%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP083^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n024.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 08:55:24 AM UTC 2026
% Result : Theorem 2.23s 1.24s
% Output : Refutation 2.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 70 ( 20 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 210 ( 19 ~; 3 |; 0 &; 184 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 53 ( 52 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 146 ( 143 usr; 13 con; 0-8 aty)
% Number of variables : 23 ( 0 ^; 21 !; 2 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
set_Pr1311924359et_val: $tType ).
thf(type_def_7,type,
set_Pr699757092de_val: $tType ).
thf(type_def_8,type,
set_Pr701036849de_val: $tType ).
thf(type_def_9,type,
set_Pr978022247et_val: $tType ).
thf(type_def_10,type,
set_Pr2105655784l_node: $tType ).
thf(type_def_11,type,
set_Pr700443783al_val: $tType ).
thf(type_def_12,type,
set_set_val: $tType ).
thf(type_def_13,type,
set_node: $tType ).
thf(type_def_14,type,
set_val: $tType ).
thf(type_def_15,type,
g: $tType ).
thf(type_def_16,type,
node: $tType ).
thf(type_def_17,type,
list_P561207620_edgeD: $tType ).
thf(type_def_18,type,
list_node: $tType ).
thf(type_def_19,type,
produc1432036078de_val: $tType ).
thf(type_def_20,type,
option_list_val: $tType ).
thf(type_def_21,type,
option_set_val: $tType ).
thf(type_def_22,type,
list_P88441325et_val: $tType ).
thf(type_def_23,type,
set_Pr1587248327et_val: $tType ).
thf(type_def_24,type,
list_P729276995de_val: $tType ).
thf(type_def_25,type,
set_Pr819703837de_val: $tType ).
thf(type_def_26,type,
list_P2089461677et_val: $tType ).
thf(type_def_27,type,
list_P1414038306l_node: $tType ).
thf(type_def_28,type,
set_Pr574789832l_node: $tType ).
thf(type_def_29,type,
list_P940784845al_val: $tType ).
thf(type_def_30,type,
set_Pr1157324199al_val: $tType ).
thf(type_def_31,type,
list_P1108777338de_val: $tType ).
thf(type_def_32,type,
set_Pr1245322836de_val: $tType ).
thf(type_def_33,type,
list_P12184414et_val: $tType ).
thf(type_def_34,type,
set_Pr1320419588et_val: $tType ).
thf(type_def_35,type,
list_P1127016369e_node: $tType ).
thf(type_def_36,type,
set_Pr9085835e_node: $tType ).
thf(type_def_37,type,
list_P1820443774de_val: $tType ).
thf(type_def_38,type,
list_P844977291de_val: $tType ).
thf(type_def_39,type,
list_P761482893et_val: $tType ).
thf(type_def_40,type,
list_P1078858818l_node: $tType ).
thf(type_def_41,type,
list_P1811375021al_val: $tType ).
thf(type_def_42,type,
list_set_val: $tType ).
thf(type_def_43,type,
list_val: $tType ).
thf(type_def_44,type,
val: $tType ).
thf(type_def_45,type,
produc1324971431et_val: $tType ).
thf(type_def_46,type,
produc1904584935et_val: $tType ).
thf(type_def_47,type,
produc452075965de_val: $tType ).
thf(type_def_48,type,
produc1013974930l_node: $tType ).
thf(type_def_49,type,
produc782216903al_val: $tType ).
thf(type_def_50,type,
produc1615737844de_val: $tType ).
thf(type_def_51,type,
produc1062784462et_val: $tType ).
thf(type_def_52,type,
produc951622955e_node: $tType ).
thf(type_def_53,type,
produc1664334075de_val: $tType ).
thf(type_def_54,type,
produc1858904199et_val: $tType ).
thf(type_def_55,type,
produc1946948786l_node: $tType ).
thf(type_def_56,type,
product_prod_val_val: $tType ).
thf(type_def_57,type,
var: $tType ).
thf(func_def_0,type,
list_P88441325et_val: $tType ).
thf(func_def_1,type,
set_Pr1587248327et_val: $tType ).
thf(func_def_2,type,
produc1904584935et_val: $tType ).
thf(func_def_3,type,
list_P729276995de_val: $tType ).
thf(func_def_4,type,
set_Pr819703837de_val: $tType ).
thf(func_def_5,type,
produc452075965de_val: $tType ).
thf(func_def_6,type,
list_P1108777338de_val: $tType ).
thf(func_def_7,type,
list_P844977291de_val: $tType ).
thf(func_def_8,type,
set_Pr1245322836de_val: $tType ).
thf(func_def_9,type,
set_Pr701036849de_val: $tType ).
thf(func_def_10,type,
list_P2089461677et_val: $tType ).
thf(func_def_11,type,
set_Pr1311924359et_val: $tType ).
thf(func_def_12,type,
produc1615737844de_val: $tType ).
thf(func_def_13,type,
produc1664334075de_val: $tType ).
thf(func_def_14,type,
list_P12184414et_val: $tType ).
thf(func_def_15,type,
list_P1414038306l_node: $tType ).
thf(func_def_16,type,
list_P761482893et_val: $tType ).
thf(func_def_17,type,
list_P940784845al_val: $tType ).
thf(func_def_18,type,
set_Pr1320419588et_val: $tType ).
thf(func_def_19,type,
set_Pr574789832l_node: $tType ).
thf(func_def_20,type,
set_Pr978022247et_val: $tType ).
thf(func_def_21,type,
set_Pr1157324199al_val: $tType ).
thf(func_def_22,type,
produc1324971431et_val: $tType ).
thf(func_def_23,type,
list_P561207620_edgeD: $tType ).
thf(func_def_24,type,
list_P1127016369e_node: $tType ).
thf(func_def_25,type,
list_P1078858818l_node: $tType ).
thf(func_def_26,type,
list_P1820443774de_val: $tType ).
thf(func_def_27,type,
set_Pr9085835e_node: $tType ).
thf(func_def_28,type,
list_P1811375021al_val: $tType ).
thf(func_def_29,type,
set_Pr2105655784l_node: $tType ).
thf(func_def_30,type,
set_Pr699757092de_val: $tType ).
thf(func_def_31,type,
produc1062784462et_val: $tType ).
thf(func_def_32,type,
produc1013974930l_node: $tType ).
thf(func_def_33,type,
set_Pr700443783al_val: $tType ).
thf(func_def_34,type,
produc1858904199et_val: $tType ).
thf(func_def_35,type,
produc782216903al_val: $tType ).
thf(func_def_36,type,
produc951622955e_node: $tType ).
thf(func_def_37,type,
option_list_val: $tType ).
thf(func_def_38,type,
produc1946948786l_node: $tType ).
thf(func_def_39,type,
produc1432036078de_val: $tType ).
thf(func_def_40,type,
product_prod_val_val: $tType ).
thf(func_def_41,type,
option_set_val: $tType ).
thf(func_def_42,type,
list_set_val: $tType ).
thf(func_def_43,type,
set_set_val: $tType ).
thf(func_def_44,type,
list_node: $tType ).
thf(func_def_45,type,
list_val: $tType ).
thf(func_def_46,type,
set_node: $tType ).
thf(func_def_47,type,
set_val: $tType ).
thf(func_def_48,type,
node: $tType ).
thf(func_def_49,type,
var: $tType ).
thf(func_def_50,type,
val: $tType ).
thf(func_def_51,type,
g: $tType ).
thf(func_def_52,type,
finite79836624et_val: set_Pr1311924359et_val > $o ).
thf(func_def_53,type,
finite2056463621de_val: set_Pr699757092de_val > $o ).
thf(func_def_54,type,
finite781217938de_val: set_Pr701036849de_val > $o ).
thf(func_def_55,type,
finite1581417648et_val: set_Pr978022247et_val > $o ).
thf(func_def_56,type,
finite423892681l_node: set_Pr2105655784l_node > $o ).
thf(func_def_57,type,
finite759259600al_val: set_Pr700443783al_val > $o ).
thf(func_def_58,type,
finite1265617511et_val: set_set_val > $o ).
thf(func_def_59,type,
finite_finite_node: set_node > $o ).
thf(func_def_60,type,
finite_finite_val: set_val > $o ).
thf(func_def_61,type,
graph_272749361_edgeD: ( g > node > list_P561207620_edgeD ) > g > node > list_node ).
thf(func_def_62,type,
graph_1037173556_edgeD: ( g > list_node ) > ( g > node > list_P561207620_edgeD ) > g > node > list_node ).
thf(func_def_63,type,
irredu893086079de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > set_val > set_Pr1311924359et_val ).
thf(func_def_64,type,
irredu681226810de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > set_val > set_set_val ).
thf(func_def_65,type,
irredu1955035135eD_val: ( g > list_node ) > ( g > node > list_P561207620_edgeD ) > ( g > node > set_val ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > set_val > set_val > $o ).
thf(func_def_66,type,
irredu224829488eD_val: ( g > list_node ) > ( g > node > list_P561207620_edgeD ) > ( g > node > set_val ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > set_val > $o ).
thf(func_def_67,type,
sup_su1487070040et_val: option_set_val > option_set_val > option_set_val ).
thf(func_def_68,type,
sup_su2005730907et_val: set_Pr1311924359et_val > set_Pr1311924359et_val > set_Pr1311924359et_val ).
thf(func_def_69,type,
sup_su2138939728de_val: set_Pr699757092de_val > set_Pr699757092de_val > set_Pr699757092de_val ).
thf(func_def_70,type,
sup_sup_set_set_val: set_set_val > set_set_val > set_set_val ).
thf(func_def_71,type,
sup_sup_set_node: set_node > set_node > set_node ).
thf(func_def_72,type,
sup_sup_set_val: set_val > set_val > set_val ).
thf(func_def_73,type,
set_Pr1006393724et_val: list_P88441325et_val > set_Pr1587248327et_val ).
thf(func_def_74,type,
set_Pr482027474de_val: list_P729276995de_val > set_Pr819703837de_val ).
thf(func_def_75,type,
set_Pr284769596et_val: list_P2089461677et_val > set_Pr1311924359et_val ).
thf(func_def_76,type,
set_Pr1904955709l_node: list_P1414038306l_node > set_Pr574789832l_node ).
thf(func_def_77,type,
set_Pr1027623516al_val: list_P940784845al_val > set_Pr1157324199al_val ).
thf(func_def_78,type,
set_Pr1157337481de_val: list_P1108777338de_val > set_Pr1245322836de_val ).
thf(func_def_79,type,
set_Pr1953765241et_val: list_P12184414et_val > set_Pr1320419588et_val ).
thf(func_def_80,type,
set_Pr450990656e_node: list_P1127016369e_node > set_Pr9085835e_node ).
thf(func_def_81,type,
set_Pr1085970585de_val: list_P1820443774de_val > set_Pr699757092de_val ).
thf(func_def_82,type,
set_Pr434939430de_val: list_P844977291de_val > set_Pr701036849de_val ).
thf(func_def_83,type,
set_Pr2104310812et_val: list_P761482893et_val > set_Pr978022247et_val ).
thf(func_def_84,type,
set_Pr1600883293l_node: list_P1078858818l_node > set_Pr2105655784l_node ).
thf(func_def_85,type,
set_Pr102746428al_val: list_P1811375021al_val > set_Pr700443783al_val ).
thf(func_def_86,type,
set_set_val2: list_set_val > set_set_val ).
thf(func_def_87,type,
set_node2: list_node > set_node ).
thf(func_def_88,type,
set_val2: list_val > set_val ).
thf(func_def_89,type,
zip_Pr21865079et_val: list_P2089461677et_val > list_P2089461677et_val > list_P88441325et_val ).
thf(func_def_90,type,
zip_Pr1472086037de_val: list_P1820443774de_val > list_P1820443774de_val > list_P729276995de_val ).
thf(func_def_91,type,
zip_set_val_set_val: list_set_val > list_set_val > list_P2089461677et_val ).
thf(func_def_92,type,
zip_set_val_node: list_set_val > list_node > list_P1414038306l_node ).
thf(func_def_93,type,
zip_set_val_val: list_set_val > list_val > list_P940784845al_val ).
thf(func_def_94,type,
zip_no263301324de_val: list_node > list_P1820443774de_val > list_P1108777338de_val ).
thf(func_def_95,type,
zip_node_set_val: list_node > list_set_val > list_P12184414et_val ).
thf(func_def_96,type,
zip_node_node: list_node > list_node > list_P1127016369e_node ).
thf(func_def_97,type,
zip_node_val: list_node > list_val > list_P1820443774de_val ).
thf(func_def_98,type,
zip_va679686869de_val: list_val > list_P1820443774de_val > list_P844977291de_val ).
thf(func_def_99,type,
zip_val_set_val: list_val > list_set_val > list_P761482893et_val ).
thf(func_def_100,type,
zip_val_node: list_val > list_node > list_P1078858818l_node ).
thf(func_def_101,type,
zip_val_val: list_val > list_val > list_P1811375021al_val ).
thf(func_def_102,type,
dom_Pr729677986st_val: ( produc1432036078de_val > option_list_val ) > set_Pr699757092de_val ).
thf(func_def_103,type,
dom_val_list_val: ( val > option_list_val ) > set_val ).
thf(func_def_104,type,
none_list_val: option_list_val ).
thf(func_def_105,type,
some_list_val: list_val > option_list_val ).
thf(func_def_106,type,
some_set_val: set_val > option_set_val ).
thf(func_def_107,type,
bot_bo2078591731et_val: set_Pr1311924359et_val ).
thf(func_def_108,type,
bot_bo404898488de_val: set_Pr699757092de_val ).
thf(func_def_109,type,
bot_bot_set_set_val: set_set_val ).
thf(func_def_110,type,
bot_bot_set_val: set_val ).
thf(func_def_111,type,
ord_le596993316et_val: option_set_val > option_set_val > $o ).
thf(func_def_112,type,
ord_le299366439et_val: set_Pr1311924359et_val > set_Pr1311924359et_val > $o ).
thf(func_def_113,type,
ord_le1643692676de_val: set_Pr699757092de_val > set_Pr699757092de_val > $o ).
thf(func_def_114,type,
ord_le1742111550et_val: set_set_val > set_set_val > $o ).
thf(func_def_115,type,
ord_less_eq_set_node: set_node > set_node > $o ).
thf(func_def_116,type,
ord_less_eq_set_val: set_val > set_val > $o ).
thf(func_def_117,type,
ord_less_eq_node: node > node > $o ).
thf(func_def_118,type,
ord_less_eq_val: val > val > $o ).
thf(func_def_119,type,
produc1377626967et_val: produc1324971431et_val > produc1324971431et_val > produc1904584935et_val ).
thf(func_def_120,type,
produc453318901de_val: produc1432036078de_val > produc1432036078de_val > produc452075965de_val ).
thf(func_def_121,type,
produc1041633943et_val: set_val > set_val > produc1324971431et_val ).
thf(func_def_122,type,
produc2052093836l_node: set_val > node > produc1013974930l_node ).
thf(func_def_123,type,
produc1337903031al_val: set_val > val > produc782216903al_val ).
thf(func_def_124,type,
produc1162531244de_val: node > produc1432036078de_val > produc1615737844de_val ).
thf(func_def_125,type,
produc2042994048et_val: node > set_val > produc1062784462et_val ).
thf(func_def_126,type,
produc457016035e_node: node > node > produc951622955e_node ).
thf(func_def_127,type,
produc1470527136de_val: node > val > produc1432036078de_val ).
thf(func_def_128,type,
produc1571934709de_val: val > produc1432036078de_val > produc1664334075de_val ).
thf(func_def_129,type,
produc1446164855et_val: val > set_val > produc1858904199et_val ).
thf(func_def_130,type,
produc1074923692l_node: val > node > produc1946948786l_node ).
thf(func_def_131,type,
product_Pair_val_val: val > val > product_prod_val_val ).
thf(func_def_132,type,
sSA_CF139593942de_val: ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > node > set_val ).
thf(func_def_133,type,
sSA_CF178745443eD_val: ( g > list_node ) > ( g > node > list_P561207620_edgeD ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > node > set_val ).
thf(func_def_134,type,
sSA_CF1517915011eD_val: ( g > list_node ) > ( g > node > list_P561207620_edgeD ) > ( g > node > set_val ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > set_val ).
thf(func_def_135,type,
sSA_CF370335846de_val: ( g > produc1432036078de_val > option_list_val ) > g > node > set_val ).
thf(func_def_136,type,
sSA_CF848637139eD_val: ( g > list_node ) > ( g > node > list_P561207620_edgeD ) > ( g > produc1432036078de_val > option_list_val ) > g > node > set_val ).
thf(func_def_137,type,
sSA_CF551432799de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > node ).
thf(func_def_138,type,
sSA_CF1909049442de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > val > $o ).
thf(func_def_139,type,
sSA_CF794421325de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > $o ).
thf(func_def_140,type,
sSA_CF1252180629de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > val > $o ).
thf(func_def_141,type,
sSA_CF262257161de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > option_list_val ).
thf(func_def_142,type,
sSA_CF2074824714de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > $o ).
thf(func_def_143,type,
sSA_CF1660885746eD_val: ( g > list_node ) > ( g > node > list_P561207620_edgeD ) > ( g > node > set_val ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > $o ).
thf(func_def_144,type,
sSA_CF1899243830eD_val: ( g > list_node ) > ( g > node > list_P561207620_edgeD ) > ( g > node > set_val ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > $o ).
thf(func_def_145,type,
sSA_CF655860150de_val: ( g > list_node ) > ( g > node > set_val ) > g > set_val ).
thf(func_def_146,type,
collec1117167378et_val: ( produc1324971431et_val > $o ) > set_Pr1311924359et_val ).
thf(func_def_147,type,
collec370342979de_val: ( produc1432036078de_val > $o ) > set_Pr699757092de_val ).
thf(func_def_148,type,
collec885255687l_node: ( produc1946948786l_node > $o ) > set_Pr2105655784l_node ).
thf(func_def_149,type,
collec52550418al_val: ( product_prod_val_val > $o ) > set_Pr700443783al_val ).
thf(func_def_150,type,
collect_set_val: ( set_val > $o ) > set_set_val ).
thf(func_def_151,type,
collect_node: ( node > $o ) > set_node ).
thf(func_def_152,type,
collect_val: ( val > $o ) > set_val ).
thf(func_def_153,type,
insert1846469495et_val: produc1324971431et_val > set_Pr1311924359et_val > set_Pr1311924359et_val ).
thf(func_def_154,type,
insert869443870de_val: produc1432036078de_val > set_Pr699757092de_val > set_Pr699757092de_val ).
thf(func_def_155,type,
insert_set_val: set_val > set_set_val > set_set_val ).
thf(func_def_156,type,
insert_node: node > set_node > set_node ).
thf(func_def_157,type,
insert_val: val > set_val > set_val ).
thf(func_def_158,type,
transi1953622797et_val: set_Pr1311924359et_val > $o ).
thf(func_def_159,type,
transi1991289355lp_val: ( val > val > $o ) > val > val > $o ).
thf(func_def_160,type,
member1254968080et_val: produc1904584935et_val > set_Pr1587248327et_val > $o ).
thf(func_def_161,type,
member698732390de_val: produc452075965de_val > set_Pr819703837de_val > $o ).
thf(func_def_162,type,
member1711426256et_val: produc1324971431et_val > set_Pr1311924359et_val > $o ).
thf(func_def_163,type,
member76372137l_node: produc1013974930l_node > set_Pr574789832l_node > $o ).
thf(func_def_164,type,
member1110026224al_val: produc782216903al_val > set_Pr1157324199al_val > $o ).
thf(func_def_165,type,
member562853661de_val: produc1615737844de_val > set_Pr1245322836de_val > $o ).
thf(func_def_166,type,
member125181669et_val: produc1062784462et_val > set_Pr1320419588et_val > $o ).
thf(func_def_167,type,
member2110109140e_node: produc951622955e_node > set_Pr9085835e_node > $o ).
thf(func_def_168,type,
member313544709de_val: produc1432036078de_val > set_Pr699757092de_val > $o ).
thf(func_def_169,type,
member1894062994de_val: produc1664334075de_val > set_Pr701036849de_val > $o ).
thf(func_def_170,type,
member39229872et_val: produc1858904199et_val > set_Pr978022247et_val > $o ).
thf(func_def_171,type,
member828457417l_node: produc1946948786l_node > set_Pr2105655784l_node > $o ).
thf(func_def_172,type,
member1680438992al_val: product_prod_val_val > set_Pr700443783al_val > $o ).
thf(func_def_173,type,
member_set_val: set_val > set_set_val > $o ).
thf(func_def_174,type,
member_node: node > set_node > $o ).
thf(func_def_175,type,
member_val: val > set_val > $o ).
thf(func_def_176,type,
alpha_n: g > list_node ).
thf(func_def_177,type,
phi: val ).
thf(func_def_178,type,
phi_s: val ).
thf(func_def_179,type,
phi2: val ).
thf(func_def_180,type,
defs: g > node > set_val ).
thf(func_def_181,type,
g2: g ).
thf(func_def_182,type,
inEdges: g > node > list_P561207620_edgeD ).
thf(func_def_183,type,
phis: g > produc1432036078de_val > option_list_val ).
thf(func_def_184,type,
s: val ).
thf(func_def_185,type,
uses: g > node > set_val ).
thf(func_def_186,type,
var2: g > val > var ).
thf(func_def_205,type,
sK0: ( val > $o ) > set_val > val ).
thf(func_def_206,type,
sK1: ( val > $o ) > set_val > val ).
thf(func_def_207,type,
sK2: ( val > $o ) > set_val > set_val > val ).
thf(func_def_208,type,
sK3: val ).
thf(func_def_209,type,
sK4: ( val > $o ) > set_val > val ).
thf(func_def_210,type,
sK5: ( val > $o ) > set_val > val ).
thf(func_def_211,type,
sK6: ( val > $o ) > set_val > set_val > val ).
thf(func_def_213,type,
ph8:
!>[X0: $tType] : X0 ).
thf(f1035,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f1034]) ).
thf(f1034,plain,
$true != $true,
inference(superposition,[status(thm)],[f1033,f1017]) ).
thf(f1017,plain,
( $true
= ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ sK3 @ phi_s ) ),
inference(cnf_transformation,[status(thm)],[f973]) ).
thf(f973,plain,
( $true
= ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ sK3 @ phi_s ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f956,f972]) ).
thf(f972,plain,
( ? [X0: val] :
( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ X0 @ phi_s )
= $true )
=> ( $true
= ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ sK3 @ phi_s ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f956,plain,
? [X0: val] :
( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ X0 @ phi_s )
= $true ),
inference(ennf_transformation,[status(thm)],[f930]) ).
thf(f930,plain,
~ ! [X0: val] :
( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ X0 @ phi_s )
!= $true ),
inference(flattening,[status(thm)],[f580]) ).
thf(f580,plain,
~ ! [X0: val] :
( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ X0 @ phi_s )
!= $true ),
inference(fool_elimination,[status(thm)],[f579]) ).
thf(f579,plain,
~ ! [X0: val] :
~ ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ X0 @ phi_s ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
~ ! [X0: val] :
~ ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ X0 @ phi_s ),
file('/export/starexec/sandbox/tmp/tmp.ceXPxvwqcT/DTF2THF_29714.p',fact_5__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062_092_060phi_062_H_O_AphiArg_Ag_A_092_060phi_062_H_A_092_060phi_062_092_060_094sub_062s_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(f1033,plain,
! [X0: val] :
( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ X0 @ phi_s )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f1032]) ).
thf(f1032,plain,
! [X0: val] :
( ( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ X0 @ phi_s )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f989,f999]) ).
thf(f999,plain,
! [X2: val,X0: val,X1: g] :
( ( $true
= ( member_val @ X0 @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ X1 ) ) )
| ( $true
!= ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ X1 @ X2 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f954]) ).
thf(f954,plain,
! [X0: val,X1: g,X2: val] :
( ( $true
!= ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ X1 @ X2 @ X0 ) )
| ( $true
= ( member_val @ X0 @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ X1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f924]) ).
thf(f924,plain,
! [X0: val,X1: g,X2: val] :
( ( $true
= ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ X1 @ X2 @ X0 ) )
=> ( $true
= ( member_val @ X0 @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f923]) ).
thf(f923,plain,
! [X0: val,X1: g,X2: val] :
( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ X1 @ X2 @ X0 )
=> ( member_val @ X0 @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ X1 ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
! [X3: val,X1: g,X2: val] :
( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ X1 @ X2 @ X3 )
=> ( member_val @ X3 @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ceXPxvwqcT/DTF2THF_29714.p',fact_6_phiArg__in__allVars) ).
thf(f989,plain,
( ( member_val @ phi_s @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f927]) ).
thf(f927,plain,
( ( member_val @ phi_s @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2 ) )
!= $true ),
inference(flattening,[status(thm)],[f742]) ).
thf(f742,plain,
( ( member_val @ phi_s @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2 ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f741]) ).
thf(f741,plain,
~ ( member_val @ phi_s @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2 ) ),
inference(rectify,[status(thm)],[f355]) ).
thf(f355,negated_conjecture,
~ ( member_val @ phi_s @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2 ) ),
inference(negated_conjecture,[status(cth)],[f354]) ).
thf(f354,conjecture,
member_val @ phi_s @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2 ),
file('/export/starexec/sandbox/tmp/tmp.ceXPxvwqcT/DTF2THF_29714.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : ITP083^1 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.06/0.25 % Computer : n024.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 300
% 0.06/0.25 % DateTime : Tue Feb 24 03:25:40 EST 2026
% 0.06/0.25 % CPUTime :
% 0.06/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.06/0.33 ---- Original DTF file ---
% 0.06/0.33 thf(spec,logic,$$dhol).
% 0.06/0.33 %------------------------------------------------------------------------------
% 0.06/0.33 % File : ITP083^1 : TPTP v9.2.1. Released v7.5.0.
% 0.06/0.33 % Domain : Interactive Theorem Proving
% 0.06/0.33 % Problem : Sledgehammer Irreducible problem prob_641__6629180_1
% 0.06/0.33 % Version : Especial.
% 0.06/0.33 % English :
% 0.06/0.33
% 0.06/0.33 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.06/0.33 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.06/0.33 % Source : [Des21]
% 0.06/0.33 % Names : Irreducible/prob_641__6629180_1 [Des21]
% 0.06/0.33
% 0.06/0.33 % Status : Theorem
% 0.06/0.33 % Rating : 0.22 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0
% 0.06/0.33 % Syntax : Number of formulae : 541 ( 183 unt; 187 typ; 0 def)
% 0.06/0.33 % Number of atoms : 948 ( 275 equ; 0 cnn)
% 0.06/0.33 % Maximal formula atoms : 7 ( 2 avg)
% 0.06/0.33 % Number of connectives : 3285 ( 114 ~; 12 |; 66 &;2729 @)
% 0.06/0.33 % ( 0 <=>; 364 =>; 0 <=; 0 <~>)
% 0.06/0.33 % Maximal formula depth : 22 ( 6 avg)
% 0.06/0.33 % Number of types : 53 ( 52 usr)
% 0.06/0.33 % Number of type conns : 511 ( 511 >; 0 *; 0 +; 0 <<)
% 0.06/0.33 % Number of symbols : 136 ( 135 usr; 10 con; 0-8 aty)
% 0.06/0.33 % Number of variables : 937 ( 98 ^; 800 !; 39 ?; 937 :)
% 0.06/0.33 % SPC : TH0_THM_EQU_NAR
% 0.06/0.33
% 0.06/0.33 % Comments : This file was generated by Sledgehammer 2021-02-23 15:43:41.217
% 0.06/0.33 %------------------------------------------------------------------------------
% 0.06/0.33 % Could-be-implicit typings (52)
% 0.06/0.33 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_Itf__val_J_Mt__Set__Oset_Itf__val_J_J_Mt__Product____Type__Oprod_It__Set__Oset_Itf__val_J_Mt__Set__Oset_Itf__val_J_J_J_J,type,
% 0.06/0.33 list_P88441325et_val: $tType ).
% 0.06/0.33
% 0.06/0.33 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_Itf__val_J_Mt__Set__Oset_Itf__val_J_J_Mt__Product____Type__Oprod_It__Set__Oset_Itf__val_J_Mt__Set__Oset_Itf__val_J_J_J_J,type,
% 0.06/0.33 set_Pr1587248327et_val: $tType ).
% 0.06/0.33
% 0.06/0.33 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_Itf__val_J_Mt__Set__Oset_Itf__val_J_J_Mt__Product____Type__Oprod_It__Set__Oset_Itf__val_J_Mt__Set__Oset_Itf__val_J_J_J,type,
% 0.06/0.33 produc1904584935et_val: $tType ).
% 0.06/0.33
% 0.06/0.33 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__node_Mtf__val_J_Mt__Product____Type__Oprod_Itf__node_Mtf__val_J_J_J,type,
% 0.06/0.33 list_P729276995de_val: $tType ).
% 0.06/0.33
% 0.06/0.33 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__node_Mtf__val_J_Mt__Product____Type__Oprod_Itf__node_Mtf__val_J_J_J,type,
% 0.06/0.33 set_Pr819703837de_val: $tType ).
% 0.06/0.33
% 0.06/0.33 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__node_Mtf__val_J_Mt__Product____Type__Oprod_Itf__node_Mtf__val_J_J,type,
% 0.06/0.33 produc452075965de_val: $tType ).
% 0.06/0.33
% 0.06/0.33 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_Itf__node_Mt__Product____Type__Oprod_Itf__node_Mtf__val_J_J_J,type,
% 0.06/0.33 list_P1108777338de_val: $tType ).
% 0.06/0.33
% 0.06/0.33 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_Itf__val_Mt__Product____Type__Oprod_Itf__node_Mtf__val_J_J_J,type,
% 0.06/0.33 list_P844977291de_val: $tType ).
% 0.06/0.33
% 0.06/0.33 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__node_Mt__Product____Type__Oprod_Itf__node_Mtf__val_J_J_J,type,
% 0.06/0.33 set_Pr1245322836de_val: $tType ).
% 0.06/0.33
% 0.06/0.33 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__val_Mt__Product____Type__Oprod_Itf__node_Mtf__val_J_J_J,type,
% 0.06/0.33 set_Pr701036849de_val: $tType ).
% 0.06/0.33
% 0.06/0.33 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Set__Oset_Itf__val_J_Mt__Set__Oset_Itf__val_J_J_J,type,
% 0.06/0.33 list_P2089461677et_val: $tType ).
% 0.06/0.33
% 0.06/0.33 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_Itf__val_J_Mt__Set__Oset_Itf__val_J_J_J,type,
% 0.06/0.33 set_Pr1311924359et_val: $tType ).
% 0.06/0.33
% 0.06/0.33 thf(ty_n_t__Product____Type__Oprod_Itf__node_Mt__Product____Type__Oprod_Itf__node_Mtf__val_J_J,type,
% 0.06/0.33 produc1615737844de_val: $tType ).
% 0.06/0.33
% 0.06/0.33 thf(ty_n_t__Product____Type__Oprod_Itf__val_Mt__Product____Type__Oprod_Itf__node_Mtf__val_J_J,type,
% 0.06/0.33 produc1664334075de_val: $tType ).
% 0.06/0.33
% 0.06/0.33 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_Itf__node_Mt__Set__Oset_Itf__val_J_J_J,type,
% 0.06/0.33 list_P12184414et_val: $tType ).
% 0.06/0.33
% 0.06/0.33 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Set__Oset_Itf__val_J_Mtf__node_J_J,type,
% 0.06/0.33 list_P1414038306l_node: $tType ).
% 0.06/0.33
% 0.06/0.33 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_Itf__val_Mt__Set__Oset_Itf__val_J_J_J,type,
% 0.06/0.33 list_P761482893et_val: $tType ).
% 0.06/0.33
% 0.06/0.33 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Set__Oset_Itf__val_J_Mtf__val_J_J,type,
% 0.06/0.33 list_P940784845al_val: $tType ).
% 0.06/0.33
% 0.06/0.33 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__node_Mt__Set__Oset_Itf__val_J_J_J,type,
% 0.06/0.33 set_Pr1320419588et_val: $tType ).
% 0.06/0.33
% 0.06/0.33 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_Itf__val_J_Mtf__node_J_J,type,
% 0.06/0.33 set_Pr574789832l_node: $tType ).
% 0.06/0.33
% 0.06/0.33 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__val_Mt__Set__Oset_Itf__val_J_J_J,type,
% 0.06/0.33 set_Pr978022247et_val: $tType ).
% 0.06/0.33
% 0.06/0.33 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_Itf__val_J_Mtf__val_J_J,type,
% 0.06/0.33 set_Pr1157324199al_val: $tType ).
% 0.06/0.33
% 0.06/0.33 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_Itf__val_J_Mt__Set__Oset_Itf__val_J_J,type,
% 0.06/0.33 produc1324971431et_val: $tType ).
% 0.06/0.33
% 0.06/0.33 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_Itf__node_Mtf__edgeD_J_J,type,
% 0.06/0.33 list_P561207620_edgeD: $tType ).
% 0.06/0.33
% 0.06/0.33 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_Itf__node_Mtf__node_J_J,type,
% 0.06/0.33 list_P1127016369e_node: $tType ).
% 0.06/0.33
% 0.06/0.33 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_Itf__val_Mtf__node_J_J,type,
% 0.06/0.33 list_P1078858818l_node: $tType ).
% 0.06/0.33
% 0.06/0.33 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_Itf__node_Mtf__val_J_J,type,
% 0.06/0.33 list_P1820443774de_val: $tType ).
% 0.06/0.33
% 0.06/0.33 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__node_Mtf__node_J_J,type,
% 0.06/0.33 set_Pr9085835e_node: $tType ).
% 0.06/0.33
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% 0.06/0.33 % \<open>\<And>thesis. (\<And>\<phi>'. phiArg g \<phi>' \<phi>\<^sub>s \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
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% 0.06/0.33 ! [G: g,V: val,V2: val] :
% 0.06/0.33 ( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G @ V @ V2 )
% 0.06/0.33 => ( member_val @ V2 @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % phiArg_in_allVars
% 0.06/0.33 thf(fact_7_uses__in__vars,axiom,
% 0.06/0.33 ! [V: val,G: g,N: node] :
% 0.06/0.33 ( ( member_val @ V @ ( uses @ G @ N ) )
% 0.06/0.33 => ( member_val @ V @ ( sSA_CF655860150de_val @ alpha_n @ uses @ G ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % uses_in_vars
% 0.06/0.33 thf(fact_8_trivial__in__allVars,axiom,
% 0.06/0.33 ! [G: g,V: val] :
% 0.06/0.33 ( ( sSA_CF1899243830eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G @ V )
% 0.06/0.33 => ( member_val @ V @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % trivial_in_allVars
% 0.06/0.33 thf(fact_9_liveVal__in__allVars,axiom,
% 0.06/0.33 ! [G: g,V: val] :
% 0.06/0.33 ( ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ G @ V )
% 0.06/0.33 => ( member_val @ V @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % liveVal_in_allVars
% 0.06/0.33 thf(fact_10_allVars__finite,axiom,
% 0.06/0.33 ! [G: g] : ( finite_finite_val @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) ) ).
% 0.06/0.33
% 0.06/0.33 % allVars_finite
% 0.06/0.33 thf(fact_11_uses__in__allUses,axiom,
% 0.06/0.33 ! [V: val,G: g,N: node] :
% 0.06/0.33 ( ( member_val @ V @ ( uses @ G @ N ) )
% 0.06/0.33 => ( member_val @ V @ ( sSA_CF178745443eD_val @ alpha_n @ inEdges @ uses @ phis @ G @ N ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % uses_in_allUses
% 0.06/0.33 thf(fact_12_redundant__def,axiom,
% 0.06/0.33 ! [G: g] :
% 0.06/0.33 ( ( sSA_CF1660885746eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G )
% 0.06/0.33 = ( ? [X: val] :
% 0.06/0.33 ( ( member_val @ X @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 0.06/0.33 & ( sSA_CF1899243830eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G @ X ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % redundant_def
% 0.06/0.33 thf(fact_13_trivial__def,axiom,
% 0.06/0.33 ! [G: g,V: val] :
% 0.06/0.33 ( ( sSA_CF1899243830eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G @ V )
% 0.06/0.33 = ( ? [X: val] :
% 0.06/0.33 ( ( member_val @ X @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 0.06/0.33 & ( sSA_CF1909049442de_val @ alpha_n @ defs @ phis @ G @ V @ X ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % trivial_def
% 0.06/0.33 thf(fact_14__092_060open_062_092_060not_062_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062s_A_092_060noteq_062_AdefNode_Ag_As_092_060close_062,axiom,
% 0.06/0.33 ( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_s )
% 0.06/0.33 = ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ s ) ) ).
% 0.06/0.33
% 0.06/0.33 % \<open>\<not> defNode g \<phi>\<^sub>s \<noteq> defNode g s\<close>
% 0.06/0.33 thf(fact_15_defs__uses__disjoint_H,axiom,
% 0.06/0.33 ! [N: node,G: g,V: val] :
% 0.06/0.33 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.06/0.33 => ( ( member_val @ V @ ( defs @ G @ N ) )
% 0.06/0.33 => ~ ( member_val @ V @ ( uses @ G @ N ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % defs_uses_disjoint'
% 0.06/0.33 thf(fact_16_livePhi,axiom,
% 0.06/0.33 ! [G: g,V: val,V2: val] :
% 0.06/0.33 ( ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ G @ V )
% 0.06/0.33 => ( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G @ V @ V2 )
% 0.06/0.33 => ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ G @ V2 ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % livePhi
% 0.06/0.33 thf(fact_17_phiArg__distinct__nodes,axiom,
% 0.06/0.33 ! [G: g,P: val,Q: val] :
% 0.06/0.33 ( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G @ P @ Q )
% 0.06/0.33 => ( ( P != Q )
% 0.06/0.33 => ( ( member_val @ P @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 0.06/0.33 => ( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ P )
% 0.06/0.33 != ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ Q ) ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % phiArg_distinct_nodes
% 0.06/0.33 thf(fact_18_phiArgs__def__distinct,axiom,
% 0.06/0.33 ! [G: g,P: val,Q: val,R: val] :
% 0.06/0.33 ( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G @ P @ Q )
% 0.06/0.33 => ( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G @ P @ R )
% 0.06/0.33 => ( ( Q != R )
% 0.06/0.33 => ( ( member_val @ P @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 0.06/0.33 => ( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ Q )
% 0.06/0.33 != ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ R ) ) ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % phiArgs_def_distinct
% 0.06/0.33 thf(fact_19_uses__in___092_060alpha_062n,axiom,
% 0.06/0.33 ! [V: val,G: g,N: node] :
% 0.06/0.33 ( ( member_val @ V @ ( uses @ G @ N ) )
% 0.06/0.33 => ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % uses_in_\<alpha>n
% 0.06/0.33 thf(fact_20_defs__finite,axiom,
% 0.06/0.33 ! [G: g,N: node] : ( finite_finite_val @ ( defs @ G @ N ) ) ).
% 0.06/0.33
% 0.06/0.33 % defs_finite
% 0.06/0.33 thf(fact_21_varsE,axiom,
% 0.06/0.33 ! [V: val,G: g] :
% 0.06/0.33 ( ( member_val @ V @ ( sSA_CF655860150de_val @ alpha_n @ uses @ G ) )
% 0.06/0.33 => ~ ! [N2: node] :
% 0.06/0.33 ( ( member_node @ N2 @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.06/0.33 => ~ ( member_val @ V @ ( uses @ G @ N2 ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % varsE
% 0.06/0.33 thf(fact_22_vars__finite,axiom,
% 0.06/0.33 ! [G: g] : ( finite_finite_val @ ( sSA_CF655860150de_val @ alpha_n @ uses @ G ) ) ).
% 0.06/0.33
% 0.06/0.33 % vars_finite
% 0.06/0.33 thf(fact_23_liveSimple,axiom,
% 0.06/0.33 ! [N: node,G: g,Val: val] :
% 0.06/0.33 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.06/0.33 => ( ( member_val @ Val @ ( uses @ G @ N ) )
% 0.06/0.33 => ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ G @ Val ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % liveSimple
% 0.06/0.33 thf(fact_24_liveVal_Osimps,axiom,
% 0.06/0.33 ! [G: g,A: val] :
% 0.06/0.33 ( ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ G @ A )
% 0.06/0.33 = ( ? [N3: node,Val2: val] :
% 0.06/0.33 ( ( A = Val2 )
% 0.06/0.33 & ( member_node @ N3 @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.06/0.33 & ( member_val @ Val2 @ ( uses @ G @ N3 ) ) )
% 0.06/0.33 | ? [V3: val,V4: val] :
% 0.06/0.33 ( ( A = V4 )
% 0.06/0.33 & ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ G @ V3 )
% 0.06/0.33 & ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G @ V3 @ V4 ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % liveVal.simps
% 0.06/0.33 thf(fact_25_liveVal_Oinducts,axiom,
% 0.06/0.33 ! [G: g,X2: val,P2: val > $o] :
% 0.06/0.33 ( ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ G @ X2 )
% 0.06/0.33 => ( ! [N2: node,Val3: val] :
% 0.06/0.33 ( ( member_node @ N2 @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.06/0.33 => ( ( member_val @ Val3 @ ( uses @ G @ N2 ) )
% 0.06/0.33 => ( P2 @ Val3 ) ) )
% 0.06/0.33 => ( ! [V5: val,V6: val] :
% 0.06/0.33 ( ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ G @ V5 )
% 0.06/0.33 => ( ( P2 @ V5 )
% 0.06/0.33 => ( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G @ V5 @ V6 )
% 0.06/0.33 => ( P2 @ V6 ) ) ) )
% 0.06/0.33 => ( P2 @ X2 ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % liveVal.inducts
% 0.06/0.33 thf(fact_26_liveVal_Ocases,axiom,
% 0.06/0.33 ! [G: g,A: val] :
% 0.06/0.33 ( ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ G @ A )
% 0.06/0.33 => ( ! [N2: node] :
% 0.06/0.33 ( ( member_node @ N2 @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.06/0.33 => ~ ( member_val @ A @ ( uses @ G @ N2 ) ) )
% 0.06/0.33 => ~ ! [V5: val] :
% 0.06/0.33 ( ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ G @ V5 )
% 0.06/0.33 => ~ ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G @ V5 @ A ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % liveVal.cases
% 0.06/0.33 thf(fact_27_allUses__finite,axiom,
% 0.06/0.33 ! [N: node,G: g] :
% 0.06/0.33 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.06/0.33 => ( finite_finite_val @ ( sSA_CF178745443eD_val @ alpha_n @ inEdges @ uses @ phis @ G @ N ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % allUses_finite
% 0.06/0.33 thf(fact_28_defNode_I1_J,axiom,
% 0.06/0.33 ! [V: val,G: g] :
% 0.06/0.33 ( ( member_val @ V @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 0.06/0.33 => ( member_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ V ) @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % defNode(1)
% 0.06/0.33 thf(fact_29_uses__finite,axiom,
% 0.06/0.33 ! [G: g,N: node] : ( finite_finite_val @ ( uses @ G @ N ) ) ).
% 0.06/0.33
% 0.06/0.33 % uses_finite
% 0.06/0.33 thf(fact_30_eq,axiom,
% 0.06/0.33 ( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_s )
% 0.06/0.33 = ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ s ) ) ).
% 0.06/0.33
% 0.06/0.33 % eq
% 0.06/0.33 thf(fact_31_allUses__in__allVars,axiom,
% 0.06/0.33 ! [V: val,G: g,N: node] :
% 0.06/0.33 ( ( member_val @ V @ ( sSA_CF178745443eD_val @ alpha_n @ inEdges @ uses @ phis @ G @ N ) )
% 0.06/0.33 => ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.06/0.33 => ( member_val @ V @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % allUses_in_allVars
% 0.06/0.33 thf(fact_32_phiUses__in__allUses,axiom,
% 0.06/0.33 ! [V: val,G: g,N: node] :
% 0.06/0.33 ( ( member_val @ V @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ G @ N ) )
% 0.06/0.33 => ( member_val @ V @ ( sSA_CF178745443eD_val @ alpha_n @ inEdges @ uses @ phis @ G @ N ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % phiUses_in_allUses
% 0.06/0.33 thf(fact_33_phiUses__finite,axiom,
% 0.06/0.33 ! [N: node,G: g] :
% 0.06/0.33 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.06/0.33 => ( finite_finite_val @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ G @ N ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % phiUses_finite
% 0.06/0.33 thf(fact_34_defNode_I2_J,axiom,
% 0.06/0.33 ! [V: val,G: g] :
% 0.06/0.33 ( ( member_val @ V @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 0.06/0.33 => ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ V ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % defNode(2)
% 0.06/0.33 thf(fact_35_defNode__ex1,axiom,
% 0.06/0.33 ! [V: val,G: g] :
% 0.06/0.33 ( ( member_val @ V @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 0.06/0.33 => ? [X3: node] :
% 0.06/0.33 ( ( member_node @ X3 @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.06/0.33 & ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ X3 ) )
% 0.06/0.33 & ! [Y: node] :
% 0.06/0.33 ( ( ( member_node @ Y @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.06/0.33 & ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ Y ) ) )
% 0.06/0.33 => ( Y = X3 ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % defNode_ex1
% 0.06/0.33 thf(fact_36_allVars__in__allDefs,axiom,
% 0.06/0.33 ! [V: val,G: g] :
% 0.06/0.33 ( ( member_val @ V @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 0.06/0.33 => ? [X3: node] :
% 0.06/0.33 ( ( member_node @ X3 @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.06/0.33 & ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ X3 ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % allVars_in_allDefs
% 0.06/0.33 thf(fact_37_List_Ofinite__set,axiom,
% 0.06/0.33 ! [Xs: list_P844977291de_val] : ( finite781217938de_val @ ( set_Pr434939430de_val @ Xs ) ) ).
% 0.06/0.33
% 0.06/0.33 % List.finite_set
% 0.06/0.33 thf(fact_38_List_Ofinite__set,axiom,
% 0.06/0.33 ! [Xs: list_P761482893et_val] : ( finite1581417648et_val @ ( set_Pr2104310812et_val @ Xs ) ) ).
% 0.06/0.33
% 0.06/0.33 % List.finite_set
% 0.06/0.33 thf(fact_39_List_Ofinite__set,axiom,
% 0.06/0.33 ! [Xs: list_P1078858818l_node] : ( finite423892681l_node @ ( set_Pr1600883293l_node @ Xs ) ) ).
% 0.06/0.33
% 0.06/0.33 % List.finite_set
% 0.06/0.33 thf(fact_40_List_Ofinite__set,axiom,
% 0.06/0.33 ! [Xs: list_P1811375021al_val] : ( finite759259600al_val @ ( set_Pr102746428al_val @ Xs ) ) ).
% 0.06/0.33
% 0.06/0.33 % List.finite_set
% 0.06/0.33 thf(fact_41_List_Ofinite__set,axiom,
% 0.06/0.33 ! [Xs: list_set_val] : ( finite1265617511et_val @ ( set_set_val2 @ Xs ) ) ).
% 0.06/0.33
% 0.06/0.33 % List.finite_set
% 0.06/0.33 thf(fact_42_List_Ofinite__set,axiom,
% 0.06/0.33 ! [Xs: list_node] : ( finite_finite_node @ ( set_node2 @ Xs ) ) ).
% 0.06/0.33
% 0.06/0.33 % List.finite_set
% 0.06/0.33 thf(fact_43_List_Ofinite__set,axiom,
% 0.06/0.33 ! [Xs: list_val] : ( finite_finite_val @ ( set_val2 @ Xs ) ) ).
% 0.06/0.33
% 0.06/0.33 % List.finite_set
% 0.06/0.33 thf(fact_44_List_Ofinite__set,axiom,
% 0.06/0.33 ! [Xs: list_P2089461677et_val] : ( finite79836624et_val @ ( set_Pr284769596et_val @ Xs ) ) ).
% 0.06/0.33
% 0.06/0.33 % List.finite_set
% 0.06/0.33 thf(fact_45_List_Ofinite__set,axiom,
% 0.06/0.33 ! [Xs: list_P1820443774de_val] : ( finite2056463621de_val @ ( set_Pr1085970585de_val @ Xs ) ) ).
% 0.06/0.33
% 0.06/0.33 % List.finite_set
% 0.06/0.33 thf(fact_46_phiDefs__finite,axiom,
% 0.06/0.33 ! [G: g,N: node] : ( finite_finite_val @ ( sSA_CF370335846de_val @ phis @ G @ N ) ) ).
% 0.06/0.33
% 0.06/0.33 % phiDefs_finite
% 0.06/0.33 thf(fact_47_allDefs__finite,axiom,
% 0.06/0.33 ! [N: node,G: g] :
% 0.06/0.33 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.06/0.33 => ( finite_finite_val @ ( sSA_CF139593942de_val @ defs @ phis @ G @ N ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % allDefs_finite
% 0.06/0.33 thf(fact_48_assms_I5_J,axiom,
% 0.06/0.33 ( ( var2 @ g2 @ phi )
% 0.06/0.33 = ( var2 @ g2 @ s ) ) ).
% 0.06/0.33
% 0.06/0.33 % assms(5)
% 0.06/0.33 thf(fact_49_CFG__SSA__wf__base_Oredundant__def,axiom,
% 0.06/0.33 ( sSA_CF1660885746eD_val
% 0.06/0.33 = ( ^ [Alpha_n: g > list_node,InEdges: g > node > list_P561207620_edgeD,Defs: g > node > set_val,Uses: g > node > set_val,Phis: g > produc1432036078de_val > option_list_val,G2: g] :
% 0.06/0.33 ? [X: val] :
% 0.06/0.33 ( ( member_val @ X @ ( sSA_CF1517915011eD_val @ Alpha_n @ InEdges @ Defs @ Uses @ Phis @ G2 ) )
% 0.06/0.33 & ( sSA_CF1899243830eD_val @ Alpha_n @ InEdges @ Defs @ Uses @ Phis @ G2 @ X ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % CFG_SSA_wf_base.redundant_def
% 0.06/0.33 thf(fact_50_defs__in__allDefs,axiom,
% 0.06/0.33 ! [V: val,G: g,N: node] :
% 0.06/0.33 ( ( member_val @ V @ ( defs @ G @ N ) )
% 0.06/0.33 => ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ N ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % defs_in_allDefs
% 0.06/0.33 thf(fact_51_phiDefs__in__allDefs,axiom,
% 0.06/0.33 ! [V: val,G: g,N: node] :
% 0.06/0.33 ( ( member_val @ V @ ( sSA_CF370335846de_val @ phis @ G @ N ) )
% 0.06/0.33 => ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ N ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % phiDefs_in_allDefs
% 0.06/0.33 thf(fact_52_allDefs__disjoint_H,axiom,
% 0.06/0.33 ! [N: node,G: g,M: node,V: val] :
% 0.06/0.33 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.06/0.33 => ( ( member_node @ M @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.06/0.33 => ( ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ N ) )
% 0.06/0.33 => ( ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ M ) )
% 0.06/0.33 => ( N = M ) ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % allDefs_disjoint'
% 0.06/0.33 thf(fact_53_mem__Collect__eq,axiom,
% 0.06/0.33 ! [A: produc1946948786l_node,P2: produc1946948786l_node > $o] :
% 0.06/0.33 ( ( member828457417l_node @ A @ ( collec885255687l_node @ P2 ) )
% 0.06/0.33 = ( P2 @ A ) ) ).
% 0.06/0.33
% 0.06/0.33 % mem_Collect_eq
% 0.06/0.33 thf(fact_54_mem__Collect__eq,axiom,
% 0.06/0.33 ! [A: product_prod_val_val,P2: product_prod_val_val > $o] :
% 0.06/0.33 ( ( member1680438992al_val @ A @ ( collec52550418al_val @ P2 ) )
% 0.06/0.33 = ( P2 @ A ) ) ).
% 0.06/0.33
% 0.06/0.33 % mem_Collect_eq
% 0.06/0.33 thf(fact_55_mem__Collect__eq,axiom,
% 0.06/0.33 ! [A: val,P2: val > $o] :
% 0.06/0.33 ( ( member_val @ A @ ( collect_val @ P2 ) )
% 0.06/0.33 = ( P2 @ A ) ) ).
% 0.06/0.33
% 0.06/0.33 % mem_Collect_eq
% 0.06/0.33 thf(fact_56_mem__Collect__eq,axiom,
% 0.06/0.33 ! [A: node,P2: node > $o] :
% 0.06/0.33 ( ( member_node @ A @ ( collect_node @ P2 ) )
% 0.06/0.33 = ( P2 @ A ) ) ).
% 0.06/0.33
% 0.06/0.33 % mem_Collect_eq
% 0.06/0.33 thf(fact_57_mem__Collect__eq,axiom,
% 0.06/0.33 ! [A: set_val,P2: set_val > $o] :
% 0.06/0.33 ( ( member_set_val @ A @ ( collect_set_val @ P2 ) )
% 0.06/0.33 = ( P2 @ A ) ) ).
% 0.06/0.33
% 0.06/0.33 % mem_Collect_eq
% 0.06/0.33 thf(fact_58_mem__Collect__eq,axiom,
% 0.06/0.33 ! [A: produc1432036078de_val,P2: produc1432036078de_val > $o] :
% 0.06/0.33 ( ( member313544709de_val @ A @ ( collec370342979de_val @ P2 ) )
% 0.06/0.33 = ( P2 @ A ) ) ).
% 0.06/0.33
% 0.06/0.33 % mem_Collect_eq
% 0.06/0.33 thf(fact_59_mem__Collect__eq,axiom,
% 0.06/0.33 ! [A: produc1324971431et_val,P2: produc1324971431et_val > $o] :
% 0.06/0.33 ( ( member1711426256et_val @ A @ ( collec1117167378et_val @ P2 ) )
% 0.06/0.33 = ( P2 @ A ) ) ).
% 0.06/0.33
% 0.06/0.33 % mem_Collect_eq
% 0.06/0.33 thf(fact_60_Collect__mem__eq,axiom,
% 0.06/0.33 ! [A2: set_val] :
% 0.06/0.33 ( ( collect_val
% 0.06/0.33 @ ^ [X: val] : ( member_val @ X @ A2 ) )
% 0.06/0.33 = A2 ) ).
% 0.06/0.33
% 0.06/0.33 % Collect_mem_eq
% 0.06/0.33 thf(fact_61_Collect__mem__eq,axiom,
% 0.06/0.33 ! [A2: set_node] :
% 0.06/0.33 ( ( collect_node
% 0.06/0.33 @ ^ [X: node] : ( member_node @ X @ A2 ) )
% 0.06/0.33 = A2 ) ).
% 0.06/0.33
% 0.06/0.33 % Collect_mem_eq
% 0.06/0.33 thf(fact_62_Collect__mem__eq,axiom,
% 0.06/0.33 ! [A2: set_set_val] :
% 0.06/0.33 ( ( collect_set_val
% 0.06/0.33 @ ^ [X: set_val] : ( member_set_val @ X @ A2 ) )
% 0.06/0.33 = A2 ) ).
% 0.06/0.33
% 0.06/0.33 % Collect_mem_eq
% 0.06/0.33 thf(fact_63_Collect__mem__eq,axiom,
% 0.06/0.33 ! [A2: set_Pr699757092de_val] :
% 0.06/0.33 ( ( collec370342979de_val
% 0.06/0.33 @ ^ [X: produc1432036078de_val] : ( member313544709de_val @ X @ A2 ) )
% 0.06/0.33 = A2 ) ).
% 0.06/0.33
% 0.06/0.33 % Collect_mem_eq
% 0.06/0.33 thf(fact_64_Collect__mem__eq,axiom,
% 0.06/0.33 ! [A2: set_Pr1311924359et_val] :
% 0.06/0.33 ( ( collec1117167378et_val
% 0.06/0.33 @ ^ [X: produc1324971431et_val] : ( member1711426256et_val @ X @ A2 ) )
% 0.06/0.33 = A2 ) ).
% 0.06/0.33
% 0.06/0.33 % Collect_mem_eq
% 0.06/0.33 thf(fact_65_phiArg__same__var,axiom,
% 0.06/0.33 ! [G: g,P: val,Q: val] :
% 0.06/0.33 ( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G @ P @ Q )
% 0.06/0.33 => ( ( var2 @ G @ Q )
% 0.06/0.33 = ( var2 @ G @ P ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % phiArg_same_var
% 0.06/0.33 thf(fact_66_vars__eq,axiom,
% 0.06/0.33 ( ( var2 @ g2 @ phi )
% 0.06/0.33 = ( var2 @ g2 @ phi_s ) ) ).
% 0.06/0.33
% 0.06/0.33 % vars_eq
% 0.06/0.33 thf(fact_67_allDefs__var__disjoint,axiom,
% 0.06/0.33 ! [N: node,G: g,V: val,V2: val] :
% 0.06/0.33 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.06/0.33 => ( ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ N ) )
% 0.06/0.33 => ( ( member_val @ V2 @ ( sSA_CF139593942de_val @ defs @ phis @ G @ N ) )
% 0.06/0.33 => ( ( V != V2 )
% 0.06/0.33 => ( ( var2 @ G @ V2 )
% 0.06/0.33 != ( var2 @ G @ V ) ) ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % allDefs_var_disjoint
% 0.06/0.33 thf(fact_68_defNode__var__disjoint,axiom,
% 0.06/0.33 ! [P: val,G: g,Q: val] :
% 0.06/0.33 ( ( member_val @ P @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 0.06/0.33 => ( ( member_val @ Q @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 0.06/0.33 => ( ( P != Q )
% 0.06/0.33 => ( ( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ P )
% 0.06/0.33 = ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ Q ) )
% 0.06/0.33 => ( ( var2 @ G @ P )
% 0.06/0.33 != ( var2 @ G @ Q ) ) ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % defNode_var_disjoint
% 0.06/0.33 thf(fact_69_defNode__eq,axiom,
% 0.06/0.33 ! [N: node,G: g,V: val] :
% 0.06/0.33 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.06/0.33 => ( ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ N ) )
% 0.06/0.33 => ( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ V )
% 0.06/0.33 = N ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % defNode_eq
% 0.06/0.33 thf(fact_70_allDefs__in__allVars,axiom,
% 0.06/0.33 ! [V: val,G: g,N: node] :
% 0.06/0.33 ( ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ N ) )
% 0.06/0.33 => ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.06/0.33 => ( member_val @ V @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % allDefs_in_allVars
% 0.06/0.33 thf(fact_71_pruned__def,axiom,
% 0.06/0.33 ! [G: g] :
% 0.06/0.33 ( ( sSA_CF2074824714de_val @ alpha_n @ defs @ uses @ phis @ G )
% 0.06/0.33 = ( ! [X: node] :
% 0.06/0.33 ( ( member_node @ X @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.06/0.33 => ! [Val2: val] :
% 0.06/0.33 ( ( member_val @ Val2 @ ( sSA_CF370335846de_val @ phis @ G @ X ) )
% 0.06/0.33 => ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ G @ Val2 ) ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % pruned_def
% 0.06/0.33 thf(fact_72_CFG__SSA__base_OphiUses_Ocong,axiom,
% 0.06/0.33 sSA_CF848637139eD_val = sSA_CF848637139eD_val ).
% 0.06/0.33
% 0.06/0.33 % CFG_SSA_base.phiUses.cong
% 0.06/0.33 thf(fact_73_CFG__SSA__base_OphiDefs_Ocong,axiom,
% 0.06/0.33 sSA_CF370335846de_val = sSA_CF370335846de_val ).
% 0.06/0.33
% 0.06/0.33 % CFG_SSA_base.phiDefs.cong
% 0.06/0.33 thf(fact_74_CFG__SSA__base_OallDefs_Ocong,axiom,
% 0.06/0.33 sSA_CF139593942de_val = sSA_CF139593942de_val ).
% 0.06/0.33
% 0.06/0.33 % CFG_SSA_base.allDefs.cong
% 0.06/0.33 thf(fact_75_CFG__SSA__wf__base_OdefNode_Ocong,axiom,
% 0.06/0.33 sSA_CF551432799de_val = sSA_CF551432799de_val ).
% 0.06/0.33
% 0.06/0.33 % CFG_SSA_wf_base.defNode.cong
% 0.06/0.33 thf(fact_76_CFG__SSA__base_OallVars_Ocong,axiom,
% 0.06/0.33 sSA_CF1517915011eD_val = sSA_CF1517915011eD_val ).
% 0.06/0.33
% 0.06/0.33 % CFG_SSA_base.allVars.cong
% 0.06/0.33 thf(fact_77_CFG__SSA__wf__base_OphiArg_Ocong,axiom,
% 0.06/0.33 sSA_CF1252180629de_val = sSA_CF1252180629de_val ).
% 0.06/0.33
% 0.06/0.33 % CFG_SSA_wf_base.phiArg.cong
% 0.06/0.33 thf(fact_78_CFG__SSA__base_OallUses_Ocong,axiom,
% 0.06/0.33 sSA_CF178745443eD_val = sSA_CF178745443eD_val ).
% 0.06/0.33
% 0.06/0.33 % CFG_SSA_base.allUses.cong
% 0.06/0.33 thf(fact_79_CFG__SSA__wf__base_OliveVal_Ocong,axiom,
% 0.06/0.33 sSA_CF794421325de_val = sSA_CF794421325de_val ).
% 0.06/0.33
% 0.06/0.33 % CFG_SSA_wf_base.liveVal.cong
% 0.06/0.33 thf(fact_80_CFG__SSA__wf__base_Otrivial_Ocong,axiom,
% 0.06/0.33 sSA_CF1899243830eD_val = sSA_CF1899243830eD_val ).
% 0.06/0.33
% 0.06/0.33 % CFG_SSA_wf_base.trivial.cong
% 0.06/0.33 thf(fact_81_CFG__base_Ovars_Ocong,axiom,
% 0.06/0.33 sSA_CF655860150de_val = sSA_CF655860150de_val ).
% 0.06/0.33
% 0.06/0.33 % CFG_base.vars.cong
% 0.06/0.33 thf(fact_82_CFG__SSA__wf__base_OisTrivialPhi_Ocong,axiom,
% 0.06/0.33 sSA_CF1909049442de_val = sSA_CF1909049442de_val ).
% 0.06/0.33
% 0.06/0.33 % CFG_SSA_wf_base.isTrivialPhi.cong
% 0.06/0.33 thf(fact_83_CFG__SSA__wf__base_Oredundant_Ocong,axiom,
% 0.06/0.33 sSA_CF1660885746eD_val = sSA_CF1660885746eD_val ).
% 0.06/0.33
% 0.06/0.33 % CFG_SSA_wf_base.redundant.cong
% 0.06/0.33 thf(fact_84_finite__list,axiom,
% 0.06/0.33 ! [A2: set_node] :
% 0.06/0.33 ( ( finite_finite_node @ A2 )
% 0.06/0.33 => ? [Xs2: list_node] :
% 0.06/0.33 ( ( set_node2 @ Xs2 )
% 0.06/0.33 = A2 ) ) ).
% 0.06/0.33
% 0.06/0.33 % finite_list
% 0.06/0.33 thf(fact_85_finite__list,axiom,
% 0.06/0.33 ! [A2: set_val] :
% 0.06/0.33 ( ( finite_finite_val @ A2 )
% 0.06/0.33 => ? [Xs2: list_val] :
% 0.06/0.33 ( ( set_val2 @ Xs2 )
% 0.06/0.33 = A2 ) ) ).
% 0.06/0.33
% 0.06/0.33 % finite_list
% 0.06/0.33 thf(fact_86_finite__list,axiom,
% 0.06/0.33 ! [A2: set_Pr1311924359et_val] :
% 0.06/0.33 ( ( finite79836624et_val @ A2 )
% 0.06/0.33 => ? [Xs2: list_P2089461677et_val] :
% 0.06/0.33 ( ( set_Pr284769596et_val @ Xs2 )
% 0.06/0.33 = A2 ) ) ).
% 0.06/0.33
% 0.06/0.33 % finite_list
% 0.06/0.33 thf(fact_87_finite__list,axiom,
% 0.06/0.33 ! [A2: set_Pr699757092de_val] :
% 0.06/0.33 ( ( finite2056463621de_val @ A2 )
% 0.06/0.33 => ? [Xs2: list_P1820443774de_val] :
% 0.06/0.33 ( ( set_Pr1085970585de_val @ Xs2 )
% 0.06/0.33 = A2 ) ) ).
% 0.06/0.33
% 0.06/0.33 % finite_list
% 0.06/0.33 thf(fact_88_CFG__SSA__wf__base_OliveSimple,axiom,
% 0.06/0.33 ! [N: node,Alpha_n2: g > list_node,G: g,Val: val,Uses2: g > node > set_val,Defs2: g > node > set_val,Phis2: g > produc1432036078de_val > option_list_val] :
% 0.06/0.33 ( ( member_node @ N @ ( set_node2 @ ( Alpha_n2 @ G ) ) )
% 0.06/0.33 => ( ( member_val @ Val @ ( Uses2 @ G @ N ) )
% 0.06/0.33 => ( sSA_CF794421325de_val @ Alpha_n2 @ Defs2 @ Uses2 @ Phis2 @ G @ Val ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % CFG_SSA_wf_base.liveSimple
% 0.06/0.33 thf(fact_89_CFG__SSA__wf__base_OlivePhi,axiom,
% 0.06/0.33 ! [Alpha_n2: g > list_node,Defs2: g > node > set_val,Uses2: g > node > set_val,Phis2: g > produc1432036078de_val > option_list_val,G: g,V: val,V2: val] :
% 0.06/0.33 ( ( sSA_CF794421325de_val @ Alpha_n2 @ Defs2 @ Uses2 @ Phis2 @ G @ V )
% 0.06/0.33 => ( ( sSA_CF1252180629de_val @ Alpha_n2 @ Defs2 @ Phis2 @ G @ V @ V2 )
% 0.06/0.33 => ( sSA_CF794421325de_val @ Alpha_n2 @ Defs2 @ Uses2 @ Phis2 @ G @ V2 ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % CFG_SSA_wf_base.livePhi
% 0.06/0.33 thf(fact_90_CFG__SSA__wf__base_OliveVal_Oinducts,axiom,
% 0.06/0.33 ! [Alpha_n2: g > list_node,Defs2: g > node > set_val,Uses2: g > node > set_val,Phis2: g > produc1432036078de_val > option_list_val,G: g,X2: val,P2: val > $o] :
% 0.06/0.33 ( ( sSA_CF794421325de_val @ Alpha_n2 @ Defs2 @ Uses2 @ Phis2 @ G @ X2 )
% 0.06/0.33 => ( ! [N2: node,Val3: val] :
% 0.06/0.33 ( ( member_node @ N2 @ ( set_node2 @ ( Alpha_n2 @ G ) ) )
% 0.06/0.33 => ( ( member_val @ Val3 @ ( Uses2 @ G @ N2 ) )
% 0.06/0.33 => ( P2 @ Val3 ) ) )
% 0.06/0.33 => ( ! [V5: val,V6: val] :
% 0.06/0.33 ( ( sSA_CF794421325de_val @ Alpha_n2 @ Defs2 @ Uses2 @ Phis2 @ G @ V5 )
% 0.06/0.33 => ( ( P2 @ V5 )
% 0.06/0.33 => ( ( sSA_CF1252180629de_val @ Alpha_n2 @ Defs2 @ Phis2 @ G @ V5 @ V6 )
% 0.06/0.33 => ( P2 @ V6 ) ) ) )
% 0.06/0.33 => ( P2 @ X2 ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % CFG_SSA_wf_base.liveVal.inducts
% 0.06/0.33 thf(fact_91_CFG__SSA__wf__base_OliveVal_Osimps,axiom,
% 0.06/0.33 ( sSA_CF794421325de_val
% 0.06/0.33 = ( ^ [Alpha_n: g > list_node,Defs: g > node > set_val,Uses: g > node > set_val,Phis: g > produc1432036078de_val > option_list_val,G2: g,A3: val] :
% 0.06/0.33 ( ? [N3: node,Val2: val] :
% 0.06/0.33 ( ( A3 = Val2 )
% 0.06/0.33 & ( member_node @ N3 @ ( set_node2 @ ( Alpha_n @ G2 ) ) )
% 0.06/0.33 & ( member_val @ Val2 @ ( Uses @ G2 @ N3 ) ) )
% 0.06/0.33 | ? [V3: val,V4: val] :
% 0.06/0.33 ( ( A3 = V4 )
% 0.06/0.33 & ( sSA_CF794421325de_val @ Alpha_n @ Defs @ Uses @ Phis @ G2 @ V3 )
% 0.06/0.33 & ( sSA_CF1252180629de_val @ Alpha_n @ Defs @ Phis @ G2 @ V3 @ V4 ) ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % CFG_SSA_wf_base.liveVal.simps
% 0.06/0.33 thf(fact_92_CFG__SSA__wf__base_OliveVal_Ocases,axiom,
% 0.06/0.33 ! [Alpha_n2: g > list_node,Defs2: g > node > set_val,Uses2: g > node > set_val,Phis2: g > produc1432036078de_val > option_list_val,G: g,A: val] :
% 0.06/0.33 ( ( sSA_CF794421325de_val @ Alpha_n2 @ Defs2 @ Uses2 @ Phis2 @ G @ A )
% 0.06/0.33 => ( ! [N2: node] :
% 0.06/0.33 ( ( member_node @ N2 @ ( set_node2 @ ( Alpha_n2 @ G ) ) )
% 0.06/0.33 => ~ ( member_val @ A @ ( Uses2 @ G @ N2 ) ) )
% 0.06/0.33 => ~ ! [V5: val] :
% 0.06/0.33 ( ( sSA_CF794421325de_val @ Alpha_n2 @ Defs2 @ Uses2 @ Phis2 @ G @ V5 )
% 0.06/0.33 => ~ ( sSA_CF1252180629de_val @ Alpha_n2 @ Defs2 @ Phis2 @ G @ V5 @ A ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % CFG_SSA_wf_base.liveVal.cases
% 0.06/0.33 thf(fact_93_CFG__SSA__wf__base_Otrivial__def,axiom,
% 0.06/0.33 ( sSA_CF1899243830eD_val
% 0.06/0.33 = ( ^ [Alpha_n: g > list_node,InEdges: g > node > list_P561207620_edgeD,Defs: g > node > set_val,Uses: g > node > set_val,Phis: g > produc1432036078de_val > option_list_val,G2: g,V3: val] :
% 0.06/0.33 ? [X: val] :
% 0.06/0.33 ( ( member_val @ X @ ( sSA_CF1517915011eD_val @ Alpha_n @ InEdges @ Defs @ Uses @ Phis @ G2 ) )
% 0.06/0.33 & ( sSA_CF1909049442de_val @ Alpha_n @ Defs @ Phis @ G2 @ V3 @ X ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % CFG_SSA_wf_base.trivial_def
% 0.06/0.33 thf(fact_94_condensation__finite,axiom,
% 0.06/0.33 ! [G: g,P2: set_val] : ( finite79836624et_val @ ( irredu893086079de_val @ alpha_n @ defs @ phis @ G @ P2 ) ) ).
% 0.06/0.33
% 0.06/0.33 % condensation_finite
% 0.06/0.33 thf(fact_95_phiUses__exI_H,axiom,
% 0.06/0.33 ! [G: g,P: val,Q: val] :
% 0.06/0.33 ( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G @ P @ Q )
% 0.06/0.33 => ( ( member_val @ P @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 0.06/0.33 => ~ ! [M2: node] :
% 0.06/0.33 ( ( member_val @ Q @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ G @ M2 ) )
% 0.06/0.33 => ~ ( member_node @ M2 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ P ) ) ) ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % phiUses_exI'
% 0.06/0.33 thf(fact_96_allUses__def,axiom,
% 0.06/0.33 ! [G: g,N: node] :
% 0.06/0.33 ( ( sSA_CF178745443eD_val @ alpha_n @ inEdges @ uses @ phis @ G @ N )
% 0.06/0.33 = ( sup_sup_set_val @ ( uses @ G @ N ) @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ G @ N ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % allUses_def
% 0.06/0.33 thf(fact_97_phiArg__trancl__same__var,axiom,
% 0.06/0.33 ! [G: g,Phi2: val,N: val] :
% 0.06/0.33 ( ( transi1991289355lp_val @ ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G ) @ Phi2 @ N )
% 0.06/0.33 => ( ( var2 @ G @ Phi2 )
% 0.06/0.33 = ( var2 @ G @ N ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % phiArg_trancl_same_var
% 0.06/0.33 thf(fact_98_allDefs__def,axiom,
% 0.06/0.33 ! [G: g,N: node] :
% 0.06/0.33 ( ( sSA_CF139593942de_val @ defs @ phis @ G @ N )
% 0.06/0.33 = ( sup_sup_set_val @ ( defs @ G @ N ) @ ( sSA_CF370335846de_val @ phis @ G @ N ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % allDefs_def
% 0.06/0.33 thf(fact_99_CFG__SSA__wf__base_Opruned__def,axiom,
% 0.06/0.33 ( sSA_CF2074824714de_val
% 0.06/0.33 = ( ^ [Alpha_n: g > list_node,Defs: g > node > set_val,Uses: g > node > set_val,Phis: g > produc1432036078de_val > option_list_val,G2: g] :
% 0.06/0.33 ! [X: node] :
% 0.06/0.33 ( ( member_node @ X @ ( set_node2 @ ( Alpha_n @ G2 ) ) )
% 0.06/0.33 => ! [Val2: val] :
% 0.06/0.33 ( ( member_val @ Val2 @ ( sSA_CF370335846de_val @ Phis @ G2 @ X ) )
% 0.06/0.33 => ( sSA_CF794421325de_val @ Alpha_n @ Defs @ Uses @ Phis @ G2 @ Val2 ) ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % CFG_SSA_wf_base.pruned_def
% 0.06/0.33 thf(fact_100_defNode__cases,axiom,
% 0.06/0.33 ! [V: val,G: g] :
% 0.06/0.33 ( ( member_val @ V @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 0.06/0.33 => ( ~ ( member_val @ V @ ( defs @ G @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ V ) ) )
% 0.06/0.33 => ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ G @ V )
% 0.06/0.33 != none_list_val ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % defNode_cases
% 0.06/0.33 thf(fact_101_simpleDef__not__phi,axiom,
% 0.06/0.33 ! [N: node,G: g,V: val] :
% 0.06/0.33 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.06/0.33 => ( ( member_val @ V @ ( defs @ G @ N ) )
% 0.06/0.33 => ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ G @ V )
% 0.06/0.33 = none_list_val ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % simpleDef_not_phi
% 0.06/0.33 thf(fact_102_finite__Un,axiom,
% 0.06/0.33 ! [F: set_Pr1311924359et_val,G3: set_Pr1311924359et_val] :
% 0.06/0.33 ( ( finite79836624et_val @ ( sup_su2005730907et_val @ F @ G3 ) )
% 0.06/0.33 = ( ( finite79836624et_val @ F )
% 0.06/0.33 & ( finite79836624et_val @ G3 ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % finite_Un
% 0.06/0.33 thf(fact_103_finite__Un,axiom,
% 0.06/0.33 ! [F: set_Pr699757092de_val,G3: set_Pr699757092de_val] :
% 0.06/0.33 ( ( finite2056463621de_val @ ( sup_su2138939728de_val @ F @ G3 ) )
% 0.06/0.33 = ( ( finite2056463621de_val @ F )
% 0.06/0.33 & ( finite2056463621de_val @ G3 ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % finite_Un
% 0.06/0.33 thf(fact_104_finite__Un,axiom,
% 0.06/0.33 ! [F: set_val,G3: set_val] :
% 0.06/0.33 ( ( finite_finite_val @ ( sup_sup_set_val @ F @ G3 ) )
% 0.06/0.33 = ( ( finite_finite_val @ F )
% 0.06/0.33 & ( finite_finite_val @ G3 ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % finite_Un
% 0.06/0.33 thf(fact_105_trivial__phi,axiom,
% 0.06/0.33 ! [G: g,V: val] :
% 0.06/0.33 ( ( sSA_CF1899243830eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G @ V )
% 0.06/0.33 => ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ G @ V )
% 0.06/0.33 != none_list_val ) ) ).
% 0.06/0.33
% 0.06/0.33 % trivial_phi
% 0.06/0.33 thf(fact_106_phiArg__exI,axiom,
% 0.06/0.33 ! [M: node,G: g,V: val] :
% 0.06/0.33 ( ( member_node @ M @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ V ) ) ) )
% 0.06/0.33 => ( ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ G @ V )
% 0.06/0.33 != none_list_val )
% 0.06/0.33 => ( ( member_val @ V @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 0.06/0.33 => ~ ! [V6: val] :
% 0.06/0.33 ( ( member_val @ V6 @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ G @ M ) )
% 0.06/0.33 => ~ ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G @ V @ V6 ) ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % phiArg_exI
% 0.06/0.33 thf(fact_107_CFG__SSA__wf__base_Ophi_Ocong,axiom,
% 0.06/0.33 sSA_CF262257161de_val = sSA_CF262257161de_val ).
% 0.06/0.33
% 0.06/0.33 % CFG_SSA_wf_base.phi.cong
% 0.06/0.33 thf(fact_108_infinite__Un,axiom,
% 0.06/0.33 ! [S: set_Pr1311924359et_val,T: set_Pr1311924359et_val] :
% 0.06/0.33 ( ( ~ ( finite79836624et_val @ ( sup_su2005730907et_val @ S @ T ) ) )
% 0.06/0.33 = ( ~ ( finite79836624et_val @ S )
% 0.06/0.33 | ~ ( finite79836624et_val @ T ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % infinite_Un
% 0.06/0.33 thf(fact_109_infinite__Un,axiom,
% 0.06/0.33 ! [S: set_Pr699757092de_val,T: set_Pr699757092de_val] :
% 0.06/0.33 ( ( ~ ( finite2056463621de_val @ ( sup_su2138939728de_val @ S @ T ) ) )
% 0.06/0.33 = ( ~ ( finite2056463621de_val @ S )
% 0.06/0.33 | ~ ( finite2056463621de_val @ T ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % infinite_Un
% 0.06/0.33 thf(fact_110_infinite__Un,axiom,
% 0.06/0.33 ! [S: set_val,T: set_val] :
% 0.06/0.33 ( ( ~ ( finite_finite_val @ ( sup_sup_set_val @ S @ T ) ) )
% 0.06/0.33 = ( ~ ( finite_finite_val @ S )
% 0.06/0.33 | ~ ( finite_finite_val @ T ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % infinite_Un
% 0.06/0.33 thf(fact_111_Un__infinite,axiom,
% 0.06/0.33 ! [S: set_Pr1311924359et_val,T: set_Pr1311924359et_val] :
% 0.06/0.33 ( ~ ( finite79836624et_val @ S )
% 0.06/0.33 => ~ ( finite79836624et_val @ ( sup_su2005730907et_val @ S @ T ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % Un_infinite
% 0.06/0.33 thf(fact_112_Un__infinite,axiom,
% 0.06/0.33 ! [S: set_Pr699757092de_val,T: set_Pr699757092de_val] :
% 0.06/0.33 ( ~ ( finite2056463621de_val @ S )
% 0.06/0.33 => ~ ( finite2056463621de_val @ ( sup_su2138939728de_val @ S @ T ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % Un_infinite
% 0.06/0.33 thf(fact_113_Un__infinite,axiom,
% 0.06/0.33 ! [S: set_val,T: set_val] :
% 0.06/0.33 ( ~ ( finite_finite_val @ S )
% 0.06/0.33 => ~ ( finite_finite_val @ ( sup_sup_set_val @ S @ T ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % Un_infinite
% 0.06/0.33 thf(fact_114_finite__UnI,axiom,
% 0.06/0.33 ! [F: set_Pr1311924359et_val,G3: set_Pr1311924359et_val] :
% 0.06/0.33 ( ( finite79836624et_val @ F )
% 0.06/0.33 => ( ( finite79836624et_val @ G3 )
% 0.06/0.33 => ( finite79836624et_val @ ( sup_su2005730907et_val @ F @ G3 ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % finite_UnI
% 0.06/0.33 thf(fact_115_finite__UnI,axiom,
% 0.06/0.33 ! [F: set_Pr699757092de_val,G3: set_Pr699757092de_val] :
% 0.06/0.33 ( ( finite2056463621de_val @ F )
% 0.06/0.33 => ( ( finite2056463621de_val @ G3 )
% 0.06/0.33 => ( finite2056463621de_val @ ( sup_su2138939728de_val @ F @ G3 ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % finite_UnI
% 0.06/0.33 thf(fact_116_finite__UnI,axiom,
% 0.06/0.33 ! [F: set_val,G3: set_val] :
% 0.06/0.33 ( ( finite_finite_val @ F )
% 0.06/0.33 => ( ( finite_finite_val @ G3 )
% 0.06/0.33 => ( finite_finite_val @ ( sup_sup_set_val @ F @ G3 ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % finite_UnI
% 0.06/0.33 thf(fact_117_CFG__SSA__Transformed_Ocondensation__edges_Ocong,axiom,
% 0.06/0.33 irredu893086079de_val = irredu893086079de_val ).
% 0.06/0.33
% 0.06/0.33 % CFG_SSA_Transformed.condensation_edges.cong
% 0.06/0.33 thf(fact_118_CFG__SSA__wf__base_Opruned_Ocong,axiom,
% 0.06/0.33 sSA_CF2074824714de_val = sSA_CF2074824714de_val ).
% 0.06/0.33
% 0.06/0.33 % CFG_SSA_wf_base.pruned.cong
% 0.06/0.33 thf(fact_119_CFG__SSA__base_OallDefs__def,axiom,
% 0.06/0.33 ( sSA_CF139593942de_val
% 0.06/0.33 = ( ^ [Defs: g > node > set_val,Phis: g > produc1432036078de_val > option_list_val,G2: g,N3: node] : ( sup_sup_set_val @ ( Defs @ G2 @ N3 ) @ ( sSA_CF370335846de_val @ Phis @ G2 @ N3 ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % CFG_SSA_base.allDefs_def
% 0.06/0.33 thf(fact_120_CFG__SSA__base_OallUses__def,axiom,
% 0.06/0.33 ( sSA_CF178745443eD_val
% 0.06/0.33 = ( ^ [Alpha_n: g > list_node,InEdges: g > node > list_P561207620_edgeD,Uses: g > node > set_val,Phis: g > produc1432036078de_val > option_list_val,G2: g,N3: node] : ( sup_sup_set_val @ ( Uses @ G2 @ N3 ) @ ( sSA_CF848637139eD_val @ Alpha_n @ InEdges @ Phis @ G2 @ N3 ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % CFG_SSA_base.allUses_def
% 0.06/0.33 thf(fact_121_phi__phiDefs,axiom,
% 0.06/0.33 ! [G: g,V: val,Vs: list_val] :
% 0.06/0.33 ( ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ G @ V )
% 0.06/0.33 = ( some_list_val @ Vs ) )
% 0.06/0.33 => ( member_val @ V @ ( sSA_CF370335846de_val @ phis @ G @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ V ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % phi_phiDefs
% 0.06/0.33 thf(fact_122_condensation__acyclic,axiom,
% 0.06/0.33 ! [G: g,P2: set_val] : ( transi1953622797et_val @ ( irredu893086079de_val @ alpha_n @ defs @ phis @ G @ P2 ) ) ).
% 0.06/0.33
% 0.06/0.33 % condensation_acyclic
% 0.06/0.33 thf(fact_123_phi__def,axiom,
% 0.06/0.33 ! [G: g,V: val] :
% 0.06/0.33 ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ G @ V )
% 0.06/0.33 = ( phis @ G @ ( produc1470527136de_val @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ V ) @ V ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % phi_def
% 0.06/0.33 thf(fact_124_phiArg__def,axiom,
% 0.06/0.33 ! [G: g,V: val,V2: val] :
% 0.06/0.33 ( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G @ V @ V2 )
% 0.06/0.33 = ( ? [Vs2: list_val] :
% 0.06/0.33 ( ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ G @ V )
% 0.06/0.33 = ( some_list_val @ Vs2 ) )
% 0.06/0.33 & ( member_val @ V2 @ ( set_val2 @ Vs2 ) ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % phiArg_def
% 0.06/0.33 thf(fact_125_phi__finite,axiom,
% 0.06/0.33 ! [G: g] : ( finite_finite_val @ ( dom_val_list_val @ ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ G ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % phi_finite
% 0.06/0.33 thf(fact_126_redundant__scc__phis,axiom,
% 0.06/0.33 ! [G: g,P2: set_val,Scc: set_val,X2: val] :
% 0.06/0.33 ( ( irredu224829488eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G @ P2 )
% 0.06/0.33 => ( ( member_set_val @ Scc @ ( irredu681226810de_val @ alpha_n @ defs @ phis @ G @ P2 ) )
% 0.06/0.33 => ( ( member_val @ X2 @ Scc )
% 0.06/0.33 => ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ G @ X2 )
% 0.06/0.33 != none_list_val ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % redundant_scc_phis
% 0.06/0.33 thf(fact_127_phis__disj_I2_J,axiom,
% 0.06/0.33 ! [G: g,N: node,V: val,Vs: list_val,N4: node,Vs3: list_val] :
% 0.06/0.33 ( ( ( phis @ G @ ( produc1470527136de_val @ N @ V ) )
% 0.06/0.33 = ( some_list_val @ Vs ) )
% 0.06/0.33 => ( ( ( phis @ G @ ( produc1470527136de_val @ N4 @ V ) )
% 0.06/0.33 = ( some_list_val @ Vs3 ) )
% 0.06/0.33 => ( Vs = Vs3 ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % phis_disj(2)
% 0.06/0.33 thf(fact_128_phis__disj_I1_J,axiom,
% 0.06/0.33 ! [G: g,N: node,V: val,Vs: list_val,N4: node,Vs3: list_val] :
% 0.06/0.33 ( ( ( phis @ G @ ( produc1470527136de_val @ N @ V ) )
% 0.06/0.33 = ( some_list_val @ Vs ) )
% 0.06/0.33 => ( ( ( phis @ G @ ( produc1470527136de_val @ N4 @ V ) )
% 0.06/0.33 = ( some_list_val @ Vs3 ) )
% 0.06/0.33 => ( N = N4 ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % phis_disj(1)
% 0.06/0.33 thf(fact_129_phis__in___092_060alpha_062n,axiom,
% 0.06/0.33 ! [G: g,N: node,V: val,Vs: list_val] :
% 0.06/0.33 ( ( ( phis @ G @ ( produc1470527136de_val @ N @ V ) )
% 0.06/0.33 = ( some_list_val @ Vs ) )
% 0.06/0.33 => ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % phis_in_\<alpha>n
% 0.06/0.33 thf(fact_130_phis__same__var,axiom,
% 0.06/0.33 ! [G: g,N: node,V: val,Vs: list_val,V2: val] :
% 0.06/0.33 ( ( ( phis @ G @ ( produc1470527136de_val @ N @ V ) )
% 0.06/0.33 = ( some_list_val @ Vs ) )
% 0.06/0.33 => ( ( member_val @ V2 @ ( set_val2 @ Vs ) )
% 0.06/0.33 => ( ( var2 @ G @ V2 )
% 0.06/0.33 = ( var2 @ G @ V ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % phis_same_var
% 0.06/0.33 thf(fact_131_phis__phi,axiom,
% 0.06/0.33 ! [G: g,N: node,V: val,Vs: list_val] :
% 0.06/0.33 ( ( ( phis @ G @ ( produc1470527136de_val @ N @ V ) )
% 0.06/0.33 = ( some_list_val @ Vs ) )
% 0.06/0.33 => ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ G @ V )
% 0.06/0.33 = ( some_list_val @ Vs ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % phis_phi
% 0.06/0.33 thf(fact_132_phiUses__exI,axiom,
% 0.06/0.33 ! [M: node,G: g,N: node,V: val,Vs: list_val] :
% 0.06/0.33 ( ( member_node @ M @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ N ) ) )
% 0.06/0.33 => ( ( ( phis @ G @ ( produc1470527136de_val @ N @ V ) )
% 0.06/0.33 = ( some_list_val @ Vs ) )
% 0.06/0.33 => ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.06/0.33 => ~ ! [V6: val] :
% 0.06/0.33 ( ( member_val @ V6 @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ G @ M ) )
% 0.06/0.33 => ~ ( member_val @ V6 @ ( set_val2 @ Vs ) ) ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % phiUses_exI
% 0.06/0.33 thf(fact_133_CFG__SSA__Transformed_Ocondensation__nodes_Ocong,axiom,
% 0.06/0.33 irredu681226810de_val = irredu681226810de_val ).
% 0.06/0.33
% 0.06/0.33 % CFG_SSA_Transformed.condensation_nodes.cong
% 0.06/0.33 thf(fact_134_CFG__SSA__Transformed_Oredundant__set_Ocong,axiom,
% 0.06/0.33 irredu224829488eD_val = irredu224829488eD_val ).
% 0.06/0.33
% 0.06/0.33 % CFG_SSA_Transformed.redundant_set.cong
% 0.06/0.33 thf(fact_135_CFG__SSA__wf__base_Ophi__def,axiom,
% 0.06/0.33 ( sSA_CF262257161de_val
% 0.06/0.33 = ( ^ [Alpha_n: g > list_node,Defs: g > node > set_val,Phis: g > produc1432036078de_val > option_list_val,G2: g,V3: val] : ( Phis @ G2 @ ( produc1470527136de_val @ ( sSA_CF551432799de_val @ Alpha_n @ Defs @ Phis @ G2 @ V3 ) @ V3 ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % CFG_SSA_wf_base.phi_def
% 0.06/0.33 thf(fact_136_CFG__SSA__wf__base_OphiArg__def,axiom,
% 0.06/0.33 ( sSA_CF1252180629de_val
% 0.06/0.33 = ( ^ [Alpha_n: g > list_node,Defs: g > node > set_val,Phis: g > produc1432036078de_val > option_list_val,G2: g,V3: val,V4: val] :
% 0.06/0.33 ? [Vs2: list_val] :
% 0.06/0.33 ( ( ( sSA_CF262257161de_val @ Alpha_n @ Defs @ Phis @ G2 @ V3 )
% 0.06/0.33 = ( some_list_val @ Vs2 ) )
% 0.06/0.33 & ( member_val @ V4 @ ( set_val2 @ Vs2 ) ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % CFG_SSA_wf_base.phiArg_def
% 0.06/0.33 thf(fact_137_phiUsesI,axiom,
% 0.06/0.33 ! [N4: node,G: g,V2: val,Vs: list_val,N: node,V: val] :
% 0.06/0.33 ( ( member_node @ N4 @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.06/0.33 => ( ( ( phis @ G @ ( produc1470527136de_val @ N4 @ V2 ) )
% 0.06/0.33 = ( some_list_val @ Vs ) )
% 0.06/0.33 => ( ( member313544709de_val @ ( produc1470527136de_val @ N @ V ) @ ( set_Pr1085970585de_val @ ( zip_node_val @ ( graph_272749361_edgeD @ inEdges @ G @ N4 ) @ Vs ) ) )
% 0.06/0.33 => ( member_val @ V @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ G @ N ) ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % phiUsesI
% 0.06/0.33 thf(fact_138_scc__in__P,axiom,
% 0.06/0.33 ! [Scc: set_val,G: g,P2: set_val] :
% 0.06/0.33 ( ( member_set_val @ Scc @ ( irredu681226810de_val @ alpha_n @ defs @ phis @ G @ P2 ) )
% 0.06/0.33 => ( ord_less_eq_set_val @ Scc @ P2 ) ) ).
% 0.06/0.33
% 0.06/0.33 % scc_in_P
% 0.06/0.33 thf(fact_139_not__None__eq,axiom,
% 0.06/0.33 ! [X2: option_list_val] :
% 0.06/0.33 ( ( X2 != none_list_val )
% 0.06/0.33 = ( ? [Y2: list_val] :
% 0.06/0.33 ( X2
% 0.06/0.33 = ( some_list_val @ Y2 ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % not_None_eq
% 0.06/0.33 thf(fact_140_not__Some__eq,axiom,
% 0.06/0.33 ! [X2: option_list_val] :
% 0.06/0.33 ( ( ! [Y2: list_val] :
% 0.06/0.33 ( X2
% 0.06/0.33 != ( some_list_val @ Y2 ) ) )
% 0.06/0.33 = ( X2 = none_list_val ) ) ).
% 0.06/0.33
% 0.06/0.33 % not_Some_eq
% 0.06/0.33 thf(fact_141_sup__Some,axiom,
% 0.06/0.33 ! [X2: set_val,Y3: set_val] :
% 0.06/0.33 ( ( sup_su1487070040et_val @ ( some_set_val @ X2 ) @ ( some_set_val @ Y3 ) )
% 0.06/0.33 = ( some_set_val @ ( sup_sup_set_val @ X2 @ Y3 ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % sup_Some
% 0.06/0.33 thf(fact_142_option_Oinject,axiom,
% 0.06/0.33 ! [X22: list_val,Y22: list_val] :
% 0.06/0.33 ( ( ( some_list_val @ X22 )
% 0.06/0.33 = ( some_list_val @ Y22 ) )
% 0.06/0.33 = ( X22 = Y22 ) ) ).
% 0.06/0.33
% 0.06/0.33 % option.inject
% 0.06/0.33 thf(fact_143_less__eq__option__Some,axiom,
% 0.06/0.33 ! [X2: set_val,Y3: set_val] :
% 0.06/0.33 ( ( ord_le596993316et_val @ ( some_set_val @ X2 ) @ ( some_set_val @ Y3 ) )
% 0.06/0.33 = ( ord_less_eq_set_val @ X2 @ Y3 ) ) ).
% 0.06/0.33
% 0.06/0.33 % less_eq_option_Some
% 0.06/0.33 thf(fact_144_zip__same,axiom,
% 0.06/0.33 ! [A: produc1324971431et_val,B: produc1324971431et_val,Xs: list_P2089461677et_val] :
% 0.06/0.33 ( ( member1254968080et_val @ ( produc1377626967et_val @ A @ B ) @ ( set_Pr1006393724et_val @ ( zip_Pr21865079et_val @ Xs @ Xs ) ) )
% 0.06/0.33 = ( ( member1711426256et_val @ A @ ( set_Pr284769596et_val @ Xs ) )
% 0.06/0.33 & ( A = B ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % zip_same
% 0.06/0.33 thf(fact_145_zip__same,axiom,
% 0.06/0.33 ! [A: node,B: node,Xs: list_node] :
% 0.06/0.33 ( ( member2110109140e_node @ ( produc457016035e_node @ A @ B ) @ ( set_Pr450990656e_node @ ( zip_node_node @ Xs @ Xs ) ) )
% 0.06/0.33 = ( ( member_node @ A @ ( set_node2 @ Xs ) )
% 0.06/0.33 & ( A = B ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % zip_same
% 0.06/0.33 thf(fact_146_zip__same,axiom,
% 0.06/0.33 ! [A: val,B: val,Xs: list_val] :
% 0.06/0.33 ( ( member1680438992al_val @ ( product_Pair_val_val @ A @ B ) @ ( set_Pr102746428al_val @ ( zip_val_val @ Xs @ Xs ) ) )
% 0.06/0.33 = ( ( member_val @ A @ ( set_val2 @ Xs ) )
% 0.06/0.33 & ( A = B ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % zip_same
% 0.06/0.33 thf(fact_147_zip__same,axiom,
% 0.06/0.33 ! [A: produc1432036078de_val,B: produc1432036078de_val,Xs: list_P1820443774de_val] :
% 0.06/0.33 ( ( member698732390de_val @ ( produc453318901de_val @ A @ B ) @ ( set_Pr482027474de_val @ ( zip_Pr1472086037de_val @ Xs @ Xs ) ) )
% 0.06/0.33 = ( ( member313544709de_val @ A @ ( set_Pr1085970585de_val @ Xs ) )
% 0.06/0.33 & ( A = B ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % zip_same
% 0.06/0.33 thf(fact_148_zip__same,axiom,
% 0.06/0.33 ! [A: set_val,B: set_val,Xs: list_set_val] :
% 0.06/0.33 ( ( member1711426256et_val @ ( produc1041633943et_val @ A @ B ) @ ( set_Pr284769596et_val @ ( zip_set_val_set_val @ Xs @ Xs ) ) )
% 0.06/0.33 = ( ( member_set_val @ A @ ( set_set_val2 @ Xs ) )
% 0.06/0.33 & ( A = B ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % zip_same
% 0.06/0.33 thf(fact_149__C1_C,axiom,
% 0.06/0.33 ! [G: g,P2: set_val] :
% 0.06/0.33 ( ( irredu224829488eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G @ P2 )
% 0.06/0.33 => ? [Scc2: set_val] :
% 0.06/0.33 ( ( ord_less_eq_set_val @ Scc2 @ P2 )
% 0.06/0.33 & ( irredu1955035135eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G @ P2 @ Scc2 ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % "1"
% 0.06/0.33 thf(fact_150_phiUsesE,axiom,
% 0.06/0.33 ! [V: val,G: g,N: node] :
% 0.06/0.33 ( ( member_val @ V @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ G @ N ) )
% 0.06/0.33 => ~ ! [N5: node] :
% 0.06/0.33 ( ( member_node @ N5 @ ( set_node2 @ ( graph_1037173556_edgeD @ alpha_n @ inEdges @ G @ N ) ) )
% 0.06/0.33 => ! [V6: val,Vs4: list_val] :
% 0.06/0.33 ( ( member313544709de_val @ ( produc1470527136de_val @ N @ V ) @ ( set_Pr1085970585de_val @ ( zip_node_val @ ( graph_272749361_edgeD @ inEdges @ G @ N5 ) @ Vs4 ) ) )
% 0.06/0.33 => ( ( phis @ G @ ( produc1470527136de_val @ N5 @ V6 ) )
% 0.06/0.33 != ( some_list_val @ Vs4 ) ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % phiUsesE
% 0.06/0.33 thf(fact_151_finite__has__minimal2,axiom,
% 0.06/0.33 ! [A2: set_node,A: node] :
% 0.06/0.33 ( ( finite_finite_node @ A2 )
% 0.06/0.33 => ( ( member_node @ A @ A2 )
% 0.06/0.33 => ? [X3: node] :
% 0.06/0.33 ( ( member_node @ X3 @ A2 )
% 0.06/0.33 & ( ord_less_eq_node @ X3 @ A )
% 0.06/0.33 & ! [Xa: node] :
% 0.06/0.33 ( ( member_node @ Xa @ A2 )
% 0.06/0.33 => ( ( ord_less_eq_node @ Xa @ X3 )
% 0.06/0.33 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % finite_has_minimal2
% 0.06/0.33 thf(fact_152_finite__has__minimal2,axiom,
% 0.06/0.33 ! [A2: set_val,A: val] :
% 0.06/0.33 ( ( finite_finite_val @ A2 )
% 0.06/0.33 => ( ( member_val @ A @ A2 )
% 0.06/0.33 => ? [X3: val] :
% 0.06/0.33 ( ( member_val @ X3 @ A2 )
% 0.06/0.33 & ( ord_less_eq_val @ X3 @ A )
% 0.06/0.33 & ! [Xa: val] :
% 0.06/0.33 ( ( member_val @ Xa @ A2 )
% 0.06/0.33 => ( ( ord_less_eq_val @ Xa @ X3 )
% 0.06/0.33 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % finite_has_minimal2
% 0.06/0.33 thf(fact_153_finite__has__minimal2,axiom,
% 0.06/0.33 ! [A2: set_set_val,A: set_val] :
% 0.06/0.33 ( ( finite1265617511et_val @ A2 )
% 0.06/0.33 => ( ( member_set_val @ A @ A2 )
% 0.06/0.33 => ? [X3: set_val] :
% 0.06/0.33 ( ( member_set_val @ X3 @ A2 )
% 0.06/0.33 & ( ord_less_eq_set_val @ X3 @ A )
% 0.06/0.33 & ! [Xa: set_val] :
% 0.06/0.33 ( ( member_set_val @ Xa @ A2 )
% 0.06/0.33 => ( ( ord_less_eq_set_val @ Xa @ X3 )
% 0.06/0.33 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % finite_has_minimal2
% 0.06/0.33 thf(fact_154_finite__has__maximal2,axiom,
% 0.06/0.33 ! [A2: set_node,A: node] :
% 0.06/0.33 ( ( finite_finite_node @ A2 )
% 0.06/0.33 => ( ( member_node @ A @ A2 )
% 0.06/0.33 => ? [X3: node] :
% 0.06/0.33 ( ( member_node @ X3 @ A2 )
% 0.06/0.33 & ( ord_less_eq_node @ A @ X3 )
% 0.06/0.33 & ! [Xa: node] :
% 0.06/0.33 ( ( member_node @ Xa @ A2 )
% 0.06/0.33 => ( ( ord_less_eq_node @ X3 @ Xa )
% 0.06/0.33 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % finite_has_maximal2
% 0.06/0.33 thf(fact_155_finite__has__maximal2,axiom,
% 0.06/0.33 ! [A2: set_val,A: val] :
% 0.06/0.33 ( ( finite_finite_val @ A2 )
% 0.06/0.33 => ( ( member_val @ A @ A2 )
% 0.06/0.33 => ? [X3: val] :
% 0.06/0.33 ( ( member_val @ X3 @ A2 )
% 0.06/0.33 & ( ord_less_eq_val @ A @ X3 )
% 0.06/0.33 & ! [Xa: val] :
% 0.06/0.33 ( ( member_val @ Xa @ A2 )
% 0.06/0.33 => ( ( ord_less_eq_val @ X3 @ Xa )
% 0.06/0.33 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % finite_has_maximal2
% 0.06/0.33 thf(fact_156_finite__has__maximal2,axiom,
% 0.06/0.33 ! [A2: set_set_val,A: set_val] :
% 0.06/0.33 ( ( finite1265617511et_val @ A2 )
% 0.06/0.33 => ( ( member_set_val @ A @ A2 )
% 0.06/0.33 => ? [X3: set_val] :
% 0.06/0.33 ( ( member_set_val @ X3 @ A2 )
% 0.06/0.33 & ( ord_less_eq_set_val @ A @ X3 )
% 0.06/0.33 & ! [Xa: set_val] :
% 0.06/0.33 ( ( member_set_val @ Xa @ A2 )
% 0.06/0.33 => ( ( ord_less_eq_set_val @ X3 @ Xa )
% 0.06/0.33 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % finite_has_maximal2
% 0.06/0.33 thf(fact_157_subset__code_I1_J,axiom,
% 0.06/0.33 ! [Xs: list_set_val,B2: set_set_val] :
% 0.06/0.33 ( ( ord_le1742111550et_val @ ( set_set_val2 @ Xs ) @ B2 )
% 0.06/0.33 = ( ! [X: set_val] :
% 0.06/0.33 ( ( member_set_val @ X @ ( set_set_val2 @ Xs ) )
% 0.06/0.33 => ( member_set_val @ X @ B2 ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % subset_code(1)
% 0.06/0.33 thf(fact_158_subset__code_I1_J,axiom,
% 0.06/0.33 ! [Xs: list_P2089461677et_val,B2: set_Pr1311924359et_val] :
% 0.06/0.33 ( ( ord_le299366439et_val @ ( set_Pr284769596et_val @ Xs ) @ B2 )
% 0.06/0.33 = ( ! [X: produc1324971431et_val] :
% 0.06/0.33 ( ( member1711426256et_val @ X @ ( set_Pr284769596et_val @ Xs ) )
% 0.06/0.33 => ( member1711426256et_val @ X @ B2 ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % subset_code(1)
% 0.06/0.33 thf(fact_159_subset__code_I1_J,axiom,
% 0.06/0.33 ! [Xs: list_node,B2: set_node] :
% 0.06/0.33 ( ( ord_less_eq_set_node @ ( set_node2 @ Xs ) @ B2 )
% 0.06/0.33 = ( ! [X: node] :
% 0.06/0.33 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 0.06/0.33 => ( member_node @ X @ B2 ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % subset_code(1)
% 0.06/0.33 thf(fact_160_subset__code_I1_J,axiom,
% 0.06/0.33 ! [Xs: list_P1820443774de_val,B2: set_Pr699757092de_val] :
% 0.06/0.33 ( ( ord_le1643692676de_val @ ( set_Pr1085970585de_val @ Xs ) @ B2 )
% 0.06/0.33 = ( ! [X: produc1432036078de_val] :
% 0.06/0.33 ( ( member313544709de_val @ X @ ( set_Pr1085970585de_val @ Xs ) )
% 0.06/0.33 => ( member313544709de_val @ X @ B2 ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % subset_code(1)
% 0.06/0.33 thf(fact_161_subset__code_I1_J,axiom,
% 0.06/0.33 ! [Xs: list_val,B2: set_val] :
% 0.06/0.33 ( ( ord_less_eq_set_val @ ( set_val2 @ Xs ) @ B2 )
% 0.06/0.33 = ( ! [X: val] :
% 0.06/0.33 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 0.06/0.33 => ( member_val @ X @ B2 ) ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % subset_code(1)
% 0.06/0.33 thf(fact_162_rev__finite__subset,axiom,
% 0.06/0.33 ! [B2: set_Pr1311924359et_val,A2: set_Pr1311924359et_val] :
% 0.06/0.33 ( ( finite79836624et_val @ B2 )
% 0.06/0.33 => ( ( ord_le299366439et_val @ A2 @ B2 )
% 0.06/0.33 => ( finite79836624et_val @ A2 ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % rev_finite_subset
% 0.06/0.33 thf(fact_163_rev__finite__subset,axiom,
% 0.06/0.33 ! [B2: set_Pr699757092de_val,A2: set_Pr699757092de_val] :
% 0.06/0.33 ( ( finite2056463621de_val @ B2 )
% 0.06/0.33 => ( ( ord_le1643692676de_val @ A2 @ B2 )
% 0.06/0.33 => ( finite2056463621de_val @ A2 ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % rev_finite_subset
% 0.06/0.33 thf(fact_164_rev__finite__subset,axiom,
% 0.06/0.33 ! [B2: set_val,A2: set_val] :
% 0.06/0.33 ( ( finite_finite_val @ B2 )
% 0.06/0.33 => ( ( ord_less_eq_set_val @ A2 @ B2 )
% 0.06/0.33 => ( finite_finite_val @ A2 ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % rev_finite_subset
% 0.06/0.33 thf(fact_165_infinite__super,axiom,
% 0.06/0.33 ! [S: set_Pr1311924359et_val,T: set_Pr1311924359et_val] :
% 0.06/0.33 ( ( ord_le299366439et_val @ S @ T )
% 0.06/0.33 => ( ~ ( finite79836624et_val @ S )
% 0.06/0.33 => ~ ( finite79836624et_val @ T ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % infinite_super
% 0.06/0.33 thf(fact_166_infinite__super,axiom,
% 0.06/0.33 ! [S: set_Pr699757092de_val,T: set_Pr699757092de_val] :
% 0.06/0.33 ( ( ord_le1643692676de_val @ S @ T )
% 0.06/0.33 => ( ~ ( finite2056463621de_val @ S )
% 0.06/0.33 => ~ ( finite2056463621de_val @ T ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % infinite_super
% 0.06/0.33 thf(fact_167_infinite__super,axiom,
% 0.06/0.33 ! [S: set_val,T: set_val] :
% 0.06/0.33 ( ( ord_less_eq_set_val @ S @ T )
% 0.06/0.33 => ( ~ ( finite_finite_val @ S )
% 0.06/0.33 => ~ ( finite_finite_val @ T ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % infinite_super
% 0.06/0.33 thf(fact_168_finite__subset,axiom,
% 0.06/0.33 ! [A2: set_Pr1311924359et_val,B2: set_Pr1311924359et_val] :
% 0.06/0.33 ( ( ord_le299366439et_val @ A2 @ B2 )
% 0.06/0.33 => ( ( finite79836624et_val @ B2 )
% 0.06/0.33 => ( finite79836624et_val @ A2 ) ) ) ).
% 0.06/0.33
% 0.06/0.33 % finite_subset
% 0.06/0.33 thf(fact_169_finite__subset,axiom,
% 0.06/0.33 ! [A2: set_Pr699757092de_val,B2: set_Pr699757092de_val] :
% 0.06/0.33 ( ( ord_le1643692676de_val @ A2 @ B2 )
% 0.06/0.34 => ( ( finite2056463621de_val @ B2 )
% 0.06/0.34 => ( finite2056463621de_val @ A2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % finite_subset
% 0.06/0.34 thf(fact_170_finite__subset,axiom,
% 0.06/0.34 ! [A2: set_val,B2: set_val] :
% 0.06/0.34 ( ( ord_less_eq_set_val @ A2 @ B2 )
% 0.06/0.34 => ( ( finite_finite_val @ B2 )
% 0.06/0.34 => ( finite_finite_val @ A2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % finite_subset
% 0.06/0.34 thf(fact_171_in__set__zipE,axiom,
% 0.06/0.34 ! [X2: node,Y3: node,Xs: list_node,Ys: list_node] :
% 0.06/0.34 ( ( member2110109140e_node @ ( produc457016035e_node @ X2 @ Y3 ) @ ( set_Pr450990656e_node @ ( zip_node_node @ Xs @ Ys ) ) )
% 0.06/0.34 => ~ ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 0.06/0.34 => ~ ( member_node @ Y3 @ ( set_node2 @ Ys ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % in_set_zipE
% 0.06/0.34 thf(fact_172_in__set__zipE,axiom,
% 0.06/0.34 ! [X2: val,Y3: node,Xs: list_val,Ys: list_node] :
% 0.06/0.34 ( ( member828457417l_node @ ( produc1074923692l_node @ X2 @ Y3 ) @ ( set_Pr1600883293l_node @ ( zip_val_node @ Xs @ Ys ) ) )
% 0.06/0.34 => ~ ( ( member_val @ X2 @ ( set_val2 @ Xs ) )
% 0.06/0.34 => ~ ( member_node @ Y3 @ ( set_node2 @ Ys ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % in_set_zipE
% 0.06/0.34 thf(fact_173_in__set__zipE,axiom,
% 0.06/0.34 ! [X2: val,Y3: val,Xs: list_val,Ys: list_val] :
% 0.06/0.34 ( ( member1680438992al_val @ ( product_Pair_val_val @ X2 @ Y3 ) @ ( set_Pr102746428al_val @ ( zip_val_val @ Xs @ Ys ) ) )
% 0.06/0.34 => ~ ( ( member_val @ X2 @ ( set_val2 @ Xs ) )
% 0.06/0.34 => ~ ( member_val @ Y3 @ ( set_val2 @ Ys ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % in_set_zipE
% 0.06/0.34 thf(fact_174_in__set__zipE,axiom,
% 0.06/0.34 ! [X2: node,Y3: val,Xs: list_node,Ys: list_val] :
% 0.06/0.34 ( ( member313544709de_val @ ( produc1470527136de_val @ X2 @ Y3 ) @ ( set_Pr1085970585de_val @ ( zip_node_val @ Xs @ Ys ) ) )
% 0.06/0.34 => ~ ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 0.06/0.34 => ~ ( member_val @ Y3 @ ( set_val2 @ Ys ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % in_set_zipE
% 0.06/0.34 thf(fact_175_in__set__zipE,axiom,
% 0.06/0.34 ! [X2: set_val,Y3: node,Xs: list_set_val,Ys: list_node] :
% 0.06/0.34 ( ( member76372137l_node @ ( produc2052093836l_node @ X2 @ Y3 ) @ ( set_Pr1904955709l_node @ ( zip_set_val_node @ Xs @ Ys ) ) )
% 0.06/0.34 => ~ ( ( member_set_val @ X2 @ ( set_set_val2 @ Xs ) )
% 0.06/0.34 => ~ ( member_node @ Y3 @ ( set_node2 @ Ys ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % in_set_zipE
% 0.06/0.34 thf(fact_176_in__set__zipE,axiom,
% 0.06/0.34 ! [X2: set_val,Y3: val,Xs: list_set_val,Ys: list_val] :
% 0.06/0.34 ( ( member1110026224al_val @ ( produc1337903031al_val @ X2 @ Y3 ) @ ( set_Pr1027623516al_val @ ( zip_set_val_val @ Xs @ Ys ) ) )
% 0.06/0.34 => ~ ( ( member_set_val @ X2 @ ( set_set_val2 @ Xs ) )
% 0.06/0.34 => ~ ( member_val @ Y3 @ ( set_val2 @ Ys ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % in_set_zipE
% 0.06/0.34 thf(fact_177_in__set__zipE,axiom,
% 0.06/0.34 ! [X2: node,Y3: set_val,Xs: list_node,Ys: list_set_val] :
% 0.06/0.34 ( ( member125181669et_val @ ( produc2042994048et_val @ X2 @ Y3 ) @ ( set_Pr1953765241et_val @ ( zip_node_set_val @ Xs @ Ys ) ) )
% 0.06/0.34 => ~ ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 0.06/0.34 => ~ ( member_set_val @ Y3 @ ( set_set_val2 @ Ys ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % in_set_zipE
% 0.06/0.34 thf(fact_178_in__set__zipE,axiom,
% 0.06/0.34 ! [X2: val,Y3: set_val,Xs: list_val,Ys: list_set_val] :
% 0.06/0.34 ( ( member39229872et_val @ ( produc1446164855et_val @ X2 @ Y3 ) @ ( set_Pr2104310812et_val @ ( zip_val_set_val @ Xs @ Ys ) ) )
% 0.06/0.34 => ~ ( ( member_val @ X2 @ ( set_val2 @ Xs ) )
% 0.06/0.34 => ~ ( member_set_val @ Y3 @ ( set_set_val2 @ Ys ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % in_set_zipE
% 0.06/0.34 thf(fact_179_in__set__zipE,axiom,
% 0.06/0.34 ! [X2: node,Y3: produc1432036078de_val,Xs: list_node,Ys: list_P1820443774de_val] :
% 0.06/0.34 ( ( member562853661de_val @ ( produc1162531244de_val @ X2 @ Y3 ) @ ( set_Pr1157337481de_val @ ( zip_no263301324de_val @ Xs @ Ys ) ) )
% 0.06/0.34 => ~ ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 0.06/0.34 => ~ ( member313544709de_val @ Y3 @ ( set_Pr1085970585de_val @ Ys ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % in_set_zipE
% 0.06/0.34 thf(fact_180_in__set__zipE,axiom,
% 0.06/0.34 ! [X2: val,Y3: produc1432036078de_val,Xs: list_val,Ys: list_P1820443774de_val] :
% 0.06/0.34 ( ( member1894062994de_val @ ( produc1571934709de_val @ X2 @ Y3 ) @ ( set_Pr434939430de_val @ ( zip_va679686869de_val @ Xs @ Ys ) ) )
% 0.06/0.34 => ~ ( ( member_val @ X2 @ ( set_val2 @ Xs ) )
% 0.06/0.34 => ~ ( member313544709de_val @ Y3 @ ( set_Pr1085970585de_val @ Ys ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % in_set_zipE
% 0.06/0.34 thf(fact_181_set__zip__leftD,axiom,
% 0.06/0.34 ! [X2: node,Y3: val,Xs: list_node,Ys: list_val] :
% 0.06/0.34 ( ( member313544709de_val @ ( produc1470527136de_val @ X2 @ Y3 ) @ ( set_Pr1085970585de_val @ ( zip_node_val @ Xs @ Ys ) ) )
% 0.06/0.34 => ( member_node @ X2 @ ( set_node2 @ Xs ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % set_zip_leftD
% 0.06/0.34 thf(fact_182_set__zip__leftD,axiom,
% 0.06/0.34 ! [X2: set_val,Y3: set_val,Xs: list_set_val,Ys: list_set_val] :
% 0.06/0.34 ( ( member1711426256et_val @ ( produc1041633943et_val @ X2 @ Y3 ) @ ( set_Pr284769596et_val @ ( zip_set_val_set_val @ Xs @ Ys ) ) )
% 0.06/0.34 => ( member_set_val @ X2 @ ( set_set_val2 @ Xs ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % set_zip_leftD
% 0.06/0.34 thf(fact_183_set__zip__rightD,axiom,
% 0.06/0.34 ! [X2: node,Y3: val,Xs: list_node,Ys: list_val] :
% 0.06/0.34 ( ( member313544709de_val @ ( produc1470527136de_val @ X2 @ Y3 ) @ ( set_Pr1085970585de_val @ ( zip_node_val @ Xs @ Ys ) ) )
% 0.06/0.34 => ( member_val @ Y3 @ ( set_val2 @ Ys ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % set_zip_rightD
% 0.06/0.34 thf(fact_184_set__zip__rightD,axiom,
% 0.06/0.34 ! [X2: set_val,Y3: set_val,Xs: list_set_val,Ys: list_set_val] :
% 0.06/0.34 ( ( member1711426256et_val @ ( produc1041633943et_val @ X2 @ Y3 ) @ ( set_Pr284769596et_val @ ( zip_set_val_set_val @ Xs @ Ys ) ) )
% 0.06/0.34 => ( member_set_val @ Y3 @ ( set_set_val2 @ Ys ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % set_zip_rightD
% 0.06/0.34 thf(fact_185_combine__options__cases,axiom,
% 0.06/0.34 ! [X2: option_list_val,P2: option_list_val > option_list_val > $o,Y3: option_list_val] :
% 0.06/0.34 ( ( ( X2 = none_list_val )
% 0.06/0.34 => ( P2 @ X2 @ Y3 ) )
% 0.06/0.34 => ( ( ( Y3 = none_list_val )
% 0.06/0.34 => ( P2 @ X2 @ Y3 ) )
% 0.06/0.34 => ( ! [A4: list_val,B3: list_val] :
% 0.06/0.34 ( ( X2
% 0.06/0.34 = ( some_list_val @ A4 ) )
% 0.06/0.34 => ( ( Y3
% 0.06/0.34 = ( some_list_val @ B3 ) )
% 0.06/0.34 => ( P2 @ X2 @ Y3 ) ) )
% 0.06/0.34 => ( P2 @ X2 @ Y3 ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % combine_options_cases
% 0.06/0.34 thf(fact_186_split__option__all,axiom,
% 0.06/0.34 ( ( ^ [P3: option_list_val > $o] :
% 0.06/0.34 ! [X4: option_list_val] : ( P3 @ X4 ) )
% 0.06/0.34 = ( ^ [P4: option_list_val > $o] :
% 0.06/0.34 ( ( P4 @ none_list_val )
% 0.06/0.34 & ! [X: list_val] : ( P4 @ ( some_list_val @ X ) ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % split_option_all
% 0.06/0.34 thf(fact_187_split__option__ex,axiom,
% 0.06/0.34 ( ( ^ [P3: option_list_val > $o] :
% 0.06/0.34 ? [X4: option_list_val] : ( P3 @ X4 ) )
% 0.06/0.34 = ( ^ [P4: option_list_val > $o] :
% 0.06/0.34 ( ( P4 @ none_list_val )
% 0.06/0.34 | ? [X: list_val] : ( P4 @ ( some_list_val @ X ) ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % split_option_ex
% 0.06/0.34 thf(fact_188_option_Oinducts,axiom,
% 0.06/0.34 ! [P2: option_list_val > $o,Option: option_list_val] :
% 0.06/0.34 ( ( P2 @ none_list_val )
% 0.06/0.34 => ( ! [X3: list_val] : ( P2 @ ( some_list_val @ X3 ) )
% 0.06/0.34 => ( P2 @ Option ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % option.inducts
% 0.06/0.34 thf(fact_189_option_Oexhaust,axiom,
% 0.06/0.34 ! [Y3: option_list_val] :
% 0.06/0.34 ( ( Y3 != none_list_val )
% 0.06/0.34 => ~ ! [X23: list_val] :
% 0.06/0.34 ( Y3
% 0.06/0.34 != ( some_list_val @ X23 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % option.exhaust
% 0.06/0.34 thf(fact_190_option_OdiscI,axiom,
% 0.06/0.34 ! [Option: option_list_val,X22: list_val] :
% 0.06/0.34 ( ( Option
% 0.06/0.34 = ( some_list_val @ X22 ) )
% 0.06/0.34 => ( Option != none_list_val ) ) ).
% 0.06/0.34
% 0.06/0.34 % option.discI
% 0.06/0.34 thf(fact_191_option_Odistinct_I1_J,axiom,
% 0.06/0.34 ! [X22: list_val] :
% 0.06/0.34 ( none_list_val
% 0.06/0.34 != ( some_list_val @ X22 ) ) ).
% 0.06/0.34
% 0.06/0.34 % option.distinct(1)
% 0.06/0.34 thf(fact_192_Ex__condensation__leaf,axiom,
% 0.06/0.34 ! [P2: set_val,G: g] :
% 0.06/0.34 ( ( P2 != bot_bot_set_val )
% 0.06/0.34 => ? [Leaf: set_val] :
% 0.06/0.34 ( ( member_set_val @ Leaf @ ( irredu681226810de_val @ alpha_n @ defs @ phis @ G @ P2 ) )
% 0.06/0.34 & ! [Scc3: set_val] :
% 0.06/0.34 ~ ( member1711426256et_val @ ( produc1041633943et_val @ Leaf @ Scc3 ) @ ( irredu893086079de_val @ alpha_n @ defs @ phis @ G @ P2 ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % Ex_condensation_leaf
% 0.06/0.34 thf(fact_193_Un__subset__iff,axiom,
% 0.06/0.34 ! [A2: set_val,B2: set_val,C: set_val] :
% 0.06/0.34 ( ( ord_less_eq_set_val @ ( sup_sup_set_val @ A2 @ B2 ) @ C )
% 0.06/0.34 = ( ( ord_less_eq_set_val @ A2 @ C )
% 0.06/0.34 & ( ord_less_eq_set_val @ B2 @ C ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % Un_subset_iff
% 0.06/0.34 thf(fact_194_le__sup__iff,axiom,
% 0.06/0.34 ! [X2: set_val,Y3: set_val,Z: set_val] :
% 0.06/0.34 ( ( ord_less_eq_set_val @ ( sup_sup_set_val @ X2 @ Y3 ) @ Z )
% 0.06/0.34 = ( ( ord_less_eq_set_val @ X2 @ Z )
% 0.06/0.34 & ( ord_less_eq_set_val @ Y3 @ Z ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % le_sup_iff
% 0.06/0.34 thf(fact_195_sup_Obounded__iff,axiom,
% 0.06/0.34 ! [B: set_val,C2: set_val,A: set_val] :
% 0.06/0.34 ( ( ord_less_eq_set_val @ ( sup_sup_set_val @ B @ C2 ) @ A )
% 0.06/0.34 = ( ( ord_less_eq_set_val @ B @ A )
% 0.06/0.34 & ( ord_less_eq_set_val @ C2 @ A ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % sup.bounded_iff
% 0.06/0.34 thf(fact_196_subset__antisym,axiom,
% 0.06/0.34 ! [A2: set_val,B2: set_val] :
% 0.06/0.34 ( ( ord_less_eq_set_val @ A2 @ B2 )
% 0.06/0.34 => ( ( ord_less_eq_set_val @ B2 @ A2 )
% 0.06/0.34 => ( A2 = B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % subset_antisym
% 0.06/0.34 thf(fact_197_subsetI,axiom,
% 0.06/0.34 ! [A2: set_node,B2: set_node] :
% 0.06/0.34 ( ! [X3: node] :
% 0.06/0.34 ( ( member_node @ X3 @ A2 )
% 0.06/0.34 => ( member_node @ X3 @ B2 ) )
% 0.06/0.34 => ( ord_less_eq_set_node @ A2 @ B2 ) ) ).
% 0.06/0.34
% 0.06/0.34 % subsetI
% 0.06/0.34 thf(fact_198_subsetI,axiom,
% 0.06/0.34 ! [A2: set_set_val,B2: set_set_val] :
% 0.06/0.34 ( ! [X3: set_val] :
% 0.06/0.34 ( ( member_set_val @ X3 @ A2 )
% 0.06/0.34 => ( member_set_val @ X3 @ B2 ) )
% 0.06/0.34 => ( ord_le1742111550et_val @ A2 @ B2 ) ) ).
% 0.06/0.34
% 0.06/0.34 % subsetI
% 0.06/0.34 thf(fact_199_subsetI,axiom,
% 0.06/0.34 ! [A2: set_Pr699757092de_val,B2: set_Pr699757092de_val] :
% 0.06/0.34 ( ! [X3: produc1432036078de_val] :
% 0.06/0.34 ( ( member313544709de_val @ X3 @ A2 )
% 0.06/0.34 => ( member313544709de_val @ X3 @ B2 ) )
% 0.06/0.34 => ( ord_le1643692676de_val @ A2 @ B2 ) ) ).
% 0.06/0.34
% 0.06/0.34 % subsetI
% 0.06/0.34 thf(fact_200_subsetI,axiom,
% 0.06/0.34 ! [A2: set_Pr1311924359et_val,B2: set_Pr1311924359et_val] :
% 0.06/0.34 ( ! [X3: produc1324971431et_val] :
% 0.06/0.34 ( ( member1711426256et_val @ X3 @ A2 )
% 0.06/0.34 => ( member1711426256et_val @ X3 @ B2 ) )
% 0.06/0.34 => ( ord_le299366439et_val @ A2 @ B2 ) ) ).
% 0.06/0.34
% 0.06/0.34 % subsetI
% 0.06/0.34 thf(fact_201_subsetI,axiom,
% 0.06/0.34 ! [A2: set_val,B2: set_val] :
% 0.06/0.34 ( ! [X3: val] :
% 0.06/0.34 ( ( member_val @ X3 @ A2 )
% 0.06/0.34 => ( member_val @ X3 @ B2 ) )
% 0.06/0.34 => ( ord_less_eq_set_val @ A2 @ B2 ) ) ).
% 0.06/0.34
% 0.06/0.34 % subsetI
% 0.06/0.34 thf(fact_202_sup_Oright__idem,axiom,
% 0.06/0.34 ! [A: set_val,B: set_val] :
% 0.06/0.34 ( ( sup_sup_set_val @ ( sup_sup_set_val @ A @ B ) @ B )
% 0.06/0.34 = ( sup_sup_set_val @ A @ B ) ) ).
% 0.06/0.34
% 0.06/0.34 % sup.right_idem
% 0.06/0.34 thf(fact_203_sup__left__idem,axiom,
% 0.06/0.34 ! [X2: set_val,Y3: set_val] :
% 0.06/0.34 ( ( sup_sup_set_val @ X2 @ ( sup_sup_set_val @ X2 @ Y3 ) )
% 0.06/0.34 = ( sup_sup_set_val @ X2 @ Y3 ) ) ).
% 0.06/0.34
% 0.06/0.34 % sup_left_idem
% 0.06/0.34 thf(fact_204_sup_Oleft__idem,axiom,
% 0.06/0.34 ! [A: set_val,B: set_val] :
% 0.06/0.34 ( ( sup_sup_set_val @ A @ ( sup_sup_set_val @ A @ B ) )
% 0.06/0.34 = ( sup_sup_set_val @ A @ B ) ) ).
% 0.06/0.34
% 0.06/0.34 % sup.left_idem
% 0.06/0.34 thf(fact_205_sup__idem,axiom,
% 0.06/0.34 ! [X2: set_val] :
% 0.06/0.34 ( ( sup_sup_set_val @ X2 @ X2 )
% 0.06/0.34 = X2 ) ).
% 0.06/0.34
% 0.06/0.34 % sup_idem
% 0.06/0.34 thf(fact_206_sup_Oidem,axiom,
% 0.06/0.34 ! [A: set_val] :
% 0.06/0.34 ( ( sup_sup_set_val @ A @ A )
% 0.06/0.34 = A ) ).
% 0.06/0.34
% 0.06/0.34 % sup.idem
% 0.06/0.34 thf(fact_207_Un__iff,axiom,
% 0.06/0.34 ! [C2: node,A2: set_node,B2: set_node] :
% 0.06/0.34 ( ( member_node @ C2 @ ( sup_sup_set_node @ A2 @ B2 ) )
% 0.06/0.34 = ( ( member_node @ C2 @ A2 )
% 0.06/0.34 | ( member_node @ C2 @ B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % Un_iff
% 0.06/0.34 thf(fact_208_Un__iff,axiom,
% 0.06/0.34 ! [C2: set_val,A2: set_set_val,B2: set_set_val] :
% 0.06/0.34 ( ( member_set_val @ C2 @ ( sup_sup_set_set_val @ A2 @ B2 ) )
% 0.06/0.34 = ( ( member_set_val @ C2 @ A2 )
% 0.06/0.34 | ( member_set_val @ C2 @ B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % Un_iff
% 0.06/0.34 thf(fact_209_Un__iff,axiom,
% 0.06/0.34 ! [C2: produc1432036078de_val,A2: set_Pr699757092de_val,B2: set_Pr699757092de_val] :
% 0.06/0.34 ( ( member313544709de_val @ C2 @ ( sup_su2138939728de_val @ A2 @ B2 ) )
% 0.06/0.34 = ( ( member313544709de_val @ C2 @ A2 )
% 0.06/0.34 | ( member313544709de_val @ C2 @ B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % Un_iff
% 0.06/0.34 thf(fact_210_Un__iff,axiom,
% 0.06/0.34 ! [C2: produc1324971431et_val,A2: set_Pr1311924359et_val,B2: set_Pr1311924359et_val] :
% 0.06/0.34 ( ( member1711426256et_val @ C2 @ ( sup_su2005730907et_val @ A2 @ B2 ) )
% 0.06/0.34 = ( ( member1711426256et_val @ C2 @ A2 )
% 0.06/0.34 | ( member1711426256et_val @ C2 @ B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % Un_iff
% 0.06/0.34 thf(fact_211_Un__iff,axiom,
% 0.06/0.34 ! [C2: val,A2: set_val,B2: set_val] :
% 0.06/0.34 ( ( member_val @ C2 @ ( sup_sup_set_val @ A2 @ B2 ) )
% 0.06/0.34 = ( ( member_val @ C2 @ A2 )
% 0.06/0.34 | ( member_val @ C2 @ B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % Un_iff
% 0.06/0.34 thf(fact_212_UnCI,axiom,
% 0.06/0.34 ! [C2: node,B2: set_node,A2: set_node] :
% 0.06/0.34 ( ( ~ ( member_node @ C2 @ B2 )
% 0.06/0.34 => ( member_node @ C2 @ A2 ) )
% 0.06/0.34 => ( member_node @ C2 @ ( sup_sup_set_node @ A2 @ B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % UnCI
% 0.06/0.34 thf(fact_213_UnCI,axiom,
% 0.06/0.34 ! [C2: set_val,B2: set_set_val,A2: set_set_val] :
% 0.06/0.34 ( ( ~ ( member_set_val @ C2 @ B2 )
% 0.06/0.34 => ( member_set_val @ C2 @ A2 ) )
% 0.06/0.34 => ( member_set_val @ C2 @ ( sup_sup_set_set_val @ A2 @ B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % UnCI
% 0.06/0.34 thf(fact_214_UnCI,axiom,
% 0.06/0.34 ! [C2: produc1432036078de_val,B2: set_Pr699757092de_val,A2: set_Pr699757092de_val] :
% 0.06/0.34 ( ( ~ ( member313544709de_val @ C2 @ B2 )
% 0.06/0.34 => ( member313544709de_val @ C2 @ A2 ) )
% 0.06/0.34 => ( member313544709de_val @ C2 @ ( sup_su2138939728de_val @ A2 @ B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % UnCI
% 0.06/0.34 thf(fact_215_UnCI,axiom,
% 0.06/0.34 ! [C2: produc1324971431et_val,B2: set_Pr1311924359et_val,A2: set_Pr1311924359et_val] :
% 0.06/0.34 ( ( ~ ( member1711426256et_val @ C2 @ B2 )
% 0.06/0.34 => ( member1711426256et_val @ C2 @ A2 ) )
% 0.06/0.34 => ( member1711426256et_val @ C2 @ ( sup_su2005730907et_val @ A2 @ B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % UnCI
% 0.06/0.34 thf(fact_216_UnCI,axiom,
% 0.06/0.34 ! [C2: val,B2: set_val,A2: set_val] :
% 0.06/0.34 ( ( ~ ( member_val @ C2 @ B2 )
% 0.06/0.34 => ( member_val @ C2 @ A2 ) )
% 0.06/0.34 => ( member_val @ C2 @ ( sup_sup_set_val @ A2 @ B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % UnCI
% 0.06/0.34 thf(fact_217_subset__empty,axiom,
% 0.06/0.34 ! [A2: set_val] :
% 0.06/0.34 ( ( ord_less_eq_set_val @ A2 @ bot_bot_set_val )
% 0.06/0.34 = ( A2 = bot_bot_set_val ) ) ).
% 0.06/0.34
% 0.06/0.34 % subset_empty
% 0.06/0.34 thf(fact_218_empty__subsetI,axiom,
% 0.06/0.34 ! [A2: set_val] : ( ord_less_eq_set_val @ bot_bot_set_val @ A2 ) ).
% 0.06/0.34
% 0.06/0.34 % empty_subsetI
% 0.06/0.34 thf(fact_219_sup__bot__left,axiom,
% 0.06/0.34 ! [X2: set_val] :
% 0.06/0.34 ( ( sup_sup_set_val @ bot_bot_set_val @ X2 )
% 0.06/0.34 = X2 ) ).
% 0.06/0.34
% 0.06/0.34 % sup_bot_left
% 0.06/0.34 thf(fact_220_sup__bot__right,axiom,
% 0.06/0.34 ! [X2: set_val] :
% 0.06/0.34 ( ( sup_sup_set_val @ X2 @ bot_bot_set_val )
% 0.06/0.34 = X2 ) ).
% 0.06/0.34
% 0.06/0.34 % sup_bot_right
% 0.06/0.34 thf(fact_221_bot__eq__sup__iff,axiom,
% 0.06/0.34 ! [X2: set_val,Y3: set_val] :
% 0.06/0.34 ( ( bot_bot_set_val
% 0.06/0.34 = ( sup_sup_set_val @ X2 @ Y3 ) )
% 0.06/0.34 = ( ( X2 = bot_bot_set_val )
% 0.06/0.34 & ( Y3 = bot_bot_set_val ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % bot_eq_sup_iff
% 0.06/0.34 thf(fact_222_sup__eq__bot__iff,axiom,
% 0.06/0.34 ! [X2: set_val,Y3: set_val] :
% 0.06/0.34 ( ( ( sup_sup_set_val @ X2 @ Y3 )
% 0.06/0.34 = bot_bot_set_val )
% 0.06/0.34 = ( ( X2 = bot_bot_set_val )
% 0.06/0.34 & ( Y3 = bot_bot_set_val ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % sup_eq_bot_iff
% 0.06/0.34 thf(fact_223_sup__bot_Oeq__neutr__iff,axiom,
% 0.06/0.34 ! [A: set_val,B: set_val] :
% 0.06/0.34 ( ( ( sup_sup_set_val @ A @ B )
% 0.06/0.34 = bot_bot_set_val )
% 0.06/0.34 = ( ( A = bot_bot_set_val )
% 0.06/0.34 & ( B = bot_bot_set_val ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % sup_bot.eq_neutr_iff
% 0.06/0.34 thf(fact_224_sup__bot_Oleft__neutral,axiom,
% 0.06/0.34 ! [A: set_val] :
% 0.06/0.34 ( ( sup_sup_set_val @ bot_bot_set_val @ A )
% 0.06/0.34 = A ) ).
% 0.06/0.34
% 0.06/0.34 % sup_bot.left_neutral
% 0.06/0.34 thf(fact_225_sup__bot_Oneutr__eq__iff,axiom,
% 0.06/0.34 ! [A: set_val,B: set_val] :
% 0.06/0.34 ( ( bot_bot_set_val
% 0.06/0.34 = ( sup_sup_set_val @ A @ B ) )
% 0.06/0.34 = ( ( A = bot_bot_set_val )
% 0.06/0.34 & ( B = bot_bot_set_val ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % sup_bot.neutr_eq_iff
% 0.06/0.34 thf(fact_226_sup__bot_Oright__neutral,axiom,
% 0.06/0.34 ! [A: set_val] :
% 0.06/0.34 ( ( sup_sup_set_val @ A @ bot_bot_set_val )
% 0.06/0.34 = A ) ).
% 0.06/0.34
% 0.06/0.34 % sup_bot.right_neutral
% 0.06/0.34 thf(fact_227_Un__empty,axiom,
% 0.06/0.34 ! [A2: set_val,B2: set_val] :
% 0.06/0.34 ( ( ( sup_sup_set_val @ A2 @ B2 )
% 0.06/0.34 = bot_bot_set_val )
% 0.06/0.34 = ( ( A2 = bot_bot_set_val )
% 0.06/0.34 & ( B2 = bot_bot_set_val ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % Un_empty
% 0.06/0.34 thf(fact_228_old_Osuccessors__predecessors,axiom,
% 0.06/0.34 ! [N: node,G: g,M: node] :
% 0.06/0.34 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.06/0.34 => ( ( member_node @ N @ ( set_node2 @ ( graph_1037173556_edgeD @ alpha_n @ inEdges @ G @ M ) ) )
% 0.06/0.34 = ( member_node @ M @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ N ) ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % old.successors_predecessors
% 0.06/0.34 thf(fact_229_Un__empty__left,axiom,
% 0.06/0.34 ! [B2: set_val] :
% 0.06/0.34 ( ( sup_sup_set_val @ bot_bot_set_val @ B2 )
% 0.06/0.34 = B2 ) ).
% 0.06/0.34
% 0.06/0.34 % Un_empty_left
% 0.06/0.34 thf(fact_230_Un__empty__right,axiom,
% 0.06/0.34 ! [A2: set_val] :
% 0.06/0.34 ( ( sup_sup_set_val @ A2 @ bot_bot_set_val )
% 0.06/0.34 = A2 ) ).
% 0.06/0.34
% 0.06/0.34 % Un_empty_right
% 0.06/0.34 thf(fact_231_infinite__imp__nonempty,axiom,
% 0.06/0.34 ! [S: set_Pr1311924359et_val] :
% 0.06/0.34 ( ~ ( finite79836624et_val @ S )
% 0.06/0.34 => ( S != bot_bo2078591731et_val ) ) ).
% 0.06/0.34
% 0.06/0.34 % infinite_imp_nonempty
% 0.06/0.34 thf(fact_232_infinite__imp__nonempty,axiom,
% 0.06/0.34 ! [S: set_Pr699757092de_val] :
% 0.06/0.34 ( ~ ( finite2056463621de_val @ S )
% 0.06/0.34 => ( S != bot_bo404898488de_val ) ) ).
% 0.06/0.34
% 0.06/0.34 % infinite_imp_nonempty
% 0.06/0.34 thf(fact_233_infinite__imp__nonempty,axiom,
% 0.06/0.34 ! [S: set_val] :
% 0.06/0.34 ( ~ ( finite_finite_val @ S )
% 0.06/0.34 => ( S != bot_bot_set_val ) ) ).
% 0.06/0.34
% 0.06/0.34 % infinite_imp_nonempty
% 0.06/0.34 thf(fact_234_finite_OemptyI,axiom,
% 0.06/0.34 finite79836624et_val @ bot_bo2078591731et_val ).
% 0.06/0.34
% 0.06/0.34 % finite.emptyI
% 0.06/0.34 thf(fact_235_finite_OemptyI,axiom,
% 0.06/0.34 finite2056463621de_val @ bot_bo404898488de_val ).
% 0.06/0.34
% 0.06/0.34 % finite.emptyI
% 0.06/0.34 thf(fact_236_finite_OemptyI,axiom,
% 0.06/0.34 finite_finite_val @ bot_bot_set_val ).
% 0.06/0.34
% 0.06/0.34 % finite.emptyI
% 0.06/0.34 thf(fact_237_CFG__SSA__Transformed_Oredundant__scc_Ocong,axiom,
% 0.06/0.34 irredu1955035135eD_val = irredu1955035135eD_val ).
% 0.06/0.34
% 0.06/0.34 % CFG_SSA_Transformed.redundant_scc.cong
% 0.06/0.34 thf(fact_238_finite__has__maximal,axiom,
% 0.06/0.34 ! [A2: set_val] :
% 0.06/0.34 ( ( finite_finite_val @ A2 )
% 0.06/0.34 => ( ( A2 != bot_bot_set_val )
% 0.06/0.34 => ? [X3: val] :
% 0.06/0.34 ( ( member_val @ X3 @ A2 )
% 0.06/0.34 & ! [Xa: val] :
% 0.06/0.34 ( ( member_val @ Xa @ A2 )
% 0.06/0.34 => ( ( ord_less_eq_val @ X3 @ Xa )
% 0.06/0.34 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % finite_has_maximal
% 0.06/0.34 thf(fact_239_finite__has__maximal,axiom,
% 0.06/0.34 ! [A2: set_set_val] :
% 0.06/0.34 ( ( finite1265617511et_val @ A2 )
% 0.06/0.34 => ( ( A2 != bot_bot_set_set_val )
% 0.06/0.34 => ? [X3: set_val] :
% 0.06/0.34 ( ( member_set_val @ X3 @ A2 )
% 0.06/0.34 & ! [Xa: set_val] :
% 0.06/0.34 ( ( member_set_val @ Xa @ A2 )
% 0.06/0.34 => ( ( ord_less_eq_set_val @ X3 @ Xa )
% 0.06/0.34 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % finite_has_maximal
% 0.06/0.34 thf(fact_240_finite__has__minimal,axiom,
% 0.06/0.34 ! [A2: set_val] :
% 0.06/0.34 ( ( finite_finite_val @ A2 )
% 0.06/0.34 => ( ( A2 != bot_bot_set_val )
% 0.06/0.34 => ? [X3: val] :
% 0.06/0.34 ( ( member_val @ X3 @ A2 )
% 0.06/0.34 & ! [Xa: val] :
% 0.06/0.34 ( ( member_val @ Xa @ A2 )
% 0.06/0.34 => ( ( ord_less_eq_val @ Xa @ X3 )
% 0.06/0.34 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % finite_has_minimal
% 0.06/0.34 thf(fact_241_finite__has__minimal,axiom,
% 0.06/0.34 ! [A2: set_set_val] :
% 0.06/0.34 ( ( finite1265617511et_val @ A2 )
% 0.06/0.34 => ( ( A2 != bot_bot_set_set_val )
% 0.06/0.34 => ? [X3: set_val] :
% 0.06/0.34 ( ( member_set_val @ X3 @ A2 )
% 0.06/0.34 & ! [Xa: set_val] :
% 0.06/0.34 ( ( member_set_val @ Xa @ A2 )
% 0.06/0.34 => ( ( ord_less_eq_set_val @ Xa @ X3 )
% 0.06/0.34 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % finite_has_minimal
% 0.06/0.34 thf(fact_242_Collect__mono__iff,axiom,
% 0.06/0.34 ! [P2: val > $o,Q2: val > $o] :
% 0.06/0.34 ( ( ord_less_eq_set_val @ ( collect_val @ P2 ) @ ( collect_val @ Q2 ) )
% 0.06/0.34 = ( ! [X: val] :
% 0.06/0.34 ( ( P2 @ X )
% 0.06/0.34 => ( Q2 @ X ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % Collect_mono_iff
% 0.06/0.34 thf(fact_243_set__eq__subset,axiom,
% 0.06/0.34 ( ( ^ [Y4: set_val,Z2: set_val] : ( Y4 = Z2 ) )
% 0.06/0.34 = ( ^ [A5: set_val,B4: set_val] :
% 0.06/0.34 ( ( ord_less_eq_set_val @ A5 @ B4 )
% 0.06/0.34 & ( ord_less_eq_set_val @ B4 @ A5 ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % set_eq_subset
% 0.06/0.34 thf(fact_244_subset__trans,axiom,
% 0.06/0.34 ! [A2: set_val,B2: set_val,C: set_val] :
% 0.06/0.34 ( ( ord_less_eq_set_val @ A2 @ B2 )
% 0.06/0.34 => ( ( ord_less_eq_set_val @ B2 @ C )
% 0.06/0.34 => ( ord_less_eq_set_val @ A2 @ C ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % subset_trans
% 0.06/0.34 thf(fact_245_Collect__mono,axiom,
% 0.06/0.34 ! [P2: val > $o,Q2: val > $o] :
% 0.06/0.34 ( ! [X3: val] :
% 0.06/0.34 ( ( P2 @ X3 )
% 0.06/0.34 => ( Q2 @ X3 ) )
% 0.06/0.34 => ( ord_less_eq_set_val @ ( collect_val @ P2 ) @ ( collect_val @ Q2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % Collect_mono
% 0.06/0.34 thf(fact_246_subset__refl,axiom,
% 0.06/0.34 ! [A2: set_val] : ( ord_less_eq_set_val @ A2 @ A2 ) ).
% 0.06/0.34
% 0.06/0.34 % subset_refl
% 0.06/0.34 thf(fact_247_subset__iff,axiom,
% 0.06/0.34 ( ord_less_eq_set_node
% 0.06/0.34 = ( ^ [A5: set_node,B4: set_node] :
% 0.06/0.34 ! [T2: node] :
% 0.06/0.34 ( ( member_node @ T2 @ A5 )
% 0.06/0.34 => ( member_node @ T2 @ B4 ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % subset_iff
% 0.06/0.34 thf(fact_248_subset__iff,axiom,
% 0.06/0.34 ( ord_le1742111550et_val
% 0.06/0.34 = ( ^ [A5: set_set_val,B4: set_set_val] :
% 0.06/0.34 ! [T2: set_val] :
% 0.06/0.34 ( ( member_set_val @ T2 @ A5 )
% 0.06/0.34 => ( member_set_val @ T2 @ B4 ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % subset_iff
% 0.06/0.34 thf(fact_249_subset__iff,axiom,
% 0.06/0.34 ( ord_le1643692676de_val
% 0.06/0.34 = ( ^ [A5: set_Pr699757092de_val,B4: set_Pr699757092de_val] :
% 0.06/0.34 ! [T2: produc1432036078de_val] :
% 0.06/0.34 ( ( member313544709de_val @ T2 @ A5 )
% 0.06/0.34 => ( member313544709de_val @ T2 @ B4 ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % subset_iff
% 0.06/0.34 thf(fact_250_subset__iff,axiom,
% 0.06/0.34 ( ord_le299366439et_val
% 0.06/0.34 = ( ^ [A5: set_Pr1311924359et_val,B4: set_Pr1311924359et_val] :
% 0.06/0.34 ! [T2: produc1324971431et_val] :
% 0.06/0.34 ( ( member1711426256et_val @ T2 @ A5 )
% 0.06/0.34 => ( member1711426256et_val @ T2 @ B4 ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % subset_iff
% 0.06/0.34 thf(fact_251_subset__iff,axiom,
% 0.06/0.34 ( ord_less_eq_set_val
% 0.06/0.34 = ( ^ [A5: set_val,B4: set_val] :
% 0.06/0.34 ! [T2: val] :
% 0.06/0.34 ( ( member_val @ T2 @ A5 )
% 0.06/0.34 => ( member_val @ T2 @ B4 ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % subset_iff
% 0.06/0.34 thf(fact_252_equalityD2,axiom,
% 0.06/0.34 ! [A2: set_val,B2: set_val] :
% 0.06/0.34 ( ( A2 = B2 )
% 0.06/0.34 => ( ord_less_eq_set_val @ B2 @ A2 ) ) ).
% 0.06/0.34
% 0.06/0.34 % equalityD2
% 0.06/0.34 thf(fact_253_equalityD1,axiom,
% 0.06/0.34 ! [A2: set_val,B2: set_val] :
% 0.06/0.34 ( ( A2 = B2 )
% 0.06/0.34 => ( ord_less_eq_set_val @ A2 @ B2 ) ) ).
% 0.06/0.34
% 0.06/0.34 % equalityD1
% 0.06/0.34 thf(fact_254_subset__eq,axiom,
% 0.06/0.34 ( ord_less_eq_set_node
% 0.06/0.34 = ( ^ [A5: set_node,B4: set_node] :
% 0.06/0.34 ! [X: node] :
% 0.06/0.34 ( ( member_node @ X @ A5 )
% 0.06/0.34 => ( member_node @ X @ B4 ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % subset_eq
% 0.06/0.34 thf(fact_255_subset__eq,axiom,
% 0.06/0.34 ( ord_le1742111550et_val
% 0.06/0.34 = ( ^ [A5: set_set_val,B4: set_set_val] :
% 0.06/0.34 ! [X: set_val] :
% 0.06/0.34 ( ( member_set_val @ X @ A5 )
% 0.06/0.34 => ( member_set_val @ X @ B4 ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % subset_eq
% 0.06/0.34 thf(fact_256_subset__eq,axiom,
% 0.06/0.34 ( ord_le1643692676de_val
% 0.06/0.34 = ( ^ [A5: set_Pr699757092de_val,B4: set_Pr699757092de_val] :
% 0.06/0.34 ! [X: produc1432036078de_val] :
% 0.06/0.34 ( ( member313544709de_val @ X @ A5 )
% 0.06/0.34 => ( member313544709de_val @ X @ B4 ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % subset_eq
% 0.06/0.34 thf(fact_257_subset__eq,axiom,
% 0.06/0.34 ( ord_le299366439et_val
% 0.06/0.34 = ( ^ [A5: set_Pr1311924359et_val,B4: set_Pr1311924359et_val] :
% 0.06/0.34 ! [X: produc1324971431et_val] :
% 0.06/0.34 ( ( member1711426256et_val @ X @ A5 )
% 0.06/0.34 => ( member1711426256et_val @ X @ B4 ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % subset_eq
% 0.06/0.34 thf(fact_258_subset__eq,axiom,
% 0.06/0.34 ( ord_less_eq_set_val
% 0.06/0.34 = ( ^ [A5: set_val,B4: set_val] :
% 0.06/0.34 ! [X: val] :
% 0.06/0.34 ( ( member_val @ X @ A5 )
% 0.06/0.34 => ( member_val @ X @ B4 ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % subset_eq
% 0.06/0.34 thf(fact_259_equalityE,axiom,
% 0.06/0.34 ! [A2: set_val,B2: set_val] :
% 0.06/0.34 ( ( A2 = B2 )
% 0.06/0.34 => ~ ( ( ord_less_eq_set_val @ A2 @ B2 )
% 0.06/0.34 => ~ ( ord_less_eq_set_val @ B2 @ A2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % equalityE
% 0.06/0.34 thf(fact_260_subsetD,axiom,
% 0.06/0.34 ! [A2: set_node,B2: set_node,C2: node] :
% 0.06/0.34 ( ( ord_less_eq_set_node @ A2 @ B2 )
% 0.06/0.34 => ( ( member_node @ C2 @ A2 )
% 0.06/0.34 => ( member_node @ C2 @ B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % subsetD
% 0.06/0.34 thf(fact_261_subsetD,axiom,
% 0.06/0.34 ! [A2: set_set_val,B2: set_set_val,C2: set_val] :
% 0.06/0.34 ( ( ord_le1742111550et_val @ A2 @ B2 )
% 0.06/0.34 => ( ( member_set_val @ C2 @ A2 )
% 0.06/0.34 => ( member_set_val @ C2 @ B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % subsetD
% 0.06/0.34 thf(fact_262_subsetD,axiom,
% 0.06/0.34 ! [A2: set_Pr699757092de_val,B2: set_Pr699757092de_val,C2: produc1432036078de_val] :
% 0.06/0.34 ( ( ord_le1643692676de_val @ A2 @ B2 )
% 0.06/0.34 => ( ( member313544709de_val @ C2 @ A2 )
% 0.06/0.34 => ( member313544709de_val @ C2 @ B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % subsetD
% 0.06/0.34 thf(fact_263_subsetD,axiom,
% 0.06/0.34 ! [A2: set_Pr1311924359et_val,B2: set_Pr1311924359et_val,C2: produc1324971431et_val] :
% 0.06/0.34 ( ( ord_le299366439et_val @ A2 @ B2 )
% 0.06/0.34 => ( ( member1711426256et_val @ C2 @ A2 )
% 0.06/0.34 => ( member1711426256et_val @ C2 @ B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % subsetD
% 0.06/0.34 thf(fact_264_subsetD,axiom,
% 0.06/0.34 ! [A2: set_val,B2: set_val,C2: val] :
% 0.06/0.34 ( ( ord_less_eq_set_val @ A2 @ B2 )
% 0.06/0.34 => ( ( member_val @ C2 @ A2 )
% 0.06/0.34 => ( member_val @ C2 @ B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % subsetD
% 0.06/0.34 thf(fact_265_in__mono,axiom,
% 0.06/0.34 ! [A2: set_node,B2: set_node,X2: node] :
% 0.06/0.34 ( ( ord_less_eq_set_node @ A2 @ B2 )
% 0.06/0.34 => ( ( member_node @ X2 @ A2 )
% 0.06/0.34 => ( member_node @ X2 @ B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % in_mono
% 0.06/0.34 thf(fact_266_in__mono,axiom,
% 0.06/0.34 ! [A2: set_set_val,B2: set_set_val,X2: set_val] :
% 0.06/0.34 ( ( ord_le1742111550et_val @ A2 @ B2 )
% 0.06/0.34 => ( ( member_set_val @ X2 @ A2 )
% 0.06/0.34 => ( member_set_val @ X2 @ B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % in_mono
% 0.06/0.34 thf(fact_267_in__mono,axiom,
% 0.06/0.34 ! [A2: set_Pr699757092de_val,B2: set_Pr699757092de_val,X2: produc1432036078de_val] :
% 0.06/0.34 ( ( ord_le1643692676de_val @ A2 @ B2 )
% 0.06/0.34 => ( ( member313544709de_val @ X2 @ A2 )
% 0.06/0.34 => ( member313544709de_val @ X2 @ B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % in_mono
% 0.06/0.34 thf(fact_268_in__mono,axiom,
% 0.06/0.34 ! [A2: set_Pr1311924359et_val,B2: set_Pr1311924359et_val,X2: produc1324971431et_val] :
% 0.06/0.34 ( ( ord_le299366439et_val @ A2 @ B2 )
% 0.06/0.34 => ( ( member1711426256et_val @ X2 @ A2 )
% 0.06/0.34 => ( member1711426256et_val @ X2 @ B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % in_mono
% 0.06/0.34 thf(fact_269_in__mono,axiom,
% 0.06/0.34 ! [A2: set_val,B2: set_val,X2: val] :
% 0.06/0.34 ( ( ord_less_eq_set_val @ A2 @ B2 )
% 0.06/0.34 => ( ( member_val @ X2 @ A2 )
% 0.06/0.34 => ( member_val @ X2 @ B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % in_mono
% 0.06/0.34 thf(fact_270_sup__left__commute,axiom,
% 0.06/0.34 ! [X2: set_val,Y3: set_val,Z: set_val] :
% 0.06/0.34 ( ( sup_sup_set_val @ X2 @ ( sup_sup_set_val @ Y3 @ Z ) )
% 0.06/0.34 = ( sup_sup_set_val @ Y3 @ ( sup_sup_set_val @ X2 @ Z ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % sup_left_commute
% 0.06/0.34 thf(fact_271_sup_Oleft__commute,axiom,
% 0.06/0.34 ! [B: set_val,A: set_val,C2: set_val] :
% 0.06/0.34 ( ( sup_sup_set_val @ B @ ( sup_sup_set_val @ A @ C2 ) )
% 0.06/0.34 = ( sup_sup_set_val @ A @ ( sup_sup_set_val @ B @ C2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % sup.left_commute
% 0.06/0.34 thf(fact_272_sup__commute,axiom,
% 0.06/0.34 ( sup_sup_set_val
% 0.06/0.34 = ( ^ [X: set_val,Y2: set_val] : ( sup_sup_set_val @ Y2 @ X ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % sup_commute
% 0.06/0.34 thf(fact_273_sup_Ocommute,axiom,
% 0.06/0.34 ( sup_sup_set_val
% 0.06/0.34 = ( ^ [A3: set_val,B5: set_val] : ( sup_sup_set_val @ B5 @ A3 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % sup.commute
% 0.06/0.34 thf(fact_274_sup__assoc,axiom,
% 0.06/0.34 ! [X2: set_val,Y3: set_val,Z: set_val] :
% 0.06/0.34 ( ( sup_sup_set_val @ ( sup_sup_set_val @ X2 @ Y3 ) @ Z )
% 0.06/0.34 = ( sup_sup_set_val @ X2 @ ( sup_sup_set_val @ Y3 @ Z ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % sup_assoc
% 0.06/0.34 thf(fact_275_sup_Oassoc,axiom,
% 0.06/0.34 ! [A: set_val,B: set_val,C2: set_val] :
% 0.06/0.34 ( ( sup_sup_set_val @ ( sup_sup_set_val @ A @ B ) @ C2 )
% 0.06/0.34 = ( sup_sup_set_val @ A @ ( sup_sup_set_val @ B @ C2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % sup.assoc
% 0.06/0.34 thf(fact_276_boolean__algebra__cancel_Osup2,axiom,
% 0.06/0.34 ! [B2: set_val,K: set_val,B: set_val,A: set_val] :
% 0.06/0.34 ( ( B2
% 0.06/0.34 = ( sup_sup_set_val @ K @ B ) )
% 0.06/0.34 => ( ( sup_sup_set_val @ A @ B2 )
% 0.06/0.34 = ( sup_sup_set_val @ K @ ( sup_sup_set_val @ A @ B ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % boolean_algebra_cancel.sup2
% 0.06/0.34 thf(fact_277_boolean__algebra__cancel_Osup1,axiom,
% 0.06/0.34 ! [A2: set_val,K: set_val,A: set_val,B: set_val] :
% 0.06/0.34 ( ( A2
% 0.06/0.34 = ( sup_sup_set_val @ K @ A ) )
% 0.06/0.34 => ( ( sup_sup_set_val @ A2 @ B )
% 0.06/0.34 = ( sup_sup_set_val @ K @ ( sup_sup_set_val @ A @ B ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % boolean_algebra_cancel.sup1
% 0.06/0.34 thf(fact_278_inf__sup__aci_I5_J,axiom,
% 0.06/0.34 ( sup_sup_set_val
% 0.06/0.34 = ( ^ [X: set_val,Y2: set_val] : ( sup_sup_set_val @ Y2 @ X ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % inf_sup_aci(5)
% 0.06/0.34 thf(fact_279_inf__sup__aci_I6_J,axiom,
% 0.06/0.34 ! [X2: set_val,Y3: set_val,Z: set_val] :
% 0.06/0.34 ( ( sup_sup_set_val @ ( sup_sup_set_val @ X2 @ Y3 ) @ Z )
% 0.06/0.34 = ( sup_sup_set_val @ X2 @ ( sup_sup_set_val @ Y3 @ Z ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % inf_sup_aci(6)
% 0.06/0.34 thf(fact_280_inf__sup__aci_I7_J,axiom,
% 0.06/0.34 ! [X2: set_val,Y3: set_val,Z: set_val] :
% 0.06/0.34 ( ( sup_sup_set_val @ X2 @ ( sup_sup_set_val @ Y3 @ Z ) )
% 0.06/0.34 = ( sup_sup_set_val @ Y3 @ ( sup_sup_set_val @ X2 @ Z ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % inf_sup_aci(7)
% 0.06/0.34 thf(fact_281_inf__sup__aci_I8_J,axiom,
% 0.06/0.34 ! [X2: set_val,Y3: set_val] :
% 0.06/0.34 ( ( sup_sup_set_val @ X2 @ ( sup_sup_set_val @ X2 @ Y3 ) )
% 0.06/0.34 = ( sup_sup_set_val @ X2 @ Y3 ) ) ).
% 0.06/0.34
% 0.06/0.34 % inf_sup_aci(8)
% 0.06/0.34 thf(fact_282_Un__left__commute,axiom,
% 0.06/0.34 ! [A2: set_val,B2: set_val,C: set_val] :
% 0.06/0.34 ( ( sup_sup_set_val @ A2 @ ( sup_sup_set_val @ B2 @ C ) )
% 0.06/0.34 = ( sup_sup_set_val @ B2 @ ( sup_sup_set_val @ A2 @ C ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % Un_left_commute
% 0.06/0.34 thf(fact_283_Un__left__absorb,axiom,
% 0.06/0.34 ! [A2: set_val,B2: set_val] :
% 0.06/0.34 ( ( sup_sup_set_val @ A2 @ ( sup_sup_set_val @ A2 @ B2 ) )
% 0.06/0.34 = ( sup_sup_set_val @ A2 @ B2 ) ) ).
% 0.06/0.34
% 0.06/0.34 % Un_left_absorb
% 0.06/0.34 thf(fact_284_Un__commute,axiom,
% 0.06/0.34 ( sup_sup_set_val
% 0.06/0.34 = ( ^ [A5: set_val,B4: set_val] : ( sup_sup_set_val @ B4 @ A5 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % Un_commute
% 0.06/0.34 thf(fact_285_Un__absorb,axiom,
% 0.06/0.34 ! [A2: set_val] :
% 0.06/0.34 ( ( sup_sup_set_val @ A2 @ A2 )
% 0.06/0.34 = A2 ) ).
% 0.06/0.34
% 0.06/0.34 % Un_absorb
% 0.06/0.34 thf(fact_286_Un__assoc,axiom,
% 0.06/0.34 ! [A2: set_val,B2: set_val,C: set_val] :
% 0.06/0.34 ( ( sup_sup_set_val @ ( sup_sup_set_val @ A2 @ B2 ) @ C )
% 0.06/0.34 = ( sup_sup_set_val @ A2 @ ( sup_sup_set_val @ B2 @ C ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % Un_assoc
% 0.06/0.34 thf(fact_287_ball__Un,axiom,
% 0.06/0.34 ! [A2: set_val,B2: set_val,P2: val > $o] :
% 0.06/0.34 ( ( ! [X: val] :
% 0.06/0.34 ( ( member_val @ X @ ( sup_sup_set_val @ A2 @ B2 ) )
% 0.06/0.34 => ( P2 @ X ) ) )
% 0.06/0.34 = ( ! [X: val] :
% 0.06/0.34 ( ( member_val @ X @ A2 )
% 0.06/0.34 => ( P2 @ X ) )
% 0.06/0.34 & ! [X: val] :
% 0.06/0.34 ( ( member_val @ X @ B2 )
% 0.06/0.34 => ( P2 @ X ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % ball_Un
% 0.06/0.34 thf(fact_288_bex__Un,axiom,
% 0.06/0.34 ! [A2: set_val,B2: set_val,P2: val > $o] :
% 0.06/0.34 ( ( ? [X: val] :
% 0.06/0.34 ( ( member_val @ X @ ( sup_sup_set_val @ A2 @ B2 ) )
% 0.06/0.34 & ( P2 @ X ) ) )
% 0.06/0.34 = ( ? [X: val] :
% 0.06/0.34 ( ( member_val @ X @ A2 )
% 0.06/0.34 & ( P2 @ X ) )
% 0.06/0.34 | ? [X: val] :
% 0.06/0.34 ( ( member_val @ X @ B2 )
% 0.06/0.34 & ( P2 @ X ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % bex_Un
% 0.06/0.34 thf(fact_289_UnI2,axiom,
% 0.06/0.34 ! [C2: node,B2: set_node,A2: set_node] :
% 0.06/0.34 ( ( member_node @ C2 @ B2 )
% 0.06/0.34 => ( member_node @ C2 @ ( sup_sup_set_node @ A2 @ B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % UnI2
% 0.06/0.34 thf(fact_290_UnI2,axiom,
% 0.06/0.34 ! [C2: set_val,B2: set_set_val,A2: set_set_val] :
% 0.06/0.34 ( ( member_set_val @ C2 @ B2 )
% 0.06/0.34 => ( member_set_val @ C2 @ ( sup_sup_set_set_val @ A2 @ B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % UnI2
% 0.06/0.34 thf(fact_291_UnI2,axiom,
% 0.06/0.34 ! [C2: produc1432036078de_val,B2: set_Pr699757092de_val,A2: set_Pr699757092de_val] :
% 0.06/0.34 ( ( member313544709de_val @ C2 @ B2 )
% 0.06/0.34 => ( member313544709de_val @ C2 @ ( sup_su2138939728de_val @ A2 @ B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % UnI2
% 0.06/0.34 thf(fact_292_UnI2,axiom,
% 0.06/0.34 ! [C2: produc1324971431et_val,B2: set_Pr1311924359et_val,A2: set_Pr1311924359et_val] :
% 0.06/0.34 ( ( member1711426256et_val @ C2 @ B2 )
% 0.06/0.34 => ( member1711426256et_val @ C2 @ ( sup_su2005730907et_val @ A2 @ B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % UnI2
% 0.06/0.34 thf(fact_293_UnI2,axiom,
% 0.06/0.34 ! [C2: val,B2: set_val,A2: set_val] :
% 0.06/0.34 ( ( member_val @ C2 @ B2 )
% 0.06/0.34 => ( member_val @ C2 @ ( sup_sup_set_val @ A2 @ B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % UnI2
% 0.06/0.34 thf(fact_294_UnI1,axiom,
% 0.06/0.34 ! [C2: node,A2: set_node,B2: set_node] :
% 0.06/0.34 ( ( member_node @ C2 @ A2 )
% 0.06/0.34 => ( member_node @ C2 @ ( sup_sup_set_node @ A2 @ B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % UnI1
% 0.06/0.34 thf(fact_295_UnI1,axiom,
% 0.06/0.34 ! [C2: set_val,A2: set_set_val,B2: set_set_val] :
% 0.06/0.34 ( ( member_set_val @ C2 @ A2 )
% 0.06/0.34 => ( member_set_val @ C2 @ ( sup_sup_set_set_val @ A2 @ B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % UnI1
% 0.06/0.34 thf(fact_296_UnI1,axiom,
% 0.06/0.34 ! [C2: produc1432036078de_val,A2: set_Pr699757092de_val,B2: set_Pr699757092de_val] :
% 0.06/0.34 ( ( member313544709de_val @ C2 @ A2 )
% 0.06/0.34 => ( member313544709de_val @ C2 @ ( sup_su2138939728de_val @ A2 @ B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % UnI1
% 0.06/0.34 thf(fact_297_UnI1,axiom,
% 0.06/0.34 ! [C2: produc1324971431et_val,A2: set_Pr1311924359et_val,B2: set_Pr1311924359et_val] :
% 0.06/0.34 ( ( member1711426256et_val @ C2 @ A2 )
% 0.06/0.34 => ( member1711426256et_val @ C2 @ ( sup_su2005730907et_val @ A2 @ B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % UnI1
% 0.06/0.34 thf(fact_298_UnI1,axiom,
% 0.06/0.34 ! [C2: val,A2: set_val,B2: set_val] :
% 0.06/0.34 ( ( member_val @ C2 @ A2 )
% 0.06/0.34 => ( member_val @ C2 @ ( sup_sup_set_val @ A2 @ B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % UnI1
% 0.06/0.34 thf(fact_299_UnE,axiom,
% 0.06/0.34 ! [C2: node,A2: set_node,B2: set_node] :
% 0.06/0.34 ( ( member_node @ C2 @ ( sup_sup_set_node @ A2 @ B2 ) )
% 0.06/0.34 => ( ~ ( member_node @ C2 @ A2 )
% 0.06/0.34 => ( member_node @ C2 @ B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % UnE
% 0.06/0.34 thf(fact_300_UnE,axiom,
% 0.06/0.34 ! [C2: set_val,A2: set_set_val,B2: set_set_val] :
% 0.06/0.34 ( ( member_set_val @ C2 @ ( sup_sup_set_set_val @ A2 @ B2 ) )
% 0.06/0.34 => ( ~ ( member_set_val @ C2 @ A2 )
% 0.06/0.34 => ( member_set_val @ C2 @ B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % UnE
% 0.06/0.34 thf(fact_301_UnE,axiom,
% 0.06/0.34 ! [C2: produc1432036078de_val,A2: set_Pr699757092de_val,B2: set_Pr699757092de_val] :
% 0.06/0.34 ( ( member313544709de_val @ C2 @ ( sup_su2138939728de_val @ A2 @ B2 ) )
% 0.06/0.34 => ( ~ ( member313544709de_val @ C2 @ A2 )
% 0.06/0.34 => ( member313544709de_val @ C2 @ B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % UnE
% 0.06/0.34 thf(fact_302_UnE,axiom,
% 0.06/0.34 ! [C2: produc1324971431et_val,A2: set_Pr1311924359et_val,B2: set_Pr1311924359et_val] :
% 0.06/0.34 ( ( member1711426256et_val @ C2 @ ( sup_su2005730907et_val @ A2 @ B2 ) )
% 0.06/0.34 => ( ~ ( member1711426256et_val @ C2 @ A2 )
% 0.06/0.34 => ( member1711426256et_val @ C2 @ B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % UnE
% 0.06/0.34 thf(fact_303_UnE,axiom,
% 0.06/0.34 ! [C2: val,A2: set_val,B2: set_val] :
% 0.06/0.34 ( ( member_val @ C2 @ ( sup_sup_set_val @ A2 @ B2 ) )
% 0.06/0.34 => ( ~ ( member_val @ C2 @ A2 )
% 0.06/0.34 => ( member_val @ C2 @ B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % UnE
% 0.06/0.34 thf(fact_304_sup_OcoboundedI2,axiom,
% 0.06/0.34 ! [C2: set_val,B: set_val,A: set_val] :
% 0.06/0.34 ( ( ord_less_eq_set_val @ C2 @ B )
% 0.06/0.34 => ( ord_less_eq_set_val @ C2 @ ( sup_sup_set_val @ A @ B ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % sup.coboundedI2
% 0.06/0.34 thf(fact_305_sup_OcoboundedI1,axiom,
% 0.06/0.34 ! [C2: set_val,A: set_val,B: set_val] :
% 0.06/0.34 ( ( ord_less_eq_set_val @ C2 @ A )
% 0.06/0.34 => ( ord_less_eq_set_val @ C2 @ ( sup_sup_set_val @ A @ B ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % sup.coboundedI1
% 0.06/0.34 thf(fact_306_sup_Oabsorb__iff2,axiom,
% 0.06/0.34 ( ord_less_eq_set_val
% 0.06/0.34 = ( ^ [A3: set_val,B5: set_val] :
% 0.06/0.34 ( ( sup_sup_set_val @ A3 @ B5 )
% 0.06/0.34 = B5 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % sup.absorb_iff2
% 0.06/0.34 thf(fact_307_sup_Oabsorb__iff1,axiom,
% 0.06/0.34 ( ord_less_eq_set_val
% 0.06/0.34 = ( ^ [B5: set_val,A3: set_val] :
% 0.06/0.34 ( ( sup_sup_set_val @ A3 @ B5 )
% 0.06/0.34 = A3 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % sup.absorb_iff1
% 0.06/0.34 thf(fact_308_sup_Ocobounded2,axiom,
% 0.06/0.34 ! [B: set_val,A: set_val] : ( ord_less_eq_set_val @ B @ ( sup_sup_set_val @ A @ B ) ) ).
% 0.06/0.34
% 0.06/0.34 % sup.cobounded2
% 0.06/0.34 thf(fact_309_sup_Ocobounded1,axiom,
% 0.06/0.34 ! [A: set_val,B: set_val] : ( ord_less_eq_set_val @ A @ ( sup_sup_set_val @ A @ B ) ) ).
% 0.06/0.34
% 0.06/0.34 % sup.cobounded1
% 0.06/0.34 thf(fact_310_sup_Oorder__iff,axiom,
% 0.06/0.34 ( ord_less_eq_set_val
% 0.06/0.34 = ( ^ [B5: set_val,A3: set_val] :
% 0.06/0.34 ( A3
% 0.06/0.34 = ( sup_sup_set_val @ A3 @ B5 ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % sup.order_iff
% 0.06/0.34 thf(fact_311_sup_OboundedI,axiom,
% 0.06/0.34 ! [B: set_val,A: set_val,C2: set_val] :
% 0.06/0.34 ( ( ord_less_eq_set_val @ B @ A )
% 0.06/0.34 => ( ( ord_less_eq_set_val @ C2 @ A )
% 0.06/0.34 => ( ord_less_eq_set_val @ ( sup_sup_set_val @ B @ C2 ) @ A ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % sup.boundedI
% 0.06/0.34 thf(fact_312_sup_OboundedE,axiom,
% 0.06/0.34 ! [B: set_val,C2: set_val,A: set_val] :
% 0.06/0.34 ( ( ord_less_eq_set_val @ ( sup_sup_set_val @ B @ C2 ) @ A )
% 0.06/0.34 => ~ ( ( ord_less_eq_set_val @ B @ A )
% 0.06/0.34 => ~ ( ord_less_eq_set_val @ C2 @ A ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % sup.boundedE
% 0.06/0.34 thf(fact_313_sup__absorb2,axiom,
% 0.06/0.34 ! [X2: set_val,Y3: set_val] :
% 0.06/0.34 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 0.06/0.34 => ( ( sup_sup_set_val @ X2 @ Y3 )
% 0.06/0.34 = Y3 ) ) ).
% 0.06/0.34
% 0.06/0.34 % sup_absorb2
% 0.06/0.34 thf(fact_314_sup__absorb1,axiom,
% 0.06/0.34 ! [Y3: set_val,X2: set_val] :
% 0.06/0.34 ( ( ord_less_eq_set_val @ Y3 @ X2 )
% 0.06/0.34 => ( ( sup_sup_set_val @ X2 @ Y3 )
% 0.06/0.34 = X2 ) ) ).
% 0.06/0.34
% 0.06/0.34 % sup_absorb1
% 0.06/0.34 thf(fact_315_sup_Oabsorb2,axiom,
% 0.06/0.34 ! [A: set_val,B: set_val] :
% 0.06/0.34 ( ( ord_less_eq_set_val @ A @ B )
% 0.06/0.34 => ( ( sup_sup_set_val @ A @ B )
% 0.06/0.34 = B ) ) ).
% 0.06/0.34
% 0.06/0.34 % sup.absorb2
% 0.06/0.34 thf(fact_316_sup_Oabsorb1,axiom,
% 0.06/0.34 ! [B: set_val,A: set_val] :
% 0.06/0.34 ( ( ord_less_eq_set_val @ B @ A )
% 0.06/0.34 => ( ( sup_sup_set_val @ A @ B )
% 0.06/0.34 = A ) ) ).
% 0.06/0.34
% 0.06/0.34 % sup.absorb1
% 0.06/0.34 thf(fact_317_sup__unique,axiom,
% 0.06/0.34 ! [F2: set_val > set_val > set_val,X2: set_val,Y3: set_val] :
% 0.06/0.34 ( ! [X3: set_val,Y5: set_val] : ( ord_less_eq_set_val @ X3 @ ( F2 @ X3 @ Y5 ) )
% 0.06/0.34 => ( ! [X3: set_val,Y5: set_val] : ( ord_less_eq_set_val @ Y5 @ ( F2 @ X3 @ Y5 ) )
% 0.06/0.34 => ( ! [X3: set_val,Y5: set_val,Z3: set_val] :
% 0.06/0.34 ( ( ord_less_eq_set_val @ Y5 @ X3 )
% 0.06/0.34 => ( ( ord_less_eq_set_val @ Z3 @ X3 )
% 0.06/0.34 => ( ord_less_eq_set_val @ ( F2 @ Y5 @ Z3 ) @ X3 ) ) )
% 0.06/0.34 => ( ( sup_sup_set_val @ X2 @ Y3 )
% 0.06/0.34 = ( F2 @ X2 @ Y3 ) ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % sup_unique
% 0.06/0.34 thf(fact_318_sup_OorderI,axiom,
% 0.06/0.34 ! [A: set_val,B: set_val] :
% 0.06/0.34 ( ( A
% 0.06/0.34 = ( sup_sup_set_val @ A @ B ) )
% 0.06/0.34 => ( ord_less_eq_set_val @ B @ A ) ) ).
% 0.06/0.34
% 0.06/0.34 % sup.orderI
% 0.06/0.34 thf(fact_319_sup_OorderE,axiom,
% 0.06/0.34 ! [B: set_val,A: set_val] :
% 0.06/0.34 ( ( ord_less_eq_set_val @ B @ A )
% 0.06/0.34 => ( A
% 0.06/0.34 = ( sup_sup_set_val @ A @ B ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % sup.orderE
% 0.06/0.34 thf(fact_320_le__iff__sup,axiom,
% 0.06/0.34 ( ord_less_eq_set_val
% 0.06/0.34 = ( ^ [X: set_val,Y2: set_val] :
% 0.06/0.34 ( ( sup_sup_set_val @ X @ Y2 )
% 0.06/0.34 = Y2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % le_iff_sup
% 0.06/0.34 thf(fact_321_sup__least,axiom,
% 0.06/0.34 ! [Y3: set_val,X2: set_val,Z: set_val] :
% 0.06/0.34 ( ( ord_less_eq_set_val @ Y3 @ X2 )
% 0.06/0.34 => ( ( ord_less_eq_set_val @ Z @ X2 )
% 0.06/0.34 => ( ord_less_eq_set_val @ ( sup_sup_set_val @ Y3 @ Z ) @ X2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % sup_least
% 0.06/0.34 thf(fact_322_sup__mono,axiom,
% 0.06/0.34 ! [A: set_val,C2: set_val,B: set_val,D: set_val] :
% 0.06/0.34 ( ( ord_less_eq_set_val @ A @ C2 )
% 0.06/0.34 => ( ( ord_less_eq_set_val @ B @ D )
% 0.06/0.34 => ( ord_less_eq_set_val @ ( sup_sup_set_val @ A @ B ) @ ( sup_sup_set_val @ C2 @ D ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % sup_mono
% 0.06/0.34 thf(fact_323_sup_Omono,axiom,
% 0.06/0.34 ! [C2: set_val,A: set_val,D: set_val,B: set_val] :
% 0.06/0.34 ( ( ord_less_eq_set_val @ C2 @ A )
% 0.06/0.34 => ( ( ord_less_eq_set_val @ D @ B )
% 0.06/0.34 => ( ord_less_eq_set_val @ ( sup_sup_set_val @ C2 @ D ) @ ( sup_sup_set_val @ A @ B ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % sup.mono
% 0.06/0.34 thf(fact_324_le__supI2,axiom,
% 0.06/0.34 ! [X2: set_val,B: set_val,A: set_val] :
% 0.06/0.34 ( ( ord_less_eq_set_val @ X2 @ B )
% 0.06/0.34 => ( ord_less_eq_set_val @ X2 @ ( sup_sup_set_val @ A @ B ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % le_supI2
% 0.06/0.34 thf(fact_325_le__supI1,axiom,
% 0.06/0.34 ! [X2: set_val,A: set_val,B: set_val] :
% 0.06/0.34 ( ( ord_less_eq_set_val @ X2 @ A )
% 0.06/0.34 => ( ord_less_eq_set_val @ X2 @ ( sup_sup_set_val @ A @ B ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % le_supI1
% 0.06/0.34 thf(fact_326_sup__ge2,axiom,
% 0.06/0.34 ! [Y3: set_val,X2: set_val] : ( ord_less_eq_set_val @ Y3 @ ( sup_sup_set_val @ X2 @ Y3 ) ) ).
% 0.06/0.34
% 0.06/0.34 % sup_ge2
% 0.06/0.34 thf(fact_327_sup__ge1,axiom,
% 0.06/0.34 ! [X2: set_val,Y3: set_val] : ( ord_less_eq_set_val @ X2 @ ( sup_sup_set_val @ X2 @ Y3 ) ) ).
% 0.06/0.34
% 0.06/0.34 % sup_ge1
% 0.06/0.34 thf(fact_328_le__supI,axiom,
% 0.06/0.34 ! [A: set_val,X2: set_val,B: set_val] :
% 0.06/0.34 ( ( ord_less_eq_set_val @ A @ X2 )
% 0.06/0.34 => ( ( ord_less_eq_set_val @ B @ X2 )
% 0.06/0.34 => ( ord_less_eq_set_val @ ( sup_sup_set_val @ A @ B ) @ X2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % le_supI
% 0.06/0.34 thf(fact_329_le__supE,axiom,
% 0.06/0.34 ! [A: set_val,B: set_val,X2: set_val] :
% 0.06/0.34 ( ( ord_less_eq_set_val @ ( sup_sup_set_val @ A @ B ) @ X2 )
% 0.06/0.34 => ~ ( ( ord_less_eq_set_val @ A @ X2 )
% 0.06/0.34 => ~ ( ord_less_eq_set_val @ B @ X2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % le_supE
% 0.06/0.34 thf(fact_330_inf__sup__ord_I3_J,axiom,
% 0.06/0.34 ! [X2: set_val,Y3: set_val] : ( ord_less_eq_set_val @ X2 @ ( sup_sup_set_val @ X2 @ Y3 ) ) ).
% 0.06/0.34
% 0.06/0.34 % inf_sup_ord(3)
% 0.06/0.34 thf(fact_331_inf__sup__ord_I4_J,axiom,
% 0.06/0.34 ! [Y3: set_val,X2: set_val] : ( ord_less_eq_set_val @ Y3 @ ( sup_sup_set_val @ X2 @ Y3 ) ) ).
% 0.06/0.34
% 0.06/0.34 % inf_sup_ord(4)
% 0.06/0.34 thf(fact_332_subset__Un__eq,axiom,
% 0.06/0.34 ( ord_less_eq_set_val
% 0.06/0.34 = ( ^ [A5: set_val,B4: set_val] :
% 0.06/0.34 ( ( sup_sup_set_val @ A5 @ B4 )
% 0.06/0.34 = B4 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % subset_Un_eq
% 0.06/0.34 thf(fact_333_subset__UnE,axiom,
% 0.06/0.34 ! [C: set_val,A2: set_val,B2: set_val] :
% 0.06/0.34 ( ( ord_less_eq_set_val @ C @ ( sup_sup_set_val @ A2 @ B2 ) )
% 0.06/0.34 => ~ ! [A6: set_val] :
% 0.06/0.34 ( ( ord_less_eq_set_val @ A6 @ A2 )
% 0.06/0.34 => ! [B6: set_val] :
% 0.06/0.34 ( ( ord_less_eq_set_val @ B6 @ B2 )
% 0.06/0.34 => ( C
% 0.06/0.34 != ( sup_sup_set_val @ A6 @ B6 ) ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % subset_UnE
% 0.06/0.34 thf(fact_334_Un__absorb2,axiom,
% 0.06/0.34 ! [B2: set_val,A2: set_val] :
% 0.06/0.34 ( ( ord_less_eq_set_val @ B2 @ A2 )
% 0.06/0.34 => ( ( sup_sup_set_val @ A2 @ B2 )
% 0.06/0.34 = A2 ) ) ).
% 0.06/0.34
% 0.06/0.34 % Un_absorb2
% 0.06/0.34 thf(fact_335_Un__absorb1,axiom,
% 0.06/0.34 ! [A2: set_val,B2: set_val] :
% 0.06/0.34 ( ( ord_less_eq_set_val @ A2 @ B2 )
% 0.06/0.34 => ( ( sup_sup_set_val @ A2 @ B2 )
% 0.06/0.34 = B2 ) ) ).
% 0.06/0.34
% 0.06/0.34 % Un_absorb1
% 0.06/0.34 thf(fact_336_Un__upper2,axiom,
% 0.06/0.34 ! [B2: set_val,A2: set_val] : ( ord_less_eq_set_val @ B2 @ ( sup_sup_set_val @ A2 @ B2 ) ) ).
% 0.06/0.34
% 0.06/0.34 % Un_upper2
% 0.06/0.34 thf(fact_337_Un__upper1,axiom,
% 0.06/0.34 ! [A2: set_val,B2: set_val] : ( ord_less_eq_set_val @ A2 @ ( sup_sup_set_val @ A2 @ B2 ) ) ).
% 0.06/0.34
% 0.06/0.34 % Un_upper1
% 0.06/0.34 thf(fact_338_Un__least,axiom,
% 0.06/0.34 ! [A2: set_val,C: set_val,B2: set_val] :
% 0.06/0.34 ( ( ord_less_eq_set_val @ A2 @ C )
% 0.06/0.34 => ( ( ord_less_eq_set_val @ B2 @ C )
% 0.06/0.34 => ( ord_less_eq_set_val @ ( sup_sup_set_val @ A2 @ B2 ) @ C ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % Un_least
% 0.06/0.34 thf(fact_339_Un__mono,axiom,
% 0.06/0.34 ! [A2: set_val,C: set_val,B2: set_val,D2: set_val] :
% 0.06/0.34 ( ( ord_less_eq_set_val @ A2 @ C )
% 0.06/0.34 => ( ( ord_less_eq_set_val @ B2 @ D2 )
% 0.06/0.34 => ( ord_less_eq_set_val @ ( sup_sup_set_val @ A2 @ B2 ) @ ( sup_sup_set_val @ C @ D2 ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % Un_mono
% 0.06/0.34 thf(fact_340_redundant__set__def,axiom,
% 0.06/0.34 ! [G: g,P2: set_val] :
% 0.06/0.34 ( ( irredu224829488eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G @ P2 )
% 0.06/0.34 = ( ( P2 != bot_bot_set_val )
% 0.06/0.34 & ( ord_less_eq_set_val @ P2 @ ( dom_val_list_val @ ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ G ) ) )
% 0.06/0.34 & ? [X: val] :
% 0.06/0.34 ( ( member_val @ X @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 0.06/0.34 & ! [Y2: val] :
% 0.06/0.34 ( ( member_val @ Y2 @ P2 )
% 0.06/0.34 => ! [Phi3: val] :
% 0.06/0.34 ( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G @ Y2 @ Phi3 )
% 0.06/0.34 => ( member_val @ Phi3 @ ( sup_sup_set_val @ P2 @ ( insert_val @ X @ bot_bot_set_val ) ) ) ) ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % redundant_set_def
% 0.06/0.34 thf(fact_341_phi__no__closed__loop,axiom,
% 0.06/0.34 ! [P: val,G: g,Vs: list_val] :
% 0.06/0.34 ( ( member_val @ P @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 0.06/0.34 => ( ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ G @ P )
% 0.06/0.34 = ( some_list_val @ Vs ) )
% 0.06/0.34 => ( ( set_val2 @ Vs )
% 0.06/0.34 != ( insert_val @ P @ bot_bot_set_val ) ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % phi_no_closed_loop
% 0.06/0.34 thf(fact_342_dom__eq__empty__conv,axiom,
% 0.06/0.34 ! [F2: produc1432036078de_val > option_list_val] :
% 0.06/0.34 ( ( ( dom_Pr729677986st_val @ F2 )
% 0.06/0.34 = bot_bo404898488de_val )
% 0.06/0.34 = ( F2
% 0.06/0.34 = ( ^ [X: produc1432036078de_val] : none_list_val ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % dom_eq_empty_conv
% 0.06/0.34 thf(fact_343_dom__eq__empty__conv,axiom,
% 0.06/0.34 ! [F2: val > option_list_val] :
% 0.06/0.34 ( ( ( dom_val_list_val @ F2 )
% 0.06/0.34 = bot_bot_set_val )
% 0.06/0.34 = ( F2
% 0.06/0.34 = ( ^ [X: val] : none_list_val ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % dom_eq_empty_conv
% 0.06/0.34 thf(fact_344_phis__finite,axiom,
% 0.06/0.34 ! [G: g] : ( finite2056463621de_val @ ( dom_Pr729677986st_val @ ( phis @ G ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % phis_finite
% 0.06/0.34 thf(fact_345_insert__subset,axiom,
% 0.06/0.34 ! [X2: node,A2: set_node,B2: set_node] :
% 0.06/0.34 ( ( ord_less_eq_set_node @ ( insert_node @ X2 @ A2 ) @ B2 )
% 0.06/0.34 = ( ( member_node @ X2 @ B2 )
% 0.06/0.34 & ( ord_less_eq_set_node @ A2 @ B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % insert_subset
% 0.06/0.34 thf(fact_346_insert__subset,axiom,
% 0.06/0.34 ! [X2: set_val,A2: set_set_val,B2: set_set_val] :
% 0.06/0.34 ( ( ord_le1742111550et_val @ ( insert_set_val @ X2 @ A2 ) @ B2 )
% 0.06/0.34 = ( ( member_set_val @ X2 @ B2 )
% 0.06/0.34 & ( ord_le1742111550et_val @ A2 @ B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % insert_subset
% 0.06/0.34 thf(fact_347_insert__subset,axiom,
% 0.06/0.34 ! [X2: produc1432036078de_val,A2: set_Pr699757092de_val,B2: set_Pr699757092de_val] :
% 0.06/0.34 ( ( ord_le1643692676de_val @ ( insert869443870de_val @ X2 @ A2 ) @ B2 )
% 0.06/0.34 = ( ( member313544709de_val @ X2 @ B2 )
% 0.06/0.34 & ( ord_le1643692676de_val @ A2 @ B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % insert_subset
% 0.06/0.34 thf(fact_348_insert__subset,axiom,
% 0.06/0.34 ! [X2: produc1324971431et_val,A2: set_Pr1311924359et_val,B2: set_Pr1311924359et_val] :
% 0.06/0.34 ( ( ord_le299366439et_val @ ( insert1846469495et_val @ X2 @ A2 ) @ B2 )
% 0.06/0.34 = ( ( member1711426256et_val @ X2 @ B2 )
% 0.06/0.34 & ( ord_le299366439et_val @ A2 @ B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % insert_subset
% 0.06/0.34 thf(fact_349_insert__subset,axiom,
% 0.06/0.34 ! [X2: val,A2: set_val,B2: set_val] :
% 0.06/0.34 ( ( ord_less_eq_set_val @ ( insert_val @ X2 @ A2 ) @ B2 )
% 0.06/0.34 = ( ( member_val @ X2 @ B2 )
% 0.06/0.34 & ( ord_less_eq_set_val @ A2 @ B2 ) ) ) ).
% 0.06/0.34
% 0.06/0.34 % insert_subset
% 0.06/0.34 thf(fact_350_finite__insert,axiom,
% 0.06/0.34 ! [A: val,A2: set_val] :
% 0.06/0.34 ( ( finite_finite_val @ ( insert_val @ A @ A2 ) )
% 0.06/0.34 = ( finite_finite_val @ A2 ) ) ).
% 0.06/0.34
% 0.06/0.34 % finite_insert
% 0.06/0.34 thf(fact_351_finite__insert,axiom,
% 0.06/0.34 ! [A: produc1324971431et_val,A2: set_Pr1311924359et_val] :
% 0.06/0.34 ( ( finite79836624et_val @ ( insert1846469495et_val @ A @ A2 ) )
% 0.06/0.34 = ( finite79836624et_val @ A2 ) ) ).
% 0.06/0.34
% 0.06/0.34 % finite_insert
% 0.06/0.34 thf(fact_352_finite__insert,axiom,
% 0.06/0.34 ! [A: produc1432036078de_val,A2: set_Pr699757092de_val] :
% 0.06/0.34 ( ( finite2056463621de_val @ ( insert869443870de_val @ A @ A2 ) )
% 0.06/0.34 = ( finite2056463621de_val @ A2 ) ) ).
% 0.06/0.34
% 0.06/0.34 % finite_insert
% 0.06/0.34
% 0.06/0.34 % Conjectures (1)
% 0.06/0.34 thf(conj_0,conjecture,
% 0.06/0.34 member_val @ phi_s @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2 ) ).
% 0.06/0.34
% 0.06/0.34 %------------------------------------------------------------------------------
% 0.06/0.34 ------------------------
% 2.07/1.15 ---- Embedded in THF ---
% 2.07/1.15 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.07/1.15 %%% Generated on Tue Feb 24 03:25:41 EST 2026
% 2.07/1.15 %%% using '$$dhol' embedding, version 1.3.0.
% 2.07/1.15 %%% Logic specification used:
% 2.07/1.15 %%% thf(spec, logic, $$dhol).
% 2.07/1.15
% 2.07/1.15 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.ceXPxvwqcT/DTF2DTF29714.p
% See solution above
% 2.07/1.15 ------------------------
% 2.07/1.19 ---- Cleaned THF ---
% 2.07/1.19 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_Itf__val_J_Mt__Set__Oset_Itf__val_J_J_Mt__Product____Type__Oprod_It__Set__Oset_Itf__val_J_Mt__Set__Oset_Itf__val_J_J_J_J,type,
% 2.07/1.19 list_P88441325et_val: $tType ).
% 2.07/1.19
% 2.07/1.19 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_Itf__val_J_Mt__Set__Oset_Itf__val_J_J_Mt__Product____Type__Oprod_It__Set__Oset_Itf__val_J_Mt__Set__Oset_Itf__val_J_J_J_J,type,
% 2.07/1.19 set_Pr1587248327et_val: $tType ).
% 2.07/1.19
% 2.07/1.19 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_Itf__val_J_Mt__Set__Oset_Itf__val_J_J_Mt__Product____Type__Oprod_It__Set__Oset_Itf__val_J_Mt__Set__Oset_Itf__val_J_J_J,type,
% 2.07/1.19 produc1904584935et_val: $tType ).
% 2.07/1.19
% 2.07/1.19 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__node_Mtf__val_J_Mt__Product____Type__Oprod_Itf__node_Mtf__val_J_J_J,type,
% 2.07/1.19 list_P729276995de_val: $tType ).
% 2.07/1.19
% 2.07/1.19 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__node_Mtf__val_J_Mt__Product____Type__Oprod_Itf__node_Mtf__val_J_J_J,type,
% 2.07/1.19 set_Pr819703837de_val: $tType ).
% 2.07/1.19
% 2.07/1.19 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__node_Mtf__val_J_Mt__Product____Type__Oprod_Itf__node_Mtf__val_J_J,type,
% 2.07/1.19 produc452075965de_val: $tType ).
% 2.07/1.19
% 2.07/1.19 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_Itf__node_Mt__Product____Type__Oprod_Itf__node_Mtf__val_J_J_J,type,
% 2.07/1.19 list_P1108777338de_val: $tType ).
% 2.07/1.19
% 2.07/1.19 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_Itf__val_Mt__Product____Type__Oprod_Itf__node_Mtf__val_J_J_J,type,
% 2.07/1.19 list_P844977291de_val: $tType ).
% 2.07/1.19
% 2.07/1.19 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__node_Mt__Product____Type__Oprod_Itf__node_Mtf__val_J_J_J,type,
% 2.07/1.19 set_Pr1245322836de_val: $tType ).
% 2.07/1.19
% 2.07/1.19 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__val_Mt__Product____Type__Oprod_Itf__node_Mtf__val_J_J_J,type,
% 2.07/1.19 set_Pr701036849de_val: $tType ).
% 2.07/1.19
% 2.07/1.19 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Set__Oset_Itf__val_J_Mt__Set__Oset_Itf__val_J_J_J,type,
% 2.07/1.19 list_P2089461677et_val: $tType ).
% 2.07/1.19
% 2.07/1.19 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_Itf__val_J_Mt__Set__Oset_Itf__val_J_J_J,type,
% 2.07/1.19 set_Pr1311924359et_val: $tType ).
% 2.07/1.19
% 2.07/1.19 thf(ty_n_t__Product____Type__Oprod_Itf__node_Mt__Product____Type__Oprod_Itf__node_Mtf__val_J_J,type,
% 2.07/1.19 produc1615737844de_val: $tType ).
% 2.07/1.19
% 2.07/1.19 thf(ty_n_t__Product____Type__Oprod_Itf__val_Mt__Product____Type__Oprod_Itf__node_Mtf__val_J_J,type,
% 2.07/1.19 produc1664334075de_val: $tType ).
% 2.07/1.19
% 2.07/1.19 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_Itf__node_Mt__Set__Oset_Itf__val_J_J_J,type,
% 2.07/1.19 list_P12184414et_val: $tType ).
% 2.07/1.19
% 2.07/1.19 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Set__Oset_Itf__val_J_Mtf__node_J_J,type,
% 2.07/1.19 list_P1414038306l_node: $tType ).
% 2.07/1.19
% 2.07/1.19 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_Itf__val_Mt__Set__Oset_Itf__val_J_J_J,type,
% 2.07/1.19 list_P761482893et_val: $tType ).
% 2.07/1.19
% 2.07/1.19 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Set__Oset_Itf__val_J_Mtf__val_J_J,type,
% 2.07/1.19 list_P940784845al_val: $tType ).
% 2.07/1.19
% 2.07/1.19 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__node_Mt__Set__Oset_Itf__val_J_J_J,type,
% 2.07/1.19 set_Pr1320419588et_val: $tType ).
% 2.07/1.19
% 2.07/1.19 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_Itf__val_J_Mtf__node_J_J,type,
% 2.07/1.19 set_Pr574789832l_node: $tType ).
% 2.07/1.19
% 2.07/1.19 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__val_Mt__Set__Oset_Itf__val_J_J_J,type,
% 2.07/1.19 set_Pr978022247et_val: $tType ).
% 2.07/1.19
% 2.07/1.19 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_Itf__val_J_Mtf__val_J_J,type,
% 2.07/1.19 set_Pr1157324199al_val: $tType ).
% 2.07/1.19
% 2.07/1.19 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_Itf__val_J_Mt__Set__Oset_Itf__val_J_J,type,
% 2.07/1.19 produc1324971431et_val: $tType ).
% 2.07/1.19
% 2.07/1.19 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_Itf__node_Mtf__edgeD_J_J,type,
% 2.07/1.19 list_P561207620_edgeD: $tType ).
% 2.07/1.19
% 2.07/1.19 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_Itf__node_Mtf__node_J_J,type,
% 2.07/1.19 list_P1127016369e_node: $tType ).
% 2.07/1.19
% 2.07/1.19 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_Itf__val_Mtf__node_J_J,type,
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% 2.07/1.19 ord_le596993316et_val: option_set_val > option_set_val > $o ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_Itf__val_J_Mt__Set__Oset_Itf__val_J_J_J,type,
% 2.07/1.19 ord_le299366439et_val: set_Pr1311924359et_val > set_Pr1311924359et_val > $o ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_Itf__node_Mtf__val_J_J,type,
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% 2.07/1.19
% 2.07/1.19 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_Itf__val_J_J,type,
% 2.07/1.19 ord_le1742111550et_val: set_set_val > set_set_val > $o ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__node_J,type,
% 2.07/1.19 ord_less_eq_set_node: set_node > set_node > $o ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__val_J,type,
% 2.07/1.19 ord_less_eq_set_val: set_val > set_val > $o ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_Orderings_Oord__class_Oless__eq_001tf__node,type,
% 2.07/1.19 ord_less_eq_node: node > node > $o ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_Orderings_Oord__class_Oless__eq_001tf__val,type,
% 2.07/1.19 ord_less_eq_val: val > val > $o ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Set__Oset_Itf__val_J_Mt__Set__Oset_Itf__val_J_J_001t__Product____Type__Oprod_It__Set__Oset_Itf__val_J_Mt__Set__Oset_Itf__val_J_J,type,
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% 2.07/1.19
% 2.07/1.19 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_Itf__node_Mtf__val_J_001t__Product____Type__Oprod_Itf__node_Mtf__val_J,type,
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% 2.07/1.19
% 2.07/1.19 thf(sy_c_Product__Type_OPair_001t__Set__Oset_Itf__val_J_001t__Set__Oset_Itf__val_J,type,
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% 2.07/1.19
% 2.07/1.19 thf(sy_c_Product__Type_OPair_001t__Set__Oset_Itf__val_J_001tf__node,type,
% 2.07/1.19 produc2052093836l_node: set_val > node > produc1013974930l_node ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_Product__Type_OPair_001t__Set__Oset_Itf__val_J_001tf__val,type,
% 2.07/1.19 produc1337903031al_val: set_val > val > produc782216903al_val ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_Product__Type_OPair_001tf__node_001t__Product____Type__Oprod_Itf__node_Mtf__val_J,type,
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% 2.07/1.19
% 2.07/1.19 thf(sy_c_Product__Type_OPair_001tf__node_001t__Set__Oset_Itf__val_J,type,
% 2.07/1.19 produc2042994048et_val: node > set_val > produc1062784462et_val ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_Product__Type_OPair_001tf__node_001tf__node,type,
% 2.07/1.19 produc457016035e_node: node > node > produc951622955e_node ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_Product__Type_OPair_001tf__node_001tf__val,type,
% 2.07/1.19 produc1470527136de_val: node > val > produc1432036078de_val ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_Product__Type_OPair_001tf__val_001t__Product____Type__Oprod_Itf__node_Mtf__val_J,type,
% 2.07/1.19 produc1571934709de_val: val > produc1432036078de_val > produc1664334075de_val ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_Product__Type_OPair_001tf__val_001t__Set__Oset_Itf__val_J,type,
% 2.07/1.19 produc1446164855et_val: val > set_val > produc1858904199et_val ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_Product__Type_OPair_001tf__val_001tf__node,type,
% 2.07/1.19 produc1074923692l_node: val > node > produc1946948786l_node ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_Product__Type_OPair_001tf__val_001tf__val,type,
% 2.07/1.19 product_Pair_val_val: val > val > product_prod_val_val ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_SSA__CFG_OCFG__SSA__base_OallDefs_001tf__g_001tf__node_001tf__val,type,
% 2.07/1.19 sSA_CF139593942de_val: ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > node > set_val ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_SSA__CFG_OCFG__SSA__base_OallUses_001tf__g_001tf__node_001tf__edgeD_001tf__val,type,
% 2.07/1.19 sSA_CF178745443eD_val: ( g > list_node ) > ( g > node > list_P561207620_edgeD ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > node > set_val ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_SSA__CFG_OCFG__SSA__base_OallVars_001tf__g_001tf__node_001tf__edgeD_001tf__val,type,
% 2.07/1.19 sSA_CF1517915011eD_val: ( g > list_node ) > ( g > node > list_P561207620_edgeD ) > ( g > node > set_val ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > set_val ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_SSA__CFG_OCFG__SSA__base_OphiDefs_001tf__g_001tf__node_001tf__val,type,
% 2.07/1.19 sSA_CF370335846de_val: ( g > produc1432036078de_val > option_list_val ) > g > node > set_val ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_SSA__CFG_OCFG__SSA__base_OphiUses_001tf__g_001tf__node_001tf__edgeD_001tf__val,type,
% 2.07/1.19 sSA_CF848637139eD_val: ( g > list_node ) > ( g > node > list_P561207620_edgeD ) > ( g > produc1432036078de_val > option_list_val ) > g > node > set_val ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OdefNode_001tf__g_001tf__node_001tf__val,type,
% 2.07/1.19 sSA_CF551432799de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > node ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OisTrivialPhi_001tf__g_001tf__node_001tf__val,type,
% 2.07/1.19 sSA_CF1909049442de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > val > $o ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OliveVal_001tf__g_001tf__node_001tf__val,type,
% 2.07/1.19 sSA_CF794421325de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > $o ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OphiArg_001tf__g_001tf__node_001tf__val,type,
% 2.07/1.19 sSA_CF1252180629de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > val > $o ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_Ophi_001tf__g_001tf__node_001tf__val,type,
% 2.07/1.19 sSA_CF262257161de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > option_list_val ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_Opruned_001tf__g_001tf__node_001tf__val,type,
% 2.07/1.19 sSA_CF2074824714de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > $o ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_Oredundant_001tf__g_001tf__node_001tf__edgeD_001tf__val,type,
% 2.07/1.19 sSA_CF1660885746eD_val: ( g > list_node ) > ( g > node > list_P561207620_edgeD ) > ( g > node > set_val ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > $o ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_Otrivial_001tf__g_001tf__node_001tf__edgeD_001tf__val,type,
% 2.07/1.19 sSA_CF1899243830eD_val: ( g > list_node ) > ( g > node > list_P561207620_edgeD ) > ( g > node > set_val ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > $o ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_SSA__CFG_OCFG__base_Ovars_001tf__g_001tf__node_001tf__val,type,
% 2.07/1.19 sSA_CF655860150de_val: ( g > list_node ) > ( g > node > set_val ) > g > set_val ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Set__Oset_Itf__val_J_Mt__Set__Oset_Itf__val_J_J,type,
% 2.07/1.19 collec1117167378et_val: ( produc1324971431et_val > $o ) > set_Pr1311924359et_val ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_Itf__node_Mtf__val_J,type,
% 2.07/1.19 collec370342979de_val: ( produc1432036078de_val > $o ) > set_Pr699757092de_val ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_Itf__val_Mtf__node_J,type,
% 2.07/1.19 collec885255687l_node: ( produc1946948786l_node > $o ) > set_Pr2105655784l_node ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_Itf__val_Mtf__val_J,type,
% 2.07/1.19 collec52550418al_val: ( product_prod_val_val > $o ) > set_Pr700443783al_val ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_Set_OCollect_001t__Set__Oset_Itf__val_J,type,
% 2.07/1.19 collect_set_val: ( set_val > $o ) > set_set_val ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_Set_OCollect_001tf__node,type,
% 2.07/1.19 collect_node: ( node > $o ) > set_node ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_Set_OCollect_001tf__val,type,
% 2.07/1.19 collect_val: ( val > $o ) > set_val ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Set__Oset_Itf__val_J_Mt__Set__Oset_Itf__val_J_J,type,
% 2.07/1.19 insert1846469495et_val: produc1324971431et_val > set_Pr1311924359et_val > set_Pr1311924359et_val ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_Itf__node_Mtf__val_J,type,
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% 2.07/1.19
% 2.07/1.19 thf(sy_c_Set_Oinsert_001t__Set__Oset_Itf__val_J,type,
% 2.07/1.19 insert_set_val: set_val > set_set_val > set_set_val ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_Set_Oinsert_001tf__node,type,
% 2.07/1.19 insert_node: node > set_node > set_node ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_Set_Oinsert_001tf__val,type,
% 2.07/1.19 insert_val: val > set_val > set_val ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_Transitive__Closure_Oacyclic_001t__Set__Oset_Itf__val_J,type,
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% 2.07/1.19
% 2.07/1.19 thf(sy_c_Transitive__Closure_Otranclp_001tf__val,type,
% 2.07/1.19 transi1991289355lp_val: ( val > val > $o ) > val > val > $o ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_Itf__val_J_Mt__Set__Oset_Itf__val_J_J_Mt__Product____Type__Oprod_It__Set__Oset_Itf__val_J_Mt__Set__Oset_Itf__val_J_J_J,type,
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% 2.07/1.19
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% 2.07/1.19
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% 2.07/1.19
% 2.07/1.19 thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_Itf__val_J_Mtf__val_J,type,
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% 2.07/1.19
% 2.07/1.19 thf(sy_c_member_001t__Product____Type__Oprod_Itf__node_Mt__Product____Type__Oprod_Itf__node_Mtf__val_J_J,type,
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% 2.07/1.19
% 2.07/1.19 thf(sy_c_member_001t__Product____Type__Oprod_Itf__node_Mt__Set__Oset_Itf__val_J_J,type,
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% 2.07/1.19
% 2.07/1.19 thf(sy_c_member_001t__Product____Type__Oprod_Itf__node_Mtf__node_J,type,
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% 2.07/1.19
% 2.07/1.19 thf(sy_c_member_001t__Product____Type__Oprod_Itf__node_Mtf__val_J,type,
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% 2.07/1.19
% 2.07/1.19 thf(sy_c_member_001t__Product____Type__Oprod_Itf__val_Mt__Product____Type__Oprod_Itf__node_Mtf__val_J_J,type,
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% 2.07/1.19 thf(sy_c_member_001t__Product____Type__Oprod_Itf__val_Mtf__node_J,type,
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% 2.07/1.19
% 2.07/1.19 thf(sy_c_member_001t__Set__Oset_Itf__val_J,type,
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% 2.07/1.19
% 2.07/1.19 thf(sy_c_member_001tf__node,type,
% 2.07/1.19 member_node: node > set_node > $o ).
% 2.07/1.19
% 2.07/1.19 thf(sy_c_member_001tf__val,type,
% 2.07/1.19 member_val: val > set_val > $o ).
% 2.07/1.19
% 2.07/1.19 thf(sy_v__092_060alpha_062n,type,
% 2.07/1.19 alpha_n: g > list_node ).
% 2.07/1.19
% 2.07/1.19 thf(sy_v__092_060phi_062,type,
% 2.07/1.19 phi: val ).
% 2.07/1.19
% 2.07/1.19 thf(sy_v__092_060phi_062_092_060_094sub_062s,type,
% 2.07/1.19 phi_s: val ).
% 2.07/1.19
% 2.07/1.19 thf(sy_v__092_060phi_062_H____,type,
% 2.07/1.19 phi2: val ).
% 2.07/1.19
% 2.07/1.19 thf(sy_v_defs,type,
% 2.07/1.19 defs: g > node > set_val ).
% 2.07/1.19
% 2.07/1.19 thf(sy_v_g,type,
% 2.07/1.19 g2: g ).
% 2.07/1.19
% 2.07/1.19 thf(sy_v_inEdges_H,type,
% 2.07/1.19 inEdges: g > node > list_P561207620_edgeD ).
% 2.07/1.19
% 2.07/1.19 thf(sy_v_phis,type,
% 2.07/1.19 phis: g > produc1432036078de_val > option_list_val ).
% 2.07/1.19
% 2.07/1.19 thf(sy_v_s,type,
% 2.07/1.19 s: val ).
% 2.07/1.19
% 2.07/1.19 thf(sy_v_uses,type,
% 2.07/1.19 uses: g > node > set_val ).
% 2.07/1.19
% 2.07/1.19 thf(sy_v_var,type,
% 2.07/1.19 var2: g > val > var ).
% 2.07/1.19
% 2.07/1.19 thf(fact_0_assms_I4_J,axiom,
% 2.07/1.19 phi_s != s ).
% 2.07/1.19
% 2.07/1.19 thf(fact_1_False,axiom,
% 2.07/1.19 phi != phi_s ).
% 2.07/1.19
% 2.07/1.19 thf(fact_2__092_060open_062phiArg_Ag_A_092_060phi_062_H_A_092_060phi_062_092_060_094sub_062s_092_060close_062,axiom,
% 2.07/1.19 sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ phi2 @ phi_s ).
% 2.07/1.19
% 2.07/1.19 thf(fact_3_assms_I3_J,axiom,
% 2.07/1.19 member_val @ s @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2 ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_4_assms_I2_J,axiom,
% 2.07/1.19 member_val @ phi @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2 ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_5__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062_092_060phi_062_H_O_AphiArg_Ag_A_092_060phi_062_H_A_092_060phi_062_092_060_094sub_062s_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 2.07/1.19 ~ ! [Phi: val] :
% 2.07/1.19 ~ ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ Phi @ phi_s ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_6_phiArg__in__allVars,axiom,
% 2.07/1.19 ! [G: g,V: val,V2: val] :
% 2.07/1.19 ( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G @ V @ V2 )
% 2.07/1.19 => ( member_val @ V2 @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_7_uses__in__vars,axiom,
% 2.07/1.19 ! [V: val,G: g,N: node] :
% 2.07/1.19 ( ( member_val @ V @ ( uses @ G @ N ) )
% 2.07/1.19 => ( member_val @ V @ ( sSA_CF655860150de_val @ alpha_n @ uses @ G ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_8_trivial__in__allVars,axiom,
% 2.07/1.19 ! [G: g,V: val] :
% 2.07/1.19 ( ( sSA_CF1899243830eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G @ V )
% 2.07/1.19 => ( member_val @ V @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_9_liveVal__in__allVars,axiom,
% 2.07/1.19 ! [G: g,V: val] :
% 2.07/1.19 ( ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ G @ V )
% 2.07/1.19 => ( member_val @ V @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_10_allVars__finite,axiom,
% 2.07/1.19 ! [G: g] : ( finite_finite_val @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_11_uses__in__allUses,axiom,
% 2.07/1.19 ! [V: val,G: g,N: node] :
% 2.07/1.19 ( ( member_val @ V @ ( uses @ G @ N ) )
% 2.07/1.19 => ( member_val @ V @ ( sSA_CF178745443eD_val @ alpha_n @ inEdges @ uses @ phis @ G @ N ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_12_redundant__def,axiom,
% 2.07/1.19 ! [G: g] :
% 2.07/1.19 ( ( sSA_CF1660885746eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G )
% 2.07/1.19 = ( ? [X: val] :
% 2.07/1.19 ( ( member_val @ X @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 2.07/1.19 & ( sSA_CF1899243830eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G @ X ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_13_trivial__def,axiom,
% 2.07/1.19 ! [G: g,V: val] :
% 2.07/1.19 ( ( sSA_CF1899243830eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G @ V )
% 2.07/1.19 = ( ? [X: val] :
% 2.07/1.19 ( ( member_val @ X @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 2.07/1.19 & ( sSA_CF1909049442de_val @ alpha_n @ defs @ phis @ G @ V @ X ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_14__092_060open_062_092_060not_062_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062s_A_092_060noteq_062_AdefNode_Ag_As_092_060close_062,axiom,
% 2.07/1.19 ( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_s )
% 2.07/1.19 = ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ s ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_15_defs__uses__disjoint_H,axiom,
% 2.07/1.19 ! [N: node,G: g,V: val] :
% 2.07/1.19 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.07/1.19 => ( ( member_val @ V @ ( defs @ G @ N ) )
% 2.07/1.19 => ~ ( member_val @ V @ ( uses @ G @ N ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_16_livePhi,axiom,
% 2.07/1.19 ! [G: g,V: val,V2: val] :
% 2.07/1.19 ( ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ G @ V )
% 2.07/1.19 => ( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G @ V @ V2 )
% 2.07/1.19 => ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ G @ V2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_17_phiArg__distinct__nodes,axiom,
% 2.07/1.19 ! [G: g,P: val,Q: val] :
% 2.07/1.19 ( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G @ P @ Q )
% 2.07/1.19 => ( ( P != Q )
% 2.07/1.19 => ( ( member_val @ P @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 2.07/1.19 => ( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ P )
% 2.07/1.19 != ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ Q ) ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_18_phiArgs__def__distinct,axiom,
% 2.07/1.19 ! [G: g,P: val,Q: val,R: val] :
% 2.07/1.19 ( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G @ P @ Q )
% 2.07/1.19 => ( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G @ P @ R )
% 2.07/1.19 => ( ( Q != R )
% 2.07/1.19 => ( ( member_val @ P @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 2.07/1.19 => ( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ Q )
% 2.07/1.19 != ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ R ) ) ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_19_uses__in___092_060alpha_062n,axiom,
% 2.07/1.19 ! [V: val,G: g,N: node] :
% 2.07/1.19 ( ( member_val @ V @ ( uses @ G @ N ) )
% 2.07/1.19 => ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_20_defs__finite,axiom,
% 2.07/1.19 ! [G: g,N: node] : ( finite_finite_val @ ( defs @ G @ N ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_21_varsE,axiom,
% 2.07/1.19 ! [V: val,G: g] :
% 2.07/1.19 ( ( member_val @ V @ ( sSA_CF655860150de_val @ alpha_n @ uses @ G ) )
% 2.07/1.19 => ~ ! [N2: node] :
% 2.07/1.19 ( ( member_node @ N2 @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.07/1.19 => ~ ( member_val @ V @ ( uses @ G @ N2 ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_22_vars__finite,axiom,
% 2.07/1.19 ! [G: g] : ( finite_finite_val @ ( sSA_CF655860150de_val @ alpha_n @ uses @ G ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_23_liveSimple,axiom,
% 2.07/1.19 ! [N: node,G: g,Val: val] :
% 2.07/1.19 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.07/1.19 => ( ( member_val @ Val @ ( uses @ G @ N ) )
% 2.07/1.19 => ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ G @ Val ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_24_liveVal_Osimps,axiom,
% 2.07/1.19 ! [G: g,A: val] :
% 2.07/1.19 ( ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ G @ A )
% 2.07/1.19 = ( ? [N3: node,Val2: val] :
% 2.07/1.19 ( ( A = Val2 )
% 2.07/1.19 & ( member_node @ N3 @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.07/1.19 & ( member_val @ Val2 @ ( uses @ G @ N3 ) ) )
% 2.07/1.19 | ? [V3: val,V4: val] :
% 2.07/1.19 ( ( A = V4 )
% 2.07/1.19 & ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ G @ V3 )
% 2.07/1.19 & ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G @ V3 @ V4 ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_25_liveVal_Oinducts,axiom,
% 2.07/1.19 ! [G: g,X2: val,P2: val > $o] :
% 2.07/1.19 ( ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ G @ X2 )
% 2.07/1.19 => ( ! [N2: node,Val3: val] :
% 2.07/1.19 ( ( member_node @ N2 @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.07/1.19 => ( ( member_val @ Val3 @ ( uses @ G @ N2 ) )
% 2.07/1.19 => ( P2 @ Val3 ) ) )
% 2.07/1.19 => ( ! [V5: val,V6: val] :
% 2.07/1.19 ( ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ G @ V5 )
% 2.07/1.19 => ( ( P2 @ V5 )
% 2.07/1.19 => ( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G @ V5 @ V6 )
% 2.07/1.19 => ( P2 @ V6 ) ) ) )
% 2.07/1.19 => ( P2 @ X2 ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_26_liveVal_Ocases,axiom,
% 2.07/1.19 ! [G: g,A: val] :
% 2.07/1.19 ( ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ G @ A )
% 2.07/1.19 => ( ! [N2: node] :
% 2.07/1.19 ( ( member_node @ N2 @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.07/1.19 => ~ ( member_val @ A @ ( uses @ G @ N2 ) ) )
% 2.07/1.19 => ~ ! [V5: val] :
% 2.07/1.19 ( ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ G @ V5 )
% 2.07/1.19 => ~ ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G @ V5 @ A ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_27_allUses__finite,axiom,
% 2.07/1.19 ! [N: node,G: g] :
% 2.07/1.19 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.07/1.19 => ( finite_finite_val @ ( sSA_CF178745443eD_val @ alpha_n @ inEdges @ uses @ phis @ G @ N ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_28_defNode_I1_J,axiom,
% 2.07/1.19 ! [V: val,G: g] :
% 2.07/1.19 ( ( member_val @ V @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 2.07/1.19 => ( member_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ V ) @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_29_uses__finite,axiom,
% 2.07/1.19 ! [G: g,N: node] : ( finite_finite_val @ ( uses @ G @ N ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_30_eq,axiom,
% 2.07/1.19 ( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_s )
% 2.07/1.19 = ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ s ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_31_allUses__in__allVars,axiom,
% 2.07/1.19 ! [V: val,G: g,N: node] :
% 2.07/1.19 ( ( member_val @ V @ ( sSA_CF178745443eD_val @ alpha_n @ inEdges @ uses @ phis @ G @ N ) )
% 2.07/1.19 => ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.07/1.19 => ( member_val @ V @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_32_phiUses__in__allUses,axiom,
% 2.07/1.19 ! [V: val,G: g,N: node] :
% 2.07/1.19 ( ( member_val @ V @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ G @ N ) )
% 2.07/1.19 => ( member_val @ V @ ( sSA_CF178745443eD_val @ alpha_n @ inEdges @ uses @ phis @ G @ N ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_33_phiUses__finite,axiom,
% 2.07/1.19 ! [N: node,G: g] :
% 2.07/1.19 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.07/1.19 => ( finite_finite_val @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ G @ N ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_34_defNode_I2_J,axiom,
% 2.07/1.19 ! [V: val,G: g] :
% 2.07/1.19 ( ( member_val @ V @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 2.07/1.19 => ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ V ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_35_defNode__ex1,axiom,
% 2.07/1.19 ! [V: val,G: g] :
% 2.07/1.19 ( ( member_val @ V @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 2.07/1.19 => ? [X3: node] :
% 2.07/1.19 ( ( member_node @ X3 @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.07/1.19 & ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ X3 ) )
% 2.07/1.19 & ! [Y: node] :
% 2.07/1.19 ( ( ( member_node @ Y @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.07/1.19 & ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ Y ) ) )
% 2.07/1.19 => ( Y = X3 ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_36_allVars__in__allDefs,axiom,
% 2.07/1.19 ! [V: val,G: g] :
% 2.07/1.19 ( ( member_val @ V @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 2.07/1.19 => ? [X3: node] :
% 2.07/1.19 ( ( member_node @ X3 @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.07/1.19 & ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ X3 ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_37_List_Ofinite__set,axiom,
% 2.07/1.19 ! [Xs: list_P844977291de_val] : ( finite781217938de_val @ ( set_Pr434939430de_val @ Xs ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_38_List_Ofinite__set,axiom,
% 2.07/1.19 ! [Xs: list_P761482893et_val] : ( finite1581417648et_val @ ( set_Pr2104310812et_val @ Xs ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_39_List_Ofinite__set,axiom,
% 2.07/1.19 ! [Xs: list_P1078858818l_node] : ( finite423892681l_node @ ( set_Pr1600883293l_node @ Xs ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_40_List_Ofinite__set,axiom,
% 2.07/1.19 ! [Xs: list_P1811375021al_val] : ( finite759259600al_val @ ( set_Pr102746428al_val @ Xs ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_41_List_Ofinite__set,axiom,
% 2.07/1.19 ! [Xs: list_set_val] : ( finite1265617511et_val @ ( set_set_val2 @ Xs ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_42_List_Ofinite__set,axiom,
% 2.07/1.19 ! [Xs: list_node] : ( finite_finite_node @ ( set_node2 @ Xs ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_43_List_Ofinite__set,axiom,
% 2.07/1.19 ! [Xs: list_val] : ( finite_finite_val @ ( set_val2 @ Xs ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_44_List_Ofinite__set,axiom,
% 2.07/1.19 ! [Xs: list_P2089461677et_val] : ( finite79836624et_val @ ( set_Pr284769596et_val @ Xs ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_45_List_Ofinite__set,axiom,
% 2.07/1.19 ! [Xs: list_P1820443774de_val] : ( finite2056463621de_val @ ( set_Pr1085970585de_val @ Xs ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_46_phiDefs__finite,axiom,
% 2.07/1.19 ! [G: g,N: node] : ( finite_finite_val @ ( sSA_CF370335846de_val @ phis @ G @ N ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_47_allDefs__finite,axiom,
% 2.07/1.19 ! [N: node,G: g] :
% 2.07/1.19 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.07/1.19 => ( finite_finite_val @ ( sSA_CF139593942de_val @ defs @ phis @ G @ N ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_48_assms_I5_J,axiom,
% 2.07/1.19 ( ( var2 @ g2 @ phi )
% 2.07/1.19 = ( var2 @ g2 @ s ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_49_CFG__SSA__wf__base_Oredundant__def,axiom,
% 2.07/1.19 ( sSA_CF1660885746eD_val
% 2.07/1.19 = ( ^ [Alpha_n: g > list_node,InEdges: g > node > list_P561207620_edgeD,Defs: g > node > set_val,Uses: g > node > set_val,Phis: g > produc1432036078de_val > option_list_val,G2: g] :
% 2.07/1.19 ? [X: val] :
% 2.07/1.19 ( ( member_val @ X @ ( sSA_CF1517915011eD_val @ Alpha_n @ InEdges @ Defs @ Uses @ Phis @ G2 ) )
% 2.07/1.19 & ( sSA_CF1899243830eD_val @ Alpha_n @ InEdges @ Defs @ Uses @ Phis @ G2 @ X ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_50_defs__in__allDefs,axiom,
% 2.07/1.19 ! [V: val,G: g,N: node] :
% 2.07/1.19 ( ( member_val @ V @ ( defs @ G @ N ) )
% 2.07/1.19 => ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ N ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_51_phiDefs__in__allDefs,axiom,
% 2.07/1.19 ! [V: val,G: g,N: node] :
% 2.07/1.19 ( ( member_val @ V @ ( sSA_CF370335846de_val @ phis @ G @ N ) )
% 2.07/1.19 => ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ N ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_52_allDefs__disjoint_H,axiom,
% 2.07/1.19 ! [N: node,G: g,M: node,V: val] :
% 2.07/1.19 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.07/1.19 => ( ( member_node @ M @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.07/1.19 => ( ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ N ) )
% 2.07/1.19 => ( ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ M ) )
% 2.07/1.19 => ( N = M ) ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_53_mem__Collect__eq,axiom,
% 2.07/1.19 ! [A: produc1946948786l_node,P2: produc1946948786l_node > $o] :
% 2.07/1.19 ( ( member828457417l_node @ A @ ( collec885255687l_node @ P2 ) )
% 2.07/1.19 = ( P2 @ A ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_54_mem__Collect__eq,axiom,
% 2.07/1.19 ! [A: product_prod_val_val,P2: product_prod_val_val > $o] :
% 2.07/1.19 ( ( member1680438992al_val @ A @ ( collec52550418al_val @ P2 ) )
% 2.07/1.19 = ( P2 @ A ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_55_mem__Collect__eq,axiom,
% 2.07/1.19 ! [A: val,P2: val > $o] :
% 2.07/1.19 ( ( member_val @ A @ ( collect_val @ P2 ) )
% 2.07/1.19 = ( P2 @ A ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_56_mem__Collect__eq,axiom,
% 2.07/1.19 ! [A: node,P2: node > $o] :
% 2.07/1.19 ( ( member_node @ A @ ( collect_node @ P2 ) )
% 2.07/1.19 = ( P2 @ A ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_57_mem__Collect__eq,axiom,
% 2.07/1.19 ! [A: set_val,P2: set_val > $o] :
% 2.07/1.19 ( ( member_set_val @ A @ ( collect_set_val @ P2 ) )
% 2.07/1.19 = ( P2 @ A ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_58_mem__Collect__eq,axiom,
% 2.07/1.19 ! [A: produc1432036078de_val,P2: produc1432036078de_val > $o] :
% 2.07/1.19 ( ( member313544709de_val @ A @ ( collec370342979de_val @ P2 ) )
% 2.07/1.19 = ( P2 @ A ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_59_mem__Collect__eq,axiom,
% 2.07/1.19 ! [A: produc1324971431et_val,P2: produc1324971431et_val > $o] :
% 2.07/1.19 ( ( member1711426256et_val @ A @ ( collec1117167378et_val @ P2 ) )
% 2.07/1.19 = ( P2 @ A ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_60_Collect__mem__eq,axiom,
% 2.07/1.19 ! [A2: set_val] :
% 2.07/1.19 ( ( collect_val
% 2.07/1.19 @ ^ [X: val] : ( member_val @ X @ A2 ) )
% 2.07/1.19 = A2 ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_61_Collect__mem__eq,axiom,
% 2.07/1.19 ! [A2: set_node] :
% 2.07/1.19 ( ( collect_node
% 2.07/1.19 @ ^ [X: node] : ( member_node @ X @ A2 ) )
% 2.07/1.19 = A2 ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_62_Collect__mem__eq,axiom,
% 2.07/1.19 ! [A2: set_set_val] :
% 2.07/1.19 ( ( collect_set_val
% 2.07/1.19 @ ^ [X: set_val] : ( member_set_val @ X @ A2 ) )
% 2.07/1.19 = A2 ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_63_Collect__mem__eq,axiom,
% 2.07/1.19 ! [A2: set_Pr699757092de_val] :
% 2.07/1.19 ( ( collec370342979de_val
% 2.07/1.19 @ ^ [X: produc1432036078de_val] : ( member313544709de_val @ X @ A2 ) )
% 2.07/1.19 = A2 ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_64_Collect__mem__eq,axiom,
% 2.07/1.19 ! [A2: set_Pr1311924359et_val] :
% 2.07/1.19 ( ( collec1117167378et_val
% 2.07/1.19 @ ^ [X: produc1324971431et_val] : ( member1711426256et_val @ X @ A2 ) )
% 2.07/1.19 = A2 ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_65_phiArg__same__var,axiom,
% 2.07/1.19 ! [G: g,P: val,Q: val] :
% 2.07/1.19 ( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G @ P @ Q )
% 2.07/1.19 => ( ( var2 @ G @ Q )
% 2.07/1.19 = ( var2 @ G @ P ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_66_vars__eq,axiom,
% 2.07/1.19 ( ( var2 @ g2 @ phi )
% 2.07/1.19 = ( var2 @ g2 @ phi_s ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_67_allDefs__var__disjoint,axiom,
% 2.07/1.19 ! [N: node,G: g,V: val,V2: val] :
% 2.07/1.19 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.07/1.19 => ( ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ N ) )
% 2.07/1.19 => ( ( member_val @ V2 @ ( sSA_CF139593942de_val @ defs @ phis @ G @ N ) )
% 2.07/1.19 => ( ( V != V2 )
% 2.07/1.19 => ( ( var2 @ G @ V2 )
% 2.07/1.19 != ( var2 @ G @ V ) ) ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_68_defNode__var__disjoint,axiom,
% 2.07/1.19 ! [P: val,G: g,Q: val] :
% 2.07/1.19 ( ( member_val @ P @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 2.07/1.19 => ( ( member_val @ Q @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 2.07/1.19 => ( ( P != Q )
% 2.07/1.19 => ( ( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ P )
% 2.07/1.19 = ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ Q ) )
% 2.07/1.19 => ( ( var2 @ G @ P )
% 2.07/1.19 != ( var2 @ G @ Q ) ) ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_69_defNode__eq,axiom,
% 2.07/1.19 ! [N: node,G: g,V: val] :
% 2.07/1.19 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.07/1.19 => ( ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ N ) )
% 2.07/1.19 => ( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ V )
% 2.07/1.19 = N ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_70_allDefs__in__allVars,axiom,
% 2.07/1.19 ! [V: val,G: g,N: node] :
% 2.07/1.19 ( ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ N ) )
% 2.07/1.19 => ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.07/1.19 => ( member_val @ V @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_71_pruned__def,axiom,
% 2.07/1.19 ! [G: g] :
% 2.07/1.19 ( ( sSA_CF2074824714de_val @ alpha_n @ defs @ uses @ phis @ G )
% 2.07/1.19 = ( ! [X: node] :
% 2.07/1.19 ( ( member_node @ X @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.07/1.19 => ! [Val2: val] :
% 2.07/1.19 ( ( member_val @ Val2 @ ( sSA_CF370335846de_val @ phis @ G @ X ) )
% 2.07/1.19 => ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ G @ Val2 ) ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_72_CFG__SSA__base_OphiUses_Ocong,axiom,
% 2.07/1.19 sSA_CF848637139eD_val = sSA_CF848637139eD_val ).
% 2.07/1.19
% 2.07/1.19 thf(fact_73_CFG__SSA__base_OphiDefs_Ocong,axiom,
% 2.07/1.19 sSA_CF370335846de_val = sSA_CF370335846de_val ).
% 2.07/1.19
% 2.07/1.19 thf(fact_74_CFG__SSA__base_OallDefs_Ocong,axiom,
% 2.07/1.19 sSA_CF139593942de_val = sSA_CF139593942de_val ).
% 2.07/1.19
% 2.07/1.19 thf(fact_75_CFG__SSA__wf__base_OdefNode_Ocong,axiom,
% 2.07/1.19 sSA_CF551432799de_val = sSA_CF551432799de_val ).
% 2.07/1.19
% 2.07/1.19 thf(fact_76_CFG__SSA__base_OallVars_Ocong,axiom,
% 2.07/1.19 sSA_CF1517915011eD_val = sSA_CF1517915011eD_val ).
% 2.07/1.19
% 2.07/1.19 thf(fact_77_CFG__SSA__wf__base_OphiArg_Ocong,axiom,
% 2.07/1.19 sSA_CF1252180629de_val = sSA_CF1252180629de_val ).
% 2.07/1.19
% 2.07/1.19 thf(fact_78_CFG__SSA__base_OallUses_Ocong,axiom,
% 2.07/1.19 sSA_CF178745443eD_val = sSA_CF178745443eD_val ).
% 2.07/1.19
% 2.07/1.19 thf(fact_79_CFG__SSA__wf__base_OliveVal_Ocong,axiom,
% 2.07/1.19 sSA_CF794421325de_val = sSA_CF794421325de_val ).
% 2.07/1.19
% 2.07/1.19 thf(fact_80_CFG__SSA__wf__base_Otrivial_Ocong,axiom,
% 2.07/1.19 sSA_CF1899243830eD_val = sSA_CF1899243830eD_val ).
% 2.07/1.19
% 2.07/1.19 thf(fact_81_CFG__base_Ovars_Ocong,axiom,
% 2.07/1.19 sSA_CF655860150de_val = sSA_CF655860150de_val ).
% 2.07/1.19
% 2.07/1.19 thf(fact_82_CFG__SSA__wf__base_OisTrivialPhi_Ocong,axiom,
% 2.07/1.19 sSA_CF1909049442de_val = sSA_CF1909049442de_val ).
% 2.07/1.19
% 2.07/1.19 thf(fact_83_CFG__SSA__wf__base_Oredundant_Ocong,axiom,
% 2.07/1.19 sSA_CF1660885746eD_val = sSA_CF1660885746eD_val ).
% 2.07/1.19
% 2.07/1.19 thf(fact_84_finite__list,axiom,
% 2.07/1.19 ! [A2: set_node] :
% 2.07/1.19 ( ( finite_finite_node @ A2 )
% 2.07/1.19 => ? [Xs2: list_node] :
% 2.07/1.19 ( ( set_node2 @ Xs2 )
% 2.07/1.19 = A2 ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_85_finite__list,axiom,
% 2.07/1.19 ! [A2: set_val] :
% 2.07/1.19 ( ( finite_finite_val @ A2 )
% 2.07/1.19 => ? [Xs2: list_val] :
% 2.07/1.19 ( ( set_val2 @ Xs2 )
% 2.07/1.19 = A2 ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_86_finite__list,axiom,
% 2.07/1.19 ! [A2: set_Pr1311924359et_val] :
% 2.07/1.19 ( ( finite79836624et_val @ A2 )
% 2.07/1.19 => ? [Xs2: list_P2089461677et_val] :
% 2.07/1.19 ( ( set_Pr284769596et_val @ Xs2 )
% 2.07/1.19 = A2 ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_87_finite__list,axiom,
% 2.07/1.19 ! [A2: set_Pr699757092de_val] :
% 2.07/1.19 ( ( finite2056463621de_val @ A2 )
% 2.07/1.19 => ? [Xs2: list_P1820443774de_val] :
% 2.07/1.19 ( ( set_Pr1085970585de_val @ Xs2 )
% 2.07/1.19 = A2 ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_88_CFG__SSA__wf__base_OliveSimple,axiom,
% 2.07/1.19 ! [N: node,Alpha_n2: g > list_node,G: g,Val: val,Uses2: g > node > set_val,Defs2: g > node > set_val,Phis2: g > produc1432036078de_val > option_list_val] :
% 2.07/1.19 ( ( member_node @ N @ ( set_node2 @ ( Alpha_n2 @ G ) ) )
% 2.07/1.19 => ( ( member_val @ Val @ ( Uses2 @ G @ N ) )
% 2.07/1.19 => ( sSA_CF794421325de_val @ Alpha_n2 @ Defs2 @ Uses2 @ Phis2 @ G @ Val ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_89_CFG__SSA__wf__base_OlivePhi,axiom,
% 2.07/1.19 ! [Alpha_n2: g > list_node,Defs2: g > node > set_val,Uses2: g > node > set_val,Phis2: g > produc1432036078de_val > option_list_val,G: g,V: val,V2: val] :
% 2.07/1.19 ( ( sSA_CF794421325de_val @ Alpha_n2 @ Defs2 @ Uses2 @ Phis2 @ G @ V )
% 2.07/1.19 => ( ( sSA_CF1252180629de_val @ Alpha_n2 @ Defs2 @ Phis2 @ G @ V @ V2 )
% 2.07/1.19 => ( sSA_CF794421325de_val @ Alpha_n2 @ Defs2 @ Uses2 @ Phis2 @ G @ V2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_90_CFG__SSA__wf__base_OliveVal_Oinducts,axiom,
% 2.07/1.19 ! [Alpha_n2: g > list_node,Defs2: g > node > set_val,Uses2: g > node > set_val,Phis2: g > produc1432036078de_val > option_list_val,G: g,X2: val,P2: val > $o] :
% 2.07/1.19 ( ( sSA_CF794421325de_val @ Alpha_n2 @ Defs2 @ Uses2 @ Phis2 @ G @ X2 )
% 2.07/1.19 => ( ! [N2: node,Val3: val] :
% 2.07/1.19 ( ( member_node @ N2 @ ( set_node2 @ ( Alpha_n2 @ G ) ) )
% 2.07/1.19 => ( ( member_val @ Val3 @ ( Uses2 @ G @ N2 ) )
% 2.07/1.19 => ( P2 @ Val3 ) ) )
% 2.07/1.19 => ( ! [V5: val,V6: val] :
% 2.07/1.19 ( ( sSA_CF794421325de_val @ Alpha_n2 @ Defs2 @ Uses2 @ Phis2 @ G @ V5 )
% 2.07/1.19 => ( ( P2 @ V5 )
% 2.07/1.19 => ( ( sSA_CF1252180629de_val @ Alpha_n2 @ Defs2 @ Phis2 @ G @ V5 @ V6 )
% 2.07/1.19 => ( P2 @ V6 ) ) ) )
% 2.07/1.19 => ( P2 @ X2 ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_91_CFG__SSA__wf__base_OliveVal_Osimps,axiom,
% 2.07/1.19 ( sSA_CF794421325de_val
% 2.07/1.19 = ( ^ [Alpha_n: g > list_node,Defs: g > node > set_val,Uses: g > node > set_val,Phis: g > produc1432036078de_val > option_list_val,G2: g,A3: val] :
% 2.07/1.19 ( ? [N3: node,Val2: val] :
% 2.07/1.19 ( ( A3 = Val2 )
% 2.07/1.19 & ( member_node @ N3 @ ( set_node2 @ ( Alpha_n @ G2 ) ) )
% 2.07/1.19 & ( member_val @ Val2 @ ( Uses @ G2 @ N3 ) ) )
% 2.07/1.19 | ? [V3: val,V4: val] :
% 2.07/1.19 ( ( A3 = V4 )
% 2.07/1.19 & ( sSA_CF794421325de_val @ Alpha_n @ Defs @ Uses @ Phis @ G2 @ V3 )
% 2.07/1.19 & ( sSA_CF1252180629de_val @ Alpha_n @ Defs @ Phis @ G2 @ V3 @ V4 ) ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_92_CFG__SSA__wf__base_OliveVal_Ocases,axiom,
% 2.07/1.19 ! [Alpha_n2: g > list_node,Defs2: g > node > set_val,Uses2: g > node > set_val,Phis2: g > produc1432036078de_val > option_list_val,G: g,A: val] :
% 2.07/1.19 ( ( sSA_CF794421325de_val @ Alpha_n2 @ Defs2 @ Uses2 @ Phis2 @ G @ A )
% 2.07/1.19 => ( ! [N2: node] :
% 2.07/1.19 ( ( member_node @ N2 @ ( set_node2 @ ( Alpha_n2 @ G ) ) )
% 2.07/1.19 => ~ ( member_val @ A @ ( Uses2 @ G @ N2 ) ) )
% 2.07/1.19 => ~ ! [V5: val] :
% 2.07/1.19 ( ( sSA_CF794421325de_val @ Alpha_n2 @ Defs2 @ Uses2 @ Phis2 @ G @ V5 )
% 2.07/1.19 => ~ ( sSA_CF1252180629de_val @ Alpha_n2 @ Defs2 @ Phis2 @ G @ V5 @ A ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_93_CFG__SSA__wf__base_Otrivial__def,axiom,
% 2.07/1.19 ( sSA_CF1899243830eD_val
% 2.07/1.19 = ( ^ [Alpha_n: g > list_node,InEdges: g > node > list_P561207620_edgeD,Defs: g > node > set_val,Uses: g > node > set_val,Phis: g > produc1432036078de_val > option_list_val,G2: g,V3: val] :
% 2.07/1.19 ? [X: val] :
% 2.07/1.19 ( ( member_val @ X @ ( sSA_CF1517915011eD_val @ Alpha_n @ InEdges @ Defs @ Uses @ Phis @ G2 ) )
% 2.07/1.19 & ( sSA_CF1909049442de_val @ Alpha_n @ Defs @ Phis @ G2 @ V3 @ X ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_94_condensation__finite,axiom,
% 2.07/1.19 ! [G: g,P2: set_val] : ( finite79836624et_val @ ( irredu893086079de_val @ alpha_n @ defs @ phis @ G @ P2 ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_95_phiUses__exI_H,axiom,
% 2.07/1.19 ! [G: g,P: val,Q: val] :
% 2.07/1.19 ( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G @ P @ Q )
% 2.07/1.19 => ( ( member_val @ P @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 2.07/1.19 => ~ ! [M2: node] :
% 2.07/1.19 ( ( member_val @ Q @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ G @ M2 ) )
% 2.07/1.19 => ~ ( member_node @ M2 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ P ) ) ) ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_96_allUses__def,axiom,
% 2.07/1.19 ! [G: g,N: node] :
% 2.07/1.19 ( ( sSA_CF178745443eD_val @ alpha_n @ inEdges @ uses @ phis @ G @ N )
% 2.07/1.19 = ( sup_sup_set_val @ ( uses @ G @ N ) @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ G @ N ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_97_phiArg__trancl__same__var,axiom,
% 2.07/1.19 ! [G: g,Phi2: val,N: val] :
% 2.07/1.19 ( ( transi1991289355lp_val @ ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G ) @ Phi2 @ N )
% 2.07/1.19 => ( ( var2 @ G @ Phi2 )
% 2.07/1.19 = ( var2 @ G @ N ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_98_allDefs__def,axiom,
% 2.07/1.19 ! [G: g,N: node] :
% 2.07/1.19 ( ( sSA_CF139593942de_val @ defs @ phis @ G @ N )
% 2.07/1.19 = ( sup_sup_set_val @ ( defs @ G @ N ) @ ( sSA_CF370335846de_val @ phis @ G @ N ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_99_CFG__SSA__wf__base_Opruned__def,axiom,
% 2.07/1.19 ( sSA_CF2074824714de_val
% 2.07/1.19 = ( ^ [Alpha_n: g > list_node,Defs: g > node > set_val,Uses: g > node > set_val,Phis: g > produc1432036078de_val > option_list_val,G2: g] :
% 2.07/1.19 ! [X: node] :
% 2.07/1.19 ( ( member_node @ X @ ( set_node2 @ ( Alpha_n @ G2 ) ) )
% 2.07/1.19 => ! [Val2: val] :
% 2.07/1.19 ( ( member_val @ Val2 @ ( sSA_CF370335846de_val @ Phis @ G2 @ X ) )
% 2.07/1.19 => ( sSA_CF794421325de_val @ Alpha_n @ Defs @ Uses @ Phis @ G2 @ Val2 ) ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_100_defNode__cases,axiom,
% 2.07/1.19 ! [V: val,G: g] :
% 2.07/1.19 ( ( member_val @ V @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 2.07/1.19 => ( ~ ( member_val @ V @ ( defs @ G @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ V ) ) )
% 2.07/1.19 => ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ G @ V )
% 2.07/1.19 != none_list_val ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_101_simpleDef__not__phi,axiom,
% 2.07/1.19 ! [N: node,G: g,V: val] :
% 2.07/1.19 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.07/1.19 => ( ( member_val @ V @ ( defs @ G @ N ) )
% 2.07/1.19 => ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ G @ V )
% 2.07/1.19 = none_list_val ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_102_finite__Un,axiom,
% 2.07/1.19 ! [F: set_Pr1311924359et_val,G3: set_Pr1311924359et_val] :
% 2.07/1.19 ( ( finite79836624et_val @ ( sup_su2005730907et_val @ F @ G3 ) )
% 2.07/1.19 = ( ( finite79836624et_val @ F )
% 2.07/1.19 & ( finite79836624et_val @ G3 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_103_finite__Un,axiom,
% 2.07/1.19 ! [F: set_Pr699757092de_val,G3: set_Pr699757092de_val] :
% 2.07/1.19 ( ( finite2056463621de_val @ ( sup_su2138939728de_val @ F @ G3 ) )
% 2.07/1.19 = ( ( finite2056463621de_val @ F )
% 2.07/1.19 & ( finite2056463621de_val @ G3 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_104_finite__Un,axiom,
% 2.07/1.19 ! [F: set_val,G3: set_val] :
% 2.07/1.19 ( ( finite_finite_val @ ( sup_sup_set_val @ F @ G3 ) )
% 2.07/1.19 = ( ( finite_finite_val @ F )
% 2.07/1.19 & ( finite_finite_val @ G3 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_105_trivial__phi,axiom,
% 2.07/1.19 ! [G: g,V: val] :
% 2.07/1.19 ( ( sSA_CF1899243830eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G @ V )
% 2.07/1.19 => ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ G @ V )
% 2.07/1.19 != none_list_val ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_106_phiArg__exI,axiom,
% 2.07/1.19 ! [M: node,G: g,V: val] :
% 2.07/1.19 ( ( member_node @ M @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ V ) ) ) )
% 2.07/1.19 => ( ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ G @ V )
% 2.07/1.19 != none_list_val )
% 2.07/1.19 => ( ( member_val @ V @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 2.07/1.19 => ~ ! [V6: val] :
% 2.07/1.19 ( ( member_val @ V6 @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ G @ M ) )
% 2.07/1.19 => ~ ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G @ V @ V6 ) ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_107_CFG__SSA__wf__base_Ophi_Ocong,axiom,
% 2.07/1.19 sSA_CF262257161de_val = sSA_CF262257161de_val ).
% 2.07/1.19
% 2.07/1.19 thf(fact_108_infinite__Un,axiom,
% 2.07/1.19 ! [S: set_Pr1311924359et_val,T: set_Pr1311924359et_val] :
% 2.07/1.19 ( ( ~ ( finite79836624et_val @ ( sup_su2005730907et_val @ S @ T ) ) )
% 2.07/1.19 = ( ~ ( finite79836624et_val @ S )
% 2.07/1.19 | ~ ( finite79836624et_val @ T ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_109_infinite__Un,axiom,
% 2.07/1.19 ! [S: set_Pr699757092de_val,T: set_Pr699757092de_val] :
% 2.07/1.19 ( ( ~ ( finite2056463621de_val @ ( sup_su2138939728de_val @ S @ T ) ) )
% 2.07/1.19 = ( ~ ( finite2056463621de_val @ S )
% 2.07/1.19 | ~ ( finite2056463621de_val @ T ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_110_infinite__Un,axiom,
% 2.07/1.19 ! [S: set_val,T: set_val] :
% 2.07/1.19 ( ( ~ ( finite_finite_val @ ( sup_sup_set_val @ S @ T ) ) )
% 2.07/1.19 = ( ~ ( finite_finite_val @ S )
% 2.07/1.19 | ~ ( finite_finite_val @ T ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_111_Un__infinite,axiom,
% 2.07/1.19 ! [S: set_Pr1311924359et_val,T: set_Pr1311924359et_val] :
% 2.07/1.19 ( ~ ( finite79836624et_val @ S )
% 2.07/1.19 => ~ ( finite79836624et_val @ ( sup_su2005730907et_val @ S @ T ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_112_Un__infinite,axiom,
% 2.07/1.19 ! [S: set_Pr699757092de_val,T: set_Pr699757092de_val] :
% 2.07/1.19 ( ~ ( finite2056463621de_val @ S )
% 2.07/1.19 => ~ ( finite2056463621de_val @ ( sup_su2138939728de_val @ S @ T ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_113_Un__infinite,axiom,
% 2.07/1.19 ! [S: set_val,T: set_val] :
% 2.07/1.19 ( ~ ( finite_finite_val @ S )
% 2.07/1.19 => ~ ( finite_finite_val @ ( sup_sup_set_val @ S @ T ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_114_finite__UnI,axiom,
% 2.07/1.19 ! [F: set_Pr1311924359et_val,G3: set_Pr1311924359et_val] :
% 2.07/1.19 ( ( finite79836624et_val @ F )
% 2.07/1.19 => ( ( finite79836624et_val @ G3 )
% 2.07/1.19 => ( finite79836624et_val @ ( sup_su2005730907et_val @ F @ G3 ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_115_finite__UnI,axiom,
% 2.07/1.19 ! [F: set_Pr699757092de_val,G3: set_Pr699757092de_val] :
% 2.07/1.19 ( ( finite2056463621de_val @ F )
% 2.07/1.19 => ( ( finite2056463621de_val @ G3 )
% 2.07/1.19 => ( finite2056463621de_val @ ( sup_su2138939728de_val @ F @ G3 ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_116_finite__UnI,axiom,
% 2.07/1.19 ! [F: set_val,G3: set_val] :
% 2.07/1.19 ( ( finite_finite_val @ F )
% 2.07/1.19 => ( ( finite_finite_val @ G3 )
% 2.07/1.19 => ( finite_finite_val @ ( sup_sup_set_val @ F @ G3 ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_117_CFG__SSA__Transformed_Ocondensation__edges_Ocong,axiom,
% 2.07/1.19 irredu893086079de_val = irredu893086079de_val ).
% 2.07/1.19
% 2.07/1.19 thf(fact_118_CFG__SSA__wf__base_Opruned_Ocong,axiom,
% 2.07/1.19 sSA_CF2074824714de_val = sSA_CF2074824714de_val ).
% 2.07/1.19
% 2.07/1.19 thf(fact_119_CFG__SSA__base_OallDefs__def,axiom,
% 2.07/1.19 ( sSA_CF139593942de_val
% 2.07/1.19 = ( ^ [Defs: g > node > set_val,Phis: g > produc1432036078de_val > option_list_val,G2: g,N3: node] : ( sup_sup_set_val @ ( Defs @ G2 @ N3 ) @ ( sSA_CF370335846de_val @ Phis @ G2 @ N3 ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_120_CFG__SSA__base_OallUses__def,axiom,
% 2.07/1.19 ( sSA_CF178745443eD_val
% 2.07/1.19 = ( ^ [Alpha_n: g > list_node,InEdges: g > node > list_P561207620_edgeD,Uses: g > node > set_val,Phis: g > produc1432036078de_val > option_list_val,G2: g,N3: node] : ( sup_sup_set_val @ ( Uses @ G2 @ N3 ) @ ( sSA_CF848637139eD_val @ Alpha_n @ InEdges @ Phis @ G2 @ N3 ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_121_phi__phiDefs,axiom,
% 2.07/1.19 ! [G: g,V: val,Vs: list_val] :
% 2.07/1.19 ( ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ G @ V )
% 2.07/1.19 = ( some_list_val @ Vs ) )
% 2.07/1.19 => ( member_val @ V @ ( sSA_CF370335846de_val @ phis @ G @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ V ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_122_condensation__acyclic,axiom,
% 2.07/1.19 ! [G: g,P2: set_val] : ( transi1953622797et_val @ ( irredu893086079de_val @ alpha_n @ defs @ phis @ G @ P2 ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_123_phi__def,axiom,
% 2.07/1.19 ! [G: g,V: val] :
% 2.07/1.19 ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ G @ V )
% 2.07/1.19 = ( phis @ G @ ( produc1470527136de_val @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ V ) @ V ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_124_phiArg__def,axiom,
% 2.07/1.19 ! [G: g,V: val,V2: val] :
% 2.07/1.19 ( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G @ V @ V2 )
% 2.07/1.19 = ( ? [Vs2: list_val] :
% 2.07/1.19 ( ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ G @ V )
% 2.07/1.19 = ( some_list_val @ Vs2 ) )
% 2.07/1.19 & ( member_val @ V2 @ ( set_val2 @ Vs2 ) ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_125_phi__finite,axiom,
% 2.07/1.19 ! [G: g] : ( finite_finite_val @ ( dom_val_list_val @ ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ G ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_126_redundant__scc__phis,axiom,
% 2.07/1.19 ! [G: g,P2: set_val,Scc: set_val,X2: val] :
% 2.07/1.19 ( ( irredu224829488eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G @ P2 )
% 2.07/1.19 => ( ( member_set_val @ Scc @ ( irredu681226810de_val @ alpha_n @ defs @ phis @ G @ P2 ) )
% 2.07/1.19 => ( ( member_val @ X2 @ Scc )
% 2.07/1.19 => ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ G @ X2 )
% 2.07/1.19 != none_list_val ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_127_phis__disj_I2_J,axiom,
% 2.07/1.19 ! [G: g,N: node,V: val,Vs: list_val,N4: node,Vs3: list_val] :
% 2.07/1.19 ( ( ( phis @ G @ ( produc1470527136de_val @ N @ V ) )
% 2.07/1.19 = ( some_list_val @ Vs ) )
% 2.07/1.19 => ( ( ( phis @ G @ ( produc1470527136de_val @ N4 @ V ) )
% 2.07/1.19 = ( some_list_val @ Vs3 ) )
% 2.07/1.19 => ( Vs = Vs3 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_128_phis__disj_I1_J,axiom,
% 2.07/1.19 ! [G: g,N: node,V: val,Vs: list_val,N4: node,Vs3: list_val] :
% 2.07/1.19 ( ( ( phis @ G @ ( produc1470527136de_val @ N @ V ) )
% 2.07/1.19 = ( some_list_val @ Vs ) )
% 2.07/1.19 => ( ( ( phis @ G @ ( produc1470527136de_val @ N4 @ V ) )
% 2.07/1.19 = ( some_list_val @ Vs3 ) )
% 2.07/1.19 => ( N = N4 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_129_phis__in___092_060alpha_062n,axiom,
% 2.07/1.19 ! [G: g,N: node,V: val,Vs: list_val] :
% 2.07/1.19 ( ( ( phis @ G @ ( produc1470527136de_val @ N @ V ) )
% 2.07/1.19 = ( some_list_val @ Vs ) )
% 2.07/1.19 => ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_130_phis__same__var,axiom,
% 2.07/1.19 ! [G: g,N: node,V: val,Vs: list_val,V2: val] :
% 2.07/1.19 ( ( ( phis @ G @ ( produc1470527136de_val @ N @ V ) )
% 2.07/1.19 = ( some_list_val @ Vs ) )
% 2.07/1.19 => ( ( member_val @ V2 @ ( set_val2 @ Vs ) )
% 2.07/1.19 => ( ( var2 @ G @ V2 )
% 2.07/1.19 = ( var2 @ G @ V ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_131_phis__phi,axiom,
% 2.07/1.19 ! [G: g,N: node,V: val,Vs: list_val] :
% 2.07/1.19 ( ( ( phis @ G @ ( produc1470527136de_val @ N @ V ) )
% 2.07/1.19 = ( some_list_val @ Vs ) )
% 2.07/1.19 => ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ G @ V )
% 2.07/1.19 = ( some_list_val @ Vs ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_132_phiUses__exI,axiom,
% 2.07/1.19 ! [M: node,G: g,N: node,V: val,Vs: list_val] :
% 2.07/1.19 ( ( member_node @ M @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ N ) ) )
% 2.07/1.19 => ( ( ( phis @ G @ ( produc1470527136de_val @ N @ V ) )
% 2.07/1.19 = ( some_list_val @ Vs ) )
% 2.07/1.19 => ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.07/1.19 => ~ ! [V6: val] :
% 2.07/1.19 ( ( member_val @ V6 @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ G @ M ) )
% 2.07/1.19 => ~ ( member_val @ V6 @ ( set_val2 @ Vs ) ) ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_133_CFG__SSA__Transformed_Ocondensation__nodes_Ocong,axiom,
% 2.07/1.19 irredu681226810de_val = irredu681226810de_val ).
% 2.07/1.19
% 2.07/1.19 thf(fact_134_CFG__SSA__Transformed_Oredundant__set_Ocong,axiom,
% 2.07/1.19 irredu224829488eD_val = irredu224829488eD_val ).
% 2.07/1.19
% 2.07/1.19 thf(fact_135_CFG__SSA__wf__base_Ophi__def,axiom,
% 2.07/1.19 ( sSA_CF262257161de_val
% 2.07/1.19 = ( ^ [Alpha_n: g > list_node,Defs: g > node > set_val,Phis: g > produc1432036078de_val > option_list_val,G2: g,V3: val] : ( Phis @ G2 @ ( produc1470527136de_val @ ( sSA_CF551432799de_val @ Alpha_n @ Defs @ Phis @ G2 @ V3 ) @ V3 ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_136_CFG__SSA__wf__base_OphiArg__def,axiom,
% 2.07/1.19 ( sSA_CF1252180629de_val
% 2.07/1.19 = ( ^ [Alpha_n: g > list_node,Defs: g > node > set_val,Phis: g > produc1432036078de_val > option_list_val,G2: g,V3: val,V4: val] :
% 2.07/1.19 ? [Vs2: list_val] :
% 2.07/1.19 ( ( ( sSA_CF262257161de_val @ Alpha_n @ Defs @ Phis @ G2 @ V3 )
% 2.07/1.19 = ( some_list_val @ Vs2 ) )
% 2.07/1.19 & ( member_val @ V4 @ ( set_val2 @ Vs2 ) ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_137_phiUsesI,axiom,
% 2.07/1.19 ! [N4: node,G: g,V2: val,Vs: list_val,N: node,V: val] :
% 2.07/1.19 ( ( member_node @ N4 @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.07/1.19 => ( ( ( phis @ G @ ( produc1470527136de_val @ N4 @ V2 ) )
% 2.07/1.19 = ( some_list_val @ Vs ) )
% 2.07/1.19 => ( ( member313544709de_val @ ( produc1470527136de_val @ N @ V ) @ ( set_Pr1085970585de_val @ ( zip_node_val @ ( graph_272749361_edgeD @ inEdges @ G @ N4 ) @ Vs ) ) )
% 2.07/1.19 => ( member_val @ V @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ G @ N ) ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_138_scc__in__P,axiom,
% 2.07/1.19 ! [Scc: set_val,G: g,P2: set_val] :
% 2.07/1.19 ( ( member_set_val @ Scc @ ( irredu681226810de_val @ alpha_n @ defs @ phis @ G @ P2 ) )
% 2.07/1.19 => ( ord_less_eq_set_val @ Scc @ P2 ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_139_not__None__eq,axiom,
% 2.07/1.19 ! [X2: option_list_val] :
% 2.07/1.19 ( ( X2 != none_list_val )
% 2.07/1.19 = ( ? [Y2: list_val] :
% 2.07/1.19 ( X2
% 2.07/1.19 = ( some_list_val @ Y2 ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_140_not__Some__eq,axiom,
% 2.07/1.19 ! [X2: option_list_val] :
% 2.07/1.19 ( ( ! [Y2: list_val] :
% 2.07/1.19 ( X2
% 2.07/1.19 != ( some_list_val @ Y2 ) ) )
% 2.07/1.19 = ( X2 = none_list_val ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_141_sup__Some,axiom,
% 2.07/1.19 ! [X2: set_val,Y3: set_val] :
% 2.07/1.19 ( ( sup_su1487070040et_val @ ( some_set_val @ X2 ) @ ( some_set_val @ Y3 ) )
% 2.07/1.19 = ( some_set_val @ ( sup_sup_set_val @ X2 @ Y3 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_142_option_Oinject,axiom,
% 2.07/1.19 ! [X22: list_val,Y22: list_val] :
% 2.07/1.19 ( ( ( some_list_val @ X22 )
% 2.07/1.19 = ( some_list_val @ Y22 ) )
% 2.07/1.19 = ( X22 = Y22 ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_143_less__eq__option__Some,axiom,
% 2.07/1.19 ! [X2: set_val,Y3: set_val] :
% 2.07/1.19 ( ( ord_le596993316et_val @ ( some_set_val @ X2 ) @ ( some_set_val @ Y3 ) )
% 2.07/1.19 = ( ord_less_eq_set_val @ X2 @ Y3 ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_144_zip__same,axiom,
% 2.07/1.19 ! [A: produc1324971431et_val,B: produc1324971431et_val,Xs: list_P2089461677et_val] :
% 2.07/1.19 ( ( member1254968080et_val @ ( produc1377626967et_val @ A @ B ) @ ( set_Pr1006393724et_val @ ( zip_Pr21865079et_val @ Xs @ Xs ) ) )
% 2.07/1.19 = ( ( member1711426256et_val @ A @ ( set_Pr284769596et_val @ Xs ) )
% 2.07/1.19 & ( A = B ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_145_zip__same,axiom,
% 2.07/1.19 ! [A: node,B: node,Xs: list_node] :
% 2.07/1.19 ( ( member2110109140e_node @ ( produc457016035e_node @ A @ B ) @ ( set_Pr450990656e_node @ ( zip_node_node @ Xs @ Xs ) ) )
% 2.07/1.19 = ( ( member_node @ A @ ( set_node2 @ Xs ) )
% 2.07/1.19 & ( A = B ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_146_zip__same,axiom,
% 2.07/1.19 ! [A: val,B: val,Xs: list_val] :
% 2.07/1.19 ( ( member1680438992al_val @ ( product_Pair_val_val @ A @ B ) @ ( set_Pr102746428al_val @ ( zip_val_val @ Xs @ Xs ) ) )
% 2.07/1.19 = ( ( member_val @ A @ ( set_val2 @ Xs ) )
% 2.07/1.19 & ( A = B ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_147_zip__same,axiom,
% 2.07/1.19 ! [A: produc1432036078de_val,B: produc1432036078de_val,Xs: list_P1820443774de_val] :
% 2.07/1.19 ( ( member698732390de_val @ ( produc453318901de_val @ A @ B ) @ ( set_Pr482027474de_val @ ( zip_Pr1472086037de_val @ Xs @ Xs ) ) )
% 2.07/1.19 = ( ( member313544709de_val @ A @ ( set_Pr1085970585de_val @ Xs ) )
% 2.07/1.19 & ( A = B ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_148_zip__same,axiom,
% 2.07/1.19 ! [A: set_val,B: set_val,Xs: list_set_val] :
% 2.07/1.19 ( ( member1711426256et_val @ ( produc1041633943et_val @ A @ B ) @ ( set_Pr284769596et_val @ ( zip_set_val_set_val @ Xs @ Xs ) ) )
% 2.07/1.19 = ( ( member_set_val @ A @ ( set_set_val2 @ Xs ) )
% 2.07/1.19 & ( A = B ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_149__C1_C,axiom,
% 2.07/1.19 ! [G: g,P2: set_val] :
% 2.07/1.19 ( ( irredu224829488eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G @ P2 )
% 2.07/1.19 => ? [Scc2: set_val] :
% 2.07/1.19 ( ( ord_less_eq_set_val @ Scc2 @ P2 )
% 2.07/1.19 & ( irredu1955035135eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G @ P2 @ Scc2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_150_phiUsesE,axiom,
% 2.07/1.19 ! [V: val,G: g,N: node] :
% 2.07/1.19 ( ( member_val @ V @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ G @ N ) )
% 2.07/1.19 => ~ ! [N5: node] :
% 2.07/1.19 ( ( member_node @ N5 @ ( set_node2 @ ( graph_1037173556_edgeD @ alpha_n @ inEdges @ G @ N ) ) )
% 2.07/1.19 => ! [V6: val,Vs4: list_val] :
% 2.07/1.19 ( ( member313544709de_val @ ( produc1470527136de_val @ N @ V ) @ ( set_Pr1085970585de_val @ ( zip_node_val @ ( graph_272749361_edgeD @ inEdges @ G @ N5 ) @ Vs4 ) ) )
% 2.07/1.19 => ( ( phis @ G @ ( produc1470527136de_val @ N5 @ V6 ) )
% 2.07/1.19 != ( some_list_val @ Vs4 ) ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_151_finite__has__minimal2,axiom,
% 2.07/1.19 ! [A2: set_node,A: node] :
% 2.07/1.19 ( ( finite_finite_node @ A2 )
% 2.07/1.19 => ( ( member_node @ A @ A2 )
% 2.07/1.19 => ? [X3: node] :
% 2.07/1.19 ( ( member_node @ X3 @ A2 )
% 2.07/1.19 & ( ord_less_eq_node @ X3 @ A )
% 2.07/1.19 & ! [Xa: node] :
% 2.07/1.19 ( ( member_node @ Xa @ A2 )
% 2.07/1.19 => ( ( ord_less_eq_node @ Xa @ X3 )
% 2.07/1.19 => ( X3 = Xa ) ) ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_152_finite__has__minimal2,axiom,
% 2.07/1.19 ! [A2: set_val,A: val] :
% 2.07/1.19 ( ( finite_finite_val @ A2 )
% 2.07/1.19 => ( ( member_val @ A @ A2 )
% 2.07/1.19 => ? [X3: val] :
% 2.07/1.19 ( ( member_val @ X3 @ A2 )
% 2.07/1.19 & ( ord_less_eq_val @ X3 @ A )
% 2.07/1.19 & ! [Xa: val] :
% 2.07/1.19 ( ( member_val @ Xa @ A2 )
% 2.07/1.19 => ( ( ord_less_eq_val @ Xa @ X3 )
% 2.07/1.19 => ( X3 = Xa ) ) ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_153_finite__has__minimal2,axiom,
% 2.07/1.19 ! [A2: set_set_val,A: set_val] :
% 2.07/1.19 ( ( finite1265617511et_val @ A2 )
% 2.07/1.19 => ( ( member_set_val @ A @ A2 )
% 2.07/1.19 => ? [X3: set_val] :
% 2.07/1.19 ( ( member_set_val @ X3 @ A2 )
% 2.07/1.19 & ( ord_less_eq_set_val @ X3 @ A )
% 2.07/1.19 & ! [Xa: set_val] :
% 2.07/1.19 ( ( member_set_val @ Xa @ A2 )
% 2.07/1.19 => ( ( ord_less_eq_set_val @ Xa @ X3 )
% 2.07/1.19 => ( X3 = Xa ) ) ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_154_finite__has__maximal2,axiom,
% 2.07/1.19 ! [A2: set_node,A: node] :
% 2.07/1.19 ( ( finite_finite_node @ A2 )
% 2.07/1.19 => ( ( member_node @ A @ A2 )
% 2.07/1.19 => ? [X3: node] :
% 2.07/1.19 ( ( member_node @ X3 @ A2 )
% 2.07/1.19 & ( ord_less_eq_node @ A @ X3 )
% 2.07/1.19 & ! [Xa: node] :
% 2.07/1.19 ( ( member_node @ Xa @ A2 )
% 2.07/1.19 => ( ( ord_less_eq_node @ X3 @ Xa )
% 2.07/1.19 => ( X3 = Xa ) ) ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_155_finite__has__maximal2,axiom,
% 2.07/1.19 ! [A2: set_val,A: val] :
% 2.07/1.19 ( ( finite_finite_val @ A2 )
% 2.07/1.19 => ( ( member_val @ A @ A2 )
% 2.07/1.19 => ? [X3: val] :
% 2.07/1.19 ( ( member_val @ X3 @ A2 )
% 2.07/1.19 & ( ord_less_eq_val @ A @ X3 )
% 2.07/1.19 & ! [Xa: val] :
% 2.07/1.19 ( ( member_val @ Xa @ A2 )
% 2.07/1.19 => ( ( ord_less_eq_val @ X3 @ Xa )
% 2.07/1.19 => ( X3 = Xa ) ) ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_156_finite__has__maximal2,axiom,
% 2.07/1.19 ! [A2: set_set_val,A: set_val] :
% 2.07/1.19 ( ( finite1265617511et_val @ A2 )
% 2.07/1.19 => ( ( member_set_val @ A @ A2 )
% 2.07/1.19 => ? [X3: set_val] :
% 2.07/1.19 ( ( member_set_val @ X3 @ A2 )
% 2.07/1.19 & ( ord_less_eq_set_val @ A @ X3 )
% 2.07/1.19 & ! [Xa: set_val] :
% 2.07/1.19 ( ( member_set_val @ Xa @ A2 )
% 2.07/1.19 => ( ( ord_less_eq_set_val @ X3 @ Xa )
% 2.07/1.19 => ( X3 = Xa ) ) ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_157_subset__code_I1_J,axiom,
% 2.07/1.19 ! [Xs: list_set_val,B2: set_set_val] :
% 2.07/1.19 ( ( ord_le1742111550et_val @ ( set_set_val2 @ Xs ) @ B2 )
% 2.07/1.19 = ( ! [X: set_val] :
% 2.07/1.19 ( ( member_set_val @ X @ ( set_set_val2 @ Xs ) )
% 2.07/1.19 => ( member_set_val @ X @ B2 ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_158_subset__code_I1_J,axiom,
% 2.07/1.19 ! [Xs: list_P2089461677et_val,B2: set_Pr1311924359et_val] :
% 2.07/1.19 ( ( ord_le299366439et_val @ ( set_Pr284769596et_val @ Xs ) @ B2 )
% 2.07/1.19 = ( ! [X: produc1324971431et_val] :
% 2.07/1.19 ( ( member1711426256et_val @ X @ ( set_Pr284769596et_val @ Xs ) )
% 2.07/1.19 => ( member1711426256et_val @ X @ B2 ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_159_subset__code_I1_J,axiom,
% 2.07/1.19 ! [Xs: list_node,B2: set_node] :
% 2.07/1.19 ( ( ord_less_eq_set_node @ ( set_node2 @ Xs ) @ B2 )
% 2.07/1.19 = ( ! [X: node] :
% 2.07/1.19 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 2.07/1.19 => ( member_node @ X @ B2 ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_160_subset__code_I1_J,axiom,
% 2.07/1.19 ! [Xs: list_P1820443774de_val,B2: set_Pr699757092de_val] :
% 2.07/1.19 ( ( ord_le1643692676de_val @ ( set_Pr1085970585de_val @ Xs ) @ B2 )
% 2.07/1.19 = ( ! [X: produc1432036078de_val] :
% 2.07/1.19 ( ( member313544709de_val @ X @ ( set_Pr1085970585de_val @ Xs ) )
% 2.07/1.19 => ( member313544709de_val @ X @ B2 ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_161_subset__code_I1_J,axiom,
% 2.07/1.19 ! [Xs: list_val,B2: set_val] :
% 2.07/1.19 ( ( ord_less_eq_set_val @ ( set_val2 @ Xs ) @ B2 )
% 2.07/1.19 = ( ! [X: val] :
% 2.07/1.19 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 2.07/1.19 => ( member_val @ X @ B2 ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_162_rev__finite__subset,axiom,
% 2.07/1.19 ! [B2: set_Pr1311924359et_val,A2: set_Pr1311924359et_val] :
% 2.07/1.19 ( ( finite79836624et_val @ B2 )
% 2.07/1.19 => ( ( ord_le299366439et_val @ A2 @ B2 )
% 2.07/1.19 => ( finite79836624et_val @ A2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_163_rev__finite__subset,axiom,
% 2.07/1.19 ! [B2: set_Pr699757092de_val,A2: set_Pr699757092de_val] :
% 2.07/1.19 ( ( finite2056463621de_val @ B2 )
% 2.07/1.19 => ( ( ord_le1643692676de_val @ A2 @ B2 )
% 2.07/1.19 => ( finite2056463621de_val @ A2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_164_rev__finite__subset,axiom,
% 2.07/1.19 ! [B2: set_val,A2: set_val] :
% 2.07/1.19 ( ( finite_finite_val @ B2 )
% 2.07/1.19 => ( ( ord_less_eq_set_val @ A2 @ B2 )
% 2.07/1.19 => ( finite_finite_val @ A2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_165_infinite__super,axiom,
% 2.07/1.19 ! [S: set_Pr1311924359et_val,T: set_Pr1311924359et_val] :
% 2.07/1.19 ( ( ord_le299366439et_val @ S @ T )
% 2.07/1.19 => ( ~ ( finite79836624et_val @ S )
% 2.07/1.19 => ~ ( finite79836624et_val @ T ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_166_infinite__super,axiom,
% 2.07/1.19 ! [S: set_Pr699757092de_val,T: set_Pr699757092de_val] :
% 2.07/1.19 ( ( ord_le1643692676de_val @ S @ T )
% 2.07/1.19 => ( ~ ( finite2056463621de_val @ S )
% 2.07/1.19 => ~ ( finite2056463621de_val @ T ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_167_infinite__super,axiom,
% 2.07/1.19 ! [S: set_val,T: set_val] :
% 2.07/1.19 ( ( ord_less_eq_set_val @ S @ T )
% 2.07/1.19 => ( ~ ( finite_finite_val @ S )
% 2.07/1.19 => ~ ( finite_finite_val @ T ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_168_finite__subset,axiom,
% 2.07/1.19 ! [A2: set_Pr1311924359et_val,B2: set_Pr1311924359et_val] :
% 2.07/1.19 ( ( ord_le299366439et_val @ A2 @ B2 )
% 2.07/1.19 => ( ( finite79836624et_val @ B2 )
% 2.07/1.19 => ( finite79836624et_val @ A2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_169_finite__subset,axiom,
% 2.07/1.19 ! [A2: set_Pr699757092de_val,B2: set_Pr699757092de_val] :
% 2.07/1.19 ( ( ord_le1643692676de_val @ A2 @ B2 )
% 2.07/1.19 => ( ( finite2056463621de_val @ B2 )
% 2.07/1.19 => ( finite2056463621de_val @ A2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_170_finite__subset,axiom,
% 2.07/1.19 ! [A2: set_val,B2: set_val] :
% 2.07/1.19 ( ( ord_less_eq_set_val @ A2 @ B2 )
% 2.07/1.19 => ( ( finite_finite_val @ B2 )
% 2.07/1.19 => ( finite_finite_val @ A2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_171_in__set__zipE,axiom,
% 2.07/1.19 ! [X2: node,Y3: node,Xs: list_node,Ys: list_node] :
% 2.07/1.19 ( ( member2110109140e_node @ ( produc457016035e_node @ X2 @ Y3 ) @ ( set_Pr450990656e_node @ ( zip_node_node @ Xs @ Ys ) ) )
% 2.07/1.19 => ~ ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 2.07/1.19 => ~ ( member_node @ Y3 @ ( set_node2 @ Ys ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_172_in__set__zipE,axiom,
% 2.07/1.19 ! [X2: val,Y3: node,Xs: list_val,Ys: list_node] :
% 2.07/1.19 ( ( member828457417l_node @ ( produc1074923692l_node @ X2 @ Y3 ) @ ( set_Pr1600883293l_node @ ( zip_val_node @ Xs @ Ys ) ) )
% 2.07/1.19 => ~ ( ( member_val @ X2 @ ( set_val2 @ Xs ) )
% 2.07/1.19 => ~ ( member_node @ Y3 @ ( set_node2 @ Ys ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_173_in__set__zipE,axiom,
% 2.07/1.19 ! [X2: val,Y3: val,Xs: list_val,Ys: list_val] :
% 2.07/1.19 ( ( member1680438992al_val @ ( product_Pair_val_val @ X2 @ Y3 ) @ ( set_Pr102746428al_val @ ( zip_val_val @ Xs @ Ys ) ) )
% 2.07/1.19 => ~ ( ( member_val @ X2 @ ( set_val2 @ Xs ) )
% 2.07/1.19 => ~ ( member_val @ Y3 @ ( set_val2 @ Ys ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_174_in__set__zipE,axiom,
% 2.07/1.19 ! [X2: node,Y3: val,Xs: list_node,Ys: list_val] :
% 2.07/1.19 ( ( member313544709de_val @ ( produc1470527136de_val @ X2 @ Y3 ) @ ( set_Pr1085970585de_val @ ( zip_node_val @ Xs @ Ys ) ) )
% 2.07/1.19 => ~ ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 2.07/1.19 => ~ ( member_val @ Y3 @ ( set_val2 @ Ys ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_175_in__set__zipE,axiom,
% 2.07/1.19 ! [X2: set_val,Y3: node,Xs: list_set_val,Ys: list_node] :
% 2.07/1.19 ( ( member76372137l_node @ ( produc2052093836l_node @ X2 @ Y3 ) @ ( set_Pr1904955709l_node @ ( zip_set_val_node @ Xs @ Ys ) ) )
% 2.07/1.19 => ~ ( ( member_set_val @ X2 @ ( set_set_val2 @ Xs ) )
% 2.07/1.19 => ~ ( member_node @ Y3 @ ( set_node2 @ Ys ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_176_in__set__zipE,axiom,
% 2.07/1.19 ! [X2: set_val,Y3: val,Xs: list_set_val,Ys: list_val] :
% 2.07/1.19 ( ( member1110026224al_val @ ( produc1337903031al_val @ X2 @ Y3 ) @ ( set_Pr1027623516al_val @ ( zip_set_val_val @ Xs @ Ys ) ) )
% 2.07/1.19 => ~ ( ( member_set_val @ X2 @ ( set_set_val2 @ Xs ) )
% 2.07/1.19 => ~ ( member_val @ Y3 @ ( set_val2 @ Ys ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_177_in__set__zipE,axiom,
% 2.07/1.19 ! [X2: node,Y3: set_val,Xs: list_node,Ys: list_set_val] :
% 2.07/1.19 ( ( member125181669et_val @ ( produc2042994048et_val @ X2 @ Y3 ) @ ( set_Pr1953765241et_val @ ( zip_node_set_val @ Xs @ Ys ) ) )
% 2.07/1.19 => ~ ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 2.07/1.19 => ~ ( member_set_val @ Y3 @ ( set_set_val2 @ Ys ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_178_in__set__zipE,axiom,
% 2.07/1.19 ! [X2: val,Y3: set_val,Xs: list_val,Ys: list_set_val] :
% 2.07/1.19 ( ( member39229872et_val @ ( produc1446164855et_val @ X2 @ Y3 ) @ ( set_Pr2104310812et_val @ ( zip_val_set_val @ Xs @ Ys ) ) )
% 2.07/1.19 => ~ ( ( member_val @ X2 @ ( set_val2 @ Xs ) )
% 2.07/1.19 => ~ ( member_set_val @ Y3 @ ( set_set_val2 @ Ys ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_179_in__set__zipE,axiom,
% 2.07/1.19 ! [X2: node,Y3: produc1432036078de_val,Xs: list_node,Ys: list_P1820443774de_val] :
% 2.07/1.19 ( ( member562853661de_val @ ( produc1162531244de_val @ X2 @ Y3 ) @ ( set_Pr1157337481de_val @ ( zip_no263301324de_val @ Xs @ Ys ) ) )
% 2.07/1.19 => ~ ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 2.07/1.19 => ~ ( member313544709de_val @ Y3 @ ( set_Pr1085970585de_val @ Ys ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_180_in__set__zipE,axiom,
% 2.07/1.19 ! [X2: val,Y3: produc1432036078de_val,Xs: list_val,Ys: list_P1820443774de_val] :
% 2.07/1.19 ( ( member1894062994de_val @ ( produc1571934709de_val @ X2 @ Y3 ) @ ( set_Pr434939430de_val @ ( zip_va679686869de_val @ Xs @ Ys ) ) )
% 2.07/1.19 => ~ ( ( member_val @ X2 @ ( set_val2 @ Xs ) )
% 2.07/1.19 => ~ ( member313544709de_val @ Y3 @ ( set_Pr1085970585de_val @ Ys ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_181_set__zip__leftD,axiom,
% 2.07/1.19 ! [X2: node,Y3: val,Xs: list_node,Ys: list_val] :
% 2.07/1.19 ( ( member313544709de_val @ ( produc1470527136de_val @ X2 @ Y3 ) @ ( set_Pr1085970585de_val @ ( zip_node_val @ Xs @ Ys ) ) )
% 2.07/1.19 => ( member_node @ X2 @ ( set_node2 @ Xs ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_182_set__zip__leftD,axiom,
% 2.07/1.19 ! [X2: set_val,Y3: set_val,Xs: list_set_val,Ys: list_set_val] :
% 2.07/1.19 ( ( member1711426256et_val @ ( produc1041633943et_val @ X2 @ Y3 ) @ ( set_Pr284769596et_val @ ( zip_set_val_set_val @ Xs @ Ys ) ) )
% 2.07/1.19 => ( member_set_val @ X2 @ ( set_set_val2 @ Xs ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_183_set__zip__rightD,axiom,
% 2.07/1.19 ! [X2: node,Y3: val,Xs: list_node,Ys: list_val] :
% 2.07/1.19 ( ( member313544709de_val @ ( produc1470527136de_val @ X2 @ Y3 ) @ ( set_Pr1085970585de_val @ ( zip_node_val @ Xs @ Ys ) ) )
% 2.07/1.19 => ( member_val @ Y3 @ ( set_val2 @ Ys ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_184_set__zip__rightD,axiom,
% 2.07/1.19 ! [X2: set_val,Y3: set_val,Xs: list_set_val,Ys: list_set_val] :
% 2.07/1.19 ( ( member1711426256et_val @ ( produc1041633943et_val @ X2 @ Y3 ) @ ( set_Pr284769596et_val @ ( zip_set_val_set_val @ Xs @ Ys ) ) )
% 2.07/1.19 => ( member_set_val @ Y3 @ ( set_set_val2 @ Ys ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_185_combine__options__cases,axiom,
% 2.07/1.19 ! [X2: option_list_val,P2: option_list_val > option_list_val > $o,Y3: option_list_val] :
% 2.07/1.19 ( ( ( X2 = none_list_val )
% 2.07/1.19 => ( P2 @ X2 @ Y3 ) )
% 2.07/1.19 => ( ( ( Y3 = none_list_val )
% 2.07/1.19 => ( P2 @ X2 @ Y3 ) )
% 2.07/1.19 => ( ! [A4: list_val,B3: list_val] :
% 2.07/1.19 ( ( X2
% 2.07/1.19 = ( some_list_val @ A4 ) )
% 2.07/1.19 => ( ( Y3
% 2.07/1.19 = ( some_list_val @ B3 ) )
% 2.07/1.19 => ( P2 @ X2 @ Y3 ) ) )
% 2.07/1.19 => ( P2 @ X2 @ Y3 ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_186_split__option__all,axiom,
% 2.07/1.19 ( ( ^ [P3: option_list_val > $o] :
% 2.07/1.19 ! [X4: option_list_val] : ( P3 @ X4 ) )
% 2.07/1.19 = ( ^ [P4: option_list_val > $o] :
% 2.07/1.19 ( ( P4 @ none_list_val )
% 2.07/1.19 & ! [X: list_val] : ( P4 @ ( some_list_val @ X ) ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_187_split__option__ex,axiom,
% 2.07/1.19 ( ( ^ [P3: option_list_val > $o] :
% 2.07/1.19 ? [X4: option_list_val] : ( P3 @ X4 ) )
% 2.07/1.19 = ( ^ [P4: option_list_val > $o] :
% 2.07/1.19 ( ( P4 @ none_list_val )
% 2.07/1.19 | ? [X: list_val] : ( P4 @ ( some_list_val @ X ) ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_188_option_Oinducts,axiom,
% 2.07/1.19 ! [P2: option_list_val > $o,Option: option_list_val] :
% 2.07/1.19 ( ( P2 @ none_list_val )
% 2.07/1.19 => ( ! [X3: list_val] : ( P2 @ ( some_list_val @ X3 ) )
% 2.07/1.19 => ( P2 @ Option ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_189_option_Oexhaust,axiom,
% 2.07/1.19 ! [Y3: option_list_val] :
% 2.07/1.19 ( ( Y3 != none_list_val )
% 2.07/1.19 => ~ ! [X23: list_val] :
% 2.07/1.19 ( Y3
% 2.07/1.19 != ( some_list_val @ X23 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_190_option_OdiscI,axiom,
% 2.07/1.19 ! [Option: option_list_val,X22: list_val] :
% 2.07/1.19 ( ( Option
% 2.07/1.19 = ( some_list_val @ X22 ) )
% 2.07/1.19 => ( Option != none_list_val ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_191_option_Odistinct_I1_J,axiom,
% 2.07/1.19 ! [X22: list_val] :
% 2.07/1.19 ( none_list_val
% 2.07/1.19 != ( some_list_val @ X22 ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_192_Ex__condensation__leaf,axiom,
% 2.07/1.19 ! [P2: set_val,G: g] :
% 2.07/1.19 ( ( P2 != bot_bot_set_val )
% 2.07/1.19 => ? [Leaf: set_val] :
% 2.07/1.19 ( ( member_set_val @ Leaf @ ( irredu681226810de_val @ alpha_n @ defs @ phis @ G @ P2 ) )
% 2.07/1.19 & ! [Scc3: set_val] :
% 2.07/1.19 ~ ( member1711426256et_val @ ( produc1041633943et_val @ Leaf @ Scc3 ) @ ( irredu893086079de_val @ alpha_n @ defs @ phis @ G @ P2 ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_193_Un__subset__iff,axiom,
% 2.07/1.19 ! [A2: set_val,B2: set_val,C: set_val] :
% 2.07/1.19 ( ( ord_less_eq_set_val @ ( sup_sup_set_val @ A2 @ B2 ) @ C )
% 2.07/1.19 = ( ( ord_less_eq_set_val @ A2 @ C )
% 2.07/1.19 & ( ord_less_eq_set_val @ B2 @ C ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_194_le__sup__iff,axiom,
% 2.07/1.19 ! [X2: set_val,Y3: set_val,Z: set_val] :
% 2.07/1.19 ( ( ord_less_eq_set_val @ ( sup_sup_set_val @ X2 @ Y3 ) @ Z )
% 2.07/1.19 = ( ( ord_less_eq_set_val @ X2 @ Z )
% 2.07/1.19 & ( ord_less_eq_set_val @ Y3 @ Z ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_195_sup_Obounded__iff,axiom,
% 2.07/1.19 ! [B: set_val,C2: set_val,A: set_val] :
% 2.07/1.19 ( ( ord_less_eq_set_val @ ( sup_sup_set_val @ B @ C2 ) @ A )
% 2.07/1.19 = ( ( ord_less_eq_set_val @ B @ A )
% 2.07/1.19 & ( ord_less_eq_set_val @ C2 @ A ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_196_subset__antisym,axiom,
% 2.07/1.19 ! [A2: set_val,B2: set_val] :
% 2.07/1.19 ( ( ord_less_eq_set_val @ A2 @ B2 )
% 2.07/1.19 => ( ( ord_less_eq_set_val @ B2 @ A2 )
% 2.07/1.19 => ( A2 = B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_197_subsetI,axiom,
% 2.07/1.19 ! [A2: set_node,B2: set_node] :
% 2.07/1.19 ( ! [X3: node] :
% 2.07/1.19 ( ( member_node @ X3 @ A2 )
% 2.07/1.19 => ( member_node @ X3 @ B2 ) )
% 2.07/1.19 => ( ord_less_eq_set_node @ A2 @ B2 ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_198_subsetI,axiom,
% 2.07/1.19 ! [A2: set_set_val,B2: set_set_val] :
% 2.07/1.19 ( ! [X3: set_val] :
% 2.07/1.19 ( ( member_set_val @ X3 @ A2 )
% 2.07/1.19 => ( member_set_val @ X3 @ B2 ) )
% 2.07/1.19 => ( ord_le1742111550et_val @ A2 @ B2 ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_199_subsetI,axiom,
% 2.07/1.19 ! [A2: set_Pr699757092de_val,B2: set_Pr699757092de_val] :
% 2.07/1.19 ( ! [X3: produc1432036078de_val] :
% 2.07/1.19 ( ( member313544709de_val @ X3 @ A2 )
% 2.07/1.19 => ( member313544709de_val @ X3 @ B2 ) )
% 2.07/1.19 => ( ord_le1643692676de_val @ A2 @ B2 ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_200_subsetI,axiom,
% 2.07/1.19 ! [A2: set_Pr1311924359et_val,B2: set_Pr1311924359et_val] :
% 2.07/1.19 ( ! [X3: produc1324971431et_val] :
% 2.07/1.19 ( ( member1711426256et_val @ X3 @ A2 )
% 2.07/1.19 => ( member1711426256et_val @ X3 @ B2 ) )
% 2.07/1.19 => ( ord_le299366439et_val @ A2 @ B2 ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_201_subsetI,axiom,
% 2.07/1.19 ! [A2: set_val,B2: set_val] :
% 2.07/1.19 ( ! [X3: val] :
% 2.07/1.19 ( ( member_val @ X3 @ A2 )
% 2.07/1.19 => ( member_val @ X3 @ B2 ) )
% 2.07/1.19 => ( ord_less_eq_set_val @ A2 @ B2 ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_202_sup_Oright__idem,axiom,
% 2.07/1.19 ! [A: set_val,B: set_val] :
% 2.07/1.19 ( ( sup_sup_set_val @ ( sup_sup_set_val @ A @ B ) @ B )
% 2.07/1.19 = ( sup_sup_set_val @ A @ B ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_203_sup__left__idem,axiom,
% 2.07/1.19 ! [X2: set_val,Y3: set_val] :
% 2.07/1.19 ( ( sup_sup_set_val @ X2 @ ( sup_sup_set_val @ X2 @ Y3 ) )
% 2.07/1.19 = ( sup_sup_set_val @ X2 @ Y3 ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_204_sup_Oleft__idem,axiom,
% 2.07/1.19 ! [A: set_val,B: set_val] :
% 2.07/1.19 ( ( sup_sup_set_val @ A @ ( sup_sup_set_val @ A @ B ) )
% 2.07/1.19 = ( sup_sup_set_val @ A @ B ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_205_sup__idem,axiom,
% 2.07/1.19 ! [X2: set_val] :
% 2.07/1.19 ( ( sup_sup_set_val @ X2 @ X2 )
% 2.07/1.19 = X2 ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_206_sup_Oidem,axiom,
% 2.07/1.19 ! [A: set_val] :
% 2.07/1.19 ( ( sup_sup_set_val @ A @ A )
% 2.07/1.19 = A ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_207_Un__iff,axiom,
% 2.07/1.19 ! [C2: node,A2: set_node,B2: set_node] :
% 2.07/1.19 ( ( member_node @ C2 @ ( sup_sup_set_node @ A2 @ B2 ) )
% 2.07/1.19 = ( ( member_node @ C2 @ A2 )
% 2.07/1.19 | ( member_node @ C2 @ B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_208_Un__iff,axiom,
% 2.07/1.19 ! [C2: set_val,A2: set_set_val,B2: set_set_val] :
% 2.07/1.19 ( ( member_set_val @ C2 @ ( sup_sup_set_set_val @ A2 @ B2 ) )
% 2.07/1.19 = ( ( member_set_val @ C2 @ A2 )
% 2.07/1.19 | ( member_set_val @ C2 @ B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_209_Un__iff,axiom,
% 2.07/1.19 ! [C2: produc1432036078de_val,A2: set_Pr699757092de_val,B2: set_Pr699757092de_val] :
% 2.07/1.19 ( ( member313544709de_val @ C2 @ ( sup_su2138939728de_val @ A2 @ B2 ) )
% 2.07/1.19 = ( ( member313544709de_val @ C2 @ A2 )
% 2.07/1.19 | ( member313544709de_val @ C2 @ B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_210_Un__iff,axiom,
% 2.07/1.19 ! [C2: produc1324971431et_val,A2: set_Pr1311924359et_val,B2: set_Pr1311924359et_val] :
% 2.07/1.19 ( ( member1711426256et_val @ C2 @ ( sup_su2005730907et_val @ A2 @ B2 ) )
% 2.07/1.19 = ( ( member1711426256et_val @ C2 @ A2 )
% 2.07/1.19 | ( member1711426256et_val @ C2 @ B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_211_Un__iff,axiom,
% 2.07/1.19 ! [C2: val,A2: set_val,B2: set_val] :
% 2.07/1.19 ( ( member_val @ C2 @ ( sup_sup_set_val @ A2 @ B2 ) )
% 2.07/1.19 = ( ( member_val @ C2 @ A2 )
% 2.07/1.19 | ( member_val @ C2 @ B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_212_UnCI,axiom,
% 2.07/1.19 ! [C2: node,B2: set_node,A2: set_node] :
% 2.07/1.19 ( ( ~ ( member_node @ C2 @ B2 )
% 2.07/1.19 => ( member_node @ C2 @ A2 ) )
% 2.07/1.19 => ( member_node @ C2 @ ( sup_sup_set_node @ A2 @ B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_213_UnCI,axiom,
% 2.07/1.19 ! [C2: set_val,B2: set_set_val,A2: set_set_val] :
% 2.07/1.19 ( ( ~ ( member_set_val @ C2 @ B2 )
% 2.07/1.19 => ( member_set_val @ C2 @ A2 ) )
% 2.07/1.19 => ( member_set_val @ C2 @ ( sup_sup_set_set_val @ A2 @ B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_214_UnCI,axiom,
% 2.07/1.19 ! [C2: produc1432036078de_val,B2: set_Pr699757092de_val,A2: set_Pr699757092de_val] :
% 2.07/1.19 ( ( ~ ( member313544709de_val @ C2 @ B2 )
% 2.07/1.19 => ( member313544709de_val @ C2 @ A2 ) )
% 2.07/1.19 => ( member313544709de_val @ C2 @ ( sup_su2138939728de_val @ A2 @ B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_215_UnCI,axiom,
% 2.07/1.19 ! [C2: produc1324971431et_val,B2: set_Pr1311924359et_val,A2: set_Pr1311924359et_val] :
% 2.07/1.19 ( ( ~ ( member1711426256et_val @ C2 @ B2 )
% 2.07/1.19 => ( member1711426256et_val @ C2 @ A2 ) )
% 2.07/1.19 => ( member1711426256et_val @ C2 @ ( sup_su2005730907et_val @ A2 @ B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_216_UnCI,axiom,
% 2.07/1.19 ! [C2: val,B2: set_val,A2: set_val] :
% 2.07/1.19 ( ( ~ ( member_val @ C2 @ B2 )
% 2.07/1.19 => ( member_val @ C2 @ A2 ) )
% 2.07/1.19 => ( member_val @ C2 @ ( sup_sup_set_val @ A2 @ B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_217_subset__empty,axiom,
% 2.07/1.19 ! [A2: set_val] :
% 2.07/1.19 ( ( ord_less_eq_set_val @ A2 @ bot_bot_set_val )
% 2.07/1.19 = ( A2 = bot_bot_set_val ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_218_empty__subsetI,axiom,
% 2.07/1.19 ! [A2: set_val] : ( ord_less_eq_set_val @ bot_bot_set_val @ A2 ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_219_sup__bot__left,axiom,
% 2.07/1.19 ! [X2: set_val] :
% 2.07/1.19 ( ( sup_sup_set_val @ bot_bot_set_val @ X2 )
% 2.07/1.19 = X2 ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_220_sup__bot__right,axiom,
% 2.07/1.19 ! [X2: set_val] :
% 2.07/1.19 ( ( sup_sup_set_val @ X2 @ bot_bot_set_val )
% 2.07/1.19 = X2 ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_221_bot__eq__sup__iff,axiom,
% 2.07/1.19 ! [X2: set_val,Y3: set_val] :
% 2.07/1.19 ( ( bot_bot_set_val
% 2.07/1.19 = ( sup_sup_set_val @ X2 @ Y3 ) )
% 2.07/1.19 = ( ( X2 = bot_bot_set_val )
% 2.07/1.19 & ( Y3 = bot_bot_set_val ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_222_sup__eq__bot__iff,axiom,
% 2.07/1.19 ! [X2: set_val,Y3: set_val] :
% 2.07/1.19 ( ( ( sup_sup_set_val @ X2 @ Y3 )
% 2.07/1.19 = bot_bot_set_val )
% 2.07/1.19 = ( ( X2 = bot_bot_set_val )
% 2.07/1.19 & ( Y3 = bot_bot_set_val ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_223_sup__bot_Oeq__neutr__iff,axiom,
% 2.07/1.19 ! [A: set_val,B: set_val] :
% 2.07/1.19 ( ( ( sup_sup_set_val @ A @ B )
% 2.07/1.19 = bot_bot_set_val )
% 2.07/1.19 = ( ( A = bot_bot_set_val )
% 2.07/1.19 & ( B = bot_bot_set_val ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_224_sup__bot_Oleft__neutral,axiom,
% 2.07/1.19 ! [A: set_val] :
% 2.07/1.19 ( ( sup_sup_set_val @ bot_bot_set_val @ A )
% 2.07/1.19 = A ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_225_sup__bot_Oneutr__eq__iff,axiom,
% 2.07/1.19 ! [A: set_val,B: set_val] :
% 2.07/1.19 ( ( bot_bot_set_val
% 2.07/1.19 = ( sup_sup_set_val @ A @ B ) )
% 2.07/1.19 = ( ( A = bot_bot_set_val )
% 2.07/1.19 & ( B = bot_bot_set_val ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_226_sup__bot_Oright__neutral,axiom,
% 2.07/1.19 ! [A: set_val] :
% 2.07/1.19 ( ( sup_sup_set_val @ A @ bot_bot_set_val )
% 2.07/1.19 = A ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_227_Un__empty,axiom,
% 2.07/1.19 ! [A2: set_val,B2: set_val] :
% 2.07/1.19 ( ( ( sup_sup_set_val @ A2 @ B2 )
% 2.07/1.19 = bot_bot_set_val )
% 2.07/1.19 = ( ( A2 = bot_bot_set_val )
% 2.07/1.19 & ( B2 = bot_bot_set_val ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_228_old_Osuccessors__predecessors,axiom,
% 2.07/1.19 ! [N: node,G: g,M: node] :
% 2.07/1.19 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.07/1.19 => ( ( member_node @ N @ ( set_node2 @ ( graph_1037173556_edgeD @ alpha_n @ inEdges @ G @ M ) ) )
% 2.07/1.19 = ( member_node @ M @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ N ) ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_229_Un__empty__left,axiom,
% 2.07/1.19 ! [B2: set_val] :
% 2.07/1.19 ( ( sup_sup_set_val @ bot_bot_set_val @ B2 )
% 2.07/1.19 = B2 ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_230_Un__empty__right,axiom,
% 2.07/1.19 ! [A2: set_val] :
% 2.07/1.19 ( ( sup_sup_set_val @ A2 @ bot_bot_set_val )
% 2.07/1.19 = A2 ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_231_infinite__imp__nonempty,axiom,
% 2.07/1.19 ! [S: set_Pr1311924359et_val] :
% 2.07/1.19 ( ~ ( finite79836624et_val @ S )
% 2.07/1.19 => ( S != bot_bo2078591731et_val ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_232_infinite__imp__nonempty,axiom,
% 2.07/1.19 ! [S: set_Pr699757092de_val] :
% 2.07/1.19 ( ~ ( finite2056463621de_val @ S )
% 2.07/1.19 => ( S != bot_bo404898488de_val ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_233_infinite__imp__nonempty,axiom,
% 2.07/1.19 ! [S: set_val] :
% 2.07/1.19 ( ~ ( finite_finite_val @ S )
% 2.07/1.19 => ( S != bot_bot_set_val ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_234_finite_OemptyI,axiom,
% 2.07/1.19 finite79836624et_val @ bot_bo2078591731et_val ).
% 2.07/1.19
% 2.07/1.19 thf(fact_235_finite_OemptyI,axiom,
% 2.07/1.19 finite2056463621de_val @ bot_bo404898488de_val ).
% 2.07/1.19
% 2.07/1.19 thf(fact_236_finite_OemptyI,axiom,
% 2.07/1.19 finite_finite_val @ bot_bot_set_val ).
% 2.07/1.19
% 2.07/1.19 thf(fact_237_CFG__SSA__Transformed_Oredundant__scc_Ocong,axiom,
% 2.07/1.19 irredu1955035135eD_val = irredu1955035135eD_val ).
% 2.07/1.19
% 2.07/1.19 thf(fact_238_finite__has__maximal,axiom,
% 2.07/1.19 ! [A2: set_val] :
% 2.07/1.19 ( ( finite_finite_val @ A2 )
% 2.07/1.19 => ( ( A2 != bot_bot_set_val )
% 2.07/1.19 => ? [X3: val] :
% 2.07/1.19 ( ( member_val @ X3 @ A2 )
% 2.07/1.19 & ! [Xa: val] :
% 2.07/1.19 ( ( member_val @ Xa @ A2 )
% 2.07/1.19 => ( ( ord_less_eq_val @ X3 @ Xa )
% 2.07/1.19 => ( X3 = Xa ) ) ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_239_finite__has__maximal,axiom,
% 2.07/1.19 ! [A2: set_set_val] :
% 2.07/1.19 ( ( finite1265617511et_val @ A2 )
% 2.07/1.19 => ( ( A2 != bot_bot_set_set_val )
% 2.07/1.19 => ? [X3: set_val] :
% 2.07/1.19 ( ( member_set_val @ X3 @ A2 )
% 2.07/1.19 & ! [Xa: set_val] :
% 2.07/1.19 ( ( member_set_val @ Xa @ A2 )
% 2.07/1.19 => ( ( ord_less_eq_set_val @ X3 @ Xa )
% 2.07/1.19 => ( X3 = Xa ) ) ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_240_finite__has__minimal,axiom,
% 2.07/1.19 ! [A2: set_val] :
% 2.07/1.19 ( ( finite_finite_val @ A2 )
% 2.07/1.19 => ( ( A2 != bot_bot_set_val )
% 2.07/1.19 => ? [X3: val] :
% 2.07/1.19 ( ( member_val @ X3 @ A2 )
% 2.07/1.19 & ! [Xa: val] :
% 2.07/1.19 ( ( member_val @ Xa @ A2 )
% 2.07/1.19 => ( ( ord_less_eq_val @ Xa @ X3 )
% 2.07/1.19 => ( X3 = Xa ) ) ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_241_finite__has__minimal,axiom,
% 2.07/1.19 ! [A2: set_set_val] :
% 2.07/1.19 ( ( finite1265617511et_val @ A2 )
% 2.07/1.19 => ( ( A2 != bot_bot_set_set_val )
% 2.07/1.19 => ? [X3: set_val] :
% 2.07/1.19 ( ( member_set_val @ X3 @ A2 )
% 2.07/1.19 & ! [Xa: set_val] :
% 2.07/1.19 ( ( member_set_val @ Xa @ A2 )
% 2.07/1.19 => ( ( ord_less_eq_set_val @ Xa @ X3 )
% 2.07/1.19 => ( X3 = Xa ) ) ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_242_Collect__mono__iff,axiom,
% 2.07/1.19 ! [P2: val > $o,Q2: val > $o] :
% 2.07/1.19 ( ( ord_less_eq_set_val @ ( collect_val @ P2 ) @ ( collect_val @ Q2 ) )
% 2.07/1.19 = ( ! [X: val] :
% 2.07/1.19 ( ( P2 @ X )
% 2.07/1.19 => ( Q2 @ X ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_243_set__eq__subset,axiom,
% 2.07/1.19 ( ( ^ [Y4: set_val,Z2: set_val] : ( Y4 = Z2 ) )
% 2.07/1.19 = ( ^ [A5: set_val,B4: set_val] :
% 2.07/1.19 ( ( ord_less_eq_set_val @ A5 @ B4 )
% 2.07/1.19 & ( ord_less_eq_set_val @ B4 @ A5 ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_244_subset__trans,axiom,
% 2.07/1.19 ! [A2: set_val,B2: set_val,C: set_val] :
% 2.07/1.19 ( ( ord_less_eq_set_val @ A2 @ B2 )
% 2.07/1.19 => ( ( ord_less_eq_set_val @ B2 @ C )
% 2.07/1.19 => ( ord_less_eq_set_val @ A2 @ C ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_245_Collect__mono,axiom,
% 2.07/1.19 ! [P2: val > $o,Q2: val > $o] :
% 2.07/1.19 ( ! [X3: val] :
% 2.07/1.19 ( ( P2 @ X3 )
% 2.07/1.19 => ( Q2 @ X3 ) )
% 2.07/1.19 => ( ord_less_eq_set_val @ ( collect_val @ P2 ) @ ( collect_val @ Q2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_246_subset__refl,axiom,
% 2.07/1.19 ! [A2: set_val] : ( ord_less_eq_set_val @ A2 @ A2 ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_247_subset__iff,axiom,
% 2.07/1.19 ( ord_less_eq_set_node
% 2.07/1.19 = ( ^ [A5: set_node,B4: set_node] :
% 2.07/1.19 ! [T2: node] :
% 2.07/1.19 ( ( member_node @ T2 @ A5 )
% 2.07/1.19 => ( member_node @ T2 @ B4 ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_248_subset__iff,axiom,
% 2.07/1.19 ( ord_le1742111550et_val
% 2.07/1.19 = ( ^ [A5: set_set_val,B4: set_set_val] :
% 2.07/1.19 ! [T2: set_val] :
% 2.07/1.19 ( ( member_set_val @ T2 @ A5 )
% 2.07/1.19 => ( member_set_val @ T2 @ B4 ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_249_subset__iff,axiom,
% 2.07/1.19 ( ord_le1643692676de_val
% 2.07/1.19 = ( ^ [A5: set_Pr699757092de_val,B4: set_Pr699757092de_val] :
% 2.07/1.19 ! [T2: produc1432036078de_val] :
% 2.07/1.19 ( ( member313544709de_val @ T2 @ A5 )
% 2.07/1.19 => ( member313544709de_val @ T2 @ B4 ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_250_subset__iff,axiom,
% 2.07/1.19 ( ord_le299366439et_val
% 2.07/1.19 = ( ^ [A5: set_Pr1311924359et_val,B4: set_Pr1311924359et_val] :
% 2.07/1.19 ! [T2: produc1324971431et_val] :
% 2.07/1.19 ( ( member1711426256et_val @ T2 @ A5 )
% 2.07/1.19 => ( member1711426256et_val @ T2 @ B4 ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_251_subset__iff,axiom,
% 2.07/1.19 ( ord_less_eq_set_val
% 2.07/1.19 = ( ^ [A5: set_val,B4: set_val] :
% 2.07/1.19 ! [T2: val] :
% 2.07/1.19 ( ( member_val @ T2 @ A5 )
% 2.07/1.19 => ( member_val @ T2 @ B4 ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_252_equalityD2,axiom,
% 2.07/1.19 ! [A2: set_val,B2: set_val] :
% 2.07/1.19 ( ( A2 = B2 )
% 2.07/1.19 => ( ord_less_eq_set_val @ B2 @ A2 ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_253_equalityD1,axiom,
% 2.07/1.19 ! [A2: set_val,B2: set_val] :
% 2.07/1.19 ( ( A2 = B2 )
% 2.07/1.19 => ( ord_less_eq_set_val @ A2 @ B2 ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_254_subset__eq,axiom,
% 2.07/1.19 ( ord_less_eq_set_node
% 2.07/1.19 = ( ^ [A5: set_node,B4: set_node] :
% 2.07/1.19 ! [X: node] :
% 2.07/1.19 ( ( member_node @ X @ A5 )
% 2.07/1.19 => ( member_node @ X @ B4 ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_255_subset__eq,axiom,
% 2.07/1.19 ( ord_le1742111550et_val
% 2.07/1.19 = ( ^ [A5: set_set_val,B4: set_set_val] :
% 2.07/1.19 ! [X: set_val] :
% 2.07/1.19 ( ( member_set_val @ X @ A5 )
% 2.07/1.19 => ( member_set_val @ X @ B4 ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_256_subset__eq,axiom,
% 2.07/1.19 ( ord_le1643692676de_val
% 2.07/1.19 = ( ^ [A5: set_Pr699757092de_val,B4: set_Pr699757092de_val] :
% 2.07/1.19 ! [X: produc1432036078de_val] :
% 2.07/1.19 ( ( member313544709de_val @ X @ A5 )
% 2.07/1.19 => ( member313544709de_val @ X @ B4 ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_257_subset__eq,axiom,
% 2.07/1.19 ( ord_le299366439et_val
% 2.07/1.19 = ( ^ [A5: set_Pr1311924359et_val,B4: set_Pr1311924359et_val] :
% 2.07/1.19 ! [X: produc1324971431et_val] :
% 2.07/1.19 ( ( member1711426256et_val @ X @ A5 )
% 2.07/1.19 => ( member1711426256et_val @ X @ B4 ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_258_subset__eq,axiom,
% 2.07/1.19 ( ord_less_eq_set_val
% 2.07/1.19 = ( ^ [A5: set_val,B4: set_val] :
% 2.07/1.19 ! [X: val] :
% 2.07/1.19 ( ( member_val @ X @ A5 )
% 2.07/1.19 => ( member_val @ X @ B4 ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_259_equalityE,axiom,
% 2.07/1.19 ! [A2: set_val,B2: set_val] :
% 2.07/1.19 ( ( A2 = B2 )
% 2.07/1.19 => ~ ( ( ord_less_eq_set_val @ A2 @ B2 )
% 2.07/1.19 => ~ ( ord_less_eq_set_val @ B2 @ A2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_260_subsetD,axiom,
% 2.07/1.19 ! [A2: set_node,B2: set_node,C2: node] :
% 2.07/1.19 ( ( ord_less_eq_set_node @ A2 @ B2 )
% 2.07/1.19 => ( ( member_node @ C2 @ A2 )
% 2.07/1.19 => ( member_node @ C2 @ B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_261_subsetD,axiom,
% 2.07/1.19 ! [A2: set_set_val,B2: set_set_val,C2: set_val] :
% 2.07/1.19 ( ( ord_le1742111550et_val @ A2 @ B2 )
% 2.07/1.19 => ( ( member_set_val @ C2 @ A2 )
% 2.07/1.19 => ( member_set_val @ C2 @ B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_262_subsetD,axiom,
% 2.07/1.19 ! [A2: set_Pr699757092de_val,B2: set_Pr699757092de_val,C2: produc1432036078de_val] :
% 2.07/1.19 ( ( ord_le1643692676de_val @ A2 @ B2 )
% 2.07/1.19 => ( ( member313544709de_val @ C2 @ A2 )
% 2.07/1.19 => ( member313544709de_val @ C2 @ B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_263_subsetD,axiom,
% 2.07/1.19 ! [A2: set_Pr1311924359et_val,B2: set_Pr1311924359et_val,C2: produc1324971431et_val] :
% 2.07/1.19 ( ( ord_le299366439et_val @ A2 @ B2 )
% 2.07/1.19 => ( ( member1711426256et_val @ C2 @ A2 )
% 2.07/1.19 => ( member1711426256et_val @ C2 @ B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_264_subsetD,axiom,
% 2.07/1.19 ! [A2: set_val,B2: set_val,C2: val] :
% 2.07/1.19 ( ( ord_less_eq_set_val @ A2 @ B2 )
% 2.07/1.19 => ( ( member_val @ C2 @ A2 )
% 2.07/1.19 => ( member_val @ C2 @ B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_265_in__mono,axiom,
% 2.07/1.19 ! [A2: set_node,B2: set_node,X2: node] :
% 2.07/1.19 ( ( ord_less_eq_set_node @ A2 @ B2 )
% 2.07/1.19 => ( ( member_node @ X2 @ A2 )
% 2.07/1.19 => ( member_node @ X2 @ B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_266_in__mono,axiom,
% 2.07/1.19 ! [A2: set_set_val,B2: set_set_val,X2: set_val] :
% 2.07/1.19 ( ( ord_le1742111550et_val @ A2 @ B2 )
% 2.07/1.19 => ( ( member_set_val @ X2 @ A2 )
% 2.07/1.19 => ( member_set_val @ X2 @ B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_267_in__mono,axiom,
% 2.07/1.19 ! [A2: set_Pr699757092de_val,B2: set_Pr699757092de_val,X2: produc1432036078de_val] :
% 2.07/1.19 ( ( ord_le1643692676de_val @ A2 @ B2 )
% 2.07/1.19 => ( ( member313544709de_val @ X2 @ A2 )
% 2.07/1.19 => ( member313544709de_val @ X2 @ B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_268_in__mono,axiom,
% 2.07/1.19 ! [A2: set_Pr1311924359et_val,B2: set_Pr1311924359et_val,X2: produc1324971431et_val] :
% 2.07/1.19 ( ( ord_le299366439et_val @ A2 @ B2 )
% 2.07/1.19 => ( ( member1711426256et_val @ X2 @ A2 )
% 2.07/1.19 => ( member1711426256et_val @ X2 @ B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_269_in__mono,axiom,
% 2.07/1.19 ! [A2: set_val,B2: set_val,X2: val] :
% 2.07/1.19 ( ( ord_less_eq_set_val @ A2 @ B2 )
% 2.07/1.19 => ( ( member_val @ X2 @ A2 )
% 2.07/1.19 => ( member_val @ X2 @ B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_270_sup__left__commute,axiom,
% 2.07/1.19 ! [X2: set_val,Y3: set_val,Z: set_val] :
% 2.07/1.19 ( ( sup_sup_set_val @ X2 @ ( sup_sup_set_val @ Y3 @ Z ) )
% 2.07/1.19 = ( sup_sup_set_val @ Y3 @ ( sup_sup_set_val @ X2 @ Z ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_271_sup_Oleft__commute,axiom,
% 2.07/1.19 ! [B: set_val,A: set_val,C2: set_val] :
% 2.07/1.19 ( ( sup_sup_set_val @ B @ ( sup_sup_set_val @ A @ C2 ) )
% 2.07/1.19 = ( sup_sup_set_val @ A @ ( sup_sup_set_val @ B @ C2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_272_sup__commute,axiom,
% 2.07/1.19 ( sup_sup_set_val
% 2.07/1.19 = ( ^ [X: set_val,Y2: set_val] : ( sup_sup_set_val @ Y2 @ X ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_273_sup_Ocommute,axiom,
% 2.07/1.19 ( sup_sup_set_val
% 2.07/1.19 = ( ^ [A3: set_val,B5: set_val] : ( sup_sup_set_val @ B5 @ A3 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_274_sup__assoc,axiom,
% 2.07/1.19 ! [X2: set_val,Y3: set_val,Z: set_val] :
% 2.07/1.19 ( ( sup_sup_set_val @ ( sup_sup_set_val @ X2 @ Y3 ) @ Z )
% 2.07/1.19 = ( sup_sup_set_val @ X2 @ ( sup_sup_set_val @ Y3 @ Z ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_275_sup_Oassoc,axiom,
% 2.07/1.19 ! [A: set_val,B: set_val,C2: set_val] :
% 2.07/1.19 ( ( sup_sup_set_val @ ( sup_sup_set_val @ A @ B ) @ C2 )
% 2.07/1.19 = ( sup_sup_set_val @ A @ ( sup_sup_set_val @ B @ C2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_276_boolean__algebra__cancel_Osup2,axiom,
% 2.07/1.19 ! [B2: set_val,K: set_val,B: set_val,A: set_val] :
% 2.07/1.19 ( ( B2
% 2.07/1.19 = ( sup_sup_set_val @ K @ B ) )
% 2.07/1.19 => ( ( sup_sup_set_val @ A @ B2 )
% 2.07/1.19 = ( sup_sup_set_val @ K @ ( sup_sup_set_val @ A @ B ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_277_boolean__algebra__cancel_Osup1,axiom,
% 2.07/1.19 ! [A2: set_val,K: set_val,A: set_val,B: set_val] :
% 2.07/1.19 ( ( A2
% 2.07/1.19 = ( sup_sup_set_val @ K @ A ) )
% 2.07/1.19 => ( ( sup_sup_set_val @ A2 @ B )
% 2.07/1.19 = ( sup_sup_set_val @ K @ ( sup_sup_set_val @ A @ B ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_278_inf__sup__aci_I5_J,axiom,
% 2.07/1.19 ( sup_sup_set_val
% 2.07/1.19 = ( ^ [X: set_val,Y2: set_val] : ( sup_sup_set_val @ Y2 @ X ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_279_inf__sup__aci_I6_J,axiom,
% 2.07/1.19 ! [X2: set_val,Y3: set_val,Z: set_val] :
% 2.07/1.19 ( ( sup_sup_set_val @ ( sup_sup_set_val @ X2 @ Y3 ) @ Z )
% 2.07/1.19 = ( sup_sup_set_val @ X2 @ ( sup_sup_set_val @ Y3 @ Z ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_280_inf__sup__aci_I7_J,axiom,
% 2.07/1.19 ! [X2: set_val,Y3: set_val,Z: set_val] :
% 2.07/1.19 ( ( sup_sup_set_val @ X2 @ ( sup_sup_set_val @ Y3 @ Z ) )
% 2.07/1.19 = ( sup_sup_set_val @ Y3 @ ( sup_sup_set_val @ X2 @ Z ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_281_inf__sup__aci_I8_J,axiom,
% 2.07/1.19 ! [X2: set_val,Y3: set_val] :
% 2.07/1.19 ( ( sup_sup_set_val @ X2 @ ( sup_sup_set_val @ X2 @ Y3 ) )
% 2.07/1.19 = ( sup_sup_set_val @ X2 @ Y3 ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_282_Un__left__commute,axiom,
% 2.07/1.19 ! [A2: set_val,B2: set_val,C: set_val] :
% 2.07/1.19 ( ( sup_sup_set_val @ A2 @ ( sup_sup_set_val @ B2 @ C ) )
% 2.07/1.19 = ( sup_sup_set_val @ B2 @ ( sup_sup_set_val @ A2 @ C ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_283_Un__left__absorb,axiom,
% 2.07/1.19 ! [A2: set_val,B2: set_val] :
% 2.07/1.19 ( ( sup_sup_set_val @ A2 @ ( sup_sup_set_val @ A2 @ B2 ) )
% 2.07/1.19 = ( sup_sup_set_val @ A2 @ B2 ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_284_Un__commute,axiom,
% 2.07/1.19 ( sup_sup_set_val
% 2.07/1.19 = ( ^ [A5: set_val,B4: set_val] : ( sup_sup_set_val @ B4 @ A5 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_285_Un__absorb,axiom,
% 2.07/1.19 ! [A2: set_val] :
% 2.07/1.19 ( ( sup_sup_set_val @ A2 @ A2 )
% 2.07/1.19 = A2 ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_286_Un__assoc,axiom,
% 2.07/1.19 ! [A2: set_val,B2: set_val,C: set_val] :
% 2.07/1.19 ( ( sup_sup_set_val @ ( sup_sup_set_val @ A2 @ B2 ) @ C )
% 2.07/1.19 = ( sup_sup_set_val @ A2 @ ( sup_sup_set_val @ B2 @ C ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_287_ball__Un,axiom,
% 2.07/1.19 ! [A2: set_val,B2: set_val,P2: val > $o] :
% 2.07/1.19 ( ( ! [X: val] :
% 2.07/1.19 ( ( member_val @ X @ ( sup_sup_set_val @ A2 @ B2 ) )
% 2.07/1.19 => ( P2 @ X ) ) )
% 2.07/1.19 = ( ! [X: val] :
% 2.07/1.19 ( ( member_val @ X @ A2 )
% 2.07/1.19 => ( P2 @ X ) )
% 2.07/1.19 & ! [X: val] :
% 2.07/1.19 ( ( member_val @ X @ B2 )
% 2.07/1.19 => ( P2 @ X ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_288_bex__Un,axiom,
% 2.07/1.19 ! [A2: set_val,B2: set_val,P2: val > $o] :
% 2.07/1.19 ( ( ? [X: val] :
% 2.07/1.19 ( ( member_val @ X @ ( sup_sup_set_val @ A2 @ B2 ) )
% 2.07/1.19 & ( P2 @ X ) ) )
% 2.07/1.19 = ( ? [X: val] :
% 2.07/1.19 ( ( member_val @ X @ A2 )
% 2.07/1.19 & ( P2 @ X ) )
% 2.07/1.19 | ? [X: val] :
% 2.07/1.19 ( ( member_val @ X @ B2 )
% 2.07/1.19 & ( P2 @ X ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_289_UnI2,axiom,
% 2.07/1.19 ! [C2: node,B2: set_node,A2: set_node] :
% 2.07/1.19 ( ( member_node @ C2 @ B2 )
% 2.07/1.19 => ( member_node @ C2 @ ( sup_sup_set_node @ A2 @ B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_290_UnI2,axiom,
% 2.07/1.19 ! [C2: set_val,B2: set_set_val,A2: set_set_val] :
% 2.07/1.19 ( ( member_set_val @ C2 @ B2 )
% 2.07/1.19 => ( member_set_val @ C2 @ ( sup_sup_set_set_val @ A2 @ B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_291_UnI2,axiom,
% 2.07/1.19 ! [C2: produc1432036078de_val,B2: set_Pr699757092de_val,A2: set_Pr699757092de_val] :
% 2.07/1.19 ( ( member313544709de_val @ C2 @ B2 )
% 2.07/1.19 => ( member313544709de_val @ C2 @ ( sup_su2138939728de_val @ A2 @ B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_292_UnI2,axiom,
% 2.07/1.19 ! [C2: produc1324971431et_val,B2: set_Pr1311924359et_val,A2: set_Pr1311924359et_val] :
% 2.07/1.19 ( ( member1711426256et_val @ C2 @ B2 )
% 2.07/1.19 => ( member1711426256et_val @ C2 @ ( sup_su2005730907et_val @ A2 @ B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_293_UnI2,axiom,
% 2.07/1.19 ! [C2: val,B2: set_val,A2: set_val] :
% 2.07/1.19 ( ( member_val @ C2 @ B2 )
% 2.07/1.19 => ( member_val @ C2 @ ( sup_sup_set_val @ A2 @ B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_294_UnI1,axiom,
% 2.07/1.19 ! [C2: node,A2: set_node,B2: set_node] :
% 2.07/1.19 ( ( member_node @ C2 @ A2 )
% 2.07/1.19 => ( member_node @ C2 @ ( sup_sup_set_node @ A2 @ B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_295_UnI1,axiom,
% 2.07/1.19 ! [C2: set_val,A2: set_set_val,B2: set_set_val] :
% 2.07/1.19 ( ( member_set_val @ C2 @ A2 )
% 2.07/1.19 => ( member_set_val @ C2 @ ( sup_sup_set_set_val @ A2 @ B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_296_UnI1,axiom,
% 2.07/1.19 ! [C2: produc1432036078de_val,A2: set_Pr699757092de_val,B2: set_Pr699757092de_val] :
% 2.07/1.19 ( ( member313544709de_val @ C2 @ A2 )
% 2.07/1.19 => ( member313544709de_val @ C2 @ ( sup_su2138939728de_val @ A2 @ B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_297_UnI1,axiom,
% 2.07/1.19 ! [C2: produc1324971431et_val,A2: set_Pr1311924359et_val,B2: set_Pr1311924359et_val] :
% 2.07/1.19 ( ( member1711426256et_val @ C2 @ A2 )
% 2.07/1.19 => ( member1711426256et_val @ C2 @ ( sup_su2005730907et_val @ A2 @ B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_298_UnI1,axiom,
% 2.07/1.19 ! [C2: val,A2: set_val,B2: set_val] :
% 2.07/1.19 ( ( member_val @ C2 @ A2 )
% 2.07/1.19 => ( member_val @ C2 @ ( sup_sup_set_val @ A2 @ B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_299_UnE,axiom,
% 2.07/1.19 ! [C2: node,A2: set_node,B2: set_node] :
% 2.07/1.19 ( ( member_node @ C2 @ ( sup_sup_set_node @ A2 @ B2 ) )
% 2.07/1.19 => ( ~ ( member_node @ C2 @ A2 )
% 2.07/1.19 => ( member_node @ C2 @ B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_300_UnE,axiom,
% 2.07/1.19 ! [C2: set_val,A2: set_set_val,B2: set_set_val] :
% 2.07/1.19 ( ( member_set_val @ C2 @ ( sup_sup_set_set_val @ A2 @ B2 ) )
% 2.07/1.19 => ( ~ ( member_set_val @ C2 @ A2 )
% 2.07/1.19 => ( member_set_val @ C2 @ B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_301_UnE,axiom,
% 2.07/1.19 ! [C2: produc1432036078de_val,A2: set_Pr699757092de_val,B2: set_Pr699757092de_val] :
% 2.07/1.19 ( ( member313544709de_val @ C2 @ ( sup_su2138939728de_val @ A2 @ B2 ) )
% 2.07/1.19 => ( ~ ( member313544709de_val @ C2 @ A2 )
% 2.07/1.19 => ( member313544709de_val @ C2 @ B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_302_UnE,axiom,
% 2.07/1.19 ! [C2: produc1324971431et_val,A2: set_Pr1311924359et_val,B2: set_Pr1311924359et_val] :
% 2.07/1.19 ( ( member1711426256et_val @ C2 @ ( sup_su2005730907et_val @ A2 @ B2 ) )
% 2.07/1.19 => ( ~ ( member1711426256et_val @ C2 @ A2 )
% 2.07/1.19 => ( member1711426256et_val @ C2 @ B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_303_UnE,axiom,
% 2.07/1.19 ! [C2: val,A2: set_val,B2: set_val] :
% 2.07/1.19 ( ( member_val @ C2 @ ( sup_sup_set_val @ A2 @ B2 ) )
% 2.07/1.19 => ( ~ ( member_val @ C2 @ A2 )
% 2.07/1.19 => ( member_val @ C2 @ B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_304_sup_OcoboundedI2,axiom,
% 2.07/1.19 ! [C2: set_val,B: set_val,A: set_val] :
% 2.07/1.19 ( ( ord_less_eq_set_val @ C2 @ B )
% 2.07/1.19 => ( ord_less_eq_set_val @ C2 @ ( sup_sup_set_val @ A @ B ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_305_sup_OcoboundedI1,axiom,
% 2.07/1.19 ! [C2: set_val,A: set_val,B: set_val] :
% 2.07/1.19 ( ( ord_less_eq_set_val @ C2 @ A )
% 2.07/1.19 => ( ord_less_eq_set_val @ C2 @ ( sup_sup_set_val @ A @ B ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_306_sup_Oabsorb__iff2,axiom,
% 2.07/1.19 ( ord_less_eq_set_val
% 2.07/1.19 = ( ^ [A3: set_val,B5: set_val] :
% 2.07/1.19 ( ( sup_sup_set_val @ A3 @ B5 )
% 2.07/1.19 = B5 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_307_sup_Oabsorb__iff1,axiom,
% 2.07/1.19 ( ord_less_eq_set_val
% 2.07/1.19 = ( ^ [B5: set_val,A3: set_val] :
% 2.07/1.19 ( ( sup_sup_set_val @ A3 @ B5 )
% 2.07/1.19 = A3 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_308_sup_Ocobounded2,axiom,
% 2.07/1.19 ! [B: set_val,A: set_val] : ( ord_less_eq_set_val @ B @ ( sup_sup_set_val @ A @ B ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_309_sup_Ocobounded1,axiom,
% 2.07/1.19 ! [A: set_val,B: set_val] : ( ord_less_eq_set_val @ A @ ( sup_sup_set_val @ A @ B ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_310_sup_Oorder__iff,axiom,
% 2.07/1.19 ( ord_less_eq_set_val
% 2.07/1.19 = ( ^ [B5: set_val,A3: set_val] :
% 2.07/1.19 ( A3
% 2.07/1.19 = ( sup_sup_set_val @ A3 @ B5 ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_311_sup_OboundedI,axiom,
% 2.07/1.19 ! [B: set_val,A: set_val,C2: set_val] :
% 2.07/1.19 ( ( ord_less_eq_set_val @ B @ A )
% 2.07/1.19 => ( ( ord_less_eq_set_val @ C2 @ A )
% 2.07/1.19 => ( ord_less_eq_set_val @ ( sup_sup_set_val @ B @ C2 ) @ A ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_312_sup_OboundedE,axiom,
% 2.07/1.19 ! [B: set_val,C2: set_val,A: set_val] :
% 2.07/1.19 ( ( ord_less_eq_set_val @ ( sup_sup_set_val @ B @ C2 ) @ A )
% 2.07/1.19 => ~ ( ( ord_less_eq_set_val @ B @ A )
% 2.07/1.19 => ~ ( ord_less_eq_set_val @ C2 @ A ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_313_sup__absorb2,axiom,
% 2.07/1.19 ! [X2: set_val,Y3: set_val] :
% 2.07/1.19 ( ( ord_less_eq_set_val @ X2 @ Y3 )
% 2.07/1.19 => ( ( sup_sup_set_val @ X2 @ Y3 )
% 2.07/1.19 = Y3 ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_314_sup__absorb1,axiom,
% 2.07/1.19 ! [Y3: set_val,X2: set_val] :
% 2.07/1.19 ( ( ord_less_eq_set_val @ Y3 @ X2 )
% 2.07/1.19 => ( ( sup_sup_set_val @ X2 @ Y3 )
% 2.07/1.19 = X2 ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_315_sup_Oabsorb2,axiom,
% 2.07/1.19 ! [A: set_val,B: set_val] :
% 2.07/1.19 ( ( ord_less_eq_set_val @ A @ B )
% 2.07/1.19 => ( ( sup_sup_set_val @ A @ B )
% 2.07/1.19 = B ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_316_sup_Oabsorb1,axiom,
% 2.07/1.19 ! [B: set_val,A: set_val] :
% 2.07/1.19 ( ( ord_less_eq_set_val @ B @ A )
% 2.07/1.19 => ( ( sup_sup_set_val @ A @ B )
% 2.07/1.19 = A ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_317_sup__unique,axiom,
% 2.07/1.19 ! [F2: set_val > set_val > set_val,X2: set_val,Y3: set_val] :
% 2.07/1.19 ( ! [X3: set_val,Y5: set_val] : ( ord_less_eq_set_val @ X3 @ ( F2 @ X3 @ Y5 ) )
% 2.07/1.19 => ( ! [X3: set_val,Y5: set_val] : ( ord_less_eq_set_val @ Y5 @ ( F2 @ X3 @ Y5 ) )
% 2.07/1.19 => ( ! [X3: set_val,Y5: set_val,Z3: set_val] :
% 2.07/1.19 ( ( ord_less_eq_set_val @ Y5 @ X3 )
% 2.07/1.19 => ( ( ord_less_eq_set_val @ Z3 @ X3 )
% 2.07/1.19 => ( ord_less_eq_set_val @ ( F2 @ Y5 @ Z3 ) @ X3 ) ) )
% 2.07/1.19 => ( ( sup_sup_set_val @ X2 @ Y3 )
% 2.07/1.19 = ( F2 @ X2 @ Y3 ) ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_318_sup_OorderI,axiom,
% 2.07/1.19 ! [A: set_val,B: set_val] :
% 2.07/1.19 ( ( A
% 2.07/1.19 = ( sup_sup_set_val @ A @ B ) )
% 2.07/1.19 => ( ord_less_eq_set_val @ B @ A ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_319_sup_OorderE,axiom,
% 2.07/1.19 ! [B: set_val,A: set_val] :
% 2.07/1.19 ( ( ord_less_eq_set_val @ B @ A )
% 2.07/1.19 => ( A
% 2.07/1.19 = ( sup_sup_set_val @ A @ B ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_320_le__iff__sup,axiom,
% 2.07/1.19 ( ord_less_eq_set_val
% 2.07/1.19 = ( ^ [X: set_val,Y2: set_val] :
% 2.07/1.19 ( ( sup_sup_set_val @ X @ Y2 )
% 2.07/1.19 = Y2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_321_sup__least,axiom,
% 2.07/1.19 ! [Y3: set_val,X2: set_val,Z: set_val] :
% 2.07/1.19 ( ( ord_less_eq_set_val @ Y3 @ X2 )
% 2.07/1.19 => ( ( ord_less_eq_set_val @ Z @ X2 )
% 2.07/1.19 => ( ord_less_eq_set_val @ ( sup_sup_set_val @ Y3 @ Z ) @ X2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_322_sup__mono,axiom,
% 2.07/1.19 ! [A: set_val,C2: set_val,B: set_val,D: set_val] :
% 2.07/1.19 ( ( ord_less_eq_set_val @ A @ C2 )
% 2.07/1.19 => ( ( ord_less_eq_set_val @ B @ D )
% 2.07/1.19 => ( ord_less_eq_set_val @ ( sup_sup_set_val @ A @ B ) @ ( sup_sup_set_val @ C2 @ D ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_323_sup_Omono,axiom,
% 2.07/1.19 ! [C2: set_val,A: set_val,D: set_val,B: set_val] :
% 2.07/1.19 ( ( ord_less_eq_set_val @ C2 @ A )
% 2.07/1.19 => ( ( ord_less_eq_set_val @ D @ B )
% 2.07/1.19 => ( ord_less_eq_set_val @ ( sup_sup_set_val @ C2 @ D ) @ ( sup_sup_set_val @ A @ B ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_324_le__supI2,axiom,
% 2.07/1.19 ! [X2: set_val,B: set_val,A: set_val] :
% 2.07/1.19 ( ( ord_less_eq_set_val @ X2 @ B )
% 2.07/1.19 => ( ord_less_eq_set_val @ X2 @ ( sup_sup_set_val @ A @ B ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_325_le__supI1,axiom,
% 2.07/1.19 ! [X2: set_val,A: set_val,B: set_val] :
% 2.07/1.19 ( ( ord_less_eq_set_val @ X2 @ A )
% 2.07/1.19 => ( ord_less_eq_set_val @ X2 @ ( sup_sup_set_val @ A @ B ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_326_sup__ge2,axiom,
% 2.07/1.19 ! [Y3: set_val,X2: set_val] : ( ord_less_eq_set_val @ Y3 @ ( sup_sup_set_val @ X2 @ Y3 ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_327_sup__ge1,axiom,
% 2.07/1.19 ! [X2: set_val,Y3: set_val] : ( ord_less_eq_set_val @ X2 @ ( sup_sup_set_val @ X2 @ Y3 ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_328_le__supI,axiom,
% 2.07/1.19 ! [A: set_val,X2: set_val,B: set_val] :
% 2.07/1.19 ( ( ord_less_eq_set_val @ A @ X2 )
% 2.07/1.19 => ( ( ord_less_eq_set_val @ B @ X2 )
% 2.07/1.19 => ( ord_less_eq_set_val @ ( sup_sup_set_val @ A @ B ) @ X2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_329_le__supE,axiom,
% 2.07/1.19 ! [A: set_val,B: set_val,X2: set_val] :
% 2.07/1.19 ( ( ord_less_eq_set_val @ ( sup_sup_set_val @ A @ B ) @ X2 )
% 2.07/1.19 => ~ ( ( ord_less_eq_set_val @ A @ X2 )
% 2.07/1.19 => ~ ( ord_less_eq_set_val @ B @ X2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_330_inf__sup__ord_I3_J,axiom,
% 2.07/1.19 ! [X2: set_val,Y3: set_val] : ( ord_less_eq_set_val @ X2 @ ( sup_sup_set_val @ X2 @ Y3 ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_331_inf__sup__ord_I4_J,axiom,
% 2.07/1.19 ! [Y3: set_val,X2: set_val] : ( ord_less_eq_set_val @ Y3 @ ( sup_sup_set_val @ X2 @ Y3 ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_332_subset__Un__eq,axiom,
% 2.07/1.19 ( ord_less_eq_set_val
% 2.07/1.19 = ( ^ [A5: set_val,B4: set_val] :
% 2.07/1.19 ( ( sup_sup_set_val @ A5 @ B4 )
% 2.07/1.19 = B4 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_333_subset__UnE,axiom,
% 2.07/1.19 ! [C: set_val,A2: set_val,B2: set_val] :
% 2.07/1.19 ( ( ord_less_eq_set_val @ C @ ( sup_sup_set_val @ A2 @ B2 ) )
% 2.07/1.19 => ~ ! [A6: set_val] :
% 2.07/1.19 ( ( ord_less_eq_set_val @ A6 @ A2 )
% 2.07/1.19 => ! [B6: set_val] :
% 2.07/1.19 ( ( ord_less_eq_set_val @ B6 @ B2 )
% 2.07/1.19 => ( C
% 2.07/1.19 != ( sup_sup_set_val @ A6 @ B6 ) ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_334_Un__absorb2,axiom,
% 2.07/1.19 ! [B2: set_val,A2: set_val] :
% 2.07/1.19 ( ( ord_less_eq_set_val @ B2 @ A2 )
% 2.07/1.19 => ( ( sup_sup_set_val @ A2 @ B2 )
% 2.07/1.19 = A2 ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_335_Un__absorb1,axiom,
% 2.07/1.19 ! [A2: set_val,B2: set_val] :
% 2.07/1.19 ( ( ord_less_eq_set_val @ A2 @ B2 )
% 2.07/1.19 => ( ( sup_sup_set_val @ A2 @ B2 )
% 2.07/1.19 = B2 ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_336_Un__upper2,axiom,
% 2.07/1.19 ! [B2: set_val,A2: set_val] : ( ord_less_eq_set_val @ B2 @ ( sup_sup_set_val @ A2 @ B2 ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_337_Un__upper1,axiom,
% 2.07/1.19 ! [A2: set_val,B2: set_val] : ( ord_less_eq_set_val @ A2 @ ( sup_sup_set_val @ A2 @ B2 ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_338_Un__least,axiom,
% 2.07/1.19 ! [A2: set_val,C: set_val,B2: set_val] :
% 2.07/1.19 ( ( ord_less_eq_set_val @ A2 @ C )
% 2.07/1.19 => ( ( ord_less_eq_set_val @ B2 @ C )
% 2.07/1.19 => ( ord_less_eq_set_val @ ( sup_sup_set_val @ A2 @ B2 ) @ C ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_339_Un__mono,axiom,
% 2.07/1.19 ! [A2: set_val,C: set_val,B2: set_val,D2: set_val] :
% 2.07/1.19 ( ( ord_less_eq_set_val @ A2 @ C )
% 2.07/1.19 => ( ( ord_less_eq_set_val @ B2 @ D2 )
% 2.07/1.19 => ( ord_less_eq_set_val @ ( sup_sup_set_val @ A2 @ B2 ) @ ( sup_sup_set_val @ C @ D2 ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_340_redundant__set__def,axiom,
% 2.07/1.19 ! [G: g,P2: set_val] :
% 2.07/1.19 ( ( irredu224829488eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G @ P2 )
% 2.07/1.19 = ( ( P2 != bot_bot_set_val )
% 2.07/1.19 & ( ord_less_eq_set_val @ P2 @ ( dom_val_list_val @ ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ G ) ) )
% 2.07/1.19 & ? [X: val] :
% 2.07/1.19 ( ( member_val @ X @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 2.07/1.19 & ! [Y2: val] :
% 2.07/1.19 ( ( member_val @ Y2 @ P2 )
% 2.07/1.19 => ! [Phi3: val] :
% 2.07/1.19 ( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ G @ Y2 @ Phi3 )
% 2.07/1.19 => ( member_val @ Phi3 @ ( sup_sup_set_val @ P2 @ ( insert_val @ X @ bot_bot_set_val ) ) ) ) ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_341_phi__no__closed__loop,axiom,
% 2.07/1.19 ! [P: val,G: g,Vs: list_val] :
% 2.07/1.19 ( ( member_val @ P @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ G ) )
% 2.07/1.19 => ( ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ G @ P )
% 2.07/1.19 = ( some_list_val @ Vs ) )
% 2.07/1.19 => ( ( set_val2 @ Vs )
% 2.07/1.19 != ( insert_val @ P @ bot_bot_set_val ) ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_342_dom__eq__empty__conv,axiom,
% 2.07/1.19 ! [F2: produc1432036078de_val > option_list_val] :
% 2.07/1.19 ( ( ( dom_Pr729677986st_val @ F2 )
% 2.07/1.19 = bot_bo404898488de_val )
% 2.07/1.19 = ( F2
% 2.07/1.19 = ( ^ [X: produc1432036078de_val] : none_list_val ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_343_dom__eq__empty__conv,axiom,
% 2.07/1.19 ! [F2: val > option_list_val] :
% 2.07/1.19 ( ( ( dom_val_list_val @ F2 )
% 2.07/1.19 = bot_bot_set_val )
% 2.07/1.19 = ( F2
% 2.07/1.19 = ( ^ [X: val] : none_list_val ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_344_phis__finite,axiom,
% 2.07/1.19 ! [G: g] : ( finite2056463621de_val @ ( dom_Pr729677986st_val @ ( phis @ G ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_345_insert__subset,axiom,
% 2.07/1.19 ! [X2: node,A2: set_node,B2: set_node] :
% 2.07/1.19 ( ( ord_less_eq_set_node @ ( insert_node @ X2 @ A2 ) @ B2 )
% 2.07/1.19 = ( ( member_node @ X2 @ B2 )
% 2.07/1.19 & ( ord_less_eq_set_node @ A2 @ B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_346_insert__subset,axiom,
% 2.07/1.19 ! [X2: set_val,A2: set_set_val,B2: set_set_val] :
% 2.07/1.19 ( ( ord_le1742111550et_val @ ( insert_set_val @ X2 @ A2 ) @ B2 )
% 2.07/1.19 = ( ( member_set_val @ X2 @ B2 )
% 2.07/1.19 & ( ord_le1742111550et_val @ A2 @ B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_347_insert__subset,axiom,
% 2.07/1.19 ! [X2: produc1432036078de_val,A2: set_Pr699757092de_val,B2: set_Pr699757092de_val] :
% 2.07/1.19 ( ( ord_le1643692676de_val @ ( insert869443870de_val @ X2 @ A2 ) @ B2 )
% 2.07/1.19 = ( ( member313544709de_val @ X2 @ B2 )
% 2.07/1.19 & ( ord_le1643692676de_val @ A2 @ B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_348_insert__subset,axiom,
% 2.07/1.19 ! [X2: produc1324971431et_val,A2: set_Pr1311924359et_val,B2: set_Pr1311924359et_val] :
% 2.07/1.19 ( ( ord_le299366439et_val @ ( insert1846469495et_val @ X2 @ A2 ) @ B2 )
% 2.07/1.19 = ( ( member1711426256et_val @ X2 @ B2 )
% 2.07/1.19 & ( ord_le299366439et_val @ A2 @ B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_349_insert__subset,axiom,
% 2.07/1.19 ! [X2: val,A2: set_val,B2: set_val] :
% 2.07/1.19 ( ( ord_less_eq_set_val @ ( insert_val @ X2 @ A2 ) @ B2 )
% 2.07/1.19 = ( ( member_val @ X2 @ B2 )
% 2.07/1.19 & ( ord_less_eq_set_val @ A2 @ B2 ) ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_350_finite__insert,axiom,
% 2.07/1.19 ! [A: val,A2: set_val] :
% 2.07/1.19 ( ( finite_finite_val @ ( insert_val @ A @ A2 ) )
% 2.07/1.19 = ( finite_finite_val @ A2 ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_351_finite__insert,axiom,
% 2.07/1.19 ! [A: produc1324971431et_val,A2: set_Pr1311924359et_val] :
% 2.07/1.19 ( ( finite79836624et_val @ ( insert1846469495et_val @ A @ A2 ) )
% 2.07/1.19 = ( finite79836624et_val @ A2 ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(fact_352_finite__insert,axiom,
% 2.07/1.19 ! [A: produc1432036078de_val,A2: set_Pr699757092de_val] :
% 2.07/1.19 ( ( finite2056463621de_val @ ( insert869443870de_val @ A @ A2 ) )
% 2.07/1.19 = ( finite2056463621de_val @ A2 ) ) ).
% 2.07/1.19
% 2.07/1.19 thf(conj_0,conjecture,
% 2.07/1.19 member_val @ phi_s @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2 ) ).
% 2.07/1.19 ------------------------
% 2.23/1.21 % (29825)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_29714 for (2999ds/275Mi)
% 2.23/1.21 % (29823)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29714 for (2999ds/2Mi)
% 2.23/1.21 % (29820)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29714 for (2999ds/183Mi)
% 2.23/1.21 % (29821)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_29714 for (2999ds/4Mi)
% 2.23/1.21 % (29824)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_29714 for (2999ds/2Mi)
% 2.23/1.21 % (29822)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_29714 for (2999ds/27Mi)
% 2.23/1.21 % (29826)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29714 for (2999ds/18Mi)
% 2.23/1.21 % (29823)Instruction limit reached!
% 2.23/1.21 % (29823)------------------------------
% 2.23/1.21 % (29823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.23/1.21 % (29823)Termination reason: Unknown
% 2.23/1.21 % (29823)Termination phase: shuffling
% 2.23/1.21
% 2.23/1.21 % (29823)Memory used [KB]: 1407
% 2.23/1.21 % (29823)Time elapsed: 0.002 s
% 2.23/1.21 % (29823)Instructions burned: 2 (million)
% 2.23/1.21 % (29823)------------------------------
% 2.23/1.21 % (29823)------------------------------
% 2.23/1.21 % (29824)Instruction limit reached!
% 2.23/1.21 % (29824)------------------------------
% 2.23/1.21 % (29824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.23/1.21 % (29824)Termination reason: Unknown
% 2.23/1.21 % (29824)Termination phase: shuffling
% 2.23/1.21
% 2.23/1.21 % (29824)Memory used [KB]: 1407
% 2.23/1.21 % (29824)Time elapsed: 0.002 s
% 2.23/1.21 % (29824)Instructions burned: 2 (million)
% 2.23/1.21 % (29824)------------------------------
% 2.23/1.21 % (29824)------------------------------
% 2.23/1.21 % (29821)Instruction limit reached!
% 2.23/1.21 % (29821)------------------------------
% 2.23/1.21 % (29821)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.23/1.21 % (29821)Termination reason: Unknown
% 2.23/1.21 % (29821)Termination phase: shuffling
% 2.23/1.21
% 2.23/1.21 % (29821)Memory used [KB]: 1535
% 2.23/1.21 % (29821)Time elapsed: 0.003 s
% 2.23/1.21 % (29821)Instructions burned: 5 (million)
% 2.23/1.21 % (29821)------------------------------
% 2.23/1.21 % (29821)------------------------------
% 2.23/1.22 % (29826)Instruction limit reached!
% 2.23/1.22 % (29826)------------------------------
% 2.23/1.22 % (29826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.23/1.22 % (29826)Termination reason: Unknown
% 2.23/1.22 % (29826)Termination phase: shuffling
% 2.23/1.22
% 2.23/1.22 % (29826)Memory used [KB]: 1663
% 2.23/1.22 % (29826)Time elapsed: 0.007 s
% 2.23/1.22 % (29826)Instructions burned: 19 (million)
% 2.23/1.22 % (29826)------------------------------
% 2.23/1.22 % (29826)------------------------------
% 2.23/1.22 % (29822)Instruction limit reached!
% 2.23/1.22 % (29822)------------------------------
% 2.23/1.22 % (29822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.23/1.22 % (29822)Termination reason: Unknown
% 2.23/1.22 % (29822)Termination phase: shuffling
% 2.23/1.22
% 2.23/1.22 % (29822)Memory used [KB]: 1918
% 2.23/1.22 % (29822)Time elapsed: 0.010 s
% 2.23/1.22 % (29822)Instructions burned: 28 (million)
% 2.23/1.22 % (29822)------------------------------
% 2.23/1.22 % (29822)------------------------------
% 2.23/1.22 % (29827)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_29714 for (2999ds/3Mi)
% 2.23/1.22 % (29828)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_29714 for (2999ds/37Mi)
% 2.23/1.22 % (29829)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_29714 for (2999ds/15Mi)
% 2.23/1.22 % (29827)Instruction limit reached!
% 2.23/1.22 % (29827)------------------------------
% 2.23/1.22 % (29827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.23/1.22 % (29827)Termination reason: Unknown
% 2.23/1.22 % (29827)Termination phase: shuffling
% 2.23/1.22
% 2.23/1.22 % (29827)Memory used [KB]: 1535
% 2.23/1.22 % (29827)Time elapsed: 0.002 s
% 2.23/1.22 % (29827)Instructions burned: 3 (million)
% 2.23/1.22 % (29827)------------------------------
% 2.23/1.22 % (29827)------------------------------
% 2.23/1.23 % (29830)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_29714 for (2999ds/3Mi)
% 2.23/1.23 % (29829)Instruction limit reached!
% 2.23/1.23 % (29829)------------------------------
% 2.23/1.23 % (29829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.23/1.23 % (29829)Termination reason: Unknown
% 2.23/1.23 % (29829)Termination phase: shuffling
% 2.23/1.23
% 2.23/1.23 % (29829)Memory used [KB]: 1663
% 2.23/1.23 % (29829)Time elapsed: 0.006 s
% 2.23/1.23 % (29829)Instructions burned: 16 (million)
% 2.23/1.23 % (29829)------------------------------
% 2.23/1.23 % (29829)------------------------------
% 2.23/1.23 % (29830)Instruction limit reached!
% 2.23/1.23 % (29830)------------------------------
% 2.23/1.23 % (29830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.23/1.23 % (29830)Termination reason: Unknown
% 2.23/1.23 % (29830)Termination phase: shuffling
% 2.23/1.23
% 2.23/1.23 % (29830)Memory used [KB]: 1407
% 2.23/1.23 % (29830)Time elapsed: 0.002 s
% 2.23/1.23 % (29830)Instructions burned: 3 (million)
% 2.23/1.23 % (29830)------------------------------
% 2.23/1.23 % (29830)------------------------------
% 2.23/1.23 % (29831)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_29714 for (2999ds/1041Mi)
% 2.23/1.23 % (29828)Instruction limit reached!
% 2.23/1.23 % (29828)------------------------------
% 2.23/1.23 % (29828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.23/1.23 % (29828)Termination reason: Unknown
% 2.23/1.23 % (29828)Termination phase: shuffling
% 2.23/1.23
% 2.23/1.23 % (29828)Memory used [KB]: 2174
% 2.23/1.23 % (29828)Time elapsed: 0.011 s
% 2.23/1.23 % (29828)Instructions burned: 38 (million)
% 2.23/1.23 % (29828)------------------------------
% 2.23/1.23 % (29828)------------------------------
% 2.23/1.23 % (29832)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_29714 for (2999ds/7Mi)
% 2.23/1.24 % (29832)Instruction limit reached!
% 2.23/1.24 % (29832)------------------------------
% 2.23/1.24 % (29832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.23/1.24 % (29832)Termination reason: Unknown
% 2.23/1.24 % (29832)Termination phase: shuffling
% 2.23/1.24
% 2.23/1.24 % (29832)Memory used [KB]: 1535
% 2.23/1.24 % (29832)Time elapsed: 0.003 s
% 2.23/1.24 % (29832)Instructions burned: 7 (million)
% 2.23/1.24 % (29832)------------------------------
% 2.23/1.24 % (29832)------------------------------
% 2.23/1.24 % (29825)First to succeed.
% 2.23/1.24 % (29825)Refutation found. Thanks to Tanya!
% 2.23/1.24 % SZS status Theorem for DTF2THF_29714
% 2.23/1.24 % SZS output start Proof for DTF2THF_29714
% 2.23/1.24 thf(type_def_5, type, set_Pr1311924359et_val: $tType).
% 2.23/1.24 thf(type_def_7, type, set_Pr699757092de_val: $tType).
% 2.23/1.24 thf(type_def_8, type, set_Pr701036849de_val: $tType).
% 2.23/1.24 thf(type_def_9, type, set_Pr978022247et_val: $tType).
% 2.23/1.24 thf(type_def_10, type, set_Pr2105655784l_node: $tType).
% 2.23/1.24 thf(type_def_11, type, set_Pr700443783al_val: $tType).
% 2.23/1.24 thf(type_def_12, type, set_set_val: $tType).
% 2.23/1.24 thf(type_def_13, type, set_node: $tType).
% 2.23/1.24 thf(type_def_14, type, set_val: $tType).
% 2.23/1.24 thf(type_def_15, type, g: $tType).
% 2.23/1.24 thf(type_def_16, type, node: $tType).
% 2.23/1.24 thf(type_def_17, type, list_P561207620_edgeD: $tType).
% 2.23/1.24 thf(type_def_18, type, list_node: $tType).
% 2.23/1.24 thf(type_def_19, type, produc1432036078de_val: $tType).
% 2.23/1.24 thf(type_def_20, type, option_list_val: $tType).
% 2.23/1.24 thf(type_def_21, type, option_set_val: $tType).
% 2.23/1.24 thf(type_def_22, type, list_P88441325et_val: $tType).
% 2.23/1.24 thf(type_def_23, type, set_Pr1587248327et_val: $tType).
% 2.23/1.24 thf(type_def_24, type, list_P729276995de_val: $tType).
% 2.23/1.24 thf(type_def_25, type, set_Pr819703837de_val: $tType).
% 2.23/1.24 thf(type_def_26, type, list_P2089461677et_val: $tType).
% 2.23/1.24 thf(type_def_27, type, list_P1414038306l_node: $tType).
% 2.23/1.24 thf(type_def_28, type, set_Pr574789832l_node: $tType).
% 2.23/1.24 thf(type_def_29, type, list_P940784845al_val: $tType).
% 2.23/1.24 thf(type_def_30, type, set_Pr1157324199al_val: $tType).
% 2.23/1.24 thf(type_def_31, type, list_P1108777338de_val: $tType).
% 2.23/1.24 thf(type_def_32, type, set_Pr1245322836de_val: $tType).
% 2.23/1.24 thf(type_def_33, type, list_P12184414et_val: $tType).
% 2.23/1.24 thf(type_def_34, type, set_Pr1320419588et_val: $tType).
% 2.23/1.24 thf(type_def_35, type, list_P1127016369e_node: $tType).
% 2.23/1.24 thf(type_def_36, type, set_Pr9085835e_node: $tType).
% 2.23/1.24 thf(type_def_37, type, list_P1820443774de_val: $tType).
% 2.23/1.24 thf(type_def_38, type, list_P844977291de_val: $tType).
% 2.23/1.24 thf(type_def_39, type, list_P761482893et_val: $tType).
% 2.23/1.24 thf(type_def_40, type, list_P1078858818l_node: $tType).
% 2.23/1.24 thf(type_def_41, type, list_P1811375021al_val: $tType).
% 2.23/1.24 thf(type_def_42, type, list_set_val: $tType).
% 2.23/1.24 thf(type_def_43, type, list_val: $tType).
% 2.23/1.24 thf(type_def_44, type, val: $tType).
% 2.23/1.24 thf(type_def_45, type, produc1324971431et_val: $tType).
% 2.23/1.24 thf(type_def_46, type, produc1904584935et_val: $tType).
% 2.23/1.24 thf(type_def_47, type, produc452075965de_val: $tType).
% 2.23/1.24 thf(type_def_48, type, produc1013974930l_node: $tType).
% 2.23/1.24 thf(type_def_49, type, produc782216903al_val: $tType).
% 2.23/1.24 thf(type_def_50, type, produc1615737844de_val: $tType).
% 2.23/1.24 thf(type_def_51, type, produc1062784462et_val: $tType).
% 2.23/1.24 thf(type_def_52, type, produc951622955e_node: $tType).
% 2.23/1.24 thf(type_def_53, type, produc1664334075de_val: $tType).
% 2.23/1.24 thf(type_def_54, type, produc1858904199et_val: $tType).
% 2.23/1.24 thf(type_def_55, type, produc1946948786l_node: $tType).
% 2.23/1.24 thf(type_def_56, type, product_prod_val_val: $tType).
% 2.23/1.24 thf(type_def_57, type, var: $tType).
% 2.23/1.24 thf(func_def_0, type, list_P88441325et_val: $tType).
% 2.23/1.24 thf(func_def_1, type, set_Pr1587248327et_val: $tType).
% 2.23/1.24 thf(func_def_2, type, produc1904584935et_val: $tType).
% 2.23/1.24 thf(func_def_3, type, list_P729276995de_val: $tType).
% 2.23/1.24 thf(func_def_4, type, set_Pr819703837de_val: $tType).
% 2.23/1.24 thf(func_def_5, type, produc452075965de_val: $tType).
% 2.23/1.24 thf(func_def_6, type, list_P1108777338de_val: $tType).
% 2.23/1.24 thf(func_def_7, type, list_P844977291de_val: $tType).
% 2.23/1.24 thf(func_def_8, type, set_Pr1245322836de_val: $tType).
% 2.23/1.24 thf(func_def_9, type, set_Pr701036849de_val: $tType).
% 2.23/1.24 thf(func_def_10, type, list_P2089461677et_val: $tType).
% 2.23/1.24 thf(func_def_11, type, set_Pr1311924359et_val: $tType).
% 2.23/1.24 thf(func_def_12, type, produc1615737844de_val: $tType).
% 2.23/1.24 thf(func_def_13, type, produc1664334075de_val: $tType).
% 2.23/1.24 thf(func_def_14, type, list_P12184414et_val: $tType).
% 2.23/1.24 thf(func_def_15, type, list_P1414038306l_node: $tType).
% 2.23/1.24 thf(func_def_16, type, list_P761482893et_val: $tType).
% 2.23/1.24 thf(func_def_17, type, list_P940784845al_val: $tType).
% 2.23/1.24 thf(func_def_18, type, set_Pr1320419588et_val: $tType).
% 2.23/1.24 thf(func_def_19, type, set_Pr574789832l_node: $tType).
% 2.23/1.24 thf(func_def_20, type, set_Pr978022247et_val: $tType).
% 2.23/1.24 thf(func_def_21, type, set_Pr1157324199al_val: $tType).
% 2.23/1.24 thf(func_def_22, type, produc1324971431et_val: $tType).
% 2.23/1.24 thf(func_def_23, type, list_P561207620_edgeD: $tType).
% 2.23/1.24 thf(func_def_24, type, list_P1127016369e_node: $tType).
% 2.23/1.24 thf(func_def_25, type, list_P1078858818l_node: $tType).
% 2.23/1.24 thf(func_def_26, type, list_P1820443774de_val: $tType).
% 2.23/1.24 thf(func_def_27, type, set_Pr9085835e_node: $tType).
% 2.23/1.24 thf(func_def_28, type, list_P1811375021al_val: $tType).
% 2.23/1.24 thf(func_def_29, type, set_Pr2105655784l_node: $tType).
% 2.23/1.24 thf(func_def_30, type, set_Pr699757092de_val: $tType).
% 2.23/1.24 thf(func_def_31, type, produc1062784462et_val: $tType).
% 2.23/1.24 thf(func_def_32, type, produc1013974930l_node: $tType).
% 2.23/1.24 thf(func_def_33, type, set_Pr700443783al_val: $tType).
% 2.23/1.24 thf(func_def_34, type, produc1858904199et_val: $tType).
% 2.23/1.24 thf(func_def_35, type, produc782216903al_val: $tType).
% 2.23/1.24 thf(func_def_36, type, produc951622955e_node: $tType).
% 2.23/1.24 thf(func_def_37, type, option_list_val: $tType).
% 2.23/1.24 thf(func_def_38, type, produc1946948786l_node: $tType).
% 2.23/1.24 thf(func_def_39, type, produc1432036078de_val: $tType).
% 2.23/1.24 thf(func_def_40, type, product_prod_val_val: $tType).
% 2.23/1.24 thf(func_def_41, type, option_set_val: $tType).
% 2.23/1.24 thf(func_def_42, type, list_set_val: $tType).
% 2.23/1.24 thf(func_def_43, type, set_set_val: $tType).
% 2.23/1.24 thf(func_def_44, type, list_node: $tType).
% 2.23/1.24 thf(func_def_45, type, list_val: $tType).
% 2.23/1.24 thf(func_def_46, type, set_node: $tType).
% 2.23/1.24 thf(func_def_47, type, set_val: $tType).
% 2.23/1.24 thf(func_def_48, type, node: $tType).
% 2.23/1.24 thf(func_def_49, type, var: $tType).
% 2.23/1.24 thf(func_def_50, type, val: $tType).
% 2.23/1.24 thf(func_def_51, type, g: $tType).
% 2.23/1.24 thf(func_def_52, type, finite79836624et_val: set_Pr1311924359et_val > $o).
% 2.23/1.24 thf(func_def_53, type, finite2056463621de_val: set_Pr699757092de_val > $o).
% 2.23/1.24 thf(func_def_54, type, finite781217938de_val: set_Pr701036849de_val > $o).
% 2.23/1.24 thf(func_def_55, type, finite1581417648et_val: set_Pr978022247et_val > $o).
% 2.23/1.24 thf(func_def_56, type, finite423892681l_node: set_Pr2105655784l_node > $o).
% 2.23/1.24 thf(func_def_57, type, finite759259600al_val: set_Pr700443783al_val > $o).
% 2.23/1.24 thf(func_def_58, type, finite1265617511et_val: set_set_val > $o).
% 2.23/1.24 thf(func_def_59, type, finite_finite_node: set_node > $o).
% 2.23/1.24 thf(func_def_60, type, finite_finite_val: set_val > $o).
% 2.23/1.24 thf(func_def_61, type, graph_272749361_edgeD: (g > node > list_P561207620_edgeD) > g > node > list_node).
% 2.23/1.24 thf(func_def_62, type, graph_1037173556_edgeD: (g > list_node) > (g > node > list_P561207620_edgeD) > g > node > list_node).
% 2.23/1.24 thf(func_def_63, type, irredu893086079de_val: (g > list_node) > (g > node > set_val) > (g > produc1432036078de_val > option_list_val) > g > set_val > set_Pr1311924359et_val).
% 2.23/1.24 thf(func_def_64, type, irredu681226810de_val: (g > list_node) > (g > node > set_val) > (g > produc1432036078de_val > option_list_val) > g > set_val > set_set_val).
% 2.23/1.24 thf(func_def_65, type, irredu1955035135eD_val: (g > list_node) > (g > node > list_P561207620_edgeD) > (g > node > set_val) > (g > node > set_val) > (g > produc1432036078de_val > option_list_val) > g > set_val > set_val > $o).
% 2.23/1.24 thf(func_def_66, type, irredu224829488eD_val: (g > list_node) > (g > node > list_P561207620_edgeD) > (g > node > set_val) > (g > node > set_val) > (g > produc1432036078de_val > option_list_val) > g > set_val > $o).
% 2.23/1.24 thf(func_def_67, type, sup_su1487070040et_val: option_set_val > option_set_val > option_set_val).
% 2.23/1.24 thf(func_def_68, type, sup_su2005730907et_val: set_Pr1311924359et_val > set_Pr1311924359et_val > set_Pr1311924359et_val).
% 2.23/1.24 thf(func_def_69, type, sup_su2138939728de_val: set_Pr699757092de_val > set_Pr699757092de_val > set_Pr699757092de_val).
% 2.23/1.24 thf(func_def_70, type, sup_sup_set_set_val: set_set_val > set_set_val > set_set_val).
% 2.23/1.24 thf(func_def_71, type, sup_sup_set_node: set_node > set_node > set_node).
% 2.23/1.24 thf(func_def_72, type, sup_sup_set_val: set_val > set_val > set_val).
% 2.23/1.24 thf(func_def_73, type, set_Pr1006393724et_val: list_P88441325et_val > set_Pr1587248327et_val).
% 2.23/1.24 thf(func_def_74, type, set_Pr482027474de_val: list_P729276995de_val > set_Pr819703837de_val).
% 2.23/1.24 thf(func_def_75, type, set_Pr284769596et_val: list_P2089461677et_val > set_Pr1311924359et_val).
% 2.23/1.24 thf(func_def_76, type, set_Pr1904955709l_node: list_P1414038306l_node > set_Pr574789832l_node).
% 2.23/1.24 thf(func_def_77, type, set_Pr1027623516al_val: list_P940784845al_val > set_Pr1157324199al_val).
% 2.23/1.24 thf(func_def_78, type, set_Pr1157337481de_val: list_P1108777338de_val > set_Pr1245322836de_val).
% 2.23/1.24 thf(func_def_79, type, set_Pr1953765241et_val: list_P12184414et_val > set_Pr1320419588et_val).
% 2.23/1.24 thf(func_def_80, type, set_Pr450990656e_node: list_P1127016369e_node > set_Pr9085835e_node).
% 2.23/1.24 thf(func_def_81, type, set_Pr1085970585de_val: list_P1820443774de_val > set_Pr699757092de_val).
% 2.23/1.24 thf(func_def_82, type, set_Pr434939430de_val: list_P844977291de_val > set_Pr701036849de_val).
% 2.23/1.24 thf(func_def_83, type, set_Pr2104310812et_val: list_P761482893et_val > set_Pr978022247et_val).
% 2.23/1.24 thf(func_def_84, type, set_Pr1600883293l_node: list_P1078858818l_node > set_Pr2105655784l_node).
% 2.23/1.24 thf(func_def_85, type, set_Pr102746428al_val: list_P1811375021al_val > set_Pr700443783al_val).
% 2.23/1.24 thf(func_def_86, type, set_set_val2: list_set_val > set_set_val).
% 2.23/1.24 thf(func_def_87, type, set_node2: list_node > set_node).
% 2.23/1.24 thf(func_def_88, type, set_val2: list_val > set_val).
% 2.23/1.24 thf(func_def_89, type, zip_Pr21865079et_val: list_P2089461677et_val > list_P2089461677et_val > list_P88441325et_val).
% 2.23/1.24 thf(func_def_90, type, zip_Pr1472086037de_val: list_P1820443774de_val > list_P1820443774de_val > list_P729276995de_val).
% 2.23/1.24 thf(func_def_91, type, zip_set_val_set_val: list_set_val > list_set_val > list_P2089461677et_val).
% 2.23/1.24 thf(func_def_92, type, zip_set_val_node: list_set_val > list_node > list_P1414038306l_node).
% 2.23/1.24 thf(func_def_93, type, zip_set_val_val: list_set_val > list_val > list_P940784845al_val).
% 2.23/1.24 thf(func_def_94, type, zip_no263301324de_val: list_node > list_P1820443774de_val > list_P1108777338de_val).
% 2.23/1.24 thf(func_def_95, type, zip_node_set_val: list_node > list_set_val > list_P12184414et_val).
% 2.23/1.24 thf(func_def_96, type, zip_node_node: list_node > list_node > list_P1127016369e_node).
% 2.23/1.24 thf(func_def_97, type, zip_node_val: list_node > list_val > list_P1820443774de_val).
% 2.23/1.24 thf(func_def_98, type, zip_va679686869de_val: list_val > list_P1820443774de_val > list_P844977291de_val).
% 2.23/1.24 thf(func_def_99, type, zip_val_set_val: list_val > list_set_val > list_P761482893et_val).
% 2.23/1.24 thf(func_def_100, type, zip_val_node: list_val > list_node > list_P1078858818l_node).
% 2.23/1.24 thf(func_def_101, type, zip_val_val: list_val > list_val > list_P1811375021al_val).
% 2.23/1.24 thf(func_def_102, type, dom_Pr729677986st_val: (produc1432036078de_val > option_list_val) > set_Pr699757092de_val).
% 2.23/1.24 thf(func_def_103, type, dom_val_list_val: (val > option_list_val) > set_val).
% 2.23/1.24 thf(func_def_104, type, none_list_val: option_list_val).
% 2.23/1.24 thf(func_def_105, type, some_list_val: list_val > option_list_val).
% 2.23/1.24 thf(func_def_106, type, some_set_val: set_val > option_set_val).
% 2.23/1.24 thf(func_def_107, type, bot_bo2078591731et_val: set_Pr1311924359et_val).
% 2.23/1.24 thf(func_def_108, type, bot_bo404898488de_val: set_Pr699757092de_val).
% 2.23/1.24 thf(func_def_109, type, bot_bot_set_set_val: set_set_val).
% 2.23/1.24 thf(func_def_110, type, bot_bot_set_val: set_val).
% 2.23/1.24 thf(func_def_111, type, ord_le596993316et_val: option_set_val > option_set_val > $o).
% 2.23/1.24 thf(func_def_112, type, ord_le299366439et_val: set_Pr1311924359et_val > set_Pr1311924359et_val > $o).
% 2.23/1.24 thf(func_def_113, type, ord_le1643692676de_val: set_Pr699757092de_val > set_Pr699757092de_val > $o).
% 2.23/1.24 thf(func_def_114, type, ord_le1742111550et_val: set_set_val > set_set_val > $o).
% 2.23/1.24 thf(func_def_115, type, ord_less_eq_set_node: set_node > set_node > $o).
% 2.23/1.24 thf(func_def_116, type, ord_less_eq_set_val: set_val > set_val > $o).
% 2.23/1.24 thf(func_def_117, type, ord_less_eq_node: node > node > $o).
% 2.23/1.24 thf(func_def_118, type, ord_less_eq_val: val > val > $o).
% 2.23/1.24 thf(func_def_119, type, produc1377626967et_val: produc1324971431et_val > produc1324971431et_val > produc1904584935et_val).
% 2.23/1.24 thf(func_def_120, type, produc453318901de_val: produc1432036078de_val > produc1432036078de_val > produc452075965de_val).
% 2.23/1.24 thf(func_def_121, type, produc1041633943et_val: set_val > set_val > produc1324971431et_val).
% 2.23/1.24 thf(func_def_122, type, produc2052093836l_node: set_val > node > produc1013974930l_node).
% 2.23/1.24 thf(func_def_123, type, produc1337903031al_val: set_val > val > produc782216903al_val).
% 2.23/1.24 thf(func_def_124, type, produc1162531244de_val: node > produc1432036078de_val > produc1615737844de_val).
% 2.23/1.24 thf(func_def_125, type, produc2042994048et_val: node > set_val > produc1062784462et_val).
% 2.23/1.24 thf(func_def_126, type, produc457016035e_node: node > node > produc951622955e_node).
% 2.23/1.24 thf(func_def_127, type, produc1470527136de_val: node > val > produc1432036078de_val).
% 2.23/1.24 thf(func_def_128, type, produc1571934709de_val: val > produc1432036078de_val > produc1664334075de_val).
% 2.23/1.24 thf(func_def_129, type, produc1446164855et_val: val > set_val > produc1858904199et_val).
% 2.23/1.24 thf(func_def_130, type, produc1074923692l_node: val > node > produc1946948786l_node).
% 2.23/1.24 thf(func_def_131, type, product_Pair_val_val: val > val > product_prod_val_val).
% 2.23/1.24 thf(func_def_132, type, sSA_CF139593942de_val: (g > node > set_val) > (g > produc1432036078de_val > option_list_val) > g > node > set_val).
% 2.23/1.24 thf(func_def_133, type, sSA_CF178745443eD_val: (g > list_node) > (g > node > list_P561207620_edgeD) > (g > node > set_val) > (g > produc1432036078de_val > option_list_val) > g > node > set_val).
% 2.23/1.24 thf(func_def_134, type, sSA_CF1517915011eD_val: (g > list_node) > (g > node > list_P561207620_edgeD) > (g > node > set_val) > (g > node > set_val) > (g > produc1432036078de_val > option_list_val) > g > set_val).
% 2.23/1.24 thf(func_def_135, type, sSA_CF370335846de_val: (g > produc1432036078de_val > option_list_val) > g > node > set_val).
% 2.23/1.24 thf(func_def_136, type, sSA_CF848637139eD_val: (g > list_node) > (g > node > list_P561207620_edgeD) > (g > produc1432036078de_val > option_list_val) > g > node > set_val).
% 2.23/1.24 thf(func_def_137, type, sSA_CF551432799de_val: (g > list_node) > (g > node > set_val) > (g > produc1432036078de_val > option_list_val) > g > val > node).
% 2.23/1.24 thf(func_def_138, type, sSA_CF1909049442de_val: (g > list_node) > (g > node > set_val) > (g > produc1432036078de_val > option_list_val) > g > val > val > $o).
% 2.23/1.24 thf(func_def_139, type, sSA_CF794421325de_val: (g > list_node) > (g > node > set_val) > (g > node > set_val) > (g > produc1432036078de_val > option_list_val) > g > val > $o).
% 2.23/1.24 thf(func_def_140, type, sSA_CF1252180629de_val: (g > list_node) > (g > node > set_val) > (g > produc1432036078de_val > option_list_val) > g > val > val > $o).
% 2.23/1.24 thf(func_def_141, type, sSA_CF262257161de_val: (g > list_node) > (g > node > set_val) > (g > produc1432036078de_val > option_list_val) > g > val > option_list_val).
% 2.23/1.24 thf(func_def_142, type, sSA_CF2074824714de_val: (g > list_node) > (g > node > set_val) > (g > node > set_val) > (g > produc1432036078de_val > option_list_val) > g > $o).
% 2.23/1.24 thf(func_def_143, type, sSA_CF1660885746eD_val: (g > list_node) > (g > node > list_P561207620_edgeD) > (g > node > set_val) > (g > node > set_val) > (g > produc1432036078de_val > option_list_val) > g > $o).
% 2.23/1.24 thf(func_def_144, type, sSA_CF1899243830eD_val: (g > list_node) > (g > node > list_P561207620_edgeD) > (g > node > set_val) > (g > node > set_val) > (g > produc1432036078de_val > option_list_val) > g > val > $o).
% 2.23/1.24 thf(func_def_145, type, sSA_CF655860150de_val: (g > list_node) > (g > node > set_val) > g > set_val).
% 2.23/1.24 thf(func_def_146, type, collec1117167378et_val: (produc1324971431et_val > $o) > set_Pr1311924359et_val).
% 2.23/1.24 thf(func_def_147, type, collec370342979de_val: (produc1432036078de_val > $o) > set_Pr699757092de_val).
% 2.23/1.24 thf(func_def_148, type, collec885255687l_node: (produc1946948786l_node > $o) > set_Pr2105655784l_node).
% 2.23/1.24 thf(func_def_149, type, collec52550418al_val: (product_prod_val_val > $o) > set_Pr700443783al_val).
% 2.23/1.24 thf(func_def_150, type, collect_set_val: (set_val > $o) > set_set_val).
% 2.23/1.24 thf(func_def_151, type, collect_node: (node > $o) > set_node).
% 2.23/1.24 thf(func_def_152, type, collect_val: (val > $o) > set_val).
% 2.23/1.24 thf(func_def_153, type, insert1846469495et_val: produc1324971431et_val > set_Pr1311924359et_val > set_Pr1311924359et_val).
% 2.23/1.24 thf(func_def_154, type, insert869443870de_val: produc1432036078de_val > set_Pr699757092de_val > set_Pr699757092de_val).
% 2.23/1.24 thf(func_def_155, type, insert_set_val: set_val > set_set_val > set_set_val).
% 2.23/1.24 thf(func_def_156, type, insert_node: node > set_node > set_node).
% 2.23/1.24 thf(func_def_157, type, insert_val: val > set_val > set_val).
% 2.23/1.24 thf(func_def_158, type, transi1953622797et_val: set_Pr1311924359et_val > $o).
% 2.23/1.24 thf(func_def_159, type, transi1991289355lp_val: (val > val > $o) > val > val > $o).
% 2.23/1.24 thf(func_def_160, type, member1254968080et_val: produc1904584935et_val > set_Pr1587248327et_val > $o).
% 2.23/1.24 thf(func_def_161, type, member698732390de_val: produc452075965de_val > set_Pr819703837de_val > $o).
% 2.23/1.24 thf(func_def_162, type, member1711426256et_val: produc1324971431et_val > set_Pr1311924359et_val > $o).
% 2.23/1.24 thf(func_def_163, type, member76372137l_node: produc1013974930l_node > set_Pr574789832l_node > $o).
% 2.23/1.24 thf(func_def_164, type, member1110026224al_val: produc782216903al_val > set_Pr1157324199al_val > $o).
% 2.23/1.24 thf(func_def_165, type, member562853661de_val: produc1615737844de_val > set_Pr1245322836de_val > $o).
% 2.23/1.24 thf(func_def_166, type, member125181669et_val: produc1062784462et_val > set_Pr1320419588et_val > $o).
% 2.23/1.24 thf(func_def_167, type, member2110109140e_node: produc951622955e_node > set_Pr9085835e_node > $o).
% 2.23/1.24 thf(func_def_168, type, member313544709de_val: produc1432036078de_val > set_Pr699757092de_val > $o).
% 2.23/1.24 thf(func_def_169, type, member1894062994de_val: produc1664334075de_val > set_Pr701036849de_val > $o).
% 2.23/1.24 thf(func_def_170, type, member39229872et_val: produc1858904199et_val > set_Pr978022247et_val > $o).
% 2.23/1.24 thf(func_def_171, type, member828457417l_node: produc1946948786l_node > set_Pr2105655784l_node > $o).
% 2.23/1.24 thf(func_def_172, type, member1680438992al_val: product_prod_val_val > set_Pr700443783al_val > $o).
% 2.23/1.24 thf(func_def_173, type, member_set_val: set_val > set_set_val > $o).
% 2.23/1.24 thf(func_def_174, type, member_node: node > set_node > $o).
% 2.23/1.24 thf(func_def_175, type, member_val: val > set_val > $o).
% 2.23/1.24 thf(func_def_176, type, alpha_n: g > list_node).
% 2.23/1.24 thf(func_def_177, type, phi: val).
% 2.23/1.24 thf(func_def_178, type, phi_s: val).
% 2.23/1.24 thf(func_def_179, type, phi2: val).
% 2.23/1.24 thf(func_def_180, type, defs: g > node > set_val).
% 2.23/1.24 thf(func_def_181, type, g2: g).
% 2.23/1.24 thf(func_def_182, type, inEdges: g > node > list_P561207620_edgeD).
% 2.23/1.24 thf(func_def_183, type, phis: g > produc1432036078de_val > option_list_val).
% 2.23/1.24 thf(func_def_184, type, s: val).
% 2.23/1.24 thf(func_def_185, type, uses: g > node > set_val).
% 2.23/1.24 thf(func_def_186, type, var2: g > val > var).
% 2.23/1.24 thf(func_def_205, type, sK0: (val > $o) > set_val > val).
% 2.23/1.24 thf(func_def_206, type, sK1: (val > $o) > set_val > val).
% 2.23/1.24 thf(func_def_207, type, sK2: (val > $o) > set_val > set_val > val).
% 2.23/1.24 thf(func_def_208, type, sK3: val).
% 2.23/1.24 thf(func_def_209, type, sK4: (val > $o) > set_val > val).
% 2.23/1.24 thf(func_def_210, type, sK5: (val > $o) > set_val > val).
% 2.23/1.24 thf(func_def_211, type, sK6: (val > $o) > set_val > set_val > val).
% 2.23/1.24 thf(func_def_213, type, ph8: !>[X0: $tType]:(X0)).
% 2.23/1.24 thf(f1035,plain,(
% 2.23/1.24 $false),
% 2.23/1.24 inference(trivial_inequality_removal,[status(thm)],[f1034])).
% 2.23/1.24 thf(f1034,plain,(
% 2.23/1.24 ($true != $true)),
% 2.23/1.24 inference(superposition,[status(thm)],[f1033,f1017])).
% 2.23/1.24 thf(f1017,plain,(
% 2.23/1.24 ($true = (sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ sK3 @ phi_s))),
% 2.23/1.24 inference(cnf_transformation,[status(thm)],[f973])).
% 2.23/1.24 thf(f973,plain,(
% 2.23/1.24 ($true = (sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ sK3 @ phi_s))),
% 2.23/1.24 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f956,f972])).
% 2.23/1.24 thf(f972,plain,(
% 2.23/1.24 ? [X0 : val] : ((sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ X0 @ phi_s) = $true) => ($true = (sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ sK3 @ phi_s))),
% 2.23/1.24 introduced(definition,[],[choice_axiom])).
% 2.23/1.24 thf(f956,plain,(
% 2.23/1.24 ? [X0 : val] : ((sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ X0 @ phi_s) = $true)),
% 2.23/1.24 inference(ennf_transformation,[status(thm)],[f930])).
% 2.23/1.24 thf(f930,plain,(
% 2.23/1.24 ~! [X0 : val] : ((sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ X0 @ phi_s) != $true)),
% 2.23/1.24 inference(flattening,[status(thm)],[f580])).
% 2.23/1.24 thf(f580,plain,(
% 2.23/1.24 ~! [X0 : val] : ~((sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ X0 @ phi_s) = $true)),
% 2.23/1.24 inference(fool_elimination,[status(thm)],[f579])).
% 2.23/1.24 thf(f579,plain,(
% 2.23/1.24 ~! [X0 : val] : ~(sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ X0 @ phi_s)),
% 2.23/1.24 inference(rectify,[status(thm)],[f6])).
% 2.23/1.24 thf(f6,axiom,(
% 2.23/1.24 ~! [X0 : val] : ~(sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ X0 @ phi_s)),
% 2.23/1.24 file('/export/starexec/sandbox/tmp/tmp.ceXPxvwqcT/DTF2THF_29714.p',fact_5__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062_092_060phi_062_H_O_AphiArg_Ag_A_092_060phi_062_H_A_092_060phi_062_092_060_094sub_062s_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062)).
% 2.23/1.24 thf(f1033,plain,(
% 2.23/1.24 ( ! [X0 : val] : (((sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ X0 @ phi_s) != $true)) )),
% 2.23/1.24 inference(trivial_inequality_removal,[status(thm)],[f1032])).
% 2.23/1.24 thf(f1032,plain,(
% 2.23/1.24 ( ! [X0 : val] : (((sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ X0 @ phi_s) != $true) | ($true != $true)) )),
% 2.23/1.24 inference(superposition,[status(thm)],[f989,f999])).
% 2.23/1.24 thf(f999,plain,(
% 2.23/1.24 ( ! [X2 : val,X0 : val,X1 : g] : (($true = (member_val @ X0 @ (sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ X1))) | ($true != (sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ X1 @ X2 @ X0))) )),
% 2.23/1.24 inference(cnf_transformation,[status(thm)],[f954])).
% 2.23/1.24 thf(f954,plain,(
% 2.23/1.24 ! [X0 : val,X1 : g,X2 : val] : (($true != (sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ X1 @ X2 @ X0)) | ($true = (member_val @ X0 @ (sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ X1))))),
% 2.23/1.24 inference(ennf_transformation,[status(thm)],[f924])).
% 2.23/1.24 thf(f924,plain,(
% 2.23/1.24 ! [X0 : val,X1 : g,X2 : val] : (($true = (sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ X1 @ X2 @ X0)) => ($true = (member_val @ X0 @ (sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ X1))))),
% 2.23/1.24 inference(fool_elimination,[status(thm)],[f923])).
% 2.23/1.24 thf(f923,plain,(
% 2.23/1.24 ! [X0 : val,X1 : g,X2 : val] : ((sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ X1 @ X2 @ X0) => (member_val @ X0 @ (sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ X1)))),
% 2.23/1.24 inference(rectify,[status(thm)],[f7])).
% 2.23/1.24 thf(f7,axiom,(
% 2.23/1.24 ! [X3 : val,X1 : g,X2 : val] : ((sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ X1 @ X2 @ X3) => (member_val @ X3 @ (sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ X1)))),
% 2.23/1.24 file('/export/starexec/sandbox/tmp/tmp.ceXPxvwqcT/DTF2THF_29714.p',fact_6_phiArg__in__allVars)).
% 2.23/1.24 thf(f989,plain,(
% 2.23/1.24 ((member_val @ phi_s @ (sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2)) != $true)),
% 2.23/1.24 inference(cnf_transformation,[status(thm)],[f927])).
% 2.23/1.24 thf(f927,plain,(
% 2.23/1.24 ((member_val @ phi_s @ (sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2)) != $true)),
% 2.23/1.24 inference(flattening,[status(thm)],[f742])).
% 2.23/1.24 thf(f742,plain,(
% 2.23/1.24 ~((member_val @ phi_s @ (sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2)) = $true)),
% 2.23/1.24 inference(fool_elimination,[status(thm)],[f741])).
% 2.23/1.24 thf(f741,plain,(
% 2.23/1.24 ~(member_val @ phi_s @ (sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2))),
% 2.23/1.24 inference(rectify,[status(thm)],[f355])).
% 2.23/1.24 thf(f355,negated_conjecture,(
% 2.23/1.24 ~(member_val @ phi_s @ (sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2))),
% 2.23/1.24 inference(negated_conjecture,[status(cth)],[f354])).
% 2.23/1.24 thf(f354,conjecture,(
% 2.23/1.24 (member_val @ phi_s @ (sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2))),
% 2.23/1.24 file('/export/starexec/sandbox/tmp/tmp.ceXPxvwqcT/DTF2THF_29714.p',conj_0)).
% 2.23/1.24 % SZS output end Proof for DTF2THF_29714
% 2.23/1.24 % (29825)------------------------------
% 2.23/1.24 % (29825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.23/1.24 % (29825)Termination reason: Refutation
% 2.23/1.24
% 2.23/1.24 % (29825)Memory used [KB]: 6524
% 2.23/1.24 % (29825)Time elapsed: 0.025 s
% 2.23/1.24 % (29825)Instructions burned: 76 (million)
% 2.23/1.24 % (29825)------------------------------
% 2.23/1.24 % (29825)------------------------------
% 2.23/1.24 % (29819)Success in time 0.04 s
%------------------------------------------------------------------------------