) ).

thf(f1448,plain,
    ! [X2: set_nat,X1: nat] :
      ( ( member_nat @ X1 @ ( insert_nat @ X1 @ X2 ) )
      = $true ),
    inference(equality_resolution,[status(thm)],[f1300]) ).

thf(f1300,plain,
    ! [X2: set_nat,X0: nat,X1: nat] :
      ( ( $true
        = ( member_nat @ X1 @ ( insert_nat @ X0 @ X2 ) ) )
      | ( X0 != X1 ) ),
    inference(cnf_transformation,[status(thm)],[f1114]) ).

thf(f1114,plain,
    ! [X0: nat,X1: nat,X2: set_nat] :
      ( ( ( $true
          = ( member_nat @ X1 @ ( insert_nat @ X0 @ X2 ) ) )
        | ( ( X0 != X1 )
          & ( $true
           != ( member_nat @ X1 @ X2 ) ) ) )
      & ( ( X0 = X1 )
        | ( $true
          = ( member_nat @ X1 @ X2 ) )
        | ( $true
         != ( member_nat @ X1 @ ( insert_nat @ X0 @ X2 ) ) ) ) ),
    inference(flattening,[status(thm)],[f1113]) ).

thf(f1113,plain,
    ! [X0: nat,X1: nat,X2: set_nat] :
      ( ( ( $true
          = ( member_nat @ X1 @ ( insert_nat @ X0 @ X2 ) ) )
        | ( ( X0 != X1 )
          & ( $true
           != ( member_nat @ X1 @ X2 ) ) ) )
      & ( ( X0 = X1 )
        | ( $true
          = ( member_nat @ X1 @ X2 ) )
        | ( $true
         != ( member_nat @ X1 @ ( insert_nat @ X0 @ X2 ) ) ) ) ),
    inference(nnf_transformation,[status(thm)],[f814]) ).

thf(f814,plain,
    ! [X0: nat,X1: nat,X2: set_nat] :
      ( ( $true
        = ( member_nat @ X1 @ ( insert_nat @ X0 @ X2 ) ) )
    <=> ( ( X0 = X1 )
        | ( $true
          = ( member_nat @ X1 @ X2 ) ) ) ),
    inference(fool_elimination,[status(thm)],[f813]) ).

thf(f813,plain,
    ! [X0: nat,X1: nat,X2: set_nat] :
      ( ( ( member_nat @ X1 @ ( insert_nat @ X0 @ X2 ) )
        = ( X0 = X1 ) )
      | ( member_nat @ X1 @ X2 ) ),
    inference(rectify,[status(thm)],[f245]) ).

thf(f245,axiom,
    ! [X1: nat,X0: nat,X15: set_nat] :
      ( ( ( member_nat @ X0 @ ( insert_nat @ X1 @ X15 ) )
        = ( X0 = X1 ) )
      | ( member_nat @ X0 @ X15 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.XpaU65CC0V/DTF2THF_20438.p',fact_244_insert__iff) ).

thf(f3182,plain,
    ( ( ( member_nat @ zero_zero_nat @ ( insert_nat @ zero_zero_nat @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ) )
     != $true )
    | ( ( ord_less_eq_set_nat @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) @ ( insert_nat @ zero_zero_nat @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ) )
     != $true )
    | spl46_1 ),
    inference(trivial_inequality_removal,[status(thm)],[f3180]) ).

thf(f3180,plain,
    ( ( ( member_nat @ zero_zero_nat @ ( insert_nat @ zero_zero_nat @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ) )
     != $true )
    | ( $true != $true )
    | ( ( ord_less_eq_set_nat @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) @ ( insert_nat @ zero_zero_nat @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ) )
     != $true )
    | spl46_1 ),
    inference(superposition,[status(thm)],[f3166,f1330]) ).

thf(f1330,plain,
    ! [X2: set_nat,X0: nat,X1: set_nat] :
      ( ( $true
        = ( ord_less_eq_set_nat @ ( insert_nat @ X0 @ X2 ) @ X1 ) )
      | ( $true
       != ( member_nat @ X0 @ X1 ) )
      | ( $true
       != ( ord_less_eq_set_nat @ X2 @ X1 ) ) ),
    inference(cnf_transformation,[status(thm)],[f1136]) ).

thf(f1136,plain,
    ! [X0: nat,X1: set_nat,X2: set_nat] :
      ( ( ( $true
          = ( ord_less_eq_set_nat @ ( insert_nat @ X0 @ X2 ) @ X1 ) )
        | ( $true
         != ( member_nat @ X0 @ X1 ) )
        | ( $true
         != ( ord_less_eq_set_nat @ X2 @ X1 ) ) )
      & ( ( ( $true
            = ( member_nat @ X0 @ X1 ) )
          & ( $true
            = ( ord_less_eq_set_nat @ X2 @ X1 ) ) )
        | ( $true
         != ( ord_less_eq_set_nat @ ( insert_nat @ X0 @ X2 ) @ X1 ) ) ) ),
    inference(flattening,[status(thm)],[f1135]) ).

thf(f1135,plain,
    ! [X0: nat,X1: set_nat,X2: set_nat] :
      ( ( ( $true
          = ( ord_less_eq_set_nat @ ( insert_nat @ X0 @ X2 ) @ X1 ) )
        | ( $true
         != ( member_nat @ X0 @ X1 ) )
        | ( $true
         != ( ord_less_eq_set_nat @ X2 @ X1 ) ) )
      & ( ( ( $true
            = ( member_nat @ X0 @ X1 ) )
          & ( $true
            = ( ord_less_eq_set_nat @ X2 @ X1 ) ) )
        | ( $true
         != ( ord_less_eq_set_nat @ ( insert_nat @ X0 @ X2 ) @ X1 ) ) ) ),
    inference(nnf_transformation,[status(thm)],[f630]) ).

thf(f630,plain,
    ! [X0: nat,X1: set_nat,X2: set_nat] :
      ( ( $true
        = ( ord_less_eq_set_nat @ ( insert_nat @ X0 @ X2 ) @ X1 ) )
    <=> ( ( $true
          = ( member_nat @ X0 @ X1 ) )
        & ( $true
          = ( ord_less_eq_set_nat @ X2 @ X1 ) ) ) ),
    inference(fool_elimination,[status(thm)],[f629]) ).

thf(f629,plain,
    ! [X0: nat,X1: set_nat,X2: set_nat] :
      ( ( ( ord_less_eq_set_nat @ ( insert_nat @ X0 @ X2 ) @ X1 )
        = ( member_nat @ X0 @ X1 ) )
      & ( ord_less_eq_set_nat @ X2 @ X1 ) ),
    inference(rectify,[status(thm)],[f178]) ).

thf(f178,axiom,
    ! [X8: nat,X43: set_nat,X15: set_nat] :
      ( ( ( ord_less_eq_set_nat @ ( insert_nat @ X8 @ X15 ) @ X43 )
        = ( member_nat @ X8 @ X43 ) )
      & ( ord_less_eq_set_nat @ X15 @ X43 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.XpaU65CC0V/DTF2THF_20438.p',fact_177_insert__subset) ).

thf(f3166,plain,
    ( ( $true
     != ( ord_less_eq_set_nat @ ( insert_nat @ zero_zero_nat @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ) @ ( insert_nat @ zero_zero_nat @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ) ) )
    | spl46_1 ),
    inference(trivial_inequality_removal,[status(thm)],[f3159]) ).

thf(f3159,plain,
    ( ( $true
     != ( ord_less_eq_set_nat @ ( insert_nat @ zero_zero_nat @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ) @ ( insert_nat @ zero_zero_nat @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ) ) )
    | ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ ( insert_nat @ zero_zero_nat @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ) ) )
     != ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ ( insert_nat @ zero_zero_nat @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ) ) ) )
    | spl46_1 ),
    inference(superposition,[status(thm)],[f2700,f1424]) ).

thf(f1424,plain,
    ! [X2: standard_Constant_a,X0: nat,X1: nat] :
      ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ X2 @ ( product_Pair_nat_nat @ X0 @ X1 ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ X0 @ ( insert_nat @ X1 @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ) ) )
      = ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ X2 @ ( product_Pair_nat_nat @ X0 @ X1 ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ X0 @ ( insert_nat @ X1 @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ) ) ) ) ),
    inference(definition_unfolding,[status(thm)],[f1354,f1232,f1232]) ).

thf(f1354,plain,
    ! [X2: standard_Constant_a,X0: nat,X1: nat] :
      ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ X2 @ ( product_Pair_nat_nat @ X0 @ X1 ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ X0 @ ( insert_nat @ X1 @ bot_bot_set_nat ) ) )
      = ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ X2 @ ( product_Pair_nat_nat @ X0 @ X1 ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ X0 @ ( insert_nat @ X1 @ bot_bot_set_nat ) ) ) ) ),
    inference(cnf_transformation,[status(thm)],[f937]) ).

thf(f937,plain,
    ! [X0: nat,X1: nat,X2: standard_Constant_a] :
      ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ X2 @ ( product_Pair_nat_nat @ X0 @ X1 ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ X0 @ ( insert_nat @ X1 @ bot_bot_set_nat ) ) )
      = ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ X2 @ ( product_Pair_nat_nat @ X0 @ X1 ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ X0 @ ( insert_nat @ X1 @ bot_bot_set_nat ) ) ) ) ),
    inference(rectify,[status(thm)],[f8]) ).

thf(f8,axiom,
    ! [X1: nat,X2: nat,X0: standard_Constant_a] :
      ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ X0 @ ( product_Pair_nat_nat @ X1 @ X2 ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ X1 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) )
      = ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ X0 @ ( product_Pair_nat_nat @ X1 @ X2 ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ X1 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.XpaU65CC0V/DTF2THF_20438.p',fact_7_graph__single) ).

thf(f2700,plain,
    ( ! [X0: set_nat] :
        ( ( ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ X0 ) ) )
         != ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ X0 ) ) )
        | ( $true
         != ( ord_less_eq_set_nat @ X0 @ ( insert_nat @ zero_zero_nat @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ) ) ) )
    | spl46_1 ),
    inference(superposition,[status(thm)],[f1475,f1428]) ).

thf(f1428,plain,
    ! [X2: nat,X1: set_nat] :
      ( ( ( insert_nat @ X2 @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) )
        = ( insert_nat @ X2 @ X1 ) )
      | ( $true
       != ( ord_less_eq_set_nat @ X1 @ ( insert_nat @ X2 @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ) ) ) ),
    inference(equality_resolution,[status(thm)],[f1400]) ).

thf(f1400,plain,
    ! [X2: nat,X0: nat,X1: set_nat] :
      ( ( ( insert_nat @ X0 @ X1 )
        = ( insert_nat @ X2 @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ) )
      | ( X0 != X2 )
      | ( $true
       != ( ord_less_eq_set_nat @ X1 @ ( insert_nat @ X2 @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ) ) ) ),
    inference(definition_unfolding,[status(thm)],[f1197,f1232,f1232]) ).

thf(f1197,plain,
    ! [X2: nat,X0: nat,X1: set_nat] :
      ( ( ( insert_nat @ X2 @ bot_bot_set_nat )
        = ( insert_nat @ X0 @ X1 ) )
      | ( X0 != X2 )
      | ( $true
       != ( ord_less_eq_set_nat @ X1 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ),
    inference(cnf_transformation,[status(thm)],[f1052]) ).

thf(f1475,plain,
    ( ( ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ) ) )
     != ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ) ) )
    | spl46_1 ),
    inference(avatar_component_clause,[status(thm)],[f1474]) ).

thf(f1474,definition,
    ( spl46_1
  <=> ( ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ) ) )
      = ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ) ) ) ),
    introduced(definition,[new_symbols(naming,[spl46_1])],[avatar_definition]) ).

thf(f1491,plain,
    ( ~ spl46_1
    | ~ spl46_2
    | ~ spl46_3
    | ~ spl46_4
    | ~ spl46_5
    | ~ spl46_6 ),
    inference(avatar_split_clause,[status(thm)],[f1409,f1489,f1486,f1483,f1480,f1477,f1474]) ).

thf(f1409,plain,
    ( ( ( unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) )
     != $true )
    | ( g
     != ( restri1162247455um_a_b @ g ) )
    | ( ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ) ) ) ) @ ( labele577278695um_a_b @ g ) )
     != $true )
    | ( ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ) ) )
     != ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ) ) )
    | ( ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ) ) ) @ ( labele1939049654um_a_b @ g ) )
     != $true )
    | ( ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) )
     != ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ ( domain1368163076um_a_b @ bot_bo575978147um_a_b ) ) ) ) ) ),
    inference(definition_unfolding,[status(thm)],[f1265,f1232,f1232,f1232,f1232,f1232]) ).

thf(f1265,plain,
    ( ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
     != ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ) )
    | ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) )
     != ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) )
    | ( ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) @ ( labele577278695um_a_b @ g ) )
     != $true )
    | ( g
     != ( restri1162247455um_a_b @ g ) )
    | ( ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) @ ( labele1939049654um_a_b @ g ) )
     != $true )
    | ( ( unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) )
     != $true ) ),
    inference(cnf_transformation,[status(thm)],[f1025]) ).

thf(f1025,plain,
    ( ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
     != ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ) )
    | ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) )
     != ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) )
    | ( ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) @ ( labele577278695um_a_b @ g ) )
     != $true )
    | ( g
     != ( restri1162247455um_a_b @ g ) )
    | ( ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) @ ( labele1939049654um_a_b @ g ) )
     != $true )
    | ( ( unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) )
     != $true ) ),
    inference(ennf_transformation,[status(thm)],[f666]) ).

thf(f666,plain,
    ~ ( ( ( unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) )
        = $true )
      & ( g
        = ( restri1162247455um_a_b @ g ) )
      & ( ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) @ ( labele1939049654um_a_b @ g ) )
        = $true )
      & ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) )
        = ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) )
      & ( ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) @ ( labele577278695um_a_b @ g ) )
        = $true )
      & ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
        = ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ) ) ),
    inference(fool_elimination,[status(thm)],[f665]) ).

thf(f665,plain,
    ~ ( ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) )
        = ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) )
      & ( g
        = ( restri1162247455um_a_b @ g ) )
      & ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
        = ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ) )
      & ( unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) )
      & ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) @ ( labele577278695um_a_b @ g ) )
      & ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) @ ( labele1939049654um_a_b @ g ) ) ),
    inference(rectify,[status(thm)],[f354]) ).

thf(f354,negated_conjecture,
    ~ ( ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) )
        = ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) )
      & ( g
        = ( restri1162247455um_a_b @ g ) )
      & ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
        = ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ) )
      & ( unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) )
      & ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) @ ( labele577278695um_a_b @ g ) )
      & ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) @ ( labele1939049654um_a_b @ g ) ) ),
    inference(negated_conjecture,[status(cth)],[f353]) ).

thf(f353,conjecture,
    ( ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) )
      = ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) )
    & ( g
      = ( restri1162247455um_a_b @ g ) )
    & ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
      = ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ) )
    & ( unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) )
    & ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) @ ( labele577278695um_a_b @ g ) )
    & ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) @ ( labele1939049654um_a_b @ g ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.XpaU65CC0V/DTF2THF_20438.p',conj_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ITP179^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13  % Command  : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33  % Computer : n029.cluster.edu
% 0.16/0.33  % Model    : x86_64 x86_64
% 0.16/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33  % Memory   : 8042.1875MB
% 0.16/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33  % CPULimit : 300
% 0.16/0.33  % WCLimit  : 300
% 0.16/0.33  % DateTime : Tue Feb 24 08:28:59 EST 2026
% 0.16/0.34  % CPUTime  : 
% 0.16/0.34  Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.45  ---- Original DTF file ---
% 0.29/0.46  thf(spec,logic,$$dhol).
% 0.29/0.46  %------------------------------------------------------------------------------
% 0.29/0.46  % File     : ITP179^1 : TPTP v9.2.1. Released v7.5.0.
% 0.29/0.46  % Domain   : Interactive Theorem Proving
% 0.29/0.46  % Problem  : Sledgehammer StandardRules problem prob_555__5392816_1
% 0.29/0.46  % Version  : Especial.
% 0.29/0.46  % English  :
% 0.29/0.46  
% 0.29/0.46  % Refs     : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.29/0.46  %          : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.29/0.46  % Source   : [Des21]
% 0.29/0.46  % Names    : StandardRules/prob_555__5392816_1 [Des21]
% 0.29/0.46  
% 0.29/0.46  % Status   : Theorem
% 0.29/0.46  % Rating   : 0.11 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.15 v8.1.0, 0.18 v7.5.0
% 0.29/0.46  % Syntax   : Number of formulae    :  554 ( 231 unt; 201 typ;   0 def)
% 0.29/0.46  %            Number of atoms       :  847 ( 345 equ;   0 cnn)
% 0.29/0.46  %            Maximal formula atoms :    6 (   2 avg)
% 0.29/0.46  %            Number of connectives : 2464 ( 112   ~;   9   |;  56   &;2064   @)
% 0.29/0.46  %                                         (   0 <=>; 223  =>;   0  <=;   0 <~>)
% 0.29/0.46  %            Maximal formula depth :   18 (   5 avg)
% 0.29/0.46  %            Number of types       :   55 (  54 usr)
% 0.29/0.46  %            Number of type conns  :  262 ( 262   >;   0   *;   0   +;   0  <<)
% 0.29/0.46  %            Number of symbols     :  148 ( 147 usr;  27 con; 0-3 aty)
% 0.29/0.46  %            Number of variables   :  835 (  20   ^; 788   !;  27   ?; 835   :)
% 0.29/0.46  % SPC      : TH0_THM_EQU_NAR
% 0.29/0.46  
% 0.29/0.46  % Comments : This file was generated by Sledgehammer 2021-02-23 15:38:59.416
% 0.29/0.46  %------------------------------------------------------------------------------
% 0.29/0.46  % Could-be-implicit typings (54)
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% 0.29/0.46  thf(sy_v_G,type,
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% 0.29/0.46  thf(sy_v_l,type,
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% 0.29/0.46  
% 0.29/0.46  thf(sy_v_v____,type,
% 0.29/0.46      v: sum_sum_a_b ).
% 0.29/0.46  
% 0.29/0.46  % Relevant facts (352)
% 0.29/0.46  thf(fact_0_g,axiom,
% 0.29/0.46      ( g
% 0.29/0.46      = ( restri1162247455um_a_b @ g ) ) ).
% 0.29/0.46  
% 0.29/0.46  % g
% 0.29/0.46  thf(fact_1_v,axiom,
% 0.29/0.46      member_Sum_sum_a_b @ v @ ( labele577278695um_a_b @ g ) ).
% 0.29/0.46  
% 0.29/0.46  % v
% 0.29/0.46  thf(fact_2__092_060open_062edge__preserving_A_123_I0_058_058_063_Hc1_M_Av_J_125_A_123_IS__Idt_M_A0_058_058_063_Hc1_M_A0_058_058_063_Hc1_J_125_A_Iedges_AG_J_092_060close_062,axiom,
% 0.29/0.46      edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( labele1939049654um_a_b @ g ) ).
% 0.29/0.46  
% 0.29/0.46  % \<open>edge_preserving {(0::?'c1, v)} {(S_Idt, 0::?'c1, 0::?'c1)} (edges G)\<close>
% 0.29/0.46  thf(fact_3_r,axiom,
% 0.29/0.46      ord_le192794300um_a_b @ ( image_256773707um_a_b @ f @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) @ ( labele577278695um_a_b @ g ) ).
% 0.29/0.46  
% 0.29/0.46  % r
% 0.29/0.46  thf(fact_4_f,axiom,
% 0.29/0.46      ( f
% 0.29/0.46      = ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ) ).
% 0.29/0.46  
% 0.29/0.46  % f
% 0.29/0.46  thf(fact_5_d,axiom,
% 0.29/0.46      ( ( domain1368163076um_a_b @ f )
% 0.29/0.46      = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ).
% 0.29/0.46  
% 0.29/0.46  % d
% 0.29/0.46  thf(fact_6_graph__single,axiom,
% 0.29/0.46      ! [A: standard_Constant_a,B: sum_sum_a_b,C: sum_sum_a_b] :
% 0.29/0.46        ( ( labele1729654377um_a_b @ ( insert323157027um_a_b @ ( produc1697725733um_a_b @ A @ ( produc176426981um_a_b @ B @ C ) ) @ bot_bo1262634813um_a_b ) @ ( insert_Sum_sum_a_b @ B @ ( insert_Sum_sum_a_b @ C @ bot_bo1491243248um_a_b ) ) )
% 0.29/0.46        = ( restri1162247455um_a_b @ ( labele1729654377um_a_b @ ( insert323157027um_a_b @ ( produc1697725733um_a_b @ A @ ( produc176426981um_a_b @ B @ C ) ) @ bot_bo1262634813um_a_b ) @ ( insert_Sum_sum_a_b @ B @ ( insert_Sum_sum_a_b @ C @ bot_bo1491243248um_a_b ) ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % graph_single
% 0.29/0.46  thf(fact_7_graph__single,axiom,
% 0.29/0.46      ! [A: standard_Constant_a,B: nat,C: nat] :
% 0.29/0.46        ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ A @ ( product_Pair_nat_nat @ B @ C ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ B @ ( insert_nat @ C @ bot_bot_set_nat ) ) )
% 0.29/0.46        = ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ A @ ( product_Pair_nat_nat @ B @ C ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ B @ ( insert_nat @ C @ bot_bot_set_nat ) ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % graph_single
% 0.29/0.46  thf(fact_8__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062v_O_A_I0_M_Av_J_A_092_060in_062_Af_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.29/0.46      ~ ! [V: sum_sum_a_b] :
% 0.29/0.46          ~ ( member1294585472um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ V ) @ f ) ).
% 0.29/0.46  
% 0.29/0.46  % \<open>\<And>thesis. (\<And>v. (0, v) \<in> f \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.29/0.46  thf(fact_9_u,axiom,
% 0.29/0.46      unival2092813468um_a_b @ f ).
% 0.29/0.46  
% 0.29/0.46  % u
% 0.29/0.46  thf(fact_10_Domain__insert,axiom,
% 0.29/0.46      ! [A: standard_Constant_a,B: product_prod_nat_nat,R: set_Pr1647387645at_nat] :
% 0.29/0.46        ( ( domain1060562500at_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ A @ B ) @ R ) )
% 0.29/0.46        = ( insert1909710879tant_a @ A @ ( domain1060562500at_nat @ R ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain_insert
% 0.29/0.46  thf(fact_11_Domain__insert,axiom,
% 0.29/0.46      ! [A: nat,B: nat,R: set_Pr1986765409at_nat] :
% 0.29/0.46        ( ( domain_nat_nat @ ( insert271595217at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R ) )
% 0.29/0.46        = ( insert_nat @ A @ ( domain_nat_nat @ R ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain_insert
% 0.29/0.46  thf(fact_12_Domain__insert,axiom,
% 0.29/0.46      ! [A: nat,B: sum_sum_a_b,R: set_Pr1174980151um_a_b] :
% 0.29/0.46        ( ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ A @ B ) @ R ) )
% 0.29/0.46        = ( insert_nat @ A @ ( domain1368163076um_a_b @ R ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain_insert
% 0.29/0.46  thf(fact_13_Domain__insert,axiom,
% 0.29/0.46      ! [A: standard_Constant_a,B: produc1548871597um_a_b,R: set_Pr409224873um_a_b] :
% 0.29/0.46        ( ( domain1362581744um_a_b @ ( insert323157027um_a_b @ ( produc1697725733um_a_b @ A @ B ) @ R ) )
% 0.29/0.46        = ( insert1909710879tant_a @ A @ ( domain1362581744um_a_b @ R ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain_insert
% 0.29/0.46  thf(fact_14_Domain__insert,axiom,
% 0.29/0.46      ! [A: sum_sum_a_b,B: sum_sum_a_b,R: set_Pr1916610317um_a_b] :
% 0.29/0.46        ( ( domain2069673178um_a_b @ ( insert1435405693um_a_b @ ( produc176426981um_a_b @ A @ B ) @ R ) )
% 0.29/0.46        = ( insert_Sum_sum_a_b @ A @ ( domain2069673178um_a_b @ R ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain_insert
% 0.29/0.46  thf(fact_15_Image__singleton__iff,axiom,
% 0.29/0.46      ! [B: nat,R: set_Pr1986765409at_nat,A: nat] :
% 0.29/0.46        ( ( member_nat @ B @ ( image_nat_nat @ R @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.29/0.46        = ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Image_singleton_iff
% 0.29/0.46  thf(fact_16_Image__singleton__iff,axiom,
% 0.29/0.46      ! [B: sum_sum_a_b,R: set_Pr1174980151um_a_b,A: nat] :
% 0.29/0.46        ( ( member_Sum_sum_a_b @ B @ ( image_256773707um_a_b @ R @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.29/0.46        = ( member1294585472um_a_b @ ( produc1808556047um_a_b @ A @ B ) @ R ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Image_singleton_iff
% 0.29/0.46  thf(fact_17_Image__singleton__iff,axiom,
% 0.29/0.46      ! [B: sum_sum_a_b,R: set_Pr1994339542um_a_b,A: standard_Constant_a] :
% 0.29/0.46        ( ( member_Sum_sum_a_b @ B @ ( image_2129435242um_a_b @ R @ ( insert1909710879tant_a @ A @ bot_bo1160111033tant_a ) ) )
% 0.29/0.46        = ( member1641046175um_a_b @ ( produc584843310um_a_b @ A @ B ) @ R ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Image_singleton_iff
% 0.29/0.46  thf(fact_18_Image__singleton__iff,axiom,
% 0.29/0.46      ! [B: product_prod_nat_nat,R: set_Pr1647387645at_nat,A: standard_Constant_a] :
% 0.29/0.46        ( ( member701585322at_nat @ B @ ( image_127502653at_nat @ R @ ( insert1909710879tant_a @ A @ bot_bo1160111033tant_a ) ) )
% 0.29/0.46        = ( member1696759390at_nat @ ( produc407553657at_nat @ A @ B ) @ R ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Image_singleton_iff
% 0.29/0.46  thf(fact_19_Image__singleton__iff,axiom,
% 0.29/0.46      ! [B: sum_sum_a_b,R: set_Pr195945996um_a_b,A: product_prod_nat_nat] :
% 0.29/0.46        ( ( member_Sum_sum_a_b @ B @ ( image_1754351636um_a_b @ R @ ( insert271595217at_nat @ A @ bot_bo2130386637at_nat ) ) )
% 0.29/0.46        = ( member585880557um_a_b @ ( produc1872245072um_a_b @ A @ B ) @ R ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Image_singleton_iff
% 0.29/0.46  thf(fact_20_Image__singleton__iff,axiom,
% 0.29/0.46      ! [B: produc1124793815um_a_b,R: set_Pr1618094130um_a_b,A: nat] :
% 0.29/0.46        ( ( member1294585472um_a_b @ B @ ( image_1228479730um_a_b @ R @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.29/0.46        = ( member1139034387um_a_b @ ( produc1346373166um_a_b @ A @ B ) @ R ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Image_singleton_iff
% 0.29/0.46  thf(fact_21_Image__singleton__iff,axiom,
% 0.29/0.46      ! [B: sum_sum_a_b,R: set_Pr1916610317um_a_b,A: sum_sum_a_b] :
% 0.29/0.46        ( ( member_Sum_sum_a_b @ B @ ( image_1918588449um_a_b @ R @ ( insert_Sum_sum_a_b @ A @ bot_bo1491243248um_a_b ) ) )
% 0.29/0.46        = ( member947389014um_a_b @ ( produc176426981um_a_b @ A @ B ) @ R ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Image_singleton_iff
% 0.29/0.46  thf(fact_22_Image__singleton__iff,axiom,
% 0.29/0.46      ! [B: produc1124793815um_a_b,R: set_Pr326391507um_a_b,A: standard_Constant_a] :
% 0.29/0.46        ( ( member1294585472um_a_b @ B @ ( image_1179143699um_a_b @ R @ ( insert1909710879tant_a @ A @ bot_bo1160111033tant_a ) ) )
% 0.29/0.46        = ( member1502344244um_a_b @ ( produc414524239um_a_b @ A @ B ) @ R ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Image_singleton_iff
% 0.29/0.46  thf(fact_23_Image__singleton__iff,axiom,
% 0.29/0.46      ! [B: produc1124793815um_a_b,R: set_Pr386468381um_a_b,A: product_prod_nat_nat] :
% 0.29/0.46        ( ( member1294585472um_a_b @ B @ ( image_320480233um_a_b @ R @ ( insert271595217at_nat @ A @ bot_bo2130386637at_nat ) ) )
% 0.29/0.46        = ( member834135910um_a_b @ ( produc335036333um_a_b @ A @ B ) @ R ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Image_singleton_iff
% 0.29/0.46  thf(fact_24_Image__singleton__iff,axiom,
% 0.29/0.46      ! [B: sum_sum_a_b,R: set_Pr653770722um_a_b,A: produc1124793815um_a_b] :
% 0.29/0.46        ( ( member_Sum_sum_a_b @ B @ ( image_869585130um_a_b @ R @ ( insert983991207um_a_b @ A @ bot_bo575978147um_a_b ) ) )
% 0.29/0.46        = ( member748122307um_a_b @ ( produc831476262um_a_b @ A @ B ) @ R ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Image_singleton_iff
% 0.29/0.46  thf(fact_25_graph__empty__e,axiom,
% 0.29/0.46      ! [V2: set_nat] :
% 0.29/0.46        ( ( labele16114835_a_nat @ bot_bo810816657at_nat @ V2 )
% 0.29/0.46        = ( restri572569417_a_nat @ ( labele16114835_a_nat @ bot_bo810816657at_nat @ V2 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % graph_empty_e
% 0.29/0.46  thf(fact_26_graph__empty__e,axiom,
% 0.29/0.46      ! [V2: set_Sum_sum_a_b] :
% 0.29/0.46        ( ( labele1729654377um_a_b @ bot_bo1262634813um_a_b @ V2 )
% 0.29/0.46        = ( restri1162247455um_a_b @ ( labele1729654377um_a_b @ bot_bo1262634813um_a_b @ V2 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % graph_empty_e
% 0.29/0.46  thf(fact_27_labeled__graph_Ocollapse,axiom,
% 0.29/0.46      ! [Labeled_graph: labele935650037_a_nat] :
% 0.29/0.46        ( ( labele16114835_a_nat @ ( labele195203296_a_nat @ Labeled_graph ) @ ( labele1810595089_a_nat @ Labeled_graph ) )
% 0.29/0.46        = Labeled_graph ) ).
% 0.29/0.46  
% 0.29/0.46  % labeled_graph.collapse
% 0.29/0.46  thf(fact_28_labeled__graph_Ocollapse,axiom,
% 0.29/0.46      ! [Labeled_graph: labele431970251um_a_b] :
% 0.29/0.46        ( ( labele1729654377um_a_b @ ( labele1939049654um_a_b @ Labeled_graph ) @ ( labele577278695um_a_b @ Labeled_graph ) )
% 0.29/0.46        = Labeled_graph ) ).
% 0.29/0.46  
% 0.29/0.46  % labeled_graph.collapse
% 0.29/0.46  thf(fact_29_Domain__empty,axiom,
% 0.29/0.46      ( ( domain_nat_nat @ bot_bo2130386637at_nat )
% 0.29/0.46      = bot_bot_set_nat ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain_empty
% 0.29/0.46  thf(fact_30_Domain__empty,axiom,
% 0.29/0.46      ( ( domain1060562500at_nat @ bot_bo810816657at_nat )
% 0.29/0.46      = bot_bo1160111033tant_a ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain_empty
% 0.29/0.46  thf(fact_31_Domain__empty,axiom,
% 0.29/0.46      ( ( domain1368163076um_a_b @ bot_bo575978147um_a_b )
% 0.29/0.46      = bot_bot_set_nat ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain_empty
% 0.29/0.46  thf(fact_32_Domain__empty,axiom,
% 0.29/0.46      ( ( domain2069673178um_a_b @ bot_bo225809273um_a_b )
% 0.29/0.46      = bot_bo1491243248um_a_b ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain_empty
% 0.29/0.46  thf(fact_33_Domain__empty,axiom,
% 0.29/0.46      ( ( domain1362581744um_a_b @ bot_bo1262634813um_a_b )
% 0.29/0.46      = bot_bo1160111033tant_a ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain_empty
% 0.29/0.46  thf(fact_34_Image__empty1,axiom,
% 0.29/0.46      ! [X: set_St761939237tant_a] :
% 0.29/0.46        ( ( image_127502653at_nat @ bot_bo810816657at_nat @ X )
% 0.29/0.46        = bot_bo2130386637at_nat ) ).
% 0.29/0.46  
% 0.29/0.46  % Image_empty1
% 0.29/0.46  thf(fact_35_Image__empty1,axiom,
% 0.29/0.46      ! [X: set_nat] :
% 0.29/0.46        ( ( image_256773707um_a_b @ bot_bo575978147um_a_b @ X )
% 0.29/0.46        = bot_bo1491243248um_a_b ) ).
% 0.29/0.46  
% 0.29/0.46  % Image_empty1
% 0.29/0.46  thf(fact_36_Image__empty1,axiom,
% 0.29/0.46      ! [X: set_Sum_sum_a_b] :
% 0.29/0.46        ( ( image_1918588449um_a_b @ bot_bo225809273um_a_b @ X )
% 0.29/0.46        = bot_bo1491243248um_a_b ) ).
% 0.29/0.46  
% 0.29/0.46  % Image_empty1
% 0.29/0.46  thf(fact_37_Image__empty1,axiom,
% 0.29/0.46      ! [X: set_St761939237tant_a] :
% 0.29/0.46        ( ( image_2023280617um_a_b @ bot_bo1262634813um_a_b @ X )
% 0.29/0.46        = bot_bo225809273um_a_b ) ).
% 0.29/0.46  
% 0.29/0.46  % Image_empty1
% 0.29/0.46  thf(fact_38_restrict__idemp,axiom,
% 0.29/0.46      ! [X2: labele935650037_a_nat] :
% 0.29/0.46        ( ( restri572569417_a_nat @ ( restri572569417_a_nat @ X2 ) )
% 0.29/0.46        = ( restri572569417_a_nat @ X2 ) ) ).
% 0.29/0.46  
% 0.29/0.46  % restrict_idemp
% 0.29/0.46  thf(fact_39_restrict__idemp,axiom,
% 0.29/0.46      ! [X2: labele431970251um_a_b] :
% 0.29/0.46        ( ( restri1162247455um_a_b @ ( restri1162247455um_a_b @ X2 ) )
% 0.29/0.46        = ( restri1162247455um_a_b @ X2 ) ) ).
% 0.29/0.46  
% 0.29/0.46  % restrict_idemp
% 0.29/0.46  thf(fact_40_labeled__graph_Oinject,axiom,
% 0.29/0.46      ! [X1: set_Pr1647387645at_nat,X22: set_nat,Y1: set_Pr1647387645at_nat,Y2: set_nat] :
% 0.29/0.46        ( ( ( labele16114835_a_nat @ X1 @ X22 )
% 0.29/0.46          = ( labele16114835_a_nat @ Y1 @ Y2 ) )
% 0.29/0.46        = ( ( X1 = Y1 )
% 0.29/0.46          & ( X22 = Y2 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % labeled_graph.inject
% 0.29/0.46  thf(fact_41_labeled__graph_Oinject,axiom,
% 0.29/0.46      ! [X1: set_Pr409224873um_a_b,X22: set_Sum_sum_a_b,Y1: set_Pr409224873um_a_b,Y2: set_Sum_sum_a_b] :
% 0.29/0.46        ( ( ( labele1729654377um_a_b @ X1 @ X22 )
% 0.29/0.46          = ( labele1729654377um_a_b @ Y1 @ Y2 ) )
% 0.29/0.46        = ( ( X1 = Y1 )
% 0.29/0.46          & ( X22 = Y2 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % labeled_graph.inject
% 0.29/0.46  thf(fact_42_v__gr,axiom,
% 0.29/0.46      ! [A2: sum_sum_a_b,B2: sum_sum_a_b] :
% 0.29/0.46        ( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ standard_S_Idt_a @ ( produc176426981um_a_b @ A2 @ B2 ) ) @ ( labele1939049654um_a_b @ g ) )
% 0.29/0.46        = ( ( member_Sum_sum_a_b @ A2 @ ( labele577278695um_a_b @ g ) )
% 0.29/0.46          & ( B2 = A2 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % v_gr
% 0.29/0.46  thf(fact_43__092_060open_062_IS__Idt_M_Av_M_Av_J_A_092_060in_062_Aedges_AG_092_060close_062,axiom,
% 0.29/0.46      member1998628618um_a_b @ ( produc1697725733um_a_b @ standard_S_Idt_a @ ( produc176426981um_a_b @ v @ v ) ) @ ( labele1939049654um_a_b @ g ) ).
% 0.29/0.46  
% 0.29/0.46  % \<open>(S_Idt, v, v) \<in> edges G\<close>
% 0.29/0.46  thf(fact_44_ImageI,axiom,
% 0.29/0.46      ! [A: nat,B: nat,R: set_Pr1986765409at_nat,A3: set_nat] :
% 0.29/0.46        ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R )
% 0.29/0.46       => ( ( member_nat @ A @ A3 )
% 0.29/0.46         => ( member_nat @ B @ ( image_nat_nat @ R @ A3 ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % ImageI
% 0.29/0.46  thf(fact_45_ImageI,axiom,
% 0.29/0.46      ! [A: nat,B: sum_sum_a_b,R: set_Pr1174980151um_a_b,A3: set_nat] :
% 0.29/0.46        ( ( member1294585472um_a_b @ ( produc1808556047um_a_b @ A @ B ) @ R )
% 0.29/0.46       => ( ( member_nat @ A @ A3 )
% 0.29/0.46         => ( member_Sum_sum_a_b @ B @ ( image_256773707um_a_b @ R @ A3 ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % ImageI
% 0.29/0.46  thf(fact_46_ImageI,axiom,
% 0.29/0.46      ! [A: standard_Constant_a,B: product_prod_nat_nat,R: set_Pr1647387645at_nat,A3: set_St761939237tant_a] :
% 0.29/0.46        ( ( member1696759390at_nat @ ( produc407553657at_nat @ A @ B ) @ R )
% 0.29/0.46       => ( ( member1632892294tant_a @ A @ A3 )
% 0.29/0.46         => ( member701585322at_nat @ B @ ( image_127502653at_nat @ R @ A3 ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % ImageI
% 0.29/0.46  thf(fact_47_ImageI,axiom,
% 0.29/0.46      ! [A: sum_sum_a_b,B: sum_sum_a_b,R: set_Pr1916610317um_a_b,A3: set_Sum_sum_a_b] :
% 0.29/0.46        ( ( member947389014um_a_b @ ( produc176426981um_a_b @ A @ B ) @ R )
% 0.29/0.46       => ( ( member_Sum_sum_a_b @ A @ A3 )
% 0.29/0.46         => ( member_Sum_sum_a_b @ B @ ( image_1918588449um_a_b @ R @ A3 ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % ImageI
% 0.29/0.46  thf(fact_48_ImageI,axiom,
% 0.29/0.46      ! [A: sum_sum_a_b,B: produc1124793815um_a_b,R: set_Pr1783309276um_a_b,A3: set_Sum_sum_a_b] :
% 0.29/0.46        ( ( member485470653um_a_b @ ( produc1637282520um_a_b @ A @ B ) @ R )
% 0.29/0.46       => ( ( member_Sum_sum_a_b @ A @ A3 )
% 0.29/0.46         => ( member1294585472um_a_b @ B @ ( image_1675391388um_a_b @ R @ A3 ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % ImageI
% 0.29/0.46  thf(fact_49_ImageI,axiom,
% 0.29/0.46      ! [A: produc1124793815um_a_b,B: sum_sum_a_b,R: set_Pr653770722um_a_b,A3: set_Pr1174980151um_a_b] :
% 0.29/0.46        ( ( member748122307um_a_b @ ( produc831476262um_a_b @ A @ B ) @ R )
% 0.29/0.46       => ( ( member1294585472um_a_b @ A @ A3 )
% 0.29/0.46         => ( member_Sum_sum_a_b @ B @ ( image_869585130um_a_b @ R @ A3 ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % ImageI
% 0.29/0.46  thf(fact_50_ImageI,axiom,
% 0.29/0.46      ! [A: standard_Constant_a,B: produc1548871597um_a_b,R: set_Pr409224873um_a_b,A3: set_St761939237tant_a] :
% 0.29/0.46        ( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ A @ B ) @ R )
% 0.29/0.46       => ( ( member1632892294tant_a @ A @ A3 )
% 0.29/0.46         => ( member947389014um_a_b @ B @ ( image_2023280617um_a_b @ R @ A3 ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % ImageI
% 0.29/0.46  thf(fact_51_ImageI,axiom,
% 0.29/0.46      ! [A: produc1124793815um_a_b,B: produc1124793815um_a_b,R: set_Pr45173959um_a_b,A3: set_Pr1174980151um_a_b] :
% 0.29/0.46        ( ( member429827856um_a_b @ ( produc27163479um_a_b @ A @ B ) @ R )
% 0.29/0.46       => ( ( member1294585472um_a_b @ A @ A3 )
% 0.29/0.46         => ( member1294585472um_a_b @ B @ ( image_1464989587um_a_b @ R @ A3 ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % ImageI
% 0.29/0.46  thf(fact_52_ImageI,axiom,
% 0.29/0.46      ! [A: sum_sum_a_b,B: produc1963079155um_a_b,R: set_Pr1558970842um_a_b,A3: set_Sum_sum_a_b] :
% 0.29/0.46        ( ( member1641922979um_a_b @ ( produc230853810um_a_b @ A @ B ) @ R )
% 0.29/0.46       => ( ( member_Sum_sum_a_b @ A @ A3 )
% 0.29/0.46         => ( member1998628618um_a_b @ B @ ( image_1482984686um_a_b @ R @ A3 ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % ImageI
% 0.29/0.46  thf(fact_53_ImageI,axiom,
% 0.29/0.46      ! [A: produc1963079155um_a_b,B: sum_sum_a_b,R: set_Pr1121389018um_a_b,A3: set_Pr409224873um_a_b] :
% 0.29/0.46        ( ( member1590479267um_a_b @ ( produc522766386um_a_b @ A @ B ) @ R )
% 0.29/0.46       => ( ( member1998628618um_a_b @ A @ A3 )
% 0.29/0.46         => ( member_Sum_sum_a_b @ B @ ( image_1774897262um_a_b @ R @ A3 ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % ImageI
% 0.29/0.46  thf(fact_54_Image__empty2,axiom,
% 0.29/0.46      ! [R2: set_Pr1986765409at_nat] :
% 0.29/0.46        ( ( image_nat_nat @ R2 @ bot_bot_set_nat )
% 0.29/0.46        = bot_bot_set_nat ) ).
% 0.29/0.46  
% 0.29/0.46  % Image_empty2
% 0.29/0.46  thf(fact_55_Image__empty2,axiom,
% 0.29/0.46      ! [R2: set_Pr1174980151um_a_b] :
% 0.29/0.46        ( ( image_256773707um_a_b @ R2 @ bot_bot_set_nat )
% 0.29/0.46        = bot_bo1491243248um_a_b ) ).
% 0.29/0.46  
% 0.29/0.46  % Image_empty2
% 0.29/0.46  thf(fact_56_Image__empty2,axiom,
% 0.29/0.46      ! [R2: set_Pr375490359_b_nat] :
% 0.29/0.46        ( ( image_1117854795_b_nat @ R2 @ bot_bo1491243248um_a_b )
% 0.29/0.46        = bot_bot_set_nat ) ).
% 0.29/0.46  
% 0.29/0.46  % Image_empty2
% 0.29/0.46  thf(fact_57_Image__empty2,axiom,
% 0.29/0.46      ! [R2: set_Pr1618094130um_a_b] :
% 0.29/0.46        ( ( image_1228479730um_a_b @ R2 @ bot_bot_set_nat )
% 0.29/0.46        = bot_bo575978147um_a_b ) ).
% 0.29/0.46  
% 0.29/0.46  % Image_empty2
% 0.29/0.46  thf(fact_58_Image__empty2,axiom,
% 0.29/0.46      ! [R2: set_Pr1902304780_b_nat] :
% 0.29/0.46        ( ( image_128716052_b_nat @ R2 @ bot_bo575978147um_a_b )
% 0.29/0.46        = bot_bot_set_nat ) ).
% 0.29/0.46  
% 0.29/0.46  % Image_empty2
% 0.29/0.46  thf(fact_59_Image__empty2,axiom,
% 0.29/0.46      ! [R2: set_Pr1916610317um_a_b] :
% 0.29/0.46        ( ( image_1918588449um_a_b @ R2 @ bot_bo1491243248um_a_b )
% 0.29/0.46        = bot_bo1491243248um_a_b ) ).
% 0.29/0.46  
% 0.29/0.46  % Image_empty2
% 0.29/0.46  thf(fact_60_Image__empty2,axiom,
% 0.29/0.46      ! [R2: set_Pr689416536at_nat] :
% 0.29/0.46        ( ( image_452296684at_nat @ R2 @ bot_bo810816657at_nat )
% 0.29/0.46        = bot_bot_set_nat ) ).
% 0.29/0.46  
% 0.29/0.46  % Image_empty2
% 0.29/0.46  thf(fact_61_Image__empty2,axiom,
% 0.29/0.46      ! [R2: set_Pr1134469976at_nat] :
% 0.29/0.46        ( ( image_489788268at_nat @ R2 @ bot_bot_set_nat )
% 0.29/0.46        = bot_bo810816657at_nat ) ).
% 0.29/0.46  
% 0.29/0.46  % Image_empty2
% 0.29/0.46  thf(fact_62_Image__empty2,axiom,
% 0.29/0.46      ! [R2: set_Pr1155046920um_a_b] :
% 0.29/0.46        ( ( image_166667464um_a_b @ R2 @ bot_bot_set_nat )
% 0.29/0.46        = bot_bo225809273um_a_b ) ).
% 0.29/0.46  
% 0.29/0.46  % Image_empty2
% 0.29/0.46  thf(fact_63_Image__empty2,axiom,
% 0.29/0.46      ! [R2: set_Pr653770722um_a_b] :
% 0.29/0.46        ( ( image_869585130um_a_b @ R2 @ bot_bo575978147um_a_b )
% 0.29/0.46        = bot_bo1491243248um_a_b ) ).
% 0.29/0.46  
% 0.29/0.46  % Image_empty2
% 0.29/0.46  thf(fact_64_vertices__restrict,axiom,
% 0.29/0.46      ! [G: labele935650037_a_nat] :
% 0.29/0.46        ( ( labele1810595089_a_nat @ ( restri572569417_a_nat @ G ) )
% 0.29/0.46        = ( labele1810595089_a_nat @ G ) ) ).
% 0.29/0.46  
% 0.29/0.46  % vertices_restrict
% 0.29/0.46  thf(fact_65_vertices__restrict,axiom,
% 0.29/0.46      ! [G: labele431970251um_a_b] :
% 0.29/0.46        ( ( labele577278695um_a_b @ ( restri1162247455um_a_b @ G ) )
% 0.29/0.46        = ( labele577278695um_a_b @ G ) ) ).
% 0.29/0.46  
% 0.29/0.46  % vertices_restrict
% 0.29/0.46  thf(fact_66__092_060open_062graph__homomorphism_A_ILG_A_123_125_A_1230_125_J_AG_Af_092_060close_062,axiom,
% 0.29/0.46      graph_1452133198um_a_b @ ( labele16114835_a_nat @ bot_bo810816657at_nat @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) @ g @ f ).
% 0.29/0.46  
% 0.29/0.46  % \<open>graph_homomorphism (LG {} {0}) G f\<close>
% 0.29/0.46  thf(fact_67_labeled__graph_Oexhaust,axiom,
% 0.29/0.46      ! [Y: labele935650037_a_nat] :
% 0.29/0.46        ~ ! [X12: set_Pr1647387645at_nat,X23: set_nat] :
% 0.29/0.46            ( Y
% 0.29/0.46           != ( labele16114835_a_nat @ X12 @ X23 ) ) ).
% 0.29/0.46  
% 0.29/0.46  % labeled_graph.exhaust
% 0.29/0.46  thf(fact_68_labeled__graph_Oexhaust,axiom,
% 0.29/0.46      ! [Y: labele431970251um_a_b] :
% 0.29/0.46        ~ ! [X12: set_Pr409224873um_a_b,X23: set_Sum_sum_a_b] :
% 0.29/0.46            ( Y
% 0.29/0.46           != ( labele1729654377um_a_b @ X12 @ X23 ) ) ).
% 0.29/0.46  
% 0.29/0.46  % labeled_graph.exhaust
% 0.29/0.46  thf(fact_69_labeled__graph_Oinduct,axiom,
% 0.29/0.46      ! [P: labele935650037_a_nat > $o,Labeled_graph: labele935650037_a_nat] :
% 0.29/0.46        ( ! [X1a: set_Pr1647387645at_nat,X2a: set_nat] : ( P @ ( labele16114835_a_nat @ X1a @ X2a ) )
% 0.29/0.46       => ( P @ Labeled_graph ) ) ).
% 0.29/0.46  
% 0.29/0.46  % labeled_graph.induct
% 0.29/0.46  thf(fact_70_labeled__graph_Oinduct,axiom,
% 0.29/0.46      ! [P: labele431970251um_a_b > $o,Labeled_graph: labele431970251um_a_b] :
% 0.29/0.46        ( ! [X1a: set_Pr409224873um_a_b,X2a: set_Sum_sum_a_b] : ( P @ ( labele1729654377um_a_b @ X1a @ X2a ) )
% 0.29/0.46       => ( P @ Labeled_graph ) ) ).
% 0.29/0.46  
% 0.29/0.46  % labeled_graph.induct
% 0.29/0.46  thf(fact_71_rev__ImageI,axiom,
% 0.29/0.46      ! [A: nat,A3: set_nat,B: nat,R: set_Pr1986765409at_nat] :
% 0.29/0.46        ( ( member_nat @ A @ A3 )
% 0.29/0.46       => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R )
% 0.29/0.46         => ( member_nat @ B @ ( image_nat_nat @ R @ A3 ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % rev_ImageI
% 0.29/0.46  thf(fact_72_rev__ImageI,axiom,
% 0.29/0.46      ! [A: nat,A3: set_nat,B: sum_sum_a_b,R: set_Pr1174980151um_a_b] :
% 0.29/0.46        ( ( member_nat @ A @ A3 )
% 0.29/0.46       => ( ( member1294585472um_a_b @ ( produc1808556047um_a_b @ A @ B ) @ R )
% 0.29/0.46         => ( member_Sum_sum_a_b @ B @ ( image_256773707um_a_b @ R @ A3 ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % rev_ImageI
% 0.29/0.46  thf(fact_73_rev__ImageI,axiom,
% 0.29/0.46      ! [A: standard_Constant_a,A3: set_St761939237tant_a,B: product_prod_nat_nat,R: set_Pr1647387645at_nat] :
% 0.29/0.46        ( ( member1632892294tant_a @ A @ A3 )
% 0.29/0.46       => ( ( member1696759390at_nat @ ( produc407553657at_nat @ A @ B ) @ R )
% 0.29/0.46         => ( member701585322at_nat @ B @ ( image_127502653at_nat @ R @ A3 ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % rev_ImageI
% 0.29/0.46  thf(fact_74_rev__ImageI,axiom,
% 0.29/0.46      ! [A: sum_sum_a_b,A3: set_Sum_sum_a_b,B: sum_sum_a_b,R: set_Pr1916610317um_a_b] :
% 0.29/0.46        ( ( member_Sum_sum_a_b @ A @ A3 )
% 0.29/0.46       => ( ( member947389014um_a_b @ ( produc176426981um_a_b @ A @ B ) @ R )
% 0.29/0.46         => ( member_Sum_sum_a_b @ B @ ( image_1918588449um_a_b @ R @ A3 ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % rev_ImageI
% 0.29/0.46  thf(fact_75_rev__ImageI,axiom,
% 0.29/0.46      ! [A: sum_sum_a_b,A3: set_Sum_sum_a_b,B: produc1124793815um_a_b,R: set_Pr1783309276um_a_b] :
% 0.29/0.46        ( ( member_Sum_sum_a_b @ A @ A3 )
% 0.29/0.46       => ( ( member485470653um_a_b @ ( produc1637282520um_a_b @ A @ B ) @ R )
% 0.29/0.46         => ( member1294585472um_a_b @ B @ ( image_1675391388um_a_b @ R @ A3 ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % rev_ImageI
% 0.29/0.46  thf(fact_76_rev__ImageI,axiom,
% 0.29/0.46      ! [A: produc1124793815um_a_b,A3: set_Pr1174980151um_a_b,B: sum_sum_a_b,R: set_Pr653770722um_a_b] :
% 0.29/0.46        ( ( member1294585472um_a_b @ A @ A3 )
% 0.29/0.46       => ( ( member748122307um_a_b @ ( produc831476262um_a_b @ A @ B ) @ R )
% 0.29/0.46         => ( member_Sum_sum_a_b @ B @ ( image_869585130um_a_b @ R @ A3 ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % rev_ImageI
% 0.29/0.46  thf(fact_77_rev__ImageI,axiom,
% 0.29/0.46      ! [A: standard_Constant_a,A3: set_St761939237tant_a,B: produc1548871597um_a_b,R: set_Pr409224873um_a_b] :
% 0.29/0.46        ( ( member1632892294tant_a @ A @ A3 )
% 0.29/0.46       => ( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ A @ B ) @ R )
% 0.29/0.46         => ( member947389014um_a_b @ B @ ( image_2023280617um_a_b @ R @ A3 ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % rev_ImageI
% 0.29/0.46  thf(fact_78_rev__ImageI,axiom,
% 0.29/0.46      ! [A: produc1124793815um_a_b,A3: set_Pr1174980151um_a_b,B: produc1124793815um_a_b,R: set_Pr45173959um_a_b] :
% 0.29/0.46        ( ( member1294585472um_a_b @ A @ A3 )
% 0.29/0.46       => ( ( member429827856um_a_b @ ( produc27163479um_a_b @ A @ B ) @ R )
% 0.29/0.46         => ( member1294585472um_a_b @ B @ ( image_1464989587um_a_b @ R @ A3 ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % rev_ImageI
% 0.29/0.46  thf(fact_79_rev__ImageI,axiom,
% 0.29/0.46      ! [A: sum_sum_a_b,A3: set_Sum_sum_a_b,B: produc1963079155um_a_b,R: set_Pr1558970842um_a_b] :
% 0.29/0.46        ( ( member_Sum_sum_a_b @ A @ A3 )
% 0.29/0.46       => ( ( member1641922979um_a_b @ ( produc230853810um_a_b @ A @ B ) @ R )
% 0.29/0.46         => ( member1998628618um_a_b @ B @ ( image_1482984686um_a_b @ R @ A3 ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % rev_ImageI
% 0.29/0.46  thf(fact_80_rev__ImageI,axiom,
% 0.29/0.46      ! [A: produc1963079155um_a_b,A3: set_Pr409224873um_a_b,B: sum_sum_a_b,R: set_Pr1121389018um_a_b] :
% 0.29/0.46        ( ( member1998628618um_a_b @ A @ A3 )
% 0.29/0.46       => ( ( member1590479267um_a_b @ ( produc522766386um_a_b @ A @ B ) @ R )
% 0.29/0.46         => ( member_Sum_sum_a_b @ B @ ( image_1774897262um_a_b @ R @ A3 ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % rev_ImageI
% 0.29/0.46  thf(fact_81_Image__iff,axiom,
% 0.29/0.46      ! [B: product_prod_nat_nat,R: set_Pr1647387645at_nat,A3: set_St761939237tant_a] :
% 0.29/0.46        ( ( member701585322at_nat @ B @ ( image_127502653at_nat @ R @ A3 ) )
% 0.29/0.46        = ( ? [X3: standard_Constant_a] :
% 0.29/0.46              ( ( member1632892294tant_a @ X3 @ A3 )
% 0.29/0.46              & ( member1696759390at_nat @ ( produc407553657at_nat @ X3 @ B ) @ R ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Image_iff
% 0.29/0.46  thf(fact_82_Image__iff,axiom,
% 0.29/0.46      ! [B: nat,R: set_Pr1986765409at_nat,A3: set_nat] :
% 0.29/0.46        ( ( member_nat @ B @ ( image_nat_nat @ R @ A3 ) )
% 0.29/0.46        = ( ? [X3: nat] :
% 0.29/0.46              ( ( member_nat @ X3 @ A3 )
% 0.29/0.46              & ( member701585322at_nat @ ( product_Pair_nat_nat @ X3 @ B ) @ R ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Image_iff
% 0.29/0.46  thf(fact_83_Image__iff,axiom,
% 0.29/0.46      ! [B: sum_sum_a_b,R: set_Pr1174980151um_a_b,A3: set_nat] :
% 0.29/0.46        ( ( member_Sum_sum_a_b @ B @ ( image_256773707um_a_b @ R @ A3 ) )
% 0.29/0.46        = ( ? [X3: nat] :
% 0.29/0.46              ( ( member_nat @ X3 @ A3 )
% 0.29/0.46              & ( member1294585472um_a_b @ ( produc1808556047um_a_b @ X3 @ B ) @ R ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Image_iff
% 0.29/0.46  thf(fact_84_Image__iff,axiom,
% 0.29/0.46      ! [B: produc1548871597um_a_b,R: set_Pr409224873um_a_b,A3: set_St761939237tant_a] :
% 0.29/0.46        ( ( member947389014um_a_b @ B @ ( image_2023280617um_a_b @ R @ A3 ) )
% 0.29/0.46        = ( ? [X3: standard_Constant_a] :
% 0.29/0.46              ( ( member1632892294tant_a @ X3 @ A3 )
% 0.29/0.46              & ( member1998628618um_a_b @ ( produc1697725733um_a_b @ X3 @ B ) @ R ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Image_iff
% 0.29/0.46  thf(fact_85_Image__iff,axiom,
% 0.29/0.46      ! [B: sum_sum_a_b,R: set_Pr1916610317um_a_b,A3: set_Sum_sum_a_b] :
% 0.29/0.46        ( ( member_Sum_sum_a_b @ B @ ( image_1918588449um_a_b @ R @ A3 ) )
% 0.29/0.46        = ( ? [X3: sum_sum_a_b] :
% 0.29/0.46              ( ( member_Sum_sum_a_b @ X3 @ A3 )
% 0.29/0.46              & ( member947389014um_a_b @ ( produc176426981um_a_b @ X3 @ B ) @ R ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Image_iff
% 0.29/0.46  thf(fact_86_ImageE,axiom,
% 0.29/0.46      ! [B: nat,R: set_Pr1986765409at_nat,A3: set_nat] :
% 0.29/0.46        ( ( member_nat @ B @ ( image_nat_nat @ R @ A3 ) )
% 0.29/0.46       => ~ ! [X4: nat] :
% 0.29/0.46              ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X4 @ B ) @ R )
% 0.29/0.46             => ~ ( member_nat @ X4 @ A3 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % ImageE
% 0.29/0.46  thf(fact_87_ImageE,axiom,
% 0.29/0.46      ! [B: sum_sum_a_b,R: set_Pr1174980151um_a_b,A3: set_nat] :
% 0.29/0.46        ( ( member_Sum_sum_a_b @ B @ ( image_256773707um_a_b @ R @ A3 ) )
% 0.29/0.46       => ~ ! [X4: nat] :
% 0.29/0.46              ( ( member1294585472um_a_b @ ( produc1808556047um_a_b @ X4 @ B ) @ R )
% 0.29/0.46             => ~ ( member_nat @ X4 @ A3 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % ImageE
% 0.29/0.46  thf(fact_88_ImageE,axiom,
% 0.29/0.46      ! [B: product_prod_nat_nat,R: set_Pr1647387645at_nat,A3: set_St761939237tant_a] :
% 0.29/0.46        ( ( member701585322at_nat @ B @ ( image_127502653at_nat @ R @ A3 ) )
% 0.29/0.46       => ~ ! [X4: standard_Constant_a] :
% 0.29/0.46              ( ( member1696759390at_nat @ ( produc407553657at_nat @ X4 @ B ) @ R )
% 0.29/0.46             => ~ ( member1632892294tant_a @ X4 @ A3 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % ImageE
% 0.29/0.46  thf(fact_89_ImageE,axiom,
% 0.29/0.46      ! [B: sum_sum_a_b,R: set_Pr1916610317um_a_b,A3: set_Sum_sum_a_b] :
% 0.29/0.46        ( ( member_Sum_sum_a_b @ B @ ( image_1918588449um_a_b @ R @ A3 ) )
% 0.29/0.46       => ~ ! [X4: sum_sum_a_b] :
% 0.29/0.46              ( ( member947389014um_a_b @ ( produc176426981um_a_b @ X4 @ B ) @ R )
% 0.29/0.46             => ~ ( member_Sum_sum_a_b @ X4 @ A3 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % ImageE
% 0.29/0.46  thf(fact_90_ImageE,axiom,
% 0.29/0.46      ! [B: sum_sum_a_b,R: set_Pr653770722um_a_b,A3: set_Pr1174980151um_a_b] :
% 0.29/0.46        ( ( member_Sum_sum_a_b @ B @ ( image_869585130um_a_b @ R @ A3 ) )
% 0.29/0.46       => ~ ! [X4: produc1124793815um_a_b] :
% 0.29/0.46              ( ( member748122307um_a_b @ ( produc831476262um_a_b @ X4 @ B ) @ R )
% 0.29/0.46             => ~ ( member1294585472um_a_b @ X4 @ A3 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % ImageE
% 0.29/0.46  thf(fact_91_ImageE,axiom,
% 0.29/0.46      ! [B: produc1124793815um_a_b,R: set_Pr1783309276um_a_b,A3: set_Sum_sum_a_b] :
% 0.29/0.46        ( ( member1294585472um_a_b @ B @ ( image_1675391388um_a_b @ R @ A3 ) )
% 0.29/0.46       => ~ ! [X4: sum_sum_a_b] :
% 0.29/0.46              ( ( member485470653um_a_b @ ( produc1637282520um_a_b @ X4 @ B ) @ R )
% 0.29/0.46             => ~ ( member_Sum_sum_a_b @ X4 @ A3 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % ImageE
% 0.29/0.46  thf(fact_92_ImageE,axiom,
% 0.29/0.46      ! [B: produc1548871597um_a_b,R: set_Pr409224873um_a_b,A3: set_St761939237tant_a] :
% 0.29/0.46        ( ( member947389014um_a_b @ B @ ( image_2023280617um_a_b @ R @ A3 ) )
% 0.29/0.46       => ~ ! [X4: standard_Constant_a] :
% 0.29/0.46              ( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ X4 @ B ) @ R )
% 0.29/0.46             => ~ ( member1632892294tant_a @ X4 @ A3 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % ImageE
% 0.29/0.46  thf(fact_93_ImageE,axiom,
% 0.29/0.46      ! [B: produc1124793815um_a_b,R: set_Pr45173959um_a_b,A3: set_Pr1174980151um_a_b] :
% 0.29/0.46        ( ( member1294585472um_a_b @ B @ ( image_1464989587um_a_b @ R @ A3 ) )
% 0.29/0.46       => ~ ! [X4: produc1124793815um_a_b] :
% 0.29/0.46              ( ( member429827856um_a_b @ ( produc27163479um_a_b @ X4 @ B ) @ R )
% 0.29/0.46             => ~ ( member1294585472um_a_b @ X4 @ A3 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % ImageE
% 0.29/0.46  thf(fact_94_ImageE,axiom,
% 0.29/0.46      ! [B: sum_sum_a_b,R: set_Pr1121389018um_a_b,A3: set_Pr409224873um_a_b] :
% 0.29/0.46        ( ( member_Sum_sum_a_b @ B @ ( image_1774897262um_a_b @ R @ A3 ) )
% 0.29/0.46       => ~ ! [X4: produc1963079155um_a_b] :
% 0.29/0.46              ( ( member1590479267um_a_b @ ( produc522766386um_a_b @ X4 @ B ) @ R )
% 0.29/0.46             => ~ ( member1998628618um_a_b @ X4 @ A3 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % ImageE
% 0.29/0.46  thf(fact_95_ImageE,axiom,
% 0.29/0.46      ! [B: produc1963079155um_a_b,R: set_Pr1558970842um_a_b,A3: set_Sum_sum_a_b] :
% 0.29/0.46        ( ( member1998628618um_a_b @ B @ ( image_1482984686um_a_b @ R @ A3 ) )
% 0.29/0.46       => ~ ! [X4: sum_sum_a_b] :
% 0.29/0.46              ( ( member1641922979um_a_b @ ( produc230853810um_a_b @ X4 @ B ) @ R )
% 0.29/0.46             => ~ ( member_Sum_sum_a_b @ X4 @ A3 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % ImageE
% 0.29/0.46  thf(fact_96_Image__mono,axiom,
% 0.29/0.46      ! [R3: set_Pr1174980151um_a_b,R: set_Pr1174980151um_a_b,A4: set_nat,A3: set_nat] :
% 0.29/0.46        ( ( ord_le823954903um_a_b @ R3 @ R )
% 0.29/0.46       => ( ( ord_less_eq_set_nat @ A4 @ A3 )
% 0.29/0.46         => ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ R3 @ A4 ) @ ( image_256773707um_a_b @ R @ A3 ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Image_mono
% 0.29/0.46  thf(fact_97_Image__mono,axiom,
% 0.29/0.46      ! [R3: set_Pr1916610317um_a_b,R: set_Pr1916610317um_a_b,A4: set_Sum_sum_a_b,A3: set_Sum_sum_a_b] :
% 0.29/0.46        ( ( ord_le1059794605um_a_b @ R3 @ R )
% 0.29/0.46       => ( ( ord_le192794300um_a_b @ A4 @ A3 )
% 0.29/0.46         => ( ord_le192794300um_a_b @ ( image_1918588449um_a_b @ R3 @ A4 ) @ ( image_1918588449um_a_b @ R @ A3 ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Image_mono
% 0.29/0.46  thf(fact_98_Domain_Oinducts,axiom,
% 0.29/0.46      ! [X2: standard_Constant_a,R: set_Pr1647387645at_nat,P: standard_Constant_a > $o] :
% 0.29/0.46        ( ( member1632892294tant_a @ X2 @ ( domain1060562500at_nat @ R ) )
% 0.29/0.46       => ( ! [A5: standard_Constant_a,B3: product_prod_nat_nat] :
% 0.29/0.46              ( ( member1696759390at_nat @ ( produc407553657at_nat @ A5 @ B3 ) @ R )
% 0.29/0.46             => ( P @ A5 ) )
% 0.29/0.46         => ( P @ X2 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain.inducts
% 0.29/0.46  thf(fact_99_Domain_Oinducts,axiom,
% 0.29/0.46      ! [X2: nat,R: set_Pr1986765409at_nat,P: nat > $o] :
% 0.29/0.46        ( ( member_nat @ X2 @ ( domain_nat_nat @ R ) )
% 0.29/0.46       => ( ! [A5: nat,B3: nat] :
% 0.29/0.46              ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A5 @ B3 ) @ R )
% 0.29/0.46             => ( P @ A5 ) )
% 0.29/0.46         => ( P @ X2 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain.inducts
% 0.29/0.46  thf(fact_100_Domain_Oinducts,axiom,
% 0.29/0.46      ! [X2: nat,R: set_Pr1174980151um_a_b,P: nat > $o] :
% 0.29/0.46        ( ( member_nat @ X2 @ ( domain1368163076um_a_b @ R ) )
% 0.29/0.46       => ( ! [A5: nat,B3: sum_sum_a_b] :
% 0.29/0.46              ( ( member1294585472um_a_b @ ( produc1808556047um_a_b @ A5 @ B3 ) @ R )
% 0.29/0.46             => ( P @ A5 ) )
% 0.29/0.46         => ( P @ X2 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain.inducts
% 0.29/0.46  thf(fact_101_Domain_Oinducts,axiom,
% 0.29/0.46      ! [X2: standard_Constant_a,R: set_Pr409224873um_a_b,P: standard_Constant_a > $o] :
% 0.29/0.46        ( ( member1632892294tant_a @ X2 @ ( domain1362581744um_a_b @ R ) )
% 0.29/0.46       => ( ! [A5: standard_Constant_a,B3: produc1548871597um_a_b] :
% 0.29/0.46              ( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ A5 @ B3 ) @ R )
% 0.29/0.46             => ( P @ A5 ) )
% 0.29/0.46         => ( P @ X2 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain.inducts
% 0.29/0.46  thf(fact_102_Domain_Oinducts,axiom,
% 0.29/0.46      ! [X2: sum_sum_a_b,R: set_Pr1916610317um_a_b,P: sum_sum_a_b > $o] :
% 0.29/0.46        ( ( member_Sum_sum_a_b @ X2 @ ( domain2069673178um_a_b @ R ) )
% 0.29/0.46       => ( ! [A5: sum_sum_a_b,B3: sum_sum_a_b] :
% 0.29/0.46              ( ( member947389014um_a_b @ ( produc176426981um_a_b @ A5 @ B3 ) @ R )
% 0.29/0.46             => ( P @ A5 ) )
% 0.29/0.46         => ( P @ X2 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain.inducts
% 0.29/0.46  thf(fact_103_Domain_ODomainI,axiom,
% 0.29/0.46      ! [A: standard_Constant_a,B: product_prod_nat_nat,R: set_Pr1647387645at_nat] :
% 0.29/0.46        ( ( member1696759390at_nat @ ( produc407553657at_nat @ A @ B ) @ R )
% 0.29/0.46       => ( member1632892294tant_a @ A @ ( domain1060562500at_nat @ R ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain.DomainI
% 0.29/0.46  thf(fact_104_Domain_ODomainI,axiom,
% 0.29/0.46      ! [A: nat,B: nat,R: set_Pr1986765409at_nat] :
% 0.29/0.46        ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R )
% 0.29/0.46       => ( member_nat @ A @ ( domain_nat_nat @ R ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain.DomainI
% 0.29/0.46  thf(fact_105_Domain_ODomainI,axiom,
% 0.29/0.46      ! [A: nat,B: sum_sum_a_b,R: set_Pr1174980151um_a_b] :
% 0.29/0.46        ( ( member1294585472um_a_b @ ( produc1808556047um_a_b @ A @ B ) @ R )
% 0.29/0.46       => ( member_nat @ A @ ( domain1368163076um_a_b @ R ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain.DomainI
% 0.29/0.46  thf(fact_106_Domain_ODomainI,axiom,
% 0.29/0.46      ! [A: standard_Constant_a,B: produc1548871597um_a_b,R: set_Pr409224873um_a_b] :
% 0.29/0.46        ( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ A @ B ) @ R )
% 0.29/0.46       => ( member1632892294tant_a @ A @ ( domain1362581744um_a_b @ R ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain.DomainI
% 0.29/0.46  thf(fact_107_Domain_ODomainI,axiom,
% 0.29/0.46      ! [A: sum_sum_a_b,B: sum_sum_a_b,R: set_Pr1916610317um_a_b] :
% 0.29/0.46        ( ( member947389014um_a_b @ ( produc176426981um_a_b @ A @ B ) @ R )
% 0.29/0.46       => ( member_Sum_sum_a_b @ A @ ( domain2069673178um_a_b @ R ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain.DomainI
% 0.29/0.46  thf(fact_108_Domain_Osimps,axiom,
% 0.29/0.46      ! [A: standard_Constant_a,R: set_Pr1647387645at_nat] :
% 0.29/0.46        ( ( member1632892294tant_a @ A @ ( domain1060562500at_nat @ R ) )
% 0.29/0.46        = ( ? [A6: standard_Constant_a,B4: product_prod_nat_nat] :
% 0.29/0.46              ( ( A = A6 )
% 0.29/0.46              & ( member1696759390at_nat @ ( produc407553657at_nat @ A6 @ B4 ) @ R ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain.simps
% 0.29/0.46  thf(fact_109_Domain_Osimps,axiom,
% 0.29/0.46      ! [A: nat,R: set_Pr1986765409at_nat] :
% 0.29/0.46        ( ( member_nat @ A @ ( domain_nat_nat @ R ) )
% 0.29/0.46        = ( ? [A6: nat,B4: nat] :
% 0.29/0.46              ( ( A = A6 )
% 0.29/0.46              & ( member701585322at_nat @ ( product_Pair_nat_nat @ A6 @ B4 ) @ R ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain.simps
% 0.29/0.46  thf(fact_110_Domain_Osimps,axiom,
% 0.29/0.46      ! [A: nat,R: set_Pr1174980151um_a_b] :
% 0.29/0.46        ( ( member_nat @ A @ ( domain1368163076um_a_b @ R ) )
% 0.29/0.46        = ( ? [A6: nat,B4: sum_sum_a_b] :
% 0.29/0.46              ( ( A = A6 )
% 0.29/0.46              & ( member1294585472um_a_b @ ( produc1808556047um_a_b @ A6 @ B4 ) @ R ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain.simps
% 0.29/0.46  thf(fact_111_Domain_Osimps,axiom,
% 0.29/0.46      ! [A: standard_Constant_a,R: set_Pr409224873um_a_b] :
% 0.29/0.46        ( ( member1632892294tant_a @ A @ ( domain1362581744um_a_b @ R ) )
% 0.29/0.46        = ( ? [A6: standard_Constant_a,B4: produc1548871597um_a_b] :
% 0.29/0.46              ( ( A = A6 )
% 0.29/0.46              & ( member1998628618um_a_b @ ( produc1697725733um_a_b @ A6 @ B4 ) @ R ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain.simps
% 0.29/0.46  thf(fact_112_Domain_Osimps,axiom,
% 0.29/0.46      ! [A: sum_sum_a_b,R: set_Pr1916610317um_a_b] :
% 0.29/0.46        ( ( member_Sum_sum_a_b @ A @ ( domain2069673178um_a_b @ R ) )
% 0.29/0.46        = ( ? [A6: sum_sum_a_b,B4: sum_sum_a_b] :
% 0.29/0.46              ( ( A = A6 )
% 0.29/0.46              & ( member947389014um_a_b @ ( produc176426981um_a_b @ A6 @ B4 ) @ R ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain.simps
% 0.29/0.46  thf(fact_113_Domain_Ocases,axiom,
% 0.29/0.46      ! [A: standard_Constant_a,R: set_Pr1647387645at_nat] :
% 0.29/0.46        ( ( member1632892294tant_a @ A @ ( domain1060562500at_nat @ R ) )
% 0.29/0.46       => ~ ! [B3: product_prod_nat_nat] :
% 0.29/0.46              ~ ( member1696759390at_nat @ ( produc407553657at_nat @ A @ B3 ) @ R ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain.cases
% 0.29/0.46  thf(fact_114_Domain_Ocases,axiom,
% 0.29/0.46      ! [A: nat,R: set_Pr1986765409at_nat] :
% 0.29/0.46        ( ( member_nat @ A @ ( domain_nat_nat @ R ) )
% 0.29/0.46       => ~ ! [B3: nat] :
% 0.29/0.46              ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B3 ) @ R ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain.cases
% 0.29/0.46  thf(fact_115_Domain_Ocases,axiom,
% 0.29/0.46      ! [A: nat,R: set_Pr1174980151um_a_b] :
% 0.29/0.46        ( ( member_nat @ A @ ( domain1368163076um_a_b @ R ) )
% 0.29/0.46       => ~ ! [B3: sum_sum_a_b] :
% 0.29/0.46              ~ ( member1294585472um_a_b @ ( produc1808556047um_a_b @ A @ B3 ) @ R ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain.cases
% 0.29/0.46  thf(fact_116_Domain_Ocases,axiom,
% 0.29/0.46      ! [A: standard_Constant_a,R: set_Pr409224873um_a_b] :
% 0.29/0.46        ( ( member1632892294tant_a @ A @ ( domain1362581744um_a_b @ R ) )
% 0.29/0.46       => ~ ! [B3: produc1548871597um_a_b] :
% 0.29/0.46              ~ ( member1998628618um_a_b @ ( produc1697725733um_a_b @ A @ B3 ) @ R ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain.cases
% 0.29/0.46  thf(fact_117_Domain_Ocases,axiom,
% 0.29/0.46      ! [A: sum_sum_a_b,R: set_Pr1916610317um_a_b] :
% 0.29/0.46        ( ( member_Sum_sum_a_b @ A @ ( domain2069673178um_a_b @ R ) )
% 0.29/0.46       => ~ ! [B3: sum_sum_a_b] :
% 0.29/0.46              ~ ( member947389014um_a_b @ ( produc176426981um_a_b @ A @ B3 ) @ R ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain.cases
% 0.29/0.46  thf(fact_118_Domain__iff,axiom,
% 0.29/0.46      ! [A: standard_Constant_a,R: set_Pr1647387645at_nat] :
% 0.29/0.46        ( ( member1632892294tant_a @ A @ ( domain1060562500at_nat @ R ) )
% 0.29/0.46        = ( ? [Y3: product_prod_nat_nat] : ( member1696759390at_nat @ ( produc407553657at_nat @ A @ Y3 ) @ R ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain_iff
% 0.29/0.46  thf(fact_119_Domain__iff,axiom,
% 0.29/0.46      ! [A: nat,R: set_Pr1986765409at_nat] :
% 0.29/0.46        ( ( member_nat @ A @ ( domain_nat_nat @ R ) )
% 0.29/0.46        = ( ? [Y3: nat] : ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ Y3 ) @ R ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain_iff
% 0.29/0.46  thf(fact_120_Domain__iff,axiom,
% 0.29/0.46      ! [A: nat,R: set_Pr1174980151um_a_b] :
% 0.29/0.46        ( ( member_nat @ A @ ( domain1368163076um_a_b @ R ) )
% 0.29/0.46        = ( ? [Y3: sum_sum_a_b] : ( member1294585472um_a_b @ ( produc1808556047um_a_b @ A @ Y3 ) @ R ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain_iff
% 0.29/0.46  thf(fact_121_Domain__iff,axiom,
% 0.29/0.46      ! [A: standard_Constant_a,R: set_Pr409224873um_a_b] :
% 0.29/0.46        ( ( member1632892294tant_a @ A @ ( domain1362581744um_a_b @ R ) )
% 0.29/0.46        = ( ? [Y3: produc1548871597um_a_b] : ( member1998628618um_a_b @ ( produc1697725733um_a_b @ A @ Y3 ) @ R ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain_iff
% 0.29/0.46  thf(fact_122_Domain__iff,axiom,
% 0.29/0.46      ! [A: sum_sum_a_b,R: set_Pr1916610317um_a_b] :
% 0.29/0.46        ( ( member_Sum_sum_a_b @ A @ ( domain2069673178um_a_b @ R ) )
% 0.29/0.46        = ( ? [Y3: sum_sum_a_b] : ( member947389014um_a_b @ ( produc176426981um_a_b @ A @ Y3 ) @ R ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain_iff
% 0.29/0.46  thf(fact_123_DomainE,axiom,
% 0.29/0.46      ! [A: standard_Constant_a,R: set_Pr1647387645at_nat] :
% 0.29/0.46        ( ( member1632892294tant_a @ A @ ( domain1060562500at_nat @ R ) )
% 0.29/0.46       => ~ ! [B3: product_prod_nat_nat] :
% 0.29/0.46              ~ ( member1696759390at_nat @ ( produc407553657at_nat @ A @ B3 ) @ R ) ) ).
% 0.29/0.46  
% 0.29/0.46  % DomainE
% 0.29/0.46  thf(fact_124_DomainE,axiom,
% 0.29/0.46      ! [A: nat,R: set_Pr1986765409at_nat] :
% 0.29/0.46        ( ( member_nat @ A @ ( domain_nat_nat @ R ) )
% 0.29/0.46       => ~ ! [B3: nat] :
% 0.29/0.46              ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B3 ) @ R ) ) ).
% 0.29/0.46  
% 0.29/0.46  % DomainE
% 0.29/0.46  thf(fact_125_DomainE,axiom,
% 0.29/0.46      ! [A: nat,R: set_Pr1174980151um_a_b] :
% 0.29/0.46        ( ( member_nat @ A @ ( domain1368163076um_a_b @ R ) )
% 0.29/0.46       => ~ ! [B3: sum_sum_a_b] :
% 0.29/0.46              ~ ( member1294585472um_a_b @ ( produc1808556047um_a_b @ A @ B3 ) @ R ) ) ).
% 0.29/0.46  
% 0.29/0.46  % DomainE
% 0.29/0.46  thf(fact_126_DomainE,axiom,
% 0.29/0.46      ! [A: standard_Constant_a,R: set_Pr409224873um_a_b] :
% 0.29/0.46        ( ( member1632892294tant_a @ A @ ( domain1362581744um_a_b @ R ) )
% 0.29/0.46       => ~ ! [B3: produc1548871597um_a_b] :
% 0.29/0.46              ~ ( member1998628618um_a_b @ ( produc1697725733um_a_b @ A @ B3 ) @ R ) ) ).
% 0.29/0.46  
% 0.29/0.46  % DomainE
% 0.29/0.46  thf(fact_127_DomainE,axiom,
% 0.29/0.46      ! [A: sum_sum_a_b,R: set_Pr1916610317um_a_b] :
% 0.29/0.46        ( ( member_Sum_sum_a_b @ A @ ( domain2069673178um_a_b @ R ) )
% 0.29/0.46       => ~ ! [B3: sum_sum_a_b] :
% 0.29/0.46              ~ ( member947389014um_a_b @ ( produc176426981um_a_b @ A @ B3 ) @ R ) ) ).
% 0.29/0.46  
% 0.29/0.46  % DomainE
% 0.29/0.46  thf(fact_128_Domain__mono,axiom,
% 0.29/0.46      ! [R: set_Pr1174980151um_a_b,S: set_Pr1174980151um_a_b] :
% 0.29/0.46        ( ( ord_le823954903um_a_b @ R @ S )
% 0.29/0.46       => ( ord_less_eq_set_nat @ ( domain1368163076um_a_b @ R ) @ ( domain1368163076um_a_b @ S ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain_mono
% 0.29/0.46  thf(fact_129_Domain__mono,axiom,
% 0.29/0.46      ! [R: set_Pr409224873um_a_b,S: set_Pr409224873um_a_b] :
% 0.29/0.46        ( ( ord_le615126793um_a_b @ R @ S )
% 0.29/0.46       => ( ord_le1739761029tant_a @ ( domain1362581744um_a_b @ R ) @ ( domain1362581744um_a_b @ S ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain_mono
% 0.29/0.46  thf(fact_130_Domain__mono,axiom,
% 0.29/0.46      ! [R: set_Pr1986765409at_nat,S: set_Pr1986765409at_nat] :
% 0.29/0.46        ( ( ord_le841296385at_nat @ R @ S )
% 0.29/0.46       => ( ord_less_eq_set_nat @ ( domain_nat_nat @ R ) @ ( domain_nat_nat @ S ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain_mono
% 0.29/0.46  thf(fact_131_Domain__mono,axiom,
% 0.29/0.46      ! [R: set_Pr1647387645at_nat,S: set_Pr1647387645at_nat] :
% 0.29/0.46        ( ( ord_le1909159005at_nat @ R @ S )
% 0.29/0.46       => ( ord_le1739761029tant_a @ ( domain1060562500at_nat @ R ) @ ( domain1060562500at_nat @ S ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain_mono
% 0.29/0.46  thf(fact_132_Domain__mono,axiom,
% 0.29/0.46      ! [R: set_Pr1916610317um_a_b,S: set_Pr1916610317um_a_b] :
% 0.29/0.46        ( ( ord_le1059794605um_a_b @ R @ S )
% 0.29/0.46       => ( ord_le192794300um_a_b @ ( domain2069673178um_a_b @ R ) @ ( domain2069673178um_a_b @ S ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain_mono
% 0.29/0.46  thf(fact_133_labeled__graph_Oexpand,axiom,
% 0.29/0.46      ! [Labeled_graph: labele935650037_a_nat,Labeled_graph2: labele935650037_a_nat] :
% 0.29/0.46        ( ( ( ( labele195203296_a_nat @ Labeled_graph )
% 0.29/0.46            = ( labele195203296_a_nat @ Labeled_graph2 ) )
% 0.29/0.46          & ( ( labele1810595089_a_nat @ Labeled_graph )
% 0.29/0.46            = ( labele1810595089_a_nat @ Labeled_graph2 ) ) )
% 0.29/0.46       => ( Labeled_graph = Labeled_graph2 ) ) ).
% 0.29/0.46  
% 0.29/0.46  % labeled_graph.expand
% 0.29/0.46  thf(fact_134_labeled__graph_Oexpand,axiom,
% 0.29/0.46      ! [Labeled_graph: labele431970251um_a_b,Labeled_graph2: labele431970251um_a_b] :
% 0.29/0.46        ( ( ( ( labele1939049654um_a_b @ Labeled_graph )
% 0.29/0.46            = ( labele1939049654um_a_b @ Labeled_graph2 ) )
% 0.29/0.46          & ( ( labele577278695um_a_b @ Labeled_graph )
% 0.29/0.46            = ( labele577278695um_a_b @ Labeled_graph2 ) ) )
% 0.29/0.46       => ( Labeled_graph = Labeled_graph2 ) ) ).
% 0.29/0.46  
% 0.29/0.46  % labeled_graph.expand
% 0.29/0.46  thf(fact_135_labeled__graph_Osel_I2_J,axiom,
% 0.29/0.46      ! [X1: set_Pr1647387645at_nat,X22: set_nat] :
% 0.29/0.46        ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ X1 @ X22 ) )
% 0.29/0.46        = X22 ) ).
% 0.29/0.46  
% 0.29/0.46  % labeled_graph.sel(2)
% 0.29/0.46  thf(fact_136_labeled__graph_Osel_I2_J,axiom,
% 0.29/0.46      ! [X1: set_Pr409224873um_a_b,X22: set_Sum_sum_a_b] :
% 0.29/0.46        ( ( labele577278695um_a_b @ ( labele1729654377um_a_b @ X1 @ X22 ) )
% 0.29/0.46        = X22 ) ).
% 0.29/0.46  
% 0.29/0.46  % labeled_graph.sel(2)
% 0.29/0.46  thf(fact_137_labeled__graph_Osel_I1_J,axiom,
% 0.29/0.46      ! [X1: set_Pr1647387645at_nat,X22: set_nat] :
% 0.29/0.46        ( ( labele195203296_a_nat @ ( labele16114835_a_nat @ X1 @ X22 ) )
% 0.29/0.46        = X1 ) ).
% 0.29/0.46  
% 0.29/0.46  % labeled_graph.sel(1)
% 0.29/0.46  thf(fact_138_labeled__graph_Osel_I1_J,axiom,
% 0.29/0.46      ! [X1: set_Pr409224873um_a_b,X22: set_Sum_sum_a_b] :
% 0.29/0.46        ( ( labele1939049654um_a_b @ ( labele1729654377um_a_b @ X1 @ X22 ) )
% 0.29/0.46        = X1 ) ).
% 0.29/0.46  
% 0.29/0.46  % labeled_graph.sel(1)
% 0.29/0.46  thf(fact_139_Domain__empty__iff,axiom,
% 0.29/0.46      ! [R: set_Pr1647387645at_nat] :
% 0.29/0.46        ( ( ( domain1060562500at_nat @ R )
% 0.29/0.46          = bot_bo1160111033tant_a )
% 0.29/0.46        = ( R = bot_bo810816657at_nat ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain_empty_iff
% 0.29/0.46  thf(fact_140_Domain__empty__iff,axiom,
% 0.29/0.46      ! [R: set_Pr409224873um_a_b] :
% 0.29/0.46        ( ( ( domain1362581744um_a_b @ R )
% 0.29/0.46          = bot_bo1160111033tant_a )
% 0.29/0.46        = ( R = bot_bo1262634813um_a_b ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain_empty_iff
% 0.29/0.46  thf(fact_141_Domain__empty__iff,axiom,
% 0.29/0.46      ! [R: set_Pr1986765409at_nat] :
% 0.29/0.46        ( ( ( domain_nat_nat @ R )
% 0.29/0.46          = bot_bot_set_nat )
% 0.29/0.46        = ( R = bot_bo2130386637at_nat ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain_empty_iff
% 0.29/0.46  thf(fact_142_Domain__empty__iff,axiom,
% 0.29/0.46      ! [R: set_Pr1174980151um_a_b] :
% 0.29/0.46        ( ( ( domain1368163076um_a_b @ R )
% 0.29/0.46          = bot_bot_set_nat )
% 0.29/0.46        = ( R = bot_bo575978147um_a_b ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain_empty_iff
% 0.29/0.46  thf(fact_143_Domain__empty__iff,axiom,
% 0.29/0.46      ! [R: set_Pr1916610317um_a_b] :
% 0.29/0.46        ( ( ( domain2069673178um_a_b @ R )
% 0.29/0.46          = bot_bo1491243248um_a_b )
% 0.29/0.46        = ( R = bot_bo225809273um_a_b ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Domain_empty_iff
% 0.29/0.46  thf(fact_144_edge__preserving__atomic,axiom,
% 0.29/0.46      ! [H1: set_Pr375490359_b_nat,E1: set_Pr409224873um_a_b,E2: set_Pr1647387645at_nat,V1: sum_sum_a_b,V12: nat,V22: sum_sum_a_b,V23: nat,K: standard_Constant_a] :
% 0.29/0.46        ( ( edge_p749155930tant_a @ H1 @ E1 @ E2 )
% 0.29/0.46       => ( ( member1249152_b_nat @ ( produc522153487_b_nat @ V1 @ V12 ) @ H1 )
% 0.29/0.46         => ( ( member1249152_b_nat @ ( produc522153487_b_nat @ V22 @ V23 ) @ H1 )
% 0.29/0.46           => ( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ K @ ( produc176426981um_a_b @ V1 @ V22 ) ) @ E1 )
% 0.29/0.46             => ( member1696759390at_nat @ ( produc407553657at_nat @ K @ ( product_Pair_nat_nat @ V12 @ V23 ) ) @ E2 ) ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % edge_preserving_atomic
% 0.29/0.46  thf(fact_145_edge__preserving__atomic,axiom,
% 0.29/0.46      ! [H1: set_Pr1986765409at_nat,E1: set_Pr1647387645at_nat,E2: set_Pr1647387645at_nat,V1: nat,V12: nat,V22: nat,V23: nat,K: standard_Constant_a] :
% 0.29/0.46        ( ( edge_p170421892tant_a @ H1 @ E1 @ E2 )
% 0.29/0.46       => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ V1 @ V12 ) @ H1 )
% 0.29/0.46         => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ V22 @ V23 ) @ H1 )
% 0.29/0.46           => ( ( member1696759390at_nat @ ( produc407553657at_nat @ K @ ( product_Pair_nat_nat @ V1 @ V22 ) ) @ E1 )
% 0.29/0.46             => ( member1696759390at_nat @ ( produc407553657at_nat @ K @ ( product_Pair_nat_nat @ V12 @ V23 ) ) @ E2 ) ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % edge_preserving_atomic
% 0.29/0.46  thf(fact_146_edge__preserving__atomic,axiom,
% 0.29/0.46      ! [H1: set_Pr1916610317um_a_b,E1: set_Pr409224873um_a_b,E2: set_Pr409224873um_a_b,V1: sum_sum_a_b,V12: sum_sum_a_b,V22: sum_sum_a_b,V23: sum_sum_a_b,K: standard_Constant_a] :
% 0.29/0.46        ( ( edge_p1871801392tant_a @ H1 @ E1 @ E2 )
% 0.29/0.46       => ( ( member947389014um_a_b @ ( produc176426981um_a_b @ V1 @ V12 ) @ H1 )
% 0.29/0.46         => ( ( member947389014um_a_b @ ( produc176426981um_a_b @ V22 @ V23 ) @ H1 )
% 0.29/0.46           => ( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ K @ ( produc176426981um_a_b @ V1 @ V22 ) ) @ E1 )
% 0.29/0.46             => ( member1998628618um_a_b @ ( produc1697725733um_a_b @ K @ ( produc176426981um_a_b @ V12 @ V23 ) ) @ E2 ) ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % edge_preserving_atomic
% 0.29/0.46  thf(fact_147_edge__preserving__atomic,axiom,
% 0.29/0.46      ! [H1: set_Pr1174980151um_a_b,E1: set_Pr1647387645at_nat,E2: set_Pr409224873um_a_b,V1: nat,V12: sum_sum_a_b,V22: nat,V23: sum_sum_a_b,K: standard_Constant_a] :
% 0.29/0.46        ( ( edge_p1382426714tant_a @ H1 @ E1 @ E2 )
% 0.29/0.46       => ( ( member1294585472um_a_b @ ( produc1808556047um_a_b @ V1 @ V12 ) @ H1 )
% 0.29/0.46         => ( ( member1294585472um_a_b @ ( produc1808556047um_a_b @ V22 @ V23 ) @ H1 )
% 0.29/0.46           => ( ( member1696759390at_nat @ ( produc407553657at_nat @ K @ ( product_Pair_nat_nat @ V1 @ V22 ) ) @ E1 )
% 0.29/0.46             => ( member1998628618um_a_b @ ( produc1697725733um_a_b @ K @ ( produc176426981um_a_b @ V12 @ V23 ) ) @ E2 ) ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % edge_preserving_atomic
% 0.29/0.46  thf(fact_148_labeled__graph_Oexhaust__sel,axiom,
% 0.29/0.46      ! [Labeled_graph: labele935650037_a_nat] :
% 0.29/0.46        ( Labeled_graph
% 0.29/0.46        = ( labele16114835_a_nat @ ( labele195203296_a_nat @ Labeled_graph ) @ ( labele1810595089_a_nat @ Labeled_graph ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % labeled_graph.exhaust_sel
% 0.29/0.46  thf(fact_149_labeled__graph_Oexhaust__sel,axiom,
% 0.29/0.46      ! [Labeled_graph: labele431970251um_a_b] :
% 0.29/0.46        ( Labeled_graph
% 0.29/0.46        = ( labele1729654377um_a_b @ ( labele1939049654um_a_b @ Labeled_graph ) @ ( labele577278695um_a_b @ Labeled_graph ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % labeled_graph.exhaust_sel
% 0.29/0.46  thf(fact_150_singleton__insert__inj__eq_H,axiom,
% 0.29/0.46      ! [A: standard_Constant_a,A3: set_St761939237tant_a,B: standard_Constant_a] :
% 0.29/0.46        ( ( ( insert1909710879tant_a @ A @ A3 )
% 0.29/0.46          = ( insert1909710879tant_a @ B @ bot_bo1160111033tant_a ) )
% 0.29/0.46        = ( ( A = B )
% 0.29/0.46          & ( ord_le1739761029tant_a @ A3 @ ( insert1909710879tant_a @ B @ bot_bo1160111033tant_a ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % singleton_insert_inj_eq'
% 0.29/0.46  thf(fact_151_singleton__insert__inj__eq_H,axiom,
% 0.29/0.46      ! [A: product_prod_nat_nat,A3: set_Pr1986765409at_nat,B: product_prod_nat_nat] :
% 0.29/0.46        ( ( ( insert271595217at_nat @ A @ A3 )
% 0.29/0.46          = ( insert271595217at_nat @ B @ bot_bo2130386637at_nat ) )
% 0.29/0.46        = ( ( A = B )
% 0.29/0.46          & ( ord_le841296385at_nat @ A3 @ ( insert271595217at_nat @ B @ bot_bo2130386637at_nat ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % singleton_insert_inj_eq'
% 0.29/0.46  thf(fact_152_singleton__insert__inj__eq_H,axiom,
% 0.29/0.46      ! [A: produc1032616263at_nat,A3: set_Pr1647387645at_nat,B: produc1032616263at_nat] :
% 0.29/0.46        ( ( ( insert1625259895at_nat @ A @ A3 )
% 0.29/0.46          = ( insert1625259895at_nat @ B @ bot_bo810816657at_nat ) )
% 0.29/0.46        = ( ( A = B )
% 0.29/0.46          & ( ord_le1909159005at_nat @ A3 @ ( insert1625259895at_nat @ B @ bot_bo810816657at_nat ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % singleton_insert_inj_eq'
% 0.29/0.46  thf(fact_153_singleton__insert__inj__eq_H,axiom,
% 0.29/0.46      ! [A: nat,A3: set_nat,B: nat] :
% 0.29/0.46        ( ( ( insert_nat @ A @ A3 )
% 0.29/0.46          = ( insert_nat @ B @ bot_bot_set_nat ) )
% 0.29/0.46        = ( ( A = B )
% 0.29/0.46          & ( ord_less_eq_set_nat @ A3 @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % singleton_insert_inj_eq'
% 0.29/0.46  thf(fact_154_singleton__insert__inj__eq_H,axiom,
% 0.29/0.46      ! [A: produc1124793815um_a_b,A3: set_Pr1174980151um_a_b,B: produc1124793815um_a_b] :
% 0.29/0.46        ( ( ( insert983991207um_a_b @ A @ A3 )
% 0.29/0.46          = ( insert983991207um_a_b @ B @ bot_bo575978147um_a_b ) )
% 0.29/0.46        = ( ( A = B )
% 0.29/0.46          & ( ord_le823954903um_a_b @ A3 @ ( insert983991207um_a_b @ B @ bot_bo575978147um_a_b ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % singleton_insert_inj_eq'
% 0.29/0.46  thf(fact_155_singleton__insert__inj__eq_H,axiom,
% 0.29/0.46      ! [A: produc1548871597um_a_b,A3: set_Pr1916610317um_a_b,B: produc1548871597um_a_b] :
% 0.29/0.46        ( ( ( insert1435405693um_a_b @ A @ A3 )
% 0.29/0.46          = ( insert1435405693um_a_b @ B @ bot_bo225809273um_a_b ) )
% 0.29/0.46        = ( ( A = B )
% 0.29/0.46          & ( ord_le1059794605um_a_b @ A3 @ ( insert1435405693um_a_b @ B @ bot_bo225809273um_a_b ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % singleton_insert_inj_eq'
% 0.29/0.46  thf(fact_156_singleton__insert__inj__eq_H,axiom,
% 0.29/0.46      ! [A: produc1963079155um_a_b,A3: set_Pr409224873um_a_b,B: produc1963079155um_a_b] :
% 0.29/0.46        ( ( ( insert323157027um_a_b @ A @ A3 )
% 0.29/0.46          = ( insert323157027um_a_b @ B @ bot_bo1262634813um_a_b ) )
% 0.29/0.46        = ( ( A = B )
% 0.29/0.46          & ( ord_le615126793um_a_b @ A3 @ ( insert323157027um_a_b @ B @ bot_bo1262634813um_a_b ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % singleton_insert_inj_eq'
% 0.29/0.46  thf(fact_157_singleton__insert__inj__eq_H,axiom,
% 0.29/0.46      ! [A: sum_sum_a_b,A3: set_Sum_sum_a_b,B: sum_sum_a_b] :
% 0.29/0.46        ( ( ( insert_Sum_sum_a_b @ A @ A3 )
% 0.29/0.46          = ( insert_Sum_sum_a_b @ B @ bot_bo1491243248um_a_b ) )
% 0.29/0.46        = ( ( A = B )
% 0.29/0.46          & ( ord_le192794300um_a_b @ A3 @ ( insert_Sum_sum_a_b @ B @ bot_bo1491243248um_a_b ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % singleton_insert_inj_eq'
% 0.29/0.46  thf(fact_158_singleton__insert__inj__eq,axiom,
% 0.29/0.46      ! [B: standard_Constant_a,A: standard_Constant_a,A3: set_St761939237tant_a] :
% 0.29/0.46        ( ( ( insert1909710879tant_a @ B @ bot_bo1160111033tant_a )
% 0.29/0.46          = ( insert1909710879tant_a @ A @ A3 ) )
% 0.29/0.46        = ( ( A = B )
% 0.29/0.46          & ( ord_le1739761029tant_a @ A3 @ ( insert1909710879tant_a @ B @ bot_bo1160111033tant_a ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % singleton_insert_inj_eq
% 0.29/0.46  thf(fact_159_singleton__insert__inj__eq,axiom,
% 0.29/0.46      ! [B: product_prod_nat_nat,A: product_prod_nat_nat,A3: set_Pr1986765409at_nat] :
% 0.29/0.46        ( ( ( insert271595217at_nat @ B @ bot_bo2130386637at_nat )
% 0.29/0.46          = ( insert271595217at_nat @ A @ A3 ) )
% 0.29/0.46        = ( ( A = B )
% 0.29/0.46          & ( ord_le841296385at_nat @ A3 @ ( insert271595217at_nat @ B @ bot_bo2130386637at_nat ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % singleton_insert_inj_eq
% 0.29/0.46  thf(fact_160_singleton__insert__inj__eq,axiom,
% 0.29/0.46      ! [B: produc1032616263at_nat,A: produc1032616263at_nat,A3: set_Pr1647387645at_nat] :
% 0.29/0.46        ( ( ( insert1625259895at_nat @ B @ bot_bo810816657at_nat )
% 0.29/0.46          = ( insert1625259895at_nat @ A @ A3 ) )
% 0.29/0.46        = ( ( A = B )
% 0.29/0.46          & ( ord_le1909159005at_nat @ A3 @ ( insert1625259895at_nat @ B @ bot_bo810816657at_nat ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % singleton_insert_inj_eq
% 0.29/0.46  thf(fact_161_singleton__insert__inj__eq,axiom,
% 0.29/0.46      ! [B: nat,A: nat,A3: set_nat] :
% 0.29/0.46        ( ( ( insert_nat @ B @ bot_bot_set_nat )
% 0.29/0.46          = ( insert_nat @ A @ A3 ) )
% 0.29/0.46        = ( ( A = B )
% 0.29/0.46          & ( ord_less_eq_set_nat @ A3 @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % singleton_insert_inj_eq
% 0.29/0.46  thf(fact_162_singleton__insert__inj__eq,axiom,
% 0.29/0.46      ! [B: produc1124793815um_a_b,A: produc1124793815um_a_b,A3: set_Pr1174980151um_a_b] :
% 0.29/0.46        ( ( ( insert983991207um_a_b @ B @ bot_bo575978147um_a_b )
% 0.29/0.46          = ( insert983991207um_a_b @ A @ A3 ) )
% 0.29/0.46        = ( ( A = B )
% 0.29/0.46          & ( ord_le823954903um_a_b @ A3 @ ( insert983991207um_a_b @ B @ bot_bo575978147um_a_b ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % singleton_insert_inj_eq
% 0.29/0.46  thf(fact_163_singleton__insert__inj__eq,axiom,
% 0.29/0.46      ! [B: produc1548871597um_a_b,A: produc1548871597um_a_b,A3: set_Pr1916610317um_a_b] :
% 0.29/0.46        ( ( ( insert1435405693um_a_b @ B @ bot_bo225809273um_a_b )
% 0.29/0.46          = ( insert1435405693um_a_b @ A @ A3 ) )
% 0.29/0.46        = ( ( A = B )
% 0.29/0.46          & ( ord_le1059794605um_a_b @ A3 @ ( insert1435405693um_a_b @ B @ bot_bo225809273um_a_b ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % singleton_insert_inj_eq
% 0.29/0.46  thf(fact_164_singleton__insert__inj__eq,axiom,
% 0.29/0.46      ! [B: produc1963079155um_a_b,A: produc1963079155um_a_b,A3: set_Pr409224873um_a_b] :
% 0.29/0.46        ( ( ( insert323157027um_a_b @ B @ bot_bo1262634813um_a_b )
% 0.29/0.46          = ( insert323157027um_a_b @ A @ A3 ) )
% 0.29/0.46        = ( ( A = B )
% 0.29/0.46          & ( ord_le615126793um_a_b @ A3 @ ( insert323157027um_a_b @ B @ bot_bo1262634813um_a_b ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % singleton_insert_inj_eq
% 0.29/0.46  thf(fact_165_singleton__insert__inj__eq,axiom,
% 0.29/0.46      ! [B: sum_sum_a_b,A: sum_sum_a_b,A3: set_Sum_sum_a_b] :
% 0.29/0.46        ( ( ( insert_Sum_sum_a_b @ B @ bot_bo1491243248um_a_b )
% 0.29/0.46          = ( insert_Sum_sum_a_b @ A @ A3 ) )
% 0.29/0.46        = ( ( A = B )
% 0.29/0.46          & ( ord_le192794300um_a_b @ A3 @ ( insert_Sum_sum_a_b @ B @ bot_bo1491243248um_a_b ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % singleton_insert_inj_eq
% 0.29/0.46  thf(fact_166_univalent__empty,axiom,
% 0.29/0.46      unival860567212at_nat @ bot_bo810816657at_nat ).
% 0.29/0.46  
% 0.29/0.46  % univalent_empty
% 0.29/0.46  thf(fact_167_univalent__empty,axiom,
% 0.29/0.46      unival118648434um_a_b @ bot_bo225809273um_a_b ).
% 0.29/0.46  
% 0.29/0.46  % univalent_empty
% 0.29/0.46  thf(fact_168_univalent__empty,axiom,
% 0.29/0.46      unival1487587672um_a_b @ bot_bo1262634813um_a_b ).
% 0.29/0.46  
% 0.29/0.46  % univalent_empty
% 0.29/0.46  thf(fact_169_univalent__empty,axiom,
% 0.29/0.46      unival2092813468um_a_b @ bot_bo575978147um_a_b ).
% 0.29/0.46  
% 0.29/0.46  % univalent_empty
% 0.29/0.46  thf(fact_170_mem__Collect__eq,axiom,
% 0.29/0.46      ! [A: sum_sum_a_b,P: sum_sum_a_b > $o] :
% 0.29/0.46        ( ( member_Sum_sum_a_b @ A @ ( collect_Sum_sum_a_b @ P ) )
% 0.29/0.46        = ( P @ A ) ) ).
% 0.29/0.46  
% 0.29/0.46  % mem_Collect_eq
% 0.29/0.46  thf(fact_171_mem__Collect__eq,axiom,
% 0.29/0.46      ! [A: produc1124793815um_a_b,P: produc1124793815um_a_b > $o] :
% 0.29/0.46        ( ( member1294585472um_a_b @ A @ ( collec492052930um_a_b @ P ) )
% 0.29/0.46        = ( P @ A ) ) ).
% 0.29/0.46  
% 0.29/0.46  % mem_Collect_eq
% 0.29/0.46  thf(fact_172_mem__Collect__eq,axiom,
% 0.29/0.46      ! [A: produc1963079155um_a_b,P: produc1963079155um_a_b > $o] :
% 0.29/0.46        ( ( member1998628618um_a_b @ A @ ( collec1254333256um_a_b @ P ) )
% 0.29/0.46        = ( P @ A ) ) ).
% 0.29/0.46  
% 0.29/0.46  % mem_Collect_eq
% 0.29/0.46  thf(fact_173_Collect__mem__eq,axiom,
% 0.29/0.46      ! [A3: set_Sum_sum_a_b] :
% 0.29/0.46        ( ( collect_Sum_sum_a_b
% 0.29/0.46          @ ^ [X3: sum_sum_a_b] : ( member_Sum_sum_a_b @ X3 @ A3 ) )
% 0.29/0.46        = A3 ) ).
% 0.29/0.46  
% 0.29/0.46  % Collect_mem_eq
% 0.29/0.46  thf(fact_174_Collect__mem__eq,axiom,
% 0.29/0.46      ! [A3: set_Pr1174980151um_a_b] :
% 0.29/0.46        ( ( collec492052930um_a_b
% 0.29/0.46          @ ^ [X3: produc1124793815um_a_b] : ( member1294585472um_a_b @ X3 @ A3 ) )
% 0.29/0.46        = A3 ) ).
% 0.29/0.46  
% 0.29/0.46  % Collect_mem_eq
% 0.29/0.46  thf(fact_175_Collect__mem__eq,axiom,
% 0.29/0.46      ! [A3: set_Pr409224873um_a_b] :
% 0.29/0.46        ( ( collec1254333256um_a_b
% 0.29/0.46          @ ^ [X3: produc1963079155um_a_b] : ( member1998628618um_a_b @ X3 @ A3 ) )
% 0.29/0.46        = A3 ) ).
% 0.29/0.46  
% 0.29/0.46  % Collect_mem_eq
% 0.29/0.46  thf(fact_176_insert__subset,axiom,
% 0.29/0.46      ! [X2: produc1032616263at_nat,A3: set_Pr1647387645at_nat,B5: set_Pr1647387645at_nat] :
% 0.29/0.46        ( ( ord_le1909159005at_nat @ ( insert1625259895at_nat @ X2 @ A3 ) @ B5 )
% 0.29/0.46        = ( ( member1696759390at_nat @ X2 @ B5 )
% 0.29/0.46          & ( ord_le1909159005at_nat @ A3 @ B5 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % insert_subset
% 0.29/0.46  thf(fact_177_insert__subset,axiom,
% 0.29/0.46      ! [X2: nat,A3: set_nat,B5: set_nat] :
% 0.29/0.46        ( ( ord_less_eq_set_nat @ ( insert_nat @ X2 @ A3 ) @ B5 )
% 0.29/0.46        = ( ( member_nat @ X2 @ B5 )
% 0.29/0.46          & ( ord_less_eq_set_nat @ A3 @ B5 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % insert_subset
% 0.29/0.46  thf(fact_178_insert__subset,axiom,
% 0.29/0.46      ! [X2: produc1548871597um_a_b,A3: set_Pr1916610317um_a_b,B5: set_Pr1916610317um_a_b] :
% 0.29/0.46        ( ( ord_le1059794605um_a_b @ ( insert1435405693um_a_b @ X2 @ A3 ) @ B5 )
% 0.29/0.46        = ( ( member947389014um_a_b @ X2 @ B5 )
% 0.29/0.46          & ( ord_le1059794605um_a_b @ A3 @ B5 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % insert_subset
% 0.29/0.46  thf(fact_179_insert__subset,axiom,
% 0.29/0.46      ! [X2: standard_Constant_a,A3: set_St761939237tant_a,B5: set_St761939237tant_a] :
% 0.29/0.46        ( ( ord_le1739761029tant_a @ ( insert1909710879tant_a @ X2 @ A3 ) @ B5 )
% 0.29/0.46        = ( ( member1632892294tant_a @ X2 @ B5 )
% 0.29/0.46          & ( ord_le1739761029tant_a @ A3 @ B5 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % insert_subset
% 0.29/0.46  thf(fact_180_insert__subset,axiom,
% 0.29/0.46      ! [X2: product_prod_nat_nat,A3: set_Pr1986765409at_nat,B5: set_Pr1986765409at_nat] :
% 0.29/0.46        ( ( ord_le841296385at_nat @ ( insert271595217at_nat @ X2 @ A3 ) @ B5 )
% 0.29/0.46        = ( ( member701585322at_nat @ X2 @ B5 )
% 0.29/0.46          & ( ord_le841296385at_nat @ A3 @ B5 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % insert_subset
% 0.29/0.46  thf(fact_181_insert__subset,axiom,
% 0.29/0.46      ! [X2: produc1124793815um_a_b,A3: set_Pr1174980151um_a_b,B5: set_Pr1174980151um_a_b] :
% 0.29/0.46        ( ( ord_le823954903um_a_b @ ( insert983991207um_a_b @ X2 @ A3 ) @ B5 )
% 0.29/0.46        = ( ( member1294585472um_a_b @ X2 @ B5 )
% 0.29/0.46          & ( ord_le823954903um_a_b @ A3 @ B5 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % insert_subset
% 0.29/0.46  thf(fact_182_insert__subset,axiom,
% 0.29/0.46      ! [X2: produc1963079155um_a_b,A3: set_Pr409224873um_a_b,B5: set_Pr409224873um_a_b] :
% 0.29/0.46        ( ( ord_le615126793um_a_b @ ( insert323157027um_a_b @ X2 @ A3 ) @ B5 )
% 0.29/0.46        = ( ( member1998628618um_a_b @ X2 @ B5 )
% 0.29/0.46          & ( ord_le615126793um_a_b @ A3 @ B5 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % insert_subset
% 0.29/0.46  thf(fact_183_insert__subset,axiom,
% 0.29/0.46      ! [X2: sum_sum_a_b,A3: set_Sum_sum_a_b,B5: set_Sum_sum_a_b] :
% 0.29/0.46        ( ( ord_le192794300um_a_b @ ( insert_Sum_sum_a_b @ X2 @ A3 ) @ B5 )
% 0.29/0.46        = ( ( member_Sum_sum_a_b @ X2 @ B5 )
% 0.29/0.46          & ( ord_le192794300um_a_b @ A3 @ B5 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % insert_subset
% 0.29/0.46  thf(fact_184_singletonI,axiom,
% 0.29/0.46      ! [A: standard_Constant_a] : ( member1632892294tant_a @ A @ ( insert1909710879tant_a @ A @ bot_bo1160111033tant_a ) ) ).
% 0.29/0.46  
% 0.29/0.46  % singletonI
% 0.29/0.46  thf(fact_185_singletonI,axiom,
% 0.29/0.46      ! [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( insert271595217at_nat @ A @ bot_bo2130386637at_nat ) ) ).
% 0.29/0.46  
% 0.29/0.46  % singletonI
% 0.29/0.46  thf(fact_186_singletonI,axiom,
% 0.29/0.46      ! [A: produc1032616263at_nat] : ( member1696759390at_nat @ A @ ( insert1625259895at_nat @ A @ bot_bo810816657at_nat ) ) ).
% 0.29/0.46  
% 0.29/0.46  % singletonI
% 0.29/0.46  thf(fact_187_singletonI,axiom,
% 0.29/0.46      ! [A: nat] : ( member_nat @ A @ ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 0.29/0.46  
% 0.29/0.46  % singletonI
% 0.29/0.46  thf(fact_188_singletonI,axiom,
% 0.29/0.46      ! [A: produc1124793815um_a_b] : ( member1294585472um_a_b @ A @ ( insert983991207um_a_b @ A @ bot_bo575978147um_a_b ) ) ).
% 0.29/0.46  
% 0.29/0.46  % singletonI
% 0.29/0.46  thf(fact_189_singletonI,axiom,
% 0.29/0.46      ! [A: produc1548871597um_a_b] : ( member947389014um_a_b @ A @ ( insert1435405693um_a_b @ A @ bot_bo225809273um_a_b ) ) ).
% 0.29/0.46  
% 0.29/0.46  % singletonI
% 0.29/0.46  thf(fact_190_singletonI,axiom,
% 0.29/0.46      ! [A: produc1963079155um_a_b] : ( member1998628618um_a_b @ A @ ( insert323157027um_a_b @ A @ bot_bo1262634813um_a_b ) ) ).
% 0.29/0.46  
% 0.29/0.46  % singletonI
% 0.29/0.46  thf(fact_191_singletonI,axiom,
% 0.29/0.46      ! [A: sum_sum_a_b] : ( member_Sum_sum_a_b @ A @ ( insert_Sum_sum_a_b @ A @ bot_bo1491243248um_a_b ) ) ).
% 0.29/0.46  
% 0.29/0.46  % singletonI
% 0.29/0.46  thf(fact_192_empty__subsetI,axiom,
% 0.29/0.46      ! [A3: set_Pr1647387645at_nat] : ( ord_le1909159005at_nat @ bot_bo810816657at_nat @ A3 ) ).
% 0.29/0.46  
% 0.29/0.46  % empty_subsetI
% 0.29/0.46  thf(fact_193_empty__subsetI,axiom,
% 0.29/0.46      ! [A3: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A3 ) ).
% 0.29/0.46  
% 0.29/0.46  % empty_subsetI
% 0.29/0.46  thf(fact_194_empty__subsetI,axiom,
% 0.29/0.46      ! [A3: set_Pr1174980151um_a_b] : ( ord_le823954903um_a_b @ bot_bo575978147um_a_b @ A3 ) ).
% 0.29/0.46  
% 0.29/0.46  % empty_subsetI
% 0.29/0.46  thf(fact_195_empty__subsetI,axiom,
% 0.29/0.46      ! [A3: set_Pr1916610317um_a_b] : ( ord_le1059794605um_a_b @ bot_bo225809273um_a_b @ A3 ) ).
% 0.29/0.46  
% 0.29/0.46  % empty_subsetI
% 0.29/0.46  thf(fact_196_empty__subsetI,axiom,
% 0.29/0.46      ! [A3: set_Pr409224873um_a_b] : ( ord_le615126793um_a_b @ bot_bo1262634813um_a_b @ A3 ) ).
% 0.29/0.46  
% 0.29/0.46  % empty_subsetI
% 0.29/0.46  thf(fact_197_empty__subsetI,axiom,
% 0.29/0.46      ! [A3: set_Sum_sum_a_b] : ( ord_le192794300um_a_b @ bot_bo1491243248um_a_b @ A3 ) ).
% 0.29/0.46  
% 0.29/0.46  % empty_subsetI
% 0.29/0.46  thf(fact_198_subset__empty,axiom,
% 0.29/0.46      ! [A3: set_Pr1647387645at_nat] :
% 0.29/0.46        ( ( ord_le1909159005at_nat @ A3 @ bot_bo810816657at_nat )
% 0.29/0.46        = ( A3 = bot_bo810816657at_nat ) ) ).
% 0.29/0.46  
% 0.29/0.46  % subset_empty
% 0.29/0.46  thf(fact_199_subset__empty,axiom,
% 0.29/0.46      ! [A3: set_nat] :
% 0.29/0.46        ( ( ord_less_eq_set_nat @ A3 @ bot_bot_set_nat )
% 0.29/0.46        = ( A3 = bot_bot_set_nat ) ) ).
% 0.29/0.46  
% 0.29/0.46  % subset_empty
% 0.29/0.46  thf(fact_200_subset__empty,axiom,
% 0.29/0.46      ! [A3: set_Pr1174980151um_a_b] :
% 0.29/0.46        ( ( ord_le823954903um_a_b @ A3 @ bot_bo575978147um_a_b )
% 0.29/0.46        = ( A3 = bot_bo575978147um_a_b ) ) ).
% 0.29/0.46  
% 0.29/0.46  % subset_empty
% 0.29/0.46  thf(fact_201_subset__empty,axiom,
% 0.29/0.46      ! [A3: set_Pr1916610317um_a_b] :
% 0.29/0.46        ( ( ord_le1059794605um_a_b @ A3 @ bot_bo225809273um_a_b )
% 0.29/0.46        = ( A3 = bot_bo225809273um_a_b ) ) ).
% 0.29/0.46  
% 0.29/0.46  % subset_empty
% 0.29/0.46  thf(fact_202_subset__empty,axiom,
% 0.29/0.46      ! [A3: set_Pr409224873um_a_b] :
% 0.29/0.46        ( ( ord_le615126793um_a_b @ A3 @ bot_bo1262634813um_a_b )
% 0.29/0.46        = ( A3 = bot_bo1262634813um_a_b ) ) ).
% 0.29/0.46  
% 0.29/0.46  % subset_empty
% 0.29/0.46  thf(fact_203_subset__empty,axiom,
% 0.29/0.46      ! [A3: set_Sum_sum_a_b] :
% 0.29/0.46        ( ( ord_le192794300um_a_b @ A3 @ bot_bo1491243248um_a_b )
% 0.29/0.46        = ( A3 = bot_bo1491243248um_a_b ) ) ).
% 0.29/0.46  
% 0.29/0.46  % subset_empty
% 0.29/0.46  thf(fact_204_le__zero__eq,axiom,
% 0.29/0.46      ! [N: nat] :
% 0.29/0.46        ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 0.29/0.46        = ( N = zero_zero_nat ) ) ).
% 0.29/0.46  
% 0.29/0.46  % le_zero_eq
% 0.29/0.46  thf(fact_205_reflexivity__rule__def,axiom,
% 0.29/0.46      ( standa63370785tant_a
% 0.29/0.46      = ( ^ [T: standard_Constant_a] : ( produc1676969687_a_nat @ ( labele16114835_a_nat @ bot_bo810816657at_nat @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ T @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % reflexivity_rule_def
% 0.29/0.46  thf(fact_206_nonempty__rule__def,axiom,
% 0.29/0.46      ( standa1410829644tant_a
% 0.29/0.46      = ( produc1676969687_a_nat @ ( labele16114835_a_nat @ bot_bo810816657at_nat @ bot_bot_set_nat ) @ ( labele16114835_a_nat @ bot_bo810816657at_nat @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % nonempty_rule_def
% 0.29/0.46  thf(fact_207_empty__iff,axiom,
% 0.29/0.46      ! [C: produc1032616263at_nat] :
% 0.29/0.46        ~ ( member1696759390at_nat @ C @ bot_bo810816657at_nat ) ).
% 0.29/0.46  
% 0.29/0.46  % empty_iff
% 0.29/0.46  thf(fact_208_empty__iff,axiom,
% 0.29/0.46      ! [C: nat] :
% 0.29/0.46        ~ ( member_nat @ C @ bot_bot_set_nat ) ).
% 0.29/0.46  
% 0.29/0.46  % empty_iff
% 0.29/0.46  thf(fact_209_empty__iff,axiom,
% 0.29/0.46      ! [C: produc1124793815um_a_b] :
% 0.29/0.46        ~ ( member1294585472um_a_b @ C @ bot_bo575978147um_a_b ) ).
% 0.29/0.46  
% 0.29/0.46  % empty_iff
% 0.29/0.46  thf(fact_210_empty__iff,axiom,
% 0.29/0.46      ! [C: produc1548871597um_a_b] :
% 0.29/0.46        ~ ( member947389014um_a_b @ C @ bot_bo225809273um_a_b ) ).
% 0.29/0.46  
% 0.29/0.46  % empty_iff
% 0.29/0.46  thf(fact_211_empty__iff,axiom,
% 0.29/0.46      ! [C: produc1963079155um_a_b] :
% 0.29/0.46        ~ ( member1998628618um_a_b @ C @ bot_bo1262634813um_a_b ) ).
% 0.29/0.46  
% 0.29/0.46  % empty_iff
% 0.29/0.46  thf(fact_212_empty__iff,axiom,
% 0.29/0.46      ! [C: sum_sum_a_b] :
% 0.29/0.46        ~ ( member_Sum_sum_a_b @ C @ bot_bo1491243248um_a_b ) ).
% 0.29/0.46  
% 0.29/0.46  % empty_iff
% 0.29/0.46  thf(fact_213_all__not__in__conv,axiom,
% 0.29/0.46      ! [A3: set_Pr1647387645at_nat] :
% 0.29/0.46        ( ( ! [X3: produc1032616263at_nat] :
% 0.29/0.46              ~ ( member1696759390at_nat @ X3 @ A3 ) )
% 0.29/0.46        = ( A3 = bot_bo810816657at_nat ) ) ).
% 0.29/0.46  
% 0.29/0.46  % all_not_in_conv
% 0.29/0.46  thf(fact_214_all__not__in__conv,axiom,
% 0.29/0.46      ! [A3: set_nat] :
% 0.29/0.46        ( ( ! [X3: nat] :
% 0.29/0.46              ~ ( member_nat @ X3 @ A3 ) )
% 0.29/0.46        = ( A3 = bot_bot_set_nat ) ) ).
% 0.29/0.46  
% 0.29/0.46  % all_not_in_conv
% 0.29/0.46  thf(fact_215_all__not__in__conv,axiom,
% 0.29/0.46      ! [A3: set_Pr1174980151um_a_b] :
% 0.29/0.46        ( ( ! [X3: produc1124793815um_a_b] :
% 0.29/0.46              ~ ( member1294585472um_a_b @ X3 @ A3 ) )
% 0.29/0.46        = ( A3 = bot_bo575978147um_a_b ) ) ).
% 0.29/0.46  
% 0.29/0.46  % all_not_in_conv
% 0.29/0.46  thf(fact_216_all__not__in__conv,axiom,
% 0.29/0.46      ! [A3: set_Pr1916610317um_a_b] :
% 0.29/0.46        ( ( ! [X3: produc1548871597um_a_b] :
% 0.29/0.46              ~ ( member947389014um_a_b @ X3 @ A3 ) )
% 0.29/0.46        = ( A3 = bot_bo225809273um_a_b ) ) ).
% 0.29/0.46  
% 0.29/0.46  % all_not_in_conv
% 0.29/0.46  thf(fact_217_all__not__in__conv,axiom,
% 0.29/0.46      ! [A3: set_Pr409224873um_a_b] :
% 0.29/0.46        ( ( ! [X3: produc1963079155um_a_b] :
% 0.29/0.46              ~ ( member1998628618um_a_b @ X3 @ A3 ) )
% 0.29/0.46        = ( A3 = bot_bo1262634813um_a_b ) ) ).
% 0.29/0.46  
% 0.29/0.46  % all_not_in_conv
% 0.29/0.46  thf(fact_218_all__not__in__conv,axiom,
% 0.29/0.46      ! [A3: set_Sum_sum_a_b] :
% 0.29/0.46        ( ( ! [X3: sum_sum_a_b] :
% 0.29/0.46              ~ ( member_Sum_sum_a_b @ X3 @ A3 ) )
% 0.29/0.46        = ( A3 = bot_bo1491243248um_a_b ) ) ).
% 0.29/0.46  
% 0.29/0.46  % all_not_in_conv
% 0.29/0.46  thf(fact_219_Collect__empty__eq,axiom,
% 0.29/0.46      ! [P: produc1032616263at_nat > $o] :
% 0.29/0.46        ( ( ( collec52779676at_nat @ P )
% 0.29/0.46          = bot_bo810816657at_nat )
% 0.29/0.46        = ( ! [X3: produc1032616263at_nat] :
% 0.29/0.46              ~ ( P @ X3 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Collect_empty_eq
% 0.29/0.46  thf(fact_220_Collect__empty__eq,axiom,
% 0.29/0.46      ! [P: nat > $o] :
% 0.29/0.46        ( ( ( collect_nat @ P )
% 0.29/0.46          = bot_bot_set_nat )
% 0.29/0.46        = ( ! [X3: nat] :
% 0.29/0.46              ~ ( P @ X3 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Collect_empty_eq
% 0.29/0.46  thf(fact_221_Collect__empty__eq,axiom,
% 0.29/0.46      ! [P: produc1124793815um_a_b > $o] :
% 0.29/0.46        ( ( ( collec492052930um_a_b @ P )
% 0.29/0.46          = bot_bo575978147um_a_b )
% 0.29/0.46        = ( ! [X3: produc1124793815um_a_b] :
% 0.29/0.46              ~ ( P @ X3 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Collect_empty_eq
% 0.29/0.46  thf(fact_222_Collect__empty__eq,axiom,
% 0.29/0.46      ! [P: produc1548871597um_a_b > $o] :
% 0.29/0.46        ( ( ( collec1769032088um_a_b @ P )
% 0.29/0.46          = bot_bo225809273um_a_b )
% 0.29/0.46        = ( ! [X3: produc1548871597um_a_b] :
% 0.29/0.46              ~ ( P @ X3 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Collect_empty_eq
% 0.29/0.46  thf(fact_223_Collect__empty__eq,axiom,
% 0.29/0.46      ! [P: produc1963079155um_a_b > $o] :
% 0.29/0.46        ( ( ( collec1254333256um_a_b @ P )
% 0.29/0.46          = bot_bo1262634813um_a_b )
% 0.29/0.46        = ( ! [X3: produc1963079155um_a_b] :
% 0.29/0.46              ~ ( P @ X3 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Collect_empty_eq
% 0.29/0.46  thf(fact_224_Collect__empty__eq,axiom,
% 0.29/0.46      ! [P: sum_sum_a_b > $o] :
% 0.29/0.46        ( ( ( collect_Sum_sum_a_b @ P )
% 0.29/0.46          = bot_bo1491243248um_a_b )
% 0.29/0.46        = ( ! [X3: sum_sum_a_b] :
% 0.29/0.46              ~ ( P @ X3 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % Collect_empty_eq
% 0.29/0.46  thf(fact_225_empty__Collect__eq,axiom,
% 0.29/0.46      ! [P: produc1032616263at_nat > $o] :
% 0.29/0.46        ( ( bot_bo810816657at_nat
% 0.29/0.46          = ( collec52779676at_nat @ P ) )
% 0.29/0.46        = ( ! [X3: produc1032616263at_nat] :
% 0.29/0.46              ~ ( P @ X3 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % empty_Collect_eq
% 0.29/0.46  thf(fact_226_empty__Collect__eq,axiom,
% 0.29/0.46      ! [P: nat > $o] :
% 0.29/0.46        ( ( bot_bot_set_nat
% 0.29/0.46          = ( collect_nat @ P ) )
% 0.29/0.46        = ( ! [X3: nat] :
% 0.29/0.46              ~ ( P @ X3 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % empty_Collect_eq
% 0.29/0.46  thf(fact_227_empty__Collect__eq,axiom,
% 0.29/0.46      ! [P: produc1124793815um_a_b > $o] :
% 0.29/0.46        ( ( bot_bo575978147um_a_b
% 0.29/0.46          = ( collec492052930um_a_b @ P ) )
% 0.29/0.46        = ( ! [X3: produc1124793815um_a_b] :
% 0.29/0.46              ~ ( P @ X3 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % empty_Collect_eq
% 0.29/0.46  thf(fact_228_empty__Collect__eq,axiom,
% 0.29/0.46      ! [P: produc1548871597um_a_b > $o] :
% 0.29/0.46        ( ( bot_bo225809273um_a_b
% 0.29/0.46          = ( collec1769032088um_a_b @ P ) )
% 0.29/0.46        = ( ! [X3: produc1548871597um_a_b] :
% 0.29/0.46              ~ ( P @ X3 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % empty_Collect_eq
% 0.29/0.46  thf(fact_229_empty__Collect__eq,axiom,
% 0.29/0.46      ! [P: produc1963079155um_a_b > $o] :
% 0.29/0.46        ( ( bot_bo1262634813um_a_b
% 0.29/0.46          = ( collec1254333256um_a_b @ P ) )
% 0.29/0.46        = ( ! [X3: produc1963079155um_a_b] :
% 0.29/0.46              ~ ( P @ X3 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % empty_Collect_eq
% 0.29/0.46  thf(fact_230_empty__Collect__eq,axiom,
% 0.29/0.46      ! [P: sum_sum_a_b > $o] :
% 0.29/0.46        ( ( bot_bo1491243248um_a_b
% 0.29/0.46          = ( collect_Sum_sum_a_b @ P ) )
% 0.29/0.46        = ( ! [X3: sum_sum_a_b] :
% 0.29/0.46              ~ ( P @ X3 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % empty_Collect_eq
% 0.29/0.46  thf(fact_231_subsetI,axiom,
% 0.29/0.46      ! [A3: set_Pr1174980151um_a_b,B5: set_Pr1174980151um_a_b] :
% 0.29/0.46        ( ! [X4: produc1124793815um_a_b] :
% 0.29/0.46            ( ( member1294585472um_a_b @ X4 @ A3 )
% 0.29/0.46           => ( member1294585472um_a_b @ X4 @ B5 ) )
% 0.29/0.46       => ( ord_le823954903um_a_b @ A3 @ B5 ) ) ).
% 0.29/0.46  
% 0.29/0.46  % subsetI
% 0.29/0.46  thf(fact_232_subsetI,axiom,
% 0.29/0.46      ! [A3: set_Pr409224873um_a_b,B5: set_Pr409224873um_a_b] :
% 0.29/0.46        ( ! [X4: produc1963079155um_a_b] :
% 0.29/0.46            ( ( member1998628618um_a_b @ X4 @ A3 )
% 0.29/0.46           => ( member1998628618um_a_b @ X4 @ B5 ) )
% 0.29/0.46       => ( ord_le615126793um_a_b @ A3 @ B5 ) ) ).
% 0.29/0.46  
% 0.29/0.46  % subsetI
% 0.29/0.46  thf(fact_233_subsetI,axiom,
% 0.29/0.46      ! [A3: set_Sum_sum_a_b,B5: set_Sum_sum_a_b] :
% 0.29/0.46        ( ! [X4: sum_sum_a_b] :
% 0.29/0.46            ( ( member_Sum_sum_a_b @ X4 @ A3 )
% 0.29/0.46           => ( member_Sum_sum_a_b @ X4 @ B5 ) )
% 0.29/0.46       => ( ord_le192794300um_a_b @ A3 @ B5 ) ) ).
% 0.29/0.46  
% 0.29/0.46  % subsetI
% 0.29/0.46  thf(fact_234_subset__antisym,axiom,
% 0.29/0.46      ! [A3: set_Sum_sum_a_b,B5: set_Sum_sum_a_b] :
% 0.29/0.46        ( ( ord_le192794300um_a_b @ A3 @ B5 )
% 0.29/0.46       => ( ( ord_le192794300um_a_b @ B5 @ A3 )
% 0.29/0.46         => ( A3 = B5 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % subset_antisym
% 0.29/0.46  thf(fact_235_insertCI,axiom,
% 0.29/0.46      ! [A: produc1032616263at_nat,B5: set_Pr1647387645at_nat,B: produc1032616263at_nat] :
% 0.29/0.46        ( ( ~ ( member1696759390at_nat @ A @ B5 )
% 0.29/0.46         => ( A = B ) )
% 0.29/0.46       => ( member1696759390at_nat @ A @ ( insert1625259895at_nat @ B @ B5 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % insertCI
% 0.29/0.46  thf(fact_236_insertCI,axiom,
% 0.29/0.46      ! [A: nat,B5: set_nat,B: nat] :
% 0.29/0.46        ( ( ~ ( member_nat @ A @ B5 )
% 0.29/0.46         => ( A = B ) )
% 0.29/0.46       => ( member_nat @ A @ ( insert_nat @ B @ B5 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % insertCI
% 0.29/0.46  thf(fact_237_insertCI,axiom,
% 0.29/0.46      ! [A: produc1548871597um_a_b,B5: set_Pr1916610317um_a_b,B: produc1548871597um_a_b] :
% 0.29/0.46        ( ( ~ ( member947389014um_a_b @ A @ B5 )
% 0.29/0.46         => ( A = B ) )
% 0.29/0.46       => ( member947389014um_a_b @ A @ ( insert1435405693um_a_b @ B @ B5 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % insertCI
% 0.29/0.46  thf(fact_238_insertCI,axiom,
% 0.29/0.46      ! [A: standard_Constant_a,B5: set_St761939237tant_a,B: standard_Constant_a] :
% 0.29/0.46        ( ( ~ ( member1632892294tant_a @ A @ B5 )
% 0.29/0.46         => ( A = B ) )
% 0.29/0.46       => ( member1632892294tant_a @ A @ ( insert1909710879tant_a @ B @ B5 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % insertCI
% 0.29/0.46  thf(fact_239_insertCI,axiom,
% 0.29/0.46      ! [A: product_prod_nat_nat,B5: set_Pr1986765409at_nat,B: product_prod_nat_nat] :
% 0.29/0.46        ( ( ~ ( member701585322at_nat @ A @ B5 )
% 0.29/0.46         => ( A = B ) )
% 0.29/0.46       => ( member701585322at_nat @ A @ ( insert271595217at_nat @ B @ B5 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % insertCI
% 0.29/0.46  thf(fact_240_insertCI,axiom,
% 0.29/0.46      ! [A: sum_sum_a_b,B5: set_Sum_sum_a_b,B: sum_sum_a_b] :
% 0.29/0.46        ( ( ~ ( member_Sum_sum_a_b @ A @ B5 )
% 0.29/0.46         => ( A = B ) )
% 0.29/0.46       => ( member_Sum_sum_a_b @ A @ ( insert_Sum_sum_a_b @ B @ B5 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % insertCI
% 0.29/0.46  thf(fact_241_insertCI,axiom,
% 0.29/0.46      ! [A: produc1124793815um_a_b,B5: set_Pr1174980151um_a_b,B: produc1124793815um_a_b] :
% 0.29/0.46        ( ( ~ ( member1294585472um_a_b @ A @ B5 )
% 0.29/0.46         => ( A = B ) )
% 0.29/0.46       => ( member1294585472um_a_b @ A @ ( insert983991207um_a_b @ B @ B5 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % insertCI
% 0.29/0.46  thf(fact_242_insertCI,axiom,
% 0.29/0.46      ! [A: produc1963079155um_a_b,B5: set_Pr409224873um_a_b,B: produc1963079155um_a_b] :
% 0.29/0.46        ( ( ~ ( member1998628618um_a_b @ A @ B5 )
% 0.29/0.46         => ( A = B ) )
% 0.29/0.46       => ( member1998628618um_a_b @ A @ ( insert323157027um_a_b @ B @ B5 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % insertCI
% 0.29/0.46  thf(fact_243_insert__iff,axiom,
% 0.29/0.46      ! [A: produc1032616263at_nat,B: produc1032616263at_nat,A3: set_Pr1647387645at_nat] :
% 0.29/0.46        ( ( member1696759390at_nat @ A @ ( insert1625259895at_nat @ B @ A3 ) )
% 0.29/0.46        = ( ( A = B )
% 0.29/0.46          | ( member1696759390at_nat @ A @ A3 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % insert_iff
% 0.29/0.46  thf(fact_244_insert__iff,axiom,
% 0.29/0.46      ! [A: nat,B: nat,A3: set_nat] :
% 0.29/0.46        ( ( member_nat @ A @ ( insert_nat @ B @ A3 ) )
% 0.29/0.46        = ( ( A = B )
% 0.29/0.46          | ( member_nat @ A @ A3 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % insert_iff
% 0.29/0.46  thf(fact_245_insert__iff,axiom,
% 0.29/0.46      ! [A: produc1548871597um_a_b,B: produc1548871597um_a_b,A3: set_Pr1916610317um_a_b] :
% 0.29/0.46        ( ( member947389014um_a_b @ A @ ( insert1435405693um_a_b @ B @ A3 ) )
% 0.29/0.46        = ( ( A = B )
% 0.29/0.46          | ( member947389014um_a_b @ A @ A3 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % insert_iff
% 0.29/0.46  thf(fact_246_insert__iff,axiom,
% 0.29/0.46      ! [A: standard_Constant_a,B: standard_Constant_a,A3: set_St761939237tant_a] :
% 0.29/0.46        ( ( member1632892294tant_a @ A @ ( insert1909710879tant_a @ B @ A3 ) )
% 0.29/0.46        = ( ( A = B )
% 0.29/0.46          | ( member1632892294tant_a @ A @ A3 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % insert_iff
% 0.29/0.46  thf(fact_247_insert__iff,axiom,
% 0.29/0.46      ! [A: product_prod_nat_nat,B: product_prod_nat_nat,A3: set_Pr1986765409at_nat] :
% 0.29/0.46        ( ( member701585322at_nat @ A @ ( insert271595217at_nat @ B @ A3 ) )
% 0.29/0.46        = ( ( A = B )
% 0.29/0.46          | ( member701585322at_nat @ A @ A3 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % insert_iff
% 0.29/0.46  thf(fact_248_insert__iff,axiom,
% 0.29/0.46      ! [A: sum_sum_a_b,B: sum_sum_a_b,A3: set_Sum_sum_a_b] :
% 0.29/0.46        ( ( member_Sum_sum_a_b @ A @ ( insert_Sum_sum_a_b @ B @ A3 ) )
% 0.29/0.46        = ( ( A = B )
% 0.29/0.46          | ( member_Sum_sum_a_b @ A @ A3 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % insert_iff
% 0.29/0.46  thf(fact_249_insert__iff,axiom,
% 0.29/0.46      ! [A: produc1124793815um_a_b,B: produc1124793815um_a_b,A3: set_Pr1174980151um_a_b] :
% 0.29/0.46        ( ( member1294585472um_a_b @ A @ ( insert983991207um_a_b @ B @ A3 ) )
% 0.29/0.46        = ( ( A = B )
% 0.29/0.46          | ( member1294585472um_a_b @ A @ A3 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % insert_iff
% 0.29/0.46  thf(fact_250_insert__iff,axiom,
% 0.29/0.46      ! [A: produc1963079155um_a_b,B: produc1963079155um_a_b,A3: set_Pr409224873um_a_b] :
% 0.29/0.46        ( ( member1998628618um_a_b @ A @ ( insert323157027um_a_b @ B @ A3 ) )
% 0.29/0.46        = ( ( A = B )
% 0.29/0.46          | ( member1998628618um_a_b @ A @ A3 ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % insert_iff
% 0.29/0.46  thf(fact_251_insert__absorb2,axiom,
% 0.29/0.46      ! [X2: produc1032616263at_nat,A3: set_Pr1647387645at_nat] :
% 0.29/0.46        ( ( insert1625259895at_nat @ X2 @ ( insert1625259895at_nat @ X2 @ A3 ) )
% 0.29/0.46        = ( insert1625259895at_nat @ X2 @ A3 ) ) ).
% 0.29/0.46  
% 0.29/0.46  % insert_absorb2
% 0.29/0.46  thf(fact_252_insert__absorb2,axiom,
% 0.29/0.46      ! [X2: nat,A3: set_nat] :
% 0.29/0.46        ( ( insert_nat @ X2 @ ( insert_nat @ X2 @ A3 ) )
% 0.29/0.46        = ( insert_nat @ X2 @ A3 ) ) ).
% 0.29/0.46  
% 0.29/0.46  % insert_absorb2
% 0.29/0.46  thf(fact_253_insert__absorb2,axiom,
% 0.29/0.46      ! [X2: produc1124793815um_a_b,A3: set_Pr1174980151um_a_b] :
% 0.29/0.46        ( ( insert983991207um_a_b @ X2 @ ( insert983991207um_a_b @ X2 @ A3 ) )
% 0.29/0.46        = ( insert983991207um_a_b @ X2 @ A3 ) ) ).
% 0.29/0.46  
% 0.29/0.46  % insert_absorb2
% 0.29/0.46  thf(fact_254_insert__absorb2,axiom,
% 0.29/0.46      ! [X2: produc1963079155um_a_b,A3: set_Pr409224873um_a_b] :
% 0.29/0.46        ( ( insert323157027um_a_b @ X2 @ ( insert323157027um_a_b @ X2 @ A3 ) )
% 0.29/0.46        = ( insert323157027um_a_b @ X2 @ A3 ) ) ).
% 0.29/0.46  
% 0.29/0.46  % insert_absorb2
% 0.29/0.46  thf(fact_255_insert__absorb2,axiom,
% 0.29/0.46      ! [X2: sum_sum_a_b,A3: set_Sum_sum_a_b] :
% 0.29/0.46        ( ( insert_Sum_sum_a_b @ X2 @ ( insert_Sum_sum_a_b @ X2 @ A3 ) )
% 0.29/0.46        = ( insert_Sum_sum_a_b @ X2 @ A3 ) ) ).
% 0.29/0.46  
% 0.29/0.46  % insert_absorb2
% 0.29/0.46  thf(fact_256_insert__absorb2,axiom,
% 0.29/0.46      ! [X2: produc1548871597um_a_b,A3: set_Pr1916610317um_a_b] :
% 0.29/0.46        ( ( insert1435405693um_a_b @ X2 @ ( insert1435405693um_a_b @ X2 @ A3 ) )
% 0.29/0.46        = ( insert1435405693um_a_b @ X2 @ A3 ) ) ).
% 0.29/0.46  
% 0.29/0.46  % insert_absorb2
% 0.29/0.46  thf(fact_257_insert__absorb2,axiom,
% 0.29/0.46      ! [X2: standard_Constant_a,A3: set_St761939237tant_a] :
% 0.29/0.46        ( ( insert1909710879tant_a @ X2 @ ( insert1909710879tant_a @ X2 @ A3 ) )
% 0.29/0.46        = ( insert1909710879tant_a @ X2 @ A3 ) ) ).
% 0.29/0.46  
% 0.29/0.46  % insert_absorb2
% 0.29/0.46  thf(fact_258_insert__absorb2,axiom,
% 0.29/0.46      ! [X2: product_prod_nat_nat,A3: set_Pr1986765409at_nat] :
% 0.29/0.46        ( ( insert271595217at_nat @ X2 @ ( insert271595217at_nat @ X2 @ A3 ) )
% 0.29/0.46        = ( insert271595217at_nat @ X2 @ A3 ) ) ).
% 0.29/0.46  
% 0.29/0.46  % insert_absorb2
% 0.29/0.46  thf(fact_259_graph__homomorphism__empty,axiom,
% 0.29/0.46      ! [G: labele935650037_a_nat,F: set_Pr1986765409at_nat] :
% 0.29/0.46        ( ( graph_2130075512at_nat @ ( labele16114835_a_nat @ bot_bo810816657at_nat @ bot_bot_set_nat ) @ G @ F )
% 0.29/0.46        = ( ( F = bot_bo2130386637at_nat )
% 0.29/0.46          & ( G
% 0.29/0.46            = ( restri572569417_a_nat @ G ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % graph_homomorphism_empty
% 0.29/0.46  thf(fact_260_graph__homomorphism__empty,axiom,
% 0.29/0.46      ! [G: labele935650037_a_nat,F: set_Pr375490359_b_nat] :
% 0.29/0.46        ( ( graph_165730638_b_nat @ ( labele1729654377um_a_b @ bot_bo1262634813um_a_b @ bot_bo1491243248um_a_b ) @ G @ F )
% 0.29/0.46        = ( ( F = bot_bo1923972003_b_nat )
% 0.29/0.46          & ( G
% 0.29/0.46            = ( restri572569417_a_nat @ G ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % graph_homomorphism_empty
% 0.29/0.46  thf(fact_261_graph__homomorphism__empty,axiom,
% 0.29/0.46      ! [G: labele431970251um_a_b,F: set_Pr1174980151um_a_b] :
% 0.29/0.46        ( ( graph_1452133198um_a_b @ ( labele16114835_a_nat @ bot_bo810816657at_nat @ bot_bot_set_nat ) @ G @ F )
% 0.29/0.46        = ( ( F = bot_bo575978147um_a_b )
% 0.29/0.46          & ( G
% 0.29/0.46            = ( restri1162247455um_a_b @ G ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % graph_homomorphism_empty
% 0.29/0.46  thf(fact_262_graph__homomorphism__empty,axiom,
% 0.29/0.46      ! [G: labele935650037_a_nat,F: set_Pr1902304780_b_nat] :
% 0.29/0.46        ( ( graph_1203757137_b_nat @ ( labele2034032468um_a_b @ bot_bo1208513655um_a_b @ bot_bo575978147um_a_b ) @ G @ F )
% 0.29/0.46        = ( ( F = bot_bo949957280_b_nat )
% 0.29/0.46          & ( G
% 0.29/0.46            = ( restri572569417_a_nat @ G ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % graph_homomorphism_empty
% 0.29/0.46  thf(fact_263_graph__homomorphism__empty,axiom,
% 0.29/0.46      ! [G: labele431970251um_a_b,F: set_Pr1916610317um_a_b] :
% 0.29/0.46        ( ( graph_611893540um_a_b @ ( labele1729654377um_a_b @ bot_bo1262634813um_a_b @ bot_bo1491243248um_a_b ) @ G @ F )
% 0.29/0.46        = ( ( F = bot_bo225809273um_a_b )
% 0.29/0.46          & ( G
% 0.29/0.46            = ( restri1162247455um_a_b @ G ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % graph_homomorphism_empty
% 0.29/0.46  thf(fact_264_graph__homomorphism__empty,axiom,
% 0.29/0.46      ! [G: labele935650037_a_nat,F: set_Pr689416536at_nat] :
% 0.29/0.46        ( ( graph_149544303at_nat @ ( labele1813985418at_nat @ bot_bo1524397311at_nat @ bot_bo810816657at_nat ) @ G @ F )
% 0.29/0.46        = ( ( F = bot_bo1582968772at_nat )
% 0.29/0.46          & ( G
% 0.29/0.46            = ( restri572569417_a_nat @ G ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % graph_homomorphism_empty
% 0.29/0.46  thf(fact_265_graph__homomorphism__empty,axiom,
% 0.29/0.46      ! [G: labele431970251um_a_b,F: set_Pr653770722um_a_b] :
% 0.29/0.46        ( ( graph_502887975um_a_b @ ( labele2034032468um_a_b @ bot_bo1208513655um_a_b @ bot_bo575978147um_a_b ) @ G @ F )
% 0.29/0.46        = ( ( F = bot_bo1892785270um_a_b )
% 0.29/0.46          & ( G
% 0.29/0.46            = ( restri1162247455um_a_b @ G ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % graph_homomorphism_empty
% 0.29/0.46  thf(fact_266_graph__homomorphism__empty,axiom,
% 0.29/0.46      ! [G: labele935650037_a_nat,F: set_Pr507214050_b_nat] :
% 0.29/0.46        ( ( graph_1815313447_b_nat @ ( labele989994um_a_b @ bot_bo1262778871um_a_b @ bot_bo225809273um_a_b ) @ G @ F )
% 0.29/0.46        = ( ( F = bot_bo1746228598_b_nat )
% 0.29/0.46          & ( G
% 0.29/0.46            = ( restri572569417_a_nat @ G ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % graph_homomorphism_empty
% 0.29/0.46  thf(fact_267_graph__homomorphism__empty,axiom,
% 0.29/0.46      ! [G: labele431970251um_a_b,F: set_Pr304595758um_a_b] :
% 0.29/0.46        ( ( graph_166346565um_a_b @ ( labele1813985418at_nat @ bot_bo1524397311at_nat @ bot_bo810816657at_nat ) @ G @ F )
% 0.29/0.46        = ( ( F = bot_bo627753370um_a_b )
% 0.29/0.46          & ( G
% 0.29/0.46            = ( restri1162247455um_a_b @ G ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % graph_homomorphism_empty
% 0.29/0.46  thf(fact_268_graph__homomorphism__empty,axiom,
% 0.29/0.46      ! [G: labele431970251um_a_b,F: set_Pr55236280um_a_b] :
% 0.29/0.46        ( ( graph_1763806717um_a_b @ ( labele989994um_a_b @ bot_bo1262778871um_a_b @ bot_bo225809273um_a_b ) @ G @ F )
% 0.29/0.46        = ( ( F = bot_bo1217542988um_a_b )
% 0.29/0.46          & ( G
% 0.29/0.46            = ( restri1162247455um_a_b @ G ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % graph_homomorphism_empty
% 0.29/0.46  thf(fact_269_edge__preserving__subset,axiom,
% 0.29/0.46      ! [R_1: set_Pr1174980151um_a_b,R_2: set_Pr1174980151um_a_b,E_1: set_Pr1647387645at_nat,E_2: set_Pr1647387645at_nat,G: set_Pr409224873um_a_b] :
% 0.29/0.46        ( ( ord_le823954903um_a_b @ R_1 @ R_2 )
% 0.29/0.46       => ( ( ord_le1909159005at_nat @ E_1 @ E_2 )
% 0.29/0.46         => ( ( edge_p1382426714tant_a @ R_2 @ E_2 @ G )
% 0.29/0.46           => ( edge_p1382426714tant_a @ R_1 @ E_1 @ G ) ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % edge_preserving_subset
% 0.29/0.46  thf(fact_270_subrelI,axiom,
% 0.29/0.46      ! [R: set_Pr1647387645at_nat,S: set_Pr1647387645at_nat] :
% 0.29/0.46        ( ! [X4: standard_Constant_a,Y4: product_prod_nat_nat] :
% 0.29/0.46            ( ( member1696759390at_nat @ ( produc407553657at_nat @ X4 @ Y4 ) @ R )
% 0.29/0.46           => ( member1696759390at_nat @ ( produc407553657at_nat @ X4 @ Y4 ) @ S ) )
% 0.29/0.46       => ( ord_le1909159005at_nat @ R @ S ) ) ).
% 0.29/0.46  
% 0.29/0.46  % subrelI
% 0.29/0.46  thf(fact_271_subrelI,axiom,
% 0.29/0.46      ! [R: set_Pr1986765409at_nat,S: set_Pr1986765409at_nat] :
% 0.29/0.46        ( ! [X4: nat,Y4: nat] :
% 0.29/0.46            ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) @ R )
% 0.29/0.46           => ( member701585322at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) @ S ) )
% 0.29/0.46       => ( ord_le841296385at_nat @ R @ S ) ) ).
% 0.29/0.46  
% 0.29/0.46  % subrelI
% 0.29/0.46  thf(fact_272_subrelI,axiom,
% 0.29/0.46      ! [R: set_Pr1174980151um_a_b,S: set_Pr1174980151um_a_b] :
% 0.29/0.46        ( ! [X4: nat,Y4: sum_sum_a_b] :
% 0.29/0.46            ( ( member1294585472um_a_b @ ( produc1808556047um_a_b @ X4 @ Y4 ) @ R )
% 0.29/0.46           => ( member1294585472um_a_b @ ( produc1808556047um_a_b @ X4 @ Y4 ) @ S ) )
% 0.29/0.46       => ( ord_le823954903um_a_b @ R @ S ) ) ).
% 0.29/0.46  
% 0.29/0.46  % subrelI
% 0.29/0.46  thf(fact_273_subrelI,axiom,
% 0.29/0.46      ! [R: set_Pr409224873um_a_b,S: set_Pr409224873um_a_b] :
% 0.29/0.46        ( ! [X4: standard_Constant_a,Y4: produc1548871597um_a_b] :
% 0.29/0.46            ( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ X4 @ Y4 ) @ R )
% 0.29/0.46           => ( member1998628618um_a_b @ ( produc1697725733um_a_b @ X4 @ Y4 ) @ S ) )
% 0.29/0.46       => ( ord_le615126793um_a_b @ R @ S ) ) ).
% 0.29/0.46  
% 0.29/0.46  % subrelI
% 0.29/0.46  thf(fact_274_subrelI,axiom,
% 0.29/0.46      ! [R: set_Pr1916610317um_a_b,S: set_Pr1916610317um_a_b] :
% 0.29/0.46        ( ! [X4: sum_sum_a_b,Y4: sum_sum_a_b] :
% 0.29/0.46            ( ( member947389014um_a_b @ ( produc176426981um_a_b @ X4 @ Y4 ) @ R )
% 0.29/0.46           => ( member947389014um_a_b @ ( produc176426981um_a_b @ X4 @ Y4 ) @ S ) )
% 0.29/0.46       => ( ord_le1059794605um_a_b @ R @ S ) ) ).
% 0.29/0.46  
% 0.29/0.46  % subrelI
% 0.29/0.46  thf(fact_275_restrict__subsD,axiom,
% 0.29/0.46      ! [G: labele935650037_a_nat] :
% 0.29/0.46        ( ( ord_le1909159005at_nat @ ( labele195203296_a_nat @ G ) @ ( labele195203296_a_nat @ ( restri572569417_a_nat @ G ) ) )
% 0.29/0.46       => ( G
% 0.29/0.46          = ( restri572569417_a_nat @ G ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % restrict_subsD
% 0.29/0.46  thf(fact_276_restrict__subsD,axiom,
% 0.29/0.46      ! [G: labele431970251um_a_b] :
% 0.29/0.46        ( ( ord_le615126793um_a_b @ ( labele1939049654um_a_b @ G ) @ ( labele1939049654um_a_b @ ( restri1162247455um_a_b @ G ) ) )
% 0.29/0.46       => ( G
% 0.29/0.46          = ( restri1162247455um_a_b @ G ) ) ) ).
% 0.29/0.46  
% 0.29/0.46  % restrict_subsD
% 0.29/0.46  thf(fact_277_zero__reorient,axiom,
% 0.29/0.46      ! [X2: nat] :
% 0.29/0.46        ( ( zero_zero_nat = X2 )
% 0.29/0.46        = ( X2 = zero_zero_nat ) ) ).
% 0.29/0.46  
% 0.29/0.46  % zero_reorient
% 0.29/0.46  thf(fact_278_emptyE,axiom,
% 0.29/0.46      ! [A: produc1032616263at_nat] :
% 0.29/0.46        ~ ( member1696759390at_nat @ A @ bot_bo810816657at_nat ) ).
% 0.29/0.46  
% 0.29/0.46  % emptyE
% 0.29/0.46  thf(fact_279_emptyE,axiom,
% 0.29/0.46      ! [A: nat] :
% 0.29/0.46        ~ ( member_nat @ A @ bot_bot_set_nat ) ).
% 0.29/0.46  
% 0.29/0.46  % emptyE
% 0.29/0.46  thf(fact_280_emptyE,axiom,
% 0.29/0.46      ! [A: produc1124793815um_a_b] :
% 0.29/0.46        ~ ( member1294585472um_a_b @ A @ bot_bo575978147um_a_b ) ).
% 0.29/0.46  
% 0.29/0.46  % emptyE
% 0.29/0.46  thf(fact_281_emptyE,axiom,
% 0.29/0.46      ! [A: produc1548871597um_a_b] :
% 0.29/0.46        ~ ( member947389014um_a_b @ A @ bot_bo225809273um_a_b ) ).
% 0.29/0.46  
% 0.29/0.46  % emptyE
% 0.29/0.46  thf(fact_282_emptyE,axiom,
% 0.29/0.46      ! [A: produc1963079155um_a_b] :
% 0.29/0.46        ~ ( member1998628618um_a_b @ A @ bot_bo1262634813um_a_b ) ).
% 0.29/0.46  
% 0.29/0.46  % emptyE
% 0.29/0.46  thf(fact_283_emptyE,axiom,
% 0.29/0.46      ! [A: sum_sum_a_b] :
% 0.29/0.46        ~ ( member_Sum_sum_a_b @ A @ bot_bo1491243248um_a_b ) ).
% 0.29/0.46  
% 0.29/0.46  % emptyE
% 0.29/0.46  thf(fact_284_equals0D,axiom,
% 0.29/0.46      ! [A3: set_Pr1647387645at_nat,A: produc1032616263at_nat] :
% 0.29/0.46        ( ( A3 = bot_bo810816657at_nat )
% 0.29/0.46       => ~ ( member1696759390at_nat @ A @ A3 ) ) ).
% 0.29/0.46  
% 0.29/0.46  % equals0D
% 0.29/0.46  thf(fact_285_equals0D,axiom,
% 0.29/0.46      ! [A3: set_nat,A: nat] :
% 0.29/0.46        ( ( A3 = bot_bot_set_nat )
% 0.29/0.46       => ~ ( member_nat @ A @ A3 ) ) ).
% 0.29/0.46  
% 0.29/0.46  % equals0D
% 0.29/0.46  thf(fact_286_equals0D,axiom,
% 0.29/0.46      ! [A3: set_Pr1174980151um_a_b,A: produc1124793815um_a_b] :
% 0.29/0.46        ( ( A3 = bot_bo575978147um_a_b )
% 0.29/0.46       => ~ ( member1294585472um_a_b @ A @ A3 ) ) ).
% 0.29/0.46  
% 0.29/0.46  % equals0D
% 0.29/0.46  thf(fact_287_equals0D,axiom,
% 0.29/0.46      ! [A3: set_Pr1916610317um_a_b,A: produc1548871597um_a_b] :
% 0.29/0.46        ( ( A3 = bot_bo225809273um_a_b )
% 0.29/0.46       => ~ ( member947389014um_a_b @ A @ A3 ) ) ).
% 0.29/0.46  
% 0.29/0.46  % equals0D
% 0.29/0.46  thf(fact_288_equals0D,axiom,
% 0.29/0.46      ! [A3: set_Pr409224873um_a_b,A: produc1963079155um_a_b] :
% 0.29/0.46        ( ( A3 = bot_bo1262634813um_a_b )
% 0.29/0.46       => ~ ( member1998628618um_a_b @ A @ A3 ) ) ).
% 0.29/0.46  
% 0.29/0.46  % equals0D
% 0.29/0.46  thf(fact_289_equals0D,axiom,
% 0.29/0.46      ! [A3: set_Sum_sum_a_b,A: sum_sum_a_b] :
% 0.29/0.46        ( ( A3 = bot_bo1491243248um_a_b )
% 0.29/0.46       => ~ ( member_Sum_sum_a_b @ A @ A3 ) ) ).
% 0.29/0.46  
% 0.29/0.46  % equals0D
% 0.29/0.46  thf(fact_290_equals0I,axiom,
% 0.29/0.46      ! [A3: set_Pr1647387645at_nat] :
% 0.29/0.46        ( ! [Y4: produc1032616263at_nat] :
% 0.29/0.46            ~ ( member1696759390at_nat @ Y4 @ A3 )
% 0.29/0.46       => ( A3 = bot_bo810816657at_nat ) ) ).
% 0.29/0.46  
% 0.29/0.46  % equals0I
% 0.29/0.46  thf(fact_291_equals0I,axiom,
% 0.29/0.46      ! [A3: set_nat] :
% 0.29/0.46        ( ! [Y4: nat] :
% 0.29/0.46            ~ ( member_nat @ Y4 @ A3 )
% 0.29/0.46       => ( A3 = bot_bot_set_nat ) ) ).
% 0.29/0.46  
% 0.29/0.46  % equals0I
% 0.29/0.46  thf(fact_292_equals0I,axiom,
% 0.29/0.46      ! [A3: set_Pr1174980151um_a_b] :
% 0.29/0.46        ( ! [Y4: produc1124793815um_a_b] :
% 0.29/0.46            ~ ( member1294585472um_a_b @ Y4 @ A3 )
% 0.29/0.46       => ( A3 = bot_bo575978147um_a_b ) ) ).
% 0.29/0.46  
% 0.29/0.46  % equals0I
% 0.29/0.46  thf(fact_293_equals0I,axiom,
% 0.29/0.46      ! [A3: set_Pr1916610317um_a_b] :
% 0.29/0.46        ( ! [Y4: produc1548871597um_a_b] :
% 0.29/0.46            ~ ( member947389014um_a_b @ Y4 @ A3 )
% 0.29/0.46       => ( A3 = bot_bo225809273um_a_b ) ) ).
% 0.29/0.46  
% 0.29/0.46  % equals0I
% 0.29/0.46  thf(fact_294_equals0I,axiom,
% 0.29/0.46      ! [A3: set_Pr409224873um_a_b] :
% 0.29/0.46        ( ! [Y4: produc1963079155um_a_b] :
% 0.29/0.46            ~ ( member1998628618um_a_b @ Y4 @ A3 )
% 0.29/0.46       => ( A3 = bot_bo1262634813um_a_b ) ) ).
% 0.29/0.46  
% 0.29/0.46  % equals0I
% 0.29/0.46  thf(fact_295_equals0I,axiom,
% 0.29/0.46      ! [A3: set_Sum_sum_a_b] :
% 0.29/0.46        ( ! [Y4: sum_sum_a_b] :
% 0.29/0.46            ~ ( member_Sum_sum_a_b @ Y4 @ A3 )
% 0.29/0.46       => ( A3 = bot_bo1491243248um_a_b ) ) ).
% 0.29/0.46  
% 0.29/0.46  % equals0I
% 0.29/0.46  thf(fact_296_ex__in__conv,axiom,
% 0.29/0.46      ! [A3: set_Pr1647387645at_nat] :
% 0.29/0.46        ( ( ? [X3: produc1032616263at_nat] : ( member1696759390at_nat @ X3 @ A3 ) )
% 0.29/0.46        = ( A3 != bot_bo810816657at_nat ) ) ).
% 0.29/0.46  
% 0.29/0.46  % ex_in_conv
% 0.29/0.46  thf(fact_297_ex__in__conv,axiom,
% 0.29/0.46      ! [A3: set_nat] :
% 0.29/0.46        ( ( ? [X3: nat] : ( member_nat @ X3 @ A3 ) )
% 0.29/0.46        = ( A3 != bot_bot_set_nat ) ) ).
% 0.29/0.46  
% 0.29/0.46  % ex_in_conv
% 0.29/0.46  thf(fact_298_ex__in__conv,axiom,
% 0.29/0.46      ! [A3: set_Pr1174980151um_a_b] :
% 0.29/0.46        ( ( ? [X3: produc1124793815um_a_b] : ( member1294585472um_a_b @ X3 @ A3 ) )
% 0.29/0.46        = ( A3 != bot_bo575978147um_a_b ) ) ).
% 0.29/0.46  
% 0.29/0.46  % ex_in_conv
% 0.29/0.46  thf(fact_299_ex__in__conv,axiom,
% 0.29/0.46      ! [A3: set_Pr1916610317um_a_b] :
% 0.29/0.46        ( ( ? [X3: produc1548871597um_a_b] : ( member947389014um_a_b @ X3 @ A3 ) )
% 0.29/0.46        = ( A3 != bot_bo225809273um_a_b ) ) ).
% 0.29/0.46  
% 0.29/0.46  % ex_in_conv
% 0.29/0.46  thf(fact_300_ex__in__conv,axiom,
% 0.29/0.46      ! [A3: set_Pr409224873um_a_b] :
% 0.29/0.47        ( ( ? [X3: produc1963079155um_a_b] : ( member1998628618um_a_b @ X3 @ A3 ) )
% 0.29/0.47        = ( A3 != bot_bo1262634813um_a_b ) ) ).
% 0.29/0.47  
% 0.29/0.47  % ex_in_conv
% 0.29/0.47  thf(fact_301_ex__in__conv,axiom,
% 0.29/0.47      ! [A3: set_Sum_sum_a_b] :
% 0.29/0.47        ( ( ? [X3: sum_sum_a_b] : ( member_Sum_sum_a_b @ X3 @ A3 ) )
% 0.29/0.47        = ( A3 != bot_bo1491243248um_a_b ) ) ).
% 0.29/0.47  
% 0.29/0.47  % ex_in_conv
% 0.29/0.47  thf(fact_302_in__mono,axiom,
% 0.29/0.47      ! [A3: set_Pr1174980151um_a_b,B5: set_Pr1174980151um_a_b,X2: produc1124793815um_a_b] :
% 0.29/0.47        ( ( ord_le823954903um_a_b @ A3 @ B5 )
% 0.29/0.47       => ( ( member1294585472um_a_b @ X2 @ A3 )
% 0.29/0.47         => ( member1294585472um_a_b @ X2 @ B5 ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % in_mono
% 0.29/0.47  thf(fact_303_in__mono,axiom,
% 0.29/0.47      ! [A3: set_Pr409224873um_a_b,B5: set_Pr409224873um_a_b,X2: produc1963079155um_a_b] :
% 0.29/0.47        ( ( ord_le615126793um_a_b @ A3 @ B5 )
% 0.29/0.47       => ( ( member1998628618um_a_b @ X2 @ A3 )
% 0.29/0.47         => ( member1998628618um_a_b @ X2 @ B5 ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % in_mono
% 0.29/0.47  thf(fact_304_in__mono,axiom,
% 0.29/0.47      ! [A3: set_Sum_sum_a_b,B5: set_Sum_sum_a_b,X2: sum_sum_a_b] :
% 0.29/0.47        ( ( ord_le192794300um_a_b @ A3 @ B5 )
% 0.29/0.47       => ( ( member_Sum_sum_a_b @ X2 @ A3 )
% 0.29/0.47         => ( member_Sum_sum_a_b @ X2 @ B5 ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % in_mono
% 0.29/0.47  thf(fact_305_subsetD,axiom,
% 0.29/0.47      ! [A3: set_Pr1174980151um_a_b,B5: set_Pr1174980151um_a_b,C: produc1124793815um_a_b] :
% 0.29/0.47        ( ( ord_le823954903um_a_b @ A3 @ B5 )
% 0.29/0.47       => ( ( member1294585472um_a_b @ C @ A3 )
% 0.29/0.47         => ( member1294585472um_a_b @ C @ B5 ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % subsetD
% 0.29/0.47  thf(fact_306_subsetD,axiom,
% 0.29/0.47      ! [A3: set_Pr409224873um_a_b,B5: set_Pr409224873um_a_b,C: produc1963079155um_a_b] :
% 0.29/0.47        ( ( ord_le615126793um_a_b @ A3 @ B5 )
% 0.29/0.47       => ( ( member1998628618um_a_b @ C @ A3 )
% 0.29/0.47         => ( member1998628618um_a_b @ C @ B5 ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % subsetD
% 0.29/0.47  thf(fact_307_subsetD,axiom,
% 0.29/0.47      ! [A3: set_Sum_sum_a_b,B5: set_Sum_sum_a_b,C: sum_sum_a_b] :
% 0.29/0.47        ( ( ord_le192794300um_a_b @ A3 @ B5 )
% 0.29/0.47       => ( ( member_Sum_sum_a_b @ C @ A3 )
% 0.29/0.47         => ( member_Sum_sum_a_b @ C @ B5 ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % subsetD
% 0.29/0.47  thf(fact_308_equalityE,axiom,
% 0.29/0.47      ! [A3: set_Sum_sum_a_b,B5: set_Sum_sum_a_b] :
% 0.29/0.47        ( ( A3 = B5 )
% 0.29/0.47       => ~ ( ( ord_le192794300um_a_b @ A3 @ B5 )
% 0.29/0.47           => ~ ( ord_le192794300um_a_b @ B5 @ A3 ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % equalityE
% 0.29/0.47  thf(fact_309_subset__eq,axiom,
% 0.29/0.47      ( ord_le823954903um_a_b
% 0.29/0.47      = ( ^ [A7: set_Pr1174980151um_a_b,B6: set_Pr1174980151um_a_b] :
% 0.29/0.47          ! [X3: produc1124793815um_a_b] :
% 0.29/0.47            ( ( member1294585472um_a_b @ X3 @ A7 )
% 0.29/0.47           => ( member1294585472um_a_b @ X3 @ B6 ) ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % subset_eq
% 0.29/0.47  thf(fact_310_subset__eq,axiom,
% 0.29/0.47      ( ord_le615126793um_a_b
% 0.29/0.47      = ( ^ [A7: set_Pr409224873um_a_b,B6: set_Pr409224873um_a_b] :
% 0.29/0.47          ! [X3: produc1963079155um_a_b] :
% 0.29/0.47            ( ( member1998628618um_a_b @ X3 @ A7 )
% 0.29/0.47           => ( member1998628618um_a_b @ X3 @ B6 ) ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % subset_eq
% 0.29/0.47  thf(fact_311_subset__eq,axiom,
% 0.29/0.47      ( ord_le192794300um_a_b
% 0.29/0.47      = ( ^ [A7: set_Sum_sum_a_b,B6: set_Sum_sum_a_b] :
% 0.29/0.47          ! [X3: sum_sum_a_b] :
% 0.29/0.47            ( ( member_Sum_sum_a_b @ X3 @ A7 )
% 0.29/0.47           => ( member_Sum_sum_a_b @ X3 @ B6 ) ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % subset_eq
% 0.29/0.47  thf(fact_312_equalityD1,axiom,
% 0.29/0.47      ! [A3: set_Sum_sum_a_b,B5: set_Sum_sum_a_b] :
% 0.29/0.47        ( ( A3 = B5 )
% 0.29/0.47       => ( ord_le192794300um_a_b @ A3 @ B5 ) ) ).
% 0.29/0.47  
% 0.29/0.47  % equalityD1
% 0.29/0.47  thf(fact_313_equalityD2,axiom,
% 0.29/0.47      ! [A3: set_Sum_sum_a_b,B5: set_Sum_sum_a_b] :
% 0.29/0.47        ( ( A3 = B5 )
% 0.29/0.47       => ( ord_le192794300um_a_b @ B5 @ A3 ) ) ).
% 0.29/0.47  
% 0.29/0.47  % equalityD2
% 0.29/0.47  thf(fact_314_subset__iff,axiom,
% 0.29/0.47      ( ord_le823954903um_a_b
% 0.29/0.47      = ( ^ [A7: set_Pr1174980151um_a_b,B6: set_Pr1174980151um_a_b] :
% 0.29/0.47          ! [T: produc1124793815um_a_b] :
% 0.29/0.47            ( ( member1294585472um_a_b @ T @ A7 )
% 0.29/0.47           => ( member1294585472um_a_b @ T @ B6 ) ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % subset_iff
% 0.29/0.47  thf(fact_315_subset__iff,axiom,
% 0.29/0.47      ( ord_le615126793um_a_b
% 0.29/0.47      = ( ^ [A7: set_Pr409224873um_a_b,B6: set_Pr409224873um_a_b] :
% 0.29/0.47          ! [T: produc1963079155um_a_b] :
% 0.29/0.47            ( ( member1998628618um_a_b @ T @ A7 )
% 0.29/0.47           => ( member1998628618um_a_b @ T @ B6 ) ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % subset_iff
% 0.29/0.47  thf(fact_316_subset__iff,axiom,
% 0.29/0.47      ( ord_le192794300um_a_b
% 0.29/0.47      = ( ^ [A7: set_Sum_sum_a_b,B6: set_Sum_sum_a_b] :
% 0.29/0.47          ! [T: sum_sum_a_b] :
% 0.29/0.47            ( ( member_Sum_sum_a_b @ T @ A7 )
% 0.29/0.47           => ( member_Sum_sum_a_b @ T @ B6 ) ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % subset_iff
% 0.29/0.47  thf(fact_317_subset__refl,axiom,
% 0.29/0.47      ! [A3: set_Sum_sum_a_b] : ( ord_le192794300um_a_b @ A3 @ A3 ) ).
% 0.29/0.47  
% 0.29/0.47  % subset_refl
% 0.29/0.47  thf(fact_318_Collect__mono,axiom,
% 0.29/0.47      ! [P: sum_sum_a_b > $o,Q: sum_sum_a_b > $o] :
% 0.29/0.47        ( ! [X4: sum_sum_a_b] :
% 0.29/0.47            ( ( P @ X4 )
% 0.29/0.47           => ( Q @ X4 ) )
% 0.29/0.47       => ( ord_le192794300um_a_b @ ( collect_Sum_sum_a_b @ P ) @ ( collect_Sum_sum_a_b @ Q ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % Collect_mono
% 0.29/0.47  thf(fact_319_subset__trans,axiom,
% 0.29/0.47      ! [A3: set_Sum_sum_a_b,B5: set_Sum_sum_a_b,C2: set_Sum_sum_a_b] :
% 0.29/0.47        ( ( ord_le192794300um_a_b @ A3 @ B5 )
% 0.29/0.47       => ( ( ord_le192794300um_a_b @ B5 @ C2 )
% 0.29/0.47         => ( ord_le192794300um_a_b @ A3 @ C2 ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % subset_trans
% 0.29/0.47  thf(fact_320_set__eq__subset,axiom,
% 0.29/0.47      ( ( ^ [Y5: set_Sum_sum_a_b,Z: set_Sum_sum_a_b] : ( Y5 = Z ) )
% 0.29/0.47      = ( ^ [A7: set_Sum_sum_a_b,B6: set_Sum_sum_a_b] :
% 0.29/0.47            ( ( ord_le192794300um_a_b @ A7 @ B6 )
% 0.29/0.47            & ( ord_le192794300um_a_b @ B6 @ A7 ) ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % set_eq_subset
% 0.29/0.47  thf(fact_321_Collect__mono__iff,axiom,
% 0.29/0.47      ! [P: sum_sum_a_b > $o,Q: sum_sum_a_b > $o] :
% 0.29/0.47        ( ( ord_le192794300um_a_b @ ( collect_Sum_sum_a_b @ P ) @ ( collect_Sum_sum_a_b @ Q ) )
% 0.29/0.47        = ( ! [X3: sum_sum_a_b] :
% 0.29/0.47              ( ( P @ X3 )
% 0.29/0.47             => ( Q @ X3 ) ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % Collect_mono_iff
% 0.29/0.47  thf(fact_322_insertE,axiom,
% 0.29/0.47      ! [A: produc1032616263at_nat,B: produc1032616263at_nat,A3: set_Pr1647387645at_nat] :
% 0.29/0.47        ( ( member1696759390at_nat @ A @ ( insert1625259895at_nat @ B @ A3 ) )
% 0.29/0.47       => ( ( A != B )
% 0.29/0.47         => ( member1696759390at_nat @ A @ A3 ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % insertE
% 0.29/0.47  thf(fact_323_insertE,axiom,
% 0.29/0.47      ! [A: nat,B: nat,A3: set_nat] :
% 0.29/0.47        ( ( member_nat @ A @ ( insert_nat @ B @ A3 ) )
% 0.29/0.47       => ( ( A != B )
% 0.29/0.47         => ( member_nat @ A @ A3 ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % insertE
% 0.29/0.47  thf(fact_324_insertE,axiom,
% 0.29/0.47      ! [A: produc1548871597um_a_b,B: produc1548871597um_a_b,A3: set_Pr1916610317um_a_b] :
% 0.29/0.47        ( ( member947389014um_a_b @ A @ ( insert1435405693um_a_b @ B @ A3 ) )
% 0.29/0.47       => ( ( A != B )
% 0.29/0.47         => ( member947389014um_a_b @ A @ A3 ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % insertE
% 0.29/0.47  thf(fact_325_insertE,axiom,
% 0.29/0.47      ! [A: standard_Constant_a,B: standard_Constant_a,A3: set_St761939237tant_a] :
% 0.29/0.47        ( ( member1632892294tant_a @ A @ ( insert1909710879tant_a @ B @ A3 ) )
% 0.29/0.47       => ( ( A != B )
% 0.29/0.47         => ( member1632892294tant_a @ A @ A3 ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % insertE
% 0.29/0.47  thf(fact_326_insertE,axiom,
% 0.29/0.47      ! [A: product_prod_nat_nat,B: product_prod_nat_nat,A3: set_Pr1986765409at_nat] :
% 0.29/0.47        ( ( member701585322at_nat @ A @ ( insert271595217at_nat @ B @ A3 ) )
% 0.29/0.47       => ( ( A != B )
% 0.29/0.47         => ( member701585322at_nat @ A @ A3 ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % insertE
% 0.29/0.47  thf(fact_327_insertE,axiom,
% 0.29/0.47      ! [A: sum_sum_a_b,B: sum_sum_a_b,A3: set_Sum_sum_a_b] :
% 0.29/0.47        ( ( member_Sum_sum_a_b @ A @ ( insert_Sum_sum_a_b @ B @ A3 ) )
% 0.29/0.47       => ( ( A != B )
% 0.29/0.47         => ( member_Sum_sum_a_b @ A @ A3 ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % insertE
% 0.29/0.47  thf(fact_328_insertE,axiom,
% 0.29/0.47      ! [A: produc1124793815um_a_b,B: produc1124793815um_a_b,A3: set_Pr1174980151um_a_b] :
% 0.29/0.47        ( ( member1294585472um_a_b @ A @ ( insert983991207um_a_b @ B @ A3 ) )
% 0.29/0.47       => ( ( A != B )
% 0.29/0.47         => ( member1294585472um_a_b @ A @ A3 ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % insertE
% 0.29/0.47  thf(fact_329_insertE,axiom,
% 0.29/0.47      ! [A: produc1963079155um_a_b,B: produc1963079155um_a_b,A3: set_Pr409224873um_a_b] :
% 0.29/0.47        ( ( member1998628618um_a_b @ A @ ( insert323157027um_a_b @ B @ A3 ) )
% 0.29/0.47       => ( ( A != B )
% 0.29/0.47         => ( member1998628618um_a_b @ A @ A3 ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % insertE
% 0.29/0.47  thf(fact_330_insertI1,axiom,
% 0.29/0.47      ! [A: product_prod_nat_nat,B5: set_Pr1986765409at_nat] : ( member701585322at_nat @ A @ ( insert271595217at_nat @ A @ B5 ) ) ).
% 0.29/0.47  
% 0.29/0.47  % insertI1
% 0.29/0.47  thf(fact_331_insertI1,axiom,
% 0.29/0.47      ! [A: sum_sum_a_b,B5: set_Sum_sum_a_b] : ( member_Sum_sum_a_b @ A @ ( insert_Sum_sum_a_b @ A @ B5 ) ) ).
% 0.29/0.47  
% 0.29/0.47  % insertI1
% 0.29/0.47  thf(fact_332_insertI1,axiom,
% 0.29/0.47      ! [A: produc1124793815um_a_b,B5: set_Pr1174980151um_a_b] : ( member1294585472um_a_b @ A @ ( insert983991207um_a_b @ A @ B5 ) ) ).
% 0.29/0.47  
% 0.29/0.47  % insertI1
% 0.29/0.47  thf(fact_333_insertI1,axiom,
% 0.29/0.47      ! [A: produc1963079155um_a_b,B5: set_Pr409224873um_a_b] : ( member1998628618um_a_b @ A @ ( insert323157027um_a_b @ A @ B5 ) ) ).
% 0.29/0.47  
% 0.29/0.47  % insertI1
% 0.29/0.47  thf(fact_334_le0,axiom,
% 0.29/0.47      ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.29/0.47  
% 0.29/0.47  % le0
% 0.29/0.47  thf(fact_335_bot__nat__0_Oextremum,axiom,
% 0.29/0.47      ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 0.29/0.47  
% 0.29/0.47  % bot_nat_0.extremum
% 0.29/0.47  thf(fact_336_Nat_Oex__has__greatest__nat,axiom,
% 0.29/0.47      ! [P: nat > $o,K: nat,B: nat] :
% 0.29/0.47        ( ( P @ K )
% 0.29/0.47       => ( ! [Y4: nat] :
% 0.29/0.47              ( ( P @ Y4 )
% 0.29/0.47             => ( ord_less_eq_nat @ Y4 @ B ) )
% 0.29/0.47         => ? [X4: nat] :
% 0.29/0.47              ( ( P @ X4 )
% 0.29/0.47              & ! [Y6: nat] :
% 0.29/0.47                  ( ( P @ Y6 )
% 0.29/0.47                 => ( ord_less_eq_nat @ Y6 @ X4 ) ) ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % Nat.ex_has_greatest_nat
% 0.29/0.47  thf(fact_337_nat__le__linear,axiom,
% 0.29/0.47      ! [M: nat,N: nat] :
% 0.29/0.47        ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.47        | ( ord_less_eq_nat @ N @ M ) ) ).
% 0.29/0.47  
% 0.29/0.47  % nat_le_linear
% 0.29/0.47  thf(fact_338_le__antisym,axiom,
% 0.29/0.47      ! [M: nat,N: nat] :
% 0.29/0.47        ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.47       => ( ( ord_less_eq_nat @ N @ M )
% 0.29/0.47         => ( M = N ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % le_antisym
% 0.29/0.47  thf(fact_339_eq__imp__le,axiom,
% 0.29/0.47      ! [M: nat,N: nat] :
% 0.29/0.47        ( ( M = N )
% 0.29/0.47       => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.29/0.47  
% 0.29/0.47  % eq_imp_le
% 0.29/0.47  thf(fact_340_le__trans,axiom,
% 0.29/0.47      ! [I: nat,J: nat,K: nat] :
% 0.29/0.47        ( ( ord_less_eq_nat @ I @ J )
% 0.29/0.47       => ( ( ord_less_eq_nat @ J @ K )
% 0.29/0.47         => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % le_trans
% 0.29/0.47  thf(fact_341_le__refl,axiom,
% 0.29/0.47      ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 0.29/0.47  
% 0.29/0.47  % le_refl
% 0.29/0.47  thf(fact_342_bot__nat__def,axiom,
% 0.29/0.47      bot_bot_nat = zero_zero_nat ).
% 0.29/0.47  
% 0.29/0.47  % bot_nat_def
% 0.29/0.47  thf(fact_343_bot__nat__0_Oextremum__uniqueI,axiom,
% 0.29/0.47      ! [A: nat] :
% 0.29/0.47        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.29/0.47       => ( A = zero_zero_nat ) ) ).
% 0.29/0.47  
% 0.29/0.47  % bot_nat_0.extremum_uniqueI
% 0.29/0.47  thf(fact_344_bot__nat__0_Oextremum__unique,axiom,
% 0.29/0.47      ! [A: nat] :
% 0.29/0.47        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.29/0.47        = ( A = zero_zero_nat ) ) ).
% 0.29/0.47  
% 0.29/0.47  % bot_nat_0.extremum_unique
% 0.29/0.47  thf(fact_345_le__0__eq,axiom,
% 0.29/0.47      ! [N: nat] :
% 0.29/0.47        ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 0.29/0.47        = ( N = zero_zero_nat ) ) ).
% 0.29/0.47  
% 0.29/0.47  % le_0_eq
% 0.29/0.47  thf(fact_346_less__eq__nat_Osimps_I1_J,axiom,
% 0.29/0.47      ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.29/0.47  
% 0.29/0.47  % less_eq_nat.simps(1)
% 0.29/0.47  thf(fact_347_gr_I1_J,axiom,
% 0.29/0.47      ( ( getRel1465196352um_a_b @ standard_S_Idt_a @ g )
% 0.29/0.47      = ( id_on_Sum_sum_a_b @ ( labele577278695um_a_b @ g ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  % gr(1)
% 0.29/0.47  thf(fact_348_gr_I2_J,axiom,
% 0.29/0.47      ( ( getRel1465196352um_a_b @ standard_S_Bot_a @ g )
% 0.29/0.47      = bot_bo225809273um_a_b ) ).
% 0.29/0.47  
% 0.29/0.47  % gr(2)
% 0.29/0.47  thf(fact_349__092_060open_062maintained_A_Isymmetry__rule_AS__Idt_J_AG_092_060close_062,axiom,
% 0.29/0.47      mainta522127984um_a_b @ ( standa997693288tant_a @ standard_S_Idt_a ) @ g ).
% 0.29/0.47  
% 0.29/0.47  % \<open>maintained (symmetry_rule S_Idt) G\<close>
% 0.29/0.47  thf(fact_350__092_060open_062maintained_A_Itransitive__rule_AS__Idt_J_AG_092_060close_062,axiom,
% 0.29/0.47      mainta522127984um_a_b @ ( standa1795879409tant_a @ standard_S_Idt_a ) @ g ).
% 0.29/0.47  
% 0.29/0.47  % \<open>maintained (transitive_rule S_Idt) G\<close>
% 0.29/0.47  thf(fact_351__092_060open_062maintained_A_Icongruence__rule_AS__Idt_Al_J_AG_092_060close_062,axiom,
% 0.29/0.47      mainta522127984um_a_b @ ( standa1343274079tant_a @ standard_S_Idt_a @ l ) @ g ).
% 0.29/0.47  
% 0.29/0.47  % \<open>maintained (congruence_rule S_Idt l) G\<close>
% 0.29/0.47  
% 0.29/0.47  % Conjectures (1)
% 0.29/0.47  thf(conj_0,conjecture,
% 0.29/0.47      ( ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 0.29/0.47        = ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ) )
% 0.29/0.47      & ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) )
% 0.29/0.47        = ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) )
% 0.29/0.47      & ( g
% 0.29/0.47        = ( restri1162247455um_a_b @ g ) )
% 0.29/0.47      & ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) @ ( labele577278695um_a_b @ g ) )
% 0.29/0.47      & ( unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) )
% 0.29/0.47      & ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) @ ( labele1939049654um_a_b @ g ) ) ) ).
% 0.29/0.47  
% 0.29/0.47  %------------------------------------------------------------------------------
% 0.29/0.47  ------------------------
% 2.81/1.52  ---- Embedded in THF ---
% 2.81/1.53  %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.81/1.53  %%% Generated on Tue Feb 24 08:29:00 EST 2026
% 2.81/1.53  %%% using '$$dhol' embedding, version 1.3.0.
% 2.81/1.53  %%% Logic specification used:
% 2.81/1.53  %%% thf(spec, logic, $$dhol).
% 2.81/1.53  
% 2.81/1.53  % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.XpaU65CC0V/DTF2DTF20438.p
% See solution above
% 2.81/1.53  ------------------------
% 2.81/1.57  ---- Cleaned THF ---
% 2.81/1.57  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
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% 2.81/1.57  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Sum____Type__Osum_Itf__a_Mtf__b_J_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_Mt__Product____Type__Oprod_It__Sum____Type__Osum_Itf__a_Mtf__b_J_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_J_J_J,type,
% 2.81/1.57      set_Pr1429673827um_a_b: $tType ).
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% 2.81/1.57  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_J_J_J,type,
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% 2.81/1.57  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_It__Sum____Type__Osum_Itf__a_Mtf__b_J_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_J_J_J,type,
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% 2.81/1.57  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_It__Sum____Type__Osum_Itf__a_Mtf__b_J_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_J_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_J,type,
% 2.81/1.57      set_Pr1121389018um_a_b: $tType ).
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% 2.81/1.57  thf(ty_n_t__Product____Type__Oprod_It__Sum____Type__Osum_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_It__Sum____Type__Osum_Itf__a_Mtf__b_J_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_J_J,type,
% 2.81/1.57      produc1733247354um_a_b: $tType ).
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% 2.81/1.57  thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_It__Sum____Type__Osum_Itf__a_Mtf__b_J_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_J_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J,type,
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% 2.81/1.57  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,
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% 2.81/1.57  thf(ty_n_t__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
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% 2.81/1.57  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_J,type,
% 2.81/1.57      set_Pr304595758um_a_b: $tType ).
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% 2.81/1.57  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_It__Sum____Type__Osum_Itf__a_Mtf__b_J_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_J_J,type,
% 2.81/1.57      set_Pr409224873um_a_b: $tType ).
% 2.81/1.57  
% 2.81/1.57  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_J_J,type,
% 2.81/1.57      set_Pr45173959um_a_b: $tType ).
% 2.81/1.57  
% 2.81/1.57  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Nat__Onat_J_J,type,
% 2.81/1.57      set_Pr689416536at_nat: $tType ).
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% 2.81/1.57  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
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% 2.81/1.57  thf(ty_n_t__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_It__Sum____Type__Osum_Itf__a_Mtf__b_J_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_J,type,
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% 2.81/1.57  thf(ty_n_t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_It__Sum____Type__Osum_Itf__a_Mtf__b_J_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_J,type,
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% 2.81/1.57  thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_J,type,
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% 2.81/1.57  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__Sum____Type__Osum_Itf__a_Mtf__b_J_J_J_J,type,
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% 2.81/1.57  thf(ty_n_t__LabeledGraphs__Olabeled____graph_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_J,type,
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% 2.81/1.57  thf(ty_n_t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_J,type,
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% 2.81/1.57  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__Sum____Type__Osum_Itf__a_Mtf__b_J_J_J,type,
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% 2.81/1.57  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_J_J,type,
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% 2.81/1.57  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Sum____Type__Osum_Itf__a_Mtf__b_J_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_Mt__Nat__Onat_J_J,type,
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% 2.81/1.57  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_J,type,
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% 2.81/1.57  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,
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% 2.81/1.57  thf(ty_n_t__Product____Type__Oprod_It__Sum____Type__Osum_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_J,type,
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% 2.81/1.57  thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J,type,
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% 2.81/1.57  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_Mt__Nat__Onat_J_J,type,
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% 2.81/1.57  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_J,type,
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% 2.81/1.57  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_J_J,type,
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% 2.81/1.57  thf(ty_n_t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J,type,
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% 2.81/1.57  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_Itf__a_Mtf__b_J_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_J,type,
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% 2.81/1.57  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Sum____Type__Osum_Itf__a_Mtf__b_J_Mt__Nat__Onat_J_J,type,
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% 2.81/1.57  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_J,type,
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% 2.81/1.57  thf(ty_n_t__Set__Oset_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_J,type,
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% 2.81/1.57  thf(ty_n_t__LabeledGraphSemantics__OStandard____Constant_Itf__a_J,type,
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% 2.81/1.57  thf(ty_n_t__Set__Oset_It__Sum____Type__Osum_Itf__a_Mtf__b_J_J,type,
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% 2.81/1.57  thf(ty_n_t__Sum____Type__Osum_Itf__a_Mtf__b_J,type,
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% 2.81/1.57  thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
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% 2.81/1.57  thf(ty_n_t__Nat__Onat,type,
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% 2.81/1.57  thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
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% 2.81/1.57  thf(sy_c_LabeledGraphSemantics_OStandard__Constant_OS__Bot_001tf__a,type,
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% 2.81/1.57  thf(sy_c_LabeledGraphSemantics_OStandard__Constant_OS__Idt_001tf__a,type,
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% 2.81/1.57  thf(sy_c_LabeledGraphSemantics_OgetRel_001t__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_001t__Sum____Type__Osum_Itf__a_Mtf__b_J,type,
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% 2.81/1.57  thf(sy_c_LabeledGraphs_Oedge__preserving_001t__Nat__Onat_001t__Sum____Type__Osum_Itf__a_Mtf__b_J_001t__LabeledGraphSemantics__OStandard____Constant_Itf__a_J,type,
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% 2.81/1.57  thf(sy_c_LabeledGraphs_Oedge__preserving_001t__Sum____Type__Osum_Itf__a_Mtf__b_J_001t__Nat__Onat_001t__LabeledGraphSemantics__OStandard____Constant_Itf__a_J,type,
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% 2.81/1.57      insert_Sum_sum_a_b: sum_sum_a_b > set_Sum_sum_a_b > set_Sum_sum_a_b ).
% 2.81/1.57  
% 2.81/1.57  thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Ocongruence__rule_001t__LabeledGraphSemantics__OStandard____Constant_Itf__a_J,type,
% 2.81/1.57      standa1343274079tant_a: standard_Constant_a > standard_Constant_a > produc1871334759_a_nat ).
% 2.81/1.57  
% 2.81/1.57  thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Ononempty__rule_001t__LabeledGraphSemantics__OStandard____Constant_Itf__a_J,type,
% 2.81/1.57      standa1410829644tant_a: produc1871334759_a_nat ).
% 2.81/1.57  
% 2.81/1.57  thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Oreflexivity__rule_001t__LabeledGraphSemantics__OStandard____Constant_Itf__a_J,type,
% 2.81/1.57      standa63370785tant_a: standard_Constant_a > produc1871334759_a_nat ).
% 2.81/1.57  
% 2.81/1.57  thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Osymmetry__rule_001t__LabeledGraphSemantics__OStandard____Constant_Itf__a_J,type,
% 2.81/1.57      standa997693288tant_a: standard_Constant_a > produc1871334759_a_nat ).
% 2.81/1.57  
% 2.81/1.57  thf(sy_c_StandardRules__Mirabelle__iljqcenreq_Otransitive__rule_001t__LabeledGraphSemantics__OStandard____Constant_Itf__a_J,type,
% 2.81/1.57      standa1795879409tant_a: standard_Constant_a > produc1871334759_a_nat ).
% 2.81/1.57  
% 2.81/1.57  thf(sy_c_member_001t__LabeledGraphSemantics__OStandard____Constant_Itf__a_J,type,
% 2.81/1.57      member1632892294tant_a: standard_Constant_a > set_St761939237tant_a > $o ).
% 2.81/1.57  
% 2.81/1.57  thf(sy_c_member_001t__Nat__Onat,type,
% 2.81/1.57      member_nat: nat > set_nat > $o ).
% 2.81/1.57  
% 2.81/1.57  thf(sy_c_member_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.81/1.57      member1696759390at_nat: produc1032616263at_nat > set_Pr1647387645at_nat > $o ).
% 2.81/1.57  
% 2.81/1.57  thf(sy_c_member_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_J,type,
% 2.81/1.57      member1502344244um_a_b: produc1003469085um_a_b > set_Pr326391507um_a_b > $o ).
% 2.81/1.57  
% 2.81/1.57  thf(sy_c_member_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_It__Sum____Type__Osum_Itf__a_Mtf__b_J_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_J,type,
% 2.81/1.57      member1998628618um_a_b: produc1963079155um_a_b > set_Pr409224873um_a_b > $o ).
% 2.81/1.57  
% 2.81/1.57  thf(sy_c_member_001t__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J,type,
% 2.81/1.57      member1641046175um_a_b: produc1394389750um_a_b > set_Pr1994339542um_a_b > $o ).
% 2.81/1.57  
% 2.81/1.57  thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.81/1.57      member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
% 2.81/1.57  
% 2.81/1.57  thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_J,type,
% 2.81/1.57      member1139034387um_a_b: produc204140796um_a_b > set_Pr1618094130um_a_b > $o ).
% 2.81/1.57  
% 2.81/1.57  thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J,type,
% 2.81/1.57      member1294585472um_a_b: produc1124793815um_a_b > set_Pr1174980151um_a_b > $o ).
% 2.81/1.57  
% 2.81/1.57  thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_It__Sum____Type__Osum_Itf__a_Mtf__b_J_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_J_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J,type,
% 2.81/1.57      member1590479267um_a_b: produc1681803642um_a_b > set_Pr1121389018um_a_b > $o ).
% 2.81/1.57  
% 2.81/1.57  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__Sum____Type__Osum_Itf__a_Mtf__b_J_J_J,type,
% 2.81/1.57      member834135910um_a_b: produc1546082365um_a_b > set_Pr386468381um_a_b > $o ).
% 2.81/1.57  
% 2.81/1.57  thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J,type,
% 2.81/1.57      member585880557um_a_b: produc1798470614um_a_b > set_Pr195945996um_a_b > $o ).
% 2.81/1.57  
% 2.81/1.57  thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_J,type,
% 2.81/1.57      member429827856um_a_b: produc1918750183um_a_b > set_Pr45173959um_a_b > $o ).
% 2.81/1.57  
% 2.81/1.57  thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J,type,
% 2.81/1.57      member748122307um_a_b: produc585753260um_a_b > set_Pr653770722um_a_b > $o ).
% 2.81/1.57  
% 2.81/1.57  thf(sy_c_member_001t__Product____Type__Oprod_It__Sum____Type__Osum_Itf__a_Mtf__b_J_Mt__Nat__Onat_J,type,
% 2.81/1.57      member1249152_b_nat: produc1978941143_b_nat > set_Pr375490359_b_nat > $o ).
% 2.81/1.57  
% 2.81/1.57  thf(sy_c_member_001t__Product____Type__Oprod_It__Sum____Type__Osum_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__LabeledGraphSemantics__OStandard____Constant_Itf__a_J_Mt__Product____Type__Oprod_It__Sum____Type__Osum_Itf__a_Mtf__b_J_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_J_J,type,
% 2.81/1.57      member1641922979um_a_b: produc1733247354um_a_b > set_Pr1558970842um_a_b > $o ).
% 2.81/1.57  
% 2.81/1.57  thf(sy_c_member_001t__Product____Type__Oprod_It__Sum____Type__Osum_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J_J,type,
% 2.81/1.57      member485470653um_a_b: produc323101606um_a_b > set_Pr1783309276um_a_b > $o ).
% 2.81/1.57  
% 2.81/1.57  thf(sy_c_member_001t__Product____Type__Oprod_It__Sum____Type__Osum_Itf__a_Mtf__b_J_Mt__Sum____Type__Osum_Itf__a_Mtf__b_J_J,type,
% 2.81/1.57      member947389014um_a_b: produc1548871597um_a_b > set_Pr1916610317um_a_b > $o ).
% 2.81/1.57  
% 2.81/1.57  thf(sy_c_member_001t__Sum____Type__Osum_Itf__a_Mtf__b_J,type,
% 2.81/1.57      member_Sum_sum_a_b: sum_sum_a_b > set_Sum_sum_a_b > $o ).
% 2.81/1.57  
% 2.81/1.57  thf(sy_v_G,type,
% 2.81/1.57      g: labele431970251um_a_b ).
% 2.81/1.57  
% 2.81/1.57  thf(sy_v_f____,type,
% 2.81/1.57      f: set_Pr1174980151um_a_b ).
% 2.81/1.57  
% 2.81/1.57  thf(sy_v_l,type,
% 2.81/1.57      l: standard_Constant_a ).
% 2.81/1.57  
% 2.81/1.57  thf(sy_v_v____,type,
% 2.81/1.57      v: sum_sum_a_b ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_0_g,axiom,
% 2.81/1.57      ( g
% 2.81/1.57      = ( restri1162247455um_a_b @ g ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_1_v,axiom,
% 2.81/1.57      member_Sum_sum_a_b @ v @ ( labele577278695um_a_b @ g ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_2__092_060open_062edge__preserving_A_123_I0_058_058_063_Hc1_M_Av_J_125_A_123_IS__Idt_M_A0_058_058_063_Hc1_M_A0_058_058_063_Hc1_J_125_A_Iedges_AG_J_092_060close_062,axiom,
% 2.81/1.57      edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( labele1939049654um_a_b @ g ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_3_r,axiom,
% 2.81/1.57      ord_le192794300um_a_b @ ( image_256773707um_a_b @ f @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) @ ( labele577278695um_a_b @ g ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_4_f,axiom,
% 2.81/1.57      ( f
% 2.81/1.57      = ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_5_d,axiom,
% 2.81/1.57      ( ( domain1368163076um_a_b @ f )
% 2.81/1.57      = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_6_graph__single,axiom,
% 2.81/1.57      ! [A: standard_Constant_a,B: sum_sum_a_b,C: sum_sum_a_b] :
% 2.81/1.57        ( ( labele1729654377um_a_b @ ( insert323157027um_a_b @ ( produc1697725733um_a_b @ A @ ( produc176426981um_a_b @ B @ C ) ) @ bot_bo1262634813um_a_b ) @ ( insert_Sum_sum_a_b @ B @ ( insert_Sum_sum_a_b @ C @ bot_bo1491243248um_a_b ) ) )
% 2.81/1.57        = ( restri1162247455um_a_b @ ( labele1729654377um_a_b @ ( insert323157027um_a_b @ ( produc1697725733um_a_b @ A @ ( produc176426981um_a_b @ B @ C ) ) @ bot_bo1262634813um_a_b ) @ ( insert_Sum_sum_a_b @ B @ ( insert_Sum_sum_a_b @ C @ bot_bo1491243248um_a_b ) ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_7_graph__single,axiom,
% 2.81/1.57      ! [A: standard_Constant_a,B: nat,C: nat] :
% 2.81/1.57        ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ A @ ( product_Pair_nat_nat @ B @ C ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ B @ ( insert_nat @ C @ bot_bot_set_nat ) ) )
% 2.81/1.57        = ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ A @ ( product_Pair_nat_nat @ B @ C ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ B @ ( insert_nat @ C @ bot_bot_set_nat ) ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_8__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062v_O_A_I0_M_Av_J_A_092_060in_062_Af_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 2.81/1.57      ~ ! [V: sum_sum_a_b] :
% 2.81/1.57          ~ ( member1294585472um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ V ) @ f ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_9_u,axiom,
% 2.81/1.57      unival2092813468um_a_b @ f ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_10_Domain__insert,axiom,
% 2.81/1.57      ! [A: standard_Constant_a,B: product_prod_nat_nat,R: set_Pr1647387645at_nat] :
% 2.81/1.57        ( ( domain1060562500at_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ A @ B ) @ R ) )
% 2.81/1.57        = ( insert1909710879tant_a @ A @ ( domain1060562500at_nat @ R ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_11_Domain__insert,axiom,
% 2.81/1.57      ! [A: nat,B: nat,R: set_Pr1986765409at_nat] :
% 2.81/1.57        ( ( domain_nat_nat @ ( insert271595217at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R ) )
% 2.81/1.57        = ( insert_nat @ A @ ( domain_nat_nat @ R ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_12_Domain__insert,axiom,
% 2.81/1.57      ! [A: nat,B: sum_sum_a_b,R: set_Pr1174980151um_a_b] :
% 2.81/1.57        ( ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ A @ B ) @ R ) )
% 2.81/1.57        = ( insert_nat @ A @ ( domain1368163076um_a_b @ R ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_13_Domain__insert,axiom,
% 2.81/1.57      ! [A: standard_Constant_a,B: produc1548871597um_a_b,R: set_Pr409224873um_a_b] :
% 2.81/1.57        ( ( domain1362581744um_a_b @ ( insert323157027um_a_b @ ( produc1697725733um_a_b @ A @ B ) @ R ) )
% 2.81/1.57        = ( insert1909710879tant_a @ A @ ( domain1362581744um_a_b @ R ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_14_Domain__insert,axiom,
% 2.81/1.57      ! [A: sum_sum_a_b,B: sum_sum_a_b,R: set_Pr1916610317um_a_b] :
% 2.81/1.57        ( ( domain2069673178um_a_b @ ( insert1435405693um_a_b @ ( produc176426981um_a_b @ A @ B ) @ R ) )
% 2.81/1.57        = ( insert_Sum_sum_a_b @ A @ ( domain2069673178um_a_b @ R ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_15_Image__singleton__iff,axiom,
% 2.81/1.57      ! [B: nat,R: set_Pr1986765409at_nat,A: nat] :
% 2.81/1.57        ( ( member_nat @ B @ ( image_nat_nat @ R @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 2.81/1.57        = ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_16_Image__singleton__iff,axiom,
% 2.81/1.57      ! [B: sum_sum_a_b,R: set_Pr1174980151um_a_b,A: nat] :
% 2.81/1.57        ( ( member_Sum_sum_a_b @ B @ ( image_256773707um_a_b @ R @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 2.81/1.57        = ( member1294585472um_a_b @ ( produc1808556047um_a_b @ A @ B ) @ R ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_17_Image__singleton__iff,axiom,
% 2.81/1.57      ! [B: sum_sum_a_b,R: set_Pr1994339542um_a_b,A: standard_Constant_a] :
% 2.81/1.57        ( ( member_Sum_sum_a_b @ B @ ( image_2129435242um_a_b @ R @ ( insert1909710879tant_a @ A @ bot_bo1160111033tant_a ) ) )
% 2.81/1.57        = ( member1641046175um_a_b @ ( produc584843310um_a_b @ A @ B ) @ R ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_18_Image__singleton__iff,axiom,
% 2.81/1.57      ! [B: product_prod_nat_nat,R: set_Pr1647387645at_nat,A: standard_Constant_a] :
% 2.81/1.57        ( ( member701585322at_nat @ B @ ( image_127502653at_nat @ R @ ( insert1909710879tant_a @ A @ bot_bo1160111033tant_a ) ) )
% 2.81/1.57        = ( member1696759390at_nat @ ( produc407553657at_nat @ A @ B ) @ R ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_19_Image__singleton__iff,axiom,
% 2.81/1.57      ! [B: sum_sum_a_b,R: set_Pr195945996um_a_b,A: product_prod_nat_nat] :
% 2.81/1.57        ( ( member_Sum_sum_a_b @ B @ ( image_1754351636um_a_b @ R @ ( insert271595217at_nat @ A @ bot_bo2130386637at_nat ) ) )
% 2.81/1.57        = ( member585880557um_a_b @ ( produc1872245072um_a_b @ A @ B ) @ R ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_20_Image__singleton__iff,axiom,
% 2.81/1.57      ! [B: produc1124793815um_a_b,R: set_Pr1618094130um_a_b,A: nat] :
% 2.81/1.57        ( ( member1294585472um_a_b @ B @ ( image_1228479730um_a_b @ R @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 2.81/1.57        = ( member1139034387um_a_b @ ( produc1346373166um_a_b @ A @ B ) @ R ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_21_Image__singleton__iff,axiom,
% 2.81/1.57      ! [B: sum_sum_a_b,R: set_Pr1916610317um_a_b,A: sum_sum_a_b] :
% 2.81/1.57        ( ( member_Sum_sum_a_b @ B @ ( image_1918588449um_a_b @ R @ ( insert_Sum_sum_a_b @ A @ bot_bo1491243248um_a_b ) ) )
% 2.81/1.57        = ( member947389014um_a_b @ ( produc176426981um_a_b @ A @ B ) @ R ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_22_Image__singleton__iff,axiom,
% 2.81/1.57      ! [B: produc1124793815um_a_b,R: set_Pr326391507um_a_b,A: standard_Constant_a] :
% 2.81/1.57        ( ( member1294585472um_a_b @ B @ ( image_1179143699um_a_b @ R @ ( insert1909710879tant_a @ A @ bot_bo1160111033tant_a ) ) )
% 2.81/1.57        = ( member1502344244um_a_b @ ( produc414524239um_a_b @ A @ B ) @ R ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_23_Image__singleton__iff,axiom,
% 2.81/1.57      ! [B: produc1124793815um_a_b,R: set_Pr386468381um_a_b,A: product_prod_nat_nat] :
% 2.81/1.57        ( ( member1294585472um_a_b @ B @ ( image_320480233um_a_b @ R @ ( insert271595217at_nat @ A @ bot_bo2130386637at_nat ) ) )
% 2.81/1.57        = ( member834135910um_a_b @ ( produc335036333um_a_b @ A @ B ) @ R ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_24_Image__singleton__iff,axiom,
% 2.81/1.57      ! [B: sum_sum_a_b,R: set_Pr653770722um_a_b,A: produc1124793815um_a_b] :
% 2.81/1.57        ( ( member_Sum_sum_a_b @ B @ ( image_869585130um_a_b @ R @ ( insert983991207um_a_b @ A @ bot_bo575978147um_a_b ) ) )
% 2.81/1.57        = ( member748122307um_a_b @ ( produc831476262um_a_b @ A @ B ) @ R ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_25_graph__empty__e,axiom,
% 2.81/1.57      ! [V2: set_nat] :
% 2.81/1.57        ( ( labele16114835_a_nat @ bot_bo810816657at_nat @ V2 )
% 2.81/1.57        = ( restri572569417_a_nat @ ( labele16114835_a_nat @ bot_bo810816657at_nat @ V2 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_26_graph__empty__e,axiom,
% 2.81/1.57      ! [V2: set_Sum_sum_a_b] :
% 2.81/1.57        ( ( labele1729654377um_a_b @ bot_bo1262634813um_a_b @ V2 )
% 2.81/1.57        = ( restri1162247455um_a_b @ ( labele1729654377um_a_b @ bot_bo1262634813um_a_b @ V2 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_27_labeled__graph_Ocollapse,axiom,
% 2.81/1.57      ! [Labeled_graph: labele935650037_a_nat] :
% 2.81/1.57        ( ( labele16114835_a_nat @ ( labele195203296_a_nat @ Labeled_graph ) @ ( labele1810595089_a_nat @ Labeled_graph ) )
% 2.81/1.57        = Labeled_graph ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_28_labeled__graph_Ocollapse,axiom,
% 2.81/1.57      ! [Labeled_graph: labele431970251um_a_b] :
% 2.81/1.57        ( ( labele1729654377um_a_b @ ( labele1939049654um_a_b @ Labeled_graph ) @ ( labele577278695um_a_b @ Labeled_graph ) )
% 2.81/1.57        = Labeled_graph ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_29_Domain__empty,axiom,
% 2.81/1.57      ( ( domain_nat_nat @ bot_bo2130386637at_nat )
% 2.81/1.57      = bot_bot_set_nat ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_30_Domain__empty,axiom,
% 2.81/1.57      ( ( domain1060562500at_nat @ bot_bo810816657at_nat )
% 2.81/1.57      = bot_bo1160111033tant_a ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_31_Domain__empty,axiom,
% 2.81/1.57      ( ( domain1368163076um_a_b @ bot_bo575978147um_a_b )
% 2.81/1.57      = bot_bot_set_nat ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_32_Domain__empty,axiom,
% 2.81/1.57      ( ( domain2069673178um_a_b @ bot_bo225809273um_a_b )
% 2.81/1.57      = bot_bo1491243248um_a_b ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_33_Domain__empty,axiom,
% 2.81/1.57      ( ( domain1362581744um_a_b @ bot_bo1262634813um_a_b )
% 2.81/1.57      = bot_bo1160111033tant_a ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_34_Image__empty1,axiom,
% 2.81/1.57      ! [X: set_St761939237tant_a] :
% 2.81/1.57        ( ( image_127502653at_nat @ bot_bo810816657at_nat @ X )
% 2.81/1.57        = bot_bo2130386637at_nat ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_35_Image__empty1,axiom,
% 2.81/1.57      ! [X: set_nat] :
% 2.81/1.57        ( ( image_256773707um_a_b @ bot_bo575978147um_a_b @ X )
% 2.81/1.57        = bot_bo1491243248um_a_b ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_36_Image__empty1,axiom,
% 2.81/1.57      ! [X: set_Sum_sum_a_b] :
% 2.81/1.57        ( ( image_1918588449um_a_b @ bot_bo225809273um_a_b @ X )
% 2.81/1.57        = bot_bo1491243248um_a_b ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_37_Image__empty1,axiom,
% 2.81/1.57      ! [X: set_St761939237tant_a] :
% 2.81/1.57        ( ( image_2023280617um_a_b @ bot_bo1262634813um_a_b @ X )
% 2.81/1.57        = bot_bo225809273um_a_b ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_38_restrict__idemp,axiom,
% 2.81/1.57      ! [X2: labele935650037_a_nat] :
% 2.81/1.57        ( ( restri572569417_a_nat @ ( restri572569417_a_nat @ X2 ) )
% 2.81/1.57        = ( restri572569417_a_nat @ X2 ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_39_restrict__idemp,axiom,
% 2.81/1.57      ! [X2: labele431970251um_a_b] :
% 2.81/1.57        ( ( restri1162247455um_a_b @ ( restri1162247455um_a_b @ X2 ) )
% 2.81/1.57        = ( restri1162247455um_a_b @ X2 ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_40_labeled__graph_Oinject,axiom,
% 2.81/1.57      ! [X1: set_Pr1647387645at_nat,X22: set_nat,Y1: set_Pr1647387645at_nat,Y2: set_nat] :
% 2.81/1.57        ( ( ( labele16114835_a_nat @ X1 @ X22 )
% 2.81/1.57          = ( labele16114835_a_nat @ Y1 @ Y2 ) )
% 2.81/1.57        = ( ( X1 = Y1 )
% 2.81/1.57          & ( X22 = Y2 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_41_labeled__graph_Oinject,axiom,
% 2.81/1.57      ! [X1: set_Pr409224873um_a_b,X22: set_Sum_sum_a_b,Y1: set_Pr409224873um_a_b,Y2: set_Sum_sum_a_b] :
% 2.81/1.57        ( ( ( labele1729654377um_a_b @ X1 @ X22 )
% 2.81/1.57          = ( labele1729654377um_a_b @ Y1 @ Y2 ) )
% 2.81/1.57        = ( ( X1 = Y1 )
% 2.81/1.57          & ( X22 = Y2 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_42_v__gr,axiom,
% 2.81/1.57      ! [A2: sum_sum_a_b,B2: sum_sum_a_b] :
% 2.81/1.57        ( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ standard_S_Idt_a @ ( produc176426981um_a_b @ A2 @ B2 ) ) @ ( labele1939049654um_a_b @ g ) )
% 2.81/1.57        = ( ( member_Sum_sum_a_b @ A2 @ ( labele577278695um_a_b @ g ) )
% 2.81/1.57          & ( B2 = A2 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_43__092_060open_062_IS__Idt_M_Av_M_Av_J_A_092_060in_062_Aedges_AG_092_060close_062,axiom,
% 2.81/1.57      member1998628618um_a_b @ ( produc1697725733um_a_b @ standard_S_Idt_a @ ( produc176426981um_a_b @ v @ v ) ) @ ( labele1939049654um_a_b @ g ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_44_ImageI,axiom,
% 2.81/1.57      ! [A: nat,B: nat,R: set_Pr1986765409at_nat,A3: set_nat] :
% 2.81/1.57        ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R )
% 2.81/1.57       => ( ( member_nat @ A @ A3 )
% 2.81/1.57         => ( member_nat @ B @ ( image_nat_nat @ R @ A3 ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_45_ImageI,axiom,
% 2.81/1.57      ! [A: nat,B: sum_sum_a_b,R: set_Pr1174980151um_a_b,A3: set_nat] :
% 2.81/1.57        ( ( member1294585472um_a_b @ ( produc1808556047um_a_b @ A @ B ) @ R )
% 2.81/1.57       => ( ( member_nat @ A @ A3 )
% 2.81/1.57         => ( member_Sum_sum_a_b @ B @ ( image_256773707um_a_b @ R @ A3 ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_46_ImageI,axiom,
% 2.81/1.57      ! [A: standard_Constant_a,B: product_prod_nat_nat,R: set_Pr1647387645at_nat,A3: set_St761939237tant_a] :
% 2.81/1.57        ( ( member1696759390at_nat @ ( produc407553657at_nat @ A @ B ) @ R )
% 2.81/1.57       => ( ( member1632892294tant_a @ A @ A3 )
% 2.81/1.57         => ( member701585322at_nat @ B @ ( image_127502653at_nat @ R @ A3 ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_47_ImageI,axiom,
% 2.81/1.57      ! [A: sum_sum_a_b,B: sum_sum_a_b,R: set_Pr1916610317um_a_b,A3: set_Sum_sum_a_b] :
% 2.81/1.57        ( ( member947389014um_a_b @ ( produc176426981um_a_b @ A @ B ) @ R )
% 2.81/1.57       => ( ( member_Sum_sum_a_b @ A @ A3 )
% 2.81/1.57         => ( member_Sum_sum_a_b @ B @ ( image_1918588449um_a_b @ R @ A3 ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_48_ImageI,axiom,
% 2.81/1.57      ! [A: sum_sum_a_b,B: produc1124793815um_a_b,R: set_Pr1783309276um_a_b,A3: set_Sum_sum_a_b] :
% 2.81/1.57        ( ( member485470653um_a_b @ ( produc1637282520um_a_b @ A @ B ) @ R )
% 2.81/1.57       => ( ( member_Sum_sum_a_b @ A @ A3 )
% 2.81/1.57         => ( member1294585472um_a_b @ B @ ( image_1675391388um_a_b @ R @ A3 ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_49_ImageI,axiom,
% 2.81/1.57      ! [A: produc1124793815um_a_b,B: sum_sum_a_b,R: set_Pr653770722um_a_b,A3: set_Pr1174980151um_a_b] :
% 2.81/1.57        ( ( member748122307um_a_b @ ( produc831476262um_a_b @ A @ B ) @ R )
% 2.81/1.57       => ( ( member1294585472um_a_b @ A @ A3 )
% 2.81/1.57         => ( member_Sum_sum_a_b @ B @ ( image_869585130um_a_b @ R @ A3 ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_50_ImageI,axiom,
% 2.81/1.57      ! [A: standard_Constant_a,B: produc1548871597um_a_b,R: set_Pr409224873um_a_b,A3: set_St761939237tant_a] :
% 2.81/1.57        ( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ A @ B ) @ R )
% 2.81/1.57       => ( ( member1632892294tant_a @ A @ A3 )
% 2.81/1.57         => ( member947389014um_a_b @ B @ ( image_2023280617um_a_b @ R @ A3 ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_51_ImageI,axiom,
% 2.81/1.57      ! [A: produc1124793815um_a_b,B: produc1124793815um_a_b,R: set_Pr45173959um_a_b,A3: set_Pr1174980151um_a_b] :
% 2.81/1.57        ( ( member429827856um_a_b @ ( produc27163479um_a_b @ A @ B ) @ R )
% 2.81/1.57       => ( ( member1294585472um_a_b @ A @ A3 )
% 2.81/1.57         => ( member1294585472um_a_b @ B @ ( image_1464989587um_a_b @ R @ A3 ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_52_ImageI,axiom,
% 2.81/1.57      ! [A: sum_sum_a_b,B: produc1963079155um_a_b,R: set_Pr1558970842um_a_b,A3: set_Sum_sum_a_b] :
% 2.81/1.57        ( ( member1641922979um_a_b @ ( produc230853810um_a_b @ A @ B ) @ R )
% 2.81/1.57       => ( ( member_Sum_sum_a_b @ A @ A3 )
% 2.81/1.57         => ( member1998628618um_a_b @ B @ ( image_1482984686um_a_b @ R @ A3 ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_53_ImageI,axiom,
% 2.81/1.57      ! [A: produc1963079155um_a_b,B: sum_sum_a_b,R: set_Pr1121389018um_a_b,A3: set_Pr409224873um_a_b] :
% 2.81/1.57        ( ( member1590479267um_a_b @ ( produc522766386um_a_b @ A @ B ) @ R )
% 2.81/1.57       => ( ( member1998628618um_a_b @ A @ A3 )
% 2.81/1.57         => ( member_Sum_sum_a_b @ B @ ( image_1774897262um_a_b @ R @ A3 ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_54_Image__empty2,axiom,
% 2.81/1.57      ! [R2: set_Pr1986765409at_nat] :
% 2.81/1.57        ( ( image_nat_nat @ R2 @ bot_bot_set_nat )
% 2.81/1.57        = bot_bot_set_nat ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_55_Image__empty2,axiom,
% 2.81/1.57      ! [R2: set_Pr1174980151um_a_b] :
% 2.81/1.57        ( ( image_256773707um_a_b @ R2 @ bot_bot_set_nat )
% 2.81/1.57        = bot_bo1491243248um_a_b ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_56_Image__empty2,axiom,
% 2.81/1.57      ! [R2: set_Pr375490359_b_nat] :
% 2.81/1.57        ( ( image_1117854795_b_nat @ R2 @ bot_bo1491243248um_a_b )
% 2.81/1.57        = bot_bot_set_nat ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_57_Image__empty2,axiom,
% 2.81/1.57      ! [R2: set_Pr1618094130um_a_b] :
% 2.81/1.57        ( ( image_1228479730um_a_b @ R2 @ bot_bot_set_nat )
% 2.81/1.57        = bot_bo575978147um_a_b ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_58_Image__empty2,axiom,
% 2.81/1.57      ! [R2: set_Pr1902304780_b_nat] :
% 2.81/1.57        ( ( image_128716052_b_nat @ R2 @ bot_bo575978147um_a_b )
% 2.81/1.57        = bot_bot_set_nat ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_59_Image__empty2,axiom,
% 2.81/1.57      ! [R2: set_Pr1916610317um_a_b] :
% 2.81/1.57        ( ( image_1918588449um_a_b @ R2 @ bot_bo1491243248um_a_b )
% 2.81/1.57        = bot_bo1491243248um_a_b ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_60_Image__empty2,axiom,
% 2.81/1.57      ! [R2: set_Pr689416536at_nat] :
% 2.81/1.57        ( ( image_452296684at_nat @ R2 @ bot_bo810816657at_nat )
% 2.81/1.57        = bot_bot_set_nat ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_61_Image__empty2,axiom,
% 2.81/1.57      ! [R2: set_Pr1134469976at_nat] :
% 2.81/1.57        ( ( image_489788268at_nat @ R2 @ bot_bot_set_nat )
% 2.81/1.57        = bot_bo810816657at_nat ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_62_Image__empty2,axiom,
% 2.81/1.57      ! [R2: set_Pr1155046920um_a_b] :
% 2.81/1.57        ( ( image_166667464um_a_b @ R2 @ bot_bot_set_nat )
% 2.81/1.57        = bot_bo225809273um_a_b ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_63_Image__empty2,axiom,
% 2.81/1.57      ! [R2: set_Pr653770722um_a_b] :
% 2.81/1.57        ( ( image_869585130um_a_b @ R2 @ bot_bo575978147um_a_b )
% 2.81/1.57        = bot_bo1491243248um_a_b ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_64_vertices__restrict,axiom,
% 2.81/1.57      ! [G: labele935650037_a_nat] :
% 2.81/1.57        ( ( labele1810595089_a_nat @ ( restri572569417_a_nat @ G ) )
% 2.81/1.57        = ( labele1810595089_a_nat @ G ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_65_vertices__restrict,axiom,
% 2.81/1.57      ! [G: labele431970251um_a_b] :
% 2.81/1.57        ( ( labele577278695um_a_b @ ( restri1162247455um_a_b @ G ) )
% 2.81/1.57        = ( labele577278695um_a_b @ G ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_66__092_060open_062graph__homomorphism_A_ILG_A_123_125_A_1230_125_J_AG_Af_092_060close_062,axiom,
% 2.81/1.57      graph_1452133198um_a_b @ ( labele16114835_a_nat @ bot_bo810816657at_nat @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) @ g @ f ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_67_labeled__graph_Oexhaust,axiom,
% 2.81/1.57      ! [Y: labele935650037_a_nat] :
% 2.81/1.57        ~ ! [X12: set_Pr1647387645at_nat,X23: set_nat] :
% 2.81/1.57            ( Y
% 2.81/1.57           != ( labele16114835_a_nat @ X12 @ X23 ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_68_labeled__graph_Oexhaust,axiom,
% 2.81/1.57      ! [Y: labele431970251um_a_b] :
% 2.81/1.57        ~ ! [X12: set_Pr409224873um_a_b,X23: set_Sum_sum_a_b] :
% 2.81/1.57            ( Y
% 2.81/1.57           != ( labele1729654377um_a_b @ X12 @ X23 ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_69_labeled__graph_Oinduct,axiom,
% 2.81/1.57      ! [P: labele935650037_a_nat > $o,Labeled_graph: labele935650037_a_nat] :
% 2.81/1.57        ( ! [X1a: set_Pr1647387645at_nat,X2a: set_nat] : ( P @ ( labele16114835_a_nat @ X1a @ X2a ) )
% 2.81/1.57       => ( P @ Labeled_graph ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_70_labeled__graph_Oinduct,axiom,
% 2.81/1.57      ! [P: labele431970251um_a_b > $o,Labeled_graph: labele431970251um_a_b] :
% 2.81/1.57        ( ! [X1a: set_Pr409224873um_a_b,X2a: set_Sum_sum_a_b] : ( P @ ( labele1729654377um_a_b @ X1a @ X2a ) )
% 2.81/1.57       => ( P @ Labeled_graph ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_71_rev__ImageI,axiom,
% 2.81/1.57      ! [A: nat,A3: set_nat,B: nat,R: set_Pr1986765409at_nat] :
% 2.81/1.57        ( ( member_nat @ A @ A3 )
% 2.81/1.57       => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R )
% 2.81/1.57         => ( member_nat @ B @ ( image_nat_nat @ R @ A3 ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_72_rev__ImageI,axiom,
% 2.81/1.57      ! [A: nat,A3: set_nat,B: sum_sum_a_b,R: set_Pr1174980151um_a_b] :
% 2.81/1.57        ( ( member_nat @ A @ A3 )
% 2.81/1.57       => ( ( member1294585472um_a_b @ ( produc1808556047um_a_b @ A @ B ) @ R )
% 2.81/1.57         => ( member_Sum_sum_a_b @ B @ ( image_256773707um_a_b @ R @ A3 ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_73_rev__ImageI,axiom,
% 2.81/1.57      ! [A: standard_Constant_a,A3: set_St761939237tant_a,B: product_prod_nat_nat,R: set_Pr1647387645at_nat] :
% 2.81/1.57        ( ( member1632892294tant_a @ A @ A3 )
% 2.81/1.57       => ( ( member1696759390at_nat @ ( produc407553657at_nat @ A @ B ) @ R )
% 2.81/1.57         => ( member701585322at_nat @ B @ ( image_127502653at_nat @ R @ A3 ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_74_rev__ImageI,axiom,
% 2.81/1.57      ! [A: sum_sum_a_b,A3: set_Sum_sum_a_b,B: sum_sum_a_b,R: set_Pr1916610317um_a_b] :
% 2.81/1.57        ( ( member_Sum_sum_a_b @ A @ A3 )
% 2.81/1.57       => ( ( member947389014um_a_b @ ( produc176426981um_a_b @ A @ B ) @ R )
% 2.81/1.57         => ( member_Sum_sum_a_b @ B @ ( image_1918588449um_a_b @ R @ A3 ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_75_rev__ImageI,axiom,
% 2.81/1.57      ! [A: sum_sum_a_b,A3: set_Sum_sum_a_b,B: produc1124793815um_a_b,R: set_Pr1783309276um_a_b] :
% 2.81/1.57        ( ( member_Sum_sum_a_b @ A @ A3 )
% 2.81/1.57       => ( ( member485470653um_a_b @ ( produc1637282520um_a_b @ A @ B ) @ R )
% 2.81/1.57         => ( member1294585472um_a_b @ B @ ( image_1675391388um_a_b @ R @ A3 ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_76_rev__ImageI,axiom,
% 2.81/1.57      ! [A: produc1124793815um_a_b,A3: set_Pr1174980151um_a_b,B: sum_sum_a_b,R: set_Pr653770722um_a_b] :
% 2.81/1.57        ( ( member1294585472um_a_b @ A @ A3 )
% 2.81/1.57       => ( ( member748122307um_a_b @ ( produc831476262um_a_b @ A @ B ) @ R )
% 2.81/1.57         => ( member_Sum_sum_a_b @ B @ ( image_869585130um_a_b @ R @ A3 ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_77_rev__ImageI,axiom,
% 2.81/1.57      ! [A: standard_Constant_a,A3: set_St761939237tant_a,B: produc1548871597um_a_b,R: set_Pr409224873um_a_b] :
% 2.81/1.57        ( ( member1632892294tant_a @ A @ A3 )
% 2.81/1.57       => ( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ A @ B ) @ R )
% 2.81/1.57         => ( member947389014um_a_b @ B @ ( image_2023280617um_a_b @ R @ A3 ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_78_rev__ImageI,axiom,
% 2.81/1.57      ! [A: produc1124793815um_a_b,A3: set_Pr1174980151um_a_b,B: produc1124793815um_a_b,R: set_Pr45173959um_a_b] :
% 2.81/1.57        ( ( member1294585472um_a_b @ A @ A3 )
% 2.81/1.57       => ( ( member429827856um_a_b @ ( produc27163479um_a_b @ A @ B ) @ R )
% 2.81/1.57         => ( member1294585472um_a_b @ B @ ( image_1464989587um_a_b @ R @ A3 ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_79_rev__ImageI,axiom,
% 2.81/1.57      ! [A: sum_sum_a_b,A3: set_Sum_sum_a_b,B: produc1963079155um_a_b,R: set_Pr1558970842um_a_b] :
% 2.81/1.57        ( ( member_Sum_sum_a_b @ A @ A3 )
% 2.81/1.57       => ( ( member1641922979um_a_b @ ( produc230853810um_a_b @ A @ B ) @ R )
% 2.81/1.57         => ( member1998628618um_a_b @ B @ ( image_1482984686um_a_b @ R @ A3 ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_80_rev__ImageI,axiom,
% 2.81/1.57      ! [A: produc1963079155um_a_b,A3: set_Pr409224873um_a_b,B: sum_sum_a_b,R: set_Pr1121389018um_a_b] :
% 2.81/1.57        ( ( member1998628618um_a_b @ A @ A3 )
% 2.81/1.57       => ( ( member1590479267um_a_b @ ( produc522766386um_a_b @ A @ B ) @ R )
% 2.81/1.57         => ( member_Sum_sum_a_b @ B @ ( image_1774897262um_a_b @ R @ A3 ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_81_Image__iff,axiom,
% 2.81/1.57      ! [B: product_prod_nat_nat,R: set_Pr1647387645at_nat,A3: set_St761939237tant_a] :
% 2.81/1.57        ( ( member701585322at_nat @ B @ ( image_127502653at_nat @ R @ A3 ) )
% 2.81/1.57        = ( ? [X3: standard_Constant_a] :
% 2.81/1.57              ( ( member1632892294tant_a @ X3 @ A3 )
% 2.81/1.57              & ( member1696759390at_nat @ ( produc407553657at_nat @ X3 @ B ) @ R ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_82_Image__iff,axiom,
% 2.81/1.57      ! [B: nat,R: set_Pr1986765409at_nat,A3: set_nat] :
% 2.81/1.57        ( ( member_nat @ B @ ( image_nat_nat @ R @ A3 ) )
% 2.81/1.57        = ( ? [X3: nat] :
% 2.81/1.57              ( ( member_nat @ X3 @ A3 )
% 2.81/1.57              & ( member701585322at_nat @ ( product_Pair_nat_nat @ X3 @ B ) @ R ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_83_Image__iff,axiom,
% 2.81/1.57      ! [B: sum_sum_a_b,R: set_Pr1174980151um_a_b,A3: set_nat] :
% 2.81/1.57        ( ( member_Sum_sum_a_b @ B @ ( image_256773707um_a_b @ R @ A3 ) )
% 2.81/1.57        = ( ? [X3: nat] :
% 2.81/1.57              ( ( member_nat @ X3 @ A3 )
% 2.81/1.57              & ( member1294585472um_a_b @ ( produc1808556047um_a_b @ X3 @ B ) @ R ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_84_Image__iff,axiom,
% 2.81/1.57      ! [B: produc1548871597um_a_b,R: set_Pr409224873um_a_b,A3: set_St761939237tant_a] :
% 2.81/1.57        ( ( member947389014um_a_b @ B @ ( image_2023280617um_a_b @ R @ A3 ) )
% 2.81/1.57        = ( ? [X3: standard_Constant_a] :
% 2.81/1.57              ( ( member1632892294tant_a @ X3 @ A3 )
% 2.81/1.57              & ( member1998628618um_a_b @ ( produc1697725733um_a_b @ X3 @ B ) @ R ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_85_Image__iff,axiom,
% 2.81/1.57      ! [B: sum_sum_a_b,R: set_Pr1916610317um_a_b,A3: set_Sum_sum_a_b] :
% 2.81/1.57        ( ( member_Sum_sum_a_b @ B @ ( image_1918588449um_a_b @ R @ A3 ) )
% 2.81/1.57        = ( ? [X3: sum_sum_a_b] :
% 2.81/1.57              ( ( member_Sum_sum_a_b @ X3 @ A3 )
% 2.81/1.57              & ( member947389014um_a_b @ ( produc176426981um_a_b @ X3 @ B ) @ R ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_86_ImageE,axiom,
% 2.81/1.57      ! [B: nat,R: set_Pr1986765409at_nat,A3: set_nat] :
% 2.81/1.57        ( ( member_nat @ B @ ( image_nat_nat @ R @ A3 ) )
% 2.81/1.57       => ~ ! [X4: nat] :
% 2.81/1.57              ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X4 @ B ) @ R )
% 2.81/1.57             => ~ ( member_nat @ X4 @ A3 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_87_ImageE,axiom,
% 2.81/1.57      ! [B: sum_sum_a_b,R: set_Pr1174980151um_a_b,A3: set_nat] :
% 2.81/1.57        ( ( member_Sum_sum_a_b @ B @ ( image_256773707um_a_b @ R @ A3 ) )
% 2.81/1.57       => ~ ! [X4: nat] :
% 2.81/1.57              ( ( member1294585472um_a_b @ ( produc1808556047um_a_b @ X4 @ B ) @ R )
% 2.81/1.57             => ~ ( member_nat @ X4 @ A3 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_88_ImageE,axiom,
% 2.81/1.57      ! [B: product_prod_nat_nat,R: set_Pr1647387645at_nat,A3: set_St761939237tant_a] :
% 2.81/1.57        ( ( member701585322at_nat @ B @ ( image_127502653at_nat @ R @ A3 ) )
% 2.81/1.57       => ~ ! [X4: standard_Constant_a] :
% 2.81/1.57              ( ( member1696759390at_nat @ ( produc407553657at_nat @ X4 @ B ) @ R )
% 2.81/1.57             => ~ ( member1632892294tant_a @ X4 @ A3 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_89_ImageE,axiom,
% 2.81/1.57      ! [B: sum_sum_a_b,R: set_Pr1916610317um_a_b,A3: set_Sum_sum_a_b] :
% 2.81/1.57        ( ( member_Sum_sum_a_b @ B @ ( image_1918588449um_a_b @ R @ A3 ) )
% 2.81/1.57       => ~ ! [X4: sum_sum_a_b] :
% 2.81/1.57              ( ( member947389014um_a_b @ ( produc176426981um_a_b @ X4 @ B ) @ R )
% 2.81/1.57             => ~ ( member_Sum_sum_a_b @ X4 @ A3 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_90_ImageE,axiom,
% 2.81/1.57      ! [B: sum_sum_a_b,R: set_Pr653770722um_a_b,A3: set_Pr1174980151um_a_b] :
% 2.81/1.57        ( ( member_Sum_sum_a_b @ B @ ( image_869585130um_a_b @ R @ A3 ) )
% 2.81/1.57       => ~ ! [X4: produc1124793815um_a_b] :
% 2.81/1.57              ( ( member748122307um_a_b @ ( produc831476262um_a_b @ X4 @ B ) @ R )
% 2.81/1.57             => ~ ( member1294585472um_a_b @ X4 @ A3 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_91_ImageE,axiom,
% 2.81/1.57      ! [B: produc1124793815um_a_b,R: set_Pr1783309276um_a_b,A3: set_Sum_sum_a_b] :
% 2.81/1.57        ( ( member1294585472um_a_b @ B @ ( image_1675391388um_a_b @ R @ A3 ) )
% 2.81/1.57       => ~ ! [X4: sum_sum_a_b] :
% 2.81/1.57              ( ( member485470653um_a_b @ ( produc1637282520um_a_b @ X4 @ B ) @ R )
% 2.81/1.57             => ~ ( member_Sum_sum_a_b @ X4 @ A3 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_92_ImageE,axiom,
% 2.81/1.57      ! [B: produc1548871597um_a_b,R: set_Pr409224873um_a_b,A3: set_St761939237tant_a] :
% 2.81/1.57        ( ( member947389014um_a_b @ B @ ( image_2023280617um_a_b @ R @ A3 ) )
% 2.81/1.57       => ~ ! [X4: standard_Constant_a] :
% 2.81/1.57              ( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ X4 @ B ) @ R )
% 2.81/1.57             => ~ ( member1632892294tant_a @ X4 @ A3 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_93_ImageE,axiom,
% 2.81/1.57      ! [B: produc1124793815um_a_b,R: set_Pr45173959um_a_b,A3: set_Pr1174980151um_a_b] :
% 2.81/1.57        ( ( member1294585472um_a_b @ B @ ( image_1464989587um_a_b @ R @ A3 ) )
% 2.81/1.57       => ~ ! [X4: produc1124793815um_a_b] :
% 2.81/1.57              ( ( member429827856um_a_b @ ( produc27163479um_a_b @ X4 @ B ) @ R )
% 2.81/1.57             => ~ ( member1294585472um_a_b @ X4 @ A3 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_94_ImageE,axiom,
% 2.81/1.57      ! [B: sum_sum_a_b,R: set_Pr1121389018um_a_b,A3: set_Pr409224873um_a_b] :
% 2.81/1.57        ( ( member_Sum_sum_a_b @ B @ ( image_1774897262um_a_b @ R @ A3 ) )
% 2.81/1.57       => ~ ! [X4: produc1963079155um_a_b] :
% 2.81/1.57              ( ( member1590479267um_a_b @ ( produc522766386um_a_b @ X4 @ B ) @ R )
% 2.81/1.57             => ~ ( member1998628618um_a_b @ X4 @ A3 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_95_ImageE,axiom,
% 2.81/1.57      ! [B: produc1963079155um_a_b,R: set_Pr1558970842um_a_b,A3: set_Sum_sum_a_b] :
% 2.81/1.57        ( ( member1998628618um_a_b @ B @ ( image_1482984686um_a_b @ R @ A3 ) )
% 2.81/1.57       => ~ ! [X4: sum_sum_a_b] :
% 2.81/1.57              ( ( member1641922979um_a_b @ ( produc230853810um_a_b @ X4 @ B ) @ R )
% 2.81/1.57             => ~ ( member_Sum_sum_a_b @ X4 @ A3 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_96_Image__mono,axiom,
% 2.81/1.57      ! [R3: set_Pr1174980151um_a_b,R: set_Pr1174980151um_a_b,A4: set_nat,A3: set_nat] :
% 2.81/1.57        ( ( ord_le823954903um_a_b @ R3 @ R )
% 2.81/1.57       => ( ( ord_less_eq_set_nat @ A4 @ A3 )
% 2.81/1.57         => ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ R3 @ A4 ) @ ( image_256773707um_a_b @ R @ A3 ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_97_Image__mono,axiom,
% 2.81/1.57      ! [R3: set_Pr1916610317um_a_b,R: set_Pr1916610317um_a_b,A4: set_Sum_sum_a_b,A3: set_Sum_sum_a_b] :
% 2.81/1.57        ( ( ord_le1059794605um_a_b @ R3 @ R )
% 2.81/1.57       => ( ( ord_le192794300um_a_b @ A4 @ A3 )
% 2.81/1.57         => ( ord_le192794300um_a_b @ ( image_1918588449um_a_b @ R3 @ A4 ) @ ( image_1918588449um_a_b @ R @ A3 ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_98_Domain_Oinducts,axiom,
% 2.81/1.57      ! [X2: standard_Constant_a,R: set_Pr1647387645at_nat,P: standard_Constant_a > $o] :
% 2.81/1.57        ( ( member1632892294tant_a @ X2 @ ( domain1060562500at_nat @ R ) )
% 2.81/1.57       => ( ! [A5: standard_Constant_a,B3: product_prod_nat_nat] :
% 2.81/1.57              ( ( member1696759390at_nat @ ( produc407553657at_nat @ A5 @ B3 ) @ R )
% 2.81/1.57             => ( P @ A5 ) )
% 2.81/1.57         => ( P @ X2 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_99_Domain_Oinducts,axiom,
% 2.81/1.57      ! [X2: nat,R: set_Pr1986765409at_nat,P: nat > $o] :
% 2.81/1.57        ( ( member_nat @ X2 @ ( domain_nat_nat @ R ) )
% 2.81/1.57       => ( ! [A5: nat,B3: nat] :
% 2.81/1.57              ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A5 @ B3 ) @ R )
% 2.81/1.57             => ( P @ A5 ) )
% 2.81/1.57         => ( P @ X2 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_100_Domain_Oinducts,axiom,
% 2.81/1.57      ! [X2: nat,R: set_Pr1174980151um_a_b,P: nat > $o] :
% 2.81/1.57        ( ( member_nat @ X2 @ ( domain1368163076um_a_b @ R ) )
% 2.81/1.57       => ( ! [A5: nat,B3: sum_sum_a_b] :
% 2.81/1.57              ( ( member1294585472um_a_b @ ( produc1808556047um_a_b @ A5 @ B3 ) @ R )
% 2.81/1.57             => ( P @ A5 ) )
% 2.81/1.57         => ( P @ X2 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_101_Domain_Oinducts,axiom,
% 2.81/1.57      ! [X2: standard_Constant_a,R: set_Pr409224873um_a_b,P: standard_Constant_a > $o] :
% 2.81/1.57        ( ( member1632892294tant_a @ X2 @ ( domain1362581744um_a_b @ R ) )
% 2.81/1.57       => ( ! [A5: standard_Constant_a,B3: produc1548871597um_a_b] :
% 2.81/1.57              ( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ A5 @ B3 ) @ R )
% 2.81/1.57             => ( P @ A5 ) )
% 2.81/1.57         => ( P @ X2 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_102_Domain_Oinducts,axiom,
% 2.81/1.57      ! [X2: sum_sum_a_b,R: set_Pr1916610317um_a_b,P: sum_sum_a_b > $o] :
% 2.81/1.57        ( ( member_Sum_sum_a_b @ X2 @ ( domain2069673178um_a_b @ R ) )
% 2.81/1.57       => ( ! [A5: sum_sum_a_b,B3: sum_sum_a_b] :
% 2.81/1.57              ( ( member947389014um_a_b @ ( produc176426981um_a_b @ A5 @ B3 ) @ R )
% 2.81/1.57             => ( P @ A5 ) )
% 2.81/1.57         => ( P @ X2 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_103_Domain_ODomainI,axiom,
% 2.81/1.57      ! [A: standard_Constant_a,B: product_prod_nat_nat,R: set_Pr1647387645at_nat] :
% 2.81/1.57        ( ( member1696759390at_nat @ ( produc407553657at_nat @ A @ B ) @ R )
% 2.81/1.57       => ( member1632892294tant_a @ A @ ( domain1060562500at_nat @ R ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_104_Domain_ODomainI,axiom,
% 2.81/1.57      ! [A: nat,B: nat,R: set_Pr1986765409at_nat] :
% 2.81/1.57        ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R )
% 2.81/1.57       => ( member_nat @ A @ ( domain_nat_nat @ R ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_105_Domain_ODomainI,axiom,
% 2.81/1.57      ! [A: nat,B: sum_sum_a_b,R: set_Pr1174980151um_a_b] :
% 2.81/1.57        ( ( member1294585472um_a_b @ ( produc1808556047um_a_b @ A @ B ) @ R )
% 2.81/1.57       => ( member_nat @ A @ ( domain1368163076um_a_b @ R ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_106_Domain_ODomainI,axiom,
% 2.81/1.57      ! [A: standard_Constant_a,B: produc1548871597um_a_b,R: set_Pr409224873um_a_b] :
% 2.81/1.57        ( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ A @ B ) @ R )
% 2.81/1.57       => ( member1632892294tant_a @ A @ ( domain1362581744um_a_b @ R ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_107_Domain_ODomainI,axiom,
% 2.81/1.57      ! [A: sum_sum_a_b,B: sum_sum_a_b,R: set_Pr1916610317um_a_b] :
% 2.81/1.57        ( ( member947389014um_a_b @ ( produc176426981um_a_b @ A @ B ) @ R )
% 2.81/1.57       => ( member_Sum_sum_a_b @ A @ ( domain2069673178um_a_b @ R ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_108_Domain_Osimps,axiom,
% 2.81/1.57      ! [A: standard_Constant_a,R: set_Pr1647387645at_nat] :
% 2.81/1.57        ( ( member1632892294tant_a @ A @ ( domain1060562500at_nat @ R ) )
% 2.81/1.57        = ( ? [A6: standard_Constant_a,B4: product_prod_nat_nat] :
% 2.81/1.57              ( ( A = A6 )
% 2.81/1.57              & ( member1696759390at_nat @ ( produc407553657at_nat @ A6 @ B4 ) @ R ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_109_Domain_Osimps,axiom,
% 2.81/1.57      ! [A: nat,R: set_Pr1986765409at_nat] :
% 2.81/1.57        ( ( member_nat @ A @ ( domain_nat_nat @ R ) )
% 2.81/1.57        = ( ? [A6: nat,B4: nat] :
% 2.81/1.57              ( ( A = A6 )
% 2.81/1.57              & ( member701585322at_nat @ ( product_Pair_nat_nat @ A6 @ B4 ) @ R ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_110_Domain_Osimps,axiom,
% 2.81/1.57      ! [A: nat,R: set_Pr1174980151um_a_b] :
% 2.81/1.57        ( ( member_nat @ A @ ( domain1368163076um_a_b @ R ) )
% 2.81/1.57        = ( ? [A6: nat,B4: sum_sum_a_b] :
% 2.81/1.57              ( ( A = A6 )
% 2.81/1.57              & ( member1294585472um_a_b @ ( produc1808556047um_a_b @ A6 @ B4 ) @ R ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_111_Domain_Osimps,axiom,
% 2.81/1.57      ! [A: standard_Constant_a,R: set_Pr409224873um_a_b] :
% 2.81/1.57        ( ( member1632892294tant_a @ A @ ( domain1362581744um_a_b @ R ) )
% 2.81/1.57        = ( ? [A6: standard_Constant_a,B4: produc1548871597um_a_b] :
% 2.81/1.57              ( ( A = A6 )
% 2.81/1.57              & ( member1998628618um_a_b @ ( produc1697725733um_a_b @ A6 @ B4 ) @ R ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_112_Domain_Osimps,axiom,
% 2.81/1.57      ! [A: sum_sum_a_b,R: set_Pr1916610317um_a_b] :
% 2.81/1.57        ( ( member_Sum_sum_a_b @ A @ ( domain2069673178um_a_b @ R ) )
% 2.81/1.57        = ( ? [A6: sum_sum_a_b,B4: sum_sum_a_b] :
% 2.81/1.57              ( ( A = A6 )
% 2.81/1.57              & ( member947389014um_a_b @ ( produc176426981um_a_b @ A6 @ B4 ) @ R ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_113_Domain_Ocases,axiom,
% 2.81/1.57      ! [A: standard_Constant_a,R: set_Pr1647387645at_nat] :
% 2.81/1.57        ( ( member1632892294tant_a @ A @ ( domain1060562500at_nat @ R ) )
% 2.81/1.57       => ~ ! [B3: product_prod_nat_nat] :
% 2.81/1.57              ~ ( member1696759390at_nat @ ( produc407553657at_nat @ A @ B3 ) @ R ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_114_Domain_Ocases,axiom,
% 2.81/1.57      ! [A: nat,R: set_Pr1986765409at_nat] :
% 2.81/1.57        ( ( member_nat @ A @ ( domain_nat_nat @ R ) )
% 2.81/1.57       => ~ ! [B3: nat] :
% 2.81/1.57              ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B3 ) @ R ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_115_Domain_Ocases,axiom,
% 2.81/1.57      ! [A: nat,R: set_Pr1174980151um_a_b] :
% 2.81/1.57        ( ( member_nat @ A @ ( domain1368163076um_a_b @ R ) )
% 2.81/1.57       => ~ ! [B3: sum_sum_a_b] :
% 2.81/1.57              ~ ( member1294585472um_a_b @ ( produc1808556047um_a_b @ A @ B3 ) @ R ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_116_Domain_Ocases,axiom,
% 2.81/1.57      ! [A: standard_Constant_a,R: set_Pr409224873um_a_b] :
% 2.81/1.57        ( ( member1632892294tant_a @ A @ ( domain1362581744um_a_b @ R ) )
% 2.81/1.57       => ~ ! [B3: produc1548871597um_a_b] :
% 2.81/1.57              ~ ( member1998628618um_a_b @ ( produc1697725733um_a_b @ A @ B3 ) @ R ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_117_Domain_Ocases,axiom,
% 2.81/1.57      ! [A: sum_sum_a_b,R: set_Pr1916610317um_a_b] :
% 2.81/1.57        ( ( member_Sum_sum_a_b @ A @ ( domain2069673178um_a_b @ R ) )
% 2.81/1.57       => ~ ! [B3: sum_sum_a_b] :
% 2.81/1.57              ~ ( member947389014um_a_b @ ( produc176426981um_a_b @ A @ B3 ) @ R ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_118_Domain__iff,axiom,
% 2.81/1.57      ! [A: standard_Constant_a,R: set_Pr1647387645at_nat] :
% 2.81/1.57        ( ( member1632892294tant_a @ A @ ( domain1060562500at_nat @ R ) )
% 2.81/1.57        = ( ? [Y3: product_prod_nat_nat] : ( member1696759390at_nat @ ( produc407553657at_nat @ A @ Y3 ) @ R ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_119_Domain__iff,axiom,
% 2.81/1.57      ! [A: nat,R: set_Pr1986765409at_nat] :
% 2.81/1.57        ( ( member_nat @ A @ ( domain_nat_nat @ R ) )
% 2.81/1.57        = ( ? [Y3: nat] : ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ Y3 ) @ R ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_120_Domain__iff,axiom,
% 2.81/1.57      ! [A: nat,R: set_Pr1174980151um_a_b] :
% 2.81/1.57        ( ( member_nat @ A @ ( domain1368163076um_a_b @ R ) )
% 2.81/1.57        = ( ? [Y3: sum_sum_a_b] : ( member1294585472um_a_b @ ( produc1808556047um_a_b @ A @ Y3 ) @ R ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_121_Domain__iff,axiom,
% 2.81/1.57      ! [A: standard_Constant_a,R: set_Pr409224873um_a_b] :
% 2.81/1.57        ( ( member1632892294tant_a @ A @ ( domain1362581744um_a_b @ R ) )
% 2.81/1.57        = ( ? [Y3: produc1548871597um_a_b] : ( member1998628618um_a_b @ ( produc1697725733um_a_b @ A @ Y3 ) @ R ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_122_Domain__iff,axiom,
% 2.81/1.57      ! [A: sum_sum_a_b,R: set_Pr1916610317um_a_b] :
% 2.81/1.57        ( ( member_Sum_sum_a_b @ A @ ( domain2069673178um_a_b @ R ) )
% 2.81/1.57        = ( ? [Y3: sum_sum_a_b] : ( member947389014um_a_b @ ( produc176426981um_a_b @ A @ Y3 ) @ R ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_123_DomainE,axiom,
% 2.81/1.57      ! [A: standard_Constant_a,R: set_Pr1647387645at_nat] :
% 2.81/1.57        ( ( member1632892294tant_a @ A @ ( domain1060562500at_nat @ R ) )
% 2.81/1.57       => ~ ! [B3: product_prod_nat_nat] :
% 2.81/1.57              ~ ( member1696759390at_nat @ ( produc407553657at_nat @ A @ B3 ) @ R ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_124_DomainE,axiom,
% 2.81/1.57      ! [A: nat,R: set_Pr1986765409at_nat] :
% 2.81/1.57        ( ( member_nat @ A @ ( domain_nat_nat @ R ) )
% 2.81/1.57       => ~ ! [B3: nat] :
% 2.81/1.57              ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B3 ) @ R ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_125_DomainE,axiom,
% 2.81/1.57      ! [A: nat,R: set_Pr1174980151um_a_b] :
% 2.81/1.57        ( ( member_nat @ A @ ( domain1368163076um_a_b @ R ) )
% 2.81/1.57       => ~ ! [B3: sum_sum_a_b] :
% 2.81/1.57              ~ ( member1294585472um_a_b @ ( produc1808556047um_a_b @ A @ B3 ) @ R ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_126_DomainE,axiom,
% 2.81/1.57      ! [A: standard_Constant_a,R: set_Pr409224873um_a_b] :
% 2.81/1.57        ( ( member1632892294tant_a @ A @ ( domain1362581744um_a_b @ R ) )
% 2.81/1.57       => ~ ! [B3: produc1548871597um_a_b] :
% 2.81/1.57              ~ ( member1998628618um_a_b @ ( produc1697725733um_a_b @ A @ B3 ) @ R ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_127_DomainE,axiom,
% 2.81/1.57      ! [A: sum_sum_a_b,R: set_Pr1916610317um_a_b] :
% 2.81/1.57        ( ( member_Sum_sum_a_b @ A @ ( domain2069673178um_a_b @ R ) )
% 2.81/1.57       => ~ ! [B3: sum_sum_a_b] :
% 2.81/1.57              ~ ( member947389014um_a_b @ ( produc176426981um_a_b @ A @ B3 ) @ R ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_128_Domain__mono,axiom,
% 2.81/1.57      ! [R: set_Pr1174980151um_a_b,S: set_Pr1174980151um_a_b] :
% 2.81/1.57        ( ( ord_le823954903um_a_b @ R @ S )
% 2.81/1.57       => ( ord_less_eq_set_nat @ ( domain1368163076um_a_b @ R ) @ ( domain1368163076um_a_b @ S ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_129_Domain__mono,axiom,
% 2.81/1.57      ! [R: set_Pr409224873um_a_b,S: set_Pr409224873um_a_b] :
% 2.81/1.57        ( ( ord_le615126793um_a_b @ R @ S )
% 2.81/1.57       => ( ord_le1739761029tant_a @ ( domain1362581744um_a_b @ R ) @ ( domain1362581744um_a_b @ S ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_130_Domain__mono,axiom,
% 2.81/1.57      ! [R: set_Pr1986765409at_nat,S: set_Pr1986765409at_nat] :
% 2.81/1.57        ( ( ord_le841296385at_nat @ R @ S )
% 2.81/1.57       => ( ord_less_eq_set_nat @ ( domain_nat_nat @ R ) @ ( domain_nat_nat @ S ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_131_Domain__mono,axiom,
% 2.81/1.57      ! [R: set_Pr1647387645at_nat,S: set_Pr1647387645at_nat] :
% 2.81/1.57        ( ( ord_le1909159005at_nat @ R @ S )
% 2.81/1.57       => ( ord_le1739761029tant_a @ ( domain1060562500at_nat @ R ) @ ( domain1060562500at_nat @ S ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_132_Domain__mono,axiom,
% 2.81/1.57      ! [R: set_Pr1916610317um_a_b,S: set_Pr1916610317um_a_b] :
% 2.81/1.57        ( ( ord_le1059794605um_a_b @ R @ S )
% 2.81/1.57       => ( ord_le192794300um_a_b @ ( domain2069673178um_a_b @ R ) @ ( domain2069673178um_a_b @ S ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_133_labeled__graph_Oexpand,axiom,
% 2.81/1.57      ! [Labeled_graph: labele935650037_a_nat,Labeled_graph2: labele935650037_a_nat] :
% 2.81/1.57        ( ( ( ( labele195203296_a_nat @ Labeled_graph )
% 2.81/1.57            = ( labele195203296_a_nat @ Labeled_graph2 ) )
% 2.81/1.57          & ( ( labele1810595089_a_nat @ Labeled_graph )
% 2.81/1.57            = ( labele1810595089_a_nat @ Labeled_graph2 ) ) )
% 2.81/1.57       => ( Labeled_graph = Labeled_graph2 ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_134_labeled__graph_Oexpand,axiom,
% 2.81/1.57      ! [Labeled_graph: labele431970251um_a_b,Labeled_graph2: labele431970251um_a_b] :
% 2.81/1.57        ( ( ( ( labele1939049654um_a_b @ Labeled_graph )
% 2.81/1.57            = ( labele1939049654um_a_b @ Labeled_graph2 ) )
% 2.81/1.57          & ( ( labele577278695um_a_b @ Labeled_graph )
% 2.81/1.57            = ( labele577278695um_a_b @ Labeled_graph2 ) ) )
% 2.81/1.57       => ( Labeled_graph = Labeled_graph2 ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_135_labeled__graph_Osel_I2_J,axiom,
% 2.81/1.57      ! [X1: set_Pr1647387645at_nat,X22: set_nat] :
% 2.81/1.57        ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ X1 @ X22 ) )
% 2.81/1.57        = X22 ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_136_labeled__graph_Osel_I2_J,axiom,
% 2.81/1.57      ! [X1: set_Pr409224873um_a_b,X22: set_Sum_sum_a_b] :
% 2.81/1.57        ( ( labele577278695um_a_b @ ( labele1729654377um_a_b @ X1 @ X22 ) )
% 2.81/1.57        = X22 ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_137_labeled__graph_Osel_I1_J,axiom,
% 2.81/1.57      ! [X1: set_Pr1647387645at_nat,X22: set_nat] :
% 2.81/1.57        ( ( labele195203296_a_nat @ ( labele16114835_a_nat @ X1 @ X22 ) )
% 2.81/1.57        = X1 ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_138_labeled__graph_Osel_I1_J,axiom,
% 2.81/1.57      ! [X1: set_Pr409224873um_a_b,X22: set_Sum_sum_a_b] :
% 2.81/1.57        ( ( labele1939049654um_a_b @ ( labele1729654377um_a_b @ X1 @ X22 ) )
% 2.81/1.57        = X1 ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_139_Domain__empty__iff,axiom,
% 2.81/1.57      ! [R: set_Pr1647387645at_nat] :
% 2.81/1.57        ( ( ( domain1060562500at_nat @ R )
% 2.81/1.57          = bot_bo1160111033tant_a )
% 2.81/1.57        = ( R = bot_bo810816657at_nat ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_140_Domain__empty__iff,axiom,
% 2.81/1.57      ! [R: set_Pr409224873um_a_b] :
% 2.81/1.57        ( ( ( domain1362581744um_a_b @ R )
% 2.81/1.57          = bot_bo1160111033tant_a )
% 2.81/1.57        = ( R = bot_bo1262634813um_a_b ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_141_Domain__empty__iff,axiom,
% 2.81/1.57      ! [R: set_Pr1986765409at_nat] :
% 2.81/1.57        ( ( ( domain_nat_nat @ R )
% 2.81/1.57          = bot_bot_set_nat )
% 2.81/1.57        = ( R = bot_bo2130386637at_nat ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_142_Domain__empty__iff,axiom,
% 2.81/1.57      ! [R: set_Pr1174980151um_a_b] :
% 2.81/1.57        ( ( ( domain1368163076um_a_b @ R )
% 2.81/1.57          = bot_bot_set_nat )
% 2.81/1.57        = ( R = bot_bo575978147um_a_b ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_143_Domain__empty__iff,axiom,
% 2.81/1.57      ! [R: set_Pr1916610317um_a_b] :
% 2.81/1.57        ( ( ( domain2069673178um_a_b @ R )
% 2.81/1.57          = bot_bo1491243248um_a_b )
% 2.81/1.57        = ( R = bot_bo225809273um_a_b ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_144_edge__preserving__atomic,axiom,
% 2.81/1.57      ! [H1: set_Pr375490359_b_nat,E1: set_Pr409224873um_a_b,E2: set_Pr1647387645at_nat,V1: sum_sum_a_b,V12: nat,V22: sum_sum_a_b,V23: nat,K: standard_Constant_a] :
% 2.81/1.57        ( ( edge_p749155930tant_a @ H1 @ E1 @ E2 )
% 2.81/1.57       => ( ( member1249152_b_nat @ ( produc522153487_b_nat @ V1 @ V12 ) @ H1 )
% 2.81/1.57         => ( ( member1249152_b_nat @ ( produc522153487_b_nat @ V22 @ V23 ) @ H1 )
% 2.81/1.57           => ( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ K @ ( produc176426981um_a_b @ V1 @ V22 ) ) @ E1 )
% 2.81/1.57             => ( member1696759390at_nat @ ( produc407553657at_nat @ K @ ( product_Pair_nat_nat @ V12 @ V23 ) ) @ E2 ) ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_145_edge__preserving__atomic,axiom,
% 2.81/1.57      ! [H1: set_Pr1986765409at_nat,E1: set_Pr1647387645at_nat,E2: set_Pr1647387645at_nat,V1: nat,V12: nat,V22: nat,V23: nat,K: standard_Constant_a] :
% 2.81/1.57        ( ( edge_p170421892tant_a @ H1 @ E1 @ E2 )
% 2.81/1.57       => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ V1 @ V12 ) @ H1 )
% 2.81/1.57         => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ V22 @ V23 ) @ H1 )
% 2.81/1.57           => ( ( member1696759390at_nat @ ( produc407553657at_nat @ K @ ( product_Pair_nat_nat @ V1 @ V22 ) ) @ E1 )
% 2.81/1.57             => ( member1696759390at_nat @ ( produc407553657at_nat @ K @ ( product_Pair_nat_nat @ V12 @ V23 ) ) @ E2 ) ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_146_edge__preserving__atomic,axiom,
% 2.81/1.57      ! [H1: set_Pr1916610317um_a_b,E1: set_Pr409224873um_a_b,E2: set_Pr409224873um_a_b,V1: sum_sum_a_b,V12: sum_sum_a_b,V22: sum_sum_a_b,V23: sum_sum_a_b,K: standard_Constant_a] :
% 2.81/1.57        ( ( edge_p1871801392tant_a @ H1 @ E1 @ E2 )
% 2.81/1.57       => ( ( member947389014um_a_b @ ( produc176426981um_a_b @ V1 @ V12 ) @ H1 )
% 2.81/1.57         => ( ( member947389014um_a_b @ ( produc176426981um_a_b @ V22 @ V23 ) @ H1 )
% 2.81/1.57           => ( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ K @ ( produc176426981um_a_b @ V1 @ V22 ) ) @ E1 )
% 2.81/1.57             => ( member1998628618um_a_b @ ( produc1697725733um_a_b @ K @ ( produc176426981um_a_b @ V12 @ V23 ) ) @ E2 ) ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_147_edge__preserving__atomic,axiom,
% 2.81/1.57      ! [H1: set_Pr1174980151um_a_b,E1: set_Pr1647387645at_nat,E2: set_Pr409224873um_a_b,V1: nat,V12: sum_sum_a_b,V22: nat,V23: sum_sum_a_b,K: standard_Constant_a] :
% 2.81/1.57        ( ( edge_p1382426714tant_a @ H1 @ E1 @ E2 )
% 2.81/1.57       => ( ( member1294585472um_a_b @ ( produc1808556047um_a_b @ V1 @ V12 ) @ H1 )
% 2.81/1.57         => ( ( member1294585472um_a_b @ ( produc1808556047um_a_b @ V22 @ V23 ) @ H1 )
% 2.81/1.57           => ( ( member1696759390at_nat @ ( produc407553657at_nat @ K @ ( product_Pair_nat_nat @ V1 @ V22 ) ) @ E1 )
% 2.81/1.57             => ( member1998628618um_a_b @ ( produc1697725733um_a_b @ K @ ( produc176426981um_a_b @ V12 @ V23 ) ) @ E2 ) ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_148_labeled__graph_Oexhaust__sel,axiom,
% 2.81/1.57      ! [Labeled_graph: labele935650037_a_nat] :
% 2.81/1.57        ( Labeled_graph
% 2.81/1.57        = ( labele16114835_a_nat @ ( labele195203296_a_nat @ Labeled_graph ) @ ( labele1810595089_a_nat @ Labeled_graph ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_149_labeled__graph_Oexhaust__sel,axiom,
% 2.81/1.57      ! [Labeled_graph: labele431970251um_a_b] :
% 2.81/1.57        ( Labeled_graph
% 2.81/1.57        = ( labele1729654377um_a_b @ ( labele1939049654um_a_b @ Labeled_graph ) @ ( labele577278695um_a_b @ Labeled_graph ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_150_singleton__insert__inj__eq_H,axiom,
% 2.81/1.57      ! [A: standard_Constant_a,A3: set_St761939237tant_a,B: standard_Constant_a] :
% 2.81/1.57        ( ( ( insert1909710879tant_a @ A @ A3 )
% 2.81/1.57          = ( insert1909710879tant_a @ B @ bot_bo1160111033tant_a ) )
% 2.81/1.57        = ( ( A = B )
% 2.81/1.57          & ( ord_le1739761029tant_a @ A3 @ ( insert1909710879tant_a @ B @ bot_bo1160111033tant_a ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_151_singleton__insert__inj__eq_H,axiom,
% 2.81/1.57      ! [A: product_prod_nat_nat,A3: set_Pr1986765409at_nat,B: product_prod_nat_nat] :
% 2.81/1.57        ( ( ( insert271595217at_nat @ A @ A3 )
% 2.81/1.57          = ( insert271595217at_nat @ B @ bot_bo2130386637at_nat ) )
% 2.81/1.57        = ( ( A = B )
% 2.81/1.57          & ( ord_le841296385at_nat @ A3 @ ( insert271595217at_nat @ B @ bot_bo2130386637at_nat ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_152_singleton__insert__inj__eq_H,axiom,
% 2.81/1.57      ! [A: produc1032616263at_nat,A3: set_Pr1647387645at_nat,B: produc1032616263at_nat] :
% 2.81/1.57        ( ( ( insert1625259895at_nat @ A @ A3 )
% 2.81/1.57          = ( insert1625259895at_nat @ B @ bot_bo810816657at_nat ) )
% 2.81/1.57        = ( ( A = B )
% 2.81/1.57          & ( ord_le1909159005at_nat @ A3 @ ( insert1625259895at_nat @ B @ bot_bo810816657at_nat ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_153_singleton__insert__inj__eq_H,axiom,
% 2.81/1.57      ! [A: nat,A3: set_nat,B: nat] :
% 2.81/1.57        ( ( ( insert_nat @ A @ A3 )
% 2.81/1.57          = ( insert_nat @ B @ bot_bot_set_nat ) )
% 2.81/1.57        = ( ( A = B )
% 2.81/1.57          & ( ord_less_eq_set_nat @ A3 @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_154_singleton__insert__inj__eq_H,axiom,
% 2.81/1.57      ! [A: produc1124793815um_a_b,A3: set_Pr1174980151um_a_b,B: produc1124793815um_a_b] :
% 2.81/1.57        ( ( ( insert983991207um_a_b @ A @ A3 )
% 2.81/1.57          = ( insert983991207um_a_b @ B @ bot_bo575978147um_a_b ) )
% 2.81/1.57        = ( ( A = B )
% 2.81/1.57          & ( ord_le823954903um_a_b @ A3 @ ( insert983991207um_a_b @ B @ bot_bo575978147um_a_b ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_155_singleton__insert__inj__eq_H,axiom,
% 2.81/1.57      ! [A: produc1548871597um_a_b,A3: set_Pr1916610317um_a_b,B: produc1548871597um_a_b] :
% 2.81/1.57        ( ( ( insert1435405693um_a_b @ A @ A3 )
% 2.81/1.57          = ( insert1435405693um_a_b @ B @ bot_bo225809273um_a_b ) )
% 2.81/1.57        = ( ( A = B )
% 2.81/1.57          & ( ord_le1059794605um_a_b @ A3 @ ( insert1435405693um_a_b @ B @ bot_bo225809273um_a_b ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_156_singleton__insert__inj__eq_H,axiom,
% 2.81/1.57      ! [A: produc1963079155um_a_b,A3: set_Pr409224873um_a_b,B: produc1963079155um_a_b] :
% 2.81/1.57        ( ( ( insert323157027um_a_b @ A @ A3 )
% 2.81/1.57          = ( insert323157027um_a_b @ B @ bot_bo1262634813um_a_b ) )
% 2.81/1.57        = ( ( A = B )
% 2.81/1.57          & ( ord_le615126793um_a_b @ A3 @ ( insert323157027um_a_b @ B @ bot_bo1262634813um_a_b ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_157_singleton__insert__inj__eq_H,axiom,
% 2.81/1.57      ! [A: sum_sum_a_b,A3: set_Sum_sum_a_b,B: sum_sum_a_b] :
% 2.81/1.57        ( ( ( insert_Sum_sum_a_b @ A @ A3 )
% 2.81/1.57          = ( insert_Sum_sum_a_b @ B @ bot_bo1491243248um_a_b ) )
% 2.81/1.57        = ( ( A = B )
% 2.81/1.57          & ( ord_le192794300um_a_b @ A3 @ ( insert_Sum_sum_a_b @ B @ bot_bo1491243248um_a_b ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_158_singleton__insert__inj__eq,axiom,
% 2.81/1.57      ! [B: standard_Constant_a,A: standard_Constant_a,A3: set_St761939237tant_a] :
% 2.81/1.57        ( ( ( insert1909710879tant_a @ B @ bot_bo1160111033tant_a )
% 2.81/1.57          = ( insert1909710879tant_a @ A @ A3 ) )
% 2.81/1.57        = ( ( A = B )
% 2.81/1.57          & ( ord_le1739761029tant_a @ A3 @ ( insert1909710879tant_a @ B @ bot_bo1160111033tant_a ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_159_singleton__insert__inj__eq,axiom,
% 2.81/1.57      ! [B: product_prod_nat_nat,A: product_prod_nat_nat,A3: set_Pr1986765409at_nat] :
% 2.81/1.57        ( ( ( insert271595217at_nat @ B @ bot_bo2130386637at_nat )
% 2.81/1.57          = ( insert271595217at_nat @ A @ A3 ) )
% 2.81/1.57        = ( ( A = B )
% 2.81/1.57          & ( ord_le841296385at_nat @ A3 @ ( insert271595217at_nat @ B @ bot_bo2130386637at_nat ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_160_singleton__insert__inj__eq,axiom,
% 2.81/1.57      ! [B: produc1032616263at_nat,A: produc1032616263at_nat,A3: set_Pr1647387645at_nat] :
% 2.81/1.57        ( ( ( insert1625259895at_nat @ B @ bot_bo810816657at_nat )
% 2.81/1.57          = ( insert1625259895at_nat @ A @ A3 ) )
% 2.81/1.57        = ( ( A = B )
% 2.81/1.57          & ( ord_le1909159005at_nat @ A3 @ ( insert1625259895at_nat @ B @ bot_bo810816657at_nat ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_161_singleton__insert__inj__eq,axiom,
% 2.81/1.57      ! [B: nat,A: nat,A3: set_nat] :
% 2.81/1.57        ( ( ( insert_nat @ B @ bot_bot_set_nat )
% 2.81/1.57          = ( insert_nat @ A @ A3 ) )
% 2.81/1.57        = ( ( A = B )
% 2.81/1.57          & ( ord_less_eq_set_nat @ A3 @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_162_singleton__insert__inj__eq,axiom,
% 2.81/1.57      ! [B: produc1124793815um_a_b,A: produc1124793815um_a_b,A3: set_Pr1174980151um_a_b] :
% 2.81/1.57        ( ( ( insert983991207um_a_b @ B @ bot_bo575978147um_a_b )
% 2.81/1.57          = ( insert983991207um_a_b @ A @ A3 ) )
% 2.81/1.57        = ( ( A = B )
% 2.81/1.57          & ( ord_le823954903um_a_b @ A3 @ ( insert983991207um_a_b @ B @ bot_bo575978147um_a_b ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_163_singleton__insert__inj__eq,axiom,
% 2.81/1.57      ! [B: produc1548871597um_a_b,A: produc1548871597um_a_b,A3: set_Pr1916610317um_a_b] :
% 2.81/1.57        ( ( ( insert1435405693um_a_b @ B @ bot_bo225809273um_a_b )
% 2.81/1.57          = ( insert1435405693um_a_b @ A @ A3 ) )
% 2.81/1.57        = ( ( A = B )
% 2.81/1.57          & ( ord_le1059794605um_a_b @ A3 @ ( insert1435405693um_a_b @ B @ bot_bo225809273um_a_b ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_164_singleton__insert__inj__eq,axiom,
% 2.81/1.57      ! [B: produc1963079155um_a_b,A: produc1963079155um_a_b,A3: set_Pr409224873um_a_b] :
% 2.81/1.57        ( ( ( insert323157027um_a_b @ B @ bot_bo1262634813um_a_b )
% 2.81/1.57          = ( insert323157027um_a_b @ A @ A3 ) )
% 2.81/1.57        = ( ( A = B )
% 2.81/1.57          & ( ord_le615126793um_a_b @ A3 @ ( insert323157027um_a_b @ B @ bot_bo1262634813um_a_b ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_165_singleton__insert__inj__eq,axiom,
% 2.81/1.57      ! [B: sum_sum_a_b,A: sum_sum_a_b,A3: set_Sum_sum_a_b] :
% 2.81/1.57        ( ( ( insert_Sum_sum_a_b @ B @ bot_bo1491243248um_a_b )
% 2.81/1.57          = ( insert_Sum_sum_a_b @ A @ A3 ) )
% 2.81/1.57        = ( ( A = B )
% 2.81/1.57          & ( ord_le192794300um_a_b @ A3 @ ( insert_Sum_sum_a_b @ B @ bot_bo1491243248um_a_b ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_166_univalent__empty,axiom,
% 2.81/1.57      unival860567212at_nat @ bot_bo810816657at_nat ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_167_univalent__empty,axiom,
% 2.81/1.57      unival118648434um_a_b @ bot_bo225809273um_a_b ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_168_univalent__empty,axiom,
% 2.81/1.57      unival1487587672um_a_b @ bot_bo1262634813um_a_b ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_169_univalent__empty,axiom,
% 2.81/1.57      unival2092813468um_a_b @ bot_bo575978147um_a_b ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_170_mem__Collect__eq,axiom,
% 2.81/1.57      ! [A: sum_sum_a_b,P: sum_sum_a_b > $o] :
% 2.81/1.57        ( ( member_Sum_sum_a_b @ A @ ( collect_Sum_sum_a_b @ P ) )
% 2.81/1.57        = ( P @ A ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_171_mem__Collect__eq,axiom,
% 2.81/1.57      ! [A: produc1124793815um_a_b,P: produc1124793815um_a_b > $o] :
% 2.81/1.57        ( ( member1294585472um_a_b @ A @ ( collec492052930um_a_b @ P ) )
% 2.81/1.57        = ( P @ A ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_172_mem__Collect__eq,axiom,
% 2.81/1.57      ! [A: produc1963079155um_a_b,P: produc1963079155um_a_b > $o] :
% 2.81/1.57        ( ( member1998628618um_a_b @ A @ ( collec1254333256um_a_b @ P ) )
% 2.81/1.57        = ( P @ A ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_173_Collect__mem__eq,axiom,
% 2.81/1.57      ! [A3: set_Sum_sum_a_b] :
% 2.81/1.57        ( ( collect_Sum_sum_a_b
% 2.81/1.57          @ ^ [X3: sum_sum_a_b] : ( member_Sum_sum_a_b @ X3 @ A3 ) )
% 2.81/1.57        = A3 ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_174_Collect__mem__eq,axiom,
% 2.81/1.57      ! [A3: set_Pr1174980151um_a_b] :
% 2.81/1.57        ( ( collec492052930um_a_b
% 2.81/1.57          @ ^ [X3: produc1124793815um_a_b] : ( member1294585472um_a_b @ X3 @ A3 ) )
% 2.81/1.57        = A3 ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_175_Collect__mem__eq,axiom,
% 2.81/1.57      ! [A3: set_Pr409224873um_a_b] :
% 2.81/1.57        ( ( collec1254333256um_a_b
% 2.81/1.57          @ ^ [X3: produc1963079155um_a_b] : ( member1998628618um_a_b @ X3 @ A3 ) )
% 2.81/1.57        = A3 ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_176_insert__subset,axiom,
% 2.81/1.57      ! [X2: produc1032616263at_nat,A3: set_Pr1647387645at_nat,B5: set_Pr1647387645at_nat] :
% 2.81/1.57        ( ( ord_le1909159005at_nat @ ( insert1625259895at_nat @ X2 @ A3 ) @ B5 )
% 2.81/1.57        = ( ( member1696759390at_nat @ X2 @ B5 )
% 2.81/1.57          & ( ord_le1909159005at_nat @ A3 @ B5 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_177_insert__subset,axiom,
% 2.81/1.57      ! [X2: nat,A3: set_nat,B5: set_nat] :
% 2.81/1.57        ( ( ord_less_eq_set_nat @ ( insert_nat @ X2 @ A3 ) @ B5 )
% 2.81/1.57        = ( ( member_nat @ X2 @ B5 )
% 2.81/1.57          & ( ord_less_eq_set_nat @ A3 @ B5 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_178_insert__subset,axiom,
% 2.81/1.57      ! [X2: produc1548871597um_a_b,A3: set_Pr1916610317um_a_b,B5: set_Pr1916610317um_a_b] :
% 2.81/1.57        ( ( ord_le1059794605um_a_b @ ( insert1435405693um_a_b @ X2 @ A3 ) @ B5 )
% 2.81/1.57        = ( ( member947389014um_a_b @ X2 @ B5 )
% 2.81/1.57          & ( ord_le1059794605um_a_b @ A3 @ B5 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_179_insert__subset,axiom,
% 2.81/1.57      ! [X2: standard_Constant_a,A3: set_St761939237tant_a,B5: set_St761939237tant_a] :
% 2.81/1.57        ( ( ord_le1739761029tant_a @ ( insert1909710879tant_a @ X2 @ A3 ) @ B5 )
% 2.81/1.57        = ( ( member1632892294tant_a @ X2 @ B5 )
% 2.81/1.57          & ( ord_le1739761029tant_a @ A3 @ B5 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_180_insert__subset,axiom,
% 2.81/1.57      ! [X2: product_prod_nat_nat,A3: set_Pr1986765409at_nat,B5: set_Pr1986765409at_nat] :
% 2.81/1.57        ( ( ord_le841296385at_nat @ ( insert271595217at_nat @ X2 @ A3 ) @ B5 )
% 2.81/1.57        = ( ( member701585322at_nat @ X2 @ B5 )
% 2.81/1.57          & ( ord_le841296385at_nat @ A3 @ B5 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_181_insert__subset,axiom,
% 2.81/1.57      ! [X2: produc1124793815um_a_b,A3: set_Pr1174980151um_a_b,B5: set_Pr1174980151um_a_b] :
% 2.81/1.57        ( ( ord_le823954903um_a_b @ ( insert983991207um_a_b @ X2 @ A3 ) @ B5 )
% 2.81/1.57        = ( ( member1294585472um_a_b @ X2 @ B5 )
% 2.81/1.57          & ( ord_le823954903um_a_b @ A3 @ B5 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_182_insert__subset,axiom,
% 2.81/1.57      ! [X2: produc1963079155um_a_b,A3: set_Pr409224873um_a_b,B5: set_Pr409224873um_a_b] :
% 2.81/1.57        ( ( ord_le615126793um_a_b @ ( insert323157027um_a_b @ X2 @ A3 ) @ B5 )
% 2.81/1.57        = ( ( member1998628618um_a_b @ X2 @ B5 )
% 2.81/1.57          & ( ord_le615126793um_a_b @ A3 @ B5 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_183_insert__subset,axiom,
% 2.81/1.57      ! [X2: sum_sum_a_b,A3: set_Sum_sum_a_b,B5: set_Sum_sum_a_b] :
% 2.81/1.57        ( ( ord_le192794300um_a_b @ ( insert_Sum_sum_a_b @ X2 @ A3 ) @ B5 )
% 2.81/1.57        = ( ( member_Sum_sum_a_b @ X2 @ B5 )
% 2.81/1.57          & ( ord_le192794300um_a_b @ A3 @ B5 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_184_singletonI,axiom,
% 2.81/1.57      ! [A: standard_Constant_a] : ( member1632892294tant_a @ A @ ( insert1909710879tant_a @ A @ bot_bo1160111033tant_a ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_185_singletonI,axiom,
% 2.81/1.57      ! [A: product_prod_nat_nat] : ( member701585322at_nat @ A @ ( insert271595217at_nat @ A @ bot_bo2130386637at_nat ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_186_singletonI,axiom,
% 2.81/1.57      ! [A: produc1032616263at_nat] : ( member1696759390at_nat @ A @ ( insert1625259895at_nat @ A @ bot_bo810816657at_nat ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_187_singletonI,axiom,
% 2.81/1.57      ! [A: nat] : ( member_nat @ A @ ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_188_singletonI,axiom,
% 2.81/1.57      ! [A: produc1124793815um_a_b] : ( member1294585472um_a_b @ A @ ( insert983991207um_a_b @ A @ bot_bo575978147um_a_b ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_189_singletonI,axiom,
% 2.81/1.57      ! [A: produc1548871597um_a_b] : ( member947389014um_a_b @ A @ ( insert1435405693um_a_b @ A @ bot_bo225809273um_a_b ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_190_singletonI,axiom,
% 2.81/1.57      ! [A: produc1963079155um_a_b] : ( member1998628618um_a_b @ A @ ( insert323157027um_a_b @ A @ bot_bo1262634813um_a_b ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_191_singletonI,axiom,
% 2.81/1.57      ! [A: sum_sum_a_b] : ( member_Sum_sum_a_b @ A @ ( insert_Sum_sum_a_b @ A @ bot_bo1491243248um_a_b ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_192_empty__subsetI,axiom,
% 2.81/1.57      ! [A3: set_Pr1647387645at_nat] : ( ord_le1909159005at_nat @ bot_bo810816657at_nat @ A3 ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_193_empty__subsetI,axiom,
% 2.81/1.57      ! [A3: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A3 ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_194_empty__subsetI,axiom,
% 2.81/1.57      ! [A3: set_Pr1174980151um_a_b] : ( ord_le823954903um_a_b @ bot_bo575978147um_a_b @ A3 ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_195_empty__subsetI,axiom,
% 2.81/1.57      ! [A3: set_Pr1916610317um_a_b] : ( ord_le1059794605um_a_b @ bot_bo225809273um_a_b @ A3 ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_196_empty__subsetI,axiom,
% 2.81/1.57      ! [A3: set_Pr409224873um_a_b] : ( ord_le615126793um_a_b @ bot_bo1262634813um_a_b @ A3 ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_197_empty__subsetI,axiom,
% 2.81/1.57      ! [A3: set_Sum_sum_a_b] : ( ord_le192794300um_a_b @ bot_bo1491243248um_a_b @ A3 ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_198_subset__empty,axiom,
% 2.81/1.57      ! [A3: set_Pr1647387645at_nat] :
% 2.81/1.57        ( ( ord_le1909159005at_nat @ A3 @ bot_bo810816657at_nat )
% 2.81/1.57        = ( A3 = bot_bo810816657at_nat ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_199_subset__empty,axiom,
% 2.81/1.57      ! [A3: set_nat] :
% 2.81/1.57        ( ( ord_less_eq_set_nat @ A3 @ bot_bot_set_nat )
% 2.81/1.57        = ( A3 = bot_bot_set_nat ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_200_subset__empty,axiom,
% 2.81/1.57      ! [A3: set_Pr1174980151um_a_b] :
% 2.81/1.57        ( ( ord_le823954903um_a_b @ A3 @ bot_bo575978147um_a_b )
% 2.81/1.57        = ( A3 = bot_bo575978147um_a_b ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_201_subset__empty,axiom,
% 2.81/1.57      ! [A3: set_Pr1916610317um_a_b] :
% 2.81/1.57        ( ( ord_le1059794605um_a_b @ A3 @ bot_bo225809273um_a_b )
% 2.81/1.57        = ( A3 = bot_bo225809273um_a_b ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_202_subset__empty,axiom,
% 2.81/1.57      ! [A3: set_Pr409224873um_a_b] :
% 2.81/1.57        ( ( ord_le615126793um_a_b @ A3 @ bot_bo1262634813um_a_b )
% 2.81/1.57        = ( A3 = bot_bo1262634813um_a_b ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_203_subset__empty,axiom,
% 2.81/1.57      ! [A3: set_Sum_sum_a_b] :
% 2.81/1.57        ( ( ord_le192794300um_a_b @ A3 @ bot_bo1491243248um_a_b )
% 2.81/1.57        = ( A3 = bot_bo1491243248um_a_b ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_204_le__zero__eq,axiom,
% 2.81/1.57      ! [N: nat] :
% 2.81/1.57        ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 2.81/1.57        = ( N = zero_zero_nat ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_205_reflexivity__rule__def,axiom,
% 2.81/1.57      ( standa63370785tant_a
% 2.81/1.57      = ( ^ [T: standard_Constant_a] : ( produc1676969687_a_nat @ ( labele16114835_a_nat @ bot_bo810816657at_nat @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ T @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_206_nonempty__rule__def,axiom,
% 2.81/1.57      ( standa1410829644tant_a
% 2.81/1.57      = ( produc1676969687_a_nat @ ( labele16114835_a_nat @ bot_bo810816657at_nat @ bot_bot_set_nat ) @ ( labele16114835_a_nat @ bot_bo810816657at_nat @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_207_empty__iff,axiom,
% 2.81/1.57      ! [C: produc1032616263at_nat] :
% 2.81/1.57        ~ ( member1696759390at_nat @ C @ bot_bo810816657at_nat ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_208_empty__iff,axiom,
% 2.81/1.57      ! [C: nat] :
% 2.81/1.57        ~ ( member_nat @ C @ bot_bot_set_nat ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_209_empty__iff,axiom,
% 2.81/1.57      ! [C: produc1124793815um_a_b] :
% 2.81/1.57        ~ ( member1294585472um_a_b @ C @ bot_bo575978147um_a_b ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_210_empty__iff,axiom,
% 2.81/1.57      ! [C: produc1548871597um_a_b] :
% 2.81/1.57        ~ ( member947389014um_a_b @ C @ bot_bo225809273um_a_b ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_211_empty__iff,axiom,
% 2.81/1.57      ! [C: produc1963079155um_a_b] :
% 2.81/1.57        ~ ( member1998628618um_a_b @ C @ bot_bo1262634813um_a_b ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_212_empty__iff,axiom,
% 2.81/1.57      ! [C: sum_sum_a_b] :
% 2.81/1.57        ~ ( member_Sum_sum_a_b @ C @ bot_bo1491243248um_a_b ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_213_all__not__in__conv,axiom,
% 2.81/1.57      ! [A3: set_Pr1647387645at_nat] :
% 2.81/1.57        ( ( ! [X3: produc1032616263at_nat] :
% 2.81/1.57              ~ ( member1696759390at_nat @ X3 @ A3 ) )
% 2.81/1.57        = ( A3 = bot_bo810816657at_nat ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_214_all__not__in__conv,axiom,
% 2.81/1.57      ! [A3: set_nat] :
% 2.81/1.57        ( ( ! [X3: nat] :
% 2.81/1.57              ~ ( member_nat @ X3 @ A3 ) )
% 2.81/1.57        = ( A3 = bot_bot_set_nat ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_215_all__not__in__conv,axiom,
% 2.81/1.57      ! [A3: set_Pr1174980151um_a_b] :
% 2.81/1.57        ( ( ! [X3: produc1124793815um_a_b] :
% 2.81/1.57              ~ ( member1294585472um_a_b @ X3 @ A3 ) )
% 2.81/1.57        = ( A3 = bot_bo575978147um_a_b ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_216_all__not__in__conv,axiom,
% 2.81/1.57      ! [A3: set_Pr1916610317um_a_b] :
% 2.81/1.57        ( ( ! [X3: produc1548871597um_a_b] :
% 2.81/1.57              ~ ( member947389014um_a_b @ X3 @ A3 ) )
% 2.81/1.57        = ( A3 = bot_bo225809273um_a_b ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_217_all__not__in__conv,axiom,
% 2.81/1.57      ! [A3: set_Pr409224873um_a_b] :
% 2.81/1.57        ( ( ! [X3: produc1963079155um_a_b] :
% 2.81/1.57              ~ ( member1998628618um_a_b @ X3 @ A3 ) )
% 2.81/1.57        = ( A3 = bot_bo1262634813um_a_b ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_218_all__not__in__conv,axiom,
% 2.81/1.57      ! [A3: set_Sum_sum_a_b] :
% 2.81/1.57        ( ( ! [X3: sum_sum_a_b] :
% 2.81/1.57              ~ ( member_Sum_sum_a_b @ X3 @ A3 ) )
% 2.81/1.57        = ( A3 = bot_bo1491243248um_a_b ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_219_Collect__empty__eq,axiom,
% 2.81/1.57      ! [P: produc1032616263at_nat > $o] :
% 2.81/1.57        ( ( ( collec52779676at_nat @ P )
% 2.81/1.57          = bot_bo810816657at_nat )
% 2.81/1.57        = ( ! [X3: produc1032616263at_nat] :
% 2.81/1.57              ~ ( P @ X3 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_220_Collect__empty__eq,axiom,
% 2.81/1.57      ! [P: nat > $o] :
% 2.81/1.57        ( ( ( collect_nat @ P )
% 2.81/1.57          = bot_bot_set_nat )
% 2.81/1.57        = ( ! [X3: nat] :
% 2.81/1.57              ~ ( P @ X3 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_221_Collect__empty__eq,axiom,
% 2.81/1.57      ! [P: produc1124793815um_a_b > $o] :
% 2.81/1.57        ( ( ( collec492052930um_a_b @ P )
% 2.81/1.57          = bot_bo575978147um_a_b )
% 2.81/1.57        = ( ! [X3: produc1124793815um_a_b] :
% 2.81/1.57              ~ ( P @ X3 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_222_Collect__empty__eq,axiom,
% 2.81/1.57      ! [P: produc1548871597um_a_b > $o] :
% 2.81/1.57        ( ( ( collec1769032088um_a_b @ P )
% 2.81/1.57          = bot_bo225809273um_a_b )
% 2.81/1.57        = ( ! [X3: produc1548871597um_a_b] :
% 2.81/1.57              ~ ( P @ X3 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_223_Collect__empty__eq,axiom,
% 2.81/1.57      ! [P: produc1963079155um_a_b > $o] :
% 2.81/1.57        ( ( ( collec1254333256um_a_b @ P )
% 2.81/1.57          = bot_bo1262634813um_a_b )
% 2.81/1.57        = ( ! [X3: produc1963079155um_a_b] :
% 2.81/1.57              ~ ( P @ X3 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_224_Collect__empty__eq,axiom,
% 2.81/1.57      ! [P: sum_sum_a_b > $o] :
% 2.81/1.57        ( ( ( collect_Sum_sum_a_b @ P )
% 2.81/1.57          = bot_bo1491243248um_a_b )
% 2.81/1.57        = ( ! [X3: sum_sum_a_b] :
% 2.81/1.57              ~ ( P @ X3 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_225_empty__Collect__eq,axiom,
% 2.81/1.57      ! [P: produc1032616263at_nat > $o] :
% 2.81/1.57        ( ( bot_bo810816657at_nat
% 2.81/1.57          = ( collec52779676at_nat @ P ) )
% 2.81/1.57        = ( ! [X3: produc1032616263at_nat] :
% 2.81/1.57              ~ ( P @ X3 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_226_empty__Collect__eq,axiom,
% 2.81/1.57      ! [P: nat > $o] :
% 2.81/1.57        ( ( bot_bot_set_nat
% 2.81/1.57          = ( collect_nat @ P ) )
% 2.81/1.57        = ( ! [X3: nat] :
% 2.81/1.57              ~ ( P @ X3 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_227_empty__Collect__eq,axiom,
% 2.81/1.57      ! [P: produc1124793815um_a_b > $o] :
% 2.81/1.57        ( ( bot_bo575978147um_a_b
% 2.81/1.57          = ( collec492052930um_a_b @ P ) )
% 2.81/1.57        = ( ! [X3: produc1124793815um_a_b] :
% 2.81/1.57              ~ ( P @ X3 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_228_empty__Collect__eq,axiom,
% 2.81/1.57      ! [P: produc1548871597um_a_b > $o] :
% 2.81/1.57        ( ( bot_bo225809273um_a_b
% 2.81/1.57          = ( collec1769032088um_a_b @ P ) )
% 2.81/1.57        = ( ! [X3: produc1548871597um_a_b] :
% 2.81/1.57              ~ ( P @ X3 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_229_empty__Collect__eq,axiom,
% 2.81/1.57      ! [P: produc1963079155um_a_b > $o] :
% 2.81/1.57        ( ( bot_bo1262634813um_a_b
% 2.81/1.57          = ( collec1254333256um_a_b @ P ) )
% 2.81/1.57        = ( ! [X3: produc1963079155um_a_b] :
% 2.81/1.57              ~ ( P @ X3 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_230_empty__Collect__eq,axiom,
% 2.81/1.57      ! [P: sum_sum_a_b > $o] :
% 2.81/1.57        ( ( bot_bo1491243248um_a_b
% 2.81/1.57          = ( collect_Sum_sum_a_b @ P ) )
% 2.81/1.57        = ( ! [X3: sum_sum_a_b] :
% 2.81/1.57              ~ ( P @ X3 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_231_subsetI,axiom,
% 2.81/1.57      ! [A3: set_Pr1174980151um_a_b,B5: set_Pr1174980151um_a_b] :
% 2.81/1.57        ( ! [X4: produc1124793815um_a_b] :
% 2.81/1.57            ( ( member1294585472um_a_b @ X4 @ A3 )
% 2.81/1.57           => ( member1294585472um_a_b @ X4 @ B5 ) )
% 2.81/1.57       => ( ord_le823954903um_a_b @ A3 @ B5 ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_232_subsetI,axiom,
% 2.81/1.57      ! [A3: set_Pr409224873um_a_b,B5: set_Pr409224873um_a_b] :
% 2.81/1.57        ( ! [X4: produc1963079155um_a_b] :
% 2.81/1.57            ( ( member1998628618um_a_b @ X4 @ A3 )
% 2.81/1.57           => ( member1998628618um_a_b @ X4 @ B5 ) )
% 2.81/1.57       => ( ord_le615126793um_a_b @ A3 @ B5 ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_233_subsetI,axiom,
% 2.81/1.57      ! [A3: set_Sum_sum_a_b,B5: set_Sum_sum_a_b] :
% 2.81/1.57        ( ! [X4: sum_sum_a_b] :
% 2.81/1.57            ( ( member_Sum_sum_a_b @ X4 @ A3 )
% 2.81/1.57           => ( member_Sum_sum_a_b @ X4 @ B5 ) )
% 2.81/1.57       => ( ord_le192794300um_a_b @ A3 @ B5 ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_234_subset__antisym,axiom,
% 2.81/1.57      ! [A3: set_Sum_sum_a_b,B5: set_Sum_sum_a_b] :
% 2.81/1.57        ( ( ord_le192794300um_a_b @ A3 @ B5 )
% 2.81/1.57       => ( ( ord_le192794300um_a_b @ B5 @ A3 )
% 2.81/1.57         => ( A3 = B5 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_235_insertCI,axiom,
% 2.81/1.57      ! [A: produc1032616263at_nat,B5: set_Pr1647387645at_nat,B: produc1032616263at_nat] :
% 2.81/1.57        ( ( ~ ( member1696759390at_nat @ A @ B5 )
% 2.81/1.57         => ( A = B ) )
% 2.81/1.57       => ( member1696759390at_nat @ A @ ( insert1625259895at_nat @ B @ B5 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_236_insertCI,axiom,
% 2.81/1.57      ! [A: nat,B5: set_nat,B: nat] :
% 2.81/1.57        ( ( ~ ( member_nat @ A @ B5 )
% 2.81/1.57         => ( A = B ) )
% 2.81/1.57       => ( member_nat @ A @ ( insert_nat @ B @ B5 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_237_insertCI,axiom,
% 2.81/1.57      ! [A: produc1548871597um_a_b,B5: set_Pr1916610317um_a_b,B: produc1548871597um_a_b] :
% 2.81/1.57        ( ( ~ ( member947389014um_a_b @ A @ B5 )
% 2.81/1.57         => ( A = B ) )
% 2.81/1.57       => ( member947389014um_a_b @ A @ ( insert1435405693um_a_b @ B @ B5 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_238_insertCI,axiom,
% 2.81/1.57      ! [A: standard_Constant_a,B5: set_St761939237tant_a,B: standard_Constant_a] :
% 2.81/1.57        ( ( ~ ( member1632892294tant_a @ A @ B5 )
% 2.81/1.57         => ( A = B ) )
% 2.81/1.57       => ( member1632892294tant_a @ A @ ( insert1909710879tant_a @ B @ B5 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_239_insertCI,axiom,
% 2.81/1.57      ! [A: product_prod_nat_nat,B5: set_Pr1986765409at_nat,B: product_prod_nat_nat] :
% 2.81/1.57        ( ( ~ ( member701585322at_nat @ A @ B5 )
% 2.81/1.57         => ( A = B ) )
% 2.81/1.57       => ( member701585322at_nat @ A @ ( insert271595217at_nat @ B @ B5 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_240_insertCI,axiom,
% 2.81/1.57      ! [A: sum_sum_a_b,B5: set_Sum_sum_a_b,B: sum_sum_a_b] :
% 2.81/1.57        ( ( ~ ( member_Sum_sum_a_b @ A @ B5 )
% 2.81/1.57         => ( A = B ) )
% 2.81/1.57       => ( member_Sum_sum_a_b @ A @ ( insert_Sum_sum_a_b @ B @ B5 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_241_insertCI,axiom,
% 2.81/1.57      ! [A: produc1124793815um_a_b,B5: set_Pr1174980151um_a_b,B: produc1124793815um_a_b] :
% 2.81/1.57        ( ( ~ ( member1294585472um_a_b @ A @ B5 )
% 2.81/1.57         => ( A = B ) )
% 2.81/1.57       => ( member1294585472um_a_b @ A @ ( insert983991207um_a_b @ B @ B5 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_242_insertCI,axiom,
% 2.81/1.57      ! [A: produc1963079155um_a_b,B5: set_Pr409224873um_a_b,B: produc1963079155um_a_b] :
% 2.81/1.57        ( ( ~ ( member1998628618um_a_b @ A @ B5 )
% 2.81/1.57         => ( A = B ) )
% 2.81/1.57       => ( member1998628618um_a_b @ A @ ( insert323157027um_a_b @ B @ B5 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_243_insert__iff,axiom,
% 2.81/1.57      ! [A: produc1032616263at_nat,B: produc1032616263at_nat,A3: set_Pr1647387645at_nat] :
% 2.81/1.57        ( ( member1696759390at_nat @ A @ ( insert1625259895at_nat @ B @ A3 ) )
% 2.81/1.57        = ( ( A = B )
% 2.81/1.57          | ( member1696759390at_nat @ A @ A3 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_244_insert__iff,axiom,
% 2.81/1.57      ! [A: nat,B: nat,A3: set_nat] :
% 2.81/1.57        ( ( member_nat @ A @ ( insert_nat @ B @ A3 ) )
% 2.81/1.57        = ( ( A = B )
% 2.81/1.57          | ( member_nat @ A @ A3 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_245_insert__iff,axiom,
% 2.81/1.57      ! [A: produc1548871597um_a_b,B: produc1548871597um_a_b,A3: set_Pr1916610317um_a_b] :
% 2.81/1.57        ( ( member947389014um_a_b @ A @ ( insert1435405693um_a_b @ B @ A3 ) )
% 2.81/1.57        = ( ( A = B )
% 2.81/1.57          | ( member947389014um_a_b @ A @ A3 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_246_insert__iff,axiom,
% 2.81/1.57      ! [A: standard_Constant_a,B: standard_Constant_a,A3: set_St761939237tant_a] :
% 2.81/1.57        ( ( member1632892294tant_a @ A @ ( insert1909710879tant_a @ B @ A3 ) )
% 2.81/1.57        = ( ( A = B )
% 2.81/1.57          | ( member1632892294tant_a @ A @ A3 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_247_insert__iff,axiom,
% 2.81/1.57      ! [A: product_prod_nat_nat,B: product_prod_nat_nat,A3: set_Pr1986765409at_nat] :
% 2.81/1.57        ( ( member701585322at_nat @ A @ ( insert271595217at_nat @ B @ A3 ) )
% 2.81/1.57        = ( ( A = B )
% 2.81/1.57          | ( member701585322at_nat @ A @ A3 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_248_insert__iff,axiom,
% 2.81/1.57      ! [A: sum_sum_a_b,B: sum_sum_a_b,A3: set_Sum_sum_a_b] :
% 2.81/1.57        ( ( member_Sum_sum_a_b @ A @ ( insert_Sum_sum_a_b @ B @ A3 ) )
% 2.81/1.57        = ( ( A = B )
% 2.81/1.57          | ( member_Sum_sum_a_b @ A @ A3 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_249_insert__iff,axiom,
% 2.81/1.57      ! [A: produc1124793815um_a_b,B: produc1124793815um_a_b,A3: set_Pr1174980151um_a_b] :
% 2.81/1.57        ( ( member1294585472um_a_b @ A @ ( insert983991207um_a_b @ B @ A3 ) )
% 2.81/1.57        = ( ( A = B )
% 2.81/1.57          | ( member1294585472um_a_b @ A @ A3 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_250_insert__iff,axiom,
% 2.81/1.57      ! [A: produc1963079155um_a_b,B: produc1963079155um_a_b,A3: set_Pr409224873um_a_b] :
% 2.81/1.57        ( ( member1998628618um_a_b @ A @ ( insert323157027um_a_b @ B @ A3 ) )
% 2.81/1.57        = ( ( A = B )
% 2.81/1.57          | ( member1998628618um_a_b @ A @ A3 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_251_insert__absorb2,axiom,
% 2.81/1.57      ! [X2: produc1032616263at_nat,A3: set_Pr1647387645at_nat] :
% 2.81/1.57        ( ( insert1625259895at_nat @ X2 @ ( insert1625259895at_nat @ X2 @ A3 ) )
% 2.81/1.57        = ( insert1625259895at_nat @ X2 @ A3 ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_252_insert__absorb2,axiom,
% 2.81/1.57      ! [X2: nat,A3: set_nat] :
% 2.81/1.57        ( ( insert_nat @ X2 @ ( insert_nat @ X2 @ A3 ) )
% 2.81/1.57        = ( insert_nat @ X2 @ A3 ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_253_insert__absorb2,axiom,
% 2.81/1.57      ! [X2: produc1124793815um_a_b,A3: set_Pr1174980151um_a_b] :
% 2.81/1.57        ( ( insert983991207um_a_b @ X2 @ ( insert983991207um_a_b @ X2 @ A3 ) )
% 2.81/1.57        = ( insert983991207um_a_b @ X2 @ A3 ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_254_insert__absorb2,axiom,
% 2.81/1.57      ! [X2: produc1963079155um_a_b,A3: set_Pr409224873um_a_b] :
% 2.81/1.57        ( ( insert323157027um_a_b @ X2 @ ( insert323157027um_a_b @ X2 @ A3 ) )
% 2.81/1.57        = ( insert323157027um_a_b @ X2 @ A3 ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_255_insert__absorb2,axiom,
% 2.81/1.57      ! [X2: sum_sum_a_b,A3: set_Sum_sum_a_b] :
% 2.81/1.57        ( ( insert_Sum_sum_a_b @ X2 @ ( insert_Sum_sum_a_b @ X2 @ A3 ) )
% 2.81/1.57        = ( insert_Sum_sum_a_b @ X2 @ A3 ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_256_insert__absorb2,axiom,
% 2.81/1.57      ! [X2: produc1548871597um_a_b,A3: set_Pr1916610317um_a_b] :
% 2.81/1.57        ( ( insert1435405693um_a_b @ X2 @ ( insert1435405693um_a_b @ X2 @ A3 ) )
% 2.81/1.57        = ( insert1435405693um_a_b @ X2 @ A3 ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_257_insert__absorb2,axiom,
% 2.81/1.57      ! [X2: standard_Constant_a,A3: set_St761939237tant_a] :
% 2.81/1.57        ( ( insert1909710879tant_a @ X2 @ ( insert1909710879tant_a @ X2 @ A3 ) )
% 2.81/1.57        = ( insert1909710879tant_a @ X2 @ A3 ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_258_insert__absorb2,axiom,
% 2.81/1.57      ! [X2: product_prod_nat_nat,A3: set_Pr1986765409at_nat] :
% 2.81/1.57        ( ( insert271595217at_nat @ X2 @ ( insert271595217at_nat @ X2 @ A3 ) )
% 2.81/1.57        = ( insert271595217at_nat @ X2 @ A3 ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_259_graph__homomorphism__empty,axiom,
% 2.81/1.57      ! [G: labele935650037_a_nat,F: set_Pr1986765409at_nat] :
% 2.81/1.57        ( ( graph_2130075512at_nat @ ( labele16114835_a_nat @ bot_bo810816657at_nat @ bot_bot_set_nat ) @ G @ F )
% 2.81/1.57        = ( ( F = bot_bo2130386637at_nat )
% 2.81/1.57          & ( G
% 2.81/1.57            = ( restri572569417_a_nat @ G ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_260_graph__homomorphism__empty,axiom,
% 2.81/1.57      ! [G: labele935650037_a_nat,F: set_Pr375490359_b_nat] :
% 2.81/1.57        ( ( graph_165730638_b_nat @ ( labele1729654377um_a_b @ bot_bo1262634813um_a_b @ bot_bo1491243248um_a_b ) @ G @ F )
% 2.81/1.57        = ( ( F = bot_bo1923972003_b_nat )
% 2.81/1.57          & ( G
% 2.81/1.57            = ( restri572569417_a_nat @ G ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_261_graph__homomorphism__empty,axiom,
% 2.81/1.57      ! [G: labele431970251um_a_b,F: set_Pr1174980151um_a_b] :
% 2.81/1.57        ( ( graph_1452133198um_a_b @ ( labele16114835_a_nat @ bot_bo810816657at_nat @ bot_bot_set_nat ) @ G @ F )
% 2.81/1.57        = ( ( F = bot_bo575978147um_a_b )
% 2.81/1.57          & ( G
% 2.81/1.57            = ( restri1162247455um_a_b @ G ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_262_graph__homomorphism__empty,axiom,
% 2.81/1.57      ! [G: labele935650037_a_nat,F: set_Pr1902304780_b_nat] :
% 2.81/1.57        ( ( graph_1203757137_b_nat @ ( labele2034032468um_a_b @ bot_bo1208513655um_a_b @ bot_bo575978147um_a_b ) @ G @ F )
% 2.81/1.57        = ( ( F = bot_bo949957280_b_nat )
% 2.81/1.57          & ( G
% 2.81/1.57            = ( restri572569417_a_nat @ G ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_263_graph__homomorphism__empty,axiom,
% 2.81/1.57      ! [G: labele431970251um_a_b,F: set_Pr1916610317um_a_b] :
% 2.81/1.57        ( ( graph_611893540um_a_b @ ( labele1729654377um_a_b @ bot_bo1262634813um_a_b @ bot_bo1491243248um_a_b ) @ G @ F )
% 2.81/1.57        = ( ( F = bot_bo225809273um_a_b )
% 2.81/1.57          & ( G
% 2.81/1.57            = ( restri1162247455um_a_b @ G ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_264_graph__homomorphism__empty,axiom,
% 2.81/1.57      ! [G: labele935650037_a_nat,F: set_Pr689416536at_nat] :
% 2.81/1.57        ( ( graph_149544303at_nat @ ( labele1813985418at_nat @ bot_bo1524397311at_nat @ bot_bo810816657at_nat ) @ G @ F )
% 2.81/1.57        = ( ( F = bot_bo1582968772at_nat )
% 2.81/1.57          & ( G
% 2.81/1.57            = ( restri572569417_a_nat @ G ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_265_graph__homomorphism__empty,axiom,
% 2.81/1.57      ! [G: labele431970251um_a_b,F: set_Pr653770722um_a_b] :
% 2.81/1.57        ( ( graph_502887975um_a_b @ ( labele2034032468um_a_b @ bot_bo1208513655um_a_b @ bot_bo575978147um_a_b ) @ G @ F )
% 2.81/1.57        = ( ( F = bot_bo1892785270um_a_b )
% 2.81/1.57          & ( G
% 2.81/1.57            = ( restri1162247455um_a_b @ G ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_266_graph__homomorphism__empty,axiom,
% 2.81/1.57      ! [G: labele935650037_a_nat,F: set_Pr507214050_b_nat] :
% 2.81/1.57        ( ( graph_1815313447_b_nat @ ( labele989994um_a_b @ bot_bo1262778871um_a_b @ bot_bo225809273um_a_b ) @ G @ F )
% 2.81/1.57        = ( ( F = bot_bo1746228598_b_nat )
% 2.81/1.57          & ( G
% 2.81/1.57            = ( restri572569417_a_nat @ G ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_267_graph__homomorphism__empty,axiom,
% 2.81/1.57      ! [G: labele431970251um_a_b,F: set_Pr304595758um_a_b] :
% 2.81/1.57        ( ( graph_166346565um_a_b @ ( labele1813985418at_nat @ bot_bo1524397311at_nat @ bot_bo810816657at_nat ) @ G @ F )
% 2.81/1.57        = ( ( F = bot_bo627753370um_a_b )
% 2.81/1.57          & ( G
% 2.81/1.57            = ( restri1162247455um_a_b @ G ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_268_graph__homomorphism__empty,axiom,
% 2.81/1.57      ! [G: labele431970251um_a_b,F: set_Pr55236280um_a_b] :
% 2.81/1.57        ( ( graph_1763806717um_a_b @ ( labele989994um_a_b @ bot_bo1262778871um_a_b @ bot_bo225809273um_a_b ) @ G @ F )
% 2.81/1.57        = ( ( F = bot_bo1217542988um_a_b )
% 2.81/1.57          & ( G
% 2.81/1.57            = ( restri1162247455um_a_b @ G ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_269_edge__preserving__subset,axiom,
% 2.81/1.57      ! [R_1: set_Pr1174980151um_a_b,R_2: set_Pr1174980151um_a_b,E_1: set_Pr1647387645at_nat,E_2: set_Pr1647387645at_nat,G: set_Pr409224873um_a_b] :
% 2.81/1.57        ( ( ord_le823954903um_a_b @ R_1 @ R_2 )
% 2.81/1.57       => ( ( ord_le1909159005at_nat @ E_1 @ E_2 )
% 2.81/1.57         => ( ( edge_p1382426714tant_a @ R_2 @ E_2 @ G )
% 2.81/1.57           => ( edge_p1382426714tant_a @ R_1 @ E_1 @ G ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_270_subrelI,axiom,
% 2.81/1.57      ! [R: set_Pr1647387645at_nat,S: set_Pr1647387645at_nat] :
% 2.81/1.57        ( ! [X4: standard_Constant_a,Y4: product_prod_nat_nat] :
% 2.81/1.57            ( ( member1696759390at_nat @ ( produc407553657at_nat @ X4 @ Y4 ) @ R )
% 2.81/1.57           => ( member1696759390at_nat @ ( produc407553657at_nat @ X4 @ Y4 ) @ S ) )
% 2.81/1.57       => ( ord_le1909159005at_nat @ R @ S ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_271_subrelI,axiom,
% 2.81/1.57      ! [R: set_Pr1986765409at_nat,S: set_Pr1986765409at_nat] :
% 2.81/1.57        ( ! [X4: nat,Y4: nat] :
% 2.81/1.57            ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) @ R )
% 2.81/1.57           => ( member701585322at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) @ S ) )
% 2.81/1.57       => ( ord_le841296385at_nat @ R @ S ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_272_subrelI,axiom,
% 2.81/1.57      ! [R: set_Pr1174980151um_a_b,S: set_Pr1174980151um_a_b] :
% 2.81/1.57        ( ! [X4: nat,Y4: sum_sum_a_b] :
% 2.81/1.57            ( ( member1294585472um_a_b @ ( produc1808556047um_a_b @ X4 @ Y4 ) @ R )
% 2.81/1.57           => ( member1294585472um_a_b @ ( produc1808556047um_a_b @ X4 @ Y4 ) @ S ) )
% 2.81/1.57       => ( ord_le823954903um_a_b @ R @ S ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_273_subrelI,axiom,
% 2.81/1.57      ! [R: set_Pr409224873um_a_b,S: set_Pr409224873um_a_b] :
% 2.81/1.57        ( ! [X4: standard_Constant_a,Y4: produc1548871597um_a_b] :
% 2.81/1.57            ( ( member1998628618um_a_b @ ( produc1697725733um_a_b @ X4 @ Y4 ) @ R )
% 2.81/1.57           => ( member1998628618um_a_b @ ( produc1697725733um_a_b @ X4 @ Y4 ) @ S ) )
% 2.81/1.57       => ( ord_le615126793um_a_b @ R @ S ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_274_subrelI,axiom,
% 2.81/1.57      ! [R: set_Pr1916610317um_a_b,S: set_Pr1916610317um_a_b] :
% 2.81/1.57        ( ! [X4: sum_sum_a_b,Y4: sum_sum_a_b] :
% 2.81/1.57            ( ( member947389014um_a_b @ ( produc176426981um_a_b @ X4 @ Y4 ) @ R )
% 2.81/1.57           => ( member947389014um_a_b @ ( produc176426981um_a_b @ X4 @ Y4 ) @ S ) )
% 2.81/1.57       => ( ord_le1059794605um_a_b @ R @ S ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_275_restrict__subsD,axiom,
% 2.81/1.57      ! [G: labele935650037_a_nat] :
% 2.81/1.57        ( ( ord_le1909159005at_nat @ ( labele195203296_a_nat @ G ) @ ( labele195203296_a_nat @ ( restri572569417_a_nat @ G ) ) )
% 2.81/1.57       => ( G
% 2.81/1.57          = ( restri572569417_a_nat @ G ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_276_restrict__subsD,axiom,
% 2.81/1.57      ! [G: labele431970251um_a_b] :
% 2.81/1.57        ( ( ord_le615126793um_a_b @ ( labele1939049654um_a_b @ G ) @ ( labele1939049654um_a_b @ ( restri1162247455um_a_b @ G ) ) )
% 2.81/1.57       => ( G
% 2.81/1.57          = ( restri1162247455um_a_b @ G ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_277_zero__reorient,axiom,
% 2.81/1.57      ! [X2: nat] :
% 2.81/1.57        ( ( zero_zero_nat = X2 )
% 2.81/1.57        = ( X2 = zero_zero_nat ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_278_emptyE,axiom,
% 2.81/1.57      ! [A: produc1032616263at_nat] :
% 2.81/1.57        ~ ( member1696759390at_nat @ A @ bot_bo810816657at_nat ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_279_emptyE,axiom,
% 2.81/1.57      ! [A: nat] :
% 2.81/1.57        ~ ( member_nat @ A @ bot_bot_set_nat ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_280_emptyE,axiom,
% 2.81/1.57      ! [A: produc1124793815um_a_b] :
% 2.81/1.57        ~ ( member1294585472um_a_b @ A @ bot_bo575978147um_a_b ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_281_emptyE,axiom,
% 2.81/1.57      ! [A: produc1548871597um_a_b] :
% 2.81/1.57        ~ ( member947389014um_a_b @ A @ bot_bo225809273um_a_b ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_282_emptyE,axiom,
% 2.81/1.57      ! [A: produc1963079155um_a_b] :
% 2.81/1.57        ~ ( member1998628618um_a_b @ A @ bot_bo1262634813um_a_b ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_283_emptyE,axiom,
% 2.81/1.57      ! [A: sum_sum_a_b] :
% 2.81/1.57        ~ ( member_Sum_sum_a_b @ A @ bot_bo1491243248um_a_b ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_284_equals0D,axiom,
% 2.81/1.57      ! [A3: set_Pr1647387645at_nat,A: produc1032616263at_nat] :
% 2.81/1.57        ( ( A3 = bot_bo810816657at_nat )
% 2.81/1.57       => ~ ( member1696759390at_nat @ A @ A3 ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_285_equals0D,axiom,
% 2.81/1.57      ! [A3: set_nat,A: nat] :
% 2.81/1.57        ( ( A3 = bot_bot_set_nat )
% 2.81/1.57       => ~ ( member_nat @ A @ A3 ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_286_equals0D,axiom,
% 2.81/1.57      ! [A3: set_Pr1174980151um_a_b,A: produc1124793815um_a_b] :
% 2.81/1.57        ( ( A3 = bot_bo575978147um_a_b )
% 2.81/1.57       => ~ ( member1294585472um_a_b @ A @ A3 ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_287_equals0D,axiom,
% 2.81/1.57      ! [A3: set_Pr1916610317um_a_b,A: produc1548871597um_a_b] :
% 2.81/1.57        ( ( A3 = bot_bo225809273um_a_b )
% 2.81/1.57       => ~ ( member947389014um_a_b @ A @ A3 ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_288_equals0D,axiom,
% 2.81/1.57      ! [A3: set_Pr409224873um_a_b,A: produc1963079155um_a_b] :
% 2.81/1.57        ( ( A3 = bot_bo1262634813um_a_b )
% 2.81/1.57       => ~ ( member1998628618um_a_b @ A @ A3 ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_289_equals0D,axiom,
% 2.81/1.57      ! [A3: set_Sum_sum_a_b,A: sum_sum_a_b] :
% 2.81/1.57        ( ( A3 = bot_bo1491243248um_a_b )
% 2.81/1.57       => ~ ( member_Sum_sum_a_b @ A @ A3 ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_290_equals0I,axiom,
% 2.81/1.57      ! [A3: set_Pr1647387645at_nat] :
% 2.81/1.57        ( ! [Y4: produc1032616263at_nat] :
% 2.81/1.57            ~ ( member1696759390at_nat @ Y4 @ A3 )
% 2.81/1.57       => ( A3 = bot_bo810816657at_nat ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_291_equals0I,axiom,
% 2.81/1.57      ! [A3: set_nat] :
% 2.81/1.57        ( ! [Y4: nat] :
% 2.81/1.57            ~ ( member_nat @ Y4 @ A3 )
% 2.81/1.57       => ( A3 = bot_bot_set_nat ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_292_equals0I,axiom,
% 2.81/1.57      ! [A3: set_Pr1174980151um_a_b] :
% 2.81/1.57        ( ! [Y4: produc1124793815um_a_b] :
% 2.81/1.57            ~ ( member1294585472um_a_b @ Y4 @ A3 )
% 2.81/1.57       => ( A3 = bot_bo575978147um_a_b ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_293_equals0I,axiom,
% 2.81/1.57      ! [A3: set_Pr1916610317um_a_b] :
% 2.81/1.57        ( ! [Y4: produc1548871597um_a_b] :
% 2.81/1.57            ~ ( member947389014um_a_b @ Y4 @ A3 )
% 2.81/1.57       => ( A3 = bot_bo225809273um_a_b ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_294_equals0I,axiom,
% 2.81/1.57      ! [A3: set_Pr409224873um_a_b] :
% 2.81/1.57        ( ! [Y4: produc1963079155um_a_b] :
% 2.81/1.57            ~ ( member1998628618um_a_b @ Y4 @ A3 )
% 2.81/1.57       => ( A3 = bot_bo1262634813um_a_b ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_295_equals0I,axiom,
% 2.81/1.57      ! [A3: set_Sum_sum_a_b] :
% 2.81/1.57        ( ! [Y4: sum_sum_a_b] :
% 2.81/1.57            ~ ( member_Sum_sum_a_b @ Y4 @ A3 )
% 2.81/1.57       => ( A3 = bot_bo1491243248um_a_b ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_296_ex__in__conv,axiom,
% 2.81/1.57      ! [A3: set_Pr1647387645at_nat] :
% 2.81/1.57        ( ( ? [X3: produc1032616263at_nat] : ( member1696759390at_nat @ X3 @ A3 ) )
% 2.81/1.57        = ( A3 != bot_bo810816657at_nat ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_297_ex__in__conv,axiom,
% 2.81/1.57      ! [A3: set_nat] :
% 2.81/1.57        ( ( ? [X3: nat] : ( member_nat @ X3 @ A3 ) )
% 2.81/1.57        = ( A3 != bot_bot_set_nat ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_298_ex__in__conv,axiom,
% 2.81/1.57      ! [A3: set_Pr1174980151um_a_b] :
% 2.81/1.57        ( ( ? [X3: produc1124793815um_a_b] : ( member1294585472um_a_b @ X3 @ A3 ) )
% 2.81/1.57        = ( A3 != bot_bo575978147um_a_b ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_299_ex__in__conv,axiom,
% 2.81/1.57      ! [A3: set_Pr1916610317um_a_b] :
% 2.81/1.57        ( ( ? [X3: produc1548871597um_a_b] : ( member947389014um_a_b @ X3 @ A3 ) )
% 2.81/1.57        = ( A3 != bot_bo225809273um_a_b ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_300_ex__in__conv,axiom,
% 2.81/1.57      ! [A3: set_Pr409224873um_a_b] :
% 2.81/1.57        ( ( ? [X3: produc1963079155um_a_b] : ( member1998628618um_a_b @ X3 @ A3 ) )
% 2.81/1.57        = ( A3 != bot_bo1262634813um_a_b ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_301_ex__in__conv,axiom,
% 2.81/1.57      ! [A3: set_Sum_sum_a_b] :
% 2.81/1.57        ( ( ? [X3: sum_sum_a_b] : ( member_Sum_sum_a_b @ X3 @ A3 ) )
% 2.81/1.57        = ( A3 != bot_bo1491243248um_a_b ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_302_in__mono,axiom,
% 2.81/1.57      ! [A3: set_Pr1174980151um_a_b,B5: set_Pr1174980151um_a_b,X2: produc1124793815um_a_b] :
% 2.81/1.57        ( ( ord_le823954903um_a_b @ A3 @ B5 )
% 2.81/1.57       => ( ( member1294585472um_a_b @ X2 @ A3 )
% 2.81/1.57         => ( member1294585472um_a_b @ X2 @ B5 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_303_in__mono,axiom,
% 2.81/1.57      ! [A3: set_Pr409224873um_a_b,B5: set_Pr409224873um_a_b,X2: produc1963079155um_a_b] :
% 2.81/1.57        ( ( ord_le615126793um_a_b @ A3 @ B5 )
% 2.81/1.57       => ( ( member1998628618um_a_b @ X2 @ A3 )
% 2.81/1.57         => ( member1998628618um_a_b @ X2 @ B5 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_304_in__mono,axiom,
% 2.81/1.57      ! [A3: set_Sum_sum_a_b,B5: set_Sum_sum_a_b,X2: sum_sum_a_b] :
% 2.81/1.57        ( ( ord_le192794300um_a_b @ A3 @ B5 )
% 2.81/1.57       => ( ( member_Sum_sum_a_b @ X2 @ A3 )
% 2.81/1.57         => ( member_Sum_sum_a_b @ X2 @ B5 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_305_subsetD,axiom,
% 2.81/1.57      ! [A3: set_Pr1174980151um_a_b,B5: set_Pr1174980151um_a_b,C: produc1124793815um_a_b] :
% 2.81/1.57        ( ( ord_le823954903um_a_b @ A3 @ B5 )
% 2.81/1.57       => ( ( member1294585472um_a_b @ C @ A3 )
% 2.81/1.57         => ( member1294585472um_a_b @ C @ B5 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_306_subsetD,axiom,
% 2.81/1.57      ! [A3: set_Pr409224873um_a_b,B5: set_Pr409224873um_a_b,C: produc1963079155um_a_b] :
% 2.81/1.57        ( ( ord_le615126793um_a_b @ A3 @ B5 )
% 2.81/1.57       => ( ( member1998628618um_a_b @ C @ A3 )
% 2.81/1.57         => ( member1998628618um_a_b @ C @ B5 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_307_subsetD,axiom,
% 2.81/1.57      ! [A3: set_Sum_sum_a_b,B5: set_Sum_sum_a_b,C: sum_sum_a_b] :
% 2.81/1.57        ( ( ord_le192794300um_a_b @ A3 @ B5 )
% 2.81/1.57       => ( ( member_Sum_sum_a_b @ C @ A3 )
% 2.81/1.57         => ( member_Sum_sum_a_b @ C @ B5 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_308_equalityE,axiom,
% 2.81/1.57      ! [A3: set_Sum_sum_a_b,B5: set_Sum_sum_a_b] :
% 2.81/1.57        ( ( A3 = B5 )
% 2.81/1.57       => ~ ( ( ord_le192794300um_a_b @ A3 @ B5 )
% 2.81/1.57           => ~ ( ord_le192794300um_a_b @ B5 @ A3 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_309_subset__eq,axiom,
% 2.81/1.57      ( ord_le823954903um_a_b
% 2.81/1.57      = ( ^ [A7: set_Pr1174980151um_a_b,B6: set_Pr1174980151um_a_b] :
% 2.81/1.57          ! [X3: produc1124793815um_a_b] :
% 2.81/1.57            ( ( member1294585472um_a_b @ X3 @ A7 )
% 2.81/1.57           => ( member1294585472um_a_b @ X3 @ B6 ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_310_subset__eq,axiom,
% 2.81/1.57      ( ord_le615126793um_a_b
% 2.81/1.57      = ( ^ [A7: set_Pr409224873um_a_b,B6: set_Pr409224873um_a_b] :
% 2.81/1.57          ! [X3: produc1963079155um_a_b] :
% 2.81/1.57            ( ( member1998628618um_a_b @ X3 @ A7 )
% 2.81/1.57           => ( member1998628618um_a_b @ X3 @ B6 ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_311_subset__eq,axiom,
% 2.81/1.57      ( ord_le192794300um_a_b
% 2.81/1.57      = ( ^ [A7: set_Sum_sum_a_b,B6: set_Sum_sum_a_b] :
% 2.81/1.57          ! [X3: sum_sum_a_b] :
% 2.81/1.57            ( ( member_Sum_sum_a_b @ X3 @ A7 )
% 2.81/1.57           => ( member_Sum_sum_a_b @ X3 @ B6 ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_312_equalityD1,axiom,
% 2.81/1.57      ! [A3: set_Sum_sum_a_b,B5: set_Sum_sum_a_b] :
% 2.81/1.57        ( ( A3 = B5 )
% 2.81/1.57       => ( ord_le192794300um_a_b @ A3 @ B5 ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_313_equalityD2,axiom,
% 2.81/1.57      ! [A3: set_Sum_sum_a_b,B5: set_Sum_sum_a_b] :
% 2.81/1.57        ( ( A3 = B5 )
% 2.81/1.57       => ( ord_le192794300um_a_b @ B5 @ A3 ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_314_subset__iff,axiom,
% 2.81/1.57      ( ord_le823954903um_a_b
% 2.81/1.57      = ( ^ [A7: set_Pr1174980151um_a_b,B6: set_Pr1174980151um_a_b] :
% 2.81/1.57          ! [T: produc1124793815um_a_b] :
% 2.81/1.57            ( ( member1294585472um_a_b @ T @ A7 )
% 2.81/1.57           => ( member1294585472um_a_b @ T @ B6 ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_315_subset__iff,axiom,
% 2.81/1.57      ( ord_le615126793um_a_b
% 2.81/1.57      = ( ^ [A7: set_Pr409224873um_a_b,B6: set_Pr409224873um_a_b] :
% 2.81/1.57          ! [T: produc1963079155um_a_b] :
% 2.81/1.57            ( ( member1998628618um_a_b @ T @ A7 )
% 2.81/1.57           => ( member1998628618um_a_b @ T @ B6 ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_316_subset__iff,axiom,
% 2.81/1.57      ( ord_le192794300um_a_b
% 2.81/1.57      = ( ^ [A7: set_Sum_sum_a_b,B6: set_Sum_sum_a_b] :
% 2.81/1.57          ! [T: sum_sum_a_b] :
% 2.81/1.57            ( ( member_Sum_sum_a_b @ T @ A7 )
% 2.81/1.57           => ( member_Sum_sum_a_b @ T @ B6 ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_317_subset__refl,axiom,
% 2.81/1.57      ! [A3: set_Sum_sum_a_b] : ( ord_le192794300um_a_b @ A3 @ A3 ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_318_Collect__mono,axiom,
% 2.81/1.57      ! [P: sum_sum_a_b > $o,Q: sum_sum_a_b > $o] :
% 2.81/1.57        ( ! [X4: sum_sum_a_b] :
% 2.81/1.57            ( ( P @ X4 )
% 2.81/1.57           => ( Q @ X4 ) )
% 2.81/1.57       => ( ord_le192794300um_a_b @ ( collect_Sum_sum_a_b @ P ) @ ( collect_Sum_sum_a_b @ Q ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_319_subset__trans,axiom,
% 2.81/1.57      ! [A3: set_Sum_sum_a_b,B5: set_Sum_sum_a_b,C2: set_Sum_sum_a_b] :
% 2.81/1.57        ( ( ord_le192794300um_a_b @ A3 @ B5 )
% 2.81/1.57       => ( ( ord_le192794300um_a_b @ B5 @ C2 )
% 2.81/1.57         => ( ord_le192794300um_a_b @ A3 @ C2 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_320_set__eq__subset,axiom,
% 2.81/1.57      ( ( ^ [Y5: set_Sum_sum_a_b,Z: set_Sum_sum_a_b] : ( Y5 = Z ) )
% 2.81/1.57      = ( ^ [A7: set_Sum_sum_a_b,B6: set_Sum_sum_a_b] :
% 2.81/1.57            ( ( ord_le192794300um_a_b @ A7 @ B6 )
% 2.81/1.57            & ( ord_le192794300um_a_b @ B6 @ A7 ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_321_Collect__mono__iff,axiom,
% 2.81/1.57      ! [P: sum_sum_a_b > $o,Q: sum_sum_a_b > $o] :
% 2.81/1.57        ( ( ord_le192794300um_a_b @ ( collect_Sum_sum_a_b @ P ) @ ( collect_Sum_sum_a_b @ Q ) )
% 2.81/1.57        = ( ! [X3: sum_sum_a_b] :
% 2.81/1.57              ( ( P @ X3 )
% 2.81/1.57             => ( Q @ X3 ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_322_insertE,axiom,
% 2.81/1.57      ! [A: produc1032616263at_nat,B: produc1032616263at_nat,A3: set_Pr1647387645at_nat] :
% 2.81/1.57        ( ( member1696759390at_nat @ A @ ( insert1625259895at_nat @ B @ A3 ) )
% 2.81/1.57       => ( ( A != B )
% 2.81/1.57         => ( member1696759390at_nat @ A @ A3 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_323_insertE,axiom,
% 2.81/1.57      ! [A: nat,B: nat,A3: set_nat] :
% 2.81/1.57        ( ( member_nat @ A @ ( insert_nat @ B @ A3 ) )
% 2.81/1.57       => ( ( A != B )
% 2.81/1.57         => ( member_nat @ A @ A3 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_324_insertE,axiom,
% 2.81/1.57      ! [A: produc1548871597um_a_b,B: produc1548871597um_a_b,A3: set_Pr1916610317um_a_b] :
% 2.81/1.57        ( ( member947389014um_a_b @ A @ ( insert1435405693um_a_b @ B @ A3 ) )
% 2.81/1.57       => ( ( A != B )
% 2.81/1.57         => ( member947389014um_a_b @ A @ A3 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_325_insertE,axiom,
% 2.81/1.57      ! [A: standard_Constant_a,B: standard_Constant_a,A3: set_St761939237tant_a] :
% 2.81/1.57        ( ( member1632892294tant_a @ A @ ( insert1909710879tant_a @ B @ A3 ) )
% 2.81/1.57       => ( ( A != B )
% 2.81/1.57         => ( member1632892294tant_a @ A @ A3 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_326_insertE,axiom,
% 2.81/1.57      ! [A: product_prod_nat_nat,B: product_prod_nat_nat,A3: set_Pr1986765409at_nat] :
% 2.81/1.57        ( ( member701585322at_nat @ A @ ( insert271595217at_nat @ B @ A3 ) )
% 2.81/1.57       => ( ( A != B )
% 2.81/1.57         => ( member701585322at_nat @ A @ A3 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_327_insertE,axiom,
% 2.81/1.57      ! [A: sum_sum_a_b,B: sum_sum_a_b,A3: set_Sum_sum_a_b] :
% 2.81/1.57        ( ( member_Sum_sum_a_b @ A @ ( insert_Sum_sum_a_b @ B @ A3 ) )
% 2.81/1.57       => ( ( A != B )
% 2.81/1.57         => ( member_Sum_sum_a_b @ A @ A3 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_328_insertE,axiom,
% 2.81/1.57      ! [A: produc1124793815um_a_b,B: produc1124793815um_a_b,A3: set_Pr1174980151um_a_b] :
% 2.81/1.57        ( ( member1294585472um_a_b @ A @ ( insert983991207um_a_b @ B @ A3 ) )
% 2.81/1.57       => ( ( A != B )
% 2.81/1.57         => ( member1294585472um_a_b @ A @ A3 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_329_insertE,axiom,
% 2.81/1.57      ! [A: produc1963079155um_a_b,B: produc1963079155um_a_b,A3: set_Pr409224873um_a_b] :
% 2.81/1.57        ( ( member1998628618um_a_b @ A @ ( insert323157027um_a_b @ B @ A3 ) )
% 2.81/1.57       => ( ( A != B )
% 2.81/1.57         => ( member1998628618um_a_b @ A @ A3 ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_330_insertI1,axiom,
% 2.81/1.57      ! [A: product_prod_nat_nat,B5: set_Pr1986765409at_nat] : ( member701585322at_nat @ A @ ( insert271595217at_nat @ A @ B5 ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_331_insertI1,axiom,
% 2.81/1.57      ! [A: sum_sum_a_b,B5: set_Sum_sum_a_b] : ( member_Sum_sum_a_b @ A @ ( insert_Sum_sum_a_b @ A @ B5 ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_332_insertI1,axiom,
% 2.81/1.57      ! [A: produc1124793815um_a_b,B5: set_Pr1174980151um_a_b] : ( member1294585472um_a_b @ A @ ( insert983991207um_a_b @ A @ B5 ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_333_insertI1,axiom,
% 2.81/1.57      ! [A: produc1963079155um_a_b,B5: set_Pr409224873um_a_b] : ( member1998628618um_a_b @ A @ ( insert323157027um_a_b @ A @ B5 ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_334_le0,axiom,
% 2.81/1.57      ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_335_bot__nat__0_Oextremum,axiom,
% 2.81/1.57      ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_336_Nat_Oex__has__greatest__nat,axiom,
% 2.81/1.57      ! [P: nat > $o,K: nat,B: nat] :
% 2.81/1.57        ( ( P @ K )
% 2.81/1.57       => ( ! [Y4: nat] :
% 2.81/1.57              ( ( P @ Y4 )
% 2.81/1.57             => ( ord_less_eq_nat @ Y4 @ B ) )
% 2.81/1.57         => ? [X4: nat] :
% 2.81/1.57              ( ( P @ X4 )
% 2.81/1.57              & ! [Y6: nat] :
% 2.81/1.57                  ( ( P @ Y6 )
% 2.81/1.57                 => ( ord_less_eq_nat @ Y6 @ X4 ) ) ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_337_nat__le__linear,axiom,
% 2.81/1.57      ! [M: nat,N: nat] :
% 2.81/1.57        ( ( ord_less_eq_nat @ M @ N )
% 2.81/1.57        | ( ord_less_eq_nat @ N @ M ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_338_le__antisym,axiom,
% 2.81/1.57      ! [M: nat,N: nat] :
% 2.81/1.57        ( ( ord_less_eq_nat @ M @ N )
% 2.81/1.57       => ( ( ord_less_eq_nat @ N @ M )
% 2.81/1.57         => ( M = N ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_339_eq__imp__le,axiom,
% 2.81/1.57      ! [M: nat,N: nat] :
% 2.81/1.57        ( ( M = N )
% 2.81/1.57       => ( ord_less_eq_nat @ M @ N ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_340_le__trans,axiom,
% 2.81/1.57      ! [I: nat,J: nat,K: nat] :
% 2.81/1.57        ( ( ord_less_eq_nat @ I @ J )
% 2.81/1.57       => ( ( ord_less_eq_nat @ J @ K )
% 2.81/1.57         => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_341_le__refl,axiom,
% 2.81/1.57      ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_342_bot__nat__def,axiom,
% 2.81/1.57      bot_bot_nat = zero_zero_nat ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_343_bot__nat__0_Oextremum__uniqueI,axiom,
% 2.81/1.57      ! [A: nat] :
% 2.81/1.57        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 2.81/1.57       => ( A = zero_zero_nat ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_344_bot__nat__0_Oextremum__unique,axiom,
% 2.81/1.57      ! [A: nat] :
% 2.81/1.57        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 2.81/1.57        = ( A = zero_zero_nat ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_345_le__0__eq,axiom,
% 2.81/1.57      ! [N: nat] :
% 2.81/1.57        ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 2.81/1.57        = ( N = zero_zero_nat ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_346_less__eq__nat_Osimps_I1_J,axiom,
% 2.81/1.57      ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_347_gr_I1_J,axiom,
% 2.81/1.57      ( ( getRel1465196352um_a_b @ standard_S_Idt_a @ g )
% 2.81/1.57      = ( id_on_Sum_sum_a_b @ ( labele577278695um_a_b @ g ) ) ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_348_gr_I2_J,axiom,
% 2.81/1.57      ( ( getRel1465196352um_a_b @ standard_S_Bot_a @ g )
% 2.81/1.57      = bot_bo225809273um_a_b ) ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_349__092_060open_062maintained_A_Isymmetry__rule_AS__Idt_J_AG_092_060close_062,axiom,
% 2.81/1.57      mainta522127984um_a_b @ ( standa997693288tant_a @ standard_S_Idt_a ) @ g ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_350__092_060open_062maintained_A_Itransitive__rule_AS__Idt_J_AG_092_060close_062,axiom,
% 2.81/1.57      mainta522127984um_a_b @ ( standa1795879409tant_a @ standard_S_Idt_a ) @ g ).
% 2.81/1.57  
% 2.81/1.57  thf(fact_351__092_060open_062maintained_A_Icongruence__rule_AS__Idt_Al_J_AG_092_060close_062,axiom,
% 2.81/1.57      mainta522127984um_a_b @ ( standa1343274079tant_a @ standard_S_Idt_a @ l ) @ g ).
% 2.81/1.57  
% 2.81/1.57  thf(conj_0,conjecture,
% 2.81/1.57      ( ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 2.81/1.57        = ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ) )
% 2.81/1.57      & ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) )
% 2.81/1.57        = ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) )
% 2.81/1.57      & ( g
% 2.81/1.57        = ( restri1162247455um_a_b @ g ) )
% 2.81/1.57      & ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) @ ( labele577278695um_a_b @ g ) )
% 2.81/1.57      & ( unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) )
% 2.81/1.57      & ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) @ ( labele1939049654um_a_b @ g ) ) ) ).
% 2.81/1.57  ------------------------
% 2.94/1.61  % (20542)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_20438 for (2999ds/2Mi)
% 2.94/1.61  % (20539)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_20438 for (2999ds/4Mi)
% 2.94/1.61  % (20538)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20438 for (2999ds/183Mi)
% 2.94/1.61  % (20542)Instruction limit reached!
% 2.94/1.61  % (20542)------------------------------
% 2.94/1.61  % (20542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.61  % (20542)Termination reason: Unknown
% 2.94/1.61  % (20542)Termination phase: shuffling
% 2.94/1.61  
% 2.94/1.61  % (20542)Memory used [KB]: 1535
% 2.94/1.61  % (20542)Time elapsed: 0.002 s
% 2.94/1.61  % (20542)Instructions burned: 2 (million)
% 2.94/1.61  % (20542)------------------------------
% 2.94/1.61  % (20542)------------------------------
% 2.94/1.61  % (20539)Instruction limit reached!
% 2.94/1.61  % (20539)------------------------------
% 2.94/1.61  % (20539)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.61  % (20539)Termination reason: Unknown
% 2.94/1.61  % (20539)Termination phase: shuffling
% 2.94/1.61  
% 2.94/1.61  % (20539)Memory used [KB]: 1535
% 2.94/1.61  % (20539)Time elapsed: 0.003 s
% 2.94/1.61  % (20539)Instructions burned: 4 (million)
% 2.94/1.61  % (20539)------------------------------
% 2.94/1.61  % (20539)------------------------------
% 2.94/1.62  % (20541)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20438 for (2999ds/2Mi)
% 2.94/1.62  % (20540)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_20438 for (2999ds/27Mi)
% 2.94/1.62  % (20543)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_20438 for (2999ds/275Mi)
% 2.94/1.62  % (20544)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20438 for (2999ds/18Mi)
% 2.94/1.62  % (20541)Instruction limit reached!
% 2.94/1.62  % (20541)------------------------------
% 2.94/1.62  % (20541)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.62  % (20541)Termination reason: Unknown
% 2.94/1.62  % (20541)Termination phase: shuffling
% 2.94/1.62  
% 2.94/1.62  % (20541)Memory used [KB]: 1535
% 2.94/1.62  % (20541)Time elapsed: 0.004 s
% 2.94/1.62  % (20541)Instructions burned: 3 (million)
% 2.94/1.62  % (20541)------------------------------
% 2.94/1.62  % (20541)------------------------------
% 2.94/1.62  % (20545)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_20438 for (2999ds/3Mi)
% 2.94/1.62  % (20546)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_20438 for (2999ds/37Mi)
% 2.94/1.62  % (20545)Instruction limit reached!
% 2.94/1.62  % (20545)------------------------------
% 2.94/1.62  % (20545)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.62  % (20545)Termination reason: Unknown
% 2.94/1.62  % (20545)Termination phase: shuffling
% 2.94/1.62  
% 2.94/1.62  % (20545)Memory used [KB]: 1535
% 2.94/1.62  % (20545)Time elapsed: 0.002 s
% 2.94/1.62  % (20545)Instructions burned: 3 (million)
% 2.94/1.62  % (20545)------------------------------
% 2.94/1.62  % (20545)------------------------------
% 2.94/1.63  % (20544)Instruction limit reached!
% 2.94/1.63  % (20544)------------------------------
% 2.94/1.63  % (20544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.63  % (20544)Termination reason: Unknown
% 2.94/1.63  % (20544)Termination phase: shuffling
% 2.94/1.63  
% 2.94/1.63  % (20544)Memory used [KB]: 1918
% 2.94/1.63  % (20544)Time elapsed: 0.014 s
% 2.94/1.63  % (20544)Instructions burned: 19 (million)
% 2.94/1.63  % (20544)------------------------------
% 2.94/1.63  % (20544)------------------------------
% 2.94/1.63  % (20548)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_20438 for (2999ds/3Mi)
% 2.94/1.63  % (20546)Instruction limit reached!
% 2.94/1.63  % (20546)------------------------------
% 2.94/1.63  % (20546)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.63  % (20546)Termination reason: Unknown
% 2.94/1.63  % (20546)Termination phase: shuffling
% 2.94/1.63  
% 2.94/1.63  % (20546)Memory used [KB]: 2302
% 2.94/1.63  % (20546)Time elapsed: 0.011 s
% 2.94/1.63  % (20546)Instructions burned: 37 (million)
% 2.94/1.63  % (20546)------------------------------
% 2.94/1.63  % (20546)------------------------------
% 2.94/1.63  % (20548)Instruction limit reached!
% 2.94/1.63  % (20548)------------------------------
% 2.94/1.63  % (20548)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.63  % (20548)Termination reason: Unknown
% 2.94/1.63  % (20548)Termination phase: shuffling
% 2.94/1.63  
% 2.94/1.63  % (20548)Memory used [KB]: 1535
% 2.94/1.63  % (20548)Time elapsed: 0.002 s
% 2.94/1.63  % (20548)Instructions burned: 3 (million)
% 2.94/1.63  % (20548)------------------------------
% 2.94/1.63  % (20548)------------------------------
% 2.94/1.63  % (20540)Instruction limit reached!
% 2.94/1.63  % (20540)------------------------------
% 2.94/1.63  % (20540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.63  % (20540)Termination reason: Unknown
% 2.94/1.63  % (20540)Termination phase: Property scanning
% 2.94/1.63  
% 2.94/1.63  % (20540)Memory used [KB]: 1918
% 2.94/1.63  % (20540)Time elapsed: 0.018 s
% 2.94/1.63  % (20540)Instructions burned: 27 (million)
% 2.94/1.63  % (20540)------------------------------
% 2.94/1.63  % (20540)------------------------------
% 2.94/1.64  % (20547)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_20438 for (2999ds/15Mi)
% 2.94/1.64  % (20550)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_20438 for (2999ds/7Mi)
% 2.94/1.64  % (20551)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_20438 for (2999ds/16Mi)
% 2.94/1.64  % (20550)Instruction limit reached!
% 2.94/1.64  % (20550)------------------------------
% 2.94/1.64  % (20550)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.64  % (20550)Termination reason: Unknown
% 2.94/1.64  % (20550)Termination phase: shuffling
% 2.94/1.64  
% 2.94/1.64  % (20550)Memory used [KB]: 1663
% 2.94/1.64  % (20550)Time elapsed: 0.004 s
% 2.94/1.64  % (20550)Instructions burned: 9 (million)
% 2.94/1.64  % (20550)------------------------------
% 2.94/1.64  % (20550)------------------------------
% 2.94/1.64  % (20549)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_20438 for (2999ds/1041Mi)
% 2.94/1.64  % (20551)Instruction limit reached!
% 2.94/1.64  % (20551)------------------------------
% 2.94/1.64  % (20551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.64  % (20551)Termination reason: Unknown
% 2.94/1.64  % (20551)Termination phase: shuffling
% 2.94/1.64  
% 2.94/1.64  % (20551)Memory used [KB]: 1791
% 2.94/1.64  % (20551)Time elapsed: 0.006 s
% 2.94/1.64  % (20551)Instructions burned: 16 (million)
% 2.94/1.64  % (20551)------------------------------
% 2.94/1.64  % (20551)------------------------------
% 2.94/1.64  % (20547)Instruction limit reached!
% 2.94/1.64  % (20547)------------------------------
% 2.94/1.64  % (20547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.64  % (20547)Termination reason: Unknown
% 2.94/1.64  % (20547)Termination phase: shuffling
% 2.94/1.64  
% 2.94/1.64  % (20547)Memory used [KB]: 1918
% 2.94/1.64  % (20547)Time elapsed: 0.011 s
% 2.94/1.64  % (20547)Instructions burned: 17 (million)
% 2.94/1.64  % (20547)------------------------------
% 2.94/1.64  % (20547)------------------------------
% 2.94/1.64  % (20552)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_20438 for (2999ds/3Mi)
% 2.94/1.65  % (20552)Instruction limit reached!
% 2.94/1.65  % (20552)------------------------------
% 2.94/1.65  % (20552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.65  % (20552)Termination reason: Unknown
% 2.94/1.65  % (20552)Termination phase: shuffling
% 2.94/1.65  
% 2.94/1.65  % (20552)Memory used [KB]: 1535
% 2.94/1.65  % (20552)Time elapsed: 0.003 s
% 2.94/1.65  % (20552)Instructions burned: 4 (million)
% 2.94/1.65  % (20552)------------------------------
% 2.94/1.65  % (20552)------------------------------
% 2.94/1.65  % (20553)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_20438 for (2999ds/3Mi)
% 2.94/1.65  % (20553)Instruction limit reached!
% 2.94/1.65  % (20553)------------------------------
% 2.94/1.65  % (20553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.65  % (20553)Termination reason: Unknown
% 2.94/1.65  % (20553)Termination phase: shuffling
% 2.94/1.65  
% 2.94/1.65  % (20553)Memory used [KB]: 1535
% 2.94/1.65  % (20553)Time elapsed: 0.002 s
% 2.94/1.65  % (20553)Instructions burned: 3 (million)
% 2.94/1.65  % (20553)------------------------------
% 2.94/1.65  % (20553)------------------------------
% 2.94/1.65  % (20554)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_20438 for (2999ds/7Mi)
% 2.94/1.66  % (20557)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_20438 for (2999ds/4Mi)
% 2.94/1.66  % (20555)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_20438 for (2999ds/3Mi)
% 2.94/1.66  % (20554)Instruction limit reached!
% 2.94/1.66  % (20554)------------------------------
% 2.94/1.66  % (20554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.66  % (20554)Termination reason: Unknown
% 2.94/1.66  % (20554)Termination phase: shuffling
% 2.94/1.66  
% 2.94/1.66  % (20554)Memory used [KB]: 1663
% 2.94/1.66  % (20554)Time elapsed: 0.004 s
% 2.94/1.66  % (20554)Instructions burned: 10 (million)
% 2.94/1.66  % (20554)------------------------------
% 2.94/1.66  % (20554)------------------------------
% 2.94/1.66  % (20555)Instruction limit reached!
% 2.94/1.66  % (20555)------------------------------
% 2.94/1.66  % (20555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.66  % (20555)Termination reason: Unknown
% 2.94/1.66  % (20555)Termination phase: shuffling
% 2.94/1.66  
% 2.94/1.66  % (20555)Memory used [KB]: 1535
% 2.94/1.66  % (20555)Time elapsed: 0.003 s
% 2.94/1.66  % (20555)Instructions burned: 4 (million)
% 2.94/1.66  % (20555)------------------------------
% 2.94/1.66  % (20555)------------------------------
% 2.94/1.66  % (20557)Instruction limit reached!
% 2.94/1.66  % (20557)------------------------------
% 2.94/1.66  % (20557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.66  % (20557)Termination reason: Unknown
% 2.94/1.66  % (20557)Termination phase: shuffling
% 2.94/1.66  
% 2.94/1.66  % (20557)Memory used [KB]: 1535
% 2.94/1.66  % (20557)Time elapsed: 0.003 s
% 2.94/1.66  % (20557)Instructions burned: 6 (million)
% 2.94/1.66  % (20557)------------------------------
% 2.94/1.66  % (20557)------------------------------
% 2.94/1.66  % (20558)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_20438 for (2999ds/18Mi)
% 2.94/1.66  % (20543)Refutation not found, incomplete strategy
% 2.94/1.66  % (20543)------------------------------
% 2.94/1.66  % (20543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.66  % (20543)Termination reason: Refutation not found, incomplete strategy
% 2.94/1.66  
% 2.94/1.66  
% 2.94/1.66  % (20543)Memory used [KB]: 7036
% 2.94/1.66  % (20543)Time elapsed: 0.050 s
% 2.94/1.66  % (20543)Instructions burned: 81 (million)
% 2.94/1.66  % (20543)------------------------------
% 2.94/1.66  % (20543)------------------------------
% 2.94/1.67  % (20559)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_20438 for (2999ds/710Mi)
% 2.94/1.67  % (20538)Instruction limit reached!
% 2.94/1.67  % (20538)------------------------------
% 2.94/1.67  % (20538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.67  % (20538)Termination reason: Unknown
% 2.94/1.67  % (20538)Termination phase: Saturation
% 2.94/1.67  
% 2.94/1.67  % (20538)Memory used [KB]: 7419
% 2.94/1.67  % (20538)Time elapsed: 0.059 s
% 2.94/1.67  % (20538)Instructions burned: 183 (million)
% 2.94/1.67  % (20538)------------------------------
% 2.94/1.67  % (20538)------------------------------
% 2.94/1.67  % (20558)Instruction limit reached!
% 2.94/1.67  % (20558)------------------------------
% 2.94/1.67  % (20558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.67  % (20558)Termination reason: Unknown
% 2.94/1.67  % (20561)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_20438 for (2999ds/902Mi)
% 2.94/1.67  % (20558)Termination phase: shuffling
% 2.94/1.67  
% 2.94/1.67  % (20558)Memory used [KB]: 1918
% 2.94/1.67  % (20558)Time elapsed: 0.007 s
% 2.94/1.67  % (20558)Instructions burned: 19 (million)
% 2.94/1.67  % (20558)------------------------------
% 2.94/1.67  % (20558)------------------------------
% 2.94/1.67  % (20560)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_20438 for (2999ds/6Mi)
% 2.94/1.67  % (20560)Instruction limit reached!
% 2.94/1.67  % (20560)------------------------------
% 2.94/1.67  % (20560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.67  % (20560)Termination reason: Unknown
% 2.94/1.67  % (20560)Termination phase: shuffling
% 2.94/1.67  
% 2.94/1.67  % (20560)Memory used [KB]: 1535
% 2.94/1.67  % (20560)Time elapsed: 0.004 s
% 2.94/1.67  % (20560)Instructions burned: 6 (million)
% 2.94/1.67  % (20560)------------------------------
% 2.94/1.67  % (20560)------------------------------
% 2.94/1.68  % (20564)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_20438 for (2999ds/6Mi)
% 2.94/1.68  % (20563)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_20438 for (2999ds/5Mi)
% 2.94/1.68  % (20564)Instruction limit reached!
% 2.94/1.68  % (20564)------------------------------
% 2.94/1.68  % (20564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.68  % (20564)Termination reason: Unknown
% 2.94/1.68  % (20564)Termination phase: shuffling
% 2.94/1.68  
% 2.94/1.68  % (20564)Memory used [KB]: 1663
% 2.94/1.68  % (20564)Time elapsed: 0.003 s
% 2.94/1.68  % (20564)Instructions burned: 7 (million)
% 2.94/1.68  % (20564)------------------------------
% 2.94/1.68  % (20564)------------------------------
% 2.94/1.68  % (20563)Instruction limit reached!
% 2.94/1.68  % (20563)------------------------------
% 2.94/1.68  % (20563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.68  % (20563)Termination reason: Unknown
% 2.94/1.68  % (20563)Termination phase: shuffling
% 2.94/1.68  
% 2.94/1.68  % (20563)Memory used [KB]: 1663
% 2.94/1.68  % (20563)Time elapsed: 0.004 s
% 2.94/1.68  % (20563)Instructions burned: 7 (million)
% 2.94/1.68  % (20563)------------------------------
% 2.94/1.68  % (20563)------------------------------
% 2.94/1.68  % (20565)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_20438 for (2999ds/377Mi)
% 2.94/1.68  % (20562)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_20438 for (2999ds/21Mi)
% 2.94/1.69  % (20566)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_20438 for (2998ds/779Mi)
% 2.94/1.69  % (20567)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_20438 for (2998ds/19Mi)
% 2.94/1.70  % (20567)Instruction limit reached!
% 2.94/1.70  % (20567)------------------------------
% 2.94/1.70  % (20567)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.70  % (20567)Termination reason: Unknown
% 2.94/1.70  % (20567)Termination phase: shuffling
% 2.94/1.70  
% 2.94/1.70  % (20567)Memory used [KB]: 2046
% 2.94/1.70  % (20567)Time elapsed: 0.007 s
% 2.94/1.70  % (20567)Instructions burned: 20 (million)
% 2.94/1.70  % (20567)------------------------------
% 2.94/1.70  % (20567)------------------------------
% 2.94/1.70  % (20562)Instruction limit reached!
% 2.94/1.70  % (20562)------------------------------
% 2.94/1.70  % (20562)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.70  % (20562)Termination reason: Unknown
% 2.94/1.70  % (20562)Termination phase: shuffling
% 2.94/1.70  
% 2.94/1.70  % (20562)Memory used [KB]: 1918
% 2.94/1.70  % (20562)Time elapsed: 0.015 s
% 2.94/1.70  % (20562)Instructions burned: 21 (million)
% 2.94/1.70  % (20562)------------------------------
% 2.94/1.70  % (20562)------------------------------
% 2.94/1.71  % (20568)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_20438 for (2998ds/879Mi)
% 2.94/1.71  % (20569)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_20438 for (2998ds/17Mi)
% 2.94/1.72  % (20569)Instruction limit reached!
% 2.94/1.72  % (20569)------------------------------
% 2.94/1.72  % (20569)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.72  % (20569)Termination reason: Unknown
% 2.94/1.72  % (20569)Termination phase: shuffling
% 2.94/1.72  
% 2.94/1.72  % (20569)Memory used [KB]: 1791
% 2.94/1.72  % (20569)Time elapsed: 0.007 s
% 2.94/1.72  % (20569)Instructions burned: 17 (million)
% 2.94/1.72  % (20569)------------------------------
% 2.94/1.72  % (20569)------------------------------
% 2.94/1.73  % (20570)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_20438 for (2998ds/3Mi)
% 2.94/1.73  % (20570)Instruction limit reached!
% 2.94/1.73  % (20570)------------------------------
% 2.94/1.73  % (20570)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.73  % (20570)Termination reason: Unknown
% 2.94/1.73  % (20570)Termination phase: shuffling
% 2.94/1.73  
% 2.94/1.73  % (20570)Memory used [KB]: 1535
% 2.94/1.73  % (20570)Time elapsed: 0.003 s
% 2.94/1.73  % (20570)Instructions burned: 3 (million)
% 2.94/1.73  % (20570)------------------------------
% 2.94/1.73  % (20570)------------------------------
% 2.94/1.74  % (20571)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_20438 for (2998ds/30Mi)
% 2.94/1.75  % (20571)Instruction limit reached!
% 2.94/1.75  % (20571)------------------------------
% 2.94/1.75  % (20571)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.75  % (20571)Termination reason: Unknown
% 2.94/1.75  % (20571)Termination phase: Property scanning
% 2.94/1.75  
% 2.94/1.75  % (20571)Memory used [KB]: 1918
% 2.94/1.75  % (20571)Time elapsed: 0.012 s
% 2.94/1.75  % (20571)Instructions burned: 33 (million)
% 2.94/1.75  % (20571)------------------------------
% 2.94/1.75  % (20571)------------------------------
% 2.94/1.76  % (20572)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_20438 for (2998ds/127Mi)
% 2.94/1.80  % (20572)Instruction limit reached!
% 2.94/1.80  % (20572)------------------------------
% 2.94/1.80  % (20572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.80  % (20572)Termination reason: Unknown
% 2.94/1.80  % (20572)Termination phase: Saturation
% 2.94/1.80  
% 2.94/1.80  % (20572)Memory used [KB]: 7164
% 2.94/1.80  % (20572)Time elapsed: 0.041 s
% 2.94/1.80  % (20572)Instructions burned: 127 (million)
% 2.94/1.80  % (20572)------------------------------
% 2.94/1.80  % (20572)------------------------------
% 2.94/1.81  % (20565)Instruction limit reached!
% 2.94/1.81  % (20565)------------------------------
% 2.94/1.81  % (20565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.81  % (20565)Termination reason: Unknown
% 2.94/1.81  % (20565)Termination phase: Saturation
% 2.94/1.81  
% 2.94/1.81  % (20565)Memory used [KB]: 8699
% 2.94/1.81  % (20565)Time elapsed: 0.128 s
% 2.94/1.81  % (20565)Instructions burned: 378 (million)
% 2.94/1.81  % (20565)------------------------------
% 2.94/1.81  % (20565)------------------------------
% 2.94/1.81  % (20573)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_20438 for (2997ds/100Mi)
% 2.94/1.82  % (20574)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_20438 for (2997ds/3Mi)
% 2.94/1.82  % (20574)Instruction limit reached!
% 2.94/1.82  % (20574)------------------------------
% 2.94/1.82  % (20574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.82  % (20574)Termination reason: Unknown
% 2.94/1.82  % (20574)Termination phase: shuffling
% 2.94/1.82  
% 2.94/1.82  % (20574)Memory used [KB]: 1535
% 2.94/1.82  % (20574)Time elapsed: 0.002 s
% 2.94/1.82  % (20574)Instructions burned: 3 (million)
% 2.94/1.82  % (20574)------------------------------
% 2.94/1.82  % (20574)------------------------------
% 2.94/1.83  % (20575)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_20438 for (2997ds/20Mi)
% 2.94/1.84  % (20575)Instruction limit reached!
% 2.94/1.84  % (20575)------------------------------
% 2.94/1.84  % (20575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.84  % (20575)Termination reason: Unknown
% 2.94/1.84  % (20575)Termination phase: Property scanning
% 2.94/1.84  
% 2.94/1.84  % (20575)Memory used [KB]: 1918
% 2.94/1.84  % (20575)Time elapsed: 0.009 s
% 2.94/1.84  % (20575)Instructions burned: 22 (million)
% 2.94/1.84  % (20575)------------------------------
% 2.94/1.84  % (20575)------------------------------
% 2.94/1.84  % (20573)Instruction limit reached!
% 2.94/1.84  % (20573)------------------------------
% 2.94/1.84  % (20573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.84  % (20573)Termination reason: Unknown
% 2.94/1.84  % (20573)Termination phase: Function definition elimination
% 2.94/1.84  
% 2.94/1.84  % (20573)Memory used [KB]: 2558
% 2.94/1.84  % (20573)Time elapsed: 0.030 s
% 2.94/1.84  % (20573)Instructions burned: 102 (million)
% 2.94/1.84  % (20573)------------------------------
% 2.94/1.84  % (20573)------------------------------
% 2.94/1.85  % (20576)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_20438 for (2997ds/86Mi)
% 2.94/1.85  % (20577)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_20438 for (2997ds/107Mi)
% 2.94/1.87  % (20576)Instruction limit reached!
% 2.94/1.87  % (20576)------------------------------
% 2.94/1.87  % (20576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.87  % (20576)Termination reason: Unknown
% 2.94/1.87  % (20576)Termination phase: Saturation
% 2.94/1.87  
% 2.94/1.87  % (20576)Memory used [KB]: 2302
% 2.94/1.87  % (20576)Time elapsed: 0.027 s
% 2.94/1.87  % (20576)Instructions burned: 87 (million)
% 2.94/1.87  % (20576)------------------------------
% 2.94/1.87  % (20576)------------------------------
% 2.94/1.88  % (20578)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_20438 for (2997ds/39Mi)
% 2.94/1.88  % (20577)Instruction limit reached!
% 2.94/1.88  % (20577)------------------------------
% 2.94/1.88  % (20577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.88  % (20577)Termination reason: Unknown
% 2.94/1.88  % (20577)Termination phase: Saturation
% 2.94/1.88  
% 2.94/1.88  % (20577)Memory used [KB]: 7036
% 2.94/1.88  % (20577)Time elapsed: 0.034 s
% 2.94/1.88  % (20577)Instructions burned: 107 (million)
% 2.94/1.88  % (20577)------------------------------
% 2.94/1.88  % (20577)------------------------------
% 2.94/1.89  % (20559)Instruction limit reached!
% 2.94/1.89  % (20559)------------------------------
% 2.94/1.89  % (20559)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.89  % (20559)Termination reason: Unknown
% 2.94/1.89  % (20559)Termination phase: Saturation
% 2.94/1.89  
% 2.94/1.89  % (20559)Memory used [KB]: 7931
% 2.94/1.89  % (20559)Time elapsed: 0.221 s
% 2.94/1.89  % (20559)Instructions burned: 711 (million)
% 2.94/1.89  % (20559)------------------------------
% 2.94/1.89  % (20559)------------------------------
% 2.94/1.89  % (20579)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_20438 for (2996ds/448Mi)
% 2.94/1.89  % (20578)Instruction limit reached!
% 2.94/1.89  % (20578)------------------------------
% 2.94/1.89  % (20578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.90  % (20578)Termination reason: Unknown
% 2.94/1.90  % (20578)Termination phase: shuffling
% 2.94/1.90  
% 2.94/1.90  % (20578)Memory used [KB]: 2302
% 2.94/1.90  % (20578)Time elapsed: 0.013 s
% 2.94/1.90  % (20578)Instructions burned: 40 (million)
% 2.94/1.90  % (20578)------------------------------
% 2.94/1.90  % (20578)------------------------------
% 2.94/1.90  % (20580)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_20438 for (2996ds/46Mi)
% 2.94/1.91  % (20581)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_20438 for (2996ds/98Mi)
% 2.94/1.91  % (20580)Instruction limit reached!
% 2.94/1.91  % (20580)------------------------------
% 2.94/1.91  % (20580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.91  % (20580)Termination reason: Unknown
% 2.94/1.91  % (20580)Termination phase: Preprocessing 1
% 2.94/1.91  
% 2.94/1.91  % (20580)Memory used [KB]: 1918
% 2.94/1.91  % (20580)Time elapsed: 0.015 s
% 2.94/1.91  % (20580)Instructions burned: 48 (million)
% 2.94/1.91  % (20580)------------------------------
% 2.94/1.91  % (20580)------------------------------
% 2.94/1.92  % (20566)Instruction limit reached!
% 2.94/1.92  % (20566)------------------------------
% 2.94/1.92  % (20566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.92  % (20566)Termination reason: Unknown
% 2.94/1.92  % (20566)Termination phase: Saturation
% 2.94/1.92  
% 2.94/1.92  % (20566)Memory used [KB]: 9850
% 2.94/1.92  % (20566)Time elapsed: 0.230 s
% 2.94/1.92  % (20566)Instructions burned: 780 (million)
% 2.94/1.92  % (20566)------------------------------
% 2.94/1.92  % (20566)------------------------------
% 2.94/1.92  % (20582)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_20438 for (2996ds/507Mi)
% 2.94/1.93  % (20583)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_20438 for (2996ds/149Mi)
% 2.94/1.93  % (20561)Instruction limit reached!
% 2.94/1.93  % (20561)------------------------------
% 2.94/1.93  % (20561)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.93  % (20561)Termination reason: Unknown
% 2.94/1.93  % (20561)Termination phase: Saturation
% 2.94/1.93  
% 2.94/1.93  % (20561)Memory used [KB]: 8315
% 2.94/1.93  % (20561)Time elapsed: 0.264 s
% 2.94/1.93  % (20561)Instructions burned: 903 (million)
% 2.94/1.93  % (20561)------------------------------
% 2.94/1.93  % (20561)------------------------------
% 2.94/1.93  % (20581)Instruction limit reached!
% 2.94/1.93  % (20581)------------------------------
% 2.94/1.93  % (20581)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.93  % (20581)Termination reason: Unknown
% 2.94/1.93  % (20581)Termination phase: Property scanning
% 2.94/1.93  
% 2.94/1.93  % (20581)Memory used [KB]: 2558
% 2.94/1.93  % (20581)Time elapsed: 0.029 s
% 2.94/1.93  % (20581)Instructions burned: 100 (million)
% 2.94/1.93  % (20581)------------------------------
% 2.94/1.93  % (20581)------------------------------
% 2.94/1.94  % (20584)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_20438 for (2996ds/39Mi)
% 2.94/1.94  % (20585)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_20438 for (2996ds/6Mi)
% 2.94/1.95  % (20585)Instruction limit reached!
% 2.94/1.95  % (20585)------------------------------
% 2.94/1.95  % (20585)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.95  % (20585)Termination reason: Unknown
% 2.94/1.95  % (20585)Termination phase: shuffling
% 2.94/1.95  
% 2.94/1.95  % (20585)Memory used [KB]: 1663
% 2.94/1.95  % (20585)Time elapsed: 0.003 s
% 2.94/1.95  % (20585)Instructions burned: 6 (million)
% 2.94/1.95  % (20585)------------------------------
% 2.94/1.95  % (20585)------------------------------
% 2.94/1.95  % (20584)Instruction limit reached!
% 2.94/1.95  % (20584)------------------------------
% 2.94/1.95  % (20584)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.95  % (20584)Termination reason: Unknown
% 2.94/1.95  % (20584)Termination phase: Unused predicate definition removal
% 2.94/1.95  
% 2.94/1.95  % (20584)Memory used [KB]: 2046
% 2.94/1.95  % (20584)Time elapsed: 0.013 s
% 2.94/1.95  % (20584)Instructions burned: 41 (million)
% 2.94/1.95  % (20584)------------------------------
% 2.94/1.95  % (20584)------------------------------
% 2.94/1.96  % (20586)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_20438 for (2996ds/1087Mi)
% 2.94/1.96  % (20582)Refutation not found, incomplete strategy
% 2.94/1.96  % (20582)------------------------------
% 2.94/1.96  % (20582)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.96  % (20582)Termination reason: Refutation not found, incomplete strategy
% 2.94/1.96  
% 2.94/1.96  
% 2.94/1.96  % (20582)Memory used [KB]: 7675
% 2.94/1.96  % (20582)Time elapsed: 0.038 s
% 2.94/1.96  % (20582)Instructions burned: 126 (million)
% 2.94/1.96  % (20582)------------------------------
% 2.94/1.96  % (20582)------------------------------
% 2.94/1.96  % (20587)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_20438 for (2996ds/47Mi)
% 2.94/1.97  % (20588)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_20438 for (2996ds/44Mi)
% 2.94/1.97  % (20583)Instruction limit reached!
% 2.94/1.97  % (20583)------------------------------
% 2.94/1.97  % (20583)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.97  % (20583)Termination reason: Unknown
% 2.94/1.97  % (20583)Termination phase: Saturation
% 2.94/1.97  
% 2.94/1.97  % (20583)Memory used [KB]: 7419
% 2.94/1.97  % (20583)Time elapsed: 0.045 s
% 2.94/1.97  % (20583)Instructions burned: 151 (million)
% 2.94/1.97  % (20583)------------------------------
% 2.94/1.97  % (20583)------------------------------
% 2.94/1.98  % (20587)Instruction limit reached!
% 2.94/1.98  % (20587)------------------------------
% 2.94/1.98  % (20587)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.98  % (20587)Termination reason: Unknown
% 2.94/1.98  % (20587)Termination phase: Preprocessing 3
% 2.94/1.98  
% 2.94/1.98  % (20587)Memory used [KB]: 2174
% 2.94/1.98  % (20587)Time elapsed: 0.015 s
% 2.94/1.98  % (20587)Instructions burned: 48 (million)
% 2.94/1.98  % (20587)------------------------------
% 2.94/1.98  % (20587)------------------------------
% 2.94/1.98  % (20588)Instruction limit reached!
% 2.94/1.98  % (20588)------------------------------
% 2.94/1.98  % (20588)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/1.98  % (20588)Termination reason: Unknown
% 2.94/1.98  % (20588)Termination phase: shuffling
% 2.94/1.98  
% 2.94/1.98  % (20588)Memory used [KB]: 2430
% 2.94/1.98  % (20588)Time elapsed: 0.013 s
% 2.94/1.98  % (20588)Instructions burned: 44 (million)
% 2.94/1.98  % (20588)------------------------------
% 2.94/1.98  % (20588)------------------------------
% 2.94/1.98  % (20589)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_20438 for (2996ds/432Mi)
% 2.94/1.98  % (20590)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_20438 for (2996ds/62Mi)
% 2.94/1.99  % (20591)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_20438 for (2996ds/31Mi)
% 2.94/2.00  % (20591)Instruction limit reached!
% 2.94/2.00  % (20591)------------------------------
% 2.94/2.00  % (20591)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/2.00  % (20591)Termination reason: Unknown
% 2.94/2.00  % (20591)Termination phase: Property scanning
% 2.94/2.00  
% 2.94/2.00  % (20591)Memory used [KB]: 1918
% 2.94/2.00  % (20591)Time elapsed: 0.011 s
% 2.94/2.00  % (20591)Instructions burned: 33 (million)
% 2.94/2.00  % (20591)------------------------------
% 2.94/2.00  % (20591)------------------------------
% 2.94/2.00  % (20568)Instruction limit reached!
% 2.94/2.00  % (20568)------------------------------
% 2.94/2.00  % (20568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/2.00  % (20568)Termination reason: Unknown
% 2.94/2.00  % (20568)Termination phase: Saturation
% 2.94/2.00  
% 2.94/2.00  % (20568)Memory used [KB]: 8699
% 2.94/2.00  % (20568)Time elapsed: 0.293 s
% 2.94/2.00  % (20568)Instructions burned: 881 (million)
% 2.94/2.00  % (20568)------------------------------
% 2.94/2.00  % (20568)------------------------------
% 2.94/2.00  % (20549)Instruction limit reached!
% 2.94/2.00  % (20549)------------------------------
% 2.94/2.00  % (20549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/2.00  % (20549)Termination reason: Unknown
% 2.94/2.00  % (20549)Termination phase: Saturation
% 2.94/2.00  
% 2.94/2.00  % (20549)Memory used [KB]: 10362
% 2.94/2.00  % (20549)Time elapsed: 0.358 s
% 2.94/2.00  % (20549)Instructions burned: 1041 (million)
% 2.94/2.00  % (20549)------------------------------
% 2.94/2.00  % (20549)------------------------------
% 2.94/2.00  % (20590)Instruction limit reached!
% 2.94/2.00  % (20590)------------------------------
% 2.94/2.00  % (20590)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.94/2.00  % (20590)Termination reason: Unknown
% 2.94/2.00  % (20590)Termination phase: Property scanning
% 2.94/2.00  
% 2.94/2.00  % (20590)Memory used [KB]: 2430
% 2.94/2.00  % (20590)Time elapsed: 0.018 s
% 2.94/2.00  % (20590)Instructions burned: 65 (million)
% 2.94/2.00  % (20590)------------------------------
% 2.94/2.00  % (20590)------------------------------
% 2.94/2.01  % (20593)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_20438 for (2995ds/453Mi)
% 2.94/2.01  % (20594)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_20438 for (2995ds/71Mi)
% 2.94/2.01  % (20595)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_20438 for (2995ds/83Mi)
% 2.94/2.01  % (20592)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_20438 for (2995ds/96Mi)
% 5.75/2.03  % (20594)Instruction limit reached!
% 5.75/2.03  % (20594)------------------------------
% 5.75/2.03  % (20594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.75/2.03  % (20594)Termination reason: Unknown
% 5.75/2.03  % (20594)Termination phase: Property scanning
% 5.75/2.03  
% 5.75/2.03  % (20594)Memory used [KB]: 2302
% 5.75/2.03  % (20594)Time elapsed: 0.022 s
% 5.75/2.03  % (20594)Instructions burned: 74 (million)
% 5.75/2.03  % (20594)------------------------------
% 5.75/2.03  % (20594)------------------------------
% 5.75/2.04  % (20595)Instruction limit reached!
% 5.75/2.04  % (20595)------------------------------
% 5.75/2.04  % (20595)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.75/2.04  % (20595)Termination reason: Unknown
% 5.75/2.04  % (20595)Termination phase: Saturation
% 5.75/2.04  
% 5.75/2.04  % (20595)Memory used [KB]: 6652
% 5.75/2.04  % (20595)Time elapsed: 0.026 s
% 5.75/2.04  % (20595)Instructions burned: 84 (million)
% 5.75/2.04  % (20595)------------------------------
% 5.75/2.04  % (20595)------------------------------
% 5.75/2.04  % (20592)Instruction limit reached!
% 5.75/2.04  % (20592)------------------------------
% 5.75/2.04  % (20592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.75/2.04  % (20592)Termination reason: Unknown
% 5.75/2.04  % (20592)Termination phase: Saturation
% 5.75/2.04  
% 5.75/2.04  % (20592)Memory used [KB]: 6908
% 5.75/2.04  % (20592)Time elapsed: 0.028 s
% 5.75/2.04  % (20592)Instructions burned: 98 (million)
% 5.75/2.04  % (20592)------------------------------
% 5.75/2.04  % (20592)------------------------------
% 5.75/2.04  % (20596)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_20438 for (2995ds/11Mi)
% 5.75/2.04  % (20579)Instruction limit reached!
% 5.75/2.04  % (20579)------------------------------
% 5.75/2.04  % (20579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.75/2.04  % (20579)Termination reason: Unknown
% 5.75/2.04  % (20579)Termination phase: Saturation
% 5.75/2.04  
% 5.75/2.04  % (20579)Memory used [KB]: 9338
% 5.75/2.04  % (20579)Time elapsed: 0.140 s
% 5.75/2.04  % (20579)Instructions burned: 450 (million)
% 5.75/2.04  % (20579)------------------------------
% 5.75/2.04  % (20579)------------------------------
% 5.75/2.04  % (20596)Instruction limit reached!
% 5.75/2.04  % (20596)------------------------------
% 5.75/2.04  % (20596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.75/2.04  % (20596)Termination reason: Unknown
% 5.75/2.04  % (20596)Termination phase: shuffling
% 5.75/2.04  
% 5.75/2.04  % (20596)Memory used [KB]: 1791
% 5.75/2.04  % (20596)Time elapsed: 0.005 s
% 5.75/2.04  % (20596)Instructions burned: 14 (million)
% 5.75/2.04  % (20596)------------------------------
% 5.75/2.04  % (20596)------------------------------
% 5.75/2.05  % (20597)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_20438 for (2995ds/41Mi)
% 5.75/2.05  % (20598)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_20438 for (2995ds/6Mi)
% 5.75/2.05  % (20598)Instruction limit reached!
% 5.75/2.05  % (20598)------------------------------
% 5.75/2.05  % (20598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.75/2.05  % (20598)Termination reason: Unknown
% 5.75/2.05  % (20598)Termination phase: shuffling
% 5.75/2.05  
% 5.75/2.05  % (20598)Memory used [KB]: 1535
% 5.75/2.05  % (20598)Time elapsed: 0.003 s
% 5.75/2.05  % (20598)Instructions burned: 6 (million)
% 5.75/2.05  % (20598)------------------------------
% 5.75/2.05  % (20598)------------------------------
% 5.75/2.05  % (20599)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_20438 for (2995ds/150Mi)
% 5.75/2.05  % (20600)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_20438 for (2995ds/343Mi)
% 5.75/2.06  % (20597)Instruction limit reached!
% 5.75/2.06  % (20597)------------------------------
% 5.75/2.06  % (20597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.75/2.06  % (20597)Termination reason: Unknown
% 5.75/2.06  % (20597)Termination phase: shuffling
% 5.75/2.06  
% 5.75/2.06  % (20597)Memory used [KB]: 2430
% 5.75/2.06  % (20597)Time elapsed: 0.012 s
% 5.75/2.06  % (20597)Instructions burned: 41 (million)
% 5.75/2.06  % (20597)------------------------------
% 5.75/2.06  % (20597)------------------------------
% 5.75/2.06  % (20601)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_20438 for (2995ds/109Mi)
% 5.75/2.07  % (20602)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_20438 for (2995ds/253Mi)
% 5.75/2.09  % (20601)Instruction limit reached!
% 5.75/2.09  % (20601)------------------------------
% 5.75/2.09  % (20601)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.75/2.09  % (20601)Termination reason: Unknown
% 5.75/2.09  % (20601)Termination phase: Saturation
% 5.75/2.09  
% 5.75/2.09  % (20601)Memory used [KB]: 7036
% 5.75/2.09  % (20601)Time elapsed: 0.032 s
% 5.75/2.09  % (20601)Instructions burned: 111 (million)
% 5.75/2.09  % (20601)------------------------------
% 5.75/2.09  % (20601)------------------------------
% 5.75/2.10  % (20599)Instruction limit reached!
% 5.75/2.10  % (20599)------------------------------
% 5.75/2.10  % (20599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.75/2.10  % (20599)Termination reason: Unknown
% 5.75/2.10  % (20599)Termination phase: Saturation
% 5.75/2.10  
% 5.75/2.10  % (20599)Memory used [KB]: 7419
% 5.75/2.10  % (20599)Time elapsed: 0.046 s
% 5.75/2.10  % (20599)Instructions burned: 152 (million)
% 5.75/2.10  % (20599)------------------------------
% 5.75/2.10  % (20599)------------------------------
% 5.75/2.10  % (20603)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_20438 for (2994ds/140Mi)
% 5.75/2.11  % (20604)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_20438 for (2994ds/614Mi)
% 5.75/2.11  % (20589)Instruction limit reached!
% 5.75/2.11  % (20589)------------------------------
% 5.75/2.11  % (20589)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.75/2.11  % (20589)Termination reason: Unknown
% 5.75/2.11  % (20589)Termination phase: Saturation
% 5.75/2.11  
% 5.75/2.11  % (20589)Memory used [KB]: 4093
% 5.75/2.11  % (20589)Time elapsed: 0.131 s
% 5.75/2.11  % (20589)Instructions burned: 434 (million)
% 5.75/2.11  % (20589)------------------------------
% 5.75/2.11  % (20589)------------------------------
% 6.23/2.12  % (20605)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_20438 for (2994ds/202Mi)
% 6.23/2.14  % (20593)Instruction limit reached!
% 6.23/2.14  % (20593)------------------------------
% 6.23/2.14  % (20593)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.23/2.14  % (20593)Termination reason: Unknown
% 6.23/2.14  % (20593)Termination phase: Saturation
% 6.23/2.14  
% 6.23/2.14  % (20593)Memory used [KB]: 8187
% 6.23/2.14  % (20593)Time elapsed: 0.152 s
% 6.23/2.14  % (20593)Instructions burned: 454 (million)
% 6.23/2.14  % (20593)------------------------------
% 6.23/2.14  % (20593)------------------------------
% 6.23/2.14  % (20603)Instruction limit reached!
% 6.23/2.14  % (20603)------------------------------
% 6.23/2.14  % (20603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.23/2.14  % (20603)Termination reason: Unknown
% 6.23/2.14  % (20603)Termination phase: Saturation
% 6.23/2.14  
% 6.23/2.14  % (20603)Memory used [KB]: 7291
% 6.23/2.14  % (20603)Time elapsed: 0.045 s
% 6.23/2.14  % (20603)Instructions burned: 141 (million)
% 6.23/2.14  % (20603)------------------------------
% 6.23/2.14  % (20603)------------------------------
% 6.23/2.14  % (20602)Instruction limit reached!
% 6.23/2.14  % (20602)------------------------------
% 6.23/2.14  % (20602)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.23/2.14  % (20602)Termination reason: Unknown
% 6.23/2.14  % (20602)Termination phase: Saturation
% 6.23/2.14  
% 6.23/2.14  % (20602)Memory used [KB]: 7547
% 6.23/2.14  % (20602)Time elapsed: 0.079 s
% 6.23/2.14  % (20602)Instructions burned: 255 (million)
% 6.23/2.14  % (20602)------------------------------
% 6.23/2.14  % (20602)------------------------------
% 6.23/2.15  % (20606)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_20438 for (2994ds/339Mi)
% 6.23/2.15  % (20607)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_20438 for (2994ds/283Mi)
% 6.23/2.15  % (20608)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_20438 for (2994ds/134Mi)
% 6.23/2.16  % (20600)Instruction limit reached!
% 6.23/2.16  % (20600)------------------------------
% 6.23/2.16  % (20600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.23/2.16  % (20600)Termination reason: Unknown
% 6.23/2.16  % (20600)Termination phase: Saturation
% 6.23/2.16  
% 6.23/2.16  % (20600)Memory used [KB]: 8059
% 6.23/2.16  % (20600)Time elapsed: 0.109 s
% 6.23/2.16  % (20600)Instructions burned: 343 (million)
% 6.23/2.16  % (20600)------------------------------
% 6.23/2.16  % (20600)------------------------------
% 6.23/2.17  % (20609)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_20438 for (2994ds/298Mi)
% 6.23/2.18  % (20605)Instruction limit reached!
% 6.23/2.18  % (20605)------------------------------
% 6.23/2.18  % (20605)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.23/2.18  % (20605)Termination reason: Unknown
% 6.23/2.18  % (20605)Termination phase: Saturation
% 6.23/2.18  
% 6.23/2.18  % (20605)Memory used [KB]: 7419
% 6.23/2.18  % (20605)Time elapsed: 0.063 s
% 6.23/2.18  % (20605)Instructions burned: 202 (million)
% 6.23/2.18  % (20605)------------------------------
% 6.23/2.18  % (20605)------------------------------
% 6.23/2.19  % (20608)Instruction limit reached!
% 6.23/2.19  % (20608)------------------------------
% 6.23/2.19  % (20608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.23/2.19  % (20608)Termination reason: Unknown
% 6.23/2.19  % (20608)Termination phase: Saturation
% 6.23/2.19  
% 6.23/2.19  % (20608)Memory used [KB]: 7164
% 6.23/2.19  % (20608)Time elapsed: 0.039 s
% 6.23/2.19  % (20608)Instructions burned: 135 (million)
% 6.23/2.19  % (20608)------------------------------
% 6.23/2.19  % (20608)------------------------------
% 6.23/2.19  % (20610)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_20438 for (2993ds/192Mi)
% 6.84/2.20  % (20611)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_20438 for (2993ds/258Mi)
% 6.84/2.24  % (20607)Instruction limit reached!
% 6.84/2.24  % (20607)------------------------------
% 6.84/2.24  % (20607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.84/2.24  % (20607)Termination reason: Unknown
% 6.84/2.24  % (20607)Termination phase: Saturation
% 6.84/2.24  
% 6.84/2.24  % (20607)Memory used [KB]: 7803
% 6.84/2.24  % (20607)Time elapsed: 0.084 s
% 6.84/2.24  % (20607)Instructions burned: 283 (million)
% 6.84/2.24  % (20607)------------------------------
% 6.84/2.24  % (20607)------------------------------
% 6.84/2.24  % (20610)Refutation not found, incomplete strategy
% 6.84/2.24  % (20610)------------------------------
% 6.84/2.24  % (20610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.84/2.24  % (20610)Termination reason: Refutation not found, incomplete strategy
% 6.84/2.24  
% 6.84/2.24  
% 6.84/2.24  % (20610)Memory used [KB]: 8187
% 6.84/2.24  % (20610)Time elapsed: 0.050 s
% 6.84/2.24  % (20610)Instructions burned: 163 (million)
% 6.84/2.24  % (20610)------------------------------
% 6.84/2.24  % (20610)------------------------------
% 6.84/2.25  % (20612)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_20438 for (2993ds/90Mi)
% 6.84/2.25  % (20613)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_20438 for (2993ds/231Mi)
% 6.84/2.25  % (20606)Instruction limit reached!
% 6.84/2.25  % (20606)------------------------------
% 6.84/2.25  % (20606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.84/2.25  % (20606)Termination reason: Unknown
% 6.84/2.25  % (20606)Termination phase: Saturation
% 6.84/2.25  
% 6.84/2.25  % (20606)Memory used [KB]: 8187
% 6.84/2.25  % (20606)Time elapsed: 0.105 s
% 6.84/2.25  % (20606)Instructions burned: 341 (million)
% 6.84/2.25  % (20606)------------------------------
% 6.84/2.25  % (20606)------------------------------
% 6.84/2.25  % (20609)Instruction limit reached!
% 6.84/2.25  % (20609)------------------------------
% 6.84/2.25  % (20609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.84/2.25  % (20609)Termination reason: Unknown
% 6.84/2.25  % (20609)Termination phase: Saturation
% 6.84/2.25  
% 6.84/2.25  % (20609)Memory used [KB]: 9083
% 6.84/2.25  % (20609)Time elapsed: 0.083 s
% 6.84/2.25  % (20609)Instructions burned: 300 (million)
% 6.84/2.25  % (20609)------------------------------
% 6.84/2.25  % (20609)------------------------------
% 6.84/2.26  % (20614)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_20438 for (2993ds/458Mi)
% 6.84/2.26  % (20615)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_20438 for (2993ds/31Mi)
% 6.84/2.27  % (20612)Instruction limit reached!
% 6.84/2.27  % (20612)------------------------------
% 6.84/2.27  % (20612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.84/2.27  % (20612)Termination reason: Unknown
% 6.84/2.27  % (20612)Termination phase: Saturation
% 6.84/2.27  
% 6.84/2.27  % (20612)Memory used [KB]: 6908
% 6.84/2.27  % (20612)Time elapsed: 0.027 s
% 6.84/2.27  % (20612)Instructions burned: 92 (million)
% 6.84/2.27  % (20612)------------------------------
% 6.84/2.27  % (20612)------------------------------
% 6.84/2.27  % (20615)Instruction limit reached!
% 6.84/2.27  % (20615)------------------------------
% 6.84/2.27  % (20615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.84/2.27  % (20615)Termination reason: Unknown
% 6.84/2.27  % (20615)Termination phase: Property scanning
% 6.84/2.27  
% 6.84/2.27  % (20615)Memory used [KB]: 1918
% 6.84/2.27  % (20615)Time elapsed: 0.011 s
% 6.84/2.27  % (20615)Instructions burned: 32 (million)
% 6.84/2.27  % (20615)------------------------------
% 6.84/2.27  % (20615)------------------------------
% 6.84/2.28  % (20611)Instruction limit reached!
% 6.84/2.28  % (20611)------------------------------
% 6.84/2.28  % (20611)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.84/2.28  % (20611)Termination reason: Unknown
% 6.84/2.28  % (20611)Termination phase: Saturation
% 6.84/2.28  
% 6.84/2.28  % (20611)Memory used [KB]: 8059
% 6.84/2.28  % (20611)Time elapsed: 0.079 s
% 6.84/2.28  % (20611)Instructions burned: 261 (million)
% 6.84/2.28  % (20611)------------------------------
% 6.84/2.28  % (20611)------------------------------
% 6.84/2.28  % (20616)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_20438 for (2993ds/297Mi)
% 6.84/2.28  % (20617)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_20438 for (2993ds/987Mi)
% 6.84/2.29  % (20618)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_20438 for (2993ds/182Mi)
% 6.84/2.29  % (20586)First to succeed.
% 6.84/2.29  % (20604)Instruction limit reached!
% 6.84/2.29  % (20604)------------------------------
% 6.84/2.29  % (20604)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.84/2.29  % (20604)Termination reason: Unknown
% 6.84/2.29  % (20604)Termination phase: Saturation
% 6.84/2.29  
% 6.84/2.29  % (20604)Memory used [KB]: 9083
% 6.84/2.29  % (20604)Time elapsed: 0.189 s
% 6.84/2.29  % (20604)Instructions burned: 614 (million)
% 6.84/2.29  % (20604)------------------------------
% 6.84/2.29  % (20604)------------------------------
% 7.63/2.30  % (20586)Refutation found. Thanks to Tanya!
% 7.63/2.30  % SZS status Theorem for DTF2THF_20438
% 7.63/2.30  % SZS output start Proof for DTF2THF_20438
% 7.63/2.30  thf(type_def_5, type, nat: $tType).
% 7.63/2.30  thf(type_def_6, type, standard_Constant_a: $tType).
% 7.63/2.30  thf(type_def_7, type, labele431970251um_a_b: $tType).
% 7.63/2.30  thf(type_def_8, type, set_Pr1916610317um_a_b: $tType).
% 7.63/2.30  thf(type_def_10, type, set_Pr1986765409at_nat: $tType).
% 7.63/2.30  thf(type_def_11, type, set_Pr1647387645at_nat: $tType).
% 7.63/2.30  thf(type_def_12, type, set_Pr1174980151um_a_b: $tType).
% 7.63/2.30  thf(type_def_13, type, set_Pr409224873um_a_b: $tType).
% 7.63/2.30  thf(type_def_14, type, set_Pr375490359_b_nat: $tType).
% 7.63/2.30  thf(type_def_15, type, labele935650037_a_nat: $tType).
% 7.63/2.30  thf(type_def_16, type, labele498606060at_nat: $tType).
% 7.63/2.30  thf(type_def_17, type, set_Pr689416536at_nat: $tType).
% 7.63/2.30  thf(type_def_18, type, set_Pr304595758um_a_b: $tType).
% 7.63/2.30  thf(type_def_19, type, labele261019144um_a_b: $tType).
% 7.63/2.30  thf(type_def_20, type, set_Pr1902304780_b_nat: $tType).
% 7.63/2.30  thf(type_def_21, type, set_Pr653770722um_a_b: $tType).
% 7.63/2.30  thf(type_def_22, type, labele1191284958um_a_b: $tType).
% 7.63/2.30  thf(type_def_23, type, set_Pr507214050_b_nat: $tType).
% 7.63/2.30  thf(type_def_24, type, set_Pr55236280um_a_b: $tType).
% 7.63/2.30  thf(type_def_25, type, set_nat: $tType).
% 7.63/2.30  thf(type_def_26, type, set_Pr1355257963at_nat: $tType).
% 7.63/2.30  thf(type_def_27, type, set_Pr2065572323um_a_b: $tType).
% 7.63/2.30  thf(type_def_28, type, set_Pr1429673827um_a_b: $tType).
% 7.63/2.30  thf(type_def_29, type, set_Sum_sum_a_b: $tType).
% 7.63/2.30  thf(type_def_30, type, set_St761939237tant_a: $tType).
% 7.63/2.30  thf(type_def_31, type, product_prod_nat_nat: $tType).
% 7.63/2.30  thf(type_def_32, type, produc1032616263at_nat: $tType).
% 7.63/2.30  thf(type_def_33, type, produc1124793815um_a_b: $tType).
% 7.63/2.30  thf(type_def_34, type, produc1003469085um_a_b: $tType).
% 7.63/2.30  thf(type_def_35, type, produc1548871597um_a_b: $tType).
% 7.63/2.30  thf(type_def_36, type, produc1963079155um_a_b: $tType).
% 7.63/2.30  thf(type_def_37, type, sum_sum_a_b: $tType).
% 7.63/2.30  thf(type_def_38, type, produc1394389750um_a_b: $tType).
% 7.63/2.30  thf(type_def_39, type, produc1871334759_a_nat: $tType).
% 7.63/2.30  thf(type_def_40, type, produc204140796um_a_b: $tType).
% 7.63/2.30  thf(type_def_41, type, produc1681803642um_a_b: $tType).
% 7.63/2.30  thf(type_def_42, type, produc1546082365um_a_b: $tType).
% 7.63/2.30  thf(type_def_43, type, produc1798470614um_a_b: $tType).
% 7.63/2.30  thf(type_def_44, type, produc1918750183um_a_b: $tType).
% 7.63/2.30  thf(type_def_45, type, produc585753260um_a_b: $tType).
% 7.63/2.30  thf(type_def_46, type, produc1978941143_b_nat: $tType).
% 7.63/2.30  thf(type_def_47, type, produc1733247354um_a_b: $tType).
% 7.63/2.30  thf(type_def_48, type, produc323101606um_a_b: $tType).
% 7.63/2.30  thf(type_def_49, type, set_Pr326391507um_a_b: $tType).
% 7.63/2.30  thf(type_def_50, type, set_Pr1994339542um_a_b: $tType).
% 7.63/2.30  thf(type_def_51, type, set_Pr1134469976at_nat: $tType).
% 7.63/2.30  thf(type_def_52, type, set_Pr1618094130um_a_b: $tType).
% 7.63/2.30  thf(type_def_53, type, set_Pr1155046920um_a_b: $tType).
% 7.63/2.30  thf(type_def_54, type, set_Pr1121389018um_a_b: $tType).
% 7.63/2.30  thf(type_def_55, type, set_Pr386468381um_a_b: $tType).
% 7.63/2.30  thf(type_def_56, type, set_Pr195945996um_a_b: $tType).
% 7.63/2.30  thf(type_def_57, type, set_Pr45173959um_a_b: $tType).
% 7.63/2.30  thf(type_def_58, type, set_Pr1558970842um_a_b: $tType).
% 7.63/2.30  thf(type_def_59, type, set_Pr1783309276um_a_b: $tType).
% 7.63/2.30  thf(func_def_0, type, set_Pr1355257963at_nat: $tType).
% 7.63/2.30  thf(func_def_1, type, set_Pr1429673827um_a_b: $tType).
% 7.63/2.30  thf(func_def_2, type, set_Pr2065572323um_a_b: $tType).
% 7.63/2.30  thf(func_def_3, type, set_Pr1558970842um_a_b: $tType).
% 7.63/2.30  thf(func_def_4, type, set_Pr1121389018um_a_b: $tType).
% 7.63/2.30  thf(func_def_5, type, produc1733247354um_a_b: $tType).
% 7.63/2.30  thf(func_def_6, type, produc1681803642um_a_b: $tType).
% 7.63/2.30  thf(func_def_7, type, produc1871334759_a_nat: $tType).
% 7.63/2.30  thf(func_def_8, type, labele498606060at_nat: $tType).
% 7.63/2.30  thf(func_def_9, type, set_Pr304595758um_a_b: $tType).
% 7.63/2.30  thf(func_def_10, type, set_Pr409224873um_a_b: $tType).
% 7.63/2.30  thf(func_def_11, type, set_Pr45173959um_a_b: $tType).
% 7.63/2.30  thf(func_def_12, type, set_Pr689416536at_nat: $tType).
% 7.63/2.30  thf(func_def_13, type, set_Pr1134469976at_nat: $tType).
% 7.63/2.30  thf(func_def_14, type, labele1191284958um_a_b: $tType).
% 7.63/2.30  thf(func_def_15, type, produc1963079155um_a_b: $tType).
% 7.63/2.30  thf(func_def_16, type, produc1918750183um_a_b: $tType).
% 7.63/2.30  thf(func_def_17, type, set_Pr55236280um_a_b: $tType).
% 7.63/2.30  thf(func_def_18, type, set_Pr326391507um_a_b: $tType).
% 7.63/2.30  thf(func_def_19, type, set_Pr386468381um_a_b: $tType).
% 7.63/2.30  thf(func_def_20, type, labele261019144um_a_b: $tType).
% 7.63/2.30  thf(func_def_21, type, produc1003469085um_a_b: $tType).
% 7.63/2.30  thf(func_def_22, type, produc1546082365um_a_b: $tType).
% 7.63/2.30  thf(func_def_23, type, set_Pr1783309276um_a_b: $tType).
% 7.63/2.30  thf(func_def_24, type, set_Pr507214050_b_nat: $tType).
% 7.63/2.30  thf(func_def_25, type, set_Pr653770722um_a_b: $tType).
% 7.63/2.30  thf(func_def_26, type, set_Pr1155046920um_a_b: $tType).
% 7.63/2.30  thf(func_def_27, type, set_Pr1647387645at_nat: $tType).
% 7.63/2.30  thf(func_def_28, type, produc323101606um_a_b: $tType).
% 7.63/2.30  thf(func_def_29, type, produc585753260um_a_b: $tType).
% 7.63/2.30  thf(func_def_30, type, produc1032616263at_nat: $tType).
% 7.63/2.30  thf(func_def_31, type, set_Pr1994339542um_a_b: $tType).
% 7.63/2.30  thf(func_def_32, type, set_Pr1902304780_b_nat: $tType).
% 7.63/2.30  thf(func_def_33, type, set_Pr195945996um_a_b: $tType).
% 7.63/2.30  thf(func_def_34, type, set_Pr1618094130um_a_b: $tType).
% 7.63/2.30  thf(func_def_35, type, labele431970251um_a_b: $tType).
% 7.63/2.30  thf(func_def_36, type, produc1394389750um_a_b: $tType).
% 7.63/2.30  thf(func_def_37, type, produc1798470614um_a_b: $tType).
% 7.63/2.30  thf(func_def_38, type, produc204140796um_a_b: $tType).
% 7.63/2.30  thf(func_def_39, type, set_Pr1916610317um_a_b: $tType).
% 7.63/2.30  thf(func_def_40, type, labele935650037_a_nat: $tType).
% 7.63/2.30  thf(func_def_41, type, produc1548871597um_a_b: $tType).
% 7.63/2.30  thf(func_def_42, type, set_Pr375490359_b_nat: $tType).
% 7.63/2.30  thf(func_def_43, type, set_Pr1174980151um_a_b: $tType).
% 7.63/2.30  thf(func_def_44, type, produc1978941143_b_nat: $tType).
% 7.63/2.30  thf(func_def_45, type, produc1124793815um_a_b: $tType).
% 7.63/2.30  thf(func_def_46, type, set_St761939237tant_a: $tType).
% 7.63/2.30  thf(func_def_47, type, set_Pr1986765409at_nat: $tType).
% 7.63/2.30  thf(func_def_48, type, standard_Constant_a: $tType).
% 7.63/2.30  thf(func_def_49, type, product_prod_nat_nat: $tType).
% 7.63/2.30  thf(func_def_50, type, set_Sum_sum_a_b: $tType).
% 7.63/2.30  thf(func_def_51, type, sum_sum_a_b: $tType).
% 7.63/2.30  thf(func_def_52, type, set_nat: $tType).
% 7.63/2.30  thf(func_def_53, type, nat: $tType).
% 7.63/2.30  thf(func_def_54, type, zero_zero_nat: nat).
% 7.63/2.30  thf(func_def_55, type, standard_S_Bot_a: standard_Constant_a).
% 7.63/2.30  thf(func_def_56, type, standard_S_Idt_a: standard_Constant_a).
% 7.63/2.30  thf(func_def_57, type, getRel1465196352um_a_b: standard_Constant_a > labele431970251um_a_b > set_Pr1916610317um_a_b).
% 7.63/2.30  thf(func_def_58, type, edge_p170421892tant_a: set_Pr1986765409at_nat > set_Pr1647387645at_nat > set_Pr1647387645at_nat > $o).
% 7.63/2.30  thf(func_def_59, type, edge_p1382426714tant_a: set_Pr1174980151um_a_b > set_Pr1647387645at_nat > set_Pr409224873um_a_b > $o).
% 7.63/2.30  thf(func_def_60, type, edge_p749155930tant_a: set_Pr375490359_b_nat > set_Pr409224873um_a_b > set_Pr1647387645at_nat > $o).
% 7.63/2.30  thf(func_def_61, type, edge_p1871801392tant_a: set_Pr1916610317um_a_b > set_Pr409224873um_a_b > set_Pr409224873um_a_b > $o).
% 7.63/2.30  thf(func_def_62, type, graph_2130075512at_nat: labele935650037_a_nat > labele935650037_a_nat > set_Pr1986765409at_nat > $o).
% 7.63/2.30  thf(func_def_63, type, graph_1452133198um_a_b: labele935650037_a_nat > labele431970251um_a_b > set_Pr1174980151um_a_b > $o).
% 7.63/2.30  thf(func_def_64, type, graph_149544303at_nat: labele498606060at_nat > labele935650037_a_nat > set_Pr689416536at_nat > $o).
% 7.63/2.30  thf(func_def_65, type, graph_166346565um_a_b: labele498606060at_nat > labele431970251um_a_b > set_Pr304595758um_a_b > $o).
% 7.63/2.30  thf(func_def_66, type, graph_1203757137_b_nat: labele261019144um_a_b > labele935650037_a_nat > set_Pr1902304780_b_nat > $o).
% 7.63/2.30  thf(func_def_67, type, graph_502887975um_a_b: labele261019144um_a_b > labele431970251um_a_b > set_Pr653770722um_a_b > $o).
% 7.63/2.30  thf(func_def_68, type, graph_1815313447_b_nat: labele1191284958um_a_b > labele935650037_a_nat > set_Pr507214050_b_nat > $o).
% 7.63/2.30  thf(func_def_69, type, graph_1763806717um_a_b: labele1191284958um_a_b > labele431970251um_a_b > set_Pr55236280um_a_b > $o).
% 7.63/2.30  thf(func_def_70, type, graph_165730638_b_nat: labele431970251um_a_b > labele935650037_a_nat > set_Pr375490359_b_nat > $o).
% 7.63/2.30  thf(func_def_71, type, graph_611893540um_a_b: labele431970251um_a_b > labele431970251um_a_b > set_Pr1916610317um_a_b > $o).
% 7.63/2.30  thf(func_def_72, type, labele16114835_a_nat: set_Pr1647387645at_nat > set_nat > labele935650037_a_nat).
% 7.63/2.30  thf(func_def_73, type, labele1813985418at_nat: set_Pr1355257963at_nat > set_Pr1647387645at_nat > labele498606060at_nat).
% 7.63/2.30  thf(func_def_74, type, labele2034032468um_a_b: set_Pr2065572323um_a_b > set_Pr1174980151um_a_b > labele261019144um_a_b).
% 7.63/2.30  thf(func_def_75, type, labele989994um_a_b: set_Pr1429673827um_a_b > set_Pr1916610317um_a_b > labele1191284958um_a_b).
% 7.63/2.30  thf(func_def_76, type, labele1729654377um_a_b: set_Pr409224873um_a_b > set_Sum_sum_a_b > labele431970251um_a_b).
% 7.63/2.30  thf(func_def_77, type, labele195203296_a_nat: labele935650037_a_nat > set_Pr1647387645at_nat).
% 7.63/2.30  thf(func_def_78, type, labele1939049654um_a_b: labele431970251um_a_b > set_Pr409224873um_a_b).
% 7.63/2.30  thf(func_def_79, type, labele1810595089_a_nat: labele935650037_a_nat > set_nat).
% 7.63/2.30  thf(func_def_80, type, labele577278695um_a_b: labele431970251um_a_b > set_Sum_sum_a_b).
% 7.63/2.30  thf(func_def_81, type, restri572569417_a_nat: labele935650037_a_nat > labele935650037_a_nat).
% 7.63/2.30  thf(func_def_82, type, restri1162247455um_a_b: labele431970251um_a_b > labele431970251um_a_b).
% 7.63/2.30  thf(func_def_83, type, unival860567212at_nat: set_Pr1647387645at_nat > $o).
% 7.63/2.30  thf(func_def_84, type, unival1487587672um_a_b: set_Pr409224873um_a_b > $o).
% 7.63/2.30  thf(func_def_85, type, unival2092813468um_a_b: set_Pr1174980151um_a_b > $o).
% 7.63/2.30  thf(func_def_86, type, unival118648434um_a_b: set_Pr1916610317um_a_b > $o).
% 7.63/2.30  thf(func_def_87, type, bot_bot_nat: nat).
% 7.63/2.30  thf(func_def_88, type, bot_bo1160111033tant_a: set_St761939237tant_a).
% 7.63/2.30  thf(func_def_89, type, bot_bot_set_nat: set_nat).
% 7.63/2.30  thf(func_def_90, type, bot_bo810816657at_nat: set_Pr1647387645at_nat).
% 7.63/2.30  thf(func_def_91, type, bot_bo1524397311at_nat: set_Pr1355257963at_nat).
% 7.63/2.30  thf(func_def_92, type, bot_bo1208513655um_a_b: set_Pr2065572323um_a_b).
% 7.63/2.30  thf(func_def_93, type, bot_bo1262778871um_a_b: set_Pr1429673827um_a_b).
% 7.63/2.30  thf(func_def_94, type, bot_bo1262634813um_a_b: set_Pr409224873um_a_b).
% 7.63/2.30  thf(func_def_95, type, bot_bo2130386637at_nat: set_Pr1986765409at_nat).
% 7.63/2.30  thf(func_def_96, type, bot_bo575978147um_a_b: set_Pr1174980151um_a_b).
% 7.63/2.30  thf(func_def_97, type, bot_bo1582968772at_nat: set_Pr689416536at_nat).
% 7.63/2.30  thf(func_def_98, type, bot_bo627753370um_a_b: set_Pr304595758um_a_b).
% 7.63/2.30  thf(func_def_99, type, bot_bo949957280_b_nat: set_Pr1902304780_b_nat).
% 7.63/2.30  thf(func_def_100, type, bot_bo1892785270um_a_b: set_Pr653770722um_a_b).
% 7.63/2.30  thf(func_def_101, type, bot_bo1746228598_b_nat: set_Pr507214050_b_nat).
% 7.63/2.30  thf(func_def_102, type, bot_bo1217542988um_a_b: set_Pr55236280um_a_b).
% 7.63/2.30  thf(func_def_103, type, bot_bo1923972003_b_nat: set_Pr375490359_b_nat).
% 7.63/2.30  thf(func_def_104, type, bot_bo225809273um_a_b: set_Pr1916610317um_a_b).
% 7.63/2.30  thf(func_def_105, type, bot_bo1491243248um_a_b: set_Sum_sum_a_b).
% 7.63/2.30  thf(func_def_106, type, ord_less_eq_nat: nat > nat > $o).
% 7.63/2.30  thf(func_def_107, type, ord_le1739761029tant_a: set_St761939237tant_a > set_St761939237tant_a > $o).
% 7.63/2.30  thf(func_def_108, type, ord_less_eq_set_nat: set_nat > set_nat > $o).
% 7.63/2.30  thf(func_def_109, type, ord_le1909159005at_nat: set_Pr1647387645at_nat > set_Pr1647387645at_nat > $o).
% 7.63/2.30  thf(func_def_110, type, ord_le615126793um_a_b: set_Pr409224873um_a_b > set_Pr409224873um_a_b > $o).
% 7.63/2.30  thf(func_def_111, type, ord_le841296385at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > $o).
% 7.63/2.30  thf(func_def_112, type, ord_le823954903um_a_b: set_Pr1174980151um_a_b > set_Pr1174980151um_a_b > $o).
% 7.63/2.30  thf(func_def_113, type, ord_le1059794605um_a_b: set_Pr1916610317um_a_b > set_Pr1916610317um_a_b > $o).
% 7.63/2.30  thf(func_def_114, type, ord_le192794300um_a_b: set_Sum_sum_a_b > set_Sum_sum_a_b > $o).
% 7.63/2.30  thf(func_def_115, type, produc407553657at_nat: standard_Constant_a > product_prod_nat_nat > produc1032616263at_nat).
% 7.63/2.30  thf(func_def_116, type, produc414524239um_a_b: standard_Constant_a > produc1124793815um_a_b > produc1003469085um_a_b).
% 7.63/2.30  thf(func_def_117, type, produc1697725733um_a_b: standard_Constant_a > produc1548871597um_a_b > produc1963079155um_a_b).
% 7.63/2.30  thf(func_def_118, type, produc584843310um_a_b: standard_Constant_a > sum_sum_a_b > produc1394389750um_a_b).
% 7.63/2.30  thf(func_def_119, type, produc1676969687_a_nat: labele935650037_a_nat > labele935650037_a_nat > produc1871334759_a_nat).
% 7.63/2.30  thf(func_def_120, type, product_Pair_nat_nat: nat > nat > product_prod_nat_nat).
% 7.63/2.30  thf(func_def_121, type, produc1346373166um_a_b: nat > produc1124793815um_a_b > produc204140796um_a_b).
% 7.63/2.30  thf(func_def_122, type, produc1808556047um_a_b: nat > sum_sum_a_b > produc1124793815um_a_b).
% 7.63/2.30  thf(func_def_123, type, produc522766386um_a_b: produc1963079155um_a_b > sum_sum_a_b > produc1681803642um_a_b).
% 7.63/2.30  thf(func_def_124, type, produc335036333um_a_b: product_prod_nat_nat > produc1124793815um_a_b > produc1546082365um_a_b).
% 7.63/2.30  thf(func_def_125, type, produc1872245072um_a_b: product_prod_nat_nat > sum_sum_a_b > produc1798470614um_a_b).
% 7.63/2.30  thf(func_def_126, type, produc27163479um_a_b: produc1124793815um_a_b > produc1124793815um_a_b > produc1918750183um_a_b).
% 7.63/2.30  thf(func_def_127, type, produc831476262um_a_b: produc1124793815um_a_b > sum_sum_a_b > produc585753260um_a_b).
% 7.63/2.30  thf(func_def_128, type, produc522153487_b_nat: sum_sum_a_b > nat > produc1978941143_b_nat).
% 7.63/2.30  thf(func_def_129, type, produc230853810um_a_b: sum_sum_a_b > produc1963079155um_a_b > produc1733247354um_a_b).
% 7.63/2.30  thf(func_def_130, type, produc1637282520um_a_b: sum_sum_a_b > produc1124793815um_a_b > produc323101606um_a_b).
% 7.63/2.30  thf(func_def_131, type, produc176426981um_a_b: sum_sum_a_b > sum_sum_a_b > produc1548871597um_a_b).
% 7.63/2.30  thf(func_def_132, type, domain1060562500at_nat: set_Pr1647387645at_nat > set_St761939237tant_a).
% 7.63/2.30  thf(func_def_133, type, domain1362581744um_a_b: set_Pr409224873um_a_b > set_St761939237tant_a).
% 7.63/2.30  thf(func_def_134, type, domain_nat_nat: set_Pr1986765409at_nat > set_nat).
% 7.63/2.30  thf(func_def_135, type, domain1368163076um_a_b: set_Pr1174980151um_a_b > set_nat).
% 7.63/2.30  thf(func_def_136, type, domain2069673178um_a_b: set_Pr1916610317um_a_b > set_Sum_sum_a_b).
% 7.63/2.30  thf(func_def_137, type, id_on_Sum_sum_a_b: set_Sum_sum_a_b > set_Pr1916610317um_a_b).
% 7.63/2.30  thf(func_def_138, type, image_127502653at_nat: set_Pr1647387645at_nat > set_St761939237tant_a > set_Pr1986765409at_nat).
% 7.63/2.30  thf(func_def_139, type, image_1179143699um_a_b: set_Pr326391507um_a_b > set_St761939237tant_a > set_Pr1174980151um_a_b).
% 7.63/2.30  thf(func_def_140, type, image_2023280617um_a_b: set_Pr409224873um_a_b > set_St761939237tant_a > set_Pr1916610317um_a_b).
% 7.63/2.30  thf(func_def_141, type, image_2129435242um_a_b: set_Pr1994339542um_a_b > set_St761939237tant_a > set_Sum_sum_a_b).
% 7.63/2.30  thf(func_def_142, type, image_nat_nat: set_Pr1986765409at_nat > set_nat > set_nat).
% 7.63/2.30  thf(func_def_143, type, image_489788268at_nat: set_Pr1134469976at_nat > set_nat > set_Pr1647387645at_nat).
% 7.63/2.30  thf(func_def_144, type, image_1228479730um_a_b: set_Pr1618094130um_a_b > set_nat > set_Pr1174980151um_a_b).
% 7.63/2.30  thf(func_def_145, type, image_166667464um_a_b: set_Pr1155046920um_a_b > set_nat > set_Pr1916610317um_a_b).
% 7.63/2.30  thf(func_def_146, type, image_256773707um_a_b: set_Pr1174980151um_a_b > set_nat > set_Sum_sum_a_b).
% 7.63/2.30  thf(func_def_147, type, image_452296684at_nat: set_Pr689416536at_nat > set_Pr1647387645at_nat > set_nat).
% 7.63/2.30  thf(func_def_148, type, image_1774897262um_a_b: set_Pr1121389018um_a_b > set_Pr409224873um_a_b > set_Sum_sum_a_b).
% 7.63/2.30  thf(func_def_149, type, image_320480233um_a_b: set_Pr386468381um_a_b > set_Pr1986765409at_nat > set_Pr1174980151um_a_b).
% 7.63/2.30  thf(func_def_150, type, image_1754351636um_a_b: set_Pr195945996um_a_b > set_Pr1986765409at_nat > set_Sum_sum_a_b).
% 7.63/2.30  thf(func_def_151, type, image_128716052_b_nat: set_Pr1902304780_b_nat > set_Pr1174980151um_a_b > set_nat).
% 7.63/2.30  thf(func_def_152, type, image_1464989587um_a_b: set_Pr45173959um_a_b > set_Pr1174980151um_a_b > set_Pr1174980151um_a_b).
% 7.63/2.30  thf(func_def_153, type, image_869585130um_a_b: set_Pr653770722um_a_b > set_Pr1174980151um_a_b > set_Sum_sum_a_b).
% 7.63/2.30  thf(func_def_154, type, image_1117854795_b_nat: set_Pr375490359_b_nat > set_Sum_sum_a_b > set_nat).
% 7.63/2.30  thf(func_def_155, type, image_1482984686um_a_b: set_Pr1558970842um_a_b > set_Sum_sum_a_b > set_Pr409224873um_a_b).
% 7.63/2.30  thf(func_def_156, type, image_1675391388um_a_b: set_Pr1783309276um_a_b > set_Sum_sum_a_b > set_Pr1174980151um_a_b).
% 7.63/2.30  thf(func_def_157, type, image_1918588449um_a_b: set_Pr1916610317um_a_b > set_Sum_sum_a_b > set_Sum_sum_a_b).
% 7.63/2.30  thf(func_def_158, type, mainta522127984um_a_b: produc1871334759_a_nat > labele431970251um_a_b > $o).
% 7.63/2.30  thf(func_def_159, type, collect_nat: (nat > $o) > set_nat).
% 7.63/2.30  thf(func_def_160, type, collec52779676at_nat: (produc1032616263at_nat > $o) > set_Pr1647387645at_nat).
% 7.63/2.30  thf(func_def_161, type, collec1254333256um_a_b: (produc1963079155um_a_b > $o) > set_Pr409224873um_a_b).
% 7.63/2.30  thf(func_def_162, type, collec492052930um_a_b: (produc1124793815um_a_b > $o) > set_Pr1174980151um_a_b).
% 7.63/2.30  thf(func_def_163, type, collec1769032088um_a_b: (produc1548871597um_a_b > $o) > set_Pr1916610317um_a_b).
% 7.63/2.30  thf(func_def_164, type, collect_Sum_sum_a_b: (sum_sum_a_b > $o) > set_Sum_sum_a_b).
% 7.63/2.30  thf(func_def_165, type, insert1909710879tant_a: standard_Constant_a > set_St761939237tant_a > set_St761939237tant_a).
% 7.63/2.30  thf(func_def_166, type, insert_nat: nat > set_nat > set_nat).
% 7.63/2.30  thf(func_def_167, type, insert1625259895at_nat: produc1032616263at_nat > set_Pr1647387645at_nat > set_Pr1647387645at_nat).
% 7.63/2.30  thf(func_def_168, type, insert323157027um_a_b: produc1963079155um_a_b > set_Pr409224873um_a_b > set_Pr409224873um_a_b).
% 7.63/2.30  thf(func_def_169, type, insert271595217at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat).
% 7.63/2.30  thf(func_def_170, type, insert983991207um_a_b: produc1124793815um_a_b > set_Pr1174980151um_a_b > set_Pr1174980151um_a_b).
% 7.63/2.30  thf(func_def_171, type, insert1435405693um_a_b: produc1548871597um_a_b > set_Pr1916610317um_a_b > set_Pr1916610317um_a_b).
% 7.63/2.30  thf(func_def_172, type, insert_Sum_sum_a_b: sum_sum_a_b > set_Sum_sum_a_b > set_Sum_sum_a_b).
% 7.63/2.30  thf(func_def_173, type, standa1343274079tant_a: standard_Constant_a > standard_Constant_a > produc1871334759_a_nat).
% 7.63/2.30  thf(func_def_174, type, standa1410829644tant_a: produc1871334759_a_nat).
% 7.63/2.30  thf(func_def_175, type, standa63370785tant_a: standard_Constant_a > produc1871334759_a_nat).
% 7.63/2.30  thf(func_def_176, type, standa997693288tant_a: standard_Constant_a > produc1871334759_a_nat).
% 7.63/2.30  thf(func_def_177, type, standa1795879409tant_a: standard_Constant_a > produc1871334759_a_nat).
% 7.63/2.30  thf(func_def_178, type, member1632892294tant_a: standard_Constant_a > set_St761939237tant_a > $o).
% 7.63/2.30  thf(func_def_179, type, member_nat: nat > set_nat > $o).
% 7.63/2.30  thf(func_def_180, type, member1696759390at_nat: produc1032616263at_nat > set_Pr1647387645at_nat > $o).
% 7.63/2.30  thf(func_def_181, type, member1502344244um_a_b: produc1003469085um_a_b > set_Pr326391507um_a_b > $o).
% 7.63/2.30  thf(func_def_182, type, member1998628618um_a_b: produc1963079155um_a_b > set_Pr409224873um_a_b > $o).
% 7.63/2.30  thf(func_def_183, type, member1641046175um_a_b: produc1394389750um_a_b > set_Pr1994339542um_a_b > $o).
% 7.63/2.30  thf(func_def_184, type, member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o).
% 7.63/2.30  thf(func_def_185, type, member1139034387um_a_b: produc204140796um_a_b > set_Pr1618094130um_a_b > $o).
% 7.63/2.30  thf(func_def_186, type, member1294585472um_a_b: produc1124793815um_a_b > set_Pr1174980151um_a_b > $o).
% 7.63/2.30  thf(func_def_187, type, member1590479267um_a_b: produc1681803642um_a_b > set_Pr1121389018um_a_b > $o).
% 7.63/2.30  thf(func_def_188, type, member834135910um_a_b: produc1546082365um_a_b > set_Pr386468381um_a_b > $o).
% 7.63/2.30  thf(func_def_189, type, member585880557um_a_b: produc1798470614um_a_b > set_Pr195945996um_a_b > $o).
% 7.63/2.30  thf(func_def_190, type, member429827856um_a_b: produc1918750183um_a_b > set_Pr45173959um_a_b > $o).
% 7.63/2.30  thf(func_def_191, type, member748122307um_a_b: produc585753260um_a_b > set_Pr653770722um_a_b > $o).
% 7.63/2.30  thf(func_def_192, type, member1249152_b_nat: produc1978941143_b_nat > set_Pr375490359_b_nat > $o).
% 7.63/2.30  thf(func_def_193, type, member1641922979um_a_b: produc1733247354um_a_b > set_Pr1558970842um_a_b > $o).
% 7.63/2.30  thf(func_def_194, type, member485470653um_a_b: produc323101606um_a_b > set_Pr1783309276um_a_b > $o).
% 7.63/2.30  thf(func_def_195, type, member947389014um_a_b: produc1548871597um_a_b > set_Pr1916610317um_a_b > $o).
% 7.63/2.30  thf(func_def_196, type, member_Sum_sum_a_b: sum_sum_a_b > set_Sum_sum_a_b > $o).
% 7.63/2.30  thf(func_def_197, type, g: labele431970251um_a_b).
% 7.63/2.30  thf(func_def_198, type, f: set_Pr1174980151um_a_b).
% 7.63/2.30  thf(func_def_199, type, l: standard_Constant_a).
% 7.63/2.30  thf(func_def_200, type, v: sum_sum_a_b).
% 7.63/2.30  thf(func_def_212, type, sK0: standard_Constant_a > set_Pr1647387645at_nat > product_prod_nat_nat).
% 7.63/2.30  thf(func_def_213, type, sK1: set_nat > nat).
% 7.63/2.30  thf(func_def_214, type, sK2: nat > set_Pr1174980151um_a_b > sum_sum_a_b).
% 7.63/2.30  thf(func_def_215, type, sK3: nat > set_Pr1174980151um_a_b > nat).
% 7.63/2.30  thf(func_def_216, type, sK4: nat > set_Pr1986765409at_nat > nat).
% 7.63/2.30  thf(func_def_217, type, sK5: labele431970251um_a_b > set_Pr409224873um_a_b).
% 7.63/2.30  thf(func_def_218, type, sK6: labele431970251um_a_b > set_Sum_sum_a_b).
% 7.63/2.30  thf(func_def_219, type, sK7: set_Pr1647387645at_nat > produc1032616263at_nat).
% 7.63/2.30  thf(func_def_220, type, sK8: nat > set_Pr1174980151um_a_b > sum_sum_a_b).
% 7.63/2.30  thf(func_def_221, type, sK9: set_Pr1174980151um_a_b > produc1124793815um_a_b).
% 7.63/2.30  thf(func_def_222, type, sK10: (labele935650037_a_nat > $o) > set_nat).
% 7.63/2.30  thf(func_def_223, type, sK11: (labele935650037_a_nat > $o) > set_Pr1647387645at_nat).
% 7.63/2.30  thf(func_def_224, type, sK12: set_Pr1174980151um_a_b > nat > sum_sum_a_b).
% 7.63/2.30  thf(func_def_225, type, sK13: set_Pr1174980151um_a_b > produc1124793815um_a_b).
% 7.63/2.30  thf(func_def_226, type, sK14: set_Pr1174980151um_a_b > produc1124793815um_a_b).
% 7.63/2.30  thf(func_def_227, type, sK15: set_Pr1174980151um_a_b > set_Pr1174980151um_a_b > nat).
% 7.63/2.30  thf(func_def_228, type, sK16: set_Pr1174980151um_a_b > set_Pr1174980151um_a_b > sum_sum_a_b).
% 7.63/2.30  thf(func_def_229, type, sK17: (labele431970251um_a_b > $o) > set_Sum_sum_a_b).
% 7.63/2.30  thf(func_def_230, type, sK18: (labele431970251um_a_b > $o) > set_Pr409224873um_a_b).
% 7.63/2.30  thf(func_def_231, type, sK19: (standard_Constant_a > $o) > set_Pr1647387645at_nat > standard_Constant_a).
% 7.63/2.30  thf(func_def_232, type, sK20: (standard_Constant_a > $o) > set_Pr1647387645at_nat > product_prod_nat_nat).
% 7.63/2.30  thf(func_def_233, type, sK21: set_Pr1647387645at_nat > standard_Constant_a > product_prod_nat_nat).
% 7.63/2.30  thf(func_def_234, type, sK22: set_Pr1986765409at_nat > (nat > $o) > nat).
% 7.63/2.30  thf(func_def_235, type, sK23: set_Pr1986765409at_nat > (nat > $o) > nat).
% 7.63/2.30  thf(func_def_236, type, sK24: set_Pr1986765409at_nat > nat > nat).
% 7.63/2.30  thf(func_def_237, type, sK25: set_Pr1647387645at_nat > produc1032616263at_nat).
% 7.63/2.30  thf(func_def_238, type, sK26: set_Pr1986765409at_nat > nat > nat).
% 7.63/2.30  thf(func_def_239, type, sK27: sum_sum_a_b > set_Pr1174980151um_a_b > set_nat > nat).
% 7.63/2.30  thf(func_def_240, type, sK28: set_Pr1174980151um_a_b > (nat > $o) > sum_sum_a_b).
% 7.63/2.30  thf(func_def_241, type, sK29: set_Pr1174980151um_a_b > (nat > $o) > nat).
% 7.63/2.30  thf(func_def_242, type, sK30: sum_sum_a_b).
% 7.63/2.30  thf(func_def_243, type, sK31: nat > set_Pr1174980151um_a_b > sum_sum_a_b).
% 7.63/2.30  thf(func_def_244, type, sK32: set_Pr1647387645at_nat > produc1032616263at_nat).
% 7.63/2.30  thf(func_def_245, type, sK33: set_Sum_sum_a_b > set_Sum_sum_a_b > sum_sum_a_b).
% 7.63/2.30  thf(func_def_246, type, sK34: set_Pr1986765409at_nat > nat > nat).
% 7.63/2.30  thf(func_def_247, type, sK35: set_Pr1986765409at_nat > nat > nat).
% 7.63/2.30  thf(func_def_248, type, sK36: set_nat > nat).
% 7.63/2.30  thf(func_def_249, type, sK37: standard_Constant_a > set_Pr1647387645at_nat > standard_Constant_a).
% 7.63/2.30  thf(func_def_250, type, sK38: standard_Constant_a > set_Pr1647387645at_nat > product_prod_nat_nat).
% 7.63/2.30  thf(func_def_251, type, sK39: sum_sum_a_b > set_Pr1174980151um_a_b > set_nat > nat).
% 7.63/2.30  thf(func_def_252, type, sK40: set_nat > nat).
% 7.63/2.30  thf(func_def_253, type, sK41: labele935650037_a_nat > set_Pr1647387645at_nat).
% 7.63/2.30  thf(func_def_254, type, sK42: labele935650037_a_nat > set_nat).
% 7.63/2.30  thf(func_def_255, type, sK43: standard_Constant_a > set_Pr1647387645at_nat > product_prod_nat_nat).
% 7.63/2.30  thf(func_def_256, type, sK44: set_Pr1647387645at_nat > set_Pr1647387645at_nat > product_prod_nat_nat).
% 7.63/2.30  thf(func_def_257, type, sK45: set_Pr1647387645at_nat > set_Pr1647387645at_nat > standard_Constant_a).
% 7.63/2.30  thf(func_def_260, type, ph47: !>[X0: $tType]:(X0)).
% 7.63/2.30  thf(f3283,plain,(
% 7.63/2.30    $false),
% 7.63/2.30    inference(avatar_sat_refutation,[status(thm)],[f1491,f3269,f3271,f3274,f3277,f3279,f3282])).
% 7.63/2.30  thf(f3282,plain,(
% 7.63/2.30    spl46_6),
% 7.63/2.30    inference(avatar_contradiction_clause,[status(thm)],[f3281])).
% 7.63/2.30  thf(f3281,plain,(
% 7.63/2.30    $false | spl46_6),
% 7.63/2.30    inference(subsumption_resolution,[status(thm)],[f3280,f1358])).
% 7.63/2.30  thf(f1358,plain,(
% 7.63/2.30    ((edge_p1382426714tant_a @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (labele1939049654um_a_b @ g)) = $true)),
% 7.63/2.30    inference(cnf_transformation,[status(thm)],[f610])).
% 7.63/2.30  thf(f610,plain,(
% 7.63/2.30    ((edge_p1382426714tant_a @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (labele1939049654um_a_b @ g)) = $true)),
% 7.63/2.30    inference(fool_elimination,[status(thm)],[f609])).
% 7.63/2.30  thf(f609,plain,(
% 7.63/2.30    (edge_p1382426714tant_a @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (labele1939049654um_a_b @ g))),
% 7.63/2.30    inference(rectify,[status(thm)],[f3])).
% 7.63/2.30  thf(f3,axiom,(
% 7.63/2.30    (edge_p1382426714tant_a @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (labele1939049654um_a_b @ g))),
% 7.63/2.30    file('/export/starexec/sandbox2/tmp/tmp.XpaU65CC0V/DTF2THF_20438.p',fact_2__092_060open_062edge__preserving_A_123_I0_058_058_063_Hc1_M_Av_J_125_A_123_IS__Idt_M_A0_058_058_063_Hc1_M_A0_058_058_063_Hc1_J_125_A_Iedges_AG_J_092_060close_062)).
% 7.63/2.30  thf(f3280,plain,(
% 7.63/2.30    ((edge_p1382426714tant_a @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (labele1939049654um_a_b @ g)) != $true) | spl46_6),
% 7.63/2.30    inference(forward_demodulation,[status(thm)],[f1490,f1313])).
% 7.63/2.30  thf(f1313,plain,(
% 7.63/2.30    ( ! [X0 : set_nat,X1 : set_Pr1647387645at_nat] : (((labele195203296_a_nat @ (labele16114835_a_nat @ X1 @ X0)) = X1)) )),
% 7.63/2.30    inference(cnf_transformation,[status(thm)],[f943])).
% 7.63/2.30  thf(f943,plain,(
% 7.63/2.30    ! [X0 : set_nat,X1 : set_Pr1647387645at_nat] : ((labele195203296_a_nat @ (labele16114835_a_nat @ X1 @ X0)) = X1)),
% 7.63/2.30    inference(rectify,[status(thm)],[f138])).
% 7.63/2.30  thf(f138,axiom,(
% 7.63/2.30    ! [X10 : set_nat,X9 : set_Pr1647387645at_nat] : ((labele195203296_a_nat @ (labele16114835_a_nat @ X9 @ X10)) = X9)),
% 7.63/2.30    file('/export/starexec/sandbox2/tmp/tmp.XpaU65CC0V/DTF2THF_20438.p',fact_137_labeled__graph_Osel_I1_J)).
% 7.63/2.30  thf(f1490,plain,(
% 7.63/2.30    ((edge_p1382426714tant_a @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (labele195203296_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ (domain1368163076um_a_b @ bot_bo575978147um_a_b)))) @ (labele1939049654um_a_b @ g)) != $true) | spl46_6),
% 7.63/2.30    inference(avatar_component_clause,[status(thm)],[f1489])).
% 7.63/2.30  thf(f1489,definition,(
% 7.63/2.30    spl46_6 <=> ((edge_p1382426714tant_a @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (labele195203296_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ (domain1368163076um_a_b @ bot_bo575978147um_a_b)))) @ (labele1939049654um_a_b @ g)) = $true)),
% 7.63/2.30    introduced(definition,[new_symbols(naming,[spl46_6])],[avatar_definition])).
% 7.63/2.30  thf(f3279,plain,(
% 7.63/2.30    spl46_5),
% 7.63/2.30    inference(avatar_contradiction_clause,[status(thm)],[f3278])).
% 7.63/2.30  thf(f3278,plain,(
% 7.63/2.30    $false | spl46_5),
% 7.63/2.30    inference(subsumption_resolution,[status(thm)],[f1487,f1417])).
% 7.63/2.30  thf(f1417,plain,(
% 7.63/2.30    ((unival2092813468um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b)) = $true)),
% 7.63/2.30    inference(definition_unfolding,[status(thm)],[f1295,f1375])).
% 7.63/2.30  thf(f1375,plain,(
% 7.63/2.30    ((insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) = f)),
% 7.63/2.30    inference(cnf_transformation,[status(thm)],[f5])).
% 7.63/2.30  thf(f5,axiom,(
% 7.63/2.30    ((insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) = f)),
% 7.63/2.30    file('/export/starexec/sandbox2/tmp/tmp.XpaU65CC0V/DTF2THF_20438.p',fact_4_f)).
% 7.63/2.30  thf(f1295,plain,(
% 7.63/2.30    ((unival2092813468um_a_b @ f) = $true)),
% 7.63/2.30    inference(cnf_transformation,[status(thm)],[f862])).
% 7.63/2.30  thf(f862,plain,(
% 7.63/2.30    ((unival2092813468um_a_b @ f) = $true)),
% 7.63/2.30    inference(fool_elimination,[status(thm)],[f861])).
% 7.63/2.30  thf(f861,plain,(
% 7.63/2.30    (unival2092813468um_a_b @ f)),
% 7.63/2.30    inference(rectify,[status(thm)],[f10])).
% 7.63/2.30  thf(f10,axiom,(
% 7.63/2.30    (unival2092813468um_a_b @ f)),
% 7.63/2.30    file('/export/starexec/sandbox2/tmp/tmp.XpaU65CC0V/DTF2THF_20438.p',fact_9_u)).
% 7.63/2.30  thf(f1487,plain,(
% 7.63/2.30    ((unival2092813468um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b)) != $true) | spl46_5),
% 7.63/2.30    inference(avatar_component_clause,[status(thm)],[f1486])).
% 7.63/2.30  thf(f1486,definition,(
% 7.63/2.30    spl46_5 <=> ((unival2092813468um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b)) = $true)),
% 7.63/2.30    introduced(definition,[new_symbols(naming,[spl46_5])],[avatar_definition])).
% 7.63/2.30  thf(f3277,plain,(
% 7.63/2.30    spl46_4),
% 7.63/2.30    inference(avatar_contradiction_clause,[status(thm)],[f3276])).
% 7.63/2.30  thf(f3276,plain,(
% 7.63/2.30    $false | spl46_4),
% 7.63/2.30    inference(subsumption_resolution,[status(thm)],[f3275,f1411])).
% 7.63/2.30  thf(f1411,plain,(
% 7.63/2.30    ($true = (ord_le192794300um_a_b @ (image_256773707um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (insert_nat @ zero_zero_nat @ (domain1368163076um_a_b @ bot_bo575978147um_a_b))) @ (labele577278695um_a_b @ g)))),
% 7.63/2.30    inference(definition_unfolding,[status(thm)],[f1279,f1375,f1232])).
% 7.63/2.30  thf(f1232,plain,(
% 7.63/2.30    (bot_bot_set_nat = (domain1368163076um_a_b @ bot_bo575978147um_a_b))),
% 7.63/2.30    inference(cnf_transformation,[status(thm)],[f32])).
% 7.63/2.30  thf(f32,axiom,(
% 7.63/2.30    (bot_bot_set_nat = (domain1368163076um_a_b @ bot_bo575978147um_a_b))),
% 7.63/2.30    file('/export/starexec/sandbox2/tmp/tmp.XpaU65CC0V/DTF2THF_20438.p',fact_31_Domain__empty)).
% 7.63/2.30  thf(f1279,plain,(
% 7.63/2.30    ((ord_le192794300um_a_b @ (image_256773707um_a_b @ f @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)) @ (labele577278695um_a_b @ g)) = $true)),
% 7.63/2.30    inference(cnf_transformation,[status(thm)],[f526])).
% 7.63/2.30  thf(f526,plain,(
% 7.63/2.30    ((ord_le192794300um_a_b @ (image_256773707um_a_b @ f @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)) @ (labele577278695um_a_b @ g)) = $true)),
% 7.63/2.30    inference(fool_elimination,[status(thm)],[f525])).
% 7.63/2.30  thf(f525,plain,(
% 7.63/2.30    (ord_le192794300um_a_b @ (image_256773707um_a_b @ f @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)) @ (labele577278695um_a_b @ g))),
% 7.63/2.30    inference(rectify,[status(thm)],[f4])).
% 7.63/2.30  thf(f4,axiom,(
% 7.63/2.30    (ord_le192794300um_a_b @ (image_256773707um_a_b @ f @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)) @ (labele577278695um_a_b @ g))),
% 7.63/2.30    file('/export/starexec/sandbox2/tmp/tmp.XpaU65CC0V/DTF2THF_20438.p',fact_3_r)).
% 7.63/2.30  thf(f3275,plain,(
% 7.63/2.30    ($true != (ord_le192794300um_a_b @ (image_256773707um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (insert_nat @ zero_zero_nat @ (domain1368163076um_a_b @ bot_bo575978147um_a_b))) @ (labele577278695um_a_b @ g))) | spl46_4),
% 7.63/2.30    inference(forward_demodulation,[status(thm)],[f1484,f1398])).
% 7.63/2.30  thf(f1398,plain,(
% 7.63/2.30    ( ! [X0 : set_nat,X1 : set_Pr1647387645at_nat] : (((labele1810595089_a_nat @ (labele16114835_a_nat @ X1 @ X0)) = X0)) )),
% 7.63/2.30    inference(cnf_transformation,[status(thm)],[f944])).
% 7.63/2.30  thf(f944,plain,(
% 7.63/2.30    ! [X0 : set_nat,X1 : set_Pr1647387645at_nat] : ((labele1810595089_a_nat @ (labele16114835_a_nat @ X1 @ X0)) = X0)),
% 7.63/2.30    inference(rectify,[status(thm)],[f136])).
% 7.63/2.30  thf(f136,axiom,(
% 7.63/2.30    ! [X10 : set_nat,X9 : set_Pr1647387645at_nat] : ((labele1810595089_a_nat @ (labele16114835_a_nat @ X9 @ X10)) = X10)),
% 7.63/2.30    file('/export/starexec/sandbox2/tmp/tmp.XpaU65CC0V/DTF2THF_20438.p',fact_135_labeled__graph_Osel_I2_J)).
% 7.63/2.30  thf(f1484,plain,(
% 7.63/2.30    ((ord_le192794300um_a_b @ (image_256773707um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (labele1810595089_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ (domain1368163076um_a_b @ bot_bo575978147um_a_b))))) @ (labele577278695um_a_b @ g)) != $true) | spl46_4),
% 7.63/2.30    inference(avatar_component_clause,[status(thm)],[f1483])).
% 7.63/2.30  thf(f1483,definition,(
% 7.63/2.30    spl46_4 <=> ((ord_le192794300um_a_b @ (image_256773707um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (labele1810595089_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ (domain1368163076um_a_b @ bot_bo575978147um_a_b))))) @ (labele577278695um_a_b @ g)) = $true)),
% 7.63/2.30    introduced(definition,[new_symbols(naming,[spl46_4])],[avatar_definition])).
% 7.63/2.30  thf(f3274,plain,(
% 7.63/2.30    spl46_3),
% 7.63/2.30    inference(avatar_contradiction_clause,[status(thm)],[f3273])).
% 7.63/2.30  thf(f3273,plain,(
% 7.63/2.30    $false | spl46_3),
% 7.63/2.30    inference(subsumption_resolution,[status(thm)],[f3272,f1343])).
% 7.63/2.30  thf(f1343,plain,(
% 7.63/2.30    ( ! [X2 : sum_sum_a_b,X0 : set_Pr1174980151um_a_b,X1 : nat] : (((insert_nat @ X1 @ (domain1368163076um_a_b @ X0)) = (domain1368163076um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ X1 @ X2) @ X0)))) )),
% 7.63/2.30    inference(cnf_transformation,[status(thm)],[f964])).
% 7.63/2.30  thf(f964,plain,(
% 7.63/2.30    ! [X0 : set_Pr1174980151um_a_b,X1 : nat,X2 : sum_sum_a_b] : ((insert_nat @ X1 @ (domain1368163076um_a_b @ X0)) = (domain1368163076um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ X1 @ X2) @ X0)))),
% 7.63/2.30    inference(rectify,[status(thm)],[f13])).
% 7.63/2.30  thf(f13,axiom,(
% 7.63/2.30    ! [X4 : set_Pr1174980151um_a_b,X0 : nat,X1 : sum_sum_a_b] : ((domain1368163076um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ X0 @ X1) @ X4)) = (insert_nat @ X0 @ (domain1368163076um_a_b @ X4)))),
% 7.63/2.30    file('/export/starexec/sandbox2/tmp/tmp.XpaU65CC0V/DTF2THF_20438.p',fact_12_Domain__insert)).
% 7.63/2.30  thf(f3272,plain,(
% 7.63/2.30    ((domain1368163076um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b)) != (insert_nat @ zero_zero_nat @ (domain1368163076um_a_b @ bot_bo575978147um_a_b))) | spl46_3),
% 7.63/2.30    inference(forward_demodulation,[status(thm)],[f1481,f1398])).
% 7.63/2.30  thf(f1481,plain,(
% 7.63/2.30    ((domain1368163076um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b)) != (labele1810595089_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ (domain1368163076um_a_b @ bot_bo575978147um_a_b))))) | spl46_3),
% 7.63/2.30    inference(avatar_component_clause,[status(thm)],[f1480])).
% 7.63/2.30  thf(f1480,definition,(
% 7.63/2.30    spl46_3 <=> ((domain1368163076um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b)) = (labele1810595089_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ (domain1368163076um_a_b @ bot_bo575978147um_a_b)))))),
% 7.63/2.30    introduced(definition,[new_symbols(naming,[spl46_3])],[avatar_definition])).
% 7.63/2.30  thf(f3271,plain,(
% 7.63/2.30    spl46_2),
% 7.63/2.30    inference(avatar_contradiction_clause,[status(thm)],[f3270])).
% 7.63/2.30  thf(f3270,plain,(
% 7.63/2.30    $false | spl46_2),
% 7.63/2.30    inference(subsumption_resolution,[status(thm)],[f1478,f1208])).
% 7.63/2.30  thf(f1208,plain,(
% 7.63/2.30    (g = (restri1162247455um_a_b @ g))),
% 7.63/2.30    inference(cnf_transformation,[status(thm)],[f1])).
% 7.63/2.30  thf(f1,axiom,(
% 7.63/2.30    (g = (restri1162247455um_a_b @ g))),
% 7.63/2.30    file('/export/starexec/sandbox2/tmp/tmp.XpaU65CC0V/DTF2THF_20438.p',fact_0_g)).
% 7.63/2.30  thf(f1478,plain,(
% 7.63/2.30    (g != (restri1162247455um_a_b @ g)) | spl46_2),
% 7.63/2.30    inference(avatar_component_clause,[status(thm)],[f1477])).
% 7.63/2.30  thf(f1477,definition,(
% 7.63/2.30    spl46_2 <=> (g = (restri1162247455um_a_b @ g))),
% 7.63/2.30    introduced(definition,[new_symbols(naming,[spl46_2])],[avatar_definition])).
% 7.63/2.30  thf(f3269,plain,(
% 7.63/2.30    spl46_1),
% 7.63/2.30    inference(avatar_contradiction_clause,[status(thm)],[f3268])).
% 7.63/2.30  thf(f3268,plain,(
% 7.63/2.30    $false | spl46_1),
% 7.63/2.30    inference(equality_resolution,[status(thm)],[f3228])).
% 7.63/2.30  thf(f3228,plain,(
% 7.63/2.30    ( ! [X0 : nat] : (((insert_nat @ X0 @ (domain1368163076um_a_b @ bot_bo575978147um_a_b)) != (insert_nat @ zero_zero_nat @ (domain1368163076um_a_b @ bot_bo575978147um_a_b)))) ) | spl46_1),
% 7.63/2.30    inference(trivial_inequality_removal,[status(thm)],[f3227])).
% 7.63/2.30  thf(f3227,plain,(
% 7.63/2.30    ( ! [X0 : nat] : (($true != $true) | ((insert_nat @ X0 @ (domain1368163076um_a_b @ bot_bo575978147um_a_b)) != (insert_nat @ zero_zero_nat @ (domain1368163076um_a_b @ bot_bo575978147um_a_b)))) ) | spl46_1),
% 7.63/2.30    inference(superposition,[status(thm)],[f3184,f1402])).
% 7.63/2.30  thf(f1402,plain,(
% 7.63/2.30    ( ! [X2 : nat,X0 : nat,X1 : set_nat] : (($true = (ord_less_eq_set_nat @ X1 @ (insert_nat @ X2 @ (domain1368163076um_a_b @ bot_bo575978147um_a_b)))) | ((insert_nat @ X0 @ X1) != (insert_nat @ X2 @ (domain1368163076um_a_b @ bot_bo575978147um_a_b)))) )),
% 7.63/2.30    inference(definition_unfolding,[status(thm)],[f1195,f1232,f1232])).
% 7.63/2.30  thf(f1195,plain,(
% 7.63/2.30    ( ! [X2 : nat,X0 : nat,X1 : set_nat] : (($true = (ord_less_eq_set_nat @ X1 @ (insert_nat @ X2 @ bot_bot_set_nat))) | ((insert_nat @ X2 @ bot_bot_set_nat) != (insert_nat @ X0 @ X1))) )),
% 7.63/2.30    inference(cnf_transformation,[status(thm)],[f1052])).
% 7.63/2.30  thf(f1052,plain,(
% 7.63/2.30    ! [X0 : nat,X1 : set_nat,X2 : nat] : ((((insert_nat @ X2 @ bot_bot_set_nat) = (insert_nat @ X0 @ X1)) | (X0 != X2) | ($true != (ord_less_eq_set_nat @ X1 @ (insert_nat @ X2 @ bot_bot_set_nat)))) & (((X0 = X2) & ($true = (ord_less_eq_set_nat @ X1 @ (insert_nat @ X2 @ bot_bot_set_nat)))) | ((insert_nat @ X2 @ bot_bot_set_nat) != (insert_nat @ X0 @ X1))))),
% 7.63/2.30    inference(flattening,[status(thm)],[f1051])).
% 7.63/2.30  thf(f1051,plain,(
% 7.63/2.30    ! [X0 : nat,X1 : set_nat,X2 : nat] : ((((insert_nat @ X2 @ bot_bot_set_nat) = (insert_nat @ X0 @ X1)) | ((X0 != X2) | ($true != (ord_less_eq_set_nat @ X1 @ (insert_nat @ X2 @ bot_bot_set_nat))))) & (((X0 = X2) & ($true = (ord_less_eq_set_nat @ X1 @ (insert_nat @ X2 @ bot_bot_set_nat)))) | ((insert_nat @ X2 @ bot_bot_set_nat) != (insert_nat @ X0 @ X1))))),
% 7.63/2.30    inference(nnf_transformation,[status(thm)],[f357])).
% 7.63/2.30  thf(f357,plain,(
% 7.63/2.30    ! [X0 : nat,X1 : set_nat,X2 : nat] : (((insert_nat @ X2 @ bot_bot_set_nat) = (insert_nat @ X0 @ X1)) <=> ((X0 = X2) & ($true = (ord_less_eq_set_nat @ X1 @ (insert_nat @ X2 @ bot_bot_set_nat)))))),
% 7.63/2.30    inference(fool_elimination,[status(thm)],[f356])).
% 7.63/2.30  thf(f356,plain,(
% 7.63/2.30    ! [X0 : nat,X1 : set_nat,X2 : nat] : (((insert_nat @ X2 @ bot_bot_set_nat) = (insert_nat @ X0 @ X1)) = (ord_less_eq_set_nat @ X1 @ (insert_nat @ X2 @ bot_bot_set_nat)) & (X0 = X2))),
% 7.63/2.30    inference(rectify,[status(thm)],[f154])).
% 7.63/2.30  thf(f154,axiom,(
% 7.63/2.30    ! [X0 : nat,X15 : set_nat,X1 : nat] : (((insert_nat @ X0 @ X15) = (insert_nat @ X1 @ bot_bot_set_nat)) = (ord_less_eq_set_nat @ X15 @ (insert_nat @ X1 @ bot_bot_set_nat)) & (X0 = X1))),
% 7.63/2.30    file('/export/starexec/sandbox2/tmp/tmp.XpaU65CC0V/DTF2THF_20438.p',fact_153_singleton__insert__inj__eq_H)).
% 7.63/2.30  thf(f3184,plain,(
% 7.63/2.30    ((ord_less_eq_set_nat @ (domain1368163076um_a_b @ bot_bo575978147um_a_b) @ (insert_nat @ zero_zero_nat @ (domain1368163076um_a_b @ bot_bo575978147um_a_b))) != $true) | spl46_1),
% 7.63/2.30    inference(subsumption_resolution,[status(thm)],[f3182,f1448])).
% 7.63/2.30  thf(f1448,plain,(
% 7.63/2.30    ( ! [X2 : set_nat,X1 : nat] : (((member_nat @ X1 @ (insert_nat @ X1 @ X2)) = $true)) )),
% 7.63/2.30    inference(equality_resolution,[status(thm)],[f1300])).
% 7.63/2.30  thf(f1300,plain,(
% 7.63/2.30    ( ! [X2 : set_nat,X0 : nat,X1 : nat] : (($true = (member_nat @ X1 @ (insert_nat @ X0 @ X2))) | (X0 != X1)) )),
% 7.63/2.30    inference(cnf_transformation,[status(thm)],[f1114])).
% 7.63/2.30  thf(f1114,plain,(
% 7.63/2.30    ! [X0 : nat,X1 : nat,X2 : set_nat] : ((($true = (member_nat @ X1 @ (insert_nat @ X0 @ X2))) | ((X0 != X1) & ($true != (member_nat @ X1 @ X2)))) & ((X0 = X1) | ($true = (member_nat @ X1 @ X2)) | ($true != (member_nat @ X1 @ (insert_nat @ X0 @ X2)))))),
% 7.63/2.30    inference(flattening,[status(thm)],[f1113])).
% 7.63/2.30  thf(f1113,plain,(
% 7.63/2.30    ! [X0 : nat,X1 : nat,X2 : set_nat] : ((($true = (member_nat @ X1 @ (insert_nat @ X0 @ X2))) | ((X0 != X1) & ($true != (member_nat @ X1 @ X2)))) & (((X0 = X1) | ($true = (member_nat @ X1 @ X2))) | ($true != (member_nat @ X1 @ (insert_nat @ X0 @ X2)))))),
% 7.63/2.30    inference(nnf_transformation,[status(thm)],[f814])).
% 7.63/2.30  thf(f814,plain,(
% 7.63/2.30    ! [X0 : nat,X1 : nat,X2 : set_nat] : (($true = (member_nat @ X1 @ (insert_nat @ X0 @ X2))) <=> ((X0 = X1) | ($true = (member_nat @ X1 @ X2))))),
% 7.63/2.30    inference(fool_elimination,[status(thm)],[f813])).
% 7.63/2.30  thf(f813,plain,(
% 7.63/2.30    ! [X0 : nat,X1 : nat,X2 : set_nat] : ((member_nat @ X1 @ (insert_nat @ X0 @ X2)) = (X0 = X1) | (member_nat @ X1 @ X2))),
% 7.63/2.30    inference(rectify,[status(thm)],[f245])).
% 7.63/2.30  thf(f245,axiom,(
% 7.63/2.30    ! [X1 : nat,X0 : nat,X15 : set_nat] : ((member_nat @ X0 @ (insert_nat @ X1 @ X15)) = (X0 = X1) | (member_nat @ X0 @ X15))),
% 7.63/2.30    file('/export/starexec/sandbox2/tmp/tmp.XpaU65CC0V/DTF2THF_20438.p',fact_244_insert__iff)).
% 7.63/2.30  thf(f3182,plain,(
% 7.63/2.30    ((member_nat @ zero_zero_nat @ (insert_nat @ zero_zero_nat @ (domain1368163076um_a_b @ bot_bo575978147um_a_b))) != $true) | ((ord_less_eq_set_nat @ (domain1368163076um_a_b @ bot_bo575978147um_a_b) @ (insert_nat @ zero_zero_nat @ (domain1368163076um_a_b @ bot_bo575978147um_a_b))) != $true) | spl46_1),
% 7.63/2.30    inference(trivial_inequality_removal,[status(thm)],[f3180])).
% 7.63/2.30  thf(f3180,plain,(
% 7.63/2.30    ((member_nat @ zero_zero_nat @ (insert_nat @ zero_zero_nat @ (domain1368163076um_a_b @ bot_bo575978147um_a_b))) != $true) | ($true != $true) | ((ord_less_eq_set_nat @ (domain1368163076um_a_b @ bot_bo575978147um_a_b) @ (insert_nat @ zero_zero_nat @ (domain1368163076um_a_b @ bot_bo575978147um_a_b))) != $true) | spl46_1),
% 7.63/2.30    inference(superposition,[status(thm)],[f3166,f1330])).
% 7.63/2.30  thf(f1330,plain,(
% 7.63/2.30    ( ! [X2 : set_nat,X0 : nat,X1 : set_nat] : (($true = (ord_less_eq_set_nat @ (insert_nat @ X0 @ X2) @ X1)) | ($true != (member_nat @ X0 @ X1)) | ($true != (ord_less_eq_set_nat @ X2 @ X1))) )),
% 7.63/2.30    inference(cnf_transformation,[status(thm)],[f1136])).
% 7.63/2.30  thf(f1136,plain,(
% 7.63/2.30    ! [X0 : nat,X1 : set_nat,X2 : set_nat] : ((($true = (ord_less_eq_set_nat @ (insert_nat @ X0 @ X2) @ X1)) | ($true != (member_nat @ X0 @ X1)) | ($true != (ord_less_eq_set_nat @ X2 @ X1))) & ((($true = (member_nat @ X0 @ X1)) & ($true = (ord_less_eq_set_nat @ X2 @ X1))) | ($true != (ord_less_eq_set_nat @ (insert_nat @ X0 @ X2) @ X1))))),
% 7.63/2.30    inference(flattening,[status(thm)],[f1135])).
% 7.63/2.30  thf(f1135,plain,(
% 7.63/2.30    ! [X0 : nat,X1 : set_nat,X2 : set_nat] : ((($true = (ord_less_eq_set_nat @ (insert_nat @ X0 @ X2) @ X1)) | (($true != (member_nat @ X0 @ X1)) | ($true != (ord_less_eq_set_nat @ X2 @ X1)))) & ((($true = (member_nat @ X0 @ X1)) & ($true = (ord_less_eq_set_nat @ X2 @ X1))) | ($true != (ord_less_eq_set_nat @ (insert_nat @ X0 @ X2) @ X1))))),
% 7.63/2.30    inference(nnf_transformation,[status(thm)],[f630])).
% 7.63/2.30  thf(f630,plain,(
% 7.63/2.30    ! [X0 : nat,X1 : set_nat,X2 : set_nat] : (($true = (ord_less_eq_set_nat @ (insert_nat @ X0 @ X2) @ X1)) <=> (($true = (member_nat @ X0 @ X1)) & ($true = (ord_less_eq_set_nat @ X2 @ X1))))),
% 7.63/2.30    inference(fool_elimination,[status(thm)],[f629])).
% 7.63/2.30  thf(f629,plain,(
% 7.63/2.30    ! [X0 : nat,X1 : set_nat,X2 : set_nat] : ((ord_less_eq_set_nat @ (insert_nat @ X0 @ X2) @ X1) = (member_nat @ X0 @ X1) & (ord_less_eq_set_nat @ X2 @ X1))),
% 7.63/2.30    inference(rectify,[status(thm)],[f178])).
% 7.63/2.30  thf(f178,axiom,(
% 7.63/2.30    ! [X8 : nat,X43 : set_nat,X15 : set_nat] : ((ord_less_eq_set_nat @ (insert_nat @ X8 @ X15) @ X43) = (member_nat @ X8 @ X43) & (ord_less_eq_set_nat @ X15 @ X43))),
% 7.63/2.30    file('/export/starexec/sandbox2/tmp/tmp.XpaU65CC0V/DTF2THF_20438.p',fact_177_insert__subset)).
% 7.63/2.30  thf(f3166,plain,(
% 7.63/2.30    ($true != (ord_less_eq_set_nat @ (insert_nat @ zero_zero_nat @ (domain1368163076um_a_b @ bot_bo575978147um_a_b)) @ (insert_nat @ zero_zero_nat @ (domain1368163076um_a_b @ bot_bo575978147um_a_b)))) | spl46_1),
% 7.63/2.30    inference(trivial_inequality_removal,[status(thm)],[f3159])).
% 7.63/2.30  thf(f3159,plain,(
% 7.63/2.30    ($true != (ord_less_eq_set_nat @ (insert_nat @ zero_zero_nat @ (domain1368163076um_a_b @ bot_bo575978147um_a_b)) @ (insert_nat @ zero_zero_nat @ (domain1368163076um_a_b @ bot_bo575978147um_a_b)))) | ((labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ (insert_nat @ zero_zero_nat @ (domain1368163076um_a_b @ bot_bo575978147um_a_b)))) != (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ (insert_nat @ zero_zero_nat @ (domain1368163076um_a_b @ bot_bo575978147um_a_b))))) | spl46_1),
% 7.63/2.30    inference(superposition,[status(thm)],[f2700,f1424])).
% 7.63/2.30  thf(f1424,plain,(
% 7.63/2.30    ( ! [X2 : standard_Constant_a,X0 : nat,X1 : nat] : (((labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ X2 @ (product_Pair_nat_nat @ X0 @ X1)) @ bot_bo810816657at_nat) @ (insert_nat @ X0 @ (insert_nat @ X1 @ (domain1368163076um_a_b @ bot_bo575978147um_a_b)))) = (restri572569417_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ X2 @ (product_Pair_nat_nat @ X0 @ X1)) @ bot_bo810816657at_nat) @ (insert_nat @ X0 @ (insert_nat @ X1 @ (domain1368163076um_a_b @ bot_bo575978147um_a_b))))))) )),
% 7.63/2.30    inference(definition_unfolding,[status(thm)],[f1354,f1232,f1232])).
% 7.63/2.30  thf(f1354,plain,(
% 7.63/2.30    ( ! [X2 : standard_Constant_a,X0 : nat,X1 : nat] : (((labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ X2 @ (product_Pair_nat_nat @ X0 @ X1)) @ bot_bo810816657at_nat) @ (insert_nat @ X0 @ (insert_nat @ X1 @ bot_bot_set_nat))) = (restri572569417_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ X2 @ (product_Pair_nat_nat @ X0 @ X1)) @ bot_bo810816657at_nat) @ (insert_nat @ X0 @ (insert_nat @ X1 @ bot_bot_set_nat)))))) )),
% 7.63/2.30    inference(cnf_transformation,[status(thm)],[f937])).
% 7.63/2.30  thf(f937,plain,(
% 7.63/2.30    ! [X0 : nat,X1 : nat,X2 : standard_Constant_a] : ((labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ X2 @ (product_Pair_nat_nat @ X0 @ X1)) @ bot_bo810816657at_nat) @ (insert_nat @ X0 @ (insert_nat @ X1 @ bot_bot_set_nat))) = (restri572569417_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ X2 @ (product_Pair_nat_nat @ X0 @ X1)) @ bot_bo810816657at_nat) @ (insert_nat @ X0 @ (insert_nat @ X1 @ bot_bot_set_nat)))))),
% 7.63/2.30    inference(rectify,[status(thm)],[f8])).
% 7.63/2.30  thf(f8,axiom,(
% 7.63/2.30    ! [X1 : nat,X2 : nat,X0 : standard_Constant_a] : ((labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ X0 @ (product_Pair_nat_nat @ X1 @ X2)) @ bot_bo810816657at_nat) @ (insert_nat @ X1 @ (insert_nat @ X2 @ bot_bot_set_nat))) = (restri572569417_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ X0 @ (product_Pair_nat_nat @ X1 @ X2)) @ bot_bo810816657at_nat) @ (insert_nat @ X1 @ (insert_nat @ X2 @ bot_bot_set_nat)))))),
% 7.63/2.30    file('/export/starexec/sandbox2/tmp/tmp.XpaU65CC0V/DTF2THF_20438.p',fact_7_graph__single)).
% 7.63/2.30  thf(f2700,plain,(
% 7.63/2.30    ( ! [X0 : set_nat] : (((restri572569417_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ X0))) != (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ X0))) | ($true != (ord_less_eq_set_nat @ X0 @ (insert_nat @ zero_zero_nat @ (domain1368163076um_a_b @ bot_bo575978147um_a_b))))) ) | spl46_1),
% 7.63/2.30    inference(superposition,[status(thm)],[f1475,f1428])).
% 7.63/2.30  thf(f1428,plain,(
% 7.63/2.30    ( ! [X2 : nat,X1 : set_nat] : (((insert_nat @ X2 @ (domain1368163076um_a_b @ bot_bo575978147um_a_b)) = (insert_nat @ X2 @ X1)) | ($true != (ord_less_eq_set_nat @ X1 @ (insert_nat @ X2 @ (domain1368163076um_a_b @ bot_bo575978147um_a_b))))) )),
% 7.63/2.30    inference(equality_resolution,[status(thm)],[f1400])).
% 7.63/2.30  thf(f1400,plain,(
% 7.63/2.30    ( ! [X2 : nat,X0 : nat,X1 : set_nat] : (((insert_nat @ X0 @ X1) = (insert_nat @ X2 @ (domain1368163076um_a_b @ bot_bo575978147um_a_b))) | (X0 != X2) | ($true != (ord_less_eq_set_nat @ X1 @ (insert_nat @ X2 @ (domain1368163076um_a_b @ bot_bo575978147um_a_b))))) )),
% 7.63/2.30    inference(definition_unfolding,[status(thm)],[f1197,f1232,f1232])).
% 7.63/2.30  thf(f1197,plain,(
% 7.63/2.30    ( ! [X2 : nat,X0 : nat,X1 : set_nat] : (((insert_nat @ X2 @ bot_bot_set_nat) = (insert_nat @ X0 @ X1)) | (X0 != X2) | ($true != (ord_less_eq_set_nat @ X1 @ (insert_nat @ X2 @ bot_bot_set_nat)))) )),
% 7.63/2.30    inference(cnf_transformation,[status(thm)],[f1052])).
% 7.63/2.30  thf(f1475,plain,(
% 7.63/2.30    ((restri572569417_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ (domain1368163076um_a_b @ bot_bo575978147um_a_b)))) != (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ (domain1368163076um_a_b @ bot_bo575978147um_a_b)))) | spl46_1),
% 7.63/2.30    inference(avatar_component_clause,[status(thm)],[f1474])).
% 7.63/2.30  thf(f1474,definition,(
% 7.63/2.30    spl46_1 <=> ((restri572569417_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ (domain1368163076um_a_b @ bot_bo575978147um_a_b)))) = (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ (domain1368163076um_a_b @ bot_bo575978147um_a_b))))),
% 7.63/2.30    introduced(definition,[new_symbols(naming,[spl46_1])],[avatar_definition])).
% 7.63/2.30  thf(f1491,plain,(
% 7.63/2.30    ~spl46_1 | ~spl46_2 | ~spl46_3 | ~spl46_4 | ~spl46_5 | ~spl46_6),
% 7.63/2.30    inference(avatar_split_clause,[status(thm)],[f1409,f1489,f1486,f1483,f1480,f1477,f1474])).
% 7.63/2.30  thf(f1409,plain,(
% 7.63/2.30    ((unival2092813468um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b)) != $true) | (g != (restri1162247455um_a_b @ g)) | ((ord_le192794300um_a_b @ (image_256773707um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (labele1810595089_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ (domain1368163076um_a_b @ bot_bo575978147um_a_b))))) @ (labele577278695um_a_b @ g)) != $true) | ((restri572569417_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ (domain1368163076um_a_b @ bot_bo575978147um_a_b)))) != (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ (domain1368163076um_a_b @ bot_bo575978147um_a_b)))) | ((edge_p1382426714tant_a @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (labele195203296_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ (domain1368163076um_a_b @ bot_bo575978147um_a_b)))) @ (labele1939049654um_a_b @ g)) != $true) | ((domain1368163076um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b)) != (labele1810595089_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ (domain1368163076um_a_b @ bot_bo575978147um_a_b)))))),
% 7.63/2.30    inference(definition_unfolding,[status(thm)],[f1265,f1232,f1232,f1232,f1232,f1232])).
% 7.63/2.30  thf(f1265,plain,(
% 7.63/2.30    ((labele1810595089_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))) != (domain1368163076um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b))) | ((labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)) != (restri572569417_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)))) | ((ord_le192794300um_a_b @ (image_256773707um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (labele1810595089_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)))) @ (labele577278695um_a_b @ g)) != $true) | (g != (restri1162247455um_a_b @ g)) | ((edge_p1382426714tant_a @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (labele195203296_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))) @ (labele1939049654um_a_b @ g)) != $true) | ((unival2092813468um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b)) != $true)),
% 7.63/2.30    inference(cnf_transformation,[status(thm)],[f1025])).
% 7.63/2.30  thf(f1025,plain,(
% 7.63/2.30    ((labele1810595089_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))) != (domain1368163076um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b))) | ((labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)) != (restri572569417_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)))) | ((ord_le192794300um_a_b @ (image_256773707um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (labele1810595089_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)))) @ (labele577278695um_a_b @ g)) != $true) | (g != (restri1162247455um_a_b @ g)) | ((edge_p1382426714tant_a @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (labele195203296_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))) @ (labele1939049654um_a_b @ g)) != $true) | ((unival2092813468um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b)) != $true)),
% 7.63/2.30    inference(ennf_transformation,[status(thm)],[f666])).
% 7.63/2.30  thf(f666,plain,(
% 7.63/2.30    ~(((unival2092813468um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b)) = $true) & (g = (restri1162247455um_a_b @ g)) & ((edge_p1382426714tant_a @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (labele195203296_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))) @ (labele1939049654um_a_b @ g)) = $true) & ((labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)) = (restri572569417_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)))) & ((ord_le192794300um_a_b @ (image_256773707um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (labele1810595089_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)))) @ (labele577278695um_a_b @ g)) = $true) & ((labele1810595089_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))) = (domain1368163076um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b))))),
% 7.63/2.30    inference(fool_elimination,[status(thm)],[f665])).
% 7.63/2.30  thf(f665,plain,(
% 7.63/2.30    ~(((labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)) = (restri572569417_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)))) & (g = (restri1162247455um_a_b @ g)) & ((labele1810595089_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))) = (domain1368163076um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b))) & (unival2092813468um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b)) & (ord_le192794300um_a_b @ (image_256773707um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (labele1810595089_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)))) @ (labele577278695um_a_b @ g)) & (edge_p1382426714tant_a @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (labele195203296_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))) @ (labele1939049654um_a_b @ g)))),
% 7.63/2.30    inference(rectify,[status(thm)],[f354])).
% 7.63/2.30  thf(f354,negated_conjecture,(
% 7.63/2.30    ~(((labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)) = (restri572569417_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)))) & (g = (restri1162247455um_a_b @ g)) & ((labele1810595089_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))) = (domain1368163076um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b))) & (unival2092813468um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b)) & (ord_le192794300um_a_b @ (image_256773707um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (labele1810595089_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)))) @ (labele577278695um_a_b @ g)) & (edge_p1382426714tant_a @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (labele195203296_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))) @ (labele1939049654um_a_b @ g)))),
% 7.63/2.30    inference(negated_conjecture,[status(cth)],[f353])).
% 7.63/2.30  thf(f353,conjecture,(
% 7.63/2.30    ((labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)) = (restri572569417_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)))) & (g = (restri1162247455um_a_b @ g)) & ((labele1810595089_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))) = (domain1368163076um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b))) & (unival2092813468um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b)) & (ord_le192794300um_a_b @ (image_256773707um_a_b @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (labele1810595089_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat)))) @ (labele577278695um_a_b @ g)) & (edge_p1382426714tant_a @ (insert983991207um_a_b @ (produc1808556047um_a_b @ zero_zero_nat @ v) @ bot_bo575978147um_a_b) @ (labele195203296_a_nat @ (labele16114835_a_nat @ (insert1625259895at_nat @ (produc407553657at_nat @ standard_S_Idt_a @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)) @ bot_bo810816657at_nat) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))) @ (labele1939049654um_a_b @ g))),
% 7.63/2.30    file('/export/starexec/sandbox2/tmp/tmp.XpaU65CC0V/DTF2THF_20438.p',conj_0)).
% 7.63/2.30  % SZS output end Proof for DTF2THF_20438
% 7.63/2.30  % (20586)------------------------------
% 7.63/2.30  % (20586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.63/2.30  % (20586)Termination reason: Refutation
% 7.63/2.30  
% 7.63/2.30  % (20586)Memory used [KB]: 8187
% 7.63/2.30  % (20586)Time elapsed: 0.338 s
% 7.63/2.30  % (20586)Instructions burned: 987 (million)
% 7.63/2.30  % (20586)------------------------------
% 7.63/2.30  % (20586)------------------------------
% 7.63/2.30  % (20537)Success in time 0.718 s
%------------------------------------------------------------------------------