%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP039^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n031.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 08:55:03 AM UTC 2026
% Result : Theorem 3.20s 1.75s
% Output : Refutation 3.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 17
% Syntax : Number of formulae : 133 ( 4 unt; 0 typ; 14 def)
% Number of atoms : 1088 ( 283 equ; 0 cnn)
% Maximal formula atoms : 12 ( 8 avg)
% Number of connectives : 1883 ( 238 ~; 331 |; 23 &;1256 @)
% ( 15 <=>; 18 =>; 0 <=; 2 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 27 ( 26 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 151 ( 148 usr; 28 con; 0-10 aty)
% Number of variables : 168 ( 0 ^; 144 !; 24 ?; 168 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
formula_a_b_c: $tType ).
thf(type_def_7,type,
denota231621370t_unit: $tType ).
thf(type_def_8,type,
set_Su1783761653um_b_c: $tType ).
thf(type_def_9,type,
produc190496183real_c: $tType ).
thf(type_def_10,type,
set_Sum_sum_c_c: $tType ).
thf(type_def_11,type,
set_Pr1389752855real_c: $tType ).
thf(type_def_12,type,
denota610675952t_unit: $tType ).
thf(type_def_13,type,
formula_sf_sc_sz: $tType ).
thf(type_def_14,type,
set_Pr60491591eal_sz: $tType ).
thf(type_def_15,type,
sz: $tType ).
thf(type_def_16,type,
sf: $tType ).
thf(type_def_17,type,
sc: $tType ).
thf(type_def_18,type,
produc866628903_sc_sz: $tType ).
thf(type_def_19,type,
finite1398487019real_c: $tType ).
thf(type_def_20,type,
set_Pr1169339874_sc_sz: $tType ).
thf(type_def_21,type,
produc1821101996_sc_sz: $tType ).
thf(type_def_22,type,
list_f1238882004_sc_sz: $tType ).
thf(type_def_23,type,
produc640052711real_c: $tType ).
thf(type_def_24,type,
produc999471430t_unit: $tType ).
thf(type_def_25,type,
set_De208295462t_unit: $tType ).
thf(type_def_26,type,
set_Pr1774599175_sc_sz: $tType ).
thf(type_def_27,type,
set_Fi1407883041real_c: $tType ).
thf(type_def_28,type,
set_Pr754230471real_c: $tType ).
thf(type_def_29,type,
set_Pr2041213564t_unit: $tType ).
thf(type_def_30,type,
set_o: $tType ).
thf(type_def_31,type,
produc1149990247eal_sz: $tType ).
thf(func_def_0,type,
set_Pr754230471real_c: $tType ).
thf(func_def_1,type,
produc640052711real_c: $tType ).
thf(func_def_2,type,
set_Pr2041213564t_unit: $tType ).
thf(func_def_3,type,
set_Pr1169339874_sc_sz: $tType ).
thf(func_def_4,type,
produc999471430t_unit: $tType ).
thf(func_def_5,type,
produc1821101996_sc_sz: $tType ).
thf(func_def_6,type,
set_Pr60491591eal_sz: $tType ).
thf(func_def_7,type,
set_Pr1389752855real_c: $tType ).
thf(func_def_8,type,
set_Pr1774599175_sc_sz: $tType ).
thf(func_def_9,type,
produc1149990247eal_sz: $tType ).
thf(func_def_10,type,
produc190496183real_c: $tType ).
thf(func_def_11,type,
produc866628903_sc_sz: $tType ).
thf(func_def_12,type,
set_De208295462t_unit: $tType ).
thf(func_def_13,type,
denota610675952t_unit: $tType ).
thf(func_def_14,type,
denota231621370t_unit: $tType ).
thf(func_def_15,type,
set_Su1783761653um_b_c: $tType ).
thf(func_def_16,type,
set_Fi1407883041real_c: $tType ).
thf(func_def_17,type,
finite1398487019real_c: $tType ).
thf(func_def_18,type,
list_f1238882004_sc_sz: $tType ).
thf(func_def_19,type,
set_Sum_sum_c_c: $tType ).
thf(func_def_20,type,
formula_sf_sc_sz: $tType ).
thf(func_def_21,type,
formula_a_b_c: $tType ).
thf(func_def_22,type,
set_o: $tType ).
thf(func_def_23,type,
sz: $tType ).
thf(func_def_24,type,
sf: $tType ).
thf(func_def_25,type,
sc: $tType ).
thf(func_def_26,type,
coinci501627771_a_b_c: formula_a_b_c > $o ).
thf(func_def_27,type,
denota69106024_a_b_c: denota231621370t_unit > denota231621370t_unit > set_Su1783761653um_b_c > $o ).
thf(func_def_28,type,
denota1997846518gree_c: produc190496183real_c > produc190496183real_c > set_Sum_sum_c_c > $o ).
thf(func_def_29,type,
denota968303861_a_b_c: denota231621370t_unit > formula_a_b_c > set_Pr1389752855real_c ).
thf(func_def_30,type,
denota1711272799_sc_sz: denota610675952t_unit > formula_sf_sc_sz > set_Pr60491591eal_sz ).
thf(func_def_31,type,
denota1946510237_sc_sz: formula_sf_sc_sz > $o ).
thf(func_def_32,type,
denota1579475975_sc_sz: denota610675952t_unit > $o ).
thf(func_def_33,type,
ids_sz_sf_sc: sz > sz > sz > sf > sf > sf > sc > sc > sc > sc > $o ).
thf(func_def_34,type,
top_to1399053141c_sz_o: denota610675952t_unit > produc866628903_sc_sz > $o ).
thf(func_def_35,type,
top_to964419200al_c_o: finite1398487019real_c > finite1398487019real_c > $o ).
thf(func_def_36,type,
top_to1499569298_sc_sz: set_Pr1169339874_sc_sz ).
thf(func_def_37,type,
top_to226056039real_c: set_Pr1389752855real_c ).
thf(func_def_38,type,
top_to1660572043um_c_c: set_Sum_sum_c_c ).
thf(func_def_39,type,
produc789536734_sc_sz: denota610675952t_unit > produc866628903_sc_sz > produc1821101996_sc_sz ).
thf(func_def_40,type,
produc394644079real_c: finite1398487019real_c > finite1398487019real_c > produc190496183real_c ).
thf(func_def_41,type,
produc1822718231_sc_sz: list_f1238882004_sc_sz > list_f1238882004_sc_sz > produc866628903_sc_sz ).
thf(func_def_42,type,
produc1687028567real_c: produc190496183real_c > produc190496183real_c > produc640052711real_c ).
thf(func_def_43,type,
produc502616768t_unit: produc866628903_sc_sz > denota610675952t_unit > produc999471430t_unit ).
thf(func_def_44,type,
produc159603053_sc_sz: set_De208295462t_unit > ( denota610675952t_unit > set_Pr1774599175_sc_sz ) > set_Pr1169339874_sc_sz ).
thf(func_def_45,type,
produc563345056real_c: set_Fi1407883041real_c > ( finite1398487019real_c > set_Fi1407883041real_c ) > set_Pr1389752855real_c ).
thf(func_def_46,type,
produc1017530376real_c: set_Pr1389752855real_c > ( produc190496183real_c > set_Pr1389752855real_c ) > set_Pr754230471real_c ).
thf(func_def_47,type,
produc2020166735t_unit: set_Pr1774599175_sc_sz > ( produc866628903_sc_sz > set_De208295462t_unit ) > set_Pr2041213564t_unit ).
thf(func_def_48,type,
produc793407943_sc_sz: ( denota610675952t_unit > denota610675952t_unit ) > produc999471430t_unit > produc999471430t_unit ).
thf(func_def_49,type,
produc981295297real_c: ( finite1398487019real_c > finite1398487019real_c ) > produc190496183real_c > produc190496183real_c ).
thf(func_def_50,type,
produc233219286_sc_sz: ( list_f1238882004_sc_sz > list_f1238882004_sc_sz ) > produc866628903_sc_sz > produc866628903_sc_sz ).
thf(func_def_51,type,
produc2089853305real_c: ( produc190496183real_c > produc190496183real_c ) > produc640052711real_c > produc640052711real_c ).
thf(func_def_52,type,
produc1959054510t_unit: ( produc866628903_sc_sz > produc866628903_sc_sz ) > produc1821101996_sc_sz > produc1821101996_sc_sz ).
thf(func_def_53,type,
produc1086673900c_sz_o: ( produc1821101996_sc_sz > $o ) > denota610675952t_unit > produc866628903_sc_sz > $o ).
thf(func_def_54,type,
produc753314315real_c: ( produc1821101996_sc_sz > produc190496183real_c ) > denota610675952t_unit > produc866628903_sc_sz > produc190496183real_c ).
thf(func_def_55,type,
produc1827049067real_c: ( produc1821101996_sc_sz > set_Pr1389752855real_c ) > denota610675952t_unit > produc866628903_sc_sz > set_Pr1389752855real_c ).
thf(func_def_56,type,
produc1716060341al_c_o: ( produc190496183real_c > $o ) > finite1398487019real_c > finite1398487019real_c > $o ).
thf(func_def_57,type,
produc1119115220real_c: ( produc190496183real_c > produc190496183real_c ) > finite1398487019real_c > finite1398487019real_c > produc190496183real_c ).
thf(func_def_58,type,
produc880541325c_sz_o: ( produc866628903_sc_sz > $o ) > list_f1238882004_sc_sz > list_f1238882004_sc_sz > $o ).
thf(func_def_59,type,
produc440529997al_c_o: ( produc640052711real_c > $o ) > produc190496183real_c > produc190496183real_c > $o ).
thf(func_def_60,type,
produc38128778unit_o: ( produc999471430t_unit > $o ) > produc866628903_sc_sz > denota610675952t_unit > $o ).
thf(func_def_61,type,
produc295339066_sc_sz: ( produc999471430t_unit > produc1821101996_sc_sz ) > produc866628903_sc_sz > denota610675952t_unit > produc1821101996_sc_sz ).
thf(func_def_62,type,
produc198687651c_sz_o: ( denota610675952t_unit > produc866628903_sc_sz > $o ) > produc1821101996_sc_sz > $o ).
thf(func_def_63,type,
produc383750338real_c: ( denota610675952t_unit > produc866628903_sc_sz > produc190496183real_c ) > produc1821101996_sc_sz > produc190496183real_c ).
thf(func_def_64,type,
produc1894848802real_c: ( denota610675952t_unit > produc866628903_sc_sz > set_Pr1389752855real_c ) > produc1821101996_sc_sz > set_Pr1389752855real_c ).
thf(func_def_65,type,
produc1442549981real_c: ( finite1398487019real_c > finite1398487019real_c > produc190496183real_c ) > produc190496183real_c > produc190496183real_c ).
thf(func_def_66,type,
produc2099580355_sc_sz: ( produc866628903_sc_sz > denota610675952t_unit > produc1821101996_sc_sz ) > produc999471430t_unit > produc1821101996_sc_sz ).
thf(func_def_67,type,
produc403791768_sc_sz: ( denota610675952t_unit > denota610675952t_unit ) > ( produc866628903_sc_sz > produc866628903_sc_sz ) > produc1821101996_sc_sz > produc1821101996_sc_sz ).
thf(func_def_68,type,
produc1612557567real_c: ( denota610675952t_unit > finite1398487019real_c ) > ( produc866628903_sc_sz > finite1398487019real_c ) > produc1821101996_sc_sz > produc190496183real_c ).
thf(func_def_69,type,
produc1784590311_sc_sz: ( finite1398487019real_c > denota610675952t_unit ) > ( finite1398487019real_c > produc866628903_sc_sz ) > produc190496183real_c > produc1821101996_sc_sz ).
thf(func_def_70,type,
produc368345510real_c: ( finite1398487019real_c > finite1398487019real_c ) > ( finite1398487019real_c > finite1398487019real_c ) > produc190496183real_c > produc190496183real_c ).
thf(func_def_71,type,
produc619560141c_sz_o: ( denota610675952t_unit > produc866628903_sc_sz > $o ) > produc1821101996_sc_sz > $o ).
thf(func_def_72,type,
produc1920474870real_c: ( denota610675952t_unit > produc866628903_sc_sz > finite1398487019real_c ) > produc1821101996_sc_sz > finite1398487019real_c ).
thf(func_def_73,type,
produc448466487_sc_sz: ( denota610675952t_unit > produc866628903_sc_sz > produc1821101996_sc_sz ) > produc1821101996_sc_sz > produc1821101996_sc_sz ).
thf(func_def_74,type,
produc1575513068real_c: ( denota610675952t_unit > produc866628903_sc_sz > produc190496183real_c ) > produc1821101996_sc_sz > produc190496183real_c ).
thf(func_def_75,type,
produc2068697644real_c: ( denota610675952t_unit > produc866628903_sc_sz > set_Fi1407883041real_c ) > produc1821101996_sc_sz > set_Fi1407883041real_c ).
thf(func_def_76,type,
produc237521996real_c: ( denota610675952t_unit > produc866628903_sc_sz > set_Pr1389752855real_c ) > produc1821101996_sc_sz > set_Pr1389752855real_c ).
thf(func_def_77,type,
produc353381908al_c_o: ( finite1398487019real_c > finite1398487019real_c > $o ) > produc190496183real_c > $o ).
thf(func_def_78,type,
produc567249007real_c: ( finite1398487019real_c > finite1398487019real_c > finite1398487019real_c ) > produc190496183real_c > finite1398487019real_c ).
thf(func_def_79,type,
produc107375667real_c: ( finite1398487019real_c > finite1398487019real_c > produc190496183real_c ) > produc190496183real_c > produc190496183real_c ).
thf(func_def_80,type,
produc1341776291_sc_sz: ( finite1398487019real_c > finite1398487019real_c > produc866628903_sc_sz ) > produc190496183real_c > produc866628903_sc_sz ).
thf(func_def_81,type,
produc29022117real_c: ( finite1398487019real_c > finite1398487019real_c > set_Fi1407883041real_c ) > produc190496183real_c > set_Fi1407883041real_c ).
thf(func_def_82,type,
produc923381907real_c: ( finite1398487019real_c > finite1398487019real_c > set_Pr1389752855real_c ) > produc190496183real_c > set_Pr1389752855real_c ).
thf(func_def_83,type,
produc642283651_sc_sz: ( finite1398487019real_c > finite1398487019real_c > set_Pr1774599175_sc_sz ) > produc190496183real_c > set_Pr1774599175_sc_sz ).
thf(func_def_84,type,
produc2039065452c_sz_o: ( list_f1238882004_sc_sz > list_f1238882004_sc_sz > $o ) > produc866628903_sc_sz > $o ).
thf(func_def_85,type,
produc236226839real_c: ( list_f1238882004_sc_sz > list_f1238882004_sc_sz > finite1398487019real_c ) > produc866628903_sc_sz > finite1398487019real_c ).
thf(func_def_86,type,
produc126255499real_c: ( list_f1238882004_sc_sz > list_f1238882004_sc_sz > produc190496183real_c ) > produc866628903_sc_sz > produc190496183real_c ).
thf(func_def_87,type,
produc1449736269real_c: ( list_f1238882004_sc_sz > list_f1238882004_sc_sz > set_Fi1407883041real_c ) > produc866628903_sc_sz > set_Fi1407883041real_c ).
thf(func_def_88,type,
produc6841835real_c: ( list_f1238882004_sc_sz > list_f1238882004_sc_sz > set_Pr1389752855real_c ) > produc866628903_sc_sz > set_Pr1389752855real_c ).
thf(func_def_89,type,
produc1563580891_sc_sz: ( list_f1238882004_sc_sz > list_f1238882004_sc_sz > set_Pr1774599175_sc_sz ) > produc866628903_sc_sz > set_Pr1774599175_sc_sz ).
thf(func_def_90,type,
produc1726730540al_c_o: ( produc190496183real_c > produc190496183real_c > $o ) > produc640052711real_c > $o ).
thf(func_def_91,type,
produc344593239real_c: ( produc190496183real_c > produc190496183real_c > finite1398487019real_c ) > produc640052711real_c > finite1398487019real_c ).
thf(func_def_92,type,
produc1066779277real_c: ( produc190496183real_c > produc190496183real_c > set_Fi1407883041real_c ) > produc640052711real_c > set_Fi1407883041real_c ).
thf(func_def_93,type,
produc1718498667unit_o: ( produc866628903_sc_sz > denota610675952t_unit > $o ) > produc999471430t_unit > $o ).
thf(func_def_94,type,
produc1753599960real_c: ( produc866628903_sc_sz > denota610675952t_unit > finite1398487019real_c ) > produc999471430t_unit > finite1398487019real_c ).
thf(func_def_95,type,
produc435149849_sc_sz: ( produc866628903_sc_sz > denota610675952t_unit > produc1821101996_sc_sz ) > produc999471430t_unit > produc1821101996_sc_sz ).
thf(func_def_96,type,
produc645763722real_c: ( produc866628903_sc_sz > denota610675952t_unit > produc190496183real_c ) > produc999471430t_unit > produc190496183real_c ).
thf(func_def_97,type,
produc1368849166real_c: ( produc866628903_sc_sz > denota610675952t_unit > set_Fi1407883041real_c ) > produc999471430t_unit > set_Fi1407883041real_c ).
thf(func_def_98,type,
produc593754858real_c: ( produc866628903_sc_sz > denota610675952t_unit > set_Pr1389752855real_c ) > produc999471430t_unit > set_Pr1389752855real_c ).
thf(func_def_99,type,
produc1503602930_sc_sz: produc1821101996_sc_sz > denota610675952t_unit ).
thf(func_def_100,type,
produc532048446_sc_sz: produc1821101996_sc_sz > produc999471430t_unit ).
thf(func_def_101,type,
produc704157711real_c: produc190496183real_c > produc190496183real_c ).
thf(func_def_102,type,
produc1145837239_sc_sz: produc866628903_sc_sz > produc866628903_sc_sz ).
thf(func_def_103,type,
produc350724343real_c: produc640052711real_c > produc640052711real_c ).
thf(func_def_104,type,
produc245128480t_unit: produc999471430t_unit > produc1821101996_sc_sz ).
thf(func_def_105,type,
produc3751594real_c: set_Fi1407883041real_c > set_Fi1407883041real_c > set_Pr1389752855real_c ).
thf(func_def_106,type,
inv_im1827249322real_c: set_Pr1389752855real_c > ( finite1398487019real_c > finite1398487019real_c ) > set_Pr1389752855real_c ).
thf(func_def_107,type,
collec230941376real_c: ( finite1398487019real_c > $o ) > set_Fi1407883041real_c ).
thf(func_def_108,type,
collec1199592193_sc_sz: ( produc1821101996_sc_sz > $o ) > set_Pr1169339874_sc_sz ).
thf(func_def_109,type,
collec1643251106real_c: ( produc190496183real_c > $o ) > set_Pr1389752855real_c ).
thf(func_def_110,type,
collec2036662930_sc_sz: ( produc866628903_sc_sz > $o ) > set_Pr1774599175_sc_sz ).
thf(func_def_111,type,
collec1126017874real_c: ( produc640052711real_c > $o ) > set_Pr754230471real_c ).
thf(func_def_112,type,
collec377961627t_unit: ( produc999471430t_unit > $o ) > set_Pr2041213564t_unit ).
thf(func_def_113,type,
image_1514048989real_c: ( finite1398487019real_c > finite1398487019real_c ) > set_Fi1407883041real_c > set_Fi1407883041real_c ).
thf(func_def_114,type,
image_1461287749real_c: ( finite1398487019real_c > produc190496183real_c ) > set_Fi1407883041real_c > set_Pr1389752855real_c ).
thf(func_def_115,type,
image_290183605_sc_sz: ( finite1398487019real_c > produc866628903_sc_sz ) > set_Fi1407883041real_c > set_Pr1774599175_sc_sz ).
thf(func_def_116,type,
image_1746662005real_c: ( finite1398487019real_c > produc640052711real_c ) > set_Fi1407883041real_c > set_Pr754230471real_c ).
thf(func_def_117,type,
image_1641704997c_sz_o: ( produc1821101996_sc_sz > $o ) > set_Pr1169339874_sc_sz > set_o ).
thf(func_def_118,type,
image_1268968350real_c: ( produc1821101996_sc_sz > finite1398487019real_c ) > set_Pr1169339874_sc_sz > set_Fi1407883041real_c ).
thf(func_def_119,type,
image_1726193375_sc_sz: ( produc1821101996_sc_sz > produc1821101996_sc_sz ) > set_Pr1169339874_sc_sz > set_Pr1169339874_sc_sz ).
thf(func_def_120,type,
image_386905412real_c: ( produc1821101996_sc_sz > produc190496183real_c ) > set_Pr1169339874_sc_sz > set_Pr1389752855real_c ).
thf(func_def_121,type,
image_904562809t_unit: ( produc1821101996_sc_sz > produc999471430t_unit ) > set_Pr1169339874_sc_sz > set_Pr2041213564t_unit ).
thf(func_def_122,type,
image_14429021real_c: ( produc190496183real_c > finite1398487019real_c ) > set_Pr1389752855real_c > set_Fi1407883041real_c ).
thf(func_def_123,type,
image_1259833374_sc_sz: ( produc190496183real_c > produc1821101996_sc_sz ) > set_Pr1389752855real_c > set_Pr1169339874_sc_sz ).
thf(func_def_124,type,
image_738229701real_c: ( produc190496183real_c > produc190496183real_c ) > set_Pr1389752855real_c > set_Pr1389752855real_c ).
thf(func_def_125,type,
image_388766773_sc_sz: ( produc190496183real_c > produc866628903_sc_sz ) > set_Pr1389752855real_c > set_Pr1774599175_sc_sz ).
thf(func_def_126,type,
image_1332486093real_c: ( produc866628903_sc_sz > finite1398487019real_c ) > set_Pr1774599175_sc_sz > set_Fi1407883041real_c ).
thf(func_def_127,type,
image_226055310_sc_sz: ( produc866628903_sc_sz > produc1821101996_sc_sz ) > set_Pr1774599175_sc_sz > set_Pr1169339874_sc_sz ).
thf(func_def_128,type,
image_1121381717real_c: ( produc866628903_sc_sz > produc190496183real_c ) > set_Pr1774599175_sc_sz > set_Pr1389752855real_c ).
thf(func_def_129,type,
image_1313166277_sc_sz: ( produc866628903_sc_sz > produc866628903_sc_sz ) > set_Pr1774599175_sc_sz > set_Pr1774599175_sc_sz ).
thf(func_def_130,type,
image_768765061real_c: ( produc866628903_sc_sz > produc640052711real_c ) > set_Pr1774599175_sc_sz > set_Pr754230471real_c ).
thf(func_def_131,type,
image_1551908392t_unit: ( produc866628903_sc_sz > produc999471430t_unit ) > set_Pr1774599175_sc_sz > set_Pr2041213564t_unit ).
thf(func_def_132,type,
image_124598413real_c: ( produc640052711real_c > finite1398487019real_c ) > set_Pr754230471real_c > set_Fi1407883041real_c ).
thf(func_def_133,type,
image_2041365445real_c: ( produc640052711real_c > produc640052711real_c ) > set_Pr754230471real_c > set_Pr754230471real_c ).
thf(func_def_134,type,
image_1269062456real_c: ( produc999471430t_unit > finite1398487019real_c ) > set_Pr2041213564t_unit > set_Fi1407883041real_c ).
thf(func_def_135,type,
image_1426741113_sc_sz: ( produc999471430t_unit > produc1821101996_sc_sz ) > set_Pr2041213564t_unit > set_Pr1169339874_sc_sz ).
thf(func_def_136,type,
static_FVF_a_b_c: formula_a_b_c > set_Sum_sum_c_c ).
thf(func_def_137,type,
static_SIGF_a_b_c: formula_a_b_c > set_Su1783761653um_b_c ).
thf(func_def_138,type,
equiv_a_b_c: formula_a_b_c > formula_a_b_c > formula_a_b_c ).
thf(func_def_139,type,
implies_a_b_c: formula_a_b_c > formula_a_b_c > formula_a_b_c ).
thf(func_def_140,type,
predic913887884_sf_sz: sc > formula_sf_sc_sz ).
thf(func_def_141,type,
p_sc_sf_sz: sc > formula_sf_sc_sz ).
thf(func_def_142,type,
member_o: $o > set_o > $o ).
thf(func_def_143,type,
member754147591t_unit: denota610675952t_unit > set_De208295462t_unit > $o ).
thf(func_def_144,type,
member1261661570real_c: finite1398487019real_c > set_Fi1407883041real_c > $o ).
thf(func_def_145,type,
member1057565379_sc_sz: produc1821101996_sc_sz > set_Pr1169339874_sc_sz > $o ).
thf(func_def_146,type,
member1895684704real_c: produc190496183real_c > set_Pr1389752855real_c > $o ).
thf(func_def_147,type,
member630771088eal_sz: produc1149990247eal_sz > set_Pr60491591eal_sz > $o ).
thf(func_def_148,type,
member245028432_sc_sz: produc866628903_sc_sz > set_Pr1774599175_sc_sz > $o ).
thf(func_def_149,type,
member346808080real_c: produc640052711real_c > set_Pr754230471real_c > $o ).
thf(func_def_150,type,
member235934813t_unit: produc999471430t_unit > set_Pr2041213564t_unit > $o ).
thf(func_def_151,type,
phi: formula_a_b_c ).
thf(func_def_171,type,
sK0: denota231621370t_unit ).
thf(func_def_172,type,
sK1: produc190496183real_c ).
thf(func_def_173,type,
sK2: denota231621370t_unit ).
thf(func_def_174,type,
sK3: produc190496183real_c ).
thf(func_def_175,type,
sK4: produc190496183real_c ).
thf(func_def_176,type,
sK5: produc190496183real_c ).
thf(func_def_177,type,
sK6: denota231621370t_unit ).
thf(func_def_178,type,
sK7: denota231621370t_unit ).
thf(f1504,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f970,f987,f996,f1005,f1006,f1011,f1012,f1013,f1017,f1023,f1024,f1025,f1026,f1027,f1032,f1033,f1034,f1035,f1071,f1169,f1190,f1432,f1439,f1443,f1484,f1500,f1503]) ).
thf(f1503,plain,
( spl8_10
| ~ spl8_1
| ~ spl8_9
| ~ spl8_12
| ~ spl8_14 ),
inference(avatar_split_clause,[status(thm)],[f1502,f1029,f1015,f998,f963,f1002]) ).
thf(f1002,definition,
( spl8_10
<=> ( ( member1895684704real_c @ sK1 @ ( denota968303861_a_b_c @ sK0 @ phi ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl8_10])],[avatar_definition]) ).
thf(f963,definition,
( spl8_1
<=> ( ( denota1997846518gree_c @ sK1 @ sK3 @ ( static_FVF_a_b_c @ phi ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl8_1])],[avatar_definition]) ).
thf(f998,definition,
( spl8_9
<=> ( $false
= ( member1895684704real_c @ sK3 @ ( denota968303861_a_b_c @ sK2 @ phi ) ) ) ),
introduced(definition,[new_symbols(naming,[spl8_9])],[avatar_definition]) ).
thf(f1015,definition,
( spl8_12
<=> ! [X13: produc190496183real_c,X14: denota231621370t_unit,X12: produc190496183real_c,X15: denota231621370t_unit] :
( ( ( denota69106024_a_b_c @ X15 @ X14 @ ( static_SIGF_a_b_c @ phi ) )
!= $true )
| ( ( denota1997846518gree_c @ X13 @ X12 @ ( static_FVF_a_b_c @ phi ) )
!= $true )
| ( $false
= ( member1895684704real_c @ X13 @ ( denota968303861_a_b_c @ X15 @ phi ) ) )
| ( $true
= ( member1895684704real_c @ X12 @ ( denota968303861_a_b_c @ X14 @ phi ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl8_12])],[avatar_definition]) ).
thf(f1029,definition,
( spl8_14
<=> ( $true
= ( denota69106024_a_b_c @ sK0 @ sK2 @ ( static_SIGF_a_b_c @ phi ) ) ) ),
introduced(definition,[new_symbols(naming,[spl8_14])],[avatar_definition]) ).
thf(f1502,plain,
( ( ( member1895684704real_c @ sK1 @ ( denota968303861_a_b_c @ sK0 @ phi ) )
= $false )
| ~ spl8_1
| ~ spl8_9
| ~ spl8_12
| ~ spl8_14 ),
inference(trivial_inequality_removal,[status(thm)],[f1501]) ).
thf(f1501,plain,
( ( ( member1895684704real_c @ sK1 @ ( denota968303861_a_b_c @ sK0 @ phi ) )
= $false )
| ( $false = $true )
| ~ spl8_1
| ~ spl8_9
| ~ spl8_12
| ~ spl8_14 ),
inference(forward_demodulation,[status(thm)],[f1464,f1000]) ).
thf(f1000,plain,
( ( $false
= ( member1895684704real_c @ sK3 @ ( denota968303861_a_b_c @ sK2 @ phi ) ) )
| ~ spl8_9 ),
inference(avatar_component_clause,[status(thm)],[f998]) ).
thf(f1464,plain,
( ( ( member1895684704real_c @ sK3 @ ( denota968303861_a_b_c @ sK2 @ phi ) )
= $true )
| ( ( member1895684704real_c @ sK1 @ ( denota968303861_a_b_c @ sK0 @ phi ) )
= $false )
| ~ spl8_1
| ~ spl8_12
| ~ spl8_14 ),
inference(trivial_inequality_removal,[status(thm)],[f1457]) ).
thf(f1457,plain,
( ( ( member1895684704real_c @ sK1 @ ( denota968303861_a_b_c @ sK0 @ phi ) )
= $false )
| ( ( member1895684704real_c @ sK3 @ ( denota968303861_a_b_c @ sK2 @ phi ) )
= $true )
| ( $true != $true )
| ~ spl8_1
| ~ spl8_12
| ~ spl8_14 ),
inference(superposition,[status(thm)],[f1200,f1031]) ).
thf(f1031,plain,
( ( $true
= ( denota69106024_a_b_c @ sK0 @ sK2 @ ( static_SIGF_a_b_c @ phi ) ) )
| ~ spl8_14 ),
inference(avatar_component_clause,[status(thm)],[f1029]) ).
thf(f1200,plain,
( ! [X0: denota231621370t_unit,X1: denota231621370t_unit] :
( ( $true
!= ( denota69106024_a_b_c @ X0 @ X1 @ ( static_SIGF_a_b_c @ phi ) ) )
| ( ( member1895684704real_c @ sK3 @ ( denota968303861_a_b_c @ X1 @ phi ) )
= $true )
| ( ( member1895684704real_c @ sK1 @ ( denota968303861_a_b_c @ X0 @ phi ) )
= $false ) )
| ~ spl8_1
| ~ spl8_12 ),
inference(trivial_inequality_removal,[status(thm)],[f1199]) ).
thf(f1199,plain,
( ! [X0: denota231621370t_unit,X1: denota231621370t_unit] :
( ( $true
!= ( denota69106024_a_b_c @ X0 @ X1 @ ( static_SIGF_a_b_c @ phi ) ) )
| ( ( member1895684704real_c @ sK1 @ ( denota968303861_a_b_c @ X0 @ phi ) )
= $false )
| ( $true != $true )
| ( ( member1895684704real_c @ sK3 @ ( denota968303861_a_b_c @ X1 @ phi ) )
= $true ) )
| ~ spl8_1
| ~ spl8_12 ),
inference(superposition,[status(thm)],[f1016,f965]) ).
thf(f965,plain,
( ( ( denota1997846518gree_c @ sK1 @ sK3 @ ( static_FVF_a_b_c @ phi ) )
= $true )
| ~ spl8_1 ),
inference(avatar_component_clause,[status(thm)],[f963]) ).
thf(f1016,plain,
( ! [X14: denota231621370t_unit,X15: denota231621370t_unit,X12: produc190496183real_c,X13: produc190496183real_c] :
( ( ( denota1997846518gree_c @ X13 @ X12 @ ( static_FVF_a_b_c @ phi ) )
!= $true )
| ( ( denota69106024_a_b_c @ X15 @ X14 @ ( static_SIGF_a_b_c @ phi ) )
!= $true )
| ( $true
= ( member1895684704real_c @ X12 @ ( denota968303861_a_b_c @ X14 @ phi ) ) )
| ( $false
= ( member1895684704real_c @ X13 @ ( denota968303861_a_b_c @ X15 @ phi ) ) ) )
| ~ spl8_12 ),
inference(avatar_component_clause,[status(thm)],[f1015]) ).
thf(f1500,plain,
( ~ spl8_5
| ~ spl8_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f1499]) ).
thf(f1499,plain,
( $false
| ~ spl8_5
| ~ spl8_10 ),
inference(trivial_inequality_removal,[status(thm)],[f1498]) ).
thf(f1498,plain,
( ( $false = $true )
| ~ spl8_5
| ~ spl8_10 ),
inference(forward_demodulation,[status(thm)],[f982,f1004]) ).
thf(f1004,plain,
( ( ( member1895684704real_c @ sK1 @ ( denota968303861_a_b_c @ sK0 @ phi ) )
= $false )
| ~ spl8_10 ),
inference(avatar_component_clause,[status(thm)],[f1002]) ).
thf(f982,plain,
( ( ( member1895684704real_c @ sK1 @ ( denota968303861_a_b_c @ sK0 @ phi ) )
= $true )
| ~ spl8_5 ),
inference(avatar_component_clause,[status(thm)],[f980]) ).
thf(f980,definition,
( spl8_5
<=> ( ( member1895684704real_c @ sK1 @ ( denota968303861_a_b_c @ sK0 @ phi ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl8_5])],[avatar_definition]) ).
thf(f1484,plain,
( ~ spl8_4
| ~ spl8_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f1483]) ).
thf(f1483,plain,
( $false
| ~ spl8_4
| ~ spl8_9 ),
inference(trivial_inequality_removal,[status(thm)],[f1465]) ).
thf(f1465,plain,
( ( $false = $true )
| ~ spl8_4
| ~ spl8_9 ),
inference(superposition,[status(thm)],[f1000,f978]) ).
thf(f978,plain,
( ( ( member1895684704real_c @ sK3 @ ( denota968303861_a_b_c @ sK2 @ phi ) )
= $true )
| ~ spl8_4 ),
inference(avatar_component_clause,[status(thm)],[f976]) ).
thf(f976,definition,
( spl8_4
<=> ( ( member1895684704real_c @ sK3 @ ( denota968303861_a_b_c @ sK2 @ phi ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl8_4])],[avatar_definition]) ).
thf(f1443,plain,
( ~ spl8_2
| spl8_7
| ~ spl8_8
| ~ spl8_11
| ~ spl8_13 ),
inference(avatar_contradiction_clause,[status(thm)],[f1442]) ).
thf(f1442,plain,
( $false
| ~ spl8_2
| spl8_7
| ~ spl8_8
| ~ spl8_11
| ~ spl8_13 ),
inference(trivial_inequality_removal,[status(thm)],[f1441]) ).
thf(f1441,plain,
( ( $false = $true )
| ~ spl8_2
| spl8_7
| ~ spl8_8
| ~ spl8_11
| ~ spl8_13 ),
inference(forward_demodulation,[status(thm)],[f1440,f995]) ).
thf(f995,plain,
( ( $false
= ( member1895684704real_c @ sK5 @ ( denota968303861_a_b_c @ sK7 @ phi ) ) )
| ~ spl8_8 ),
inference(avatar_component_clause,[status(thm)],[f993]) ).
thf(f993,definition,
( spl8_8
<=> ( $false
= ( member1895684704real_c @ sK5 @ ( denota968303861_a_b_c @ sK7 @ phi ) ) ) ),
introduced(definition,[new_symbols(naming,[spl8_8])],[avatar_definition]) ).
thf(f1440,plain,
( ( $true
= ( member1895684704real_c @ sK5 @ ( denota968303861_a_b_c @ sK7 @ phi ) ) )
| ~ spl8_2
| spl8_7
| ~ spl8_11
| ~ spl8_13 ),
inference(subsumption_resolution,[status(thm)],[f1345,f990]) ).
thf(f990,plain,
( ( $false
!= ( member1895684704real_c @ sK4 @ ( denota968303861_a_b_c @ sK6 @ phi ) ) )
| spl8_7 ),
inference(avatar_component_clause,[status(thm)],[f989]) ).
thf(f989,definition,
( spl8_7
<=> ( $false
= ( member1895684704real_c @ sK4 @ ( denota968303861_a_b_c @ sK6 @ phi ) ) ) ),
introduced(definition,[new_symbols(naming,[spl8_7])],[avatar_definition]) ).
thf(f1345,plain,
( ( $true
= ( member1895684704real_c @ sK5 @ ( denota968303861_a_b_c @ sK7 @ phi ) ) )
| ( $false
= ( member1895684704real_c @ sK4 @ ( denota968303861_a_b_c @ sK6 @ phi ) ) )
| ~ spl8_2
| ~ spl8_11
| ~ spl8_13 ),
inference(trivial_inequality_removal,[status(thm)],[f1344]) ).
thf(f1344,plain,
( ( $true != $true )
| ( $false
= ( member1895684704real_c @ sK4 @ ( denota968303861_a_b_c @ sK6 @ phi ) ) )
| ( $true
= ( member1895684704real_c @ sK5 @ ( denota968303861_a_b_c @ sK7 @ phi ) ) )
| ~ spl8_2
| ~ spl8_11
| ~ spl8_13 ),
inference(superposition,[status(thm)],[f1152,f1010]) ).
thf(f1010,plain,
( ( $true
= ( denota1997846518gree_c @ sK5 @ sK4 @ ( static_FVF_a_b_c @ phi ) ) )
| ~ spl8_11 ),
inference(avatar_component_clause,[status(thm)],[f1008]) ).
thf(f1008,definition,
( spl8_11
<=> ( $true
= ( denota1997846518gree_c @ sK5 @ sK4 @ ( static_FVF_a_b_c @ phi ) ) ) ),
introduced(definition,[new_symbols(naming,[spl8_11])],[avatar_definition]) ).
thf(f1152,plain,
( ! [X0: produc190496183real_c,X1: produc190496183real_c] :
( ( $true
!= ( denota1997846518gree_c @ X0 @ X1 @ ( static_FVF_a_b_c @ phi ) ) )
| ( $true
= ( member1895684704real_c @ X0 @ ( denota968303861_a_b_c @ sK7 @ phi ) ) )
| ( ( member1895684704real_c @ X1 @ ( denota968303861_a_b_c @ sK6 @ phi ) )
= $false ) )
| ~ spl8_2
| ~ spl8_13 ),
inference(trivial_inequality_removal,[status(thm)],[f1151]) ).
thf(f1151,plain,
( ! [X0: produc190496183real_c,X1: produc190496183real_c] :
( ( $true
= ( member1895684704real_c @ X0 @ ( denota968303861_a_b_c @ sK7 @ phi ) ) )
| ( ( member1895684704real_c @ X1 @ ( denota968303861_a_b_c @ sK6 @ phi ) )
= $false )
| ( $true
!= ( denota1997846518gree_c @ X0 @ X1 @ ( static_FVF_a_b_c @ phi ) ) )
| ( $true != $true ) )
| ~ spl8_2
| ~ spl8_13 ),
inference(superposition,[status(thm)],[f1020,f969]) ).
thf(f969,plain,
( ( $true
= ( denota69106024_a_b_c @ sK7 @ sK6 @ ( static_SIGF_a_b_c @ phi ) ) )
| ~ spl8_2 ),
inference(avatar_component_clause,[status(thm)],[f967]) ).
thf(f967,definition,
( spl8_2
<=> ( $true
= ( denota69106024_a_b_c @ sK7 @ sK6 @ ( static_SIGF_a_b_c @ phi ) ) ) ),
introduced(definition,[new_symbols(naming,[spl8_2])],[avatar_definition]) ).
thf(f1020,plain,
( ! [X10: denota231621370t_unit,X11: produc190496183real_c,X8: denota231621370t_unit,X9: produc190496183real_c] :
( ( $true
!= ( denota69106024_a_b_c @ X8 @ X10 @ ( static_SIGF_a_b_c @ phi ) ) )
| ( ( denota1997846518gree_c @ X9 @ X11 @ ( static_FVF_a_b_c @ phi ) )
!= $true )
| ( ( member1895684704real_c @ X9 @ ( denota968303861_a_b_c @ X8 @ phi ) )
= $true )
| ( ( member1895684704real_c @ X11 @ ( denota968303861_a_b_c @ X10 @ phi ) )
= $false ) )
| ~ spl8_13 ),
inference(avatar_component_clause,[status(thm)],[f1019]) ).
thf(f1019,definition,
( spl8_13
<=> ! [X10: denota231621370t_unit,X11: produc190496183real_c,X9: produc190496183real_c,X8: denota231621370t_unit] :
( ( ( denota1997846518gree_c @ X9 @ X11 @ ( static_FVF_a_b_c @ phi ) )
!= $true )
| ( ( member1895684704real_c @ X9 @ ( denota968303861_a_b_c @ X8 @ phi ) )
= $true )
| ( ( member1895684704real_c @ X11 @ ( denota968303861_a_b_c @ X10 @ phi ) )
= $false )
| ( $true
!= ( denota69106024_a_b_c @ X8 @ X10 @ ( static_SIGF_a_b_c @ phi ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl8_13])],[avatar_definition]) ).
thf(f1439,plain,
( ~ spl8_2
| ~ spl8_3
| ~ spl8_8
| ~ spl8_11
| ~ spl8_13 ),
inference(avatar_contradiction_clause,[status(thm)],[f1438]) ).
thf(f1438,plain,
( $false
| ~ spl8_2
| ~ spl8_3
| ~ spl8_8
| ~ spl8_11
| ~ spl8_13 ),
inference(trivial_inequality_removal,[status(thm)],[f1437]) ).
thf(f1437,plain,
( ( $false = $true )
| ~ spl8_2
| ~ spl8_3
| ~ spl8_8
| ~ spl8_11
| ~ spl8_13 ),
inference(forward_demodulation,[status(thm)],[f1436,f995]) ).
thf(f1436,plain,
( ( $true
= ( member1895684704real_c @ sK5 @ ( denota968303861_a_b_c @ sK7 @ phi ) ) )
| ~ spl8_2
| ~ spl8_3
| ~ spl8_11
| ~ spl8_13 ),
inference(trivial_inequality_removal,[status(thm)],[f1435]) ).
thf(f1435,plain,
( ( $true
= ( member1895684704real_c @ sK5 @ ( denota968303861_a_b_c @ sK7 @ phi ) ) )
| ( $false = $true )
| ~ spl8_2
| ~ spl8_3
| ~ spl8_11
| ~ spl8_13 ),
inference(forward_demodulation,[status(thm)],[f1345,f974]) ).
thf(f974,plain,
( ( $true
= ( member1895684704real_c @ sK4 @ ( denota968303861_a_b_c @ sK6 @ phi ) ) )
| ~ spl8_3 ),
inference(avatar_component_clause,[status(thm)],[f972]) ).
thf(f972,definition,
( spl8_3
<=> ( $true
= ( member1895684704real_c @ sK4 @ ( denota968303861_a_b_c @ sK6 @ phi ) ) ) ),
introduced(definition,[new_symbols(naming,[spl8_3])],[avatar_definition]) ).
thf(f1432,plain,
( spl8_9
| ~ spl8_1
| ~ spl8_10
| ~ spl8_13
| ~ spl8_14 ),
inference(avatar_split_clause,[status(thm)],[f1431,f1029,f1019,f1002,f963,f998]) ).
thf(f1431,plain,
( ( $false
= ( member1895684704real_c @ sK3 @ ( denota968303861_a_b_c @ sK2 @ phi ) ) )
| ~ spl8_1
| ~ spl8_10
| ~ spl8_13
| ~ spl8_14 ),
inference(trivial_inequality_removal,[status(thm)],[f1430]) ).
thf(f1430,plain,
( ( $false
= ( member1895684704real_c @ sK3 @ ( denota968303861_a_b_c @ sK2 @ phi ) ) )
| ( $false = $true )
| ~ spl8_1
| ~ spl8_10
| ~ spl8_13
| ~ spl8_14 ),
inference(forward_demodulation,[status(thm)],[f1429,f1004]) ).
thf(f1429,plain,
( ( ( member1895684704real_c @ sK1 @ ( denota968303861_a_b_c @ sK0 @ phi ) )
= $true )
| ( $false
= ( member1895684704real_c @ sK3 @ ( denota968303861_a_b_c @ sK2 @ phi ) ) )
| ~ spl8_1
| ~ spl8_13
| ~ spl8_14 ),
inference(trivial_inequality_removal,[status(thm)],[f1424]) ).
thf(f1424,plain,
( ( $true != $true )
| ( ( member1895684704real_c @ sK1 @ ( denota968303861_a_b_c @ sK0 @ phi ) )
= $true )
| ( $false
= ( member1895684704real_c @ sK3 @ ( denota968303861_a_b_c @ sK2 @ phi ) ) )
| ~ spl8_1
| ~ spl8_13
| ~ spl8_14 ),
inference(superposition,[status(thm)],[f1218,f965]) ).
thf(f1218,plain,
( ! [X0: produc190496183real_c,X1: produc190496183real_c] :
( ( $true
!= ( denota1997846518gree_c @ X0 @ X1 @ ( static_FVF_a_b_c @ phi ) ) )
| ( ( member1895684704real_c @ X0 @ ( denota968303861_a_b_c @ sK0 @ phi ) )
= $true )
| ( ( member1895684704real_c @ X1 @ ( denota968303861_a_b_c @ sK2 @ phi ) )
= $false ) )
| ~ spl8_13
| ~ spl8_14 ),
inference(trivial_inequality_removal,[status(thm)],[f1217]) ).
thf(f1217,plain,
( ! [X0: produc190496183real_c,X1: produc190496183real_c] :
( ( $true != $true )
| ( $true
!= ( denota1997846518gree_c @ X0 @ X1 @ ( static_FVF_a_b_c @ phi ) ) )
| ( ( member1895684704real_c @ X0 @ ( denota968303861_a_b_c @ sK0 @ phi ) )
= $true )
| ( ( member1895684704real_c @ X1 @ ( denota968303861_a_b_c @ sK2 @ phi ) )
= $false ) )
| ~ spl8_13
| ~ spl8_14 ),
inference(superposition,[status(thm)],[f1020,f1031]) ).
thf(f1190,plain,
( ~ spl8_6
| ~ spl8_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f1189]) ).
thf(f1189,plain,
( $false
| ~ spl8_6
| ~ spl8_8 ),
inference(trivial_inequality_removal,[status(thm)],[f1175]) ).
thf(f1175,plain,
( ( $false = $true )
| ~ spl8_6
| ~ spl8_8 ),
inference(superposition,[status(thm)],[f986,f995]) ).
thf(f986,plain,
( ( $true
= ( member1895684704real_c @ sK5 @ ( denota968303861_a_b_c @ sK7 @ phi ) ) )
| ~ spl8_6 ),
inference(avatar_component_clause,[status(thm)],[f984]) ).
thf(f984,definition,
( spl8_6
<=> ( $true
= ( member1895684704real_c @ sK5 @ ( denota968303861_a_b_c @ sK7 @ phi ) ) ) ),
introduced(definition,[new_symbols(naming,[spl8_6])],[avatar_definition]) ).
thf(f1169,plain,
( spl8_8
| ~ spl8_2
| ~ spl8_7
| ~ spl8_11
| ~ spl8_12 ),
inference(avatar_split_clause,[status(thm)],[f1168,f1015,f1008,f989,f967,f993]) ).
thf(f1168,plain,
( ( $false
= ( member1895684704real_c @ sK5 @ ( denota968303861_a_b_c @ sK7 @ phi ) ) )
| ~ spl8_2
| ~ spl8_7
| ~ spl8_11
| ~ spl8_12 ),
inference(trivial_inequality_removal,[status(thm)],[f1167]) ).
thf(f1167,plain,
( ( $false = $true )
| ( $false
= ( member1895684704real_c @ sK5 @ ( denota968303861_a_b_c @ sK7 @ phi ) ) )
| ~ spl8_2
| ~ spl8_7
| ~ spl8_11
| ~ spl8_12 ),
inference(forward_demodulation,[status(thm)],[f1164,f991]) ).
thf(f991,plain,
( ( $false
= ( member1895684704real_c @ sK4 @ ( denota968303861_a_b_c @ sK6 @ phi ) ) )
| ~ spl8_7 ),
inference(avatar_component_clause,[status(thm)],[f989]) ).
thf(f1164,plain,
( ( $false
= ( member1895684704real_c @ sK5 @ ( denota968303861_a_b_c @ sK7 @ phi ) ) )
| ( $true
= ( member1895684704real_c @ sK4 @ ( denota968303861_a_b_c @ sK6 @ phi ) ) )
| ~ spl8_2
| ~ spl8_11
| ~ spl8_12 ),
inference(trivial_inequality_removal,[status(thm)],[f1163]) ).
thf(f1163,plain,
( ( $true
= ( member1895684704real_c @ sK4 @ ( denota968303861_a_b_c @ sK6 @ phi ) ) )
| ( $true != $true )
| ( $false
= ( member1895684704real_c @ sK5 @ ( denota968303861_a_b_c @ sK7 @ phi ) ) )
| ~ spl8_2
| ~ spl8_11
| ~ spl8_12 ),
inference(superposition,[status(thm)],[f1137,f969]) ).
thf(f1137,plain,
( ! [X0: denota231621370t_unit,X1: denota231621370t_unit] :
( ( $true
!= ( denota69106024_a_b_c @ X0 @ X1 @ ( static_SIGF_a_b_c @ phi ) ) )
| ( $false
= ( member1895684704real_c @ sK5 @ ( denota968303861_a_b_c @ X0 @ phi ) ) )
| ( ( member1895684704real_c @ sK4 @ ( denota968303861_a_b_c @ X1 @ phi ) )
= $true ) )
| ~ spl8_11
| ~ spl8_12 ),
inference(trivial_inequality_removal,[status(thm)],[f1135]) ).
thf(f1135,plain,
( ! [X0: denota231621370t_unit,X1: denota231621370t_unit] :
( ( $true
!= ( denota69106024_a_b_c @ X0 @ X1 @ ( static_SIGF_a_b_c @ phi ) ) )
| ( ( member1895684704real_c @ sK4 @ ( denota968303861_a_b_c @ X1 @ phi ) )
= $true )
| ( $false
= ( member1895684704real_c @ sK5 @ ( denota968303861_a_b_c @ X0 @ phi ) ) )
| ( $true != $true ) )
| ~ spl8_11
| ~ spl8_12 ),
inference(superposition,[status(thm)],[f1016,f1010]) ).
thf(f1071,plain,
( ~ spl8_3
| ~ spl8_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f1070]) ).
thf(f1070,plain,
( $false
| ~ spl8_3
| ~ spl8_7 ),
inference(trivial_inequality_removal,[status(thm)],[f1050]) ).
thf(f1050,plain,
( ( $false = $true )
| ~ spl8_3
| ~ spl8_7 ),
inference(superposition,[status(thm)],[f991,f974]) ).
thf(f1035,plain,
( spl8_8
| spl8_14
| spl8_7 ),
inference(avatar_split_clause,[status(thm)],[f943,f989,f1029,f993]) ).
thf(f943,plain,
( ( $false
= ( member1895684704real_c @ sK4 @ ( denota968303861_a_b_c @ sK6 @ phi ) ) )
| ( $false
= ( member1895684704real_c @ sK5 @ ( denota968303861_a_b_c @ sK7 @ phi ) ) )
| ( $true
= ( denota69106024_a_b_c @ sK0 @ sK2 @ ( static_SIGF_a_b_c @ phi ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f927]) ).
thf(f927,plain,
( ( ( member1895684704real_c @ sK5 @ ( denota968303861_a_b_c @ sK7 @ phi ) )
!= ( member1895684704real_c @ sK4 @ ( denota968303861_a_b_c @ sK6 @ phi ) ) )
| ( $true
= ( denota69106024_a_b_c @ sK0 @ sK2 @ ( static_SIGF_a_b_c @ phi ) ) ) ),
inference(cnf_transformation,[status(thm)],[f919]) ).
thf(f919,plain,
( ( ( ( ( denota1997846518gree_c @ sK1 @ sK3 @ ( static_FVF_a_b_c @ phi ) )
= $true )
& ( ( member1895684704real_c @ sK1 @ ( denota968303861_a_b_c @ sK0 @ phi ) )
!= ( member1895684704real_c @ sK3 @ ( denota968303861_a_b_c @ sK2 @ phi ) ) )
& ( $true
= ( denota69106024_a_b_c @ sK0 @ sK2 @ ( static_SIGF_a_b_c @ phi ) ) ) )
| ( ( $true
= ( denota1997846518gree_c @ sK5 @ sK4 @ ( static_FVF_a_b_c @ phi ) ) )
& ( ( member1895684704real_c @ sK5 @ ( denota968303861_a_b_c @ sK7 @ phi ) )
!= ( member1895684704real_c @ sK4 @ ( denota968303861_a_b_c @ sK6 @ phi ) ) )
& ( $true
= ( denota69106024_a_b_c @ sK7 @ sK6 @ ( static_SIGF_a_b_c @ phi ) ) ) ) )
& ( ! [X8: denota231621370t_unit,X9: produc190496183real_c,X10: denota231621370t_unit,X11: produc190496183real_c] :
( ( ( denota1997846518gree_c @ X9 @ X11 @ ( static_FVF_a_b_c @ phi ) )
!= $true )
| ( ( member1895684704real_c @ X11 @ ( denota968303861_a_b_c @ X10 @ phi ) )
= ( member1895684704real_c @ X9 @ ( denota968303861_a_b_c @ X8 @ phi ) ) )
| ( $true
!= ( denota69106024_a_b_c @ X8 @ X10 @ ( static_SIGF_a_b_c @ phi ) ) ) )
| ! [X12: produc190496183real_c,X13: produc190496183real_c,X14: denota231621370t_unit,X15: denota231621370t_unit] :
( ( ( denota1997846518gree_c @ X13 @ X12 @ ( static_FVF_a_b_c @ phi ) )
!= $true )
| ( ( member1895684704real_c @ X12 @ ( denota968303861_a_b_c @ X14 @ phi ) )
= ( member1895684704real_c @ X13 @ ( denota968303861_a_b_c @ X15 @ phi ) ) )
| ( ( denota69106024_a_b_c @ X15 @ X14 @ ( static_SIGF_a_b_c @ phi ) )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7])],[f916,f918,f917]) ).
thf(f917,plain,
( ? [X0: denota231621370t_unit,X1: produc190496183real_c,X2: denota231621370t_unit,X3: produc190496183real_c] :
( ( ( denota1997846518gree_c @ X1 @ X3 @ ( static_FVF_a_b_c @ phi ) )
= $true )
& ( ( member1895684704real_c @ X1 @ ( denota968303861_a_b_c @ X0 @ phi ) )
!= ( member1895684704real_c @ X3 @ ( denota968303861_a_b_c @ X2 @ phi ) ) )
& ( $true
= ( denota69106024_a_b_c @ X0 @ X2 @ ( static_SIGF_a_b_c @ phi ) ) ) )
=> ( ( ( denota1997846518gree_c @ sK1 @ sK3 @ ( static_FVF_a_b_c @ phi ) )
= $true )
& ( ( member1895684704real_c @ sK1 @ ( denota968303861_a_b_c @ sK0 @ phi ) )
!= ( member1895684704real_c @ sK3 @ ( denota968303861_a_b_c @ sK2 @ phi ) ) )
& ( $true
= ( denota69106024_a_b_c @ sK0 @ sK2 @ ( static_SIGF_a_b_c @ phi ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f918,plain,
( ? [X4: produc190496183real_c,X5: produc190496183real_c,X6: denota231621370t_unit,X7: denota231621370t_unit] :
( ( $true
= ( denota1997846518gree_c @ X5 @ X4 @ ( static_FVF_a_b_c @ phi ) ) )
& ( ( member1895684704real_c @ X4 @ ( denota968303861_a_b_c @ X6 @ phi ) )
!= ( member1895684704real_c @ X5 @ ( denota968303861_a_b_c @ X7 @ phi ) ) )
& ( $true
= ( denota69106024_a_b_c @ X7 @ X6 @ ( static_SIGF_a_b_c @ phi ) ) ) )
=> ( ( $true
= ( denota1997846518gree_c @ sK5 @ sK4 @ ( static_FVF_a_b_c @ phi ) ) )
& ( ( member1895684704real_c @ sK5 @ ( denota968303861_a_b_c @ sK7 @ phi ) )
!= ( member1895684704real_c @ sK4 @ ( denota968303861_a_b_c @ sK6 @ phi ) ) )
& ( $true
= ( denota69106024_a_b_c @ sK7 @ sK6 @ ( static_SIGF_a_b_c @ phi ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f916,plain,
( ( ? [X0: denota231621370t_unit,X1: produc190496183real_c,X2: denota231621370t_unit,X3: produc190496183real_c] :
( ( ( denota1997846518gree_c @ X1 @ X3 @ ( static_FVF_a_b_c @ phi ) )
= $true )
& ( ( member1895684704real_c @ X1 @ ( denota968303861_a_b_c @ X0 @ phi ) )
!= ( member1895684704real_c @ X3 @ ( denota968303861_a_b_c @ X2 @ phi ) ) )
& ( $true
= ( denota69106024_a_b_c @ X0 @ X2 @ ( static_SIGF_a_b_c @ phi ) ) ) )
| ? [X4: produc190496183real_c,X5: produc190496183real_c,X6: denota231621370t_unit,X7: denota231621370t_unit] :
( ( $true
= ( denota1997846518gree_c @ X5 @ X4 @ ( static_FVF_a_b_c @ phi ) ) )
& ( ( member1895684704real_c @ X4 @ ( denota968303861_a_b_c @ X6 @ phi ) )
!= ( member1895684704real_c @ X5 @ ( denota968303861_a_b_c @ X7 @ phi ) ) )
& ( $true
= ( denota69106024_a_b_c @ X7 @ X6 @ ( static_SIGF_a_b_c @ phi ) ) ) ) )
& ( ! [X8: denota231621370t_unit,X9: produc190496183real_c,X10: denota231621370t_unit,X11: produc190496183real_c] :
( ( ( denota1997846518gree_c @ X9 @ X11 @ ( static_FVF_a_b_c @ phi ) )
!= $true )
| ( ( member1895684704real_c @ X11 @ ( denota968303861_a_b_c @ X10 @ phi ) )
= ( member1895684704real_c @ X9 @ ( denota968303861_a_b_c @ X8 @ phi ) ) )
| ( $true
!= ( denota69106024_a_b_c @ X8 @ X10 @ ( static_SIGF_a_b_c @ phi ) ) ) )
| ! [X12: produc190496183real_c,X13: produc190496183real_c,X14: denota231621370t_unit,X15: denota231621370t_unit] :
( ( ( denota1997846518gree_c @ X13 @ X12 @ ( static_FVF_a_b_c @ phi ) )
!= $true )
| ( ( member1895684704real_c @ X12 @ ( denota968303861_a_b_c @ X14 @ phi ) )
= ( member1895684704real_c @ X13 @ ( denota968303861_a_b_c @ X15 @ phi ) ) )
| ( ( denota69106024_a_b_c @ X15 @ X14 @ ( static_SIGF_a_b_c @ phi ) )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f915]) ).
thf(f915,plain,
( ( ? [X4: denota231621370t_unit,X5: produc190496183real_c,X6: denota231621370t_unit,X7: produc190496183real_c] :
( ( ( denota1997846518gree_c @ X5 @ X7 @ ( static_FVF_a_b_c @ phi ) )
= $true )
& ( ( member1895684704real_c @ X5 @ ( denota968303861_a_b_c @ X4 @ phi ) )
!= ( member1895684704real_c @ X7 @ ( denota968303861_a_b_c @ X6 @ phi ) ) )
& ( $true
= ( denota69106024_a_b_c @ X4 @ X6 @ ( static_SIGF_a_b_c @ phi ) ) ) )
| ? [X0: produc190496183real_c,X1: produc190496183real_c,X2: denota231621370t_unit,X3: denota231621370t_unit] :
( ( $true
= ( denota1997846518gree_c @ X1 @ X0 @ ( static_FVF_a_b_c @ phi ) ) )
& ( ( member1895684704real_c @ X1 @ ( denota968303861_a_b_c @ X3 @ phi ) )
!= ( member1895684704real_c @ X0 @ ( denota968303861_a_b_c @ X2 @ phi ) ) )
& ( ( denota69106024_a_b_c @ X3 @ X2 @ ( static_SIGF_a_b_c @ phi ) )
= $true ) ) )
& ( ! [X4: denota231621370t_unit,X5: produc190496183real_c,X6: denota231621370t_unit,X7: produc190496183real_c] :
( ( ( denota1997846518gree_c @ X5 @ X7 @ ( static_FVF_a_b_c @ phi ) )
!= $true )
| ( ( member1895684704real_c @ X5 @ ( denota968303861_a_b_c @ X4 @ phi ) )
= ( member1895684704real_c @ X7 @ ( denota968303861_a_b_c @ X6 @ phi ) ) )
| ( $true
!= ( denota69106024_a_b_c @ X4 @ X6 @ ( static_SIGF_a_b_c @ phi ) ) ) )
| ! [X0: produc190496183real_c,X1: produc190496183real_c,X2: denota231621370t_unit,X3: denota231621370t_unit] :
( ( $true
!= ( denota1997846518gree_c @ X1 @ X0 @ ( static_FVF_a_b_c @ phi ) ) )
| ( ( member1895684704real_c @ X1 @ ( denota968303861_a_b_c @ X3 @ phi ) )
= ( member1895684704real_c @ X0 @ ( denota968303861_a_b_c @ X2 @ phi ) ) )
| ( ( denota69106024_a_b_c @ X3 @ X2 @ ( static_SIGF_a_b_c @ phi ) )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f914]) ).
thf(f914,plain,
( ! [X0: produc190496183real_c,X1: produc190496183real_c,X2: denota231621370t_unit,X3: denota231621370t_unit] :
( ( $true
!= ( denota1997846518gree_c @ X1 @ X0 @ ( static_FVF_a_b_c @ phi ) ) )
| ( ( member1895684704real_c @ X1 @ ( denota968303861_a_b_c @ X3 @ phi ) )
= ( member1895684704real_c @ X0 @ ( denota968303861_a_b_c @ X2 @ phi ) ) )
| ( ( denota69106024_a_b_c @ X3 @ X2 @ ( static_SIGF_a_b_c @ phi ) )
!= $true ) )
<~> ! [X4: denota231621370t_unit,X5: produc190496183real_c,X6: denota231621370t_unit,X7: produc190496183real_c] :
( ( ( denota1997846518gree_c @ X5 @ X7 @ ( static_FVF_a_b_c @ phi ) )
!= $true )
| ( ( member1895684704real_c @ X5 @ ( denota968303861_a_b_c @ X4 @ phi ) )
= ( member1895684704real_c @ X7 @ ( denota968303861_a_b_c @ X6 @ phi ) ) )
| ( $true
!= ( denota69106024_a_b_c @ X4 @ X6 @ ( static_SIGF_a_b_c @ phi ) ) ) ) ),
inference(flattening,[status(thm)],[f913]) ).
thf(f913,plain,
( ! [X4: denota231621370t_unit,X5: produc190496183real_c,X6: denota231621370t_unit,X7: produc190496183real_c] :
( ( ( member1895684704real_c @ X5 @ ( denota968303861_a_b_c @ X4 @ phi ) )
= ( member1895684704real_c @ X7 @ ( denota968303861_a_b_c @ X6 @ phi ) ) )
| ( ( denota1997846518gree_c @ X5 @ X7 @ ( static_FVF_a_b_c @ phi ) )
!= $true )
| ( $true
!= ( denota69106024_a_b_c @ X4 @ X6 @ ( static_SIGF_a_b_c @ phi ) ) ) )
<~> ! [X0: produc190496183real_c,X1: produc190496183real_c,X2: denota231621370t_unit,X3: denota231621370t_unit] :
( ( ( member1895684704real_c @ X1 @ ( denota968303861_a_b_c @ X3 @ phi ) )
= ( member1895684704real_c @ X0 @ ( denota968303861_a_b_c @ X2 @ phi ) ) )
| ( $true
!= ( denota1997846518gree_c @ X1 @ X0 @ ( static_FVF_a_b_c @ phi ) ) )
| ( ( denota69106024_a_b_c @ X3 @ X2 @ ( static_SIGF_a_b_c @ phi ) )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f651]) ).
thf(f651,plain,
~ ( ! [X4: denota231621370t_unit,X5: produc190496183real_c,X6: denota231621370t_unit,X7: produc190496183real_c] :
( ( $true
= ( denota69106024_a_b_c @ X4 @ X6 @ ( static_SIGF_a_b_c @ phi ) ) )
=> ( ( ( denota1997846518gree_c @ X5 @ X7 @ ( static_FVF_a_b_c @ phi ) )
= $true )
=> ( ( member1895684704real_c @ X5 @ ( denota968303861_a_b_c @ X4 @ phi ) )
= ( member1895684704real_c @ X7 @ ( denota968303861_a_b_c @ X6 @ phi ) ) ) ) )
<=> ! [X0: produc190496183real_c,X1: produc190496183real_c,X2: denota231621370t_unit,X3: denota231621370t_unit] :
( ( ( denota69106024_a_b_c @ X3 @ X2 @ ( static_SIGF_a_b_c @ phi ) )
= $true )
=> ( ( $true
= ( denota1997846518gree_c @ X1 @ X0 @ ( static_FVF_a_b_c @ phi ) ) )
=> ( ( member1895684704real_c @ X1 @ ( denota968303861_a_b_c @ X3 @ phi ) )
= ( member1895684704real_c @ X0 @ ( denota968303861_a_b_c @ X2 @ phi ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f650]) ).
thf(f650,plain,
~ ! [X0: produc190496183real_c,X1: produc190496183real_c,X2: denota231621370t_unit,X3: denota231621370t_unit] :
( ( ( denota69106024_a_b_c @ X3 @ X2 @ ( static_SIGF_a_b_c @ phi ) )
=> ( ( denota1997846518gree_c @ X1 @ X0 @ ( static_FVF_a_b_c @ phi ) )
=> ( ( member1895684704real_c @ X1 @ ( denota968303861_a_b_c @ X3 @ phi ) )
= ( member1895684704real_c @ X0 @ ( denota968303861_a_b_c @ X2 @ phi ) ) ) ) )
= ( ! [X4: denota231621370t_unit,X5: produc190496183real_c,X6: denota231621370t_unit,X7: produc190496183real_c] :
( ( denota69106024_a_b_c @ X4 @ X6 @ ( static_SIGF_a_b_c @ phi ) )
=> ( ( denota1997846518gree_c @ X5 @ X7 @ ( static_FVF_a_b_c @ phi ) )
=> ( ( member1895684704real_c @ X5 @ ( denota968303861_a_b_c @ X4 @ phi ) )
= ( member1895684704real_c @ X7 @ ( denota968303861_a_b_c @ X6 @ phi ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f356]) ).
thf(f356,negated_conjecture,
~ ! [X2: produc190496183real_c,X1: produc190496183real_c,X4: denota231621370t_unit,X3: denota231621370t_unit] :
( ( ( denota69106024_a_b_c @ X3 @ X4 @ ( static_SIGF_a_b_c @ phi ) )
=> ( ( denota1997846518gree_c @ X1 @ X2 @ ( static_FVF_a_b_c @ phi ) )
=> ( ( member1895684704real_c @ X1 @ ( denota968303861_a_b_c @ X3 @ phi ) )
= ( member1895684704real_c @ X2 @ ( denota968303861_a_b_c @ X4 @ phi ) ) ) ) )
= ( ! [X3: denota231621370t_unit,X1: produc190496183real_c,X4: denota231621370t_unit,X2: produc190496183real_c] :
( ( denota69106024_a_b_c @ X3 @ X4 @ ( static_SIGF_a_b_c @ phi ) )
=> ( ( denota1997846518gree_c @ X1 @ X2 @ ( static_FVF_a_b_c @ phi ) )
=> ( ( member1895684704real_c @ X1 @ ( denota968303861_a_b_c @ X3 @ phi ) )
= ( member1895684704real_c @ X2 @ ( denota968303861_a_b_c @ X4 @ phi ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f355]) ).
thf(f355,conjecture,
! [X2: produc190496183real_c,X1: produc190496183real_c,X4: denota231621370t_unit,X3: denota231621370t_unit] :
( ( ( denota69106024_a_b_c @ X3 @ X4 @ ( static_SIGF_a_b_c @ phi ) )
=> ( ( denota1997846518gree_c @ X1 @ X2 @ ( static_FVF_a_b_c @ phi ) )
=> ( ( member1895684704real_c @ X1 @ ( denota968303861_a_b_c @ X3 @ phi ) )
= ( member1895684704real_c @ X2 @ ( denota968303861_a_b_c @ X4 @ phi ) ) ) ) )
= ( ! [X3: denota231621370t_unit,X1: produc190496183real_c,X4: denota231621370t_unit,X2: produc190496183real_c] :
( ( denota69106024_a_b_c @ X3 @ X4 @ ( static_SIGF_a_b_c @ phi ) )
=> ( ( denota1997846518gree_c @ X1 @ X2 @ ( static_FVF_a_b_c @ phi ) )
=> ( ( member1895684704real_c @ X1 @ ( denota968303861_a_b_c @ X3 @ phi ) )
= ( member1895684704real_c @ X2 @ ( denota968303861_a_b_c @ X4 @ phi ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.jSP0w0K04t/DTF2THF_20700.p',conj_0) ).
thf(f1034,plain,
( spl8_6
| spl8_3
| spl8_14 ),
inference(avatar_split_clause,[status(thm)],[f942,f1029,f972,f984]) ).
thf(f942,plain,
( ( $true
= ( denota69106024_a_b_c @ sK0 @ sK2 @ ( static_SIGF_a_b_c @ phi ) ) )
| ( $true
= ( member1895684704real_c @ sK4 @ ( denota968303861_a_b_c @ sK6 @ phi ) ) )
| ( $true
= ( member1895684704real_c @ sK5 @ ( denota968303861_a_b_c @ sK7 @ phi ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f927]) ).
thf(f1033,plain,
( spl8_14
| spl8_2 ),
inference(avatar_split_clause,[status(thm)],[f926,f967,f1029]) ).
thf(f926,plain,
( ( $true
= ( denota69106024_a_b_c @ sK7 @ sK6 @ ( static_SIGF_a_b_c @ phi ) ) )
| ( $true
= ( denota69106024_a_b_c @ sK0 @ sK2 @ ( static_SIGF_a_b_c @ phi ) ) ) ),
inference(cnf_transformation,[status(thm)],[f919]) ).
thf(f1032,plain,
( spl8_14
| spl8_11 ),
inference(avatar_split_clause,[status(thm)],[f928,f1008,f1029]) ).
thf(f928,plain,
( ( $true
= ( denota1997846518gree_c @ sK5 @ sK4 @ ( static_FVF_a_b_c @ phi ) ) )
| ( $true
= ( denota69106024_a_b_c @ sK0 @ sK2 @ ( static_SIGF_a_b_c @ phi ) ) ) ),
inference(cnf_transformation,[status(thm)],[f919]) ).
thf(f1027,plain,
( spl8_2
| spl8_9
| spl8_10 ),
inference(avatar_split_clause,[status(thm)],[f945,f1002,f998,f967]) ).
thf(f945,plain,
( ( $true
= ( denota69106024_a_b_c @ sK7 @ sK6 @ ( static_SIGF_a_b_c @ phi ) ) )
| ( $false
= ( member1895684704real_c @ sK3 @ ( denota968303861_a_b_c @ sK2 @ phi ) ) )
| ( ( member1895684704real_c @ sK1 @ ( denota968303861_a_b_c @ sK0 @ phi ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f929]) ).
thf(f929,plain,
( ( $true
= ( denota69106024_a_b_c @ sK7 @ sK6 @ ( static_SIGF_a_b_c @ phi ) ) )
| ( ( member1895684704real_c @ sK1 @ ( denota968303861_a_b_c @ sK0 @ phi ) )
!= ( member1895684704real_c @ sK3 @ ( denota968303861_a_b_c @ sK2 @ phi ) ) ) ),
inference(cnf_transformation,[status(thm)],[f919]) ).
thf(f1026,plain,
( spl8_4
| spl8_5
| spl8_2 ),
inference(avatar_split_clause,[status(thm)],[f944,f967,f980,f976]) ).
thf(f944,plain,
( ( $true
= ( denota69106024_a_b_c @ sK7 @ sK6 @ ( static_SIGF_a_b_c @ phi ) ) )
| ( ( member1895684704real_c @ sK3 @ ( denota968303861_a_b_c @ sK2 @ phi ) )
= $true )
| ( ( member1895684704real_c @ sK1 @ ( denota968303861_a_b_c @ sK0 @ phi ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f929]) ).
thf(f1025,plain,
( spl8_11
| spl8_9
| spl8_10 ),
inference(avatar_split_clause,[status(thm)],[f947,f1002,f998,f1008]) ).
thf(f947,plain,
( ( ( member1895684704real_c @ sK1 @ ( denota968303861_a_b_c @ sK0 @ phi ) )
= $false )
| ( $true
= ( denota1997846518gree_c @ sK5 @ sK4 @ ( static_FVF_a_b_c @ phi ) ) )
| ( $false
= ( member1895684704real_c @ sK3 @ ( denota968303861_a_b_c @ sK2 @ phi ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f931]) ).
thf(f931,plain,
( ( $true
= ( denota1997846518gree_c @ sK5 @ sK4 @ ( static_FVF_a_b_c @ phi ) ) )
| ( ( member1895684704real_c @ sK1 @ ( denota968303861_a_b_c @ sK0 @ phi ) )
!= ( member1895684704real_c @ sK3 @ ( denota968303861_a_b_c @ sK2 @ phi ) ) ) ),
inference(cnf_transformation,[status(thm)],[f919]) ).
thf(f1024,plain,
( spl8_11
| spl8_5
| spl8_4 ),
inference(avatar_split_clause,[status(thm)],[f946,f976,f980,f1008]) ).
thf(f946,plain,
( ( ( member1895684704real_c @ sK3 @ ( denota968303861_a_b_c @ sK2 @ phi ) )
= $true )
| ( ( member1895684704real_c @ sK1 @ ( denota968303861_a_b_c @ sK0 @ phi ) )
= $true )
| ( $true
= ( denota1997846518gree_c @ sK5 @ sK4 @ ( static_FVF_a_b_c @ phi ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f931]) ).
thf(f1023,plain,
( spl8_13
| spl8_13 ),
inference(avatar_split_clause,[status(thm)],[f951,f1019,f1019]) ).
thf(f951,plain,
! [X10: denota231621370t_unit,X11: produc190496183real_c,X8: denota231621370t_unit,X9: produc190496183real_c,X14: denota231621370t_unit,X15: denota231621370t_unit,X12: produc190496183real_c,X13: produc190496183real_c] :
( ( $true
= ( member1895684704real_c @ X13 @ ( denota968303861_a_b_c @ X15 @ phi ) ) )
| ( ( denota1997846518gree_c @ X13 @ X12 @ ( static_FVF_a_b_c @ phi ) )
!= $true )
| ( ( member1895684704real_c @ X9 @ ( denota968303861_a_b_c @ X8 @ phi ) )
= $true )
| ( ( member1895684704real_c @ X11 @ ( denota968303861_a_b_c @ X10 @ phi ) )
= $false )
| ( ( denota69106024_a_b_c @ X15 @ X14 @ ( static_SIGF_a_b_c @ phi ) )
!= $true )
| ( $false
= ( member1895684704real_c @ X12 @ ( denota968303861_a_b_c @ X14 @ phi ) ) )
| ( $true
!= ( denota69106024_a_b_c @ X8 @ X10 @ ( static_SIGF_a_b_c @ phi ) ) )
| ( ( denota1997846518gree_c @ X9 @ X11 @ ( static_FVF_a_b_c @ phi ) )
!= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f949]) ).
thf(f949,plain,
! [X10: denota231621370t_unit,X11: produc190496183real_c,X8: denota231621370t_unit,X9: produc190496183real_c,X14: denota231621370t_unit,X15: denota231621370t_unit,X12: produc190496183real_c,X13: produc190496183real_c] :
( ( ( denota1997846518gree_c @ X13 @ X12 @ ( static_FVF_a_b_c @ phi ) )
!= $true )
| ( ( denota69106024_a_b_c @ X15 @ X14 @ ( static_SIGF_a_b_c @ phi ) )
!= $true )
| ( $true
!= ( denota69106024_a_b_c @ X8 @ X10 @ ( static_SIGF_a_b_c @ phi ) ) )
| ( ( member1895684704real_c @ X11 @ ( denota968303861_a_b_c @ X10 @ phi ) )
= ( member1895684704real_c @ X9 @ ( denota968303861_a_b_c @ X8 @ phi ) ) )
| ( $false
= ( member1895684704real_c @ X12 @ ( denota968303861_a_b_c @ X14 @ phi ) ) )
| ( ( denota1997846518gree_c @ X9 @ X11 @ ( static_FVF_a_b_c @ phi ) )
!= $true )
| ( $true
= ( member1895684704real_c @ X13 @ ( denota968303861_a_b_c @ X15 @ phi ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f925]) ).
thf(f925,plain,
! [X10: denota231621370t_unit,X11: produc190496183real_c,X8: denota231621370t_unit,X9: produc190496183real_c,X14: denota231621370t_unit,X15: denota231621370t_unit,X12: produc190496183real_c,X13: produc190496183real_c] :
( ( ( denota1997846518gree_c @ X9 @ X11 @ ( static_FVF_a_b_c @ phi ) )
!= $true )
| ( ( denota69106024_a_b_c @ X15 @ X14 @ ( static_SIGF_a_b_c @ phi ) )
!= $true )
| ( ( denota1997846518gree_c @ X13 @ X12 @ ( static_FVF_a_b_c @ phi ) )
!= $true )
| ( ( member1895684704real_c @ X12 @ ( denota968303861_a_b_c @ X14 @ phi ) )
= ( member1895684704real_c @ X13 @ ( denota968303861_a_b_c @ X15 @ phi ) ) )
| ( ( member1895684704real_c @ X11 @ ( denota968303861_a_b_c @ X10 @ phi ) )
= ( member1895684704real_c @ X9 @ ( denota968303861_a_b_c @ X8 @ phi ) ) )
| ( $true
!= ( denota69106024_a_b_c @ X8 @ X10 @ ( static_SIGF_a_b_c @ phi ) ) ) ),
inference(cnf_transformation,[status(thm)],[f919]) ).
thf(f1017,plain,
( spl8_12
| spl8_12 ),
inference(avatar_split_clause,[status(thm)],[f952,f1015,f1015]) ).
thf(f952,plain,
! [X10: denota231621370t_unit,X11: produc190496183real_c,X8: denota231621370t_unit,X9: produc190496183real_c,X14: denota231621370t_unit,X15: denota231621370t_unit,X12: produc190496183real_c,X13: produc190496183real_c] :
( ( ( denota1997846518gree_c @ X9 @ X11 @ ( static_FVF_a_b_c @ phi ) )
!= $true )
| ( ( member1895684704real_c @ X11 @ ( denota968303861_a_b_c @ X10 @ phi ) )
= $true )
| ( ( member1895684704real_c @ X9 @ ( denota968303861_a_b_c @ X8 @ phi ) )
= $false )
| ( ( denota69106024_a_b_c @ X15 @ X14 @ ( static_SIGF_a_b_c @ phi ) )
!= $true )
| ( $true
= ( member1895684704real_c @ X12 @ ( denota968303861_a_b_c @ X14 @ phi ) ) )
| ( $false
= ( member1895684704real_c @ X13 @ ( denota968303861_a_b_c @ X15 @ phi ) ) )
| ( $true
!= ( denota69106024_a_b_c @ X8 @ X10 @ ( static_SIGF_a_b_c @ phi ) ) )
| ( ( denota1997846518gree_c @ X13 @ X12 @ ( static_FVF_a_b_c @ phi ) )
!= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f948]) ).
thf(f948,plain,
! [X10: denota231621370t_unit,X11: produc190496183real_c,X8: denota231621370t_unit,X9: produc190496183real_c,X14: denota231621370t_unit,X15: denota231621370t_unit,X12: produc190496183real_c,X13: produc190496183real_c] :
( ( ( denota69106024_a_b_c @ X15 @ X14 @ ( static_SIGF_a_b_c @ phi ) )
!= $true )
| ( $true
!= ( denota69106024_a_b_c @ X8 @ X10 @ ( static_SIGF_a_b_c @ phi ) ) )
| ( ( member1895684704real_c @ X11 @ ( denota968303861_a_b_c @ X10 @ phi ) )
= ( member1895684704real_c @ X9 @ ( denota968303861_a_b_c @ X8 @ phi ) ) )
| ( ( denota1997846518gree_c @ X13 @ X12 @ ( static_FVF_a_b_c @ phi ) )
!= $true )
| ( $false
= ( member1895684704real_c @ X13 @ ( denota968303861_a_b_c @ X15 @ phi ) ) )
| ( ( denota1997846518gree_c @ X9 @ X11 @ ( static_FVF_a_b_c @ phi ) )
!= $true )
| ( $true
= ( member1895684704real_c @ X12 @ ( denota968303861_a_b_c @ X14 @ phi ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f925]) ).
thf(f1013,plain,
( spl8_1
| spl8_8
| spl8_7 ),
inference(avatar_split_clause,[status(thm)],[f955,f989,f993,f963]) ).
thf(f955,plain,
( ( $false
= ( member1895684704real_c @ sK4 @ ( denota968303861_a_b_c @ sK6 @ phi ) ) )
| ( $false
= ( member1895684704real_c @ sK5 @ ( denota968303861_a_b_c @ sK7 @ phi ) ) )
| ( ( denota1997846518gree_c @ sK1 @ sK3 @ ( static_FVF_a_b_c @ phi ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f933]) ).
thf(f933,plain,
( ( ( member1895684704real_c @ sK5 @ ( denota968303861_a_b_c @ sK7 @ phi ) )
!= ( member1895684704real_c @ sK4 @ ( denota968303861_a_b_c @ sK6 @ phi ) ) )
| ( ( denota1997846518gree_c @ sK1 @ sK3 @ ( static_FVF_a_b_c @ phi ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f919]) ).
thf(f1012,plain,
( spl8_3
| spl8_6
| spl8_1 ),
inference(avatar_split_clause,[status(thm)],[f954,f963,f984,f972]) ).
thf(f954,plain,
( ( $true
= ( member1895684704real_c @ sK4 @ ( denota968303861_a_b_c @ sK6 @ phi ) ) )
| ( $true
= ( member1895684704real_c @ sK5 @ ( denota968303861_a_b_c @ sK7 @ phi ) ) )
| ( ( denota1997846518gree_c @ sK1 @ sK3 @ ( static_FVF_a_b_c @ phi ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f933]) ).
thf(f1011,plain,
( spl8_1
| spl8_11 ),
inference(avatar_split_clause,[status(thm)],[f934,f1008,f963]) ).
thf(f934,plain,
( ( ( denota1997846518gree_c @ sK1 @ sK3 @ ( static_FVF_a_b_c @ phi ) )
= $true )
| ( $true
= ( denota1997846518gree_c @ sK5 @ sK4 @ ( static_FVF_a_b_c @ phi ) ) ) ),
inference(cnf_transformation,[status(thm)],[f919]) ).
thf(f1006,plain,
( spl8_7
| spl8_9
| spl8_10
| spl8_8 ),
inference(avatar_split_clause,[status(thm)],[f959,f993,f1002,f998,f989]) ).
thf(f959,plain,
( ( $false
= ( member1895684704real_c @ sK3 @ ( denota968303861_a_b_c @ sK2 @ phi ) ) )
| ( $false
= ( member1895684704real_c @ sK4 @ ( denota968303861_a_b_c @ sK6 @ phi ) ) )
| ( ( member1895684704real_c @ sK1 @ ( denota968303861_a_b_c @ sK0 @ phi ) )
= $false )
| ( $false
= ( member1895684704real_c @ sK5 @ ( denota968303861_a_b_c @ sK7 @ phi ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f957]) ).
thf(f957,plain,
( ( $false
= ( member1895684704real_c @ sK3 @ ( denota968303861_a_b_c @ sK2 @ phi ) ) )
| ( ( member1895684704real_c @ sK1 @ ( denota968303861_a_b_c @ sK0 @ phi ) )
= $false )
| ( ( member1895684704real_c @ sK5 @ ( denota968303861_a_b_c @ sK7 @ phi ) )
!= ( member1895684704real_c @ sK4 @ ( denota968303861_a_b_c @ sK6 @ phi ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f930]) ).
thf(f930,plain,
( ( ( member1895684704real_c @ sK1 @ ( denota968303861_a_b_c @ sK0 @ phi ) )
!= ( member1895684704real_c @ sK3 @ ( denota968303861_a_b_c @ sK2 @ phi ) ) )
| ( ( member1895684704real_c @ sK5 @ ( denota968303861_a_b_c @ sK7 @ phi ) )
!= ( member1895684704real_c @ sK4 @ ( denota968303861_a_b_c @ sK6 @ phi ) ) ) ),
inference(cnf_transformation,[status(thm)],[f919]) ).
thf(f1005,plain,
( spl8_6
| spl8_9
| spl8_3
| spl8_10 ),
inference(avatar_split_clause,[status(thm)],[f958,f1002,f972,f998,f984]) ).
thf(f958,plain,
( ( $false
= ( member1895684704real_c @ sK3 @ ( denota968303861_a_b_c @ sK2 @ phi ) ) )
| ( ( member1895684704real_c @ sK1 @ ( denota968303861_a_b_c @ sK0 @ phi ) )
= $false )
| ( $true
= ( member1895684704real_c @ sK5 @ ( denota968303861_a_b_c @ sK7 @ phi ) ) )
| ( $true
= ( member1895684704real_c @ sK4 @ ( denota968303861_a_b_c @ sK6 @ phi ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f957]) ).
thf(f996,plain,
( spl8_7
| spl8_4
| spl8_8
| spl8_5 ),
inference(avatar_split_clause,[status(thm)],[f961,f980,f993,f976,f989]) ).
thf(f961,plain,
( ( $false
= ( member1895684704real_c @ sK5 @ ( denota968303861_a_b_c @ sK7 @ phi ) ) )
| ( ( member1895684704real_c @ sK1 @ ( denota968303861_a_b_c @ sK0 @ phi ) )
= $true )
| ( $false
= ( member1895684704real_c @ sK4 @ ( denota968303861_a_b_c @ sK6 @ phi ) ) )
| ( ( member1895684704real_c @ sK3 @ ( denota968303861_a_b_c @ sK2 @ phi ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f956]) ).
thf(f956,plain,
( ( ( member1895684704real_c @ sK1 @ ( denota968303861_a_b_c @ sK0 @ phi ) )
= $true )
| ( ( member1895684704real_c @ sK3 @ ( denota968303861_a_b_c @ sK2 @ phi ) )
= $true )
| ( ( member1895684704real_c @ sK5 @ ( denota968303861_a_b_c @ sK7 @ phi ) )
!= ( member1895684704real_c @ sK4 @ ( denota968303861_a_b_c @ sK6 @ phi ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f930]) ).
thf(f987,plain,
( spl8_3
| spl8_4
| spl8_5
| spl8_6 ),
inference(avatar_split_clause,[status(thm)],[f960,f984,f980,f976,f972]) ).
thf(f960,plain,
( ( $true
= ( member1895684704real_c @ sK4 @ ( denota968303861_a_b_c @ sK6 @ phi ) ) )
| ( ( member1895684704real_c @ sK3 @ ( denota968303861_a_b_c @ sK2 @ phi ) )
= $true )
| ( $true
= ( member1895684704real_c @ sK5 @ ( denota968303861_a_b_c @ sK7 @ phi ) ) )
| ( ( member1895684704real_c @ sK1 @ ( denota968303861_a_b_c @ sK0 @ phi ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f956]) ).
thf(f970,plain,
( spl8_1
| spl8_2 ),
inference(avatar_split_clause,[status(thm)],[f932,f967,f963]) ).
thf(f932,plain,
( ( ( denota1997846518gree_c @ sK1 @ sK3 @ ( static_FVF_a_b_c @ phi ) )
= $true )
| ( $true
= ( denota69106024_a_b_c @ sK7 @ sK6 @ ( static_SIGF_a_b_c @ phi ) ) ) ),
inference(cnf_transformation,[status(thm)],[f919]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP039^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.35 % Computer : n031.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Tue Feb 24 08:26:33 EST 2026
% 0.18/0.35 % CPUTime :
% 0.18/0.35 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.21/0.47 ---- Original DTF file ---
% 0.21/0.47 thf(spec,logic,$$dhol).
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 % File : ITP039^1 : TPTP v9.2.1. Released v7.5.0.
% 0.21/0.47 % Domain : Interactive Theorem Proving
% 0.21/0.47 % Problem : Sledgehammer Coincidence problem prob_472__7214396_1
% 0.21/0.47 % Version : Especial.
% 0.21/0.47 % English :
% 0.21/0.47
% 0.21/0.47 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.21/0.47 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.21/0.47 % Source : [Des21]
% 0.21/0.47 % Names : Coincidence/prob_472__7214396_1 [Des21]
% 0.21/0.47
% 0.21/0.47 % Status : Theorem
% 0.21/0.47 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0
% 0.21/0.47 % Syntax : Number of formulae : 507 ( 165 unt; 152 typ; 0 def)
% 0.21/0.47 % Number of atoms : 782 ( 357 equ; 0 cnn)
% 0.21/0.47 % Maximal formula atoms : 13 ( 2 avg)
% 0.21/0.47 % Number of connectives : 3134 ( 150 ~; 0 |; 45 &;2594 @)
% 0.21/0.47 % ( 0 <=>; 345 =>; 0 <=; 0 <~>)
% 0.21/0.47 % Maximal formula depth : 33 ( 9 avg)
% 0.21/0.47 % Number of types : 27 ( 26 usr)
% 0.21/0.47 % Number of type conns : 754 ( 754 >; 0 *; 0 +; 0 <<)
% 0.21/0.47 % Number of symbols : 128 ( 126 usr; 5 con; 0-10 aty)
% 0.21/0.47 % Number of variables : 1586 ( 99 ^;1462 !; 25 ?;1586 :)
% 0.21/0.47 % SPC : TH0_THM_EQU_NAR
% 0.21/0.47
% 0.21/0.47 % Comments : This file was generated by Sledgehammer 2021-02-23 15:39:39.768
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 % Could-be-implicit typings (26)
% 0.21/0.47 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J_J,type,
% 0.21/0.47 set_Pr754230471real_c: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 0.21/0.47 produc640052711real_c: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_Mt__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_J_J,type,
% 0.21/0.47 set_Pr2041213564t_unit: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_J_J,type,
% 0.21/0.47 set_Pr1169339874_sc_sz: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_Mt__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_J,type,
% 0.21/0.47 produc999471430t_unit: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_n_t__Product____Type__Oprod_It__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_J,type,
% 0.21/0.47 produc1821101996_sc_sz: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_J_J,type,
% 0.21/0.47 set_Pr60491591eal_sz: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 0.21/0.47 set_Pr1389752855real_c: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_J,type,
% 0.21/0.47 set_Pr1774599175_sc_sz: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_n_t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_J,type,
% 0.21/0.47 produc1149990247eal_sz: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_n_t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 0.21/0.47 produc190496183real_c: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J,type,
% 0.21/0.47 produc866628903_sc_sz: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_n_t__Set__Oset_It__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_J,type,
% 0.21/0.47 set_De208295462t_unit: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_n_t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J,type,
% 0.21/0.47 denota610675952t_unit: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_n_t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__a_Mtf__b_Mtf__c_Mt__Product____Type__Ounit_J,type,
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% 0.21/0.47
% 0.21/0.47 thf(ty_n_t__Set__Oset_It__Sum____Type__Osum_Itf__a_Mt__Sum____Type__Osum_Itf__b_Mtf__c_J_J_J,type,
% 0.21/0.47 set_Su1783761653um_b_c: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_n_t__Set__Oset_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 0.21/0.47 set_Fi1407883041real_c: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_n_t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J,type,
% 0.21/0.47 finite1398487019real_c: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_n_t__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J,type,
% 0.21/0.47 list_f1238882004_sc_sz: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_n_t__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J,type,
% 0.21/0.47 set_Sum_sum_c_c: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_n_t__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J,type,
% 0.21/0.47 formula_sf_sc_sz: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_n_t__Syntax__Oformula_Itf__a_Mtf__b_Mtf__c_J,type,
% 0.21/0.47 formula_a_b_c: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_n_t__Set__Oset_I_Eo_J,type,
% 0.21/0.47 set_o: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_n_tf__sz,type,
% 0.21/0.47 sz: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_n_tf__sf,type,
% 0.21/0.47 sf: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_n_tf__sc,type,
% 0.21/0.47 sc: $tType ).
% 0.21/0.47
% 0.21/0.47 % Explicit typings (126)
% 0.21/0.47 thf(sy_c_Coincidence__Mirabelle__veeocdlawq_Oids_Ocoincide__fml_001tf__a_001tf__b_001tf__c,type,
% 0.21/0.47 coinci501627771_a_b_c: formula_a_b_c > $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Denotational__Semantics_OIagree_001tf__a_001tf__b_001tf__c,type,
% 0.21/0.47 denota69106024_a_b_c: denota231621370t_unit > denota231621370t_unit > set_Su1783761653um_b_c > $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Denotational__Semantics_OVagree_001tf__c,type,
% 0.21/0.47 denota1997846518gree_c: produc190496183real_c > produc190496183real_c > set_Sum_sum_c_c > $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Denotational__Semantics_Ofml__sem_001tf__a_001tf__b_001tf__c,type,
% 0.21/0.47 denota968303861_a_b_c: denota231621370t_unit > formula_a_b_c > set_Pr1389752855real_c ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Denotational__Semantics_Ofml__sem_001tf__sf_001tf__sc_001tf__sz,type,
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% 0.21/0.47
% 0.21/0.47 thf(sy_c_Denotational__Semantics_Oids_Ovalid_001tf__sf_001tf__sc_001tf__sz,type,
% 0.21/0.47 denota1946510237_sc_sz: formula_sf_sc_sz > $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Denotational__Semantics_Ois__interp_001tf__sf_001tf__sc_001tf__sz,type,
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% 0.21/0.47
% 0.21/0.47 thf(sy_c_Ids_Oids_001tf__sz_001tf__sf_001tf__sc,type,
% 0.21/0.47 ids_sz_sf_sc: sz > sz > sz > sf > sf > sf > sc > sc > sc > sc > $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_M_Eo_J_J,type,
% 0.21/0.47 top_to1399053141c_sz_o: denota610675952t_unit > produc866628903_sc_sz > $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_M_062_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_M_Eo_J_J,type,
% 0.21/0.47 top_to964419200al_c_o: finite1398487019real_c > finite1398487019real_c > $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_J_J,type,
% 0.21/0.47 top_to1499569298_sc_sz: set_Pr1169339874_sc_sz ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 0.21/0.47 top_to226056039real_c: set_Pr1389752855real_c ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Sum____Type__Osum_Itf__c_Mtf__c_J_J,type,
% 0.21/0.47 top_to1660572043um_c_c: set_Sum_sum_c_c ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Product__Type_OPair_001t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J,type,
% 0.21/0.47 produc789536734_sc_sz: denota610675952t_unit > produc866628903_sc_sz > produc1821101996_sc_sz ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Product__Type_OPair_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J,type,
% 0.21/0.47 produc394644079real_c: finite1398487019real_c > finite1398487019real_c > produc190496183real_c ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_001t__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J,type,
% 0.21/0.47 produc1822718231_sc_sz: list_f1238882004_sc_sz > list_f1238882004_sc_sz > produc866628903_sc_sz ).
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% 0.21/0.47 produc1687028567real_c: produc190496183real_c > produc190496183real_c > produc640052711real_c ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_001t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J,type,
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% 0.21/0.47 thf(sy_c_Product__Type_OSigma_001t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J,type,
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% 0.21/0.47 member1895684704real_c: produc190496183real_c > set_Pr1389752855real_c > $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_J,type,
% 0.21/0.47 member630771088eal_sz: produc1149990247eal_sz > set_Pr60491591eal_sz > $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J,type,
% 0.21/0.47 member245028432_sc_sz: produc866628903_sc_sz > set_Pr1774599175_sc_sz > $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 0.21/0.47 member346808080real_c: produc640052711real_c > set_Pr754230471real_c > $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_Mt__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_J,type,
% 0.21/0.47 member235934813t_unit: produc999471430t_unit > set_Pr2041213564t_unit > $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v__092_060phi_062,type,
% 0.21/0.47 phi: formula_a_b_c ).
% 0.21/0.47
% 0.21/0.47 % Relevant facts (354)
% 0.21/0.47 thf(fact_0_coincide__fml__def,axiom,
% 0.21/0.47 ( coinci501627771_a_b_c
% 0.21/0.47 = ( ^ [Phi: formula_a_b_c] :
% 0.21/0.47 ! [Nu: produc190496183real_c,Nu2: produc190496183real_c,I: denota231621370t_unit,J: denota231621370t_unit] :
% 0.21/0.47 ( ( denota69106024_a_b_c @ I @ J @ ( static_SIGF_a_b_c @ Phi ) )
% 0.21/0.47 => ( ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVF_a_b_c @ Phi ) )
% 0.21/0.47 => ( ( member1895684704real_c @ Nu @ ( denota968303861_a_b_c @ I @ Phi ) )
% 0.21/0.47 = ( member1895684704real_c @ Nu2 @ ( denota968303861_a_b_c @ J @ Phi ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % coincide_fml_def
% 0.21/0.47 thf(fact_1_ids_Ocoincide__fml__def,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc,Phi2: formula_a_b_c] :
% 0.21/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.47 => ( ( coinci501627771_a_b_c @ Phi2 )
% 0.21/0.47 = ( ! [Nu: produc190496183real_c,Nu2: produc190496183real_c,I: denota231621370t_unit,J: denota231621370t_unit] :
% 0.21/0.47 ( ( denota69106024_a_b_c @ I @ J @ ( static_SIGF_a_b_c @ Phi2 ) )
% 0.21/0.47 => ( ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVF_a_b_c @ Phi2 ) )
% 0.21/0.47 => ( ( member1895684704real_c @ Nu @ ( denota968303861_a_b_c @ I @ Phi2 ) )
% 0.21/0.47 = ( member1895684704real_c @ Nu2 @ ( denota968303861_a_b_c @ J @ Phi2 ) ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.coincide_fml_def
% 0.21/0.47 thf(fact_2_Iagree__comm,axiom,
% 0.21/0.47 ! [A: denota231621370t_unit,B: denota231621370t_unit,V: set_Su1783761653um_b_c] :
% 0.21/0.47 ( ( denota69106024_a_b_c @ A @ B @ V )
% 0.21/0.47 => ( denota69106024_a_b_c @ B @ A @ V ) ) ).
% 0.21/0.47
% 0.21/0.47 % Iagree_comm
% 0.21/0.47 thf(fact_3_Iagree__refl,axiom,
% 0.21/0.47 ! [I2: denota231621370t_unit,A: set_Su1783761653um_b_c] : ( denota69106024_a_b_c @ I2 @ I2 @ A ) ).
% 0.21/0.47
% 0.21/0.47 % Iagree_refl
% 0.21/0.47 thf(fact_4_agree__comm,axiom,
% 0.21/0.47 ! [A: produc190496183real_c,B: produc190496183real_c,V: set_Sum_sum_c_c] :
% 0.21/0.47 ( ( denota1997846518gree_c @ A @ B @ V )
% 0.21/0.47 => ( denota1997846518gree_c @ B @ A @ V ) ) ).
% 0.21/0.47
% 0.21/0.47 % agree_comm
% 0.21/0.47 thf(fact_5_agree__refl,axiom,
% 0.21/0.47 ! [Nu3: produc190496183real_c,A: set_Sum_sum_c_c] : ( denota1997846518gree_c @ Nu3 @ Nu3 @ A ) ).
% 0.21/0.47
% 0.21/0.47 % agree_refl
% 0.21/0.47 thf(fact_6_iff__to__impl,axiom,
% 0.21/0.47 ! [Nu3: produc190496183real_c,I2: denota231621370t_unit,A: formula_a_b_c,B: formula_a_b_c] :
% 0.21/0.47 ( ( ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I2 @ A ) )
% 0.21/0.47 = ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I2 @ B ) ) )
% 0.21/0.47 = ( ( ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I2 @ A ) )
% 0.21/0.47 => ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I2 @ B ) ) )
% 0.21/0.47 & ( ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I2 @ B ) )
% 0.21/0.47 => ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I2 @ A ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % iff_to_impl
% 0.21/0.47 thf(fact_7_iff__sem,axiom,
% 0.21/0.47 ! [Nu3: produc190496183real_c,I2: denota231621370t_unit,A: formula_a_b_c,B: formula_a_b_c] :
% 0.21/0.47 ( ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I2 @ ( equiv_a_b_c @ A @ B ) ) )
% 0.21/0.47 = ( ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I2 @ A ) )
% 0.21/0.47 = ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I2 @ B ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % iff_sem
% 0.21/0.47 thf(fact_8_impl__sem,axiom,
% 0.21/0.47 ! [Nu3: produc190496183real_c,I2: denota231621370t_unit,A: formula_a_b_c,B: formula_a_b_c] :
% 0.21/0.47 ( ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I2 @ ( implies_a_b_c @ A @ B ) ) )
% 0.21/0.47 = ( ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I2 @ A ) )
% 0.21/0.47 => ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I2 @ B ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % impl_sem
% 0.21/0.47 thf(fact_9_P__def,axiom,
% 0.21/0.47 p_sc_sf_sz = predic913887884_sf_sz ).
% 0.21/0.47
% 0.21/0.47 % P_def
% 0.21/0.47 thf(fact_10_seq__sem_Ocases,axiom,
% 0.21/0.47 ! [X: produc1821101996_sc_sz] :
% 0.21/0.47 ~ ! [I3: denota610675952t_unit,S: produc866628903_sc_sz] :
% 0.21/0.47 ( X
% 0.21/0.47 != ( produc789536734_sc_sz @ I3 @ S ) ) ).
% 0.21/0.47
% 0.21/0.47 % seq_sem.cases
% 0.21/0.47 thf(fact_11_ids_Oseq__sem_Ocases,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc,X: produc1821101996_sc_sz] :
% 0.21/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.47 => ~ ! [I3: denota610675952t_unit,S: produc866628903_sc_sz] :
% 0.21/0.47 ( X
% 0.21/0.47 != ( produc789536734_sc_sz @ I3 @ S ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.seq_sem.cases
% 0.21/0.47 thf(fact_12_ids_Oseq__sem_Oinduct,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc,P: denota610675952t_unit > produc866628903_sc_sz > $o,A0: denota610675952t_unit,A1: produc866628903_sc_sz] :
% 0.21/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.47 => ( ! [I3: denota610675952t_unit,X_1: produc866628903_sc_sz] : ( P @ I3 @ X_1 )
% 0.21/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.seq_sem.induct
% 0.21/0.47 thf(fact_13_ids_OP__def,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc,P2: sc] :
% 0.21/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.47 => ( ( p_sc_sf_sz @ P2 )
% 0.21/0.47 = ( predic913887884_sf_sz @ P2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.P_def
% 0.21/0.47 thf(fact_14_prod_Oinject,axiom,
% 0.21/0.47 ! [X1: list_f1238882004_sc_sz,X2: list_f1238882004_sc_sz,Y1: list_f1238882004_sc_sz,Y2: list_f1238882004_sc_sz] :
% 0.21/0.47 ( ( ( produc1822718231_sc_sz @ X1 @ X2 )
% 0.21/0.47 = ( produc1822718231_sc_sz @ Y1 @ Y2 ) )
% 0.21/0.47 = ( ( X1 = Y1 )
% 0.21/0.47 & ( X2 = Y2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % prod.inject
% 0.21/0.47 thf(fact_15_prod_Oinject,axiom,
% 0.21/0.47 ! [X1: finite1398487019real_c,X2: finite1398487019real_c,Y1: finite1398487019real_c,Y2: finite1398487019real_c] :
% 0.21/0.47 ( ( ( produc394644079real_c @ X1 @ X2 )
% 0.21/0.47 = ( produc394644079real_c @ Y1 @ Y2 ) )
% 0.21/0.47 = ( ( X1 = Y1 )
% 0.21/0.47 & ( X2 = Y2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % prod.inject
% 0.21/0.47 thf(fact_16_prod_Oinject,axiom,
% 0.21/0.47 ! [X1: produc866628903_sc_sz,X2: denota610675952t_unit,Y1: produc866628903_sc_sz,Y2: denota610675952t_unit] :
% 0.21/0.47 ( ( ( produc502616768t_unit @ X1 @ X2 )
% 0.21/0.47 = ( produc502616768t_unit @ Y1 @ Y2 ) )
% 0.21/0.47 = ( ( X1 = Y1 )
% 0.21/0.47 & ( X2 = Y2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % prod.inject
% 0.21/0.47 thf(fact_17_prod_Oinject,axiom,
% 0.21/0.47 ! [X1: produc190496183real_c,X2: produc190496183real_c,Y1: produc190496183real_c,Y2: produc190496183real_c] :
% 0.21/0.47 ( ( ( produc1687028567real_c @ X1 @ X2 )
% 0.21/0.47 = ( produc1687028567real_c @ Y1 @ Y2 ) )
% 0.21/0.47 = ( ( X1 = Y1 )
% 0.21/0.47 & ( X2 = Y2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % prod.inject
% 0.21/0.47 thf(fact_18_prod_Oinject,axiom,
% 0.21/0.47 ! [X1: denota610675952t_unit,X2: produc866628903_sc_sz,Y1: denota610675952t_unit,Y2: produc866628903_sc_sz] :
% 0.21/0.47 ( ( ( produc789536734_sc_sz @ X1 @ X2 )
% 0.21/0.47 = ( produc789536734_sc_sz @ Y1 @ Y2 ) )
% 0.21/0.47 = ( ( X1 = Y1 )
% 0.21/0.47 & ( X2 = Y2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % prod.inject
% 0.21/0.47 thf(fact_19_old_Oprod_Oinject,axiom,
% 0.21/0.47 ! [A2: list_f1238882004_sc_sz,B2: list_f1238882004_sc_sz,A3: list_f1238882004_sc_sz,B3: list_f1238882004_sc_sz] :
% 0.21/0.47 ( ( ( produc1822718231_sc_sz @ A2 @ B2 )
% 0.21/0.47 = ( produc1822718231_sc_sz @ A3 @ B3 ) )
% 0.21/0.47 = ( ( A2 = A3 )
% 0.21/0.47 & ( B2 = B3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.prod.inject
% 0.21/0.47 thf(fact_20_old_Oprod_Oinject,axiom,
% 0.21/0.47 ! [A2: finite1398487019real_c,B2: finite1398487019real_c,A3: finite1398487019real_c,B3: finite1398487019real_c] :
% 0.21/0.47 ( ( ( produc394644079real_c @ A2 @ B2 )
% 0.21/0.47 = ( produc394644079real_c @ A3 @ B3 ) )
% 0.21/0.47 = ( ( A2 = A3 )
% 0.21/0.47 & ( B2 = B3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.prod.inject
% 0.21/0.47 thf(fact_21_old_Oprod_Oinject,axiom,
% 0.21/0.47 ! [A2: produc866628903_sc_sz,B2: denota610675952t_unit,A3: produc866628903_sc_sz,B3: denota610675952t_unit] :
% 0.21/0.47 ( ( ( produc502616768t_unit @ A2 @ B2 )
% 0.21/0.47 = ( produc502616768t_unit @ A3 @ B3 ) )
% 0.21/0.47 = ( ( A2 = A3 )
% 0.21/0.47 & ( B2 = B3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.prod.inject
% 0.21/0.47 thf(fact_22_old_Oprod_Oinject,axiom,
% 0.21/0.47 ! [A2: produc190496183real_c,B2: produc190496183real_c,A3: produc190496183real_c,B3: produc190496183real_c] :
% 0.21/0.47 ( ( ( produc1687028567real_c @ A2 @ B2 )
% 0.21/0.47 = ( produc1687028567real_c @ A3 @ B3 ) )
% 0.21/0.47 = ( ( A2 = A3 )
% 0.21/0.47 & ( B2 = B3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.prod.inject
% 0.21/0.47 thf(fact_23_old_Oprod_Oinject,axiom,
% 0.21/0.47 ! [A2: denota610675952t_unit,B2: produc866628903_sc_sz,A3: denota610675952t_unit,B3: produc866628903_sc_sz] :
% 0.21/0.47 ( ( ( produc789536734_sc_sz @ A2 @ B2 )
% 0.21/0.47 = ( produc789536734_sc_sz @ A3 @ B3 ) )
% 0.21/0.47 = ( ( A2 = A3 )
% 0.21/0.47 & ( B2 = B3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.prod.inject
% 0.21/0.47 thf(fact_24_prod__cases3,axiom,
% 0.21/0.47 ! [Y: produc640052711real_c] :
% 0.21/0.47 ~ ! [A4: produc190496183real_c,B4: finite1398487019real_c,C: finite1398487019real_c] :
% 0.21/0.47 ( Y
% 0.21/0.47 != ( produc1687028567real_c @ A4 @ ( produc394644079real_c @ B4 @ C ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % prod_cases3
% 0.21/0.47 thf(fact_25_prod__cases3,axiom,
% 0.21/0.47 ! [Y: produc1821101996_sc_sz] :
% 0.21/0.47 ~ ! [A4: denota610675952t_unit,B4: list_f1238882004_sc_sz,C: list_f1238882004_sc_sz] :
% 0.21/0.47 ( Y
% 0.21/0.47 != ( produc789536734_sc_sz @ A4 @ ( produc1822718231_sc_sz @ B4 @ C ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % prod_cases3
% 0.21/0.47 thf(fact_26_old_Oprod_Oinducts,axiom,
% 0.21/0.47 ! [P: produc866628903_sc_sz > $o,Prod: produc866628903_sc_sz] :
% 0.21/0.47 ( ! [A4: list_f1238882004_sc_sz,B4: list_f1238882004_sc_sz] : ( P @ ( produc1822718231_sc_sz @ A4 @ B4 ) )
% 0.21/0.47 => ( P @ Prod ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.prod.inducts
% 0.21/0.47 thf(fact_27_old_Oprod_Oinducts,axiom,
% 0.21/0.47 ! [P: produc190496183real_c > $o,Prod: produc190496183real_c] :
% 0.21/0.47 ( ! [A4: finite1398487019real_c,B4: finite1398487019real_c] : ( P @ ( produc394644079real_c @ A4 @ B4 ) )
% 0.21/0.47 => ( P @ Prod ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.prod.inducts
% 0.21/0.47 thf(fact_28_old_Oprod_Oinducts,axiom,
% 0.21/0.47 ! [P: produc999471430t_unit > $o,Prod: produc999471430t_unit] :
% 0.21/0.47 ( ! [A4: produc866628903_sc_sz,B4: denota610675952t_unit] : ( P @ ( produc502616768t_unit @ A4 @ B4 ) )
% 0.21/0.47 => ( P @ Prod ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.prod.inducts
% 0.21/0.47 thf(fact_29_old_Oprod_Oinducts,axiom,
% 0.21/0.47 ! [P: produc640052711real_c > $o,Prod: produc640052711real_c] :
% 0.21/0.47 ( ! [A4: produc190496183real_c,B4: produc190496183real_c] : ( P @ ( produc1687028567real_c @ A4 @ B4 ) )
% 0.21/0.47 => ( P @ Prod ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.prod.inducts
% 0.21/0.47 thf(fact_30_old_Oprod_Oinducts,axiom,
% 0.21/0.47 ! [P: produc1821101996_sc_sz > $o,Prod: produc1821101996_sc_sz] :
% 0.21/0.47 ( ! [A4: denota610675952t_unit,B4: produc866628903_sc_sz] : ( P @ ( produc789536734_sc_sz @ A4 @ B4 ) )
% 0.21/0.47 => ( P @ Prod ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.prod.inducts
% 0.21/0.47 thf(fact_31_old_Oprod_Oexhaust,axiom,
% 0.21/0.47 ! [Y: produc866628903_sc_sz] :
% 0.21/0.47 ~ ! [A4: list_f1238882004_sc_sz,B4: list_f1238882004_sc_sz] :
% 0.21/0.47 ( Y
% 0.21/0.47 != ( produc1822718231_sc_sz @ A4 @ B4 ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.prod.exhaust
% 0.21/0.47 thf(fact_32_old_Oprod_Oexhaust,axiom,
% 0.21/0.47 ! [Y: produc190496183real_c] :
% 0.21/0.47 ~ ! [A4: finite1398487019real_c,B4: finite1398487019real_c] :
% 0.21/0.47 ( Y
% 0.21/0.47 != ( produc394644079real_c @ A4 @ B4 ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.prod.exhaust
% 0.21/0.47 thf(fact_33_old_Oprod_Oexhaust,axiom,
% 0.21/0.47 ! [Y: produc999471430t_unit] :
% 0.21/0.47 ~ ! [A4: produc866628903_sc_sz,B4: denota610675952t_unit] :
% 0.21/0.47 ( Y
% 0.21/0.47 != ( produc502616768t_unit @ A4 @ B4 ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.prod.exhaust
% 0.21/0.47 thf(fact_34_old_Oprod_Oexhaust,axiom,
% 0.21/0.47 ! [Y: produc640052711real_c] :
% 0.21/0.47 ~ ! [A4: produc190496183real_c,B4: produc190496183real_c] :
% 0.21/0.47 ( Y
% 0.21/0.47 != ( produc1687028567real_c @ A4 @ B4 ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.prod.exhaust
% 0.21/0.47 thf(fact_35_old_Oprod_Oexhaust,axiom,
% 0.21/0.47 ! [Y: produc1821101996_sc_sz] :
% 0.21/0.47 ~ ! [A4: denota610675952t_unit,B4: produc866628903_sc_sz] :
% 0.21/0.47 ( Y
% 0.21/0.47 != ( produc789536734_sc_sz @ A4 @ B4 ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.prod.exhaust
% 0.21/0.47 thf(fact_36_Pair__inject,axiom,
% 0.21/0.47 ! [A2: list_f1238882004_sc_sz,B2: list_f1238882004_sc_sz,A3: list_f1238882004_sc_sz,B3: list_f1238882004_sc_sz] :
% 0.21/0.47 ( ( ( produc1822718231_sc_sz @ A2 @ B2 )
% 0.21/0.47 = ( produc1822718231_sc_sz @ A3 @ B3 ) )
% 0.21/0.47 => ~ ( ( A2 = A3 )
% 0.21/0.47 => ( B2 != B3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Pair_inject
% 0.21/0.47 thf(fact_37_Pair__inject,axiom,
% 0.21/0.47 ! [A2: finite1398487019real_c,B2: finite1398487019real_c,A3: finite1398487019real_c,B3: finite1398487019real_c] :
% 0.21/0.47 ( ( ( produc394644079real_c @ A2 @ B2 )
% 0.21/0.47 = ( produc394644079real_c @ A3 @ B3 ) )
% 0.21/0.47 => ~ ( ( A2 = A3 )
% 0.21/0.47 => ( B2 != B3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Pair_inject
% 0.21/0.47 thf(fact_38_Pair__inject,axiom,
% 0.21/0.47 ! [A2: produc866628903_sc_sz,B2: denota610675952t_unit,A3: produc866628903_sc_sz,B3: denota610675952t_unit] :
% 0.21/0.47 ( ( ( produc502616768t_unit @ A2 @ B2 )
% 0.21/0.47 = ( produc502616768t_unit @ A3 @ B3 ) )
% 0.21/0.47 => ~ ( ( A2 = A3 )
% 0.21/0.47 => ( B2 != B3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Pair_inject
% 0.21/0.47 thf(fact_39_Pair__inject,axiom,
% 0.21/0.47 ! [A2: produc190496183real_c,B2: produc190496183real_c,A3: produc190496183real_c,B3: produc190496183real_c] :
% 0.21/0.47 ( ( ( produc1687028567real_c @ A2 @ B2 )
% 0.21/0.47 = ( produc1687028567real_c @ A3 @ B3 ) )
% 0.21/0.47 => ~ ( ( A2 = A3 )
% 0.21/0.47 => ( B2 != B3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Pair_inject
% 0.21/0.47 thf(fact_40_Pair__inject,axiom,
% 0.21/0.47 ! [A2: denota610675952t_unit,B2: produc866628903_sc_sz,A3: denota610675952t_unit,B3: produc866628903_sc_sz] :
% 0.21/0.47 ( ( ( produc789536734_sc_sz @ A2 @ B2 )
% 0.21/0.47 = ( produc789536734_sc_sz @ A3 @ B3 ) )
% 0.21/0.47 => ~ ( ( A2 = A3 )
% 0.21/0.47 => ( B2 != B3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Pair_inject
% 0.21/0.47 thf(fact_41_prod__cases,axiom,
% 0.21/0.47 ! [P: produc866628903_sc_sz > $o,P2: produc866628903_sc_sz] :
% 0.21/0.47 ( ! [A4: list_f1238882004_sc_sz,B4: list_f1238882004_sc_sz] : ( P @ ( produc1822718231_sc_sz @ A4 @ B4 ) )
% 0.21/0.47 => ( P @ P2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % prod_cases
% 0.21/0.47 thf(fact_42_prod__cases,axiom,
% 0.21/0.47 ! [P: produc190496183real_c > $o,P2: produc190496183real_c] :
% 0.21/0.47 ( ! [A4: finite1398487019real_c,B4: finite1398487019real_c] : ( P @ ( produc394644079real_c @ A4 @ B4 ) )
% 0.21/0.47 => ( P @ P2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % prod_cases
% 0.21/0.47 thf(fact_43_prod__cases,axiom,
% 0.21/0.47 ! [P: produc999471430t_unit > $o,P2: produc999471430t_unit] :
% 0.21/0.47 ( ! [A4: produc866628903_sc_sz,B4: denota610675952t_unit] : ( P @ ( produc502616768t_unit @ A4 @ B4 ) )
% 0.21/0.47 => ( P @ P2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % prod_cases
% 0.21/0.47 thf(fact_44_prod__cases,axiom,
% 0.21/0.47 ! [P: produc640052711real_c > $o,P2: produc640052711real_c] :
% 0.21/0.47 ( ! [A4: produc190496183real_c,B4: produc190496183real_c] : ( P @ ( produc1687028567real_c @ A4 @ B4 ) )
% 0.21/0.47 => ( P @ P2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % prod_cases
% 0.21/0.47 thf(fact_45_prod__cases,axiom,
% 0.21/0.47 ! [P: produc1821101996_sc_sz > $o,P2: produc1821101996_sc_sz] :
% 0.21/0.47 ( ! [A4: denota610675952t_unit,B4: produc866628903_sc_sz] : ( P @ ( produc789536734_sc_sz @ A4 @ B4 ) )
% 0.21/0.47 => ( P @ P2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % prod_cases
% 0.21/0.47 thf(fact_46_surj__pair,axiom,
% 0.21/0.47 ! [P2: produc866628903_sc_sz] :
% 0.21/0.47 ? [X3: list_f1238882004_sc_sz,Y3: list_f1238882004_sc_sz] :
% 0.21/0.47 ( P2
% 0.21/0.47 = ( produc1822718231_sc_sz @ X3 @ Y3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % surj_pair
% 0.21/0.47 thf(fact_47_surj__pair,axiom,
% 0.21/0.47 ! [P2: produc190496183real_c] :
% 0.21/0.47 ? [X3: finite1398487019real_c,Y3: finite1398487019real_c] :
% 0.21/0.47 ( P2
% 0.21/0.47 = ( produc394644079real_c @ X3 @ Y3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % surj_pair
% 0.21/0.47 thf(fact_48_surj__pair,axiom,
% 0.21/0.47 ! [P2: produc999471430t_unit] :
% 0.21/0.47 ? [X3: produc866628903_sc_sz,Y3: denota610675952t_unit] :
% 0.21/0.47 ( P2
% 0.21/0.47 = ( produc502616768t_unit @ X3 @ Y3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % surj_pair
% 0.21/0.47 thf(fact_49_surj__pair,axiom,
% 0.21/0.47 ! [P2: produc640052711real_c] :
% 0.21/0.47 ? [X3: produc190496183real_c,Y3: produc190496183real_c] :
% 0.21/0.47 ( P2
% 0.21/0.47 = ( produc1687028567real_c @ X3 @ Y3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % surj_pair
% 0.21/0.47 thf(fact_50_surj__pair,axiom,
% 0.21/0.47 ! [P2: produc1821101996_sc_sz] :
% 0.21/0.47 ? [X3: denota610675952t_unit,Y3: produc866628903_sc_sz] :
% 0.21/0.47 ( P2
% 0.21/0.47 = ( produc789536734_sc_sz @ X3 @ Y3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % surj_pair
% 0.21/0.47 thf(fact_51_prod__induct3,axiom,
% 0.21/0.47 ! [P: produc640052711real_c > $o,X: produc640052711real_c] :
% 0.21/0.47 ( ! [A4: produc190496183real_c,B4: finite1398487019real_c,C: finite1398487019real_c] : ( P @ ( produc1687028567real_c @ A4 @ ( produc394644079real_c @ B4 @ C ) ) )
% 0.21/0.47 => ( P @ X ) ) ).
% 0.21/0.47
% 0.21/0.47 % prod_induct3
% 0.21/0.47 thf(fact_52_prod__induct3,axiom,
% 0.21/0.47 ! [P: produc1821101996_sc_sz > $o,X: produc1821101996_sc_sz] :
% 0.21/0.47 ( ! [A4: denota610675952t_unit,B4: list_f1238882004_sc_sz,C: list_f1238882004_sc_sz] : ( P @ ( produc789536734_sc_sz @ A4 @ ( produc1822718231_sc_sz @ B4 @ C ) ) )
% 0.21/0.47 => ( P @ X ) ) ).
% 0.21/0.47
% 0.21/0.47 % prod_induct3
% 0.21/0.47 thf(fact_53_mem__Collect__eq,axiom,
% 0.21/0.47 ! [A2: finite1398487019real_c,P: finite1398487019real_c > $o] :
% 0.21/0.47 ( ( member1261661570real_c @ A2 @ ( collec230941376real_c @ P ) )
% 0.21/0.47 = ( P @ A2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % mem_Collect_eq
% 0.21/0.47 thf(fact_54_mem__Collect__eq,axiom,
% 0.21/0.47 ! [A2: produc1821101996_sc_sz,P: produc1821101996_sc_sz > $o] :
% 0.21/0.47 ( ( member1057565379_sc_sz @ A2 @ ( collec1199592193_sc_sz @ P ) )
% 0.21/0.47 = ( P @ A2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % mem_Collect_eq
% 0.21/0.47 thf(fact_55_mem__Collect__eq,axiom,
% 0.21/0.47 ! [A2: produc640052711real_c,P: produc640052711real_c > $o] :
% 0.21/0.47 ( ( member346808080real_c @ A2 @ ( collec1126017874real_c @ P ) )
% 0.21/0.47 = ( P @ A2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % mem_Collect_eq
% 0.21/0.47 thf(fact_56_mem__Collect__eq,axiom,
% 0.21/0.47 ! [A2: produc999471430t_unit,P: produc999471430t_unit > $o] :
% 0.21/0.47 ( ( member235934813t_unit @ A2 @ ( collec377961627t_unit @ P ) )
% 0.21/0.47 = ( P @ A2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % mem_Collect_eq
% 0.21/0.47 thf(fact_57_mem__Collect__eq,axiom,
% 0.21/0.47 ! [A2: produc866628903_sc_sz,P: produc866628903_sc_sz > $o] :
% 0.21/0.47 ( ( member245028432_sc_sz @ A2 @ ( collec2036662930_sc_sz @ P ) )
% 0.21/0.47 = ( P @ A2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % mem_Collect_eq
% 0.21/0.47 thf(fact_58_mem__Collect__eq,axiom,
% 0.21/0.47 ! [A2: produc190496183real_c,P: produc190496183real_c > $o] :
% 0.21/0.47 ( ( member1895684704real_c @ A2 @ ( collec1643251106real_c @ P ) )
% 0.21/0.47 = ( P @ A2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % mem_Collect_eq
% 0.21/0.47 thf(fact_59_Collect__mem__eq,axiom,
% 0.21/0.47 ! [A: set_Fi1407883041real_c] :
% 0.21/0.47 ( ( collec230941376real_c
% 0.21/0.47 @ ^ [X4: finite1398487019real_c] : ( member1261661570real_c @ X4 @ A ) )
% 0.21/0.47 = A ) ).
% 0.21/0.47
% 0.21/0.47 % Collect_mem_eq
% 0.21/0.47 thf(fact_60_Collect__mem__eq,axiom,
% 0.21/0.47 ! [A: set_Pr1169339874_sc_sz] :
% 0.21/0.47 ( ( collec1199592193_sc_sz
% 0.21/0.47 @ ^ [X4: produc1821101996_sc_sz] : ( member1057565379_sc_sz @ X4 @ A ) )
% 0.21/0.47 = A ) ).
% 0.21/0.47
% 0.21/0.47 % Collect_mem_eq
% 0.21/0.47 thf(fact_61_Collect__mem__eq,axiom,
% 0.21/0.47 ! [A: set_Pr754230471real_c] :
% 0.21/0.47 ( ( collec1126017874real_c
% 0.21/0.47 @ ^ [X4: produc640052711real_c] : ( member346808080real_c @ X4 @ A ) )
% 0.21/0.47 = A ) ).
% 0.21/0.47
% 0.21/0.47 % Collect_mem_eq
% 0.21/0.47 thf(fact_62_Collect__mem__eq,axiom,
% 0.21/0.47 ! [A: set_Pr2041213564t_unit] :
% 0.21/0.47 ( ( collec377961627t_unit
% 0.21/0.47 @ ^ [X4: produc999471430t_unit] : ( member235934813t_unit @ X4 @ A ) )
% 0.21/0.47 = A ) ).
% 0.21/0.47
% 0.21/0.47 % Collect_mem_eq
% 0.21/0.47 thf(fact_63_Collect__mem__eq,axiom,
% 0.21/0.47 ! [A: set_Pr1774599175_sc_sz] :
% 0.21/0.47 ( ( collec2036662930_sc_sz
% 0.21/0.47 @ ^ [X4: produc866628903_sc_sz] : ( member245028432_sc_sz @ X4 @ A ) )
% 0.21/0.47 = A ) ).
% 0.21/0.47
% 0.21/0.47 % Collect_mem_eq
% 0.21/0.47 thf(fact_64_Collect__mem__eq,axiom,
% 0.21/0.47 ! [A: set_Pr1389752855real_c] :
% 0.21/0.47 ( ( collec1643251106real_c
% 0.21/0.47 @ ^ [X4: produc190496183real_c] : ( member1895684704real_c @ X4 @ A ) )
% 0.21/0.47 = A ) ).
% 0.21/0.47
% 0.21/0.47 % Collect_mem_eq
% 0.21/0.47 thf(fact_65_Collect__cong,axiom,
% 0.21/0.47 ! [P: produc190496183real_c > $o,Q: produc190496183real_c > $o] :
% 0.21/0.47 ( ! [X3: produc190496183real_c] :
% 0.21/0.47 ( ( P @ X3 )
% 0.21/0.47 = ( Q @ X3 ) )
% 0.21/0.47 => ( ( collec1643251106real_c @ P )
% 0.21/0.47 = ( collec1643251106real_c @ Q ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Collect_cong
% 0.21/0.47 thf(fact_66_ids_Ovne23,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.21/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.47 => ( Vid2 != Vid3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.vne23
% 0.21/0.47 thf(fact_67_ids_Ovne13,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.21/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.47 => ( Vid1 != Vid3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.vne13
% 0.21/0.47 thf(fact_68_ids_Ovne12,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.21/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.47 => ( Vid1 != Vid2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.vne12
% 0.21/0.47 thf(fact_69_ids_Opne34,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.21/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.47 => ( Pid3 != Pid4 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.pne34
% 0.21/0.47 thf(fact_70_ids_Opne24,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.21/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.47 => ( Pid2 != Pid4 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.pne24
% 0.21/0.47 thf(fact_71_ids_Opne23,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.21/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.47 => ( Pid2 != Pid3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.pne23
% 0.21/0.47 thf(fact_72_ids_Oid__simps_I24_J,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.21/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.47 => ( Pid4 != Pid3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.id_simps(24)
% 0.21/0.47 thf(fact_73_ids_Oid__simps_I23_J,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.21/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.47 => ( Pid4 != Pid2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.id_simps(23)
% 0.21/0.47 thf(fact_74_ids_Oid__simps_I22_J,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.21/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.47 => ( Pid4 != Pid1 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.id_simps(22)
% 0.21/0.47 thf(fact_75_ids_Oid__simps_I21_J,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.21/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.47 => ( Pid3 != Pid1 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.id_simps(21)
% 0.21/0.47 thf(fact_76_ids_Oid__simps_I20_J,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.21/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.47 => ( Pid3 != Pid2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.id_simps(20)
% 0.21/0.47 thf(fact_77_ids_Oid__simps_I19_J,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.21/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.47 => ( Pid2 != Pid1 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.id_simps(19)
% 0.21/0.47 thf(fact_78_ids_Oid__simps_I18_J,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.21/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.47 => ( Fid3 != Fid1 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.id_simps(18)
% 0.21/0.47 thf(fact_79_ids_Oid__simps_I17_J,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.21/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.47 => ( Fid3 != Fid2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.id_simps(17)
% 0.21/0.47 thf(fact_80_ids_Oid__simps_I16_J,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.21/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.47 => ( Fid2 != Fid1 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.id_simps(16)
% 0.21/0.47 thf(fact_81_ids_Oid__simps_I15_J,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.21/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.47 => ( Vid3 != Vid1 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.id_simps(15)
% 0.21/0.47 thf(fact_82_ids_Oid__simps_I14_J,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.21/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.47 => ( Vid3 != Vid2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.id_simps(14)
% 0.21/0.47 thf(fact_83_ids_Oid__simps_I13_J,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.21/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.47 => ( Vid2 != Vid1 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.id_simps(13)
% 0.21/0.47 thf(fact_84_ids_Oid__simps_I12_J,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.21/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.47 => ( Pid3 != Pid4 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.id_simps(12)
% 0.21/0.47 thf(fact_85_ids_Oid__simps_I11_J,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.21/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.47 => ( Pid2 != Pid4 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.id_simps(11)
% 0.21/0.47 thf(fact_86_ids_Oid__simps_I10_J,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.21/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.47 => ( Pid1 != Pid4 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.id_simps(10)
% 0.21/0.47 thf(fact_87_ids_Oid__simps_I9_J,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.21/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.47 => ( Pid1 != Pid3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.id_simps(9)
% 0.21/0.47 thf(fact_88_ids_Oid__simps_I8_J,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.21/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.47 => ( Pid2 != Pid3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.id_simps(8)
% 0.21/0.47 thf(fact_89_ids_Oid__simps_I7_J,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.21/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.47 => ( Pid1 != Pid2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.id_simps(7)
% 0.21/0.47 thf(fact_90_ids_Oid__simps_I6_J,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.21/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.47 => ( Fid1 != Fid3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.id_simps(6)
% 0.21/0.47 thf(fact_91_ids_Oid__simps_I5_J,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.21/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.47 => ( Fid2 != Fid3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.id_simps(5)
% 0.21/0.47 thf(fact_92_ids_Oid__simps_I4_J,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.21/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.47 => ( Fid1 != Fid2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.id_simps(4)
% 0.21/0.47 thf(fact_93_ids_Oid__simps_I3_J,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.21/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.47 => ( Vid1 != Vid3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.id_simps(3)
% 0.21/0.47 thf(fact_94_ids_Oid__simps_I2_J,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.21/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.47 => ( Vid2 != Vid3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.id_simps(2)
% 0.21/0.47 thf(fact_95_ids_Oid__simps_I1_J,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.21/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.47 => ( Vid1 != Vid2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.id_simps(1)
% 0.21/0.47 thf(fact_96_ids__def,axiom,
% 0.21/0.47 ( ids_sz_sf_sc
% 0.21/0.47 = ( ^ [Vid12: sz,Vid22: sz,Vid32: sz,Fid12: sf,Fid22: sf,Fid32: sf,Pid12: sc,Pid22: sc,Pid32: sc,Pid42: sc] :
% 0.21/0.47 ( ( Vid12 != Vid22 )
% 0.21/0.47 & ( Vid22 != Vid32 )
% 0.21/0.47 & ( Vid12 != Vid32 )
% 0.21/0.47 & ( Fid12 != Fid22 )
% 0.21/0.47 & ( Fid22 != Fid32 )
% 0.21/0.47 & ( Fid12 != Fid32 )
% 0.21/0.47 & ( Pid12 != Pid22 )
% 0.21/0.47 & ( Pid22 != Pid32 )
% 0.21/0.47 & ( Pid12 != Pid32 )
% 0.21/0.47 & ( Pid12 != Pid42 )
% 0.21/0.47 & ( Pid22 != Pid42 )
% 0.21/0.47 & ( Pid32 != Pid42 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids_def
% 0.21/0.47 thf(fact_97_ids_Ofne12,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.21/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.47 => ( Fid1 != Fid2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.fne12
% 0.21/0.47 thf(fact_98_ids_Ofne13,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.21/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.47 => ( Fid1 != Fid3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.fne13
% 0.21/0.47 thf(fact_99_ids_Ofne23,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.21/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.47 => ( Fid2 != Fid3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.fne23
% 0.21/0.47 thf(fact_100_ids_Ointro,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.21/0.47 ( ( Vid1 != Vid2 )
% 0.21/0.47 => ( ( Vid2 != Vid3 )
% 0.21/0.47 => ( ( Vid1 != Vid3 )
% 0.21/0.47 => ( ( Fid1 != Fid2 )
% 0.21/0.47 => ( ( Fid2 != Fid3 )
% 0.21/0.47 => ( ( Fid1 != Fid3 )
% 0.21/0.47 => ( ( Pid1 != Pid2 )
% 0.21/0.47 => ( ( Pid2 != Pid3 )
% 0.21/0.47 => ( ( Pid1 != Pid3 )
% 0.21/0.47 => ( ( Pid1 != Pid4 )
% 0.21/0.47 => ( ( Pid2 != Pid4 )
% 0.21/0.47 => ( ( Pid3 != Pid4 )
% 0.21/0.47 => ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.intro
% 0.21/0.47 thf(fact_101_ids_Opne12,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.21/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.47 => ( Pid1 != Pid2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.pne12
% 0.21/0.47 thf(fact_102_ids_Opne13,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.21/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.47 => ( Pid1 != Pid3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.pne13
% 0.21/0.47 thf(fact_103_ids_Opne14,axiom,
% 0.21/0.47 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 0.21/0.47 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.47 => ( Pid1 != Pid4 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ids.pne14
% 0.21/0.47 thf(fact_104_curry__conv,axiom,
% 0.21/0.47 ( produc1086673900c_sz_o
% 0.21/0.47 = ( ^ [F: produc1821101996_sc_sz > $o,A5: denota610675952t_unit,B5: produc866628903_sc_sz] : ( F @ ( produc789536734_sc_sz @ A5 @ B5 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % curry_conv
% 0.21/0.47 thf(fact_105_ssubst__Pair__rhs,axiom,
% 0.21/0.47 ! [R: list_f1238882004_sc_sz,S2: list_f1238882004_sc_sz,R2: set_Pr1774599175_sc_sz,S3: list_f1238882004_sc_sz] :
% 0.21/0.47 ( ( member245028432_sc_sz @ ( produc1822718231_sc_sz @ R @ S2 ) @ R2 )
% 0.21/0.47 => ( ( S3 = S2 )
% 0.21/0.47 => ( member245028432_sc_sz @ ( produc1822718231_sc_sz @ R @ S3 ) @ R2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ssubst_Pair_rhs
% 0.21/0.47 thf(fact_106_ssubst__Pair__rhs,axiom,
% 0.21/0.47 ! [R: produc866628903_sc_sz,S2: denota610675952t_unit,R2: set_Pr2041213564t_unit,S3: denota610675952t_unit] :
% 0.21/0.47 ( ( member235934813t_unit @ ( produc502616768t_unit @ R @ S2 ) @ R2 )
% 0.21/0.47 => ( ( S3 = S2 )
% 0.21/0.47 => ( member235934813t_unit @ ( produc502616768t_unit @ R @ S3 ) @ R2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ssubst_Pair_rhs
% 0.21/0.47 thf(fact_107_ssubst__Pair__rhs,axiom,
% 0.21/0.47 ! [R: produc190496183real_c,S2: produc190496183real_c,R2: set_Pr754230471real_c,S3: produc190496183real_c] :
% 0.21/0.47 ( ( member346808080real_c @ ( produc1687028567real_c @ R @ S2 ) @ R2 )
% 0.21/0.47 => ( ( S3 = S2 )
% 0.21/0.47 => ( member346808080real_c @ ( produc1687028567real_c @ R @ S3 ) @ R2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ssubst_Pair_rhs
% 0.21/0.47 thf(fact_108_ssubst__Pair__rhs,axiom,
% 0.21/0.47 ! [R: finite1398487019real_c,S2: finite1398487019real_c,R2: set_Pr1389752855real_c,S3: finite1398487019real_c] :
% 0.21/0.47 ( ( member1895684704real_c @ ( produc394644079real_c @ R @ S2 ) @ R2 )
% 0.21/0.47 => ( ( S3 = S2 )
% 0.21/0.47 => ( member1895684704real_c @ ( produc394644079real_c @ R @ S3 ) @ R2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ssubst_Pair_rhs
% 0.21/0.47 thf(fact_109_ssubst__Pair__rhs,axiom,
% 0.21/0.47 ! [R: denota610675952t_unit,S2: produc866628903_sc_sz,R2: set_Pr1169339874_sc_sz,S3: produc866628903_sc_sz] :
% 0.21/0.47 ( ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ R @ S2 ) @ R2 )
% 0.21/0.47 => ( ( S3 = S2 )
% 0.21/0.47 => ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ R @ S3 ) @ R2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ssubst_Pair_rhs
% 0.21/0.47 thf(fact_110_curryI,axiom,
% 0.21/0.47 ! [F2: produc866628903_sc_sz > $o,A2: list_f1238882004_sc_sz,B2: list_f1238882004_sc_sz] :
% 0.21/0.47 ( ( F2 @ ( produc1822718231_sc_sz @ A2 @ B2 ) )
% 0.21/0.47 => ( produc880541325c_sz_o @ F2 @ A2 @ B2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % curryI
% 0.21/0.47 thf(fact_111_curryI,axiom,
% 0.21/0.47 ! [F2: produc190496183real_c > $o,A2: finite1398487019real_c,B2: finite1398487019real_c] :
% 0.21/0.47 ( ( F2 @ ( produc394644079real_c @ A2 @ B2 ) )
% 0.21/0.48 => ( produc1716060341al_c_o @ F2 @ A2 @ B2 ) ) ).
% 0.21/0.48
% 0.21/0.48 % curryI
% 0.21/0.48 thf(fact_112_curryI,axiom,
% 0.21/0.48 ! [F2: produc999471430t_unit > $o,A2: produc866628903_sc_sz,B2: denota610675952t_unit] :
% 0.21/0.48 ( ( F2 @ ( produc502616768t_unit @ A2 @ B2 ) )
% 0.21/0.48 => ( produc38128778unit_o @ F2 @ A2 @ B2 ) ) ).
% 0.21/0.48
% 0.21/0.48 % curryI
% 0.21/0.48 thf(fact_113_curryI,axiom,
% 0.21/0.48 ! [F2: produc640052711real_c > $o,A2: produc190496183real_c,B2: produc190496183real_c] :
% 0.21/0.48 ( ( F2 @ ( produc1687028567real_c @ A2 @ B2 ) )
% 0.21/0.48 => ( produc440529997al_c_o @ F2 @ A2 @ B2 ) ) ).
% 0.21/0.48
% 0.21/0.48 % curryI
% 0.21/0.48 thf(fact_114_curryI,axiom,
% 0.21/0.48 ! [F2: produc1821101996_sc_sz > $o,A2: denota610675952t_unit,B2: produc866628903_sc_sz] :
% 0.21/0.48 ( ( F2 @ ( produc789536734_sc_sz @ A2 @ B2 ) )
% 0.21/0.48 => ( produc1086673900c_sz_o @ F2 @ A2 @ B2 ) ) ).
% 0.21/0.48
% 0.21/0.48 % curryI
% 0.21/0.48 thf(fact_115_swap__simp,axiom,
% 0.21/0.48 ! [X: list_f1238882004_sc_sz,Y: list_f1238882004_sc_sz] :
% 0.21/0.48 ( ( produc1145837239_sc_sz @ ( produc1822718231_sc_sz @ X @ Y ) )
% 0.21/0.48 = ( produc1822718231_sc_sz @ Y @ X ) ) ).
% 0.21/0.48
% 0.21/0.48 % swap_simp
% 0.21/0.48 thf(fact_116_swap__simp,axiom,
% 0.21/0.48 ! [X: produc190496183real_c,Y: produc190496183real_c] :
% 0.21/0.48 ( ( produc350724343real_c @ ( produc1687028567real_c @ X @ Y ) )
% 0.21/0.48 = ( produc1687028567real_c @ Y @ X ) ) ).
% 0.21/0.48
% 0.21/0.48 % swap_simp
% 0.21/0.48 thf(fact_117_swap__simp,axiom,
% 0.21/0.48 ! [X: finite1398487019real_c,Y: finite1398487019real_c] :
% 0.21/0.48 ( ( produc704157711real_c @ ( produc394644079real_c @ X @ Y ) )
% 0.21/0.48 = ( produc394644079real_c @ Y @ X ) ) ).
% 0.21/0.48
% 0.21/0.48 % swap_simp
% 0.21/0.48 thf(fact_118_swap__simp,axiom,
% 0.21/0.48 ! [X: produc866628903_sc_sz,Y: denota610675952t_unit] :
% 0.21/0.48 ( ( produc245128480t_unit @ ( produc502616768t_unit @ X @ Y ) )
% 0.21/0.48 = ( produc789536734_sc_sz @ Y @ X ) ) ).
% 0.21/0.48
% 0.21/0.48 % swap_simp
% 0.21/0.48 thf(fact_119_swap__simp,axiom,
% 0.21/0.48 ! [X: denota610675952t_unit,Y: produc866628903_sc_sz] :
% 0.21/0.48 ( ( produc532048446_sc_sz @ ( produc789536734_sc_sz @ X @ Y ) )
% 0.21/0.48 = ( produc502616768t_unit @ Y @ X ) ) ).
% 0.21/0.48
% 0.21/0.48 % swap_simp
% 0.21/0.48 thf(fact_120_ids_Ovalid__def,axiom,
% 0.21/0.48 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc,Phi2: formula_sf_sc_sz] :
% 0.21/0.48 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 0.21/0.48 => ( ( denota1946510237_sc_sz @ Phi2 )
% 0.21/0.48 = ( ! [I: denota610675952t_unit,Nu: produc1149990247eal_sz] :
% 0.21/0.48 ( ( denota1579475975_sc_sz @ I )
% 0.21/0.48 => ( member630771088eal_sz @ Nu @ ( denota1711272799_sc_sz @ I @ Phi2 ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % ids.valid_def
% 0.21/0.48 thf(fact_121_swap__swap,axiom,
% 0.21/0.48 ! [P2: produc999471430t_unit] :
% 0.21/0.48 ( ( produc532048446_sc_sz @ ( produc245128480t_unit @ P2 ) )
% 0.21/0.48 = P2 ) ).
% 0.21/0.48
% 0.21/0.48 % swap_swap
% 0.21/0.48 thf(fact_122_swap__swap,axiom,
% 0.21/0.48 ! [P2: produc1821101996_sc_sz] :
% 0.21/0.48 ( ( produc245128480t_unit @ ( produc532048446_sc_sz @ P2 ) )
% 0.21/0.48 = P2 ) ).
% 0.21/0.48
% 0.21/0.48 % swap_swap
% 0.21/0.48 thf(fact_123_swap__swap,axiom,
% 0.21/0.48 ! [P2: produc190496183real_c] :
% 0.21/0.48 ( ( produc704157711real_c @ ( produc704157711real_c @ P2 ) )
% 0.21/0.48 = P2 ) ).
% 0.21/0.48
% 0.21/0.48 % swap_swap
% 0.21/0.48 thf(fact_124_curryE,axiom,
% 0.21/0.48 ! [F2: produc866628903_sc_sz > $o,A2: list_f1238882004_sc_sz,B2: list_f1238882004_sc_sz] :
% 0.21/0.48 ( ( produc880541325c_sz_o @ F2 @ A2 @ B2 )
% 0.21/0.48 => ( F2 @ ( produc1822718231_sc_sz @ A2 @ B2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % curryE
% 0.21/0.48 thf(fact_125_curryE,axiom,
% 0.21/0.48 ! [F2: produc190496183real_c > $o,A2: finite1398487019real_c,B2: finite1398487019real_c] :
% 0.21/0.48 ( ( produc1716060341al_c_o @ F2 @ A2 @ B2 )
% 0.21/0.48 => ( F2 @ ( produc394644079real_c @ A2 @ B2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % curryE
% 0.21/0.48 thf(fact_126_curryE,axiom,
% 0.21/0.48 ! [F2: produc999471430t_unit > $o,A2: produc866628903_sc_sz,B2: denota610675952t_unit] :
% 0.21/0.48 ( ( produc38128778unit_o @ F2 @ A2 @ B2 )
% 0.21/0.48 => ( F2 @ ( produc502616768t_unit @ A2 @ B2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % curryE
% 0.21/0.48 thf(fact_127_curryE,axiom,
% 0.21/0.48 ! [F2: produc640052711real_c > $o,A2: produc190496183real_c,B2: produc190496183real_c] :
% 0.21/0.48 ( ( produc440529997al_c_o @ F2 @ A2 @ B2 )
% 0.21/0.48 => ( F2 @ ( produc1687028567real_c @ A2 @ B2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % curryE
% 0.21/0.48 thf(fact_128_curryE,axiom,
% 0.21/0.48 ! [F2: produc1821101996_sc_sz > $o,A2: denota610675952t_unit,B2: produc866628903_sc_sz] :
% 0.21/0.48 ( ( produc1086673900c_sz_o @ F2 @ A2 @ B2 )
% 0.21/0.48 => ( F2 @ ( produc789536734_sc_sz @ A2 @ B2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % curryE
% 0.21/0.48 thf(fact_129_curryD,axiom,
% 0.21/0.48 ! [F2: produc866628903_sc_sz > $o,A2: list_f1238882004_sc_sz,B2: list_f1238882004_sc_sz] :
% 0.21/0.48 ( ( produc880541325c_sz_o @ F2 @ A2 @ B2 )
% 0.21/0.48 => ( F2 @ ( produc1822718231_sc_sz @ A2 @ B2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % curryD
% 0.21/0.48 thf(fact_130_curryD,axiom,
% 0.21/0.48 ! [F2: produc190496183real_c > $o,A2: finite1398487019real_c,B2: finite1398487019real_c] :
% 0.21/0.48 ( ( produc1716060341al_c_o @ F2 @ A2 @ B2 )
% 0.21/0.48 => ( F2 @ ( produc394644079real_c @ A2 @ B2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % curryD
% 0.21/0.48 thf(fact_131_curryD,axiom,
% 0.21/0.48 ! [F2: produc999471430t_unit > $o,A2: produc866628903_sc_sz,B2: denota610675952t_unit] :
% 0.21/0.48 ( ( produc38128778unit_o @ F2 @ A2 @ B2 )
% 0.21/0.48 => ( F2 @ ( produc502616768t_unit @ A2 @ B2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % curryD
% 0.21/0.48 thf(fact_132_curryD,axiom,
% 0.21/0.48 ! [F2: produc640052711real_c > $o,A2: produc190496183real_c,B2: produc190496183real_c] :
% 0.21/0.48 ( ( produc440529997al_c_o @ F2 @ A2 @ B2 )
% 0.21/0.48 => ( F2 @ ( produc1687028567real_c @ A2 @ B2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % curryD
% 0.21/0.48 thf(fact_133_curryD,axiom,
% 0.21/0.48 ! [F2: produc1821101996_sc_sz > $o,A2: denota610675952t_unit,B2: produc866628903_sc_sz] :
% 0.21/0.48 ( ( produc1086673900c_sz_o @ F2 @ A2 @ B2 )
% 0.21/0.48 => ( F2 @ ( produc789536734_sc_sz @ A2 @ B2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % curryD
% 0.21/0.48 thf(fact_134_pair__in__swap__image,axiom,
% 0.21/0.48 ! [Y: list_f1238882004_sc_sz,X: list_f1238882004_sc_sz,A: set_Pr1774599175_sc_sz] :
% 0.21/0.48 ( ( member245028432_sc_sz @ ( produc1822718231_sc_sz @ Y @ X ) @ ( image_1313166277_sc_sz @ produc1145837239_sc_sz @ A ) )
% 0.21/0.48 = ( member245028432_sc_sz @ ( produc1822718231_sc_sz @ X @ Y ) @ A ) ) ).
% 0.21/0.48
% 0.21/0.48 % pair_in_swap_image
% 0.21/0.48 thf(fact_135_pair__in__swap__image,axiom,
% 0.21/0.48 ! [Y: produc190496183real_c,X: produc190496183real_c,A: set_Pr754230471real_c] :
% 0.21/0.48 ( ( member346808080real_c @ ( produc1687028567real_c @ Y @ X ) @ ( image_2041365445real_c @ produc350724343real_c @ A ) )
% 0.21/0.48 = ( member346808080real_c @ ( produc1687028567real_c @ X @ Y ) @ A ) ) ).
% 0.21/0.48
% 0.21/0.48 % pair_in_swap_image
% 0.21/0.48 thf(fact_136_pair__in__swap__image,axiom,
% 0.21/0.48 ! [Y: finite1398487019real_c,X: finite1398487019real_c,A: set_Pr1389752855real_c] :
% 0.21/0.48 ( ( member1895684704real_c @ ( produc394644079real_c @ Y @ X ) @ ( image_738229701real_c @ produc704157711real_c @ A ) )
% 0.21/0.48 = ( member1895684704real_c @ ( produc394644079real_c @ X @ Y ) @ A ) ) ).
% 0.21/0.48
% 0.21/0.48 % pair_in_swap_image
% 0.21/0.48 thf(fact_137_pair__in__swap__image,axiom,
% 0.21/0.48 ! [Y: produc866628903_sc_sz,X: denota610675952t_unit,A: set_Pr1169339874_sc_sz] :
% 0.21/0.48 ( ( member235934813t_unit @ ( produc502616768t_unit @ Y @ X ) @ ( image_904562809t_unit @ produc532048446_sc_sz @ A ) )
% 0.21/0.48 = ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ X @ Y ) @ A ) ) ).
% 0.21/0.48
% 0.21/0.48 % pair_in_swap_image
% 0.21/0.48 thf(fact_138_pair__in__swap__image,axiom,
% 0.21/0.48 ! [Y: denota610675952t_unit,X: produc866628903_sc_sz,A: set_Pr2041213564t_unit] :
% 0.21/0.48 ( ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ Y @ X ) @ ( image_1426741113_sc_sz @ produc245128480t_unit @ A ) )
% 0.21/0.48 = ( member235934813t_unit @ ( produc502616768t_unit @ X @ Y ) @ A ) ) ).
% 0.21/0.48
% 0.21/0.48 % pair_in_swap_image
% 0.21/0.48 thf(fact_139_internal__case__prod__def,axiom,
% 0.21/0.48 produc383750338real_c = produc1575513068real_c ).
% 0.21/0.48
% 0.21/0.48 % internal_case_prod_def
% 0.21/0.48 thf(fact_140_internal__case__prod__def,axiom,
% 0.21/0.48 produc198687651c_sz_o = produc619560141c_sz_o ).
% 0.21/0.48
% 0.21/0.48 % internal_case_prod_def
% 0.21/0.48 thf(fact_141_internal__case__prod__def,axiom,
% 0.21/0.48 produc1894848802real_c = produc237521996real_c ).
% 0.21/0.48
% 0.21/0.48 % internal_case_prod_def
% 0.21/0.48 thf(fact_142_internal__case__prod__def,axiom,
% 0.21/0.48 produc1442549981real_c = produc107375667real_c ).
% 0.21/0.48
% 0.21/0.48 % internal_case_prod_def
% 0.21/0.48 thf(fact_143_internal__case__prod__def,axiom,
% 0.21/0.48 produc2099580355_sc_sz = produc435149849_sc_sz ).
% 0.21/0.48
% 0.21/0.48 % internal_case_prod_def
% 0.21/0.48 thf(fact_144_apsnd__conv,axiom,
% 0.21/0.48 ! [F2: list_f1238882004_sc_sz > list_f1238882004_sc_sz,X: list_f1238882004_sc_sz,Y: list_f1238882004_sc_sz] :
% 0.21/0.48 ( ( produc233219286_sc_sz @ F2 @ ( produc1822718231_sc_sz @ X @ Y ) )
% 0.21/0.48 = ( produc1822718231_sc_sz @ X @ ( F2 @ Y ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % apsnd_conv
% 0.21/0.48 thf(fact_145_apsnd__conv,axiom,
% 0.21/0.48 ! [F2: finite1398487019real_c > finite1398487019real_c,X: finite1398487019real_c,Y: finite1398487019real_c] :
% 0.21/0.48 ( ( produc981295297real_c @ F2 @ ( produc394644079real_c @ X @ Y ) )
% 0.21/0.48 = ( produc394644079real_c @ X @ ( F2 @ Y ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % apsnd_conv
% 0.21/0.48 thf(fact_146_apsnd__conv,axiom,
% 0.21/0.48 ! [F2: denota610675952t_unit > denota610675952t_unit,X: produc866628903_sc_sz,Y: denota610675952t_unit] :
% 0.21/0.48 ( ( produc793407943_sc_sz @ F2 @ ( produc502616768t_unit @ X @ Y ) )
% 0.21/0.48 = ( produc502616768t_unit @ X @ ( F2 @ Y ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % apsnd_conv
% 0.21/0.48 thf(fact_147_apsnd__conv,axiom,
% 0.21/0.48 ! [F2: produc190496183real_c > produc190496183real_c,X: produc190496183real_c,Y: produc190496183real_c] :
% 0.21/0.48 ( ( produc2089853305real_c @ F2 @ ( produc1687028567real_c @ X @ Y ) )
% 0.21/0.48 = ( produc1687028567real_c @ X @ ( F2 @ Y ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % apsnd_conv
% 0.21/0.48 thf(fact_148_apsnd__conv,axiom,
% 0.21/0.48 ! [F2: produc866628903_sc_sz > produc866628903_sc_sz,X: denota610675952t_unit,Y: produc866628903_sc_sz] :
% 0.21/0.48 ( ( produc1959054510t_unit @ F2 @ ( produc789536734_sc_sz @ X @ Y ) )
% 0.21/0.48 = ( produc789536734_sc_sz @ X @ ( F2 @ Y ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % apsnd_conv
% 0.21/0.48 thf(fact_149_mem__case__prodI2,axiom,
% 0.21/0.48 ! [P2: produc1821101996_sc_sz,Z: produc190496183real_c,C2: denota610675952t_unit > produc866628903_sc_sz > set_Pr1389752855real_c] :
% 0.21/0.48 ( ! [A4: denota610675952t_unit,B4: produc866628903_sc_sz] :
% 0.21/0.48 ( ( P2
% 0.21/0.48 = ( produc789536734_sc_sz @ A4 @ B4 ) )
% 0.21/0.48 => ( member1895684704real_c @ Z @ ( C2 @ A4 @ B4 ) ) )
% 0.21/0.48 => ( member1895684704real_c @ Z @ ( produc237521996real_c @ C2 @ P2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mem_case_prodI2
% 0.21/0.48 thf(fact_150_mem__case__prodI2,axiom,
% 0.21/0.48 ! [P2: produc190496183real_c,Z: finite1398487019real_c,C2: finite1398487019real_c > finite1398487019real_c > set_Fi1407883041real_c] :
% 0.21/0.48 ( ! [A4: finite1398487019real_c,B4: finite1398487019real_c] :
% 0.21/0.48 ( ( P2
% 0.21/0.48 = ( produc394644079real_c @ A4 @ B4 ) )
% 0.21/0.48 => ( member1261661570real_c @ Z @ ( C2 @ A4 @ B4 ) ) )
% 0.21/0.48 => ( member1261661570real_c @ Z @ ( produc29022117real_c @ C2 @ P2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mem_case_prodI2
% 0.21/0.48 thf(fact_151_mem__case__prodI2,axiom,
% 0.21/0.48 ! [P2: produc866628903_sc_sz,Z: finite1398487019real_c,C2: list_f1238882004_sc_sz > list_f1238882004_sc_sz > set_Fi1407883041real_c] :
% 0.21/0.48 ( ! [A4: list_f1238882004_sc_sz,B4: list_f1238882004_sc_sz] :
% 0.21/0.48 ( ( P2
% 0.21/0.48 = ( produc1822718231_sc_sz @ A4 @ B4 ) )
% 0.21/0.48 => ( member1261661570real_c @ Z @ ( C2 @ A4 @ B4 ) ) )
% 0.21/0.48 => ( member1261661570real_c @ Z @ ( produc1449736269real_c @ C2 @ P2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mem_case_prodI2
% 0.21/0.48 thf(fact_152_mem__case__prodI2,axiom,
% 0.21/0.48 ! [P2: produc190496183real_c,Z: produc190496183real_c,C2: finite1398487019real_c > finite1398487019real_c > set_Pr1389752855real_c] :
% 0.21/0.48 ( ! [A4: finite1398487019real_c,B4: finite1398487019real_c] :
% 0.21/0.48 ( ( P2
% 0.21/0.48 = ( produc394644079real_c @ A4 @ B4 ) )
% 0.21/0.48 => ( member1895684704real_c @ Z @ ( C2 @ A4 @ B4 ) ) )
% 0.21/0.48 => ( member1895684704real_c @ Z @ ( produc923381907real_c @ C2 @ P2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mem_case_prodI2
% 0.21/0.48 thf(fact_153_mem__case__prodI2,axiom,
% 0.21/0.48 ! [P2: produc866628903_sc_sz,Z: produc190496183real_c,C2: list_f1238882004_sc_sz > list_f1238882004_sc_sz > set_Pr1389752855real_c] :
% 0.21/0.48 ( ! [A4: list_f1238882004_sc_sz,B4: list_f1238882004_sc_sz] :
% 0.21/0.48 ( ( P2
% 0.21/0.48 = ( produc1822718231_sc_sz @ A4 @ B4 ) )
% 0.21/0.48 => ( member1895684704real_c @ Z @ ( C2 @ A4 @ B4 ) ) )
% 0.21/0.48 => ( member1895684704real_c @ Z @ ( produc6841835real_c @ C2 @ P2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mem_case_prodI2
% 0.21/0.48 thf(fact_154_mem__case__prodI2,axiom,
% 0.21/0.48 ! [P2: produc190496183real_c,Z: produc866628903_sc_sz,C2: finite1398487019real_c > finite1398487019real_c > set_Pr1774599175_sc_sz] :
% 0.21/0.48 ( ! [A4: finite1398487019real_c,B4: finite1398487019real_c] :
% 0.21/0.48 ( ( P2
% 0.21/0.48 = ( produc394644079real_c @ A4 @ B4 ) )
% 0.21/0.48 => ( member245028432_sc_sz @ Z @ ( C2 @ A4 @ B4 ) ) )
% 0.21/0.48 => ( member245028432_sc_sz @ Z @ ( produc642283651_sc_sz @ C2 @ P2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mem_case_prodI2
% 0.21/0.48 thf(fact_155_mem__case__prodI2,axiom,
% 0.21/0.48 ! [P2: produc640052711real_c,Z: finite1398487019real_c,C2: produc190496183real_c > produc190496183real_c > set_Fi1407883041real_c] :
% 0.21/0.48 ( ! [A4: produc190496183real_c,B4: produc190496183real_c] :
% 0.21/0.48 ( ( P2
% 0.21/0.48 = ( produc1687028567real_c @ A4 @ B4 ) )
% 0.21/0.48 => ( member1261661570real_c @ Z @ ( C2 @ A4 @ B4 ) ) )
% 0.21/0.48 => ( member1261661570real_c @ Z @ ( produc1066779277real_c @ C2 @ P2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mem_case_prodI2
% 0.21/0.48 thf(fact_156_mem__case__prodI2,axiom,
% 0.21/0.48 ! [P2: produc1821101996_sc_sz,Z: finite1398487019real_c,C2: denota610675952t_unit > produc866628903_sc_sz > set_Fi1407883041real_c] :
% 0.21/0.48 ( ! [A4: denota610675952t_unit,B4: produc866628903_sc_sz] :
% 0.21/0.48 ( ( P2
% 0.21/0.48 = ( produc789536734_sc_sz @ A4 @ B4 ) )
% 0.21/0.48 => ( member1261661570real_c @ Z @ ( C2 @ A4 @ B4 ) ) )
% 0.21/0.48 => ( member1261661570real_c @ Z @ ( produc2068697644real_c @ C2 @ P2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mem_case_prodI2
% 0.21/0.48 thf(fact_157_mem__case__prodI2,axiom,
% 0.21/0.48 ! [P2: produc999471430t_unit,Z: finite1398487019real_c,C2: produc866628903_sc_sz > denota610675952t_unit > set_Fi1407883041real_c] :
% 0.21/0.48 ( ! [A4: produc866628903_sc_sz,B4: denota610675952t_unit] :
% 0.21/0.48 ( ( P2
% 0.21/0.48 = ( produc502616768t_unit @ A4 @ B4 ) )
% 0.21/0.48 => ( member1261661570real_c @ Z @ ( C2 @ A4 @ B4 ) ) )
% 0.21/0.48 => ( member1261661570real_c @ Z @ ( produc1368849166real_c @ C2 @ P2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mem_case_prodI2
% 0.21/0.48 thf(fact_158_mem__case__prodI2,axiom,
% 0.21/0.48 ! [P2: produc866628903_sc_sz,Z: produc866628903_sc_sz,C2: list_f1238882004_sc_sz > list_f1238882004_sc_sz > set_Pr1774599175_sc_sz] :
% 0.21/0.48 ( ! [A4: list_f1238882004_sc_sz,B4: list_f1238882004_sc_sz] :
% 0.21/0.48 ( ( P2
% 0.21/0.48 = ( produc1822718231_sc_sz @ A4 @ B4 ) )
% 0.21/0.48 => ( member245028432_sc_sz @ Z @ ( C2 @ A4 @ B4 ) ) )
% 0.21/0.48 => ( member245028432_sc_sz @ Z @ ( produc1563580891_sc_sz @ C2 @ P2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mem_case_prodI2
% 0.21/0.48 thf(fact_159_mem__case__prodI,axiom,
% 0.21/0.48 ! [Z: produc190496183real_c,C2: denota610675952t_unit > produc866628903_sc_sz > set_Pr1389752855real_c,A2: denota610675952t_unit,B2: produc866628903_sc_sz] :
% 0.21/0.48 ( ( member1895684704real_c @ Z @ ( C2 @ A2 @ B2 ) )
% 0.21/0.48 => ( member1895684704real_c @ Z @ ( produc237521996real_c @ C2 @ ( produc789536734_sc_sz @ A2 @ B2 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mem_case_prodI
% 0.21/0.48 thf(fact_160_mem__case__prodI,axiom,
% 0.21/0.48 ! [Z: finite1398487019real_c,C2: finite1398487019real_c > finite1398487019real_c > set_Fi1407883041real_c,A2: finite1398487019real_c,B2: finite1398487019real_c] :
% 0.21/0.48 ( ( member1261661570real_c @ Z @ ( C2 @ A2 @ B2 ) )
% 0.21/0.48 => ( member1261661570real_c @ Z @ ( produc29022117real_c @ C2 @ ( produc394644079real_c @ A2 @ B2 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mem_case_prodI
% 0.21/0.48 thf(fact_161_mem__case__prodI,axiom,
% 0.21/0.48 ! [Z: finite1398487019real_c,C2: list_f1238882004_sc_sz > list_f1238882004_sc_sz > set_Fi1407883041real_c,A2: list_f1238882004_sc_sz,B2: list_f1238882004_sc_sz] :
% 0.21/0.48 ( ( member1261661570real_c @ Z @ ( C2 @ A2 @ B2 ) )
% 0.21/0.48 => ( member1261661570real_c @ Z @ ( produc1449736269real_c @ C2 @ ( produc1822718231_sc_sz @ A2 @ B2 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mem_case_prodI
% 0.21/0.48 thf(fact_162_mem__case__prodI,axiom,
% 0.21/0.48 ! [Z: produc190496183real_c,C2: finite1398487019real_c > finite1398487019real_c > set_Pr1389752855real_c,A2: finite1398487019real_c,B2: finite1398487019real_c] :
% 0.21/0.48 ( ( member1895684704real_c @ Z @ ( C2 @ A2 @ B2 ) )
% 0.21/0.48 => ( member1895684704real_c @ Z @ ( produc923381907real_c @ C2 @ ( produc394644079real_c @ A2 @ B2 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mem_case_prodI
% 0.21/0.48 thf(fact_163_mem__case__prodI,axiom,
% 0.21/0.48 ! [Z: produc190496183real_c,C2: list_f1238882004_sc_sz > list_f1238882004_sc_sz > set_Pr1389752855real_c,A2: list_f1238882004_sc_sz,B2: list_f1238882004_sc_sz] :
% 0.21/0.48 ( ( member1895684704real_c @ Z @ ( C2 @ A2 @ B2 ) )
% 0.21/0.48 => ( member1895684704real_c @ Z @ ( produc6841835real_c @ C2 @ ( produc1822718231_sc_sz @ A2 @ B2 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mem_case_prodI
% 0.21/0.48 thf(fact_164_mem__case__prodI,axiom,
% 0.21/0.48 ! [Z: produc866628903_sc_sz,C2: finite1398487019real_c > finite1398487019real_c > set_Pr1774599175_sc_sz,A2: finite1398487019real_c,B2: finite1398487019real_c] :
% 0.21/0.48 ( ( member245028432_sc_sz @ Z @ ( C2 @ A2 @ B2 ) )
% 0.21/0.48 => ( member245028432_sc_sz @ Z @ ( produc642283651_sc_sz @ C2 @ ( produc394644079real_c @ A2 @ B2 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mem_case_prodI
% 0.21/0.48 thf(fact_165_mem__case__prodI,axiom,
% 0.21/0.48 ! [Z: finite1398487019real_c,C2: produc190496183real_c > produc190496183real_c > set_Fi1407883041real_c,A2: produc190496183real_c,B2: produc190496183real_c] :
% 0.21/0.48 ( ( member1261661570real_c @ Z @ ( C2 @ A2 @ B2 ) )
% 0.21/0.48 => ( member1261661570real_c @ Z @ ( produc1066779277real_c @ C2 @ ( produc1687028567real_c @ A2 @ B2 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mem_case_prodI
% 0.21/0.48 thf(fact_166_mem__case__prodI,axiom,
% 0.21/0.48 ! [Z: finite1398487019real_c,C2: denota610675952t_unit > produc866628903_sc_sz > set_Fi1407883041real_c,A2: denota610675952t_unit,B2: produc866628903_sc_sz] :
% 0.21/0.48 ( ( member1261661570real_c @ Z @ ( C2 @ A2 @ B2 ) )
% 0.21/0.48 => ( member1261661570real_c @ Z @ ( produc2068697644real_c @ C2 @ ( produc789536734_sc_sz @ A2 @ B2 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mem_case_prodI
% 0.21/0.48 thf(fact_167_mem__case__prodI,axiom,
% 0.21/0.48 ! [Z: finite1398487019real_c,C2: produc866628903_sc_sz > denota610675952t_unit > set_Fi1407883041real_c,A2: produc866628903_sc_sz,B2: denota610675952t_unit] :
% 0.21/0.48 ( ( member1261661570real_c @ Z @ ( C2 @ A2 @ B2 ) )
% 0.21/0.48 => ( member1261661570real_c @ Z @ ( produc1368849166real_c @ C2 @ ( produc502616768t_unit @ A2 @ B2 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mem_case_prodI
% 0.21/0.48 thf(fact_168_mem__case__prodI,axiom,
% 0.21/0.48 ! [Z: produc866628903_sc_sz,C2: list_f1238882004_sc_sz > list_f1238882004_sc_sz > set_Pr1774599175_sc_sz,A2: list_f1238882004_sc_sz,B2: list_f1238882004_sc_sz] :
% 0.21/0.48 ( ( member245028432_sc_sz @ Z @ ( C2 @ A2 @ B2 ) )
% 0.21/0.48 => ( member245028432_sc_sz @ Z @ ( produc1563580891_sc_sz @ C2 @ ( produc1822718231_sc_sz @ A2 @ B2 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mem_case_prodI
% 0.21/0.48 thf(fact_169_case__prodI2,axiom,
% 0.21/0.48 ! [P2: produc866628903_sc_sz,C2: list_f1238882004_sc_sz > list_f1238882004_sc_sz > $o] :
% 0.21/0.48 ( ! [A4: list_f1238882004_sc_sz,B4: list_f1238882004_sc_sz] :
% 0.21/0.48 ( ( P2
% 0.21/0.48 = ( produc1822718231_sc_sz @ A4 @ B4 ) )
% 0.21/0.48 => ( C2 @ A4 @ B4 ) )
% 0.21/0.48 => ( produc2039065452c_sz_o @ C2 @ P2 ) ) ).
% 0.21/0.48
% 0.21/0.48 % case_prodI2
% 0.21/0.48 thf(fact_170_case__prodI2,axiom,
% 0.21/0.48 ! [P2: produc190496183real_c,C2: finite1398487019real_c > finite1398487019real_c > $o] :
% 0.21/0.48 ( ! [A4: finite1398487019real_c,B4: finite1398487019real_c] :
% 0.21/0.48 ( ( P2
% 0.21/0.48 = ( produc394644079real_c @ A4 @ B4 ) )
% 0.21/0.48 => ( C2 @ A4 @ B4 ) )
% 0.21/0.48 => ( produc353381908al_c_o @ C2 @ P2 ) ) ).
% 0.21/0.48
% 0.21/0.48 % case_prodI2
% 0.21/0.48 thf(fact_171_case__prodI2,axiom,
% 0.21/0.48 ! [P2: produc999471430t_unit,C2: produc866628903_sc_sz > denota610675952t_unit > $o] :
% 0.21/0.48 ( ! [A4: produc866628903_sc_sz,B4: denota610675952t_unit] :
% 0.21/0.48 ( ( P2
% 0.21/0.48 = ( produc502616768t_unit @ A4 @ B4 ) )
% 0.21/0.48 => ( C2 @ A4 @ B4 ) )
% 0.21/0.48 => ( produc1718498667unit_o @ C2 @ P2 ) ) ).
% 0.21/0.48
% 0.21/0.48 % case_prodI2
% 0.21/0.48 thf(fact_172_case__prodI2,axiom,
% 0.21/0.48 ! [P2: produc640052711real_c,C2: produc190496183real_c > produc190496183real_c > $o] :
% 0.21/0.48 ( ! [A4: produc190496183real_c,B4: produc190496183real_c] :
% 0.21/0.48 ( ( P2
% 0.21/0.48 = ( produc1687028567real_c @ A4 @ B4 ) )
% 0.21/0.48 => ( C2 @ A4 @ B4 ) )
% 0.21/0.48 => ( produc1726730540al_c_o @ C2 @ P2 ) ) ).
% 0.21/0.48
% 0.21/0.48 % case_prodI2
% 0.21/0.48 thf(fact_173_case__prodI2,axiom,
% 0.21/0.48 ! [P2: produc1821101996_sc_sz,C2: denota610675952t_unit > produc866628903_sc_sz > $o] :
% 0.21/0.48 ( ! [A4: denota610675952t_unit,B4: produc866628903_sc_sz] :
% 0.21/0.48 ( ( P2
% 0.21/0.48 = ( produc789536734_sc_sz @ A4 @ B4 ) )
% 0.21/0.48 => ( C2 @ A4 @ B4 ) )
% 0.21/0.48 => ( produc619560141c_sz_o @ C2 @ P2 ) ) ).
% 0.21/0.48
% 0.21/0.48 % case_prodI2
% 0.21/0.48 thf(fact_174_case__prodI,axiom,
% 0.21/0.48 ! [F2: list_f1238882004_sc_sz > list_f1238882004_sc_sz > $o,A2: list_f1238882004_sc_sz,B2: list_f1238882004_sc_sz] :
% 0.21/0.48 ( ( F2 @ A2 @ B2 )
% 0.21/0.48 => ( produc2039065452c_sz_o @ F2 @ ( produc1822718231_sc_sz @ A2 @ B2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % case_prodI
% 0.21/0.48 thf(fact_175_case__prodI,axiom,
% 0.21/0.48 ! [F2: finite1398487019real_c > finite1398487019real_c > $o,A2: finite1398487019real_c,B2: finite1398487019real_c] :
% 0.21/0.48 ( ( F2 @ A2 @ B2 )
% 0.21/0.48 => ( produc353381908al_c_o @ F2 @ ( produc394644079real_c @ A2 @ B2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % case_prodI
% 0.21/0.48 thf(fact_176_case__prodI,axiom,
% 0.21/0.48 ! [F2: produc866628903_sc_sz > denota610675952t_unit > $o,A2: produc866628903_sc_sz,B2: denota610675952t_unit] :
% 0.21/0.48 ( ( F2 @ A2 @ B2 )
% 0.21/0.48 => ( produc1718498667unit_o @ F2 @ ( produc502616768t_unit @ A2 @ B2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % case_prodI
% 0.21/0.48 thf(fact_177_case__prodI,axiom,
% 0.21/0.48 ! [F2: produc190496183real_c > produc190496183real_c > $o,A2: produc190496183real_c,B2: produc190496183real_c] :
% 0.21/0.48 ( ( F2 @ A2 @ B2 )
% 0.21/0.48 => ( produc1726730540al_c_o @ F2 @ ( produc1687028567real_c @ A2 @ B2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % case_prodI
% 0.21/0.48 thf(fact_178_case__prodI,axiom,
% 0.21/0.48 ! [F2: denota610675952t_unit > produc866628903_sc_sz > $o,A2: denota610675952t_unit,B2: produc866628903_sc_sz] :
% 0.21/0.48 ( ( F2 @ A2 @ B2 )
% 0.21/0.48 => ( produc619560141c_sz_o @ F2 @ ( produc789536734_sc_sz @ A2 @ B2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % case_prodI
% 0.21/0.48 thf(fact_179_case__prod__conv,axiom,
% 0.21/0.48 ! [F2: denota610675952t_unit > produc866628903_sc_sz > produc190496183real_c,A2: denota610675952t_unit,B2: produc866628903_sc_sz] :
% 0.21/0.48 ( ( produc1575513068real_c @ F2 @ ( produc789536734_sc_sz @ A2 @ B2 ) )
% 0.21/0.48 = ( F2 @ A2 @ B2 ) ) ).
% 0.21/0.48
% 0.21/0.48 % case_prod_conv
% 0.21/0.48 thf(fact_180_case__prod__conv,axiom,
% 0.21/0.48 ! [F2: denota610675952t_unit > produc866628903_sc_sz > $o,A2: denota610675952t_unit,B2: produc866628903_sc_sz] :
% 0.21/0.48 ( ( produc619560141c_sz_o @ F2 @ ( produc789536734_sc_sz @ A2 @ B2 ) )
% 0.21/0.48 = ( F2 @ A2 @ B2 ) ) ).
% 0.21/0.48
% 0.21/0.48 % case_prod_conv
% 0.21/0.48 thf(fact_181_case__prod__conv,axiom,
% 0.21/0.48 ! [F2: denota610675952t_unit > produc866628903_sc_sz > set_Pr1389752855real_c,A2: denota610675952t_unit,B2: produc866628903_sc_sz] :
% 0.21/0.48 ( ( produc237521996real_c @ F2 @ ( produc789536734_sc_sz @ A2 @ B2 ) )
% 0.21/0.48 = ( F2 @ A2 @ B2 ) ) ).
% 0.21/0.48
% 0.21/0.48 % case_prod_conv
% 0.21/0.48 thf(fact_182_case__prod__conv,axiom,
% 0.21/0.48 ! [F2: finite1398487019real_c > finite1398487019real_c > produc190496183real_c,A2: finite1398487019real_c,B2: finite1398487019real_c] :
% 0.21/0.48 ( ( produc107375667real_c @ F2 @ ( produc394644079real_c @ A2 @ B2 ) )
% 0.21/0.48 = ( F2 @ A2 @ B2 ) ) ).
% 0.21/0.48
% 0.21/0.48 % case_prod_conv
% 0.21/0.48 thf(fact_183_case__prod__conv,axiom,
% 0.21/0.48 ! [F2: produc866628903_sc_sz > denota610675952t_unit > produc1821101996_sc_sz,A2: produc866628903_sc_sz,B2: denota610675952t_unit] :
% 0.21/0.48 ( ( produc435149849_sc_sz @ F2 @ ( produc502616768t_unit @ A2 @ B2 ) )
% 0.21/0.48 = ( F2 @ A2 @ B2 ) ) ).
% 0.21/0.48
% 0.21/0.48 % case_prod_conv
% 0.21/0.48 thf(fact_184_curry__case__prod,axiom,
% 0.21/0.48 ! [F2: denota610675952t_unit > produc866628903_sc_sz > produc190496183real_c] :
% 0.21/0.48 ( ( produc753314315real_c @ ( produc1575513068real_c @ F2 ) )
% 0.21/0.48 = F2 ) ).
% 0.21/0.48
% 0.21/0.48 % curry_case_prod
% 0.21/0.48 thf(fact_185_curry__case__prod,axiom,
% 0.21/0.48 ! [F2: denota610675952t_unit > produc866628903_sc_sz > $o] :
% 0.21/0.48 ( ( produc1086673900c_sz_o @ ( produc619560141c_sz_o @ F2 ) )
% 0.21/0.48 = F2 ) ).
% 0.21/0.48
% 0.21/0.48 % curry_case_prod
% 0.21/0.48 thf(fact_186_curry__case__prod,axiom,
% 0.21/0.48 ! [F2: denota610675952t_unit > produc866628903_sc_sz > set_Pr1389752855real_c] :
% 0.21/0.48 ( ( produc1827049067real_c @ ( produc237521996real_c @ F2 ) )
% 0.21/0.48 = F2 ) ).
% 0.21/0.48
% 0.21/0.48 % curry_case_prod
% 0.21/0.48 thf(fact_187_curry__case__prod,axiom,
% 0.21/0.48 ! [F2: finite1398487019real_c > finite1398487019real_c > produc190496183real_c] :
% 0.21/0.48 ( ( produc1119115220real_c @ ( produc107375667real_c @ F2 ) )
% 0.21/0.48 = F2 ) ).
% 0.21/0.48
% 0.21/0.48 % curry_case_prod
% 0.21/0.48 thf(fact_188_curry__case__prod,axiom,
% 0.21/0.48 ! [F2: produc866628903_sc_sz > denota610675952t_unit > produc1821101996_sc_sz] :
% 0.21/0.48 ( ( produc295339066_sc_sz @ ( produc435149849_sc_sz @ F2 ) )
% 0.21/0.48 = F2 ) ).
% 0.21/0.48
% 0.21/0.48 % curry_case_prod
% 0.21/0.48 thf(fact_189_case__prod__curry,axiom,
% 0.21/0.48 ! [F2: produc1821101996_sc_sz > produc190496183real_c] :
% 0.21/0.48 ( ( produc1575513068real_c @ ( produc753314315real_c @ F2 ) )
% 0.21/0.48 = F2 ) ).
% 0.21/0.48
% 0.21/0.48 % case_prod_curry
% 0.21/0.48 thf(fact_190_case__prod__curry,axiom,
% 0.21/0.48 ! [F2: produc1821101996_sc_sz > $o] :
% 0.21/0.48 ( ( produc619560141c_sz_o @ ( produc1086673900c_sz_o @ F2 ) )
% 0.21/0.48 = F2 ) ).
% 0.21/0.48
% 0.21/0.48 % case_prod_curry
% 0.21/0.48 thf(fact_191_case__prod__curry,axiom,
% 0.21/0.48 ! [F2: produc1821101996_sc_sz > set_Pr1389752855real_c] :
% 0.21/0.48 ( ( produc237521996real_c @ ( produc1827049067real_c @ F2 ) )
% 0.21/0.48 = F2 ) ).
% 0.21/0.48
% 0.21/0.48 % case_prod_curry
% 0.21/0.48 thf(fact_192_case__prod__curry,axiom,
% 0.21/0.48 ! [F2: produc190496183real_c > produc190496183real_c] :
% 0.21/0.48 ( ( produc107375667real_c @ ( produc1119115220real_c @ F2 ) )
% 0.21/0.48 = F2 ) ).
% 0.21/0.48
% 0.21/0.48 % case_prod_curry
% 0.21/0.48 thf(fact_193_case__prod__curry,axiom,
% 0.21/0.48 ! [F2: produc999471430t_unit > produc1821101996_sc_sz] :
% 0.21/0.48 ( ( produc435149849_sc_sz @ ( produc295339066_sc_sz @ F2 ) )
% 0.21/0.48 = F2 ) ).
% 0.21/0.48
% 0.21/0.48 % case_prod_curry
% 0.21/0.48 thf(fact_194_case__swap,axiom,
% 0.21/0.48 ! [F2: denota610675952t_unit > produc866628903_sc_sz > produc190496183real_c,P2: produc1821101996_sc_sz] :
% 0.21/0.48 ( ( produc645763722real_c
% 0.21/0.48 @ ^ [Y4: produc866628903_sc_sz,X4: denota610675952t_unit] : ( F2 @ X4 @ Y4 )
% 0.21/0.48 @ ( produc532048446_sc_sz @ P2 ) )
% 0.21/0.48 = ( produc1575513068real_c @ F2 @ P2 ) ) ).
% 0.21/0.48
% 0.21/0.48 % case_swap
% 0.21/0.48 thf(fact_195_case__swap,axiom,
% 0.21/0.48 ! [F2: denota610675952t_unit > produc866628903_sc_sz > $o,P2: produc1821101996_sc_sz] :
% 0.21/0.48 ( ( produc1718498667unit_o
% 0.21/0.48 @ ^ [Y4: produc866628903_sc_sz,X4: denota610675952t_unit] : ( F2 @ X4 @ Y4 )
% 0.21/0.48 @ ( produc532048446_sc_sz @ P2 ) )
% 0.21/0.48 = ( produc619560141c_sz_o @ F2 @ P2 ) ) ).
% 0.21/0.48
% 0.21/0.48 % case_swap
% 0.21/0.48 thf(fact_196_case__swap,axiom,
% 0.21/0.48 ! [F2: denota610675952t_unit > produc866628903_sc_sz > set_Pr1389752855real_c,P2: produc1821101996_sc_sz] :
% 0.21/0.48 ( ( produc593754858real_c
% 0.21/0.48 @ ^ [Y4: produc866628903_sc_sz,X4: denota610675952t_unit] : ( F2 @ X4 @ Y4 )
% 0.21/0.48 @ ( produc532048446_sc_sz @ P2 ) )
% 0.21/0.48 = ( produc237521996real_c @ F2 @ P2 ) ) ).
% 0.21/0.48
% 0.21/0.48 % case_swap
% 0.21/0.48 thf(fact_197_case__swap,axiom,
% 0.21/0.48 ! [F2: produc866628903_sc_sz > denota610675952t_unit > produc1821101996_sc_sz,P2: produc999471430t_unit] :
% 0.21/0.48 ( ( produc448466487_sc_sz
% 0.21/0.48 @ ^ [Y4: denota610675952t_unit,X4: produc866628903_sc_sz] : ( F2 @ X4 @ Y4 )
% 0.21/0.48 @ ( produc245128480t_unit @ P2 ) )
% 0.21/0.48 = ( produc435149849_sc_sz @ F2 @ P2 ) ) ).
% 0.21/0.48
% 0.21/0.48 % case_swap
% 0.21/0.48 thf(fact_198_case__swap,axiom,
% 0.21/0.48 ! [F2: produc866628903_sc_sz > denota610675952t_unit > produc190496183real_c,P2: produc999471430t_unit] :
% 0.21/0.48 ( ( produc1575513068real_c
% 0.21/0.48 @ ^ [Y4: denota610675952t_unit,X4: produc866628903_sc_sz] : ( F2 @ X4 @ Y4 )
% 0.21/0.48 @ ( produc245128480t_unit @ P2 ) )
% 0.21/0.48 = ( produc645763722real_c @ F2 @ P2 ) ) ).
% 0.21/0.48
% 0.21/0.48 % case_swap
% 0.21/0.48 thf(fact_199_case__swap,axiom,
% 0.21/0.48 ! [F2: produc866628903_sc_sz > denota610675952t_unit > $o,P2: produc999471430t_unit] :
% 0.21/0.48 ( ( produc619560141c_sz_o
% 0.21/0.48 @ ^ [Y4: denota610675952t_unit,X4: produc866628903_sc_sz] : ( F2 @ X4 @ Y4 )
% 0.21/0.48 @ ( produc245128480t_unit @ P2 ) )
% 0.21/0.48 = ( produc1718498667unit_o @ F2 @ P2 ) ) ).
% 0.21/0.48
% 0.21/0.48 % case_swap
% 0.21/0.48 thf(fact_200_case__swap,axiom,
% 0.21/0.48 ! [F2: produc866628903_sc_sz > denota610675952t_unit > set_Pr1389752855real_c,P2: produc999471430t_unit] :
% 0.21/0.48 ( ( produc237521996real_c
% 0.21/0.48 @ ^ [Y4: denota610675952t_unit,X4: produc866628903_sc_sz] : ( F2 @ X4 @ Y4 )
% 0.21/0.48 @ ( produc245128480t_unit @ P2 ) )
% 0.21/0.48 = ( produc593754858real_c @ F2 @ P2 ) ) ).
% 0.21/0.48
% 0.21/0.48 % case_swap
% 0.21/0.48 thf(fact_201_case__swap,axiom,
% 0.21/0.48 ! [F2: finite1398487019real_c > finite1398487019real_c > produc190496183real_c,P2: produc190496183real_c] :
% 0.21/0.48 ( ( produc107375667real_c
% 0.21/0.48 @ ^ [Y4: finite1398487019real_c,X4: finite1398487019real_c] : ( F2 @ X4 @ Y4 )
% 0.21/0.48 @ ( produc704157711real_c @ P2 ) )
% 0.21/0.48 = ( produc107375667real_c @ F2 @ P2 ) ) ).
% 0.21/0.48
% 0.21/0.48 % case_swap
% 0.21/0.48 thf(fact_202_case__swap,axiom,
% 0.21/0.48 ! [F2: denota610675952t_unit > produc866628903_sc_sz > produc1821101996_sc_sz,P2: produc1821101996_sc_sz] :
% 0.21/0.48 ( ( produc435149849_sc_sz
% 0.21/0.48 @ ^ [Y4: produc866628903_sc_sz,X4: denota610675952t_unit] : ( F2 @ X4 @ Y4 )
% 0.21/0.48 @ ( produc532048446_sc_sz @ P2 ) )
% 0.21/0.48 = ( produc448466487_sc_sz @ F2 @ P2 ) ) ).
% 0.21/0.48
% 0.21/0.48 % case_swap
% 0.21/0.48 thf(fact_203_pair__imageI,axiom,
% 0.21/0.48 ! [A2: finite1398487019real_c,B2: finite1398487019real_c,A: set_Pr1389752855real_c,F2: finite1398487019real_c > finite1398487019real_c > produc190496183real_c] :
% 0.21/0.48 ( ( member1895684704real_c @ ( produc394644079real_c @ A2 @ B2 ) @ A )
% 0.21/0.48 => ( member1895684704real_c @ ( F2 @ A2 @ B2 ) @ ( image_738229701real_c @ ( produc107375667real_c @ F2 ) @ A ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % pair_imageI
% 0.21/0.48 thf(fact_204_pair__imageI,axiom,
% 0.21/0.48 ! [A2: denota610675952t_unit,B2: produc866628903_sc_sz,A: set_Pr1169339874_sc_sz,F2: denota610675952t_unit > produc866628903_sc_sz > produc190496183real_c] :
% 0.21/0.48 ( ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ A2 @ B2 ) @ A )
% 0.21/0.48 => ( member1895684704real_c @ ( F2 @ A2 @ B2 ) @ ( image_386905412real_c @ ( produc1575513068real_c @ F2 ) @ A ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % pair_imageI
% 0.21/0.48 thf(fact_205_pair__imageI,axiom,
% 0.21/0.48 ! [A2: finite1398487019real_c,B2: finite1398487019real_c,A: set_Pr1389752855real_c,F2: finite1398487019real_c > finite1398487019real_c > finite1398487019real_c] :
% 0.21/0.48 ( ( member1895684704real_c @ ( produc394644079real_c @ A2 @ B2 ) @ A )
% 0.21/0.48 => ( member1261661570real_c @ ( F2 @ A2 @ B2 ) @ ( image_14429021real_c @ ( produc567249007real_c @ F2 ) @ A ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % pair_imageI
% 0.21/0.48 thf(fact_206_pair__imageI,axiom,
% 0.21/0.48 ! [A2: list_f1238882004_sc_sz,B2: list_f1238882004_sc_sz,A: set_Pr1774599175_sc_sz,F2: list_f1238882004_sc_sz > list_f1238882004_sc_sz > finite1398487019real_c] :
% 0.21/0.48 ( ( member245028432_sc_sz @ ( produc1822718231_sc_sz @ A2 @ B2 ) @ A )
% 0.21/0.48 => ( member1261661570real_c @ ( F2 @ A2 @ B2 ) @ ( image_1332486093real_c @ ( produc236226839real_c @ F2 ) @ A ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % pair_imageI
% 0.21/0.48 thf(fact_207_pair__imageI,axiom,
% 0.21/0.48 ! [A2: list_f1238882004_sc_sz,B2: list_f1238882004_sc_sz,A: set_Pr1774599175_sc_sz,F2: list_f1238882004_sc_sz > list_f1238882004_sc_sz > produc190496183real_c] :
% 0.21/0.48 ( ( member245028432_sc_sz @ ( produc1822718231_sc_sz @ A2 @ B2 ) @ A )
% 0.21/0.48 => ( member1895684704real_c @ ( F2 @ A2 @ B2 ) @ ( image_1121381717real_c @ ( produc126255499real_c @ F2 ) @ A ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % pair_imageI
% 0.21/0.48 thf(fact_208_pair__imageI,axiom,
% 0.21/0.48 ! [A2: finite1398487019real_c,B2: finite1398487019real_c,A: set_Pr1389752855real_c,F2: finite1398487019real_c > finite1398487019real_c > produc866628903_sc_sz] :
% 0.21/0.48 ( ( member1895684704real_c @ ( produc394644079real_c @ A2 @ B2 ) @ A )
% 0.21/0.48 => ( member245028432_sc_sz @ ( F2 @ A2 @ B2 ) @ ( image_388766773_sc_sz @ ( produc1341776291_sc_sz @ F2 ) @ A ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % pair_imageI
% 0.21/0.48 thf(fact_209_pair__imageI,axiom,
% 0.21/0.48 ! [A2: produc190496183real_c,B2: produc190496183real_c,A: set_Pr754230471real_c,F2: produc190496183real_c > produc190496183real_c > finite1398487019real_c] :
% 0.21/0.48 ( ( member346808080real_c @ ( produc1687028567real_c @ A2 @ B2 ) @ A )
% 0.21/0.48 => ( member1261661570real_c @ ( F2 @ A2 @ B2 ) @ ( image_124598413real_c @ ( produc344593239real_c @ F2 ) @ A ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % pair_imageI
% 0.21/0.48 thf(fact_210_pair__imageI,axiom,
% 0.21/0.48 ! [A2: denota610675952t_unit,B2: produc866628903_sc_sz,A: set_Pr1169339874_sc_sz,F2: denota610675952t_unit > produc866628903_sc_sz > $o] :
% 0.21/0.48 ( ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ A2 @ B2 ) @ A )
% 0.21/0.48 => ( member_o @ ( F2 @ A2 @ B2 ) @ ( image_1641704997c_sz_o @ ( produc619560141c_sz_o @ F2 ) @ A ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % pair_imageI
% 0.21/0.48 thf(fact_211_pair__imageI,axiom,
% 0.21/0.48 ! [A2: denota610675952t_unit,B2: produc866628903_sc_sz,A: set_Pr1169339874_sc_sz,F2: denota610675952t_unit > produc866628903_sc_sz > finite1398487019real_c] :
% 0.21/0.48 ( ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ A2 @ B2 ) @ A )
% 0.21/0.48 => ( member1261661570real_c @ ( F2 @ A2 @ B2 ) @ ( image_1268968350real_c @ ( produc1920474870real_c @ F2 ) @ A ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % pair_imageI
% 0.21/0.48 thf(fact_212_pair__imageI,axiom,
% 0.21/0.48 ! [A2: produc866628903_sc_sz,B2: denota610675952t_unit,A: set_Pr2041213564t_unit,F2: produc866628903_sc_sz > denota610675952t_unit > finite1398487019real_c] :
% 0.21/0.48 ( ( member235934813t_unit @ ( produc502616768t_unit @ A2 @ B2 ) @ A )
% 0.21/0.48 => ( member1261661570real_c @ ( F2 @ A2 @ B2 ) @ ( image_1269062456real_c @ ( produc1753599960real_c @ F2 ) @ A ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % pair_imageI
% 0.21/0.48 thf(fact_213_curry__def,axiom,
% 0.21/0.48 ( produc1086673900c_sz_o
% 0.21/0.48 = ( ^ [C3: produc1821101996_sc_sz > $o,X4: denota610675952t_unit,Y4: produc866628903_sc_sz] : ( C3 @ ( produc789536734_sc_sz @ X4 @ Y4 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % curry_def
% 0.21/0.48 thf(fact_214_curry__K,axiom,
% 0.21/0.48 ! [C2: $o] :
% 0.21/0.48 ( ( produc1086673900c_sz_o
% 0.21/0.48 @ ^ [X4: produc1821101996_sc_sz] : C2 )
% 0.21/0.48 = ( ^ [X4: denota610675952t_unit,Y4: produc866628903_sc_sz] : C2 ) ) ).
% 0.21/0.48
% 0.21/0.48 % curry_K
% 0.21/0.48 thf(fact_215_old_Oprod_Ocase,axiom,
% 0.21/0.48 ! [F2: denota610675952t_unit > produc866628903_sc_sz > produc190496183real_c,X1: denota610675952t_unit,X2: produc866628903_sc_sz] :
% 0.21/0.48 ( ( produc1575513068real_c @ F2 @ ( produc789536734_sc_sz @ X1 @ X2 ) )
% 0.21/0.48 = ( F2 @ X1 @ X2 ) ) ).
% 0.21/0.48
% 0.21/0.48 % old.prod.case
% 0.21/0.48 thf(fact_216_old_Oprod_Ocase,axiom,
% 0.21/0.48 ! [F2: denota610675952t_unit > produc866628903_sc_sz > $o,X1: denota610675952t_unit,X2: produc866628903_sc_sz] :
% 0.21/0.48 ( ( produc619560141c_sz_o @ F2 @ ( produc789536734_sc_sz @ X1 @ X2 ) )
% 0.21/0.48 = ( F2 @ X1 @ X2 ) ) ).
% 0.21/0.48
% 0.21/0.48 % old.prod.case
% 0.21/0.48 thf(fact_217_old_Oprod_Ocase,axiom,
% 0.21/0.48 ! [F2: denota610675952t_unit > produc866628903_sc_sz > set_Pr1389752855real_c,X1: denota610675952t_unit,X2: produc866628903_sc_sz] :
% 0.21/0.48 ( ( produc237521996real_c @ F2 @ ( produc789536734_sc_sz @ X1 @ X2 ) )
% 0.21/0.48 = ( F2 @ X1 @ X2 ) ) ).
% 0.21/0.48
% 0.21/0.48 % old.prod.case
% 0.21/0.48 thf(fact_218_old_Oprod_Ocase,axiom,
% 0.21/0.48 ! [F2: finite1398487019real_c > finite1398487019real_c > produc190496183real_c,X1: finite1398487019real_c,X2: finite1398487019real_c] :
% 0.21/0.48 ( ( produc107375667real_c @ F2 @ ( produc394644079real_c @ X1 @ X2 ) )
% 0.21/0.48 = ( F2 @ X1 @ X2 ) ) ).
% 0.21/0.48
% 0.21/0.48 % old.prod.case
% 0.21/0.48 thf(fact_219_old_Oprod_Ocase,axiom,
% 0.21/0.48 ! [F2: produc866628903_sc_sz > denota610675952t_unit > produc1821101996_sc_sz,X1: produc866628903_sc_sz,X2: denota610675952t_unit] :
% 0.21/0.48 ( ( produc435149849_sc_sz @ F2 @ ( produc502616768t_unit @ X1 @ X2 ) )
% 0.21/0.48 = ( F2 @ X1 @ X2 ) ) ).
% 0.21/0.48
% 0.21/0.48 % old.prod.case
% 0.21/0.48 thf(fact_220_mem__case__prodE,axiom,
% 0.21/0.48 ! [Z: produc190496183real_c,C2: denota610675952t_unit > produc866628903_sc_sz > set_Pr1389752855real_c,P2: produc1821101996_sc_sz] :
% 0.21/0.48 ( ( member1895684704real_c @ Z @ ( produc237521996real_c @ C2 @ P2 ) )
% 0.21/0.48 => ~ ! [X3: denota610675952t_unit,Y3: produc866628903_sc_sz] :
% 0.21/0.48 ( ( P2
% 0.21/0.48 = ( produc789536734_sc_sz @ X3 @ Y3 ) )
% 0.21/0.48 => ~ ( member1895684704real_c @ Z @ ( C2 @ X3 @ Y3 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mem_case_prodE
% 0.21/0.48 thf(fact_221_mem__case__prodE,axiom,
% 0.21/0.48 ! [Z: finite1398487019real_c,C2: finite1398487019real_c > finite1398487019real_c > set_Fi1407883041real_c,P2: produc190496183real_c] :
% 0.21/0.48 ( ( member1261661570real_c @ Z @ ( produc29022117real_c @ C2 @ P2 ) )
% 0.21/0.48 => ~ ! [X3: finite1398487019real_c,Y3: finite1398487019real_c] :
% 0.21/0.48 ( ( P2
% 0.21/0.48 = ( produc394644079real_c @ X3 @ Y3 ) )
% 0.21/0.48 => ~ ( member1261661570real_c @ Z @ ( C2 @ X3 @ Y3 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mem_case_prodE
% 0.21/0.48 thf(fact_222_mem__case__prodE,axiom,
% 0.21/0.48 ! [Z: finite1398487019real_c,C2: list_f1238882004_sc_sz > list_f1238882004_sc_sz > set_Fi1407883041real_c,P2: produc866628903_sc_sz] :
% 0.21/0.48 ( ( member1261661570real_c @ Z @ ( produc1449736269real_c @ C2 @ P2 ) )
% 0.21/0.48 => ~ ! [X3: list_f1238882004_sc_sz,Y3: list_f1238882004_sc_sz] :
% 0.21/0.48 ( ( P2
% 0.21/0.48 = ( produc1822718231_sc_sz @ X3 @ Y3 ) )
% 0.21/0.48 => ~ ( member1261661570real_c @ Z @ ( C2 @ X3 @ Y3 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mem_case_prodE
% 0.21/0.48 thf(fact_223_mem__case__prodE,axiom,
% 0.21/0.48 ! [Z: produc190496183real_c,C2: finite1398487019real_c > finite1398487019real_c > set_Pr1389752855real_c,P2: produc190496183real_c] :
% 0.21/0.48 ( ( member1895684704real_c @ Z @ ( produc923381907real_c @ C2 @ P2 ) )
% 0.21/0.48 => ~ ! [X3: finite1398487019real_c,Y3: finite1398487019real_c] :
% 0.21/0.48 ( ( P2
% 0.21/0.48 = ( produc394644079real_c @ X3 @ Y3 ) )
% 0.21/0.48 => ~ ( member1895684704real_c @ Z @ ( C2 @ X3 @ Y3 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mem_case_prodE
% 0.21/0.48 thf(fact_224_mem__case__prodE,axiom,
% 0.21/0.48 ! [Z: produc190496183real_c,C2: list_f1238882004_sc_sz > list_f1238882004_sc_sz > set_Pr1389752855real_c,P2: produc866628903_sc_sz] :
% 0.21/0.48 ( ( member1895684704real_c @ Z @ ( produc6841835real_c @ C2 @ P2 ) )
% 0.21/0.48 => ~ ! [X3: list_f1238882004_sc_sz,Y3: list_f1238882004_sc_sz] :
% 0.21/0.48 ( ( P2
% 0.21/0.48 = ( produc1822718231_sc_sz @ X3 @ Y3 ) )
% 0.21/0.48 => ~ ( member1895684704real_c @ Z @ ( C2 @ X3 @ Y3 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mem_case_prodE
% 0.21/0.48 thf(fact_225_mem__case__prodE,axiom,
% 0.21/0.48 ! [Z: produc866628903_sc_sz,C2: finite1398487019real_c > finite1398487019real_c > set_Pr1774599175_sc_sz,P2: produc190496183real_c] :
% 0.21/0.48 ( ( member245028432_sc_sz @ Z @ ( produc642283651_sc_sz @ C2 @ P2 ) )
% 0.21/0.48 => ~ ! [X3: finite1398487019real_c,Y3: finite1398487019real_c] :
% 0.21/0.48 ( ( P2
% 0.21/0.48 = ( produc394644079real_c @ X3 @ Y3 ) )
% 0.21/0.48 => ~ ( member245028432_sc_sz @ Z @ ( C2 @ X3 @ Y3 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mem_case_prodE
% 0.21/0.48 thf(fact_226_mem__case__prodE,axiom,
% 0.21/0.48 ! [Z: finite1398487019real_c,C2: produc190496183real_c > produc190496183real_c > set_Fi1407883041real_c,P2: produc640052711real_c] :
% 0.21/0.48 ( ( member1261661570real_c @ Z @ ( produc1066779277real_c @ C2 @ P2 ) )
% 0.21/0.48 => ~ ! [X3: produc190496183real_c,Y3: produc190496183real_c] :
% 0.21/0.48 ( ( P2
% 0.21/0.48 = ( produc1687028567real_c @ X3 @ Y3 ) )
% 0.21/0.48 => ~ ( member1261661570real_c @ Z @ ( C2 @ X3 @ Y3 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mem_case_prodE
% 0.21/0.48 thf(fact_227_mem__case__prodE,axiom,
% 0.21/0.48 ! [Z: finite1398487019real_c,C2: denota610675952t_unit > produc866628903_sc_sz > set_Fi1407883041real_c,P2: produc1821101996_sc_sz] :
% 0.21/0.48 ( ( member1261661570real_c @ Z @ ( produc2068697644real_c @ C2 @ P2 ) )
% 0.21/0.48 => ~ ! [X3: denota610675952t_unit,Y3: produc866628903_sc_sz] :
% 0.21/0.48 ( ( P2
% 0.21/0.48 = ( produc789536734_sc_sz @ X3 @ Y3 ) )
% 0.21/0.48 => ~ ( member1261661570real_c @ Z @ ( C2 @ X3 @ Y3 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mem_case_prodE
% 0.21/0.48 thf(fact_228_mem__case__prodE,axiom,
% 0.21/0.48 ! [Z: finite1398487019real_c,C2: produc866628903_sc_sz > denota610675952t_unit > set_Fi1407883041real_c,P2: produc999471430t_unit] :
% 0.21/0.48 ( ( member1261661570real_c @ Z @ ( produc1368849166real_c @ C2 @ P2 ) )
% 0.21/0.48 => ~ ! [X3: produc866628903_sc_sz,Y3: denota610675952t_unit] :
% 0.21/0.48 ( ( P2
% 0.21/0.48 = ( produc502616768t_unit @ X3 @ Y3 ) )
% 0.21/0.48 => ~ ( member1261661570real_c @ Z @ ( C2 @ X3 @ Y3 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mem_case_prodE
% 0.21/0.48 thf(fact_229_mem__case__prodE,axiom,
% 0.21/0.48 ! [Z: produc866628903_sc_sz,C2: list_f1238882004_sc_sz > list_f1238882004_sc_sz > set_Pr1774599175_sc_sz,P2: produc866628903_sc_sz] :
% 0.21/0.48 ( ( member245028432_sc_sz @ Z @ ( produc1563580891_sc_sz @ C2 @ P2 ) )
% 0.21/0.48 => ~ ! [X3: list_f1238882004_sc_sz,Y3: list_f1238882004_sc_sz] :
% 0.21/0.48 ( ( P2
% 0.21/0.48 = ( produc1822718231_sc_sz @ X3 @ Y3 ) )
% 0.21/0.48 => ~ ( member245028432_sc_sz @ Z @ ( C2 @ X3 @ Y3 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mem_case_prodE
% 0.21/0.48 thf(fact_230_prod_Ocase__distrib,axiom,
% 0.21/0.48 ! [H: $o > $o,F2: denota610675952t_unit > produc866628903_sc_sz > $o,Prod: produc1821101996_sc_sz] :
% 0.21/0.48 ( ( H @ ( produc619560141c_sz_o @ F2 @ Prod ) )
% 0.21/0.48 = ( produc619560141c_sz_o
% 0.21/0.48 @ ^ [X12: denota610675952t_unit,X22: produc866628903_sc_sz] : ( H @ ( F2 @ X12 @ X22 ) )
% 0.21/0.48 @ Prod ) ) ).
% 0.21/0.48
% 0.21/0.48 % prod.case_distrib
% 0.21/0.48 thf(fact_231_prod_Ocase__distrib,axiom,
% 0.21/0.48 ! [H: produc190496183real_c > produc190496183real_c,F2: finite1398487019real_c > finite1398487019real_c > produc190496183real_c,Prod: produc190496183real_c] :
% 0.21/0.48 ( ( H @ ( produc107375667real_c @ F2 @ Prod ) )
% 0.21/0.48 = ( produc107375667real_c
% 0.21/0.48 @ ^ [X12: finite1398487019real_c,X22: finite1398487019real_c] : ( H @ ( F2 @ X12 @ X22 ) )
% 0.21/0.48 @ Prod ) ) ).
% 0.21/0.48
% 0.21/0.48 % prod.case_distrib
% 0.21/0.48 thf(fact_232_prod_Ocase__distrib,axiom,
% 0.21/0.48 ! [H: produc190496183real_c > $o,F2: denota610675952t_unit > produc866628903_sc_sz > produc190496183real_c,Prod: produc1821101996_sc_sz] :
% 0.21/0.48 ( ( H @ ( produc1575513068real_c @ F2 @ Prod ) )
% 0.21/0.48 = ( produc619560141c_sz_o
% 0.21/0.48 @ ^ [X12: denota610675952t_unit,X22: produc866628903_sc_sz] : ( H @ ( F2 @ X12 @ X22 ) )
% 0.21/0.48 @ Prod ) ) ).
% 0.21/0.48
% 0.21/0.48 % prod.case_distrib
% 0.21/0.48 thf(fact_233_prod_Ocase__distrib,axiom,
% 0.21/0.48 ! [H: $o > produc190496183real_c,F2: denota610675952t_unit > produc866628903_sc_sz > $o,Prod: produc1821101996_sc_sz] :
% 0.21/0.48 ( ( H @ ( produc619560141c_sz_o @ F2 @ Prod ) )
% 0.21/0.48 = ( produc1575513068real_c
% 0.21/0.48 @ ^ [X12: denota610675952t_unit,X22: produc866628903_sc_sz] : ( H @ ( F2 @ X12 @ X22 ) )
% 0.21/0.48 @ Prod ) ) ).
% 0.21/0.48
% 0.21/0.48 % prod.case_distrib
% 0.21/0.48 thf(fact_234_prod_Ocase__distrib,axiom,
% 0.21/0.48 ! [H: $o > set_Pr1389752855real_c,F2: denota610675952t_unit > produc866628903_sc_sz > $o,Prod: produc1821101996_sc_sz] :
% 0.21/0.48 ( ( H @ ( produc619560141c_sz_o @ F2 @ Prod ) )
% 0.21/0.48 = ( produc237521996real_c
% 0.21/0.48 @ ^ [X12: denota610675952t_unit,X22: produc866628903_sc_sz] : ( H @ ( F2 @ X12 @ X22 ) )
% 0.21/0.48 @ Prod ) ) ).
% 0.21/0.48
% 0.21/0.48 % prod.case_distrib
% 0.21/0.48 thf(fact_235_prod_Ocase__distrib,axiom,
% 0.21/0.48 ! [H: set_Pr1389752855real_c > $o,F2: denota610675952t_unit > produc866628903_sc_sz > set_Pr1389752855real_c,Prod: produc1821101996_sc_sz] :
% 0.21/0.48 ( ( H @ ( produc237521996real_c @ F2 @ Prod ) )
% 0.21/0.48 = ( produc619560141c_sz_o
% 0.21/0.48 @ ^ [X12: denota610675952t_unit,X22: produc866628903_sc_sz] : ( H @ ( F2 @ X12 @ X22 ) )
% 0.21/0.48 @ Prod ) ) ).
% 0.21/0.48
% 0.21/0.48 % prod.case_distrib
% 0.21/0.48 thf(fact_236_prod_Ocase__distrib,axiom,
% 0.21/0.48 ! [H: produc190496183real_c > produc190496183real_c,F2: denota610675952t_unit > produc866628903_sc_sz > produc190496183real_c,Prod: produc1821101996_sc_sz] :
% 0.21/0.48 ( ( H @ ( produc1575513068real_c @ F2 @ Prod ) )
% 0.21/0.48 = ( produc1575513068real_c
% 0.21/0.48 @ ^ [X12: denota610675952t_unit,X22: produc866628903_sc_sz] : ( H @ ( F2 @ X12 @ X22 ) )
% 0.21/0.48 @ Prod ) ) ).
% 0.21/0.48
% 0.21/0.48 % prod.case_distrib
% 0.21/0.48 thf(fact_237_prod_Ocase__distrib,axiom,
% 0.21/0.48 ! [H: produc190496183real_c > set_Pr1389752855real_c,F2: denota610675952t_unit > produc866628903_sc_sz > produc190496183real_c,Prod: produc1821101996_sc_sz] :
% 0.21/0.48 ( ( H @ ( produc1575513068real_c @ F2 @ Prod ) )
% 0.21/0.48 = ( produc237521996real_c
% 0.21/0.48 @ ^ [X12: denota610675952t_unit,X22: produc866628903_sc_sz] : ( H @ ( F2 @ X12 @ X22 ) )
% 0.21/0.48 @ Prod ) ) ).
% 0.21/0.48
% 0.21/0.48 % prod.case_distrib
% 0.21/0.48 thf(fact_238_prod_Ocase__distrib,axiom,
% 0.21/0.48 ! [H: set_Pr1389752855real_c > produc190496183real_c,F2: denota610675952t_unit > produc866628903_sc_sz > set_Pr1389752855real_c,Prod: produc1821101996_sc_sz] :
% 0.21/0.48 ( ( H @ ( produc237521996real_c @ F2 @ Prod ) )
% 0.21/0.48 = ( produc1575513068real_c
% 0.21/0.48 @ ^ [X12: denota610675952t_unit,X22: produc866628903_sc_sz] : ( H @ ( F2 @ X12 @ X22 ) )
% 0.21/0.48 @ Prod ) ) ).
% 0.21/0.48
% 0.21/0.48 % prod.case_distrib
% 0.21/0.48 thf(fact_239_prod_Ocase__distrib,axiom,
% 0.21/0.48 ! [H: set_Pr1389752855real_c > set_Pr1389752855real_c,F2: denota610675952t_unit > produc866628903_sc_sz > set_Pr1389752855real_c,Prod: produc1821101996_sc_sz] :
% 0.21/0.48 ( ( H @ ( produc237521996real_c @ F2 @ Prod ) )
% 0.21/0.48 = ( produc237521996real_c
% 0.21/0.48 @ ^ [X12: denota610675952t_unit,X22: produc866628903_sc_sz] : ( H @ ( F2 @ X12 @ X22 ) )
% 0.21/0.48 @ Prod ) ) ).
% 0.21/0.48
% 0.21/0.48 % prod.case_distrib
% 0.21/0.48 thf(fact_240_cond__case__prod__eta,axiom,
% 0.21/0.48 ! [F2: denota610675952t_unit > produc866628903_sc_sz > produc190496183real_c,G: produc1821101996_sc_sz > produc190496183real_c] :
% 0.21/0.48 ( ! [X3: denota610675952t_unit,Y3: produc866628903_sc_sz] :
% 0.21/0.48 ( ( F2 @ X3 @ Y3 )
% 0.21/0.48 = ( G @ ( produc789536734_sc_sz @ X3 @ Y3 ) ) )
% 0.21/0.48 => ( ( produc1575513068real_c @ F2 )
% 0.21/0.48 = G ) ) ).
% 0.21/0.48
% 0.21/0.48 % cond_case_prod_eta
% 0.21/0.48 thf(fact_241_cond__case__prod__eta,axiom,
% 0.21/0.48 ! [F2: denota610675952t_unit > produc866628903_sc_sz > $o,G: produc1821101996_sc_sz > $o] :
% 0.21/0.48 ( ! [X3: denota610675952t_unit,Y3: produc866628903_sc_sz] :
% 0.21/0.48 ( ( F2 @ X3 @ Y3 )
% 0.21/0.48 = ( G @ ( produc789536734_sc_sz @ X3 @ Y3 ) ) )
% 0.21/0.48 => ( ( produc619560141c_sz_o @ F2 )
% 0.21/0.48 = G ) ) ).
% 0.21/0.48
% 0.21/0.48 % cond_case_prod_eta
% 0.21/0.48 thf(fact_242_cond__case__prod__eta,axiom,
% 0.21/0.48 ! [F2: denota610675952t_unit > produc866628903_sc_sz > set_Pr1389752855real_c,G: produc1821101996_sc_sz > set_Pr1389752855real_c] :
% 0.21/0.48 ( ! [X3: denota610675952t_unit,Y3: produc866628903_sc_sz] :
% 0.21/0.48 ( ( F2 @ X3 @ Y3 )
% 0.21/0.48 = ( G @ ( produc789536734_sc_sz @ X3 @ Y3 ) ) )
% 0.21/0.48 => ( ( produc237521996real_c @ F2 )
% 0.21/0.48 = G ) ) ).
% 0.21/0.48
% 0.21/0.48 % cond_case_prod_eta
% 0.21/0.48 thf(fact_243_cond__case__prod__eta,axiom,
% 0.21/0.48 ! [F2: finite1398487019real_c > finite1398487019real_c > produc190496183real_c,G: produc190496183real_c > produc190496183real_c] :
% 0.21/0.48 ( ! [X3: finite1398487019real_c,Y3: finite1398487019real_c] :
% 0.21/0.48 ( ( F2 @ X3 @ Y3 )
% 0.21/0.48 = ( G @ ( produc394644079real_c @ X3 @ Y3 ) ) )
% 0.21/0.48 => ( ( produc107375667real_c @ F2 )
% 0.21/0.48 = G ) ) ).
% 0.21/0.48
% 0.21/0.48 % cond_case_prod_eta
% 0.21/0.48 thf(fact_244_cond__case__prod__eta,axiom,
% 0.21/0.48 ! [F2: produc866628903_sc_sz > denota610675952t_unit > produc1821101996_sc_sz,G: produc999471430t_unit > produc1821101996_sc_sz] :
% 0.21/0.48 ( ! [X3: produc866628903_sc_sz,Y3: denota610675952t_unit] :
% 0.21/0.48 ( ( F2 @ X3 @ Y3 )
% 0.21/0.48 = ( G @ ( produc502616768t_unit @ X3 @ Y3 ) ) )
% 0.21/0.48 => ( ( produc435149849_sc_sz @ F2 )
% 0.21/0.48 = G ) ) ).
% 0.21/0.48
% 0.21/0.48 % cond_case_prod_eta
% 0.21/0.48 thf(fact_245_case__prod__eta,axiom,
% 0.21/0.48 ! [F2: produc1821101996_sc_sz > produc190496183real_c] :
% 0.21/0.48 ( ( produc1575513068real_c
% 0.21/0.48 @ ^ [X4: denota610675952t_unit,Y4: produc866628903_sc_sz] : ( F2 @ ( produc789536734_sc_sz @ X4 @ Y4 ) ) )
% 0.21/0.48 = F2 ) ).
% 0.21/0.48
% 0.21/0.48 % case_prod_eta
% 0.21/0.48 thf(fact_246_case__prod__eta,axiom,
% 0.21/0.48 ! [F2: produc1821101996_sc_sz > $o] :
% 0.21/0.48 ( ( produc619560141c_sz_o
% 0.21/0.48 @ ^ [X4: denota610675952t_unit,Y4: produc866628903_sc_sz] : ( F2 @ ( produc789536734_sc_sz @ X4 @ Y4 ) ) )
% 0.21/0.48 = F2 ) ).
% 0.21/0.48
% 0.21/0.48 % case_prod_eta
% 0.21/0.48 thf(fact_247_case__prod__eta,axiom,
% 0.21/0.48 ! [F2: produc1821101996_sc_sz > set_Pr1389752855real_c] :
% 0.21/0.48 ( ( produc237521996real_c
% 0.21/0.48 @ ^ [X4: denota610675952t_unit,Y4: produc866628903_sc_sz] : ( F2 @ ( produc789536734_sc_sz @ X4 @ Y4 ) ) )
% 0.21/0.48 = F2 ) ).
% 0.21/0.48
% 0.21/0.48 % case_prod_eta
% 0.21/0.48 thf(fact_248_case__prod__eta,axiom,
% 0.21/0.48 ! [F2: produc190496183real_c > produc190496183real_c] :
% 0.21/0.48 ( ( produc107375667real_c
% 0.21/0.48 @ ^ [X4: finite1398487019real_c,Y4: finite1398487019real_c] : ( F2 @ ( produc394644079real_c @ X4 @ Y4 ) ) )
% 0.21/0.48 = F2 ) ).
% 0.21/0.48
% 0.21/0.48 % case_prod_eta
% 0.21/0.48 thf(fact_249_case__prod__eta,axiom,
% 0.21/0.48 ! [F2: produc999471430t_unit > produc1821101996_sc_sz] :
% 0.21/0.48 ( ( produc435149849_sc_sz
% 0.21/0.48 @ ^ [X4: produc866628903_sc_sz,Y4: denota610675952t_unit] : ( F2 @ ( produc502616768t_unit @ X4 @ Y4 ) ) )
% 0.21/0.48 = F2 ) ).
% 0.21/0.48
% 0.21/0.48 % case_prod_eta
% 0.21/0.48 thf(fact_250_case__prodE2,axiom,
% 0.21/0.48 ! [Q: produc190496183real_c > $o,P: denota610675952t_unit > produc866628903_sc_sz > produc190496183real_c,Z: produc1821101996_sc_sz] :
% 0.21/0.48 ( ( Q @ ( produc1575513068real_c @ P @ Z ) )
% 0.21/0.48 => ~ ! [X3: denota610675952t_unit,Y3: produc866628903_sc_sz] :
% 0.21/0.48 ( ( Z
% 0.21/0.48 = ( produc789536734_sc_sz @ X3 @ Y3 ) )
% 0.21/0.48 => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % case_prodE2
% 0.21/0.48 thf(fact_251_case__prodE2,axiom,
% 0.21/0.48 ! [Q: $o > $o,P: denota610675952t_unit > produc866628903_sc_sz > $o,Z: produc1821101996_sc_sz] :
% 0.21/0.48 ( ( Q @ ( produc619560141c_sz_o @ P @ Z ) )
% 0.21/0.48 => ~ ! [X3: denota610675952t_unit,Y3: produc866628903_sc_sz] :
% 0.21/0.48 ( ( Z
% 0.21/0.48 = ( produc789536734_sc_sz @ X3 @ Y3 ) )
% 0.21/0.48 => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % case_prodE2
% 0.21/0.48 thf(fact_252_case__prodE2,axiom,
% 0.21/0.48 ! [Q: set_Pr1389752855real_c > $o,P: denota610675952t_unit > produc866628903_sc_sz > set_Pr1389752855real_c,Z: produc1821101996_sc_sz] :
% 0.21/0.48 ( ( Q @ ( produc237521996real_c @ P @ Z ) )
% 0.21/0.48 => ~ ! [X3: denota610675952t_unit,Y3: produc866628903_sc_sz] :
% 0.21/0.48 ( ( Z
% 0.21/0.48 = ( produc789536734_sc_sz @ X3 @ Y3 ) )
% 0.21/0.48 => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % case_prodE2
% 0.21/0.48 thf(fact_253_case__prodE2,axiom,
% 0.21/0.48 ! [Q: produc190496183real_c > $o,P: finite1398487019real_c > finite1398487019real_c > produc190496183real_c,Z: produc190496183real_c] :
% 0.21/0.48 ( ( Q @ ( produc107375667real_c @ P @ Z ) )
% 0.21/0.48 => ~ ! [X3: finite1398487019real_c,Y3: finite1398487019real_c] :
% 0.21/0.48 ( ( Z
% 0.21/0.48 = ( produc394644079real_c @ X3 @ Y3 ) )
% 0.21/0.48 => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % case_prodE2
% 0.21/0.48 thf(fact_254_case__prodE2,axiom,
% 0.21/0.48 ! [Q: produc1821101996_sc_sz > $o,P: produc866628903_sc_sz > denota610675952t_unit > produc1821101996_sc_sz,Z: produc999471430t_unit] :
% 0.21/0.48 ( ( Q @ ( produc435149849_sc_sz @ P @ Z ) )
% 0.21/0.48 => ~ ! [X3: produc866628903_sc_sz,Y3: denota610675952t_unit] :
% 0.21/0.48 ( ( Z
% 0.21/0.48 = ( produc502616768t_unit @ X3 @ Y3 ) )
% 0.21/0.48 => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % case_prodE2
% 0.21/0.48 thf(fact_255_case__prodE,axiom,
% 0.21/0.48 ! [C2: list_f1238882004_sc_sz > list_f1238882004_sc_sz > $o,P2: produc866628903_sc_sz] :
% 0.21/0.48 ( ( produc2039065452c_sz_o @ C2 @ P2 )
% 0.21/0.48 => ~ ! [X3: list_f1238882004_sc_sz,Y3: list_f1238882004_sc_sz] :
% 0.21/0.48 ( ( P2
% 0.21/0.48 = ( produc1822718231_sc_sz @ X3 @ Y3 ) )
% 0.21/0.48 => ~ ( C2 @ X3 @ Y3 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % case_prodE
% 0.21/0.48 thf(fact_256_case__prodE,axiom,
% 0.21/0.48 ! [C2: finite1398487019real_c > finite1398487019real_c > $o,P2: produc190496183real_c] :
% 0.21/0.48 ( ( produc353381908al_c_o @ C2 @ P2 )
% 0.21/0.48 => ~ ! [X3: finite1398487019real_c,Y3: finite1398487019real_c] :
% 0.21/0.48 ( ( P2
% 0.21/0.48 = ( produc394644079real_c @ X3 @ Y3 ) )
% 0.21/0.48 => ~ ( C2 @ X3 @ Y3 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % case_prodE
% 0.21/0.48 thf(fact_257_case__prodE,axiom,
% 0.21/0.48 ! [C2: produc866628903_sc_sz > denota610675952t_unit > $o,P2: produc999471430t_unit] :
% 0.21/0.48 ( ( produc1718498667unit_o @ C2 @ P2 )
% 0.21/0.48 => ~ ! [X3: produc866628903_sc_sz,Y3: denota610675952t_unit] :
% 0.21/0.48 ( ( P2
% 0.21/0.48 = ( produc502616768t_unit @ X3 @ Y3 ) )
% 0.21/0.48 => ~ ( C2 @ X3 @ Y3 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % case_prodE
% 0.21/0.48 thf(fact_258_case__prodE,axiom,
% 0.21/0.48 ! [C2: produc190496183real_c > produc190496183real_c > $o,P2: produc640052711real_c] :
% 0.21/0.48 ( ( produc1726730540al_c_o @ C2 @ P2 )
% 0.21/0.48 => ~ ! [X3: produc190496183real_c,Y3: produc190496183real_c] :
% 0.21/0.48 ( ( P2
% 0.21/0.48 = ( produc1687028567real_c @ X3 @ Y3 ) )
% 0.21/0.48 => ~ ( C2 @ X3 @ Y3 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % case_prodE
% 0.21/0.48 thf(fact_259_case__prodE,axiom,
% 0.21/0.48 ! [C2: denota610675952t_unit > produc866628903_sc_sz > $o,P2: produc1821101996_sc_sz] :
% 0.21/0.48 ( ( produc619560141c_sz_o @ C2 @ P2 )
% 0.21/0.48 => ~ ! [X3: denota610675952t_unit,Y3: produc866628903_sc_sz] :
% 0.21/0.48 ( ( P2
% 0.21/0.48 = ( produc789536734_sc_sz @ X3 @ Y3 ) )
% 0.21/0.48 => ~ ( C2 @ X3 @ Y3 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % case_prodE
% 0.21/0.48 thf(fact_260_case__prodD,axiom,
% 0.21/0.48 ! [F2: list_f1238882004_sc_sz > list_f1238882004_sc_sz > $o,A2: list_f1238882004_sc_sz,B2: list_f1238882004_sc_sz] :
% 0.21/0.48 ( ( produc2039065452c_sz_o @ F2 @ ( produc1822718231_sc_sz @ A2 @ B2 ) )
% 0.21/0.48 => ( F2 @ A2 @ B2 ) ) ).
% 0.21/0.48
% 0.21/0.48 % case_prodD
% 0.21/0.48 thf(fact_261_case__prodD,axiom,
% 0.21/0.48 ! [F2: finite1398487019real_c > finite1398487019real_c > $o,A2: finite1398487019real_c,B2: finite1398487019real_c] :
% 0.21/0.48 ( ( produc353381908al_c_o @ F2 @ ( produc394644079real_c @ A2 @ B2 ) )
% 0.21/0.48 => ( F2 @ A2 @ B2 ) ) ).
% 0.21/0.48
% 0.21/0.48 % case_prodD
% 0.21/0.48 thf(fact_262_case__prodD,axiom,
% 0.21/0.48 ! [F2: produc866628903_sc_sz > denota610675952t_unit > $o,A2: produc866628903_sc_sz,B2: denota610675952t_unit] :
% 0.21/0.48 ( ( produc1718498667unit_o @ F2 @ ( produc502616768t_unit @ A2 @ B2 ) )
% 0.21/0.48 => ( F2 @ A2 @ B2 ) ) ).
% 0.21/0.48
% 0.21/0.48 % case_prodD
% 0.21/0.48 thf(fact_263_case__prodD,axiom,
% 0.21/0.48 ! [F2: produc190496183real_c > produc190496183real_c > $o,A2: produc190496183real_c,B2: produc190496183real_c] :
% 0.21/0.48 ( ( produc1726730540al_c_o @ F2 @ ( produc1687028567real_c @ A2 @ B2 ) )
% 0.21/0.48 => ( F2 @ A2 @ B2 ) ) ).
% 0.21/0.48
% 0.21/0.48 % case_prodD
% 0.21/0.48 thf(fact_264_case__prodD,axiom,
% 0.21/0.48 ! [F2: denota610675952t_unit > produc866628903_sc_sz > $o,A2: denota610675952t_unit,B2: produc866628903_sc_sz] :
% 0.21/0.48 ( ( produc619560141c_sz_o @ F2 @ ( produc789536734_sc_sz @ A2 @ B2 ) )
% 0.21/0.48 => ( F2 @ A2 @ B2 ) ) ).
% 0.21/0.48
% 0.21/0.48 % case_prodD
% 0.21/0.48 thf(fact_265_image__ident,axiom,
% 0.21/0.48 ! [Y5: set_Pr1389752855real_c] :
% 0.21/0.48 ( ( image_738229701real_c
% 0.21/0.48 @ ^ [X4: produc190496183real_c] : X4
% 0.21/0.48 @ Y5 )
% 0.21/0.48 = Y5 ) ).
% 0.21/0.48
% 0.21/0.48 % image_ident
% 0.21/0.48 thf(fact_266_image__eqI,axiom,
% 0.21/0.48 ! [B2: produc190496183real_c,F2: produc190496183real_c > produc190496183real_c,X: produc190496183real_c,A: set_Pr1389752855real_c] :
% 0.21/0.48 ( ( B2
% 0.21/0.48 = ( F2 @ X ) )
% 0.21/0.48 => ( ( member1895684704real_c @ X @ A )
% 0.21/0.48 => ( member1895684704real_c @ B2 @ ( image_738229701real_c @ F2 @ A ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % image_eqI
% 0.21/0.48 thf(fact_267_image__eqI,axiom,
% 0.21/0.48 ! [B2: finite1398487019real_c,F2: finite1398487019real_c > finite1398487019real_c,X: finite1398487019real_c,A: set_Fi1407883041real_c] :
% 0.21/0.48 ( ( B2
% 0.21/0.48 = ( F2 @ X ) )
% 0.21/0.48 => ( ( member1261661570real_c @ X @ A )
% 0.21/0.48 => ( member1261661570real_c @ B2 @ ( image_1514048989real_c @ F2 @ A ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % image_eqI
% 0.21/0.48 thf(fact_268_image__eqI,axiom,
% 0.21/0.48 ! [B2: finite1398487019real_c,F2: produc190496183real_c > finite1398487019real_c,X: produc190496183real_c,A: set_Pr1389752855real_c] :
% 0.21/0.48 ( ( B2
% 0.21/0.48 = ( F2 @ X ) )
% 0.21/0.48 => ( ( member1895684704real_c @ X @ A )
% 0.21/0.48 => ( member1261661570real_c @ B2 @ ( image_14429021real_c @ F2 @ A ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % image_eqI
% 0.21/0.48 thf(fact_269_image__eqI,axiom,
% 0.21/0.48 ! [B2: produc190496183real_c,F2: finite1398487019real_c > produc190496183real_c,X: finite1398487019real_c,A: set_Fi1407883041real_c] :
% 0.21/0.48 ( ( B2
% 0.21/0.48 = ( F2 @ X ) )
% 0.21/0.48 => ( ( member1261661570real_c @ X @ A )
% 0.21/0.48 => ( member1895684704real_c @ B2 @ ( image_1461287749real_c @ F2 @ A ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % image_eqI
% 0.21/0.48 thf(fact_270_image__eqI,axiom,
% 0.21/0.48 ! [B2: produc866628903_sc_sz,F2: finite1398487019real_c > produc866628903_sc_sz,X: finite1398487019real_c,A: set_Fi1407883041real_c] :
% 0.21/0.48 ( ( B2
% 0.21/0.48 = ( F2 @ X ) )
% 0.21/0.48 => ( ( member1261661570real_c @ X @ A )
% 0.21/0.48 => ( member245028432_sc_sz @ B2 @ ( image_290183605_sc_sz @ F2 @ A ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % image_eqI
% 0.21/0.48 thf(fact_271_image__eqI,axiom,
% 0.21/0.48 ! [B2: finite1398487019real_c,F2: produc866628903_sc_sz > finite1398487019real_c,X: produc866628903_sc_sz,A: set_Pr1774599175_sc_sz] :
% 0.21/0.48 ( ( B2
% 0.21/0.48 = ( F2 @ X ) )
% 0.21/0.48 => ( ( member245028432_sc_sz @ X @ A )
% 0.21/0.48 => ( member1261661570real_c @ B2 @ ( image_1332486093real_c @ F2 @ A ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % image_eqI
% 0.21/0.48 thf(fact_272_image__eqI,axiom,
% 0.21/0.48 ! [B2: produc866628903_sc_sz,F2: produc190496183real_c > produc866628903_sc_sz,X: produc190496183real_c,A: set_Pr1389752855real_c] :
% 0.21/0.48 ( ( B2
% 0.21/0.48 = ( F2 @ X ) )
% 0.21/0.48 => ( ( member1895684704real_c @ X @ A )
% 0.21/0.48 => ( member245028432_sc_sz @ B2 @ ( image_388766773_sc_sz @ F2 @ A ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % image_eqI
% 0.21/0.48 thf(fact_273_image__eqI,axiom,
% 0.21/0.48 ! [B2: produc640052711real_c,F2: finite1398487019real_c > produc640052711real_c,X: finite1398487019real_c,A: set_Fi1407883041real_c] :
% 0.21/0.48 ( ( B2
% 0.21/0.48 = ( F2 @ X ) )
% 0.21/0.48 => ( ( member1261661570real_c @ X @ A )
% 0.21/0.48 => ( member346808080real_c @ B2 @ ( image_1746662005real_c @ F2 @ A ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % image_eqI
% 0.21/0.48 thf(fact_274_image__eqI,axiom,
% 0.21/0.48 ! [B2: finite1398487019real_c,F2: produc640052711real_c > finite1398487019real_c,X: produc640052711real_c,A: set_Pr754230471real_c] :
% 0.21/0.48 ( ( B2
% 0.21/0.48 = ( F2 @ X ) )
% 0.21/0.48 => ( ( member346808080real_c @ X @ A )
% 0.21/0.48 => ( member1261661570real_c @ B2 @ ( image_124598413real_c @ F2 @ A ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % image_eqI
% 0.21/0.48 thf(fact_275_image__eqI,axiom,
% 0.21/0.48 ! [B2: produc190496183real_c,F2: produc866628903_sc_sz > produc190496183real_c,X: produc866628903_sc_sz,A: set_Pr1774599175_sc_sz] :
% 0.21/0.48 ( ( B2
% 0.21/0.48 = ( F2 @ X ) )
% 0.21/0.48 => ( ( member245028432_sc_sz @ X @ A )
% 0.21/0.48 => ( member1895684704real_c @ B2 @ ( image_1121381717real_c @ F2 @ A ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % image_eqI
% 0.21/0.48 thf(fact_276_split__part,axiom,
% 0.21/0.48 ! [P: $o,Q: denota610675952t_unit > produc866628903_sc_sz > $o] :
% 0.21/0.48 ( ( produc619560141c_sz_o
% 0.21/0.48 @ ^ [A5: denota610675952t_unit,B5: produc866628903_sc_sz] :
% 0.21/0.48 ( P
% 0.21/0.48 & ( Q @ A5 @ B5 ) ) )
% 0.21/0.48 = ( ^ [Ab: produc1821101996_sc_sz] :
% 0.21/0.48 ( P
% 0.21/0.48 & ( produc619560141c_sz_o @ Q @ Ab ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % split_part
% 0.21/0.48 thf(fact_277_prod_Odisc__eq__case,axiom,
% 0.21/0.48 ! [Prod: produc1821101996_sc_sz] :
% 0.21/0.48 ( produc619560141c_sz_o
% 0.21/0.48 @ ^ [Uu: denota610675952t_unit,Uv: produc866628903_sc_sz] : $true
% 0.21/0.48 @ Prod ) ).
% 0.21/0.48
% 0.21/0.48 % prod.disc_eq_case
% 0.21/0.48 thf(fact_278_rev__image__eqI,axiom,
% 0.21/0.48 ! [X: produc190496183real_c,A: set_Pr1389752855real_c,B2: produc190496183real_c,F2: produc190496183real_c > produc190496183real_c] :
% 0.21/0.48 ( ( member1895684704real_c @ X @ A )
% 0.21/0.48 => ( ( B2
% 0.21/0.48 = ( F2 @ X ) )
% 0.21/0.48 => ( member1895684704real_c @ B2 @ ( image_738229701real_c @ F2 @ A ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % rev_image_eqI
% 0.21/0.48 thf(fact_279_rev__image__eqI,axiom,
% 0.21/0.48 ! [X: finite1398487019real_c,A: set_Fi1407883041real_c,B2: finite1398487019real_c,F2: finite1398487019real_c > finite1398487019real_c] :
% 0.21/0.48 ( ( member1261661570real_c @ X @ A )
% 0.21/0.48 => ( ( B2
% 0.21/0.48 = ( F2 @ X ) )
% 0.21/0.48 => ( member1261661570real_c @ B2 @ ( image_1514048989real_c @ F2 @ A ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % rev_image_eqI
% 0.21/0.48 thf(fact_280_rev__image__eqI,axiom,
% 0.21/0.48 ! [X: produc190496183real_c,A: set_Pr1389752855real_c,B2: finite1398487019real_c,F2: produc190496183real_c > finite1398487019real_c] :
% 0.21/0.48 ( ( member1895684704real_c @ X @ A )
% 0.21/0.48 => ( ( B2
% 0.21/0.48 = ( F2 @ X ) )
% 0.21/0.48 => ( member1261661570real_c @ B2 @ ( image_14429021real_c @ F2 @ A ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % rev_image_eqI
% 0.21/0.48 thf(fact_281_rev__image__eqI,axiom,
% 0.21/0.48 ! [X: finite1398487019real_c,A: set_Fi1407883041real_c,B2: produc190496183real_c,F2: finite1398487019real_c > produc190496183real_c] :
% 0.21/0.48 ( ( member1261661570real_c @ X @ A )
% 0.21/0.48 => ( ( B2
% 0.21/0.48 = ( F2 @ X ) )
% 0.21/0.48 => ( member1895684704real_c @ B2 @ ( image_1461287749real_c @ F2 @ A ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % rev_image_eqI
% 0.21/0.48 thf(fact_282_rev__image__eqI,axiom,
% 0.21/0.48 ! [X: finite1398487019real_c,A: set_Fi1407883041real_c,B2: produc866628903_sc_sz,F2: finite1398487019real_c > produc866628903_sc_sz] :
% 0.21/0.48 ( ( member1261661570real_c @ X @ A )
% 0.21/0.48 => ( ( B2
% 0.21/0.48 = ( F2 @ X ) )
% 0.21/0.48 => ( member245028432_sc_sz @ B2 @ ( image_290183605_sc_sz @ F2 @ A ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % rev_image_eqI
% 0.21/0.48 thf(fact_283_rev__image__eqI,axiom,
% 0.21/0.48 ! [X: produc866628903_sc_sz,A: set_Pr1774599175_sc_sz,B2: finite1398487019real_c,F2: produc866628903_sc_sz > finite1398487019real_c] :
% 0.21/0.48 ( ( member245028432_sc_sz @ X @ A )
% 0.21/0.48 => ( ( B2
% 0.21/0.48 = ( F2 @ X ) )
% 0.21/0.48 => ( member1261661570real_c @ B2 @ ( image_1332486093real_c @ F2 @ A ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % rev_image_eqI
% 0.21/0.48 thf(fact_284_rev__image__eqI,axiom,
% 0.21/0.48 ! [X: produc190496183real_c,A: set_Pr1389752855real_c,B2: produc866628903_sc_sz,F2: produc190496183real_c > produc866628903_sc_sz] :
% 0.21/0.48 ( ( member1895684704real_c @ X @ A )
% 0.21/0.48 => ( ( B2
% 0.21/0.48 = ( F2 @ X ) )
% 0.21/0.48 => ( member245028432_sc_sz @ B2 @ ( image_388766773_sc_sz @ F2 @ A ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % rev_image_eqI
% 0.21/0.48 thf(fact_285_rev__image__eqI,axiom,
% 0.21/0.48 ! [X: finite1398487019real_c,A: set_Fi1407883041real_c,B2: produc640052711real_c,F2: finite1398487019real_c > produc640052711real_c] :
% 0.21/0.48 ( ( member1261661570real_c @ X @ A )
% 0.21/0.48 => ( ( B2
% 0.21/0.48 = ( F2 @ X ) )
% 0.21/0.48 => ( member346808080real_c @ B2 @ ( image_1746662005real_c @ F2 @ A ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % rev_image_eqI
% 0.21/0.48 thf(fact_286_rev__image__eqI,axiom,
% 0.21/0.48 ! [X: produc640052711real_c,A: set_Pr754230471real_c,B2: finite1398487019real_c,F2: produc640052711real_c > finite1398487019real_c] :
% 0.21/0.48 ( ( member346808080real_c @ X @ A )
% 0.21/0.48 => ( ( B2
% 0.21/0.48 = ( F2 @ X ) )
% 0.21/0.48 => ( member1261661570real_c @ B2 @ ( image_124598413real_c @ F2 @ A ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % rev_image_eqI
% 0.21/0.48 thf(fact_287_rev__image__eqI,axiom,
% 0.21/0.48 ! [X: produc866628903_sc_sz,A: set_Pr1774599175_sc_sz,B2: produc190496183real_c,F2: produc866628903_sc_sz > produc190496183real_c] :
% 0.21/0.48 ( ( member245028432_sc_sz @ X @ A )
% 0.21/0.48 => ( ( B2
% 0.21/0.48 = ( F2 @ X ) )
% 0.21/0.48 => ( member1895684704real_c @ B2 @ ( image_1121381717real_c @ F2 @ A ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % rev_image_eqI
% 0.21/0.48 thf(fact_288_ball__imageD,axiom,
% 0.21/0.48 ! [F2: produc1821101996_sc_sz > produc190496183real_c,A: set_Pr1169339874_sc_sz,P: produc190496183real_c > $o] :
% 0.21/0.48 ( ! [X3: produc190496183real_c] :
% 0.21/0.48 ( ( member1895684704real_c @ X3 @ ( image_386905412real_c @ F2 @ A ) )
% 0.21/0.48 => ( P @ X3 ) )
% 0.21/0.48 => ! [X5: produc1821101996_sc_sz] :
% 0.21/0.48 ( ( member1057565379_sc_sz @ X5 @ A )
% 0.21/0.48 => ( P @ ( F2 @ X5 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % ball_imageD
% 0.21/0.48 thf(fact_289_ball__imageD,axiom,
% 0.21/0.48 ! [F2: produc1821101996_sc_sz > produc999471430t_unit,A: set_Pr1169339874_sc_sz,P: produc999471430t_unit > $o] :
% 0.21/0.48 ( ! [X3: produc999471430t_unit] :
% 0.21/0.48 ( ( member235934813t_unit @ X3 @ ( image_904562809t_unit @ F2 @ A ) )
% 0.21/0.48 => ( P @ X3 ) )
% 0.21/0.48 => ! [X5: produc1821101996_sc_sz] :
% 0.21/0.48 ( ( member1057565379_sc_sz @ X5 @ A )
% 0.21/0.48 => ( P @ ( F2 @ X5 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % ball_imageD
% 0.21/0.48 thf(fact_290_ball__imageD,axiom,
% 0.21/0.48 ! [F2: produc190496183real_c > produc1821101996_sc_sz,A: set_Pr1389752855real_c,P: produc1821101996_sc_sz > $o] :
% 0.21/0.48 ( ! [X3: produc1821101996_sc_sz] :
% 0.21/0.48 ( ( member1057565379_sc_sz @ X3 @ ( image_1259833374_sc_sz @ F2 @ A ) )
% 0.21/0.48 => ( P @ X3 ) )
% 0.21/0.48 => ! [X5: produc190496183real_c] :
% 0.21/0.48 ( ( member1895684704real_c @ X5 @ A )
% 0.21/0.48 => ( P @ ( F2 @ X5 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % ball_imageD
% 0.21/0.48 thf(fact_291_ball__imageD,axiom,
% 0.21/0.48 ! [F2: produc190496183real_c > produc190496183real_c,A: set_Pr1389752855real_c,P: produc190496183real_c > $o] :
% 0.21/0.48 ( ! [X3: produc190496183real_c] :
% 0.21/0.48 ( ( member1895684704real_c @ X3 @ ( image_738229701real_c @ F2 @ A ) )
% 0.21/0.48 => ( P @ X3 ) )
% 0.21/0.48 => ! [X5: produc190496183real_c] :
% 0.21/0.48 ( ( member1895684704real_c @ X5 @ A )
% 0.21/0.48 => ( P @ ( F2 @ X5 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % ball_imageD
% 0.21/0.48 thf(fact_292_ball__imageD,axiom,
% 0.21/0.48 ! [F2: produc999471430t_unit > produc1821101996_sc_sz,A: set_Pr2041213564t_unit,P: produc1821101996_sc_sz > $o] :
% 0.21/0.48 ( ! [X3: produc1821101996_sc_sz] :
% 0.21/0.48 ( ( member1057565379_sc_sz @ X3 @ ( image_1426741113_sc_sz @ F2 @ A ) )
% 0.21/0.48 => ( P @ X3 ) )
% 0.21/0.48 => ! [X5: produc999471430t_unit] :
% 0.21/0.48 ( ( member235934813t_unit @ X5 @ A )
% 0.21/0.48 => ( P @ ( F2 @ X5 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % ball_imageD
% 0.21/0.48 thf(fact_293_image__cong,axiom,
% 0.21/0.48 ! [M: set_Pr1389752855real_c,N: set_Pr1389752855real_c,F2: produc190496183real_c > produc1821101996_sc_sz,G: produc190496183real_c > produc1821101996_sc_sz] :
% 0.21/0.48 ( ( M = N )
% 0.21/0.48 => ( ! [X3: produc190496183real_c] :
% 0.21/0.48 ( ( member1895684704real_c @ X3 @ N )
% 0.21/0.48 => ( ( F2 @ X3 )
% 0.21/0.48 = ( G @ X3 ) ) )
% 0.21/0.48 => ( ( image_1259833374_sc_sz @ F2 @ M )
% 0.21/0.48 = ( image_1259833374_sc_sz @ G @ N ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % image_cong
% 0.21/0.48 thf(fact_294_image__cong,axiom,
% 0.21/0.48 ! [M: set_Pr1389752855real_c,N: set_Pr1389752855real_c,F2: produc190496183real_c > produc190496183real_c,G: produc190496183real_c > produc190496183real_c] :
% 0.21/0.48 ( ( M = N )
% 0.21/0.48 => ( ! [X3: produc190496183real_c] :
% 0.21/0.48 ( ( member1895684704real_c @ X3 @ N )
% 0.21/0.48 => ( ( F2 @ X3 )
% 0.21/0.48 = ( G @ X3 ) ) )
% 0.21/0.48 => ( ( image_738229701real_c @ F2 @ M )
% 0.21/0.48 = ( image_738229701real_c @ G @ N ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % image_cong
% 0.21/0.48 thf(fact_295_image__cong,axiom,
% 0.21/0.48 ! [M: set_Pr1169339874_sc_sz,N: set_Pr1169339874_sc_sz,F2: produc1821101996_sc_sz > produc190496183real_c,G: produc1821101996_sc_sz > produc190496183real_c] :
% 0.21/0.48 ( ( M = N )
% 0.21/0.48 => ( ! [X3: produc1821101996_sc_sz] :
% 0.21/0.48 ( ( member1057565379_sc_sz @ X3 @ N )
% 0.21/0.48 => ( ( F2 @ X3 )
% 0.21/0.48 = ( G @ X3 ) ) )
% 0.21/0.48 => ( ( image_386905412real_c @ F2 @ M )
% 0.21/0.48 = ( image_386905412real_c @ G @ N ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % image_cong
% 0.21/0.48 thf(fact_296_image__cong,axiom,
% 0.21/0.48 ! [M: set_Pr1169339874_sc_sz,N: set_Pr1169339874_sc_sz,F2: produc1821101996_sc_sz > produc999471430t_unit,G: produc1821101996_sc_sz > produc999471430t_unit] :
% 0.21/0.48 ( ( M = N )
% 0.21/0.48 => ( ! [X3: produc1821101996_sc_sz] :
% 0.21/0.48 ( ( member1057565379_sc_sz @ X3 @ N )
% 0.21/0.48 => ( ( F2 @ X3 )
% 0.21/0.48 = ( G @ X3 ) ) )
% 0.21/0.48 => ( ( image_904562809t_unit @ F2 @ M )
% 0.21/0.48 = ( image_904562809t_unit @ G @ N ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % image_cong
% 0.21/0.48 thf(fact_297_image__cong,axiom,
% 0.21/0.48 ! [M: set_Pr2041213564t_unit,N: set_Pr2041213564t_unit,F2: produc999471430t_unit > produc1821101996_sc_sz,G: produc999471430t_unit > produc1821101996_sc_sz] :
% 0.21/0.48 ( ( M = N )
% 0.21/0.48 => ( ! [X3: produc999471430t_unit] :
% 0.21/0.48 ( ( member235934813t_unit @ X3 @ N )
% 0.21/0.48 => ( ( F2 @ X3 )
% 0.21/0.48 = ( G @ X3 ) ) )
% 0.21/0.48 => ( ( image_1426741113_sc_sz @ F2 @ M )
% 0.21/0.48 = ( image_1426741113_sc_sz @ G @ N ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % image_cong
% 0.21/0.48 thf(fact_298_bex__imageD,axiom,
% 0.21/0.48 ! [F2: produc1821101996_sc_sz > produc190496183real_c,A: set_Pr1169339874_sc_sz,P: produc190496183real_c > $o] :
% 0.21/0.48 ( ? [X5: produc190496183real_c] :
% 0.21/0.48 ( ( member1895684704real_c @ X5 @ ( image_386905412real_c @ F2 @ A ) )
% 0.21/0.48 & ( P @ X5 ) )
% 0.21/0.48 => ? [X3: produc1821101996_sc_sz] :
% 0.21/0.48 ( ( member1057565379_sc_sz @ X3 @ A )
% 0.21/0.48 & ( P @ ( F2 @ X3 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % bex_imageD
% 0.21/0.48 thf(fact_299_bex__imageD,axiom,
% 0.21/0.48 ! [F2: produc1821101996_sc_sz > produc999471430t_unit,A: set_Pr1169339874_sc_sz,P: produc999471430t_unit > $o] :
% 0.21/0.48 ( ? [X5: produc999471430t_unit] :
% 0.21/0.48 ( ( member235934813t_unit @ X5 @ ( image_904562809t_unit @ F2 @ A ) )
% 0.21/0.48 & ( P @ X5 ) )
% 0.21/0.48 => ? [X3: produc1821101996_sc_sz] :
% 0.21/0.48 ( ( member1057565379_sc_sz @ X3 @ A )
% 0.21/0.48 & ( P @ ( F2 @ X3 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % bex_imageD
% 0.21/0.48 thf(fact_300_bex__imageD,axiom,
% 0.21/0.48 ! [F2: produc190496183real_c > produc1821101996_sc_sz,A: set_Pr1389752855real_c,P: produc1821101996_sc_sz > $o] :
% 0.21/0.48 ( ? [X5: produc1821101996_sc_sz] :
% 0.21/0.48 ( ( member1057565379_sc_sz @ X5 @ ( image_1259833374_sc_sz @ F2 @ A ) )
% 0.21/0.48 & ( P @ X5 ) )
% 0.21/0.48 => ? [X3: produc190496183real_c] :
% 0.21/0.48 ( ( member1895684704real_c @ X3 @ A )
% 0.21/0.48 & ( P @ ( F2 @ X3 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % bex_imageD
% 0.21/0.48 thf(fact_301_bex__imageD,axiom,
% 0.21/0.48 ! [F2: produc190496183real_c > produc190496183real_c,A: set_Pr1389752855real_c,P: produc190496183real_c > $o] :
% 0.21/0.48 ( ? [X5: produc190496183real_c] :
% 0.21/0.48 ( ( member1895684704real_c @ X5 @ ( image_738229701real_c @ F2 @ A ) )
% 0.21/0.48 & ( P @ X5 ) )
% 0.21/0.48 => ? [X3: produc190496183real_c] :
% 0.21/0.48 ( ( member1895684704real_c @ X3 @ A )
% 0.21/0.48 & ( P @ ( F2 @ X3 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % bex_imageD
% 0.21/0.48 thf(fact_302_bex__imageD,axiom,
% 0.21/0.48 ! [F2: produc999471430t_unit > produc1821101996_sc_sz,A: set_Pr2041213564t_unit,P: produc1821101996_sc_sz > $o] :
% 0.21/0.48 ( ? [X5: produc1821101996_sc_sz] :
% 0.21/0.48 ( ( member1057565379_sc_sz @ X5 @ ( image_1426741113_sc_sz @ F2 @ A ) )
% 0.21/0.48 & ( P @ X5 ) )
% 0.21/0.48 => ? [X3: produc999471430t_unit] :
% 0.21/0.48 ( ( member235934813t_unit @ X3 @ A )
% 0.21/0.48 & ( P @ ( F2 @ X3 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % bex_imageD
% 0.21/0.48 thf(fact_303_image__iff,axiom,
% 0.21/0.48 ! [Z: produc190496183real_c,F2: produc1821101996_sc_sz > produc190496183real_c,A: set_Pr1169339874_sc_sz] :
% 0.21/0.48 ( ( member1895684704real_c @ Z @ ( image_386905412real_c @ F2 @ A ) )
% 0.21/0.48 = ( ? [X4: produc1821101996_sc_sz] :
% 0.21/0.48 ( ( member1057565379_sc_sz @ X4 @ A )
% 0.21/0.48 & ( Z
% 0.21/0.48 = ( F2 @ X4 ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % image_iff
% 0.21/0.48 thf(fact_304_image__iff,axiom,
% 0.21/0.48 ! [Z: produc190496183real_c,F2: produc190496183real_c > produc190496183real_c,A: set_Pr1389752855real_c] :
% 0.21/0.48 ( ( member1895684704real_c @ Z @ ( image_738229701real_c @ F2 @ A ) )
% 0.21/0.48 = ( ? [X4: produc190496183real_c] :
% 0.21/0.48 ( ( member1895684704real_c @ X4 @ A )
% 0.21/0.48 & ( Z
% 0.21/0.48 = ( F2 @ X4 ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % image_iff
% 0.21/0.48 thf(fact_305_image__iff,axiom,
% 0.21/0.48 ! [Z: produc1821101996_sc_sz,F2: produc190496183real_c > produc1821101996_sc_sz,A: set_Pr1389752855real_c] :
% 0.21/0.48 ( ( member1057565379_sc_sz @ Z @ ( image_1259833374_sc_sz @ F2 @ A ) )
% 0.21/0.48 = ( ? [X4: produc190496183real_c] :
% 0.21/0.48 ( ( member1895684704real_c @ X4 @ A )
% 0.21/0.48 & ( Z
% 0.21/0.48 = ( F2 @ X4 ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % image_iff
% 0.21/0.48 thf(fact_306_image__iff,axiom,
% 0.21/0.48 ! [Z: produc1821101996_sc_sz,F2: produc999471430t_unit > produc1821101996_sc_sz,A: set_Pr2041213564t_unit] :
% 0.21/0.48 ( ( member1057565379_sc_sz @ Z @ ( image_1426741113_sc_sz @ F2 @ A ) )
% 0.21/0.48 = ( ? [X4: produc999471430t_unit] :
% 0.21/0.48 ( ( member235934813t_unit @ X4 @ A )
% 0.21/0.48 & ( Z
% 0.21/0.48 = ( F2 @ X4 ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % image_iff
% 0.21/0.48 thf(fact_307_image__iff,axiom,
% 0.21/0.48 ! [Z: produc999471430t_unit,F2: produc1821101996_sc_sz > produc999471430t_unit,A: set_Pr1169339874_sc_sz] :
% 0.21/0.48 ( ( member235934813t_unit @ Z @ ( image_904562809t_unit @ F2 @ A ) )
% 0.21/0.48 = ( ? [X4: produc1821101996_sc_sz] :
% 0.21/0.48 ( ( member1057565379_sc_sz @ X4 @ A )
% 0.21/0.48 & ( Z
% 0.21/0.48 = ( F2 @ X4 ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % image_iff
% 0.21/0.48 thf(fact_308_imageI,axiom,
% 0.21/0.48 ! [X: produc866628903_sc_sz,A: set_Pr1774599175_sc_sz,F2: produc866628903_sc_sz > produc190496183real_c] :
% 0.21/0.48 ( ( member245028432_sc_sz @ X @ A )
% 0.21/0.48 => ( member1895684704real_c @ ( F2 @ X ) @ ( image_1121381717real_c @ F2 @ A ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % imageI
% 0.21/0.48 thf(fact_309_imageI,axiom,
% 0.21/0.48 ! [X: produc866628903_sc_sz,A: set_Pr1774599175_sc_sz,F2: produc866628903_sc_sz > finite1398487019real_c] :
% 0.21/0.48 ( ( member245028432_sc_sz @ X @ A )
% 0.21/0.48 => ( member1261661570real_c @ ( F2 @ X ) @ ( image_1332486093real_c @ F2 @ A ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % imageI
% 0.21/0.48 thf(fact_310_imageI,axiom,
% 0.21/0.48 ! [X: produc866628903_sc_sz,A: set_Pr1774599175_sc_sz,F2: produc866628903_sc_sz > produc1821101996_sc_sz] :
% 0.21/0.48 ( ( member245028432_sc_sz @ X @ A )
% 0.21/0.48 => ( member1057565379_sc_sz @ ( F2 @ X ) @ ( image_226055310_sc_sz @ F2 @ A ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % imageI
% 0.21/0.48 thf(fact_311_imageI,axiom,
% 0.21/0.48 ! [X: produc866628903_sc_sz,A: set_Pr1774599175_sc_sz,F2: produc866628903_sc_sz > produc640052711real_c] :
% 0.21/0.48 ( ( member245028432_sc_sz @ X @ A )
% 0.21/0.48 => ( member346808080real_c @ ( F2 @ X ) @ ( image_768765061real_c @ F2 @ A ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % imageI
% 0.21/0.48 thf(fact_312_imageI,axiom,
% 0.21/0.48 ! [X: produc866628903_sc_sz,A: set_Pr1774599175_sc_sz,F2: produc866628903_sc_sz > produc999471430t_unit] :
% 0.21/0.48 ( ( member245028432_sc_sz @ X @ A )
% 0.21/0.48 => ( member235934813t_unit @ ( F2 @ X ) @ ( image_1551908392t_unit @ F2 @ A ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % imageI
% 0.21/0.48 thf(fact_313_imageI,axiom,
% 0.21/0.48 ! [X: produc866628903_sc_sz,A: set_Pr1774599175_sc_sz,F2: produc866628903_sc_sz > produc866628903_sc_sz] :
% 0.21/0.48 ( ( member245028432_sc_sz @ X @ A )
% 0.21/0.48 => ( member245028432_sc_sz @ ( F2 @ X ) @ ( image_1313166277_sc_sz @ F2 @ A ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % imageI
% 0.21/0.48 thf(fact_314_imageI,axiom,
% 0.21/0.48 ! [X: produc190496183real_c,A: set_Pr1389752855real_c,F2: produc190496183real_c > produc190496183real_c] :
% 0.21/0.48 ( ( member1895684704real_c @ X @ A )
% 0.21/0.48 => ( member1895684704real_c @ ( F2 @ X ) @ ( image_738229701real_c @ F2 @ A ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % imageI
% 0.21/0.48 thf(fact_315_Compr__image__eq,axiom,
% 0.21/0.48 ! [F2: produc190496183real_c > produc190496183real_c,A: set_Pr1389752855real_c,P: produc190496183real_c > $o] :
% 0.21/0.48 ( ( collec1643251106real_c
% 0.21/0.48 @ ^ [X4: produc190496183real_c] :
% 0.21/0.48 ( ( member1895684704real_c @ X4 @ ( image_738229701real_c @ F2 @ A ) )
% 0.21/0.48 & ( P @ X4 ) ) )
% 0.21/0.48 = ( image_738229701real_c @ F2
% 0.21/0.48 @ ( collec1643251106real_c
% 0.21/0.48 @ ^ [X4: produc190496183real_c] :
% 0.21/0.48 ( ( member1895684704real_c @ X4 @ A )
% 0.21/0.48 & ( P @ ( F2 @ X4 ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % Compr_image_eq
% 0.21/0.48 thf(fact_316_imageE,axiom,
% 0.21/0.48 ! [B2: produc190496183real_c,F2: produc190496183real_c > produc190496183real_c,A: set_Pr1389752855real_c] :
% 0.21/0.48 ( ( member1895684704real_c @ B2 @ ( image_738229701real_c @ F2 @ A ) )
% 0.21/0.48 => ~ ! [X3: produc190496183real_c] :
% 0.21/0.48 ( ( B2
% 0.21/0.48 = ( F2 @ X3 ) )
% 0.21/0.48 => ~ ( member1895684704real_c @ X3 @ A ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % imageE
% 0.21/0.48 thf(fact_317_case__prod__Pair__iden,axiom,
% 0.21/0.48 ! [P2: produc1821101996_sc_sz] :
% 0.21/0.48 ( ( produc448466487_sc_sz @ produc789536734_sc_sz @ P2 )
% 0.21/0.48 = P2 ) ).
% 0.21/0.48
% 0.21/0.48 % case_prod_Pair_iden
% 0.21/0.48 thf(fact_318_pred__equals__eq2,axiom,
% 0.21/0.48 ! [R2: set_Pr1389752855real_c,S4: set_Pr1389752855real_c] :
% 0.21/0.48 ( ( ( ^ [X4: finite1398487019real_c,Y4: finite1398487019real_c] : ( member1895684704real_c @ ( produc394644079real_c @ X4 @ Y4 ) @ R2 ) )
% 0.21/0.48 = ( ^ [X4: finite1398487019real_c,Y4: finite1398487019real_c] : ( member1895684704real_c @ ( produc394644079real_c @ X4 @ Y4 ) @ S4 ) ) )
% 0.21/0.48 = ( R2 = S4 ) ) ).
% 0.21/0.48
% 0.21/0.48 % pred_equals_eq2
% 0.21/0.48 thf(fact_319_pred__equals__eq2,axiom,
% 0.21/0.48 ! [R2: set_Pr1169339874_sc_sz,S4: set_Pr1169339874_sc_sz] :
% 0.21/0.48 ( ( ( ^ [X4: denota610675952t_unit,Y4: produc866628903_sc_sz] : ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ X4 @ Y4 ) @ R2 ) )
% 0.21/0.48 = ( ^ [X4: denota610675952t_unit,Y4: produc866628903_sc_sz] : ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ X4 @ Y4 ) @ S4 ) ) )
% 0.21/0.48 = ( R2 = S4 ) ) ).
% 0.21/0.48
% 0.21/0.48 % pred_equals_eq2
% 0.21/0.48 thf(fact_320_mem__Sigma__iff,axiom,
% 0.21/0.48 ! [A2: produc190496183real_c,B2: produc190496183real_c,A: set_Pr1389752855real_c,B: produc190496183real_c > set_Pr1389752855real_c] :
% 0.21/0.48 ( ( member346808080real_c @ ( produc1687028567real_c @ A2 @ B2 ) @ ( produc1017530376real_c @ A @ B ) )
% 0.21/0.48 = ( ( member1895684704real_c @ A2 @ A )
% 0.21/0.48 & ( member1895684704real_c @ B2 @ ( B @ A2 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mem_Sigma_iff
% 0.21/0.48 thf(fact_321_mem__Sigma__iff,axiom,
% 0.21/0.48 ! [A2: finite1398487019real_c,B2: finite1398487019real_c,A: set_Fi1407883041real_c,B: finite1398487019real_c > set_Fi1407883041real_c] :
% 0.21/0.48 ( ( member1895684704real_c @ ( produc394644079real_c @ A2 @ B2 ) @ ( produc563345056real_c @ A @ B ) )
% 0.21/0.48 = ( ( member1261661570real_c @ A2 @ A )
% 0.21/0.48 & ( member1261661570real_c @ B2 @ ( B @ A2 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mem_Sigma_iff
% 0.21/0.48 thf(fact_322_mem__Sigma__iff,axiom,
% 0.21/0.48 ! [A2: denota610675952t_unit,B2: produc866628903_sc_sz,A: set_De208295462t_unit,B: denota610675952t_unit > set_Pr1774599175_sc_sz] :
% 0.21/0.48 ( ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ A2 @ B2 ) @ ( produc159603053_sc_sz @ A @ B ) )
% 0.21/0.48 = ( ( member754147591t_unit @ A2 @ A )
% 0.21/0.48 & ( member245028432_sc_sz @ B2 @ ( B @ A2 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % mem_Sigma_iff
% 0.21/0.48 thf(fact_323_SigmaI,axiom,
% 0.21/0.48 ! [A2: finite1398487019real_c,A: set_Fi1407883041real_c,B2: finite1398487019real_c,B: finite1398487019real_c > set_Fi1407883041real_c] :
% 0.21/0.48 ( ( member1261661570real_c @ A2 @ A )
% 0.21/0.48 => ( ( member1261661570real_c @ B2 @ ( B @ A2 ) )
% 0.21/0.48 => ( member1895684704real_c @ ( produc394644079real_c @ A2 @ B2 ) @ ( produc563345056real_c @ A @ B ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % SigmaI
% 0.21/0.48 thf(fact_324_SigmaI,axiom,
% 0.21/0.48 ! [A2: produc190496183real_c,A: set_Pr1389752855real_c,B2: produc190496183real_c,B: produc190496183real_c > set_Pr1389752855real_c] :
% 0.21/0.48 ( ( member1895684704real_c @ A2 @ A )
% 0.21/0.48 => ( ( member1895684704real_c @ B2 @ ( B @ A2 ) )
% 0.21/0.48 => ( member346808080real_c @ ( produc1687028567real_c @ A2 @ B2 ) @ ( produc1017530376real_c @ A @ B ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % SigmaI
% 0.21/0.48 thf(fact_325_SigmaI,axiom,
% 0.21/0.48 ! [A2: denota610675952t_unit,A: set_De208295462t_unit,B2: produc866628903_sc_sz,B: denota610675952t_unit > set_Pr1774599175_sc_sz] :
% 0.21/0.48 ( ( member754147591t_unit @ A2 @ A )
% 0.21/0.48 => ( ( member245028432_sc_sz @ B2 @ ( B @ A2 ) )
% 0.21/0.48 => ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ A2 @ B2 ) @ ( produc159603053_sc_sz @ A @ B ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % SigmaI
% 0.21/0.48 thf(fact_326_SigmaE2,axiom,
% 0.21/0.48 ! [A2: produc190496183real_c,B2: produc190496183real_c,A: set_Pr1389752855real_c,B: produc190496183real_c > set_Pr1389752855real_c] :
% 0.21/0.48 ( ( member346808080real_c @ ( produc1687028567real_c @ A2 @ B2 ) @ ( produc1017530376real_c @ A @ B ) )
% 0.21/0.48 => ~ ( ( member1895684704real_c @ A2 @ A )
% 0.21/0.48 => ~ ( member1895684704real_c @ B2 @ ( B @ A2 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % SigmaE2
% 0.21/0.48 thf(fact_327_SigmaE2,axiom,
% 0.21/0.48 ! [A2: finite1398487019real_c,B2: finite1398487019real_c,A: set_Fi1407883041real_c,B: finite1398487019real_c > set_Fi1407883041real_c] :
% 0.21/0.48 ( ( member1895684704real_c @ ( produc394644079real_c @ A2 @ B2 ) @ ( produc563345056real_c @ A @ B ) )
% 0.21/0.48 => ~ ( ( member1261661570real_c @ A2 @ A )
% 0.21/0.48 => ~ ( member1261661570real_c @ B2 @ ( B @ A2 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % SigmaE2
% 0.21/0.48 thf(fact_328_SigmaE2,axiom,
% 0.21/0.48 ! [A2: denota610675952t_unit,B2: produc866628903_sc_sz,A: set_De208295462t_unit,B: denota610675952t_unit > set_Pr1774599175_sc_sz] :
% 0.21/0.48 ( ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ A2 @ B2 ) @ ( produc159603053_sc_sz @ A @ B ) )
% 0.21/0.48 => ~ ( ( member754147591t_unit @ A2 @ A )
% 0.21/0.48 => ~ ( member245028432_sc_sz @ B2 @ ( B @ A2 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % SigmaE2
% 0.21/0.48 thf(fact_329_SigmaD2,axiom,
% 0.21/0.48 ! [A2: finite1398487019real_c,B2: finite1398487019real_c,A: set_Fi1407883041real_c,B: finite1398487019real_c > set_Fi1407883041real_c] :
% 0.21/0.48 ( ( member1895684704real_c @ ( produc394644079real_c @ A2 @ B2 ) @ ( produc563345056real_c @ A @ B ) )
% 0.21/0.48 => ( member1261661570real_c @ B2 @ ( B @ A2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % SigmaD2
% 0.21/0.48 thf(fact_330_SigmaD2,axiom,
% 0.21/0.48 ! [A2: denota610675952t_unit,B2: produc866628903_sc_sz,A: set_De208295462t_unit,B: denota610675952t_unit > set_Pr1774599175_sc_sz] :
% 0.21/0.48 ( ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ A2 @ B2 ) @ ( produc159603053_sc_sz @ A @ B ) )
% 0.21/0.48 => ( member245028432_sc_sz @ B2 @ ( B @ A2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % SigmaD2
% 0.21/0.48 thf(fact_331_SigmaD1,axiom,
% 0.21/0.48 ! [A2: finite1398487019real_c,B2: finite1398487019real_c,A: set_Fi1407883041real_c,B: finite1398487019real_c > set_Fi1407883041real_c] :
% 0.21/0.48 ( ( member1895684704real_c @ ( produc394644079real_c @ A2 @ B2 ) @ ( produc563345056real_c @ A @ B ) )
% 0.21/0.48 => ( member1261661570real_c @ A2 @ A ) ) ).
% 0.21/0.48
% 0.21/0.48 % SigmaD1
% 0.21/0.48 thf(fact_332_SigmaD1,axiom,
% 0.21/0.48 ! [A2: denota610675952t_unit,B2: produc866628903_sc_sz,A: set_De208295462t_unit,B: denota610675952t_unit > set_Pr1774599175_sc_sz] :
% 0.21/0.48 ( ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ A2 @ B2 ) @ ( produc159603053_sc_sz @ A @ B ) )
% 0.21/0.48 => ( member754147591t_unit @ A2 @ A ) ) ).
% 0.21/0.48
% 0.21/0.48 % SigmaD1
% 0.21/0.48 thf(fact_333_SigmaE,axiom,
% 0.21/0.48 ! [C2: produc640052711real_c,A: set_Pr1389752855real_c,B: produc190496183real_c > set_Pr1389752855real_c] :
% 0.21/0.48 ( ( member346808080real_c @ C2 @ ( produc1017530376real_c @ A @ B ) )
% 0.21/0.48 => ~ ! [X3: produc190496183real_c] :
% 0.21/0.48 ( ( member1895684704real_c @ X3 @ A )
% 0.21/0.48 => ! [Y3: produc190496183real_c] :
% 0.21/0.48 ( ( member1895684704real_c @ Y3 @ ( B @ X3 ) )
% 0.21/0.48 => ( C2
% 0.21/0.48 != ( produc1687028567real_c @ X3 @ Y3 ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % SigmaE
% 0.21/0.48 thf(fact_334_SigmaE,axiom,
% 0.21/0.48 ! [C2: produc190496183real_c,A: set_Fi1407883041real_c,B: finite1398487019real_c > set_Fi1407883041real_c] :
% 0.21/0.48 ( ( member1895684704real_c @ C2 @ ( produc563345056real_c @ A @ B ) )
% 0.21/0.48 => ~ ! [X3: finite1398487019real_c] :
% 0.21/0.48 ( ( member1261661570real_c @ X3 @ A )
% 0.21/0.48 => ! [Y3: finite1398487019real_c] :
% 0.21/0.48 ( ( member1261661570real_c @ Y3 @ ( B @ X3 ) )
% 0.21/0.48 => ( C2
% 0.21/0.48 != ( produc394644079real_c @ X3 @ Y3 ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % SigmaE
% 0.21/0.48 thf(fact_335_SigmaE,axiom,
% 0.21/0.48 ! [C2: produc1821101996_sc_sz,A: set_De208295462t_unit,B: denota610675952t_unit > set_Pr1774599175_sc_sz] :
% 0.21/0.48 ( ( member1057565379_sc_sz @ C2 @ ( produc159603053_sc_sz @ A @ B ) )
% 0.21/0.48 => ~ ! [X3: denota610675952t_unit] :
% 0.21/0.48 ( ( member754147591t_unit @ X3 @ A )
% 0.21/0.48 => ! [Y3: produc866628903_sc_sz] :
% 0.21/0.48 ( ( member245028432_sc_sz @ Y3 @ ( B @ X3 ) )
% 0.21/0.48 => ( C2
% 0.21/0.48 != ( produc789536734_sc_sz @ X3 @ Y3 ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % SigmaE
% 0.21/0.48 thf(fact_336_swap__product,axiom,
% 0.21/0.48 ! [A: set_Pr1774599175_sc_sz,B: set_De208295462t_unit] :
% 0.21/0.48 ( ( image_1426741113_sc_sz
% 0.21/0.48 @ ( produc435149849_sc_sz
% 0.21/0.48 @ ^ [I4: produc866628903_sc_sz,J2: denota610675952t_unit] : ( produc789536734_sc_sz @ J2 @ I4 ) )
% 0.21/0.48 @ ( produc2020166735t_unit @ A
% 0.21/0.48 @ ^ [Uu: produc866628903_sc_sz] : B ) )
% 0.21/0.48 = ( produc159603053_sc_sz @ B
% 0.21/0.48 @ ^ [Uu: denota610675952t_unit] : A ) ) ).
% 0.21/0.48
% 0.21/0.48 % swap_product
% 0.21/0.48 thf(fact_337_member__product,axiom,
% 0.21/0.48 ! [X: produc190496183real_c,A: set_Fi1407883041real_c,B: set_Fi1407883041real_c] :
% 0.21/0.48 ( ( member1895684704real_c @ X @ ( produc3751594real_c @ A @ B ) )
% 0.21/0.48 = ( member1895684704real_c @ X
% 0.21/0.48 @ ( produc563345056real_c @ A
% 0.21/0.48 @ ^ [Uu: finite1398487019real_c] : B ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % member_product
% 0.21/0.48 thf(fact_338_map__prod__simp,axiom,
% 0.21/0.48 ! [F2: denota610675952t_unit > denota610675952t_unit,G: produc866628903_sc_sz > produc866628903_sc_sz,A2: denota610675952t_unit,B2: produc866628903_sc_sz] :
% 0.21/0.48 ( ( produc403791768_sc_sz @ F2 @ G @ ( produc789536734_sc_sz @ A2 @ B2 ) )
% 0.21/0.48 = ( produc789536734_sc_sz @ ( F2 @ A2 ) @ ( G @ B2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % map_prod_simp
% 0.21/0.48 thf(fact_339_in__inv__image,axiom,
% 0.21/0.48 ! [X: finite1398487019real_c,Y: finite1398487019real_c,R: set_Pr1389752855real_c,F2: finite1398487019real_c > finite1398487019real_c] :
% 0.21/0.48 ( ( member1895684704real_c @ ( produc394644079real_c @ X @ Y ) @ ( inv_im1827249322real_c @ R @ F2 ) )
% 0.21/0.48 = ( member1895684704real_c @ ( produc394644079real_c @ ( F2 @ X ) @ ( F2 @ Y ) ) @ R ) ) ).
% 0.21/0.48
% 0.21/0.48 % in_inv_image
% 0.21/0.48 thf(fact_340_map__prod__imageI,axiom,
% 0.21/0.48 ! [A2: finite1398487019real_c,B2: finite1398487019real_c,R2: set_Pr1389752855real_c,F2: finite1398487019real_c > finite1398487019real_c,G: finite1398487019real_c > finite1398487019real_c] :
% 0.21/0.48 ( ( member1895684704real_c @ ( produc394644079real_c @ A2 @ B2 ) @ R2 )
% 0.21/0.48 => ( member1895684704real_c @ ( produc394644079real_c @ ( F2 @ A2 ) @ ( G @ B2 ) ) @ ( image_738229701real_c @ ( produc368345510real_c @ F2 @ G ) @ R2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % map_prod_imageI
% 0.21/0.48 thf(fact_341_map__prod__imageI,axiom,
% 0.21/0.48 ! [A2: finite1398487019real_c,B2: finite1398487019real_c,R2: set_Pr1389752855real_c,F2: finite1398487019real_c > denota610675952t_unit,G: finite1398487019real_c > produc866628903_sc_sz] :
% 0.21/0.48 ( ( member1895684704real_c @ ( produc394644079real_c @ A2 @ B2 ) @ R2 )
% 0.21/0.48 => ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ ( F2 @ A2 ) @ ( G @ B2 ) ) @ ( image_1259833374_sc_sz @ ( produc1784590311_sc_sz @ F2 @ G ) @ R2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % map_prod_imageI
% 0.21/0.48 thf(fact_342_map__prod__imageI,axiom,
% 0.21/0.48 ! [A2: denota610675952t_unit,B2: produc866628903_sc_sz,R2: set_Pr1169339874_sc_sz,F2: denota610675952t_unit > finite1398487019real_c,G: produc866628903_sc_sz > finite1398487019real_c] :
% 0.21/0.48 ( ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ A2 @ B2 ) @ R2 )
% 0.21/0.48 => ( member1895684704real_c @ ( produc394644079real_c @ ( F2 @ A2 ) @ ( G @ B2 ) ) @ ( image_386905412real_c @ ( produc1612557567real_c @ F2 @ G ) @ R2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % map_prod_imageI
% 0.21/0.48 thf(fact_343_map__prod__imageI,axiom,
% 0.21/0.48 ! [A2: denota610675952t_unit,B2: produc866628903_sc_sz,R2: set_Pr1169339874_sc_sz,F2: denota610675952t_unit > denota610675952t_unit,G: produc866628903_sc_sz > produc866628903_sc_sz] :
% 0.21/0.48 ( ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ A2 @ B2 ) @ R2 )
% 0.21/0.48 => ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ ( F2 @ A2 ) @ ( G @ B2 ) ) @ ( image_1726193375_sc_sz @ ( produc403791768_sc_sz @ F2 @ G ) @ R2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % map_prod_imageI
% 0.21/0.48 thf(fact_344_prod__fun__imageE,axiom,
% 0.21/0.48 ! [C2: produc190496183real_c,F2: finite1398487019real_c > finite1398487019real_c,G: finite1398487019real_c > finite1398487019real_c,R2: set_Pr1389752855real_c] :
% 0.21/0.48 ( ( member1895684704real_c @ C2 @ ( image_738229701real_c @ ( produc368345510real_c @ F2 @ G ) @ R2 ) )
% 0.21/0.48 => ~ ! [X3: finite1398487019real_c,Y3: finite1398487019real_c] :
% 0.21/0.48 ( ( C2
% 0.21/0.48 = ( produc394644079real_c @ ( F2 @ X3 ) @ ( G @ Y3 ) ) )
% 0.21/0.48 => ~ ( member1895684704real_c @ ( produc394644079real_c @ X3 @ Y3 ) @ R2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % prod_fun_imageE
% 0.21/0.48 thf(fact_345_prod__fun__imageE,axiom,
% 0.21/0.48 ! [C2: produc190496183real_c,F2: denota610675952t_unit > finite1398487019real_c,G: produc866628903_sc_sz > finite1398487019real_c,R2: set_Pr1169339874_sc_sz] :
% 0.21/0.48 ( ( member1895684704real_c @ C2 @ ( image_386905412real_c @ ( produc1612557567real_c @ F2 @ G ) @ R2 ) )
% 0.21/0.48 => ~ ! [X3: denota610675952t_unit,Y3: produc866628903_sc_sz] :
% 0.21/0.48 ( ( C2
% 0.21/0.48 = ( produc394644079real_c @ ( F2 @ X3 ) @ ( G @ Y3 ) ) )
% 0.21/0.48 => ~ ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ X3 @ Y3 ) @ R2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % prod_fun_imageE
% 0.21/0.48 thf(fact_346_prod__fun__imageE,axiom,
% 0.21/0.48 ! [C2: produc1821101996_sc_sz,F2: finite1398487019real_c > denota610675952t_unit,G: finite1398487019real_c > produc866628903_sc_sz,R2: set_Pr1389752855real_c] :
% 0.21/0.48 ( ( member1057565379_sc_sz @ C2 @ ( image_1259833374_sc_sz @ ( produc1784590311_sc_sz @ F2 @ G ) @ R2 ) )
% 0.21/0.48 => ~ ! [X3: finite1398487019real_c,Y3: finite1398487019real_c] :
% 0.21/0.48 ( ( C2
% 0.21/0.48 = ( produc789536734_sc_sz @ ( F2 @ X3 ) @ ( G @ Y3 ) ) )
% 0.21/0.48 => ~ ( member1895684704real_c @ ( produc394644079real_c @ X3 @ Y3 ) @ R2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % prod_fun_imageE
% 0.21/0.48 thf(fact_347_prod__fun__imageE,axiom,
% 0.21/0.48 ! [C2: produc1821101996_sc_sz,F2: denota610675952t_unit > denota610675952t_unit,G: produc866628903_sc_sz > produc866628903_sc_sz,R2: set_Pr1169339874_sc_sz] :
% 0.21/0.48 ( ( member1057565379_sc_sz @ C2 @ ( image_1726193375_sc_sz @ ( produc403791768_sc_sz @ F2 @ G ) @ R2 ) )
% 0.21/0.48 => ~ ! [X3: denota610675952t_unit,Y3: produc866628903_sc_sz] :
% 0.21/0.48 ( ( C2
% 0.21/0.48 = ( produc789536734_sc_sz @ ( F2 @ X3 ) @ ( G @ Y3 ) ) )
% 0.21/0.48 => ~ ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ X3 @ Y3 ) @ R2 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % prod_fun_imageE
% 0.21/0.48 thf(fact_348_Vagree__univ,axiom,
% 0.21/0.48 ! [A2: finite1398487019real_c,B2: finite1398487019real_c,C2: finite1398487019real_c,D: finite1398487019real_c] :
% 0.21/0.48 ( ( denota1997846518gree_c @ ( produc394644079real_c @ A2 @ B2 ) @ ( produc394644079real_c @ C2 @ D ) @ top_to1660572043um_c_c )
% 0.21/0.48 => ( ( A2 = C2 )
% 0.21/0.48 & ( B2 = D ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % Vagree_univ
% 0.21/0.48 thf(fact_349_agree__UNIV__eq,axiom,
% 0.21/0.48 ! [Nu3: produc190496183real_c,Omega: produc190496183real_c] :
% 0.21/0.48 ( ( denota1997846518gree_c @ Nu3 @ Omega @ top_to1660572043um_c_c )
% 0.21/0.48 => ( Nu3 = Omega ) ) ).
% 0.21/0.48
% 0.21/0.48 % agree_UNIV_eq
% 0.21/0.48 thf(fact_350_top__empty__eq2,axiom,
% 0.21/0.48 ( top_to964419200al_c_o
% 0.21/0.48 = ( ^ [X4: finite1398487019real_c,Y4: finite1398487019real_c] : ( member1895684704real_c @ ( produc394644079real_c @ X4 @ Y4 ) @ top_to226056039real_c ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % top_empty_eq2
% 0.21/0.48 thf(fact_351_top__empty__eq2,axiom,
% 0.21/0.48 ( top_to1399053141c_sz_o
% 0.21/0.48 = ( ^ [X4: denota610675952t_unit,Y4: produc866628903_sc_sz] : ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ X4 @ Y4 ) @ top_to1499569298_sc_sz ) ) ) ).
% 0.21/0.48
% 0.21/0.48 % top_empty_eq2
% 0.21/0.48 thf(fact_352_fst__conv,axiom,
% 0.21/0.48 ! [X1: denota610675952t_unit,X2: produc866628903_sc_sz] :
% 0.21/0.48 ( ( produc1503602930_sc_sz @ ( produc789536734_sc_sz @ X1 @ X2 ) )
% 0.21/0.48 = X1 ) ).
% 0.21/0.48
% 0.21/0.48 % fst_conv
% 0.21/0.48 thf(fact_353_fst__eqD,axiom,
% 0.21/0.48 ! [X: denota610675952t_unit,Y: produc866628903_sc_sz,A2: denota610675952t_unit] :
% 0.21/0.48 ( ( ( produc1503602930_sc_sz @ ( produc789536734_sc_sz @ X @ Y ) )
% 0.21/0.48 = A2 )
% 0.21/0.48 => ( X = A2 ) ) ).
% 0.21/0.48
% 0.21/0.48 % fst_eqD
% 0.21/0.48
% 0.21/0.48 % Conjectures (1)
% 0.21/0.48 thf(conj_0,conjecture,
% 0.21/0.48 ( ( ! [Nu: produc190496183real_c,Nu2: produc190496183real_c,I: denota231621370t_unit,J: denota231621370t_unit] :
% 0.21/0.48 ( ( denota69106024_a_b_c @ I @ J @ ( static_SIGF_a_b_c @ phi ) )
% 0.21/0.48 => ( ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVF_a_b_c @ phi ) )
% 0.21/0.48 => ( ( member1895684704real_c @ Nu @ ( denota968303861_a_b_c @ I @ phi ) )
% 0.21/0.48 = ( member1895684704real_c @ Nu2 @ ( denota968303861_a_b_c @ J @ phi ) ) ) ) ) )
% 0.21/0.48 = ( ! [Nu: produc190496183real_c,Nu2: produc190496183real_c,I: denota231621370t_unit,J: denota231621370t_unit] :
% 0.21/0.48 ( ( denota69106024_a_b_c @ I @ J @ ( static_SIGF_a_b_c @ phi ) )
% 0.21/0.48 => ( ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVF_a_b_c @ phi ) )
% 0.21/0.48 => ( ( member1895684704real_c @ Nu @ ( denota968303861_a_b_c @ I @ phi ) )
% 0.21/0.48 = ( member1895684704real_c @ Nu2 @ ( denota968303861_a_b_c @ J @ phi ) ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 %------------------------------------------------------------------------------
% 0.21/0.48 ------------------------
% 3.14/1.62 ---- Embedded in THF ---
% 3.14/1.62 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.14/1.62 %%% Generated on Tue Feb 24 08:26:34 EST 2026
% 3.14/1.62 %%% using '$$dhol' embedding, version 1.3.0.
% 3.14/1.62 %%% Logic specification used:
% 3.14/1.62 %%% thf(spec, logic, $$dhol).
% 3.14/1.62
% 3.14/1.62 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.jSP0w0K04t/DTF2DTF20700.p
% See solution above
% 3.14/1.62 ------------------------
% 3.14/1.66 ---- Cleaned THF ---
% 3.14/1.66 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J_J,type,
% 3.14/1.66 set_Pr754230471real_c: $tType ).
% 3.14/1.66
% 3.14/1.66 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 3.14/1.66 produc640052711real_c: $tType ).
% 3.14/1.66
% 3.14/1.66 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_Mt__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_J_J,type,
% 3.14/1.66 set_Pr2041213564t_unit: $tType ).
% 3.14/1.66
% 3.14/1.66 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_J_J,type,
% 3.14/1.66 set_Pr1169339874_sc_sz: $tType ).
% 3.14/1.66
% 3.14/1.66 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_Mt__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_J,type,
% 3.14/1.66 produc999471430t_unit: $tType ).
% 3.14/1.66
% 3.14/1.66 thf(ty_n_t__Product____Type__Oprod_It__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_J,type,
% 3.14/1.66 produc1821101996_sc_sz: $tType ).
% 3.14/1.66
% 3.14/1.66 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_J_J,type,
% 3.14/1.66 set_Pr60491591eal_sz: $tType ).
% 3.14/1.66
% 3.14/1.66 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 3.14/1.66 set_Pr1389752855real_c: $tType ).
% 3.14/1.66
% 3.14/1.66 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_J,type,
% 3.14/1.66 set_Pr1774599175_sc_sz: $tType ).
% 3.14/1.66
% 3.14/1.66 thf(ty_n_t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_J,type,
% 3.14/1.66 produc1149990247eal_sz: $tType ).
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% 3.14/1.66 produc2099580355_sc_sz: ( produc866628903_sc_sz > denota610675952t_unit > produc1821101996_sc_sz ) > produc999471430t_unit > produc1821101996_sc_sz ).
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% 3.14/1.66 produc403791768_sc_sz: ( denota610675952t_unit > denota610675952t_unit ) > ( produc866628903_sc_sz > produc866628903_sc_sz ) > produc1821101996_sc_sz > produc1821101996_sc_sz ).
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% 3.14/1.66 produc1784590311_sc_sz: ( finite1398487019real_c > denota610675952t_unit ) > ( finite1398487019real_c > produc866628903_sc_sz ) > produc190496183real_c > produc1821101996_sc_sz ).
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% 3.14/1.66
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% 3.14/1.66 produc1920474870real_c: ( denota610675952t_unit > produc866628903_sc_sz > finite1398487019real_c ) > produc1821101996_sc_sz > finite1398487019real_c ).
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% 3.14/1.66 produc448466487_sc_sz: ( denota610675952t_unit > produc866628903_sc_sz > produc1821101996_sc_sz ) > produc1821101996_sc_sz > produc1821101996_sc_sz ).
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% 3.14/1.66 produc237521996real_c: ( denota610675952t_unit > produc866628903_sc_sz > set_Pr1389752855real_c ) > produc1821101996_sc_sz > set_Pr1389752855real_c ).
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% 3.14/1.66 produc107375667real_c: ( finite1398487019real_c > finite1398487019real_c > produc190496183real_c ) > produc190496183real_c > produc190496183real_c ).
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% 3.14/1.66 produc1341776291_sc_sz: ( finite1398487019real_c > finite1398487019real_c > produc866628903_sc_sz ) > produc190496183real_c > produc866628903_sc_sz ).
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% 3.14/1.66 produc642283651_sc_sz: ( finite1398487019real_c > finite1398487019real_c > set_Pr1774599175_sc_sz ) > produc190496183real_c > set_Pr1774599175_sc_sz ).
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% 3.14/1.66
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% 3.14/1.66 produc6841835real_c: ( list_f1238882004_sc_sz > list_f1238882004_sc_sz > set_Pr1389752855real_c ) > produc866628903_sc_sz > set_Pr1389752855real_c ).
% 3.14/1.66
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% 3.14/1.66 produc1563580891_sc_sz: ( list_f1238882004_sc_sz > list_f1238882004_sc_sz > set_Pr1774599175_sc_sz ) > produc866628903_sc_sz > set_Pr1774599175_sc_sz ).
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% 3.14/1.66 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_001t__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J,type,
% 3.14/1.66 image_388766773_sc_sz: ( produc190496183real_c > produc866628903_sc_sz ) > set_Pr1389752855real_c > set_Pr1774599175_sc_sz ).
% 3.14/1.66
% 3.14/1.66 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J,type,
% 3.14/1.66 image_1332486093real_c: ( produc866628903_sc_sz > finite1398487019real_c ) > set_Pr1774599175_sc_sz > set_Fi1407883041real_c ).
% 3.14/1.66
% 3.14/1.66 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_001t__Product____Type__Oprod_It__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_J,type,
% 3.14/1.66 image_226055310_sc_sz: ( produc866628903_sc_sz > produc1821101996_sc_sz ) > set_Pr1774599175_sc_sz > set_Pr1169339874_sc_sz ).
% 3.14/1.66
% 3.14/1.66 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_001t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 3.14/1.66 image_1121381717real_c: ( produc866628903_sc_sz > produc190496183real_c ) > set_Pr1774599175_sc_sz > set_Pr1389752855real_c ).
% 3.14/1.66
% 3.14/1.66 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_001t__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J,type,
% 3.14/1.66 image_1313166277_sc_sz: ( produc866628903_sc_sz > produc866628903_sc_sz ) > set_Pr1774599175_sc_sz > set_Pr1774599175_sc_sz ).
% 3.14/1.66
% 3.14/1.66 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 3.14/1.66 image_768765061real_c: ( produc866628903_sc_sz > produc640052711real_c ) > set_Pr1774599175_sc_sz > set_Pr754230471real_c ).
% 3.14/1.66
% 3.14/1.66 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_Mt__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_J,type,
% 3.14/1.66 image_1551908392t_unit: ( produc866628903_sc_sz > produc999471430t_unit ) > set_Pr1774599175_sc_sz > set_Pr2041213564t_unit ).
% 3.14/1.66
% 3.14/1.66 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J,type,
% 3.14/1.66 image_124598413real_c: ( produc640052711real_c > finite1398487019real_c ) > set_Pr754230471real_c > set_Fi1407883041real_c ).
% 3.14/1.66
% 3.14/1.66 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 3.14/1.66 image_2041365445real_c: ( produc640052711real_c > produc640052711real_c ) > set_Pr754230471real_c > set_Pr754230471real_c ).
% 3.14/1.66
% 3.14/1.66 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_Mt__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_J_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J,type,
% 3.14/1.66 image_1269062456real_c: ( produc999471430t_unit > finite1398487019real_c ) > set_Pr2041213564t_unit > set_Fi1407883041real_c ).
% 3.14/1.66
% 3.14/1.66 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_Mt__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_J_001t__Product____Type__Oprod_It__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_J,type,
% 3.14/1.66 image_1426741113_sc_sz: ( produc999471430t_unit > produc1821101996_sc_sz ) > set_Pr2041213564t_unit > set_Pr1169339874_sc_sz ).
% 3.14/1.66
% 3.14/1.66 thf(sy_c_Static__Semantics_OFVF_001tf__a_001tf__b_001tf__c,type,
% 3.14/1.66 static_FVF_a_b_c: formula_a_b_c > set_Sum_sum_c_c ).
% 3.14/1.66
% 3.14/1.66 thf(sy_c_Static__Semantics_OSIGF_001tf__a_001tf__b_001tf__c,type,
% 3.14/1.66 static_SIGF_a_b_c: formula_a_b_c > set_Su1783761653um_b_c ).
% 3.14/1.66
% 3.14/1.66 thf(sy_c_Syntax_OEquiv_001tf__a_001tf__b_001tf__c,type,
% 3.14/1.66 equiv_a_b_c: formula_a_b_c > formula_a_b_c > formula_a_b_c ).
% 3.14/1.66
% 3.14/1.66 thf(sy_c_Syntax_OImplies_001tf__a_001tf__b_001tf__c,type,
% 3.14/1.66 implies_a_b_c: formula_a_b_c > formula_a_b_c > formula_a_b_c ).
% 3.14/1.66
% 3.14/1.66 thf(sy_c_Syntax_OPredicational_001tf__sc_001tf__sf_001tf__sz,type,
% 3.14/1.66 predic913887884_sf_sz: sc > formula_sf_sc_sz ).
% 3.14/1.66
% 3.14/1.66 thf(sy_c_Syntax_Oids_OP_001tf__sc_001tf__sf_001tf__sz,type,
% 3.14/1.66 p_sc_sf_sz: sc > formula_sf_sc_sz ).
% 3.14/1.66
% 3.14/1.66 thf(sy_c_member_001_Eo,type,
% 3.14/1.66 member_o: $o > set_o > $o ).
% 3.14/1.66
% 3.14/1.66 thf(sy_c_member_001t__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J,type,
% 3.14/1.66 member754147591t_unit: denota610675952t_unit > set_De208295462t_unit > $o ).
% 3.14/1.66
% 3.14/1.66 thf(sy_c_member_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J,type,
% 3.14/1.66 member1261661570real_c: finite1398487019real_c > set_Fi1407883041real_c > $o ).
% 3.14/1.66
% 3.14/1.66 thf(sy_c_member_001t__Product____Type__Oprod_It__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_J,type,
% 3.14/1.66 member1057565379_sc_sz: produc1821101996_sc_sz > set_Pr1169339874_sc_sz > $o ).
% 3.14/1.66
% 3.14/1.66 thf(sy_c_member_001t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 3.14/1.66 member1895684704real_c: produc190496183real_c > set_Pr1389752855real_c > $o ).
% 3.14/1.66
% 3.14/1.66 thf(sy_c_member_001t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_J,type,
% 3.14/1.66 member630771088eal_sz: produc1149990247eal_sz > set_Pr60491591eal_sz > $o ).
% 3.14/1.66
% 3.14/1.66 thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J,type,
% 3.14/1.66 member245028432_sc_sz: produc866628903_sc_sz > set_Pr1774599175_sc_sz > $o ).
% 3.14/1.66
% 3.14/1.66 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 3.14/1.66 member346808080real_c: produc640052711real_c > set_Pr754230471real_c > $o ).
% 3.14/1.66
% 3.14/1.66 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_Mt__List__Olist_It__Syntax__Oformula_Itf__sf_Mtf__sc_Mtf__sz_J_J_J_Mt__Denotational____Semantics__Ointerp__Ointerp____ext_Itf__sf_Mtf__sc_Mtf__sz_Mt__Product____Type__Ounit_J_J,type,
% 3.14/1.66 member235934813t_unit: produc999471430t_unit > set_Pr2041213564t_unit > $o ).
% 3.14/1.66
% 3.14/1.66 thf(sy_v__092_060phi_062,type,
% 3.14/1.66 phi: formula_a_b_c ).
% 3.14/1.66
% 3.14/1.66 thf(fact_0_coincide__fml__def,axiom,
% 3.14/1.66 ( coinci501627771_a_b_c
% 3.14/1.66 = ( ^ [Phi: formula_a_b_c] :
% 3.14/1.66 ! [Nu: produc190496183real_c,Nu2: produc190496183real_c,I: denota231621370t_unit,J: denota231621370t_unit] :
% 3.14/1.66 ( ( denota69106024_a_b_c @ I @ J @ ( static_SIGF_a_b_c @ Phi ) )
% 3.14/1.66 => ( ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVF_a_b_c @ Phi ) )
% 3.14/1.66 => ( ( member1895684704real_c @ Nu @ ( denota968303861_a_b_c @ I @ Phi ) )
% 3.14/1.66 = ( member1895684704real_c @ Nu2 @ ( denota968303861_a_b_c @ J @ Phi ) ) ) ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_1_ids_Ocoincide__fml__def,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc,Phi2: formula_a_b_c] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ( ( coinci501627771_a_b_c @ Phi2 )
% 3.14/1.66 = ( ! [Nu: produc190496183real_c,Nu2: produc190496183real_c,I: denota231621370t_unit,J: denota231621370t_unit] :
% 3.14/1.66 ( ( denota69106024_a_b_c @ I @ J @ ( static_SIGF_a_b_c @ Phi2 ) )
% 3.14/1.66 => ( ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVF_a_b_c @ Phi2 ) )
% 3.14/1.66 => ( ( member1895684704real_c @ Nu @ ( denota968303861_a_b_c @ I @ Phi2 ) )
% 3.14/1.66 = ( member1895684704real_c @ Nu2 @ ( denota968303861_a_b_c @ J @ Phi2 ) ) ) ) ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_2_Iagree__comm,axiom,
% 3.14/1.66 ! [A: denota231621370t_unit,B: denota231621370t_unit,V: set_Su1783761653um_b_c] :
% 3.14/1.66 ( ( denota69106024_a_b_c @ A @ B @ V )
% 3.14/1.66 => ( denota69106024_a_b_c @ B @ A @ V ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_3_Iagree__refl,axiom,
% 3.14/1.66 ! [I2: denota231621370t_unit,A: set_Su1783761653um_b_c] : ( denota69106024_a_b_c @ I2 @ I2 @ A ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_4_agree__comm,axiom,
% 3.14/1.66 ! [A: produc190496183real_c,B: produc190496183real_c,V: set_Sum_sum_c_c] :
% 3.14/1.66 ( ( denota1997846518gree_c @ A @ B @ V )
% 3.14/1.66 => ( denota1997846518gree_c @ B @ A @ V ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_5_agree__refl,axiom,
% 3.14/1.66 ! [Nu3: produc190496183real_c,A: set_Sum_sum_c_c] : ( denota1997846518gree_c @ Nu3 @ Nu3 @ A ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_6_iff__to__impl,axiom,
% 3.14/1.66 ! [Nu3: produc190496183real_c,I2: denota231621370t_unit,A: formula_a_b_c,B: formula_a_b_c] :
% 3.14/1.66 ( ( ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I2 @ A ) )
% 3.14/1.66 = ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I2 @ B ) ) )
% 3.14/1.66 = ( ( ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I2 @ A ) )
% 3.14/1.66 => ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I2 @ B ) ) )
% 3.14/1.66 & ( ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I2 @ B ) )
% 3.14/1.66 => ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I2 @ A ) ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_7_iff__sem,axiom,
% 3.14/1.66 ! [Nu3: produc190496183real_c,I2: denota231621370t_unit,A: formula_a_b_c,B: formula_a_b_c] :
% 3.14/1.66 ( ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I2 @ ( equiv_a_b_c @ A @ B ) ) )
% 3.14/1.66 = ( ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I2 @ A ) )
% 3.14/1.66 = ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I2 @ B ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_8_impl__sem,axiom,
% 3.14/1.66 ! [Nu3: produc190496183real_c,I2: denota231621370t_unit,A: formula_a_b_c,B: formula_a_b_c] :
% 3.14/1.66 ( ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I2 @ ( implies_a_b_c @ A @ B ) ) )
% 3.14/1.66 = ( ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I2 @ A ) )
% 3.14/1.66 => ( member1895684704real_c @ Nu3 @ ( denota968303861_a_b_c @ I2 @ B ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_9_P__def,axiom,
% 3.14/1.66 p_sc_sf_sz = predic913887884_sf_sz ).
% 3.14/1.66
% 3.14/1.66 thf(fact_10_seq__sem_Ocases,axiom,
% 3.14/1.66 ! [X: produc1821101996_sc_sz] :
% 3.14/1.66 ~ ! [I3: denota610675952t_unit,S: produc866628903_sc_sz] :
% 3.14/1.66 ( X
% 3.14/1.66 != ( produc789536734_sc_sz @ I3 @ S ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_11_ids_Oseq__sem_Ocases,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc,X: produc1821101996_sc_sz] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ~ ! [I3: denota610675952t_unit,S: produc866628903_sc_sz] :
% 3.14/1.66 ( X
% 3.14/1.66 != ( produc789536734_sc_sz @ I3 @ S ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_12_ids_Oseq__sem_Oinduct,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc,P: denota610675952t_unit > produc866628903_sc_sz > $o,A0: denota610675952t_unit,A1: produc866628903_sc_sz] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ( ! [I3: denota610675952t_unit,X_1: produc866628903_sc_sz] : ( P @ I3 @ X_1 )
% 3.14/1.66 => ( P @ A0 @ A1 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_13_ids_OP__def,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc,P2: sc] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ( ( p_sc_sf_sz @ P2 )
% 3.14/1.66 = ( predic913887884_sf_sz @ P2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_14_prod_Oinject,axiom,
% 3.14/1.66 ! [X1: list_f1238882004_sc_sz,X2: list_f1238882004_sc_sz,Y1: list_f1238882004_sc_sz,Y2: list_f1238882004_sc_sz] :
% 3.14/1.66 ( ( ( produc1822718231_sc_sz @ X1 @ X2 )
% 3.14/1.66 = ( produc1822718231_sc_sz @ Y1 @ Y2 ) )
% 3.14/1.66 = ( ( X1 = Y1 )
% 3.14/1.66 & ( X2 = Y2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_15_prod_Oinject,axiom,
% 3.14/1.66 ! [X1: finite1398487019real_c,X2: finite1398487019real_c,Y1: finite1398487019real_c,Y2: finite1398487019real_c] :
% 3.14/1.66 ( ( ( produc394644079real_c @ X1 @ X2 )
% 3.14/1.66 = ( produc394644079real_c @ Y1 @ Y2 ) )
% 3.14/1.66 = ( ( X1 = Y1 )
% 3.14/1.66 & ( X2 = Y2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_16_prod_Oinject,axiom,
% 3.14/1.66 ! [X1: produc866628903_sc_sz,X2: denota610675952t_unit,Y1: produc866628903_sc_sz,Y2: denota610675952t_unit] :
% 3.14/1.66 ( ( ( produc502616768t_unit @ X1 @ X2 )
% 3.14/1.66 = ( produc502616768t_unit @ Y1 @ Y2 ) )
% 3.14/1.66 = ( ( X1 = Y1 )
% 3.14/1.66 & ( X2 = Y2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_17_prod_Oinject,axiom,
% 3.14/1.66 ! [X1: produc190496183real_c,X2: produc190496183real_c,Y1: produc190496183real_c,Y2: produc190496183real_c] :
% 3.14/1.66 ( ( ( produc1687028567real_c @ X1 @ X2 )
% 3.14/1.66 = ( produc1687028567real_c @ Y1 @ Y2 ) )
% 3.14/1.66 = ( ( X1 = Y1 )
% 3.14/1.66 & ( X2 = Y2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_18_prod_Oinject,axiom,
% 3.14/1.66 ! [X1: denota610675952t_unit,X2: produc866628903_sc_sz,Y1: denota610675952t_unit,Y2: produc866628903_sc_sz] :
% 3.14/1.66 ( ( ( produc789536734_sc_sz @ X1 @ X2 )
% 3.14/1.66 = ( produc789536734_sc_sz @ Y1 @ Y2 ) )
% 3.14/1.66 = ( ( X1 = Y1 )
% 3.14/1.66 & ( X2 = Y2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_19_old_Oprod_Oinject,axiom,
% 3.14/1.66 ! [A2: list_f1238882004_sc_sz,B2: list_f1238882004_sc_sz,A3: list_f1238882004_sc_sz,B3: list_f1238882004_sc_sz] :
% 3.14/1.66 ( ( ( produc1822718231_sc_sz @ A2 @ B2 )
% 3.14/1.66 = ( produc1822718231_sc_sz @ A3 @ B3 ) )
% 3.14/1.66 = ( ( A2 = A3 )
% 3.14/1.66 & ( B2 = B3 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_20_old_Oprod_Oinject,axiom,
% 3.14/1.66 ! [A2: finite1398487019real_c,B2: finite1398487019real_c,A3: finite1398487019real_c,B3: finite1398487019real_c] :
% 3.14/1.66 ( ( ( produc394644079real_c @ A2 @ B2 )
% 3.14/1.66 = ( produc394644079real_c @ A3 @ B3 ) )
% 3.14/1.66 = ( ( A2 = A3 )
% 3.14/1.66 & ( B2 = B3 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_21_old_Oprod_Oinject,axiom,
% 3.14/1.66 ! [A2: produc866628903_sc_sz,B2: denota610675952t_unit,A3: produc866628903_sc_sz,B3: denota610675952t_unit] :
% 3.14/1.66 ( ( ( produc502616768t_unit @ A2 @ B2 )
% 3.14/1.66 = ( produc502616768t_unit @ A3 @ B3 ) )
% 3.14/1.66 = ( ( A2 = A3 )
% 3.14/1.66 & ( B2 = B3 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_22_old_Oprod_Oinject,axiom,
% 3.14/1.66 ! [A2: produc190496183real_c,B2: produc190496183real_c,A3: produc190496183real_c,B3: produc190496183real_c] :
% 3.14/1.66 ( ( ( produc1687028567real_c @ A2 @ B2 )
% 3.14/1.66 = ( produc1687028567real_c @ A3 @ B3 ) )
% 3.14/1.66 = ( ( A2 = A3 )
% 3.14/1.66 & ( B2 = B3 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_23_old_Oprod_Oinject,axiom,
% 3.14/1.66 ! [A2: denota610675952t_unit,B2: produc866628903_sc_sz,A3: denota610675952t_unit,B3: produc866628903_sc_sz] :
% 3.14/1.66 ( ( ( produc789536734_sc_sz @ A2 @ B2 )
% 3.14/1.66 = ( produc789536734_sc_sz @ A3 @ B3 ) )
% 3.14/1.66 = ( ( A2 = A3 )
% 3.14/1.66 & ( B2 = B3 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_24_prod__cases3,axiom,
% 3.14/1.66 ! [Y: produc640052711real_c] :
% 3.14/1.66 ~ ! [A4: produc190496183real_c,B4: finite1398487019real_c,C: finite1398487019real_c] :
% 3.14/1.66 ( Y
% 3.14/1.66 != ( produc1687028567real_c @ A4 @ ( produc394644079real_c @ B4 @ C ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_25_prod__cases3,axiom,
% 3.14/1.66 ! [Y: produc1821101996_sc_sz] :
% 3.14/1.66 ~ ! [A4: denota610675952t_unit,B4: list_f1238882004_sc_sz,C: list_f1238882004_sc_sz] :
% 3.14/1.66 ( Y
% 3.14/1.66 != ( produc789536734_sc_sz @ A4 @ ( produc1822718231_sc_sz @ B4 @ C ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_26_old_Oprod_Oinducts,axiom,
% 3.14/1.66 ! [P: produc866628903_sc_sz > $o,Prod: produc866628903_sc_sz] :
% 3.14/1.66 ( ! [A4: list_f1238882004_sc_sz,B4: list_f1238882004_sc_sz] : ( P @ ( produc1822718231_sc_sz @ A4 @ B4 ) )
% 3.14/1.66 => ( P @ Prod ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_27_old_Oprod_Oinducts,axiom,
% 3.14/1.66 ! [P: produc190496183real_c > $o,Prod: produc190496183real_c] :
% 3.14/1.66 ( ! [A4: finite1398487019real_c,B4: finite1398487019real_c] : ( P @ ( produc394644079real_c @ A4 @ B4 ) )
% 3.14/1.66 => ( P @ Prod ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_28_old_Oprod_Oinducts,axiom,
% 3.14/1.66 ! [P: produc999471430t_unit > $o,Prod: produc999471430t_unit] :
% 3.14/1.66 ( ! [A4: produc866628903_sc_sz,B4: denota610675952t_unit] : ( P @ ( produc502616768t_unit @ A4 @ B4 ) )
% 3.14/1.66 => ( P @ Prod ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_29_old_Oprod_Oinducts,axiom,
% 3.14/1.66 ! [P: produc640052711real_c > $o,Prod: produc640052711real_c] :
% 3.14/1.66 ( ! [A4: produc190496183real_c,B4: produc190496183real_c] : ( P @ ( produc1687028567real_c @ A4 @ B4 ) )
% 3.14/1.66 => ( P @ Prod ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_30_old_Oprod_Oinducts,axiom,
% 3.14/1.66 ! [P: produc1821101996_sc_sz > $o,Prod: produc1821101996_sc_sz] :
% 3.14/1.66 ( ! [A4: denota610675952t_unit,B4: produc866628903_sc_sz] : ( P @ ( produc789536734_sc_sz @ A4 @ B4 ) )
% 3.14/1.66 => ( P @ Prod ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_31_old_Oprod_Oexhaust,axiom,
% 3.14/1.66 ! [Y: produc866628903_sc_sz] :
% 3.14/1.66 ~ ! [A4: list_f1238882004_sc_sz,B4: list_f1238882004_sc_sz] :
% 3.14/1.66 ( Y
% 3.14/1.66 != ( produc1822718231_sc_sz @ A4 @ B4 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_32_old_Oprod_Oexhaust,axiom,
% 3.14/1.66 ! [Y: produc190496183real_c] :
% 3.14/1.66 ~ ! [A4: finite1398487019real_c,B4: finite1398487019real_c] :
% 3.14/1.66 ( Y
% 3.14/1.66 != ( produc394644079real_c @ A4 @ B4 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_33_old_Oprod_Oexhaust,axiom,
% 3.14/1.66 ! [Y: produc999471430t_unit] :
% 3.14/1.66 ~ ! [A4: produc866628903_sc_sz,B4: denota610675952t_unit] :
% 3.14/1.66 ( Y
% 3.14/1.66 != ( produc502616768t_unit @ A4 @ B4 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_34_old_Oprod_Oexhaust,axiom,
% 3.14/1.66 ! [Y: produc640052711real_c] :
% 3.14/1.66 ~ ! [A4: produc190496183real_c,B4: produc190496183real_c] :
% 3.14/1.66 ( Y
% 3.14/1.66 != ( produc1687028567real_c @ A4 @ B4 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_35_old_Oprod_Oexhaust,axiom,
% 3.14/1.66 ! [Y: produc1821101996_sc_sz] :
% 3.14/1.66 ~ ! [A4: denota610675952t_unit,B4: produc866628903_sc_sz] :
% 3.14/1.66 ( Y
% 3.14/1.66 != ( produc789536734_sc_sz @ A4 @ B4 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_36_Pair__inject,axiom,
% 3.14/1.66 ! [A2: list_f1238882004_sc_sz,B2: list_f1238882004_sc_sz,A3: list_f1238882004_sc_sz,B3: list_f1238882004_sc_sz] :
% 3.14/1.66 ( ( ( produc1822718231_sc_sz @ A2 @ B2 )
% 3.14/1.66 = ( produc1822718231_sc_sz @ A3 @ B3 ) )
% 3.14/1.66 => ~ ( ( A2 = A3 )
% 3.14/1.66 => ( B2 != B3 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_37_Pair__inject,axiom,
% 3.14/1.66 ! [A2: finite1398487019real_c,B2: finite1398487019real_c,A3: finite1398487019real_c,B3: finite1398487019real_c] :
% 3.14/1.66 ( ( ( produc394644079real_c @ A2 @ B2 )
% 3.14/1.66 = ( produc394644079real_c @ A3 @ B3 ) )
% 3.14/1.66 => ~ ( ( A2 = A3 )
% 3.14/1.66 => ( B2 != B3 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_38_Pair__inject,axiom,
% 3.14/1.66 ! [A2: produc866628903_sc_sz,B2: denota610675952t_unit,A3: produc866628903_sc_sz,B3: denota610675952t_unit] :
% 3.14/1.66 ( ( ( produc502616768t_unit @ A2 @ B2 )
% 3.14/1.66 = ( produc502616768t_unit @ A3 @ B3 ) )
% 3.14/1.66 => ~ ( ( A2 = A3 )
% 3.14/1.66 => ( B2 != B3 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_39_Pair__inject,axiom,
% 3.14/1.66 ! [A2: produc190496183real_c,B2: produc190496183real_c,A3: produc190496183real_c,B3: produc190496183real_c] :
% 3.14/1.66 ( ( ( produc1687028567real_c @ A2 @ B2 )
% 3.14/1.66 = ( produc1687028567real_c @ A3 @ B3 ) )
% 3.14/1.66 => ~ ( ( A2 = A3 )
% 3.14/1.66 => ( B2 != B3 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_40_Pair__inject,axiom,
% 3.14/1.66 ! [A2: denota610675952t_unit,B2: produc866628903_sc_sz,A3: denota610675952t_unit,B3: produc866628903_sc_sz] :
% 3.14/1.66 ( ( ( produc789536734_sc_sz @ A2 @ B2 )
% 3.14/1.66 = ( produc789536734_sc_sz @ A3 @ B3 ) )
% 3.14/1.66 => ~ ( ( A2 = A3 )
% 3.14/1.66 => ( B2 != B3 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_41_prod__cases,axiom,
% 3.14/1.66 ! [P: produc866628903_sc_sz > $o,P2: produc866628903_sc_sz] :
% 3.14/1.66 ( ! [A4: list_f1238882004_sc_sz,B4: list_f1238882004_sc_sz] : ( P @ ( produc1822718231_sc_sz @ A4 @ B4 ) )
% 3.14/1.66 => ( P @ P2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_42_prod__cases,axiom,
% 3.14/1.66 ! [P: produc190496183real_c > $o,P2: produc190496183real_c] :
% 3.14/1.66 ( ! [A4: finite1398487019real_c,B4: finite1398487019real_c] : ( P @ ( produc394644079real_c @ A4 @ B4 ) )
% 3.14/1.66 => ( P @ P2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_43_prod__cases,axiom,
% 3.14/1.66 ! [P: produc999471430t_unit > $o,P2: produc999471430t_unit] :
% 3.14/1.66 ( ! [A4: produc866628903_sc_sz,B4: denota610675952t_unit] : ( P @ ( produc502616768t_unit @ A4 @ B4 ) )
% 3.14/1.66 => ( P @ P2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_44_prod__cases,axiom,
% 3.14/1.66 ! [P: produc640052711real_c > $o,P2: produc640052711real_c] :
% 3.14/1.66 ( ! [A4: produc190496183real_c,B4: produc190496183real_c] : ( P @ ( produc1687028567real_c @ A4 @ B4 ) )
% 3.14/1.66 => ( P @ P2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_45_prod__cases,axiom,
% 3.14/1.66 ! [P: produc1821101996_sc_sz > $o,P2: produc1821101996_sc_sz] :
% 3.14/1.66 ( ! [A4: denota610675952t_unit,B4: produc866628903_sc_sz] : ( P @ ( produc789536734_sc_sz @ A4 @ B4 ) )
% 3.14/1.66 => ( P @ P2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_46_surj__pair,axiom,
% 3.14/1.66 ! [P2: produc866628903_sc_sz] :
% 3.14/1.66 ? [X3: list_f1238882004_sc_sz,Y3: list_f1238882004_sc_sz] :
% 3.14/1.66 ( P2
% 3.14/1.66 = ( produc1822718231_sc_sz @ X3 @ Y3 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_47_surj__pair,axiom,
% 3.14/1.66 ! [P2: produc190496183real_c] :
% 3.14/1.66 ? [X3: finite1398487019real_c,Y3: finite1398487019real_c] :
% 3.14/1.66 ( P2
% 3.14/1.66 = ( produc394644079real_c @ X3 @ Y3 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_48_surj__pair,axiom,
% 3.14/1.66 ! [P2: produc999471430t_unit] :
% 3.14/1.66 ? [X3: produc866628903_sc_sz,Y3: denota610675952t_unit] :
% 3.14/1.66 ( P2
% 3.14/1.66 = ( produc502616768t_unit @ X3 @ Y3 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_49_surj__pair,axiom,
% 3.14/1.66 ! [P2: produc640052711real_c] :
% 3.14/1.66 ? [X3: produc190496183real_c,Y3: produc190496183real_c] :
% 3.14/1.66 ( P2
% 3.14/1.66 = ( produc1687028567real_c @ X3 @ Y3 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_50_surj__pair,axiom,
% 3.14/1.66 ! [P2: produc1821101996_sc_sz] :
% 3.14/1.66 ? [X3: denota610675952t_unit,Y3: produc866628903_sc_sz] :
% 3.14/1.66 ( P2
% 3.14/1.66 = ( produc789536734_sc_sz @ X3 @ Y3 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_51_prod__induct3,axiom,
% 3.14/1.66 ! [P: produc640052711real_c > $o,X: produc640052711real_c] :
% 3.14/1.66 ( ! [A4: produc190496183real_c,B4: finite1398487019real_c,C: finite1398487019real_c] : ( P @ ( produc1687028567real_c @ A4 @ ( produc394644079real_c @ B4 @ C ) ) )
% 3.14/1.66 => ( P @ X ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_52_prod__induct3,axiom,
% 3.14/1.66 ! [P: produc1821101996_sc_sz > $o,X: produc1821101996_sc_sz] :
% 3.14/1.66 ( ! [A4: denota610675952t_unit,B4: list_f1238882004_sc_sz,C: list_f1238882004_sc_sz] : ( P @ ( produc789536734_sc_sz @ A4 @ ( produc1822718231_sc_sz @ B4 @ C ) ) )
% 3.14/1.66 => ( P @ X ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_53_mem__Collect__eq,axiom,
% 3.14/1.66 ! [A2: finite1398487019real_c,P: finite1398487019real_c > $o] :
% 3.14/1.66 ( ( member1261661570real_c @ A2 @ ( collec230941376real_c @ P ) )
% 3.14/1.66 = ( P @ A2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_54_mem__Collect__eq,axiom,
% 3.14/1.66 ! [A2: produc1821101996_sc_sz,P: produc1821101996_sc_sz > $o] :
% 3.14/1.66 ( ( member1057565379_sc_sz @ A2 @ ( collec1199592193_sc_sz @ P ) )
% 3.14/1.66 = ( P @ A2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_55_mem__Collect__eq,axiom,
% 3.14/1.66 ! [A2: produc640052711real_c,P: produc640052711real_c > $o] :
% 3.14/1.66 ( ( member346808080real_c @ A2 @ ( collec1126017874real_c @ P ) )
% 3.14/1.66 = ( P @ A2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_56_mem__Collect__eq,axiom,
% 3.14/1.66 ! [A2: produc999471430t_unit,P: produc999471430t_unit > $o] :
% 3.14/1.66 ( ( member235934813t_unit @ A2 @ ( collec377961627t_unit @ P ) )
% 3.14/1.66 = ( P @ A2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_57_mem__Collect__eq,axiom,
% 3.14/1.66 ! [A2: produc866628903_sc_sz,P: produc866628903_sc_sz > $o] :
% 3.14/1.66 ( ( member245028432_sc_sz @ A2 @ ( collec2036662930_sc_sz @ P ) )
% 3.14/1.66 = ( P @ A2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_58_mem__Collect__eq,axiom,
% 3.14/1.66 ! [A2: produc190496183real_c,P: produc190496183real_c > $o] :
% 3.14/1.66 ( ( member1895684704real_c @ A2 @ ( collec1643251106real_c @ P ) )
% 3.14/1.66 = ( P @ A2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_59_Collect__mem__eq,axiom,
% 3.14/1.66 ! [A: set_Fi1407883041real_c] :
% 3.14/1.66 ( ( collec230941376real_c
% 3.14/1.66 @ ^ [X4: finite1398487019real_c] : ( member1261661570real_c @ X4 @ A ) )
% 3.14/1.66 = A ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_60_Collect__mem__eq,axiom,
% 3.14/1.66 ! [A: set_Pr1169339874_sc_sz] :
% 3.14/1.66 ( ( collec1199592193_sc_sz
% 3.14/1.66 @ ^ [X4: produc1821101996_sc_sz] : ( member1057565379_sc_sz @ X4 @ A ) )
% 3.14/1.66 = A ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_61_Collect__mem__eq,axiom,
% 3.14/1.66 ! [A: set_Pr754230471real_c] :
% 3.14/1.66 ( ( collec1126017874real_c
% 3.14/1.66 @ ^ [X4: produc640052711real_c] : ( member346808080real_c @ X4 @ A ) )
% 3.14/1.66 = A ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_62_Collect__mem__eq,axiom,
% 3.14/1.66 ! [A: set_Pr2041213564t_unit] :
% 3.14/1.66 ( ( collec377961627t_unit
% 3.14/1.66 @ ^ [X4: produc999471430t_unit] : ( member235934813t_unit @ X4 @ A ) )
% 3.14/1.66 = A ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_63_Collect__mem__eq,axiom,
% 3.14/1.66 ! [A: set_Pr1774599175_sc_sz] :
% 3.14/1.66 ( ( collec2036662930_sc_sz
% 3.14/1.66 @ ^ [X4: produc866628903_sc_sz] : ( member245028432_sc_sz @ X4 @ A ) )
% 3.14/1.66 = A ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_64_Collect__mem__eq,axiom,
% 3.14/1.66 ! [A: set_Pr1389752855real_c] :
% 3.14/1.66 ( ( collec1643251106real_c
% 3.14/1.66 @ ^ [X4: produc190496183real_c] : ( member1895684704real_c @ X4 @ A ) )
% 3.14/1.66 = A ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_65_Collect__cong,axiom,
% 3.14/1.66 ! [P: produc190496183real_c > $o,Q: produc190496183real_c > $o] :
% 3.14/1.66 ( ! [X3: produc190496183real_c] :
% 3.14/1.66 ( ( P @ X3 )
% 3.14/1.66 = ( Q @ X3 ) )
% 3.14/1.66 => ( ( collec1643251106real_c @ P )
% 3.14/1.66 = ( collec1643251106real_c @ Q ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_66_ids_Ovne23,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ( Vid2 != Vid3 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_67_ids_Ovne13,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ( Vid1 != Vid3 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_68_ids_Ovne12,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ( Vid1 != Vid2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_69_ids_Opne34,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ( Pid3 != Pid4 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_70_ids_Opne24,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ( Pid2 != Pid4 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_71_ids_Opne23,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ( Pid2 != Pid3 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_72_ids_Oid__simps_I24_J,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ( Pid4 != Pid3 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_73_ids_Oid__simps_I23_J,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ( Pid4 != Pid2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_74_ids_Oid__simps_I22_J,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ( Pid4 != Pid1 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_75_ids_Oid__simps_I21_J,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ( Pid3 != Pid1 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_76_ids_Oid__simps_I20_J,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ( Pid3 != Pid2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_77_ids_Oid__simps_I19_J,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ( Pid2 != Pid1 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_78_ids_Oid__simps_I18_J,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ( Fid3 != Fid1 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_79_ids_Oid__simps_I17_J,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ( Fid3 != Fid2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_80_ids_Oid__simps_I16_J,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ( Fid2 != Fid1 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_81_ids_Oid__simps_I15_J,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ( Vid3 != Vid1 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_82_ids_Oid__simps_I14_J,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ( Vid3 != Vid2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_83_ids_Oid__simps_I13_J,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ( Vid2 != Vid1 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_84_ids_Oid__simps_I12_J,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ( Pid3 != Pid4 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_85_ids_Oid__simps_I11_J,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ( Pid2 != Pid4 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_86_ids_Oid__simps_I10_J,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ( Pid1 != Pid4 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_87_ids_Oid__simps_I9_J,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ( Pid1 != Pid3 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_88_ids_Oid__simps_I8_J,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ( Pid2 != Pid3 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_89_ids_Oid__simps_I7_J,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ( Pid1 != Pid2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_90_ids_Oid__simps_I6_J,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ( Fid1 != Fid3 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_91_ids_Oid__simps_I5_J,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ( Fid2 != Fid3 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_92_ids_Oid__simps_I4_J,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ( Fid1 != Fid2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_93_ids_Oid__simps_I3_J,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ( Vid1 != Vid3 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_94_ids_Oid__simps_I2_J,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ( Vid2 != Vid3 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_95_ids_Oid__simps_I1_J,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ( Vid1 != Vid2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_96_ids__def,axiom,
% 3.14/1.66 ( ids_sz_sf_sc
% 3.14/1.66 = ( ^ [Vid12: sz,Vid22: sz,Vid32: sz,Fid12: sf,Fid22: sf,Fid32: sf,Pid12: sc,Pid22: sc,Pid32: sc,Pid42: sc] :
% 3.14/1.66 ( ( Vid12 != Vid22 )
% 3.14/1.66 & ( Vid22 != Vid32 )
% 3.14/1.66 & ( Vid12 != Vid32 )
% 3.14/1.66 & ( Fid12 != Fid22 )
% 3.14/1.66 & ( Fid22 != Fid32 )
% 3.14/1.66 & ( Fid12 != Fid32 )
% 3.14/1.66 & ( Pid12 != Pid22 )
% 3.14/1.66 & ( Pid22 != Pid32 )
% 3.14/1.66 & ( Pid12 != Pid32 )
% 3.14/1.66 & ( Pid12 != Pid42 )
% 3.14/1.66 & ( Pid22 != Pid42 )
% 3.14/1.66 & ( Pid32 != Pid42 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_97_ids_Ofne12,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ( Fid1 != Fid2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_98_ids_Ofne13,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ( Fid1 != Fid3 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_99_ids_Ofne23,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ( Fid2 != Fid3 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_100_ids_Ointro,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 3.14/1.66 ( ( Vid1 != Vid2 )
% 3.14/1.66 => ( ( Vid2 != Vid3 )
% 3.14/1.66 => ( ( Vid1 != Vid3 )
% 3.14/1.66 => ( ( Fid1 != Fid2 )
% 3.14/1.66 => ( ( Fid2 != Fid3 )
% 3.14/1.66 => ( ( Fid1 != Fid3 )
% 3.14/1.66 => ( ( Pid1 != Pid2 )
% 3.14/1.66 => ( ( Pid2 != Pid3 )
% 3.14/1.66 => ( ( Pid1 != Pid3 )
% 3.14/1.66 => ( ( Pid1 != Pid4 )
% 3.14/1.66 => ( ( Pid2 != Pid4 )
% 3.14/1.66 => ( ( Pid3 != Pid4 )
% 3.14/1.66 => ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_101_ids_Opne12,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ( Pid1 != Pid2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_102_ids_Opne13,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ( Pid1 != Pid3 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_103_ids_Opne14,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ( Pid1 != Pid4 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_104_curry__conv,axiom,
% 3.14/1.66 ( produc1086673900c_sz_o
% 3.14/1.66 = ( ^ [F: produc1821101996_sc_sz > $o,A5: denota610675952t_unit,B5: produc866628903_sc_sz] : ( F @ ( produc789536734_sc_sz @ A5 @ B5 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_105_ssubst__Pair__rhs,axiom,
% 3.14/1.66 ! [R: list_f1238882004_sc_sz,S2: list_f1238882004_sc_sz,R2: set_Pr1774599175_sc_sz,S3: list_f1238882004_sc_sz] :
% 3.14/1.66 ( ( member245028432_sc_sz @ ( produc1822718231_sc_sz @ R @ S2 ) @ R2 )
% 3.14/1.66 => ( ( S3 = S2 )
% 3.14/1.66 => ( member245028432_sc_sz @ ( produc1822718231_sc_sz @ R @ S3 ) @ R2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_106_ssubst__Pair__rhs,axiom,
% 3.14/1.66 ! [R: produc866628903_sc_sz,S2: denota610675952t_unit,R2: set_Pr2041213564t_unit,S3: denota610675952t_unit] :
% 3.14/1.66 ( ( member235934813t_unit @ ( produc502616768t_unit @ R @ S2 ) @ R2 )
% 3.14/1.66 => ( ( S3 = S2 )
% 3.14/1.66 => ( member235934813t_unit @ ( produc502616768t_unit @ R @ S3 ) @ R2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_107_ssubst__Pair__rhs,axiom,
% 3.14/1.66 ! [R: produc190496183real_c,S2: produc190496183real_c,R2: set_Pr754230471real_c,S3: produc190496183real_c] :
% 3.14/1.66 ( ( member346808080real_c @ ( produc1687028567real_c @ R @ S2 ) @ R2 )
% 3.14/1.66 => ( ( S3 = S2 )
% 3.14/1.66 => ( member346808080real_c @ ( produc1687028567real_c @ R @ S3 ) @ R2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_108_ssubst__Pair__rhs,axiom,
% 3.14/1.66 ! [R: finite1398487019real_c,S2: finite1398487019real_c,R2: set_Pr1389752855real_c,S3: finite1398487019real_c] :
% 3.14/1.66 ( ( member1895684704real_c @ ( produc394644079real_c @ R @ S2 ) @ R2 )
% 3.14/1.66 => ( ( S3 = S2 )
% 3.14/1.66 => ( member1895684704real_c @ ( produc394644079real_c @ R @ S3 ) @ R2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_109_ssubst__Pair__rhs,axiom,
% 3.14/1.66 ! [R: denota610675952t_unit,S2: produc866628903_sc_sz,R2: set_Pr1169339874_sc_sz,S3: produc866628903_sc_sz] :
% 3.14/1.66 ( ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ R @ S2 ) @ R2 )
% 3.14/1.66 => ( ( S3 = S2 )
% 3.14/1.66 => ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ R @ S3 ) @ R2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_110_curryI,axiom,
% 3.14/1.66 ! [F2: produc866628903_sc_sz > $o,A2: list_f1238882004_sc_sz,B2: list_f1238882004_sc_sz] :
% 3.14/1.66 ( ( F2 @ ( produc1822718231_sc_sz @ A2 @ B2 ) )
% 3.14/1.66 => ( produc880541325c_sz_o @ F2 @ A2 @ B2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_111_curryI,axiom,
% 3.14/1.66 ! [F2: produc190496183real_c > $o,A2: finite1398487019real_c,B2: finite1398487019real_c] :
% 3.14/1.66 ( ( F2 @ ( produc394644079real_c @ A2 @ B2 ) )
% 3.14/1.66 => ( produc1716060341al_c_o @ F2 @ A2 @ B2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_112_curryI,axiom,
% 3.14/1.66 ! [F2: produc999471430t_unit > $o,A2: produc866628903_sc_sz,B2: denota610675952t_unit] :
% 3.14/1.66 ( ( F2 @ ( produc502616768t_unit @ A2 @ B2 ) )
% 3.14/1.66 => ( produc38128778unit_o @ F2 @ A2 @ B2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_113_curryI,axiom,
% 3.14/1.66 ! [F2: produc640052711real_c > $o,A2: produc190496183real_c,B2: produc190496183real_c] :
% 3.14/1.66 ( ( F2 @ ( produc1687028567real_c @ A2 @ B2 ) )
% 3.14/1.66 => ( produc440529997al_c_o @ F2 @ A2 @ B2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_114_curryI,axiom,
% 3.14/1.66 ! [F2: produc1821101996_sc_sz > $o,A2: denota610675952t_unit,B2: produc866628903_sc_sz] :
% 3.14/1.66 ( ( F2 @ ( produc789536734_sc_sz @ A2 @ B2 ) )
% 3.14/1.66 => ( produc1086673900c_sz_o @ F2 @ A2 @ B2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_115_swap__simp,axiom,
% 3.14/1.66 ! [X: list_f1238882004_sc_sz,Y: list_f1238882004_sc_sz] :
% 3.14/1.66 ( ( produc1145837239_sc_sz @ ( produc1822718231_sc_sz @ X @ Y ) )
% 3.14/1.66 = ( produc1822718231_sc_sz @ Y @ X ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_116_swap__simp,axiom,
% 3.14/1.66 ! [X: produc190496183real_c,Y: produc190496183real_c] :
% 3.14/1.66 ( ( produc350724343real_c @ ( produc1687028567real_c @ X @ Y ) )
% 3.14/1.66 = ( produc1687028567real_c @ Y @ X ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_117_swap__simp,axiom,
% 3.14/1.66 ! [X: finite1398487019real_c,Y: finite1398487019real_c] :
% 3.14/1.66 ( ( produc704157711real_c @ ( produc394644079real_c @ X @ Y ) )
% 3.14/1.66 = ( produc394644079real_c @ Y @ X ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_118_swap__simp,axiom,
% 3.14/1.66 ! [X: produc866628903_sc_sz,Y: denota610675952t_unit] :
% 3.14/1.66 ( ( produc245128480t_unit @ ( produc502616768t_unit @ X @ Y ) )
% 3.14/1.66 = ( produc789536734_sc_sz @ Y @ X ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_119_swap__simp,axiom,
% 3.14/1.66 ! [X: denota610675952t_unit,Y: produc866628903_sc_sz] :
% 3.14/1.66 ( ( produc532048446_sc_sz @ ( produc789536734_sc_sz @ X @ Y ) )
% 3.14/1.66 = ( produc502616768t_unit @ Y @ X ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_120_ids_Ovalid__def,axiom,
% 3.14/1.66 ! [Vid1: sz,Vid2: sz,Vid3: sz,Fid1: sf,Fid2: sf,Fid3: sf,Pid1: sc,Pid2: sc,Pid3: sc,Pid4: sc,Phi2: formula_sf_sc_sz] :
% 3.14/1.66 ( ( ids_sz_sf_sc @ Vid1 @ Vid2 @ Vid3 @ Fid1 @ Fid2 @ Fid3 @ Pid1 @ Pid2 @ Pid3 @ Pid4 )
% 3.14/1.66 => ( ( denota1946510237_sc_sz @ Phi2 )
% 3.14/1.66 = ( ! [I: denota610675952t_unit,Nu: produc1149990247eal_sz] :
% 3.14/1.66 ( ( denota1579475975_sc_sz @ I )
% 3.14/1.66 => ( member630771088eal_sz @ Nu @ ( denota1711272799_sc_sz @ I @ Phi2 ) ) ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_121_swap__swap,axiom,
% 3.14/1.66 ! [P2: produc999471430t_unit] :
% 3.14/1.66 ( ( produc532048446_sc_sz @ ( produc245128480t_unit @ P2 ) )
% 3.14/1.66 = P2 ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_122_swap__swap,axiom,
% 3.14/1.66 ! [P2: produc1821101996_sc_sz] :
% 3.14/1.66 ( ( produc245128480t_unit @ ( produc532048446_sc_sz @ P2 ) )
% 3.14/1.66 = P2 ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_123_swap__swap,axiom,
% 3.14/1.66 ! [P2: produc190496183real_c] :
% 3.14/1.66 ( ( produc704157711real_c @ ( produc704157711real_c @ P2 ) )
% 3.14/1.66 = P2 ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_124_curryE,axiom,
% 3.14/1.66 ! [F2: produc866628903_sc_sz > $o,A2: list_f1238882004_sc_sz,B2: list_f1238882004_sc_sz] :
% 3.14/1.66 ( ( produc880541325c_sz_o @ F2 @ A2 @ B2 )
% 3.14/1.66 => ( F2 @ ( produc1822718231_sc_sz @ A2 @ B2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_125_curryE,axiom,
% 3.14/1.66 ! [F2: produc190496183real_c > $o,A2: finite1398487019real_c,B2: finite1398487019real_c] :
% 3.14/1.66 ( ( produc1716060341al_c_o @ F2 @ A2 @ B2 )
% 3.14/1.66 => ( F2 @ ( produc394644079real_c @ A2 @ B2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_126_curryE,axiom,
% 3.14/1.66 ! [F2: produc999471430t_unit > $o,A2: produc866628903_sc_sz,B2: denota610675952t_unit] :
% 3.14/1.66 ( ( produc38128778unit_o @ F2 @ A2 @ B2 )
% 3.14/1.66 => ( F2 @ ( produc502616768t_unit @ A2 @ B2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_127_curryE,axiom,
% 3.14/1.66 ! [F2: produc640052711real_c > $o,A2: produc190496183real_c,B2: produc190496183real_c] :
% 3.14/1.66 ( ( produc440529997al_c_o @ F2 @ A2 @ B2 )
% 3.14/1.66 => ( F2 @ ( produc1687028567real_c @ A2 @ B2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_128_curryE,axiom,
% 3.14/1.66 ! [F2: produc1821101996_sc_sz > $o,A2: denota610675952t_unit,B2: produc866628903_sc_sz] :
% 3.14/1.66 ( ( produc1086673900c_sz_o @ F2 @ A2 @ B2 )
% 3.14/1.66 => ( F2 @ ( produc789536734_sc_sz @ A2 @ B2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_129_curryD,axiom,
% 3.14/1.66 ! [F2: produc866628903_sc_sz > $o,A2: list_f1238882004_sc_sz,B2: list_f1238882004_sc_sz] :
% 3.14/1.66 ( ( produc880541325c_sz_o @ F2 @ A2 @ B2 )
% 3.14/1.66 => ( F2 @ ( produc1822718231_sc_sz @ A2 @ B2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_130_curryD,axiom,
% 3.14/1.66 ! [F2: produc190496183real_c > $o,A2: finite1398487019real_c,B2: finite1398487019real_c] :
% 3.14/1.66 ( ( produc1716060341al_c_o @ F2 @ A2 @ B2 )
% 3.14/1.66 => ( F2 @ ( produc394644079real_c @ A2 @ B2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_131_curryD,axiom,
% 3.14/1.66 ! [F2: produc999471430t_unit > $o,A2: produc866628903_sc_sz,B2: denota610675952t_unit] :
% 3.14/1.66 ( ( produc38128778unit_o @ F2 @ A2 @ B2 )
% 3.14/1.66 => ( F2 @ ( produc502616768t_unit @ A2 @ B2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_132_curryD,axiom,
% 3.14/1.66 ! [F2: produc640052711real_c > $o,A2: produc190496183real_c,B2: produc190496183real_c] :
% 3.14/1.66 ( ( produc440529997al_c_o @ F2 @ A2 @ B2 )
% 3.14/1.66 => ( F2 @ ( produc1687028567real_c @ A2 @ B2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_133_curryD,axiom,
% 3.14/1.66 ! [F2: produc1821101996_sc_sz > $o,A2: denota610675952t_unit,B2: produc866628903_sc_sz] :
% 3.14/1.66 ( ( produc1086673900c_sz_o @ F2 @ A2 @ B2 )
% 3.14/1.66 => ( F2 @ ( produc789536734_sc_sz @ A2 @ B2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_134_pair__in__swap__image,axiom,
% 3.14/1.66 ! [Y: list_f1238882004_sc_sz,X: list_f1238882004_sc_sz,A: set_Pr1774599175_sc_sz] :
% 3.14/1.66 ( ( member245028432_sc_sz @ ( produc1822718231_sc_sz @ Y @ X ) @ ( image_1313166277_sc_sz @ produc1145837239_sc_sz @ A ) )
% 3.14/1.66 = ( member245028432_sc_sz @ ( produc1822718231_sc_sz @ X @ Y ) @ A ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_135_pair__in__swap__image,axiom,
% 3.14/1.66 ! [Y: produc190496183real_c,X: produc190496183real_c,A: set_Pr754230471real_c] :
% 3.14/1.66 ( ( member346808080real_c @ ( produc1687028567real_c @ Y @ X ) @ ( image_2041365445real_c @ produc350724343real_c @ A ) )
% 3.14/1.66 = ( member346808080real_c @ ( produc1687028567real_c @ X @ Y ) @ A ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_136_pair__in__swap__image,axiom,
% 3.14/1.66 ! [Y: finite1398487019real_c,X: finite1398487019real_c,A: set_Pr1389752855real_c] :
% 3.14/1.66 ( ( member1895684704real_c @ ( produc394644079real_c @ Y @ X ) @ ( image_738229701real_c @ produc704157711real_c @ A ) )
% 3.14/1.66 = ( member1895684704real_c @ ( produc394644079real_c @ X @ Y ) @ A ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_137_pair__in__swap__image,axiom,
% 3.14/1.66 ! [Y: produc866628903_sc_sz,X: denota610675952t_unit,A: set_Pr1169339874_sc_sz] :
% 3.14/1.66 ( ( member235934813t_unit @ ( produc502616768t_unit @ Y @ X ) @ ( image_904562809t_unit @ produc532048446_sc_sz @ A ) )
% 3.14/1.66 = ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ X @ Y ) @ A ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_138_pair__in__swap__image,axiom,
% 3.14/1.66 ! [Y: denota610675952t_unit,X: produc866628903_sc_sz,A: set_Pr2041213564t_unit] :
% 3.14/1.66 ( ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ Y @ X ) @ ( image_1426741113_sc_sz @ produc245128480t_unit @ A ) )
% 3.14/1.66 = ( member235934813t_unit @ ( produc502616768t_unit @ X @ Y ) @ A ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_139_internal__case__prod__def,axiom,
% 3.14/1.66 produc383750338real_c = produc1575513068real_c ).
% 3.14/1.66
% 3.14/1.66 thf(fact_140_internal__case__prod__def,axiom,
% 3.14/1.66 produc198687651c_sz_o = produc619560141c_sz_o ).
% 3.14/1.66
% 3.14/1.66 thf(fact_141_internal__case__prod__def,axiom,
% 3.14/1.66 produc1894848802real_c = produc237521996real_c ).
% 3.14/1.66
% 3.14/1.66 thf(fact_142_internal__case__prod__def,axiom,
% 3.14/1.66 produc1442549981real_c = produc107375667real_c ).
% 3.14/1.66
% 3.14/1.66 thf(fact_143_internal__case__prod__def,axiom,
% 3.14/1.66 produc2099580355_sc_sz = produc435149849_sc_sz ).
% 3.14/1.66
% 3.14/1.66 thf(fact_144_apsnd__conv,axiom,
% 3.14/1.66 ! [F2: list_f1238882004_sc_sz > list_f1238882004_sc_sz,X: list_f1238882004_sc_sz,Y: list_f1238882004_sc_sz] :
% 3.14/1.66 ( ( produc233219286_sc_sz @ F2 @ ( produc1822718231_sc_sz @ X @ Y ) )
% 3.14/1.66 = ( produc1822718231_sc_sz @ X @ ( F2 @ Y ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_145_apsnd__conv,axiom,
% 3.14/1.66 ! [F2: finite1398487019real_c > finite1398487019real_c,X: finite1398487019real_c,Y: finite1398487019real_c] :
% 3.14/1.66 ( ( produc981295297real_c @ F2 @ ( produc394644079real_c @ X @ Y ) )
% 3.14/1.66 = ( produc394644079real_c @ X @ ( F2 @ Y ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_146_apsnd__conv,axiom,
% 3.14/1.66 ! [F2: denota610675952t_unit > denota610675952t_unit,X: produc866628903_sc_sz,Y: denota610675952t_unit] :
% 3.14/1.66 ( ( produc793407943_sc_sz @ F2 @ ( produc502616768t_unit @ X @ Y ) )
% 3.14/1.66 = ( produc502616768t_unit @ X @ ( F2 @ Y ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_147_apsnd__conv,axiom,
% 3.14/1.66 ! [F2: produc190496183real_c > produc190496183real_c,X: produc190496183real_c,Y: produc190496183real_c] :
% 3.14/1.66 ( ( produc2089853305real_c @ F2 @ ( produc1687028567real_c @ X @ Y ) )
% 3.14/1.66 = ( produc1687028567real_c @ X @ ( F2 @ Y ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_148_apsnd__conv,axiom,
% 3.14/1.66 ! [F2: produc866628903_sc_sz > produc866628903_sc_sz,X: denota610675952t_unit,Y: produc866628903_sc_sz] :
% 3.14/1.66 ( ( produc1959054510t_unit @ F2 @ ( produc789536734_sc_sz @ X @ Y ) )
% 3.14/1.66 = ( produc789536734_sc_sz @ X @ ( F2 @ Y ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_149_mem__case__prodI2,axiom,
% 3.14/1.66 ! [P2: produc1821101996_sc_sz,Z: produc190496183real_c,C2: denota610675952t_unit > produc866628903_sc_sz > set_Pr1389752855real_c] :
% 3.14/1.66 ( ! [A4: denota610675952t_unit,B4: produc866628903_sc_sz] :
% 3.14/1.66 ( ( P2
% 3.14/1.66 = ( produc789536734_sc_sz @ A4 @ B4 ) )
% 3.14/1.66 => ( member1895684704real_c @ Z @ ( C2 @ A4 @ B4 ) ) )
% 3.14/1.66 => ( member1895684704real_c @ Z @ ( produc237521996real_c @ C2 @ P2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_150_mem__case__prodI2,axiom,
% 3.14/1.66 ! [P2: produc190496183real_c,Z: finite1398487019real_c,C2: finite1398487019real_c > finite1398487019real_c > set_Fi1407883041real_c] :
% 3.14/1.66 ( ! [A4: finite1398487019real_c,B4: finite1398487019real_c] :
% 3.14/1.66 ( ( P2
% 3.14/1.66 = ( produc394644079real_c @ A4 @ B4 ) )
% 3.14/1.66 => ( member1261661570real_c @ Z @ ( C2 @ A4 @ B4 ) ) )
% 3.14/1.66 => ( member1261661570real_c @ Z @ ( produc29022117real_c @ C2 @ P2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_151_mem__case__prodI2,axiom,
% 3.14/1.66 ! [P2: produc866628903_sc_sz,Z: finite1398487019real_c,C2: list_f1238882004_sc_sz > list_f1238882004_sc_sz > set_Fi1407883041real_c] :
% 3.14/1.66 ( ! [A4: list_f1238882004_sc_sz,B4: list_f1238882004_sc_sz] :
% 3.14/1.66 ( ( P2
% 3.14/1.66 = ( produc1822718231_sc_sz @ A4 @ B4 ) )
% 3.14/1.66 => ( member1261661570real_c @ Z @ ( C2 @ A4 @ B4 ) ) )
% 3.14/1.66 => ( member1261661570real_c @ Z @ ( produc1449736269real_c @ C2 @ P2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_152_mem__case__prodI2,axiom,
% 3.14/1.66 ! [P2: produc190496183real_c,Z: produc190496183real_c,C2: finite1398487019real_c > finite1398487019real_c > set_Pr1389752855real_c] :
% 3.14/1.66 ( ! [A4: finite1398487019real_c,B4: finite1398487019real_c] :
% 3.14/1.66 ( ( P2
% 3.14/1.66 = ( produc394644079real_c @ A4 @ B4 ) )
% 3.14/1.66 => ( member1895684704real_c @ Z @ ( C2 @ A4 @ B4 ) ) )
% 3.14/1.66 => ( member1895684704real_c @ Z @ ( produc923381907real_c @ C2 @ P2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_153_mem__case__prodI2,axiom,
% 3.14/1.66 ! [P2: produc866628903_sc_sz,Z: produc190496183real_c,C2: list_f1238882004_sc_sz > list_f1238882004_sc_sz > set_Pr1389752855real_c] :
% 3.14/1.66 ( ! [A4: list_f1238882004_sc_sz,B4: list_f1238882004_sc_sz] :
% 3.14/1.66 ( ( P2
% 3.14/1.66 = ( produc1822718231_sc_sz @ A4 @ B4 ) )
% 3.14/1.66 => ( member1895684704real_c @ Z @ ( C2 @ A4 @ B4 ) ) )
% 3.14/1.66 => ( member1895684704real_c @ Z @ ( produc6841835real_c @ C2 @ P2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_154_mem__case__prodI2,axiom,
% 3.14/1.66 ! [P2: produc190496183real_c,Z: produc866628903_sc_sz,C2: finite1398487019real_c > finite1398487019real_c > set_Pr1774599175_sc_sz] :
% 3.14/1.66 ( ! [A4: finite1398487019real_c,B4: finite1398487019real_c] :
% 3.14/1.66 ( ( P2
% 3.14/1.66 = ( produc394644079real_c @ A4 @ B4 ) )
% 3.14/1.66 => ( member245028432_sc_sz @ Z @ ( C2 @ A4 @ B4 ) ) )
% 3.14/1.66 => ( member245028432_sc_sz @ Z @ ( produc642283651_sc_sz @ C2 @ P2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_155_mem__case__prodI2,axiom,
% 3.14/1.66 ! [P2: produc640052711real_c,Z: finite1398487019real_c,C2: produc190496183real_c > produc190496183real_c > set_Fi1407883041real_c] :
% 3.14/1.66 ( ! [A4: produc190496183real_c,B4: produc190496183real_c] :
% 3.14/1.66 ( ( P2
% 3.14/1.66 = ( produc1687028567real_c @ A4 @ B4 ) )
% 3.14/1.66 => ( member1261661570real_c @ Z @ ( C2 @ A4 @ B4 ) ) )
% 3.14/1.66 => ( member1261661570real_c @ Z @ ( produc1066779277real_c @ C2 @ P2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_156_mem__case__prodI2,axiom,
% 3.14/1.66 ! [P2: produc1821101996_sc_sz,Z: finite1398487019real_c,C2: denota610675952t_unit > produc866628903_sc_sz > set_Fi1407883041real_c] :
% 3.14/1.66 ( ! [A4: denota610675952t_unit,B4: produc866628903_sc_sz] :
% 3.14/1.66 ( ( P2
% 3.14/1.66 = ( produc789536734_sc_sz @ A4 @ B4 ) )
% 3.14/1.66 => ( member1261661570real_c @ Z @ ( C2 @ A4 @ B4 ) ) )
% 3.14/1.66 => ( member1261661570real_c @ Z @ ( produc2068697644real_c @ C2 @ P2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_157_mem__case__prodI2,axiom,
% 3.14/1.66 ! [P2: produc999471430t_unit,Z: finite1398487019real_c,C2: produc866628903_sc_sz > denota610675952t_unit > set_Fi1407883041real_c] :
% 3.14/1.66 ( ! [A4: produc866628903_sc_sz,B4: denota610675952t_unit] :
% 3.14/1.66 ( ( P2
% 3.14/1.66 = ( produc502616768t_unit @ A4 @ B4 ) )
% 3.14/1.66 => ( member1261661570real_c @ Z @ ( C2 @ A4 @ B4 ) ) )
% 3.14/1.66 => ( member1261661570real_c @ Z @ ( produc1368849166real_c @ C2 @ P2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_158_mem__case__prodI2,axiom,
% 3.14/1.66 ! [P2: produc866628903_sc_sz,Z: produc866628903_sc_sz,C2: list_f1238882004_sc_sz > list_f1238882004_sc_sz > set_Pr1774599175_sc_sz] :
% 3.14/1.66 ( ! [A4: list_f1238882004_sc_sz,B4: list_f1238882004_sc_sz] :
% 3.14/1.66 ( ( P2
% 3.14/1.66 = ( produc1822718231_sc_sz @ A4 @ B4 ) )
% 3.14/1.66 => ( member245028432_sc_sz @ Z @ ( C2 @ A4 @ B4 ) ) )
% 3.14/1.66 => ( member245028432_sc_sz @ Z @ ( produc1563580891_sc_sz @ C2 @ P2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_159_mem__case__prodI,axiom,
% 3.14/1.66 ! [Z: produc190496183real_c,C2: denota610675952t_unit > produc866628903_sc_sz > set_Pr1389752855real_c,A2: denota610675952t_unit,B2: produc866628903_sc_sz] :
% 3.14/1.66 ( ( member1895684704real_c @ Z @ ( C2 @ A2 @ B2 ) )
% 3.14/1.66 => ( member1895684704real_c @ Z @ ( produc237521996real_c @ C2 @ ( produc789536734_sc_sz @ A2 @ B2 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_160_mem__case__prodI,axiom,
% 3.14/1.66 ! [Z: finite1398487019real_c,C2: finite1398487019real_c > finite1398487019real_c > set_Fi1407883041real_c,A2: finite1398487019real_c,B2: finite1398487019real_c] :
% 3.14/1.66 ( ( member1261661570real_c @ Z @ ( C2 @ A2 @ B2 ) )
% 3.14/1.66 => ( member1261661570real_c @ Z @ ( produc29022117real_c @ C2 @ ( produc394644079real_c @ A2 @ B2 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_161_mem__case__prodI,axiom,
% 3.14/1.66 ! [Z: finite1398487019real_c,C2: list_f1238882004_sc_sz > list_f1238882004_sc_sz > set_Fi1407883041real_c,A2: list_f1238882004_sc_sz,B2: list_f1238882004_sc_sz] :
% 3.14/1.66 ( ( member1261661570real_c @ Z @ ( C2 @ A2 @ B2 ) )
% 3.14/1.66 => ( member1261661570real_c @ Z @ ( produc1449736269real_c @ C2 @ ( produc1822718231_sc_sz @ A2 @ B2 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_162_mem__case__prodI,axiom,
% 3.14/1.66 ! [Z: produc190496183real_c,C2: finite1398487019real_c > finite1398487019real_c > set_Pr1389752855real_c,A2: finite1398487019real_c,B2: finite1398487019real_c] :
% 3.14/1.66 ( ( member1895684704real_c @ Z @ ( C2 @ A2 @ B2 ) )
% 3.14/1.66 => ( member1895684704real_c @ Z @ ( produc923381907real_c @ C2 @ ( produc394644079real_c @ A2 @ B2 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_163_mem__case__prodI,axiom,
% 3.14/1.66 ! [Z: produc190496183real_c,C2: list_f1238882004_sc_sz > list_f1238882004_sc_sz > set_Pr1389752855real_c,A2: list_f1238882004_sc_sz,B2: list_f1238882004_sc_sz] :
% 3.14/1.66 ( ( member1895684704real_c @ Z @ ( C2 @ A2 @ B2 ) )
% 3.14/1.66 => ( member1895684704real_c @ Z @ ( produc6841835real_c @ C2 @ ( produc1822718231_sc_sz @ A2 @ B2 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_164_mem__case__prodI,axiom,
% 3.14/1.66 ! [Z: produc866628903_sc_sz,C2: finite1398487019real_c > finite1398487019real_c > set_Pr1774599175_sc_sz,A2: finite1398487019real_c,B2: finite1398487019real_c] :
% 3.14/1.66 ( ( member245028432_sc_sz @ Z @ ( C2 @ A2 @ B2 ) )
% 3.14/1.66 => ( member245028432_sc_sz @ Z @ ( produc642283651_sc_sz @ C2 @ ( produc394644079real_c @ A2 @ B2 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_165_mem__case__prodI,axiom,
% 3.14/1.66 ! [Z: finite1398487019real_c,C2: produc190496183real_c > produc190496183real_c > set_Fi1407883041real_c,A2: produc190496183real_c,B2: produc190496183real_c] :
% 3.14/1.66 ( ( member1261661570real_c @ Z @ ( C2 @ A2 @ B2 ) )
% 3.14/1.66 => ( member1261661570real_c @ Z @ ( produc1066779277real_c @ C2 @ ( produc1687028567real_c @ A2 @ B2 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_166_mem__case__prodI,axiom,
% 3.14/1.66 ! [Z: finite1398487019real_c,C2: denota610675952t_unit > produc866628903_sc_sz > set_Fi1407883041real_c,A2: denota610675952t_unit,B2: produc866628903_sc_sz] :
% 3.14/1.66 ( ( member1261661570real_c @ Z @ ( C2 @ A2 @ B2 ) )
% 3.14/1.66 => ( member1261661570real_c @ Z @ ( produc2068697644real_c @ C2 @ ( produc789536734_sc_sz @ A2 @ B2 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_167_mem__case__prodI,axiom,
% 3.14/1.66 ! [Z: finite1398487019real_c,C2: produc866628903_sc_sz > denota610675952t_unit > set_Fi1407883041real_c,A2: produc866628903_sc_sz,B2: denota610675952t_unit] :
% 3.14/1.66 ( ( member1261661570real_c @ Z @ ( C2 @ A2 @ B2 ) )
% 3.14/1.66 => ( member1261661570real_c @ Z @ ( produc1368849166real_c @ C2 @ ( produc502616768t_unit @ A2 @ B2 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_168_mem__case__prodI,axiom,
% 3.14/1.66 ! [Z: produc866628903_sc_sz,C2: list_f1238882004_sc_sz > list_f1238882004_sc_sz > set_Pr1774599175_sc_sz,A2: list_f1238882004_sc_sz,B2: list_f1238882004_sc_sz] :
% 3.14/1.66 ( ( member245028432_sc_sz @ Z @ ( C2 @ A2 @ B2 ) )
% 3.14/1.66 => ( member245028432_sc_sz @ Z @ ( produc1563580891_sc_sz @ C2 @ ( produc1822718231_sc_sz @ A2 @ B2 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_169_case__prodI2,axiom,
% 3.14/1.66 ! [P2: produc866628903_sc_sz,C2: list_f1238882004_sc_sz > list_f1238882004_sc_sz > $o] :
% 3.14/1.66 ( ! [A4: list_f1238882004_sc_sz,B4: list_f1238882004_sc_sz] :
% 3.14/1.66 ( ( P2
% 3.14/1.66 = ( produc1822718231_sc_sz @ A4 @ B4 ) )
% 3.14/1.66 => ( C2 @ A4 @ B4 ) )
% 3.14/1.66 => ( produc2039065452c_sz_o @ C2 @ P2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_170_case__prodI2,axiom,
% 3.14/1.66 ! [P2: produc190496183real_c,C2: finite1398487019real_c > finite1398487019real_c > $o] :
% 3.14/1.66 ( ! [A4: finite1398487019real_c,B4: finite1398487019real_c] :
% 3.14/1.66 ( ( P2
% 3.14/1.66 = ( produc394644079real_c @ A4 @ B4 ) )
% 3.14/1.66 => ( C2 @ A4 @ B4 ) )
% 3.14/1.66 => ( produc353381908al_c_o @ C2 @ P2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_171_case__prodI2,axiom,
% 3.14/1.66 ! [P2: produc999471430t_unit,C2: produc866628903_sc_sz > denota610675952t_unit > $o] :
% 3.14/1.66 ( ! [A4: produc866628903_sc_sz,B4: denota610675952t_unit] :
% 3.14/1.66 ( ( P2
% 3.14/1.66 = ( produc502616768t_unit @ A4 @ B4 ) )
% 3.14/1.66 => ( C2 @ A4 @ B4 ) )
% 3.14/1.66 => ( produc1718498667unit_o @ C2 @ P2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_172_case__prodI2,axiom,
% 3.14/1.66 ! [P2: produc640052711real_c,C2: produc190496183real_c > produc190496183real_c > $o] :
% 3.14/1.66 ( ! [A4: produc190496183real_c,B4: produc190496183real_c] :
% 3.14/1.66 ( ( P2
% 3.14/1.66 = ( produc1687028567real_c @ A4 @ B4 ) )
% 3.14/1.66 => ( C2 @ A4 @ B4 ) )
% 3.14/1.66 => ( produc1726730540al_c_o @ C2 @ P2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_173_case__prodI2,axiom,
% 3.14/1.66 ! [P2: produc1821101996_sc_sz,C2: denota610675952t_unit > produc866628903_sc_sz > $o] :
% 3.14/1.66 ( ! [A4: denota610675952t_unit,B4: produc866628903_sc_sz] :
% 3.14/1.66 ( ( P2
% 3.14/1.66 = ( produc789536734_sc_sz @ A4 @ B4 ) )
% 3.14/1.66 => ( C2 @ A4 @ B4 ) )
% 3.14/1.66 => ( produc619560141c_sz_o @ C2 @ P2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_174_case__prodI,axiom,
% 3.14/1.66 ! [F2: list_f1238882004_sc_sz > list_f1238882004_sc_sz > $o,A2: list_f1238882004_sc_sz,B2: list_f1238882004_sc_sz] :
% 3.14/1.66 ( ( F2 @ A2 @ B2 )
% 3.14/1.66 => ( produc2039065452c_sz_o @ F2 @ ( produc1822718231_sc_sz @ A2 @ B2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_175_case__prodI,axiom,
% 3.14/1.66 ! [F2: finite1398487019real_c > finite1398487019real_c > $o,A2: finite1398487019real_c,B2: finite1398487019real_c] :
% 3.14/1.66 ( ( F2 @ A2 @ B2 )
% 3.14/1.66 => ( produc353381908al_c_o @ F2 @ ( produc394644079real_c @ A2 @ B2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_176_case__prodI,axiom,
% 3.14/1.66 ! [F2: produc866628903_sc_sz > denota610675952t_unit > $o,A2: produc866628903_sc_sz,B2: denota610675952t_unit] :
% 3.14/1.66 ( ( F2 @ A2 @ B2 )
% 3.14/1.66 => ( produc1718498667unit_o @ F2 @ ( produc502616768t_unit @ A2 @ B2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_177_case__prodI,axiom,
% 3.14/1.66 ! [F2: produc190496183real_c > produc190496183real_c > $o,A2: produc190496183real_c,B2: produc190496183real_c] :
% 3.14/1.66 ( ( F2 @ A2 @ B2 )
% 3.14/1.66 => ( produc1726730540al_c_o @ F2 @ ( produc1687028567real_c @ A2 @ B2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_178_case__prodI,axiom,
% 3.14/1.66 ! [F2: denota610675952t_unit > produc866628903_sc_sz > $o,A2: denota610675952t_unit,B2: produc866628903_sc_sz] :
% 3.14/1.66 ( ( F2 @ A2 @ B2 )
% 3.14/1.66 => ( produc619560141c_sz_o @ F2 @ ( produc789536734_sc_sz @ A2 @ B2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_179_case__prod__conv,axiom,
% 3.14/1.66 ! [F2: denota610675952t_unit > produc866628903_sc_sz > produc190496183real_c,A2: denota610675952t_unit,B2: produc866628903_sc_sz] :
% 3.14/1.66 ( ( produc1575513068real_c @ F2 @ ( produc789536734_sc_sz @ A2 @ B2 ) )
% 3.14/1.66 = ( F2 @ A2 @ B2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_180_case__prod__conv,axiom,
% 3.14/1.66 ! [F2: denota610675952t_unit > produc866628903_sc_sz > $o,A2: denota610675952t_unit,B2: produc866628903_sc_sz] :
% 3.14/1.66 ( ( produc619560141c_sz_o @ F2 @ ( produc789536734_sc_sz @ A2 @ B2 ) )
% 3.14/1.66 = ( F2 @ A2 @ B2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_181_case__prod__conv,axiom,
% 3.14/1.66 ! [F2: denota610675952t_unit > produc866628903_sc_sz > set_Pr1389752855real_c,A2: denota610675952t_unit,B2: produc866628903_sc_sz] :
% 3.14/1.66 ( ( produc237521996real_c @ F2 @ ( produc789536734_sc_sz @ A2 @ B2 ) )
% 3.14/1.66 = ( F2 @ A2 @ B2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_182_case__prod__conv,axiom,
% 3.14/1.66 ! [F2: finite1398487019real_c > finite1398487019real_c > produc190496183real_c,A2: finite1398487019real_c,B2: finite1398487019real_c] :
% 3.14/1.66 ( ( produc107375667real_c @ F2 @ ( produc394644079real_c @ A2 @ B2 ) )
% 3.14/1.66 = ( F2 @ A2 @ B2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_183_case__prod__conv,axiom,
% 3.14/1.66 ! [F2: produc866628903_sc_sz > denota610675952t_unit > produc1821101996_sc_sz,A2: produc866628903_sc_sz,B2: denota610675952t_unit] :
% 3.14/1.66 ( ( produc435149849_sc_sz @ F2 @ ( produc502616768t_unit @ A2 @ B2 ) )
% 3.14/1.66 = ( F2 @ A2 @ B2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_184_curry__case__prod,axiom,
% 3.14/1.66 ! [F2: denota610675952t_unit > produc866628903_sc_sz > produc190496183real_c] :
% 3.14/1.66 ( ( produc753314315real_c @ ( produc1575513068real_c @ F2 ) )
% 3.14/1.66 = F2 ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_185_curry__case__prod,axiom,
% 3.14/1.66 ! [F2: denota610675952t_unit > produc866628903_sc_sz > $o] :
% 3.14/1.66 ( ( produc1086673900c_sz_o @ ( produc619560141c_sz_o @ F2 ) )
% 3.14/1.66 = F2 ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_186_curry__case__prod,axiom,
% 3.14/1.66 ! [F2: denota610675952t_unit > produc866628903_sc_sz > set_Pr1389752855real_c] :
% 3.14/1.66 ( ( produc1827049067real_c @ ( produc237521996real_c @ F2 ) )
% 3.14/1.66 = F2 ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_187_curry__case__prod,axiom,
% 3.14/1.66 ! [F2: finite1398487019real_c > finite1398487019real_c > produc190496183real_c] :
% 3.14/1.66 ( ( produc1119115220real_c @ ( produc107375667real_c @ F2 ) )
% 3.14/1.66 = F2 ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_188_curry__case__prod,axiom,
% 3.14/1.66 ! [F2: produc866628903_sc_sz > denota610675952t_unit > produc1821101996_sc_sz] :
% 3.14/1.66 ( ( produc295339066_sc_sz @ ( produc435149849_sc_sz @ F2 ) )
% 3.14/1.66 = F2 ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_189_case__prod__curry,axiom,
% 3.14/1.66 ! [F2: produc1821101996_sc_sz > produc190496183real_c] :
% 3.14/1.66 ( ( produc1575513068real_c @ ( produc753314315real_c @ F2 ) )
% 3.14/1.66 = F2 ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_190_case__prod__curry,axiom,
% 3.14/1.66 ! [F2: produc1821101996_sc_sz > $o] :
% 3.14/1.66 ( ( produc619560141c_sz_o @ ( produc1086673900c_sz_o @ F2 ) )
% 3.14/1.66 = F2 ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_191_case__prod__curry,axiom,
% 3.14/1.66 ! [F2: produc1821101996_sc_sz > set_Pr1389752855real_c] :
% 3.14/1.66 ( ( produc237521996real_c @ ( produc1827049067real_c @ F2 ) )
% 3.14/1.66 = F2 ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_192_case__prod__curry,axiom,
% 3.14/1.66 ! [F2: produc190496183real_c > produc190496183real_c] :
% 3.14/1.66 ( ( produc107375667real_c @ ( produc1119115220real_c @ F2 ) )
% 3.14/1.66 = F2 ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_193_case__prod__curry,axiom,
% 3.14/1.66 ! [F2: produc999471430t_unit > produc1821101996_sc_sz] :
% 3.14/1.66 ( ( produc435149849_sc_sz @ ( produc295339066_sc_sz @ F2 ) )
% 3.14/1.66 = F2 ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_194_case__swap,axiom,
% 3.14/1.66 ! [F2: denota610675952t_unit > produc866628903_sc_sz > produc190496183real_c,P2: produc1821101996_sc_sz] :
% 3.14/1.66 ( ( produc645763722real_c
% 3.14/1.66 @ ^ [Y4: produc866628903_sc_sz,X4: denota610675952t_unit] : ( F2 @ X4 @ Y4 )
% 3.14/1.66 @ ( produc532048446_sc_sz @ P2 ) )
% 3.14/1.66 = ( produc1575513068real_c @ F2 @ P2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_195_case__swap,axiom,
% 3.14/1.66 ! [F2: denota610675952t_unit > produc866628903_sc_sz > $o,P2: produc1821101996_sc_sz] :
% 3.14/1.66 ( ( produc1718498667unit_o
% 3.14/1.66 @ ^ [Y4: produc866628903_sc_sz,X4: denota610675952t_unit] : ( F2 @ X4 @ Y4 )
% 3.14/1.66 @ ( produc532048446_sc_sz @ P2 ) )
% 3.14/1.66 = ( produc619560141c_sz_o @ F2 @ P2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_196_case__swap,axiom,
% 3.14/1.66 ! [F2: denota610675952t_unit > produc866628903_sc_sz > set_Pr1389752855real_c,P2: produc1821101996_sc_sz] :
% 3.14/1.66 ( ( produc593754858real_c
% 3.14/1.66 @ ^ [Y4: produc866628903_sc_sz,X4: denota610675952t_unit] : ( F2 @ X4 @ Y4 )
% 3.14/1.66 @ ( produc532048446_sc_sz @ P2 ) )
% 3.14/1.66 = ( produc237521996real_c @ F2 @ P2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_197_case__swap,axiom,
% 3.14/1.66 ! [F2: produc866628903_sc_sz > denota610675952t_unit > produc1821101996_sc_sz,P2: produc999471430t_unit] :
% 3.14/1.66 ( ( produc448466487_sc_sz
% 3.14/1.66 @ ^ [Y4: denota610675952t_unit,X4: produc866628903_sc_sz] : ( F2 @ X4 @ Y4 )
% 3.14/1.66 @ ( produc245128480t_unit @ P2 ) )
% 3.14/1.66 = ( produc435149849_sc_sz @ F2 @ P2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_198_case__swap,axiom,
% 3.14/1.66 ! [F2: produc866628903_sc_sz > denota610675952t_unit > produc190496183real_c,P2: produc999471430t_unit] :
% 3.14/1.66 ( ( produc1575513068real_c
% 3.14/1.66 @ ^ [Y4: denota610675952t_unit,X4: produc866628903_sc_sz] : ( F2 @ X4 @ Y4 )
% 3.14/1.66 @ ( produc245128480t_unit @ P2 ) )
% 3.14/1.66 = ( produc645763722real_c @ F2 @ P2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_199_case__swap,axiom,
% 3.14/1.66 ! [F2: produc866628903_sc_sz > denota610675952t_unit > $o,P2: produc999471430t_unit] :
% 3.14/1.66 ( ( produc619560141c_sz_o
% 3.14/1.66 @ ^ [Y4: denota610675952t_unit,X4: produc866628903_sc_sz] : ( F2 @ X4 @ Y4 )
% 3.14/1.66 @ ( produc245128480t_unit @ P2 ) )
% 3.14/1.66 = ( produc1718498667unit_o @ F2 @ P2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_200_case__swap,axiom,
% 3.14/1.66 ! [F2: produc866628903_sc_sz > denota610675952t_unit > set_Pr1389752855real_c,P2: produc999471430t_unit] :
% 3.14/1.66 ( ( produc237521996real_c
% 3.14/1.66 @ ^ [Y4: denota610675952t_unit,X4: produc866628903_sc_sz] : ( F2 @ X4 @ Y4 )
% 3.14/1.66 @ ( produc245128480t_unit @ P2 ) )
% 3.14/1.66 = ( produc593754858real_c @ F2 @ P2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_201_case__swap,axiom,
% 3.14/1.66 ! [F2: finite1398487019real_c > finite1398487019real_c > produc190496183real_c,P2: produc190496183real_c] :
% 3.14/1.66 ( ( produc107375667real_c
% 3.14/1.66 @ ^ [Y4: finite1398487019real_c,X4: finite1398487019real_c] : ( F2 @ X4 @ Y4 )
% 3.14/1.66 @ ( produc704157711real_c @ P2 ) )
% 3.14/1.66 = ( produc107375667real_c @ F2 @ P2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_202_case__swap,axiom,
% 3.14/1.66 ! [F2: denota610675952t_unit > produc866628903_sc_sz > produc1821101996_sc_sz,P2: produc1821101996_sc_sz] :
% 3.14/1.66 ( ( produc435149849_sc_sz
% 3.14/1.66 @ ^ [Y4: produc866628903_sc_sz,X4: denota610675952t_unit] : ( F2 @ X4 @ Y4 )
% 3.14/1.66 @ ( produc532048446_sc_sz @ P2 ) )
% 3.14/1.66 = ( produc448466487_sc_sz @ F2 @ P2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_203_pair__imageI,axiom,
% 3.14/1.66 ! [A2: finite1398487019real_c,B2: finite1398487019real_c,A: set_Pr1389752855real_c,F2: finite1398487019real_c > finite1398487019real_c > produc190496183real_c] :
% 3.14/1.66 ( ( member1895684704real_c @ ( produc394644079real_c @ A2 @ B2 ) @ A )
% 3.14/1.66 => ( member1895684704real_c @ ( F2 @ A2 @ B2 ) @ ( image_738229701real_c @ ( produc107375667real_c @ F2 ) @ A ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_204_pair__imageI,axiom,
% 3.14/1.66 ! [A2: denota610675952t_unit,B2: produc866628903_sc_sz,A: set_Pr1169339874_sc_sz,F2: denota610675952t_unit > produc866628903_sc_sz > produc190496183real_c] :
% 3.14/1.66 ( ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ A2 @ B2 ) @ A )
% 3.14/1.66 => ( member1895684704real_c @ ( F2 @ A2 @ B2 ) @ ( image_386905412real_c @ ( produc1575513068real_c @ F2 ) @ A ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_205_pair__imageI,axiom,
% 3.14/1.66 ! [A2: finite1398487019real_c,B2: finite1398487019real_c,A: set_Pr1389752855real_c,F2: finite1398487019real_c > finite1398487019real_c > finite1398487019real_c] :
% 3.14/1.66 ( ( member1895684704real_c @ ( produc394644079real_c @ A2 @ B2 ) @ A )
% 3.14/1.66 => ( member1261661570real_c @ ( F2 @ A2 @ B2 ) @ ( image_14429021real_c @ ( produc567249007real_c @ F2 ) @ A ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_206_pair__imageI,axiom,
% 3.14/1.66 ! [A2: list_f1238882004_sc_sz,B2: list_f1238882004_sc_sz,A: set_Pr1774599175_sc_sz,F2: list_f1238882004_sc_sz > list_f1238882004_sc_sz > finite1398487019real_c] :
% 3.14/1.66 ( ( member245028432_sc_sz @ ( produc1822718231_sc_sz @ A2 @ B2 ) @ A )
% 3.14/1.66 => ( member1261661570real_c @ ( F2 @ A2 @ B2 ) @ ( image_1332486093real_c @ ( produc236226839real_c @ F2 ) @ A ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_207_pair__imageI,axiom,
% 3.14/1.66 ! [A2: list_f1238882004_sc_sz,B2: list_f1238882004_sc_sz,A: set_Pr1774599175_sc_sz,F2: list_f1238882004_sc_sz > list_f1238882004_sc_sz > produc190496183real_c] :
% 3.14/1.66 ( ( member245028432_sc_sz @ ( produc1822718231_sc_sz @ A2 @ B2 ) @ A )
% 3.14/1.66 => ( member1895684704real_c @ ( F2 @ A2 @ B2 ) @ ( image_1121381717real_c @ ( produc126255499real_c @ F2 ) @ A ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_208_pair__imageI,axiom,
% 3.14/1.66 ! [A2: finite1398487019real_c,B2: finite1398487019real_c,A: set_Pr1389752855real_c,F2: finite1398487019real_c > finite1398487019real_c > produc866628903_sc_sz] :
% 3.14/1.66 ( ( member1895684704real_c @ ( produc394644079real_c @ A2 @ B2 ) @ A )
% 3.14/1.66 => ( member245028432_sc_sz @ ( F2 @ A2 @ B2 ) @ ( image_388766773_sc_sz @ ( produc1341776291_sc_sz @ F2 ) @ A ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_209_pair__imageI,axiom,
% 3.14/1.66 ! [A2: produc190496183real_c,B2: produc190496183real_c,A: set_Pr754230471real_c,F2: produc190496183real_c > produc190496183real_c > finite1398487019real_c] :
% 3.14/1.66 ( ( member346808080real_c @ ( produc1687028567real_c @ A2 @ B2 ) @ A )
% 3.14/1.66 => ( member1261661570real_c @ ( F2 @ A2 @ B2 ) @ ( image_124598413real_c @ ( produc344593239real_c @ F2 ) @ A ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_210_pair__imageI,axiom,
% 3.14/1.66 ! [A2: denota610675952t_unit,B2: produc866628903_sc_sz,A: set_Pr1169339874_sc_sz,F2: denota610675952t_unit > produc866628903_sc_sz > $o] :
% 3.14/1.66 ( ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ A2 @ B2 ) @ A )
% 3.14/1.66 => ( member_o @ ( F2 @ A2 @ B2 ) @ ( image_1641704997c_sz_o @ ( produc619560141c_sz_o @ F2 ) @ A ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_211_pair__imageI,axiom,
% 3.14/1.66 ! [A2: denota610675952t_unit,B2: produc866628903_sc_sz,A: set_Pr1169339874_sc_sz,F2: denota610675952t_unit > produc866628903_sc_sz > finite1398487019real_c] :
% 3.14/1.66 ( ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ A2 @ B2 ) @ A )
% 3.14/1.66 => ( member1261661570real_c @ ( F2 @ A2 @ B2 ) @ ( image_1268968350real_c @ ( produc1920474870real_c @ F2 ) @ A ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_212_pair__imageI,axiom,
% 3.14/1.66 ! [A2: produc866628903_sc_sz,B2: denota610675952t_unit,A: set_Pr2041213564t_unit,F2: produc866628903_sc_sz > denota610675952t_unit > finite1398487019real_c] :
% 3.14/1.66 ( ( member235934813t_unit @ ( produc502616768t_unit @ A2 @ B2 ) @ A )
% 3.14/1.66 => ( member1261661570real_c @ ( F2 @ A2 @ B2 ) @ ( image_1269062456real_c @ ( produc1753599960real_c @ F2 ) @ A ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_213_curry__def,axiom,
% 3.14/1.66 ( produc1086673900c_sz_o
% 3.14/1.66 = ( ^ [C3: produc1821101996_sc_sz > $o,X4: denota610675952t_unit,Y4: produc866628903_sc_sz] : ( C3 @ ( produc789536734_sc_sz @ X4 @ Y4 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_214_curry__K,axiom,
% 3.14/1.66 ! [C2: $o] :
% 3.14/1.66 ( ( produc1086673900c_sz_o
% 3.14/1.66 @ ^ [X4: produc1821101996_sc_sz] : C2 )
% 3.14/1.66 = ( ^ [X4: denota610675952t_unit,Y4: produc866628903_sc_sz] : C2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_215_old_Oprod_Ocase,axiom,
% 3.14/1.66 ! [F2: denota610675952t_unit > produc866628903_sc_sz > produc190496183real_c,X1: denota610675952t_unit,X2: produc866628903_sc_sz] :
% 3.14/1.66 ( ( produc1575513068real_c @ F2 @ ( produc789536734_sc_sz @ X1 @ X2 ) )
% 3.14/1.66 = ( F2 @ X1 @ X2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_216_old_Oprod_Ocase,axiom,
% 3.14/1.66 ! [F2: denota610675952t_unit > produc866628903_sc_sz > $o,X1: denota610675952t_unit,X2: produc866628903_sc_sz] :
% 3.14/1.66 ( ( produc619560141c_sz_o @ F2 @ ( produc789536734_sc_sz @ X1 @ X2 ) )
% 3.14/1.66 = ( F2 @ X1 @ X2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_217_old_Oprod_Ocase,axiom,
% 3.14/1.66 ! [F2: denota610675952t_unit > produc866628903_sc_sz > set_Pr1389752855real_c,X1: denota610675952t_unit,X2: produc866628903_sc_sz] :
% 3.14/1.66 ( ( produc237521996real_c @ F2 @ ( produc789536734_sc_sz @ X1 @ X2 ) )
% 3.14/1.66 = ( F2 @ X1 @ X2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_218_old_Oprod_Ocase,axiom,
% 3.14/1.66 ! [F2: finite1398487019real_c > finite1398487019real_c > produc190496183real_c,X1: finite1398487019real_c,X2: finite1398487019real_c] :
% 3.14/1.66 ( ( produc107375667real_c @ F2 @ ( produc394644079real_c @ X1 @ X2 ) )
% 3.14/1.66 = ( F2 @ X1 @ X2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_219_old_Oprod_Ocase,axiom,
% 3.14/1.66 ! [F2: produc866628903_sc_sz > denota610675952t_unit > produc1821101996_sc_sz,X1: produc866628903_sc_sz,X2: denota610675952t_unit] :
% 3.14/1.66 ( ( produc435149849_sc_sz @ F2 @ ( produc502616768t_unit @ X1 @ X2 ) )
% 3.14/1.66 = ( F2 @ X1 @ X2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_220_mem__case__prodE,axiom,
% 3.14/1.66 ! [Z: produc190496183real_c,C2: denota610675952t_unit > produc866628903_sc_sz > set_Pr1389752855real_c,P2: produc1821101996_sc_sz] :
% 3.14/1.66 ( ( member1895684704real_c @ Z @ ( produc237521996real_c @ C2 @ P2 ) )
% 3.14/1.66 => ~ ! [X3: denota610675952t_unit,Y3: produc866628903_sc_sz] :
% 3.14/1.66 ( ( P2
% 3.14/1.66 = ( produc789536734_sc_sz @ X3 @ Y3 ) )
% 3.14/1.66 => ~ ( member1895684704real_c @ Z @ ( C2 @ X3 @ Y3 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_221_mem__case__prodE,axiom,
% 3.14/1.66 ! [Z: finite1398487019real_c,C2: finite1398487019real_c > finite1398487019real_c > set_Fi1407883041real_c,P2: produc190496183real_c] :
% 3.14/1.66 ( ( member1261661570real_c @ Z @ ( produc29022117real_c @ C2 @ P2 ) )
% 3.14/1.66 => ~ ! [X3: finite1398487019real_c,Y3: finite1398487019real_c] :
% 3.14/1.66 ( ( P2
% 3.14/1.66 = ( produc394644079real_c @ X3 @ Y3 ) )
% 3.14/1.66 => ~ ( member1261661570real_c @ Z @ ( C2 @ X3 @ Y3 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_222_mem__case__prodE,axiom,
% 3.14/1.66 ! [Z: finite1398487019real_c,C2: list_f1238882004_sc_sz > list_f1238882004_sc_sz > set_Fi1407883041real_c,P2: produc866628903_sc_sz] :
% 3.14/1.66 ( ( member1261661570real_c @ Z @ ( produc1449736269real_c @ C2 @ P2 ) )
% 3.14/1.66 => ~ ! [X3: list_f1238882004_sc_sz,Y3: list_f1238882004_sc_sz] :
% 3.14/1.66 ( ( P2
% 3.14/1.66 = ( produc1822718231_sc_sz @ X3 @ Y3 ) )
% 3.14/1.66 => ~ ( member1261661570real_c @ Z @ ( C2 @ X3 @ Y3 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_223_mem__case__prodE,axiom,
% 3.14/1.66 ! [Z: produc190496183real_c,C2: finite1398487019real_c > finite1398487019real_c > set_Pr1389752855real_c,P2: produc190496183real_c] :
% 3.14/1.66 ( ( member1895684704real_c @ Z @ ( produc923381907real_c @ C2 @ P2 ) )
% 3.14/1.66 => ~ ! [X3: finite1398487019real_c,Y3: finite1398487019real_c] :
% 3.14/1.66 ( ( P2
% 3.14/1.66 = ( produc394644079real_c @ X3 @ Y3 ) )
% 3.14/1.66 => ~ ( member1895684704real_c @ Z @ ( C2 @ X3 @ Y3 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_224_mem__case__prodE,axiom,
% 3.14/1.66 ! [Z: produc190496183real_c,C2: list_f1238882004_sc_sz > list_f1238882004_sc_sz > set_Pr1389752855real_c,P2: produc866628903_sc_sz] :
% 3.14/1.66 ( ( member1895684704real_c @ Z @ ( produc6841835real_c @ C2 @ P2 ) )
% 3.14/1.66 => ~ ! [X3: list_f1238882004_sc_sz,Y3: list_f1238882004_sc_sz] :
% 3.14/1.66 ( ( P2
% 3.14/1.66 = ( produc1822718231_sc_sz @ X3 @ Y3 ) )
% 3.14/1.66 => ~ ( member1895684704real_c @ Z @ ( C2 @ X3 @ Y3 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_225_mem__case__prodE,axiom,
% 3.14/1.66 ! [Z: produc866628903_sc_sz,C2: finite1398487019real_c > finite1398487019real_c > set_Pr1774599175_sc_sz,P2: produc190496183real_c] :
% 3.14/1.66 ( ( member245028432_sc_sz @ Z @ ( produc642283651_sc_sz @ C2 @ P2 ) )
% 3.14/1.66 => ~ ! [X3: finite1398487019real_c,Y3: finite1398487019real_c] :
% 3.14/1.66 ( ( P2
% 3.14/1.66 = ( produc394644079real_c @ X3 @ Y3 ) )
% 3.14/1.66 => ~ ( member245028432_sc_sz @ Z @ ( C2 @ X3 @ Y3 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_226_mem__case__prodE,axiom,
% 3.14/1.66 ! [Z: finite1398487019real_c,C2: produc190496183real_c > produc190496183real_c > set_Fi1407883041real_c,P2: produc640052711real_c] :
% 3.14/1.66 ( ( member1261661570real_c @ Z @ ( produc1066779277real_c @ C2 @ P2 ) )
% 3.14/1.66 => ~ ! [X3: produc190496183real_c,Y3: produc190496183real_c] :
% 3.14/1.66 ( ( P2
% 3.14/1.66 = ( produc1687028567real_c @ X3 @ Y3 ) )
% 3.14/1.66 => ~ ( member1261661570real_c @ Z @ ( C2 @ X3 @ Y3 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_227_mem__case__prodE,axiom,
% 3.14/1.66 ! [Z: finite1398487019real_c,C2: denota610675952t_unit > produc866628903_sc_sz > set_Fi1407883041real_c,P2: produc1821101996_sc_sz] :
% 3.14/1.66 ( ( member1261661570real_c @ Z @ ( produc2068697644real_c @ C2 @ P2 ) )
% 3.14/1.66 => ~ ! [X3: denota610675952t_unit,Y3: produc866628903_sc_sz] :
% 3.14/1.66 ( ( P2
% 3.14/1.66 = ( produc789536734_sc_sz @ X3 @ Y3 ) )
% 3.14/1.66 => ~ ( member1261661570real_c @ Z @ ( C2 @ X3 @ Y3 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_228_mem__case__prodE,axiom,
% 3.14/1.66 ! [Z: finite1398487019real_c,C2: produc866628903_sc_sz > denota610675952t_unit > set_Fi1407883041real_c,P2: produc999471430t_unit] :
% 3.14/1.66 ( ( member1261661570real_c @ Z @ ( produc1368849166real_c @ C2 @ P2 ) )
% 3.14/1.66 => ~ ! [X3: produc866628903_sc_sz,Y3: denota610675952t_unit] :
% 3.14/1.66 ( ( P2
% 3.14/1.66 = ( produc502616768t_unit @ X3 @ Y3 ) )
% 3.14/1.66 => ~ ( member1261661570real_c @ Z @ ( C2 @ X3 @ Y3 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_229_mem__case__prodE,axiom,
% 3.14/1.66 ! [Z: produc866628903_sc_sz,C2: list_f1238882004_sc_sz > list_f1238882004_sc_sz > set_Pr1774599175_sc_sz,P2: produc866628903_sc_sz] :
% 3.14/1.66 ( ( member245028432_sc_sz @ Z @ ( produc1563580891_sc_sz @ C2 @ P2 ) )
% 3.14/1.66 => ~ ! [X3: list_f1238882004_sc_sz,Y3: list_f1238882004_sc_sz] :
% 3.14/1.66 ( ( P2
% 3.14/1.66 = ( produc1822718231_sc_sz @ X3 @ Y3 ) )
% 3.14/1.66 => ~ ( member245028432_sc_sz @ Z @ ( C2 @ X3 @ Y3 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_230_prod_Ocase__distrib,axiom,
% 3.14/1.66 ! [H: $o > $o,F2: denota610675952t_unit > produc866628903_sc_sz > $o,Prod: produc1821101996_sc_sz] :
% 3.14/1.66 ( ( H @ ( produc619560141c_sz_o @ F2 @ Prod ) )
% 3.14/1.66 = ( produc619560141c_sz_o
% 3.14/1.66 @ ^ [X12: denota610675952t_unit,X22: produc866628903_sc_sz] : ( H @ ( F2 @ X12 @ X22 ) )
% 3.14/1.66 @ Prod ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_231_prod_Ocase__distrib,axiom,
% 3.14/1.66 ! [H: produc190496183real_c > produc190496183real_c,F2: finite1398487019real_c > finite1398487019real_c > produc190496183real_c,Prod: produc190496183real_c] :
% 3.14/1.66 ( ( H @ ( produc107375667real_c @ F2 @ Prod ) )
% 3.14/1.66 = ( produc107375667real_c
% 3.14/1.66 @ ^ [X12: finite1398487019real_c,X22: finite1398487019real_c] : ( H @ ( F2 @ X12 @ X22 ) )
% 3.14/1.66 @ Prod ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_232_prod_Ocase__distrib,axiom,
% 3.14/1.66 ! [H: produc190496183real_c > $o,F2: denota610675952t_unit > produc866628903_sc_sz > produc190496183real_c,Prod: produc1821101996_sc_sz] :
% 3.14/1.66 ( ( H @ ( produc1575513068real_c @ F2 @ Prod ) )
% 3.14/1.66 = ( produc619560141c_sz_o
% 3.14/1.66 @ ^ [X12: denota610675952t_unit,X22: produc866628903_sc_sz] : ( H @ ( F2 @ X12 @ X22 ) )
% 3.14/1.66 @ Prod ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_233_prod_Ocase__distrib,axiom,
% 3.14/1.66 ! [H: $o > produc190496183real_c,F2: denota610675952t_unit > produc866628903_sc_sz > $o,Prod: produc1821101996_sc_sz] :
% 3.14/1.66 ( ( H @ ( produc619560141c_sz_o @ F2 @ Prod ) )
% 3.14/1.66 = ( produc1575513068real_c
% 3.14/1.66 @ ^ [X12: denota610675952t_unit,X22: produc866628903_sc_sz] : ( H @ ( F2 @ X12 @ X22 ) )
% 3.14/1.66 @ Prod ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_234_prod_Ocase__distrib,axiom,
% 3.14/1.66 ! [H: $o > set_Pr1389752855real_c,F2: denota610675952t_unit > produc866628903_sc_sz > $o,Prod: produc1821101996_sc_sz] :
% 3.14/1.66 ( ( H @ ( produc619560141c_sz_o @ F2 @ Prod ) )
% 3.14/1.66 = ( produc237521996real_c
% 3.14/1.66 @ ^ [X12: denota610675952t_unit,X22: produc866628903_sc_sz] : ( H @ ( F2 @ X12 @ X22 ) )
% 3.14/1.66 @ Prod ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_235_prod_Ocase__distrib,axiom,
% 3.14/1.66 ! [H: set_Pr1389752855real_c > $o,F2: denota610675952t_unit > produc866628903_sc_sz > set_Pr1389752855real_c,Prod: produc1821101996_sc_sz] :
% 3.14/1.66 ( ( H @ ( produc237521996real_c @ F2 @ Prod ) )
% 3.14/1.66 = ( produc619560141c_sz_o
% 3.14/1.66 @ ^ [X12: denota610675952t_unit,X22: produc866628903_sc_sz] : ( H @ ( F2 @ X12 @ X22 ) )
% 3.14/1.66 @ Prod ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_236_prod_Ocase__distrib,axiom,
% 3.14/1.66 ! [H: produc190496183real_c > produc190496183real_c,F2: denota610675952t_unit > produc866628903_sc_sz > produc190496183real_c,Prod: produc1821101996_sc_sz] :
% 3.14/1.66 ( ( H @ ( produc1575513068real_c @ F2 @ Prod ) )
% 3.14/1.66 = ( produc1575513068real_c
% 3.14/1.66 @ ^ [X12: denota610675952t_unit,X22: produc866628903_sc_sz] : ( H @ ( F2 @ X12 @ X22 ) )
% 3.14/1.66 @ Prod ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_237_prod_Ocase__distrib,axiom,
% 3.14/1.66 ! [H: produc190496183real_c > set_Pr1389752855real_c,F2: denota610675952t_unit > produc866628903_sc_sz > produc190496183real_c,Prod: produc1821101996_sc_sz] :
% 3.14/1.66 ( ( H @ ( produc1575513068real_c @ F2 @ Prod ) )
% 3.14/1.66 = ( produc237521996real_c
% 3.14/1.66 @ ^ [X12: denota610675952t_unit,X22: produc866628903_sc_sz] : ( H @ ( F2 @ X12 @ X22 ) )
% 3.14/1.66 @ Prod ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_238_prod_Ocase__distrib,axiom,
% 3.14/1.66 ! [H: set_Pr1389752855real_c > produc190496183real_c,F2: denota610675952t_unit > produc866628903_sc_sz > set_Pr1389752855real_c,Prod: produc1821101996_sc_sz] :
% 3.14/1.66 ( ( H @ ( produc237521996real_c @ F2 @ Prod ) )
% 3.14/1.66 = ( produc1575513068real_c
% 3.14/1.66 @ ^ [X12: denota610675952t_unit,X22: produc866628903_sc_sz] : ( H @ ( F2 @ X12 @ X22 ) )
% 3.14/1.66 @ Prod ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_239_prod_Ocase__distrib,axiom,
% 3.14/1.66 ! [H: set_Pr1389752855real_c > set_Pr1389752855real_c,F2: denota610675952t_unit > produc866628903_sc_sz > set_Pr1389752855real_c,Prod: produc1821101996_sc_sz] :
% 3.14/1.66 ( ( H @ ( produc237521996real_c @ F2 @ Prod ) )
% 3.14/1.66 = ( produc237521996real_c
% 3.14/1.66 @ ^ [X12: denota610675952t_unit,X22: produc866628903_sc_sz] : ( H @ ( F2 @ X12 @ X22 ) )
% 3.14/1.66 @ Prod ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_240_cond__case__prod__eta,axiom,
% 3.14/1.66 ! [F2: denota610675952t_unit > produc866628903_sc_sz > produc190496183real_c,G: produc1821101996_sc_sz > produc190496183real_c] :
% 3.14/1.66 ( ! [X3: denota610675952t_unit,Y3: produc866628903_sc_sz] :
% 3.14/1.66 ( ( F2 @ X3 @ Y3 )
% 3.14/1.66 = ( G @ ( produc789536734_sc_sz @ X3 @ Y3 ) ) )
% 3.14/1.66 => ( ( produc1575513068real_c @ F2 )
% 3.14/1.66 = G ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_241_cond__case__prod__eta,axiom,
% 3.14/1.66 ! [F2: denota610675952t_unit > produc866628903_sc_sz > $o,G: produc1821101996_sc_sz > $o] :
% 3.14/1.66 ( ! [X3: denota610675952t_unit,Y3: produc866628903_sc_sz] :
% 3.14/1.66 ( ( F2 @ X3 @ Y3 )
% 3.14/1.66 = ( G @ ( produc789536734_sc_sz @ X3 @ Y3 ) ) )
% 3.14/1.66 => ( ( produc619560141c_sz_o @ F2 )
% 3.14/1.66 = G ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_242_cond__case__prod__eta,axiom,
% 3.14/1.66 ! [F2: denota610675952t_unit > produc866628903_sc_sz > set_Pr1389752855real_c,G: produc1821101996_sc_sz > set_Pr1389752855real_c] :
% 3.14/1.66 ( ! [X3: denota610675952t_unit,Y3: produc866628903_sc_sz] :
% 3.14/1.66 ( ( F2 @ X3 @ Y3 )
% 3.14/1.66 = ( G @ ( produc789536734_sc_sz @ X3 @ Y3 ) ) )
% 3.14/1.66 => ( ( produc237521996real_c @ F2 )
% 3.14/1.66 = G ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_243_cond__case__prod__eta,axiom,
% 3.14/1.66 ! [F2: finite1398487019real_c > finite1398487019real_c > produc190496183real_c,G: produc190496183real_c > produc190496183real_c] :
% 3.14/1.66 ( ! [X3: finite1398487019real_c,Y3: finite1398487019real_c] :
% 3.14/1.66 ( ( F2 @ X3 @ Y3 )
% 3.14/1.66 = ( G @ ( produc394644079real_c @ X3 @ Y3 ) ) )
% 3.14/1.66 => ( ( produc107375667real_c @ F2 )
% 3.14/1.66 = G ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_244_cond__case__prod__eta,axiom,
% 3.14/1.66 ! [F2: produc866628903_sc_sz > denota610675952t_unit > produc1821101996_sc_sz,G: produc999471430t_unit > produc1821101996_sc_sz] :
% 3.14/1.66 ( ! [X3: produc866628903_sc_sz,Y3: denota610675952t_unit] :
% 3.14/1.66 ( ( F2 @ X3 @ Y3 )
% 3.14/1.66 = ( G @ ( produc502616768t_unit @ X3 @ Y3 ) ) )
% 3.14/1.66 => ( ( produc435149849_sc_sz @ F2 )
% 3.14/1.66 = G ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_245_case__prod__eta,axiom,
% 3.14/1.66 ! [F2: produc1821101996_sc_sz > produc190496183real_c] :
% 3.14/1.66 ( ( produc1575513068real_c
% 3.14/1.66 @ ^ [X4: denota610675952t_unit,Y4: produc866628903_sc_sz] : ( F2 @ ( produc789536734_sc_sz @ X4 @ Y4 ) ) )
% 3.14/1.66 = F2 ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_246_case__prod__eta,axiom,
% 3.14/1.66 ! [F2: produc1821101996_sc_sz > $o] :
% 3.14/1.66 ( ( produc619560141c_sz_o
% 3.14/1.66 @ ^ [X4: denota610675952t_unit,Y4: produc866628903_sc_sz] : ( F2 @ ( produc789536734_sc_sz @ X4 @ Y4 ) ) )
% 3.14/1.66 = F2 ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_247_case__prod__eta,axiom,
% 3.14/1.66 ! [F2: produc1821101996_sc_sz > set_Pr1389752855real_c] :
% 3.14/1.66 ( ( produc237521996real_c
% 3.14/1.66 @ ^ [X4: denota610675952t_unit,Y4: produc866628903_sc_sz] : ( F2 @ ( produc789536734_sc_sz @ X4 @ Y4 ) ) )
% 3.14/1.66 = F2 ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_248_case__prod__eta,axiom,
% 3.14/1.66 ! [F2: produc190496183real_c > produc190496183real_c] :
% 3.14/1.66 ( ( produc107375667real_c
% 3.14/1.66 @ ^ [X4: finite1398487019real_c,Y4: finite1398487019real_c] : ( F2 @ ( produc394644079real_c @ X4 @ Y4 ) ) )
% 3.14/1.66 = F2 ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_249_case__prod__eta,axiom,
% 3.14/1.66 ! [F2: produc999471430t_unit > produc1821101996_sc_sz] :
% 3.14/1.66 ( ( produc435149849_sc_sz
% 3.14/1.66 @ ^ [X4: produc866628903_sc_sz,Y4: denota610675952t_unit] : ( F2 @ ( produc502616768t_unit @ X4 @ Y4 ) ) )
% 3.14/1.66 = F2 ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_250_case__prodE2,axiom,
% 3.14/1.66 ! [Q: produc190496183real_c > $o,P: denota610675952t_unit > produc866628903_sc_sz > produc190496183real_c,Z: produc1821101996_sc_sz] :
% 3.14/1.66 ( ( Q @ ( produc1575513068real_c @ P @ Z ) )
% 3.14/1.66 => ~ ! [X3: denota610675952t_unit,Y3: produc866628903_sc_sz] :
% 3.14/1.66 ( ( Z
% 3.14/1.66 = ( produc789536734_sc_sz @ X3 @ Y3 ) )
% 3.14/1.66 => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_251_case__prodE2,axiom,
% 3.14/1.66 ! [Q: $o > $o,P: denota610675952t_unit > produc866628903_sc_sz > $o,Z: produc1821101996_sc_sz] :
% 3.14/1.66 ( ( Q @ ( produc619560141c_sz_o @ P @ Z ) )
% 3.14/1.66 => ~ ! [X3: denota610675952t_unit,Y3: produc866628903_sc_sz] :
% 3.14/1.66 ( ( Z
% 3.14/1.66 = ( produc789536734_sc_sz @ X3 @ Y3 ) )
% 3.14/1.66 => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_252_case__prodE2,axiom,
% 3.14/1.66 ! [Q: set_Pr1389752855real_c > $o,P: denota610675952t_unit > produc866628903_sc_sz > set_Pr1389752855real_c,Z: produc1821101996_sc_sz] :
% 3.14/1.66 ( ( Q @ ( produc237521996real_c @ P @ Z ) )
% 3.14/1.66 => ~ ! [X3: denota610675952t_unit,Y3: produc866628903_sc_sz] :
% 3.14/1.66 ( ( Z
% 3.14/1.66 = ( produc789536734_sc_sz @ X3 @ Y3 ) )
% 3.14/1.66 => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_253_case__prodE2,axiom,
% 3.14/1.66 ! [Q: produc190496183real_c > $o,P: finite1398487019real_c > finite1398487019real_c > produc190496183real_c,Z: produc190496183real_c] :
% 3.14/1.66 ( ( Q @ ( produc107375667real_c @ P @ Z ) )
% 3.14/1.66 => ~ ! [X3: finite1398487019real_c,Y3: finite1398487019real_c] :
% 3.14/1.66 ( ( Z
% 3.14/1.66 = ( produc394644079real_c @ X3 @ Y3 ) )
% 3.14/1.66 => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_254_case__prodE2,axiom,
% 3.14/1.66 ! [Q: produc1821101996_sc_sz > $o,P: produc866628903_sc_sz > denota610675952t_unit > produc1821101996_sc_sz,Z: produc999471430t_unit] :
% 3.14/1.66 ( ( Q @ ( produc435149849_sc_sz @ P @ Z ) )
% 3.14/1.66 => ~ ! [X3: produc866628903_sc_sz,Y3: denota610675952t_unit] :
% 3.14/1.66 ( ( Z
% 3.14/1.66 = ( produc502616768t_unit @ X3 @ Y3 ) )
% 3.14/1.66 => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_255_case__prodE,axiom,
% 3.14/1.66 ! [C2: list_f1238882004_sc_sz > list_f1238882004_sc_sz > $o,P2: produc866628903_sc_sz] :
% 3.14/1.66 ( ( produc2039065452c_sz_o @ C2 @ P2 )
% 3.14/1.66 => ~ ! [X3: list_f1238882004_sc_sz,Y3: list_f1238882004_sc_sz] :
% 3.14/1.66 ( ( P2
% 3.14/1.66 = ( produc1822718231_sc_sz @ X3 @ Y3 ) )
% 3.14/1.66 => ~ ( C2 @ X3 @ Y3 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_256_case__prodE,axiom,
% 3.14/1.66 ! [C2: finite1398487019real_c > finite1398487019real_c > $o,P2: produc190496183real_c] :
% 3.14/1.66 ( ( produc353381908al_c_o @ C2 @ P2 )
% 3.14/1.66 => ~ ! [X3: finite1398487019real_c,Y3: finite1398487019real_c] :
% 3.14/1.66 ( ( P2
% 3.14/1.66 = ( produc394644079real_c @ X3 @ Y3 ) )
% 3.14/1.66 => ~ ( C2 @ X3 @ Y3 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_257_case__prodE,axiom,
% 3.14/1.66 ! [C2: produc866628903_sc_sz > denota610675952t_unit > $o,P2: produc999471430t_unit] :
% 3.14/1.66 ( ( produc1718498667unit_o @ C2 @ P2 )
% 3.14/1.66 => ~ ! [X3: produc866628903_sc_sz,Y3: denota610675952t_unit] :
% 3.14/1.66 ( ( P2
% 3.14/1.66 = ( produc502616768t_unit @ X3 @ Y3 ) )
% 3.14/1.66 => ~ ( C2 @ X3 @ Y3 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_258_case__prodE,axiom,
% 3.14/1.66 ! [C2: produc190496183real_c > produc190496183real_c > $o,P2: produc640052711real_c] :
% 3.14/1.66 ( ( produc1726730540al_c_o @ C2 @ P2 )
% 3.14/1.66 => ~ ! [X3: produc190496183real_c,Y3: produc190496183real_c] :
% 3.14/1.66 ( ( P2
% 3.14/1.66 = ( produc1687028567real_c @ X3 @ Y3 ) )
% 3.14/1.66 => ~ ( C2 @ X3 @ Y3 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_259_case__prodE,axiom,
% 3.14/1.66 ! [C2: denota610675952t_unit > produc866628903_sc_sz > $o,P2: produc1821101996_sc_sz] :
% 3.14/1.66 ( ( produc619560141c_sz_o @ C2 @ P2 )
% 3.14/1.66 => ~ ! [X3: denota610675952t_unit,Y3: produc866628903_sc_sz] :
% 3.14/1.66 ( ( P2
% 3.14/1.66 = ( produc789536734_sc_sz @ X3 @ Y3 ) )
% 3.14/1.66 => ~ ( C2 @ X3 @ Y3 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_260_case__prodD,axiom,
% 3.14/1.66 ! [F2: list_f1238882004_sc_sz > list_f1238882004_sc_sz > $o,A2: list_f1238882004_sc_sz,B2: list_f1238882004_sc_sz] :
% 3.14/1.66 ( ( produc2039065452c_sz_o @ F2 @ ( produc1822718231_sc_sz @ A2 @ B2 ) )
% 3.14/1.66 => ( F2 @ A2 @ B2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_261_case__prodD,axiom,
% 3.14/1.66 ! [F2: finite1398487019real_c > finite1398487019real_c > $o,A2: finite1398487019real_c,B2: finite1398487019real_c] :
% 3.14/1.66 ( ( produc353381908al_c_o @ F2 @ ( produc394644079real_c @ A2 @ B2 ) )
% 3.14/1.66 => ( F2 @ A2 @ B2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_262_case__prodD,axiom,
% 3.14/1.66 ! [F2: produc866628903_sc_sz > denota610675952t_unit > $o,A2: produc866628903_sc_sz,B2: denota610675952t_unit] :
% 3.14/1.66 ( ( produc1718498667unit_o @ F2 @ ( produc502616768t_unit @ A2 @ B2 ) )
% 3.14/1.66 => ( F2 @ A2 @ B2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_263_case__prodD,axiom,
% 3.14/1.66 ! [F2: produc190496183real_c > produc190496183real_c > $o,A2: produc190496183real_c,B2: produc190496183real_c] :
% 3.14/1.66 ( ( produc1726730540al_c_o @ F2 @ ( produc1687028567real_c @ A2 @ B2 ) )
% 3.14/1.66 => ( F2 @ A2 @ B2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_264_case__prodD,axiom,
% 3.14/1.66 ! [F2: denota610675952t_unit > produc866628903_sc_sz > $o,A2: denota610675952t_unit,B2: produc866628903_sc_sz] :
% 3.14/1.66 ( ( produc619560141c_sz_o @ F2 @ ( produc789536734_sc_sz @ A2 @ B2 ) )
% 3.14/1.66 => ( F2 @ A2 @ B2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_265_image__ident,axiom,
% 3.14/1.66 ! [Y5: set_Pr1389752855real_c] :
% 3.14/1.66 ( ( image_738229701real_c
% 3.14/1.66 @ ^ [X4: produc190496183real_c] : X4
% 3.14/1.66 @ Y5 )
% 3.14/1.66 = Y5 ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_266_image__eqI,axiom,
% 3.14/1.66 ! [B2: produc190496183real_c,F2: produc190496183real_c > produc190496183real_c,X: produc190496183real_c,A: set_Pr1389752855real_c] :
% 3.14/1.66 ( ( B2
% 3.14/1.66 = ( F2 @ X ) )
% 3.14/1.66 => ( ( member1895684704real_c @ X @ A )
% 3.14/1.66 => ( member1895684704real_c @ B2 @ ( image_738229701real_c @ F2 @ A ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_267_image__eqI,axiom,
% 3.14/1.66 ! [B2: finite1398487019real_c,F2: finite1398487019real_c > finite1398487019real_c,X: finite1398487019real_c,A: set_Fi1407883041real_c] :
% 3.14/1.66 ( ( B2
% 3.14/1.66 = ( F2 @ X ) )
% 3.14/1.66 => ( ( member1261661570real_c @ X @ A )
% 3.14/1.66 => ( member1261661570real_c @ B2 @ ( image_1514048989real_c @ F2 @ A ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_268_image__eqI,axiom,
% 3.14/1.66 ! [B2: finite1398487019real_c,F2: produc190496183real_c > finite1398487019real_c,X: produc190496183real_c,A: set_Pr1389752855real_c] :
% 3.14/1.66 ( ( B2
% 3.14/1.66 = ( F2 @ X ) )
% 3.14/1.66 => ( ( member1895684704real_c @ X @ A )
% 3.14/1.66 => ( member1261661570real_c @ B2 @ ( image_14429021real_c @ F2 @ A ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_269_image__eqI,axiom,
% 3.14/1.66 ! [B2: produc190496183real_c,F2: finite1398487019real_c > produc190496183real_c,X: finite1398487019real_c,A: set_Fi1407883041real_c] :
% 3.14/1.66 ( ( B2
% 3.14/1.66 = ( F2 @ X ) )
% 3.14/1.66 => ( ( member1261661570real_c @ X @ A )
% 3.14/1.66 => ( member1895684704real_c @ B2 @ ( image_1461287749real_c @ F2 @ A ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_270_image__eqI,axiom,
% 3.14/1.66 ! [B2: produc866628903_sc_sz,F2: finite1398487019real_c > produc866628903_sc_sz,X: finite1398487019real_c,A: set_Fi1407883041real_c] :
% 3.14/1.66 ( ( B2
% 3.14/1.66 = ( F2 @ X ) )
% 3.14/1.66 => ( ( member1261661570real_c @ X @ A )
% 3.14/1.66 => ( member245028432_sc_sz @ B2 @ ( image_290183605_sc_sz @ F2 @ A ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_271_image__eqI,axiom,
% 3.14/1.66 ! [B2: finite1398487019real_c,F2: produc866628903_sc_sz > finite1398487019real_c,X: produc866628903_sc_sz,A: set_Pr1774599175_sc_sz] :
% 3.14/1.66 ( ( B2
% 3.14/1.66 = ( F2 @ X ) )
% 3.14/1.66 => ( ( member245028432_sc_sz @ X @ A )
% 3.14/1.66 => ( member1261661570real_c @ B2 @ ( image_1332486093real_c @ F2 @ A ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_272_image__eqI,axiom,
% 3.14/1.66 ! [B2: produc866628903_sc_sz,F2: produc190496183real_c > produc866628903_sc_sz,X: produc190496183real_c,A: set_Pr1389752855real_c] :
% 3.14/1.66 ( ( B2
% 3.14/1.66 = ( F2 @ X ) )
% 3.14/1.66 => ( ( member1895684704real_c @ X @ A )
% 3.14/1.66 => ( member245028432_sc_sz @ B2 @ ( image_388766773_sc_sz @ F2 @ A ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_273_image__eqI,axiom,
% 3.14/1.66 ! [B2: produc640052711real_c,F2: finite1398487019real_c > produc640052711real_c,X: finite1398487019real_c,A: set_Fi1407883041real_c] :
% 3.14/1.66 ( ( B2
% 3.14/1.66 = ( F2 @ X ) )
% 3.14/1.66 => ( ( member1261661570real_c @ X @ A )
% 3.14/1.66 => ( member346808080real_c @ B2 @ ( image_1746662005real_c @ F2 @ A ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_274_image__eqI,axiom,
% 3.14/1.66 ! [B2: finite1398487019real_c,F2: produc640052711real_c > finite1398487019real_c,X: produc640052711real_c,A: set_Pr754230471real_c] :
% 3.14/1.66 ( ( B2
% 3.14/1.66 = ( F2 @ X ) )
% 3.14/1.66 => ( ( member346808080real_c @ X @ A )
% 3.14/1.66 => ( member1261661570real_c @ B2 @ ( image_124598413real_c @ F2 @ A ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_275_image__eqI,axiom,
% 3.14/1.66 ! [B2: produc190496183real_c,F2: produc866628903_sc_sz > produc190496183real_c,X: produc866628903_sc_sz,A: set_Pr1774599175_sc_sz] :
% 3.14/1.66 ( ( B2
% 3.14/1.66 = ( F2 @ X ) )
% 3.14/1.66 => ( ( member245028432_sc_sz @ X @ A )
% 3.14/1.66 => ( member1895684704real_c @ B2 @ ( image_1121381717real_c @ F2 @ A ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_276_split__part,axiom,
% 3.14/1.66 ! [P: $o,Q: denota610675952t_unit > produc866628903_sc_sz > $o] :
% 3.14/1.66 ( ( produc619560141c_sz_o
% 3.14/1.66 @ ^ [A5: denota610675952t_unit,B5: produc866628903_sc_sz] :
% 3.14/1.66 ( P
% 3.14/1.66 & ( Q @ A5 @ B5 ) ) )
% 3.14/1.66 = ( ^ [Ab: produc1821101996_sc_sz] :
% 3.14/1.66 ( P
% 3.14/1.66 & ( produc619560141c_sz_o @ Q @ Ab ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_277_prod_Odisc__eq__case,axiom,
% 3.14/1.66 ! [Prod: produc1821101996_sc_sz] :
% 3.14/1.66 ( produc619560141c_sz_o
% 3.14/1.66 @ ^ [Uu: denota610675952t_unit,Uv: produc866628903_sc_sz] : $true
% 3.14/1.66 @ Prod ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_278_rev__image__eqI,axiom,
% 3.14/1.66 ! [X: produc190496183real_c,A: set_Pr1389752855real_c,B2: produc190496183real_c,F2: produc190496183real_c > produc190496183real_c] :
% 3.14/1.66 ( ( member1895684704real_c @ X @ A )
% 3.14/1.66 => ( ( B2
% 3.14/1.66 = ( F2 @ X ) )
% 3.14/1.66 => ( member1895684704real_c @ B2 @ ( image_738229701real_c @ F2 @ A ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_279_rev__image__eqI,axiom,
% 3.14/1.66 ! [X: finite1398487019real_c,A: set_Fi1407883041real_c,B2: finite1398487019real_c,F2: finite1398487019real_c > finite1398487019real_c] :
% 3.14/1.66 ( ( member1261661570real_c @ X @ A )
% 3.14/1.66 => ( ( B2
% 3.14/1.66 = ( F2 @ X ) )
% 3.14/1.66 => ( member1261661570real_c @ B2 @ ( image_1514048989real_c @ F2 @ A ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_280_rev__image__eqI,axiom,
% 3.14/1.66 ! [X: produc190496183real_c,A: set_Pr1389752855real_c,B2: finite1398487019real_c,F2: produc190496183real_c > finite1398487019real_c] :
% 3.14/1.66 ( ( member1895684704real_c @ X @ A )
% 3.14/1.66 => ( ( B2
% 3.14/1.66 = ( F2 @ X ) )
% 3.14/1.66 => ( member1261661570real_c @ B2 @ ( image_14429021real_c @ F2 @ A ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_281_rev__image__eqI,axiom,
% 3.14/1.66 ! [X: finite1398487019real_c,A: set_Fi1407883041real_c,B2: produc190496183real_c,F2: finite1398487019real_c > produc190496183real_c] :
% 3.14/1.66 ( ( member1261661570real_c @ X @ A )
% 3.14/1.66 => ( ( B2
% 3.14/1.66 = ( F2 @ X ) )
% 3.14/1.66 => ( member1895684704real_c @ B2 @ ( image_1461287749real_c @ F2 @ A ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_282_rev__image__eqI,axiom,
% 3.14/1.66 ! [X: finite1398487019real_c,A: set_Fi1407883041real_c,B2: produc866628903_sc_sz,F2: finite1398487019real_c > produc866628903_sc_sz] :
% 3.14/1.66 ( ( member1261661570real_c @ X @ A )
% 3.14/1.66 => ( ( B2
% 3.14/1.66 = ( F2 @ X ) )
% 3.14/1.66 => ( member245028432_sc_sz @ B2 @ ( image_290183605_sc_sz @ F2 @ A ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_283_rev__image__eqI,axiom,
% 3.14/1.66 ! [X: produc866628903_sc_sz,A: set_Pr1774599175_sc_sz,B2: finite1398487019real_c,F2: produc866628903_sc_sz > finite1398487019real_c] :
% 3.14/1.66 ( ( member245028432_sc_sz @ X @ A )
% 3.14/1.66 => ( ( B2
% 3.14/1.66 = ( F2 @ X ) )
% 3.14/1.66 => ( member1261661570real_c @ B2 @ ( image_1332486093real_c @ F2 @ A ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_284_rev__image__eqI,axiom,
% 3.14/1.66 ! [X: produc190496183real_c,A: set_Pr1389752855real_c,B2: produc866628903_sc_sz,F2: produc190496183real_c > produc866628903_sc_sz] :
% 3.14/1.66 ( ( member1895684704real_c @ X @ A )
% 3.14/1.66 => ( ( B2
% 3.14/1.66 = ( F2 @ X ) )
% 3.14/1.66 => ( member245028432_sc_sz @ B2 @ ( image_388766773_sc_sz @ F2 @ A ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_285_rev__image__eqI,axiom,
% 3.14/1.66 ! [X: finite1398487019real_c,A: set_Fi1407883041real_c,B2: produc640052711real_c,F2: finite1398487019real_c > produc640052711real_c] :
% 3.14/1.66 ( ( member1261661570real_c @ X @ A )
% 3.14/1.66 => ( ( B2
% 3.14/1.66 = ( F2 @ X ) )
% 3.14/1.66 => ( member346808080real_c @ B2 @ ( image_1746662005real_c @ F2 @ A ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_286_rev__image__eqI,axiom,
% 3.14/1.66 ! [X: produc640052711real_c,A: set_Pr754230471real_c,B2: finite1398487019real_c,F2: produc640052711real_c > finite1398487019real_c] :
% 3.14/1.66 ( ( member346808080real_c @ X @ A )
% 3.14/1.66 => ( ( B2
% 3.14/1.66 = ( F2 @ X ) )
% 3.14/1.66 => ( member1261661570real_c @ B2 @ ( image_124598413real_c @ F2 @ A ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_287_rev__image__eqI,axiom,
% 3.14/1.66 ! [X: produc866628903_sc_sz,A: set_Pr1774599175_sc_sz,B2: produc190496183real_c,F2: produc866628903_sc_sz > produc190496183real_c] :
% 3.14/1.66 ( ( member245028432_sc_sz @ X @ A )
% 3.14/1.66 => ( ( B2
% 3.14/1.66 = ( F2 @ X ) )
% 3.14/1.66 => ( member1895684704real_c @ B2 @ ( image_1121381717real_c @ F2 @ A ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_288_ball__imageD,axiom,
% 3.14/1.66 ! [F2: produc1821101996_sc_sz > produc190496183real_c,A: set_Pr1169339874_sc_sz,P: produc190496183real_c > $o] :
% 3.14/1.66 ( ! [X3: produc190496183real_c] :
% 3.14/1.66 ( ( member1895684704real_c @ X3 @ ( image_386905412real_c @ F2 @ A ) )
% 3.14/1.66 => ( P @ X3 ) )
% 3.14/1.66 => ! [X5: produc1821101996_sc_sz] :
% 3.14/1.66 ( ( member1057565379_sc_sz @ X5 @ A )
% 3.14/1.66 => ( P @ ( F2 @ X5 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_289_ball__imageD,axiom,
% 3.14/1.66 ! [F2: produc1821101996_sc_sz > produc999471430t_unit,A: set_Pr1169339874_sc_sz,P: produc999471430t_unit > $o] :
% 3.14/1.66 ( ! [X3: produc999471430t_unit] :
% 3.14/1.66 ( ( member235934813t_unit @ X3 @ ( image_904562809t_unit @ F2 @ A ) )
% 3.14/1.66 => ( P @ X3 ) )
% 3.14/1.66 => ! [X5: produc1821101996_sc_sz] :
% 3.14/1.66 ( ( member1057565379_sc_sz @ X5 @ A )
% 3.14/1.66 => ( P @ ( F2 @ X5 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_290_ball__imageD,axiom,
% 3.14/1.66 ! [F2: produc190496183real_c > produc1821101996_sc_sz,A: set_Pr1389752855real_c,P: produc1821101996_sc_sz > $o] :
% 3.14/1.66 ( ! [X3: produc1821101996_sc_sz] :
% 3.14/1.66 ( ( member1057565379_sc_sz @ X3 @ ( image_1259833374_sc_sz @ F2 @ A ) )
% 3.14/1.66 => ( P @ X3 ) )
% 3.14/1.66 => ! [X5: produc190496183real_c] :
% 3.14/1.66 ( ( member1895684704real_c @ X5 @ A )
% 3.14/1.66 => ( P @ ( F2 @ X5 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_291_ball__imageD,axiom,
% 3.14/1.66 ! [F2: produc190496183real_c > produc190496183real_c,A: set_Pr1389752855real_c,P: produc190496183real_c > $o] :
% 3.14/1.66 ( ! [X3: produc190496183real_c] :
% 3.14/1.66 ( ( member1895684704real_c @ X3 @ ( image_738229701real_c @ F2 @ A ) )
% 3.14/1.66 => ( P @ X3 ) )
% 3.14/1.66 => ! [X5: produc190496183real_c] :
% 3.14/1.66 ( ( member1895684704real_c @ X5 @ A )
% 3.14/1.66 => ( P @ ( F2 @ X5 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_292_ball__imageD,axiom,
% 3.14/1.66 ! [F2: produc999471430t_unit > produc1821101996_sc_sz,A: set_Pr2041213564t_unit,P: produc1821101996_sc_sz > $o] :
% 3.14/1.66 ( ! [X3: produc1821101996_sc_sz] :
% 3.14/1.66 ( ( member1057565379_sc_sz @ X3 @ ( image_1426741113_sc_sz @ F2 @ A ) )
% 3.14/1.66 => ( P @ X3 ) )
% 3.14/1.66 => ! [X5: produc999471430t_unit] :
% 3.14/1.66 ( ( member235934813t_unit @ X5 @ A )
% 3.14/1.66 => ( P @ ( F2 @ X5 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_293_image__cong,axiom,
% 3.14/1.66 ! [M: set_Pr1389752855real_c,N: set_Pr1389752855real_c,F2: produc190496183real_c > produc1821101996_sc_sz,G: produc190496183real_c > produc1821101996_sc_sz] :
% 3.14/1.66 ( ( M = N )
% 3.14/1.66 => ( ! [X3: produc190496183real_c] :
% 3.14/1.66 ( ( member1895684704real_c @ X3 @ N )
% 3.14/1.66 => ( ( F2 @ X3 )
% 3.14/1.66 = ( G @ X3 ) ) )
% 3.14/1.66 => ( ( image_1259833374_sc_sz @ F2 @ M )
% 3.14/1.66 = ( image_1259833374_sc_sz @ G @ N ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_294_image__cong,axiom,
% 3.14/1.66 ! [M: set_Pr1389752855real_c,N: set_Pr1389752855real_c,F2: produc190496183real_c > produc190496183real_c,G: produc190496183real_c > produc190496183real_c] :
% 3.14/1.66 ( ( M = N )
% 3.14/1.66 => ( ! [X3: produc190496183real_c] :
% 3.14/1.66 ( ( member1895684704real_c @ X3 @ N )
% 3.14/1.66 => ( ( F2 @ X3 )
% 3.14/1.66 = ( G @ X3 ) ) )
% 3.14/1.66 => ( ( image_738229701real_c @ F2 @ M )
% 3.14/1.66 = ( image_738229701real_c @ G @ N ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_295_image__cong,axiom,
% 3.14/1.66 ! [M: set_Pr1169339874_sc_sz,N: set_Pr1169339874_sc_sz,F2: produc1821101996_sc_sz > produc190496183real_c,G: produc1821101996_sc_sz > produc190496183real_c] :
% 3.14/1.66 ( ( M = N )
% 3.14/1.66 => ( ! [X3: produc1821101996_sc_sz] :
% 3.14/1.66 ( ( member1057565379_sc_sz @ X3 @ N )
% 3.14/1.66 => ( ( F2 @ X3 )
% 3.14/1.66 = ( G @ X3 ) ) )
% 3.14/1.66 => ( ( image_386905412real_c @ F2 @ M )
% 3.14/1.66 = ( image_386905412real_c @ G @ N ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_296_image__cong,axiom,
% 3.14/1.66 ! [M: set_Pr1169339874_sc_sz,N: set_Pr1169339874_sc_sz,F2: produc1821101996_sc_sz > produc999471430t_unit,G: produc1821101996_sc_sz > produc999471430t_unit] :
% 3.14/1.66 ( ( M = N )
% 3.14/1.66 => ( ! [X3: produc1821101996_sc_sz] :
% 3.14/1.66 ( ( member1057565379_sc_sz @ X3 @ N )
% 3.14/1.66 => ( ( F2 @ X3 )
% 3.14/1.66 = ( G @ X3 ) ) )
% 3.14/1.66 => ( ( image_904562809t_unit @ F2 @ M )
% 3.14/1.66 = ( image_904562809t_unit @ G @ N ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_297_image__cong,axiom,
% 3.14/1.66 ! [M: set_Pr2041213564t_unit,N: set_Pr2041213564t_unit,F2: produc999471430t_unit > produc1821101996_sc_sz,G: produc999471430t_unit > produc1821101996_sc_sz] :
% 3.14/1.66 ( ( M = N )
% 3.14/1.66 => ( ! [X3: produc999471430t_unit] :
% 3.14/1.66 ( ( member235934813t_unit @ X3 @ N )
% 3.14/1.66 => ( ( F2 @ X3 )
% 3.14/1.66 = ( G @ X3 ) ) )
% 3.14/1.66 => ( ( image_1426741113_sc_sz @ F2 @ M )
% 3.14/1.66 = ( image_1426741113_sc_sz @ G @ N ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_298_bex__imageD,axiom,
% 3.14/1.66 ! [F2: produc1821101996_sc_sz > produc190496183real_c,A: set_Pr1169339874_sc_sz,P: produc190496183real_c > $o] :
% 3.14/1.66 ( ? [X5: produc190496183real_c] :
% 3.14/1.66 ( ( member1895684704real_c @ X5 @ ( image_386905412real_c @ F2 @ A ) )
% 3.14/1.66 & ( P @ X5 ) )
% 3.14/1.66 => ? [X3: produc1821101996_sc_sz] :
% 3.14/1.66 ( ( member1057565379_sc_sz @ X3 @ A )
% 3.14/1.66 & ( P @ ( F2 @ X3 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_299_bex__imageD,axiom,
% 3.14/1.66 ! [F2: produc1821101996_sc_sz > produc999471430t_unit,A: set_Pr1169339874_sc_sz,P: produc999471430t_unit > $o] :
% 3.14/1.66 ( ? [X5: produc999471430t_unit] :
% 3.14/1.66 ( ( member235934813t_unit @ X5 @ ( image_904562809t_unit @ F2 @ A ) )
% 3.14/1.66 & ( P @ X5 ) )
% 3.14/1.66 => ? [X3: produc1821101996_sc_sz] :
% 3.14/1.66 ( ( member1057565379_sc_sz @ X3 @ A )
% 3.14/1.66 & ( P @ ( F2 @ X3 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_300_bex__imageD,axiom,
% 3.14/1.66 ! [F2: produc190496183real_c > produc1821101996_sc_sz,A: set_Pr1389752855real_c,P: produc1821101996_sc_sz > $o] :
% 3.14/1.66 ( ? [X5: produc1821101996_sc_sz] :
% 3.14/1.66 ( ( member1057565379_sc_sz @ X5 @ ( image_1259833374_sc_sz @ F2 @ A ) )
% 3.14/1.66 & ( P @ X5 ) )
% 3.14/1.66 => ? [X3: produc190496183real_c] :
% 3.14/1.66 ( ( member1895684704real_c @ X3 @ A )
% 3.14/1.66 & ( P @ ( F2 @ X3 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_301_bex__imageD,axiom,
% 3.14/1.66 ! [F2: produc190496183real_c > produc190496183real_c,A: set_Pr1389752855real_c,P: produc190496183real_c > $o] :
% 3.14/1.66 ( ? [X5: produc190496183real_c] :
% 3.14/1.66 ( ( member1895684704real_c @ X5 @ ( image_738229701real_c @ F2 @ A ) )
% 3.14/1.66 & ( P @ X5 ) )
% 3.14/1.66 => ? [X3: produc190496183real_c] :
% 3.14/1.66 ( ( member1895684704real_c @ X3 @ A )
% 3.14/1.66 & ( P @ ( F2 @ X3 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_302_bex__imageD,axiom,
% 3.14/1.66 ! [F2: produc999471430t_unit > produc1821101996_sc_sz,A: set_Pr2041213564t_unit,P: produc1821101996_sc_sz > $o] :
% 3.14/1.66 ( ? [X5: produc1821101996_sc_sz] :
% 3.14/1.66 ( ( member1057565379_sc_sz @ X5 @ ( image_1426741113_sc_sz @ F2 @ A ) )
% 3.14/1.66 & ( P @ X5 ) )
% 3.14/1.66 => ? [X3: produc999471430t_unit] :
% 3.14/1.66 ( ( member235934813t_unit @ X3 @ A )
% 3.14/1.66 & ( P @ ( F2 @ X3 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_303_image__iff,axiom,
% 3.14/1.66 ! [Z: produc190496183real_c,F2: produc1821101996_sc_sz > produc190496183real_c,A: set_Pr1169339874_sc_sz] :
% 3.14/1.66 ( ( member1895684704real_c @ Z @ ( image_386905412real_c @ F2 @ A ) )
% 3.14/1.66 = ( ? [X4: produc1821101996_sc_sz] :
% 3.14/1.66 ( ( member1057565379_sc_sz @ X4 @ A )
% 3.14/1.66 & ( Z
% 3.14/1.66 = ( F2 @ X4 ) ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_304_image__iff,axiom,
% 3.14/1.66 ! [Z: produc190496183real_c,F2: produc190496183real_c > produc190496183real_c,A: set_Pr1389752855real_c] :
% 3.14/1.66 ( ( member1895684704real_c @ Z @ ( image_738229701real_c @ F2 @ A ) )
% 3.14/1.66 = ( ? [X4: produc190496183real_c] :
% 3.14/1.66 ( ( member1895684704real_c @ X4 @ A )
% 3.14/1.66 & ( Z
% 3.14/1.66 = ( F2 @ X4 ) ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_305_image__iff,axiom,
% 3.14/1.66 ! [Z: produc1821101996_sc_sz,F2: produc190496183real_c > produc1821101996_sc_sz,A: set_Pr1389752855real_c] :
% 3.14/1.66 ( ( member1057565379_sc_sz @ Z @ ( image_1259833374_sc_sz @ F2 @ A ) )
% 3.14/1.66 = ( ? [X4: produc190496183real_c] :
% 3.14/1.66 ( ( member1895684704real_c @ X4 @ A )
% 3.14/1.66 & ( Z
% 3.14/1.66 = ( F2 @ X4 ) ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_306_image__iff,axiom,
% 3.14/1.66 ! [Z: produc1821101996_sc_sz,F2: produc999471430t_unit > produc1821101996_sc_sz,A: set_Pr2041213564t_unit] :
% 3.14/1.66 ( ( member1057565379_sc_sz @ Z @ ( image_1426741113_sc_sz @ F2 @ A ) )
% 3.14/1.66 = ( ? [X4: produc999471430t_unit] :
% 3.14/1.66 ( ( member235934813t_unit @ X4 @ A )
% 3.14/1.66 & ( Z
% 3.14/1.66 = ( F2 @ X4 ) ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_307_image__iff,axiom,
% 3.14/1.66 ! [Z: produc999471430t_unit,F2: produc1821101996_sc_sz > produc999471430t_unit,A: set_Pr1169339874_sc_sz] :
% 3.14/1.66 ( ( member235934813t_unit @ Z @ ( image_904562809t_unit @ F2 @ A ) )
% 3.14/1.66 = ( ? [X4: produc1821101996_sc_sz] :
% 3.14/1.66 ( ( member1057565379_sc_sz @ X4 @ A )
% 3.14/1.66 & ( Z
% 3.14/1.66 = ( F2 @ X4 ) ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_308_imageI,axiom,
% 3.14/1.66 ! [X: produc866628903_sc_sz,A: set_Pr1774599175_sc_sz,F2: produc866628903_sc_sz > produc190496183real_c] :
% 3.14/1.66 ( ( member245028432_sc_sz @ X @ A )
% 3.14/1.66 => ( member1895684704real_c @ ( F2 @ X ) @ ( image_1121381717real_c @ F2 @ A ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_309_imageI,axiom,
% 3.14/1.66 ! [X: produc866628903_sc_sz,A: set_Pr1774599175_sc_sz,F2: produc866628903_sc_sz > finite1398487019real_c] :
% 3.14/1.66 ( ( member245028432_sc_sz @ X @ A )
% 3.14/1.66 => ( member1261661570real_c @ ( F2 @ X ) @ ( image_1332486093real_c @ F2 @ A ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_310_imageI,axiom,
% 3.14/1.66 ! [X: produc866628903_sc_sz,A: set_Pr1774599175_sc_sz,F2: produc866628903_sc_sz > produc1821101996_sc_sz] :
% 3.14/1.66 ( ( member245028432_sc_sz @ X @ A )
% 3.14/1.66 => ( member1057565379_sc_sz @ ( F2 @ X ) @ ( image_226055310_sc_sz @ F2 @ A ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_311_imageI,axiom,
% 3.14/1.66 ! [X: produc866628903_sc_sz,A: set_Pr1774599175_sc_sz,F2: produc866628903_sc_sz > produc640052711real_c] :
% 3.14/1.66 ( ( member245028432_sc_sz @ X @ A )
% 3.14/1.66 => ( member346808080real_c @ ( F2 @ X ) @ ( image_768765061real_c @ F2 @ A ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_312_imageI,axiom,
% 3.14/1.66 ! [X: produc866628903_sc_sz,A: set_Pr1774599175_sc_sz,F2: produc866628903_sc_sz > produc999471430t_unit] :
% 3.14/1.66 ( ( member245028432_sc_sz @ X @ A )
% 3.14/1.66 => ( member235934813t_unit @ ( F2 @ X ) @ ( image_1551908392t_unit @ F2 @ A ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_313_imageI,axiom,
% 3.14/1.66 ! [X: produc866628903_sc_sz,A: set_Pr1774599175_sc_sz,F2: produc866628903_sc_sz > produc866628903_sc_sz] :
% 3.14/1.66 ( ( member245028432_sc_sz @ X @ A )
% 3.14/1.66 => ( member245028432_sc_sz @ ( F2 @ X ) @ ( image_1313166277_sc_sz @ F2 @ A ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_314_imageI,axiom,
% 3.14/1.66 ! [X: produc190496183real_c,A: set_Pr1389752855real_c,F2: produc190496183real_c > produc190496183real_c] :
% 3.14/1.66 ( ( member1895684704real_c @ X @ A )
% 3.14/1.66 => ( member1895684704real_c @ ( F2 @ X ) @ ( image_738229701real_c @ F2 @ A ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_315_Compr__image__eq,axiom,
% 3.14/1.66 ! [F2: produc190496183real_c > produc190496183real_c,A: set_Pr1389752855real_c,P: produc190496183real_c > $o] :
% 3.14/1.66 ( ( collec1643251106real_c
% 3.14/1.66 @ ^ [X4: produc190496183real_c] :
% 3.14/1.66 ( ( member1895684704real_c @ X4 @ ( image_738229701real_c @ F2 @ A ) )
% 3.14/1.66 & ( P @ X4 ) ) )
% 3.14/1.66 = ( image_738229701real_c @ F2
% 3.14/1.66 @ ( collec1643251106real_c
% 3.14/1.66 @ ^ [X4: produc190496183real_c] :
% 3.14/1.66 ( ( member1895684704real_c @ X4 @ A )
% 3.14/1.66 & ( P @ ( F2 @ X4 ) ) ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_316_imageE,axiom,
% 3.14/1.66 ! [B2: produc190496183real_c,F2: produc190496183real_c > produc190496183real_c,A: set_Pr1389752855real_c] :
% 3.14/1.66 ( ( member1895684704real_c @ B2 @ ( image_738229701real_c @ F2 @ A ) )
% 3.14/1.66 => ~ ! [X3: produc190496183real_c] :
% 3.14/1.66 ( ( B2
% 3.14/1.66 = ( F2 @ X3 ) )
% 3.14/1.66 => ~ ( member1895684704real_c @ X3 @ A ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_317_case__prod__Pair__iden,axiom,
% 3.14/1.66 ! [P2: produc1821101996_sc_sz] :
% 3.14/1.66 ( ( produc448466487_sc_sz @ produc789536734_sc_sz @ P2 )
% 3.14/1.66 = P2 ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_318_pred__equals__eq2,axiom,
% 3.14/1.66 ! [R2: set_Pr1389752855real_c,S4: set_Pr1389752855real_c] :
% 3.14/1.66 ( ( ( ^ [X4: finite1398487019real_c,Y4: finite1398487019real_c] : ( member1895684704real_c @ ( produc394644079real_c @ X4 @ Y4 ) @ R2 ) )
% 3.14/1.66 = ( ^ [X4: finite1398487019real_c,Y4: finite1398487019real_c] : ( member1895684704real_c @ ( produc394644079real_c @ X4 @ Y4 ) @ S4 ) ) )
% 3.14/1.66 = ( R2 = S4 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_319_pred__equals__eq2,axiom,
% 3.14/1.66 ! [R2: set_Pr1169339874_sc_sz,S4: set_Pr1169339874_sc_sz] :
% 3.14/1.66 ( ( ( ^ [X4: denota610675952t_unit,Y4: produc866628903_sc_sz] : ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ X4 @ Y4 ) @ R2 ) )
% 3.14/1.66 = ( ^ [X4: denota610675952t_unit,Y4: produc866628903_sc_sz] : ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ X4 @ Y4 ) @ S4 ) ) )
% 3.14/1.66 = ( R2 = S4 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_320_mem__Sigma__iff,axiom,
% 3.14/1.66 ! [A2: produc190496183real_c,B2: produc190496183real_c,A: set_Pr1389752855real_c,B: produc190496183real_c > set_Pr1389752855real_c] :
% 3.14/1.66 ( ( member346808080real_c @ ( produc1687028567real_c @ A2 @ B2 ) @ ( produc1017530376real_c @ A @ B ) )
% 3.14/1.66 = ( ( member1895684704real_c @ A2 @ A )
% 3.14/1.66 & ( member1895684704real_c @ B2 @ ( B @ A2 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_321_mem__Sigma__iff,axiom,
% 3.14/1.66 ! [A2: finite1398487019real_c,B2: finite1398487019real_c,A: set_Fi1407883041real_c,B: finite1398487019real_c > set_Fi1407883041real_c] :
% 3.14/1.66 ( ( member1895684704real_c @ ( produc394644079real_c @ A2 @ B2 ) @ ( produc563345056real_c @ A @ B ) )
% 3.14/1.66 = ( ( member1261661570real_c @ A2 @ A )
% 3.14/1.66 & ( member1261661570real_c @ B2 @ ( B @ A2 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_322_mem__Sigma__iff,axiom,
% 3.14/1.66 ! [A2: denota610675952t_unit,B2: produc866628903_sc_sz,A: set_De208295462t_unit,B: denota610675952t_unit > set_Pr1774599175_sc_sz] :
% 3.14/1.66 ( ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ A2 @ B2 ) @ ( produc159603053_sc_sz @ A @ B ) )
% 3.14/1.66 = ( ( member754147591t_unit @ A2 @ A )
% 3.14/1.66 & ( member245028432_sc_sz @ B2 @ ( B @ A2 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_323_SigmaI,axiom,
% 3.14/1.66 ! [A2: finite1398487019real_c,A: set_Fi1407883041real_c,B2: finite1398487019real_c,B: finite1398487019real_c > set_Fi1407883041real_c] :
% 3.14/1.66 ( ( member1261661570real_c @ A2 @ A )
% 3.14/1.66 => ( ( member1261661570real_c @ B2 @ ( B @ A2 ) )
% 3.14/1.66 => ( member1895684704real_c @ ( produc394644079real_c @ A2 @ B2 ) @ ( produc563345056real_c @ A @ B ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_324_SigmaI,axiom,
% 3.14/1.66 ! [A2: produc190496183real_c,A: set_Pr1389752855real_c,B2: produc190496183real_c,B: produc190496183real_c > set_Pr1389752855real_c] :
% 3.14/1.66 ( ( member1895684704real_c @ A2 @ A )
% 3.14/1.66 => ( ( member1895684704real_c @ B2 @ ( B @ A2 ) )
% 3.14/1.66 => ( member346808080real_c @ ( produc1687028567real_c @ A2 @ B2 ) @ ( produc1017530376real_c @ A @ B ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_325_SigmaI,axiom,
% 3.14/1.66 ! [A2: denota610675952t_unit,A: set_De208295462t_unit,B2: produc866628903_sc_sz,B: denota610675952t_unit > set_Pr1774599175_sc_sz] :
% 3.14/1.66 ( ( member754147591t_unit @ A2 @ A )
% 3.14/1.66 => ( ( member245028432_sc_sz @ B2 @ ( B @ A2 ) )
% 3.14/1.66 => ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ A2 @ B2 ) @ ( produc159603053_sc_sz @ A @ B ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_326_SigmaE2,axiom,
% 3.14/1.66 ! [A2: produc190496183real_c,B2: produc190496183real_c,A: set_Pr1389752855real_c,B: produc190496183real_c > set_Pr1389752855real_c] :
% 3.14/1.66 ( ( member346808080real_c @ ( produc1687028567real_c @ A2 @ B2 ) @ ( produc1017530376real_c @ A @ B ) )
% 3.14/1.66 => ~ ( ( member1895684704real_c @ A2 @ A )
% 3.14/1.66 => ~ ( member1895684704real_c @ B2 @ ( B @ A2 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_327_SigmaE2,axiom,
% 3.14/1.66 ! [A2: finite1398487019real_c,B2: finite1398487019real_c,A: set_Fi1407883041real_c,B: finite1398487019real_c > set_Fi1407883041real_c] :
% 3.14/1.66 ( ( member1895684704real_c @ ( produc394644079real_c @ A2 @ B2 ) @ ( produc563345056real_c @ A @ B ) )
% 3.14/1.66 => ~ ( ( member1261661570real_c @ A2 @ A )
% 3.14/1.66 => ~ ( member1261661570real_c @ B2 @ ( B @ A2 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_328_SigmaE2,axiom,
% 3.14/1.66 ! [A2: denota610675952t_unit,B2: produc866628903_sc_sz,A: set_De208295462t_unit,B: denota610675952t_unit > set_Pr1774599175_sc_sz] :
% 3.14/1.66 ( ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ A2 @ B2 ) @ ( produc159603053_sc_sz @ A @ B ) )
% 3.14/1.66 => ~ ( ( member754147591t_unit @ A2 @ A )
% 3.14/1.66 => ~ ( member245028432_sc_sz @ B2 @ ( B @ A2 ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_329_SigmaD2,axiom,
% 3.14/1.66 ! [A2: finite1398487019real_c,B2: finite1398487019real_c,A: set_Fi1407883041real_c,B: finite1398487019real_c > set_Fi1407883041real_c] :
% 3.14/1.66 ( ( member1895684704real_c @ ( produc394644079real_c @ A2 @ B2 ) @ ( produc563345056real_c @ A @ B ) )
% 3.14/1.66 => ( member1261661570real_c @ B2 @ ( B @ A2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_330_SigmaD2,axiom,
% 3.14/1.66 ! [A2: denota610675952t_unit,B2: produc866628903_sc_sz,A: set_De208295462t_unit,B: denota610675952t_unit > set_Pr1774599175_sc_sz] :
% 3.14/1.66 ( ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ A2 @ B2 ) @ ( produc159603053_sc_sz @ A @ B ) )
% 3.14/1.66 => ( member245028432_sc_sz @ B2 @ ( B @ A2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_331_SigmaD1,axiom,
% 3.14/1.66 ! [A2: finite1398487019real_c,B2: finite1398487019real_c,A: set_Fi1407883041real_c,B: finite1398487019real_c > set_Fi1407883041real_c] :
% 3.14/1.66 ( ( member1895684704real_c @ ( produc394644079real_c @ A2 @ B2 ) @ ( produc563345056real_c @ A @ B ) )
% 3.14/1.66 => ( member1261661570real_c @ A2 @ A ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_332_SigmaD1,axiom,
% 3.14/1.66 ! [A2: denota610675952t_unit,B2: produc866628903_sc_sz,A: set_De208295462t_unit,B: denota610675952t_unit > set_Pr1774599175_sc_sz] :
% 3.14/1.66 ( ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ A2 @ B2 ) @ ( produc159603053_sc_sz @ A @ B ) )
% 3.14/1.66 => ( member754147591t_unit @ A2 @ A ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_333_SigmaE,axiom,
% 3.14/1.66 ! [C2: produc640052711real_c,A: set_Pr1389752855real_c,B: produc190496183real_c > set_Pr1389752855real_c] :
% 3.14/1.66 ( ( member346808080real_c @ C2 @ ( produc1017530376real_c @ A @ B ) )
% 3.14/1.66 => ~ ! [X3: produc190496183real_c] :
% 3.14/1.66 ( ( member1895684704real_c @ X3 @ A )
% 3.14/1.66 => ! [Y3: produc190496183real_c] :
% 3.14/1.66 ( ( member1895684704real_c @ Y3 @ ( B @ X3 ) )
% 3.14/1.66 => ( C2
% 3.14/1.66 != ( produc1687028567real_c @ X3 @ Y3 ) ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_334_SigmaE,axiom,
% 3.14/1.66 ! [C2: produc190496183real_c,A: set_Fi1407883041real_c,B: finite1398487019real_c > set_Fi1407883041real_c] :
% 3.14/1.66 ( ( member1895684704real_c @ C2 @ ( produc563345056real_c @ A @ B ) )
% 3.14/1.66 => ~ ! [X3: finite1398487019real_c] :
% 3.14/1.66 ( ( member1261661570real_c @ X3 @ A )
% 3.14/1.66 => ! [Y3: finite1398487019real_c] :
% 3.14/1.66 ( ( member1261661570real_c @ Y3 @ ( B @ X3 ) )
% 3.14/1.66 => ( C2
% 3.14/1.66 != ( produc394644079real_c @ X3 @ Y3 ) ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_335_SigmaE,axiom,
% 3.14/1.66 ! [C2: produc1821101996_sc_sz,A: set_De208295462t_unit,B: denota610675952t_unit > set_Pr1774599175_sc_sz] :
% 3.14/1.66 ( ( member1057565379_sc_sz @ C2 @ ( produc159603053_sc_sz @ A @ B ) )
% 3.14/1.66 => ~ ! [X3: denota610675952t_unit] :
% 3.14/1.66 ( ( member754147591t_unit @ X3 @ A )
% 3.14/1.66 => ! [Y3: produc866628903_sc_sz] :
% 3.14/1.66 ( ( member245028432_sc_sz @ Y3 @ ( B @ X3 ) )
% 3.14/1.66 => ( C2
% 3.14/1.66 != ( produc789536734_sc_sz @ X3 @ Y3 ) ) ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_336_swap__product,axiom,
% 3.14/1.66 ! [A: set_Pr1774599175_sc_sz,B: set_De208295462t_unit] :
% 3.14/1.66 ( ( image_1426741113_sc_sz
% 3.14/1.66 @ ( produc435149849_sc_sz
% 3.14/1.66 @ ^ [I4: produc866628903_sc_sz,J2: denota610675952t_unit] : ( produc789536734_sc_sz @ J2 @ I4 ) )
% 3.14/1.66 @ ( produc2020166735t_unit @ A
% 3.14/1.66 @ ^ [Uu: produc866628903_sc_sz] : B ) )
% 3.14/1.66 = ( produc159603053_sc_sz @ B
% 3.14/1.66 @ ^ [Uu: denota610675952t_unit] : A ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_337_member__product,axiom,
% 3.14/1.66 ! [X: produc190496183real_c,A: set_Fi1407883041real_c,B: set_Fi1407883041real_c] :
% 3.14/1.66 ( ( member1895684704real_c @ X @ ( produc3751594real_c @ A @ B ) )
% 3.14/1.66 = ( member1895684704real_c @ X
% 3.14/1.66 @ ( produc563345056real_c @ A
% 3.14/1.66 @ ^ [Uu: finite1398487019real_c] : B ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_338_map__prod__simp,axiom,
% 3.14/1.66 ! [F2: denota610675952t_unit > denota610675952t_unit,G: produc866628903_sc_sz > produc866628903_sc_sz,A2: denota610675952t_unit,B2: produc866628903_sc_sz] :
% 3.14/1.66 ( ( produc403791768_sc_sz @ F2 @ G @ ( produc789536734_sc_sz @ A2 @ B2 ) )
% 3.14/1.66 = ( produc789536734_sc_sz @ ( F2 @ A2 ) @ ( G @ B2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_339_in__inv__image,axiom,
% 3.14/1.66 ! [X: finite1398487019real_c,Y: finite1398487019real_c,R: set_Pr1389752855real_c,F2: finite1398487019real_c > finite1398487019real_c] :
% 3.14/1.66 ( ( member1895684704real_c @ ( produc394644079real_c @ X @ Y ) @ ( inv_im1827249322real_c @ R @ F2 ) )
% 3.14/1.66 = ( member1895684704real_c @ ( produc394644079real_c @ ( F2 @ X ) @ ( F2 @ Y ) ) @ R ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_340_map__prod__imageI,axiom,
% 3.14/1.66 ! [A2: finite1398487019real_c,B2: finite1398487019real_c,R2: set_Pr1389752855real_c,F2: finite1398487019real_c > finite1398487019real_c,G: finite1398487019real_c > finite1398487019real_c] :
% 3.14/1.66 ( ( member1895684704real_c @ ( produc394644079real_c @ A2 @ B2 ) @ R2 )
% 3.14/1.66 => ( member1895684704real_c @ ( produc394644079real_c @ ( F2 @ A2 ) @ ( G @ B2 ) ) @ ( image_738229701real_c @ ( produc368345510real_c @ F2 @ G ) @ R2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_341_map__prod__imageI,axiom,
% 3.14/1.66 ! [A2: finite1398487019real_c,B2: finite1398487019real_c,R2: set_Pr1389752855real_c,F2: finite1398487019real_c > denota610675952t_unit,G: finite1398487019real_c > produc866628903_sc_sz] :
% 3.14/1.66 ( ( member1895684704real_c @ ( produc394644079real_c @ A2 @ B2 ) @ R2 )
% 3.14/1.66 => ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ ( F2 @ A2 ) @ ( G @ B2 ) ) @ ( image_1259833374_sc_sz @ ( produc1784590311_sc_sz @ F2 @ G ) @ R2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_342_map__prod__imageI,axiom,
% 3.14/1.66 ! [A2: denota610675952t_unit,B2: produc866628903_sc_sz,R2: set_Pr1169339874_sc_sz,F2: denota610675952t_unit > finite1398487019real_c,G: produc866628903_sc_sz > finite1398487019real_c] :
% 3.14/1.66 ( ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ A2 @ B2 ) @ R2 )
% 3.14/1.66 => ( member1895684704real_c @ ( produc394644079real_c @ ( F2 @ A2 ) @ ( G @ B2 ) ) @ ( image_386905412real_c @ ( produc1612557567real_c @ F2 @ G ) @ R2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_343_map__prod__imageI,axiom,
% 3.14/1.66 ! [A2: denota610675952t_unit,B2: produc866628903_sc_sz,R2: set_Pr1169339874_sc_sz,F2: denota610675952t_unit > denota610675952t_unit,G: produc866628903_sc_sz > produc866628903_sc_sz] :
% 3.14/1.66 ( ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ A2 @ B2 ) @ R2 )
% 3.14/1.66 => ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ ( F2 @ A2 ) @ ( G @ B2 ) ) @ ( image_1726193375_sc_sz @ ( produc403791768_sc_sz @ F2 @ G ) @ R2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_344_prod__fun__imageE,axiom,
% 3.14/1.66 ! [C2: produc190496183real_c,F2: finite1398487019real_c > finite1398487019real_c,G: finite1398487019real_c > finite1398487019real_c,R2: set_Pr1389752855real_c] :
% 3.14/1.66 ( ( member1895684704real_c @ C2 @ ( image_738229701real_c @ ( produc368345510real_c @ F2 @ G ) @ R2 ) )
% 3.14/1.66 => ~ ! [X3: finite1398487019real_c,Y3: finite1398487019real_c] :
% 3.14/1.66 ( ( C2
% 3.14/1.66 = ( produc394644079real_c @ ( F2 @ X3 ) @ ( G @ Y3 ) ) )
% 3.14/1.66 => ~ ( member1895684704real_c @ ( produc394644079real_c @ X3 @ Y3 ) @ R2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_345_prod__fun__imageE,axiom,
% 3.14/1.66 ! [C2: produc190496183real_c,F2: denota610675952t_unit > finite1398487019real_c,G: produc866628903_sc_sz > finite1398487019real_c,R2: set_Pr1169339874_sc_sz] :
% 3.14/1.66 ( ( member1895684704real_c @ C2 @ ( image_386905412real_c @ ( produc1612557567real_c @ F2 @ G ) @ R2 ) )
% 3.14/1.66 => ~ ! [X3: denota610675952t_unit,Y3: produc866628903_sc_sz] :
% 3.14/1.66 ( ( C2
% 3.14/1.66 = ( produc394644079real_c @ ( F2 @ X3 ) @ ( G @ Y3 ) ) )
% 3.14/1.66 => ~ ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ X3 @ Y3 ) @ R2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_346_prod__fun__imageE,axiom,
% 3.14/1.66 ! [C2: produc1821101996_sc_sz,F2: finite1398487019real_c > denota610675952t_unit,G: finite1398487019real_c > produc866628903_sc_sz,R2: set_Pr1389752855real_c] :
% 3.14/1.66 ( ( member1057565379_sc_sz @ C2 @ ( image_1259833374_sc_sz @ ( produc1784590311_sc_sz @ F2 @ G ) @ R2 ) )
% 3.14/1.66 => ~ ! [X3: finite1398487019real_c,Y3: finite1398487019real_c] :
% 3.14/1.66 ( ( C2
% 3.14/1.66 = ( produc789536734_sc_sz @ ( F2 @ X3 ) @ ( G @ Y3 ) ) )
% 3.14/1.66 => ~ ( member1895684704real_c @ ( produc394644079real_c @ X3 @ Y3 ) @ R2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_347_prod__fun__imageE,axiom,
% 3.14/1.66 ! [C2: produc1821101996_sc_sz,F2: denota610675952t_unit > denota610675952t_unit,G: produc866628903_sc_sz > produc866628903_sc_sz,R2: set_Pr1169339874_sc_sz] :
% 3.14/1.66 ( ( member1057565379_sc_sz @ C2 @ ( image_1726193375_sc_sz @ ( produc403791768_sc_sz @ F2 @ G ) @ R2 ) )
% 3.14/1.66 => ~ ! [X3: denota610675952t_unit,Y3: produc866628903_sc_sz] :
% 3.14/1.66 ( ( C2
% 3.14/1.66 = ( produc789536734_sc_sz @ ( F2 @ X3 ) @ ( G @ Y3 ) ) )
% 3.14/1.66 => ~ ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ X3 @ Y3 ) @ R2 ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_348_Vagree__univ,axiom,
% 3.14/1.66 ! [A2: finite1398487019real_c,B2: finite1398487019real_c,C2: finite1398487019real_c,D: finite1398487019real_c] :
% 3.14/1.66 ( ( denota1997846518gree_c @ ( produc394644079real_c @ A2 @ B2 ) @ ( produc394644079real_c @ C2 @ D ) @ top_to1660572043um_c_c )
% 3.14/1.66 => ( ( A2 = C2 )
% 3.14/1.66 & ( B2 = D ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_349_agree__UNIV__eq,axiom,
% 3.14/1.66 ! [Nu3: produc190496183real_c,Omega: produc190496183real_c] :
% 3.14/1.66 ( ( denota1997846518gree_c @ Nu3 @ Omega @ top_to1660572043um_c_c )
% 3.14/1.66 => ( Nu3 = Omega ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_350_top__empty__eq2,axiom,
% 3.14/1.66 ( top_to964419200al_c_o
% 3.14/1.66 = ( ^ [X4: finite1398487019real_c,Y4: finite1398487019real_c] : ( member1895684704real_c @ ( produc394644079real_c @ X4 @ Y4 ) @ top_to226056039real_c ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_351_top__empty__eq2,axiom,
% 3.14/1.66 ( top_to1399053141c_sz_o
% 3.14/1.66 = ( ^ [X4: denota610675952t_unit,Y4: produc866628903_sc_sz] : ( member1057565379_sc_sz @ ( produc789536734_sc_sz @ X4 @ Y4 ) @ top_to1499569298_sc_sz ) ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_352_fst__conv,axiom,
% 3.14/1.66 ! [X1: denota610675952t_unit,X2: produc866628903_sc_sz] :
% 3.14/1.66 ( ( produc1503602930_sc_sz @ ( produc789536734_sc_sz @ X1 @ X2 ) )
% 3.14/1.66 = X1 ) ).
% 3.14/1.66
% 3.14/1.66 thf(fact_353_fst__eqD,axiom,
% 3.14/1.66 ! [X: denota610675952t_unit,Y: produc866628903_sc_sz,A2: denota610675952t_unit] :
% 3.14/1.66 ( ( ( produc1503602930_sc_sz @ ( produc789536734_sc_sz @ X @ Y ) )
% 3.14/1.66 = A2 )
% 3.14/1.66 => ( X = A2 ) ) ).
% 3.14/1.66
% 3.14/1.66 thf(conj_0,conjecture,
% 3.14/1.66 ( ( ! [Nu: produc190496183real_c,Nu2: produc190496183real_c,I: denota231621370t_unit,J: denota231621370t_unit] :
% 3.14/1.66 ( ( denota69106024_a_b_c @ I @ J @ ( static_SIGF_a_b_c @ phi ) )
% 3.14/1.66 => ( ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVF_a_b_c @ phi ) )
% 3.14/1.66 => ( ( member1895684704real_c @ Nu @ ( denota968303861_a_b_c @ I @ phi ) )
% 3.14/1.66 = ( member1895684704real_c @ Nu2 @ ( denota968303861_a_b_c @ J @ phi ) ) ) ) ) )
% 3.14/1.66 = ( ! [Nu: produc190496183real_c,Nu2: produc190496183real_c,I: denota231621370t_unit,J: denota231621370t_unit] :
% 3.14/1.66 ( ( denota69106024_a_b_c @ I @ J @ ( static_SIGF_a_b_c @ phi ) )
% 3.14/1.66 => ( ( denota1997846518gree_c @ Nu @ Nu2 @ ( static_FVF_a_b_c @ phi ) )
% 3.14/1.66 => ( ( member1895684704real_c @ Nu @ ( denota968303861_a_b_c @ I @ phi ) )
% 3.14/1.66 = ( member1895684704real_c @ Nu2 @ ( denota968303861_a_b_c @ J @ phi ) ) ) ) ) ) ) ).
% 3.14/1.66 ------------------------
% 3.20/1.70 % (20879)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20700 for (2999ds/2Mi)
% 3.20/1.70 % (20881)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_20700 for (2999ds/275Mi)
% 3.20/1.70 % (20876)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20700 for (2999ds/183Mi)
% 3.20/1.70 % (20882)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20700 for (2999ds/18Mi)
% 3.20/1.70 % (20878)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_20700 for (2999ds/27Mi)
% 3.20/1.70 % (20879)Instruction limit reached!
% 3.20/1.70 % (20879)------------------------------
% 3.20/1.70 % (20879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.70 % (20879)Termination reason: Unknown
% 3.20/1.70 % (20879)Termination phase: shuffling
% 3.20/1.70
% 3.20/1.70 % (20879)Memory used [KB]: 1535
% 3.20/1.70 % (20879)Time elapsed: 0.002 s
% 3.20/1.70 % (20879)Instructions burned: 2 (million)
% 3.20/1.70 % (20879)------------------------------
% 3.20/1.70 % (20879)------------------------------
% 3.20/1.70 % (20877)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_20700 for (2999ds/4Mi)
% 3.20/1.70 % (20880)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_20700 for (2999ds/2Mi)
% 3.20/1.71 % (20880)Instruction limit reached!
% 3.20/1.71 % (20880)------------------------------
% 3.20/1.71 % (20880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.71 % (20880)Termination reason: Unknown
% 3.20/1.71 % (20880)Termination phase: shuffling
% 3.20/1.71
% 3.20/1.71 % (20880)Memory used [KB]: 1535
% 3.20/1.71 % (20880)Time elapsed: 0.003 s
% 3.20/1.71 % (20880)Instructions burned: 2 (million)
% 3.20/1.71 % (20880)------------------------------
% 3.20/1.71 % (20880)------------------------------
% 3.20/1.71 % (20882)Instruction limit reached!
% 3.20/1.71 % (20882)------------------------------
% 3.20/1.71 % (20882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.71 % (20882)Termination reason: Unknown
% 3.20/1.71 % (20882)Termination phase: shuffling
% 3.20/1.71
% 3.20/1.71 % (20882)Memory used [KB]: 1791
% 3.20/1.71 % (20882)Time elapsed: 0.007 s
% 3.20/1.71 % (20882)Instructions burned: 19 (million)
% 3.20/1.71 % (20882)------------------------------
% 3.20/1.71 % (20882)------------------------------
% 3.20/1.71 % (20877)Instruction limit reached!
% 3.20/1.71 % (20877)------------------------------
% 3.20/1.71 % (20877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.71 % (20877)Termination reason: Unknown
% 3.20/1.71 % (20877)Termination phase: shuffling
% 3.20/1.71
% 3.20/1.71 % (20877)Memory used [KB]: 1535
% 3.20/1.71 % (20877)Time elapsed: 0.004 s
% 3.20/1.71 % (20877)Instructions burned: 4 (million)
% 3.20/1.71 % (20877)------------------------------
% 3.20/1.71 % (20877)------------------------------
% 3.20/1.71 % (20878)Instruction limit reached!
% 3.20/1.71 % (20878)------------------------------
% 3.20/1.71 % (20878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.71 % (20878)Termination reason: Unknown
% 3.20/1.71 % (20878)Termination phase: shuffling
% 3.20/1.71
% 3.20/1.71 % (20878)Memory used [KB]: 1918
% 3.20/1.71 % (20878)Time elapsed: 0.010 s
% 3.20/1.71 % (20878)Instructions burned: 27 (million)
% 3.20/1.71 % (20878)------------------------------
% 3.20/1.71 % (20878)------------------------------
% 3.20/1.71 % (20883)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_20700 for (2999ds/3Mi)
% 3.20/1.71 % (20883)Instruction limit reached!
% 3.20/1.71 % (20883)------------------------------
% 3.20/1.71 % (20883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.71 % (20883)Termination reason: Unknown
% 3.20/1.71 % (20883)Termination phase: shuffling
% 3.20/1.71
% 3.20/1.71 % (20883)Memory used [KB]: 1535
% 3.20/1.71 % (20883)Time elapsed: 0.002 s
% 3.20/1.71 % (20883)Instructions burned: 3 (million)
% 3.20/1.71 % (20883)------------------------------
% 3.20/1.71 % (20883)------------------------------
% 3.20/1.71 % (20885)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_20700 for (2999ds/15Mi)
% 3.20/1.72 % (20887)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_20700 for (2999ds/1041Mi)
% 3.20/1.72 % (20885)Instruction limit reached!
% 3.20/1.72 % (20885)------------------------------
% 3.20/1.72 % (20885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.72 % (20885)Termination reason: Unknown
% 3.20/1.72 % (20885)Termination phase: shuffling
% 3.20/1.72
% 3.20/1.72 % (20885)Memory used [KB]: 1791
% 3.20/1.72 % (20885)Time elapsed: 0.006 s
% 3.20/1.72 % (20885)Instructions burned: 16 (million)
% 3.20/1.72 % (20885)------------------------------
% 3.20/1.72 % (20885)------------------------------
% 3.20/1.72 % (20888)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_20700 for (2999ds/7Mi)
% 3.20/1.72 % (20884)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_20700 for (2999ds/37Mi)
% 3.20/1.72 % (20888)Instruction limit reached!
% 3.20/1.72 % (20888)------------------------------
% 3.20/1.72 % (20888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.72 % (20888)Termination reason: Unknown
% 3.20/1.72 % (20888)Termination phase: shuffling
% 3.20/1.72
% 3.20/1.72 % (20888)Memory used [KB]: 1663
% 3.20/1.72 % (20888)Time elapsed: 0.004 s
% 3.20/1.72 % (20888)Instructions burned: 9 (million)
% 3.20/1.72 % (20888)------------------------------
% 3.20/1.72 % (20888)------------------------------
% 3.20/1.72 % (20886)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_20700 for (2999ds/3Mi)
% 3.20/1.73 % (20886)Instruction limit reached!
% 3.20/1.73 % (20886)------------------------------
% 3.20/1.73 % (20886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.73 % (20886)Termination reason: Unknown
% 3.20/1.73 % (20886)Termination phase: shuffling
% 3.20/1.73
% 3.20/1.73 % (20886)Memory used [KB]: 1535
% 3.20/1.73 % (20886)Time elapsed: 0.004 s
% 3.20/1.73 % (20886)Instructions burned: 3 (million)
% 3.20/1.73 % (20886)------------------------------
% 3.20/1.73 % (20886)------------------------------
% 3.20/1.73 % (20889)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_20700 for (2999ds/16Mi)
% 3.20/1.73 % (20890)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_20700 for (2999ds/3Mi)
% 3.20/1.73 % (20890)Instruction limit reached!
% 3.20/1.73 % (20890)------------------------------
% 3.20/1.73 % (20890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.73 % (20890)Termination reason: Unknown
% 3.20/1.73 % (20890)Termination phase: shuffling
% 3.20/1.73
% 3.20/1.73 % (20890)Memory used [KB]: 1535
% 3.20/1.73 % (20890)Time elapsed: 0.002 s
% 3.20/1.73 % (20890)Instructions burned: 3 (million)
% 3.20/1.73 % (20890)------------------------------
% 3.20/1.73 % (20890)------------------------------
% 3.20/1.73 % (20889)Instruction limit reached!
% 3.20/1.73 % (20889)------------------------------
% 3.20/1.73 % (20889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.73 % (20889)Termination reason: Unknown
% 3.20/1.73 % (20889)Termination phase: shuffling
% 3.20/1.73
% 3.20/1.73 % (20889)Memory used [KB]: 1791
% 3.20/1.73 % (20889)Time elapsed: 0.006 s
% 3.20/1.73 % (20889)Instructions burned: 16 (million)
% 3.20/1.73 % (20889)------------------------------
% 3.20/1.73 % (20889)------------------------------
% 3.20/1.74 % (20884)Instruction limit reached!
% 3.20/1.74 % (20884)------------------------------
% 3.20/1.74 % (20884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.74 % (20884)Termination reason: Unknown
% 3.20/1.74 % (20884)Termination phase: shuffling
% 3.20/1.74
% 3.20/1.74 % (20884)Memory used [KB]: 2302
% 3.20/1.74 % (20884)Time elapsed: 0.021 s
% 3.20/1.74 % (20884)Instructions burned: 37 (million)
% 3.20/1.74 % (20884)------------------------------
% 3.20/1.74 % (20884)------------------------------
% 3.20/1.74 % (20892)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_20700 for (2999ds/7Mi)
% 3.20/1.74 % (20891)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_20700 for (2999ds/3Mi)
% 3.20/1.74 % (20893)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_20700 for (2999ds/3Mi)
% 3.20/1.74 % (20881)First to succeed.
% 3.20/1.74 % (20893)Instruction limit reached!
% 3.20/1.74 % (20893)------------------------------
% 3.20/1.74 % (20893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.74 % (20893)Termination reason: Unknown
% 3.20/1.74 % (20893)Termination phase: shuffling
% 3.20/1.74
% 3.20/1.74 % (20893)Memory used [KB]: 1535
% 3.20/1.74 % (20893)Time elapsed: 0.002 s
% 3.20/1.74 % (20893)Instructions burned: 3 (million)
% 3.20/1.74 % (20893)------------------------------
% 3.20/1.74 % (20893)------------------------------
% 3.20/1.74 % (20892)Instruction limit reached!
% 3.20/1.74 % (20892)------------------------------
% 3.20/1.74 % (20892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.74 % (20892)Termination reason: Unknown
% 3.20/1.74 % (20892)Termination phase: shuffling
% 3.20/1.74
% 3.20/1.74 % (20892)Memory used [KB]: 1663
% 3.20/1.74 % (20892)Time elapsed: 0.003 s
% 3.20/1.74 % (20892)Instructions burned: 7 (million)
% 3.20/1.74 % (20892)------------------------------
% 3.20/1.74 % (20892)------------------------------
% 3.20/1.74 % (20891)Instruction limit reached!
% 3.20/1.74 % (20891)------------------------------
% 3.20/1.74 % (20891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.74 % (20891)Termination reason: Unknown
% 3.20/1.74 % (20891)Termination phase: shuffling
% 3.20/1.74
% 3.20/1.74 % (20891)Memory used [KB]: 1535
% 3.20/1.74 % (20891)Time elapsed: 0.004 s
% 3.20/1.74 % (20891)Instructions burned: 3 (million)
% 3.20/1.74 % (20891)------------------------------
% 3.20/1.74 % (20891)------------------------------
% 3.20/1.75 % (20881)Refutation found. Thanks to Tanya!
% 3.20/1.75 % SZS status Theorem for DTF2THF_20700
% 3.20/1.75 % SZS output start Proof for DTF2THF_20700
% 3.20/1.75 thf(type_def_5, type, formula_a_b_c: $tType).
% 3.20/1.75 thf(type_def_7, type, denota231621370t_unit: $tType).
% 3.20/1.75 thf(type_def_8, type, set_Su1783761653um_b_c: $tType).
% 3.20/1.75 thf(type_def_9, type, produc190496183real_c: $tType).
% 3.20/1.75 thf(type_def_10, type, set_Sum_sum_c_c: $tType).
% 3.20/1.75 thf(type_def_11, type, set_Pr1389752855real_c: $tType).
% 3.20/1.75 thf(type_def_12, type, denota610675952t_unit: $tType).
% 3.20/1.75 thf(type_def_13, type, formula_sf_sc_sz: $tType).
% 3.20/1.75 thf(type_def_14, type, set_Pr60491591eal_sz: $tType).
% 3.20/1.75 thf(type_def_15, type, sz: $tType).
% 3.20/1.75 thf(type_def_16, type, sf: $tType).
% 3.20/1.75 thf(type_def_17, type, sc: $tType).
% 3.20/1.75 thf(type_def_18, type, produc866628903_sc_sz: $tType).
% 3.20/1.75 thf(type_def_19, type, finite1398487019real_c: $tType).
% 3.20/1.75 thf(type_def_20, type, set_Pr1169339874_sc_sz: $tType).
% 3.20/1.75 thf(type_def_21, type, produc1821101996_sc_sz: $tType).
% 3.20/1.75 thf(type_def_22, type, list_f1238882004_sc_sz: $tType).
% 3.20/1.75 thf(type_def_23, type, produc640052711real_c: $tType).
% 3.20/1.75 thf(type_def_24, type, produc999471430t_unit: $tType).
% 3.20/1.75 thf(type_def_25, type, set_De208295462t_unit: $tType).
% 3.20/1.75 thf(type_def_26, type, set_Pr1774599175_sc_sz: $tType).
% 3.20/1.75 thf(type_def_27, type, set_Fi1407883041real_c: $tType).
% 3.20/1.75 thf(type_def_28, type, set_Pr754230471real_c: $tType).
% 3.20/1.75 thf(type_def_29, type, set_Pr2041213564t_unit: $tType).
% 3.20/1.75 thf(type_def_30, type, set_o: $tType).
% 3.20/1.75 thf(type_def_31, type, produc1149990247eal_sz: $tType).
% 3.20/1.75 thf(func_def_0, type, set_Pr754230471real_c: $tType).
% 3.20/1.75 thf(func_def_1, type, produc640052711real_c: $tType).
% 3.20/1.75 thf(func_def_2, type, set_Pr2041213564t_unit: $tType).
% 3.20/1.75 thf(func_def_3, type, set_Pr1169339874_sc_sz: $tType).
% 3.20/1.75 thf(func_def_4, type, produc999471430t_unit: $tType).
% 3.20/1.75 thf(func_def_5, type, produc1821101996_sc_sz: $tType).
% 3.20/1.75 thf(func_def_6, type, set_Pr60491591eal_sz: $tType).
% 3.20/1.75 thf(func_def_7, type, set_Pr1389752855real_c: $tType).
% 3.20/1.75 thf(func_def_8, type, set_Pr1774599175_sc_sz: $tType).
% 3.20/1.75 thf(func_def_9, type, produc1149990247eal_sz: $tType).
% 3.20/1.75 thf(func_def_10, type, produc190496183real_c: $tType).
% 3.20/1.75 thf(func_def_11, type, produc866628903_sc_sz: $tType).
% 3.20/1.75 thf(func_def_12, type, set_De208295462t_unit: $tType).
% 3.20/1.75 thf(func_def_13, type, denota610675952t_unit: $tType).
% 3.20/1.75 thf(func_def_14, type, denota231621370t_unit: $tType).
% 3.20/1.75 thf(func_def_15, type, set_Su1783761653um_b_c: $tType).
% 3.20/1.75 thf(func_def_16, type, set_Fi1407883041real_c: $tType).
% 3.20/1.75 thf(func_def_17, type, finite1398487019real_c: $tType).
% 3.20/1.75 thf(func_def_18, type, list_f1238882004_sc_sz: $tType).
% 3.20/1.75 thf(func_def_19, type, set_Sum_sum_c_c: $tType).
% 3.20/1.75 thf(func_def_20, type, formula_sf_sc_sz: $tType).
% 3.20/1.75 thf(func_def_21, type, formula_a_b_c: $tType).
% 3.20/1.75 thf(func_def_22, type, set_o: $tType).
% 3.20/1.75 thf(func_def_23, type, sz: $tType).
% 3.20/1.75 thf(func_def_24, type, sf: $tType).
% 3.20/1.75 thf(func_def_25, type, sc: $tType).
% 3.20/1.75 thf(func_def_26, type, coinci501627771_a_b_c: formula_a_b_c > $o).
% 3.20/1.75 thf(func_def_27, type, denota69106024_a_b_c: denota231621370t_unit > denota231621370t_unit > set_Su1783761653um_b_c > $o).
% 3.20/1.75 thf(func_def_28, type, denota1997846518gree_c: produc190496183real_c > produc190496183real_c > set_Sum_sum_c_c > $o).
% 3.20/1.75 thf(func_def_29, type, denota968303861_a_b_c: denota231621370t_unit > formula_a_b_c > set_Pr1389752855real_c).
% 3.20/1.75 thf(func_def_30, type, denota1711272799_sc_sz: denota610675952t_unit > formula_sf_sc_sz > set_Pr60491591eal_sz).
% 3.20/1.75 thf(func_def_31, type, denota1946510237_sc_sz: formula_sf_sc_sz > $o).
% 3.20/1.75 thf(func_def_32, type, denota1579475975_sc_sz: denota610675952t_unit > $o).
% 3.20/1.75 thf(func_def_33, type, ids_sz_sf_sc: sz > sz > sz > sf > sf > sf > sc > sc > sc > sc > $o).
% 3.20/1.75 thf(func_def_34, type, top_to1399053141c_sz_o: denota610675952t_unit > produc866628903_sc_sz > $o).
% 3.20/1.75 thf(func_def_35, type, top_to964419200al_c_o: finite1398487019real_c > finite1398487019real_c > $o).
% 3.20/1.75 thf(func_def_36, type, top_to1499569298_sc_sz: set_Pr1169339874_sc_sz).
% 3.20/1.75 thf(func_def_37, type, top_to226056039real_c: set_Pr1389752855real_c).
% 3.20/1.75 thf(func_def_38, type, top_to1660572043um_c_c: set_Sum_sum_c_c).
% 3.20/1.75 thf(func_def_39, type, produc789536734_sc_sz: denota610675952t_unit > produc866628903_sc_sz > produc1821101996_sc_sz).
% 3.20/1.75 thf(func_def_40, type, produc394644079real_c: finite1398487019real_c > finite1398487019real_c > produc190496183real_c).
% 3.20/1.75 thf(func_def_41, type, produc1822718231_sc_sz: list_f1238882004_sc_sz > list_f1238882004_sc_sz > produc866628903_sc_sz).
% 3.20/1.75 thf(func_def_42, type, produc1687028567real_c: produc190496183real_c > produc190496183real_c > produc640052711real_c).
% 3.20/1.75 thf(func_def_43, type, produc502616768t_unit: produc866628903_sc_sz > denota610675952t_unit > produc999471430t_unit).
% 3.20/1.75 thf(func_def_44, type, produc159603053_sc_sz: set_De208295462t_unit > (denota610675952t_unit > set_Pr1774599175_sc_sz) > set_Pr1169339874_sc_sz).
% 3.20/1.75 thf(func_def_45, type, produc563345056real_c: set_Fi1407883041real_c > (finite1398487019real_c > set_Fi1407883041real_c) > set_Pr1389752855real_c).
% 3.20/1.75 thf(func_def_46, type, produc1017530376real_c: set_Pr1389752855real_c > (produc190496183real_c > set_Pr1389752855real_c) > set_Pr754230471real_c).
% 3.20/1.75 thf(func_def_47, type, produc2020166735t_unit: set_Pr1774599175_sc_sz > (produc866628903_sc_sz > set_De208295462t_unit) > set_Pr2041213564t_unit).
% 3.20/1.75 thf(func_def_48, type, produc793407943_sc_sz: (denota610675952t_unit > denota610675952t_unit) > produc999471430t_unit > produc999471430t_unit).
% 3.20/1.75 thf(func_def_49, type, produc981295297real_c: (finite1398487019real_c > finite1398487019real_c) > produc190496183real_c > produc190496183real_c).
% 3.20/1.75 thf(func_def_50, type, produc233219286_sc_sz: (list_f1238882004_sc_sz > list_f1238882004_sc_sz) > produc866628903_sc_sz > produc866628903_sc_sz).
% 3.20/1.75 thf(func_def_51, type, produc2089853305real_c: (produc190496183real_c > produc190496183real_c) > produc640052711real_c > produc640052711real_c).
% 3.20/1.75 thf(func_def_52, type, produc1959054510t_unit: (produc866628903_sc_sz > produc866628903_sc_sz) > produc1821101996_sc_sz > produc1821101996_sc_sz).
% 3.20/1.75 thf(func_def_53, type, produc1086673900c_sz_o: (produc1821101996_sc_sz > $o) > denota610675952t_unit > produc866628903_sc_sz > $o).
% 3.20/1.75 thf(func_def_54, type, produc753314315real_c: (produc1821101996_sc_sz > produc190496183real_c) > denota610675952t_unit > produc866628903_sc_sz > produc190496183real_c).
% 3.20/1.75 thf(func_def_55, type, produc1827049067real_c: (produc1821101996_sc_sz > set_Pr1389752855real_c) > denota610675952t_unit > produc866628903_sc_sz > set_Pr1389752855real_c).
% 3.20/1.75 thf(func_def_56, type, produc1716060341al_c_o: (produc190496183real_c > $o) > finite1398487019real_c > finite1398487019real_c > $o).
% 3.20/1.75 thf(func_def_57, type, produc1119115220real_c: (produc190496183real_c > produc190496183real_c) > finite1398487019real_c > finite1398487019real_c > produc190496183real_c).
% 3.20/1.75 thf(func_def_58, type, produc880541325c_sz_o: (produc866628903_sc_sz > $o) > list_f1238882004_sc_sz > list_f1238882004_sc_sz > $o).
% 3.20/1.75 thf(func_def_59, type, produc440529997al_c_o: (produc640052711real_c > $o) > produc190496183real_c > produc190496183real_c > $o).
% 3.20/1.75 thf(func_def_60, type, produc38128778unit_o: (produc999471430t_unit > $o) > produc866628903_sc_sz > denota610675952t_unit > $o).
% 3.20/1.75 thf(func_def_61, type, produc295339066_sc_sz: (produc999471430t_unit > produc1821101996_sc_sz) > produc866628903_sc_sz > denota610675952t_unit > produc1821101996_sc_sz).
% 3.20/1.75 thf(func_def_62, type, produc198687651c_sz_o: (denota610675952t_unit > produc866628903_sc_sz > $o) > produc1821101996_sc_sz > $o).
% 3.20/1.75 thf(func_def_63, type, produc383750338real_c: (denota610675952t_unit > produc866628903_sc_sz > produc190496183real_c) > produc1821101996_sc_sz > produc190496183real_c).
% 3.20/1.75 thf(func_def_64, type, produc1894848802real_c: (denota610675952t_unit > produc866628903_sc_sz > set_Pr1389752855real_c) > produc1821101996_sc_sz > set_Pr1389752855real_c).
% 3.20/1.75 thf(func_def_65, type, produc1442549981real_c: (finite1398487019real_c > finite1398487019real_c > produc190496183real_c) > produc190496183real_c > produc190496183real_c).
% 3.20/1.75 thf(func_def_66, type, produc2099580355_sc_sz: (produc866628903_sc_sz > denota610675952t_unit > produc1821101996_sc_sz) > produc999471430t_unit > produc1821101996_sc_sz).
% 3.20/1.75 thf(func_def_67, type, produc403791768_sc_sz: (denota610675952t_unit > denota610675952t_unit) > (produc866628903_sc_sz > produc866628903_sc_sz) > produc1821101996_sc_sz > produc1821101996_sc_sz).
% 3.20/1.75 thf(func_def_68, type, produc1612557567real_c: (denota610675952t_unit > finite1398487019real_c) > (produc866628903_sc_sz > finite1398487019real_c) > produc1821101996_sc_sz > produc190496183real_c).
% 3.20/1.75 thf(func_def_69, type, produc1784590311_sc_sz: (finite1398487019real_c > denota610675952t_unit) > (finite1398487019real_c > produc866628903_sc_sz) > produc190496183real_c > produc1821101996_sc_sz).
% 3.20/1.75 thf(func_def_70, type, produc368345510real_c: (finite1398487019real_c > finite1398487019real_c) > (finite1398487019real_c > finite1398487019real_c) > produc190496183real_c > produc190496183real_c).
% 3.20/1.75 thf(func_def_71, type, produc619560141c_sz_o: (denota610675952t_unit > produc866628903_sc_sz > $o) > produc1821101996_sc_sz > $o).
% 3.20/1.75 thf(func_def_72, type, produc1920474870real_c: (denota610675952t_unit > produc866628903_sc_sz > finite1398487019real_c) > produc1821101996_sc_sz > finite1398487019real_c).
% 3.20/1.75 thf(func_def_73, type, produc448466487_sc_sz: (denota610675952t_unit > produc866628903_sc_sz > produc1821101996_sc_sz) > produc1821101996_sc_sz > produc1821101996_sc_sz).
% 3.20/1.75 thf(func_def_74, type, produc1575513068real_c: (denota610675952t_unit > produc866628903_sc_sz > produc190496183real_c) > produc1821101996_sc_sz > produc190496183real_c).
% 3.20/1.75 thf(func_def_75, type, produc2068697644real_c: (denota610675952t_unit > produc866628903_sc_sz > set_Fi1407883041real_c) > produc1821101996_sc_sz > set_Fi1407883041real_c).
% 3.20/1.75 thf(func_def_76, type, produc237521996real_c: (denota610675952t_unit > produc866628903_sc_sz > set_Pr1389752855real_c) > produc1821101996_sc_sz > set_Pr1389752855real_c).
% 3.20/1.75 thf(func_def_77, type, produc353381908al_c_o: (finite1398487019real_c > finite1398487019real_c > $o) > produc190496183real_c > $o).
% 3.20/1.75 thf(func_def_78, type, produc567249007real_c: (finite1398487019real_c > finite1398487019real_c > finite1398487019real_c) > produc190496183real_c > finite1398487019real_c).
% 3.20/1.75 thf(func_def_79, type, produc107375667real_c: (finite1398487019real_c > finite1398487019real_c > produc190496183real_c) > produc190496183real_c > produc190496183real_c).
% 3.20/1.75 thf(func_def_80, type, produc1341776291_sc_sz: (finite1398487019real_c > finite1398487019real_c > produc866628903_sc_sz) > produc190496183real_c > produc866628903_sc_sz).
% 3.20/1.75 thf(func_def_81, type, produc29022117real_c: (finite1398487019real_c > finite1398487019real_c > set_Fi1407883041real_c) > produc190496183real_c > set_Fi1407883041real_c).
% 3.20/1.75 thf(func_def_82, type, produc923381907real_c: (finite1398487019real_c > finite1398487019real_c > set_Pr1389752855real_c) > produc190496183real_c > set_Pr1389752855real_c).
% 3.20/1.75 thf(func_def_83, type, produc642283651_sc_sz: (finite1398487019real_c > finite1398487019real_c > set_Pr1774599175_sc_sz) > produc190496183real_c > set_Pr1774599175_sc_sz).
% 3.20/1.75 thf(func_def_84, type, produc2039065452c_sz_o: (list_f1238882004_sc_sz > list_f1238882004_sc_sz > $o) > produc866628903_sc_sz > $o).
% 3.20/1.75 thf(func_def_85, type, produc236226839real_c: (list_f1238882004_sc_sz > list_f1238882004_sc_sz > finite1398487019real_c) > produc866628903_sc_sz > finite1398487019real_c).
% 3.20/1.75 thf(func_def_86, type, produc126255499real_c: (list_f1238882004_sc_sz > list_f1238882004_sc_sz > produc190496183real_c) > produc866628903_sc_sz > produc190496183real_c).
% 3.20/1.75 thf(func_def_87, type, produc1449736269real_c: (list_f1238882004_sc_sz > list_f1238882004_sc_sz > set_Fi1407883041real_c) > produc866628903_sc_sz > set_Fi1407883041real_c).
% 3.20/1.75 thf(func_def_88, type, produc6841835real_c: (list_f1238882004_sc_sz > list_f1238882004_sc_sz > set_Pr1389752855real_c) > produc866628903_sc_sz > set_Pr1389752855real_c).
% 3.20/1.75 thf(func_def_89, type, produc1563580891_sc_sz: (list_f1238882004_sc_sz > list_f1238882004_sc_sz > set_Pr1774599175_sc_sz) > produc866628903_sc_sz > set_Pr1774599175_sc_sz).
% 3.20/1.75 thf(func_def_90, type, produc1726730540al_c_o: (produc190496183real_c > produc190496183real_c > $o) > produc640052711real_c > $o).
% 3.20/1.75 thf(func_def_91, type, produc344593239real_c: (produc190496183real_c > produc190496183real_c > finite1398487019real_c) > produc640052711real_c > finite1398487019real_c).
% 3.20/1.75 thf(func_def_92, type, produc1066779277real_c: (produc190496183real_c > produc190496183real_c > set_Fi1407883041real_c) > produc640052711real_c > set_Fi1407883041real_c).
% 3.20/1.75 thf(func_def_93, type, produc1718498667unit_o: (produc866628903_sc_sz > denota610675952t_unit > $o) > produc999471430t_unit > $o).
% 3.20/1.75 thf(func_def_94, type, produc1753599960real_c: (produc866628903_sc_sz > denota610675952t_unit > finite1398487019real_c) > produc999471430t_unit > finite1398487019real_c).
% 3.20/1.75 thf(func_def_95, type, produc435149849_sc_sz: (produc866628903_sc_sz > denota610675952t_unit > produc1821101996_sc_sz) > produc999471430t_unit > produc1821101996_sc_sz).
% 3.20/1.75 thf(func_def_96, type, produc645763722real_c: (produc866628903_sc_sz > denota610675952t_unit > produc190496183real_c) > produc999471430t_unit > produc190496183real_c).
% 3.20/1.75 thf(func_def_97, type, produc1368849166real_c: (produc866628903_sc_sz > denota610675952t_unit > set_Fi1407883041real_c) > produc999471430t_unit > set_Fi1407883041real_c).
% 3.20/1.75 thf(func_def_98, type, produc593754858real_c: (produc866628903_sc_sz > denota610675952t_unit > set_Pr1389752855real_c) > produc999471430t_unit > set_Pr1389752855real_c).
% 3.20/1.75 thf(func_def_99, type, produc1503602930_sc_sz: produc1821101996_sc_sz > denota610675952t_unit).
% 3.20/1.75 thf(func_def_100, type, produc532048446_sc_sz: produc1821101996_sc_sz > produc999471430t_unit).
% 3.20/1.75 thf(func_def_101, type, produc704157711real_c: produc190496183real_c > produc190496183real_c).
% 3.20/1.75 thf(func_def_102, type, produc1145837239_sc_sz: produc866628903_sc_sz > produc866628903_sc_sz).
% 3.20/1.75 thf(func_def_103, type, produc350724343real_c: produc640052711real_c > produc640052711real_c).
% 3.20/1.75 thf(func_def_104, type, produc245128480t_unit: produc999471430t_unit > produc1821101996_sc_sz).
% 3.20/1.75 thf(func_def_105, type, produc3751594real_c: set_Fi1407883041real_c > set_Fi1407883041real_c > set_Pr1389752855real_c).
% 3.20/1.75 thf(func_def_106, type, inv_im1827249322real_c: set_Pr1389752855real_c > (finite1398487019real_c > finite1398487019real_c) > set_Pr1389752855real_c).
% 3.20/1.75 thf(func_def_107, type, collec230941376real_c: (finite1398487019real_c > $o) > set_Fi1407883041real_c).
% 3.20/1.75 thf(func_def_108, type, collec1199592193_sc_sz: (produc1821101996_sc_sz > $o) > set_Pr1169339874_sc_sz).
% 3.20/1.75 thf(func_def_109, type, collec1643251106real_c: (produc190496183real_c > $o) > set_Pr1389752855real_c).
% 3.20/1.75 thf(func_def_110, type, collec2036662930_sc_sz: (produc866628903_sc_sz > $o) > set_Pr1774599175_sc_sz).
% 3.20/1.75 thf(func_def_111, type, collec1126017874real_c: (produc640052711real_c > $o) > set_Pr754230471real_c).
% 3.20/1.75 thf(func_def_112, type, collec377961627t_unit: (produc999471430t_unit > $o) > set_Pr2041213564t_unit).
% 3.20/1.75 thf(func_def_113, type, image_1514048989real_c: (finite1398487019real_c > finite1398487019real_c) > set_Fi1407883041real_c > set_Fi1407883041real_c).
% 3.20/1.75 thf(func_def_114, type, image_1461287749real_c: (finite1398487019real_c > produc190496183real_c) > set_Fi1407883041real_c > set_Pr1389752855real_c).
% 3.20/1.75 thf(func_def_115, type, image_290183605_sc_sz: (finite1398487019real_c > produc866628903_sc_sz) > set_Fi1407883041real_c > set_Pr1774599175_sc_sz).
% 3.20/1.75 thf(func_def_116, type, image_1746662005real_c: (finite1398487019real_c > produc640052711real_c) > set_Fi1407883041real_c > set_Pr754230471real_c).
% 3.20/1.75 thf(func_def_117, type, image_1641704997c_sz_o: (produc1821101996_sc_sz > $o) > set_Pr1169339874_sc_sz > set_o).
% 3.20/1.75 thf(func_def_118, type, image_1268968350real_c: (produc1821101996_sc_sz > finite1398487019real_c) > set_Pr1169339874_sc_sz > set_Fi1407883041real_c).
% 3.20/1.75 thf(func_def_119, type, image_1726193375_sc_sz: (produc1821101996_sc_sz > produc1821101996_sc_sz) > set_Pr1169339874_sc_sz > set_Pr1169339874_sc_sz).
% 3.20/1.75 thf(func_def_120, type, image_386905412real_c: (produc1821101996_sc_sz > produc190496183real_c) > set_Pr1169339874_sc_sz > set_Pr1389752855real_c).
% 3.20/1.75 thf(func_def_121, type, image_904562809t_unit: (produc1821101996_sc_sz > produc999471430t_unit) > set_Pr1169339874_sc_sz > set_Pr2041213564t_unit).
% 3.20/1.75 thf(func_def_122, type, image_14429021real_c: (produc190496183real_c > finite1398487019real_c) > set_Pr1389752855real_c > set_Fi1407883041real_c).
% 3.20/1.75 thf(func_def_123, type, image_1259833374_sc_sz: (produc190496183real_c > produc1821101996_sc_sz) > set_Pr1389752855real_c > set_Pr1169339874_sc_sz).
% 3.20/1.75 thf(func_def_124, type, image_738229701real_c: (produc190496183real_c > produc190496183real_c) > set_Pr1389752855real_c > set_Pr1389752855real_c).
% 3.20/1.75 thf(func_def_125, type, image_388766773_sc_sz: (produc190496183real_c > produc866628903_sc_sz) > set_Pr1389752855real_c > set_Pr1774599175_sc_sz).
% 3.20/1.75 thf(func_def_126, type, image_1332486093real_c: (produc866628903_sc_sz > finite1398487019real_c) > set_Pr1774599175_sc_sz > set_Fi1407883041real_c).
% 3.20/1.75 thf(func_def_127, type, image_226055310_sc_sz: (produc866628903_sc_sz > produc1821101996_sc_sz) > set_Pr1774599175_sc_sz > set_Pr1169339874_sc_sz).
% 3.20/1.75 thf(func_def_128, type, image_1121381717real_c: (produc866628903_sc_sz > produc190496183real_c) > set_Pr1774599175_sc_sz > set_Pr1389752855real_c).
% 3.20/1.75 thf(func_def_129, type, image_1313166277_sc_sz: (produc866628903_sc_sz > produc866628903_sc_sz) > set_Pr1774599175_sc_sz > set_Pr1774599175_sc_sz).
% 3.20/1.75 thf(func_def_130, type, image_768765061real_c: (produc866628903_sc_sz > produc640052711real_c) > set_Pr1774599175_sc_sz > set_Pr754230471real_c).
% 3.20/1.75 thf(func_def_131, type, image_1551908392t_unit: (produc866628903_sc_sz > produc999471430t_unit) > set_Pr1774599175_sc_sz > set_Pr2041213564t_unit).
% 3.20/1.75 thf(func_def_132, type, image_124598413real_c: (produc640052711real_c > finite1398487019real_c) > set_Pr754230471real_c > set_Fi1407883041real_c).
% 3.20/1.75 thf(func_def_133, type, image_2041365445real_c: (produc640052711real_c > produc640052711real_c) > set_Pr754230471real_c > set_Pr754230471real_c).
% 3.20/1.75 thf(func_def_134, type, image_1269062456real_c: (produc999471430t_unit > finite1398487019real_c) > set_Pr2041213564t_unit > set_Fi1407883041real_c).
% 3.20/1.75 thf(func_def_135, type, image_1426741113_sc_sz: (produc999471430t_unit > produc1821101996_sc_sz) > set_Pr2041213564t_unit > set_Pr1169339874_sc_sz).
% 3.20/1.75 thf(func_def_136, type, static_FVF_a_b_c: formula_a_b_c > set_Sum_sum_c_c).
% 3.20/1.75 thf(func_def_137, type, static_SIGF_a_b_c: formula_a_b_c > set_Su1783761653um_b_c).
% 3.20/1.75 thf(func_def_138, type, equiv_a_b_c: formula_a_b_c > formula_a_b_c > formula_a_b_c).
% 3.20/1.75 thf(func_def_139, type, implies_a_b_c: formula_a_b_c > formula_a_b_c > formula_a_b_c).
% 3.20/1.75 thf(func_def_140, type, predic913887884_sf_sz: sc > formula_sf_sc_sz).
% 3.20/1.75 thf(func_def_141, type, p_sc_sf_sz: sc > formula_sf_sc_sz).
% 3.20/1.75 thf(func_def_142, type, member_o: $o > set_o > $o).
% 3.20/1.75 thf(func_def_143, type, member754147591t_unit: denota610675952t_unit > set_De208295462t_unit > $o).
% 3.20/1.75 thf(func_def_144, type, member1261661570real_c: finite1398487019real_c > set_Fi1407883041real_c > $o).
% 3.20/1.75 thf(func_def_145, type, member1057565379_sc_sz: produc1821101996_sc_sz > set_Pr1169339874_sc_sz > $o).
% 3.20/1.75 thf(func_def_146, type, member1895684704real_c: produc190496183real_c > set_Pr1389752855real_c > $o).
% 3.20/1.75 thf(func_def_147, type, member630771088eal_sz: produc1149990247eal_sz > set_Pr60491591eal_sz > $o).
% 3.20/1.75 thf(func_def_148, type, member245028432_sc_sz: produc866628903_sc_sz > set_Pr1774599175_sc_sz > $o).
% 3.20/1.75 thf(func_def_149, type, member346808080real_c: produc640052711real_c > set_Pr754230471real_c > $o).
% 3.20/1.75 thf(func_def_150, type, member235934813t_unit: produc999471430t_unit > set_Pr2041213564t_unit > $o).
% 3.20/1.75 thf(func_def_151, type, phi: formula_a_b_c).
% 3.20/1.75 thf(func_def_171, type, sK0: denota231621370t_unit).
% 3.20/1.75 thf(func_def_172, type, sK1: produc190496183real_c).
% 3.20/1.75 thf(func_def_173, type, sK2: denota231621370t_unit).
% 3.20/1.75 thf(func_def_174, type, sK3: produc190496183real_c).
% 3.20/1.75 thf(func_def_175, type, sK4: produc190496183real_c).
% 3.20/1.75 thf(func_def_176, type, sK5: produc190496183real_c).
% 3.20/1.75 thf(func_def_177, type, sK6: denota231621370t_unit).
% 3.20/1.75 thf(func_def_178, type, sK7: denota231621370t_unit).
% 3.20/1.75 thf(f1504,plain,(
% 3.20/1.75 $false),
% 3.20/1.75 inference(avatar_sat_refutation,[status(thm)],[f970,f987,f996,f1005,f1006,f1011,f1012,f1013,f1017,f1023,f1024,f1025,f1026,f1027,f1032,f1033,f1034,f1035,f1071,f1169,f1190,f1432,f1439,f1443,f1484,f1500,f1503])).
% 3.20/1.75 thf(f1503,plain,(
% 3.20/1.75 spl8_10 | ~spl8_1 | ~spl8_9 | ~spl8_12 | ~spl8_14),
% 3.20/1.75 inference(avatar_split_clause,[status(thm)],[f1502,f1029,f1015,f998,f963,f1002])).
% 3.20/1.75 thf(f1002,definition,(
% 3.20/1.75 spl8_10 <=> ((member1895684704real_c @ sK1 @ (denota968303861_a_b_c @ sK0 @ phi)) = $false)),
% 3.20/1.75 introduced(definition,[new_symbols(naming,[spl8_10])],[avatar_definition])).
% 3.20/1.75 thf(f963,definition,(
% 3.20/1.75 spl8_1 <=> ((denota1997846518gree_c @ sK1 @ sK3 @ (static_FVF_a_b_c @ phi)) = $true)),
% 3.20/1.75 introduced(definition,[new_symbols(naming,[spl8_1])],[avatar_definition])).
% 3.20/1.75 thf(f998,definition,(
% 3.20/1.75 spl8_9 <=> ($false = (member1895684704real_c @ sK3 @ (denota968303861_a_b_c @ sK2 @ phi)))),
% 3.20/1.75 introduced(definition,[new_symbols(naming,[spl8_9])],[avatar_definition])).
% 3.20/1.75 thf(f1015,definition,(
% 3.20/1.75 spl8_12 <=> ! [X13 : produc190496183real_c,X14 : denota231621370t_unit,X12 : produc190496183real_c,X15 : denota231621370t_unit] : (((denota69106024_a_b_c @ X15 @ X14 @ (static_SIGF_a_b_c @ phi)) != $true) | ((denota1997846518gree_c @ X13 @ X12 @ (static_FVF_a_b_c @ phi)) != $true) | ($false = (member1895684704real_c @ X13 @ (denota968303861_a_b_c @ X15 @ phi))) | ($true = (member1895684704real_c @ X12 @ (denota968303861_a_b_c @ X14 @ phi))))),
% 3.20/1.75 introduced(definition,[new_symbols(naming,[spl8_12])],[avatar_definition])).
% 3.20/1.75 thf(f1029,definition,(
% 3.20/1.75 spl8_14 <=> ($true = (denota69106024_a_b_c @ sK0 @ sK2 @ (static_SIGF_a_b_c @ phi)))),
% 3.20/1.75 introduced(definition,[new_symbols(naming,[spl8_14])],[avatar_definition])).
% 3.20/1.75 thf(f1502,plain,(
% 3.20/1.75 ((member1895684704real_c @ sK1 @ (denota968303861_a_b_c @ sK0 @ phi)) = $false) | (~spl8_1 | ~spl8_9 | ~spl8_12 | ~spl8_14)),
% 3.20/1.75 inference(trivial_inequality_removal,[status(thm)],[f1501])).
% 3.20/1.75 thf(f1501,plain,(
% 3.20/1.75 ((member1895684704real_c @ sK1 @ (denota968303861_a_b_c @ sK0 @ phi)) = $false) | ($false = $true) | (~spl8_1 | ~spl8_9 | ~spl8_12 | ~spl8_14)),
% 3.20/1.75 inference(forward_demodulation,[status(thm)],[f1464,f1000])).
% 3.20/1.75 thf(f1000,plain,(
% 3.20/1.75 ($false = (member1895684704real_c @ sK3 @ (denota968303861_a_b_c @ sK2 @ phi))) | ~spl8_9),
% 3.20/1.75 inference(avatar_component_clause,[status(thm)],[f998])).
% 3.20/1.75 thf(f1464,plain,(
% 3.20/1.75 ((member1895684704real_c @ sK3 @ (denota968303861_a_b_c @ sK2 @ phi)) = $true) | ((member1895684704real_c @ sK1 @ (denota968303861_a_b_c @ sK0 @ phi)) = $false) | (~spl8_1 | ~spl8_12 | ~spl8_14)),
% 3.20/1.75 inference(trivial_inequality_removal,[status(thm)],[f1457])).
% 3.20/1.75 thf(f1457,plain,(
% 3.20/1.75 ((member1895684704real_c @ sK1 @ (denota968303861_a_b_c @ sK0 @ phi)) = $false) | ((member1895684704real_c @ sK3 @ (denota968303861_a_b_c @ sK2 @ phi)) = $true) | ($true != $true) | (~spl8_1 | ~spl8_12 | ~spl8_14)),
% 3.20/1.75 inference(superposition,[status(thm)],[f1200,f1031])).
% 3.20/1.75 thf(f1031,plain,(
% 3.20/1.75 ($true = (denota69106024_a_b_c @ sK0 @ sK2 @ (static_SIGF_a_b_c @ phi))) | ~spl8_14),
% 3.20/1.75 inference(avatar_component_clause,[status(thm)],[f1029])).
% 3.20/1.75 thf(f1200,plain,(
% 3.20/1.75 ( ! [X0 : denota231621370t_unit,X1 : denota231621370t_unit] : (($true != (denota69106024_a_b_c @ X0 @ X1 @ (static_SIGF_a_b_c @ phi))) | ((member1895684704real_c @ sK3 @ (denota968303861_a_b_c @ X1 @ phi)) = $true) | ((member1895684704real_c @ sK1 @ (denota968303861_a_b_c @ X0 @ phi)) = $false)) ) | (~spl8_1 | ~spl8_12)),
% 3.20/1.75 inference(trivial_inequality_removal,[status(thm)],[f1199])).
% 3.20/1.75 thf(f1199,plain,(
% 3.20/1.75 ( ! [X0 : denota231621370t_unit,X1 : denota231621370t_unit] : (($true != (denota69106024_a_b_c @ X0 @ X1 @ (static_SIGF_a_b_c @ phi))) | ((member1895684704real_c @ sK1 @ (denota968303861_a_b_c @ X0 @ phi)) = $false) | ($true != $true) | ((member1895684704real_c @ sK3 @ (denota968303861_a_b_c @ X1 @ phi)) = $true)) ) | (~spl8_1 | ~spl8_12)),
% 3.20/1.75 inference(superposition,[status(thm)],[f1016,f965])).
% 3.20/1.75 thf(f965,plain,(
% 3.20/1.75 ((denota1997846518gree_c @ sK1 @ sK3 @ (static_FVF_a_b_c @ phi)) = $true) | ~spl8_1),
% 3.20/1.75 inference(avatar_component_clause,[status(thm)],[f963])).
% 3.20/1.75 thf(f1016,plain,(
% 3.20/1.75 ( ! [X14 : denota231621370t_unit,X15 : denota231621370t_unit,X12 : produc190496183real_c,X13 : produc190496183real_c] : (((denota1997846518gree_c @ X13 @ X12 @ (static_FVF_a_b_c @ phi)) != $true) | ((denota69106024_a_b_c @ X15 @ X14 @ (static_SIGF_a_b_c @ phi)) != $true) | ($true = (member1895684704real_c @ X12 @ (denota968303861_a_b_c @ X14 @ phi))) | ($false = (member1895684704real_c @ X13 @ (denota968303861_a_b_c @ X15 @ phi)))) ) | ~spl8_12),
% 3.20/1.75 inference(avatar_component_clause,[status(thm)],[f1015])).
% 3.20/1.75 thf(f1500,plain,(
% 3.20/1.75 ~spl8_5 | ~spl8_10),
% 3.20/1.75 inference(avatar_contradiction_clause,[status(thm)],[f1499])).
% 3.20/1.75 thf(f1499,plain,(
% 3.20/1.75 $false | (~spl8_5 | ~spl8_10)),
% 3.20/1.75 inference(trivial_inequality_removal,[status(thm)],[f1498])).
% 3.20/1.75 thf(f1498,plain,(
% 3.20/1.75 ($false = $true) | (~spl8_5 | ~spl8_10)),
% 3.20/1.75 inference(forward_demodulation,[status(thm)],[f982,f1004])).
% 3.20/1.75 thf(f1004,plain,(
% 3.20/1.75 ((member1895684704real_c @ sK1 @ (denota968303861_a_b_c @ sK0 @ phi)) = $false) | ~spl8_10),
% 3.20/1.75 inference(avatar_component_clause,[status(thm)],[f1002])).
% 3.20/1.75 thf(f982,plain,(
% 3.20/1.75 ((member1895684704real_c @ sK1 @ (denota968303861_a_b_c @ sK0 @ phi)) = $true) | ~spl8_5),
% 3.20/1.75 inference(avatar_component_clause,[status(thm)],[f980])).
% 3.20/1.75 thf(f980,definition,(
% 3.20/1.75 spl8_5 <=> ((member1895684704real_c @ sK1 @ (denota968303861_a_b_c @ sK0 @ phi)) = $true)),
% 3.20/1.75 introduced(definition,[new_symbols(naming,[spl8_5])],[avatar_definition])).
% 3.20/1.75 thf(f1484,plain,(
% 3.20/1.75 ~spl8_4 | ~spl8_9),
% 3.20/1.75 inference(avatar_contradiction_clause,[status(thm)],[f1483])).
% 3.20/1.75 thf(f1483,plain,(
% 3.20/1.75 $false | (~spl8_4 | ~spl8_9)),
% 3.20/1.75 inference(trivial_inequality_removal,[status(thm)],[f1465])).
% 3.20/1.75 thf(f1465,plain,(
% 3.20/1.75 ($false = $true) | (~spl8_4 | ~spl8_9)),
% 3.20/1.75 inference(superposition,[status(thm)],[f1000,f978])).
% 3.20/1.75 thf(f978,plain,(
% 3.20/1.75 ((member1895684704real_c @ sK3 @ (denota968303861_a_b_c @ sK2 @ phi)) = $true) | ~spl8_4),
% 3.20/1.75 inference(avatar_component_clause,[status(thm)],[f976])).
% 3.20/1.75 thf(f976,definition,(
% 3.20/1.75 spl8_4 <=> ((member1895684704real_c @ sK3 @ (denota968303861_a_b_c @ sK2 @ phi)) = $true)),
% 3.20/1.75 introduced(definition,[new_symbols(naming,[spl8_4])],[avatar_definition])).
% 3.20/1.75 thf(f1443,plain,(
% 3.20/1.75 ~spl8_2 | spl8_7 | ~spl8_8 | ~spl8_11 | ~spl8_13),
% 3.20/1.75 inference(avatar_contradiction_clause,[status(thm)],[f1442])).
% 3.20/1.75 thf(f1442,plain,(
% 3.20/1.75 $false | (~spl8_2 | spl8_7 | ~spl8_8 | ~spl8_11 | ~spl8_13)),
% 3.20/1.75 inference(trivial_inequality_removal,[status(thm)],[f1441])).
% 3.20/1.75 thf(f1441,plain,(
% 3.20/1.75 ($false = $true) | (~spl8_2 | spl8_7 | ~spl8_8 | ~spl8_11 | ~spl8_13)),
% 3.20/1.75 inference(forward_demodulation,[status(thm)],[f1440,f995])).
% 3.20/1.75 thf(f995,plain,(
% 3.20/1.75 ($false = (member1895684704real_c @ sK5 @ (denota968303861_a_b_c @ sK7 @ phi))) | ~spl8_8),
% 3.20/1.75 inference(avatar_component_clause,[status(thm)],[f993])).
% 3.20/1.75 thf(f993,definition,(
% 3.20/1.75 spl8_8 <=> ($false = (member1895684704real_c @ sK5 @ (denota968303861_a_b_c @ sK7 @ phi)))),
% 3.20/1.75 introduced(definition,[new_symbols(naming,[spl8_8])],[avatar_definition])).
% 3.20/1.75 thf(f1440,plain,(
% 3.20/1.75 ($true = (member1895684704real_c @ sK5 @ (denota968303861_a_b_c @ sK7 @ phi))) | (~spl8_2 | spl8_7 | ~spl8_11 | ~spl8_13)),
% 3.20/1.75 inference(subsumption_resolution,[status(thm)],[f1345,f990])).
% 3.20/1.75 thf(f990,plain,(
% 3.20/1.75 ($false != (member1895684704real_c @ sK4 @ (denota968303861_a_b_c @ sK6 @ phi))) | spl8_7),
% 3.20/1.75 inference(avatar_component_clause,[status(thm)],[f989])).
% 3.20/1.75 thf(f989,definition,(
% 3.20/1.75 spl8_7 <=> ($false = (member1895684704real_c @ sK4 @ (denota968303861_a_b_c @ sK6 @ phi)))),
% 3.20/1.75 introduced(definition,[new_symbols(naming,[spl8_7])],[avatar_definition])).
% 3.20/1.75 thf(f1345,plain,(
% 3.20/1.75 ($true = (member1895684704real_c @ sK5 @ (denota968303861_a_b_c @ sK7 @ phi))) | ($false = (member1895684704real_c @ sK4 @ (denota968303861_a_b_c @ sK6 @ phi))) | (~spl8_2 | ~spl8_11 | ~spl8_13)),
% 3.20/1.75 inference(trivial_inequality_removal,[status(thm)],[f1344])).
% 3.20/1.75 thf(f1344,plain,(
% 3.20/1.75 ($true != $true) | ($false = (member1895684704real_c @ sK4 @ (denota968303861_a_b_c @ sK6 @ phi))) | ($true = (member1895684704real_c @ sK5 @ (denota968303861_a_b_c @ sK7 @ phi))) | (~spl8_2 | ~spl8_11 | ~spl8_13)),
% 3.20/1.75 inference(superposition,[status(thm)],[f1152,f1010])).
% 3.20/1.75 thf(f1010,plain,(
% 3.20/1.75 ($true = (denota1997846518gree_c @ sK5 @ sK4 @ (static_FVF_a_b_c @ phi))) | ~spl8_11),
% 3.20/1.75 inference(avatar_component_clause,[status(thm)],[f1008])).
% 3.20/1.75 thf(f1008,definition,(
% 3.20/1.75 spl8_11 <=> ($true = (denota1997846518gree_c @ sK5 @ sK4 @ (static_FVF_a_b_c @ phi)))),
% 3.20/1.75 introduced(definition,[new_symbols(naming,[spl8_11])],[avatar_definition])).
% 3.20/1.75 thf(f1152,plain,(
% 3.20/1.75 ( ! [X0 : produc190496183real_c,X1 : produc190496183real_c] : (($true != (denota1997846518gree_c @ X0 @ X1 @ (static_FVF_a_b_c @ phi))) | ($true = (member1895684704real_c @ X0 @ (denota968303861_a_b_c @ sK7 @ phi))) | ((member1895684704real_c @ X1 @ (denota968303861_a_b_c @ sK6 @ phi)) = $false)) ) | (~spl8_2 | ~spl8_13)),
% 3.20/1.75 inference(trivial_inequality_removal,[status(thm)],[f1151])).
% 3.20/1.75 thf(f1151,plain,(
% 3.20/1.75 ( ! [X0 : produc190496183real_c,X1 : produc190496183real_c] : (($true = (member1895684704real_c @ X0 @ (denota968303861_a_b_c @ sK7 @ phi))) | ((member1895684704real_c @ X1 @ (denota968303861_a_b_c @ sK6 @ phi)) = $false) | ($true != (denota1997846518gree_c @ X0 @ X1 @ (static_FVF_a_b_c @ phi))) | ($true != $true)) ) | (~spl8_2 | ~spl8_13)),
% 3.20/1.75 inference(superposition,[status(thm)],[f1020,f969])).
% 3.20/1.75 thf(f969,plain,(
% 3.20/1.75 ($true = (denota69106024_a_b_c @ sK7 @ sK6 @ (static_SIGF_a_b_c @ phi))) | ~spl8_2),
% 3.20/1.75 inference(avatar_component_clause,[status(thm)],[f967])).
% 3.20/1.75 thf(f967,definition,(
% 3.20/1.75 spl8_2 <=> ($true = (denota69106024_a_b_c @ sK7 @ sK6 @ (static_SIGF_a_b_c @ phi)))),
% 3.20/1.75 introduced(definition,[new_symbols(naming,[spl8_2])],[avatar_definition])).
% 3.20/1.75 thf(f1020,plain,(
% 3.20/1.75 ( ! [X10 : denota231621370t_unit,X11 : produc190496183real_c,X8 : denota231621370t_unit,X9 : produc190496183real_c] : (($true != (denota69106024_a_b_c @ X8 @ X10 @ (static_SIGF_a_b_c @ phi))) | ((denota1997846518gree_c @ X9 @ X11 @ (static_FVF_a_b_c @ phi)) != $true) | ((member1895684704real_c @ X9 @ (denota968303861_a_b_c @ X8 @ phi)) = $true) | ((member1895684704real_c @ X11 @ (denota968303861_a_b_c @ X10 @ phi)) = $false)) ) | ~spl8_13),
% 3.20/1.75 inference(avatar_component_clause,[status(thm)],[f1019])).
% 3.20/1.75 thf(f1019,definition,(
% 3.20/1.75 spl8_13 <=> ! [X10 : denota231621370t_unit,X11 : produc190496183real_c,X9 : produc190496183real_c,X8 : denota231621370t_unit] : (((denota1997846518gree_c @ X9 @ X11 @ (static_FVF_a_b_c @ phi)) != $true) | ((member1895684704real_c @ X9 @ (denota968303861_a_b_c @ X8 @ phi)) = $true) | ((member1895684704real_c @ X11 @ (denota968303861_a_b_c @ X10 @ phi)) = $false) | ($true != (denota69106024_a_b_c @ X8 @ X10 @ (static_SIGF_a_b_c @ phi))))),
% 3.20/1.75 introduced(definition,[new_symbols(naming,[spl8_13])],[avatar_definition])).
% 3.20/1.75 thf(f1439,plain,(
% 3.20/1.75 ~spl8_2 | ~spl8_3 | ~spl8_8 | ~spl8_11 | ~spl8_13),
% 3.20/1.75 inference(avatar_contradiction_clause,[status(thm)],[f1438])).
% 3.20/1.75 thf(f1438,plain,(
% 3.20/1.75 $false | (~spl8_2 | ~spl8_3 | ~spl8_8 | ~spl8_11 | ~spl8_13)),
% 3.20/1.75 inference(trivial_inequality_removal,[status(thm)],[f1437])).
% 3.20/1.75 thf(f1437,plain,(
% 3.20/1.75 ($false = $true) | (~spl8_2 | ~spl8_3 | ~spl8_8 | ~spl8_11 | ~spl8_13)),
% 3.20/1.75 inference(forward_demodulation,[status(thm)],[f1436,f995])).
% 3.20/1.75 thf(f1436,plain,(
% 3.20/1.75 ($true = (member1895684704real_c @ sK5 @ (denota968303861_a_b_c @ sK7 @ phi))) | (~spl8_2 | ~spl8_3 | ~spl8_11 | ~spl8_13)),
% 3.20/1.75 inference(trivial_inequality_removal,[status(thm)],[f1435])).
% 3.20/1.75 thf(f1435,plain,(
% 3.20/1.75 ($true = (member1895684704real_c @ sK5 @ (denota968303861_a_b_c @ sK7 @ phi))) | ($false = $true) | (~spl8_2 | ~spl8_3 | ~spl8_11 | ~spl8_13)),
% 3.20/1.75 inference(forward_demodulation,[status(thm)],[f1345,f974])).
% 3.20/1.75 thf(f974,plain,(
% 3.20/1.75 ($true = (member1895684704real_c @ sK4 @ (denota968303861_a_b_c @ sK6 @ phi))) | ~spl8_3),
% 3.20/1.75 inference(avatar_component_clause,[status(thm)],[f972])).
% 3.20/1.75 thf(f972,definition,(
% 3.20/1.75 spl8_3 <=> ($true = (member1895684704real_c @ sK4 @ (denota968303861_a_b_c @ sK6 @ phi)))),
% 3.20/1.75 introduced(definition,[new_symbols(naming,[spl8_3])],[avatar_definition])).
% 3.20/1.75 thf(f1432,plain,(
% 3.20/1.75 spl8_9 | ~spl8_1 | ~spl8_10 | ~spl8_13 | ~spl8_14),
% 3.20/1.75 inference(avatar_split_clause,[status(thm)],[f1431,f1029,f1019,f1002,f963,f998])).
% 3.20/1.75 thf(f1431,plain,(
% 3.20/1.75 ($false = (member1895684704real_c @ sK3 @ (denota968303861_a_b_c @ sK2 @ phi))) | (~spl8_1 | ~spl8_10 | ~spl8_13 | ~spl8_14)),
% 3.20/1.75 inference(trivial_inequality_removal,[status(thm)],[f1430])).
% 3.20/1.75 thf(f1430,plain,(
% 3.20/1.75 ($false = (member1895684704real_c @ sK3 @ (denota968303861_a_b_c @ sK2 @ phi))) | ($false = $true) | (~spl8_1 | ~spl8_10 | ~spl8_13 | ~spl8_14)),
% 3.20/1.75 inference(forward_demodulation,[status(thm)],[f1429,f1004])).
% 3.20/1.75 thf(f1429,plain,(
% 3.20/1.75 ((member1895684704real_c @ sK1 @ (denota968303861_a_b_c @ sK0 @ phi)) = $true) | ($false = (member1895684704real_c @ sK3 @ (denota968303861_a_b_c @ sK2 @ phi))) | (~spl8_1 | ~spl8_13 | ~spl8_14)),
% 3.20/1.75 inference(trivial_inequality_removal,[status(thm)],[f1424])).
% 3.20/1.75 thf(f1424,plain,(
% 3.20/1.75 ($true != $true) | ((member1895684704real_c @ sK1 @ (denota968303861_a_b_c @ sK0 @ phi)) = $true) | ($false = (member1895684704real_c @ sK3 @ (denota968303861_a_b_c @ sK2 @ phi))) | (~spl8_1 | ~spl8_13 | ~spl8_14)),
% 3.20/1.75 inference(superposition,[status(thm)],[f1218,f965])).
% 3.20/1.75 thf(f1218,plain,(
% 3.20/1.75 ( ! [X0 : produc190496183real_c,X1 : produc190496183real_c] : (($true != (denota1997846518gree_c @ X0 @ X1 @ (static_FVF_a_b_c @ phi))) | ((member1895684704real_c @ X0 @ (denota968303861_a_b_c @ sK0 @ phi)) = $true) | ((member1895684704real_c @ X1 @ (denota968303861_a_b_c @ sK2 @ phi)) = $false)) ) | (~spl8_13 | ~spl8_14)),
% 3.20/1.75 inference(trivial_inequality_removal,[status(thm)],[f1217])).
% 3.20/1.75 thf(f1217,plain,(
% 3.20/1.75 ( ! [X0 : produc190496183real_c,X1 : produc190496183real_c] : (($true != $true) | ($true != (denota1997846518gree_c @ X0 @ X1 @ (static_FVF_a_b_c @ phi))) | ((member1895684704real_c @ X0 @ (denota968303861_a_b_c @ sK0 @ phi)) = $true) | ((member1895684704real_c @ X1 @ (denota968303861_a_b_c @ sK2 @ phi)) = $false)) ) | (~spl8_13 | ~spl8_14)),
% 3.20/1.75 inference(superposition,[status(thm)],[f1020,f1031])).
% 3.20/1.75 thf(f1190,plain,(
% 3.20/1.75 ~spl8_6 | ~spl8_8),
% 3.20/1.75 inference(avatar_contradiction_clause,[status(thm)],[f1189])).
% 3.20/1.75 thf(f1189,plain,(
% 3.20/1.75 $false | (~spl8_6 | ~spl8_8)),
% 3.20/1.75 inference(trivial_inequality_removal,[status(thm)],[f1175])).
% 3.20/1.75 thf(f1175,plain,(
% 3.20/1.75 ($false = $true) | (~spl8_6 | ~spl8_8)),
% 3.20/1.75 inference(superposition,[status(thm)],[f986,f995])).
% 3.20/1.75 thf(f986,plain,(
% 3.20/1.75 ($true = (member1895684704real_c @ sK5 @ (denota968303861_a_b_c @ sK7 @ phi))) | ~spl8_6),
% 3.20/1.75 inference(avatar_component_clause,[status(thm)],[f984])).
% 3.20/1.75 thf(f984,definition,(
% 3.20/1.75 spl8_6 <=> ($true = (member1895684704real_c @ sK5 @ (denota968303861_a_b_c @ sK7 @ phi)))),
% 3.20/1.75 introduced(definition,[new_symbols(naming,[spl8_6])],[avatar_definition])).
% 3.20/1.75 thf(f1169,plain,(
% 3.20/1.75 spl8_8 | ~spl8_2 | ~spl8_7 | ~spl8_11 | ~spl8_12),
% 3.20/1.75 inference(avatar_split_clause,[status(thm)],[f1168,f1015,f1008,f989,f967,f993])).
% 3.20/1.75 thf(f1168,plain,(
% 3.20/1.75 ($false = (member1895684704real_c @ sK5 @ (denota968303861_a_b_c @ sK7 @ phi))) | (~spl8_2 | ~spl8_7 | ~spl8_11 | ~spl8_12)),
% 3.20/1.75 inference(trivial_inequality_removal,[status(thm)],[f1167])).
% 3.20/1.75 thf(f1167,plain,(
% 3.20/1.75 ($false = $true) | ($false = (member1895684704real_c @ sK5 @ (denota968303861_a_b_c @ sK7 @ phi))) | (~spl8_2 | ~spl8_7 | ~spl8_11 | ~spl8_12)),
% 3.20/1.75 inference(forward_demodulation,[status(thm)],[f1164,f991])).
% 3.20/1.75 thf(f991,plain,(
% 3.20/1.75 ($false = (member1895684704real_c @ sK4 @ (denota968303861_a_b_c @ sK6 @ phi))) | ~spl8_7),
% 3.20/1.75 inference(avatar_component_clause,[status(thm)],[f989])).
% 3.20/1.75 thf(f1164,plain,(
% 3.20/1.75 ($false = (member1895684704real_c @ sK5 @ (denota968303861_a_b_c @ sK7 @ phi))) | ($true = (member1895684704real_c @ sK4 @ (denota968303861_a_b_c @ sK6 @ phi))) | (~spl8_2 | ~spl8_11 | ~spl8_12)),
% 3.20/1.75 inference(trivial_inequality_removal,[status(thm)],[f1163])).
% 3.20/1.75 thf(f1163,plain,(
% 3.20/1.75 ($true = (member1895684704real_c @ sK4 @ (denota968303861_a_b_c @ sK6 @ phi))) | ($true != $true) | ($false = (member1895684704real_c @ sK5 @ (denota968303861_a_b_c @ sK7 @ phi))) | (~spl8_2 | ~spl8_11 | ~spl8_12)),
% 3.20/1.75 inference(superposition,[status(thm)],[f1137,f969])).
% 3.20/1.75 thf(f1137,plain,(
% 3.20/1.75 ( ! [X0 : denota231621370t_unit,X1 : denota231621370t_unit] : (($true != (denota69106024_a_b_c @ X0 @ X1 @ (static_SIGF_a_b_c @ phi))) | ($false = (member1895684704real_c @ sK5 @ (denota968303861_a_b_c @ X0 @ phi))) | ((member1895684704real_c @ sK4 @ (denota968303861_a_b_c @ X1 @ phi)) = $true)) ) | (~spl8_11 | ~spl8_12)),
% 3.20/1.75 inference(trivial_inequality_removal,[status(thm)],[f1135])).
% 3.20/1.75 thf(f1135,plain,(
% 3.20/1.75 ( ! [X0 : denota231621370t_unit,X1 : denota231621370t_unit] : (($true != (denota69106024_a_b_c @ X0 @ X1 @ (static_SIGF_a_b_c @ phi))) | ((member1895684704real_c @ sK4 @ (denota968303861_a_b_c @ X1 @ phi)) = $true) | ($false = (member1895684704real_c @ sK5 @ (denota968303861_a_b_c @ X0 @ phi))) | ($true != $true)) ) | (~spl8_11 | ~spl8_12)),
% 3.20/1.75 inference(superposition,[status(thm)],[f1016,f1010])).
% 3.20/1.75 thf(f1071,plain,(
% 3.20/1.75 ~spl8_3 | ~spl8_7),
% 3.20/1.75 inference(avatar_contradiction_clause,[status(thm)],[f1070])).
% 3.20/1.75 thf(f1070,plain,(
% 3.20/1.75 $false | (~spl8_3 | ~spl8_7)),
% 3.20/1.75 inference(trivial_inequality_removal,[status(thm)],[f1050])).
% 3.20/1.75 thf(f1050,plain,(
% 3.20/1.75 ($false = $true) | (~spl8_3 | ~spl8_7)),
% 3.20/1.75 inference(superposition,[status(thm)],[f991,f974])).
% 3.20/1.75 thf(f1035,plain,(
% 3.20/1.75 spl8_8 | spl8_14 | spl8_7),
% 3.20/1.75 inference(avatar_split_clause,[status(thm)],[f943,f989,f1029,f993])).
% 3.20/1.75 thf(f943,plain,(
% 3.20/1.75 ($false = (member1895684704real_c @ sK4 @ (denota968303861_a_b_c @ sK6 @ phi))) | ($false = (member1895684704real_c @ sK5 @ (denota968303861_a_b_c @ sK7 @ phi))) | ($true = (denota69106024_a_b_c @ sK0 @ sK2 @ (static_SIGF_a_b_c @ phi)))),
% 3.20/1.75 inference(binary_proxy_clausification,[status(thm)],[f927])).
% 3.20/1.75 thf(f927,plain,(
% 3.20/1.75 ((member1895684704real_c @ sK5 @ (denota968303861_a_b_c @ sK7 @ phi)) != (member1895684704real_c @ sK4 @ (denota968303861_a_b_c @ sK6 @ phi))) | ($true = (denota69106024_a_b_c @ sK0 @ sK2 @ (static_SIGF_a_b_c @ phi)))),
% 3.20/1.75 inference(cnf_transformation,[status(thm)],[f919])).
% 3.20/1.75 thf(f919,plain,(
% 3.20/1.75 ((((denota1997846518gree_c @ sK1 @ sK3 @ (static_FVF_a_b_c @ phi)) = $true) & ((member1895684704real_c @ sK1 @ (denota968303861_a_b_c @ sK0 @ phi)) != (member1895684704real_c @ sK3 @ (denota968303861_a_b_c @ sK2 @ phi))) & ($true = (denota69106024_a_b_c @ sK0 @ sK2 @ (static_SIGF_a_b_c @ phi)))) | (($true = (denota1997846518gree_c @ sK5 @ sK4 @ (static_FVF_a_b_c @ phi))) & ((member1895684704real_c @ sK5 @ (denota968303861_a_b_c @ sK7 @ phi)) != (member1895684704real_c @ sK4 @ (denota968303861_a_b_c @ sK6 @ phi))) & ($true = (denota69106024_a_b_c @ sK7 @ sK6 @ (static_SIGF_a_b_c @ phi))))) & (! [X8 : denota231621370t_unit,X9 : produc190496183real_c,X10 : denota231621370t_unit,X11 : produc190496183real_c] : (((denota1997846518gree_c @ X9 @ X11 @ (static_FVF_a_b_c @ phi)) != $true) | ((member1895684704real_c @ X11 @ (denota968303861_a_b_c @ X10 @ phi)) = (member1895684704real_c @ X9 @ (denota968303861_a_b_c @ X8 @ phi))) | ($true != (denota69106024_a_b_c @ X8 @ X10 @ (static_SIGF_a_b_c @ phi)))) | ! [X12 : produc190496183real_c,X13 : produc190496183real_c,X14 : denota231621370t_unit,X15 : denota231621370t_unit] : (((denota1997846518gree_c @ X13 @ X12 @ (static_FVF_a_b_c @ phi)) != $true) | ((member1895684704real_c @ X12 @ (denota968303861_a_b_c @ X14 @ phi)) = (member1895684704real_c @ X13 @ (denota968303861_a_b_c @ X15 @ phi))) | ((denota69106024_a_b_c @ X15 @ X14 @ (static_SIGF_a_b_c @ phi)) != $true)))),
% 3.20/1.75 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7])],[f916,f918,f917])).
% 3.20/1.75 thf(f917,plain,(
% 3.20/1.75 ? [X0 : denota231621370t_unit,X1 : produc190496183real_c,X2 : denota231621370t_unit,X3 : produc190496183real_c] : (((denota1997846518gree_c @ X1 @ X3 @ (static_FVF_a_b_c @ phi)) = $true) & ((member1895684704real_c @ X1 @ (denota968303861_a_b_c @ X0 @ phi)) != (member1895684704real_c @ X3 @ (denota968303861_a_b_c @ X2 @ phi))) & ($true = (denota69106024_a_b_c @ X0 @ X2 @ (static_SIGF_a_b_c @ phi)))) => (((denota1997846518gree_c @ sK1 @ sK3 @ (static_FVF_a_b_c @ phi)) = $true) & ((member1895684704real_c @ sK1 @ (denota968303861_a_b_c @ sK0 @ phi)) != (member1895684704real_c @ sK3 @ (denota968303861_a_b_c @ sK2 @ phi))) & ($true = (denota69106024_a_b_c @ sK0 @ sK2 @ (static_SIGF_a_b_c @ phi))))),
% 3.20/1.75 introduced(definition,[],[choice_axiom])).
% 3.20/1.75 thf(f918,plain,(
% 3.20/1.75 ? [X4 : produc190496183real_c,X5 : produc190496183real_c,X6 : denota231621370t_unit,X7 : denota231621370t_unit] : (($true = (denota1997846518gree_c @ X5 @ X4 @ (static_FVF_a_b_c @ phi))) & ((member1895684704real_c @ X4 @ (denota968303861_a_b_c @ X6 @ phi)) != (member1895684704real_c @ X5 @ (denota968303861_a_b_c @ X7 @ phi))) & ($true = (denota69106024_a_b_c @ X7 @ X6 @ (static_SIGF_a_b_c @ phi)))) => (($true = (denota1997846518gree_c @ sK5 @ sK4 @ (static_FVF_a_b_c @ phi))) & ((member1895684704real_c @ sK5 @ (denota968303861_a_b_c @ sK7 @ phi)) != (member1895684704real_c @ sK4 @ (denota968303861_a_b_c @ sK6 @ phi))) & ($true = (denota69106024_a_b_c @ sK7 @ sK6 @ (static_SIGF_a_b_c @ phi))))),
% 3.20/1.75 introduced(definition,[],[choice_axiom])).
% 3.20/1.75 thf(f916,plain,(
% 3.20/1.75 (? [X0 : denota231621370t_unit,X1 : produc190496183real_c,X2 : denota231621370t_unit,X3 : produc190496183real_c] : (((denota1997846518gree_c @ X1 @ X3 @ (static_FVF_a_b_c @ phi)) = $true) & ((member1895684704real_c @ X1 @ (denota968303861_a_b_c @ X0 @ phi)) != (member1895684704real_c @ X3 @ (denota968303861_a_b_c @ X2 @ phi))) & ($true = (denota69106024_a_b_c @ X0 @ X2 @ (static_SIGF_a_b_c @ phi)))) | ? [X4 : produc190496183real_c,X5 : produc190496183real_c,X6 : denota231621370t_unit,X7 : denota231621370t_unit] : (($true = (denota1997846518gree_c @ X5 @ X4 @ (static_FVF_a_b_c @ phi))) & ((member1895684704real_c @ X4 @ (denota968303861_a_b_c @ X6 @ phi)) != (member1895684704real_c @ X5 @ (denota968303861_a_b_c @ X7 @ phi))) & ($true = (denota69106024_a_b_c @ X7 @ X6 @ (static_SIGF_a_b_c @ phi))))) & (! [X8 : denota231621370t_unit,X9 : produc190496183real_c,X10 : denota231621370t_unit,X11 : produc190496183real_c] : (((denota1997846518gree_c @ X9 @ X11 @ (static_FVF_a_b_c @ phi)) != $true) | ((member1895684704real_c @ X11 @ (denota968303861_a_b_c @ X10 @ phi)) = (member1895684704real_c @ X9 @ (denota968303861_a_b_c @ X8 @ phi))) | ($true != (denota69106024_a_b_c @ X8 @ X10 @ (static_SIGF_a_b_c @ phi)))) | ! [X12 : produc190496183real_c,X13 : produc190496183real_c,X14 : denota231621370t_unit,X15 : denota231621370t_unit] : (((denota1997846518gree_c @ X13 @ X12 @ (static_FVF_a_b_c @ phi)) != $true) | ((member1895684704real_c @ X12 @ (denota968303861_a_b_c @ X14 @ phi)) = (member1895684704real_c @ X13 @ (denota968303861_a_b_c @ X15 @ phi))) | ((denota69106024_a_b_c @ X15 @ X14 @ (static_SIGF_a_b_c @ phi)) != $true)))),
% 3.20/1.75 inference(rectify,[status(thm)],[f915])).
% 3.20/1.75 thf(f915,plain,(
% 3.20/1.75 (? [X4 : denota231621370t_unit,X5 : produc190496183real_c,X6 : denota231621370t_unit,X7 : produc190496183real_c] : (((denota1997846518gree_c @ X5 @ X7 @ (static_FVF_a_b_c @ phi)) = $true) & ((member1895684704real_c @ X5 @ (denota968303861_a_b_c @ X4 @ phi)) != (member1895684704real_c @ X7 @ (denota968303861_a_b_c @ X6 @ phi))) & ($true = (denota69106024_a_b_c @ X4 @ X6 @ (static_SIGF_a_b_c @ phi)))) | ? [X0 : produc190496183real_c,X1 : produc190496183real_c,X2 : denota231621370t_unit,X3 : denota231621370t_unit] : (($true = (denota1997846518gree_c @ X1 @ X0 @ (static_FVF_a_b_c @ phi))) & ((member1895684704real_c @ X1 @ (denota968303861_a_b_c @ X3 @ phi)) != (member1895684704real_c @ X0 @ (denota968303861_a_b_c @ X2 @ phi))) & ((denota69106024_a_b_c @ X3 @ X2 @ (static_SIGF_a_b_c @ phi)) = $true))) & (! [X4 : denota231621370t_unit,X5 : produc190496183real_c,X6 : denota231621370t_unit,X7 : produc190496183real_c] : (((denota1997846518gree_c @ X5 @ X7 @ (static_FVF_a_b_c @ phi)) != $true) | ((member1895684704real_c @ X5 @ (denota968303861_a_b_c @ X4 @ phi)) = (member1895684704real_c @ X7 @ (denota968303861_a_b_c @ X6 @ phi))) | ($true != (denota69106024_a_b_c @ X4 @ X6 @ (static_SIGF_a_b_c @ phi)))) | ! [X0 : produc190496183real_c,X1 : produc190496183real_c,X2 : denota231621370t_unit,X3 : denota231621370t_unit] : (($true != (denota1997846518gree_c @ X1 @ X0 @ (static_FVF_a_b_c @ phi))) | ((member1895684704real_c @ X1 @ (denota968303861_a_b_c @ X3 @ phi)) = (member1895684704real_c @ X0 @ (denota968303861_a_b_c @ X2 @ phi))) | ((denota69106024_a_b_c @ X3 @ X2 @ (static_SIGF_a_b_c @ phi)) != $true)))),
% 3.20/1.75 inference(nnf_transformation,[status(thm)],[f914])).
% 3.20/1.75 thf(f914,plain,(
% 3.20/1.75 ! [X0 : produc190496183real_c,X1 : produc190496183real_c,X2 : denota231621370t_unit,X3 : denota231621370t_unit] : (($true != (denota1997846518gree_c @ X1 @ X0 @ (static_FVF_a_b_c @ phi))) | ((member1895684704real_c @ X1 @ (denota968303861_a_b_c @ X3 @ phi)) = (member1895684704real_c @ X0 @ (denota968303861_a_b_c @ X2 @ phi))) | ((denota69106024_a_b_c @ X3 @ X2 @ (static_SIGF_a_b_c @ phi)) != $true)) <~> ! [X4 : denota231621370t_unit,X5 : produc190496183real_c,X6 : denota231621370t_unit,X7 : produc190496183real_c] : (((denota1997846518gree_c @ X5 @ X7 @ (static_FVF_a_b_c @ phi)) != $true) | ((member1895684704real_c @ X5 @ (denota968303861_a_b_c @ X4 @ phi)) = (member1895684704real_c @ X7 @ (denota968303861_a_b_c @ X6 @ phi))) | ($true != (denota69106024_a_b_c @ X4 @ X6 @ (static_SIGF_a_b_c @ phi))))),
% 3.20/1.75 inference(flattening,[status(thm)],[f913])).
% 3.20/1.75 thf(f913,plain,(
% 3.20/1.75 ! [X4 : denota231621370t_unit,X5 : produc190496183real_c,X6 : denota231621370t_unit,X7 : produc190496183real_c] : ((((member1895684704real_c @ X5 @ (denota968303861_a_b_c @ X4 @ phi)) = (member1895684704real_c @ X7 @ (denota968303861_a_b_c @ X6 @ phi))) | ((denota1997846518gree_c @ X5 @ X7 @ (static_FVF_a_b_c @ phi)) != $true)) | ($true != (denota69106024_a_b_c @ X4 @ X6 @ (static_SIGF_a_b_c @ phi)))) <~> ! [X0 : produc190496183real_c,X1 : produc190496183real_c,X2 : denota231621370t_unit,X3 : denota231621370t_unit] : ((((member1895684704real_c @ X1 @ (denota968303861_a_b_c @ X3 @ phi)) = (member1895684704real_c @ X0 @ (denota968303861_a_b_c @ X2 @ phi))) | ($true != (denota1997846518gree_c @ X1 @ X0 @ (static_FVF_a_b_c @ phi)))) | ((denota69106024_a_b_c @ X3 @ X2 @ (static_SIGF_a_b_c @ phi)) != $true))),
% 3.20/1.75 inference(ennf_transformation,[status(thm)],[f651])).
% 3.20/1.75 thf(f651,plain,(
% 3.20/1.75 ~(! [X4 : denota231621370t_unit,X5 : produc190496183real_c,X6 : denota231621370t_unit,X7 : produc190496183real_c] : (($true = (denota69106024_a_b_c @ X4 @ X6 @ (static_SIGF_a_b_c @ phi))) => (((denota1997846518gree_c @ X5 @ X7 @ (static_FVF_a_b_c @ phi)) = $true) => ((member1895684704real_c @ X5 @ (denota968303861_a_b_c @ X4 @ phi)) = (member1895684704real_c @ X7 @ (denota968303861_a_b_c @ X6 @ phi))))) <=> ! [X0 : produc190496183real_c,X1 : produc190496183real_c,X2 : denota231621370t_unit,X3 : denota231621370t_unit] : (((denota69106024_a_b_c @ X3 @ X2 @ (static_SIGF_a_b_c @ phi)) = $true) => (($true = (denota1997846518gree_c @ X1 @ X0 @ (static_FVF_a_b_c @ phi))) => ((member1895684704real_c @ X1 @ (denota968303861_a_b_c @ X3 @ phi)) = (member1895684704real_c @ X0 @ (denota968303861_a_b_c @ X2 @ phi))))))),
% 3.20/1.75 inference(fool_elimination,[status(thm)],[f650])).
% 3.20/1.75 thf(f650,plain,(
% 3.20/1.75 ~(! [X0 : produc190496183real_c,X1 : produc190496183real_c,X2 : denota231621370t_unit,X3 : denota231621370t_unit] : ((denota69106024_a_b_c @ X3 @ X2 @ (static_SIGF_a_b_c @ phi)) => ((denota1997846518gree_c @ X1 @ X0 @ (static_FVF_a_b_c @ phi)) => ((member1895684704real_c @ X1 @ (denota968303861_a_b_c @ X3 @ phi)) = (member1895684704real_c @ X0 @ (denota968303861_a_b_c @ X2 @ phi))))) = ! [X4 : denota231621370t_unit,X5 : produc190496183real_c,X6 : denota231621370t_unit,X7 : produc190496183real_c] : ((denota69106024_a_b_c @ X4 @ X6 @ (static_SIGF_a_b_c @ phi)) => ((denota1997846518gree_c @ X5 @ X7 @ (static_FVF_a_b_c @ phi)) => ((member1895684704real_c @ X5 @ (denota968303861_a_b_c @ X4 @ phi)) = (member1895684704real_c @ X7 @ (denota968303861_a_b_c @ X6 @ phi))))))),
% 3.20/1.75 inference(rectify,[status(thm)],[f356])).
% 3.20/1.75 thf(f356,negated_conjecture,(
% 3.20/1.75 ~(! [X2 : produc190496183real_c,X1 : produc190496183real_c,X4 : denota231621370t_unit,X3 : denota231621370t_unit] : ((denota69106024_a_b_c @ X3 @ X4 @ (static_SIGF_a_b_c @ phi)) => ((denota1997846518gree_c @ X1 @ X2 @ (static_FVF_a_b_c @ phi)) => ((member1895684704real_c @ X1 @ (denota968303861_a_b_c @ X3 @ phi)) = (member1895684704real_c @ X2 @ (denota968303861_a_b_c @ X4 @ phi))))) = ! [X3 : denota231621370t_unit,X1 : produc190496183real_c,X4 : denota231621370t_unit,X2 : produc190496183real_c] : ((denota69106024_a_b_c @ X3 @ X4 @ (static_SIGF_a_b_c @ phi)) => ((denota1997846518gree_c @ X1 @ X2 @ (static_FVF_a_b_c @ phi)) => ((member1895684704real_c @ X1 @ (denota968303861_a_b_c @ X3 @ phi)) = (member1895684704real_c @ X2 @ (denota968303861_a_b_c @ X4 @ phi))))))),
% 3.20/1.75 inference(negated_conjecture,[status(cth)],[f355])).
% 3.20/1.75 thf(f355,conjecture,(
% 3.20/1.75 (! [X2 : produc190496183real_c,X1 : produc190496183real_c,X4 : denota231621370t_unit,X3 : denota231621370t_unit] : ((denota69106024_a_b_c @ X3 @ X4 @ (static_SIGF_a_b_c @ phi)) => ((denota1997846518gree_c @ X1 @ X2 @ (static_FVF_a_b_c @ phi)) => ((member1895684704real_c @ X1 @ (denota968303861_a_b_c @ X3 @ phi)) = (member1895684704real_c @ X2 @ (denota968303861_a_b_c @ X4 @ phi))))) = ! [X3 : denota231621370t_unit,X1 : produc190496183real_c,X4 : denota231621370t_unit,X2 : produc190496183real_c] : ((denota69106024_a_b_c @ X3 @ X4 @ (static_SIGF_a_b_c @ phi)) => ((denota1997846518gree_c @ X1 @ X2 @ (static_FVF_a_b_c @ phi)) => ((member1895684704real_c @ X1 @ (denota968303861_a_b_c @ X3 @ phi)) = (member1895684704real_c @ X2 @ (denota968303861_a_b_c @ X4 @ phi))))))),
% 3.20/1.75 file('/export/starexec/sandbox2/tmp/tmp.jSP0w0K04t/DTF2THF_20700.p',conj_0)).
% 3.20/1.75 thf(f1034,plain,(
% 3.20/1.75 spl8_6 | spl8_3 | spl8_14),
% 3.20/1.75 inference(avatar_split_clause,[status(thm)],[f942,f1029,f972,f984])).
% 3.20/1.75 thf(f942,plain,(
% 3.20/1.75 ($true = (denota69106024_a_b_c @ sK0 @ sK2 @ (static_SIGF_a_b_c @ phi))) | ($true = (member1895684704real_c @ sK4 @ (denota968303861_a_b_c @ sK6 @ phi))) | ($true = (member1895684704real_c @ sK5 @ (denota968303861_a_b_c @ sK7 @ phi)))),
% 3.20/1.75 inference(binary_proxy_clausification,[status(thm)],[f927])).
% 3.20/1.75 thf(f1033,plain,(
% 3.20/1.75 spl8_14 | spl8_2),
% 3.20/1.75 inference(avatar_split_clause,[status(thm)],[f926,f967,f1029])).
% 3.20/1.75 thf(f926,plain,(
% 3.20/1.75 ($true = (denota69106024_a_b_c @ sK7 @ sK6 @ (static_SIGF_a_b_c @ phi))) | ($true = (denota69106024_a_b_c @ sK0 @ sK2 @ (static_SIGF_a_b_c @ phi)))),
% 3.20/1.75 inference(cnf_transformation,[status(thm)],[f919])).
% 3.20/1.75 thf(f1032,plain,(
% 3.20/1.75 spl8_14 | spl8_11),
% 3.20/1.75 inference(avatar_split_clause,[status(thm)],[f928,f1008,f1029])).
% 3.20/1.75 thf(f928,plain,(
% 3.20/1.75 ($true = (denota1997846518gree_c @ sK5 @ sK4 @ (static_FVF_a_b_c @ phi))) | ($true = (denota69106024_a_b_c @ sK0 @ sK2 @ (static_SIGF_a_b_c @ phi)))),
% 3.20/1.75 inference(cnf_transformation,[status(thm)],[f919])).
% 3.20/1.75 thf(f1027,plain,(
% 3.20/1.75 spl8_2 | spl8_9 | spl8_10),
% 3.20/1.75 inference(avatar_split_clause,[status(thm)],[f945,f1002,f998,f967])).
% 3.20/1.75 thf(f945,plain,(
% 3.20/1.75 ($true = (denota69106024_a_b_c @ sK7 @ sK6 @ (static_SIGF_a_b_c @ phi))) | ($false = (member1895684704real_c @ sK3 @ (denota968303861_a_b_c @ sK2 @ phi))) | ((member1895684704real_c @ sK1 @ (denota968303861_a_b_c @ sK0 @ phi)) = $false)),
% 3.20/1.75 inference(binary_proxy_clausification,[status(thm)],[f929])).
% 3.20/1.75 thf(f929,plain,(
% 3.20/1.75 ($true = (denota69106024_a_b_c @ sK7 @ sK6 @ (static_SIGF_a_b_c @ phi))) | ((member1895684704real_c @ sK1 @ (denota968303861_a_b_c @ sK0 @ phi)) != (member1895684704real_c @ sK3 @ (denota968303861_a_b_c @ sK2 @ phi)))),
% 3.20/1.75 inference(cnf_transformation,[status(thm)],[f919])).
% 3.20/1.75 thf(f1026,plain,(
% 3.20/1.75 spl8_4 | spl8_5 | spl8_2),
% 3.20/1.75 inference(avatar_split_clause,[status(thm)],[f944,f967,f980,f976])).
% 3.20/1.75 thf(f944,plain,(
% 3.20/1.75 ($true = (denota69106024_a_b_c @ sK7 @ sK6 @ (static_SIGF_a_b_c @ phi))) | ((member1895684704real_c @ sK3 @ (denota968303861_a_b_c @ sK2 @ phi)) = $true) | ((member1895684704real_c @ sK1 @ (denota968303861_a_b_c @ sK0 @ phi)) = $true)),
% 3.20/1.75 inference(binary_proxy_clausification,[status(thm)],[f929])).
% 3.20/1.75 thf(f1025,plain,(
% 3.20/1.75 spl8_11 | spl8_9 | spl8_10),
% 3.20/1.75 inference(avatar_split_clause,[status(thm)],[f947,f1002,f998,f1008])).
% 3.20/1.75 thf(f947,plain,(
% 3.20/1.75 ((member1895684704real_c @ sK1 @ (denota968303861_a_b_c @ sK0 @ phi)) = $false) | ($true = (denota1997846518gree_c @ sK5 @ sK4 @ (static_FVF_a_b_c @ phi))) | ($false = (member1895684704real_c @ sK3 @ (denota968303861_a_b_c @ sK2 @ phi)))),
% 3.20/1.75 inference(binary_proxy_clausification,[status(thm)],[f931])).
% 3.20/1.75 thf(f931,plain,(
% 3.20/1.75 ($true = (denota1997846518gree_c @ sK5 @ sK4 @ (static_FVF_a_b_c @ phi))) | ((member1895684704real_c @ sK1 @ (denota968303861_a_b_c @ sK0 @ phi)) != (member1895684704real_c @ sK3 @ (denota968303861_a_b_c @ sK2 @ phi)))),
% 3.20/1.75 inference(cnf_transformation,[status(thm)],[f919])).
% 3.20/1.75 thf(f1024,plain,(
% 3.20/1.75 spl8_11 | spl8_5 | spl8_4),
% 3.20/1.75 inference(avatar_split_clause,[status(thm)],[f946,f976,f980,f1008])).
% 3.20/1.75 thf(f946,plain,(
% 3.20/1.75 ((member1895684704real_c @ sK3 @ (denota968303861_a_b_c @ sK2 @ phi)) = $true) | ((member1895684704real_c @ sK1 @ (denota968303861_a_b_c @ sK0 @ phi)) = $true) | ($true = (denota1997846518gree_c @ sK5 @ sK4 @ (static_FVF_a_b_c @ phi)))),
% 3.20/1.75 inference(binary_proxy_clausification,[status(thm)],[f931])).
% 3.20/1.75 thf(f1023,plain,(
% 3.20/1.75 spl8_13 | spl8_13),
% 3.20/1.75 inference(avatar_split_clause,[status(thm)],[f951,f1019,f1019])).
% 3.20/1.75 thf(f951,plain,(
% 3.20/1.75 ( ! [X10 : denota231621370t_unit,X11 : produc190496183real_c,X8 : denota231621370t_unit,X9 : produc190496183real_c,X14 : denota231621370t_unit,X15 : denota231621370t_unit,X12 : produc190496183real_c,X13 : produc190496183real_c] : (($true = (member1895684704real_c @ X13 @ (denota968303861_a_b_c @ X15 @ phi))) | ((denota1997846518gree_c @ X13 @ X12 @ (static_FVF_a_b_c @ phi)) != $true) | ((member1895684704real_c @ X9 @ (denota968303861_a_b_c @ X8 @ phi)) = $true) | ((member1895684704real_c @ X11 @ (denota968303861_a_b_c @ X10 @ phi)) = $false) | ((denota69106024_a_b_c @ X15 @ X14 @ (static_SIGF_a_b_c @ phi)) != $true) | ($false = (member1895684704real_c @ X12 @ (denota968303861_a_b_c @ X14 @ phi))) | ($true != (denota69106024_a_b_c @ X8 @ X10 @ (static_SIGF_a_b_c @ phi))) | ((denota1997846518gree_c @ X9 @ X11 @ (static_FVF_a_b_c @ phi)) != $true)) )),
% 3.20/1.75 inference(binary_proxy_clausification,[status(thm)],[f949])).
% 3.20/1.75 thf(f949,plain,(
% 3.20/1.75 ( ! [X10 : denota231621370t_unit,X11 : produc190496183real_c,X8 : denota231621370t_unit,X9 : produc190496183real_c,X14 : denota231621370t_unit,X15 : denota231621370t_unit,X12 : produc190496183real_c,X13 : produc190496183real_c] : (((denota1997846518gree_c @ X13 @ X12 @ (static_FVF_a_b_c @ phi)) != $true) | ((denota69106024_a_b_c @ X15 @ X14 @ (static_SIGF_a_b_c @ phi)) != $true) | ($true != (denota69106024_a_b_c @ X8 @ X10 @ (static_SIGF_a_b_c @ phi))) | ((member1895684704real_c @ X11 @ (denota968303861_a_b_c @ X10 @ phi)) = (member1895684704real_c @ X9 @ (denota968303861_a_b_c @ X8 @ phi))) | ($false = (member1895684704real_c @ X12 @ (denota968303861_a_b_c @ X14 @ phi))) | ((denota1997846518gree_c @ X9 @ X11 @ (static_FVF_a_b_c @ phi)) != $true) | ($true = (member1895684704real_c @ X13 @ (denota968303861_a_b_c @ X15 @ phi)))) )),
% 3.20/1.75 inference(binary_proxy_clausification,[status(thm)],[f925])).
% 3.20/1.75 thf(f925,plain,(
% 3.20/1.75 ( ! [X10 : denota231621370t_unit,X11 : produc190496183real_c,X8 : denota231621370t_unit,X9 : produc190496183real_c,X14 : denota231621370t_unit,X15 : denota231621370t_unit,X12 : produc190496183real_c,X13 : produc190496183real_c] : (((denota1997846518gree_c @ X9 @ X11 @ (static_FVF_a_b_c @ phi)) != $true) | ((denota69106024_a_b_c @ X15 @ X14 @ (static_SIGF_a_b_c @ phi)) != $true) | ((denota1997846518gree_c @ X13 @ X12 @ (static_FVF_a_b_c @ phi)) != $true) | ((member1895684704real_c @ X12 @ (denota968303861_a_b_c @ X14 @ phi)) = (member1895684704real_c @ X13 @ (denota968303861_a_b_c @ X15 @ phi))) | ((member1895684704real_c @ X11 @ (denota968303861_a_b_c @ X10 @ phi)) = (member1895684704real_c @ X9 @ (denota968303861_a_b_c @ X8 @ phi))) | ($true != (denota69106024_a_b_c @ X8 @ X10 @ (static_SIGF_a_b_c @ phi)))) )),
% 3.20/1.75 inference(cnf_transformation,[status(thm)],[f919])).
% 3.20/1.75 thf(f1017,plain,(
% 3.20/1.75 spl8_12 | spl8_12),
% 3.20/1.75 inference(avatar_split_clause,[status(thm)],[f952,f1015,f1015])).
% 3.20/1.75 thf(f952,plain,(
% 3.20/1.75 ( ! [X10 : denota231621370t_unit,X11 : produc190496183real_c,X8 : denota231621370t_unit,X9 : produc190496183real_c,X14 : denota231621370t_unit,X15 : denota231621370t_unit,X12 : produc190496183real_c,X13 : produc190496183real_c] : (((denota1997846518gree_c @ X9 @ X11 @ (static_FVF_a_b_c @ phi)) != $true) | ((member1895684704real_c @ X11 @ (denota968303861_a_b_c @ X10 @ phi)) = $true) | ((member1895684704real_c @ X9 @ (denota968303861_a_b_c @ X8 @ phi)) = $false) | ((denota69106024_a_b_c @ X15 @ X14 @ (static_SIGF_a_b_c @ phi)) != $true) | ($true = (member1895684704real_c @ X12 @ (denota968303861_a_b_c @ X14 @ phi))) | ($false = (member1895684704real_c @ X13 @ (denota968303861_a_b_c @ X15 @ phi))) | ($true != (denota69106024_a_b_c @ X8 @ X10 @ (static_SIGF_a_b_c @ phi))) | ((denota1997846518gree_c @ X13 @ X12 @ (static_FVF_a_b_c @ phi)) != $true)) )),
% 3.20/1.75 inference(binary_proxy_clausification,[status(thm)],[f948])).
% 3.20/1.75 thf(f948,plain,(
% 3.20/1.75 ( ! [X10 : denota231621370t_unit,X11 : produc190496183real_c,X8 : denota231621370t_unit,X9 : produc190496183real_c,X14 : denota231621370t_unit,X15 : denota231621370t_unit,X12 : produc190496183real_c,X13 : produc190496183real_c] : (((denota69106024_a_b_c @ X15 @ X14 @ (static_SIGF_a_b_c @ phi)) != $true) | ($true != (denota69106024_a_b_c @ X8 @ X10 @ (static_SIGF_a_b_c @ phi))) | ((member1895684704real_c @ X11 @ (denota968303861_a_b_c @ X10 @ phi)) = (member1895684704real_c @ X9 @ (denota968303861_a_b_c @ X8 @ phi))) | ((denota1997846518gree_c @ X13 @ X12 @ (static_FVF_a_b_c @ phi)) != $true) | ($false = (member1895684704real_c @ X13 @ (denota968303861_a_b_c @ X15 @ phi))) | ((denota1997846518gree_c @ X9 @ X11 @ (static_FVF_a_b_c @ phi)) != $true) | ($true = (member1895684704real_c @ X12 @ (denota968303861_a_b_c @ X14 @ phi)))) )),
% 3.20/1.75 inference(binary_proxy_clausification,[status(thm)],[f925])).
% 3.20/1.75 thf(f1013,plain,(
% 3.20/1.75 spl8_1 | spl8_8 | spl8_7),
% 3.20/1.75 inference(avatar_split_clause,[status(thm)],[f955,f989,f993,f963])).
% 3.20/1.75 thf(f955,plain,(
% 3.20/1.75 ($false = (member1895684704real_c @ sK4 @ (denota968303861_a_b_c @ sK6 @ phi))) | ($false = (member1895684704real_c @ sK5 @ (denota968303861_a_b_c @ sK7 @ phi))) | ((denota1997846518gree_c @ sK1 @ sK3 @ (static_FVF_a_b_c @ phi)) = $true)),
% 3.20/1.75 inference(binary_proxy_clausification,[status(thm)],[f933])).
% 3.20/1.75 thf(f933,plain,(
% 3.20/1.75 ((member1895684704real_c @ sK5 @ (denota968303861_a_b_c @ sK7 @ phi)) != (member1895684704real_c @ sK4 @ (denota968303861_a_b_c @ sK6 @ phi))) | ((denota1997846518gree_c @ sK1 @ sK3 @ (static_FVF_a_b_c @ phi)) = $true)),
% 3.20/1.75 inference(cnf_transformation,[status(thm)],[f919])).
% 3.20/1.75 thf(f1012,plain,(
% 3.20/1.75 spl8_3 | spl8_6 | spl8_1),
% 3.20/1.75 inference(avatar_split_clause,[status(thm)],[f954,f963,f984,f972])).
% 3.20/1.75 thf(f954,plain,(
% 3.20/1.75 ($true = (member1895684704real_c @ sK4 @ (denota968303861_a_b_c @ sK6 @ phi))) | ($true = (member1895684704real_c @ sK5 @ (denota968303861_a_b_c @ sK7 @ phi))) | ((denota1997846518gree_c @ sK1 @ sK3 @ (static_FVF_a_b_c @ phi)) = $true)),
% 3.20/1.75 inference(binary_proxy_clausification,[status(thm)],[f933])).
% 3.20/1.75 thf(f1011,plain,(
% 3.20/1.75 spl8_1 | spl8_11),
% 3.20/1.75 inference(avatar_split_clause,[status(thm)],[f934,f1008,f963])).
% 3.20/1.75 thf(f934,plain,(
% 3.20/1.75 ((denota1997846518gree_c @ sK1 @ sK3 @ (static_FVF_a_b_c @ phi)) = $true) | ($true = (denota1997846518gree_c @ sK5 @ sK4 @ (static_FVF_a_b_c @ phi)))),
% 3.20/1.75 inference(cnf_transformation,[status(thm)],[f919])).
% 3.20/1.75 thf(f1006,plain,(
% 3.20/1.75 spl8_7 | spl8_9 | spl8_10 | spl8_8),
% 3.20/1.75 inference(avatar_split_clause,[status(thm)],[f959,f993,f1002,f998,f989])).
% 3.20/1.75 thf(f959,plain,(
% 3.20/1.75 ($false = (member1895684704real_c @ sK3 @ (denota968303861_a_b_c @ sK2 @ phi))) | ($false = (member1895684704real_c @ sK4 @ (denota968303861_a_b_c @ sK6 @ phi))) | ((member1895684704real_c @ sK1 @ (denota968303861_a_b_c @ sK0 @ phi)) = $false) | ($false = (member1895684704real_c @ sK5 @ (denota968303861_a_b_c @ sK7 @ phi)))),
% 3.20/1.75 inference(binary_proxy_clausification,[status(thm)],[f957])).
% 3.20/1.75 thf(f957,plain,(
% 3.20/1.75 ($false = (member1895684704real_c @ sK3 @ (denota968303861_a_b_c @ sK2 @ phi))) | ((member1895684704real_c @ sK1 @ (denota968303861_a_b_c @ sK0 @ phi)) = $false) | ((member1895684704real_c @ sK5 @ (denota968303861_a_b_c @ sK7 @ phi)) != (member1895684704real_c @ sK4 @ (denota968303861_a_b_c @ sK6 @ phi)))),
% 3.20/1.75 inference(binary_proxy_clausification,[status(thm)],[f930])).
% 3.20/1.75 thf(f930,plain,(
% 3.20/1.75 ((member1895684704real_c @ sK1 @ (denota968303861_a_b_c @ sK0 @ phi)) != (member1895684704real_c @ sK3 @ (denota968303861_a_b_c @ sK2 @ phi))) | ((member1895684704real_c @ sK5 @ (denota968303861_a_b_c @ sK7 @ phi)) != (member1895684704real_c @ sK4 @ (denota968303861_a_b_c @ sK6 @ phi)))),
% 3.20/1.75 inference(cnf_transformation,[status(thm)],[f919])).
% 3.20/1.75 thf(f1005,plain,(
% 3.20/1.75 spl8_6 | spl8_9 | spl8_3 | spl8_10),
% 3.20/1.75 inference(avatar_split_clause,[status(thm)],[f958,f1002,f972,f998,f984])).
% 3.20/1.75 thf(f958,plain,(
% 3.20/1.75 ($false = (member1895684704real_c @ sK3 @ (denota968303861_a_b_c @ sK2 @ phi))) | ((member1895684704real_c @ sK1 @ (denota968303861_a_b_c @ sK0 @ phi)) = $false) | ($true = (member1895684704real_c @ sK5 @ (denota968303861_a_b_c @ sK7 @ phi))) | ($true = (member1895684704real_c @ sK4 @ (denota968303861_a_b_c @ sK6 @ phi)))),
% 3.20/1.75 inference(binary_proxy_clausification,[status(thm)],[f957])).
% 3.20/1.75 thf(f996,plain,(
% 3.20/1.75 spl8_7 | spl8_4 | spl8_8 | spl8_5),
% 3.20/1.75 inference(avatar_split_clause,[status(thm)],[f961,f980,f993,f976,f989])).
% 3.20/1.75 thf(f961,plain,(
% 3.20/1.75 ($false = (member1895684704real_c @ sK5 @ (denota968303861_a_b_c @ sK7 @ phi))) | ((member1895684704real_c @ sK1 @ (denota968303861_a_b_c @ sK0 @ phi)) = $true) | ($false = (member1895684704real_c @ sK4 @ (denota968303861_a_b_c @ sK6 @ phi))) | ((member1895684704real_c @ sK3 @ (denota968303861_a_b_c @ sK2 @ phi)) = $true)),
% 3.20/1.75 inference(binary_proxy_clausification,[status(thm)],[f956])).
% 3.20/1.75 thf(f956,plain,(
% 3.20/1.75 ((member1895684704real_c @ sK1 @ (denota968303861_a_b_c @ sK0 @ phi)) = $true) | ((member1895684704real_c @ sK3 @ (denota968303861_a_b_c @ sK2 @ phi)) = $true) | ((member1895684704real_c @ sK5 @ (denota968303861_a_b_c @ sK7 @ phi)) != (member1895684704real_c @ sK4 @ (denota968303861_a_b_c @ sK6 @ phi)))),
% 3.20/1.75 inference(binary_proxy_clausification,[status(thm)],[f930])).
% 3.20/1.75 thf(f987,plain,(
% 3.20/1.75 spl8_3 | spl8_4 | spl8_5 | spl8_6),
% 3.20/1.75 inference(avatar_split_clause,[status(thm)],[f960,f984,f980,f976,f972])).
% 3.20/1.75 thf(f960,plain,(
% 3.20/1.75 ($true = (member1895684704real_c @ sK4 @ (denota968303861_a_b_c @ sK6 @ phi))) | ((member1895684704real_c @ sK3 @ (denota968303861_a_b_c @ sK2 @ phi)) = $true) | ($true = (member1895684704real_c @ sK5 @ (denota968303861_a_b_c @ sK7 @ phi))) | ((member1895684704real_c @ sK1 @ (denota968303861_a_b_c @ sK0 @ phi)) = $true)),
% 3.20/1.75 inference(binary_proxy_clausification,[status(thm)],[f956])).
% 3.20/1.75 thf(f970,plain,(
% 3.20/1.75 spl8_1 | spl8_2),
% 3.20/1.75 inference(avatar_split_clause,[status(thm)],[f932,f967,f963])).
% 3.20/1.75 thf(f932,plain,(
% 3.20/1.75 ((denota1997846518gree_c @ sK1 @ sK3 @ (static_FVF_a_b_c @ phi)) = $true) | ($true = (denota69106024_a_b_c @ sK7 @ sK6 @ (static_SIGF_a_b_c @ phi)))),
% 3.20/1.75 inference(cnf_transformation,[status(thm)],[f919])).
% 3.20/1.75 % SZS output end Proof for DTF2THF_20700
% 3.20/1.75 % (20881)------------------------------
% 3.20/1.75 % (20881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.20/1.75 % (20881)Termination reason: Refutation
% 3.20/1.75
% 3.20/1.75 % (20881)Memory used [KB]: 7036
% 3.20/1.75 % (20881)Time elapsed: 0.049 s
% 3.20/1.75 % (20881)Instructions burned: 144 (million)
% 3.20/1.75 % (20881)------------------------------
% 3.20/1.75 % (20881)------------------------------
% 3.20/1.75 % (20875)Success in time 0.079 s
%------------------------------------------------------------------------------