%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP092^1 : 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 : n026.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 08:55:29 AM UTC 2026
% Result : Theorem 7.09s 2.33s
% Output : Refutation 7.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 110 ( 60 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 605 ( 28 ~; 7 |; 0 &; 537 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 56 ( 55 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 169 ( 165 usr; 14 con; 0-3 aty)
% ( 28 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 130 ( 37 ^; 85 !; 8 ?; 130 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
list_P1467822637od_a_a: $tType ).
thf(type_def_7,type,
list_P601816365list_a: $tType ).
thf(type_def_8,type,
list_P1891567085od_a_a: $tType ).
thf(type_def_9,type,
list_a_nat: $tType ).
thf(type_def_10,type,
list_l1108175539od_a_a: $tType ).
thf(type_def_11,type,
list_list_a: $tType ).
thf(type_def_12,type,
list_a: $tType ).
thf(type_def_13,type,
a: $tType ).
thf(type_def_14,type,
nat: $tType ).
thf(type_def_15,type,
product_prod_a_a: $tType ).
thf(type_def_16,type,
set_Pr1948701895od_a_a: $tType ).
thf(type_def_17,type,
set_Pr800560199od_a_a: $tType ).
thf(type_def_18,type,
set_Product_prod_a_a: $tType ).
thf(type_def_19,type,
set_Pr1971762695list_a: $tType ).
thf(type_def_20,type,
set_Pr1940702919_a_nat: $tType ).
thf(type_def_21,type,
set_Pr753687879_a_nat: $tType ).
thf(type_def_22,type,
set_Pr1239640519od_a_a: $tType ).
thf(type_def_23,type,
set_Pr1742859527list_a: $tType ).
thf(type_def_24,type,
set_Pr1295299783od_a_a: $tType ).
thf(type_def_25,type,
set_Pr779272263od_a_a: $tType ).
thf(type_def_26,type,
product_prod_a_nat_a: $tType ).
thf(type_def_27,type,
list_P916011052_nat_a: $tType ).
thf(type_def_28,type,
produc657167928_a_a_a: $tType ).
thf(type_def_29,type,
list_P305489470_a_a_a: $tType ).
thf(type_def_30,type,
produc864062247list_a: $tType ).
thf(type_def_31,type,
produc664688895_a_nat: $tType ).
thf(type_def_32,type,
list_P1435957893_a_nat: $tType ).
thf(type_def_33,type,
produc1572603623od_a_a: $tType ).
thf(type_def_34,type,
produc1016684094_a_a_a: $tType ).
thf(type_def_35,type,
list_P319927492_a_a_a: $tType ).
thf(type_def_36,type,
product_prod_a_a_nat: $tType ).
thf(type_def_37,type,
list_P576104046_a_nat: $tType ).
thf(type_def_38,type,
produc1701253078od_a_a: $tType ).
thf(type_def_39,type,
list_P1175580892od_a_a: $tType ).
thf(type_def_40,type,
produc1921647824od_a_a: $tType ).
thf(type_def_41,type,
list_P1458844246od_a_a: $tType ).
thf(type_def_42,type,
set_li562223245od_a_a: $tType ).
thf(type_def_43,type,
set_a: $tType ).
thf(type_def_44,type,
produc821581462od_a_a: $tType ).
thf(type_def_45,type,
produc501911462od_a_a: $tType ).
thf(type_def_46,type,
produc1178641895_a_nat: $tType ).
thf(type_def_47,type,
produc1334933863_a_nat: $tType ).
thf(type_def_48,type,
produc657724903od_a_a: $tType ).
thf(type_def_49,type,
produc403652391list_a: $tType ).
thf(type_def_50,type,
produc205693799od_a_a: $tType ).
thf(type_def_51,type,
produc651658087od_a_a: $tType ).
thf(type_def_52,type,
pair_p125712459t_unit: $tType ).
thf(type_def_53,type,
produc1912141786_a_a_a: $tType ).
thf(type_def_54,type,
produc1990712039od_a_a: $tType ).
thf(type_def_55,type,
produc1197928545_a_a_a: $tType ).
thf(type_def_56,type,
set_Pr727105414od_a_a: $tType ).
thf(type_def_57,type,
set_Pr1525541400_a_a_a: $tType ).
thf(type_def_58,type,
set_Pr248149174od_a_a: $tType ).
thf(type_def_59,type,
set_Pr110478017_a_a_a: $tType ).
thf(type_def_60,type,
pair_p1891813445t_unit: $tType ).
thf(func_def_0,type,
set_Pr779272263od_a_a: $tType ).
thf(func_def_1,type,
produc205693799od_a_a: $tType ).
thf(func_def_2,type,
set_Pr1295299783od_a_a: $tType ).
thf(func_def_3,type,
produc1990712039od_a_a: $tType ).
thf(func_def_4,type,
produc1912141786_a_a_a: $tType ).
thf(func_def_5,type,
set_Pr727105414od_a_a: $tType ).
thf(func_def_6,type,
set_Pr1239640519od_a_a: $tType ).
thf(func_def_7,type,
produc501911462od_a_a: $tType ).
thf(func_def_8,type,
produc657724903od_a_a: $tType ).
thf(func_def_9,type,
produc821581462od_a_a: $tType ).
thf(func_def_10,type,
set_Pr800560199od_a_a: $tType ).
thf(func_def_11,type,
produc651658087od_a_a: $tType ).
thf(func_def_12,type,
set_Pr110478017_a_a_a: $tType ).
thf(func_def_13,type,
set_Pr753687879_a_nat: $tType ).
thf(func_def_14,type,
produc1197928545_a_a_a: $tType ).
thf(func_def_15,type,
list_P1891567085od_a_a: $tType ).
thf(func_def_16,type,
set_Pr1948701895od_a_a: $tType ).
thf(func_def_17,type,
set_Pr1742859527list_a: $tType ).
thf(func_def_18,type,
pair_p1891813445t_unit: $tType ).
thf(func_def_19,type,
produc1334933863_a_nat: $tType ).
thf(func_def_20,type,
list_P1435957893_a_nat: $tType ).
thf(func_def_21,type,
produc1572603623od_a_a: $tType ).
thf(func_def_22,type,
produc403652391list_a: $tType ).
thf(func_def_23,type,
list_P1175580892od_a_a: $tType ).
thf(func_def_24,type,
list_P305489470_a_a_a: $tType ).
thf(func_def_25,type,
set_Pr248149174od_a_a: $tType ).
thf(func_def_26,type,
set_Pr1525541400_a_a_a: $tType ).
thf(func_def_27,type,
pair_p125712459t_unit: $tType ).
thf(func_def_28,type,
set_Pr1940702919_a_nat: $tType ).
thf(func_def_29,type,
produc664688895_a_nat: $tType ).
thf(func_def_30,type,
produc1701253078od_a_a: $tType ).
thf(func_def_31,type,
produc657167928_a_a_a: $tType ).
thf(func_def_32,type,
list_P1458844246od_a_a: $tType ).
thf(func_def_33,type,
list_P319927492_a_a_a: $tType ).
thf(func_def_34,type,
list_P601816365list_a: $tType ).
thf(func_def_35,type,
set_Pr1971762695list_a: $tType ).
thf(func_def_36,type,
produc1178641895_a_nat: $tType ).
thf(func_def_37,type,
list_P576104046_a_nat: $tType ).
thf(func_def_38,type,
list_P916011052_nat_a: $tType ).
thf(func_def_39,type,
produc1921647824od_a_a: $tType ).
thf(func_def_40,type,
produc1016684094_a_a_a: $tType ).
thf(func_def_41,type,
produc864062247list_a: $tType ).
thf(func_def_42,type,
list_l1108175539od_a_a: $tType ).
thf(func_def_43,type,
set_li562223245od_a_a: $tType ).
thf(func_def_44,type,
product_prod_a_a_nat: $tType ).
thf(func_def_45,type,
product_prod_a_nat_a: $tType ).
thf(func_def_46,type,
list_P1467822637od_a_a: $tType ).
thf(func_def_47,type,
set_Product_prod_a_a: $tType ).
thf(func_def_48,type,
list_a_nat: $tType ).
thf(func_def_49,type,
product_prod_a_a: $tType ).
thf(func_def_50,type,
list_list_a: $tType ).
thf(func_def_51,type,
list_a: $tType ).
thf(func_def_52,type,
set_a: $tType ).
thf(func_def_53,type,
nat: $tType ).
thf(func_def_54,type,
a: $tType ).
thf(func_def_55,type,
if_lis321365491od_a_a: $o > list_P1467822637od_a_a > list_P1467822637od_a_a > list_P1467822637od_a_a ).
thf(func_def_56,type,
kurato292963650list_a: list_P601816365list_a > $o ).
thf(func_def_57,type,
kurato1404746725od_a_a: list_P1891567085od_a_a > $o ).
thf(func_def_58,type,
kurato1072996284sing_a: list_P1467822637od_a_a > $o ).
thf(func_def_59,type,
append_a_nat: list_a_nat > list_a_nat > list_a_nat ).
thf(func_def_60,type,
append2141280328od_a_a: list_l1108175539od_a_a > list_l1108175539od_a_a > list_l1108175539od_a_a ).
thf(func_def_61,type,
append_list_a: list_list_a > list_list_a > list_list_a ).
thf(func_def_62,type,
append750086082list_a: list_P601816365list_a > list_P601816365list_a > list_P601816365list_a ).
thf(func_def_63,type,
append864718978od_a_a: list_P1891567085od_a_a > list_P1891567085od_a_a > list_P1891567085od_a_a ).
thf(func_def_64,type,
append1574001858od_a_a: list_P1467822637od_a_a > list_P1467822637od_a_a > list_P1467822637od_a_a ).
thf(func_def_65,type,
append_a: list_a > list_a > list_a ).
thf(func_def_66,type,
bind_a1190333103od_a_a: list_a_nat > ( ( a > nat ) > list_P1467822637od_a_a ) > list_P1467822637od_a_a ).
thf(func_def_67,type,
bind_a_nat_a: list_a_nat > ( ( a > nat ) > list_a ) > list_a ).
thf(func_def_68,type,
bind_l618536897od_a_a: list_l1108175539od_a_a > ( list_P1467822637od_a_a > list_P1467822637od_a_a ) > list_P1467822637od_a_a ).
thf(func_def_69,type,
bind_l1307590552_a_a_a: list_l1108175539od_a_a > ( list_P1467822637od_a_a > list_a ) > list_a ).
thf(func_def_70,type,
bind_P240085581od_a_a: list_P1467822637od_a_a > ( product_prod_a_a > list_l1108175539od_a_a ) > list_l1108175539od_a_a ).
thf(func_def_71,type,
bind_P1783625031od_a_a: list_P1467822637od_a_a > ( product_prod_a_a > list_P1467822637od_a_a ) > list_P1467822637od_a_a ).
thf(func_def_72,type,
bind_P293964574_a_a_a: list_P1467822637od_a_a > ( product_prod_a_a > list_a ) > list_a ).
thf(func_def_73,type,
bind_a883992246od_a_a: list_a > ( a > list_l1108175539od_a_a ) > list_l1108175539od_a_a ).
thf(func_def_74,type,
bind_a1679112752od_a_a: list_a > ( a > list_P1467822637od_a_a ) > list_P1467822637od_a_a ).
thf(func_def_75,type,
bind_a_a: list_a > ( a > list_a ) > list_a ).
thf(func_def_76,type,
concat1878217064od_a_a: list_l1108175539od_a_a > list_P1467822637od_a_a ).
thf(func_def_77,type,
insert2123825731od_a_a: product_prod_a_a > list_P1467822637od_a_a > list_P1467822637od_a_a ).
thf(func_def_78,type,
lenlex2038501170od_a_a: set_Pr1948701895od_a_a > set_Pr800560199od_a_a ).
thf(func_def_79,type,
lenlex_a: set_Product_prod_a_a > set_Pr1971762695list_a ).
thf(func_def_80,type,
lex_Product_prod_a_a: set_Pr1948701895od_a_a > set_Pr800560199od_a_a ).
thf(func_def_81,type,
lex_a: set_Product_prod_a_a > set_Pr1971762695list_a ).
thf(func_def_82,type,
lexord_a_nat: set_Pr1940702919_a_nat > set_Pr753687879_a_nat ).
thf(func_def_83,type,
lexord1284731808od_a_a: set_Pr800560199od_a_a > set_Pr1239640519od_a_a ).
thf(func_def_84,type,
lexord_list_a: set_Pr1971762695list_a > set_Pr1742859527list_a ).
thf(func_def_85,type,
lexord931792858od_a_a: set_Pr1295299783od_a_a > set_Pr779272263od_a_a ).
thf(func_def_86,type,
lexord673907738od_a_a: set_Pr1948701895od_a_a > set_Pr800560199od_a_a ).
thf(func_def_87,type,
lexord_a: set_Product_prod_a_a > set_Pr1971762695list_a ).
thf(func_def_88,type,
cons_a_nat: ( a > nat ) > list_a_nat > list_a_nat ).
thf(func_def_89,type,
cons_l724116707od_a_a: list_P1467822637od_a_a > list_l1108175539od_a_a > list_l1108175539od_a_a ).
thf(func_def_90,type,
cons_list_a: list_a > list_list_a > list_list_a ).
thf(func_def_91,type,
cons_P896312284_nat_a: product_prod_a_nat_a > list_P916011052_nat_a > list_P916011052_nat_a ).
thf(func_def_92,type,
cons_P169173742_a_a_a: produc657167928_a_a_a > list_P305489470_a_a_a > list_P305489470_a_a_a ).
thf(func_def_93,type,
cons_P2080942813list_a: produc864062247list_a > list_P601816365list_a > list_P601816365list_a ).
thf(func_def_94,type,
cons_P659009461_a_nat: produc664688895_a_nat > list_P1435957893_a_nat > list_P1435957893_a_nat ).
thf(func_def_95,type,
cons_P1070399645od_a_a: produc1572603623od_a_a > list_P1891567085od_a_a > list_P1891567085od_a_a ).
thf(func_def_96,type,
cons_P86081012_a_a_a: produc1016684094_a_a_a > list_P319927492_a_a_a > list_P319927492_a_a_a ).
thf(func_def_97,type,
cons_P1915851550_a_nat: product_prod_a_a_nat > list_P576104046_a_nat > list_P576104046_a_nat ).
thf(func_def_98,type,
cons_P1213258892od_a_a: produc1701253078od_a_a > list_P1175580892od_a_a > list_P1175580892od_a_a ).
thf(func_def_99,type,
cons_P991044742od_a_a: produc1921647824od_a_a > list_P1458844246od_a_a > list_P1458844246od_a_a ).
thf(func_def_100,type,
cons_P1921020637od_a_a: product_prod_a_a > list_P1467822637od_a_a > list_P1467822637od_a_a ).
thf(func_def_101,type,
cons_a: a > list_a > list_a ).
thf(func_def_102,type,
nil_a_nat: list_a_nat ).
thf(func_def_103,type,
nil_li1885598003od_a_a: list_l1108175539od_a_a ).
thf(func_def_104,type,
nil_Pr1049924845od_a_a: list_P1891567085od_a_a ).
thf(func_def_105,type,
nil_Product_prod_a_a: list_P1467822637od_a_a ).
thf(func_def_106,type,
nil_a: list_a ).
thf(func_def_107,type,
set_li1284606018od_a_a: list_l1108175539od_a_a > set_li562223245od_a_a ).
thf(func_def_108,type,
set_Product_prod_a_a2: list_P1467822637od_a_a > set_Product_prod_a_a ).
thf(func_def_109,type,
set_a2: list_a > set_a ).
thf(func_def_110,type,
listrel1_a_nat: set_Pr1940702919_a_nat > set_Pr753687879_a_nat ).
thf(func_def_111,type,
listre651914124od_a_a: set_Pr800560199od_a_a > set_Pr1239640519od_a_a ).
thf(func_def_112,type,
listrel1_list_a: set_Pr1971762695list_a > set_Pr1742859527list_a ).
thf(func_def_113,type,
listre1832537542od_a_a: set_Pr1295299783od_a_a > set_Pr779272263od_a_a ).
thf(func_def_114,type,
listre944824838od_a_a: set_Pr1948701895od_a_a > set_Pr800560199od_a_a ).
thf(func_def_115,type,
listrel1_a: set_Product_prod_a_a > set_Pr1971762695list_a ).
thf(func_def_116,type,
listre2074280881od_a_a: set_Pr1948701895od_a_a > set_Pr800560199od_a_a ).
thf(func_def_117,type,
listrel_a_a: set_Product_prod_a_a > set_Pr1971762695list_a ).
thf(func_def_118,type,
maps_a836827497od_a_a: ( ( a > nat ) > list_P1467822637od_a_a ) > list_a_nat > list_P1467822637od_a_a ).
thf(func_def_119,type,
maps_a_nat_a: ( ( a > nat ) > list_a ) > list_a_nat > list_a ).
thf(func_def_120,type,
maps_l1117535867od_a_a: ( list_P1467822637od_a_a > list_P1467822637od_a_a ) > list_l1108175539od_a_a > list_P1467822637od_a_a ).
thf(func_def_121,type,
maps_l1091119186_a_a_a: ( list_P1467822637od_a_a > list_a ) > list_l1108175539od_a_a > list_a ).
thf(func_def_122,type,
maps_P739084551od_a_a: ( product_prod_a_a > list_l1108175539od_a_a ) > list_P1467822637od_a_a > list_l1108175539od_a_a ).
thf(func_def_123,type,
maps_P1529886977od_a_a: ( product_prod_a_a > list_P1467822637od_a_a ) > list_P1467822637od_a_a > list_P1467822637od_a_a ).
thf(func_def_124,type,
maps_P321755352_a_a_a: ( product_prod_a_a > list_a ) > list_P1467822637od_a_a > list_a ).
thf(func_def_125,type,
maps_a667520880od_a_a: ( a > list_l1108175539od_a_a ) > list_a > list_l1108175539od_a_a ).
thf(func_def_126,type,
maps_a1706903530od_a_a: ( a > list_P1467822637od_a_a ) > list_a > list_P1467822637od_a_a ).
thf(func_def_127,type,
maps_a_a: ( a > list_a ) > list_a > list_a ).
thf(func_def_128,type,
measures_a: list_a_nat > set_Product_prod_a_a ).
thf(func_def_129,type,
member_a_nat: list_a_nat > ( a > nat ) > $o ).
thf(func_def_130,type,
member261538120od_a_a: list_l1108175539od_a_a > list_P1467822637od_a_a > $o ).
thf(func_def_131,type,
member2070313346od_a_a: list_P1891567085od_a_a > produc1572603623od_a_a > $o ).
thf(func_def_132,type,
member1112491458od_a_a: list_P1467822637od_a_a > product_prod_a_a > $o ).
thf(func_def_133,type,
member_a: list_a > a > $o ).
thf(func_def_134,type,
subseq2115548028od_a_a: list_P1467822637od_a_a > list_l1108175539od_a_a ).
thf(func_def_135,type,
zip_a_nat_a: list_a_nat > list_a > list_P916011052_nat_a ).
thf(func_def_136,type,
zip_li245157064_a_a_a: list_l1108175539od_a_a > list_a > list_P305489470_a_a_a ).
thf(func_def_137,type,
zip_list_a_list_a: list_list_a > list_list_a > list_P601816365list_a ).
thf(func_def_138,type,
zip_Pr24086287_a_nat: list_P1467822637od_a_a > list_a_nat > list_P1435957893_a_nat ).
thf(func_def_139,type,
zip_Pr792472183od_a_a: list_P1467822637od_a_a > list_P1467822637od_a_a > list_P1891567085od_a_a ).
thf(func_def_140,type,
zip_Pr201224270_a_a_a: list_P1467822637od_a_a > list_a > list_P319927492_a_a_a ).
thf(func_def_141,type,
zip_a_a_nat: list_a > list_a_nat > list_P576104046_a_nat ).
thf(func_def_142,type,
zip_a_1969042406od_a_a: list_a > list_l1108175539od_a_a > list_P1175580892od_a_a ).
thf(func_def_143,type,
zip_a_1586372448od_a_a: list_a > list_P1467822637od_a_a > list_P1458844246od_a_a ).
thf(func_def_144,type,
zip_a_a: list_a > list_a > list_P1467822637od_a_a ).
thf(func_def_145,type,
size_s642698393od_a_a: list_P1467822637od_a_a > nat ).
thf(func_def_146,type,
size_size_list_a: list_a > nat ).
thf(func_def_147,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_148,type,
pair_co_path_a: product_prod_a_a > a > list_P1467822637od_a_a > list_P1467822637od_a_a ).
thf(func_def_149,type,
pair_co_path_rel_a: produc821581462od_a_a > produc821581462od_a_a > $o ).
thf(func_def_150,type,
pair_p2140537249od_a_a: product_prod_a_a > list_P1891567085od_a_a > list_P1467822637od_a_a ).
thf(func_def_151,type,
pair_sd_path_a: product_prod_a_a > a > list_P1467822637od_a_a > list_P1467822637od_a_a ).
thf(func_def_152,type,
pair_sd_path_rel_a: produc821581462od_a_a > produc821581462od_a_a > $o ).
thf(func_def_153,type,
invers1007791577list_a: list_P1467822637od_a_a > a > a ).
thf(func_def_154,type,
invers214109608_rel_a: produc657167928_a_a_a > produc657167928_a_a_a > $o ).
thf(func_def_155,type,
list_permutes_a: list_P1467822637od_a_a > set_a > $o ).
thf(func_def_156,type,
permut1422637723list_a: list_P1467822637od_a_a > a > a ).
thf(func_def_157,type,
produc214132118od_a_a: ( product_prod_a_a > product_prod_a_a > $o ) > list_P1467822637od_a_a > produc501911462od_a_a ).
thf(func_def_158,type,
produc1569872215_a_nat: ( a > nat ) > ( a > nat ) > produc1178641895_a_nat ).
thf(func_def_159,type,
product_Pair_a_nat_a: ( a > nat ) > a > product_prod_a_nat_a ).
thf(func_def_160,type,
produc1430747863_a_nat: list_a_nat > list_a_nat > produc1334933863_a_nat ).
thf(func_def_161,type,
produc915218007od_a_a: list_l1108175539od_a_a > list_l1108175539od_a_a > produc657724903od_a_a ).
thf(func_def_162,type,
produc2583831list_a: list_list_a > list_list_a > produc403652391list_a ).
thf(func_def_163,type,
produc461662679od_a_a: list_P1891567085od_a_a > list_P1891567085od_a_a > produc205693799od_a_a ).
thf(func_def_164,type,
produc85179863od_a_a: list_P1467822637od_a_a > list_P1467822637od_a_a > produc651658087od_a_a ).
thf(func_def_165,type,
produc998622632_a_a_a: list_P1467822637od_a_a > a > produc657167928_a_a_a ).
thf(func_def_166,type,
produc1448356631list_a: list_a > list_a > produc864062247list_a ).
thf(func_def_167,type,
produc74075722_a_a_a: pair_p125712459t_unit > produc1016684094_a_a_a > produc1912141786_a_a_a ).
thf(func_def_168,type,
produc1935643479od_a_a: produc1572603623od_a_a > produc1572603623od_a_a > produc1990712039od_a_a ).
thf(func_def_169,type,
produc825466863_a_nat: product_prod_a_a > ( a > nat ) > produc664688895_a_nat ).
thf(func_def_170,type,
produc600870406od_a_a: product_prod_a_a > produc1701253078od_a_a > produc821581462od_a_a ).
thf(func_def_171,type,
produc1474507607od_a_a: product_prod_a_a > product_prod_a_a > produc1572603623od_a_a ).
thf(func_def_172,type,
produc2061588782_a_a_a: product_prod_a_a > a > produc1016684094_a_a_a ).
thf(func_def_173,type,
product_Pair_a_a_nat: a > ( a > nat ) > product_prod_a_a_nat ).
thf(func_def_174,type,
produc575024326od_a_a: a > list_P1467822637od_a_a > produc1701253078od_a_a ).
thf(func_def_175,type,
produc1440321489_a_a_a: a > produc657167928_a_a_a > produc1197928545_a_a_a ).
thf(func_def_176,type,
produc1299253312od_a_a: a > product_prod_a_a > produc1921647824od_a_a ).
thf(func_def_177,type,
product_Pair_a_a: a > a > product_prod_a_a ).
thf(func_def_178,type,
asym_a: set_Product_prod_a_a > $o ).
thf(func_def_179,type,
irrefl76447196od_a_a: set_Pr1948701895od_a_a > $o ).
thf(func_def_180,type,
irrefl_a: set_Product_prod_a_a > $o ).
thf(func_def_181,type,
collec1811041560od_a_a: ( list_P1467822637od_a_a > $o ) > set_li562223245od_a_a ).
thf(func_def_182,type,
collec1566074578od_a_a: ( produc651658087od_a_a > $o ) > set_Pr800560199od_a_a ).
thf(func_def_183,type,
collec656258194list_a: ( produc864062247list_a > $o ) > set_Pr1971762695list_a ).
thf(func_def_184,type,
collec645855634od_a_a: ( product_prod_a_a > $o ) > set_Product_prod_a_a ).
thf(func_def_185,type,
collect_a: ( a > $o ) > set_a ).
thf(func_def_186,type,
the_el1640649244od_a_a: set_Product_prod_a_a > product_prod_a_a ).
thf(func_def_187,type,
accp_P941981633_a_a_a: ( produc657167928_a_a_a > produc657167928_a_a_a > $o ) > produc657167928_a_a_a > $o ).
thf(func_def_188,type,
accp_P1029463583od_a_a: ( produc821581462od_a_a > produc821581462od_a_a > $o ) > produc821581462od_a_a > $o ).
thf(func_def_189,type,
member1578987478od_a_a: list_P1467822637od_a_a > set_li562223245od_a_a > $o ).
thf(func_def_190,type,
member372644687od_a_a: produc501911462od_a_a > set_Pr727105414od_a_a > $o ).
thf(func_def_191,type,
member125757712_a_nat: produc1178641895_a_nat > set_Pr1940702919_a_nat > $o ).
thf(func_def_192,type,
member688761744_a_nat: produc1334933863_a_nat > set_Pr753687879_a_nat > $o ).
thf(func_def_193,type,
member8108048od_a_a: produc657724903od_a_a > set_Pr1239640519od_a_a > $o ).
thf(func_def_194,type,
member888406864list_a: produc403652391list_a > set_Pr1742859527list_a > $o ).
thf(func_def_195,type,
member1254757008od_a_a: produc205693799od_a_a > set_Pr779272263od_a_a > $o ).
thf(func_def_196,type,
member1691432592od_a_a: produc651658087od_a_a > set_Pr800560199od_a_a > $o ).
thf(func_def_197,type,
member430654177_a_a_a: produc657167928_a_a_a > set_Pr1525541400_a_a_a > $o ).
thf(func_def_198,type,
member1250517072list_a: produc864062247list_a > set_Pr1971762695list_a > $o ).
thf(func_def_199,type,
member1899387664od_a_a: produc1990712039od_a_a > set_Pr1295299783od_a_a > $o ).
thf(func_def_200,type,
member2057358096od_a_a: produc1572603623od_a_a > set_Pr1948701895od_a_a > $o ).
thf(func_def_201,type,
member1474739327od_a_a: produc1701253078od_a_a > set_Pr248149174od_a_a > $o ).
thf(func_def_202,type,
member1904151562_a_a_a: produc1197928545_a_a_a > set_Pr110478017_a_a_a > $o ).
thf(func_def_203,type,
member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
thf(func_def_204,type,
member_a2: a > set_a > $o ).
thf(func_def_205,type,
e: product_prod_a_a ).
thf(func_def_206,type,
es: list_P1467822637od_a_a ).
thf(func_def_223,type,
sK0: product_prod_a_a > a ).
thf(func_def_224,type,
sK1: product_prod_a_a > a ).
thf(func_def_225,type,
sK2: ( product_prod_a_a > $o ) > a ).
thf(func_def_226,type,
sK3: ( product_prod_a_a > $o ) > a ).
thf(func_def_227,type,
sK4: product_prod_a_a > a ).
thf(func_def_228,type,
sK5: product_prod_a_a > a ).
thf(func_def_229,type,
sK6: list_P1467822637od_a_a ).
thf(func_def_230,type,
sK7: a ).
thf(func_def_231,type,
sK8: a ).
thf(func_def_232,type,
sK9: list_P1467822637od_a_a ).
thf(func_def_233,type,
sK10: ( product_prod_a_a > $o ) > a ).
thf(func_def_234,type,
sK11: ( product_prod_a_a > $o ) > a ).
thf(func_def_236,type,
ph13:
!>[X0: $tType] : X0 ).
thf(f960,plain,
$false,
inference(equality_resolution,[status(thm)],[f906]) ).
thf(f906,plain,
! [X2: a,X3: a,X0: product_prod_a_a,X1: list_P1467822637od_a_a,X4: list_P1467822637od_a_a] :
( ( cons_P1921020637od_a_a @ X0 @ ( append1574001858od_a_a @ X1 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X2 @ X3 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X3 @ X2 ) @ X4 ) ) ) )
!= ( cons_P1921020637od_a_a @ e @ ( append1574001858od_a_a @ sK6 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ sK7 @ sK8 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ sK8 @ sK7 ) @ sK9 ) ) ) ) ),
inference(superposition,[status(thm)],[f897,f882]) ).
thf(f882,plain,
! [X2: list_P1467822637od_a_a,X1: list_P1467822637od_a_a,X4: product_prod_a_a] :
( ( cons_P1921020637od_a_a @ X4 @ ( append1574001858od_a_a @ X2 @ X1 ) )
= ( append1574001858od_a_a @ ( cons_P1921020637od_a_a @ X4 @ X2 ) @ X1 ) ),
inference(equality_resolution,[status(thm)],[f881]) ).
thf(f881,plain,
! [X2: list_P1467822637od_a_a,X0: list_P1467822637od_a_a,X1: list_P1467822637od_a_a,X4: product_prod_a_a] :
( ( ( cons_P1921020637od_a_a @ X4 @ ( append1574001858od_a_a @ X2 @ X1 ) )
= ( append1574001858od_a_a @ X0 @ X1 ) )
| ( ( cons_P1921020637od_a_a @ X4 @ X2 )
!= X0 ) ),
inference(equality_resolution,[status(thm)],[f871]) ).
thf(f871,plain,
! [X2: list_P1467822637od_a_a,X3: list_P1467822637od_a_a,X0: list_P1467822637od_a_a,X1: list_P1467822637od_a_a,X4: product_prod_a_a] :
( ( ( append1574001858od_a_a @ X0 @ X1 )
= ( cons_P1921020637od_a_a @ X4 @ X3 ) )
| ( ( append1574001858od_a_a @ X2 @ X1 )
!= X3 )
| ( ( cons_P1921020637od_a_a @ X4 @ X2 )
!= X0 ) ),
inference(cnf_transformation,[status(thm)],[f844]) ).
thf(f844,plain,
! [X0: list_P1467822637od_a_a,X1: list_P1467822637od_a_a,X2: list_P1467822637od_a_a,X3: list_P1467822637od_a_a,X4: product_prod_a_a] :
( ( ( append1574001858od_a_a @ X0 @ X1 )
= ( cons_P1921020637od_a_a @ X4 @ X3 ) )
| ( ( append1574001858od_a_a @ X2 @ X1 )
!= X3 )
| ( ( cons_P1921020637od_a_a @ X4 @ X2 )
!= X0 ) ),
inference(flattening,[status(thm)],[f843]) ).
thf(f843,plain,
! [X0: list_P1467822637od_a_a,X1: list_P1467822637od_a_a,X2: list_P1467822637od_a_a,X3: list_P1467822637od_a_a,X4: product_prod_a_a] :
( ( ( append1574001858od_a_a @ X0 @ X1 )
= ( cons_P1921020637od_a_a @ X4 @ X3 ) )
| ( ( append1574001858od_a_a @ X2 @ X1 )
!= X3 )
| ( ( cons_P1921020637od_a_a @ X4 @ X2 )
!= X0 ) ),
inference(ennf_transformation,[status(thm)],[f833]) ).
thf(f833,plain,
! [X0: list_P1467822637od_a_a,X1: list_P1467822637od_a_a,X2: list_P1467822637od_a_a,X3: list_P1467822637od_a_a,X4: product_prod_a_a] :
( ( ( cons_P1921020637od_a_a @ X4 @ X2 )
= X0 )
=> ( ( ( append1574001858od_a_a @ X2 @ X1 )
= X3 )
=> ( ( append1574001858od_a_a @ X0 @ X1 )
= ( cons_P1921020637od_a_a @ X4 @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f42]) ).
thf(f42,axiom,
! [X9: list_P1467822637od_a_a,X10: list_P1467822637od_a_a,X22: list_P1467822637od_a_a,X8: list_P1467822637od_a_a,X21: product_prod_a_a] :
( ( ( cons_P1921020637od_a_a @ X21 @ X22 )
= X9 )
=> ( ( ( append1574001858od_a_a @ X22 @ X10 )
= X8 )
=> ( ( append1574001858od_a_a @ X9 @ X10 )
= ( cons_P1921020637od_a_a @ X21 @ X8 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.3Q2PF44D5Z/DTF2THF_29473.p',fact_41_Cons__eq__appendI) ).
thf(f897,plain,
! [X2: a,X3: a,X1: list_P1467822637od_a_a,X4: list_P1467822637od_a_a] :
( ( append1574001858od_a_a @ X1 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X3 @ X2 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X2 @ X3 ) @ X4 ) ) )
!= ( cons_P1921020637od_a_a @ e @ ( append1574001858od_a_a @ sK6 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ sK7 @ sK8 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ sK8 @ sK7 ) @ sK9 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f896]) ).
thf(f896,plain,
! [X2: a,X3: a,X1: list_P1467822637od_a_a,X4: list_P1467822637od_a_a] :
( ( ( append1574001858od_a_a @ X1 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X3 @ X2 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X2 @ X3 ) @ X4 ) ) )
= ( cons_P1921020637od_a_a @ e @ ( append1574001858od_a_a @ sK6 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ sK7 @ sK8 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ sK8 @ sK7 ) @ sK9 ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f895]) ).
thf(f895,plain,
! [X2: a,X3: a,X1: list_P1467822637od_a_a,X4: list_P1467822637od_a_a] :
( $true
= ( ( append1574001858od_a_a @ X1 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X3 @ X2 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X2 @ X3 ) @ X4 ) ) )
!= ( cons_P1921020637od_a_a @ e @ ( append1574001858od_a_a @ sK6 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ sK7 @ sK8 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ sK8 @ sK7 ) @ sK9 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f894]) ).
thf(f894,plain,
! [X2: a,X3: a,X1: list_P1467822637od_a_a,X4: list_P1467822637od_a_a] :
( $true
= ( ^ [Y0: list_P1467822637od_a_a] :
( ( append1574001858od_a_a @ X1 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X3 @ X2 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X2 @ X3 ) @ Y0 ) ) )
!= ( cons_P1921020637od_a_a @ e @ ( append1574001858od_a_a @ sK6 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ sK7 @ sK8 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ sK8 @ sK7 ) @ sK9 ) ) ) ) )
@ X4 ) ),
inference(pi_clausification,[status(thm)],[f893]) ).
thf(f893,plain,
! [X2: a,X3: a,X1: list_P1467822637od_a_a] :
( $true
= ( !! @ list_P1467822637od_a_a
@ ^ [Y0: list_P1467822637od_a_a] :
( ( append1574001858od_a_a @ X1 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X3 @ X2 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X2 @ X3 ) @ Y0 ) ) )
!= ( cons_P1921020637od_a_a @ e @ ( append1574001858od_a_a @ sK6 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ sK7 @ sK8 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ sK8 @ sK7 ) @ sK9 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f892]) ).
thf(f892,plain,
! [X2: a,X3: a,X1: list_P1467822637od_a_a] :
( $true
= ( ^ [Y0: a] :
( !! @ list_P1467822637od_a_a
@ ^ [Y1: list_P1467822637od_a_a] :
( ( append1574001858od_a_a @ X1 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y0 @ X2 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X2 @ Y0 ) @ Y1 ) ) )
!= ( cons_P1921020637od_a_a @ e @ ( append1574001858od_a_a @ sK6 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ sK7 @ sK8 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ sK8 @ sK7 ) @ sK9 ) ) ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f891]) ).
thf(f891,plain,
! [X2: a,X1: list_P1467822637od_a_a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ list_P1467822637od_a_a
@ ^ [Y1: list_P1467822637od_a_a] :
( ( append1574001858od_a_a @ X1 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y0 @ X2 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X2 @ Y0 ) @ Y1 ) ) )
!= ( cons_P1921020637od_a_a @ e @ ( append1574001858od_a_a @ sK6 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ sK7 @ sK8 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ sK8 @ sK7 ) @ sK9 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f890]) ).
thf(f890,plain,
! [X2: a,X1: list_P1467822637od_a_a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ list_P1467822637od_a_a
@ ^ [Y2: list_P1467822637od_a_a] :
( ( append1574001858od_a_a @ X1 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y1 @ Y0 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y0 @ Y1 ) @ Y2 ) ) )
!= ( cons_P1921020637od_a_a @ e @ ( append1574001858od_a_a @ sK6 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ sK7 @ sK8 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ sK8 @ sK7 ) @ sK9 ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f889]) ).
thf(f889,plain,
! [X1: list_P1467822637od_a_a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ list_P1467822637od_a_a
@ ^ [Y2: list_P1467822637od_a_a] :
( ( append1574001858od_a_a @ X1 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y1 @ Y0 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y0 @ Y1 ) @ Y2 ) ) )
!= ( cons_P1921020637od_a_a @ e @ ( append1574001858od_a_a @ sK6 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ sK7 @ sK8 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ sK8 @ sK7 ) @ sK9 ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f888]) ).
thf(f888,plain,
! [X1: list_P1467822637od_a_a] :
( $true
= ( ^ [Y0: list_P1467822637od_a_a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ list_P1467822637od_a_a
@ ^ [Y3: list_P1467822637od_a_a] :
( ( append1574001858od_a_a @ Y0 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y2 @ Y1 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y1 @ Y2 ) @ Y3 ) ) )
!= ( cons_P1921020637od_a_a @ e @ ( append1574001858od_a_a @ sK6 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ sK7 @ sK8 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ sK8 @ sK7 ) @ sK9 ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f887]) ).
thf(f887,plain,
( $true
= ( !! @ list_P1467822637od_a_a
@ ^ [Y0: list_P1467822637od_a_a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ list_P1467822637od_a_a
@ ^ [Y3: list_P1467822637od_a_a] :
( ( append1574001858od_a_a @ Y0 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y2 @ Y1 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y1 @ Y2 ) @ Y3 ) ) )
!= ( cons_P1921020637od_a_a @ e @ ( append1574001858od_a_a @ sK6 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ sK7 @ sK8 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ sK8 @ sK7 ) @ sK9 ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f879]) ).
thf(f879,plain,
( $true
= ( ^ [Y0: list_P1467822637od_a_a] :
( !! @ list_P1467822637od_a_a
@ ^ [Y1: list_P1467822637od_a_a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ list_P1467822637od_a_a
@ ^ [Y4: list_P1467822637od_a_a] :
( ( append1574001858od_a_a @ Y1 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y3 @ Y2 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y2 @ Y3 ) @ Y4 ) ) )
!= Y0 ) ) ) ) )
@ ( cons_P1921020637od_a_a @ e @ ( append1574001858od_a_a @ sK6 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ sK7 @ sK8 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ sK8 @ sK7 ) @ sK9 ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f873,f874,f866]) ).
thf(f866,plain,
( es
= ( append1574001858od_a_a @ sK6 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ sK7 @ sK8 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ sK8 @ sK7 ) @ sK9 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f856]) ).
thf(f856,plain,
( es
= ( append1574001858od_a_a @ sK6 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ sK7 @ sK8 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ sK8 @ sK7 ) @ sK9 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9])],[f847,f855]) ).
thf(f855,plain,
( ? [X0: list_P1467822637od_a_a,X1: a,X2: a,X3: list_P1467822637od_a_a] :
( es
= ( append1574001858od_a_a @ X0 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X1 @ X2 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X2 @ X1 ) @ X3 ) ) ) )
=> ( es
= ( append1574001858od_a_a @ sK6 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ sK7 @ sK8 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ sK8 @ sK7 ) @ sK9 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f847,plain,
? [X0: list_P1467822637od_a_a,X1: a,X2: a,X3: list_P1467822637od_a_a] :
( es
= ( append1574001858od_a_a @ X0 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X1 @ X2 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X2 @ X1 ) @ X3 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f830]) ).
thf(f830,plain,
~ ! [X0: list_P1467822637od_a_a,X1: a,X2: a,X3: list_P1467822637od_a_a] :
( es
!= ( append1574001858od_a_a @ X0 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X1 @ X2 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X2 @ X1 ) @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f360]) ).
thf(f360,negated_conjecture,
~ ! [X63: list_P1467822637od_a_a,X33: a,X34: a,X64: list_P1467822637od_a_a] :
( es
!= ( append1574001858od_a_a @ X63 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X33 @ X34 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X34 @ X33 ) @ X64 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f359]) ).
thf(f359,conjecture,
! [X63: list_P1467822637od_a_a,X33: a,X34: a,X64: list_P1467822637od_a_a] :
( es
!= ( append1574001858od_a_a @ X63 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X33 @ X34 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X34 @ X33 ) @ X64 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.3Q2PF44D5Z/DTF2THF_29473.p',conj_0) ).
thf(f874,plain,
( kurato1072996284sing_a
= ( ^ [Y0: list_P1467822637od_a_a] :
( !! @ list_P1467822637od_a_a
@ ^ [Y1: list_P1467822637od_a_a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ list_P1467822637od_a_a
@ ^ [Y4: list_P1467822637od_a_a] :
( ( append1574001858od_a_a @ Y1 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y3 @ Y2 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y2 @ Y3 ) @ Y4 ) ) )
!= Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f611]) ).
thf(f611,plain,
( kurato1072996284sing_a
= ( ^ [Y0: list_P1467822637od_a_a] :
( !! @ list_P1467822637od_a_a
@ ^ [Y1: list_P1467822637od_a_a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( !! @ list_P1467822637od_a_a
@ ^ [Y4: list_P1467822637od_a_a] :
( ( append1574001858od_a_a @ Y1 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y3 @ Y2 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y2 @ Y3 ) @ Y4 ) ) )
!= Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f610]) ).
thf(f610,plain,
( kurato1072996284sing_a
= ( ^ [X0: list_P1467822637od_a_a] :
! [X1: list_P1467822637od_a_a,X2: a,X3: a,X4: list_P1467822637od_a_a] :
( ( append1574001858od_a_a @ X4 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X2 @ X3 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X3 @ X2 ) @ X1 ) ) )
!= X0 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( kurato1072996284sing_a
= ( ^ [X0: list_P1467822637od_a_a] :
! [X4: list_P1467822637od_a_a,X2: a,X3: a,X1: list_P1467822637od_a_a] :
( ( append1574001858od_a_a @ X1 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X2 @ X3 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X3 @ X2 ) @ X4 ) ) )
!= X0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.3Q2PF44D5Z/DTF2THF_29473.p',fact_3_progressing__def) ).
thf(f873,plain,
( ( kurato1072996284sing_a @ ( cons_P1921020637od_a_a @ e @ es ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f521]) ).
thf(f521,plain,
( ( kurato1072996284sing_a @ ( cons_P1921020637od_a_a @ e @ es ) )
= $true ),
inference(fool_elimination,[status(thm)],[f520]) ).
thf(f520,plain,
kurato1072996284sing_a @ ( cons_P1921020637od_a_a @ e @ es ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
kurato1072996284sing_a @ ( cons_P1921020637od_a_a @ e @ es ),
file('/export/starexec/sandbox2/tmp/tmp.3Q2PF44D5Z/DTF2THF_29473.p',fact_0_assms) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP092^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n026.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 08:26:25 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : ITP092^1 : TPTP v9.2.1. Released v7.5.0.
% 0.29/0.46 % Domain : Interactive Theorem Proving
% 0.29/0.46 % Problem : Sledgehammer Kuratowski problem prob_158__5524402_1
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English :
% 0.29/0.46
% 0.29/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.29/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.29/0.46 % Source : [Des21]
% 0.29/0.46 % Names : Kuratowski/prob_158__5524402_1 [Des21]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : 0.44 v9.1.0, 0.50 v8.2.0, 0.54 v8.1.0, 0.45 v7.5.0
% 0.29/0.46 % Syntax : Number of formulae : 566 ( 174 unt; 207 typ; 0 def)
% 0.29/0.46 % Number of atoms : 1080 ( 694 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 26 ( 3 avg)
% 0.29/0.46 % Number of connectives : 4874 ( 229 ~; 59 |; 141 &;3982 @)
% 0.29/0.46 % ( 0 <=>; 463 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 29 ( 8 avg)
% 0.29/0.46 % Number of types : 56 ( 55 usr)
% 0.29/0.46 % Number of type conns : 475 ( 475 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 155 ( 152 usr; 9 con; 0-3 aty)
% 0.29/0.46 % Number of variables : 1599 ( 12 ^;1498 !; 89 ?;1599 :)
% 0.29/0.46 % SPC : TH0_THM_EQU_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 15:44:40.460
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % Could-be-implicit typings (55)
% 0.29/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__a_J_Mt__Product____Type__Oprod_Itf__a_Mtf__a_J_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__a_J_Mt__Product____Type__Oprod_Itf__a_Mtf__a_J_J_J_J_J,type,
% 0.29/0.46 set_Pr779272263od_a_a: $tType ).
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% 0.29/0.46 produc205693799od_a_a: $tType ).
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% 0.29/0.46 set_Pr1295299783od_a_a: $tType ).
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% 0.29/0.46 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__a_J_Mt__Product____Type__Oprod_Itf__a_Mtf__a_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__a_J_Mt__Product____Type__Oprod_Itf__a_Mtf__a_J_J_J,type,
% 0.29/0.46 produc1990712039od_a_a: $tType ).
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% 0.29/0.46 produc1912141786_a_a_a: $tType ).
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% 0.29/0.46 produc501911462od_a_a: $tType ).
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% 0.29/0.46 es: list_P1467822637od_a_a ).
% 0.29/0.46
% 0.29/0.46 % Relevant facts (355)
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% 0.29/0.46 kurato1072996284sing_a @ ( cons_P1921020637od_a_a @ e @ es ) ).
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% 0.29/0.46 % assms
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% 0.29/0.46 ( kurato1404746725od_a_a
% 0.29/0.46 = ( ^ [P: list_P1891567085od_a_a] :
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% 0.29/0.46
% 0.29/0.46 % progressing_def
% 0.29/0.46 thf(fact_2_progressing__def,axiom,
% 0.29/0.46 ( kurato292963650list_a
% 0.29/0.46 = ( ^ [P: list_P601816365list_a] :
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% 0.29/0.46 ( P
% 0.29/0.46 != ( append750086082list_a @ Xs @ ( cons_P2080942813list_a @ ( produc1448356631list_a @ X @ Y ) @ ( cons_P2080942813list_a @ ( produc1448356631list_a @ Y @ X ) @ Ys ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % progressing_def
% 0.29/0.46 thf(fact_3_progressing__def,axiom,
% 0.29/0.46 ( kurato1072996284sing_a
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% 0.29/0.46
% 0.29/0.46 % progressing_def
% 0.29/0.46 thf(fact_4_append_Oassoc,axiom,
% 0.29/0.46 ! [A: list_a,B: list_a,C: list_a] :
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% 0.29/0.46 % append.assoc
% 0.29/0.46 thf(fact_5_append_Oassoc,axiom,
% 0.29/0.46 ! [A: list_P1891567085od_a_a,B: list_P1891567085od_a_a,C: list_P1891567085od_a_a] :
% 0.29/0.46 ( ( append864718978od_a_a @ ( append864718978od_a_a @ A @ B ) @ C )
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% 0.29/0.46
% 0.29/0.46 % append.assoc
% 0.29/0.46 thf(fact_6_append_Oassoc,axiom,
% 0.29/0.46 ! [A: list_l1108175539od_a_a,B: list_l1108175539od_a_a,C: list_l1108175539od_a_a] :
% 0.29/0.46 ( ( append2141280328od_a_a @ ( append2141280328od_a_a @ A @ B ) @ C )
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% 0.29/0.46
% 0.29/0.46 % append.assoc
% 0.29/0.46 thf(fact_7_append_Oassoc,axiom,
% 0.29/0.46 ! [A: list_P1467822637od_a_a,B: list_P1467822637od_a_a,C: list_P1467822637od_a_a] :
% 0.29/0.46 ( ( append1574001858od_a_a @ ( append1574001858od_a_a @ A @ B ) @ C )
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% 0.29/0.46 % append.assoc
% 0.29/0.46 thf(fact_8_append__assoc,axiom,
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% 0.29/0.46 % append_assoc
% 0.29/0.46 thf(fact_9_append__assoc,axiom,
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% 0.29/0.46 ( ( append864718978od_a_a @ ( append864718978od_a_a @ Xs2 @ Ys2 ) @ Zs )
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% 0.29/0.46
% 0.29/0.46 % append_assoc
% 0.29/0.46 thf(fact_10_append__assoc,axiom,
% 0.29/0.46 ! [Xs2: list_l1108175539od_a_a,Ys2: list_l1108175539od_a_a,Zs: list_l1108175539od_a_a] :
% 0.29/0.46 ( ( append2141280328od_a_a @ ( append2141280328od_a_a @ Xs2 @ Ys2 ) @ Zs )
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% 0.29/0.46 % append_assoc
% 0.29/0.46 thf(fact_11_append__assoc,axiom,
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% 0.29/0.46 % append_assoc
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% 0.29/0.46 % append_same_eq
% 0.29/0.46 thf(fact_13_append__same__eq,axiom,
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% 0.29/0.46 ( ( ( append864718978od_a_a @ Ys2 @ Xs2 )
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% 0.29/0.46 ( ( ( append2141280328od_a_a @ Ys2 @ Xs2 )
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% 0.29/0.46 % append_same_eq
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% 0.29/0.46 % same_append_eq
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% 0.29/0.46 % same_append_eq
% 0.29/0.46 thf(fact_18_same__append__eq,axiom,
% 0.29/0.46 ! [Xs2: list_l1108175539od_a_a,Ys2: list_l1108175539od_a_a,Zs: list_l1108175539od_a_a] :
% 0.29/0.46 ( ( ( append2141280328od_a_a @ Xs2 @ Ys2 )
% 0.29/0.46 = ( append2141280328od_a_a @ Xs2 @ Zs ) )
% 0.29/0.46 = ( Ys2 = Zs ) ) ).
% 0.29/0.46
% 0.29/0.46 % same_append_eq
% 0.29/0.46 thf(fact_19_same__append__eq,axiom,
% 0.29/0.46 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a] :
% 0.29/0.46 ( ( ( append1574001858od_a_a @ Xs2 @ Ys2 )
% 0.29/0.46 = ( append1574001858od_a_a @ Xs2 @ Zs ) )
% 0.29/0.46 = ( Ys2 = Zs ) ) ).
% 0.29/0.46
% 0.29/0.46 % same_append_eq
% 0.29/0.46 thf(fact_20_list_Oinject,axiom,
% 0.29/0.46 ! [X21: a,X22: list_a,Y21: a,Y22: list_a] :
% 0.29/0.46 ( ( ( cons_a @ X21 @ X22 )
% 0.29/0.46 = ( cons_a @ Y21 @ Y22 ) )
% 0.29/0.46 = ( ( X21 = Y21 )
% 0.29/0.46 & ( X22 = Y22 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % list.inject
% 0.29/0.46 thf(fact_21_list_Oinject,axiom,
% 0.29/0.46 ! [X21: produc1572603623od_a_a,X22: list_P1891567085od_a_a,Y21: produc1572603623od_a_a,Y22: list_P1891567085od_a_a] :
% 0.29/0.46 ( ( ( cons_P1070399645od_a_a @ X21 @ X22 )
% 0.29/0.46 = ( cons_P1070399645od_a_a @ Y21 @ Y22 ) )
% 0.29/0.46 = ( ( X21 = Y21 )
% 0.29/0.46 & ( X22 = Y22 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % list.inject
% 0.29/0.47 thf(fact_22_list_Oinject,axiom,
% 0.29/0.47 ! [X21: list_P1467822637od_a_a,X22: list_l1108175539od_a_a,Y21: list_P1467822637od_a_a,Y22: list_l1108175539od_a_a] :
% 0.29/0.47 ( ( ( cons_l724116707od_a_a @ X21 @ X22 )
% 0.29/0.47 = ( cons_l724116707od_a_a @ Y21 @ Y22 ) )
% 0.29/0.47 = ( ( X21 = Y21 )
% 0.29/0.47 & ( X22 = Y22 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % list.inject
% 0.29/0.47 thf(fact_23_list_Oinject,axiom,
% 0.29/0.47 ! [X21: a > nat,X22: list_a_nat,Y21: a > nat,Y22: list_a_nat] :
% 0.29/0.47 ( ( ( cons_a_nat @ X21 @ X22 )
% 0.29/0.47 = ( cons_a_nat @ Y21 @ Y22 ) )
% 0.29/0.47 = ( ( X21 = Y21 )
% 0.29/0.47 & ( X22 = Y22 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % list.inject
% 0.29/0.47 thf(fact_24_list_Oinject,axiom,
% 0.29/0.47 ! [X21: product_prod_a_a,X22: list_P1467822637od_a_a,Y21: product_prod_a_a,Y22: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( ( cons_P1921020637od_a_a @ X21 @ X22 )
% 0.29/0.47 = ( cons_P1921020637od_a_a @ Y21 @ Y22 ) )
% 0.29/0.47 = ( ( X21 = Y21 )
% 0.29/0.47 & ( X22 = Y22 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % list.inject
% 0.29/0.47 thf(fact_25_prod_Oinject,axiom,
% 0.29/0.47 ! [X1: list_P1467822637od_a_a,X2: a,Y1: list_P1467822637od_a_a,Y2: a] :
% 0.29/0.47 ( ( ( produc998622632_a_a_a @ X1 @ X2 )
% 0.29/0.47 = ( produc998622632_a_a_a @ Y1 @ Y2 ) )
% 0.29/0.47 = ( ( X1 = Y1 )
% 0.29/0.47 & ( X2 = Y2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % prod.inject
% 0.29/0.47 thf(fact_26_prod_Oinject,axiom,
% 0.29/0.47 ! [X1: list_a,X2: list_a,Y1: list_a,Y2: list_a] :
% 0.29/0.47 ( ( ( produc1448356631list_a @ X1 @ X2 )
% 0.29/0.47 = ( produc1448356631list_a @ Y1 @ Y2 ) )
% 0.29/0.47 = ( ( X1 = Y1 )
% 0.29/0.47 & ( X2 = Y2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % prod.inject
% 0.29/0.47 thf(fact_27_prod_Oinject,axiom,
% 0.29/0.47 ! [X1: product_prod_a_a > product_prod_a_a > $o,X2: list_P1467822637od_a_a,Y1: product_prod_a_a > product_prod_a_a > $o,Y2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( ( produc214132118od_a_a @ X1 @ X2 )
% 0.29/0.47 = ( produc214132118od_a_a @ Y1 @ Y2 ) )
% 0.29/0.47 = ( ( X1 = Y1 )
% 0.29/0.47 & ( X2 = Y2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % prod.inject
% 0.29/0.47 thf(fact_28_prod_Oinject,axiom,
% 0.29/0.47 ! [X1: a,X2: produc657167928_a_a_a,Y1: a,Y2: produc657167928_a_a_a] :
% 0.29/0.47 ( ( ( produc1440321489_a_a_a @ X1 @ X2 )
% 0.29/0.47 = ( produc1440321489_a_a_a @ Y1 @ Y2 ) )
% 0.29/0.47 = ( ( X1 = Y1 )
% 0.29/0.47 & ( X2 = Y2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % prod.inject
% 0.29/0.47 thf(fact_29_prod_Oinject,axiom,
% 0.29/0.47 ! [X1: a,X2: list_P1467822637od_a_a,Y1: a,Y2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( ( produc575024326od_a_a @ X1 @ X2 )
% 0.29/0.47 = ( produc575024326od_a_a @ Y1 @ Y2 ) )
% 0.29/0.47 = ( ( X1 = Y1 )
% 0.29/0.47 & ( X2 = Y2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % prod.inject
% 0.29/0.47 thf(fact_30_prod_Oinject,axiom,
% 0.29/0.47 ! [X1: a,X2: a,Y1: a,Y2: a] :
% 0.29/0.47 ( ( ( product_Pair_a_a @ X1 @ X2 )
% 0.29/0.47 = ( product_Pair_a_a @ Y1 @ Y2 ) )
% 0.29/0.47 = ( ( X1 = Y1 )
% 0.29/0.47 & ( X2 = Y2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % prod.inject
% 0.29/0.47 thf(fact_31_old_Oprod_Oinject,axiom,
% 0.29/0.47 ! [A: list_P1467822637od_a_a,B: a,A2: list_P1467822637od_a_a,B2: a] :
% 0.29/0.47 ( ( ( produc998622632_a_a_a @ A @ B )
% 0.29/0.47 = ( produc998622632_a_a_a @ A2 @ B2 ) )
% 0.29/0.47 = ( ( A = A2 )
% 0.29/0.47 & ( B = B2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % old.prod.inject
% 0.29/0.47 thf(fact_32_old_Oprod_Oinject,axiom,
% 0.29/0.47 ! [A: list_a,B: list_a,A2: list_a,B2: list_a] :
% 0.29/0.47 ( ( ( produc1448356631list_a @ A @ B )
% 0.29/0.47 = ( produc1448356631list_a @ A2 @ B2 ) )
% 0.29/0.47 = ( ( A = A2 )
% 0.29/0.47 & ( B = B2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % old.prod.inject
% 0.29/0.47 thf(fact_33_old_Oprod_Oinject,axiom,
% 0.29/0.47 ! [A: product_prod_a_a > product_prod_a_a > $o,B: list_P1467822637od_a_a,A2: product_prod_a_a > product_prod_a_a > $o,B2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( ( produc214132118od_a_a @ A @ B )
% 0.29/0.47 = ( produc214132118od_a_a @ A2 @ B2 ) )
% 0.29/0.47 = ( ( A = A2 )
% 0.29/0.47 & ( B = B2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % old.prod.inject
% 0.29/0.47 thf(fact_34_old_Oprod_Oinject,axiom,
% 0.29/0.47 ! [A: a,B: produc657167928_a_a_a,A2: a,B2: produc657167928_a_a_a] :
% 0.29/0.47 ( ( ( produc1440321489_a_a_a @ A @ B )
% 0.29/0.47 = ( produc1440321489_a_a_a @ A2 @ B2 ) )
% 0.29/0.47 = ( ( A = A2 )
% 0.29/0.47 & ( B = B2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % old.prod.inject
% 0.29/0.47 thf(fact_35_old_Oprod_Oinject,axiom,
% 0.29/0.47 ! [A: a,B: list_P1467822637od_a_a,A2: a,B2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( ( produc575024326od_a_a @ A @ B )
% 0.29/0.47 = ( produc575024326od_a_a @ A2 @ B2 ) )
% 0.29/0.47 = ( ( A = A2 )
% 0.29/0.47 & ( B = B2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % old.prod.inject
% 0.29/0.47 thf(fact_36_old_Oprod_Oinject,axiom,
% 0.29/0.47 ! [A: a,B: a,A2: a,B2: a] :
% 0.29/0.47 ( ( ( product_Pair_a_a @ A @ B )
% 0.29/0.47 = ( product_Pair_a_a @ A2 @ B2 ) )
% 0.29/0.47 = ( ( A = A2 )
% 0.29/0.47 & ( B = B2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % old.prod.inject
% 0.29/0.47 thf(fact_37_Cons__eq__appendI,axiom,
% 0.29/0.47 ! [X3: a,Xs1: list_a,Ys2: list_a,Xs2: list_a,Zs: list_a] :
% 0.29/0.47 ( ( ( cons_a @ X3 @ Xs1 )
% 0.29/0.47 = Ys2 )
% 0.29/0.47 => ( ( Xs2
% 0.29/0.47 = ( append_a @ Xs1 @ Zs ) )
% 0.29/0.47 => ( ( cons_a @ X3 @ Xs2 )
% 0.29/0.47 = ( append_a @ Ys2 @ Zs ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Cons_eq_appendI
% 0.29/0.47 thf(fact_38_Cons__eq__appendI,axiom,
% 0.29/0.47 ! [X3: produc1572603623od_a_a,Xs1: list_P1891567085od_a_a,Ys2: list_P1891567085od_a_a,Xs2: list_P1891567085od_a_a,Zs: list_P1891567085od_a_a] :
% 0.29/0.47 ( ( ( cons_P1070399645od_a_a @ X3 @ Xs1 )
% 0.29/0.47 = Ys2 )
% 0.29/0.47 => ( ( Xs2
% 0.29/0.47 = ( append864718978od_a_a @ Xs1 @ Zs ) )
% 0.29/0.47 => ( ( cons_P1070399645od_a_a @ X3 @ Xs2 )
% 0.29/0.47 = ( append864718978od_a_a @ Ys2 @ Zs ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Cons_eq_appendI
% 0.29/0.47 thf(fact_39_Cons__eq__appendI,axiom,
% 0.29/0.47 ! [X3: list_P1467822637od_a_a,Xs1: list_l1108175539od_a_a,Ys2: list_l1108175539od_a_a,Xs2: list_l1108175539od_a_a,Zs: list_l1108175539od_a_a] :
% 0.29/0.47 ( ( ( cons_l724116707od_a_a @ X3 @ Xs1 )
% 0.29/0.47 = Ys2 )
% 0.29/0.47 => ( ( Xs2
% 0.29/0.47 = ( append2141280328od_a_a @ Xs1 @ Zs ) )
% 0.29/0.47 => ( ( cons_l724116707od_a_a @ X3 @ Xs2 )
% 0.29/0.47 = ( append2141280328od_a_a @ Ys2 @ Zs ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Cons_eq_appendI
% 0.29/0.47 thf(fact_40_Cons__eq__appendI,axiom,
% 0.29/0.47 ! [X3: a > nat,Xs1: list_a_nat,Ys2: list_a_nat,Xs2: list_a_nat,Zs: list_a_nat] :
% 0.29/0.47 ( ( ( cons_a_nat @ X3 @ Xs1 )
% 0.29/0.47 = Ys2 )
% 0.29/0.47 => ( ( Xs2
% 0.29/0.47 = ( append_a_nat @ Xs1 @ Zs ) )
% 0.29/0.47 => ( ( cons_a_nat @ X3 @ Xs2 )
% 0.29/0.47 = ( append_a_nat @ Ys2 @ Zs ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Cons_eq_appendI
% 0.29/0.47 thf(fact_41_Cons__eq__appendI,axiom,
% 0.29/0.47 ! [X3: product_prod_a_a,Xs1: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Xs2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( ( cons_P1921020637od_a_a @ X3 @ Xs1 )
% 0.29/0.47 = Ys2 )
% 0.29/0.47 => ( ( Xs2
% 0.29/0.47 = ( append1574001858od_a_a @ Xs1 @ Zs ) )
% 0.29/0.47 => ( ( cons_P1921020637od_a_a @ X3 @ Xs2 )
% 0.29/0.47 = ( append1574001858od_a_a @ Ys2 @ Zs ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Cons_eq_appendI
% 0.29/0.47 thf(fact_42_append__Cons,axiom,
% 0.29/0.47 ! [X3: a,Xs2: list_a,Ys2: list_a] :
% 0.29/0.47 ( ( append_a @ ( cons_a @ X3 @ Xs2 ) @ Ys2 )
% 0.29/0.47 = ( cons_a @ X3 @ ( append_a @ Xs2 @ Ys2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % append_Cons
% 0.29/0.47 thf(fact_43_append__Cons,axiom,
% 0.29/0.47 ! [X3: produc1572603623od_a_a,Xs2: list_P1891567085od_a_a,Ys2: list_P1891567085od_a_a] :
% 0.29/0.47 ( ( append864718978od_a_a @ ( cons_P1070399645od_a_a @ X3 @ Xs2 ) @ Ys2 )
% 0.29/0.47 = ( cons_P1070399645od_a_a @ X3 @ ( append864718978od_a_a @ Xs2 @ Ys2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % append_Cons
% 0.29/0.47 thf(fact_44_append__Cons,axiom,
% 0.29/0.47 ! [X3: list_P1467822637od_a_a,Xs2: list_l1108175539od_a_a,Ys2: list_l1108175539od_a_a] :
% 0.29/0.47 ( ( append2141280328od_a_a @ ( cons_l724116707od_a_a @ X3 @ Xs2 ) @ Ys2 )
% 0.29/0.47 = ( cons_l724116707od_a_a @ X3 @ ( append2141280328od_a_a @ Xs2 @ Ys2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % append_Cons
% 0.29/0.47 thf(fact_45_append__Cons,axiom,
% 0.29/0.47 ! [X3: a > nat,Xs2: list_a_nat,Ys2: list_a_nat] :
% 0.29/0.47 ( ( append_a_nat @ ( cons_a_nat @ X3 @ Xs2 ) @ Ys2 )
% 0.29/0.47 = ( cons_a_nat @ X3 @ ( append_a_nat @ Xs2 @ Ys2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % append_Cons
% 0.29/0.47 thf(fact_46_append__Cons,axiom,
% 0.29/0.47 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( append1574001858od_a_a @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ Ys2 )
% 0.29/0.47 = ( cons_P1921020637od_a_a @ X3 @ ( append1574001858od_a_a @ Xs2 @ Ys2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % append_Cons
% 0.29/0.47 thf(fact_47_append__eq__appendI,axiom,
% 0.29/0.47 ! [Xs2: list_a,Xs1: list_a,Zs: list_a,Ys2: list_a,Us: list_a] :
% 0.29/0.47 ( ( ( append_a @ Xs2 @ Xs1 )
% 0.29/0.47 = Zs )
% 0.29/0.47 => ( ( Ys2
% 0.29/0.47 = ( append_a @ Xs1 @ Us ) )
% 0.29/0.47 => ( ( append_a @ Xs2 @ Ys2 )
% 0.29/0.47 = ( append_a @ Zs @ Us ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % append_eq_appendI
% 0.29/0.47 thf(fact_48_append__eq__appendI,axiom,
% 0.29/0.47 ! [Xs2: list_P1891567085od_a_a,Xs1: list_P1891567085od_a_a,Zs: list_P1891567085od_a_a,Ys2: list_P1891567085od_a_a,Us: list_P1891567085od_a_a] :
% 0.29/0.47 ( ( ( append864718978od_a_a @ Xs2 @ Xs1 )
% 0.29/0.47 = Zs )
% 0.29/0.47 => ( ( Ys2
% 0.29/0.47 = ( append864718978od_a_a @ Xs1 @ Us ) )
% 0.29/0.47 => ( ( append864718978od_a_a @ Xs2 @ Ys2 )
% 0.29/0.47 = ( append864718978od_a_a @ Zs @ Us ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % append_eq_appendI
% 0.29/0.47 thf(fact_49_append__eq__appendI,axiom,
% 0.29/0.47 ! [Xs2: list_l1108175539od_a_a,Xs1: list_l1108175539od_a_a,Zs: list_l1108175539od_a_a,Ys2: list_l1108175539od_a_a,Us: list_l1108175539od_a_a] :
% 0.29/0.47 ( ( ( append2141280328od_a_a @ Xs2 @ Xs1 )
% 0.29/0.47 = Zs )
% 0.29/0.47 => ( ( Ys2
% 0.29/0.47 = ( append2141280328od_a_a @ Xs1 @ Us ) )
% 0.29/0.47 => ( ( append2141280328od_a_a @ Xs2 @ Ys2 )
% 0.29/0.47 = ( append2141280328od_a_a @ Zs @ Us ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % append_eq_appendI
% 0.29/0.47 thf(fact_50_append__eq__appendI,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a,Xs1: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Us: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( ( append1574001858od_a_a @ Xs2 @ Xs1 )
% 0.29/0.47 = Zs )
% 0.29/0.47 => ( ( Ys2
% 0.29/0.47 = ( append1574001858od_a_a @ Xs1 @ Us ) )
% 0.29/0.47 => ( ( append1574001858od_a_a @ Xs2 @ Ys2 )
% 0.29/0.47 = ( append1574001858od_a_a @ Zs @ Us ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % append_eq_appendI
% 0.29/0.47 thf(fact_51_append__eq__append__conv2,axiom,
% 0.29/0.47 ! [Xs2: list_a,Ys2: list_a,Zs: list_a,Ts: list_a] :
% 0.29/0.47 ( ( ( append_a @ Xs2 @ Ys2 )
% 0.29/0.47 = ( append_a @ Zs @ Ts ) )
% 0.29/0.47 = ( ? [Us2: list_a] :
% 0.29/0.47 ( ( ( Xs2
% 0.29/0.47 = ( append_a @ Zs @ Us2 ) )
% 0.29/0.47 & ( ( append_a @ Us2 @ Ys2 )
% 0.29/0.47 = Ts ) )
% 0.29/0.47 | ( ( ( append_a @ Xs2 @ Us2 )
% 0.29/0.47 = Zs )
% 0.29/0.47 & ( Ys2
% 0.29/0.47 = ( append_a @ Us2 @ Ts ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % append_eq_append_conv2
% 0.29/0.47 thf(fact_52_append__eq__append__conv2,axiom,
% 0.29/0.47 ! [Xs2: list_P1891567085od_a_a,Ys2: list_P1891567085od_a_a,Zs: list_P1891567085od_a_a,Ts: list_P1891567085od_a_a] :
% 0.29/0.47 ( ( ( append864718978od_a_a @ Xs2 @ Ys2 )
% 0.29/0.47 = ( append864718978od_a_a @ Zs @ Ts ) )
% 0.29/0.47 = ( ? [Us2: list_P1891567085od_a_a] :
% 0.29/0.47 ( ( ( Xs2
% 0.29/0.47 = ( append864718978od_a_a @ Zs @ Us2 ) )
% 0.29/0.47 & ( ( append864718978od_a_a @ Us2 @ Ys2 )
% 0.29/0.47 = Ts ) )
% 0.29/0.47 | ( ( ( append864718978od_a_a @ Xs2 @ Us2 )
% 0.29/0.47 = Zs )
% 0.29/0.47 & ( Ys2
% 0.29/0.47 = ( append864718978od_a_a @ Us2 @ Ts ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % append_eq_append_conv2
% 0.29/0.47 thf(fact_53_append__eq__append__conv2,axiom,
% 0.29/0.47 ! [Xs2: list_l1108175539od_a_a,Ys2: list_l1108175539od_a_a,Zs: list_l1108175539od_a_a,Ts: list_l1108175539od_a_a] :
% 0.29/0.47 ( ( ( append2141280328od_a_a @ Xs2 @ Ys2 )
% 0.29/0.47 = ( append2141280328od_a_a @ Zs @ Ts ) )
% 0.29/0.47 = ( ? [Us2: list_l1108175539od_a_a] :
% 0.29/0.47 ( ( ( Xs2
% 0.29/0.47 = ( append2141280328od_a_a @ Zs @ Us2 ) )
% 0.29/0.47 & ( ( append2141280328od_a_a @ Us2 @ Ys2 )
% 0.29/0.47 = Ts ) )
% 0.29/0.47 | ( ( ( append2141280328od_a_a @ Xs2 @ Us2 )
% 0.29/0.47 = Zs )
% 0.29/0.47 & ( Ys2
% 0.29/0.47 = ( append2141280328od_a_a @ Us2 @ Ts ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % append_eq_append_conv2
% 0.29/0.47 thf(fact_54_append__eq__append__conv2,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a,Ts: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( ( append1574001858od_a_a @ Xs2 @ Ys2 )
% 0.29/0.47 = ( append1574001858od_a_a @ Zs @ Ts ) )
% 0.29/0.47 = ( ? [Us2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( ( Xs2
% 0.29/0.47 = ( append1574001858od_a_a @ Zs @ Us2 ) )
% 0.29/0.47 & ( ( append1574001858od_a_a @ Us2 @ Ys2 )
% 0.29/0.47 = Ts ) )
% 0.29/0.47 | ( ( ( append1574001858od_a_a @ Xs2 @ Us2 )
% 0.29/0.47 = Zs )
% 0.29/0.47 & ( Ys2
% 0.29/0.47 = ( append1574001858od_a_a @ Us2 @ Ts ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % append_eq_append_conv2
% 0.29/0.47 thf(fact_55_old_Oprod_Oinducts,axiom,
% 0.29/0.47 ! [P2: produc657167928_a_a_a > $o,Prod: produc657167928_a_a_a] :
% 0.29/0.47 ( ! [A3: list_P1467822637od_a_a,B3: a] : ( P2 @ ( produc998622632_a_a_a @ A3 @ B3 ) )
% 0.29/0.47 => ( P2 @ Prod ) ) ).
% 0.29/0.47
% 0.29/0.47 % old.prod.inducts
% 0.29/0.47 thf(fact_56_old_Oprod_Oinducts,axiom,
% 0.29/0.47 ! [P2: produc864062247list_a > $o,Prod: produc864062247list_a] :
% 0.29/0.47 ( ! [A3: list_a,B3: list_a] : ( P2 @ ( produc1448356631list_a @ A3 @ B3 ) )
% 0.29/0.47 => ( P2 @ Prod ) ) ).
% 0.29/0.47
% 0.29/0.47 % old.prod.inducts
% 0.29/0.47 thf(fact_57_old_Oprod_Oinducts,axiom,
% 0.29/0.47 ! [P2: produc501911462od_a_a > $o,Prod: produc501911462od_a_a] :
% 0.29/0.47 ( ! [A3: product_prod_a_a > product_prod_a_a > $o,B3: list_P1467822637od_a_a] : ( P2 @ ( produc214132118od_a_a @ A3 @ B3 ) )
% 0.29/0.47 => ( P2 @ Prod ) ) ).
% 0.29/0.47
% 0.29/0.47 % old.prod.inducts
% 0.29/0.47 thf(fact_58_old_Oprod_Oinducts,axiom,
% 0.29/0.47 ! [P2: produc1197928545_a_a_a > $o,Prod: produc1197928545_a_a_a] :
% 0.29/0.47 ( ! [A3: a,B3: produc657167928_a_a_a] : ( P2 @ ( produc1440321489_a_a_a @ A3 @ B3 ) )
% 0.29/0.47 => ( P2 @ Prod ) ) ).
% 0.29/0.47
% 0.29/0.47 % old.prod.inducts
% 0.29/0.47 thf(fact_59_old_Oprod_Oinducts,axiom,
% 0.29/0.47 ! [P2: produc1701253078od_a_a > $o,Prod: produc1701253078od_a_a] :
% 0.29/0.47 ( ! [A3: a,B3: list_P1467822637od_a_a] : ( P2 @ ( produc575024326od_a_a @ A3 @ B3 ) )
% 0.29/0.47 => ( P2 @ Prod ) ) ).
% 0.29/0.47
% 0.29/0.47 % old.prod.inducts
% 0.29/0.47 thf(fact_60_old_Oprod_Oinducts,axiom,
% 0.29/0.47 ! [P2: product_prod_a_a > $o,Prod: product_prod_a_a] :
% 0.29/0.47 ( ! [A3: a,B3: a] : ( P2 @ ( product_Pair_a_a @ A3 @ B3 ) )
% 0.29/0.47 => ( P2 @ Prod ) ) ).
% 0.29/0.47
% 0.29/0.47 % old.prod.inducts
% 0.29/0.47 thf(fact_61_old_Oprod_Oexhaust,axiom,
% 0.29/0.47 ! [Y3: produc657167928_a_a_a] :
% 0.29/0.47 ~ ! [A3: list_P1467822637od_a_a,B3: a] :
% 0.29/0.47 ( Y3
% 0.29/0.47 != ( produc998622632_a_a_a @ A3 @ B3 ) ) ).
% 0.29/0.47
% 0.29/0.47 % old.prod.exhaust
% 0.29/0.47 thf(fact_62_old_Oprod_Oexhaust,axiom,
% 0.29/0.47 ! [Y3: produc864062247list_a] :
% 0.29/0.47 ~ ! [A3: list_a,B3: list_a] :
% 0.29/0.47 ( Y3
% 0.29/0.47 != ( produc1448356631list_a @ A3 @ B3 ) ) ).
% 0.29/0.47
% 0.29/0.47 % old.prod.exhaust
% 0.29/0.47 thf(fact_63_old_Oprod_Oexhaust,axiom,
% 0.29/0.47 ! [Y3: produc501911462od_a_a] :
% 0.29/0.47 ~ ! [A3: product_prod_a_a > product_prod_a_a > $o,B3: list_P1467822637od_a_a] :
% 0.29/0.47 ( Y3
% 0.29/0.47 != ( produc214132118od_a_a @ A3 @ B3 ) ) ).
% 0.29/0.47
% 0.29/0.47 % old.prod.exhaust
% 0.29/0.47 thf(fact_64_old_Oprod_Oexhaust,axiom,
% 0.29/0.47 ! [Y3: produc1197928545_a_a_a] :
% 0.29/0.47 ~ ! [A3: a,B3: produc657167928_a_a_a] :
% 0.29/0.47 ( Y3
% 0.29/0.47 != ( produc1440321489_a_a_a @ A3 @ B3 ) ) ).
% 0.29/0.47
% 0.29/0.47 % old.prod.exhaust
% 0.29/0.47 thf(fact_65_old_Oprod_Oexhaust,axiom,
% 0.29/0.47 ! [Y3: produc1701253078od_a_a] :
% 0.29/0.47 ~ ! [A3: a,B3: list_P1467822637od_a_a] :
% 0.29/0.47 ( Y3
% 0.29/0.47 != ( produc575024326od_a_a @ A3 @ B3 ) ) ).
% 0.29/0.47
% 0.29/0.47 % old.prod.exhaust
% 0.29/0.47 thf(fact_66_old_Oprod_Oexhaust,axiom,
% 0.29/0.47 ! [Y3: product_prod_a_a] :
% 0.29/0.47 ~ ! [A3: a,B3: a] :
% 0.29/0.47 ( Y3
% 0.29/0.47 != ( product_Pair_a_a @ A3 @ B3 ) ) ).
% 0.29/0.47
% 0.29/0.47 % old.prod.exhaust
% 0.29/0.47 thf(fact_67_prod__induct3,axiom,
% 0.29/0.47 ! [P2: produc1197928545_a_a_a > $o,X3: produc1197928545_a_a_a] :
% 0.29/0.47 ( ! [A3: a,B3: list_P1467822637od_a_a,C2: a] : ( P2 @ ( produc1440321489_a_a_a @ A3 @ ( produc998622632_a_a_a @ B3 @ C2 ) ) )
% 0.29/0.47 => ( P2 @ X3 ) ) ).
% 0.29/0.47
% 0.29/0.47 % prod_induct3
% 0.29/0.47 thf(fact_68_prod__cases3,axiom,
% 0.29/0.47 ! [Y3: produc1197928545_a_a_a] :
% 0.29/0.47 ~ ! [A3: a,B3: list_P1467822637od_a_a,C2: a] :
% 0.29/0.47 ( Y3
% 0.29/0.47 != ( produc1440321489_a_a_a @ A3 @ ( produc998622632_a_a_a @ B3 @ C2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % prod_cases3
% 0.29/0.47 thf(fact_69_Pair__inject,axiom,
% 0.29/0.47 ! [A: list_P1467822637od_a_a,B: a,A2: list_P1467822637od_a_a,B2: a] :
% 0.29/0.47 ( ( ( produc998622632_a_a_a @ A @ B )
% 0.29/0.47 = ( produc998622632_a_a_a @ A2 @ B2 ) )
% 0.29/0.47 => ~ ( ( A = A2 )
% 0.29/0.47 => ( B != B2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Pair_inject
% 0.29/0.47 thf(fact_70_Pair__inject,axiom,
% 0.29/0.47 ! [A: list_a,B: list_a,A2: list_a,B2: list_a] :
% 0.29/0.47 ( ( ( produc1448356631list_a @ A @ B )
% 0.29/0.47 = ( produc1448356631list_a @ A2 @ B2 ) )
% 0.29/0.47 => ~ ( ( A = A2 )
% 0.29/0.47 => ( B != B2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Pair_inject
% 0.29/0.47 thf(fact_71_Pair__inject,axiom,
% 0.29/0.47 ! [A: product_prod_a_a > product_prod_a_a > $o,B: list_P1467822637od_a_a,A2: product_prod_a_a > product_prod_a_a > $o,B2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( ( produc214132118od_a_a @ A @ B )
% 0.29/0.47 = ( produc214132118od_a_a @ A2 @ B2 ) )
% 0.29/0.47 => ~ ( ( A = A2 )
% 0.29/0.47 => ( B != B2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Pair_inject
% 0.29/0.47 thf(fact_72_Pair__inject,axiom,
% 0.29/0.47 ! [A: a,B: produc657167928_a_a_a,A2: a,B2: produc657167928_a_a_a] :
% 0.29/0.47 ( ( ( produc1440321489_a_a_a @ A @ B )
% 0.29/0.47 = ( produc1440321489_a_a_a @ A2 @ B2 ) )
% 0.29/0.47 => ~ ( ( A = A2 )
% 0.29/0.47 => ( B != B2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Pair_inject
% 0.29/0.47 thf(fact_73_Pair__inject,axiom,
% 0.29/0.47 ! [A: a,B: list_P1467822637od_a_a,A2: a,B2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( ( produc575024326od_a_a @ A @ B )
% 0.29/0.47 = ( produc575024326od_a_a @ A2 @ B2 ) )
% 0.29/0.47 => ~ ( ( A = A2 )
% 0.29/0.47 => ( B != B2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Pair_inject
% 0.29/0.47 thf(fact_74_Pair__inject,axiom,
% 0.29/0.47 ! [A: a,B: a,A2: a,B2: a] :
% 0.29/0.47 ( ( ( product_Pair_a_a @ A @ B )
% 0.29/0.47 = ( product_Pair_a_a @ A2 @ B2 ) )
% 0.29/0.47 => ~ ( ( A = A2 )
% 0.29/0.47 => ( B != B2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Pair_inject
% 0.29/0.47 thf(fact_75_prod__cases,axiom,
% 0.29/0.47 ! [P2: produc657167928_a_a_a > $o,P3: produc657167928_a_a_a] :
% 0.29/0.47 ( ! [A3: list_P1467822637od_a_a,B3: a] : ( P2 @ ( produc998622632_a_a_a @ A3 @ B3 ) )
% 0.29/0.47 => ( P2 @ P3 ) ) ).
% 0.29/0.47
% 0.29/0.47 % prod_cases
% 0.29/0.47 thf(fact_76_prod__cases,axiom,
% 0.29/0.47 ! [P2: produc864062247list_a > $o,P3: produc864062247list_a] :
% 0.29/0.47 ( ! [A3: list_a,B3: list_a] : ( P2 @ ( produc1448356631list_a @ A3 @ B3 ) )
% 0.29/0.47 => ( P2 @ P3 ) ) ).
% 0.29/0.47
% 0.29/0.47 % prod_cases
% 0.29/0.47 thf(fact_77_prod__cases,axiom,
% 0.29/0.47 ! [P2: produc501911462od_a_a > $o,P3: produc501911462od_a_a] :
% 0.29/0.47 ( ! [A3: product_prod_a_a > product_prod_a_a > $o,B3: list_P1467822637od_a_a] : ( P2 @ ( produc214132118od_a_a @ A3 @ B3 ) )
% 0.29/0.47 => ( P2 @ P3 ) ) ).
% 0.29/0.47
% 0.29/0.47 % prod_cases
% 0.29/0.47 thf(fact_78_prod__cases,axiom,
% 0.29/0.47 ! [P2: produc1197928545_a_a_a > $o,P3: produc1197928545_a_a_a] :
% 0.29/0.47 ( ! [A3: a,B3: produc657167928_a_a_a] : ( P2 @ ( produc1440321489_a_a_a @ A3 @ B3 ) )
% 0.29/0.47 => ( P2 @ P3 ) ) ).
% 0.29/0.47
% 0.29/0.47 % prod_cases
% 0.29/0.47 thf(fact_79_prod__cases,axiom,
% 0.29/0.47 ! [P2: produc1701253078od_a_a > $o,P3: produc1701253078od_a_a] :
% 0.29/0.47 ( ! [A3: a,B3: list_P1467822637od_a_a] : ( P2 @ ( produc575024326od_a_a @ A3 @ B3 ) )
% 0.29/0.47 => ( P2 @ P3 ) ) ).
% 0.29/0.47
% 0.29/0.47 % prod_cases
% 0.29/0.47 thf(fact_80_prod__cases,axiom,
% 0.29/0.47 ! [P2: product_prod_a_a > $o,P3: product_prod_a_a] :
% 0.29/0.47 ( ! [A3: a,B3: a] : ( P2 @ ( product_Pair_a_a @ A3 @ B3 ) )
% 0.29/0.47 => ( P2 @ P3 ) ) ).
% 0.29/0.47
% 0.29/0.47 % prod_cases
% 0.29/0.47 thf(fact_81_surj__pair,axiom,
% 0.29/0.47 ! [P3: produc657167928_a_a_a] :
% 0.29/0.47 ? [X4: list_P1467822637od_a_a,Y4: a] :
% 0.29/0.47 ( P3
% 0.29/0.47 = ( produc998622632_a_a_a @ X4 @ Y4 ) ) ).
% 0.29/0.47
% 0.29/0.47 % surj_pair
% 0.29/0.47 thf(fact_82_surj__pair,axiom,
% 0.29/0.47 ! [P3: produc864062247list_a] :
% 0.29/0.47 ? [X4: list_a,Y4: list_a] :
% 0.29/0.47 ( P3
% 0.29/0.47 = ( produc1448356631list_a @ X4 @ Y4 ) ) ).
% 0.29/0.47
% 0.29/0.47 % surj_pair
% 0.29/0.47 thf(fact_83_surj__pair,axiom,
% 0.29/0.47 ! [P3: produc501911462od_a_a] :
% 0.29/0.47 ? [X4: product_prod_a_a > product_prod_a_a > $o,Y4: list_P1467822637od_a_a] :
% 0.29/0.47 ( P3
% 0.29/0.47 = ( produc214132118od_a_a @ X4 @ Y4 ) ) ).
% 0.29/0.47
% 0.29/0.47 % surj_pair
% 0.29/0.47 thf(fact_84_surj__pair,axiom,
% 0.29/0.47 ! [P3: produc1197928545_a_a_a] :
% 0.29/0.47 ? [X4: a,Y4: produc657167928_a_a_a] :
% 0.29/0.47 ( P3
% 0.29/0.47 = ( produc1440321489_a_a_a @ X4 @ Y4 ) ) ).
% 0.29/0.47
% 0.29/0.47 % surj_pair
% 0.29/0.47 thf(fact_85_surj__pair,axiom,
% 0.29/0.47 ! [P3: produc1701253078od_a_a] :
% 0.29/0.47 ? [X4: a,Y4: list_P1467822637od_a_a] :
% 0.29/0.47 ( P3
% 0.29/0.47 = ( produc575024326od_a_a @ X4 @ Y4 ) ) ).
% 0.29/0.47
% 0.29/0.47 % surj_pair
% 0.29/0.47 thf(fact_86_surj__pair,axiom,
% 0.29/0.47 ! [P3: product_prod_a_a] :
% 0.29/0.47 ? [X4: a,Y4: a] :
% 0.29/0.47 ( P3
% 0.29/0.47 = ( product_Pair_a_a @ X4 @ Y4 ) ) ).
% 0.29/0.47
% 0.29/0.47 % surj_pair
% 0.29/0.47 thf(fact_87_not__Cons__self2,axiom,
% 0.29/0.47 ! [X3: a,Xs2: list_a] :
% 0.29/0.47 ( ( cons_a @ X3 @ Xs2 )
% 0.29/0.47 != Xs2 ) ).
% 0.29/0.47
% 0.29/0.47 % not_Cons_self2
% 0.29/0.47 thf(fact_88_not__Cons__self2,axiom,
% 0.29/0.47 ! [X3: produc1572603623od_a_a,Xs2: list_P1891567085od_a_a] :
% 0.29/0.47 ( ( cons_P1070399645od_a_a @ X3 @ Xs2 )
% 0.29/0.47 != Xs2 ) ).
% 0.29/0.47
% 0.29/0.47 % not_Cons_self2
% 0.29/0.47 thf(fact_89_not__Cons__self2,axiom,
% 0.29/0.47 ! [X3: list_P1467822637od_a_a,Xs2: list_l1108175539od_a_a] :
% 0.29/0.47 ( ( cons_l724116707od_a_a @ X3 @ Xs2 )
% 0.29/0.47 != Xs2 ) ).
% 0.29/0.47
% 0.29/0.47 % not_Cons_self2
% 0.29/0.47 thf(fact_90_not__Cons__self2,axiom,
% 0.29/0.47 ! [X3: a > nat,Xs2: list_a_nat] :
% 0.29/0.47 ( ( cons_a_nat @ X3 @ Xs2 )
% 0.29/0.47 != Xs2 ) ).
% 0.29/0.47
% 0.29/0.47 % not_Cons_self2
% 0.29/0.47 thf(fact_91_not__Cons__self2,axiom,
% 0.29/0.47 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( cons_P1921020637od_a_a @ X3 @ Xs2 )
% 0.29/0.47 != Xs2 ) ).
% 0.29/0.47
% 0.29/0.47 % not_Cons_self2
% 0.29/0.47 thf(fact_92_bind__simps_I2_J,axiom,
% 0.29/0.47 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a,F: product_prod_a_a > list_P1467822637od_a_a] :
% 0.29/0.47 ( ( bind_P1783625031od_a_a @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ F )
% 0.29/0.47 = ( append1574001858od_a_a @ ( F @ X3 ) @ ( bind_P1783625031od_a_a @ Xs2 @ F ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % bind_simps(2)
% 0.29/0.47 thf(fact_93_bind__simps_I2_J,axiom,
% 0.29/0.47 ! [X3: a,Xs2: list_a,F: a > list_a] :
% 0.29/0.47 ( ( bind_a_a @ ( cons_a @ X3 @ Xs2 ) @ F )
% 0.29/0.47 = ( append_a @ ( F @ X3 ) @ ( bind_a_a @ Xs2 @ F ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % bind_simps(2)
% 0.29/0.47 thf(fact_94_bind__simps_I2_J,axiom,
% 0.29/0.47 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a,F: product_prod_a_a > list_a] :
% 0.29/0.47 ( ( bind_P293964574_a_a_a @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ F )
% 0.29/0.47 = ( append_a @ ( F @ X3 ) @ ( bind_P293964574_a_a_a @ Xs2 @ F ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % bind_simps(2)
% 0.29/0.47 thf(fact_95_bind__simps_I2_J,axiom,
% 0.29/0.47 ! [X3: a,Xs2: list_a,F: a > list_P1467822637od_a_a] :
% 0.29/0.47 ( ( bind_a1679112752od_a_a @ ( cons_a @ X3 @ Xs2 ) @ F )
% 0.29/0.47 = ( append1574001858od_a_a @ ( F @ X3 ) @ ( bind_a1679112752od_a_a @ Xs2 @ F ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % bind_simps(2)
% 0.29/0.47 thf(fact_96_bind__simps_I2_J,axiom,
% 0.29/0.47 ! [X3: a > nat,Xs2: list_a_nat,F: ( a > nat ) > list_a] :
% 0.29/0.47 ( ( bind_a_nat_a @ ( cons_a_nat @ X3 @ Xs2 ) @ F )
% 0.29/0.47 = ( append_a @ ( F @ X3 ) @ ( bind_a_nat_a @ Xs2 @ F ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % bind_simps(2)
% 0.29/0.47 thf(fact_97_bind__simps_I2_J,axiom,
% 0.29/0.47 ! [X3: a,Xs2: list_a,F: a > list_l1108175539od_a_a] :
% 0.29/0.47 ( ( bind_a883992246od_a_a @ ( cons_a @ X3 @ Xs2 ) @ F )
% 0.29/0.47 = ( append2141280328od_a_a @ ( F @ X3 ) @ ( bind_a883992246od_a_a @ Xs2 @ F ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % bind_simps(2)
% 0.29/0.47 thf(fact_98_bind__simps_I2_J,axiom,
% 0.29/0.47 ! [X3: list_P1467822637od_a_a,Xs2: list_l1108175539od_a_a,F: list_P1467822637od_a_a > list_a] :
% 0.29/0.47 ( ( bind_l1307590552_a_a_a @ ( cons_l724116707od_a_a @ X3 @ Xs2 ) @ F )
% 0.29/0.47 = ( append_a @ ( F @ X3 ) @ ( bind_l1307590552_a_a_a @ Xs2 @ F ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % bind_simps(2)
% 0.29/0.47 thf(fact_99_bind__simps_I2_J,axiom,
% 0.29/0.47 ! [X3: a > nat,Xs2: list_a_nat,F: ( a > nat ) > list_P1467822637od_a_a] :
% 0.29/0.47 ( ( bind_a1190333103od_a_a @ ( cons_a_nat @ X3 @ Xs2 ) @ F )
% 0.29/0.47 = ( append1574001858od_a_a @ ( F @ X3 ) @ ( bind_a1190333103od_a_a @ Xs2 @ F ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % bind_simps(2)
% 0.29/0.47 thf(fact_100_bind__simps_I2_J,axiom,
% 0.29/0.47 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a,F: product_prod_a_a > list_l1108175539od_a_a] :
% 0.29/0.47 ( ( bind_P240085581od_a_a @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ F )
% 0.29/0.47 = ( append2141280328od_a_a @ ( F @ X3 ) @ ( bind_P240085581od_a_a @ Xs2 @ F ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % bind_simps(2)
% 0.29/0.47 thf(fact_101_bind__simps_I2_J,axiom,
% 0.29/0.47 ! [X3: list_P1467822637od_a_a,Xs2: list_l1108175539od_a_a,F: list_P1467822637od_a_a > list_P1467822637od_a_a] :
% 0.29/0.47 ( ( bind_l618536897od_a_a @ ( cons_l724116707od_a_a @ X3 @ Xs2 ) @ F )
% 0.29/0.47 = ( append1574001858od_a_a @ ( F @ X3 ) @ ( bind_l618536897od_a_a @ Xs2 @ F ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % bind_simps(2)
% 0.29/0.47 thf(fact_102_maps__simps_I1_J,axiom,
% 0.29/0.47 ! [F: product_prod_a_a > list_P1467822637od_a_a,X3: product_prod_a_a,Xs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( maps_P1529886977od_a_a @ F @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) )
% 0.29/0.47 = ( append1574001858od_a_a @ ( F @ X3 ) @ ( maps_P1529886977od_a_a @ F @ Xs2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % maps_simps(1)
% 0.29/0.47 thf(fact_103_maps__simps_I1_J,axiom,
% 0.29/0.47 ! [F: a > list_a,X3: a,Xs2: list_a] :
% 0.29/0.47 ( ( maps_a_a @ F @ ( cons_a @ X3 @ Xs2 ) )
% 0.29/0.47 = ( append_a @ ( F @ X3 ) @ ( maps_a_a @ F @ Xs2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % maps_simps(1)
% 0.29/0.47 thf(fact_104_maps__simps_I1_J,axiom,
% 0.29/0.47 ! [F: product_prod_a_a > list_a,X3: product_prod_a_a,Xs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( maps_P321755352_a_a_a @ F @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) )
% 0.29/0.47 = ( append_a @ ( F @ X3 ) @ ( maps_P321755352_a_a_a @ F @ Xs2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % maps_simps(1)
% 0.29/0.47 thf(fact_105_maps__simps_I1_J,axiom,
% 0.29/0.47 ! [F: a > list_P1467822637od_a_a,X3: a,Xs2: list_a] :
% 0.29/0.47 ( ( maps_a1706903530od_a_a @ F @ ( cons_a @ X3 @ Xs2 ) )
% 0.29/0.47 = ( append1574001858od_a_a @ ( F @ X3 ) @ ( maps_a1706903530od_a_a @ F @ Xs2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % maps_simps(1)
% 0.29/0.47 thf(fact_106_maps__simps_I1_J,axiom,
% 0.29/0.47 ! [F: ( a > nat ) > list_a,X3: a > nat,Xs2: list_a_nat] :
% 0.29/0.47 ( ( maps_a_nat_a @ F @ ( cons_a_nat @ X3 @ Xs2 ) )
% 0.29/0.47 = ( append_a @ ( F @ X3 ) @ ( maps_a_nat_a @ F @ Xs2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % maps_simps(1)
% 0.29/0.47 thf(fact_107_maps__simps_I1_J,axiom,
% 0.29/0.47 ! [F: a > list_l1108175539od_a_a,X3: a,Xs2: list_a] :
% 0.29/0.47 ( ( maps_a667520880od_a_a @ F @ ( cons_a @ X3 @ Xs2 ) )
% 0.29/0.47 = ( append2141280328od_a_a @ ( F @ X3 ) @ ( maps_a667520880od_a_a @ F @ Xs2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % maps_simps(1)
% 0.29/0.47 thf(fact_108_maps__simps_I1_J,axiom,
% 0.29/0.47 ! [F: list_P1467822637od_a_a > list_a,X3: list_P1467822637od_a_a,Xs2: list_l1108175539od_a_a] :
% 0.29/0.47 ( ( maps_l1091119186_a_a_a @ F @ ( cons_l724116707od_a_a @ X3 @ Xs2 ) )
% 0.29/0.47 = ( append_a @ ( F @ X3 ) @ ( maps_l1091119186_a_a_a @ F @ Xs2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % maps_simps(1)
% 0.29/0.47 thf(fact_109_maps__simps_I1_J,axiom,
% 0.29/0.47 ! [F: ( a > nat ) > list_P1467822637od_a_a,X3: a > nat,Xs2: list_a_nat] :
% 0.29/0.47 ( ( maps_a836827497od_a_a @ F @ ( cons_a_nat @ X3 @ Xs2 ) )
% 0.29/0.47 = ( append1574001858od_a_a @ ( F @ X3 ) @ ( maps_a836827497od_a_a @ F @ Xs2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % maps_simps(1)
% 0.29/0.47 thf(fact_110_maps__simps_I1_J,axiom,
% 0.29/0.47 ! [F: product_prod_a_a > list_l1108175539od_a_a,X3: product_prod_a_a,Xs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( maps_P739084551od_a_a @ F @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) )
% 0.29/0.47 = ( append2141280328od_a_a @ ( F @ X3 ) @ ( maps_P739084551od_a_a @ F @ Xs2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % maps_simps(1)
% 0.29/0.47 thf(fact_111_maps__simps_I1_J,axiom,
% 0.29/0.47 ! [F: list_P1467822637od_a_a > list_P1467822637od_a_a,X3: list_P1467822637od_a_a,Xs2: list_l1108175539od_a_a] :
% 0.29/0.47 ( ( maps_l1117535867od_a_a @ F @ ( cons_l724116707od_a_a @ X3 @ Xs2 ) )
% 0.29/0.47 = ( append1574001858od_a_a @ ( F @ X3 ) @ ( maps_l1117535867od_a_a @ F @ Xs2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % maps_simps(1)
% 0.29/0.47 thf(fact_112_lexord__append__left__rightI,axiom,
% 0.29/0.47 ! [A: produc1572603623od_a_a,B: produc1572603623od_a_a,R: set_Pr1295299783od_a_a,U: list_P1891567085od_a_a,X3: list_P1891567085od_a_a,Y3: list_P1891567085od_a_a] :
% 0.29/0.47 ( ( member1899387664od_a_a @ ( produc1935643479od_a_a @ A @ B ) @ R )
% 0.29/0.47 => ( member1254757008od_a_a @ ( produc461662679od_a_a @ ( append864718978od_a_a @ U @ ( cons_P1070399645od_a_a @ A @ X3 ) ) @ ( append864718978od_a_a @ U @ ( cons_P1070399645od_a_a @ B @ Y3 ) ) ) @ ( lexord931792858od_a_a @ R ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % lexord_append_left_rightI
% 0.29/0.47 thf(fact_113_lexord__append__left__rightI,axiom,
% 0.29/0.47 ! [A: list_P1467822637od_a_a,B: list_P1467822637od_a_a,R: set_Pr800560199od_a_a,U: list_l1108175539od_a_a,X3: list_l1108175539od_a_a,Y3: list_l1108175539od_a_a] :
% 0.29/0.47 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ A @ B ) @ R )
% 0.29/0.47 => ( member8108048od_a_a @ ( produc915218007od_a_a @ ( append2141280328od_a_a @ U @ ( cons_l724116707od_a_a @ A @ X3 ) ) @ ( append2141280328od_a_a @ U @ ( cons_l724116707od_a_a @ B @ Y3 ) ) ) @ ( lexord1284731808od_a_a @ R ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % lexord_append_left_rightI
% 0.29/0.47 thf(fact_114_lexord__append__left__rightI,axiom,
% 0.29/0.47 ! [A: a > nat,B: a > nat,R: set_Pr1940702919_a_nat,U: list_a_nat,X3: list_a_nat,Y3: list_a_nat] :
% 0.29/0.47 ( ( member125757712_a_nat @ ( produc1569872215_a_nat @ A @ B ) @ R )
% 0.29/0.47 => ( member688761744_a_nat @ ( produc1430747863_a_nat @ ( append_a_nat @ U @ ( cons_a_nat @ A @ X3 ) ) @ ( append_a_nat @ U @ ( cons_a_nat @ B @ Y3 ) ) ) @ ( lexord_a_nat @ R ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % lexord_append_left_rightI
% 0.29/0.47 thf(fact_115_lexord__append__left__rightI,axiom,
% 0.29/0.47 ! [A: list_a,B: list_a,R: set_Pr1971762695list_a,U: list_list_a,X3: list_list_a,Y3: list_list_a] :
% 0.29/0.47 ( ( member1250517072list_a @ ( produc1448356631list_a @ A @ B ) @ R )
% 0.29/0.47 => ( member888406864list_a @ ( produc2583831list_a @ ( append_list_a @ U @ ( cons_list_a @ A @ X3 ) ) @ ( append_list_a @ U @ ( cons_list_a @ B @ Y3 ) ) ) @ ( lexord_list_a @ R ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % lexord_append_left_rightI
% 0.29/0.47 thf(fact_116_lexord__append__left__rightI,axiom,
% 0.29/0.47 ! [A: product_prod_a_a,B: product_prod_a_a,R: set_Pr1948701895od_a_a,U: list_P1467822637od_a_a,X3: list_P1467822637od_a_a,Y3: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B ) @ R )
% 0.29/0.47 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ U @ ( cons_P1921020637od_a_a @ A @ X3 ) ) @ ( append1574001858od_a_a @ U @ ( cons_P1921020637od_a_a @ B @ Y3 ) ) ) @ ( lexord673907738od_a_a @ R ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % lexord_append_left_rightI
% 0.29/0.47 thf(fact_117_lexord__append__left__rightI,axiom,
% 0.29/0.47 ! [A: a,B: a,R: set_Product_prod_a_a,U: list_a,X3: list_a,Y3: list_a] :
% 0.29/0.47 ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ R )
% 0.29/0.47 => ( member1250517072list_a @ ( produc1448356631list_a @ ( append_a @ U @ ( cons_a @ A @ X3 ) ) @ ( append_a @ U @ ( cons_a @ B @ Y3 ) ) ) @ ( lexord_a @ R ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % lexord_append_left_rightI
% 0.29/0.47 thf(fact_118_zip__Cons__Cons,axiom,
% 0.29/0.47 ! [X3: a,Xs2: list_a,Y3: a,Ys2: list_a] :
% 0.29/0.47 ( ( zip_a_a @ ( cons_a @ X3 @ Xs2 ) @ ( cons_a @ Y3 @ Ys2 ) )
% 0.29/0.47 = ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ ( zip_a_a @ Xs2 @ Ys2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % zip_Cons_Cons
% 0.29/0.47 thf(fact_119_zip__Cons__Cons,axiom,
% 0.29/0.47 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a,Y3: product_prod_a_a,Ys2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( zip_Pr792472183od_a_a @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ ( cons_P1921020637od_a_a @ Y3 @ Ys2 ) )
% 0.29/0.47 = ( cons_P1070399645od_a_a @ ( produc1474507607od_a_a @ X3 @ Y3 ) @ ( zip_Pr792472183od_a_a @ Xs2 @ Ys2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % zip_Cons_Cons
% 0.29/0.47 thf(fact_120_zip__Cons__Cons,axiom,
% 0.29/0.47 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a,Y3: a,Ys2: list_a] :
% 0.29/0.47 ( ( zip_Pr201224270_a_a_a @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ ( cons_a @ Y3 @ Ys2 ) )
% 0.29/0.47 = ( cons_P86081012_a_a_a @ ( produc2061588782_a_a_a @ X3 @ Y3 ) @ ( zip_Pr201224270_a_a_a @ Xs2 @ Ys2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % zip_Cons_Cons
% 0.29/0.47 thf(fact_121_zip__Cons__Cons,axiom,
% 0.29/0.47 ! [X3: a,Xs2: list_a,Y3: product_prod_a_a,Ys2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( zip_a_1586372448od_a_a @ ( cons_a @ X3 @ Xs2 ) @ ( cons_P1921020637od_a_a @ Y3 @ Ys2 ) )
% 0.29/0.47 = ( cons_P991044742od_a_a @ ( produc1299253312od_a_a @ X3 @ Y3 ) @ ( zip_a_1586372448od_a_a @ Xs2 @ Ys2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % zip_Cons_Cons
% 0.29/0.47 thf(fact_122_zip__Cons__Cons,axiom,
% 0.29/0.47 ! [X3: a,Xs2: list_a,Y3: a > nat,Ys2: list_a_nat] :
% 0.29/0.47 ( ( zip_a_a_nat @ ( cons_a @ X3 @ Xs2 ) @ ( cons_a_nat @ Y3 @ Ys2 ) )
% 0.29/0.47 = ( cons_P1915851550_a_nat @ ( product_Pair_a_a_nat @ X3 @ Y3 ) @ ( zip_a_a_nat @ Xs2 @ Ys2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % zip_Cons_Cons
% 0.29/0.47 thf(fact_123_zip__Cons__Cons,axiom,
% 0.29/0.47 ! [X3: a > nat,Xs2: list_a_nat,Y3: a,Ys2: list_a] :
% 0.29/0.47 ( ( zip_a_nat_a @ ( cons_a_nat @ X3 @ Xs2 ) @ ( cons_a @ Y3 @ Ys2 ) )
% 0.29/0.47 = ( cons_P896312284_nat_a @ ( product_Pair_a_nat_a @ X3 @ Y3 ) @ ( zip_a_nat_a @ Xs2 @ Ys2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % zip_Cons_Cons
% 0.29/0.47 thf(fact_124_zip__Cons__Cons,axiom,
% 0.29/0.47 ! [X3: list_a,Xs2: list_list_a,Y3: list_a,Ys2: list_list_a] :
% 0.29/0.47 ( ( zip_list_a_list_a @ ( cons_list_a @ X3 @ Xs2 ) @ ( cons_list_a @ Y3 @ Ys2 ) )
% 0.29/0.47 = ( cons_P2080942813list_a @ ( produc1448356631list_a @ X3 @ Y3 ) @ ( zip_list_a_list_a @ Xs2 @ Ys2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % zip_Cons_Cons
% 0.29/0.47 thf(fact_125_zip__Cons__Cons,axiom,
% 0.29/0.47 ! [X3: list_P1467822637od_a_a,Xs2: list_l1108175539od_a_a,Y3: a,Ys2: list_a] :
% 0.29/0.47 ( ( zip_li245157064_a_a_a @ ( cons_l724116707od_a_a @ X3 @ Xs2 ) @ ( cons_a @ Y3 @ Ys2 ) )
% 0.29/0.47 = ( cons_P169173742_a_a_a @ ( produc998622632_a_a_a @ X3 @ Y3 ) @ ( zip_li245157064_a_a_a @ Xs2 @ Ys2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % zip_Cons_Cons
% 0.29/0.47 thf(fact_126_zip__Cons__Cons,axiom,
% 0.29/0.47 ! [X3: a,Xs2: list_a,Y3: list_P1467822637od_a_a,Ys2: list_l1108175539od_a_a] :
% 0.29/0.47 ( ( zip_a_1969042406od_a_a @ ( cons_a @ X3 @ Xs2 ) @ ( cons_l724116707od_a_a @ Y3 @ Ys2 ) )
% 0.29/0.47 = ( cons_P1213258892od_a_a @ ( produc575024326od_a_a @ X3 @ Y3 ) @ ( zip_a_1969042406od_a_a @ Xs2 @ Ys2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % zip_Cons_Cons
% 0.29/0.47 thf(fact_127_zip__Cons__Cons,axiom,
% 0.29/0.47 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a,Y3: a > nat,Ys2: list_a_nat] :
% 0.29/0.47 ( ( zip_Pr24086287_a_nat @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ ( cons_a_nat @ Y3 @ Ys2 ) )
% 0.29/0.47 = ( cons_P659009461_a_nat @ ( produc825466863_a_nat @ X3 @ Y3 ) @ ( zip_Pr24086287_a_nat @ Xs2 @ Ys2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % zip_Cons_Cons
% 0.29/0.47 thf(fact_128_listrel1I,axiom,
% 0.29/0.47 ! [X3: produc1572603623od_a_a,Y3: produc1572603623od_a_a,R: set_Pr1295299783od_a_a,Xs2: list_P1891567085od_a_a,Us: list_P1891567085od_a_a,Vs: list_P1891567085od_a_a,Ys2: list_P1891567085od_a_a] :
% 0.29/0.47 ( ( member1899387664od_a_a @ ( produc1935643479od_a_a @ X3 @ Y3 ) @ R )
% 0.29/0.47 => ( ( Xs2
% 0.29/0.47 = ( append864718978od_a_a @ Us @ ( cons_P1070399645od_a_a @ X3 @ Vs ) ) )
% 0.29/0.47 => ( ( Ys2
% 0.29/0.47 = ( append864718978od_a_a @ Us @ ( cons_P1070399645od_a_a @ Y3 @ Vs ) ) )
% 0.29/0.47 => ( member1254757008od_a_a @ ( produc461662679od_a_a @ Xs2 @ Ys2 ) @ ( listre1832537542od_a_a @ R ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % listrel1I
% 0.29/0.47 thf(fact_129_listrel1I,axiom,
% 0.29/0.47 ! [X3: list_P1467822637od_a_a,Y3: list_P1467822637od_a_a,R: set_Pr800560199od_a_a,Xs2: list_l1108175539od_a_a,Us: list_l1108175539od_a_a,Vs: list_l1108175539od_a_a,Ys2: list_l1108175539od_a_a] :
% 0.29/0.47 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ X3 @ Y3 ) @ R )
% 0.29/0.47 => ( ( Xs2
% 0.29/0.47 = ( append2141280328od_a_a @ Us @ ( cons_l724116707od_a_a @ X3 @ Vs ) ) )
% 0.29/0.47 => ( ( Ys2
% 0.29/0.47 = ( append2141280328od_a_a @ Us @ ( cons_l724116707od_a_a @ Y3 @ Vs ) ) )
% 0.29/0.47 => ( member8108048od_a_a @ ( produc915218007od_a_a @ Xs2 @ Ys2 ) @ ( listre651914124od_a_a @ R ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % listrel1I
% 0.29/0.47 thf(fact_130_listrel1I,axiom,
% 0.29/0.47 ! [X3: a > nat,Y3: a > nat,R: set_Pr1940702919_a_nat,Xs2: list_a_nat,Us: list_a_nat,Vs: list_a_nat,Ys2: list_a_nat] :
% 0.29/0.47 ( ( member125757712_a_nat @ ( produc1569872215_a_nat @ X3 @ Y3 ) @ R )
% 0.29/0.47 => ( ( Xs2
% 0.29/0.47 = ( append_a_nat @ Us @ ( cons_a_nat @ X3 @ Vs ) ) )
% 0.29/0.47 => ( ( Ys2
% 0.29/0.47 = ( append_a_nat @ Us @ ( cons_a_nat @ Y3 @ Vs ) ) )
% 0.29/0.47 => ( member688761744_a_nat @ ( produc1430747863_a_nat @ Xs2 @ Ys2 ) @ ( listrel1_a_nat @ R ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % listrel1I
% 0.29/0.47 thf(fact_131_listrel1I,axiom,
% 0.29/0.47 ! [X3: list_a,Y3: list_a,R: set_Pr1971762695list_a,Xs2: list_list_a,Us: list_list_a,Vs: list_list_a,Ys2: list_list_a] :
% 0.29/0.47 ( ( member1250517072list_a @ ( produc1448356631list_a @ X3 @ Y3 ) @ R )
% 0.29/0.47 => ( ( Xs2
% 0.29/0.47 = ( append_list_a @ Us @ ( cons_list_a @ X3 @ Vs ) ) )
% 0.29/0.47 => ( ( Ys2
% 0.29/0.47 = ( append_list_a @ Us @ ( cons_list_a @ Y3 @ Vs ) ) )
% 0.29/0.47 => ( member888406864list_a @ ( produc2583831list_a @ Xs2 @ Ys2 ) @ ( listrel1_list_a @ R ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % listrel1I
% 0.29/0.47 thf(fact_132_listrel1I,axiom,
% 0.29/0.47 ! [X3: product_prod_a_a,Y3: product_prod_a_a,R: set_Pr1948701895od_a_a,Xs2: list_P1467822637od_a_a,Us: list_P1467822637od_a_a,Vs: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X3 @ Y3 ) @ R )
% 0.29/0.47 => ( ( Xs2
% 0.29/0.47 = ( append1574001858od_a_a @ Us @ ( cons_P1921020637od_a_a @ X3 @ Vs ) ) )
% 0.29/0.47 => ( ( Ys2
% 0.29/0.47 = ( append1574001858od_a_a @ Us @ ( cons_P1921020637od_a_a @ Y3 @ Vs ) ) )
% 0.29/0.47 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ Ys2 ) @ ( listre944824838od_a_a @ R ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % listrel1I
% 0.29/0.47 thf(fact_133_listrel1I,axiom,
% 0.29/0.47 ! [X3: a,Y3: a,R: set_Product_prod_a_a,Xs2: list_a,Us: list_a,Vs: list_a,Ys2: list_a] :
% 0.29/0.47 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R )
% 0.29/0.47 => ( ( Xs2
% 0.29/0.47 = ( append_a @ Us @ ( cons_a @ X3 @ Vs ) ) )
% 0.29/0.47 => ( ( Ys2
% 0.29/0.47 = ( append_a @ Us @ ( cons_a @ Y3 @ Vs ) ) )
% 0.29/0.47 => ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ Ys2 ) @ ( listrel1_a @ R ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % listrel1I
% 0.29/0.47 thf(fact_134_listrel1E,axiom,
% 0.29/0.47 ! [Xs2: list_P1891567085od_a_a,Ys2: list_P1891567085od_a_a,R: set_Pr1295299783od_a_a] :
% 0.29/0.47 ( ( member1254757008od_a_a @ ( produc461662679od_a_a @ Xs2 @ Ys2 ) @ ( listre1832537542od_a_a @ R ) )
% 0.29/0.47 => ~ ! [X4: produc1572603623od_a_a,Y4: produc1572603623od_a_a] :
% 0.29/0.47 ( ( member1899387664od_a_a @ ( produc1935643479od_a_a @ X4 @ Y4 ) @ R )
% 0.29/0.47 => ! [Us3: list_P1891567085od_a_a,Vs2: list_P1891567085od_a_a] :
% 0.29/0.47 ( ( Xs2
% 0.29/0.47 = ( append864718978od_a_a @ Us3 @ ( cons_P1070399645od_a_a @ X4 @ Vs2 ) ) )
% 0.29/0.47 => ( Ys2
% 0.29/0.47 != ( append864718978od_a_a @ Us3 @ ( cons_P1070399645od_a_a @ Y4 @ Vs2 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % listrel1E
% 0.29/0.47 thf(fact_135_listrel1E,axiom,
% 0.29/0.47 ! [Xs2: list_l1108175539od_a_a,Ys2: list_l1108175539od_a_a,R: set_Pr800560199od_a_a] :
% 0.29/0.47 ( ( member8108048od_a_a @ ( produc915218007od_a_a @ Xs2 @ Ys2 ) @ ( listre651914124od_a_a @ R ) )
% 0.29/0.47 => ~ ! [X4: list_P1467822637od_a_a,Y4: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ X4 @ Y4 ) @ R )
% 0.29/0.47 => ! [Us3: list_l1108175539od_a_a,Vs2: list_l1108175539od_a_a] :
% 0.29/0.47 ( ( Xs2
% 0.29/0.47 = ( append2141280328od_a_a @ Us3 @ ( cons_l724116707od_a_a @ X4 @ Vs2 ) ) )
% 0.29/0.47 => ( Ys2
% 0.29/0.47 != ( append2141280328od_a_a @ Us3 @ ( cons_l724116707od_a_a @ Y4 @ Vs2 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % listrel1E
% 0.29/0.47 thf(fact_136_listrel1E,axiom,
% 0.29/0.47 ! [Xs2: list_a_nat,Ys2: list_a_nat,R: set_Pr1940702919_a_nat] :
% 0.29/0.47 ( ( member688761744_a_nat @ ( produc1430747863_a_nat @ Xs2 @ Ys2 ) @ ( listrel1_a_nat @ R ) )
% 0.29/0.47 => ~ ! [X4: a > nat,Y4: a > nat] :
% 0.29/0.47 ( ( member125757712_a_nat @ ( produc1569872215_a_nat @ X4 @ Y4 ) @ R )
% 0.29/0.47 => ! [Us3: list_a_nat,Vs2: list_a_nat] :
% 0.29/0.47 ( ( Xs2
% 0.29/0.47 = ( append_a_nat @ Us3 @ ( cons_a_nat @ X4 @ Vs2 ) ) )
% 0.29/0.47 => ( Ys2
% 0.29/0.47 != ( append_a_nat @ Us3 @ ( cons_a_nat @ Y4 @ Vs2 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % listrel1E
% 0.29/0.47 thf(fact_137_listrel1E,axiom,
% 0.29/0.47 ! [Xs2: list_list_a,Ys2: list_list_a,R: set_Pr1971762695list_a] :
% 0.29/0.47 ( ( member888406864list_a @ ( produc2583831list_a @ Xs2 @ Ys2 ) @ ( listrel1_list_a @ R ) )
% 0.29/0.47 => ~ ! [X4: list_a,Y4: list_a] :
% 0.29/0.47 ( ( member1250517072list_a @ ( produc1448356631list_a @ X4 @ Y4 ) @ R )
% 0.29/0.47 => ! [Us3: list_list_a,Vs2: list_list_a] :
% 0.29/0.47 ( ( Xs2
% 0.29/0.47 = ( append_list_a @ Us3 @ ( cons_list_a @ X4 @ Vs2 ) ) )
% 0.29/0.47 => ( Ys2
% 0.29/0.47 != ( append_list_a @ Us3 @ ( cons_list_a @ Y4 @ Vs2 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % listrel1E
% 0.29/0.47 thf(fact_138_listrel1E,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 0.29/0.47 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ Ys2 ) @ ( listre944824838od_a_a @ R ) )
% 0.29/0.47 => ~ ! [X4: product_prod_a_a,Y4: product_prod_a_a] :
% 0.29/0.47 ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X4 @ Y4 ) @ R )
% 0.29/0.47 => ! [Us3: list_P1467822637od_a_a,Vs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( Xs2
% 0.29/0.47 = ( append1574001858od_a_a @ Us3 @ ( cons_P1921020637od_a_a @ X4 @ Vs2 ) ) )
% 0.29/0.47 => ( Ys2
% 0.29/0.47 != ( append1574001858od_a_a @ Us3 @ ( cons_P1921020637od_a_a @ Y4 @ Vs2 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % listrel1E
% 0.29/0.47 thf(fact_139_listrel1E,axiom,
% 0.29/0.47 ! [Xs2: list_a,Ys2: list_a,R: set_Product_prod_a_a] :
% 0.29/0.47 ( ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ Ys2 ) @ ( listrel1_a @ R ) )
% 0.29/0.47 => ~ ! [X4: a,Y4: a] :
% 0.29/0.47 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ R )
% 0.29/0.47 => ! [Us3: list_a,Vs2: list_a] :
% 0.29/0.47 ( ( Xs2
% 0.29/0.47 = ( append_a @ Us3 @ ( cons_a @ X4 @ Vs2 ) ) )
% 0.29/0.47 => ( Ys2
% 0.29/0.47 != ( append_a @ Us3 @ ( cons_a @ Y4 @ Vs2 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % listrel1E
% 0.29/0.47 thf(fact_140_member__rec_I1_J,axiom,
% 0.29/0.47 ! [X3: a,Xs2: list_a,Y3: a] :
% 0.29/0.47 ( ( member_a @ ( cons_a @ X3 @ Xs2 ) @ Y3 )
% 0.29/0.47 = ( ( X3 = Y3 )
% 0.29/0.47 | ( member_a @ Xs2 @ Y3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % member_rec(1)
% 0.29/0.47 thf(fact_141_member__rec_I1_J,axiom,
% 0.29/0.47 ! [X3: produc1572603623od_a_a,Xs2: list_P1891567085od_a_a,Y3: produc1572603623od_a_a] :
% 0.29/0.47 ( ( member2070313346od_a_a @ ( cons_P1070399645od_a_a @ X3 @ Xs2 ) @ Y3 )
% 0.29/0.47 = ( ( X3 = Y3 )
% 0.29/0.47 | ( member2070313346od_a_a @ Xs2 @ Y3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % member_rec(1)
% 0.29/0.47 thf(fact_142_member__rec_I1_J,axiom,
% 0.29/0.47 ! [X3: list_P1467822637od_a_a,Xs2: list_l1108175539od_a_a,Y3: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( member261538120od_a_a @ ( cons_l724116707od_a_a @ X3 @ Xs2 ) @ Y3 )
% 0.29/0.47 = ( ( X3 = Y3 )
% 0.29/0.47 | ( member261538120od_a_a @ Xs2 @ Y3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % member_rec(1)
% 0.29/0.47 thf(fact_143_member__rec_I1_J,axiom,
% 0.29/0.47 ! [X3: a > nat,Xs2: list_a_nat,Y3: a > nat] :
% 0.29/0.47 ( ( member_a_nat @ ( cons_a_nat @ X3 @ Xs2 ) @ Y3 )
% 0.29/0.47 = ( ( X3 = Y3 )
% 0.29/0.47 | ( member_a_nat @ Xs2 @ Y3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % member_rec(1)
% 0.29/0.47 thf(fact_144_member__rec_I1_J,axiom,
% 0.29/0.47 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a,Y3: product_prod_a_a] :
% 0.29/0.47 ( ( member1112491458od_a_a @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ Y3 )
% 0.29/0.47 = ( ( X3 = Y3 )
% 0.29/0.47 | ( member1112491458od_a_a @ Xs2 @ Y3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % member_rec(1)
% 0.29/0.47 thf(fact_145_ssubst__Pair__rhs,axiom,
% 0.29/0.47 ! [R: list_P1467822637od_a_a,S: list_P1467822637od_a_a,R2: set_Pr800560199od_a_a,S2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ R @ S ) @ R2 )
% 0.29/0.47 => ( ( S2 = S )
% 0.29/0.47 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ R @ S2 ) @ R2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ssubst_Pair_rhs
% 0.29/0.47 thf(fact_146_ssubst__Pair__rhs,axiom,
% 0.29/0.47 ! [R: list_P1467822637od_a_a,S: a,R2: set_Pr1525541400_a_a_a,S2: a] :
% 0.29/0.47 ( ( member430654177_a_a_a @ ( produc998622632_a_a_a @ R @ S ) @ R2 )
% 0.29/0.47 => ( ( S2 = S )
% 0.29/0.47 => ( member430654177_a_a_a @ ( produc998622632_a_a_a @ R @ S2 ) @ R2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ssubst_Pair_rhs
% 0.29/0.47 thf(fact_147_ssubst__Pair__rhs,axiom,
% 0.29/0.47 ! [R: list_a,S: list_a,R2: set_Pr1971762695list_a,S2: list_a] :
% 0.29/0.47 ( ( member1250517072list_a @ ( produc1448356631list_a @ R @ S ) @ R2 )
% 0.29/0.47 => ( ( S2 = S )
% 0.29/0.47 => ( member1250517072list_a @ ( produc1448356631list_a @ R @ S2 ) @ R2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ssubst_Pair_rhs
% 0.29/0.47 thf(fact_148_ssubst__Pair__rhs,axiom,
% 0.29/0.47 ! [R: product_prod_a_a > product_prod_a_a > $o,S: list_P1467822637od_a_a,R2: set_Pr727105414od_a_a,S2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( member372644687od_a_a @ ( produc214132118od_a_a @ R @ S ) @ R2 )
% 0.29/0.47 => ( ( S2 = S )
% 0.29/0.47 => ( member372644687od_a_a @ ( produc214132118od_a_a @ R @ S2 ) @ R2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ssubst_Pair_rhs
% 0.29/0.47 thf(fact_149_ssubst__Pair__rhs,axiom,
% 0.29/0.47 ! [R: a,S: produc657167928_a_a_a,R2: set_Pr110478017_a_a_a,S2: produc657167928_a_a_a] :
% 0.29/0.47 ( ( member1904151562_a_a_a @ ( produc1440321489_a_a_a @ R @ S ) @ R2 )
% 0.29/0.47 => ( ( S2 = S )
% 0.29/0.47 => ( member1904151562_a_a_a @ ( produc1440321489_a_a_a @ R @ S2 ) @ R2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ssubst_Pair_rhs
% 0.29/0.47 thf(fact_150_ssubst__Pair__rhs,axiom,
% 0.29/0.47 ! [R: a,S: list_P1467822637od_a_a,R2: set_Pr248149174od_a_a,S2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( member1474739327od_a_a @ ( produc575024326od_a_a @ R @ S ) @ R2 )
% 0.29/0.47 => ( ( S2 = S )
% 0.29/0.47 => ( member1474739327od_a_a @ ( produc575024326od_a_a @ R @ S2 ) @ R2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ssubst_Pair_rhs
% 0.29/0.47 thf(fact_151_ssubst__Pair__rhs,axiom,
% 0.29/0.47 ! [R: a,S: a,R2: set_Product_prod_a_a,S2: a] :
% 0.29/0.47 ( ( member449909584od_a_a @ ( product_Pair_a_a @ R @ S ) @ R2 )
% 0.29/0.47 => ( ( S2 = S )
% 0.29/0.47 => ( member449909584od_a_a @ ( product_Pair_a_a @ R @ S2 ) @ R2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ssubst_Pair_rhs
% 0.29/0.47 thf(fact_152_subdivide_Oinduct,axiom,
% 0.29/0.47 ! [P2: pair_p1891813445t_unit > produc864062247list_a > list_a > $o,A0: pair_p1891813445t_unit,A1: produc864062247list_a,A22: list_a] :
% 0.29/0.47 ( ! [G: pair_p1891813445t_unit,U2: list_a,V: list_a,X_1: list_a] : ( P2 @ G @ ( produc1448356631list_a @ U2 @ V ) @ X_1 )
% 0.29/0.47 => ( P2 @ A0 @ A1 @ A22 ) ) ).
% 0.29/0.47
% 0.29/0.47 % subdivide.induct
% 0.29/0.47 thf(fact_153_subdivide_Oinduct,axiom,
% 0.29/0.47 ! [P2: pair_p125712459t_unit > product_prod_a_a > a > $o,A0: pair_p125712459t_unit,A1: product_prod_a_a,A22: a] :
% 0.29/0.47 ( ! [G: pair_p125712459t_unit,U2: a,V: a,X_1: a] : ( P2 @ G @ ( product_Pair_a_a @ U2 @ V ) @ X_1 )
% 0.29/0.47 => ( P2 @ A0 @ A1 @ A22 ) ) ).
% 0.29/0.47
% 0.29/0.47 % subdivide.induct
% 0.29/0.47 thf(fact_154_Cons__listrel1__Cons,axiom,
% 0.29/0.47 ! [X3: produc1572603623od_a_a,Xs2: list_P1891567085od_a_a,Y3: produc1572603623od_a_a,Ys2: list_P1891567085od_a_a,R: set_Pr1295299783od_a_a] :
% 0.29/0.47 ( ( member1254757008od_a_a @ ( produc461662679od_a_a @ ( cons_P1070399645od_a_a @ X3 @ Xs2 ) @ ( cons_P1070399645od_a_a @ Y3 @ Ys2 ) ) @ ( listre1832537542od_a_a @ R ) )
% 0.29/0.47 = ( ( ( member1899387664od_a_a @ ( produc1935643479od_a_a @ X3 @ Y3 ) @ R )
% 0.29/0.47 & ( Xs2 = Ys2 ) )
% 0.29/0.47 | ( ( X3 = Y3 )
% 0.29/0.47 & ( member1254757008od_a_a @ ( produc461662679od_a_a @ Xs2 @ Ys2 ) @ ( listre1832537542od_a_a @ R ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Cons_listrel1_Cons
% 0.29/0.47 thf(fact_155_Cons__listrel1__Cons,axiom,
% 0.29/0.47 ! [X3: list_P1467822637od_a_a,Xs2: list_l1108175539od_a_a,Y3: list_P1467822637od_a_a,Ys2: list_l1108175539od_a_a,R: set_Pr800560199od_a_a] :
% 0.29/0.47 ( ( member8108048od_a_a @ ( produc915218007od_a_a @ ( cons_l724116707od_a_a @ X3 @ Xs2 ) @ ( cons_l724116707od_a_a @ Y3 @ Ys2 ) ) @ ( listre651914124od_a_a @ R ) )
% 0.29/0.47 = ( ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ X3 @ Y3 ) @ R )
% 0.29/0.47 & ( Xs2 = Ys2 ) )
% 0.29/0.47 | ( ( X3 = Y3 )
% 0.29/0.47 & ( member8108048od_a_a @ ( produc915218007od_a_a @ Xs2 @ Ys2 ) @ ( listre651914124od_a_a @ R ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Cons_listrel1_Cons
% 0.29/0.47 thf(fact_156_Cons__listrel1__Cons,axiom,
% 0.29/0.47 ! [X3: a > nat,Xs2: list_a_nat,Y3: a > nat,Ys2: list_a_nat,R: set_Pr1940702919_a_nat] :
% 0.29/0.47 ( ( member688761744_a_nat @ ( produc1430747863_a_nat @ ( cons_a_nat @ X3 @ Xs2 ) @ ( cons_a_nat @ Y3 @ Ys2 ) ) @ ( listrel1_a_nat @ R ) )
% 0.29/0.47 = ( ( ( member125757712_a_nat @ ( produc1569872215_a_nat @ X3 @ Y3 ) @ R )
% 0.29/0.47 & ( Xs2 = Ys2 ) )
% 0.29/0.47 | ( ( X3 = Y3 )
% 0.29/0.47 & ( member688761744_a_nat @ ( produc1430747863_a_nat @ Xs2 @ Ys2 ) @ ( listrel1_a_nat @ R ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Cons_listrel1_Cons
% 0.29/0.47 thf(fact_157_Cons__listrel1__Cons,axiom,
% 0.29/0.47 ! [X3: list_a,Xs2: list_list_a,Y3: list_a,Ys2: list_list_a,R: set_Pr1971762695list_a] :
% 0.29/0.47 ( ( member888406864list_a @ ( produc2583831list_a @ ( cons_list_a @ X3 @ Xs2 ) @ ( cons_list_a @ Y3 @ Ys2 ) ) @ ( listrel1_list_a @ R ) )
% 0.29/0.47 = ( ( ( member1250517072list_a @ ( produc1448356631list_a @ X3 @ Y3 ) @ R )
% 0.29/0.47 & ( Xs2 = Ys2 ) )
% 0.29/0.47 | ( ( X3 = Y3 )
% 0.29/0.47 & ( member888406864list_a @ ( produc2583831list_a @ Xs2 @ Ys2 ) @ ( listrel1_list_a @ R ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Cons_listrel1_Cons
% 0.29/0.47 thf(fact_158_Cons__listrel1__Cons,axiom,
% 0.29/0.47 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a,Y3: product_prod_a_a,Ys2: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 0.29/0.47 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ ( cons_P1921020637od_a_a @ Y3 @ Ys2 ) ) @ ( listre944824838od_a_a @ R ) )
% 0.29/0.47 = ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X3 @ Y3 ) @ R )
% 0.29/0.47 & ( Xs2 = Ys2 ) )
% 0.29/0.47 | ( ( X3 = Y3 )
% 0.29/0.47 & ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ Ys2 ) @ ( listre944824838od_a_a @ R ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Cons_listrel1_Cons
% 0.29/0.47 thf(fact_159_Cons__listrel1__Cons,axiom,
% 0.29/0.47 ! [X3: a,Xs2: list_a,Y3: a,Ys2: list_a,R: set_Product_prod_a_a] :
% 0.29/0.47 ( ( member1250517072list_a @ ( produc1448356631list_a @ ( cons_a @ X3 @ Xs2 ) @ ( cons_a @ Y3 @ Ys2 ) ) @ ( listrel1_a @ R ) )
% 0.29/0.47 = ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R )
% 0.29/0.47 & ( Xs2 = Ys2 ) )
% 0.29/0.47 | ( ( X3 = Y3 )
% 0.29/0.47 & ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ Ys2 ) @ ( listrel1_a @ R ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Cons_listrel1_Cons
% 0.29/0.47 thf(fact_160_lexord__cons__cons,axiom,
% 0.29/0.47 ! [A: produc1572603623od_a_a,X3: list_P1891567085od_a_a,B: produc1572603623od_a_a,Y3: list_P1891567085od_a_a,R: set_Pr1295299783od_a_a] :
% 0.29/0.47 ( ( member1254757008od_a_a @ ( produc461662679od_a_a @ ( cons_P1070399645od_a_a @ A @ X3 ) @ ( cons_P1070399645od_a_a @ B @ Y3 ) ) @ ( lexord931792858od_a_a @ R ) )
% 0.29/0.47 = ( ( member1899387664od_a_a @ ( produc1935643479od_a_a @ A @ B ) @ R )
% 0.29/0.47 | ( ( A = B )
% 0.29/0.47 & ( member1254757008od_a_a @ ( produc461662679od_a_a @ X3 @ Y3 ) @ ( lexord931792858od_a_a @ R ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % lexord_cons_cons
% 0.29/0.47 thf(fact_161_lexord__cons__cons,axiom,
% 0.29/0.47 ! [A: list_P1467822637od_a_a,X3: list_l1108175539od_a_a,B: list_P1467822637od_a_a,Y3: list_l1108175539od_a_a,R: set_Pr800560199od_a_a] :
% 0.29/0.47 ( ( member8108048od_a_a @ ( produc915218007od_a_a @ ( cons_l724116707od_a_a @ A @ X3 ) @ ( cons_l724116707od_a_a @ B @ Y3 ) ) @ ( lexord1284731808od_a_a @ R ) )
% 0.29/0.47 = ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ A @ B ) @ R )
% 0.29/0.47 | ( ( A = B )
% 0.29/0.47 & ( member8108048od_a_a @ ( produc915218007od_a_a @ X3 @ Y3 ) @ ( lexord1284731808od_a_a @ R ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % lexord_cons_cons
% 0.29/0.47 thf(fact_162_lexord__cons__cons,axiom,
% 0.29/0.47 ! [A: a > nat,X3: list_a_nat,B: a > nat,Y3: list_a_nat,R: set_Pr1940702919_a_nat] :
% 0.29/0.47 ( ( member688761744_a_nat @ ( produc1430747863_a_nat @ ( cons_a_nat @ A @ X3 ) @ ( cons_a_nat @ B @ Y3 ) ) @ ( lexord_a_nat @ R ) )
% 0.29/0.47 = ( ( member125757712_a_nat @ ( produc1569872215_a_nat @ A @ B ) @ R )
% 0.29/0.47 | ( ( A = B )
% 0.29/0.47 & ( member688761744_a_nat @ ( produc1430747863_a_nat @ X3 @ Y3 ) @ ( lexord_a_nat @ R ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % lexord_cons_cons
% 0.29/0.47 thf(fact_163_lexord__cons__cons,axiom,
% 0.29/0.47 ! [A: list_a,X3: list_list_a,B: list_a,Y3: list_list_a,R: set_Pr1971762695list_a] :
% 0.29/0.47 ( ( member888406864list_a @ ( produc2583831list_a @ ( cons_list_a @ A @ X3 ) @ ( cons_list_a @ B @ Y3 ) ) @ ( lexord_list_a @ R ) )
% 0.29/0.47 = ( ( member1250517072list_a @ ( produc1448356631list_a @ A @ B ) @ R )
% 0.29/0.47 | ( ( A = B )
% 0.29/0.47 & ( member888406864list_a @ ( produc2583831list_a @ X3 @ Y3 ) @ ( lexord_list_a @ R ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % lexord_cons_cons
% 0.29/0.47 thf(fact_164_lexord__cons__cons,axiom,
% 0.29/0.47 ! [A: product_prod_a_a,X3: list_P1467822637od_a_a,B: product_prod_a_a,Y3: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 0.29/0.47 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( cons_P1921020637od_a_a @ A @ X3 ) @ ( cons_P1921020637od_a_a @ B @ Y3 ) ) @ ( lexord673907738od_a_a @ R ) )
% 0.29/0.47 = ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B ) @ R )
% 0.29/0.47 | ( ( A = B )
% 0.29/0.47 & ( member1691432592od_a_a @ ( produc85179863od_a_a @ X3 @ Y3 ) @ ( lexord673907738od_a_a @ R ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % lexord_cons_cons
% 0.29/0.47 thf(fact_165_lexord__cons__cons,axiom,
% 0.29/0.47 ! [A: a,X3: list_a,B: a,Y3: list_a,R: set_Product_prod_a_a] :
% 0.29/0.47 ( ( member1250517072list_a @ ( produc1448356631list_a @ ( cons_a @ A @ X3 ) @ ( cons_a @ B @ Y3 ) ) @ ( lexord_a @ R ) )
% 0.29/0.47 = ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ R )
% 0.29/0.47 | ( ( A = B )
% 0.29/0.47 & ( member1250517072list_a @ ( produc1448356631list_a @ X3 @ Y3 ) @ ( lexord_a @ R ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % lexord_cons_cons
% 0.29/0.47 thf(fact_166_listrel1I2,axiom,
% 0.29/0.47 ! [Xs2: list_P1891567085od_a_a,Ys2: list_P1891567085od_a_a,R: set_Pr1295299783od_a_a,X3: produc1572603623od_a_a] :
% 0.29/0.47 ( ( member1254757008od_a_a @ ( produc461662679od_a_a @ Xs2 @ Ys2 ) @ ( listre1832537542od_a_a @ R ) )
% 0.29/0.47 => ( member1254757008od_a_a @ ( produc461662679od_a_a @ ( cons_P1070399645od_a_a @ X3 @ Xs2 ) @ ( cons_P1070399645od_a_a @ X3 @ Ys2 ) ) @ ( listre1832537542od_a_a @ R ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % listrel1I2
% 0.29/0.47 thf(fact_167_listrel1I2,axiom,
% 0.29/0.47 ! [Xs2: list_l1108175539od_a_a,Ys2: list_l1108175539od_a_a,R: set_Pr800560199od_a_a,X3: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( member8108048od_a_a @ ( produc915218007od_a_a @ Xs2 @ Ys2 ) @ ( listre651914124od_a_a @ R ) )
% 0.29/0.47 => ( member8108048od_a_a @ ( produc915218007od_a_a @ ( cons_l724116707od_a_a @ X3 @ Xs2 ) @ ( cons_l724116707od_a_a @ X3 @ Ys2 ) ) @ ( listre651914124od_a_a @ R ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % listrel1I2
% 0.29/0.47 thf(fact_168_listrel1I2,axiom,
% 0.29/0.47 ! [Xs2: list_a_nat,Ys2: list_a_nat,R: set_Pr1940702919_a_nat,X3: a > nat] :
% 0.29/0.47 ( ( member688761744_a_nat @ ( produc1430747863_a_nat @ Xs2 @ Ys2 ) @ ( listrel1_a_nat @ R ) )
% 0.29/0.47 => ( member688761744_a_nat @ ( produc1430747863_a_nat @ ( cons_a_nat @ X3 @ Xs2 ) @ ( cons_a_nat @ X3 @ Ys2 ) ) @ ( listrel1_a_nat @ R ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % listrel1I2
% 0.29/0.47 thf(fact_169_listrel1I2,axiom,
% 0.29/0.47 ! [Xs2: list_a,Ys2: list_a,R: set_Product_prod_a_a,X3: a] :
% 0.29/0.47 ( ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ Ys2 ) @ ( listrel1_a @ R ) )
% 0.29/0.47 => ( member1250517072list_a @ ( produc1448356631list_a @ ( cons_a @ X3 @ Xs2 ) @ ( cons_a @ X3 @ Ys2 ) ) @ ( listrel1_a @ R ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % listrel1I2
% 0.29/0.47 thf(fact_170_listrel1I2,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a,X3: product_prod_a_a] :
% 0.29/0.47 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ Ys2 ) @ ( listre944824838od_a_a @ R ) )
% 0.29/0.47 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ ( cons_P1921020637od_a_a @ X3 @ Ys2 ) ) @ ( listre944824838od_a_a @ R ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % listrel1I2
% 0.29/0.47 thf(fact_171_append__listrel1I,axiom,
% 0.29/0.47 ! [Xs2: list_P1891567085od_a_a,Ys2: list_P1891567085od_a_a,R: set_Pr1295299783od_a_a,Us: list_P1891567085od_a_a,Vs: list_P1891567085od_a_a] :
% 0.29/0.47 ( ( ( ( member1254757008od_a_a @ ( produc461662679od_a_a @ Xs2 @ Ys2 ) @ ( listre1832537542od_a_a @ R ) )
% 0.29/0.47 & ( Us = Vs ) )
% 0.29/0.47 | ( ( Xs2 = Ys2 )
% 0.29/0.47 & ( member1254757008od_a_a @ ( produc461662679od_a_a @ Us @ Vs ) @ ( listre1832537542od_a_a @ R ) ) ) )
% 0.29/0.47 => ( member1254757008od_a_a @ ( produc461662679od_a_a @ ( append864718978od_a_a @ Xs2 @ Us ) @ ( append864718978od_a_a @ Ys2 @ Vs ) ) @ ( listre1832537542od_a_a @ R ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % append_listrel1I
% 0.29/0.47 thf(fact_172_append__listrel1I,axiom,
% 0.29/0.47 ! [Xs2: list_l1108175539od_a_a,Ys2: list_l1108175539od_a_a,R: set_Pr800560199od_a_a,Us: list_l1108175539od_a_a,Vs: list_l1108175539od_a_a] :
% 0.29/0.47 ( ( ( ( member8108048od_a_a @ ( produc915218007od_a_a @ Xs2 @ Ys2 ) @ ( listre651914124od_a_a @ R ) )
% 0.29/0.47 & ( Us = Vs ) )
% 0.29/0.47 | ( ( Xs2 = Ys2 )
% 0.29/0.47 & ( member8108048od_a_a @ ( produc915218007od_a_a @ Us @ Vs ) @ ( listre651914124od_a_a @ R ) ) ) )
% 0.29/0.47 => ( member8108048od_a_a @ ( produc915218007od_a_a @ ( append2141280328od_a_a @ Xs2 @ Us ) @ ( append2141280328od_a_a @ Ys2 @ Vs ) ) @ ( listre651914124od_a_a @ R ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % append_listrel1I
% 0.29/0.47 thf(fact_173_append__listrel1I,axiom,
% 0.29/0.47 ! [Xs2: list_a,Ys2: list_a,R: set_Product_prod_a_a,Us: list_a,Vs: list_a] :
% 0.29/0.47 ( ( ( ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ Ys2 ) @ ( listrel1_a @ R ) )
% 0.29/0.47 & ( Us = Vs ) )
% 0.29/0.47 | ( ( Xs2 = Ys2 )
% 0.29/0.47 & ( member1250517072list_a @ ( produc1448356631list_a @ Us @ Vs ) @ ( listrel1_a @ R ) ) ) )
% 0.29/0.47 => ( member1250517072list_a @ ( produc1448356631list_a @ ( append_a @ Xs2 @ Us ) @ ( append_a @ Ys2 @ Vs ) ) @ ( listrel1_a @ R ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % append_listrel1I
% 0.29/0.47 thf(fact_174_append__listrel1I,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a,Us: list_P1467822637od_a_a,Vs: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ Ys2 ) @ ( listre944824838od_a_a @ R ) )
% 0.29/0.47 & ( Us = Vs ) )
% 0.29/0.47 | ( ( Xs2 = Ys2 )
% 0.29/0.47 & ( member1691432592od_a_a @ ( produc85179863od_a_a @ Us @ Vs ) @ ( listre944824838od_a_a @ R ) ) ) )
% 0.29/0.47 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ Xs2 @ Us ) @ ( append1574001858od_a_a @ Ys2 @ Vs ) ) @ ( listre944824838od_a_a @ R ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % append_listrel1I
% 0.29/0.47 thf(fact_175_lexord__linear,axiom,
% 0.29/0.47 ! [R: set_Pr800560199od_a_a,X3: list_l1108175539od_a_a,Y3: list_l1108175539od_a_a] :
% 0.29/0.47 ( ! [A3: list_P1467822637od_a_a,B3: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ A3 @ B3 ) @ R )
% 0.29/0.47 | ( A3 = B3 )
% 0.29/0.47 | ( member1691432592od_a_a @ ( produc85179863od_a_a @ B3 @ A3 ) @ R ) )
% 0.29/0.47 => ( ( member8108048od_a_a @ ( produc915218007od_a_a @ X3 @ Y3 ) @ ( lexord1284731808od_a_a @ R ) )
% 0.29/0.47 | ( X3 = Y3 )
% 0.29/0.47 | ( member8108048od_a_a @ ( produc915218007od_a_a @ Y3 @ X3 ) @ ( lexord1284731808od_a_a @ R ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % lexord_linear
% 0.29/0.47 thf(fact_176_lexord__linear,axiom,
% 0.29/0.47 ! [R: set_Pr1948701895od_a_a,X3: list_P1467822637od_a_a,Y3: list_P1467822637od_a_a] :
% 0.29/0.47 ( ! [A3: product_prod_a_a,B3: product_prod_a_a] :
% 0.29/0.47 ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A3 @ B3 ) @ R )
% 0.29/0.47 | ( A3 = B3 )
% 0.29/0.47 | ( member2057358096od_a_a @ ( produc1474507607od_a_a @ B3 @ A3 ) @ R ) )
% 0.29/0.47 => ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ X3 @ Y3 ) @ ( lexord673907738od_a_a @ R ) )
% 0.29/0.47 | ( X3 = Y3 )
% 0.29/0.47 | ( member1691432592od_a_a @ ( produc85179863od_a_a @ Y3 @ X3 ) @ ( lexord673907738od_a_a @ R ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % lexord_linear
% 0.29/0.47 thf(fact_177_lexord__linear,axiom,
% 0.29/0.47 ! [R: set_Pr1971762695list_a,X3: list_list_a,Y3: list_list_a] :
% 0.29/0.47 ( ! [A3: list_a,B3: list_a] :
% 0.29/0.47 ( ( member1250517072list_a @ ( produc1448356631list_a @ A3 @ B3 ) @ R )
% 0.29/0.47 | ( A3 = B3 )
% 0.29/0.47 | ( member1250517072list_a @ ( produc1448356631list_a @ B3 @ A3 ) @ R ) )
% 0.29/0.47 => ( ( member888406864list_a @ ( produc2583831list_a @ X3 @ Y3 ) @ ( lexord_list_a @ R ) )
% 0.29/0.47 | ( X3 = Y3 )
% 0.29/0.47 | ( member888406864list_a @ ( produc2583831list_a @ Y3 @ X3 ) @ ( lexord_list_a @ R ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % lexord_linear
% 0.29/0.47 thf(fact_178_lexord__linear,axiom,
% 0.29/0.47 ! [R: set_Product_prod_a_a,X3: list_a,Y3: list_a] :
% 0.29/0.47 ( ! [A3: a,B3: a] :
% 0.29/0.47 ( ( member449909584od_a_a @ ( product_Pair_a_a @ A3 @ B3 ) @ R )
% 0.29/0.47 | ( A3 = B3 )
% 0.29/0.47 | ( member449909584od_a_a @ ( product_Pair_a_a @ B3 @ A3 ) @ R ) )
% 0.29/0.47 => ( ( member1250517072list_a @ ( produc1448356631list_a @ X3 @ Y3 ) @ ( lexord_a @ R ) )
% 0.29/0.47 | ( X3 = Y3 )
% 0.29/0.47 | ( member1250517072list_a @ ( produc1448356631list_a @ Y3 @ X3 ) @ ( lexord_a @ R ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % lexord_linear
% 0.29/0.47 thf(fact_179_mem__Collect__eq,axiom,
% 0.29/0.47 ! [A: produc651658087od_a_a,P2: produc651658087od_a_a > $o] :
% 0.29/0.47 ( ( member1691432592od_a_a @ A @ ( collec1566074578od_a_a @ P2 ) )
% 0.29/0.47 = ( P2 @ A ) ) ).
% 0.29/0.47
% 0.29/0.47 % mem_Collect_eq
% 0.29/0.47 thf(fact_180_mem__Collect__eq,axiom,
% 0.29/0.47 ! [A: produc864062247list_a,P2: produc864062247list_a > $o] :
% 0.29/0.47 ( ( member1250517072list_a @ A @ ( collec656258194list_a @ P2 ) )
% 0.29/0.47 = ( P2 @ A ) ) ).
% 0.29/0.47
% 0.29/0.47 % mem_Collect_eq
% 0.29/0.47 thf(fact_181_mem__Collect__eq,axiom,
% 0.29/0.47 ! [A: product_prod_a_a,P2: product_prod_a_a > $o] :
% 0.29/0.47 ( ( member449909584od_a_a @ A @ ( collec645855634od_a_a @ P2 ) )
% 0.29/0.47 = ( P2 @ A ) ) ).
% 0.29/0.47
% 0.29/0.47 % mem_Collect_eq
% 0.29/0.47 thf(fact_182_mem__Collect__eq,axiom,
% 0.29/0.47 ! [A: list_P1467822637od_a_a,P2: list_P1467822637od_a_a > $o] :
% 0.29/0.47 ( ( member1578987478od_a_a @ A @ ( collec1811041560od_a_a @ P2 ) )
% 0.29/0.47 = ( P2 @ A ) ) ).
% 0.29/0.47
% 0.29/0.47 % mem_Collect_eq
% 0.29/0.47 thf(fact_183_mem__Collect__eq,axiom,
% 0.29/0.47 ! [A: a,P2: a > $o] :
% 0.29/0.47 ( ( member_a2 @ A @ ( collect_a @ P2 ) )
% 0.29/0.47 = ( P2 @ A ) ) ).
% 0.29/0.47
% 0.29/0.47 % mem_Collect_eq
% 0.29/0.47 thf(fact_184_Collect__mem__eq,axiom,
% 0.29/0.47 ! [A4: set_Pr1971762695list_a] :
% 0.29/0.47 ( ( collec656258194list_a
% 0.29/0.47 @ ^ [X: produc864062247list_a] : ( member1250517072list_a @ X @ A4 ) )
% 0.29/0.47 = A4 ) ).
% 0.29/0.47
% 0.29/0.47 % Collect_mem_eq
% 0.29/0.47 thf(fact_185_Collect__mem__eq,axiom,
% 0.29/0.47 ! [A4: set_Product_prod_a_a] :
% 0.29/0.47 ( ( collec645855634od_a_a
% 0.29/0.47 @ ^ [X: product_prod_a_a] : ( member449909584od_a_a @ X @ A4 ) )
% 0.29/0.47 = A4 ) ).
% 0.29/0.47
% 0.29/0.47 % Collect_mem_eq
% 0.29/0.47 thf(fact_186_Collect__mem__eq,axiom,
% 0.29/0.47 ! [A4: set_li562223245od_a_a] :
% 0.29/0.47 ( ( collec1811041560od_a_a
% 0.29/0.47 @ ^ [X: list_P1467822637od_a_a] : ( member1578987478od_a_a @ X @ A4 ) )
% 0.29/0.47 = A4 ) ).
% 0.29/0.47
% 0.29/0.47 % Collect_mem_eq
% 0.29/0.47 thf(fact_187_Collect__mem__eq,axiom,
% 0.29/0.47 ! [A4: set_a] :
% 0.29/0.47 ( ( collect_a
% 0.29/0.47 @ ^ [X: a] : ( member_a2 @ X @ A4 ) )
% 0.29/0.47 = A4 ) ).
% 0.29/0.47
% 0.29/0.47 % Collect_mem_eq
% 0.29/0.47 thf(fact_188_lexord__irreflexive,axiom,
% 0.29/0.47 ! [R: set_Product_prod_a_a,Xs2: list_a] :
% 0.29/0.47 ( ! [X4: a] :
% 0.29/0.47 ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ X4 ) @ R )
% 0.29/0.47 => ~ ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ Xs2 ) @ ( lexord_a @ R ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % lexord_irreflexive
% 0.29/0.47 thf(fact_189_lexord__append__leftI,axiom,
% 0.29/0.47 ! [U: list_P1467822637od_a_a,V2: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a,X3: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ U @ V2 ) @ ( lexord673907738od_a_a @ R ) )
% 0.29/0.47 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ X3 @ U ) @ ( append1574001858od_a_a @ X3 @ V2 ) ) @ ( lexord673907738od_a_a @ R ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % lexord_append_leftI
% 0.29/0.47 thf(fact_190_listrel1I1,axiom,
% 0.29/0.47 ! [X3: product_prod_a_a,Y3: product_prod_a_a,R: set_Pr1948701895od_a_a,Xs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X3 @ Y3 ) @ R )
% 0.29/0.47 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ ( cons_P1921020637od_a_a @ Y3 @ Xs2 ) ) @ ( listre944824838od_a_a @ R ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % listrel1I1
% 0.29/0.47 thf(fact_191_listrel1I1,axiom,
% 0.29/0.47 ! [X3: a,Y3: a,R: set_Product_prod_a_a,Xs2: list_a] :
% 0.29/0.47 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R )
% 0.29/0.47 => ( member1250517072list_a @ ( produc1448356631list_a @ ( cons_a @ X3 @ Xs2 ) @ ( cons_a @ Y3 @ Xs2 ) ) @ ( listrel1_a @ R ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % listrel1I1
% 0.29/0.47 thf(fact_192_Cons__listrel1E1,axiom,
% 0.29/0.47 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 0.29/0.47 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ Ys2 ) @ ( listre944824838od_a_a @ R ) )
% 0.29/0.47 => ( ! [Y4: product_prod_a_a] :
% 0.29/0.47 ( ( Ys2
% 0.29/0.47 = ( cons_P1921020637od_a_a @ Y4 @ Xs2 ) )
% 0.29/0.47 => ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X3 @ Y4 ) @ R ) )
% 0.29/0.47 => ~ ! [Zs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( Ys2
% 0.29/0.47 = ( cons_P1921020637od_a_a @ X3 @ Zs2 ) )
% 0.29/0.47 => ~ ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ Zs2 ) @ ( listre944824838od_a_a @ R ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Cons_listrel1E1
% 0.29/0.47 thf(fact_193_Cons__listrel1E1,axiom,
% 0.29/0.47 ! [X3: a,Xs2: list_a,Ys2: list_a,R: set_Product_prod_a_a] :
% 0.29/0.47 ( ( member1250517072list_a @ ( produc1448356631list_a @ ( cons_a @ X3 @ Xs2 ) @ Ys2 ) @ ( listrel1_a @ R ) )
% 0.29/0.47 => ( ! [Y4: a] :
% 0.29/0.47 ( ( Ys2
% 0.29/0.47 = ( cons_a @ Y4 @ Xs2 ) )
% 0.29/0.47 => ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y4 ) @ R ) )
% 0.29/0.47 => ~ ! [Zs2: list_a] :
% 0.29/0.47 ( ( Ys2
% 0.29/0.47 = ( cons_a @ X3 @ Zs2 ) )
% 0.29/0.47 => ~ ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ Zs2 ) @ ( listrel1_a @ R ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Cons_listrel1E1
% 0.29/0.47 thf(fact_194_Cons__listrel1E2,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a,Y3: product_prod_a_a,Ys2: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 0.29/0.47 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ ( cons_P1921020637od_a_a @ Y3 @ Ys2 ) ) @ ( listre944824838od_a_a @ R ) )
% 0.29/0.47 => ( ! [X4: product_prod_a_a] :
% 0.29/0.47 ( ( Xs2
% 0.29/0.47 = ( cons_P1921020637od_a_a @ X4 @ Ys2 ) )
% 0.29/0.47 => ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X4 @ Y3 ) @ R ) )
% 0.29/0.47 => ~ ! [Zs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( Xs2
% 0.29/0.47 = ( cons_P1921020637od_a_a @ Y3 @ Zs2 ) )
% 0.29/0.47 => ~ ( member1691432592od_a_a @ ( produc85179863od_a_a @ Zs2 @ Ys2 ) @ ( listre944824838od_a_a @ R ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Cons_listrel1E2
% 0.29/0.47 thf(fact_195_Cons__listrel1E2,axiom,
% 0.29/0.47 ! [Xs2: list_a,Y3: a,Ys2: list_a,R: set_Product_prod_a_a] :
% 0.29/0.47 ( ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ ( cons_a @ Y3 @ Ys2 ) ) @ ( listrel1_a @ R ) )
% 0.29/0.47 => ( ! [X4: a] :
% 0.29/0.47 ( ( Xs2
% 0.29/0.47 = ( cons_a @ X4 @ Ys2 ) )
% 0.29/0.47 => ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y3 ) @ R ) )
% 0.29/0.47 => ~ ! [Zs2: list_a] :
% 0.29/0.47 ( ( Xs2
% 0.29/0.47 = ( cons_a @ Y3 @ Zs2 ) )
% 0.29/0.47 => ~ ( member1250517072list_a @ ( produc1448356631list_a @ Zs2 @ Ys2 ) @ ( listrel1_a @ R ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Cons_listrel1E2
% 0.29/0.47 thf(fact_196_lexord__append__leftD,axiom,
% 0.29/0.47 ! [X3: list_P1467822637od_a_a,U: list_P1467822637od_a_a,V2: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 0.29/0.47 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ X3 @ U ) @ ( append1574001858od_a_a @ X3 @ V2 ) ) @ ( lexord673907738od_a_a @ R ) )
% 0.29/0.47 => ( ! [A3: product_prod_a_a] :
% 0.29/0.47 ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A3 @ A3 ) @ R )
% 0.29/0.47 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ U @ V2 ) @ ( lexord673907738od_a_a @ R ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % lexord_append_leftD
% 0.29/0.47 thf(fact_197_lexord__append__leftD,axiom,
% 0.29/0.47 ! [X3: list_a,U: list_a,V2: list_a,R: set_Product_prod_a_a] :
% 0.29/0.47 ( ( member1250517072list_a @ ( produc1448356631list_a @ ( append_a @ X3 @ U ) @ ( append_a @ X3 @ V2 ) ) @ ( lexord_a @ R ) )
% 0.29/0.47 => ( ! [A3: a] :
% 0.29/0.47 ~ ( member449909584od_a_a @ ( product_Pair_a_a @ A3 @ A3 ) @ R )
% 0.29/0.47 => ( member1250517072list_a @ ( produc1448356631list_a @ U @ V2 ) @ ( lexord_a @ R ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % lexord_append_leftD
% 0.29/0.47 thf(fact_198_lexord__append__rightI,axiom,
% 0.29/0.47 ! [Y3: list_P1467822637od_a_a,X3: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 0.29/0.47 ( ? [B4: product_prod_a_a,Z: list_P1467822637od_a_a] :
% 0.29/0.47 ( Y3
% 0.29/0.47 = ( cons_P1921020637od_a_a @ B4 @ Z ) )
% 0.29/0.47 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ X3 @ ( append1574001858od_a_a @ X3 @ Y3 ) ) @ ( lexord673907738od_a_a @ R ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % lexord_append_rightI
% 0.29/0.47 thf(fact_199_zip__eq__ConsE,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Xy: produc1572603623od_a_a,Xys: list_P1891567085od_a_a] :
% 0.29/0.47 ( ( ( zip_Pr792472183od_a_a @ Xs2 @ Ys2 )
% 0.29/0.47 = ( cons_P1070399645od_a_a @ Xy @ Xys ) )
% 0.29/0.47 => ~ ! [X4: product_prod_a_a,Xs3: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( Xs2
% 0.29/0.47 = ( cons_P1921020637od_a_a @ X4 @ Xs3 ) )
% 0.29/0.47 => ! [Y4: product_prod_a_a,Ys3: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( Ys2
% 0.29/0.47 = ( cons_P1921020637od_a_a @ Y4 @ Ys3 ) )
% 0.29/0.47 => ( ( Xy
% 0.29/0.47 = ( produc1474507607od_a_a @ X4 @ Y4 ) )
% 0.29/0.47 => ( Xys
% 0.29/0.47 != ( zip_Pr792472183od_a_a @ Xs3 @ Ys3 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % zip_eq_ConsE
% 0.29/0.47 thf(fact_200_zip__eq__ConsE,axiom,
% 0.29/0.47 ! [Xs2: list_a,Ys2: list_a,Xy: product_prod_a_a,Xys: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( ( zip_a_a @ Xs2 @ Ys2 )
% 0.29/0.47 = ( cons_P1921020637od_a_a @ Xy @ Xys ) )
% 0.29/0.47 => ~ ! [X4: a,Xs3: list_a] :
% 0.29/0.47 ( ( Xs2
% 0.29/0.47 = ( cons_a @ X4 @ Xs3 ) )
% 0.29/0.47 => ! [Y4: a,Ys3: list_a] :
% 0.29/0.47 ( ( Ys2
% 0.29/0.47 = ( cons_a @ Y4 @ Ys3 ) )
% 0.29/0.47 => ( ( Xy
% 0.29/0.47 = ( product_Pair_a_a @ X4 @ Y4 ) )
% 0.29/0.47 => ( Xys
% 0.29/0.47 != ( zip_a_a @ Xs3 @ Ys3 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % zip_eq_ConsE
% 0.29/0.47 thf(fact_201_subdivide_Ocases,axiom,
% 0.29/0.47 ! [X3: produc1912141786_a_a_a] :
% 0.29/0.47 ~ ! [G: pair_p125712459t_unit,U2: a,V: a,W: a] :
% 0.29/0.47 ( X3
% 0.29/0.47 != ( produc74075722_a_a_a @ G @ ( produc2061588782_a_a_a @ ( product_Pair_a_a @ U2 @ V ) @ W ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % subdivide.cases
% 0.29/0.47 thf(fact_202_lexord__same__pref__if__irrefl,axiom,
% 0.29/0.47 ! [R: set_Pr1948701895od_a_a,Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( irrefl76447196od_a_a @ R )
% 0.29/0.47 => ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ Xs2 @ Ys2 ) @ ( append1574001858od_a_a @ Xs2 @ Zs ) ) @ ( lexord673907738od_a_a @ R ) )
% 0.29/0.47 = ( member1691432592od_a_a @ ( produc85179863od_a_a @ Ys2 @ Zs ) @ ( lexord673907738od_a_a @ R ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % lexord_same_pref_if_irrefl
% 0.29/0.47 thf(fact_203_snoc__listrel1__snoc__iff,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a,X3: product_prod_a_a,Ys2: list_P1467822637od_a_a,Y3: product_prod_a_a,R: set_Pr1948701895od_a_a] :
% 0.29/0.47 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ Xs2 @ ( cons_P1921020637od_a_a @ X3 @ nil_Product_prod_a_a ) ) @ ( append1574001858od_a_a @ Ys2 @ ( cons_P1921020637od_a_a @ Y3 @ nil_Product_prod_a_a ) ) ) @ ( listre944824838od_a_a @ R ) )
% 0.29/0.47 = ( ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ Ys2 ) @ ( listre944824838od_a_a @ R ) )
% 0.29/0.47 & ( X3 = Y3 ) )
% 0.29/0.47 | ( ( Xs2 = Ys2 )
% 0.29/0.47 & ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X3 @ Y3 ) @ R ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % snoc_listrel1_snoc_iff
% 0.29/0.47 thf(fact_204_snoc__listrel1__snoc__iff,axiom,
% 0.29/0.47 ! [Xs2: list_a,X3: a,Ys2: list_a,Y3: a,R: set_Product_prod_a_a] :
% 0.29/0.47 ( ( member1250517072list_a @ ( produc1448356631list_a @ ( append_a @ Xs2 @ ( cons_a @ X3 @ nil_a ) ) @ ( append_a @ Ys2 @ ( cons_a @ Y3 @ nil_a ) ) ) @ ( listrel1_a @ R ) )
% 0.29/0.47 = ( ( ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ Ys2 ) @ ( listrel1_a @ R ) )
% 0.29/0.47 & ( X3 = Y3 ) )
% 0.29/0.47 | ( ( Xs2 = Ys2 )
% 0.29/0.47 & ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % snoc_listrel1_snoc_iff
% 0.29/0.47 thf(fact_205_lexord__Nil__left,axiom,
% 0.29/0.47 ! [Y3: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 0.29/0.47 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ nil_Product_prod_a_a @ Y3 ) @ ( lexord673907738od_a_a @ R ) )
% 0.29/0.47 = ( ? [A5: product_prod_a_a,X: list_P1467822637od_a_a] :
% 0.29/0.47 ( Y3
% 0.29/0.47 = ( cons_P1921020637od_a_a @ A5 @ X ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % lexord_Nil_left
% 0.29/0.47 thf(fact_206_lexord__same__pref__iff,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 0.29/0.47 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ Xs2 @ Ys2 ) @ ( append1574001858od_a_a @ Xs2 @ Zs ) ) @ ( lexord673907738od_a_a @ R ) )
% 0.29/0.47 = ( ? [X: product_prod_a_a] :
% 0.29/0.47 ( ( member449909584od_a_a @ X @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 0.29/0.47 & ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X @ X ) @ R ) )
% 0.29/0.47 | ( member1691432592od_a_a @ ( produc85179863od_a_a @ Ys2 @ Zs ) @ ( lexord673907738od_a_a @ R ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % lexord_same_pref_iff
% 0.29/0.47 thf(fact_207_lexord__same__pref__iff,axiom,
% 0.29/0.47 ! [Xs2: list_a,Ys2: list_a,Zs: list_a,R: set_Product_prod_a_a] :
% 0.29/0.47 ( ( member1250517072list_a @ ( produc1448356631list_a @ ( append_a @ Xs2 @ Ys2 ) @ ( append_a @ Xs2 @ Zs ) ) @ ( lexord_a @ R ) )
% 0.29/0.47 = ( ? [X: a] :
% 0.29/0.47 ( ( member_a2 @ X @ ( set_a2 @ Xs2 ) )
% 0.29/0.47 & ( member449909584od_a_a @ ( product_Pair_a_a @ X @ X ) @ R ) )
% 0.29/0.47 | ( member1250517072list_a @ ( produc1448356631list_a @ Ys2 @ Zs ) @ ( lexord_a @ R ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % lexord_same_pref_iff
% 0.29/0.47 thf(fact_208_zip__append,axiom,
% 0.29/0.47 ! [Xs2: list_a,Us: list_a,Ys2: list_a,Vs: list_a] :
% 0.29/0.47 ( ( ( size_size_list_a @ Xs2 )
% 0.29/0.47 = ( size_size_list_a @ Us ) )
% 0.29/0.47 => ( ( zip_a_a @ ( append_a @ Xs2 @ Ys2 ) @ ( append_a @ Us @ Vs ) )
% 0.29/0.47 = ( append1574001858od_a_a @ ( zip_a_a @ Xs2 @ Us ) @ ( zip_a_a @ Ys2 @ Vs ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % zip_append
% 0.29/0.47 thf(fact_209_zip__append,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a,Us: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Vs: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( ( size_s642698393od_a_a @ Xs2 )
% 0.29/0.47 = ( size_s642698393od_a_a @ Us ) )
% 0.29/0.47 => ( ( zip_Pr792472183od_a_a @ ( append1574001858od_a_a @ Xs2 @ Ys2 ) @ ( append1574001858od_a_a @ Us @ Vs ) )
% 0.29/0.47 = ( append864718978od_a_a @ ( zip_Pr792472183od_a_a @ Xs2 @ Us ) @ ( zip_Pr792472183od_a_a @ Ys2 @ Vs ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % zip_append
% 0.29/0.47 thf(fact_210_lex__append__leftD,axiom,
% 0.29/0.47 ! [R: set_Pr1948701895od_a_a,Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a] :
% 0.29/0.47 ( ! [X4: product_prod_a_a] :
% 0.29/0.47 ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X4 @ X4 ) @ R )
% 0.29/0.47 => ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ Xs2 @ Ys2 ) @ ( append1574001858od_a_a @ Xs2 @ Zs ) ) @ ( lex_Product_prod_a_a @ R ) )
% 0.29/0.47 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ Ys2 @ Zs ) @ ( lex_Product_prod_a_a @ R ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % lex_append_leftD
% 0.29/0.47 thf(fact_211_lex__append__leftD,axiom,
% 0.29/0.47 ! [R: set_Product_prod_a_a,Xs2: list_a,Ys2: list_a,Zs: list_a] :
% 0.29/0.47 ( ! [X4: a] :
% 0.29/0.47 ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ X4 ) @ R )
% 0.29/0.47 => ( ( member1250517072list_a @ ( produc1448356631list_a @ ( append_a @ Xs2 @ Ys2 ) @ ( append_a @ Xs2 @ Zs ) ) @ ( lex_a @ R ) )
% 0.29/0.47 => ( member1250517072list_a @ ( produc1448356631list_a @ Ys2 @ Zs ) @ ( lex_a @ R ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % lex_append_leftD
% 0.29/0.47 thf(fact_212_lex__append__left__iff,axiom,
% 0.29/0.47 ! [R: set_Pr1948701895od_a_a,Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a] :
% 0.29/0.47 ( ! [X4: product_prod_a_a] :
% 0.29/0.47 ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X4 @ X4 ) @ R )
% 0.29/0.47 => ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ Xs2 @ Ys2 ) @ ( append1574001858od_a_a @ Xs2 @ Zs ) ) @ ( lex_Product_prod_a_a @ R ) )
% 0.29/0.47 = ( member1691432592od_a_a @ ( produc85179863od_a_a @ Ys2 @ Zs ) @ ( lex_Product_prod_a_a @ R ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % lex_append_left_iff
% 0.29/0.47 thf(fact_213_lex__append__left__iff,axiom,
% 0.29/0.47 ! [R: set_Product_prod_a_a,Xs2: list_a,Ys2: list_a,Zs: list_a] :
% 0.29/0.47 ( ! [X4: a] :
% 0.29/0.47 ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ X4 ) @ R )
% 0.29/0.47 => ( ( member1250517072list_a @ ( produc1448356631list_a @ ( append_a @ Xs2 @ Ys2 ) @ ( append_a @ Xs2 @ Zs ) ) @ ( lex_a @ R ) )
% 0.29/0.47 = ( member1250517072list_a @ ( produc1448356631list_a @ Ys2 @ Zs ) @ ( lex_a @ R ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % lex_append_left_iff
% 0.29/0.47 thf(fact_214_append_Oright__neutral,axiom,
% 0.29/0.47 ! [A: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( append1574001858od_a_a @ A @ nil_Product_prod_a_a )
% 0.29/0.47 = A ) ).
% 0.29/0.47
% 0.29/0.47 % append.right_neutral
% 0.29/0.47 thf(fact_215_append__is__Nil__conv,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( ( append1574001858od_a_a @ Xs2 @ Ys2 )
% 0.29/0.47 = nil_Product_prod_a_a )
% 0.29/0.47 = ( ( Xs2 = nil_Product_prod_a_a )
% 0.29/0.47 & ( Ys2 = nil_Product_prod_a_a ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % append_is_Nil_conv
% 0.29/0.47 thf(fact_216_Nil__is__append__conv,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( nil_Product_prod_a_a
% 0.29/0.47 = ( append1574001858od_a_a @ Xs2 @ Ys2 ) )
% 0.29/0.47 = ( ( Xs2 = nil_Product_prod_a_a )
% 0.29/0.47 & ( Ys2 = nil_Product_prod_a_a ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Nil_is_append_conv
% 0.29/0.47 thf(fact_217_self__append__conv2,axiom,
% 0.29/0.47 ! [Ys2: list_P1467822637od_a_a,Xs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( Ys2
% 0.29/0.47 = ( append1574001858od_a_a @ Xs2 @ Ys2 ) )
% 0.29/0.47 = ( Xs2 = nil_Product_prod_a_a ) ) ).
% 0.29/0.47
% 0.29/0.47 % self_append_conv2
% 0.29/0.47 thf(fact_218_append__self__conv2,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( ( append1574001858od_a_a @ Xs2 @ Ys2 )
% 0.29/0.47 = Ys2 )
% 0.29/0.47 = ( Xs2 = nil_Product_prod_a_a ) ) ).
% 0.29/0.47
% 0.29/0.47 % append_self_conv2
% 0.29/0.47 thf(fact_219_self__append__conv,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( Xs2
% 0.29/0.47 = ( append1574001858od_a_a @ Xs2 @ Ys2 ) )
% 0.29/0.47 = ( Ys2 = nil_Product_prod_a_a ) ) ).
% 0.29/0.47
% 0.29/0.47 % self_append_conv
% 0.29/0.47 thf(fact_220_append__self__conv,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( ( append1574001858od_a_a @ Xs2 @ Ys2 )
% 0.29/0.47 = Xs2 )
% 0.29/0.47 = ( Ys2 = nil_Product_prod_a_a ) ) ).
% 0.29/0.47
% 0.29/0.47 % append_self_conv
% 0.29/0.47 thf(fact_221_append__Nil2,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( append1574001858od_a_a @ Xs2 @ nil_Product_prod_a_a )
% 0.29/0.47 = Xs2 ) ).
% 0.29/0.47
% 0.29/0.47 % append_Nil2
% 0.29/0.47 thf(fact_222_append__eq__append__conv,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Us: list_P1467822637od_a_a,Vs: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( ( ( size_s642698393od_a_a @ Xs2 )
% 0.29/0.47 = ( size_s642698393od_a_a @ Ys2 ) )
% 0.29/0.47 | ( ( size_s642698393od_a_a @ Us )
% 0.29/0.47 = ( size_s642698393od_a_a @ Vs ) ) )
% 0.29/0.47 => ( ( ( append1574001858od_a_a @ Xs2 @ Us )
% 0.29/0.47 = ( append1574001858od_a_a @ Ys2 @ Vs ) )
% 0.29/0.47 = ( ( Xs2 = Ys2 )
% 0.29/0.47 & ( Us = Vs ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % append_eq_append_conv
% 0.29/0.47 thf(fact_223_append1__eq__conv,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a,X3: product_prod_a_a,Ys2: list_P1467822637od_a_a,Y3: product_prod_a_a] :
% 0.29/0.47 ( ( ( append1574001858od_a_a @ Xs2 @ ( cons_P1921020637od_a_a @ X3 @ nil_Product_prod_a_a ) )
% 0.29/0.47 = ( append1574001858od_a_a @ Ys2 @ ( cons_P1921020637od_a_a @ Y3 @ nil_Product_prod_a_a ) ) )
% 0.29/0.47 = ( ( Xs2 = Ys2 )
% 0.29/0.47 & ( X3 = Y3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % append1_eq_conv
% 0.29/0.47 thf(fact_224_Cons__in__lex,axiom,
% 0.29/0.47 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a,Y3: product_prod_a_a,Ys2: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 0.29/0.47 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ ( cons_P1921020637od_a_a @ Y3 @ Ys2 ) ) @ ( lex_Product_prod_a_a @ R ) )
% 0.29/0.47 = ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X3 @ Y3 ) @ R )
% 0.29/0.47 & ( ( size_s642698393od_a_a @ Xs2 )
% 0.29/0.47 = ( size_s642698393od_a_a @ Ys2 ) ) )
% 0.29/0.47 | ( ( X3 = Y3 )
% 0.29/0.47 & ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ Ys2 ) @ ( lex_Product_prod_a_a @ R ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Cons_in_lex
% 0.29/0.47 thf(fact_225_Cons__in__lex,axiom,
% 0.29/0.47 ! [X3: a,Xs2: list_a,Y3: a,Ys2: list_a,R: set_Product_prod_a_a] :
% 0.29/0.47 ( ( member1250517072list_a @ ( produc1448356631list_a @ ( cons_a @ X3 @ Xs2 ) @ ( cons_a @ Y3 @ Ys2 ) ) @ ( lex_a @ R ) )
% 0.29/0.47 = ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R )
% 0.29/0.47 & ( ( size_size_list_a @ Xs2 )
% 0.29/0.47 = ( size_size_list_a @ Ys2 ) ) )
% 0.29/0.47 | ( ( X3 = Y3 )
% 0.29/0.47 & ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ Ys2 ) @ ( lex_a @ R ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Cons_in_lex
% 0.29/0.47 thf(fact_226_in__set__impl__in__set__zip1,axiom,
% 0.29/0.47 ! [Xs2: list_a,Ys2: list_a,X3: a] :
% 0.29/0.47 ( ( ( size_size_list_a @ Xs2 )
% 0.29/0.47 = ( size_size_list_a @ Ys2 ) )
% 0.29/0.47 => ( ( member_a2 @ X3 @ ( set_a2 @ Xs2 ) )
% 0.29/0.47 => ~ ! [Y4: a] :
% 0.29/0.47 ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y4 ) @ ( set_Product_prod_a_a2 @ ( zip_a_a @ Xs2 @ Ys2 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % in_set_impl_in_set_zip1
% 0.29/0.47 thf(fact_227_in__set__impl__in__set__zip2,axiom,
% 0.29/0.47 ! [Xs2: list_a,Ys2: list_a,Y3: a] :
% 0.29/0.47 ( ( ( size_size_list_a @ Xs2 )
% 0.29/0.47 = ( size_size_list_a @ Ys2 ) )
% 0.29/0.47 => ( ( member_a2 @ Y3 @ ( set_a2 @ Ys2 ) )
% 0.29/0.47 => ~ ! [X4: a] :
% 0.29/0.47 ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y3 ) @ ( set_Product_prod_a_a2 @ ( zip_a_a @ Xs2 @ Ys2 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % in_set_impl_in_set_zip2
% 0.29/0.47 thf(fact_228_list__induct4,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a,Ws: list_P1467822637od_a_a,P2: list_P1467822637od_a_a > list_P1467822637od_a_a > list_P1467822637od_a_a > list_P1467822637od_a_a > $o] :
% 0.29/0.47 ( ( ( size_s642698393od_a_a @ Xs2 )
% 0.29/0.47 = ( size_s642698393od_a_a @ Ys2 ) )
% 0.29/0.47 => ( ( ( size_s642698393od_a_a @ Ys2 )
% 0.29/0.47 = ( size_s642698393od_a_a @ Zs ) )
% 0.29/0.47 => ( ( ( size_s642698393od_a_a @ Zs )
% 0.29/0.47 = ( size_s642698393od_a_a @ Ws ) )
% 0.29/0.47 => ( ( P2 @ nil_Product_prod_a_a @ nil_Product_prod_a_a @ nil_Product_prod_a_a @ nil_Product_prod_a_a )
% 0.29/0.47 => ( ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a,Y4: product_prod_a_a,Ys4: list_P1467822637od_a_a,Z2: product_prod_a_a,Zs2: list_P1467822637od_a_a,W: product_prod_a_a,Ws2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( ( size_s642698393od_a_a @ Xs4 )
% 0.29/0.47 = ( size_s642698393od_a_a @ Ys4 ) )
% 0.29/0.47 => ( ( ( size_s642698393od_a_a @ Ys4 )
% 0.29/0.47 = ( size_s642698393od_a_a @ Zs2 ) )
% 0.29/0.47 => ( ( ( size_s642698393od_a_a @ Zs2 )
% 0.29/0.47 = ( size_s642698393od_a_a @ Ws2 ) )
% 0.29/0.47 => ( ( P2 @ Xs4 @ Ys4 @ Zs2 @ Ws2 )
% 0.29/0.47 => ( P2 @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) @ ( cons_P1921020637od_a_a @ Y4 @ Ys4 ) @ ( cons_P1921020637od_a_a @ Z2 @ Zs2 ) @ ( cons_P1921020637od_a_a @ W @ Ws2 ) ) ) ) ) )
% 0.29/0.47 => ( P2 @ Xs2 @ Ys2 @ Zs @ Ws ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % list_induct4
% 0.29/0.47 thf(fact_229_list__induct3,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a,P2: list_P1467822637od_a_a > list_P1467822637od_a_a > list_P1467822637od_a_a > $o] :
% 0.29/0.47 ( ( ( size_s642698393od_a_a @ Xs2 )
% 0.29/0.47 = ( size_s642698393od_a_a @ Ys2 ) )
% 0.29/0.47 => ( ( ( size_s642698393od_a_a @ Ys2 )
% 0.29/0.47 = ( size_s642698393od_a_a @ Zs ) )
% 0.29/0.47 => ( ( P2 @ nil_Product_prod_a_a @ nil_Product_prod_a_a @ nil_Product_prod_a_a )
% 0.29/0.47 => ( ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a,Y4: product_prod_a_a,Ys4: list_P1467822637od_a_a,Z2: product_prod_a_a,Zs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( ( size_s642698393od_a_a @ Xs4 )
% 0.29/0.47 = ( size_s642698393od_a_a @ Ys4 ) )
% 0.29/0.47 => ( ( ( size_s642698393od_a_a @ Ys4 )
% 0.29/0.47 = ( size_s642698393od_a_a @ Zs2 ) )
% 0.29/0.47 => ( ( P2 @ Xs4 @ Ys4 @ Zs2 )
% 0.29/0.47 => ( P2 @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) @ ( cons_P1921020637od_a_a @ Y4 @ Ys4 ) @ ( cons_P1921020637od_a_a @ Z2 @ Zs2 ) ) ) ) )
% 0.29/0.47 => ( P2 @ Xs2 @ Ys2 @ Zs ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % list_induct3
% 0.29/0.47 thf(fact_230_list__induct2,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,P2: list_P1467822637od_a_a > list_P1467822637od_a_a > $o] :
% 0.29/0.47 ( ( ( size_s642698393od_a_a @ Xs2 )
% 0.29/0.47 = ( size_s642698393od_a_a @ Ys2 ) )
% 0.29/0.47 => ( ( P2 @ nil_Product_prod_a_a @ nil_Product_prod_a_a )
% 0.29/0.47 => ( ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a,Y4: product_prod_a_a,Ys4: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( ( size_s642698393od_a_a @ Xs4 )
% 0.29/0.47 = ( size_s642698393od_a_a @ Ys4 ) )
% 0.29/0.47 => ( ( P2 @ Xs4 @ Ys4 )
% 0.29/0.47 => ( P2 @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) @ ( cons_P1921020637od_a_a @ Y4 @ Ys4 ) ) ) )
% 0.29/0.47 => ( P2 @ Xs2 @ Ys2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % list_induct2
% 0.29/0.47 thf(fact_231_transpose_Ocases,axiom,
% 0.29/0.47 ! [X3: list_l1108175539od_a_a] :
% 0.29/0.47 ( ( X3 != nil_li1885598003od_a_a )
% 0.29/0.47 => ( ! [Xss: list_l1108175539od_a_a] :
% 0.29/0.47 ( X3
% 0.29/0.47 != ( cons_l724116707od_a_a @ nil_Product_prod_a_a @ Xss ) )
% 0.29/0.47 => ~ ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a,Xss: list_l1108175539od_a_a] :
% 0.29/0.47 ( X3
% 0.29/0.47 != ( cons_l724116707od_a_a @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) @ Xss ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % transpose.cases
% 0.29/0.47 thf(fact_232_set__zip__rightD,axiom,
% 0.29/0.47 ! [X3: a,Y3: a,Xs2: list_a,Ys2: list_a] :
% 0.29/0.47 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ ( set_Product_prod_a_a2 @ ( zip_a_a @ Xs2 @ Ys2 ) ) )
% 0.29/0.47 => ( member_a2 @ Y3 @ ( set_a2 @ Ys2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % set_zip_rightD
% 0.29/0.47 thf(fact_233_set__zip__leftD,axiom,
% 0.29/0.47 ! [X3: a,Y3: a,Xs2: list_a,Ys2: list_a] :
% 0.29/0.47 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ ( set_Product_prod_a_a2 @ ( zip_a_a @ Xs2 @ Ys2 ) ) )
% 0.29/0.47 => ( member_a2 @ X3 @ ( set_a2 @ Xs2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % set_zip_leftD
% 0.29/0.47 thf(fact_234_in__set__zipE,axiom,
% 0.29/0.47 ! [X3: a,Y3: a,Xs2: list_a,Ys2: list_a] :
% 0.29/0.47 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ ( set_Product_prod_a_a2 @ ( zip_a_a @ Xs2 @ Ys2 ) ) )
% 0.29/0.47 => ~ ( ( member_a2 @ X3 @ ( set_a2 @ Xs2 ) )
% 0.29/0.47 => ~ ( member_a2 @ Y3 @ ( set_a2 @ Ys2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % in_set_zipE
% 0.29/0.47 thf(fact_235_zip__same,axiom,
% 0.29/0.47 ! [A: a,B: a,Xs2: list_a] :
% 0.29/0.47 ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ ( set_Product_prod_a_a2 @ ( zip_a_a @ Xs2 @ Xs2 ) ) )
% 0.29/0.47 = ( ( member_a2 @ A @ ( set_a2 @ Xs2 ) )
% 0.29/0.47 & ( A = B ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % zip_same
% 0.29/0.47 thf(fact_236_same__length__different,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( Xs2 != Ys2 )
% 0.29/0.47 => ( ( ( size_s642698393od_a_a @ Xs2 )
% 0.29/0.47 = ( size_s642698393od_a_a @ Ys2 ) )
% 0.29/0.47 => ? [Pre: list_P1467822637od_a_a,X4: product_prod_a_a,Xs3: list_P1467822637od_a_a,Y4: product_prod_a_a,Ys3: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( X4 != Y4 )
% 0.29/0.47 & ( Xs2
% 0.29/0.47 = ( append1574001858od_a_a @ Pre @ ( append1574001858od_a_a @ ( cons_P1921020637od_a_a @ X4 @ nil_Product_prod_a_a ) @ Xs3 ) ) )
% 0.29/0.47 & ( Ys2
% 0.29/0.47 = ( append1574001858od_a_a @ Pre @ ( append1574001858od_a_a @ ( cons_P1921020637od_a_a @ Y4 @ nil_Product_prod_a_a ) @ Ys3 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % same_length_different
% 0.29/0.47 thf(fact_237_list_Oset__cases,axiom,
% 0.29/0.47 ! [E: product_prod_a_a,A: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( member449909584od_a_a @ E @ ( set_Product_prod_a_a2 @ A ) )
% 0.29/0.47 => ( ! [Z22: list_P1467822637od_a_a] :
% 0.29/0.47 ( A
% 0.29/0.47 != ( cons_P1921020637od_a_a @ E @ Z22 ) )
% 0.29/0.47 => ~ ! [Z1: product_prod_a_a,Z22: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( A
% 0.29/0.47 = ( cons_P1921020637od_a_a @ Z1 @ Z22 ) )
% 0.29/0.47 => ~ ( member449909584od_a_a @ E @ ( set_Product_prod_a_a2 @ Z22 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % list.set_cases
% 0.29/0.47 thf(fact_238_set__ConsD,axiom,
% 0.29/0.47 ! [Y3: product_prod_a_a,X3: product_prod_a_a,Xs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( member449909584od_a_a @ Y3 @ ( set_Product_prod_a_a2 @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) ) )
% 0.29/0.47 => ( ( Y3 = X3 )
% 0.29/0.47 | ( member449909584od_a_a @ Y3 @ ( set_Product_prod_a_a2 @ Xs2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % set_ConsD
% 0.29/0.47 thf(fact_239_list_Oset__intros_I1_J,axiom,
% 0.29/0.47 ! [X21: product_prod_a_a,X22: list_P1467822637od_a_a] : ( member449909584od_a_a @ X21 @ ( set_Product_prod_a_a2 @ ( cons_P1921020637od_a_a @ X21 @ X22 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % list.set_intros(1)
% 0.29/0.47 thf(fact_240_list_Oset__intros_I2_J,axiom,
% 0.29/0.47 ! [Y3: product_prod_a_a,X22: list_P1467822637od_a_a,X21: product_prod_a_a] :
% 0.29/0.47 ( ( member449909584od_a_a @ Y3 @ ( set_Product_prod_a_a2 @ X22 ) )
% 0.29/0.47 => ( member449909584od_a_a @ Y3 @ ( set_Product_prod_a_a2 @ ( cons_P1921020637od_a_a @ X21 @ X22 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % list.set_intros(2)
% 0.29/0.47 thf(fact_241_lex__append__rightI,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a,Vs: list_P1467822637od_a_a,Us: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ Ys2 ) @ ( lex_Product_prod_a_a @ R ) )
% 0.29/0.47 => ( ( ( size_s642698393od_a_a @ Vs )
% 0.29/0.47 = ( size_s642698393od_a_a @ Us ) )
% 0.29/0.47 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ Xs2 @ Us ) @ ( append1574001858od_a_a @ Ys2 @ Vs ) ) @ ( lex_Product_prod_a_a @ R ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % lex_append_rightI
% 0.29/0.47 thf(fact_242_sorted__wrt_Ocases,axiom,
% 0.29/0.47 ! [X3: produc501911462od_a_a] :
% 0.29/0.47 ( ! [P4: product_prod_a_a > product_prod_a_a > $o] :
% 0.29/0.47 ( X3
% 0.29/0.47 != ( produc214132118od_a_a @ P4 @ nil_Product_prod_a_a ) )
% 0.29/0.47 => ~ ! [P4: product_prod_a_a > product_prod_a_a > $o,X4: product_prod_a_a,Ys4: list_P1467822637od_a_a] :
% 0.29/0.47 ( X3
% 0.29/0.47 != ( produc214132118od_a_a @ P4 @ ( cons_P1921020637od_a_a @ X4 @ Ys4 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % sorted_wrt.cases
% 0.29/0.47 thf(fact_243_successively_Ocases,axiom,
% 0.29/0.47 ! [X3: produc501911462od_a_a] :
% 0.29/0.47 ( ! [P4: product_prod_a_a > product_prod_a_a > $o] :
% 0.29/0.47 ( X3
% 0.29/0.47 != ( produc214132118od_a_a @ P4 @ nil_Product_prod_a_a ) )
% 0.29/0.47 => ( ! [P4: product_prod_a_a > product_prod_a_a > $o,X4: product_prod_a_a] :
% 0.29/0.47 ( X3
% 0.29/0.47 != ( produc214132118od_a_a @ P4 @ ( cons_P1921020637od_a_a @ X4 @ nil_Product_prod_a_a ) ) )
% 0.29/0.47 => ~ ! [P4: product_prod_a_a > product_prod_a_a > $o,X4: product_prod_a_a,Y4: product_prod_a_a,Xs4: list_P1467822637od_a_a] :
% 0.29/0.47 ( X3
% 0.29/0.47 != ( produc214132118od_a_a @ P4 @ ( cons_P1921020637od_a_a @ X4 @ ( cons_P1921020637od_a_a @ Y4 @ Xs4 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % successively.cases
% 0.29/0.47 thf(fact_244_map__tailrec__rev_Oinduct,axiom,
% 0.29/0.47 ! [P2: ( product_prod_a_a > product_prod_a_a ) > list_P1467822637od_a_a > list_P1467822637od_a_a > $o,A0: product_prod_a_a > product_prod_a_a,A1: list_P1467822637od_a_a,A22: list_P1467822637od_a_a] :
% 0.29/0.47 ( ! [F2: product_prod_a_a > product_prod_a_a,X_1: list_P1467822637od_a_a] : ( P2 @ F2 @ nil_Product_prod_a_a @ X_1 )
% 0.29/0.47 => ( ! [F2: product_prod_a_a > product_prod_a_a,A3: product_prod_a_a,As: list_P1467822637od_a_a,Bs: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( P2 @ F2 @ As @ ( cons_P1921020637od_a_a @ ( F2 @ A3 ) @ Bs ) )
% 0.29/0.47 => ( P2 @ F2 @ ( cons_P1921020637od_a_a @ A3 @ As ) @ Bs ) )
% 0.29/0.47 => ( P2 @ A0 @ A1 @ A22 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % map_tailrec_rev.induct
% 0.29/0.47 thf(fact_245_list__nonempty__induct,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a,P2: list_P1467822637od_a_a > $o] :
% 0.29/0.47 ( ( Xs2 != nil_Product_prod_a_a )
% 0.29/0.47 => ( ! [X4: product_prod_a_a] : ( P2 @ ( cons_P1921020637od_a_a @ X4 @ nil_Product_prod_a_a ) )
% 0.29/0.47 => ( ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( Xs4 != nil_Product_prod_a_a )
% 0.29/0.47 => ( ( P2 @ Xs4 )
% 0.29/0.47 => ( P2 @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) ) ) )
% 0.29/0.47 => ( P2 @ Xs2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % list_nonempty_induct
% 0.29/0.47 thf(fact_246_successively_Oinduct,axiom,
% 0.29/0.47 ! [P2: ( product_prod_a_a > product_prod_a_a > $o ) > list_P1467822637od_a_a > $o,A0: product_prod_a_a > product_prod_a_a > $o,A1: list_P1467822637od_a_a] :
% 0.29/0.47 ( ! [P4: product_prod_a_a > product_prod_a_a > $o] : ( P2 @ P4 @ nil_Product_prod_a_a )
% 0.29/0.47 => ( ! [P4: product_prod_a_a > product_prod_a_a > $o,X4: product_prod_a_a] : ( P2 @ P4 @ ( cons_P1921020637od_a_a @ X4 @ nil_Product_prod_a_a ) )
% 0.29/0.47 => ( ! [P4: product_prod_a_a > product_prod_a_a > $o,X4: product_prod_a_a,Y4: product_prod_a_a,Xs4: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( P2 @ P4 @ ( cons_P1921020637od_a_a @ Y4 @ Xs4 ) )
% 0.29/0.47 => ( P2 @ P4 @ ( cons_P1921020637od_a_a @ X4 @ ( cons_P1921020637od_a_a @ Y4 @ Xs4 ) ) ) )
% 0.29/0.47 => ( P2 @ A0 @ A1 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % successively.induct
% 0.29/0.47 thf(fact_247_remdups__adj_Oinduct,axiom,
% 0.29/0.47 ! [P2: list_P1467822637od_a_a > $o,A0: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( P2 @ nil_Product_prod_a_a )
% 0.29/0.47 => ( ! [X4: product_prod_a_a] : ( P2 @ ( cons_P1921020637od_a_a @ X4 @ nil_Product_prod_a_a ) )
% 0.29/0.47 => ( ! [X4: product_prod_a_a,Y4: product_prod_a_a,Xs4: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( ( X4 = Y4 )
% 0.29/0.47 => ( P2 @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) ) )
% 0.29/0.47 => ( ( ( X4 != Y4 )
% 0.29/0.47 => ( P2 @ ( cons_P1921020637od_a_a @ Y4 @ Xs4 ) ) )
% 0.29/0.47 => ( P2 @ ( cons_P1921020637od_a_a @ X4 @ ( cons_P1921020637od_a_a @ Y4 @ Xs4 ) ) ) ) )
% 0.29/0.47 => ( P2 @ A0 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % remdups_adj.induct
% 0.29/0.47 thf(fact_248_sorted__wrt_Oinduct,axiom,
% 0.29/0.47 ! [P2: ( product_prod_a_a > product_prod_a_a > $o ) > list_P1467822637od_a_a > $o,A0: product_prod_a_a > product_prod_a_a > $o,A1: list_P1467822637od_a_a] :
% 0.29/0.47 ( ! [P4: product_prod_a_a > product_prod_a_a > $o] : ( P2 @ P4 @ nil_Product_prod_a_a )
% 0.29/0.47 => ( ! [P4: product_prod_a_a > product_prod_a_a > $o,X4: product_prod_a_a,Ys4: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( P2 @ P4 @ Ys4 )
% 0.29/0.47 => ( P2 @ P4 @ ( cons_P1921020637od_a_a @ X4 @ Ys4 ) ) )
% 0.29/0.47 => ( P2 @ A0 @ A1 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % sorted_wrt.induct
% 0.29/0.47 thf(fact_249_remdups__adj_Ocases,axiom,
% 0.29/0.47 ! [X3: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( X3 != nil_Product_prod_a_a )
% 0.29/0.47 => ( ! [X4: product_prod_a_a] :
% 0.29/0.47 ( X3
% 0.29/0.47 != ( cons_P1921020637od_a_a @ X4 @ nil_Product_prod_a_a ) )
% 0.29/0.47 => ~ ! [X4: product_prod_a_a,Y4: product_prod_a_a,Xs4: list_P1467822637od_a_a] :
% 0.29/0.47 ( X3
% 0.29/0.47 != ( cons_P1921020637od_a_a @ X4 @ ( cons_P1921020637od_a_a @ Y4 @ Xs4 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % remdups_adj.cases
% 0.29/0.47 thf(fact_250_shuffles_Oinduct,axiom,
% 0.29/0.47 ! [P2: list_P1467822637od_a_a > list_P1467822637od_a_a > $o,A0: list_P1467822637od_a_a,A1: list_P1467822637od_a_a] :
% 0.29/0.47 ( ! [X_1: list_P1467822637od_a_a] : ( P2 @ nil_Product_prod_a_a @ X_1 )
% 0.29/0.47 => ( ! [Xs4: list_P1467822637od_a_a] : ( P2 @ Xs4 @ nil_Product_prod_a_a )
% 0.29/0.47 => ( ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a,Y4: product_prod_a_a,Ys4: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( P2 @ Xs4 @ ( cons_P1921020637od_a_a @ Y4 @ Ys4 ) )
% 0.29/0.47 => ( ( P2 @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) @ Ys4 )
% 0.29/0.47 => ( P2 @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) @ ( cons_P1921020637od_a_a @ Y4 @ Ys4 ) ) ) )
% 0.29/0.47 => ( P2 @ A0 @ A1 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % shuffles.induct
% 0.29/0.47 thf(fact_251_induct__list012,axiom,
% 0.29/0.47 ! [P2: list_P1467822637od_a_a > $o,Xs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( P2 @ nil_Product_prod_a_a )
% 0.29/0.47 => ( ! [X4: product_prod_a_a] : ( P2 @ ( cons_P1921020637od_a_a @ X4 @ nil_Product_prod_a_a ) )
% 0.29/0.47 => ( ! [X4: product_prod_a_a,Y4: product_prod_a_a,Zs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( P2 @ Zs2 )
% 0.29/0.47 => ( ( P2 @ ( cons_P1921020637od_a_a @ Y4 @ Zs2 ) )
% 0.29/0.47 => ( P2 @ ( cons_P1921020637od_a_a @ X4 @ ( cons_P1921020637od_a_a @ Y4 @ Zs2 ) ) ) ) )
% 0.29/0.47 => ( P2 @ Xs2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % induct_list012
% 0.29/0.47 thf(fact_252_splice_Oinduct,axiom,
% 0.29/0.47 ! [P2: list_P1467822637od_a_a > list_P1467822637od_a_a > $o,A0: list_P1467822637od_a_a,A1: list_P1467822637od_a_a] :
% 0.29/0.47 ( ! [X_1: list_P1467822637od_a_a] : ( P2 @ nil_Product_prod_a_a @ X_1 )
% 0.29/0.47 => ( ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a,Ys4: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( P2 @ Ys4 @ Xs4 )
% 0.29/0.47 => ( P2 @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) @ Ys4 ) )
% 0.29/0.47 => ( P2 @ A0 @ A1 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % splice.induct
% 0.29/0.47 thf(fact_253_list__induct2_H,axiom,
% 0.29/0.47 ! [P2: list_P1467822637od_a_a > list_P1467822637od_a_a > $o,Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( P2 @ nil_Product_prod_a_a @ nil_Product_prod_a_a )
% 0.29/0.47 => ( ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a] : ( P2 @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) @ nil_Product_prod_a_a )
% 0.29/0.47 => ( ! [Y4: product_prod_a_a,Ys4: list_P1467822637od_a_a] : ( P2 @ nil_Product_prod_a_a @ ( cons_P1921020637od_a_a @ Y4 @ Ys4 ) )
% 0.29/0.47 => ( ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a,Y4: product_prod_a_a,Ys4: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( P2 @ Xs4 @ Ys4 )
% 0.29/0.47 => ( P2 @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) @ ( cons_P1921020637od_a_a @ Y4 @ Ys4 ) ) )
% 0.29/0.47 => ( P2 @ Xs2 @ Ys2 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % list_induct2'
% 0.29/0.47 thf(fact_254_neq__Nil__conv,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( Xs2 != nil_Product_prod_a_a )
% 0.29/0.47 = ( ? [Y: product_prod_a_a,Ys: list_P1467822637od_a_a] :
% 0.29/0.47 ( Xs2
% 0.29/0.47 = ( cons_P1921020637od_a_a @ Y @ Ys ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % neq_Nil_conv
% 0.29/0.47 thf(fact_255_list_Oinducts,axiom,
% 0.29/0.47 ! [P2: list_P1467822637od_a_a > $o,List: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( P2 @ nil_Product_prod_a_a )
% 0.29/0.47 => ( ! [X12: product_prod_a_a,X23: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( P2 @ X23 )
% 0.29/0.47 => ( P2 @ ( cons_P1921020637od_a_a @ X12 @ X23 ) ) )
% 0.29/0.47 => ( P2 @ List ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % list.inducts
% 0.29/0.47 thf(fact_256_list_Oexhaust,axiom,
% 0.29/0.47 ! [Y3: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( Y3 != nil_Product_prod_a_a )
% 0.29/0.47 => ~ ! [X212: product_prod_a_a,X222: list_P1467822637od_a_a] :
% 0.29/0.47 ( Y3
% 0.29/0.47 != ( cons_P1921020637od_a_a @ X212 @ X222 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % list.exhaust
% 0.29/0.47 thf(fact_257_list_OdiscI,axiom,
% 0.29/0.47 ! [List: list_P1467822637od_a_a,X21: product_prod_a_a,X22: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( List
% 0.29/0.47 = ( cons_P1921020637od_a_a @ X21 @ X22 ) )
% 0.29/0.47 => ( List != nil_Product_prod_a_a ) ) ).
% 0.29/0.47
% 0.29/0.47 % list.discI
% 0.29/0.47 thf(fact_258_list_Odistinct_I1_J,axiom,
% 0.29/0.47 ! [X21: product_prod_a_a,X22: list_P1467822637od_a_a] :
% 0.29/0.47 ( nil_Product_prod_a_a
% 0.29/0.47 != ( cons_P1921020637od_a_a @ X21 @ X22 ) ) ).
% 0.29/0.47
% 0.29/0.47 % list.distinct(1)
% 0.29/0.47 thf(fact_259_append_Oleft__neutral,axiom,
% 0.29/0.47 ! [A: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( append1574001858od_a_a @ nil_Product_prod_a_a @ A )
% 0.29/0.47 = A ) ).
% 0.29/0.47
% 0.29/0.47 % append.left_neutral
% 0.29/0.47 thf(fact_260_append__Nil,axiom,
% 0.29/0.47 ! [Ys2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( append1574001858od_a_a @ nil_Product_prod_a_a @ Ys2 )
% 0.29/0.47 = Ys2 ) ).
% 0.29/0.47
% 0.29/0.47 % append_Nil
% 0.29/0.47 thf(fact_261_eq__Nil__appendI,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( Xs2 = Ys2 )
% 0.29/0.47 => ( Xs2
% 0.29/0.47 = ( append1574001858od_a_a @ nil_Product_prod_a_a @ Ys2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % eq_Nil_appendI
% 0.29/0.47 thf(fact_262_pcas_Ocases,axiom,
% 0.29/0.47 ! [X3: produc1197928545_a_a_a] :
% 0.29/0.47 ( ! [U2: a,V: a] :
% 0.29/0.47 ( X3
% 0.29/0.47 != ( produc1440321489_a_a_a @ U2 @ ( produc998622632_a_a_a @ nil_Product_prod_a_a @ V ) ) )
% 0.29/0.47 => ~ ! [U2: a,E2: product_prod_a_a,Es: list_P1467822637od_a_a,V: a] :
% 0.29/0.47 ( X3
% 0.29/0.47 != ( produc1440321489_a_a_a @ U2 @ ( produc998622632_a_a_a @ ( cons_P1921020637od_a_a @ E2 @ Es ) @ V ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % pcas.cases
% 0.29/0.47 thf(fact_263_progressing__Nil,axiom,
% 0.29/0.47 kurato1072996284sing_a @ nil_Product_prod_a_a ).
% 0.29/0.47
% 0.29/0.47 % progressing_Nil
% 0.29/0.47 thf(fact_264_split__list__first__prop__iff,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a,P2: product_prod_a_a > $o] :
% 0.29/0.47 ( ( ? [X: product_prod_a_a] :
% 0.29/0.47 ( ( member449909584od_a_a @ X @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 0.29/0.47 & ( P2 @ X ) ) )
% 0.29/0.47 = ( ? [Ys: list_P1467822637od_a_a,X: product_prod_a_a] :
% 0.29/0.47 ( ? [Zs3: list_P1467822637od_a_a] :
% 0.29/0.47 ( Xs2
% 0.29/0.47 = ( append1574001858od_a_a @ Ys @ ( cons_P1921020637od_a_a @ X @ Zs3 ) ) )
% 0.29/0.47 & ( P2 @ X )
% 0.29/0.47 & ! [Y: product_prod_a_a] :
% 0.29/0.47 ( ( member449909584od_a_a @ Y @ ( set_Product_prod_a_a2 @ Ys ) )
% 0.29/0.47 => ~ ( P2 @ Y ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % split_list_first_prop_iff
% 0.29/0.47 thf(fact_265_split__list__last__prop__iff,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a,P2: product_prod_a_a > $o] :
% 0.29/0.47 ( ( ? [X: product_prod_a_a] :
% 0.29/0.47 ( ( member449909584od_a_a @ X @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 0.29/0.47 & ( P2 @ X ) ) )
% 0.29/0.47 = ( ? [Ys: list_P1467822637od_a_a,X: product_prod_a_a,Zs3: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( Xs2
% 0.29/0.47 = ( append1574001858od_a_a @ Ys @ ( cons_P1921020637od_a_a @ X @ Zs3 ) ) )
% 0.29/0.47 & ( P2 @ X )
% 0.29/0.47 & ! [Y: product_prod_a_a] :
% 0.29/0.47 ( ( member449909584od_a_a @ Y @ ( set_Product_prod_a_a2 @ Zs3 ) )
% 0.29/0.47 => ~ ( P2 @ Y ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % split_list_last_prop_iff
% 0.29/0.47 thf(fact_266_in__set__conv__decomp__first,axiom,
% 0.29/0.47 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( member449909584od_a_a @ X3 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 0.29/0.47 = ( ? [Ys: list_P1467822637od_a_a,Zs3: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( Xs2
% 0.29/0.47 = ( append1574001858od_a_a @ Ys @ ( cons_P1921020637od_a_a @ X3 @ Zs3 ) ) )
% 0.29/0.47 & ~ ( member449909584od_a_a @ X3 @ ( set_Product_prod_a_a2 @ Ys ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % in_set_conv_decomp_first
% 0.29/0.47 thf(fact_267_in__set__conv__decomp__last,axiom,
% 0.29/0.47 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( member449909584od_a_a @ X3 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 0.29/0.47 = ( ? [Ys: list_P1467822637od_a_a,Zs3: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( Xs2
% 0.29/0.47 = ( append1574001858od_a_a @ Ys @ ( cons_P1921020637od_a_a @ X3 @ Zs3 ) ) )
% 0.29/0.47 & ~ ( member449909584od_a_a @ X3 @ ( set_Product_prod_a_a2 @ Zs3 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % in_set_conv_decomp_last
% 0.29/0.47 thf(fact_268_split__list__first__propE,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a,P2: product_prod_a_a > $o] :
% 0.29/0.47 ( ? [X5: product_prod_a_a] :
% 0.29/0.47 ( ( member449909584od_a_a @ X5 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 0.29/0.47 & ( P2 @ X5 ) )
% 0.29/0.47 => ~ ! [Ys4: list_P1467822637od_a_a,X4: product_prod_a_a] :
% 0.29/0.47 ( ? [Zs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( Xs2
% 0.29/0.47 = ( append1574001858od_a_a @ Ys4 @ ( cons_P1921020637od_a_a @ X4 @ Zs2 ) ) )
% 0.29/0.47 => ( ( P2 @ X4 )
% 0.29/0.47 => ~ ! [Xa: product_prod_a_a] :
% 0.29/0.47 ( ( member449909584od_a_a @ Xa @ ( set_Product_prod_a_a2 @ Ys4 ) )
% 0.29/0.47 => ~ ( P2 @ Xa ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % split_list_first_propE
% 0.29/0.47 thf(fact_269_split__list__last__propE,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a,P2: product_prod_a_a > $o] :
% 0.29/0.47 ( ? [X5: product_prod_a_a] :
% 0.29/0.47 ( ( member449909584od_a_a @ X5 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 0.29/0.47 & ( P2 @ X5 ) )
% 0.29/0.47 => ~ ! [Ys4: list_P1467822637od_a_a,X4: product_prod_a_a,Zs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( Xs2
% 0.29/0.47 = ( append1574001858od_a_a @ Ys4 @ ( cons_P1921020637od_a_a @ X4 @ Zs2 ) ) )
% 0.29/0.47 => ( ( P2 @ X4 )
% 0.29/0.47 => ~ ! [Xa: product_prod_a_a] :
% 0.29/0.47 ( ( member449909584od_a_a @ Xa @ ( set_Product_prod_a_a2 @ Zs2 ) )
% 0.29/0.47 => ~ ( P2 @ Xa ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % split_list_last_propE
% 0.29/0.47 thf(fact_270_split__list__first__prop,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a,P2: product_prod_a_a > $o] :
% 0.29/0.47 ( ? [X5: product_prod_a_a] :
% 0.29/0.47 ( ( member449909584od_a_a @ X5 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 0.29/0.47 & ( P2 @ X5 ) )
% 0.29/0.47 => ? [Ys4: list_P1467822637od_a_a,X4: product_prod_a_a] :
% 0.29/0.47 ( ? [Zs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( Xs2
% 0.29/0.47 = ( append1574001858od_a_a @ Ys4 @ ( cons_P1921020637od_a_a @ X4 @ Zs2 ) ) )
% 0.29/0.47 & ( P2 @ X4 )
% 0.29/0.47 & ! [Xa: product_prod_a_a] :
% 0.29/0.47 ( ( member449909584od_a_a @ Xa @ ( set_Product_prod_a_a2 @ Ys4 ) )
% 0.29/0.47 => ~ ( P2 @ Xa ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % split_list_first_prop
% 0.29/0.47 thf(fact_271_split__list__last__prop,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a,P2: product_prod_a_a > $o] :
% 0.29/0.47 ( ? [X5: product_prod_a_a] :
% 0.29/0.47 ( ( member449909584od_a_a @ X5 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 0.29/0.47 & ( P2 @ X5 ) )
% 0.29/0.47 => ? [Ys4: list_P1467822637od_a_a,X4: product_prod_a_a,Zs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( Xs2
% 0.29/0.47 = ( append1574001858od_a_a @ Ys4 @ ( cons_P1921020637od_a_a @ X4 @ Zs2 ) ) )
% 0.29/0.47 & ( P2 @ X4 )
% 0.29/0.47 & ! [Xa: product_prod_a_a] :
% 0.29/0.47 ( ( member449909584od_a_a @ Xa @ ( set_Product_prod_a_a2 @ Zs2 ) )
% 0.29/0.47 => ~ ( P2 @ Xa ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % split_list_last_prop
% 0.29/0.47 thf(fact_272_in__set__conv__decomp,axiom,
% 0.29/0.47 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( member449909584od_a_a @ X3 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 0.29/0.47 = ( ? [Ys: list_P1467822637od_a_a,Zs3: list_P1467822637od_a_a] :
% 0.29/0.47 ( Xs2
% 0.29/0.47 = ( append1574001858od_a_a @ Ys @ ( cons_P1921020637od_a_a @ X3 @ Zs3 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % in_set_conv_decomp
% 0.29/0.47 thf(fact_273_append__Cons__eq__iff,axiom,
% 0.29/0.47 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Xs5: list_P1467822637od_a_a,Ys5: list_P1467822637od_a_a] :
% 0.29/0.47 ( ~ ( member449909584od_a_a @ X3 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 0.29/0.47 => ( ~ ( member449909584od_a_a @ X3 @ ( set_Product_prod_a_a2 @ Ys2 ) )
% 0.29/0.47 => ( ( ( append1574001858od_a_a @ Xs2 @ ( cons_P1921020637od_a_a @ X3 @ Ys2 ) )
% 0.29/0.47 = ( append1574001858od_a_a @ Xs5 @ ( cons_P1921020637od_a_a @ X3 @ Ys5 ) ) )
% 0.29/0.47 = ( ( Xs2 = Xs5 )
% 0.29/0.47 & ( Ys2 = Ys5 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % append_Cons_eq_iff
% 0.29/0.47 thf(fact_274_split__list__propE,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a,P2: product_prod_a_a > $o] :
% 0.29/0.47 ( ? [X5: product_prod_a_a] :
% 0.29/0.47 ( ( member449909584od_a_a @ X5 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 0.29/0.47 & ( P2 @ X5 ) )
% 0.29/0.47 => ~ ! [Ys4: list_P1467822637od_a_a,X4: product_prod_a_a] :
% 0.29/0.47 ( ? [Zs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( Xs2
% 0.29/0.47 = ( append1574001858od_a_a @ Ys4 @ ( cons_P1921020637od_a_a @ X4 @ Zs2 ) ) )
% 0.29/0.47 => ~ ( P2 @ X4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % split_list_propE
% 0.29/0.47 thf(fact_275_split__list__first,axiom,
% 0.29/0.47 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( member449909584od_a_a @ X3 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 0.29/0.47 => ? [Ys4: list_P1467822637od_a_a,Zs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( Xs2
% 0.29/0.47 = ( append1574001858od_a_a @ Ys4 @ ( cons_P1921020637od_a_a @ X3 @ Zs2 ) ) )
% 0.29/0.47 & ~ ( member449909584od_a_a @ X3 @ ( set_Product_prod_a_a2 @ Ys4 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % split_list_first
% 0.29/0.47 thf(fact_276_split__list__prop,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a,P2: product_prod_a_a > $o] :
% 0.29/0.47 ( ? [X5: product_prod_a_a] :
% 0.29/0.47 ( ( member449909584od_a_a @ X5 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 0.29/0.47 & ( P2 @ X5 ) )
% 0.29/0.47 => ? [Ys4: list_P1467822637od_a_a,X4: product_prod_a_a] :
% 0.29/0.47 ( ? [Zs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( Xs2
% 0.29/0.47 = ( append1574001858od_a_a @ Ys4 @ ( cons_P1921020637od_a_a @ X4 @ Zs2 ) ) )
% 0.29/0.47 & ( P2 @ X4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % split_list_prop
% 0.29/0.47 thf(fact_277_split__list__last,axiom,
% 0.29/0.47 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( member449909584od_a_a @ X3 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 0.29/0.47 => ? [Ys4: list_P1467822637od_a_a,Zs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( Xs2
% 0.29/0.47 = ( append1574001858od_a_a @ Ys4 @ ( cons_P1921020637od_a_a @ X3 @ Zs2 ) ) )
% 0.29/0.47 & ~ ( member449909584od_a_a @ X3 @ ( set_Product_prod_a_a2 @ Zs2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % split_list_last
% 0.29/0.47 thf(fact_278_split__list,axiom,
% 0.29/0.47 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( member449909584od_a_a @ X3 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 0.29/0.47 => ? [Ys4: list_P1467822637od_a_a,Zs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( Xs2
% 0.29/0.47 = ( append1574001858od_a_a @ Ys4 @ ( cons_P1921020637od_a_a @ X3 @ Zs2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % split_list
% 0.29/0.47 thf(fact_279_rev__nonempty__induct,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a,P2: list_P1467822637od_a_a > $o] :
% 0.29/0.47 ( ( Xs2 != nil_Product_prod_a_a )
% 0.29/0.47 => ( ! [X4: product_prod_a_a] : ( P2 @ ( cons_P1921020637od_a_a @ X4 @ nil_Product_prod_a_a ) )
% 0.29/0.47 => ( ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( Xs4 != nil_Product_prod_a_a )
% 0.29/0.47 => ( ( P2 @ Xs4 )
% 0.29/0.47 => ( P2 @ ( append1574001858od_a_a @ Xs4 @ ( cons_P1921020637od_a_a @ X4 @ nil_Product_prod_a_a ) ) ) ) )
% 0.29/0.47 => ( P2 @ Xs2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % rev_nonempty_induct
% 0.29/0.47 thf(fact_280_append__eq__Cons__conv,axiom,
% 0.29/0.47 ! [Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a,X3: product_prod_a_a,Xs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( ( append1574001858od_a_a @ Ys2 @ Zs )
% 0.29/0.47 = ( cons_P1921020637od_a_a @ X3 @ Xs2 ) )
% 0.29/0.47 = ( ( ( Ys2 = nil_Product_prod_a_a )
% 0.29/0.47 & ( Zs
% 0.29/0.47 = ( cons_P1921020637od_a_a @ X3 @ Xs2 ) ) )
% 0.29/0.47 | ? [Ys6: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( Ys2
% 0.29/0.47 = ( cons_P1921020637od_a_a @ X3 @ Ys6 ) )
% 0.29/0.47 & ( ( append1574001858od_a_a @ Ys6 @ Zs )
% 0.29/0.47 = Xs2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % append_eq_Cons_conv
% 0.29/0.47 thf(fact_281_Cons__eq__append__conv,axiom,
% 0.29/0.47 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( ( cons_P1921020637od_a_a @ X3 @ Xs2 )
% 0.29/0.47 = ( append1574001858od_a_a @ Ys2 @ Zs ) )
% 0.29/0.47 = ( ( ( Ys2 = nil_Product_prod_a_a )
% 0.29/0.47 & ( ( cons_P1921020637od_a_a @ X3 @ Xs2 )
% 0.29/0.47 = Zs ) )
% 0.29/0.47 | ? [Ys6: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( ( cons_P1921020637od_a_a @ X3 @ Ys6 )
% 0.29/0.47 = Ys2 )
% 0.29/0.47 & ( Xs2
% 0.29/0.47 = ( append1574001858od_a_a @ Ys6 @ Zs ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Cons_eq_append_conv
% 0.29/0.47 thf(fact_282_rev__exhaust,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( Xs2 != nil_Product_prod_a_a )
% 0.29/0.47 => ~ ! [Ys4: list_P1467822637od_a_a,Y4: product_prod_a_a] :
% 0.29/0.47 ( Xs2
% 0.29/0.47 != ( append1574001858od_a_a @ Ys4 @ ( cons_P1921020637od_a_a @ Y4 @ nil_Product_prod_a_a ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % rev_exhaust
% 0.29/0.47 thf(fact_283_rev__induct,axiom,
% 0.29/0.47 ! [P2: list_P1467822637od_a_a > $o,Xs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( P2 @ nil_Product_prod_a_a )
% 0.29/0.47 => ( ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( P2 @ Xs4 )
% 0.29/0.47 => ( P2 @ ( append1574001858od_a_a @ Xs4 @ ( cons_P1921020637od_a_a @ X4 @ nil_Product_prod_a_a ) ) ) )
% 0.29/0.47 => ( P2 @ Xs2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % rev_induct
% 0.29/0.47 thf(fact_284_shuffles_Ocases,axiom,
% 0.29/0.47 ! [X3: produc651658087od_a_a] :
% 0.29/0.47 ( ! [Ys4: list_P1467822637od_a_a] :
% 0.29/0.47 ( X3
% 0.29/0.47 != ( produc85179863od_a_a @ nil_Product_prod_a_a @ Ys4 ) )
% 0.29/0.47 => ( ! [Xs4: list_P1467822637od_a_a] :
% 0.29/0.47 ( X3
% 0.29/0.47 != ( produc85179863od_a_a @ Xs4 @ nil_Product_prod_a_a ) )
% 0.29/0.47 => ~ ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a,Y4: product_prod_a_a,Ys4: list_P1467822637od_a_a] :
% 0.29/0.47 ( X3
% 0.29/0.47 != ( produc85179863od_a_a @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) @ ( cons_P1921020637od_a_a @ Y4 @ Ys4 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % shuffles.cases
% 0.29/0.47 thf(fact_285_sd__path_Oinduct,axiom,
% 0.29/0.47 ! [P2: product_prod_a_a > a > list_P1467822637od_a_a > $o,A0: product_prod_a_a,A1: a,A22: list_P1467822637od_a_a] :
% 0.29/0.47 ( ! [Uu: product_prod_a_a,Uv: a] : ( P2 @ Uu @ Uv @ nil_Product_prod_a_a )
% 0.29/0.47 => ( ! [U2: a,V: a,W: a,E2: product_prod_a_a,Es: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( P2 @ ( product_Pair_a_a @ U2 @ V ) @ W @ Es )
% 0.29/0.47 => ( P2 @ ( product_Pair_a_a @ U2 @ V ) @ W @ ( cons_P1921020637od_a_a @ E2 @ Es ) ) )
% 0.29/0.47 => ( P2 @ A0 @ A1 @ A22 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % sd_path.induct
% 0.29/0.47 thf(fact_286_co__path_Oinduct,axiom,
% 0.29/0.47 ! [P2: product_prod_a_a > a > list_P1467822637od_a_a > $o,A0: product_prod_a_a,A1: a,A22: list_P1467822637od_a_a] :
% 0.29/0.47 ( ! [Uu: product_prod_a_a,Uv: a] : ( P2 @ Uu @ Uv @ nil_Product_prod_a_a )
% 0.29/0.47 => ( ! [Uw: product_prod_a_a,Ux: a,E2: product_prod_a_a] : ( P2 @ Uw @ Ux @ ( cons_P1921020637od_a_a @ E2 @ nil_Product_prod_a_a ) )
% 0.29/0.47 => ( ! [U2: a,V: a,W: a,E1: product_prod_a_a,E22: product_prod_a_a,Es: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( ( ( E1
% 0.29/0.47 = ( product_Pair_a_a @ U2 @ W ) )
% 0.29/0.47 & ( E22
% 0.29/0.47 = ( product_Pair_a_a @ W @ V ) ) )
% 0.29/0.47 => ( P2 @ ( product_Pair_a_a @ U2 @ V ) @ W @ Es ) )
% 0.29/0.47 => ( ( ~ ( ( E1
% 0.29/0.47 = ( product_Pair_a_a @ U2 @ W ) )
% 0.29/0.47 & ( E22
% 0.29/0.47 = ( product_Pair_a_a @ W @ V ) ) )
% 0.29/0.47 => ( ( ( E1
% 0.29/0.47 = ( product_Pair_a_a @ V @ W ) )
% 0.29/0.47 & ( E22
% 0.29/0.47 = ( product_Pair_a_a @ W @ U2 ) ) )
% 0.29/0.47 => ( P2 @ ( product_Pair_a_a @ U2 @ V ) @ W @ Es ) ) )
% 0.29/0.47 => ( ( ~ ( ( E1
% 0.29/0.47 = ( product_Pair_a_a @ U2 @ W ) )
% 0.29/0.47 & ( E22
% 0.29/0.47 = ( product_Pair_a_a @ W @ V ) ) )
% 0.29/0.47 => ( ~ ( ( E1
% 0.29/0.47 = ( product_Pair_a_a @ V @ W ) )
% 0.29/0.47 & ( E22
% 0.29/0.47 = ( product_Pair_a_a @ W @ U2 ) ) )
% 0.29/0.47 => ( P2 @ ( product_Pair_a_a @ U2 @ V ) @ W @ ( cons_P1921020637od_a_a @ E22 @ Es ) ) ) )
% 0.29/0.47 => ( P2 @ ( product_Pair_a_a @ U2 @ V ) @ W @ ( cons_P1921020637od_a_a @ E1 @ ( cons_P1921020637od_a_a @ E22 @ Es ) ) ) ) ) )
% 0.29/0.47 => ( P2 @ A0 @ A1 @ A22 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % co_path.induct
% 0.29/0.47 thf(fact_287_sd__path_Ocases,axiom,
% 0.29/0.47 ! [X3: produc821581462od_a_a] :
% 0.29/0.47 ( ! [Uu: product_prod_a_a,Uv: a] :
% 0.29/0.47 ( X3
% 0.29/0.47 != ( produc600870406od_a_a @ Uu @ ( produc575024326od_a_a @ Uv @ nil_Product_prod_a_a ) ) )
% 0.29/0.47 => ~ ! [U2: a,V: a,W: a,E2: product_prod_a_a,Es: list_P1467822637od_a_a] :
% 0.29/0.47 ( X3
% 0.29/0.47 != ( produc600870406od_a_a @ ( product_Pair_a_a @ U2 @ V ) @ ( produc575024326od_a_a @ W @ ( cons_P1921020637od_a_a @ E2 @ Es ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % sd_path.cases
% 0.29/0.47 thf(fact_288_co__path_Ocases,axiom,
% 0.29/0.47 ! [X3: produc821581462od_a_a] :
% 0.29/0.47 ( ! [Uu: product_prod_a_a,Uv: a] :
% 0.29/0.47 ( X3
% 0.29/0.47 != ( produc600870406od_a_a @ Uu @ ( produc575024326od_a_a @ Uv @ nil_Product_prod_a_a ) ) )
% 0.29/0.47 => ( ! [Uw: product_prod_a_a,Ux: a,E2: product_prod_a_a] :
% 0.29/0.47 ( X3
% 0.29/0.47 != ( produc600870406od_a_a @ Uw @ ( produc575024326od_a_a @ Ux @ ( cons_P1921020637od_a_a @ E2 @ nil_Product_prod_a_a ) ) ) )
% 0.29/0.47 => ~ ! [U2: a,V: a,W: a,E1: product_prod_a_a,E22: product_prod_a_a,Es: list_P1467822637od_a_a] :
% 0.29/0.47 ( X3
% 0.29/0.47 != ( produc600870406od_a_a @ ( product_Pair_a_a @ U2 @ V ) @ ( produc575024326od_a_a @ W @ ( cons_P1921020637od_a_a @ E1 @ ( cons_P1921020637od_a_a @ E22 @ Es ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % co_path.cases
% 0.29/0.47 thf(fact_289_lex__append__leftI,axiom,
% 0.29/0.47 ! [Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a,Xs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ Ys2 @ Zs ) @ ( lex_Product_prod_a_a @ R ) )
% 0.29/0.47 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ Xs2 @ Ys2 ) @ ( append1574001858od_a_a @ Xs2 @ Zs ) ) @ ( lex_Product_prod_a_a @ R ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % lex_append_leftI
% 0.29/0.47 thf(fact_290_progressing__single,axiom,
% 0.29/0.47 ! [E: product_prod_a_a] : ( kurato1072996284sing_a @ ( cons_P1921020637od_a_a @ E @ nil_Product_prod_a_a ) ) ).
% 0.29/0.47
% 0.29/0.47 % progressing_single
% 0.29/0.47 thf(fact_291_lexord__partial__trans,axiom,
% 0.29/0.47 ! [Xs2: list_a,R: set_Product_prod_a_a,Ys2: list_a,Zs: list_a] :
% 0.29/0.47 ( ! [X4: a,Y4: a,Z2: a] :
% 0.29/0.47 ( ( member_a2 @ X4 @ ( set_a2 @ Xs2 ) )
% 0.29/0.47 => ( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ R )
% 0.29/0.47 => ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y4 @ Z2 ) @ R )
% 0.29/0.47 => ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Z2 ) @ R ) ) ) )
% 0.29/0.47 => ( ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ Ys2 ) @ ( lexord_a @ R ) )
% 0.29/0.47 => ( ( member1250517072list_a @ ( produc1448356631list_a @ Ys2 @ Zs ) @ ( lexord_a @ R ) )
% 0.29/0.47 => ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ Zs ) @ ( lexord_a @ R ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % lexord_partial_trans
% 0.29/0.47 thf(fact_292_lexord__sufE,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Qs: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 0.29/0.47 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ Xs2 @ Zs ) @ ( append1574001858od_a_a @ Ys2 @ Qs ) ) @ ( lexord673907738od_a_a @ R ) )
% 0.29/0.47 => ( ( Xs2 != Ys2 )
% 0.29/0.47 => ( ( ( size_s642698393od_a_a @ Xs2 )
% 0.29/0.47 = ( size_s642698393od_a_a @ Ys2 ) )
% 0.29/0.47 => ( ( ( size_s642698393od_a_a @ Zs )
% 0.29/0.47 = ( size_s642698393od_a_a @ Qs ) )
% 0.29/0.47 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ Ys2 ) @ ( lexord673907738od_a_a @ R ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % lexord_sufE
% 0.29/0.47 thf(fact_293_subset__eq__mset__impl_Ocases,axiom,
% 0.29/0.47 ! [X3: produc651658087od_a_a] :
% 0.29/0.47 ( ! [Ys4: list_P1467822637od_a_a] :
% 0.29/0.47 ( X3
% 0.29/0.47 != ( produc85179863od_a_a @ nil_Product_prod_a_a @ Ys4 ) )
% 0.29/0.47 => ~ ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a,Ys4: list_P1467822637od_a_a] :
% 0.29/0.47 ( X3
% 0.29/0.47 != ( produc85179863od_a_a @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) @ Ys4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % subset_eq_mset_impl.cases
% 0.29/0.47 thf(fact_294_asym_Oinducts,axiom,
% 0.29/0.47 ! [X3: set_Product_prod_a_a,P2: set_Product_prod_a_a > $o] :
% 0.29/0.47 ( ( asym_a @ X3 )
% 0.29/0.47 => ( ! [R3: set_Product_prod_a_a] :
% 0.29/0.47 ( ! [A6: a,B4: a] :
% 0.29/0.47 ( ( member449909584od_a_a @ ( product_Pair_a_a @ A6 @ B4 ) @ R3 )
% 0.29/0.47 => ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B4 @ A6 ) @ R3 ) )
% 0.29/0.47 => ( P2 @ R3 ) )
% 0.29/0.47 => ( P2 @ X3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % asym.inducts
% 0.29/0.47 thf(fact_295_asym_Ointros,axiom,
% 0.29/0.47 ! [R2: set_Product_prod_a_a] :
% 0.29/0.47 ( ! [A3: a,B3: a] :
% 0.29/0.47 ( ( member449909584od_a_a @ ( product_Pair_a_a @ A3 @ B3 ) @ R2 )
% 0.29/0.47 => ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B3 @ A3 ) @ R2 ) )
% 0.29/0.47 => ( asym_a @ R2 ) ) ).
% 0.29/0.47
% 0.29/0.47 % asym.intros
% 0.29/0.47 thf(fact_296_asym_Osimps,axiom,
% 0.29/0.47 ( asym_a
% 0.29/0.47 = ( ^ [A5: set_Product_prod_a_a] :
% 0.29/0.47 ? [R4: set_Product_prod_a_a] :
% 0.29/0.47 ( ( A5 = R4 )
% 0.29/0.47 & ! [X: a,Y: a] :
% 0.29/0.47 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ R4 )
% 0.29/0.47 => ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ R4 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % asym.simps
% 0.29/0.47 thf(fact_297_asym_Ocases,axiom,
% 0.29/0.47 ! [A: set_Product_prod_a_a] :
% 0.29/0.47 ( ( asym_a @ A )
% 0.29/0.47 => ! [A6: a,B4: a] :
% 0.29/0.47 ( ( member449909584od_a_a @ ( product_Pair_a_a @ A6 @ B4 ) @ A )
% 0.29/0.47 => ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B4 @ A6 ) @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % asym.cases
% 0.29/0.47 thf(fact_298_asym__iff,axiom,
% 0.29/0.47 ( asym_a
% 0.29/0.47 = ( ^ [R4: set_Product_prod_a_a] :
% 0.29/0.47 ! [X: a,Y: a] :
% 0.29/0.47 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ R4 )
% 0.29/0.47 => ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ R4 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % asym_iff
% 0.29/0.47 thf(fact_299_irreflI,axiom,
% 0.29/0.47 ! [R2: set_Product_prod_a_a] :
% 0.29/0.47 ( ! [A3: a] :
% 0.29/0.47 ~ ( member449909584od_a_a @ ( product_Pair_a_a @ A3 @ A3 ) @ R2 )
% 0.29/0.47 => ( irrefl_a @ R2 ) ) ).
% 0.29/0.47
% 0.29/0.47 % irreflI
% 0.29/0.47 thf(fact_300_irrefl__def,axiom,
% 0.29/0.47 ( irrefl_a
% 0.29/0.47 = ( ^ [R5: set_Product_prod_a_a] :
% 0.29/0.47 ! [A5: a] :
% 0.29/0.47 ~ ( member449909584od_a_a @ ( product_Pair_a_a @ A5 @ A5 ) @ R5 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % irrefl_def
% 0.29/0.47 thf(fact_301_asymD,axiom,
% 0.29/0.47 ! [R2: set_Product_prod_a_a,X3: a,Y3: a] :
% 0.29/0.47 ( ( asym_a @ R2 )
% 0.29/0.47 => ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R2 )
% 0.29/0.47 => ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y3 @ X3 ) @ R2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % asymD
% 0.29/0.47 thf(fact_302_inverse__permutation__of__list_Ocases,axiom,
% 0.29/0.47 ! [X3: produc657167928_a_a_a] :
% 0.29/0.47 ( ! [X4: a] :
% 0.29/0.47 ( X3
% 0.29/0.47 != ( produc998622632_a_a_a @ nil_Product_prod_a_a @ X4 ) )
% 0.29/0.47 => ~ ! [Y4: a,X6: a,Xs4: list_P1467822637od_a_a,X4: a] :
% 0.29/0.47 ( X3
% 0.29/0.47 != ( produc998622632_a_a_a @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y4 @ X6 ) @ Xs4 ) @ X4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % inverse_permutation_of_list.cases
% 0.29/0.47 thf(fact_303_inverse__permutation__of__list_Oinduct,axiom,
% 0.29/0.47 ! [P2: list_P1467822637od_a_a > a > $o,A0: list_P1467822637od_a_a,A1: a] :
% 0.29/0.47 ( ! [X_1: a] : ( P2 @ nil_Product_prod_a_a @ X_1 )
% 0.29/0.47 => ( ! [Y4: a,X6: a,Xs4: list_P1467822637od_a_a,X4: a] :
% 0.29/0.47 ( ( ( X4 != X6 )
% 0.29/0.47 => ( P2 @ Xs4 @ X4 ) )
% 0.29/0.47 => ( P2 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y4 @ X6 ) @ Xs4 ) @ X4 ) )
% 0.29/0.47 => ( P2 @ A0 @ A1 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % inverse_permutation_of_list.induct
% 0.29/0.47 thf(fact_304_sd__path_Osimps_I2_J,axiom,
% 0.29/0.47 ! [U: a,V2: a,W2: a,E: product_prod_a_a,Es2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( pair_sd_path_a @ ( product_Pair_a_a @ U @ V2 ) @ W2 @ ( cons_P1921020637od_a_a @ E @ Es2 ) )
% 0.29/0.47 = ( append1574001858od_a_a
% 0.29/0.47 @ ( if_lis321365491od_a_a
% 0.29/0.47 @ ( E
% 0.29/0.47 = ( product_Pair_a_a @ U @ V2 ) )
% 0.29/0.47 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ U @ W2 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ W2 @ V2 ) @ nil_Product_prod_a_a ) )
% 0.29/0.47 @ ( if_lis321365491od_a_a
% 0.29/0.47 @ ( E
% 0.29/0.47 = ( product_Pair_a_a @ V2 @ U ) )
% 0.29/0.47 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ V2 @ W2 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ W2 @ U ) @ nil_Product_prod_a_a ) )
% 0.29/0.47 @ ( cons_P1921020637od_a_a @ E @ nil_Product_prod_a_a ) ) )
% 0.29/0.47 @ ( pair_sd_path_a @ ( product_Pair_a_a @ U @ V2 ) @ W2 @ Es2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % sd_path.simps(2)
% 0.29/0.47 thf(fact_305_sd__path__id,axiom,
% 0.29/0.47 ! [X3: a,Y3: a,P3: list_P1467822637od_a_a,W2: a] :
% 0.29/0.47 ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ ( set_Product_prod_a_a2 @ P3 ) )
% 0.29/0.47 => ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y3 @ X3 ) @ ( set_Product_prod_a_a2 @ P3 ) )
% 0.29/0.47 => ( ( pair_sd_path_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ W2 @ P3 )
% 0.29/0.47 = P3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % sd_path_id
% 0.29/0.47 thf(fact_306_sd__path_Oelims,axiom,
% 0.29/0.47 ! [X3: product_prod_a_a,Xa2: a,Xb: list_P1467822637od_a_a,Y3: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( ( pair_sd_path_a @ X3 @ Xa2 @ Xb )
% 0.29/0.47 = Y3 )
% 0.29/0.47 => ( ( ( Xb = nil_Product_prod_a_a )
% 0.29/0.47 => ( Y3 != nil_Product_prod_a_a ) )
% 0.29/0.47 => ~ ! [U2: a,V: a] :
% 0.29/0.47 ( ( X3
% 0.29/0.47 = ( product_Pair_a_a @ U2 @ V ) )
% 0.29/0.47 => ! [E2: product_prod_a_a,Es: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( Xb
% 0.29/0.47 = ( cons_P1921020637od_a_a @ E2 @ Es ) )
% 0.29/0.47 => ( Y3
% 0.29/0.47 != ( append1574001858od_a_a
% 0.29/0.47 @ ( if_lis321365491od_a_a
% 0.29/0.47 @ ( E2
% 0.29/0.47 = ( product_Pair_a_a @ U2 @ V ) )
% 0.29/0.47 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ U2 @ Xa2 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Xa2 @ V ) @ nil_Product_prod_a_a ) )
% 0.29/0.47 @ ( if_lis321365491od_a_a
% 0.29/0.47 @ ( E2
% 0.29/0.47 = ( product_Pair_a_a @ V @ U2 ) )
% 0.29/0.47 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ V @ Xa2 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Xa2 @ U2 ) @ nil_Product_prod_a_a ) )
% 0.29/0.47 @ ( cons_P1921020637od_a_a @ E2 @ nil_Product_prod_a_a ) ) )
% 0.29/0.47 @ ( pair_sd_path_a @ ( product_Pair_a_a @ U2 @ V ) @ Xa2 @ Es ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % sd_path.elims
% 0.29/0.47 thf(fact_307_the__elem__set,axiom,
% 0.29/0.47 ! [X3: product_prod_a_a] :
% 0.29/0.47 ( ( the_el1640649244od_a_a @ ( set_Product_prod_a_a2 @ ( cons_P1921020637od_a_a @ X3 @ nil_Product_prod_a_a ) ) )
% 0.29/0.47 = X3 ) ).
% 0.29/0.47
% 0.29/0.47 % the_elem_set
% 0.29/0.47 thf(fact_308_sd__path_Opelims,axiom,
% 0.29/0.47 ! [X3: product_prod_a_a,Xa2: a,Xb: list_P1467822637od_a_a,Y3: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( ( pair_sd_path_a @ X3 @ Xa2 @ Xb )
% 0.29/0.47 = Y3 )
% 0.29/0.47 => ( ( accp_P1029463583od_a_a @ pair_sd_path_rel_a @ ( produc600870406od_a_a @ X3 @ ( produc575024326od_a_a @ Xa2 @ Xb ) ) )
% 0.29/0.47 => ( ( ( Xb = nil_Product_prod_a_a )
% 0.29/0.47 => ( ( Y3 = nil_Product_prod_a_a )
% 0.29/0.47 => ~ ( accp_P1029463583od_a_a @ pair_sd_path_rel_a @ ( produc600870406od_a_a @ X3 @ ( produc575024326od_a_a @ Xa2 @ nil_Product_prod_a_a ) ) ) ) )
% 0.29/0.47 => ~ ! [U2: a,V: a] :
% 0.29/0.47 ( ( X3
% 0.29/0.47 = ( product_Pair_a_a @ U2 @ V ) )
% 0.29/0.47 => ! [E2: product_prod_a_a,Es: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( Xb
% 0.29/0.47 = ( cons_P1921020637od_a_a @ E2 @ Es ) )
% 0.29/0.47 => ( ( Y3
% 0.29/0.47 = ( append1574001858od_a_a
% 0.29/0.47 @ ( if_lis321365491od_a_a
% 0.29/0.47 @ ( E2
% 0.29/0.47 = ( product_Pair_a_a @ U2 @ V ) )
% 0.29/0.47 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ U2 @ Xa2 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Xa2 @ V ) @ nil_Product_prod_a_a ) )
% 0.29/0.47 @ ( if_lis321365491od_a_a
% 0.29/0.47 @ ( E2
% 0.29/0.47 = ( product_Pair_a_a @ V @ U2 ) )
% 0.29/0.47 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ V @ Xa2 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Xa2 @ U2 ) @ nil_Product_prod_a_a ) )
% 0.29/0.47 @ ( cons_P1921020637od_a_a @ E2 @ nil_Product_prod_a_a ) ) )
% 0.29/0.47 @ ( pair_sd_path_a @ ( product_Pair_a_a @ U2 @ V ) @ Xa2 @ Es ) ) )
% 0.29/0.47 => ~ ( accp_P1029463583od_a_a @ pair_sd_path_rel_a @ ( produc600870406od_a_a @ ( product_Pair_a_a @ U2 @ V ) @ ( produc575024326od_a_a @ Xa2 @ ( cons_P1921020637od_a_a @ E2 @ Es ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % sd_path.pelims
% 0.29/0.47 thf(fact_309_list__exhaust2,axiom,
% 0.29/0.47 ! [Y3: list_P1467822637od_a_a,Ya: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( ( Y3 = nil_Product_prod_a_a )
% 0.29/0.47 => ( Ya != nil_Product_prod_a_a ) )
% 0.29/0.47 => ( ( ( Y3 = nil_Product_prod_a_a )
% 0.29/0.47 => ! [X212: product_prod_a_a,X222: list_P1467822637od_a_a] :
% 0.29/0.47 ( Ya
% 0.29/0.47 != ( cons_P1921020637od_a_a @ X212 @ X222 ) ) )
% 0.29/0.47 => ( ( ? [X212: product_prod_a_a,X222: list_P1467822637od_a_a] :
% 0.29/0.47 ( Y3
% 0.29/0.47 = ( cons_P1921020637od_a_a @ X212 @ X222 ) )
% 0.29/0.47 => ( Ya != nil_Product_prod_a_a ) )
% 0.29/0.47 => ~ ( ? [X212: product_prod_a_a,X222: list_P1467822637od_a_a] :
% 0.29/0.47 ( Y3
% 0.29/0.47 = ( cons_P1921020637od_a_a @ X212 @ X222 ) )
% 0.29/0.47 => ! [X21a: product_prod_a_a,X22a: list_P1467822637od_a_a] :
% 0.29/0.47 ( Ya
% 0.29/0.47 != ( cons_P1921020637od_a_a @ X21a @ X22a ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % list_exhaust2
% 0.29/0.47 thf(fact_310_list__exhaust__NSC,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( Xs2 != nil_Product_prod_a_a )
% 0.29/0.47 => ( ! [X4: product_prod_a_a] :
% 0.29/0.47 ( Xs2
% 0.29/0.47 != ( cons_P1921020637od_a_a @ X4 @ nil_Product_prod_a_a ) )
% 0.29/0.47 => ~ ! [X4: product_prod_a_a,Y4: product_prod_a_a,Ys4: list_P1467822637od_a_a] :
% 0.29/0.47 ( Xs2
% 0.29/0.47 != ( cons_P1921020637od_a_a @ X4 @ ( cons_P1921020637od_a_a @ Y4 @ Ys4 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % list_exhaust_NSC
% 0.29/0.47 thf(fact_311_lenlex__append2,axiom,
% 0.29/0.47 ! [R2: set_Pr1948701895od_a_a,Us: list_P1467822637od_a_a,Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( irrefl76447196od_a_a @ R2 )
% 0.29/0.47 => ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ Us @ Xs2 ) @ ( append1574001858od_a_a @ Us @ Ys2 ) ) @ ( lenlex2038501170od_a_a @ R2 ) )
% 0.29/0.47 = ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ Ys2 ) @ ( lenlex2038501170od_a_a @ R2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % lenlex_append2
% 0.29/0.47 thf(fact_312_lenlex__irreflexive,axiom,
% 0.29/0.47 ! [R: set_Product_prod_a_a,Xs2: list_a] :
% 0.29/0.47 ( ! [X4: a] :
% 0.29/0.47 ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ X4 ) @ R )
% 0.29/0.47 => ~ ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ Xs2 ) @ ( lenlex_a @ R ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % lenlex_irreflexive
% 0.29/0.47 thf(fact_313_lenlex__append1,axiom,
% 0.29/0.47 ! [Us: list_P1467822637od_a_a,Xs2: list_P1467822637od_a_a,R2: set_Pr1948701895od_a_a,Vs: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ Us @ Xs2 ) @ ( lenlex2038501170od_a_a @ R2 ) )
% 0.29/0.47 => ( ( ( size_s642698393od_a_a @ Vs )
% 0.29/0.47 = ( size_s642698393od_a_a @ Ys2 ) )
% 0.29/0.47 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ Us @ Vs ) @ ( append1574001858od_a_a @ Xs2 @ Ys2 ) ) @ ( lenlex2038501170od_a_a @ R2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % lenlex_append1
% 0.29/0.47 thf(fact_314_co__path_Opelims,axiom,
% 0.29/0.47 ! [X3: product_prod_a_a,Xa2: a,Xb: list_P1467822637od_a_a,Y3: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( ( pair_co_path_a @ X3 @ Xa2 @ Xb )
% 0.29/0.47 = Y3 )
% 0.29/0.47 => ( ( accp_P1029463583od_a_a @ pair_co_path_rel_a @ ( produc600870406od_a_a @ X3 @ ( produc575024326od_a_a @ Xa2 @ Xb ) ) )
% 0.29/0.47 => ( ( ( Xb = nil_Product_prod_a_a )
% 0.29/0.47 => ( ( Y3 = nil_Product_prod_a_a )
% 0.29/0.47 => ~ ( accp_P1029463583od_a_a @ pair_co_path_rel_a @ ( produc600870406od_a_a @ X3 @ ( produc575024326od_a_a @ Xa2 @ nil_Product_prod_a_a ) ) ) ) )
% 0.29/0.47 => ( ! [E2: product_prod_a_a] :
% 0.29/0.47 ( ( Xb
% 0.29/0.47 = ( cons_P1921020637od_a_a @ E2 @ nil_Product_prod_a_a ) )
% 0.29/0.47 => ( ( Y3
% 0.29/0.47 = ( cons_P1921020637od_a_a @ E2 @ nil_Product_prod_a_a ) )
% 0.29/0.47 => ~ ( accp_P1029463583od_a_a @ pair_co_path_rel_a @ ( produc600870406od_a_a @ X3 @ ( produc575024326od_a_a @ Xa2 @ ( cons_P1921020637od_a_a @ E2 @ nil_Product_prod_a_a ) ) ) ) ) )
% 0.29/0.47 => ~ ! [U2: a,V: a] :
% 0.29/0.47 ( ( X3
% 0.29/0.47 = ( product_Pair_a_a @ U2 @ V ) )
% 0.29/0.47 => ! [E1: product_prod_a_a,E22: product_prod_a_a,Es: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( Xb
% 0.29/0.47 = ( cons_P1921020637od_a_a @ E1 @ ( cons_P1921020637od_a_a @ E22 @ Es ) ) )
% 0.29/0.47 => ( ( ( ( ( E1
% 0.29/0.47 = ( product_Pair_a_a @ U2 @ Xa2 ) )
% 0.29/0.47 & ( E22
% 0.29/0.47 = ( product_Pair_a_a @ Xa2 @ V ) ) )
% 0.29/0.47 => ( Y3
% 0.29/0.47 = ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ U2 @ V ) @ ( pair_co_path_a @ ( product_Pair_a_a @ U2 @ V ) @ Xa2 @ Es ) ) ) )
% 0.29/0.47 & ( ~ ( ( E1
% 0.29/0.47 = ( product_Pair_a_a @ U2 @ Xa2 ) )
% 0.29/0.47 & ( E22
% 0.29/0.47 = ( product_Pair_a_a @ Xa2 @ V ) ) )
% 0.29/0.47 => ( ( ( ( E1
% 0.29/0.47 = ( product_Pair_a_a @ V @ Xa2 ) )
% 0.29/0.47 & ( E22
% 0.29/0.47 = ( product_Pair_a_a @ Xa2 @ U2 ) ) )
% 0.29/0.47 => ( Y3
% 0.29/0.47 = ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ V @ U2 ) @ ( pair_co_path_a @ ( product_Pair_a_a @ U2 @ V ) @ Xa2 @ Es ) ) ) )
% 0.29/0.47 & ( ~ ( ( E1
% 0.29/0.47 = ( product_Pair_a_a @ V @ Xa2 ) )
% 0.29/0.47 & ( E22
% 0.29/0.47 = ( product_Pair_a_a @ Xa2 @ U2 ) ) )
% 0.29/0.47 => ( Y3
% 0.29/0.47 = ( cons_P1921020637od_a_a @ E1 @ ( pair_co_path_a @ ( product_Pair_a_a @ U2 @ V ) @ Xa2 @ ( cons_P1921020637od_a_a @ E22 @ Es ) ) ) ) ) ) ) )
% 0.29/0.47 => ~ ( accp_P1029463583od_a_a @ pair_co_path_rel_a @ ( produc600870406od_a_a @ ( product_Pair_a_a @ U2 @ V ) @ ( produc575024326od_a_a @ Xa2 @ ( cons_P1921020637od_a_a @ E1 @ ( cons_P1921020637od_a_a @ E22 @ Es ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % co_path.pelims
% 0.29/0.47 thf(fact_315_pawalk__verts_Osimps_I1_J,axiom,
% 0.29/0.47 ! [U: product_prod_a_a] :
% 0.29/0.47 ( ( pair_p2140537249od_a_a @ U @ nil_Pr1049924845od_a_a )
% 0.29/0.47 = ( cons_P1921020637od_a_a @ U @ nil_Product_prod_a_a ) ) ).
% 0.29/0.47
% 0.29/0.47 % pawalk_verts.simps(1)
% 0.29/0.47 thf(fact_316_co__path_Osimps_I3_J,axiom,
% 0.29/0.47 ! [E12: product_prod_a_a,U: a,W2: a,E23: product_prod_a_a,V2: a,Es2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( ( ( E12
% 0.29/0.47 = ( product_Pair_a_a @ U @ W2 ) )
% 0.29/0.47 & ( E23
% 0.29/0.47 = ( product_Pair_a_a @ W2 @ V2 ) ) )
% 0.29/0.47 => ( ( pair_co_path_a @ ( product_Pair_a_a @ U @ V2 ) @ W2 @ ( cons_P1921020637od_a_a @ E12 @ ( cons_P1921020637od_a_a @ E23 @ Es2 ) ) )
% 0.29/0.47 = ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ U @ V2 ) @ ( pair_co_path_a @ ( product_Pair_a_a @ U @ V2 ) @ W2 @ Es2 ) ) ) )
% 0.29/0.47 & ( ~ ( ( E12
% 0.29/0.47 = ( product_Pair_a_a @ U @ W2 ) )
% 0.29/0.47 & ( E23
% 0.29/0.47 = ( product_Pair_a_a @ W2 @ V2 ) ) )
% 0.29/0.47 => ( ( ( ( E12
% 0.29/0.47 = ( product_Pair_a_a @ V2 @ W2 ) )
% 0.29/0.47 & ( E23
% 0.29/0.47 = ( product_Pair_a_a @ W2 @ U ) ) )
% 0.29/0.47 => ( ( pair_co_path_a @ ( product_Pair_a_a @ U @ V2 ) @ W2 @ ( cons_P1921020637od_a_a @ E12 @ ( cons_P1921020637od_a_a @ E23 @ Es2 ) ) )
% 0.29/0.47 = ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ V2 @ U ) @ ( pair_co_path_a @ ( product_Pair_a_a @ U @ V2 ) @ W2 @ Es2 ) ) ) )
% 0.29/0.47 & ( ~ ( ( E12
% 0.29/0.47 = ( product_Pair_a_a @ V2 @ W2 ) )
% 0.29/0.47 & ( E23
% 0.29/0.47 = ( product_Pair_a_a @ W2 @ U ) ) )
% 0.29/0.47 => ( ( pair_co_path_a @ ( product_Pair_a_a @ U @ V2 ) @ W2 @ ( cons_P1921020637od_a_a @ E12 @ ( cons_P1921020637od_a_a @ E23 @ Es2 ) ) )
% 0.29/0.47 = ( cons_P1921020637od_a_a @ E12 @ ( pair_co_path_a @ ( product_Pair_a_a @ U @ V2 ) @ W2 @ ( cons_P1921020637od_a_a @ E23 @ Es2 ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % co_path.simps(3)
% 0.29/0.47 thf(fact_317_co__path_Osimps_I2_J,axiom,
% 0.29/0.47 ! [Uw2: product_prod_a_a,Ux2: a,E: product_prod_a_a] :
% 0.29/0.47 ( ( pair_co_path_a @ Uw2 @ Ux2 @ ( cons_P1921020637od_a_a @ E @ nil_Product_prod_a_a ) )
% 0.29/0.47 = ( cons_P1921020637od_a_a @ E @ nil_Product_prod_a_a ) ) ).
% 0.29/0.47
% 0.29/0.47 % co_path.simps(2)
% 0.29/0.47 thf(fact_318_co__path_Oelims,axiom,
% 0.29/0.47 ! [X3: product_prod_a_a,Xa2: a,Xb: list_P1467822637od_a_a,Y3: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( ( pair_co_path_a @ X3 @ Xa2 @ Xb )
% 0.29/0.47 = Y3 )
% 0.29/0.47 => ( ( ( Xb = nil_Product_prod_a_a )
% 0.29/0.47 => ( Y3 != nil_Product_prod_a_a ) )
% 0.29/0.47 => ( ! [E2: product_prod_a_a] :
% 0.29/0.47 ( ( Xb
% 0.29/0.47 = ( cons_P1921020637od_a_a @ E2 @ nil_Product_prod_a_a ) )
% 0.29/0.47 => ( Y3
% 0.29/0.47 != ( cons_P1921020637od_a_a @ E2 @ nil_Product_prod_a_a ) ) )
% 0.29/0.47 => ~ ! [U2: a,V: a] :
% 0.29/0.47 ( ( X3
% 0.29/0.47 = ( product_Pair_a_a @ U2 @ V ) )
% 0.29/0.47 => ! [E1: product_prod_a_a,E22: product_prod_a_a,Es: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( Xb
% 0.29/0.47 = ( cons_P1921020637od_a_a @ E1 @ ( cons_P1921020637od_a_a @ E22 @ Es ) ) )
% 0.29/0.47 => ~ ( ( ( ( E1
% 0.29/0.47 = ( product_Pair_a_a @ U2 @ Xa2 ) )
% 0.29/0.47 & ( E22
% 0.29/0.47 = ( product_Pair_a_a @ Xa2 @ V ) ) )
% 0.29/0.47 => ( Y3
% 0.29/0.47 = ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ U2 @ V ) @ ( pair_co_path_a @ ( product_Pair_a_a @ U2 @ V ) @ Xa2 @ Es ) ) ) )
% 0.29/0.47 & ( ~ ( ( E1
% 0.29/0.47 = ( product_Pair_a_a @ U2 @ Xa2 ) )
% 0.29/0.47 & ( E22
% 0.29/0.47 = ( product_Pair_a_a @ Xa2 @ V ) ) )
% 0.29/0.47 => ( ( ( ( E1
% 0.29/0.47 = ( product_Pair_a_a @ V @ Xa2 ) )
% 0.29/0.47 & ( E22
% 0.29/0.47 = ( product_Pair_a_a @ Xa2 @ U2 ) ) )
% 0.29/0.47 => ( Y3
% 0.29/0.47 = ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ V @ U2 ) @ ( pair_co_path_a @ ( product_Pair_a_a @ U2 @ V ) @ Xa2 @ Es ) ) ) )
% 0.29/0.47 & ( ~ ( ( E1
% 0.29/0.47 = ( product_Pair_a_a @ V @ Xa2 ) )
% 0.29/0.47 & ( E22
% 0.29/0.47 = ( product_Pair_a_a @ Xa2 @ U2 ) ) )
% 0.29/0.47 => ( Y3
% 0.29/0.47 = ( cons_P1921020637od_a_a @ E1 @ ( pair_co_path_a @ ( product_Pair_a_a @ U2 @ V ) @ Xa2 @ ( cons_P1921020637od_a_a @ E22 @ Es ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % co_path.elims
% 0.29/0.47 thf(fact_319_co__sd__id,axiom,
% 0.29/0.47 ! [U: a,W2: a,P3: list_P1467822637od_a_a,V2: a] :
% 0.29/0.47 ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ U @ W2 ) @ ( set_Product_prod_a_a2 @ P3 ) )
% 0.29/0.47 => ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ V2 @ W2 ) @ ( set_Product_prod_a_a2 @ P3 ) )
% 0.29/0.47 => ( ( pair_co_path_a @ ( product_Pair_a_a @ U @ V2 ) @ W2 @ ( pair_sd_path_a @ ( product_Pair_a_a @ U @ V2 ) @ W2 @ P3 ) )
% 0.29/0.47 = P3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % co_sd_id
% 0.29/0.47 thf(fact_320_Cons__lenlex__iff,axiom,
% 0.29/0.47 ! [M: product_prod_a_a,Ms: list_P1467822637od_a_a,N: product_prod_a_a,Ns: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 0.29/0.47 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( cons_P1921020637od_a_a @ M @ Ms ) @ ( cons_P1921020637od_a_a @ N @ Ns ) ) @ ( lenlex2038501170od_a_a @ R ) )
% 0.29/0.47 = ( ( ord_less_nat @ ( size_s642698393od_a_a @ Ms ) @ ( size_s642698393od_a_a @ Ns ) )
% 0.29/0.47 | ( ( ( size_s642698393od_a_a @ Ms )
% 0.29/0.47 = ( size_s642698393od_a_a @ Ns ) )
% 0.29/0.47 & ( member2057358096od_a_a @ ( produc1474507607od_a_a @ M @ N ) @ R ) )
% 0.29/0.47 | ( ( M = N )
% 0.29/0.47 & ( member1691432592od_a_a @ ( produc85179863od_a_a @ Ms @ Ns ) @ ( lenlex2038501170od_a_a @ R ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Cons_lenlex_iff
% 0.29/0.47 thf(fact_321_Cons__lenlex__iff,axiom,
% 0.29/0.47 ! [M: a,Ms: list_a,N: a,Ns: list_a,R: set_Product_prod_a_a] :
% 0.29/0.47 ( ( member1250517072list_a @ ( produc1448356631list_a @ ( cons_a @ M @ Ms ) @ ( cons_a @ N @ Ns ) ) @ ( lenlex_a @ R ) )
% 0.29/0.47 = ( ( ord_less_nat @ ( size_size_list_a @ Ms ) @ ( size_size_list_a @ Ns ) )
% 0.29/0.47 | ( ( ( size_size_list_a @ Ms )
% 0.29/0.47 = ( size_size_list_a @ Ns ) )
% 0.29/0.47 & ( member449909584od_a_a @ ( product_Pair_a_a @ M @ N ) @ R ) )
% 0.29/0.47 | ( ( M = N )
% 0.29/0.47 & ( member1250517072list_a @ ( produc1448356631list_a @ Ms @ Ns ) @ ( lenlex_a @ R ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Cons_lenlex_iff
% 0.29/0.47 thf(fact_322_Cons__in__subseqsD,axiom,
% 0.29/0.47 ! [Y3: product_prod_a_a,Ys2: list_P1467822637od_a_a,Xs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( member1578987478od_a_a @ ( cons_P1921020637od_a_a @ Y3 @ Ys2 ) @ ( set_li1284606018od_a_a @ ( subseq2115548028od_a_a @ Xs2 ) ) )
% 0.29/0.47 => ( member1578987478od_a_a @ Ys2 @ ( set_li1284606018od_a_a @ ( subseq2115548028od_a_a @ Xs2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Cons_in_subseqsD
% 0.29/0.47 thf(fact_323_in__measures_I2_J,axiom,
% 0.29/0.47 ! [X3: a,Y3: a,F: a > nat,Fs: list_a_nat] :
% 0.29/0.47 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ ( measures_a @ ( cons_a_nat @ F @ Fs ) ) )
% 0.29/0.47 = ( ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) )
% 0.29/0.47 | ( ( ( F @ X3 )
% 0.29/0.47 = ( F @ Y3 ) )
% 0.29/0.47 & ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ ( measures_a @ Fs ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % in_measures(2)
% 0.29/0.47 thf(fact_324_inverse__permutation__of__list_Oelims,axiom,
% 0.29/0.47 ! [X3: list_P1467822637od_a_a,Xa2: a,Y3: a] :
% 0.29/0.47 ( ( ( invers1007791577list_a @ X3 @ Xa2 )
% 0.29/0.47 = Y3 )
% 0.29/0.47 => ( ( ( X3 = nil_Product_prod_a_a )
% 0.29/0.47 => ( Y3 != Xa2 ) )
% 0.29/0.47 => ~ ! [Y4: a,X6: a,Xs4: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( X3
% 0.29/0.47 = ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y4 @ X6 ) @ Xs4 ) )
% 0.29/0.47 => ~ ( ( ( Xa2 = X6 )
% 0.29/0.47 => ( Y3 = Y4 ) )
% 0.29/0.47 & ( ( Xa2 != X6 )
% 0.29/0.47 => ( Y3
% 0.29/0.47 = ( invers1007791577list_a @ Xs4 @ Xa2 ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % inverse_permutation_of_list.elims
% 0.29/0.47 thf(fact_325_in__measures_I1_J,axiom,
% 0.29/0.47 ! [X3: a,Y3: a] :
% 0.29/0.47 ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ ( measures_a @ nil_a_nat ) ) ).
% 0.29/0.47
% 0.29/0.47 % in_measures(1)
% 0.29/0.47 thf(fact_326_eval__inverse__permutation__of__list_I3_J,axiom,
% 0.29/0.47 ! [X3: a,X7: a,Y5: a,Xs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( X3 != X7 )
% 0.29/0.47 => ( ( invers1007791577list_a @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y5 @ X7 ) @ Xs2 ) @ X3 )
% 0.29/0.47 = ( invers1007791577list_a @ Xs2 @ X3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % eval_inverse_permutation_of_list(3)
% 0.29/0.47 thf(fact_327_eval__inverse__permutation__of__list_I2_J,axiom,
% 0.29/0.47 ! [X3: a,X7: a,Y3: a,Xs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( X3 = X7 )
% 0.29/0.47 => ( ( invers1007791577list_a @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y3 @ X7 ) @ Xs2 ) @ X3 )
% 0.29/0.47 = Y3 ) ) ).
% 0.29/0.47
% 0.29/0.47 % eval_inverse_permutation_of_list(2)
% 0.29/0.47 thf(fact_328_inverse__permutation__of__list_Osimps_I2_J,axiom,
% 0.29/0.47 ! [X3: a,X7: a,Y3: a,Xs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( ( X3 = X7 )
% 0.29/0.47 => ( ( invers1007791577list_a @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y3 @ X7 ) @ Xs2 ) @ X3 )
% 0.29/0.47 = Y3 ) )
% 0.29/0.47 & ( ( X3 != X7 )
% 0.29/0.47 => ( ( invers1007791577list_a @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y3 @ X7 ) @ Xs2 ) @ X3 )
% 0.29/0.47 = ( invers1007791577list_a @ Xs2 @ X3 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % inverse_permutation_of_list.simps(2)
% 0.29/0.47 thf(fact_329_measures__less,axiom,
% 0.29/0.47 ! [F: a > nat,X3: a,Y3: a,Fs: list_a_nat] :
% 0.29/0.47 ( ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) )
% 0.29/0.47 => ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ ( measures_a @ ( cons_a_nat @ F @ Fs ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % measures_less
% 0.29/0.47 thf(fact_330_inverse__permutation__of__list__unique,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a,A4: set_a,X3: a,Y3: a] :
% 0.29/0.47 ( ( list_permutes_a @ Xs2 @ A4 )
% 0.29/0.47 => ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 0.29/0.47 => ( ( invers1007791577list_a @ Xs2 @ Y3 )
% 0.29/0.47 = X3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % inverse_permutation_of_list_unique
% 0.29/0.47 thf(fact_331_eval__permutation__of__list_I3_J,axiom,
% 0.29/0.47 ! [X3: a,X7: a,Y5: a,Xs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( X3 != X7 )
% 0.29/0.47 => ( ( permut1422637723list_a @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X7 @ Y5 ) @ Xs2 ) @ X3 )
% 0.29/0.47 = ( permut1422637723list_a @ Xs2 @ X3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % eval_permutation_of_list(3)
% 0.29/0.47 thf(fact_332_eval__permutation__of__list_I2_J,axiom,
% 0.29/0.47 ! [X3: a,X7: a,Y3: a,Xs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( X3 = X7 )
% 0.29/0.47 => ( ( permut1422637723list_a @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X7 @ Y3 ) @ Xs2 ) @ X3 )
% 0.29/0.47 = Y3 ) ) ).
% 0.29/0.47
% 0.29/0.47 % eval_permutation_of_list(2)
% 0.29/0.47 thf(fact_333_permutation__of__list__unique,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a,A4: set_a,X3: a,Y3: a] :
% 0.29/0.47 ( ( list_permutes_a @ Xs2 @ A4 )
% 0.29/0.47 => ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 0.29/0.47 => ( ( permut1422637723list_a @ Xs2 @ X3 )
% 0.29/0.47 = Y3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % permutation_of_list_unique
% 0.29/0.47 thf(fact_334_permutation__of__list__Cons,axiom,
% 0.29/0.47 ! [X3: a,X7: a,Y3: a,Xs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( ( X3 = X7 )
% 0.29/0.47 => ( ( permut1422637723list_a @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ Xs2 ) @ X7 )
% 0.29/0.47 = Y3 ) )
% 0.29/0.47 & ( ( X3 != X7 )
% 0.29/0.47 => ( ( permut1422637723list_a @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ Xs2 ) @ X7 )
% 0.29/0.47 = ( permut1422637723list_a @ Xs2 @ X7 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % permutation_of_list_Cons
% 0.29/0.47 thf(fact_335_not__in__set__insert,axiom,
% 0.29/0.47 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ~ ( member449909584od_a_a @ X3 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 0.29/0.47 => ( ( insert2123825731od_a_a @ X3 @ Xs2 )
% 0.29/0.47 = ( cons_P1921020637od_a_a @ X3 @ Xs2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % not_in_set_insert
% 0.29/0.47 thf(fact_336_insert__Nil,axiom,
% 0.29/0.47 ! [X3: product_prod_a_a] :
% 0.29/0.47 ( ( insert2123825731od_a_a @ X3 @ nil_Product_prod_a_a )
% 0.29/0.47 = ( cons_P1921020637od_a_a @ X3 @ nil_Product_prod_a_a ) ) ).
% 0.29/0.47
% 0.29/0.47 % insert_Nil
% 0.29/0.47 thf(fact_337_List_Oinsert__def,axiom,
% 0.29/0.47 ( insert2123825731od_a_a
% 0.29/0.47 = ( ^ [X: product_prod_a_a,Xs: list_P1467822637od_a_a] : ( if_lis321365491od_a_a @ ( member449909584od_a_a @ X @ ( set_Product_prod_a_a2 @ Xs ) ) @ Xs @ ( cons_P1921020637od_a_a @ X @ Xs ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % List.insert_def
% 0.29/0.47 thf(fact_338_concat__eq__append__conv,axiom,
% 0.29/0.47 ! [Xss2: list_l1108175539od_a_a,Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( ( concat1878217064od_a_a @ Xss2 )
% 0.29/0.47 = ( append1574001858od_a_a @ Ys2 @ Zs ) )
% 0.29/0.47 = ( ( ( Xss2 = nil_li1885598003od_a_a )
% 0.29/0.47 => ( ( Ys2 = nil_Product_prod_a_a )
% 0.29/0.47 & ( Zs = nil_Product_prod_a_a ) ) )
% 0.29/0.47 & ( ( Xss2 != nil_li1885598003od_a_a )
% 0.29/0.47 => ? [Xss1: list_l1108175539od_a_a,Xs: list_P1467822637od_a_a,Xs6: list_P1467822637od_a_a,Xss22: list_l1108175539od_a_a] :
% 0.29/0.47 ( ( Xss2
% 0.29/0.47 = ( append2141280328od_a_a @ Xss1 @ ( cons_l724116707od_a_a @ ( append1574001858od_a_a @ Xs @ Xs6 ) @ Xss22 ) ) )
% 0.29/0.47 & ( Ys2
% 0.29/0.47 = ( append1574001858od_a_a @ ( concat1878217064od_a_a @ Xss1 ) @ Xs ) )
% 0.29/0.47 & ( Zs
% 0.29/0.47 = ( append1574001858od_a_a @ Xs6 @ ( concat1878217064od_a_a @ Xss22 ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % concat_eq_append_conv
% 0.29/0.47 thf(fact_339_inverse__permutation__of__list_Opelims,axiom,
% 0.29/0.47 ! [X3: list_P1467822637od_a_a,Xa2: a,Y3: a] :
% 0.29/0.47 ( ( ( invers1007791577list_a @ X3 @ Xa2 )
% 0.29/0.47 = Y3 )
% 0.29/0.47 => ( ( accp_P941981633_a_a_a @ invers214109608_rel_a @ ( produc998622632_a_a_a @ X3 @ Xa2 ) )
% 0.29/0.47 => ( ( ( X3 = nil_Product_prod_a_a )
% 0.29/0.47 => ( ( Y3 = Xa2 )
% 0.29/0.47 => ~ ( accp_P941981633_a_a_a @ invers214109608_rel_a @ ( produc998622632_a_a_a @ nil_Product_prod_a_a @ Xa2 ) ) ) )
% 0.29/0.47 => ~ ! [Y4: a,X6: a,Xs4: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( X3
% 0.29/0.47 = ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y4 @ X6 ) @ Xs4 ) )
% 0.29/0.47 => ( ( ( ( Xa2 = X6 )
% 0.29/0.47 => ( Y3 = Y4 ) )
% 0.29/0.47 & ( ( Xa2 != X6 )
% 0.29/0.47 => ( Y3
% 0.29/0.47 = ( invers1007791577list_a @ Xs4 @ Xa2 ) ) ) )
% 0.29/0.47 => ~ ( accp_P941981633_a_a_a @ invers214109608_rel_a @ ( produc998622632_a_a_a @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y4 @ X6 ) @ Xs4 ) @ Xa2 ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % inverse_permutation_of_list.pelims
% 0.29/0.47 thf(fact_340_concat__append,axiom,
% 0.29/0.47 ! [Xs2: list_l1108175539od_a_a,Ys2: list_l1108175539od_a_a] :
% 0.29/0.47 ( ( concat1878217064od_a_a @ ( append2141280328od_a_a @ Xs2 @ Ys2 ) )
% 0.29/0.47 = ( append1574001858od_a_a @ ( concat1878217064od_a_a @ Xs2 ) @ ( concat1878217064od_a_a @ Ys2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % concat_append
% 0.29/0.47 thf(fact_341_concat_Osimps_I2_J,axiom,
% 0.29/0.47 ! [X3: list_P1467822637od_a_a,Xs2: list_l1108175539od_a_a] :
% 0.29/0.47 ( ( concat1878217064od_a_a @ ( cons_l724116707od_a_a @ X3 @ Xs2 ) )
% 0.29/0.47 = ( append1574001858od_a_a @ X3 @ ( concat1878217064od_a_a @ Xs2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % concat.simps(2)
% 0.29/0.47 thf(fact_342_concat__eq__appendD,axiom,
% 0.29/0.47 ! [Xss2: list_l1108175539od_a_a,Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( ( concat1878217064od_a_a @ Xss2 )
% 0.29/0.47 = ( append1574001858od_a_a @ Ys2 @ Zs ) )
% 0.29/0.47 => ( ( Xss2 != nil_li1885598003od_a_a )
% 0.29/0.47 => ? [Xss12: list_l1108175539od_a_a,Xs4: list_P1467822637od_a_a,Xs3: list_P1467822637od_a_a,Xss23: list_l1108175539od_a_a] :
% 0.29/0.47 ( ( Xss2
% 0.29/0.47 = ( append2141280328od_a_a @ Xss12 @ ( cons_l724116707od_a_a @ ( append1574001858od_a_a @ Xs4 @ Xs3 ) @ Xss23 ) ) )
% 0.29/0.47 & ( Ys2
% 0.29/0.47 = ( append1574001858od_a_a @ ( concat1878217064od_a_a @ Xss12 ) @ Xs4 ) )
% 0.29/0.47 & ( Zs
% 0.29/0.47 = ( append1574001858od_a_a @ Xs3 @ ( concat1878217064od_a_a @ Xss23 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % concat_eq_appendD
% 0.29/0.47 thf(fact_343_listrel_Oinducts,axiom,
% 0.29/0.47 ! [X1: list_P1467822637od_a_a,X2: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a,P2: list_P1467822637od_a_a > list_P1467822637od_a_a > $o] :
% 0.29/0.47 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ X1 @ X2 ) @ ( listre2074280881od_a_a @ R ) )
% 0.29/0.47 => ( ( P2 @ nil_Product_prod_a_a @ nil_Product_prod_a_a )
% 0.29/0.47 => ( ! [X4: product_prod_a_a,Y4: product_prod_a_a,Xs4: list_P1467822637od_a_a,Ys4: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X4 @ Y4 ) @ R )
% 0.29/0.47 => ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs4 @ Ys4 ) @ ( listre2074280881od_a_a @ R ) )
% 0.29/0.47 => ( ( P2 @ Xs4 @ Ys4 )
% 0.29/0.47 => ( P2 @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) @ ( cons_P1921020637od_a_a @ Y4 @ Ys4 ) ) ) ) )
% 0.29/0.47 => ( P2 @ X1 @ X2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % listrel.inducts
% 0.29/0.47 thf(fact_344_listrel_Oinducts,axiom,
% 0.29/0.47 ! [X1: list_a,X2: list_a,R: set_Product_prod_a_a,P2: list_a > list_a > $o] :
% 0.29/0.47 ( ( member1250517072list_a @ ( produc1448356631list_a @ X1 @ X2 ) @ ( listrel_a_a @ R ) )
% 0.29/0.47 => ( ( P2 @ nil_a @ nil_a )
% 0.29/0.47 => ( ! [X4: a,Y4: a,Xs4: list_a,Ys4: list_a] :
% 0.29/0.47 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ R )
% 0.29/0.47 => ( ( member1250517072list_a @ ( produc1448356631list_a @ Xs4 @ Ys4 ) @ ( listrel_a_a @ R ) )
% 0.29/0.47 => ( ( P2 @ Xs4 @ Ys4 )
% 0.29/0.47 => ( P2 @ ( cons_a @ X4 @ Xs4 ) @ ( cons_a @ Y4 @ Ys4 ) ) ) ) )
% 0.29/0.47 => ( P2 @ X1 @ X2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % listrel.inducts
% 0.29/0.47 thf(fact_345_listrel_OCons,axiom,
% 0.29/0.47 ! [X3: product_prod_a_a,Y3: product_prod_a_a,R: set_Pr1948701895od_a_a,Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X3 @ Y3 ) @ R )
% 0.29/0.47 => ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ Ys2 ) @ ( listre2074280881od_a_a @ R ) )
% 0.29/0.47 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ ( cons_P1921020637od_a_a @ Y3 @ Ys2 ) ) @ ( listre2074280881od_a_a @ R ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % listrel.Cons
% 0.29/0.47 thf(fact_346_listrel_OCons,axiom,
% 0.29/0.47 ! [X3: a,Y3: a,R: set_Product_prod_a_a,Xs2: list_a,Ys2: list_a] :
% 0.29/0.47 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R )
% 0.29/0.47 => ( ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ Ys2 ) @ ( listrel_a_a @ R ) )
% 0.29/0.47 => ( member1250517072list_a @ ( produc1448356631list_a @ ( cons_a @ X3 @ Xs2 ) @ ( cons_a @ Y3 @ Ys2 ) ) @ ( listrel_a_a @ R ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % listrel.Cons
% 0.29/0.47 thf(fact_347_listrel__Cons1,axiom,
% 0.29/0.47 ! [Y3: product_prod_a_a,Ys2: list_P1467822637od_a_a,Xs2: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 0.29/0.47 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( cons_P1921020637od_a_a @ Y3 @ Ys2 ) @ Xs2 ) @ ( listre2074280881od_a_a @ R ) )
% 0.29/0.47 => ~ ! [Y4: product_prod_a_a,Ys4: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( Xs2
% 0.29/0.47 = ( cons_P1921020637od_a_a @ Y4 @ Ys4 ) )
% 0.29/0.47 => ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ Y3 @ Y4 ) @ R )
% 0.29/0.47 => ~ ( member1691432592od_a_a @ ( produc85179863od_a_a @ Ys2 @ Ys4 ) @ ( listre2074280881od_a_a @ R ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % listrel_Cons1
% 0.29/0.47 thf(fact_348_listrel__Cons1,axiom,
% 0.29/0.47 ! [Y3: a,Ys2: list_a,Xs2: list_a,R: set_Product_prod_a_a] :
% 0.29/0.47 ( ( member1250517072list_a @ ( produc1448356631list_a @ ( cons_a @ Y3 @ Ys2 ) @ Xs2 ) @ ( listrel_a_a @ R ) )
% 0.29/0.47 => ~ ! [Y4: a,Ys4: list_a] :
% 0.29/0.47 ( ( Xs2
% 0.29/0.47 = ( cons_a @ Y4 @ Ys4 ) )
% 0.29/0.47 => ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y3 @ Y4 ) @ R )
% 0.29/0.47 => ~ ( member1250517072list_a @ ( produc1448356631list_a @ Ys2 @ Ys4 ) @ ( listrel_a_a @ R ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % listrel_Cons1
% 0.29/0.47 thf(fact_349_listrel__Cons2,axiom,
% 0.29/0.47 ! [Xs2: list_P1467822637od_a_a,Y3: product_prod_a_a,Ys2: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 0.29/0.47 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ ( cons_P1921020637od_a_a @ Y3 @ Ys2 ) ) @ ( listre2074280881od_a_a @ R ) )
% 0.29/0.47 => ~ ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( Xs2
% 0.29/0.47 = ( cons_P1921020637od_a_a @ X4 @ Xs4 ) )
% 0.29/0.47 => ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X4 @ Y3 ) @ R )
% 0.29/0.47 => ~ ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs4 @ Ys2 ) @ ( listre2074280881od_a_a @ R ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % listrel_Cons2
% 0.29/0.47 thf(fact_350_listrel__Cons2,axiom,
% 0.29/0.47 ! [Xs2: list_a,Y3: a,Ys2: list_a,R: set_Product_prod_a_a] :
% 0.29/0.47 ( ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ ( cons_a @ Y3 @ Ys2 ) ) @ ( listrel_a_a @ R ) )
% 0.29/0.47 => ~ ! [X4: a,Xs4: list_a] :
% 0.29/0.47 ( ( Xs2
% 0.29/0.47 = ( cons_a @ X4 @ Xs4 ) )
% 0.29/0.47 => ( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y3 ) @ R )
% 0.29/0.47 => ~ ( member1250517072list_a @ ( produc1448356631list_a @ Xs4 @ Ys2 ) @ ( listrel_a_a @ R ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % listrel_Cons2
% 0.29/0.47 thf(fact_351_listrel_Ocases,axiom,
% 0.29/0.47 ! [A1: list_P1467822637od_a_a,A22: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 0.29/0.47 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ A1 @ A22 ) @ ( listre2074280881od_a_a @ R ) )
% 0.29/0.47 => ( ( ( A1 = nil_Product_prod_a_a )
% 0.29/0.47 => ( A22 != nil_Product_prod_a_a ) )
% 0.29/0.47 => ~ ! [X4: product_prod_a_a,Y4: product_prod_a_a,Xs4: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( A1
% 0.29/0.47 = ( cons_P1921020637od_a_a @ X4 @ Xs4 ) )
% 0.29/0.47 => ! [Ys4: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( A22
% 0.29/0.47 = ( cons_P1921020637od_a_a @ Y4 @ Ys4 ) )
% 0.29/0.47 => ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X4 @ Y4 ) @ R )
% 0.29/0.47 => ~ ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs4 @ Ys4 ) @ ( listre2074280881od_a_a @ R ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % listrel.cases
% 0.29/0.47 thf(fact_352_listrel_Ocases,axiom,
% 0.29/0.47 ! [A1: list_a,A22: list_a,R: set_Product_prod_a_a] :
% 0.29/0.47 ( ( member1250517072list_a @ ( produc1448356631list_a @ A1 @ A22 ) @ ( listrel_a_a @ R ) )
% 0.29/0.47 => ( ( ( A1 = nil_a )
% 0.29/0.47 => ( A22 != nil_a ) )
% 0.29/0.47 => ~ ! [X4: a,Y4: a,Xs4: list_a] :
% 0.29/0.47 ( ( A1
% 0.29/0.47 = ( cons_a @ X4 @ Xs4 ) )
% 0.29/0.47 => ! [Ys4: list_a] :
% 0.29/0.47 ( ( A22
% 0.29/0.47 = ( cons_a @ Y4 @ Ys4 ) )
% 0.29/0.47 => ( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ R )
% 0.29/0.47 => ~ ( member1250517072list_a @ ( produc1448356631list_a @ Xs4 @ Ys4 ) @ ( listrel_a_a @ R ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % listrel.cases
% 0.29/0.47 thf(fact_353_listrel_Osimps,axiom,
% 0.29/0.47 ! [A1: list_P1467822637od_a_a,A22: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 0.29/0.47 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ A1 @ A22 ) @ ( listre2074280881od_a_a @ R ) )
% 0.29/0.47 = ( ( ( A1 = nil_Product_prod_a_a )
% 0.29/0.47 & ( A22 = nil_Product_prod_a_a ) )
% 0.29/0.47 | ? [X: product_prod_a_a,Y: product_prod_a_a,Xs: list_P1467822637od_a_a,Ys: list_P1467822637od_a_a] :
% 0.29/0.47 ( ( A1
% 0.29/0.47 = ( cons_P1921020637od_a_a @ X @ Xs ) )
% 0.29/0.47 & ( A22
% 0.29/0.47 = ( cons_P1921020637od_a_a @ Y @ Ys ) )
% 0.29/0.47 & ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X @ Y ) @ R )
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% 3.13/1.61 thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_Itf__a_J_Mt__List__Olist_Itf__a_J_J,type,
% 3.13/1.61 member1250517072list_a: produc864062247list_a > set_Pr1971762695list_a > $o ).
% 3.13/1.61
% 3.13/1.61 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__a_J_Mt__Product____Type__Oprod_Itf__a_Mtf__a_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__a_J_Mt__Product____Type__Oprod_Itf__a_Mtf__a_J_J_J,type,
% 3.13/1.61 member1899387664od_a_a: produc1990712039od_a_a > set_Pr1295299783od_a_a > $o ).
% 3.13/1.61
% 3.13/1.61 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__a_J_Mt__Product____Type__Oprod_Itf__a_Mtf__a_J_J,type,
% 3.13/1.61 member2057358096od_a_a: produc1572603623od_a_a > set_Pr1948701895od_a_a > $o ).
% 3.13/1.61
% 3.13/1.61 thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_Mt__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_J,type,
% 3.13/1.61 member1474739327od_a_a: produc1701253078od_a_a > set_Pr248149174od_a_a > $o ).
% 3.13/1.61
% 3.13/1.61 thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_Mtf__a_J_J,type,
% 3.13/1.61 member1904151562_a_a_a: produc1197928545_a_a_a > set_Pr110478017_a_a_a > $o ).
% 3.13/1.61
% 3.13/1.61 thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_Mtf__a_J,type,
% 3.13/1.61 member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
% 3.13/1.61
% 3.13/1.61 thf(sy_c_member_001tf__a,type,
% 3.13/1.61 member_a2: a > set_a > $o ).
% 3.13/1.61
% 3.13/1.61 thf(sy_v_e,type,
% 3.13/1.61 e: product_prod_a_a ).
% 3.13/1.61
% 3.13/1.61 thf(sy_v_es,type,
% 3.13/1.61 es: list_P1467822637od_a_a ).
% 3.13/1.61
% 3.13/1.61 thf(fact_0_assms,axiom,
% 3.13/1.61 kurato1072996284sing_a @ ( cons_P1921020637od_a_a @ e @ es ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_1_progressing__def,axiom,
% 3.13/1.61 ( kurato1404746725od_a_a
% 3.13/1.61 = ( ^ [P: list_P1891567085od_a_a] :
% 3.13/1.61 ! [Xs: list_P1891567085od_a_a,X: product_prod_a_a,Y: product_prod_a_a,Ys: list_P1891567085od_a_a] :
% 3.13/1.61 ( P
% 3.13/1.61 != ( append864718978od_a_a @ Xs @ ( cons_P1070399645od_a_a @ ( produc1474507607od_a_a @ X @ Y ) @ ( cons_P1070399645od_a_a @ ( produc1474507607od_a_a @ Y @ X ) @ Ys ) ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_2_progressing__def,axiom,
% 3.13/1.61 ( kurato292963650list_a
% 3.13/1.61 = ( ^ [P: list_P601816365list_a] :
% 3.13/1.61 ! [Xs: list_P601816365list_a,X: list_a,Y: list_a,Ys: list_P601816365list_a] :
% 3.13/1.61 ( P
% 3.13/1.61 != ( append750086082list_a @ Xs @ ( cons_P2080942813list_a @ ( produc1448356631list_a @ X @ Y ) @ ( cons_P2080942813list_a @ ( produc1448356631list_a @ Y @ X ) @ Ys ) ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_3_progressing__def,axiom,
% 3.13/1.61 ( kurato1072996284sing_a
% 3.13/1.61 = ( ^ [P: list_P1467822637od_a_a] :
% 3.13/1.61 ! [Xs: list_P1467822637od_a_a,X: a,Y: a,Ys: list_P1467822637od_a_a] :
% 3.13/1.61 ( P
% 3.13/1.61 != ( append1574001858od_a_a @ Xs @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X @ Y ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y @ X ) @ Ys ) ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_4_append_Oassoc,axiom,
% 3.13/1.61 ! [A: list_a,B: list_a,C: list_a] :
% 3.13/1.61 ( ( append_a @ ( append_a @ A @ B ) @ C )
% 3.13/1.61 = ( append_a @ A @ ( append_a @ B @ C ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_5_append_Oassoc,axiom,
% 3.13/1.61 ! [A: list_P1891567085od_a_a,B: list_P1891567085od_a_a,C: list_P1891567085od_a_a] :
% 3.13/1.61 ( ( append864718978od_a_a @ ( append864718978od_a_a @ A @ B ) @ C )
% 3.13/1.61 = ( append864718978od_a_a @ A @ ( append864718978od_a_a @ B @ C ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_6_append_Oassoc,axiom,
% 3.13/1.61 ! [A: list_l1108175539od_a_a,B: list_l1108175539od_a_a,C: list_l1108175539od_a_a] :
% 3.13/1.61 ( ( append2141280328od_a_a @ ( append2141280328od_a_a @ A @ B ) @ C )
% 3.13/1.61 = ( append2141280328od_a_a @ A @ ( append2141280328od_a_a @ B @ C ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_7_append_Oassoc,axiom,
% 3.13/1.61 ! [A: list_P1467822637od_a_a,B: list_P1467822637od_a_a,C: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( append1574001858od_a_a @ ( append1574001858od_a_a @ A @ B ) @ C )
% 3.13/1.61 = ( append1574001858od_a_a @ A @ ( append1574001858od_a_a @ B @ C ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_8_append__assoc,axiom,
% 3.13/1.61 ! [Xs2: list_a,Ys2: list_a,Zs: list_a] :
% 3.13/1.61 ( ( append_a @ ( append_a @ Xs2 @ Ys2 ) @ Zs )
% 3.13/1.61 = ( append_a @ Xs2 @ ( append_a @ Ys2 @ Zs ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_9_append__assoc,axiom,
% 3.13/1.61 ! [Xs2: list_P1891567085od_a_a,Ys2: list_P1891567085od_a_a,Zs: list_P1891567085od_a_a] :
% 3.13/1.61 ( ( append864718978od_a_a @ ( append864718978od_a_a @ Xs2 @ Ys2 ) @ Zs )
% 3.13/1.61 = ( append864718978od_a_a @ Xs2 @ ( append864718978od_a_a @ Ys2 @ Zs ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_10_append__assoc,axiom,
% 3.13/1.61 ! [Xs2: list_l1108175539od_a_a,Ys2: list_l1108175539od_a_a,Zs: list_l1108175539od_a_a] :
% 3.13/1.61 ( ( append2141280328od_a_a @ ( append2141280328od_a_a @ Xs2 @ Ys2 ) @ Zs )
% 3.13/1.61 = ( append2141280328od_a_a @ Xs2 @ ( append2141280328od_a_a @ Ys2 @ Zs ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_11_append__assoc,axiom,
% 3.13/1.61 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( append1574001858od_a_a @ ( append1574001858od_a_a @ Xs2 @ Ys2 ) @ Zs )
% 3.13/1.61 = ( append1574001858od_a_a @ Xs2 @ ( append1574001858od_a_a @ Ys2 @ Zs ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_12_append__same__eq,axiom,
% 3.13/1.61 ! [Ys2: list_a,Xs2: list_a,Zs: list_a] :
% 3.13/1.61 ( ( ( append_a @ Ys2 @ Xs2 )
% 3.13/1.61 = ( append_a @ Zs @ Xs2 ) )
% 3.13/1.61 = ( Ys2 = Zs ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_13_append__same__eq,axiom,
% 3.13/1.61 ! [Ys2: list_P1891567085od_a_a,Xs2: list_P1891567085od_a_a,Zs: list_P1891567085od_a_a] :
% 3.13/1.61 ( ( ( append864718978od_a_a @ Ys2 @ Xs2 )
% 3.13/1.61 = ( append864718978od_a_a @ Zs @ Xs2 ) )
% 3.13/1.61 = ( Ys2 = Zs ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_14_append__same__eq,axiom,
% 3.13/1.61 ! [Ys2: list_l1108175539od_a_a,Xs2: list_l1108175539od_a_a,Zs: list_l1108175539od_a_a] :
% 3.13/1.61 ( ( ( append2141280328od_a_a @ Ys2 @ Xs2 )
% 3.13/1.61 = ( append2141280328od_a_a @ Zs @ Xs2 ) )
% 3.13/1.61 = ( Ys2 = Zs ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_15_append__same__eq,axiom,
% 3.13/1.61 ! [Ys2: list_P1467822637od_a_a,Xs2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( ( append1574001858od_a_a @ Ys2 @ Xs2 )
% 3.13/1.61 = ( append1574001858od_a_a @ Zs @ Xs2 ) )
% 3.13/1.61 = ( Ys2 = Zs ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_16_same__append__eq,axiom,
% 3.13/1.61 ! [Xs2: list_a,Ys2: list_a,Zs: list_a] :
% 3.13/1.61 ( ( ( append_a @ Xs2 @ Ys2 )
% 3.13/1.61 = ( append_a @ Xs2 @ Zs ) )
% 3.13/1.61 = ( Ys2 = Zs ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_17_same__append__eq,axiom,
% 3.13/1.61 ! [Xs2: list_P1891567085od_a_a,Ys2: list_P1891567085od_a_a,Zs: list_P1891567085od_a_a] :
% 3.13/1.61 ( ( ( append864718978od_a_a @ Xs2 @ Ys2 )
% 3.13/1.61 = ( append864718978od_a_a @ Xs2 @ Zs ) )
% 3.13/1.61 = ( Ys2 = Zs ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_18_same__append__eq,axiom,
% 3.13/1.61 ! [Xs2: list_l1108175539od_a_a,Ys2: list_l1108175539od_a_a,Zs: list_l1108175539od_a_a] :
% 3.13/1.61 ( ( ( append2141280328od_a_a @ Xs2 @ Ys2 )
% 3.13/1.61 = ( append2141280328od_a_a @ Xs2 @ Zs ) )
% 3.13/1.61 = ( Ys2 = Zs ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_19_same__append__eq,axiom,
% 3.13/1.61 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( ( append1574001858od_a_a @ Xs2 @ Ys2 )
% 3.13/1.61 = ( append1574001858od_a_a @ Xs2 @ Zs ) )
% 3.13/1.61 = ( Ys2 = Zs ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_20_list_Oinject,axiom,
% 3.13/1.61 ! [X21: a,X22: list_a,Y21: a,Y22: list_a] :
% 3.13/1.61 ( ( ( cons_a @ X21 @ X22 )
% 3.13/1.61 = ( cons_a @ Y21 @ Y22 ) )
% 3.13/1.61 = ( ( X21 = Y21 )
% 3.13/1.61 & ( X22 = Y22 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_21_list_Oinject,axiom,
% 3.13/1.61 ! [X21: produc1572603623od_a_a,X22: list_P1891567085od_a_a,Y21: produc1572603623od_a_a,Y22: list_P1891567085od_a_a] :
% 3.13/1.61 ( ( ( cons_P1070399645od_a_a @ X21 @ X22 )
% 3.13/1.61 = ( cons_P1070399645od_a_a @ Y21 @ Y22 ) )
% 3.13/1.61 = ( ( X21 = Y21 )
% 3.13/1.61 & ( X22 = Y22 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_22_list_Oinject,axiom,
% 3.13/1.61 ! [X21: list_P1467822637od_a_a,X22: list_l1108175539od_a_a,Y21: list_P1467822637od_a_a,Y22: list_l1108175539od_a_a] :
% 3.13/1.61 ( ( ( cons_l724116707od_a_a @ X21 @ X22 )
% 3.13/1.61 = ( cons_l724116707od_a_a @ Y21 @ Y22 ) )
% 3.13/1.61 = ( ( X21 = Y21 )
% 3.13/1.61 & ( X22 = Y22 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_23_list_Oinject,axiom,
% 3.13/1.61 ! [X21: a > nat,X22: list_a_nat,Y21: a > nat,Y22: list_a_nat] :
% 3.13/1.61 ( ( ( cons_a_nat @ X21 @ X22 )
% 3.13/1.61 = ( cons_a_nat @ Y21 @ Y22 ) )
% 3.13/1.61 = ( ( X21 = Y21 )
% 3.13/1.61 & ( X22 = Y22 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_24_list_Oinject,axiom,
% 3.13/1.61 ! [X21: product_prod_a_a,X22: list_P1467822637od_a_a,Y21: product_prod_a_a,Y22: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( ( cons_P1921020637od_a_a @ X21 @ X22 )
% 3.13/1.61 = ( cons_P1921020637od_a_a @ Y21 @ Y22 ) )
% 3.13/1.61 = ( ( X21 = Y21 )
% 3.13/1.61 & ( X22 = Y22 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_25_prod_Oinject,axiom,
% 3.13/1.61 ! [X1: list_P1467822637od_a_a,X2: a,Y1: list_P1467822637od_a_a,Y2: a] :
% 3.13/1.61 ( ( ( produc998622632_a_a_a @ X1 @ X2 )
% 3.13/1.61 = ( produc998622632_a_a_a @ Y1 @ Y2 ) )
% 3.13/1.61 = ( ( X1 = Y1 )
% 3.13/1.61 & ( X2 = Y2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_26_prod_Oinject,axiom,
% 3.13/1.61 ! [X1: list_a,X2: list_a,Y1: list_a,Y2: list_a] :
% 3.13/1.61 ( ( ( produc1448356631list_a @ X1 @ X2 )
% 3.13/1.61 = ( produc1448356631list_a @ Y1 @ Y2 ) )
% 3.13/1.61 = ( ( X1 = Y1 )
% 3.13/1.61 & ( X2 = Y2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_27_prod_Oinject,axiom,
% 3.13/1.61 ! [X1: product_prod_a_a > product_prod_a_a > $o,X2: list_P1467822637od_a_a,Y1: product_prod_a_a > product_prod_a_a > $o,Y2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( ( produc214132118od_a_a @ X1 @ X2 )
% 3.13/1.61 = ( produc214132118od_a_a @ Y1 @ Y2 ) )
% 3.13/1.61 = ( ( X1 = Y1 )
% 3.13/1.61 & ( X2 = Y2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_28_prod_Oinject,axiom,
% 3.13/1.61 ! [X1: a,X2: produc657167928_a_a_a,Y1: a,Y2: produc657167928_a_a_a] :
% 3.13/1.61 ( ( ( produc1440321489_a_a_a @ X1 @ X2 )
% 3.13/1.61 = ( produc1440321489_a_a_a @ Y1 @ Y2 ) )
% 3.13/1.61 = ( ( X1 = Y1 )
% 3.13/1.61 & ( X2 = Y2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_29_prod_Oinject,axiom,
% 3.13/1.61 ! [X1: a,X2: list_P1467822637od_a_a,Y1: a,Y2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( ( produc575024326od_a_a @ X1 @ X2 )
% 3.13/1.61 = ( produc575024326od_a_a @ Y1 @ Y2 ) )
% 3.13/1.61 = ( ( X1 = Y1 )
% 3.13/1.61 & ( X2 = Y2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_30_prod_Oinject,axiom,
% 3.13/1.61 ! [X1: a,X2: a,Y1: a,Y2: a] :
% 3.13/1.61 ( ( ( product_Pair_a_a @ X1 @ X2 )
% 3.13/1.61 = ( product_Pair_a_a @ Y1 @ Y2 ) )
% 3.13/1.61 = ( ( X1 = Y1 )
% 3.13/1.61 & ( X2 = Y2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_31_old_Oprod_Oinject,axiom,
% 3.13/1.61 ! [A: list_P1467822637od_a_a,B: a,A2: list_P1467822637od_a_a,B2: a] :
% 3.13/1.61 ( ( ( produc998622632_a_a_a @ A @ B )
% 3.13/1.61 = ( produc998622632_a_a_a @ A2 @ B2 ) )
% 3.13/1.61 = ( ( A = A2 )
% 3.13/1.61 & ( B = B2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_32_old_Oprod_Oinject,axiom,
% 3.13/1.61 ! [A: list_a,B: list_a,A2: list_a,B2: list_a] :
% 3.13/1.61 ( ( ( produc1448356631list_a @ A @ B )
% 3.13/1.61 = ( produc1448356631list_a @ A2 @ B2 ) )
% 3.13/1.61 = ( ( A = A2 )
% 3.13/1.61 & ( B = B2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_33_old_Oprod_Oinject,axiom,
% 3.13/1.61 ! [A: product_prod_a_a > product_prod_a_a > $o,B: list_P1467822637od_a_a,A2: product_prod_a_a > product_prod_a_a > $o,B2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( ( produc214132118od_a_a @ A @ B )
% 3.13/1.61 = ( produc214132118od_a_a @ A2 @ B2 ) )
% 3.13/1.61 = ( ( A = A2 )
% 3.13/1.61 & ( B = B2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_34_old_Oprod_Oinject,axiom,
% 3.13/1.61 ! [A: a,B: produc657167928_a_a_a,A2: a,B2: produc657167928_a_a_a] :
% 3.13/1.61 ( ( ( produc1440321489_a_a_a @ A @ B )
% 3.13/1.61 = ( produc1440321489_a_a_a @ A2 @ B2 ) )
% 3.13/1.61 = ( ( A = A2 )
% 3.13/1.61 & ( B = B2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_35_old_Oprod_Oinject,axiom,
% 3.13/1.61 ! [A: a,B: list_P1467822637od_a_a,A2: a,B2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( ( produc575024326od_a_a @ A @ B )
% 3.13/1.61 = ( produc575024326od_a_a @ A2 @ B2 ) )
% 3.13/1.61 = ( ( A = A2 )
% 3.13/1.61 & ( B = B2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_36_old_Oprod_Oinject,axiom,
% 3.13/1.61 ! [A: a,B: a,A2: a,B2: a] :
% 3.13/1.61 ( ( ( product_Pair_a_a @ A @ B )
% 3.13/1.61 = ( product_Pair_a_a @ A2 @ B2 ) )
% 3.13/1.61 = ( ( A = A2 )
% 3.13/1.61 & ( B = B2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_37_Cons__eq__appendI,axiom,
% 3.13/1.61 ! [X3: a,Xs1: list_a,Ys2: list_a,Xs2: list_a,Zs: list_a] :
% 3.13/1.61 ( ( ( cons_a @ X3 @ Xs1 )
% 3.13/1.61 = Ys2 )
% 3.13/1.61 => ( ( Xs2
% 3.13/1.61 = ( append_a @ Xs1 @ Zs ) )
% 3.13/1.61 => ( ( cons_a @ X3 @ Xs2 )
% 3.13/1.61 = ( append_a @ Ys2 @ Zs ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_38_Cons__eq__appendI,axiom,
% 3.13/1.61 ! [X3: produc1572603623od_a_a,Xs1: list_P1891567085od_a_a,Ys2: list_P1891567085od_a_a,Xs2: list_P1891567085od_a_a,Zs: list_P1891567085od_a_a] :
% 3.13/1.61 ( ( ( cons_P1070399645od_a_a @ X3 @ Xs1 )
% 3.13/1.61 = Ys2 )
% 3.13/1.61 => ( ( Xs2
% 3.13/1.61 = ( append864718978od_a_a @ Xs1 @ Zs ) )
% 3.13/1.61 => ( ( cons_P1070399645od_a_a @ X3 @ Xs2 )
% 3.13/1.61 = ( append864718978od_a_a @ Ys2 @ Zs ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_39_Cons__eq__appendI,axiom,
% 3.13/1.61 ! [X3: list_P1467822637od_a_a,Xs1: list_l1108175539od_a_a,Ys2: list_l1108175539od_a_a,Xs2: list_l1108175539od_a_a,Zs: list_l1108175539od_a_a] :
% 3.13/1.61 ( ( ( cons_l724116707od_a_a @ X3 @ Xs1 )
% 3.13/1.61 = Ys2 )
% 3.13/1.61 => ( ( Xs2
% 3.13/1.61 = ( append2141280328od_a_a @ Xs1 @ Zs ) )
% 3.13/1.61 => ( ( cons_l724116707od_a_a @ X3 @ Xs2 )
% 3.13/1.61 = ( append2141280328od_a_a @ Ys2 @ Zs ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_40_Cons__eq__appendI,axiom,
% 3.13/1.61 ! [X3: a > nat,Xs1: list_a_nat,Ys2: list_a_nat,Xs2: list_a_nat,Zs: list_a_nat] :
% 3.13/1.61 ( ( ( cons_a_nat @ X3 @ Xs1 )
% 3.13/1.61 = Ys2 )
% 3.13/1.61 => ( ( Xs2
% 3.13/1.61 = ( append_a_nat @ Xs1 @ Zs ) )
% 3.13/1.61 => ( ( cons_a_nat @ X3 @ Xs2 )
% 3.13/1.61 = ( append_a_nat @ Ys2 @ Zs ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_41_Cons__eq__appendI,axiom,
% 3.13/1.61 ! [X3: product_prod_a_a,Xs1: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Xs2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( ( cons_P1921020637od_a_a @ X3 @ Xs1 )
% 3.13/1.61 = Ys2 )
% 3.13/1.61 => ( ( Xs2
% 3.13/1.61 = ( append1574001858od_a_a @ Xs1 @ Zs ) )
% 3.13/1.61 => ( ( cons_P1921020637od_a_a @ X3 @ Xs2 )
% 3.13/1.61 = ( append1574001858od_a_a @ Ys2 @ Zs ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_42_append__Cons,axiom,
% 3.13/1.61 ! [X3: a,Xs2: list_a,Ys2: list_a] :
% 3.13/1.61 ( ( append_a @ ( cons_a @ X3 @ Xs2 ) @ Ys2 )
% 3.13/1.61 = ( cons_a @ X3 @ ( append_a @ Xs2 @ Ys2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_43_append__Cons,axiom,
% 3.13/1.61 ! [X3: produc1572603623od_a_a,Xs2: list_P1891567085od_a_a,Ys2: list_P1891567085od_a_a] :
% 3.13/1.61 ( ( append864718978od_a_a @ ( cons_P1070399645od_a_a @ X3 @ Xs2 ) @ Ys2 )
% 3.13/1.61 = ( cons_P1070399645od_a_a @ X3 @ ( append864718978od_a_a @ Xs2 @ Ys2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_44_append__Cons,axiom,
% 3.13/1.61 ! [X3: list_P1467822637od_a_a,Xs2: list_l1108175539od_a_a,Ys2: list_l1108175539od_a_a] :
% 3.13/1.61 ( ( append2141280328od_a_a @ ( cons_l724116707od_a_a @ X3 @ Xs2 ) @ Ys2 )
% 3.13/1.61 = ( cons_l724116707od_a_a @ X3 @ ( append2141280328od_a_a @ Xs2 @ Ys2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_45_append__Cons,axiom,
% 3.13/1.61 ! [X3: a > nat,Xs2: list_a_nat,Ys2: list_a_nat] :
% 3.13/1.61 ( ( append_a_nat @ ( cons_a_nat @ X3 @ Xs2 ) @ Ys2 )
% 3.13/1.61 = ( cons_a_nat @ X3 @ ( append_a_nat @ Xs2 @ Ys2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_46_append__Cons,axiom,
% 3.13/1.61 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( append1574001858od_a_a @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ Ys2 )
% 3.13/1.61 = ( cons_P1921020637od_a_a @ X3 @ ( append1574001858od_a_a @ Xs2 @ Ys2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_47_append__eq__appendI,axiom,
% 3.13/1.61 ! [Xs2: list_a,Xs1: list_a,Zs: list_a,Ys2: list_a,Us: list_a] :
% 3.13/1.61 ( ( ( append_a @ Xs2 @ Xs1 )
% 3.13/1.61 = Zs )
% 3.13/1.61 => ( ( Ys2
% 3.13/1.61 = ( append_a @ Xs1 @ Us ) )
% 3.13/1.61 => ( ( append_a @ Xs2 @ Ys2 )
% 3.13/1.61 = ( append_a @ Zs @ Us ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_48_append__eq__appendI,axiom,
% 3.13/1.61 ! [Xs2: list_P1891567085od_a_a,Xs1: list_P1891567085od_a_a,Zs: list_P1891567085od_a_a,Ys2: list_P1891567085od_a_a,Us: list_P1891567085od_a_a] :
% 3.13/1.61 ( ( ( append864718978od_a_a @ Xs2 @ Xs1 )
% 3.13/1.61 = Zs )
% 3.13/1.61 => ( ( Ys2
% 3.13/1.61 = ( append864718978od_a_a @ Xs1 @ Us ) )
% 3.13/1.61 => ( ( append864718978od_a_a @ Xs2 @ Ys2 )
% 3.13/1.61 = ( append864718978od_a_a @ Zs @ Us ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_49_append__eq__appendI,axiom,
% 3.13/1.61 ! [Xs2: list_l1108175539od_a_a,Xs1: list_l1108175539od_a_a,Zs: list_l1108175539od_a_a,Ys2: list_l1108175539od_a_a,Us: list_l1108175539od_a_a] :
% 3.13/1.61 ( ( ( append2141280328od_a_a @ Xs2 @ Xs1 )
% 3.13/1.61 = Zs )
% 3.13/1.61 => ( ( Ys2
% 3.13/1.61 = ( append2141280328od_a_a @ Xs1 @ Us ) )
% 3.13/1.61 => ( ( append2141280328od_a_a @ Xs2 @ Ys2 )
% 3.13/1.61 = ( append2141280328od_a_a @ Zs @ Us ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_50_append__eq__appendI,axiom,
% 3.13/1.61 ! [Xs2: list_P1467822637od_a_a,Xs1: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Us: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( ( append1574001858od_a_a @ Xs2 @ Xs1 )
% 3.13/1.61 = Zs )
% 3.13/1.61 => ( ( Ys2
% 3.13/1.61 = ( append1574001858od_a_a @ Xs1 @ Us ) )
% 3.13/1.61 => ( ( append1574001858od_a_a @ Xs2 @ Ys2 )
% 3.13/1.61 = ( append1574001858od_a_a @ Zs @ Us ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_51_append__eq__append__conv2,axiom,
% 3.13/1.61 ! [Xs2: list_a,Ys2: list_a,Zs: list_a,Ts: list_a] :
% 3.13/1.61 ( ( ( append_a @ Xs2 @ Ys2 )
% 3.13/1.61 = ( append_a @ Zs @ Ts ) )
% 3.13/1.61 = ( ? [Us2: list_a] :
% 3.13/1.61 ( ( ( Xs2
% 3.13/1.61 = ( append_a @ Zs @ Us2 ) )
% 3.13/1.61 & ( ( append_a @ Us2 @ Ys2 )
% 3.13/1.61 = Ts ) )
% 3.13/1.61 | ( ( ( append_a @ Xs2 @ Us2 )
% 3.13/1.61 = Zs )
% 3.13/1.61 & ( Ys2
% 3.13/1.61 = ( append_a @ Us2 @ Ts ) ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_52_append__eq__append__conv2,axiom,
% 3.13/1.61 ! [Xs2: list_P1891567085od_a_a,Ys2: list_P1891567085od_a_a,Zs: list_P1891567085od_a_a,Ts: list_P1891567085od_a_a] :
% 3.13/1.61 ( ( ( append864718978od_a_a @ Xs2 @ Ys2 )
% 3.13/1.61 = ( append864718978od_a_a @ Zs @ Ts ) )
% 3.13/1.61 = ( ? [Us2: list_P1891567085od_a_a] :
% 3.13/1.61 ( ( ( Xs2
% 3.13/1.61 = ( append864718978od_a_a @ Zs @ Us2 ) )
% 3.13/1.61 & ( ( append864718978od_a_a @ Us2 @ Ys2 )
% 3.13/1.61 = Ts ) )
% 3.13/1.61 | ( ( ( append864718978od_a_a @ Xs2 @ Us2 )
% 3.13/1.61 = Zs )
% 3.13/1.61 & ( Ys2
% 3.13/1.61 = ( append864718978od_a_a @ Us2 @ Ts ) ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_53_append__eq__append__conv2,axiom,
% 3.13/1.61 ! [Xs2: list_l1108175539od_a_a,Ys2: list_l1108175539od_a_a,Zs: list_l1108175539od_a_a,Ts: list_l1108175539od_a_a] :
% 3.13/1.61 ( ( ( append2141280328od_a_a @ Xs2 @ Ys2 )
% 3.13/1.61 = ( append2141280328od_a_a @ Zs @ Ts ) )
% 3.13/1.61 = ( ? [Us2: list_l1108175539od_a_a] :
% 3.13/1.61 ( ( ( Xs2
% 3.13/1.61 = ( append2141280328od_a_a @ Zs @ Us2 ) )
% 3.13/1.61 & ( ( append2141280328od_a_a @ Us2 @ Ys2 )
% 3.13/1.61 = Ts ) )
% 3.13/1.61 | ( ( ( append2141280328od_a_a @ Xs2 @ Us2 )
% 3.13/1.61 = Zs )
% 3.13/1.61 & ( Ys2
% 3.13/1.61 = ( append2141280328od_a_a @ Us2 @ Ts ) ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_54_append__eq__append__conv2,axiom,
% 3.13/1.61 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a,Ts: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( ( append1574001858od_a_a @ Xs2 @ Ys2 )
% 3.13/1.61 = ( append1574001858od_a_a @ Zs @ Ts ) )
% 3.13/1.61 = ( ? [Us2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( ( Xs2
% 3.13/1.61 = ( append1574001858od_a_a @ Zs @ Us2 ) )
% 3.13/1.61 & ( ( append1574001858od_a_a @ Us2 @ Ys2 )
% 3.13/1.61 = Ts ) )
% 3.13/1.61 | ( ( ( append1574001858od_a_a @ Xs2 @ Us2 )
% 3.13/1.61 = Zs )
% 3.13/1.61 & ( Ys2
% 3.13/1.61 = ( append1574001858od_a_a @ Us2 @ Ts ) ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_55_old_Oprod_Oinducts,axiom,
% 3.13/1.61 ! [P2: produc657167928_a_a_a > $o,Prod: produc657167928_a_a_a] :
% 3.13/1.61 ( ! [A3: list_P1467822637od_a_a,B3: a] : ( P2 @ ( produc998622632_a_a_a @ A3 @ B3 ) )
% 3.13/1.61 => ( P2 @ Prod ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_56_old_Oprod_Oinducts,axiom,
% 3.13/1.61 ! [P2: produc864062247list_a > $o,Prod: produc864062247list_a] :
% 3.13/1.61 ( ! [A3: list_a,B3: list_a] : ( P2 @ ( produc1448356631list_a @ A3 @ B3 ) )
% 3.13/1.61 => ( P2 @ Prod ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_57_old_Oprod_Oinducts,axiom,
% 3.13/1.61 ! [P2: produc501911462od_a_a > $o,Prod: produc501911462od_a_a] :
% 3.13/1.61 ( ! [A3: product_prod_a_a > product_prod_a_a > $o,B3: list_P1467822637od_a_a] : ( P2 @ ( produc214132118od_a_a @ A3 @ B3 ) )
% 3.13/1.61 => ( P2 @ Prod ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_58_old_Oprod_Oinducts,axiom,
% 3.13/1.61 ! [P2: produc1197928545_a_a_a > $o,Prod: produc1197928545_a_a_a] :
% 3.13/1.61 ( ! [A3: a,B3: produc657167928_a_a_a] : ( P2 @ ( produc1440321489_a_a_a @ A3 @ B3 ) )
% 3.13/1.61 => ( P2 @ Prod ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_59_old_Oprod_Oinducts,axiom,
% 3.13/1.61 ! [P2: produc1701253078od_a_a > $o,Prod: produc1701253078od_a_a] :
% 3.13/1.61 ( ! [A3: a,B3: list_P1467822637od_a_a] : ( P2 @ ( produc575024326od_a_a @ A3 @ B3 ) )
% 3.13/1.61 => ( P2 @ Prod ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_60_old_Oprod_Oinducts,axiom,
% 3.13/1.61 ! [P2: product_prod_a_a > $o,Prod: product_prod_a_a] :
% 3.13/1.61 ( ! [A3: a,B3: a] : ( P2 @ ( product_Pair_a_a @ A3 @ B3 ) )
% 3.13/1.61 => ( P2 @ Prod ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_61_old_Oprod_Oexhaust,axiom,
% 3.13/1.61 ! [Y3: produc657167928_a_a_a] :
% 3.13/1.61 ~ ! [A3: list_P1467822637od_a_a,B3: a] :
% 3.13/1.61 ( Y3
% 3.13/1.61 != ( produc998622632_a_a_a @ A3 @ B3 ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_62_old_Oprod_Oexhaust,axiom,
% 3.13/1.61 ! [Y3: produc864062247list_a] :
% 3.13/1.61 ~ ! [A3: list_a,B3: list_a] :
% 3.13/1.61 ( Y3
% 3.13/1.61 != ( produc1448356631list_a @ A3 @ B3 ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_63_old_Oprod_Oexhaust,axiom,
% 3.13/1.61 ! [Y3: produc501911462od_a_a] :
% 3.13/1.61 ~ ! [A3: product_prod_a_a > product_prod_a_a > $o,B3: list_P1467822637od_a_a] :
% 3.13/1.61 ( Y3
% 3.13/1.61 != ( produc214132118od_a_a @ A3 @ B3 ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_64_old_Oprod_Oexhaust,axiom,
% 3.13/1.61 ! [Y3: produc1197928545_a_a_a] :
% 3.13/1.61 ~ ! [A3: a,B3: produc657167928_a_a_a] :
% 3.13/1.61 ( Y3
% 3.13/1.61 != ( produc1440321489_a_a_a @ A3 @ B3 ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_65_old_Oprod_Oexhaust,axiom,
% 3.13/1.61 ! [Y3: produc1701253078od_a_a] :
% 3.13/1.61 ~ ! [A3: a,B3: list_P1467822637od_a_a] :
% 3.13/1.61 ( Y3
% 3.13/1.61 != ( produc575024326od_a_a @ A3 @ B3 ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_66_old_Oprod_Oexhaust,axiom,
% 3.13/1.61 ! [Y3: product_prod_a_a] :
% 3.13/1.61 ~ ! [A3: a,B3: a] :
% 3.13/1.61 ( Y3
% 3.13/1.61 != ( product_Pair_a_a @ A3 @ B3 ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_67_prod__induct3,axiom,
% 3.13/1.61 ! [P2: produc1197928545_a_a_a > $o,X3: produc1197928545_a_a_a] :
% 3.13/1.61 ( ! [A3: a,B3: list_P1467822637od_a_a,C2: a] : ( P2 @ ( produc1440321489_a_a_a @ A3 @ ( produc998622632_a_a_a @ B3 @ C2 ) ) )
% 3.13/1.61 => ( P2 @ X3 ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_68_prod__cases3,axiom,
% 3.13/1.61 ! [Y3: produc1197928545_a_a_a] :
% 3.13/1.61 ~ ! [A3: a,B3: list_P1467822637od_a_a,C2: a] :
% 3.13/1.61 ( Y3
% 3.13/1.61 != ( produc1440321489_a_a_a @ A3 @ ( produc998622632_a_a_a @ B3 @ C2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_69_Pair__inject,axiom,
% 3.13/1.61 ! [A: list_P1467822637od_a_a,B: a,A2: list_P1467822637od_a_a,B2: a] :
% 3.13/1.61 ( ( ( produc998622632_a_a_a @ A @ B )
% 3.13/1.61 = ( produc998622632_a_a_a @ A2 @ B2 ) )
% 3.13/1.61 => ~ ( ( A = A2 )
% 3.13/1.61 => ( B != B2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_70_Pair__inject,axiom,
% 3.13/1.61 ! [A: list_a,B: list_a,A2: list_a,B2: list_a] :
% 3.13/1.61 ( ( ( produc1448356631list_a @ A @ B )
% 3.13/1.61 = ( produc1448356631list_a @ A2 @ B2 ) )
% 3.13/1.61 => ~ ( ( A = A2 )
% 3.13/1.61 => ( B != B2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_71_Pair__inject,axiom,
% 3.13/1.61 ! [A: product_prod_a_a > product_prod_a_a > $o,B: list_P1467822637od_a_a,A2: product_prod_a_a > product_prod_a_a > $o,B2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( ( produc214132118od_a_a @ A @ B )
% 3.13/1.61 = ( produc214132118od_a_a @ A2 @ B2 ) )
% 3.13/1.61 => ~ ( ( A = A2 )
% 3.13/1.61 => ( B != B2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_72_Pair__inject,axiom,
% 3.13/1.61 ! [A: a,B: produc657167928_a_a_a,A2: a,B2: produc657167928_a_a_a] :
% 3.13/1.61 ( ( ( produc1440321489_a_a_a @ A @ B )
% 3.13/1.61 = ( produc1440321489_a_a_a @ A2 @ B2 ) )
% 3.13/1.61 => ~ ( ( A = A2 )
% 3.13/1.61 => ( B != B2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_73_Pair__inject,axiom,
% 3.13/1.61 ! [A: a,B: list_P1467822637od_a_a,A2: a,B2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( ( produc575024326od_a_a @ A @ B )
% 3.13/1.61 = ( produc575024326od_a_a @ A2 @ B2 ) )
% 3.13/1.61 => ~ ( ( A = A2 )
% 3.13/1.61 => ( B != B2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_74_Pair__inject,axiom,
% 3.13/1.61 ! [A: a,B: a,A2: a,B2: a] :
% 3.13/1.61 ( ( ( product_Pair_a_a @ A @ B )
% 3.13/1.61 = ( product_Pair_a_a @ A2 @ B2 ) )
% 3.13/1.61 => ~ ( ( A = A2 )
% 3.13/1.61 => ( B != B2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_75_prod__cases,axiom,
% 3.13/1.61 ! [P2: produc657167928_a_a_a > $o,P3: produc657167928_a_a_a] :
% 3.13/1.61 ( ! [A3: list_P1467822637od_a_a,B3: a] : ( P2 @ ( produc998622632_a_a_a @ A3 @ B3 ) )
% 3.13/1.61 => ( P2 @ P3 ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_76_prod__cases,axiom,
% 3.13/1.61 ! [P2: produc864062247list_a > $o,P3: produc864062247list_a] :
% 3.13/1.61 ( ! [A3: list_a,B3: list_a] : ( P2 @ ( produc1448356631list_a @ A3 @ B3 ) )
% 3.13/1.61 => ( P2 @ P3 ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_77_prod__cases,axiom,
% 3.13/1.61 ! [P2: produc501911462od_a_a > $o,P3: produc501911462od_a_a] :
% 3.13/1.61 ( ! [A3: product_prod_a_a > product_prod_a_a > $o,B3: list_P1467822637od_a_a] : ( P2 @ ( produc214132118od_a_a @ A3 @ B3 ) )
% 3.13/1.61 => ( P2 @ P3 ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_78_prod__cases,axiom,
% 3.13/1.61 ! [P2: produc1197928545_a_a_a > $o,P3: produc1197928545_a_a_a] :
% 3.13/1.61 ( ! [A3: a,B3: produc657167928_a_a_a] : ( P2 @ ( produc1440321489_a_a_a @ A3 @ B3 ) )
% 3.13/1.61 => ( P2 @ P3 ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_79_prod__cases,axiom,
% 3.13/1.61 ! [P2: produc1701253078od_a_a > $o,P3: produc1701253078od_a_a] :
% 3.13/1.61 ( ! [A3: a,B3: list_P1467822637od_a_a] : ( P2 @ ( produc575024326od_a_a @ A3 @ B3 ) )
% 3.13/1.61 => ( P2 @ P3 ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_80_prod__cases,axiom,
% 3.13/1.61 ! [P2: product_prod_a_a > $o,P3: product_prod_a_a] :
% 3.13/1.61 ( ! [A3: a,B3: a] : ( P2 @ ( product_Pair_a_a @ A3 @ B3 ) )
% 3.13/1.61 => ( P2 @ P3 ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_81_surj__pair,axiom,
% 3.13/1.61 ! [P3: produc657167928_a_a_a] :
% 3.13/1.61 ? [X4: list_P1467822637od_a_a,Y4: a] :
% 3.13/1.61 ( P3
% 3.13/1.61 = ( produc998622632_a_a_a @ X4 @ Y4 ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_82_surj__pair,axiom,
% 3.13/1.61 ! [P3: produc864062247list_a] :
% 3.13/1.61 ? [X4: list_a,Y4: list_a] :
% 3.13/1.61 ( P3
% 3.13/1.61 = ( produc1448356631list_a @ X4 @ Y4 ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_83_surj__pair,axiom,
% 3.13/1.61 ! [P3: produc501911462od_a_a] :
% 3.13/1.61 ? [X4: product_prod_a_a > product_prod_a_a > $o,Y4: list_P1467822637od_a_a] :
% 3.13/1.61 ( P3
% 3.13/1.61 = ( produc214132118od_a_a @ X4 @ Y4 ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_84_surj__pair,axiom,
% 3.13/1.61 ! [P3: produc1197928545_a_a_a] :
% 3.13/1.61 ? [X4: a,Y4: produc657167928_a_a_a] :
% 3.13/1.61 ( P3
% 3.13/1.61 = ( produc1440321489_a_a_a @ X4 @ Y4 ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_85_surj__pair,axiom,
% 3.13/1.61 ! [P3: produc1701253078od_a_a] :
% 3.13/1.61 ? [X4: a,Y4: list_P1467822637od_a_a] :
% 3.13/1.61 ( P3
% 3.13/1.61 = ( produc575024326od_a_a @ X4 @ Y4 ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_86_surj__pair,axiom,
% 3.13/1.61 ! [P3: product_prod_a_a] :
% 3.13/1.61 ? [X4: a,Y4: a] :
% 3.13/1.61 ( P3
% 3.13/1.61 = ( product_Pair_a_a @ X4 @ Y4 ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_87_not__Cons__self2,axiom,
% 3.13/1.61 ! [X3: a,Xs2: list_a] :
% 3.13/1.61 ( ( cons_a @ X3 @ Xs2 )
% 3.13/1.61 != Xs2 ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_88_not__Cons__self2,axiom,
% 3.13/1.61 ! [X3: produc1572603623od_a_a,Xs2: list_P1891567085od_a_a] :
% 3.13/1.61 ( ( cons_P1070399645od_a_a @ X3 @ Xs2 )
% 3.13/1.61 != Xs2 ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_89_not__Cons__self2,axiom,
% 3.13/1.61 ! [X3: list_P1467822637od_a_a,Xs2: list_l1108175539od_a_a] :
% 3.13/1.61 ( ( cons_l724116707od_a_a @ X3 @ Xs2 )
% 3.13/1.61 != Xs2 ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_90_not__Cons__self2,axiom,
% 3.13/1.61 ! [X3: a > nat,Xs2: list_a_nat] :
% 3.13/1.61 ( ( cons_a_nat @ X3 @ Xs2 )
% 3.13/1.61 != Xs2 ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_91_not__Cons__self2,axiom,
% 3.13/1.61 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( cons_P1921020637od_a_a @ X3 @ Xs2 )
% 3.13/1.61 != Xs2 ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_92_bind__simps_I2_J,axiom,
% 3.13/1.61 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a,F: product_prod_a_a > list_P1467822637od_a_a] :
% 3.13/1.61 ( ( bind_P1783625031od_a_a @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ F )
% 3.13/1.61 = ( append1574001858od_a_a @ ( F @ X3 ) @ ( bind_P1783625031od_a_a @ Xs2 @ F ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_93_bind__simps_I2_J,axiom,
% 3.13/1.61 ! [X3: a,Xs2: list_a,F: a > list_a] :
% 3.13/1.61 ( ( bind_a_a @ ( cons_a @ X3 @ Xs2 ) @ F )
% 3.13/1.61 = ( append_a @ ( F @ X3 ) @ ( bind_a_a @ Xs2 @ F ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_94_bind__simps_I2_J,axiom,
% 3.13/1.61 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a,F: product_prod_a_a > list_a] :
% 3.13/1.61 ( ( bind_P293964574_a_a_a @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ F )
% 3.13/1.61 = ( append_a @ ( F @ X3 ) @ ( bind_P293964574_a_a_a @ Xs2 @ F ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_95_bind__simps_I2_J,axiom,
% 3.13/1.61 ! [X3: a,Xs2: list_a,F: a > list_P1467822637od_a_a] :
% 3.13/1.61 ( ( bind_a1679112752od_a_a @ ( cons_a @ X3 @ Xs2 ) @ F )
% 3.13/1.61 = ( append1574001858od_a_a @ ( F @ X3 ) @ ( bind_a1679112752od_a_a @ Xs2 @ F ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_96_bind__simps_I2_J,axiom,
% 3.13/1.61 ! [X3: a > nat,Xs2: list_a_nat,F: ( a > nat ) > list_a] :
% 3.13/1.61 ( ( bind_a_nat_a @ ( cons_a_nat @ X3 @ Xs2 ) @ F )
% 3.13/1.61 = ( append_a @ ( F @ X3 ) @ ( bind_a_nat_a @ Xs2 @ F ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_97_bind__simps_I2_J,axiom,
% 3.13/1.61 ! [X3: a,Xs2: list_a,F: a > list_l1108175539od_a_a] :
% 3.13/1.61 ( ( bind_a883992246od_a_a @ ( cons_a @ X3 @ Xs2 ) @ F )
% 3.13/1.61 = ( append2141280328od_a_a @ ( F @ X3 ) @ ( bind_a883992246od_a_a @ Xs2 @ F ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_98_bind__simps_I2_J,axiom,
% 3.13/1.61 ! [X3: list_P1467822637od_a_a,Xs2: list_l1108175539od_a_a,F: list_P1467822637od_a_a > list_a] :
% 3.13/1.61 ( ( bind_l1307590552_a_a_a @ ( cons_l724116707od_a_a @ X3 @ Xs2 ) @ F )
% 3.13/1.61 = ( append_a @ ( F @ X3 ) @ ( bind_l1307590552_a_a_a @ Xs2 @ F ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_99_bind__simps_I2_J,axiom,
% 3.13/1.61 ! [X3: a > nat,Xs2: list_a_nat,F: ( a > nat ) > list_P1467822637od_a_a] :
% 3.13/1.61 ( ( bind_a1190333103od_a_a @ ( cons_a_nat @ X3 @ Xs2 ) @ F )
% 3.13/1.61 = ( append1574001858od_a_a @ ( F @ X3 ) @ ( bind_a1190333103od_a_a @ Xs2 @ F ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_100_bind__simps_I2_J,axiom,
% 3.13/1.61 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a,F: product_prod_a_a > list_l1108175539od_a_a] :
% 3.13/1.61 ( ( bind_P240085581od_a_a @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ F )
% 3.13/1.61 = ( append2141280328od_a_a @ ( F @ X3 ) @ ( bind_P240085581od_a_a @ Xs2 @ F ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_101_bind__simps_I2_J,axiom,
% 3.13/1.61 ! [X3: list_P1467822637od_a_a,Xs2: list_l1108175539od_a_a,F: list_P1467822637od_a_a > list_P1467822637od_a_a] :
% 3.13/1.61 ( ( bind_l618536897od_a_a @ ( cons_l724116707od_a_a @ X3 @ Xs2 ) @ F )
% 3.13/1.61 = ( append1574001858od_a_a @ ( F @ X3 ) @ ( bind_l618536897od_a_a @ Xs2 @ F ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_102_maps__simps_I1_J,axiom,
% 3.13/1.61 ! [F: product_prod_a_a > list_P1467822637od_a_a,X3: product_prod_a_a,Xs2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( maps_P1529886977od_a_a @ F @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) )
% 3.13/1.61 = ( append1574001858od_a_a @ ( F @ X3 ) @ ( maps_P1529886977od_a_a @ F @ Xs2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_103_maps__simps_I1_J,axiom,
% 3.13/1.61 ! [F: a > list_a,X3: a,Xs2: list_a] :
% 3.13/1.61 ( ( maps_a_a @ F @ ( cons_a @ X3 @ Xs2 ) )
% 3.13/1.61 = ( append_a @ ( F @ X3 ) @ ( maps_a_a @ F @ Xs2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_104_maps__simps_I1_J,axiom,
% 3.13/1.61 ! [F: product_prod_a_a > list_a,X3: product_prod_a_a,Xs2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( maps_P321755352_a_a_a @ F @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) )
% 3.13/1.61 = ( append_a @ ( F @ X3 ) @ ( maps_P321755352_a_a_a @ F @ Xs2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_105_maps__simps_I1_J,axiom,
% 3.13/1.61 ! [F: a > list_P1467822637od_a_a,X3: a,Xs2: list_a] :
% 3.13/1.61 ( ( maps_a1706903530od_a_a @ F @ ( cons_a @ X3 @ Xs2 ) )
% 3.13/1.61 = ( append1574001858od_a_a @ ( F @ X3 ) @ ( maps_a1706903530od_a_a @ F @ Xs2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_106_maps__simps_I1_J,axiom,
% 3.13/1.61 ! [F: ( a > nat ) > list_a,X3: a > nat,Xs2: list_a_nat] :
% 3.13/1.61 ( ( maps_a_nat_a @ F @ ( cons_a_nat @ X3 @ Xs2 ) )
% 3.13/1.61 = ( append_a @ ( F @ X3 ) @ ( maps_a_nat_a @ F @ Xs2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_107_maps__simps_I1_J,axiom,
% 3.13/1.61 ! [F: a > list_l1108175539od_a_a,X3: a,Xs2: list_a] :
% 3.13/1.61 ( ( maps_a667520880od_a_a @ F @ ( cons_a @ X3 @ Xs2 ) )
% 3.13/1.61 = ( append2141280328od_a_a @ ( F @ X3 ) @ ( maps_a667520880od_a_a @ F @ Xs2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_108_maps__simps_I1_J,axiom,
% 3.13/1.61 ! [F: list_P1467822637od_a_a > list_a,X3: list_P1467822637od_a_a,Xs2: list_l1108175539od_a_a] :
% 3.13/1.61 ( ( maps_l1091119186_a_a_a @ F @ ( cons_l724116707od_a_a @ X3 @ Xs2 ) )
% 3.13/1.61 = ( append_a @ ( F @ X3 ) @ ( maps_l1091119186_a_a_a @ F @ Xs2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_109_maps__simps_I1_J,axiom,
% 3.13/1.61 ! [F: ( a > nat ) > list_P1467822637od_a_a,X3: a > nat,Xs2: list_a_nat] :
% 3.13/1.61 ( ( maps_a836827497od_a_a @ F @ ( cons_a_nat @ X3 @ Xs2 ) )
% 3.13/1.61 = ( append1574001858od_a_a @ ( F @ X3 ) @ ( maps_a836827497od_a_a @ F @ Xs2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_110_maps__simps_I1_J,axiom,
% 3.13/1.61 ! [F: product_prod_a_a > list_l1108175539od_a_a,X3: product_prod_a_a,Xs2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( maps_P739084551od_a_a @ F @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) )
% 3.13/1.61 = ( append2141280328od_a_a @ ( F @ X3 ) @ ( maps_P739084551od_a_a @ F @ Xs2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_111_maps__simps_I1_J,axiom,
% 3.13/1.61 ! [F: list_P1467822637od_a_a > list_P1467822637od_a_a,X3: list_P1467822637od_a_a,Xs2: list_l1108175539od_a_a] :
% 3.13/1.61 ( ( maps_l1117535867od_a_a @ F @ ( cons_l724116707od_a_a @ X3 @ Xs2 ) )
% 3.13/1.61 = ( append1574001858od_a_a @ ( F @ X3 ) @ ( maps_l1117535867od_a_a @ F @ Xs2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_112_lexord__append__left__rightI,axiom,
% 3.13/1.61 ! [A: produc1572603623od_a_a,B: produc1572603623od_a_a,R: set_Pr1295299783od_a_a,U: list_P1891567085od_a_a,X3: list_P1891567085od_a_a,Y3: list_P1891567085od_a_a] :
% 3.13/1.61 ( ( member1899387664od_a_a @ ( produc1935643479od_a_a @ A @ B ) @ R )
% 3.13/1.61 => ( member1254757008od_a_a @ ( produc461662679od_a_a @ ( append864718978od_a_a @ U @ ( cons_P1070399645od_a_a @ A @ X3 ) ) @ ( append864718978od_a_a @ U @ ( cons_P1070399645od_a_a @ B @ Y3 ) ) ) @ ( lexord931792858od_a_a @ R ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_113_lexord__append__left__rightI,axiom,
% 3.13/1.61 ! [A: list_P1467822637od_a_a,B: list_P1467822637od_a_a,R: set_Pr800560199od_a_a,U: list_l1108175539od_a_a,X3: list_l1108175539od_a_a,Y3: list_l1108175539od_a_a] :
% 3.13/1.61 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ A @ B ) @ R )
% 3.13/1.61 => ( member8108048od_a_a @ ( produc915218007od_a_a @ ( append2141280328od_a_a @ U @ ( cons_l724116707od_a_a @ A @ X3 ) ) @ ( append2141280328od_a_a @ U @ ( cons_l724116707od_a_a @ B @ Y3 ) ) ) @ ( lexord1284731808od_a_a @ R ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_114_lexord__append__left__rightI,axiom,
% 3.13/1.61 ! [A: a > nat,B: a > nat,R: set_Pr1940702919_a_nat,U: list_a_nat,X3: list_a_nat,Y3: list_a_nat] :
% 3.13/1.61 ( ( member125757712_a_nat @ ( produc1569872215_a_nat @ A @ B ) @ R )
% 3.13/1.61 => ( member688761744_a_nat @ ( produc1430747863_a_nat @ ( append_a_nat @ U @ ( cons_a_nat @ A @ X3 ) ) @ ( append_a_nat @ U @ ( cons_a_nat @ B @ Y3 ) ) ) @ ( lexord_a_nat @ R ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_115_lexord__append__left__rightI,axiom,
% 3.13/1.61 ! [A: list_a,B: list_a,R: set_Pr1971762695list_a,U: list_list_a,X3: list_list_a,Y3: list_list_a] :
% 3.13/1.61 ( ( member1250517072list_a @ ( produc1448356631list_a @ A @ B ) @ R )
% 3.13/1.61 => ( member888406864list_a @ ( produc2583831list_a @ ( append_list_a @ U @ ( cons_list_a @ A @ X3 ) ) @ ( append_list_a @ U @ ( cons_list_a @ B @ Y3 ) ) ) @ ( lexord_list_a @ R ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_116_lexord__append__left__rightI,axiom,
% 3.13/1.61 ! [A: product_prod_a_a,B: product_prod_a_a,R: set_Pr1948701895od_a_a,U: list_P1467822637od_a_a,X3: list_P1467822637od_a_a,Y3: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B ) @ R )
% 3.13/1.61 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ U @ ( cons_P1921020637od_a_a @ A @ X3 ) ) @ ( append1574001858od_a_a @ U @ ( cons_P1921020637od_a_a @ B @ Y3 ) ) ) @ ( lexord673907738od_a_a @ R ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_117_lexord__append__left__rightI,axiom,
% 3.13/1.61 ! [A: a,B: a,R: set_Product_prod_a_a,U: list_a,X3: list_a,Y3: list_a] :
% 3.13/1.61 ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ R )
% 3.13/1.61 => ( member1250517072list_a @ ( produc1448356631list_a @ ( append_a @ U @ ( cons_a @ A @ X3 ) ) @ ( append_a @ U @ ( cons_a @ B @ Y3 ) ) ) @ ( lexord_a @ R ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_118_zip__Cons__Cons,axiom,
% 3.13/1.61 ! [X3: a,Xs2: list_a,Y3: a,Ys2: list_a] :
% 3.13/1.61 ( ( zip_a_a @ ( cons_a @ X3 @ Xs2 ) @ ( cons_a @ Y3 @ Ys2 ) )
% 3.13/1.61 = ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ ( zip_a_a @ Xs2 @ Ys2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_119_zip__Cons__Cons,axiom,
% 3.13/1.61 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a,Y3: product_prod_a_a,Ys2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( zip_Pr792472183od_a_a @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ ( cons_P1921020637od_a_a @ Y3 @ Ys2 ) )
% 3.13/1.61 = ( cons_P1070399645od_a_a @ ( produc1474507607od_a_a @ X3 @ Y3 ) @ ( zip_Pr792472183od_a_a @ Xs2 @ Ys2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_120_zip__Cons__Cons,axiom,
% 3.13/1.61 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a,Y3: a,Ys2: list_a] :
% 3.13/1.61 ( ( zip_Pr201224270_a_a_a @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ ( cons_a @ Y3 @ Ys2 ) )
% 3.13/1.61 = ( cons_P86081012_a_a_a @ ( produc2061588782_a_a_a @ X3 @ Y3 ) @ ( zip_Pr201224270_a_a_a @ Xs2 @ Ys2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_121_zip__Cons__Cons,axiom,
% 3.13/1.61 ! [X3: a,Xs2: list_a,Y3: product_prod_a_a,Ys2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( zip_a_1586372448od_a_a @ ( cons_a @ X3 @ Xs2 ) @ ( cons_P1921020637od_a_a @ Y3 @ Ys2 ) )
% 3.13/1.61 = ( cons_P991044742od_a_a @ ( produc1299253312od_a_a @ X3 @ Y3 ) @ ( zip_a_1586372448od_a_a @ Xs2 @ Ys2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_122_zip__Cons__Cons,axiom,
% 3.13/1.61 ! [X3: a,Xs2: list_a,Y3: a > nat,Ys2: list_a_nat] :
% 3.13/1.61 ( ( zip_a_a_nat @ ( cons_a @ X3 @ Xs2 ) @ ( cons_a_nat @ Y3 @ Ys2 ) )
% 3.13/1.61 = ( cons_P1915851550_a_nat @ ( product_Pair_a_a_nat @ X3 @ Y3 ) @ ( zip_a_a_nat @ Xs2 @ Ys2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_123_zip__Cons__Cons,axiom,
% 3.13/1.61 ! [X3: a > nat,Xs2: list_a_nat,Y3: a,Ys2: list_a] :
% 3.13/1.61 ( ( zip_a_nat_a @ ( cons_a_nat @ X3 @ Xs2 ) @ ( cons_a @ Y3 @ Ys2 ) )
% 3.13/1.61 = ( cons_P896312284_nat_a @ ( product_Pair_a_nat_a @ X3 @ Y3 ) @ ( zip_a_nat_a @ Xs2 @ Ys2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_124_zip__Cons__Cons,axiom,
% 3.13/1.61 ! [X3: list_a,Xs2: list_list_a,Y3: list_a,Ys2: list_list_a] :
% 3.13/1.61 ( ( zip_list_a_list_a @ ( cons_list_a @ X3 @ Xs2 ) @ ( cons_list_a @ Y3 @ Ys2 ) )
% 3.13/1.61 = ( cons_P2080942813list_a @ ( produc1448356631list_a @ X3 @ Y3 ) @ ( zip_list_a_list_a @ Xs2 @ Ys2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_125_zip__Cons__Cons,axiom,
% 3.13/1.61 ! [X3: list_P1467822637od_a_a,Xs2: list_l1108175539od_a_a,Y3: a,Ys2: list_a] :
% 3.13/1.61 ( ( zip_li245157064_a_a_a @ ( cons_l724116707od_a_a @ X3 @ Xs2 ) @ ( cons_a @ Y3 @ Ys2 ) )
% 3.13/1.61 = ( cons_P169173742_a_a_a @ ( produc998622632_a_a_a @ X3 @ Y3 ) @ ( zip_li245157064_a_a_a @ Xs2 @ Ys2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_126_zip__Cons__Cons,axiom,
% 3.13/1.61 ! [X3: a,Xs2: list_a,Y3: list_P1467822637od_a_a,Ys2: list_l1108175539od_a_a] :
% 3.13/1.61 ( ( zip_a_1969042406od_a_a @ ( cons_a @ X3 @ Xs2 ) @ ( cons_l724116707od_a_a @ Y3 @ Ys2 ) )
% 3.13/1.61 = ( cons_P1213258892od_a_a @ ( produc575024326od_a_a @ X3 @ Y3 ) @ ( zip_a_1969042406od_a_a @ Xs2 @ Ys2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_127_zip__Cons__Cons,axiom,
% 3.13/1.61 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a,Y3: a > nat,Ys2: list_a_nat] :
% 3.13/1.61 ( ( zip_Pr24086287_a_nat @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ ( cons_a_nat @ Y3 @ Ys2 ) )
% 3.13/1.61 = ( cons_P659009461_a_nat @ ( produc825466863_a_nat @ X3 @ Y3 ) @ ( zip_Pr24086287_a_nat @ Xs2 @ Ys2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_128_listrel1I,axiom,
% 3.13/1.61 ! [X3: produc1572603623od_a_a,Y3: produc1572603623od_a_a,R: set_Pr1295299783od_a_a,Xs2: list_P1891567085od_a_a,Us: list_P1891567085od_a_a,Vs: list_P1891567085od_a_a,Ys2: list_P1891567085od_a_a] :
% 3.13/1.61 ( ( member1899387664od_a_a @ ( produc1935643479od_a_a @ X3 @ Y3 ) @ R )
% 3.13/1.61 => ( ( Xs2
% 3.13/1.61 = ( append864718978od_a_a @ Us @ ( cons_P1070399645od_a_a @ X3 @ Vs ) ) )
% 3.13/1.61 => ( ( Ys2
% 3.13/1.61 = ( append864718978od_a_a @ Us @ ( cons_P1070399645od_a_a @ Y3 @ Vs ) ) )
% 3.13/1.61 => ( member1254757008od_a_a @ ( produc461662679od_a_a @ Xs2 @ Ys2 ) @ ( listre1832537542od_a_a @ R ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_129_listrel1I,axiom,
% 3.13/1.61 ! [X3: list_P1467822637od_a_a,Y3: list_P1467822637od_a_a,R: set_Pr800560199od_a_a,Xs2: list_l1108175539od_a_a,Us: list_l1108175539od_a_a,Vs: list_l1108175539od_a_a,Ys2: list_l1108175539od_a_a] :
% 3.13/1.61 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ X3 @ Y3 ) @ R )
% 3.13/1.61 => ( ( Xs2
% 3.13/1.61 = ( append2141280328od_a_a @ Us @ ( cons_l724116707od_a_a @ X3 @ Vs ) ) )
% 3.13/1.61 => ( ( Ys2
% 3.13/1.61 = ( append2141280328od_a_a @ Us @ ( cons_l724116707od_a_a @ Y3 @ Vs ) ) )
% 3.13/1.61 => ( member8108048od_a_a @ ( produc915218007od_a_a @ Xs2 @ Ys2 ) @ ( listre651914124od_a_a @ R ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_130_listrel1I,axiom,
% 3.13/1.61 ! [X3: a > nat,Y3: a > nat,R: set_Pr1940702919_a_nat,Xs2: list_a_nat,Us: list_a_nat,Vs: list_a_nat,Ys2: list_a_nat] :
% 3.13/1.61 ( ( member125757712_a_nat @ ( produc1569872215_a_nat @ X3 @ Y3 ) @ R )
% 3.13/1.61 => ( ( Xs2
% 3.13/1.61 = ( append_a_nat @ Us @ ( cons_a_nat @ X3 @ Vs ) ) )
% 3.13/1.61 => ( ( Ys2
% 3.13/1.61 = ( append_a_nat @ Us @ ( cons_a_nat @ Y3 @ Vs ) ) )
% 3.13/1.61 => ( member688761744_a_nat @ ( produc1430747863_a_nat @ Xs2 @ Ys2 ) @ ( listrel1_a_nat @ R ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_131_listrel1I,axiom,
% 3.13/1.61 ! [X3: list_a,Y3: list_a,R: set_Pr1971762695list_a,Xs2: list_list_a,Us: list_list_a,Vs: list_list_a,Ys2: list_list_a] :
% 3.13/1.61 ( ( member1250517072list_a @ ( produc1448356631list_a @ X3 @ Y3 ) @ R )
% 3.13/1.61 => ( ( Xs2
% 3.13/1.61 = ( append_list_a @ Us @ ( cons_list_a @ X3 @ Vs ) ) )
% 3.13/1.61 => ( ( Ys2
% 3.13/1.61 = ( append_list_a @ Us @ ( cons_list_a @ Y3 @ Vs ) ) )
% 3.13/1.61 => ( member888406864list_a @ ( produc2583831list_a @ Xs2 @ Ys2 ) @ ( listrel1_list_a @ R ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_132_listrel1I,axiom,
% 3.13/1.61 ! [X3: product_prod_a_a,Y3: product_prod_a_a,R: set_Pr1948701895od_a_a,Xs2: list_P1467822637od_a_a,Us: list_P1467822637od_a_a,Vs: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X3 @ Y3 ) @ R )
% 3.13/1.61 => ( ( Xs2
% 3.13/1.61 = ( append1574001858od_a_a @ Us @ ( cons_P1921020637od_a_a @ X3 @ Vs ) ) )
% 3.13/1.61 => ( ( Ys2
% 3.13/1.61 = ( append1574001858od_a_a @ Us @ ( cons_P1921020637od_a_a @ Y3 @ Vs ) ) )
% 3.13/1.61 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ Ys2 ) @ ( listre944824838od_a_a @ R ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_133_listrel1I,axiom,
% 3.13/1.61 ! [X3: a,Y3: a,R: set_Product_prod_a_a,Xs2: list_a,Us: list_a,Vs: list_a,Ys2: list_a] :
% 3.13/1.61 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R )
% 3.13/1.61 => ( ( Xs2
% 3.13/1.61 = ( append_a @ Us @ ( cons_a @ X3 @ Vs ) ) )
% 3.13/1.61 => ( ( Ys2
% 3.13/1.61 = ( append_a @ Us @ ( cons_a @ Y3 @ Vs ) ) )
% 3.13/1.61 => ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ Ys2 ) @ ( listrel1_a @ R ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_134_listrel1E,axiom,
% 3.13/1.61 ! [Xs2: list_P1891567085od_a_a,Ys2: list_P1891567085od_a_a,R: set_Pr1295299783od_a_a] :
% 3.13/1.61 ( ( member1254757008od_a_a @ ( produc461662679od_a_a @ Xs2 @ Ys2 ) @ ( listre1832537542od_a_a @ R ) )
% 3.13/1.61 => ~ ! [X4: produc1572603623od_a_a,Y4: produc1572603623od_a_a] :
% 3.13/1.61 ( ( member1899387664od_a_a @ ( produc1935643479od_a_a @ X4 @ Y4 ) @ R )
% 3.13/1.61 => ! [Us3: list_P1891567085od_a_a,Vs2: list_P1891567085od_a_a] :
% 3.13/1.61 ( ( Xs2
% 3.13/1.61 = ( append864718978od_a_a @ Us3 @ ( cons_P1070399645od_a_a @ X4 @ Vs2 ) ) )
% 3.13/1.61 => ( Ys2
% 3.13/1.61 != ( append864718978od_a_a @ Us3 @ ( cons_P1070399645od_a_a @ Y4 @ Vs2 ) ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_135_listrel1E,axiom,
% 3.13/1.61 ! [Xs2: list_l1108175539od_a_a,Ys2: list_l1108175539od_a_a,R: set_Pr800560199od_a_a] :
% 3.13/1.61 ( ( member8108048od_a_a @ ( produc915218007od_a_a @ Xs2 @ Ys2 ) @ ( listre651914124od_a_a @ R ) )
% 3.13/1.61 => ~ ! [X4: list_P1467822637od_a_a,Y4: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ X4 @ Y4 ) @ R )
% 3.13/1.61 => ! [Us3: list_l1108175539od_a_a,Vs2: list_l1108175539od_a_a] :
% 3.13/1.61 ( ( Xs2
% 3.13/1.61 = ( append2141280328od_a_a @ Us3 @ ( cons_l724116707od_a_a @ X4 @ Vs2 ) ) )
% 3.13/1.61 => ( Ys2
% 3.13/1.61 != ( append2141280328od_a_a @ Us3 @ ( cons_l724116707od_a_a @ Y4 @ Vs2 ) ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_136_listrel1E,axiom,
% 3.13/1.61 ! [Xs2: list_a_nat,Ys2: list_a_nat,R: set_Pr1940702919_a_nat] :
% 3.13/1.61 ( ( member688761744_a_nat @ ( produc1430747863_a_nat @ Xs2 @ Ys2 ) @ ( listrel1_a_nat @ R ) )
% 3.13/1.61 => ~ ! [X4: a > nat,Y4: a > nat] :
% 3.13/1.61 ( ( member125757712_a_nat @ ( produc1569872215_a_nat @ X4 @ Y4 ) @ R )
% 3.13/1.61 => ! [Us3: list_a_nat,Vs2: list_a_nat] :
% 3.13/1.61 ( ( Xs2
% 3.13/1.61 = ( append_a_nat @ Us3 @ ( cons_a_nat @ X4 @ Vs2 ) ) )
% 3.13/1.61 => ( Ys2
% 3.13/1.61 != ( append_a_nat @ Us3 @ ( cons_a_nat @ Y4 @ Vs2 ) ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_137_listrel1E,axiom,
% 3.13/1.61 ! [Xs2: list_list_a,Ys2: list_list_a,R: set_Pr1971762695list_a] :
% 3.13/1.61 ( ( member888406864list_a @ ( produc2583831list_a @ Xs2 @ Ys2 ) @ ( listrel1_list_a @ R ) )
% 3.13/1.61 => ~ ! [X4: list_a,Y4: list_a] :
% 3.13/1.61 ( ( member1250517072list_a @ ( produc1448356631list_a @ X4 @ Y4 ) @ R )
% 3.13/1.61 => ! [Us3: list_list_a,Vs2: list_list_a] :
% 3.13/1.61 ( ( Xs2
% 3.13/1.61 = ( append_list_a @ Us3 @ ( cons_list_a @ X4 @ Vs2 ) ) )
% 3.13/1.61 => ( Ys2
% 3.13/1.61 != ( append_list_a @ Us3 @ ( cons_list_a @ Y4 @ Vs2 ) ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_138_listrel1E,axiom,
% 3.13/1.61 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 3.13/1.61 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ Ys2 ) @ ( listre944824838od_a_a @ R ) )
% 3.13/1.61 => ~ ! [X4: product_prod_a_a,Y4: product_prod_a_a] :
% 3.13/1.61 ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X4 @ Y4 ) @ R )
% 3.13/1.61 => ! [Us3: list_P1467822637od_a_a,Vs2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( Xs2
% 3.13/1.61 = ( append1574001858od_a_a @ Us3 @ ( cons_P1921020637od_a_a @ X4 @ Vs2 ) ) )
% 3.13/1.61 => ( Ys2
% 3.13/1.61 != ( append1574001858od_a_a @ Us3 @ ( cons_P1921020637od_a_a @ Y4 @ Vs2 ) ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_139_listrel1E,axiom,
% 3.13/1.61 ! [Xs2: list_a,Ys2: list_a,R: set_Product_prod_a_a] :
% 3.13/1.61 ( ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ Ys2 ) @ ( listrel1_a @ R ) )
% 3.13/1.61 => ~ ! [X4: a,Y4: a] :
% 3.13/1.61 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ R )
% 3.13/1.61 => ! [Us3: list_a,Vs2: list_a] :
% 3.13/1.61 ( ( Xs2
% 3.13/1.61 = ( append_a @ Us3 @ ( cons_a @ X4 @ Vs2 ) ) )
% 3.13/1.61 => ( Ys2
% 3.13/1.61 != ( append_a @ Us3 @ ( cons_a @ Y4 @ Vs2 ) ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_140_member__rec_I1_J,axiom,
% 3.13/1.61 ! [X3: a,Xs2: list_a,Y3: a] :
% 3.13/1.61 ( ( member_a @ ( cons_a @ X3 @ Xs2 ) @ Y3 )
% 3.13/1.61 = ( ( X3 = Y3 )
% 3.13/1.61 | ( member_a @ Xs2 @ Y3 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_141_member__rec_I1_J,axiom,
% 3.13/1.61 ! [X3: produc1572603623od_a_a,Xs2: list_P1891567085od_a_a,Y3: produc1572603623od_a_a] :
% 3.13/1.61 ( ( member2070313346od_a_a @ ( cons_P1070399645od_a_a @ X3 @ Xs2 ) @ Y3 )
% 3.13/1.61 = ( ( X3 = Y3 )
% 3.13/1.61 | ( member2070313346od_a_a @ Xs2 @ Y3 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_142_member__rec_I1_J,axiom,
% 3.13/1.61 ! [X3: list_P1467822637od_a_a,Xs2: list_l1108175539od_a_a,Y3: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( member261538120od_a_a @ ( cons_l724116707od_a_a @ X3 @ Xs2 ) @ Y3 )
% 3.13/1.61 = ( ( X3 = Y3 )
% 3.13/1.61 | ( member261538120od_a_a @ Xs2 @ Y3 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_143_member__rec_I1_J,axiom,
% 3.13/1.61 ! [X3: a > nat,Xs2: list_a_nat,Y3: a > nat] :
% 3.13/1.61 ( ( member_a_nat @ ( cons_a_nat @ X3 @ Xs2 ) @ Y3 )
% 3.13/1.61 = ( ( X3 = Y3 )
% 3.13/1.61 | ( member_a_nat @ Xs2 @ Y3 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_144_member__rec_I1_J,axiom,
% 3.13/1.61 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a,Y3: product_prod_a_a] :
% 3.13/1.61 ( ( member1112491458od_a_a @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ Y3 )
% 3.13/1.61 = ( ( X3 = Y3 )
% 3.13/1.61 | ( member1112491458od_a_a @ Xs2 @ Y3 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_145_ssubst__Pair__rhs,axiom,
% 3.13/1.61 ! [R: list_P1467822637od_a_a,S: list_P1467822637od_a_a,R2: set_Pr800560199od_a_a,S2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ R @ S ) @ R2 )
% 3.13/1.61 => ( ( S2 = S )
% 3.13/1.61 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ R @ S2 ) @ R2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_146_ssubst__Pair__rhs,axiom,
% 3.13/1.61 ! [R: list_P1467822637od_a_a,S: a,R2: set_Pr1525541400_a_a_a,S2: a] :
% 3.13/1.61 ( ( member430654177_a_a_a @ ( produc998622632_a_a_a @ R @ S ) @ R2 )
% 3.13/1.61 => ( ( S2 = S )
% 3.13/1.61 => ( member430654177_a_a_a @ ( produc998622632_a_a_a @ R @ S2 ) @ R2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_147_ssubst__Pair__rhs,axiom,
% 3.13/1.61 ! [R: list_a,S: list_a,R2: set_Pr1971762695list_a,S2: list_a] :
% 3.13/1.61 ( ( member1250517072list_a @ ( produc1448356631list_a @ R @ S ) @ R2 )
% 3.13/1.61 => ( ( S2 = S )
% 3.13/1.61 => ( member1250517072list_a @ ( produc1448356631list_a @ R @ S2 ) @ R2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_148_ssubst__Pair__rhs,axiom,
% 3.13/1.61 ! [R: product_prod_a_a > product_prod_a_a > $o,S: list_P1467822637od_a_a,R2: set_Pr727105414od_a_a,S2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( member372644687od_a_a @ ( produc214132118od_a_a @ R @ S ) @ R2 )
% 3.13/1.61 => ( ( S2 = S )
% 3.13/1.61 => ( member372644687od_a_a @ ( produc214132118od_a_a @ R @ S2 ) @ R2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_149_ssubst__Pair__rhs,axiom,
% 3.13/1.61 ! [R: a,S: produc657167928_a_a_a,R2: set_Pr110478017_a_a_a,S2: produc657167928_a_a_a] :
% 3.13/1.61 ( ( member1904151562_a_a_a @ ( produc1440321489_a_a_a @ R @ S ) @ R2 )
% 3.13/1.61 => ( ( S2 = S )
% 3.13/1.61 => ( member1904151562_a_a_a @ ( produc1440321489_a_a_a @ R @ S2 ) @ R2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_150_ssubst__Pair__rhs,axiom,
% 3.13/1.61 ! [R: a,S: list_P1467822637od_a_a,R2: set_Pr248149174od_a_a,S2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( member1474739327od_a_a @ ( produc575024326od_a_a @ R @ S ) @ R2 )
% 3.13/1.61 => ( ( S2 = S )
% 3.13/1.61 => ( member1474739327od_a_a @ ( produc575024326od_a_a @ R @ S2 ) @ R2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_151_ssubst__Pair__rhs,axiom,
% 3.13/1.61 ! [R: a,S: a,R2: set_Product_prod_a_a,S2: a] :
% 3.13/1.61 ( ( member449909584od_a_a @ ( product_Pair_a_a @ R @ S ) @ R2 )
% 3.13/1.61 => ( ( S2 = S )
% 3.13/1.61 => ( member449909584od_a_a @ ( product_Pair_a_a @ R @ S2 ) @ R2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_152_subdivide_Oinduct,axiom,
% 3.13/1.61 ! [P2: pair_p1891813445t_unit > produc864062247list_a > list_a > $o,A0: pair_p1891813445t_unit,A1: produc864062247list_a,A22: list_a] :
% 3.13/1.61 ( ! [G: pair_p1891813445t_unit,U2: list_a,V: list_a,X_1: list_a] : ( P2 @ G @ ( produc1448356631list_a @ U2 @ V ) @ X_1 )
% 3.13/1.61 => ( P2 @ A0 @ A1 @ A22 ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_153_subdivide_Oinduct,axiom,
% 3.13/1.61 ! [P2: pair_p125712459t_unit > product_prod_a_a > a > $o,A0: pair_p125712459t_unit,A1: product_prod_a_a,A22: a] :
% 3.13/1.61 ( ! [G: pair_p125712459t_unit,U2: a,V: a,X_1: a] : ( P2 @ G @ ( product_Pair_a_a @ U2 @ V ) @ X_1 )
% 3.13/1.61 => ( P2 @ A0 @ A1 @ A22 ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_154_Cons__listrel1__Cons,axiom,
% 3.13/1.61 ! [X3: produc1572603623od_a_a,Xs2: list_P1891567085od_a_a,Y3: produc1572603623od_a_a,Ys2: list_P1891567085od_a_a,R: set_Pr1295299783od_a_a] :
% 3.13/1.61 ( ( member1254757008od_a_a @ ( produc461662679od_a_a @ ( cons_P1070399645od_a_a @ X3 @ Xs2 ) @ ( cons_P1070399645od_a_a @ Y3 @ Ys2 ) ) @ ( listre1832537542od_a_a @ R ) )
% 3.13/1.61 = ( ( ( member1899387664od_a_a @ ( produc1935643479od_a_a @ X3 @ Y3 ) @ R )
% 3.13/1.61 & ( Xs2 = Ys2 ) )
% 3.13/1.61 | ( ( X3 = Y3 )
% 3.13/1.61 & ( member1254757008od_a_a @ ( produc461662679od_a_a @ Xs2 @ Ys2 ) @ ( listre1832537542od_a_a @ R ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_155_Cons__listrel1__Cons,axiom,
% 3.13/1.61 ! [X3: list_P1467822637od_a_a,Xs2: list_l1108175539od_a_a,Y3: list_P1467822637od_a_a,Ys2: list_l1108175539od_a_a,R: set_Pr800560199od_a_a] :
% 3.13/1.61 ( ( member8108048od_a_a @ ( produc915218007od_a_a @ ( cons_l724116707od_a_a @ X3 @ Xs2 ) @ ( cons_l724116707od_a_a @ Y3 @ Ys2 ) ) @ ( listre651914124od_a_a @ R ) )
% 3.13/1.61 = ( ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ X3 @ Y3 ) @ R )
% 3.13/1.61 & ( Xs2 = Ys2 ) )
% 3.13/1.61 | ( ( X3 = Y3 )
% 3.13/1.61 & ( member8108048od_a_a @ ( produc915218007od_a_a @ Xs2 @ Ys2 ) @ ( listre651914124od_a_a @ R ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_156_Cons__listrel1__Cons,axiom,
% 3.13/1.61 ! [X3: a > nat,Xs2: list_a_nat,Y3: a > nat,Ys2: list_a_nat,R: set_Pr1940702919_a_nat] :
% 3.13/1.61 ( ( member688761744_a_nat @ ( produc1430747863_a_nat @ ( cons_a_nat @ X3 @ Xs2 ) @ ( cons_a_nat @ Y3 @ Ys2 ) ) @ ( listrel1_a_nat @ R ) )
% 3.13/1.61 = ( ( ( member125757712_a_nat @ ( produc1569872215_a_nat @ X3 @ Y3 ) @ R )
% 3.13/1.61 & ( Xs2 = Ys2 ) )
% 3.13/1.61 | ( ( X3 = Y3 )
% 3.13/1.61 & ( member688761744_a_nat @ ( produc1430747863_a_nat @ Xs2 @ Ys2 ) @ ( listrel1_a_nat @ R ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_157_Cons__listrel1__Cons,axiom,
% 3.13/1.61 ! [X3: list_a,Xs2: list_list_a,Y3: list_a,Ys2: list_list_a,R: set_Pr1971762695list_a] :
% 3.13/1.61 ( ( member888406864list_a @ ( produc2583831list_a @ ( cons_list_a @ X3 @ Xs2 ) @ ( cons_list_a @ Y3 @ Ys2 ) ) @ ( listrel1_list_a @ R ) )
% 3.13/1.61 = ( ( ( member1250517072list_a @ ( produc1448356631list_a @ X3 @ Y3 ) @ R )
% 3.13/1.61 & ( Xs2 = Ys2 ) )
% 3.13/1.61 | ( ( X3 = Y3 )
% 3.13/1.61 & ( member888406864list_a @ ( produc2583831list_a @ Xs2 @ Ys2 ) @ ( listrel1_list_a @ R ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_158_Cons__listrel1__Cons,axiom,
% 3.13/1.61 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a,Y3: product_prod_a_a,Ys2: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 3.13/1.61 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ ( cons_P1921020637od_a_a @ Y3 @ Ys2 ) ) @ ( listre944824838od_a_a @ R ) )
% 3.13/1.61 = ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X3 @ Y3 ) @ R )
% 3.13/1.61 & ( Xs2 = Ys2 ) )
% 3.13/1.61 | ( ( X3 = Y3 )
% 3.13/1.61 & ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ Ys2 ) @ ( listre944824838od_a_a @ R ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_159_Cons__listrel1__Cons,axiom,
% 3.13/1.61 ! [X3: a,Xs2: list_a,Y3: a,Ys2: list_a,R: set_Product_prod_a_a] :
% 3.13/1.61 ( ( member1250517072list_a @ ( produc1448356631list_a @ ( cons_a @ X3 @ Xs2 ) @ ( cons_a @ Y3 @ Ys2 ) ) @ ( listrel1_a @ R ) )
% 3.13/1.61 = ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R )
% 3.13/1.61 & ( Xs2 = Ys2 ) )
% 3.13/1.61 | ( ( X3 = Y3 )
% 3.13/1.61 & ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ Ys2 ) @ ( listrel1_a @ R ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_160_lexord__cons__cons,axiom,
% 3.13/1.61 ! [A: produc1572603623od_a_a,X3: list_P1891567085od_a_a,B: produc1572603623od_a_a,Y3: list_P1891567085od_a_a,R: set_Pr1295299783od_a_a] :
% 3.13/1.61 ( ( member1254757008od_a_a @ ( produc461662679od_a_a @ ( cons_P1070399645od_a_a @ A @ X3 ) @ ( cons_P1070399645od_a_a @ B @ Y3 ) ) @ ( lexord931792858od_a_a @ R ) )
% 3.13/1.61 = ( ( member1899387664od_a_a @ ( produc1935643479od_a_a @ A @ B ) @ R )
% 3.13/1.61 | ( ( A = B )
% 3.13/1.61 & ( member1254757008od_a_a @ ( produc461662679od_a_a @ X3 @ Y3 ) @ ( lexord931792858od_a_a @ R ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_161_lexord__cons__cons,axiom,
% 3.13/1.61 ! [A: list_P1467822637od_a_a,X3: list_l1108175539od_a_a,B: list_P1467822637od_a_a,Y3: list_l1108175539od_a_a,R: set_Pr800560199od_a_a] :
% 3.13/1.61 ( ( member8108048od_a_a @ ( produc915218007od_a_a @ ( cons_l724116707od_a_a @ A @ X3 ) @ ( cons_l724116707od_a_a @ B @ Y3 ) ) @ ( lexord1284731808od_a_a @ R ) )
% 3.13/1.61 = ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ A @ B ) @ R )
% 3.13/1.61 | ( ( A = B )
% 3.13/1.61 & ( member8108048od_a_a @ ( produc915218007od_a_a @ X3 @ Y3 ) @ ( lexord1284731808od_a_a @ R ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_162_lexord__cons__cons,axiom,
% 3.13/1.61 ! [A: a > nat,X3: list_a_nat,B: a > nat,Y3: list_a_nat,R: set_Pr1940702919_a_nat] :
% 3.13/1.61 ( ( member688761744_a_nat @ ( produc1430747863_a_nat @ ( cons_a_nat @ A @ X3 ) @ ( cons_a_nat @ B @ Y3 ) ) @ ( lexord_a_nat @ R ) )
% 3.13/1.61 = ( ( member125757712_a_nat @ ( produc1569872215_a_nat @ A @ B ) @ R )
% 3.13/1.61 | ( ( A = B )
% 3.13/1.61 & ( member688761744_a_nat @ ( produc1430747863_a_nat @ X3 @ Y3 ) @ ( lexord_a_nat @ R ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_163_lexord__cons__cons,axiom,
% 3.13/1.61 ! [A: list_a,X3: list_list_a,B: list_a,Y3: list_list_a,R: set_Pr1971762695list_a] :
% 3.13/1.61 ( ( member888406864list_a @ ( produc2583831list_a @ ( cons_list_a @ A @ X3 ) @ ( cons_list_a @ B @ Y3 ) ) @ ( lexord_list_a @ R ) )
% 3.13/1.61 = ( ( member1250517072list_a @ ( produc1448356631list_a @ A @ B ) @ R )
% 3.13/1.61 | ( ( A = B )
% 3.13/1.61 & ( member888406864list_a @ ( produc2583831list_a @ X3 @ Y3 ) @ ( lexord_list_a @ R ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_164_lexord__cons__cons,axiom,
% 3.13/1.61 ! [A: product_prod_a_a,X3: list_P1467822637od_a_a,B: product_prod_a_a,Y3: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 3.13/1.61 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( cons_P1921020637od_a_a @ A @ X3 ) @ ( cons_P1921020637od_a_a @ B @ Y3 ) ) @ ( lexord673907738od_a_a @ R ) )
% 3.13/1.61 = ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B ) @ R )
% 3.13/1.61 | ( ( A = B )
% 3.13/1.61 & ( member1691432592od_a_a @ ( produc85179863od_a_a @ X3 @ Y3 ) @ ( lexord673907738od_a_a @ R ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_165_lexord__cons__cons,axiom,
% 3.13/1.61 ! [A: a,X3: list_a,B: a,Y3: list_a,R: set_Product_prod_a_a] :
% 3.13/1.61 ( ( member1250517072list_a @ ( produc1448356631list_a @ ( cons_a @ A @ X3 ) @ ( cons_a @ B @ Y3 ) ) @ ( lexord_a @ R ) )
% 3.13/1.61 = ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ R )
% 3.13/1.61 | ( ( A = B )
% 3.13/1.61 & ( member1250517072list_a @ ( produc1448356631list_a @ X3 @ Y3 ) @ ( lexord_a @ R ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_166_listrel1I2,axiom,
% 3.13/1.61 ! [Xs2: list_P1891567085od_a_a,Ys2: list_P1891567085od_a_a,R: set_Pr1295299783od_a_a,X3: produc1572603623od_a_a] :
% 3.13/1.61 ( ( member1254757008od_a_a @ ( produc461662679od_a_a @ Xs2 @ Ys2 ) @ ( listre1832537542od_a_a @ R ) )
% 3.13/1.61 => ( member1254757008od_a_a @ ( produc461662679od_a_a @ ( cons_P1070399645od_a_a @ X3 @ Xs2 ) @ ( cons_P1070399645od_a_a @ X3 @ Ys2 ) ) @ ( listre1832537542od_a_a @ R ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_167_listrel1I2,axiom,
% 3.13/1.61 ! [Xs2: list_l1108175539od_a_a,Ys2: list_l1108175539od_a_a,R: set_Pr800560199od_a_a,X3: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( member8108048od_a_a @ ( produc915218007od_a_a @ Xs2 @ Ys2 ) @ ( listre651914124od_a_a @ R ) )
% 3.13/1.61 => ( member8108048od_a_a @ ( produc915218007od_a_a @ ( cons_l724116707od_a_a @ X3 @ Xs2 ) @ ( cons_l724116707od_a_a @ X3 @ Ys2 ) ) @ ( listre651914124od_a_a @ R ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_168_listrel1I2,axiom,
% 3.13/1.61 ! [Xs2: list_a_nat,Ys2: list_a_nat,R: set_Pr1940702919_a_nat,X3: a > nat] :
% 3.13/1.61 ( ( member688761744_a_nat @ ( produc1430747863_a_nat @ Xs2 @ Ys2 ) @ ( listrel1_a_nat @ R ) )
% 3.13/1.61 => ( member688761744_a_nat @ ( produc1430747863_a_nat @ ( cons_a_nat @ X3 @ Xs2 ) @ ( cons_a_nat @ X3 @ Ys2 ) ) @ ( listrel1_a_nat @ R ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_169_listrel1I2,axiom,
% 3.13/1.61 ! [Xs2: list_a,Ys2: list_a,R: set_Product_prod_a_a,X3: a] :
% 3.13/1.61 ( ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ Ys2 ) @ ( listrel1_a @ R ) )
% 3.13/1.61 => ( member1250517072list_a @ ( produc1448356631list_a @ ( cons_a @ X3 @ Xs2 ) @ ( cons_a @ X3 @ Ys2 ) ) @ ( listrel1_a @ R ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_170_listrel1I2,axiom,
% 3.13/1.61 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a,X3: product_prod_a_a] :
% 3.13/1.61 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ Ys2 ) @ ( listre944824838od_a_a @ R ) )
% 3.13/1.61 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ ( cons_P1921020637od_a_a @ X3 @ Ys2 ) ) @ ( listre944824838od_a_a @ R ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_171_append__listrel1I,axiom,
% 3.13/1.61 ! [Xs2: list_P1891567085od_a_a,Ys2: list_P1891567085od_a_a,R: set_Pr1295299783od_a_a,Us: list_P1891567085od_a_a,Vs: list_P1891567085od_a_a] :
% 3.13/1.61 ( ( ( ( member1254757008od_a_a @ ( produc461662679od_a_a @ Xs2 @ Ys2 ) @ ( listre1832537542od_a_a @ R ) )
% 3.13/1.61 & ( Us = Vs ) )
% 3.13/1.61 | ( ( Xs2 = Ys2 )
% 3.13/1.61 & ( member1254757008od_a_a @ ( produc461662679od_a_a @ Us @ Vs ) @ ( listre1832537542od_a_a @ R ) ) ) )
% 3.13/1.61 => ( member1254757008od_a_a @ ( produc461662679od_a_a @ ( append864718978od_a_a @ Xs2 @ Us ) @ ( append864718978od_a_a @ Ys2 @ Vs ) ) @ ( listre1832537542od_a_a @ R ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_172_append__listrel1I,axiom,
% 3.13/1.61 ! [Xs2: list_l1108175539od_a_a,Ys2: list_l1108175539od_a_a,R: set_Pr800560199od_a_a,Us: list_l1108175539od_a_a,Vs: list_l1108175539od_a_a] :
% 3.13/1.61 ( ( ( ( member8108048od_a_a @ ( produc915218007od_a_a @ Xs2 @ Ys2 ) @ ( listre651914124od_a_a @ R ) )
% 3.13/1.61 & ( Us = Vs ) )
% 3.13/1.61 | ( ( Xs2 = Ys2 )
% 3.13/1.61 & ( member8108048od_a_a @ ( produc915218007od_a_a @ Us @ Vs ) @ ( listre651914124od_a_a @ R ) ) ) )
% 3.13/1.61 => ( member8108048od_a_a @ ( produc915218007od_a_a @ ( append2141280328od_a_a @ Xs2 @ Us ) @ ( append2141280328od_a_a @ Ys2 @ Vs ) ) @ ( listre651914124od_a_a @ R ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_173_append__listrel1I,axiom,
% 3.13/1.61 ! [Xs2: list_a,Ys2: list_a,R: set_Product_prod_a_a,Us: list_a,Vs: list_a] :
% 3.13/1.61 ( ( ( ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ Ys2 ) @ ( listrel1_a @ R ) )
% 3.13/1.61 & ( Us = Vs ) )
% 3.13/1.61 | ( ( Xs2 = Ys2 )
% 3.13/1.61 & ( member1250517072list_a @ ( produc1448356631list_a @ Us @ Vs ) @ ( listrel1_a @ R ) ) ) )
% 3.13/1.61 => ( member1250517072list_a @ ( produc1448356631list_a @ ( append_a @ Xs2 @ Us ) @ ( append_a @ Ys2 @ Vs ) ) @ ( listrel1_a @ R ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_174_append__listrel1I,axiom,
% 3.13/1.61 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a,Us: list_P1467822637od_a_a,Vs: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ Ys2 ) @ ( listre944824838od_a_a @ R ) )
% 3.13/1.61 & ( Us = Vs ) )
% 3.13/1.61 | ( ( Xs2 = Ys2 )
% 3.13/1.61 & ( member1691432592od_a_a @ ( produc85179863od_a_a @ Us @ Vs ) @ ( listre944824838od_a_a @ R ) ) ) )
% 3.13/1.61 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ Xs2 @ Us ) @ ( append1574001858od_a_a @ Ys2 @ Vs ) ) @ ( listre944824838od_a_a @ R ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_175_lexord__linear,axiom,
% 3.13/1.61 ! [R: set_Pr800560199od_a_a,X3: list_l1108175539od_a_a,Y3: list_l1108175539od_a_a] :
% 3.13/1.61 ( ! [A3: list_P1467822637od_a_a,B3: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ A3 @ B3 ) @ R )
% 3.13/1.61 | ( A3 = B3 )
% 3.13/1.61 | ( member1691432592od_a_a @ ( produc85179863od_a_a @ B3 @ A3 ) @ R ) )
% 3.13/1.61 => ( ( member8108048od_a_a @ ( produc915218007od_a_a @ X3 @ Y3 ) @ ( lexord1284731808od_a_a @ R ) )
% 3.13/1.61 | ( X3 = Y3 )
% 3.13/1.61 | ( member8108048od_a_a @ ( produc915218007od_a_a @ Y3 @ X3 ) @ ( lexord1284731808od_a_a @ R ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_176_lexord__linear,axiom,
% 3.13/1.61 ! [R: set_Pr1948701895od_a_a,X3: list_P1467822637od_a_a,Y3: list_P1467822637od_a_a] :
% 3.13/1.61 ( ! [A3: product_prod_a_a,B3: product_prod_a_a] :
% 3.13/1.61 ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A3 @ B3 ) @ R )
% 3.13/1.61 | ( A3 = B3 )
% 3.13/1.61 | ( member2057358096od_a_a @ ( produc1474507607od_a_a @ B3 @ A3 ) @ R ) )
% 3.13/1.61 => ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ X3 @ Y3 ) @ ( lexord673907738od_a_a @ R ) )
% 3.13/1.61 | ( X3 = Y3 )
% 3.13/1.61 | ( member1691432592od_a_a @ ( produc85179863od_a_a @ Y3 @ X3 ) @ ( lexord673907738od_a_a @ R ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_177_lexord__linear,axiom,
% 3.13/1.61 ! [R: set_Pr1971762695list_a,X3: list_list_a,Y3: list_list_a] :
% 3.13/1.61 ( ! [A3: list_a,B3: list_a] :
% 3.13/1.61 ( ( member1250517072list_a @ ( produc1448356631list_a @ A3 @ B3 ) @ R )
% 3.13/1.61 | ( A3 = B3 )
% 3.13/1.61 | ( member1250517072list_a @ ( produc1448356631list_a @ B3 @ A3 ) @ R ) )
% 3.13/1.61 => ( ( member888406864list_a @ ( produc2583831list_a @ X3 @ Y3 ) @ ( lexord_list_a @ R ) )
% 3.13/1.61 | ( X3 = Y3 )
% 3.13/1.61 | ( member888406864list_a @ ( produc2583831list_a @ Y3 @ X3 ) @ ( lexord_list_a @ R ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_178_lexord__linear,axiom,
% 3.13/1.61 ! [R: set_Product_prod_a_a,X3: list_a,Y3: list_a] :
% 3.13/1.61 ( ! [A3: a,B3: a] :
% 3.13/1.61 ( ( member449909584od_a_a @ ( product_Pair_a_a @ A3 @ B3 ) @ R )
% 3.13/1.61 | ( A3 = B3 )
% 3.13/1.61 | ( member449909584od_a_a @ ( product_Pair_a_a @ B3 @ A3 ) @ R ) )
% 3.13/1.61 => ( ( member1250517072list_a @ ( produc1448356631list_a @ X3 @ Y3 ) @ ( lexord_a @ R ) )
% 3.13/1.61 | ( X3 = Y3 )
% 3.13/1.61 | ( member1250517072list_a @ ( produc1448356631list_a @ Y3 @ X3 ) @ ( lexord_a @ R ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_179_mem__Collect__eq,axiom,
% 3.13/1.61 ! [A: produc651658087od_a_a,P2: produc651658087od_a_a > $o] :
% 3.13/1.61 ( ( member1691432592od_a_a @ A @ ( collec1566074578od_a_a @ P2 ) )
% 3.13/1.61 = ( P2 @ A ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_180_mem__Collect__eq,axiom,
% 3.13/1.61 ! [A: produc864062247list_a,P2: produc864062247list_a > $o] :
% 3.13/1.61 ( ( member1250517072list_a @ A @ ( collec656258194list_a @ P2 ) )
% 3.13/1.61 = ( P2 @ A ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_181_mem__Collect__eq,axiom,
% 3.13/1.61 ! [A: product_prod_a_a,P2: product_prod_a_a > $o] :
% 3.13/1.61 ( ( member449909584od_a_a @ A @ ( collec645855634od_a_a @ P2 ) )
% 3.13/1.61 = ( P2 @ A ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_182_mem__Collect__eq,axiom,
% 3.13/1.61 ! [A: list_P1467822637od_a_a,P2: list_P1467822637od_a_a > $o] :
% 3.13/1.61 ( ( member1578987478od_a_a @ A @ ( collec1811041560od_a_a @ P2 ) )
% 3.13/1.61 = ( P2 @ A ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_183_mem__Collect__eq,axiom,
% 3.13/1.61 ! [A: a,P2: a > $o] :
% 3.13/1.61 ( ( member_a2 @ A @ ( collect_a @ P2 ) )
% 3.13/1.61 = ( P2 @ A ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_184_Collect__mem__eq,axiom,
% 3.13/1.61 ! [A4: set_Pr1971762695list_a] :
% 3.13/1.61 ( ( collec656258194list_a
% 3.13/1.61 @ ^ [X: produc864062247list_a] : ( member1250517072list_a @ X @ A4 ) )
% 3.13/1.61 = A4 ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_185_Collect__mem__eq,axiom,
% 3.13/1.61 ! [A4: set_Product_prod_a_a] :
% 3.13/1.61 ( ( collec645855634od_a_a
% 3.13/1.61 @ ^ [X: product_prod_a_a] : ( member449909584od_a_a @ X @ A4 ) )
% 3.13/1.61 = A4 ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_186_Collect__mem__eq,axiom,
% 3.13/1.61 ! [A4: set_li562223245od_a_a] :
% 3.13/1.61 ( ( collec1811041560od_a_a
% 3.13/1.61 @ ^ [X: list_P1467822637od_a_a] : ( member1578987478od_a_a @ X @ A4 ) )
% 3.13/1.61 = A4 ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_187_Collect__mem__eq,axiom,
% 3.13/1.61 ! [A4: set_a] :
% 3.13/1.61 ( ( collect_a
% 3.13/1.61 @ ^ [X: a] : ( member_a2 @ X @ A4 ) )
% 3.13/1.61 = A4 ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_188_lexord__irreflexive,axiom,
% 3.13/1.61 ! [R: set_Product_prod_a_a,Xs2: list_a] :
% 3.13/1.61 ( ! [X4: a] :
% 3.13/1.61 ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ X4 ) @ R )
% 3.13/1.61 => ~ ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ Xs2 ) @ ( lexord_a @ R ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_189_lexord__append__leftI,axiom,
% 3.13/1.61 ! [U: list_P1467822637od_a_a,V2: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a,X3: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ U @ V2 ) @ ( lexord673907738od_a_a @ R ) )
% 3.13/1.61 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ X3 @ U ) @ ( append1574001858od_a_a @ X3 @ V2 ) ) @ ( lexord673907738od_a_a @ R ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_190_listrel1I1,axiom,
% 3.13/1.61 ! [X3: product_prod_a_a,Y3: product_prod_a_a,R: set_Pr1948701895od_a_a,Xs2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X3 @ Y3 ) @ R )
% 3.13/1.61 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ ( cons_P1921020637od_a_a @ Y3 @ Xs2 ) ) @ ( listre944824838od_a_a @ R ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_191_listrel1I1,axiom,
% 3.13/1.61 ! [X3: a,Y3: a,R: set_Product_prod_a_a,Xs2: list_a] :
% 3.13/1.61 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R )
% 3.13/1.61 => ( member1250517072list_a @ ( produc1448356631list_a @ ( cons_a @ X3 @ Xs2 ) @ ( cons_a @ Y3 @ Xs2 ) ) @ ( listrel1_a @ R ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_192_Cons__listrel1E1,axiom,
% 3.13/1.61 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 3.13/1.61 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ Ys2 ) @ ( listre944824838od_a_a @ R ) )
% 3.13/1.61 => ( ! [Y4: product_prod_a_a] :
% 3.13/1.61 ( ( Ys2
% 3.13/1.61 = ( cons_P1921020637od_a_a @ Y4 @ Xs2 ) )
% 3.13/1.61 => ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X3 @ Y4 ) @ R ) )
% 3.13/1.61 => ~ ! [Zs2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( Ys2
% 3.13/1.61 = ( cons_P1921020637od_a_a @ X3 @ Zs2 ) )
% 3.13/1.61 => ~ ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ Zs2 ) @ ( listre944824838od_a_a @ R ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_193_Cons__listrel1E1,axiom,
% 3.13/1.61 ! [X3: a,Xs2: list_a,Ys2: list_a,R: set_Product_prod_a_a] :
% 3.13/1.61 ( ( member1250517072list_a @ ( produc1448356631list_a @ ( cons_a @ X3 @ Xs2 ) @ Ys2 ) @ ( listrel1_a @ R ) )
% 3.13/1.61 => ( ! [Y4: a] :
% 3.13/1.61 ( ( Ys2
% 3.13/1.61 = ( cons_a @ Y4 @ Xs2 ) )
% 3.13/1.61 => ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y4 ) @ R ) )
% 3.13/1.61 => ~ ! [Zs2: list_a] :
% 3.13/1.61 ( ( Ys2
% 3.13/1.61 = ( cons_a @ X3 @ Zs2 ) )
% 3.13/1.61 => ~ ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ Zs2 ) @ ( listrel1_a @ R ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_194_Cons__listrel1E2,axiom,
% 3.13/1.61 ! [Xs2: list_P1467822637od_a_a,Y3: product_prod_a_a,Ys2: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 3.13/1.61 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ ( cons_P1921020637od_a_a @ Y3 @ Ys2 ) ) @ ( listre944824838od_a_a @ R ) )
% 3.13/1.61 => ( ! [X4: product_prod_a_a] :
% 3.13/1.61 ( ( Xs2
% 3.13/1.61 = ( cons_P1921020637od_a_a @ X4 @ Ys2 ) )
% 3.13/1.61 => ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X4 @ Y3 ) @ R ) )
% 3.13/1.61 => ~ ! [Zs2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( Xs2
% 3.13/1.61 = ( cons_P1921020637od_a_a @ Y3 @ Zs2 ) )
% 3.13/1.61 => ~ ( member1691432592od_a_a @ ( produc85179863od_a_a @ Zs2 @ Ys2 ) @ ( listre944824838od_a_a @ R ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_195_Cons__listrel1E2,axiom,
% 3.13/1.61 ! [Xs2: list_a,Y3: a,Ys2: list_a,R: set_Product_prod_a_a] :
% 3.13/1.61 ( ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ ( cons_a @ Y3 @ Ys2 ) ) @ ( listrel1_a @ R ) )
% 3.13/1.61 => ( ! [X4: a] :
% 3.13/1.61 ( ( Xs2
% 3.13/1.61 = ( cons_a @ X4 @ Ys2 ) )
% 3.13/1.61 => ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y3 ) @ R ) )
% 3.13/1.61 => ~ ! [Zs2: list_a] :
% 3.13/1.61 ( ( Xs2
% 3.13/1.61 = ( cons_a @ Y3 @ Zs2 ) )
% 3.13/1.61 => ~ ( member1250517072list_a @ ( produc1448356631list_a @ Zs2 @ Ys2 ) @ ( listrel1_a @ R ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_196_lexord__append__leftD,axiom,
% 3.13/1.61 ! [X3: list_P1467822637od_a_a,U: list_P1467822637od_a_a,V2: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 3.13/1.61 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ X3 @ U ) @ ( append1574001858od_a_a @ X3 @ V2 ) ) @ ( lexord673907738od_a_a @ R ) )
% 3.13/1.61 => ( ! [A3: product_prod_a_a] :
% 3.13/1.61 ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A3 @ A3 ) @ R )
% 3.13/1.61 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ U @ V2 ) @ ( lexord673907738od_a_a @ R ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_197_lexord__append__leftD,axiom,
% 3.13/1.61 ! [X3: list_a,U: list_a,V2: list_a,R: set_Product_prod_a_a] :
% 3.13/1.61 ( ( member1250517072list_a @ ( produc1448356631list_a @ ( append_a @ X3 @ U ) @ ( append_a @ X3 @ V2 ) ) @ ( lexord_a @ R ) )
% 3.13/1.61 => ( ! [A3: a] :
% 3.13/1.61 ~ ( member449909584od_a_a @ ( product_Pair_a_a @ A3 @ A3 ) @ R )
% 3.13/1.61 => ( member1250517072list_a @ ( produc1448356631list_a @ U @ V2 ) @ ( lexord_a @ R ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_198_lexord__append__rightI,axiom,
% 3.13/1.61 ! [Y3: list_P1467822637od_a_a,X3: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 3.13/1.61 ( ? [B4: product_prod_a_a,Z: list_P1467822637od_a_a] :
% 3.13/1.61 ( Y3
% 3.13/1.61 = ( cons_P1921020637od_a_a @ B4 @ Z ) )
% 3.13/1.61 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ X3 @ ( append1574001858od_a_a @ X3 @ Y3 ) ) @ ( lexord673907738od_a_a @ R ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_199_zip__eq__ConsE,axiom,
% 3.13/1.61 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Xy: produc1572603623od_a_a,Xys: list_P1891567085od_a_a] :
% 3.13/1.61 ( ( ( zip_Pr792472183od_a_a @ Xs2 @ Ys2 )
% 3.13/1.61 = ( cons_P1070399645od_a_a @ Xy @ Xys ) )
% 3.13/1.61 => ~ ! [X4: product_prod_a_a,Xs3: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( Xs2
% 3.13/1.61 = ( cons_P1921020637od_a_a @ X4 @ Xs3 ) )
% 3.13/1.61 => ! [Y4: product_prod_a_a,Ys3: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( Ys2
% 3.13/1.61 = ( cons_P1921020637od_a_a @ Y4 @ Ys3 ) )
% 3.13/1.61 => ( ( Xy
% 3.13/1.61 = ( produc1474507607od_a_a @ X4 @ Y4 ) )
% 3.13/1.61 => ( Xys
% 3.13/1.61 != ( zip_Pr792472183od_a_a @ Xs3 @ Ys3 ) ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_200_zip__eq__ConsE,axiom,
% 3.13/1.61 ! [Xs2: list_a,Ys2: list_a,Xy: product_prod_a_a,Xys: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( ( zip_a_a @ Xs2 @ Ys2 )
% 3.13/1.61 = ( cons_P1921020637od_a_a @ Xy @ Xys ) )
% 3.13/1.61 => ~ ! [X4: a,Xs3: list_a] :
% 3.13/1.61 ( ( Xs2
% 3.13/1.61 = ( cons_a @ X4 @ Xs3 ) )
% 3.13/1.61 => ! [Y4: a,Ys3: list_a] :
% 3.13/1.61 ( ( Ys2
% 3.13/1.61 = ( cons_a @ Y4 @ Ys3 ) )
% 3.13/1.61 => ( ( Xy
% 3.13/1.61 = ( product_Pair_a_a @ X4 @ Y4 ) )
% 3.13/1.61 => ( Xys
% 3.13/1.61 != ( zip_a_a @ Xs3 @ Ys3 ) ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_201_subdivide_Ocases,axiom,
% 3.13/1.61 ! [X3: produc1912141786_a_a_a] :
% 3.13/1.61 ~ ! [G: pair_p125712459t_unit,U2: a,V: a,W: a] :
% 3.13/1.61 ( X3
% 3.13/1.61 != ( produc74075722_a_a_a @ G @ ( produc2061588782_a_a_a @ ( product_Pair_a_a @ U2 @ V ) @ W ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_202_lexord__same__pref__if__irrefl,axiom,
% 3.13/1.61 ! [R: set_Pr1948701895od_a_a,Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( irrefl76447196od_a_a @ R )
% 3.13/1.61 => ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ Xs2 @ Ys2 ) @ ( append1574001858od_a_a @ Xs2 @ Zs ) ) @ ( lexord673907738od_a_a @ R ) )
% 3.13/1.61 = ( member1691432592od_a_a @ ( produc85179863od_a_a @ Ys2 @ Zs ) @ ( lexord673907738od_a_a @ R ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_203_snoc__listrel1__snoc__iff,axiom,
% 3.13/1.61 ! [Xs2: list_P1467822637od_a_a,X3: product_prod_a_a,Ys2: list_P1467822637od_a_a,Y3: product_prod_a_a,R: set_Pr1948701895od_a_a] :
% 3.13/1.61 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ Xs2 @ ( cons_P1921020637od_a_a @ X3 @ nil_Product_prod_a_a ) ) @ ( append1574001858od_a_a @ Ys2 @ ( cons_P1921020637od_a_a @ Y3 @ nil_Product_prod_a_a ) ) ) @ ( listre944824838od_a_a @ R ) )
% 3.13/1.61 = ( ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ Ys2 ) @ ( listre944824838od_a_a @ R ) )
% 3.13/1.61 & ( X3 = Y3 ) )
% 3.13/1.61 | ( ( Xs2 = Ys2 )
% 3.13/1.61 & ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X3 @ Y3 ) @ R ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_204_snoc__listrel1__snoc__iff,axiom,
% 3.13/1.61 ! [Xs2: list_a,X3: a,Ys2: list_a,Y3: a,R: set_Product_prod_a_a] :
% 3.13/1.61 ( ( member1250517072list_a @ ( produc1448356631list_a @ ( append_a @ Xs2 @ ( cons_a @ X3 @ nil_a ) ) @ ( append_a @ Ys2 @ ( cons_a @ Y3 @ nil_a ) ) ) @ ( listrel1_a @ R ) )
% 3.13/1.61 = ( ( ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ Ys2 ) @ ( listrel1_a @ R ) )
% 3.13/1.61 & ( X3 = Y3 ) )
% 3.13/1.61 | ( ( Xs2 = Ys2 )
% 3.13/1.61 & ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_205_lexord__Nil__left,axiom,
% 3.13/1.61 ! [Y3: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 3.13/1.61 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ nil_Product_prod_a_a @ Y3 ) @ ( lexord673907738od_a_a @ R ) )
% 3.13/1.61 = ( ? [A5: product_prod_a_a,X: list_P1467822637od_a_a] :
% 3.13/1.61 ( Y3
% 3.13/1.61 = ( cons_P1921020637od_a_a @ A5 @ X ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_206_lexord__same__pref__iff,axiom,
% 3.13/1.61 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 3.13/1.61 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ Xs2 @ Ys2 ) @ ( append1574001858od_a_a @ Xs2 @ Zs ) ) @ ( lexord673907738od_a_a @ R ) )
% 3.13/1.61 = ( ? [X: product_prod_a_a] :
% 3.13/1.61 ( ( member449909584od_a_a @ X @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 3.13/1.61 & ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X @ X ) @ R ) )
% 3.13/1.61 | ( member1691432592od_a_a @ ( produc85179863od_a_a @ Ys2 @ Zs ) @ ( lexord673907738od_a_a @ R ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_207_lexord__same__pref__iff,axiom,
% 3.13/1.61 ! [Xs2: list_a,Ys2: list_a,Zs: list_a,R: set_Product_prod_a_a] :
% 3.13/1.61 ( ( member1250517072list_a @ ( produc1448356631list_a @ ( append_a @ Xs2 @ Ys2 ) @ ( append_a @ Xs2 @ Zs ) ) @ ( lexord_a @ R ) )
% 3.13/1.61 = ( ? [X: a] :
% 3.13/1.61 ( ( member_a2 @ X @ ( set_a2 @ Xs2 ) )
% 3.13/1.61 & ( member449909584od_a_a @ ( product_Pair_a_a @ X @ X ) @ R ) )
% 3.13/1.61 | ( member1250517072list_a @ ( produc1448356631list_a @ Ys2 @ Zs ) @ ( lexord_a @ R ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_208_zip__append,axiom,
% 3.13/1.61 ! [Xs2: list_a,Us: list_a,Ys2: list_a,Vs: list_a] :
% 3.13/1.61 ( ( ( size_size_list_a @ Xs2 )
% 3.13/1.61 = ( size_size_list_a @ Us ) )
% 3.13/1.61 => ( ( zip_a_a @ ( append_a @ Xs2 @ Ys2 ) @ ( append_a @ Us @ Vs ) )
% 3.13/1.61 = ( append1574001858od_a_a @ ( zip_a_a @ Xs2 @ Us ) @ ( zip_a_a @ Ys2 @ Vs ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_209_zip__append,axiom,
% 3.13/1.61 ! [Xs2: list_P1467822637od_a_a,Us: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Vs: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( ( size_s642698393od_a_a @ Xs2 )
% 3.13/1.61 = ( size_s642698393od_a_a @ Us ) )
% 3.13/1.61 => ( ( zip_Pr792472183od_a_a @ ( append1574001858od_a_a @ Xs2 @ Ys2 ) @ ( append1574001858od_a_a @ Us @ Vs ) )
% 3.13/1.61 = ( append864718978od_a_a @ ( zip_Pr792472183od_a_a @ Xs2 @ Us ) @ ( zip_Pr792472183od_a_a @ Ys2 @ Vs ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_210_lex__append__leftD,axiom,
% 3.13/1.61 ! [R: set_Pr1948701895od_a_a,Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a] :
% 3.13/1.61 ( ! [X4: product_prod_a_a] :
% 3.13/1.61 ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X4 @ X4 ) @ R )
% 3.13/1.61 => ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ Xs2 @ Ys2 ) @ ( append1574001858od_a_a @ Xs2 @ Zs ) ) @ ( lex_Product_prod_a_a @ R ) )
% 3.13/1.61 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ Ys2 @ Zs ) @ ( lex_Product_prod_a_a @ R ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_211_lex__append__leftD,axiom,
% 3.13/1.61 ! [R: set_Product_prod_a_a,Xs2: list_a,Ys2: list_a,Zs: list_a] :
% 3.13/1.61 ( ! [X4: a] :
% 3.13/1.61 ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ X4 ) @ R )
% 3.13/1.61 => ( ( member1250517072list_a @ ( produc1448356631list_a @ ( append_a @ Xs2 @ Ys2 ) @ ( append_a @ Xs2 @ Zs ) ) @ ( lex_a @ R ) )
% 3.13/1.61 => ( member1250517072list_a @ ( produc1448356631list_a @ Ys2 @ Zs ) @ ( lex_a @ R ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_212_lex__append__left__iff,axiom,
% 3.13/1.61 ! [R: set_Pr1948701895od_a_a,Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a] :
% 3.13/1.61 ( ! [X4: product_prod_a_a] :
% 3.13/1.61 ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X4 @ X4 ) @ R )
% 3.13/1.61 => ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ Xs2 @ Ys2 ) @ ( append1574001858od_a_a @ Xs2 @ Zs ) ) @ ( lex_Product_prod_a_a @ R ) )
% 3.13/1.61 = ( member1691432592od_a_a @ ( produc85179863od_a_a @ Ys2 @ Zs ) @ ( lex_Product_prod_a_a @ R ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_213_lex__append__left__iff,axiom,
% 3.13/1.61 ! [R: set_Product_prod_a_a,Xs2: list_a,Ys2: list_a,Zs: list_a] :
% 3.13/1.61 ( ! [X4: a] :
% 3.13/1.61 ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ X4 ) @ R )
% 3.13/1.61 => ( ( member1250517072list_a @ ( produc1448356631list_a @ ( append_a @ Xs2 @ Ys2 ) @ ( append_a @ Xs2 @ Zs ) ) @ ( lex_a @ R ) )
% 3.13/1.61 = ( member1250517072list_a @ ( produc1448356631list_a @ Ys2 @ Zs ) @ ( lex_a @ R ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_214_append_Oright__neutral,axiom,
% 3.13/1.61 ! [A: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( append1574001858od_a_a @ A @ nil_Product_prod_a_a )
% 3.13/1.61 = A ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_215_append__is__Nil__conv,axiom,
% 3.13/1.61 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( ( append1574001858od_a_a @ Xs2 @ Ys2 )
% 3.13/1.61 = nil_Product_prod_a_a )
% 3.13/1.61 = ( ( Xs2 = nil_Product_prod_a_a )
% 3.13/1.61 & ( Ys2 = nil_Product_prod_a_a ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_216_Nil__is__append__conv,axiom,
% 3.13/1.61 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( nil_Product_prod_a_a
% 3.13/1.61 = ( append1574001858od_a_a @ Xs2 @ Ys2 ) )
% 3.13/1.61 = ( ( Xs2 = nil_Product_prod_a_a )
% 3.13/1.61 & ( Ys2 = nil_Product_prod_a_a ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_217_self__append__conv2,axiom,
% 3.13/1.61 ! [Ys2: list_P1467822637od_a_a,Xs2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( Ys2
% 3.13/1.61 = ( append1574001858od_a_a @ Xs2 @ Ys2 ) )
% 3.13/1.61 = ( Xs2 = nil_Product_prod_a_a ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_218_append__self__conv2,axiom,
% 3.13/1.61 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( ( append1574001858od_a_a @ Xs2 @ Ys2 )
% 3.13/1.61 = Ys2 )
% 3.13/1.61 = ( Xs2 = nil_Product_prod_a_a ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_219_self__append__conv,axiom,
% 3.13/1.61 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( Xs2
% 3.13/1.61 = ( append1574001858od_a_a @ Xs2 @ Ys2 ) )
% 3.13/1.61 = ( Ys2 = nil_Product_prod_a_a ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_220_append__self__conv,axiom,
% 3.13/1.61 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( ( append1574001858od_a_a @ Xs2 @ Ys2 )
% 3.13/1.61 = Xs2 )
% 3.13/1.61 = ( Ys2 = nil_Product_prod_a_a ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_221_append__Nil2,axiom,
% 3.13/1.61 ! [Xs2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( append1574001858od_a_a @ Xs2 @ nil_Product_prod_a_a )
% 3.13/1.61 = Xs2 ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_222_append__eq__append__conv,axiom,
% 3.13/1.61 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Us: list_P1467822637od_a_a,Vs: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( ( ( size_s642698393od_a_a @ Xs2 )
% 3.13/1.61 = ( size_s642698393od_a_a @ Ys2 ) )
% 3.13/1.61 | ( ( size_s642698393od_a_a @ Us )
% 3.13/1.61 = ( size_s642698393od_a_a @ Vs ) ) )
% 3.13/1.61 => ( ( ( append1574001858od_a_a @ Xs2 @ Us )
% 3.13/1.61 = ( append1574001858od_a_a @ Ys2 @ Vs ) )
% 3.13/1.61 = ( ( Xs2 = Ys2 )
% 3.13/1.61 & ( Us = Vs ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_223_append1__eq__conv,axiom,
% 3.13/1.61 ! [Xs2: list_P1467822637od_a_a,X3: product_prod_a_a,Ys2: list_P1467822637od_a_a,Y3: product_prod_a_a] :
% 3.13/1.61 ( ( ( append1574001858od_a_a @ Xs2 @ ( cons_P1921020637od_a_a @ X3 @ nil_Product_prod_a_a ) )
% 3.13/1.61 = ( append1574001858od_a_a @ Ys2 @ ( cons_P1921020637od_a_a @ Y3 @ nil_Product_prod_a_a ) ) )
% 3.13/1.61 = ( ( Xs2 = Ys2 )
% 3.13/1.61 & ( X3 = Y3 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_224_Cons__in__lex,axiom,
% 3.13/1.61 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a,Y3: product_prod_a_a,Ys2: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 3.13/1.61 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ ( cons_P1921020637od_a_a @ Y3 @ Ys2 ) ) @ ( lex_Product_prod_a_a @ R ) )
% 3.13/1.61 = ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X3 @ Y3 ) @ R )
% 3.13/1.61 & ( ( size_s642698393od_a_a @ Xs2 )
% 3.13/1.61 = ( size_s642698393od_a_a @ Ys2 ) ) )
% 3.13/1.61 | ( ( X3 = Y3 )
% 3.13/1.61 & ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ Ys2 ) @ ( lex_Product_prod_a_a @ R ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_225_Cons__in__lex,axiom,
% 3.13/1.61 ! [X3: a,Xs2: list_a,Y3: a,Ys2: list_a,R: set_Product_prod_a_a] :
% 3.13/1.61 ( ( member1250517072list_a @ ( produc1448356631list_a @ ( cons_a @ X3 @ Xs2 ) @ ( cons_a @ Y3 @ Ys2 ) ) @ ( lex_a @ R ) )
% 3.13/1.61 = ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R )
% 3.13/1.61 & ( ( size_size_list_a @ Xs2 )
% 3.13/1.61 = ( size_size_list_a @ Ys2 ) ) )
% 3.13/1.61 | ( ( X3 = Y3 )
% 3.13/1.61 & ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ Ys2 ) @ ( lex_a @ R ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_226_in__set__impl__in__set__zip1,axiom,
% 3.13/1.61 ! [Xs2: list_a,Ys2: list_a,X3: a] :
% 3.13/1.61 ( ( ( size_size_list_a @ Xs2 )
% 3.13/1.61 = ( size_size_list_a @ Ys2 ) )
% 3.13/1.61 => ( ( member_a2 @ X3 @ ( set_a2 @ Xs2 ) )
% 3.13/1.61 => ~ ! [Y4: a] :
% 3.13/1.61 ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y4 ) @ ( set_Product_prod_a_a2 @ ( zip_a_a @ Xs2 @ Ys2 ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_227_in__set__impl__in__set__zip2,axiom,
% 3.13/1.61 ! [Xs2: list_a,Ys2: list_a,Y3: a] :
% 3.13/1.61 ( ( ( size_size_list_a @ Xs2 )
% 3.13/1.61 = ( size_size_list_a @ Ys2 ) )
% 3.13/1.61 => ( ( member_a2 @ Y3 @ ( set_a2 @ Ys2 ) )
% 3.13/1.61 => ~ ! [X4: a] :
% 3.13/1.61 ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y3 ) @ ( set_Product_prod_a_a2 @ ( zip_a_a @ Xs2 @ Ys2 ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_228_list__induct4,axiom,
% 3.13/1.61 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a,Ws: list_P1467822637od_a_a,P2: list_P1467822637od_a_a > list_P1467822637od_a_a > list_P1467822637od_a_a > list_P1467822637od_a_a > $o] :
% 3.13/1.61 ( ( ( size_s642698393od_a_a @ Xs2 )
% 3.13/1.61 = ( size_s642698393od_a_a @ Ys2 ) )
% 3.13/1.61 => ( ( ( size_s642698393od_a_a @ Ys2 )
% 3.13/1.61 = ( size_s642698393od_a_a @ Zs ) )
% 3.13/1.61 => ( ( ( size_s642698393od_a_a @ Zs )
% 3.13/1.61 = ( size_s642698393od_a_a @ Ws ) )
% 3.13/1.61 => ( ( P2 @ nil_Product_prod_a_a @ nil_Product_prod_a_a @ nil_Product_prod_a_a @ nil_Product_prod_a_a )
% 3.13/1.61 => ( ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a,Y4: product_prod_a_a,Ys4: list_P1467822637od_a_a,Z2: product_prod_a_a,Zs2: list_P1467822637od_a_a,W: product_prod_a_a,Ws2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( ( size_s642698393od_a_a @ Xs4 )
% 3.13/1.61 = ( size_s642698393od_a_a @ Ys4 ) )
% 3.13/1.61 => ( ( ( size_s642698393od_a_a @ Ys4 )
% 3.13/1.61 = ( size_s642698393od_a_a @ Zs2 ) )
% 3.13/1.61 => ( ( ( size_s642698393od_a_a @ Zs2 )
% 3.13/1.61 = ( size_s642698393od_a_a @ Ws2 ) )
% 3.13/1.61 => ( ( P2 @ Xs4 @ Ys4 @ Zs2 @ Ws2 )
% 3.13/1.61 => ( P2 @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) @ ( cons_P1921020637od_a_a @ Y4 @ Ys4 ) @ ( cons_P1921020637od_a_a @ Z2 @ Zs2 ) @ ( cons_P1921020637od_a_a @ W @ Ws2 ) ) ) ) ) )
% 3.13/1.61 => ( P2 @ Xs2 @ Ys2 @ Zs @ Ws ) ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_229_list__induct3,axiom,
% 3.13/1.61 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a,P2: list_P1467822637od_a_a > list_P1467822637od_a_a > list_P1467822637od_a_a > $o] :
% 3.13/1.61 ( ( ( size_s642698393od_a_a @ Xs2 )
% 3.13/1.61 = ( size_s642698393od_a_a @ Ys2 ) )
% 3.13/1.61 => ( ( ( size_s642698393od_a_a @ Ys2 )
% 3.13/1.61 = ( size_s642698393od_a_a @ Zs ) )
% 3.13/1.61 => ( ( P2 @ nil_Product_prod_a_a @ nil_Product_prod_a_a @ nil_Product_prod_a_a )
% 3.13/1.61 => ( ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a,Y4: product_prod_a_a,Ys4: list_P1467822637od_a_a,Z2: product_prod_a_a,Zs2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( ( size_s642698393od_a_a @ Xs4 )
% 3.13/1.61 = ( size_s642698393od_a_a @ Ys4 ) )
% 3.13/1.61 => ( ( ( size_s642698393od_a_a @ Ys4 )
% 3.13/1.61 = ( size_s642698393od_a_a @ Zs2 ) )
% 3.13/1.61 => ( ( P2 @ Xs4 @ Ys4 @ Zs2 )
% 3.13/1.61 => ( P2 @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) @ ( cons_P1921020637od_a_a @ Y4 @ Ys4 ) @ ( cons_P1921020637od_a_a @ Z2 @ Zs2 ) ) ) ) )
% 3.13/1.61 => ( P2 @ Xs2 @ Ys2 @ Zs ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_230_list__induct2,axiom,
% 3.13/1.61 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,P2: list_P1467822637od_a_a > list_P1467822637od_a_a > $o] :
% 3.13/1.61 ( ( ( size_s642698393od_a_a @ Xs2 )
% 3.13/1.61 = ( size_s642698393od_a_a @ Ys2 ) )
% 3.13/1.61 => ( ( P2 @ nil_Product_prod_a_a @ nil_Product_prod_a_a )
% 3.13/1.61 => ( ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a,Y4: product_prod_a_a,Ys4: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( ( size_s642698393od_a_a @ Xs4 )
% 3.13/1.61 = ( size_s642698393od_a_a @ Ys4 ) )
% 3.13/1.61 => ( ( P2 @ Xs4 @ Ys4 )
% 3.13/1.61 => ( P2 @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) @ ( cons_P1921020637od_a_a @ Y4 @ Ys4 ) ) ) )
% 3.13/1.61 => ( P2 @ Xs2 @ Ys2 ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_231_transpose_Ocases,axiom,
% 3.13/1.61 ! [X3: list_l1108175539od_a_a] :
% 3.13/1.61 ( ( X3 != nil_li1885598003od_a_a )
% 3.13/1.61 => ( ! [Xss: list_l1108175539od_a_a] :
% 3.13/1.61 ( X3
% 3.13/1.61 != ( cons_l724116707od_a_a @ nil_Product_prod_a_a @ Xss ) )
% 3.13/1.61 => ~ ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a,Xss: list_l1108175539od_a_a] :
% 3.13/1.61 ( X3
% 3.13/1.61 != ( cons_l724116707od_a_a @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) @ Xss ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_232_set__zip__rightD,axiom,
% 3.13/1.61 ! [X3: a,Y3: a,Xs2: list_a,Ys2: list_a] :
% 3.13/1.61 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ ( set_Product_prod_a_a2 @ ( zip_a_a @ Xs2 @ Ys2 ) ) )
% 3.13/1.61 => ( member_a2 @ Y3 @ ( set_a2 @ Ys2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_233_set__zip__leftD,axiom,
% 3.13/1.61 ! [X3: a,Y3: a,Xs2: list_a,Ys2: list_a] :
% 3.13/1.61 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ ( set_Product_prod_a_a2 @ ( zip_a_a @ Xs2 @ Ys2 ) ) )
% 3.13/1.61 => ( member_a2 @ X3 @ ( set_a2 @ Xs2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_234_in__set__zipE,axiom,
% 3.13/1.61 ! [X3: a,Y3: a,Xs2: list_a,Ys2: list_a] :
% 3.13/1.61 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ ( set_Product_prod_a_a2 @ ( zip_a_a @ Xs2 @ Ys2 ) ) )
% 3.13/1.61 => ~ ( ( member_a2 @ X3 @ ( set_a2 @ Xs2 ) )
% 3.13/1.61 => ~ ( member_a2 @ Y3 @ ( set_a2 @ Ys2 ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_235_zip__same,axiom,
% 3.13/1.61 ! [A: a,B: a,Xs2: list_a] :
% 3.13/1.61 ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ ( set_Product_prod_a_a2 @ ( zip_a_a @ Xs2 @ Xs2 ) ) )
% 3.13/1.61 = ( ( member_a2 @ A @ ( set_a2 @ Xs2 ) )
% 3.13/1.61 & ( A = B ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_236_same__length__different,axiom,
% 3.13/1.61 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( Xs2 != Ys2 )
% 3.13/1.61 => ( ( ( size_s642698393od_a_a @ Xs2 )
% 3.13/1.61 = ( size_s642698393od_a_a @ Ys2 ) )
% 3.13/1.61 => ? [Pre: list_P1467822637od_a_a,X4: product_prod_a_a,Xs3: list_P1467822637od_a_a,Y4: product_prod_a_a,Ys3: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( X4 != Y4 )
% 3.13/1.61 & ( Xs2
% 3.13/1.61 = ( append1574001858od_a_a @ Pre @ ( append1574001858od_a_a @ ( cons_P1921020637od_a_a @ X4 @ nil_Product_prod_a_a ) @ Xs3 ) ) )
% 3.13/1.61 & ( Ys2
% 3.13/1.61 = ( append1574001858od_a_a @ Pre @ ( append1574001858od_a_a @ ( cons_P1921020637od_a_a @ Y4 @ nil_Product_prod_a_a ) @ Ys3 ) ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_237_list_Oset__cases,axiom,
% 3.13/1.61 ! [E: product_prod_a_a,A: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( member449909584od_a_a @ E @ ( set_Product_prod_a_a2 @ A ) )
% 3.13/1.61 => ( ! [Z22: list_P1467822637od_a_a] :
% 3.13/1.61 ( A
% 3.13/1.61 != ( cons_P1921020637od_a_a @ E @ Z22 ) )
% 3.13/1.61 => ~ ! [Z1: product_prod_a_a,Z22: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( A
% 3.13/1.61 = ( cons_P1921020637od_a_a @ Z1 @ Z22 ) )
% 3.13/1.61 => ~ ( member449909584od_a_a @ E @ ( set_Product_prod_a_a2 @ Z22 ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_238_set__ConsD,axiom,
% 3.13/1.61 ! [Y3: product_prod_a_a,X3: product_prod_a_a,Xs2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( member449909584od_a_a @ Y3 @ ( set_Product_prod_a_a2 @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) ) )
% 3.13/1.61 => ( ( Y3 = X3 )
% 3.13/1.61 | ( member449909584od_a_a @ Y3 @ ( set_Product_prod_a_a2 @ Xs2 ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_239_list_Oset__intros_I1_J,axiom,
% 3.13/1.61 ! [X21: product_prod_a_a,X22: list_P1467822637od_a_a] : ( member449909584od_a_a @ X21 @ ( set_Product_prod_a_a2 @ ( cons_P1921020637od_a_a @ X21 @ X22 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_240_list_Oset__intros_I2_J,axiom,
% 3.13/1.61 ! [Y3: product_prod_a_a,X22: list_P1467822637od_a_a,X21: product_prod_a_a] :
% 3.13/1.61 ( ( member449909584od_a_a @ Y3 @ ( set_Product_prod_a_a2 @ X22 ) )
% 3.13/1.61 => ( member449909584od_a_a @ Y3 @ ( set_Product_prod_a_a2 @ ( cons_P1921020637od_a_a @ X21 @ X22 ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_241_lex__append__rightI,axiom,
% 3.13/1.61 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a,Vs: list_P1467822637od_a_a,Us: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ Ys2 ) @ ( lex_Product_prod_a_a @ R ) )
% 3.13/1.61 => ( ( ( size_s642698393od_a_a @ Vs )
% 3.13/1.61 = ( size_s642698393od_a_a @ Us ) )
% 3.13/1.61 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ Xs2 @ Us ) @ ( append1574001858od_a_a @ Ys2 @ Vs ) ) @ ( lex_Product_prod_a_a @ R ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_242_sorted__wrt_Ocases,axiom,
% 3.13/1.61 ! [X3: produc501911462od_a_a] :
% 3.13/1.61 ( ! [P4: product_prod_a_a > product_prod_a_a > $o] :
% 3.13/1.61 ( X3
% 3.13/1.61 != ( produc214132118od_a_a @ P4 @ nil_Product_prod_a_a ) )
% 3.13/1.61 => ~ ! [P4: product_prod_a_a > product_prod_a_a > $o,X4: product_prod_a_a,Ys4: list_P1467822637od_a_a] :
% 3.13/1.61 ( X3
% 3.13/1.61 != ( produc214132118od_a_a @ P4 @ ( cons_P1921020637od_a_a @ X4 @ Ys4 ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_243_successively_Ocases,axiom,
% 3.13/1.61 ! [X3: produc501911462od_a_a] :
% 3.13/1.61 ( ! [P4: product_prod_a_a > product_prod_a_a > $o] :
% 3.13/1.61 ( X3
% 3.13/1.61 != ( produc214132118od_a_a @ P4 @ nil_Product_prod_a_a ) )
% 3.13/1.61 => ( ! [P4: product_prod_a_a > product_prod_a_a > $o,X4: product_prod_a_a] :
% 3.13/1.61 ( X3
% 3.13/1.61 != ( produc214132118od_a_a @ P4 @ ( cons_P1921020637od_a_a @ X4 @ nil_Product_prod_a_a ) ) )
% 3.13/1.61 => ~ ! [P4: product_prod_a_a > product_prod_a_a > $o,X4: product_prod_a_a,Y4: product_prod_a_a,Xs4: list_P1467822637od_a_a] :
% 3.13/1.61 ( X3
% 3.13/1.61 != ( produc214132118od_a_a @ P4 @ ( cons_P1921020637od_a_a @ X4 @ ( cons_P1921020637od_a_a @ Y4 @ Xs4 ) ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_244_map__tailrec__rev_Oinduct,axiom,
% 3.13/1.61 ! [P2: ( product_prod_a_a > product_prod_a_a ) > list_P1467822637od_a_a > list_P1467822637od_a_a > $o,A0: product_prod_a_a > product_prod_a_a,A1: list_P1467822637od_a_a,A22: list_P1467822637od_a_a] :
% 3.13/1.61 ( ! [F2: product_prod_a_a > product_prod_a_a,X_1: list_P1467822637od_a_a] : ( P2 @ F2 @ nil_Product_prod_a_a @ X_1 )
% 3.13/1.61 => ( ! [F2: product_prod_a_a > product_prod_a_a,A3: product_prod_a_a,As: list_P1467822637od_a_a,Bs: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( P2 @ F2 @ As @ ( cons_P1921020637od_a_a @ ( F2 @ A3 ) @ Bs ) )
% 3.13/1.61 => ( P2 @ F2 @ ( cons_P1921020637od_a_a @ A3 @ As ) @ Bs ) )
% 3.13/1.61 => ( P2 @ A0 @ A1 @ A22 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_245_list__nonempty__induct,axiom,
% 3.13/1.61 ! [Xs2: list_P1467822637od_a_a,P2: list_P1467822637od_a_a > $o] :
% 3.13/1.61 ( ( Xs2 != nil_Product_prod_a_a )
% 3.13/1.61 => ( ! [X4: product_prod_a_a] : ( P2 @ ( cons_P1921020637od_a_a @ X4 @ nil_Product_prod_a_a ) )
% 3.13/1.61 => ( ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( Xs4 != nil_Product_prod_a_a )
% 3.13/1.61 => ( ( P2 @ Xs4 )
% 3.13/1.61 => ( P2 @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) ) ) )
% 3.13/1.61 => ( P2 @ Xs2 ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_246_successively_Oinduct,axiom,
% 3.13/1.61 ! [P2: ( product_prod_a_a > product_prod_a_a > $o ) > list_P1467822637od_a_a > $o,A0: product_prod_a_a > product_prod_a_a > $o,A1: list_P1467822637od_a_a] :
% 3.13/1.61 ( ! [P4: product_prod_a_a > product_prod_a_a > $o] : ( P2 @ P4 @ nil_Product_prod_a_a )
% 3.13/1.61 => ( ! [P4: product_prod_a_a > product_prod_a_a > $o,X4: product_prod_a_a] : ( P2 @ P4 @ ( cons_P1921020637od_a_a @ X4 @ nil_Product_prod_a_a ) )
% 3.13/1.61 => ( ! [P4: product_prod_a_a > product_prod_a_a > $o,X4: product_prod_a_a,Y4: product_prod_a_a,Xs4: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( P2 @ P4 @ ( cons_P1921020637od_a_a @ Y4 @ Xs4 ) )
% 3.13/1.61 => ( P2 @ P4 @ ( cons_P1921020637od_a_a @ X4 @ ( cons_P1921020637od_a_a @ Y4 @ Xs4 ) ) ) )
% 3.13/1.61 => ( P2 @ A0 @ A1 ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_247_remdups__adj_Oinduct,axiom,
% 3.13/1.61 ! [P2: list_P1467822637od_a_a > $o,A0: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( P2 @ nil_Product_prod_a_a )
% 3.13/1.61 => ( ! [X4: product_prod_a_a] : ( P2 @ ( cons_P1921020637od_a_a @ X4 @ nil_Product_prod_a_a ) )
% 3.13/1.61 => ( ! [X4: product_prod_a_a,Y4: product_prod_a_a,Xs4: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( ( X4 = Y4 )
% 3.13/1.61 => ( P2 @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) ) )
% 3.13/1.61 => ( ( ( X4 != Y4 )
% 3.13/1.61 => ( P2 @ ( cons_P1921020637od_a_a @ Y4 @ Xs4 ) ) )
% 3.13/1.61 => ( P2 @ ( cons_P1921020637od_a_a @ X4 @ ( cons_P1921020637od_a_a @ Y4 @ Xs4 ) ) ) ) )
% 3.13/1.61 => ( P2 @ A0 ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_248_sorted__wrt_Oinduct,axiom,
% 3.13/1.61 ! [P2: ( product_prod_a_a > product_prod_a_a > $o ) > list_P1467822637od_a_a > $o,A0: product_prod_a_a > product_prod_a_a > $o,A1: list_P1467822637od_a_a] :
% 3.13/1.61 ( ! [P4: product_prod_a_a > product_prod_a_a > $o] : ( P2 @ P4 @ nil_Product_prod_a_a )
% 3.13/1.61 => ( ! [P4: product_prod_a_a > product_prod_a_a > $o,X4: product_prod_a_a,Ys4: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( P2 @ P4 @ Ys4 )
% 3.13/1.61 => ( P2 @ P4 @ ( cons_P1921020637od_a_a @ X4 @ Ys4 ) ) )
% 3.13/1.61 => ( P2 @ A0 @ A1 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_249_remdups__adj_Ocases,axiom,
% 3.13/1.61 ! [X3: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( X3 != nil_Product_prod_a_a )
% 3.13/1.61 => ( ! [X4: product_prod_a_a] :
% 3.13/1.61 ( X3
% 3.13/1.61 != ( cons_P1921020637od_a_a @ X4 @ nil_Product_prod_a_a ) )
% 3.13/1.61 => ~ ! [X4: product_prod_a_a,Y4: product_prod_a_a,Xs4: list_P1467822637od_a_a] :
% 3.13/1.61 ( X3
% 3.13/1.61 != ( cons_P1921020637od_a_a @ X4 @ ( cons_P1921020637od_a_a @ Y4 @ Xs4 ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_250_shuffles_Oinduct,axiom,
% 3.13/1.61 ! [P2: list_P1467822637od_a_a > list_P1467822637od_a_a > $o,A0: list_P1467822637od_a_a,A1: list_P1467822637od_a_a] :
% 3.13/1.61 ( ! [X_1: list_P1467822637od_a_a] : ( P2 @ nil_Product_prod_a_a @ X_1 )
% 3.13/1.61 => ( ! [Xs4: list_P1467822637od_a_a] : ( P2 @ Xs4 @ nil_Product_prod_a_a )
% 3.13/1.61 => ( ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a,Y4: product_prod_a_a,Ys4: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( P2 @ Xs4 @ ( cons_P1921020637od_a_a @ Y4 @ Ys4 ) )
% 3.13/1.61 => ( ( P2 @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) @ Ys4 )
% 3.13/1.61 => ( P2 @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) @ ( cons_P1921020637od_a_a @ Y4 @ Ys4 ) ) ) )
% 3.13/1.61 => ( P2 @ A0 @ A1 ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_251_induct__list012,axiom,
% 3.13/1.61 ! [P2: list_P1467822637od_a_a > $o,Xs2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( P2 @ nil_Product_prod_a_a )
% 3.13/1.61 => ( ! [X4: product_prod_a_a] : ( P2 @ ( cons_P1921020637od_a_a @ X4 @ nil_Product_prod_a_a ) )
% 3.13/1.61 => ( ! [X4: product_prod_a_a,Y4: product_prod_a_a,Zs2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( P2 @ Zs2 )
% 3.13/1.61 => ( ( P2 @ ( cons_P1921020637od_a_a @ Y4 @ Zs2 ) )
% 3.13/1.61 => ( P2 @ ( cons_P1921020637od_a_a @ X4 @ ( cons_P1921020637od_a_a @ Y4 @ Zs2 ) ) ) ) )
% 3.13/1.61 => ( P2 @ Xs2 ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_252_splice_Oinduct,axiom,
% 3.13/1.61 ! [P2: list_P1467822637od_a_a > list_P1467822637od_a_a > $o,A0: list_P1467822637od_a_a,A1: list_P1467822637od_a_a] :
% 3.13/1.61 ( ! [X_1: list_P1467822637od_a_a] : ( P2 @ nil_Product_prod_a_a @ X_1 )
% 3.13/1.61 => ( ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a,Ys4: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( P2 @ Ys4 @ Xs4 )
% 3.13/1.61 => ( P2 @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) @ Ys4 ) )
% 3.13/1.61 => ( P2 @ A0 @ A1 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_253_list__induct2_H,axiom,
% 3.13/1.61 ! [P2: list_P1467822637od_a_a > list_P1467822637od_a_a > $o,Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( P2 @ nil_Product_prod_a_a @ nil_Product_prod_a_a )
% 3.13/1.61 => ( ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a] : ( P2 @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) @ nil_Product_prod_a_a )
% 3.13/1.61 => ( ! [Y4: product_prod_a_a,Ys4: list_P1467822637od_a_a] : ( P2 @ nil_Product_prod_a_a @ ( cons_P1921020637od_a_a @ Y4 @ Ys4 ) )
% 3.13/1.61 => ( ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a,Y4: product_prod_a_a,Ys4: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( P2 @ Xs4 @ Ys4 )
% 3.13/1.61 => ( P2 @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) @ ( cons_P1921020637od_a_a @ Y4 @ Ys4 ) ) )
% 3.13/1.61 => ( P2 @ Xs2 @ Ys2 ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_254_neq__Nil__conv,axiom,
% 3.13/1.61 ! [Xs2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( Xs2 != nil_Product_prod_a_a )
% 3.13/1.61 = ( ? [Y: product_prod_a_a,Ys: list_P1467822637od_a_a] :
% 3.13/1.61 ( Xs2
% 3.13/1.61 = ( cons_P1921020637od_a_a @ Y @ Ys ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_255_list_Oinducts,axiom,
% 3.13/1.61 ! [P2: list_P1467822637od_a_a > $o,List: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( P2 @ nil_Product_prod_a_a )
% 3.13/1.61 => ( ! [X12: product_prod_a_a,X23: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( P2 @ X23 )
% 3.13/1.61 => ( P2 @ ( cons_P1921020637od_a_a @ X12 @ X23 ) ) )
% 3.13/1.61 => ( P2 @ List ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_256_list_Oexhaust,axiom,
% 3.13/1.61 ! [Y3: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( Y3 != nil_Product_prod_a_a )
% 3.13/1.61 => ~ ! [X212: product_prod_a_a,X222: list_P1467822637od_a_a] :
% 3.13/1.61 ( Y3
% 3.13/1.61 != ( cons_P1921020637od_a_a @ X212 @ X222 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_257_list_OdiscI,axiom,
% 3.13/1.61 ! [List: list_P1467822637od_a_a,X21: product_prod_a_a,X22: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( List
% 3.13/1.61 = ( cons_P1921020637od_a_a @ X21 @ X22 ) )
% 3.13/1.61 => ( List != nil_Product_prod_a_a ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_258_list_Odistinct_I1_J,axiom,
% 3.13/1.61 ! [X21: product_prod_a_a,X22: list_P1467822637od_a_a] :
% 3.13/1.61 ( nil_Product_prod_a_a
% 3.13/1.61 != ( cons_P1921020637od_a_a @ X21 @ X22 ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_259_append_Oleft__neutral,axiom,
% 3.13/1.61 ! [A: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( append1574001858od_a_a @ nil_Product_prod_a_a @ A )
% 3.13/1.61 = A ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_260_append__Nil,axiom,
% 3.13/1.61 ! [Ys2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( append1574001858od_a_a @ nil_Product_prod_a_a @ Ys2 )
% 3.13/1.61 = Ys2 ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_261_eq__Nil__appendI,axiom,
% 3.13/1.61 ! [Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( Xs2 = Ys2 )
% 3.13/1.61 => ( Xs2
% 3.13/1.61 = ( append1574001858od_a_a @ nil_Product_prod_a_a @ Ys2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_262_pcas_Ocases,axiom,
% 3.13/1.61 ! [X3: produc1197928545_a_a_a] :
% 3.13/1.61 ( ! [U2: a,V: a] :
% 3.13/1.61 ( X3
% 3.13/1.61 != ( produc1440321489_a_a_a @ U2 @ ( produc998622632_a_a_a @ nil_Product_prod_a_a @ V ) ) )
% 3.13/1.61 => ~ ! [U2: a,E2: product_prod_a_a,Es: list_P1467822637od_a_a,V: a] :
% 3.13/1.61 ( X3
% 3.13/1.61 != ( produc1440321489_a_a_a @ U2 @ ( produc998622632_a_a_a @ ( cons_P1921020637od_a_a @ E2 @ Es ) @ V ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_263_progressing__Nil,axiom,
% 3.13/1.61 kurato1072996284sing_a @ nil_Product_prod_a_a ).
% 3.13/1.61
% 3.13/1.61 thf(fact_264_split__list__first__prop__iff,axiom,
% 3.13/1.61 ! [Xs2: list_P1467822637od_a_a,P2: product_prod_a_a > $o] :
% 3.13/1.61 ( ( ? [X: product_prod_a_a] :
% 3.13/1.61 ( ( member449909584od_a_a @ X @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 3.13/1.61 & ( P2 @ X ) ) )
% 3.13/1.61 = ( ? [Ys: list_P1467822637od_a_a,X: product_prod_a_a] :
% 3.13/1.61 ( ? [Zs3: list_P1467822637od_a_a] :
% 3.13/1.61 ( Xs2
% 3.13/1.61 = ( append1574001858od_a_a @ Ys @ ( cons_P1921020637od_a_a @ X @ Zs3 ) ) )
% 3.13/1.61 & ( P2 @ X )
% 3.13/1.61 & ! [Y: product_prod_a_a] :
% 3.13/1.61 ( ( member449909584od_a_a @ Y @ ( set_Product_prod_a_a2 @ Ys ) )
% 3.13/1.61 => ~ ( P2 @ Y ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_265_split__list__last__prop__iff,axiom,
% 3.13/1.61 ! [Xs2: list_P1467822637od_a_a,P2: product_prod_a_a > $o] :
% 3.13/1.61 ( ( ? [X: product_prod_a_a] :
% 3.13/1.61 ( ( member449909584od_a_a @ X @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 3.13/1.61 & ( P2 @ X ) ) )
% 3.13/1.61 = ( ? [Ys: list_P1467822637od_a_a,X: product_prod_a_a,Zs3: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( Xs2
% 3.13/1.61 = ( append1574001858od_a_a @ Ys @ ( cons_P1921020637od_a_a @ X @ Zs3 ) ) )
% 3.13/1.61 & ( P2 @ X )
% 3.13/1.61 & ! [Y: product_prod_a_a] :
% 3.13/1.61 ( ( member449909584od_a_a @ Y @ ( set_Product_prod_a_a2 @ Zs3 ) )
% 3.13/1.61 => ~ ( P2 @ Y ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_266_in__set__conv__decomp__first,axiom,
% 3.13/1.61 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( member449909584od_a_a @ X3 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 3.13/1.61 = ( ? [Ys: list_P1467822637od_a_a,Zs3: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( Xs2
% 3.13/1.61 = ( append1574001858od_a_a @ Ys @ ( cons_P1921020637od_a_a @ X3 @ Zs3 ) ) )
% 3.13/1.61 & ~ ( member449909584od_a_a @ X3 @ ( set_Product_prod_a_a2 @ Ys ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_267_in__set__conv__decomp__last,axiom,
% 3.13/1.61 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( member449909584od_a_a @ X3 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 3.13/1.61 = ( ? [Ys: list_P1467822637od_a_a,Zs3: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( Xs2
% 3.13/1.61 = ( append1574001858od_a_a @ Ys @ ( cons_P1921020637od_a_a @ X3 @ Zs3 ) ) )
% 3.13/1.61 & ~ ( member449909584od_a_a @ X3 @ ( set_Product_prod_a_a2 @ Zs3 ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_268_split__list__first__propE,axiom,
% 3.13/1.61 ! [Xs2: list_P1467822637od_a_a,P2: product_prod_a_a > $o] :
% 3.13/1.61 ( ? [X5: product_prod_a_a] :
% 3.13/1.61 ( ( member449909584od_a_a @ X5 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 3.13/1.61 & ( P2 @ X5 ) )
% 3.13/1.61 => ~ ! [Ys4: list_P1467822637od_a_a,X4: product_prod_a_a] :
% 3.13/1.61 ( ? [Zs2: list_P1467822637od_a_a] :
% 3.13/1.61 ( Xs2
% 3.13/1.61 = ( append1574001858od_a_a @ Ys4 @ ( cons_P1921020637od_a_a @ X4 @ Zs2 ) ) )
% 3.13/1.61 => ( ( P2 @ X4 )
% 3.13/1.61 => ~ ! [Xa: product_prod_a_a] :
% 3.13/1.61 ( ( member449909584od_a_a @ Xa @ ( set_Product_prod_a_a2 @ Ys4 ) )
% 3.13/1.61 => ~ ( P2 @ Xa ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_269_split__list__last__propE,axiom,
% 3.13/1.61 ! [Xs2: list_P1467822637od_a_a,P2: product_prod_a_a > $o] :
% 3.13/1.61 ( ? [X5: product_prod_a_a] :
% 3.13/1.61 ( ( member449909584od_a_a @ X5 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 3.13/1.61 & ( P2 @ X5 ) )
% 3.13/1.61 => ~ ! [Ys4: list_P1467822637od_a_a,X4: product_prod_a_a,Zs2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( Xs2
% 3.13/1.61 = ( append1574001858od_a_a @ Ys4 @ ( cons_P1921020637od_a_a @ X4 @ Zs2 ) ) )
% 3.13/1.61 => ( ( P2 @ X4 )
% 3.13/1.61 => ~ ! [Xa: product_prod_a_a] :
% 3.13/1.61 ( ( member449909584od_a_a @ Xa @ ( set_Product_prod_a_a2 @ Zs2 ) )
% 3.13/1.61 => ~ ( P2 @ Xa ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_270_split__list__first__prop,axiom,
% 3.13/1.61 ! [Xs2: list_P1467822637od_a_a,P2: product_prod_a_a > $o] :
% 3.13/1.61 ( ? [X5: product_prod_a_a] :
% 3.13/1.61 ( ( member449909584od_a_a @ X5 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 3.13/1.61 & ( P2 @ X5 ) )
% 3.13/1.61 => ? [Ys4: list_P1467822637od_a_a,X4: product_prod_a_a] :
% 3.13/1.61 ( ? [Zs2: list_P1467822637od_a_a] :
% 3.13/1.61 ( Xs2
% 3.13/1.61 = ( append1574001858od_a_a @ Ys4 @ ( cons_P1921020637od_a_a @ X4 @ Zs2 ) ) )
% 3.13/1.61 & ( P2 @ X4 )
% 3.13/1.61 & ! [Xa: product_prod_a_a] :
% 3.13/1.61 ( ( member449909584od_a_a @ Xa @ ( set_Product_prod_a_a2 @ Ys4 ) )
% 3.13/1.61 => ~ ( P2 @ Xa ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_271_split__list__last__prop,axiom,
% 3.13/1.61 ! [Xs2: list_P1467822637od_a_a,P2: product_prod_a_a > $o] :
% 3.13/1.61 ( ? [X5: product_prod_a_a] :
% 3.13/1.61 ( ( member449909584od_a_a @ X5 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 3.13/1.61 & ( P2 @ X5 ) )
% 3.13/1.61 => ? [Ys4: list_P1467822637od_a_a,X4: product_prod_a_a,Zs2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( Xs2
% 3.13/1.61 = ( append1574001858od_a_a @ Ys4 @ ( cons_P1921020637od_a_a @ X4 @ Zs2 ) ) )
% 3.13/1.61 & ( P2 @ X4 )
% 3.13/1.61 & ! [Xa: product_prod_a_a] :
% 3.13/1.61 ( ( member449909584od_a_a @ Xa @ ( set_Product_prod_a_a2 @ Zs2 ) )
% 3.13/1.61 => ~ ( P2 @ Xa ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_272_in__set__conv__decomp,axiom,
% 3.13/1.61 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( member449909584od_a_a @ X3 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 3.13/1.61 = ( ? [Ys: list_P1467822637od_a_a,Zs3: list_P1467822637od_a_a] :
% 3.13/1.61 ( Xs2
% 3.13/1.61 = ( append1574001858od_a_a @ Ys @ ( cons_P1921020637od_a_a @ X3 @ Zs3 ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_273_append__Cons__eq__iff,axiom,
% 3.13/1.61 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Xs5: list_P1467822637od_a_a,Ys5: list_P1467822637od_a_a] :
% 3.13/1.61 ( ~ ( member449909584od_a_a @ X3 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 3.13/1.61 => ( ~ ( member449909584od_a_a @ X3 @ ( set_Product_prod_a_a2 @ Ys2 ) )
% 3.13/1.61 => ( ( ( append1574001858od_a_a @ Xs2 @ ( cons_P1921020637od_a_a @ X3 @ Ys2 ) )
% 3.13/1.61 = ( append1574001858od_a_a @ Xs5 @ ( cons_P1921020637od_a_a @ X3 @ Ys5 ) ) )
% 3.13/1.61 = ( ( Xs2 = Xs5 )
% 3.13/1.61 & ( Ys2 = Ys5 ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_274_split__list__propE,axiom,
% 3.13/1.61 ! [Xs2: list_P1467822637od_a_a,P2: product_prod_a_a > $o] :
% 3.13/1.61 ( ? [X5: product_prod_a_a] :
% 3.13/1.61 ( ( member449909584od_a_a @ X5 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 3.13/1.61 & ( P2 @ X5 ) )
% 3.13/1.61 => ~ ! [Ys4: list_P1467822637od_a_a,X4: product_prod_a_a] :
% 3.13/1.61 ( ? [Zs2: list_P1467822637od_a_a] :
% 3.13/1.61 ( Xs2
% 3.13/1.61 = ( append1574001858od_a_a @ Ys4 @ ( cons_P1921020637od_a_a @ X4 @ Zs2 ) ) )
% 3.13/1.61 => ~ ( P2 @ X4 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_275_split__list__first,axiom,
% 3.13/1.61 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( member449909584od_a_a @ X3 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 3.13/1.61 => ? [Ys4: list_P1467822637od_a_a,Zs2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( Xs2
% 3.13/1.61 = ( append1574001858od_a_a @ Ys4 @ ( cons_P1921020637od_a_a @ X3 @ Zs2 ) ) )
% 3.13/1.61 & ~ ( member449909584od_a_a @ X3 @ ( set_Product_prod_a_a2 @ Ys4 ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_276_split__list__prop,axiom,
% 3.13/1.61 ! [Xs2: list_P1467822637od_a_a,P2: product_prod_a_a > $o] :
% 3.13/1.61 ( ? [X5: product_prod_a_a] :
% 3.13/1.61 ( ( member449909584od_a_a @ X5 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 3.13/1.61 & ( P2 @ X5 ) )
% 3.13/1.61 => ? [Ys4: list_P1467822637od_a_a,X4: product_prod_a_a] :
% 3.13/1.61 ( ? [Zs2: list_P1467822637od_a_a] :
% 3.13/1.61 ( Xs2
% 3.13/1.61 = ( append1574001858od_a_a @ Ys4 @ ( cons_P1921020637od_a_a @ X4 @ Zs2 ) ) )
% 3.13/1.61 & ( P2 @ X4 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_277_split__list__last,axiom,
% 3.13/1.61 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( member449909584od_a_a @ X3 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 3.13/1.61 => ? [Ys4: list_P1467822637od_a_a,Zs2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( Xs2
% 3.13/1.61 = ( append1574001858od_a_a @ Ys4 @ ( cons_P1921020637od_a_a @ X3 @ Zs2 ) ) )
% 3.13/1.61 & ~ ( member449909584od_a_a @ X3 @ ( set_Product_prod_a_a2 @ Zs2 ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_278_split__list,axiom,
% 3.13/1.61 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( member449909584od_a_a @ X3 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 3.13/1.61 => ? [Ys4: list_P1467822637od_a_a,Zs2: list_P1467822637od_a_a] :
% 3.13/1.61 ( Xs2
% 3.13/1.61 = ( append1574001858od_a_a @ Ys4 @ ( cons_P1921020637od_a_a @ X3 @ Zs2 ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_279_rev__nonempty__induct,axiom,
% 3.13/1.61 ! [Xs2: list_P1467822637od_a_a,P2: list_P1467822637od_a_a > $o] :
% 3.13/1.61 ( ( Xs2 != nil_Product_prod_a_a )
% 3.13/1.61 => ( ! [X4: product_prod_a_a] : ( P2 @ ( cons_P1921020637od_a_a @ X4 @ nil_Product_prod_a_a ) )
% 3.13/1.61 => ( ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( Xs4 != nil_Product_prod_a_a )
% 3.13/1.61 => ( ( P2 @ Xs4 )
% 3.13/1.61 => ( P2 @ ( append1574001858od_a_a @ Xs4 @ ( cons_P1921020637od_a_a @ X4 @ nil_Product_prod_a_a ) ) ) ) )
% 3.13/1.61 => ( P2 @ Xs2 ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_280_append__eq__Cons__conv,axiom,
% 3.13/1.61 ! [Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a,X3: product_prod_a_a,Xs2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( ( append1574001858od_a_a @ Ys2 @ Zs )
% 3.13/1.61 = ( cons_P1921020637od_a_a @ X3 @ Xs2 ) )
% 3.13/1.61 = ( ( ( Ys2 = nil_Product_prod_a_a )
% 3.13/1.61 & ( Zs
% 3.13/1.61 = ( cons_P1921020637od_a_a @ X3 @ Xs2 ) ) )
% 3.13/1.61 | ? [Ys6: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( Ys2
% 3.13/1.61 = ( cons_P1921020637od_a_a @ X3 @ Ys6 ) )
% 3.13/1.61 & ( ( append1574001858od_a_a @ Ys6 @ Zs )
% 3.13/1.61 = Xs2 ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_281_Cons__eq__append__conv,axiom,
% 3.13/1.61 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( ( cons_P1921020637od_a_a @ X3 @ Xs2 )
% 3.13/1.61 = ( append1574001858od_a_a @ Ys2 @ Zs ) )
% 3.13/1.61 = ( ( ( Ys2 = nil_Product_prod_a_a )
% 3.13/1.61 & ( ( cons_P1921020637od_a_a @ X3 @ Xs2 )
% 3.13/1.61 = Zs ) )
% 3.13/1.61 | ? [Ys6: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( ( cons_P1921020637od_a_a @ X3 @ Ys6 )
% 3.13/1.61 = Ys2 )
% 3.13/1.61 & ( Xs2
% 3.13/1.61 = ( append1574001858od_a_a @ Ys6 @ Zs ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_282_rev__exhaust,axiom,
% 3.13/1.61 ! [Xs2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( Xs2 != nil_Product_prod_a_a )
% 3.13/1.61 => ~ ! [Ys4: list_P1467822637od_a_a,Y4: product_prod_a_a] :
% 3.13/1.61 ( Xs2
% 3.13/1.61 != ( append1574001858od_a_a @ Ys4 @ ( cons_P1921020637od_a_a @ Y4 @ nil_Product_prod_a_a ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_283_rev__induct,axiom,
% 3.13/1.61 ! [P2: list_P1467822637od_a_a > $o,Xs2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( P2 @ nil_Product_prod_a_a )
% 3.13/1.61 => ( ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( P2 @ Xs4 )
% 3.13/1.61 => ( P2 @ ( append1574001858od_a_a @ Xs4 @ ( cons_P1921020637od_a_a @ X4 @ nil_Product_prod_a_a ) ) ) )
% 3.13/1.61 => ( P2 @ Xs2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_284_shuffles_Ocases,axiom,
% 3.13/1.61 ! [X3: produc651658087od_a_a] :
% 3.13/1.61 ( ! [Ys4: list_P1467822637od_a_a] :
% 3.13/1.61 ( X3
% 3.13/1.61 != ( produc85179863od_a_a @ nil_Product_prod_a_a @ Ys4 ) )
% 3.13/1.61 => ( ! [Xs4: list_P1467822637od_a_a] :
% 3.13/1.61 ( X3
% 3.13/1.61 != ( produc85179863od_a_a @ Xs4 @ nil_Product_prod_a_a ) )
% 3.13/1.61 => ~ ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a,Y4: product_prod_a_a,Ys4: list_P1467822637od_a_a] :
% 3.13/1.61 ( X3
% 3.13/1.61 != ( produc85179863od_a_a @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) @ ( cons_P1921020637od_a_a @ Y4 @ Ys4 ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_285_sd__path_Oinduct,axiom,
% 3.13/1.61 ! [P2: product_prod_a_a > a > list_P1467822637od_a_a > $o,A0: product_prod_a_a,A1: a,A22: list_P1467822637od_a_a] :
% 3.13/1.61 ( ! [Uu: product_prod_a_a,Uv: a] : ( P2 @ Uu @ Uv @ nil_Product_prod_a_a )
% 3.13/1.61 => ( ! [U2: a,V: a,W: a,E2: product_prod_a_a,Es: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( P2 @ ( product_Pair_a_a @ U2 @ V ) @ W @ Es )
% 3.13/1.61 => ( P2 @ ( product_Pair_a_a @ U2 @ V ) @ W @ ( cons_P1921020637od_a_a @ E2 @ Es ) ) )
% 3.13/1.61 => ( P2 @ A0 @ A1 @ A22 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_286_co__path_Oinduct,axiom,
% 3.13/1.61 ! [P2: product_prod_a_a > a > list_P1467822637od_a_a > $o,A0: product_prod_a_a,A1: a,A22: list_P1467822637od_a_a] :
% 3.13/1.61 ( ! [Uu: product_prod_a_a,Uv: a] : ( P2 @ Uu @ Uv @ nil_Product_prod_a_a )
% 3.13/1.61 => ( ! [Uw: product_prod_a_a,Ux: a,E2: product_prod_a_a] : ( P2 @ Uw @ Ux @ ( cons_P1921020637od_a_a @ E2 @ nil_Product_prod_a_a ) )
% 3.13/1.61 => ( ! [U2: a,V: a,W: a,E1: product_prod_a_a,E22: product_prod_a_a,Es: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( ( ( E1
% 3.13/1.61 = ( product_Pair_a_a @ U2 @ W ) )
% 3.13/1.61 & ( E22
% 3.13/1.61 = ( product_Pair_a_a @ W @ V ) ) )
% 3.13/1.61 => ( P2 @ ( product_Pair_a_a @ U2 @ V ) @ W @ Es ) )
% 3.13/1.61 => ( ( ~ ( ( E1
% 3.13/1.61 = ( product_Pair_a_a @ U2 @ W ) )
% 3.13/1.61 & ( E22
% 3.13/1.61 = ( product_Pair_a_a @ W @ V ) ) )
% 3.13/1.61 => ( ( ( E1
% 3.13/1.61 = ( product_Pair_a_a @ V @ W ) )
% 3.13/1.61 & ( E22
% 3.13/1.61 = ( product_Pair_a_a @ W @ U2 ) ) )
% 3.13/1.61 => ( P2 @ ( product_Pair_a_a @ U2 @ V ) @ W @ Es ) ) )
% 3.13/1.61 => ( ( ~ ( ( E1
% 3.13/1.61 = ( product_Pair_a_a @ U2 @ W ) )
% 3.13/1.61 & ( E22
% 3.13/1.61 = ( product_Pair_a_a @ W @ V ) ) )
% 3.13/1.61 => ( ~ ( ( E1
% 3.13/1.61 = ( product_Pair_a_a @ V @ W ) )
% 3.13/1.61 & ( E22
% 3.13/1.61 = ( product_Pair_a_a @ W @ U2 ) ) )
% 3.13/1.61 => ( P2 @ ( product_Pair_a_a @ U2 @ V ) @ W @ ( cons_P1921020637od_a_a @ E22 @ Es ) ) ) )
% 3.13/1.61 => ( P2 @ ( product_Pair_a_a @ U2 @ V ) @ W @ ( cons_P1921020637od_a_a @ E1 @ ( cons_P1921020637od_a_a @ E22 @ Es ) ) ) ) ) )
% 3.13/1.61 => ( P2 @ A0 @ A1 @ A22 ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_287_sd__path_Ocases,axiom,
% 3.13/1.61 ! [X3: produc821581462od_a_a] :
% 3.13/1.61 ( ! [Uu: product_prod_a_a,Uv: a] :
% 3.13/1.61 ( X3
% 3.13/1.61 != ( produc600870406od_a_a @ Uu @ ( produc575024326od_a_a @ Uv @ nil_Product_prod_a_a ) ) )
% 3.13/1.61 => ~ ! [U2: a,V: a,W: a,E2: product_prod_a_a,Es: list_P1467822637od_a_a] :
% 3.13/1.61 ( X3
% 3.13/1.61 != ( produc600870406od_a_a @ ( product_Pair_a_a @ U2 @ V ) @ ( produc575024326od_a_a @ W @ ( cons_P1921020637od_a_a @ E2 @ Es ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_288_co__path_Ocases,axiom,
% 3.13/1.61 ! [X3: produc821581462od_a_a] :
% 3.13/1.61 ( ! [Uu: product_prod_a_a,Uv: a] :
% 3.13/1.61 ( X3
% 3.13/1.61 != ( produc600870406od_a_a @ Uu @ ( produc575024326od_a_a @ Uv @ nil_Product_prod_a_a ) ) )
% 3.13/1.61 => ( ! [Uw: product_prod_a_a,Ux: a,E2: product_prod_a_a] :
% 3.13/1.61 ( X3
% 3.13/1.61 != ( produc600870406od_a_a @ Uw @ ( produc575024326od_a_a @ Ux @ ( cons_P1921020637od_a_a @ E2 @ nil_Product_prod_a_a ) ) ) )
% 3.13/1.61 => ~ ! [U2: a,V: a,W: a,E1: product_prod_a_a,E22: product_prod_a_a,Es: list_P1467822637od_a_a] :
% 3.13/1.61 ( X3
% 3.13/1.61 != ( produc600870406od_a_a @ ( product_Pair_a_a @ U2 @ V ) @ ( produc575024326od_a_a @ W @ ( cons_P1921020637od_a_a @ E1 @ ( cons_P1921020637od_a_a @ E22 @ Es ) ) ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_289_lex__append__leftI,axiom,
% 3.13/1.61 ! [Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a,Xs2: list_P1467822637od_a_a] :
% 3.13/1.61 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ Ys2 @ Zs ) @ ( lex_Product_prod_a_a @ R ) )
% 3.13/1.61 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ Xs2 @ Ys2 ) @ ( append1574001858od_a_a @ Xs2 @ Zs ) ) @ ( lex_Product_prod_a_a @ R ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_290_progressing__single,axiom,
% 3.13/1.61 ! [E: product_prod_a_a] : ( kurato1072996284sing_a @ ( cons_P1921020637od_a_a @ E @ nil_Product_prod_a_a ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_291_lexord__partial__trans,axiom,
% 3.13/1.61 ! [Xs2: list_a,R: set_Product_prod_a_a,Ys2: list_a,Zs: list_a] :
% 3.13/1.61 ( ! [X4: a,Y4: a,Z2: a] :
% 3.13/1.61 ( ( member_a2 @ X4 @ ( set_a2 @ Xs2 ) )
% 3.13/1.61 => ( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ R )
% 3.13/1.61 => ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y4 @ Z2 ) @ R )
% 3.13/1.61 => ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Z2 ) @ R ) ) ) )
% 3.13/1.61 => ( ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ Ys2 ) @ ( lexord_a @ R ) )
% 3.13/1.61 => ( ( member1250517072list_a @ ( produc1448356631list_a @ Ys2 @ Zs ) @ ( lexord_a @ R ) )
% 3.13/1.61 => ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ Zs ) @ ( lexord_a @ R ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_292_lexord__sufE,axiom,
% 3.13/1.61 ! [Xs2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a,Qs: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 3.13/1.61 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ Xs2 @ Zs ) @ ( append1574001858od_a_a @ Ys2 @ Qs ) ) @ ( lexord673907738od_a_a @ R ) )
% 3.13/1.61 => ( ( Xs2 != Ys2 )
% 3.13/1.61 => ( ( ( size_s642698393od_a_a @ Xs2 )
% 3.13/1.61 = ( size_s642698393od_a_a @ Ys2 ) )
% 3.13/1.61 => ( ( ( size_s642698393od_a_a @ Zs )
% 3.13/1.61 = ( size_s642698393od_a_a @ Qs ) )
% 3.13/1.61 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ Ys2 ) @ ( lexord673907738od_a_a @ R ) ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_293_subset__eq__mset__impl_Ocases,axiom,
% 3.13/1.61 ! [X3: produc651658087od_a_a] :
% 3.13/1.61 ( ! [Ys4: list_P1467822637od_a_a] :
% 3.13/1.61 ( X3
% 3.13/1.61 != ( produc85179863od_a_a @ nil_Product_prod_a_a @ Ys4 ) )
% 3.13/1.61 => ~ ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a,Ys4: list_P1467822637od_a_a] :
% 3.13/1.61 ( X3
% 3.13/1.61 != ( produc85179863od_a_a @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) @ Ys4 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_294_asym_Oinducts,axiom,
% 3.13/1.61 ! [X3: set_Product_prod_a_a,P2: set_Product_prod_a_a > $o] :
% 3.13/1.61 ( ( asym_a @ X3 )
% 3.13/1.61 => ( ! [R3: set_Product_prod_a_a] :
% 3.13/1.61 ( ! [A6: a,B4: a] :
% 3.13/1.61 ( ( member449909584od_a_a @ ( product_Pair_a_a @ A6 @ B4 ) @ R3 )
% 3.13/1.61 => ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B4 @ A6 ) @ R3 ) )
% 3.13/1.61 => ( P2 @ R3 ) )
% 3.13/1.61 => ( P2 @ X3 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_295_asym_Ointros,axiom,
% 3.13/1.61 ! [R2: set_Product_prod_a_a] :
% 3.13/1.61 ( ! [A3: a,B3: a] :
% 3.13/1.61 ( ( member449909584od_a_a @ ( product_Pair_a_a @ A3 @ B3 ) @ R2 )
% 3.13/1.61 => ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B3 @ A3 ) @ R2 ) )
% 3.13/1.61 => ( asym_a @ R2 ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_296_asym_Osimps,axiom,
% 3.13/1.61 ( asym_a
% 3.13/1.61 = ( ^ [A5: set_Product_prod_a_a] :
% 3.13/1.61 ? [R4: set_Product_prod_a_a] :
% 3.13/1.61 ( ( A5 = R4 )
% 3.13/1.61 & ! [X: a,Y: a] :
% 3.13/1.61 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ R4 )
% 3.13/1.61 => ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ R4 ) ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_297_asym_Ocases,axiom,
% 3.13/1.61 ! [A: set_Product_prod_a_a] :
% 3.13/1.61 ( ( asym_a @ A )
% 3.13/1.61 => ! [A6: a,B4: a] :
% 3.13/1.61 ( ( member449909584od_a_a @ ( product_Pair_a_a @ A6 @ B4 ) @ A )
% 3.13/1.61 => ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B4 @ A6 ) @ A ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_298_asym__iff,axiom,
% 3.13/1.61 ( asym_a
% 3.13/1.61 = ( ^ [R4: set_Product_prod_a_a] :
% 3.13/1.61 ! [X: a,Y: a] :
% 3.13/1.61 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ R4 )
% 3.13/1.61 => ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ R4 ) ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_299_irreflI,axiom,
% 3.13/1.61 ! [R2: set_Product_prod_a_a] :
% 3.13/1.61 ( ! [A3: a] :
% 3.13/1.61 ~ ( member449909584od_a_a @ ( product_Pair_a_a @ A3 @ A3 ) @ R2 )
% 3.13/1.61 => ( irrefl_a @ R2 ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_300_irrefl__def,axiom,
% 3.13/1.61 ( irrefl_a
% 3.13/1.61 = ( ^ [R5: set_Product_prod_a_a] :
% 3.13/1.61 ! [A5: a] :
% 3.13/1.61 ~ ( member449909584od_a_a @ ( product_Pair_a_a @ A5 @ A5 ) @ R5 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_301_asymD,axiom,
% 3.13/1.61 ! [R2: set_Product_prod_a_a,X3: a,Y3: a] :
% 3.13/1.61 ( ( asym_a @ R2 )
% 3.13/1.61 => ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R2 )
% 3.13/1.61 => ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y3 @ X3 ) @ R2 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_302_inverse__permutation__of__list_Ocases,axiom,
% 3.13/1.61 ! [X3: produc657167928_a_a_a] :
% 3.13/1.61 ( ! [X4: a] :
% 3.13/1.61 ( X3
% 3.13/1.61 != ( produc998622632_a_a_a @ nil_Product_prod_a_a @ X4 ) )
% 3.13/1.61 => ~ ! [Y4: a,X6: a,Xs4: list_P1467822637od_a_a,X4: a] :
% 3.13/1.61 ( X3
% 3.13/1.61 != ( produc998622632_a_a_a @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y4 @ X6 ) @ Xs4 ) @ X4 ) ) ) ).
% 3.13/1.61
% 3.13/1.61 thf(fact_303_inverse__permutation__of__list_Oinduct,axiom,
% 3.13/1.61 ! [P2: list_P1467822637od_a_a > a > $o,A0: list_P1467822637od_a_a,A1: a] :
% 3.13/1.62 ( ! [X_1: a] : ( P2 @ nil_Product_prod_a_a @ X_1 )
% 3.13/1.62 => ( ! [Y4: a,X6: a,Xs4: list_P1467822637od_a_a,X4: a] :
% 3.13/1.62 ( ( ( X4 != X6 )
% 3.13/1.62 => ( P2 @ Xs4 @ X4 ) )
% 3.13/1.62 => ( P2 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y4 @ X6 ) @ Xs4 ) @ X4 ) )
% 3.13/1.62 => ( P2 @ A0 @ A1 ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_304_sd__path_Osimps_I2_J,axiom,
% 3.13/1.62 ! [U: a,V2: a,W2: a,E: product_prod_a_a,Es2: list_P1467822637od_a_a] :
% 3.13/1.62 ( ( pair_sd_path_a @ ( product_Pair_a_a @ U @ V2 ) @ W2 @ ( cons_P1921020637od_a_a @ E @ Es2 ) )
% 3.13/1.62 = ( append1574001858od_a_a
% 3.13/1.62 @ ( if_lis321365491od_a_a
% 3.13/1.62 @ ( E
% 3.13/1.62 = ( product_Pair_a_a @ U @ V2 ) )
% 3.13/1.62 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ U @ W2 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ W2 @ V2 ) @ nil_Product_prod_a_a ) )
% 3.13/1.62 @ ( if_lis321365491od_a_a
% 3.13/1.62 @ ( E
% 3.13/1.62 = ( product_Pair_a_a @ V2 @ U ) )
% 3.13/1.62 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ V2 @ W2 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ W2 @ U ) @ nil_Product_prod_a_a ) )
% 3.13/1.62 @ ( cons_P1921020637od_a_a @ E @ nil_Product_prod_a_a ) ) )
% 3.13/1.62 @ ( pair_sd_path_a @ ( product_Pair_a_a @ U @ V2 ) @ W2 @ Es2 ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_305_sd__path__id,axiom,
% 3.13/1.62 ! [X3: a,Y3: a,P3: list_P1467822637od_a_a,W2: a] :
% 3.13/1.62 ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ ( set_Product_prod_a_a2 @ P3 ) )
% 3.13/1.62 => ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y3 @ X3 ) @ ( set_Product_prod_a_a2 @ P3 ) )
% 3.13/1.62 => ( ( pair_sd_path_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ W2 @ P3 )
% 3.13/1.62 = P3 ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_306_sd__path_Oelims,axiom,
% 3.13/1.62 ! [X3: product_prod_a_a,Xa2: a,Xb: list_P1467822637od_a_a,Y3: list_P1467822637od_a_a] :
% 3.13/1.62 ( ( ( pair_sd_path_a @ X3 @ Xa2 @ Xb )
% 3.13/1.62 = Y3 )
% 3.13/1.62 => ( ( ( Xb = nil_Product_prod_a_a )
% 3.13/1.62 => ( Y3 != nil_Product_prod_a_a ) )
% 3.13/1.62 => ~ ! [U2: a,V: a] :
% 3.13/1.62 ( ( X3
% 3.13/1.62 = ( product_Pair_a_a @ U2 @ V ) )
% 3.13/1.62 => ! [E2: product_prod_a_a,Es: list_P1467822637od_a_a] :
% 3.13/1.62 ( ( Xb
% 3.13/1.62 = ( cons_P1921020637od_a_a @ E2 @ Es ) )
% 3.13/1.62 => ( Y3
% 3.13/1.62 != ( append1574001858od_a_a
% 3.13/1.62 @ ( if_lis321365491od_a_a
% 3.13/1.62 @ ( E2
% 3.13/1.62 = ( product_Pair_a_a @ U2 @ V ) )
% 3.13/1.62 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ U2 @ Xa2 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Xa2 @ V ) @ nil_Product_prod_a_a ) )
% 3.13/1.62 @ ( if_lis321365491od_a_a
% 3.13/1.62 @ ( E2
% 3.13/1.62 = ( product_Pair_a_a @ V @ U2 ) )
% 3.13/1.62 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ V @ Xa2 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Xa2 @ U2 ) @ nil_Product_prod_a_a ) )
% 3.13/1.62 @ ( cons_P1921020637od_a_a @ E2 @ nil_Product_prod_a_a ) ) )
% 3.13/1.62 @ ( pair_sd_path_a @ ( product_Pair_a_a @ U2 @ V ) @ Xa2 @ Es ) ) ) ) ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_307_the__elem__set,axiom,
% 3.13/1.62 ! [X3: product_prod_a_a] :
% 3.13/1.62 ( ( the_el1640649244od_a_a @ ( set_Product_prod_a_a2 @ ( cons_P1921020637od_a_a @ X3 @ nil_Product_prod_a_a ) ) )
% 3.13/1.62 = X3 ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_308_sd__path_Opelims,axiom,
% 3.13/1.62 ! [X3: product_prod_a_a,Xa2: a,Xb: list_P1467822637od_a_a,Y3: list_P1467822637od_a_a] :
% 3.13/1.62 ( ( ( pair_sd_path_a @ X3 @ Xa2 @ Xb )
% 3.13/1.62 = Y3 )
% 3.13/1.62 => ( ( accp_P1029463583od_a_a @ pair_sd_path_rel_a @ ( produc600870406od_a_a @ X3 @ ( produc575024326od_a_a @ Xa2 @ Xb ) ) )
% 3.13/1.62 => ( ( ( Xb = nil_Product_prod_a_a )
% 3.13/1.62 => ( ( Y3 = nil_Product_prod_a_a )
% 3.13/1.62 => ~ ( accp_P1029463583od_a_a @ pair_sd_path_rel_a @ ( produc600870406od_a_a @ X3 @ ( produc575024326od_a_a @ Xa2 @ nil_Product_prod_a_a ) ) ) ) )
% 3.13/1.62 => ~ ! [U2: a,V: a] :
% 3.13/1.62 ( ( X3
% 3.13/1.62 = ( product_Pair_a_a @ U2 @ V ) )
% 3.13/1.62 => ! [E2: product_prod_a_a,Es: list_P1467822637od_a_a] :
% 3.13/1.62 ( ( Xb
% 3.13/1.62 = ( cons_P1921020637od_a_a @ E2 @ Es ) )
% 3.13/1.62 => ( ( Y3
% 3.13/1.62 = ( append1574001858od_a_a
% 3.13/1.62 @ ( if_lis321365491od_a_a
% 3.13/1.62 @ ( E2
% 3.13/1.62 = ( product_Pair_a_a @ U2 @ V ) )
% 3.13/1.62 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ U2 @ Xa2 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Xa2 @ V ) @ nil_Product_prod_a_a ) )
% 3.13/1.62 @ ( if_lis321365491od_a_a
% 3.13/1.62 @ ( E2
% 3.13/1.62 = ( product_Pair_a_a @ V @ U2 ) )
% 3.13/1.62 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ V @ Xa2 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Xa2 @ U2 ) @ nil_Product_prod_a_a ) )
% 3.13/1.62 @ ( cons_P1921020637od_a_a @ E2 @ nil_Product_prod_a_a ) ) )
% 3.13/1.62 @ ( pair_sd_path_a @ ( product_Pair_a_a @ U2 @ V ) @ Xa2 @ Es ) ) )
% 3.13/1.62 => ~ ( accp_P1029463583od_a_a @ pair_sd_path_rel_a @ ( produc600870406od_a_a @ ( product_Pair_a_a @ U2 @ V ) @ ( produc575024326od_a_a @ Xa2 @ ( cons_P1921020637od_a_a @ E2 @ Es ) ) ) ) ) ) ) ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_309_list__exhaust2,axiom,
% 3.13/1.62 ! [Y3: list_P1467822637od_a_a,Ya: list_P1467822637od_a_a] :
% 3.13/1.62 ( ( ( Y3 = nil_Product_prod_a_a )
% 3.13/1.62 => ( Ya != nil_Product_prod_a_a ) )
% 3.13/1.62 => ( ( ( Y3 = nil_Product_prod_a_a )
% 3.13/1.62 => ! [X212: product_prod_a_a,X222: list_P1467822637od_a_a] :
% 3.13/1.62 ( Ya
% 3.13/1.62 != ( cons_P1921020637od_a_a @ X212 @ X222 ) ) )
% 3.13/1.62 => ( ( ? [X212: product_prod_a_a,X222: list_P1467822637od_a_a] :
% 3.13/1.62 ( Y3
% 3.13/1.62 = ( cons_P1921020637od_a_a @ X212 @ X222 ) )
% 3.13/1.62 => ( Ya != nil_Product_prod_a_a ) )
% 3.13/1.62 => ~ ( ? [X212: product_prod_a_a,X222: list_P1467822637od_a_a] :
% 3.13/1.62 ( Y3
% 3.13/1.62 = ( cons_P1921020637od_a_a @ X212 @ X222 ) )
% 3.13/1.62 => ! [X21a: product_prod_a_a,X22a: list_P1467822637od_a_a] :
% 3.13/1.62 ( Ya
% 3.13/1.62 != ( cons_P1921020637od_a_a @ X21a @ X22a ) ) ) ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_310_list__exhaust__NSC,axiom,
% 3.13/1.62 ! [Xs2: list_P1467822637od_a_a] :
% 3.13/1.62 ( ( Xs2 != nil_Product_prod_a_a )
% 3.13/1.62 => ( ! [X4: product_prod_a_a] :
% 3.13/1.62 ( Xs2
% 3.13/1.62 != ( cons_P1921020637od_a_a @ X4 @ nil_Product_prod_a_a ) )
% 3.13/1.62 => ~ ! [X4: product_prod_a_a,Y4: product_prod_a_a,Ys4: list_P1467822637od_a_a] :
% 3.13/1.62 ( Xs2
% 3.13/1.62 != ( cons_P1921020637od_a_a @ X4 @ ( cons_P1921020637od_a_a @ Y4 @ Ys4 ) ) ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_311_lenlex__append2,axiom,
% 3.13/1.62 ! [R2: set_Pr1948701895od_a_a,Us: list_P1467822637od_a_a,Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a] :
% 3.13/1.62 ( ( irrefl76447196od_a_a @ R2 )
% 3.13/1.62 => ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ Us @ Xs2 ) @ ( append1574001858od_a_a @ Us @ Ys2 ) ) @ ( lenlex2038501170od_a_a @ R2 ) )
% 3.13/1.62 = ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ Ys2 ) @ ( lenlex2038501170od_a_a @ R2 ) ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_312_lenlex__irreflexive,axiom,
% 3.13/1.62 ! [R: set_Product_prod_a_a,Xs2: list_a] :
% 3.13/1.62 ( ! [X4: a] :
% 3.13/1.62 ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ X4 ) @ R )
% 3.13/1.62 => ~ ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ Xs2 ) @ ( lenlex_a @ R ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_313_lenlex__append1,axiom,
% 3.13/1.62 ! [Us: list_P1467822637od_a_a,Xs2: list_P1467822637od_a_a,R2: set_Pr1948701895od_a_a,Vs: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a] :
% 3.13/1.62 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ Us @ Xs2 ) @ ( lenlex2038501170od_a_a @ R2 ) )
% 3.13/1.62 => ( ( ( size_s642698393od_a_a @ Vs )
% 3.13/1.62 = ( size_s642698393od_a_a @ Ys2 ) )
% 3.13/1.62 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( append1574001858od_a_a @ Us @ Vs ) @ ( append1574001858od_a_a @ Xs2 @ Ys2 ) ) @ ( lenlex2038501170od_a_a @ R2 ) ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_314_co__path_Opelims,axiom,
% 3.13/1.62 ! [X3: product_prod_a_a,Xa2: a,Xb: list_P1467822637od_a_a,Y3: list_P1467822637od_a_a] :
% 3.13/1.62 ( ( ( pair_co_path_a @ X3 @ Xa2 @ Xb )
% 3.13/1.62 = Y3 )
% 3.13/1.62 => ( ( accp_P1029463583od_a_a @ pair_co_path_rel_a @ ( produc600870406od_a_a @ X3 @ ( produc575024326od_a_a @ Xa2 @ Xb ) ) )
% 3.13/1.62 => ( ( ( Xb = nil_Product_prod_a_a )
% 3.13/1.62 => ( ( Y3 = nil_Product_prod_a_a )
% 3.13/1.62 => ~ ( accp_P1029463583od_a_a @ pair_co_path_rel_a @ ( produc600870406od_a_a @ X3 @ ( produc575024326od_a_a @ Xa2 @ nil_Product_prod_a_a ) ) ) ) )
% 3.13/1.62 => ( ! [E2: product_prod_a_a] :
% 3.13/1.62 ( ( Xb
% 3.13/1.62 = ( cons_P1921020637od_a_a @ E2 @ nil_Product_prod_a_a ) )
% 3.13/1.62 => ( ( Y3
% 3.13/1.62 = ( cons_P1921020637od_a_a @ E2 @ nil_Product_prod_a_a ) )
% 3.13/1.62 => ~ ( accp_P1029463583od_a_a @ pair_co_path_rel_a @ ( produc600870406od_a_a @ X3 @ ( produc575024326od_a_a @ Xa2 @ ( cons_P1921020637od_a_a @ E2 @ nil_Product_prod_a_a ) ) ) ) ) )
% 3.13/1.62 => ~ ! [U2: a,V: a] :
% 3.13/1.62 ( ( X3
% 3.13/1.62 = ( product_Pair_a_a @ U2 @ V ) )
% 3.13/1.62 => ! [E1: product_prod_a_a,E22: product_prod_a_a,Es: list_P1467822637od_a_a] :
% 3.13/1.62 ( ( Xb
% 3.13/1.62 = ( cons_P1921020637od_a_a @ E1 @ ( cons_P1921020637od_a_a @ E22 @ Es ) ) )
% 3.13/1.62 => ( ( ( ( ( E1
% 3.13/1.62 = ( product_Pair_a_a @ U2 @ Xa2 ) )
% 3.13/1.62 & ( E22
% 3.13/1.62 = ( product_Pair_a_a @ Xa2 @ V ) ) )
% 3.13/1.62 => ( Y3
% 3.13/1.62 = ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ U2 @ V ) @ ( pair_co_path_a @ ( product_Pair_a_a @ U2 @ V ) @ Xa2 @ Es ) ) ) )
% 3.13/1.62 & ( ~ ( ( E1
% 3.13/1.62 = ( product_Pair_a_a @ U2 @ Xa2 ) )
% 3.13/1.62 & ( E22
% 3.13/1.62 = ( product_Pair_a_a @ Xa2 @ V ) ) )
% 3.13/1.62 => ( ( ( ( E1
% 3.13/1.62 = ( product_Pair_a_a @ V @ Xa2 ) )
% 3.13/1.62 & ( E22
% 3.13/1.62 = ( product_Pair_a_a @ Xa2 @ U2 ) ) )
% 3.13/1.62 => ( Y3
% 3.13/1.62 = ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ V @ U2 ) @ ( pair_co_path_a @ ( product_Pair_a_a @ U2 @ V ) @ Xa2 @ Es ) ) ) )
% 3.13/1.62 & ( ~ ( ( E1
% 3.13/1.62 = ( product_Pair_a_a @ V @ Xa2 ) )
% 3.13/1.62 & ( E22
% 3.13/1.62 = ( product_Pair_a_a @ Xa2 @ U2 ) ) )
% 3.13/1.62 => ( Y3
% 3.13/1.62 = ( cons_P1921020637od_a_a @ E1 @ ( pair_co_path_a @ ( product_Pair_a_a @ U2 @ V ) @ Xa2 @ ( cons_P1921020637od_a_a @ E22 @ Es ) ) ) ) ) ) ) )
% 3.13/1.62 => ~ ( accp_P1029463583od_a_a @ pair_co_path_rel_a @ ( produc600870406od_a_a @ ( product_Pair_a_a @ U2 @ V ) @ ( produc575024326od_a_a @ Xa2 @ ( cons_P1921020637od_a_a @ E1 @ ( cons_P1921020637od_a_a @ E22 @ Es ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_315_pawalk__verts_Osimps_I1_J,axiom,
% 3.13/1.62 ! [U: product_prod_a_a] :
% 3.13/1.62 ( ( pair_p2140537249od_a_a @ U @ nil_Pr1049924845od_a_a )
% 3.13/1.62 = ( cons_P1921020637od_a_a @ U @ nil_Product_prod_a_a ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_316_co__path_Osimps_I3_J,axiom,
% 3.13/1.62 ! [E12: product_prod_a_a,U: a,W2: a,E23: product_prod_a_a,V2: a,Es2: list_P1467822637od_a_a] :
% 3.13/1.62 ( ( ( ( E12
% 3.13/1.62 = ( product_Pair_a_a @ U @ W2 ) )
% 3.13/1.62 & ( E23
% 3.13/1.62 = ( product_Pair_a_a @ W2 @ V2 ) ) )
% 3.13/1.62 => ( ( pair_co_path_a @ ( product_Pair_a_a @ U @ V2 ) @ W2 @ ( cons_P1921020637od_a_a @ E12 @ ( cons_P1921020637od_a_a @ E23 @ Es2 ) ) )
% 3.13/1.62 = ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ U @ V2 ) @ ( pair_co_path_a @ ( product_Pair_a_a @ U @ V2 ) @ W2 @ Es2 ) ) ) )
% 3.13/1.62 & ( ~ ( ( E12
% 3.13/1.62 = ( product_Pair_a_a @ U @ W2 ) )
% 3.13/1.62 & ( E23
% 3.13/1.62 = ( product_Pair_a_a @ W2 @ V2 ) ) )
% 3.13/1.62 => ( ( ( ( E12
% 3.13/1.62 = ( product_Pair_a_a @ V2 @ W2 ) )
% 3.13/1.62 & ( E23
% 3.13/1.62 = ( product_Pair_a_a @ W2 @ U ) ) )
% 3.13/1.62 => ( ( pair_co_path_a @ ( product_Pair_a_a @ U @ V2 ) @ W2 @ ( cons_P1921020637od_a_a @ E12 @ ( cons_P1921020637od_a_a @ E23 @ Es2 ) ) )
% 3.13/1.62 = ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ V2 @ U ) @ ( pair_co_path_a @ ( product_Pair_a_a @ U @ V2 ) @ W2 @ Es2 ) ) ) )
% 3.13/1.62 & ( ~ ( ( E12
% 3.13/1.62 = ( product_Pair_a_a @ V2 @ W2 ) )
% 3.13/1.62 & ( E23
% 3.13/1.62 = ( product_Pair_a_a @ W2 @ U ) ) )
% 3.13/1.62 => ( ( pair_co_path_a @ ( product_Pair_a_a @ U @ V2 ) @ W2 @ ( cons_P1921020637od_a_a @ E12 @ ( cons_P1921020637od_a_a @ E23 @ Es2 ) ) )
% 3.13/1.62 = ( cons_P1921020637od_a_a @ E12 @ ( pair_co_path_a @ ( product_Pair_a_a @ U @ V2 ) @ W2 @ ( cons_P1921020637od_a_a @ E23 @ Es2 ) ) ) ) ) ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_317_co__path_Osimps_I2_J,axiom,
% 3.13/1.62 ! [Uw2: product_prod_a_a,Ux2: a,E: product_prod_a_a] :
% 3.13/1.62 ( ( pair_co_path_a @ Uw2 @ Ux2 @ ( cons_P1921020637od_a_a @ E @ nil_Product_prod_a_a ) )
% 3.13/1.62 = ( cons_P1921020637od_a_a @ E @ nil_Product_prod_a_a ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_318_co__path_Oelims,axiom,
% 3.13/1.62 ! [X3: product_prod_a_a,Xa2: a,Xb: list_P1467822637od_a_a,Y3: list_P1467822637od_a_a] :
% 3.13/1.62 ( ( ( pair_co_path_a @ X3 @ Xa2 @ Xb )
% 3.13/1.62 = Y3 )
% 3.13/1.62 => ( ( ( Xb = nil_Product_prod_a_a )
% 3.13/1.62 => ( Y3 != nil_Product_prod_a_a ) )
% 3.13/1.62 => ( ! [E2: product_prod_a_a] :
% 3.13/1.62 ( ( Xb
% 3.13/1.62 = ( cons_P1921020637od_a_a @ E2 @ nil_Product_prod_a_a ) )
% 3.13/1.62 => ( Y3
% 3.13/1.62 != ( cons_P1921020637od_a_a @ E2 @ nil_Product_prod_a_a ) ) )
% 3.13/1.62 => ~ ! [U2: a,V: a] :
% 3.13/1.62 ( ( X3
% 3.13/1.62 = ( product_Pair_a_a @ U2 @ V ) )
% 3.13/1.62 => ! [E1: product_prod_a_a,E22: product_prod_a_a,Es: list_P1467822637od_a_a] :
% 3.13/1.62 ( ( Xb
% 3.13/1.62 = ( cons_P1921020637od_a_a @ E1 @ ( cons_P1921020637od_a_a @ E22 @ Es ) ) )
% 3.13/1.62 => ~ ( ( ( ( E1
% 3.13/1.62 = ( product_Pair_a_a @ U2 @ Xa2 ) )
% 3.13/1.62 & ( E22
% 3.13/1.62 = ( product_Pair_a_a @ Xa2 @ V ) ) )
% 3.13/1.62 => ( Y3
% 3.13/1.62 = ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ U2 @ V ) @ ( pair_co_path_a @ ( product_Pair_a_a @ U2 @ V ) @ Xa2 @ Es ) ) ) )
% 3.13/1.62 & ( ~ ( ( E1
% 3.13/1.62 = ( product_Pair_a_a @ U2 @ Xa2 ) )
% 3.13/1.62 & ( E22
% 3.13/1.62 = ( product_Pair_a_a @ Xa2 @ V ) ) )
% 3.13/1.62 => ( ( ( ( E1
% 3.13/1.62 = ( product_Pair_a_a @ V @ Xa2 ) )
% 3.13/1.62 & ( E22
% 3.13/1.62 = ( product_Pair_a_a @ Xa2 @ U2 ) ) )
% 3.13/1.62 => ( Y3
% 3.13/1.62 = ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ V @ U2 ) @ ( pair_co_path_a @ ( product_Pair_a_a @ U2 @ V ) @ Xa2 @ Es ) ) ) )
% 3.13/1.62 & ( ~ ( ( E1
% 3.13/1.62 = ( product_Pair_a_a @ V @ Xa2 ) )
% 3.13/1.62 & ( E22
% 3.13/1.62 = ( product_Pair_a_a @ Xa2 @ U2 ) ) )
% 3.13/1.62 => ( Y3
% 3.13/1.62 = ( cons_P1921020637od_a_a @ E1 @ ( pair_co_path_a @ ( product_Pair_a_a @ U2 @ V ) @ Xa2 @ ( cons_P1921020637od_a_a @ E22 @ Es ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_319_co__sd__id,axiom,
% 3.13/1.62 ! [U: a,W2: a,P3: list_P1467822637od_a_a,V2: a] :
% 3.13/1.62 ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ U @ W2 ) @ ( set_Product_prod_a_a2 @ P3 ) )
% 3.13/1.62 => ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ V2 @ W2 ) @ ( set_Product_prod_a_a2 @ P3 ) )
% 3.13/1.62 => ( ( pair_co_path_a @ ( product_Pair_a_a @ U @ V2 ) @ W2 @ ( pair_sd_path_a @ ( product_Pair_a_a @ U @ V2 ) @ W2 @ P3 ) )
% 3.13/1.62 = P3 ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_320_Cons__lenlex__iff,axiom,
% 3.13/1.62 ! [M: product_prod_a_a,Ms: list_P1467822637od_a_a,N: product_prod_a_a,Ns: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 3.13/1.62 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( cons_P1921020637od_a_a @ M @ Ms ) @ ( cons_P1921020637od_a_a @ N @ Ns ) ) @ ( lenlex2038501170od_a_a @ R ) )
% 3.13/1.62 = ( ( ord_less_nat @ ( size_s642698393od_a_a @ Ms ) @ ( size_s642698393od_a_a @ Ns ) )
% 3.13/1.62 | ( ( ( size_s642698393od_a_a @ Ms )
% 3.13/1.62 = ( size_s642698393od_a_a @ Ns ) )
% 3.13/1.62 & ( member2057358096od_a_a @ ( produc1474507607od_a_a @ M @ N ) @ R ) )
% 3.13/1.62 | ( ( M = N )
% 3.13/1.62 & ( member1691432592od_a_a @ ( produc85179863od_a_a @ Ms @ Ns ) @ ( lenlex2038501170od_a_a @ R ) ) ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_321_Cons__lenlex__iff,axiom,
% 3.13/1.62 ! [M: a,Ms: list_a,N: a,Ns: list_a,R: set_Product_prod_a_a] :
% 3.13/1.62 ( ( member1250517072list_a @ ( produc1448356631list_a @ ( cons_a @ M @ Ms ) @ ( cons_a @ N @ Ns ) ) @ ( lenlex_a @ R ) )
% 3.13/1.62 = ( ( ord_less_nat @ ( size_size_list_a @ Ms ) @ ( size_size_list_a @ Ns ) )
% 3.13/1.62 | ( ( ( size_size_list_a @ Ms )
% 3.13/1.62 = ( size_size_list_a @ Ns ) )
% 3.13/1.62 & ( member449909584od_a_a @ ( product_Pair_a_a @ M @ N ) @ R ) )
% 3.13/1.62 | ( ( M = N )
% 3.13/1.62 & ( member1250517072list_a @ ( produc1448356631list_a @ Ms @ Ns ) @ ( lenlex_a @ R ) ) ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_322_Cons__in__subseqsD,axiom,
% 3.13/1.62 ! [Y3: product_prod_a_a,Ys2: list_P1467822637od_a_a,Xs2: list_P1467822637od_a_a] :
% 3.13/1.62 ( ( member1578987478od_a_a @ ( cons_P1921020637od_a_a @ Y3 @ Ys2 ) @ ( set_li1284606018od_a_a @ ( subseq2115548028od_a_a @ Xs2 ) ) )
% 3.13/1.62 => ( member1578987478od_a_a @ Ys2 @ ( set_li1284606018od_a_a @ ( subseq2115548028od_a_a @ Xs2 ) ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_323_in__measures_I2_J,axiom,
% 3.13/1.62 ! [X3: a,Y3: a,F: a > nat,Fs: list_a_nat] :
% 3.13/1.62 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ ( measures_a @ ( cons_a_nat @ F @ Fs ) ) )
% 3.13/1.62 = ( ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) )
% 3.13/1.62 | ( ( ( F @ X3 )
% 3.13/1.62 = ( F @ Y3 ) )
% 3.13/1.62 & ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ ( measures_a @ Fs ) ) ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_324_inverse__permutation__of__list_Oelims,axiom,
% 3.13/1.62 ! [X3: list_P1467822637od_a_a,Xa2: a,Y3: a] :
% 3.13/1.62 ( ( ( invers1007791577list_a @ X3 @ Xa2 )
% 3.13/1.62 = Y3 )
% 3.13/1.62 => ( ( ( X3 = nil_Product_prod_a_a )
% 3.13/1.62 => ( Y3 != Xa2 ) )
% 3.13/1.62 => ~ ! [Y4: a,X6: a,Xs4: list_P1467822637od_a_a] :
% 3.13/1.62 ( ( X3
% 3.13/1.62 = ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y4 @ X6 ) @ Xs4 ) )
% 3.13/1.62 => ~ ( ( ( Xa2 = X6 )
% 3.13/1.62 => ( Y3 = Y4 ) )
% 3.13/1.62 & ( ( Xa2 != X6 )
% 3.13/1.62 => ( Y3
% 3.13/1.62 = ( invers1007791577list_a @ Xs4 @ Xa2 ) ) ) ) ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_325_in__measures_I1_J,axiom,
% 3.13/1.62 ! [X3: a,Y3: a] :
% 3.13/1.62 ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ ( measures_a @ nil_a_nat ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_326_eval__inverse__permutation__of__list_I3_J,axiom,
% 3.13/1.62 ! [X3: a,X7: a,Y5: a,Xs2: list_P1467822637od_a_a] :
% 3.13/1.62 ( ( X3 != X7 )
% 3.13/1.62 => ( ( invers1007791577list_a @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y5 @ X7 ) @ Xs2 ) @ X3 )
% 3.13/1.62 = ( invers1007791577list_a @ Xs2 @ X3 ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_327_eval__inverse__permutation__of__list_I2_J,axiom,
% 3.13/1.62 ! [X3: a,X7: a,Y3: a,Xs2: list_P1467822637od_a_a] :
% 3.13/1.62 ( ( X3 = X7 )
% 3.13/1.62 => ( ( invers1007791577list_a @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y3 @ X7 ) @ Xs2 ) @ X3 )
% 3.13/1.62 = Y3 ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_328_inverse__permutation__of__list_Osimps_I2_J,axiom,
% 3.13/1.62 ! [X3: a,X7: a,Y3: a,Xs2: list_P1467822637od_a_a] :
% 3.13/1.62 ( ( ( X3 = X7 )
% 3.13/1.62 => ( ( invers1007791577list_a @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y3 @ X7 ) @ Xs2 ) @ X3 )
% 3.13/1.62 = Y3 ) )
% 3.13/1.62 & ( ( X3 != X7 )
% 3.13/1.62 => ( ( invers1007791577list_a @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y3 @ X7 ) @ Xs2 ) @ X3 )
% 3.13/1.62 = ( invers1007791577list_a @ Xs2 @ X3 ) ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_329_measures__less,axiom,
% 3.13/1.62 ! [F: a > nat,X3: a,Y3: a,Fs: list_a_nat] :
% 3.13/1.62 ( ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) )
% 3.13/1.62 => ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ ( measures_a @ ( cons_a_nat @ F @ Fs ) ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_330_inverse__permutation__of__list__unique,axiom,
% 3.13/1.62 ! [Xs2: list_P1467822637od_a_a,A4: set_a,X3: a,Y3: a] :
% 3.13/1.62 ( ( list_permutes_a @ Xs2 @ A4 )
% 3.13/1.62 => ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 3.13/1.62 => ( ( invers1007791577list_a @ Xs2 @ Y3 )
% 3.13/1.62 = X3 ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_331_eval__permutation__of__list_I3_J,axiom,
% 3.13/1.62 ! [X3: a,X7: a,Y5: a,Xs2: list_P1467822637od_a_a] :
% 3.13/1.62 ( ( X3 != X7 )
% 3.13/1.62 => ( ( permut1422637723list_a @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X7 @ Y5 ) @ Xs2 ) @ X3 )
% 3.13/1.62 = ( permut1422637723list_a @ Xs2 @ X3 ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_332_eval__permutation__of__list_I2_J,axiom,
% 3.13/1.62 ! [X3: a,X7: a,Y3: a,Xs2: list_P1467822637od_a_a] :
% 3.13/1.62 ( ( X3 = X7 )
% 3.13/1.62 => ( ( permut1422637723list_a @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X7 @ Y3 ) @ Xs2 ) @ X3 )
% 3.13/1.62 = Y3 ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_333_permutation__of__list__unique,axiom,
% 3.13/1.62 ! [Xs2: list_P1467822637od_a_a,A4: set_a,X3: a,Y3: a] :
% 3.13/1.62 ( ( list_permutes_a @ Xs2 @ A4 )
% 3.13/1.62 => ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 3.13/1.62 => ( ( permut1422637723list_a @ Xs2 @ X3 )
% 3.13/1.62 = Y3 ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_334_permutation__of__list__Cons,axiom,
% 3.13/1.62 ! [X3: a,X7: a,Y3: a,Xs2: list_P1467822637od_a_a] :
% 3.13/1.62 ( ( ( X3 = X7 )
% 3.13/1.62 => ( ( permut1422637723list_a @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ Xs2 ) @ X7 )
% 3.13/1.62 = Y3 ) )
% 3.13/1.62 & ( ( X3 != X7 )
% 3.13/1.62 => ( ( permut1422637723list_a @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ Xs2 ) @ X7 )
% 3.13/1.62 = ( permut1422637723list_a @ Xs2 @ X7 ) ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_335_not__in__set__insert,axiom,
% 3.13/1.62 ! [X3: product_prod_a_a,Xs2: list_P1467822637od_a_a] :
% 3.13/1.62 ( ~ ( member449909584od_a_a @ X3 @ ( set_Product_prod_a_a2 @ Xs2 ) )
% 3.13/1.62 => ( ( insert2123825731od_a_a @ X3 @ Xs2 )
% 3.13/1.62 = ( cons_P1921020637od_a_a @ X3 @ Xs2 ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_336_insert__Nil,axiom,
% 3.13/1.62 ! [X3: product_prod_a_a] :
% 3.13/1.62 ( ( insert2123825731od_a_a @ X3 @ nil_Product_prod_a_a )
% 3.13/1.62 = ( cons_P1921020637od_a_a @ X3 @ nil_Product_prod_a_a ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_337_List_Oinsert__def,axiom,
% 3.13/1.62 ( insert2123825731od_a_a
% 3.13/1.62 = ( ^ [X: product_prod_a_a,Xs: list_P1467822637od_a_a] : ( if_lis321365491od_a_a @ ( member449909584od_a_a @ X @ ( set_Product_prod_a_a2 @ Xs ) ) @ Xs @ ( cons_P1921020637od_a_a @ X @ Xs ) ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_338_concat__eq__append__conv,axiom,
% 3.13/1.62 ! [Xss2: list_l1108175539od_a_a,Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a] :
% 3.13/1.62 ( ( ( concat1878217064od_a_a @ Xss2 )
% 3.13/1.62 = ( append1574001858od_a_a @ Ys2 @ Zs ) )
% 3.13/1.62 = ( ( ( Xss2 = nil_li1885598003od_a_a )
% 3.13/1.62 => ( ( Ys2 = nil_Product_prod_a_a )
% 3.13/1.62 & ( Zs = nil_Product_prod_a_a ) ) )
% 3.13/1.62 & ( ( Xss2 != nil_li1885598003od_a_a )
% 3.13/1.62 => ? [Xss1: list_l1108175539od_a_a,Xs: list_P1467822637od_a_a,Xs6: list_P1467822637od_a_a,Xss22: list_l1108175539od_a_a] :
% 3.13/1.62 ( ( Xss2
% 3.13/1.62 = ( append2141280328od_a_a @ Xss1 @ ( cons_l724116707od_a_a @ ( append1574001858od_a_a @ Xs @ Xs6 ) @ Xss22 ) ) )
% 3.13/1.62 & ( Ys2
% 3.13/1.62 = ( append1574001858od_a_a @ ( concat1878217064od_a_a @ Xss1 ) @ Xs ) )
% 3.13/1.62 & ( Zs
% 3.13/1.62 = ( append1574001858od_a_a @ Xs6 @ ( concat1878217064od_a_a @ Xss22 ) ) ) ) ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_339_inverse__permutation__of__list_Opelims,axiom,
% 3.13/1.62 ! [X3: list_P1467822637od_a_a,Xa2: a,Y3: a] :
% 3.13/1.62 ( ( ( invers1007791577list_a @ X3 @ Xa2 )
% 3.13/1.62 = Y3 )
% 3.13/1.62 => ( ( accp_P941981633_a_a_a @ invers214109608_rel_a @ ( produc998622632_a_a_a @ X3 @ Xa2 ) )
% 3.13/1.62 => ( ( ( X3 = nil_Product_prod_a_a )
% 3.13/1.62 => ( ( Y3 = Xa2 )
% 3.13/1.62 => ~ ( accp_P941981633_a_a_a @ invers214109608_rel_a @ ( produc998622632_a_a_a @ nil_Product_prod_a_a @ Xa2 ) ) ) )
% 3.13/1.62 => ~ ! [Y4: a,X6: a,Xs4: list_P1467822637od_a_a] :
% 3.13/1.62 ( ( X3
% 3.13/1.62 = ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y4 @ X6 ) @ Xs4 ) )
% 3.13/1.62 => ( ( ( ( Xa2 = X6 )
% 3.13/1.62 => ( Y3 = Y4 ) )
% 3.13/1.62 & ( ( Xa2 != X6 )
% 3.13/1.62 => ( Y3
% 3.13/1.62 = ( invers1007791577list_a @ Xs4 @ Xa2 ) ) ) )
% 3.13/1.62 => ~ ( accp_P941981633_a_a_a @ invers214109608_rel_a @ ( produc998622632_a_a_a @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y4 @ X6 ) @ Xs4 ) @ Xa2 ) ) ) ) ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_340_concat__append,axiom,
% 3.13/1.62 ! [Xs2: list_l1108175539od_a_a,Ys2: list_l1108175539od_a_a] :
% 3.13/1.62 ( ( concat1878217064od_a_a @ ( append2141280328od_a_a @ Xs2 @ Ys2 ) )
% 3.13/1.62 = ( append1574001858od_a_a @ ( concat1878217064od_a_a @ Xs2 ) @ ( concat1878217064od_a_a @ Ys2 ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_341_concat_Osimps_I2_J,axiom,
% 3.13/1.62 ! [X3: list_P1467822637od_a_a,Xs2: list_l1108175539od_a_a] :
% 3.13/1.62 ( ( concat1878217064od_a_a @ ( cons_l724116707od_a_a @ X3 @ Xs2 ) )
% 3.13/1.62 = ( append1574001858od_a_a @ X3 @ ( concat1878217064od_a_a @ Xs2 ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_342_concat__eq__appendD,axiom,
% 3.13/1.62 ! [Xss2: list_l1108175539od_a_a,Ys2: list_P1467822637od_a_a,Zs: list_P1467822637od_a_a] :
% 3.13/1.62 ( ( ( concat1878217064od_a_a @ Xss2 )
% 3.13/1.62 = ( append1574001858od_a_a @ Ys2 @ Zs ) )
% 3.13/1.62 => ( ( Xss2 != nil_li1885598003od_a_a )
% 3.13/1.62 => ? [Xss12: list_l1108175539od_a_a,Xs4: list_P1467822637od_a_a,Xs3: list_P1467822637od_a_a,Xss23: list_l1108175539od_a_a] :
% 3.13/1.62 ( ( Xss2
% 3.13/1.62 = ( append2141280328od_a_a @ Xss12 @ ( cons_l724116707od_a_a @ ( append1574001858od_a_a @ Xs4 @ Xs3 ) @ Xss23 ) ) )
% 3.13/1.62 & ( Ys2
% 3.13/1.62 = ( append1574001858od_a_a @ ( concat1878217064od_a_a @ Xss12 ) @ Xs4 ) )
% 3.13/1.62 & ( Zs
% 3.13/1.62 = ( append1574001858od_a_a @ Xs3 @ ( concat1878217064od_a_a @ Xss23 ) ) ) ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_343_listrel_Oinducts,axiom,
% 3.13/1.62 ! [X1: list_P1467822637od_a_a,X2: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a,P2: list_P1467822637od_a_a > list_P1467822637od_a_a > $o] :
% 3.13/1.62 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ X1 @ X2 ) @ ( listre2074280881od_a_a @ R ) )
% 3.13/1.62 => ( ( P2 @ nil_Product_prod_a_a @ nil_Product_prod_a_a )
% 3.13/1.62 => ( ! [X4: product_prod_a_a,Y4: product_prod_a_a,Xs4: list_P1467822637od_a_a,Ys4: list_P1467822637od_a_a] :
% 3.13/1.62 ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X4 @ Y4 ) @ R )
% 3.13/1.62 => ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs4 @ Ys4 ) @ ( listre2074280881od_a_a @ R ) )
% 3.13/1.62 => ( ( P2 @ Xs4 @ Ys4 )
% 3.13/1.62 => ( P2 @ ( cons_P1921020637od_a_a @ X4 @ Xs4 ) @ ( cons_P1921020637od_a_a @ Y4 @ Ys4 ) ) ) ) )
% 3.13/1.62 => ( P2 @ X1 @ X2 ) ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_344_listrel_Oinducts,axiom,
% 3.13/1.62 ! [X1: list_a,X2: list_a,R: set_Product_prod_a_a,P2: list_a > list_a > $o] :
% 3.13/1.62 ( ( member1250517072list_a @ ( produc1448356631list_a @ X1 @ X2 ) @ ( listrel_a_a @ R ) )
% 3.13/1.62 => ( ( P2 @ nil_a @ nil_a )
% 3.13/1.62 => ( ! [X4: a,Y4: a,Xs4: list_a,Ys4: list_a] :
% 3.13/1.62 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ R )
% 3.13/1.62 => ( ( member1250517072list_a @ ( produc1448356631list_a @ Xs4 @ Ys4 ) @ ( listrel_a_a @ R ) )
% 3.13/1.62 => ( ( P2 @ Xs4 @ Ys4 )
% 3.13/1.62 => ( P2 @ ( cons_a @ X4 @ Xs4 ) @ ( cons_a @ Y4 @ Ys4 ) ) ) ) )
% 3.13/1.62 => ( P2 @ X1 @ X2 ) ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_345_listrel_OCons,axiom,
% 3.13/1.62 ! [X3: product_prod_a_a,Y3: product_prod_a_a,R: set_Pr1948701895od_a_a,Xs2: list_P1467822637od_a_a,Ys2: list_P1467822637od_a_a] :
% 3.13/1.62 ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X3 @ Y3 ) @ R )
% 3.13/1.62 => ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ Ys2 ) @ ( listre2074280881od_a_a @ R ) )
% 3.13/1.62 => ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( cons_P1921020637od_a_a @ X3 @ Xs2 ) @ ( cons_P1921020637od_a_a @ Y3 @ Ys2 ) ) @ ( listre2074280881od_a_a @ R ) ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_346_listrel_OCons,axiom,
% 3.13/1.62 ! [X3: a,Y3: a,R: set_Product_prod_a_a,Xs2: list_a,Ys2: list_a] :
% 3.13/1.62 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R )
% 3.13/1.62 => ( ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ Ys2 ) @ ( listrel_a_a @ R ) )
% 3.13/1.62 => ( member1250517072list_a @ ( produc1448356631list_a @ ( cons_a @ X3 @ Xs2 ) @ ( cons_a @ Y3 @ Ys2 ) ) @ ( listrel_a_a @ R ) ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_347_listrel__Cons1,axiom,
% 3.13/1.62 ! [Y3: product_prod_a_a,Ys2: list_P1467822637od_a_a,Xs2: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 3.13/1.62 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ ( cons_P1921020637od_a_a @ Y3 @ Ys2 ) @ Xs2 ) @ ( listre2074280881od_a_a @ R ) )
% 3.13/1.62 => ~ ! [Y4: product_prod_a_a,Ys4: list_P1467822637od_a_a] :
% 3.13/1.62 ( ( Xs2
% 3.13/1.62 = ( cons_P1921020637od_a_a @ Y4 @ Ys4 ) )
% 3.13/1.62 => ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ Y3 @ Y4 ) @ R )
% 3.13/1.62 => ~ ( member1691432592od_a_a @ ( produc85179863od_a_a @ Ys2 @ Ys4 ) @ ( listre2074280881od_a_a @ R ) ) ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_348_listrel__Cons1,axiom,
% 3.13/1.62 ! [Y3: a,Ys2: list_a,Xs2: list_a,R: set_Product_prod_a_a] :
% 3.13/1.62 ( ( member1250517072list_a @ ( produc1448356631list_a @ ( cons_a @ Y3 @ Ys2 ) @ Xs2 ) @ ( listrel_a_a @ R ) )
% 3.13/1.62 => ~ ! [Y4: a,Ys4: list_a] :
% 3.13/1.62 ( ( Xs2
% 3.13/1.62 = ( cons_a @ Y4 @ Ys4 ) )
% 3.13/1.62 => ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y3 @ Y4 ) @ R )
% 3.13/1.62 => ~ ( member1250517072list_a @ ( produc1448356631list_a @ Ys2 @ Ys4 ) @ ( listrel_a_a @ R ) ) ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_349_listrel__Cons2,axiom,
% 3.13/1.62 ! [Xs2: list_P1467822637od_a_a,Y3: product_prod_a_a,Ys2: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 3.13/1.62 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs2 @ ( cons_P1921020637od_a_a @ Y3 @ Ys2 ) ) @ ( listre2074280881od_a_a @ R ) )
% 3.13/1.62 => ~ ! [X4: product_prod_a_a,Xs4: list_P1467822637od_a_a] :
% 3.13/1.62 ( ( Xs2
% 3.13/1.62 = ( cons_P1921020637od_a_a @ X4 @ Xs4 ) )
% 3.13/1.62 => ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X4 @ Y3 ) @ R )
% 3.13/1.62 => ~ ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs4 @ Ys2 ) @ ( listre2074280881od_a_a @ R ) ) ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_350_listrel__Cons2,axiom,
% 3.13/1.62 ! [Xs2: list_a,Y3: a,Ys2: list_a,R: set_Product_prod_a_a] :
% 3.13/1.62 ( ( member1250517072list_a @ ( produc1448356631list_a @ Xs2 @ ( cons_a @ Y3 @ Ys2 ) ) @ ( listrel_a_a @ R ) )
% 3.13/1.62 => ~ ! [X4: a,Xs4: list_a] :
% 3.13/1.62 ( ( Xs2
% 3.13/1.62 = ( cons_a @ X4 @ Xs4 ) )
% 3.13/1.62 => ( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y3 ) @ R )
% 3.13/1.62 => ~ ( member1250517072list_a @ ( produc1448356631list_a @ Xs4 @ Ys2 ) @ ( listrel_a_a @ R ) ) ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_351_listrel_Ocases,axiom,
% 3.13/1.62 ! [A1: list_P1467822637od_a_a,A22: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 3.13/1.62 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ A1 @ A22 ) @ ( listre2074280881od_a_a @ R ) )
% 3.13/1.62 => ( ( ( A1 = nil_Product_prod_a_a )
% 3.13/1.62 => ( A22 != nil_Product_prod_a_a ) )
% 3.13/1.62 => ~ ! [X4: product_prod_a_a,Y4: product_prod_a_a,Xs4: list_P1467822637od_a_a] :
% 3.13/1.62 ( ( A1
% 3.13/1.62 = ( cons_P1921020637od_a_a @ X4 @ Xs4 ) )
% 3.13/1.62 => ! [Ys4: list_P1467822637od_a_a] :
% 3.13/1.62 ( ( A22
% 3.13/1.62 = ( cons_P1921020637od_a_a @ Y4 @ Ys4 ) )
% 3.13/1.62 => ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X4 @ Y4 ) @ R )
% 3.13/1.62 => ~ ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs4 @ Ys4 ) @ ( listre2074280881od_a_a @ R ) ) ) ) ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_352_listrel_Ocases,axiom,
% 3.13/1.62 ! [A1: list_a,A22: list_a,R: set_Product_prod_a_a] :
% 3.13/1.62 ( ( member1250517072list_a @ ( produc1448356631list_a @ A1 @ A22 ) @ ( listrel_a_a @ R ) )
% 3.13/1.62 => ( ( ( A1 = nil_a )
% 3.13/1.62 => ( A22 != nil_a ) )
% 3.13/1.62 => ~ ! [X4: a,Y4: a,Xs4: list_a] :
% 3.13/1.62 ( ( A1
% 3.13/1.62 = ( cons_a @ X4 @ Xs4 ) )
% 3.13/1.62 => ! [Ys4: list_a] :
% 3.13/1.62 ( ( A22
% 3.13/1.62 = ( cons_a @ Y4 @ Ys4 ) )
% 3.13/1.62 => ( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ R )
% 3.13/1.62 => ~ ( member1250517072list_a @ ( produc1448356631list_a @ Xs4 @ Ys4 ) @ ( listrel_a_a @ R ) ) ) ) ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_353_listrel_Osimps,axiom,
% 3.13/1.62 ! [A1: list_P1467822637od_a_a,A22: list_P1467822637od_a_a,R: set_Pr1948701895od_a_a] :
% 3.13/1.62 ( ( member1691432592od_a_a @ ( produc85179863od_a_a @ A1 @ A22 ) @ ( listre2074280881od_a_a @ R ) )
% 3.13/1.62 = ( ( ( A1 = nil_Product_prod_a_a )
% 3.13/1.62 & ( A22 = nil_Product_prod_a_a ) )
% 3.13/1.62 | ? [X: product_prod_a_a,Y: product_prod_a_a,Xs: list_P1467822637od_a_a,Ys: list_P1467822637od_a_a] :
% 3.13/1.62 ( ( A1
% 3.13/1.62 = ( cons_P1921020637od_a_a @ X @ Xs ) )
% 3.13/1.62 & ( A22
% 3.13/1.62 = ( cons_P1921020637od_a_a @ Y @ Ys ) )
% 3.13/1.62 & ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X @ Y ) @ R )
% 3.13/1.62 & ( member1691432592od_a_a @ ( produc85179863od_a_a @ Xs @ Ys ) @ ( listre2074280881od_a_a @ R ) ) ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(fact_354_listrel_Osimps,axiom,
% 3.13/1.62 ! [A1: list_a,A22: list_a,R: set_Product_prod_a_a] :
% 3.13/1.62 ( ( member1250517072list_a @ ( produc1448356631list_a @ A1 @ A22 ) @ ( listrel_a_a @ R ) )
% 3.13/1.62 = ( ( ( A1 = nil_a )
% 3.13/1.62 & ( A22 = nil_a ) )
% 3.13/1.62 | ? [X: a,Y: a,Xs: list_a,Ys: list_a] :
% 3.13/1.62 ( ( A1
% 3.13/1.62 = ( cons_a @ X @ Xs ) )
% 3.13/1.62 & ( A22
% 3.13/1.62 = ( cons_a @ Y @ Ys ) )
% 3.13/1.62 & ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ R )
% 3.13/1.62 & ( member1250517072list_a @ ( produc1448356631list_a @ Xs @ Ys ) @ ( listrel_a_a @ R ) ) ) ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(help_If_3_1_If_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_T,axiom,
% 3.13/1.62 ! [P2: $o] :
% 3.13/1.62 ( ( P2 = $true )
% 3.13/1.62 | ( P2 = $false ) ) ).
% 3.13/1.62
% 3.13/1.62 thf(help_If_2_1_If_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_T,axiom,
% 3.13/1.62 ! [X3: list_P1467822637od_a_a,Y3: list_P1467822637od_a_a] :
% 3.13/1.62 ( ( if_lis321365491od_a_a @ $false @ X3 @ Y3 )
% 3.13/1.62 = Y3 ) ).
% 3.13/1.62
% 3.13/1.62 thf(help_If_1_1_If_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_T,axiom,
% 3.13/1.62 ! [X3: list_P1467822637od_a_a,Y3: list_P1467822637od_a_a] :
% 3.13/1.62 ( ( if_lis321365491od_a_a @ $true @ X3 @ Y3 )
% 3.13/1.62 = X3 ) ).
% 3.13/1.62
% 3.13/1.62 thf(conj_0,conjecture,
% 3.13/1.62 ! [Xs4: list_P1467822637od_a_a,X4: a,Y4: a,Ys4: list_P1467822637od_a_a] :
% 3.13/1.62 ( es
% 3.13/1.62 != ( append1574001858od_a_a @ Xs4 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ Y4 @ X4 ) @ Ys4 ) ) ) ) ).
% 3.13/1.62 ------------------------
% 3.13/1.67 % (29688)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29473 for (2999ds/183Mi)
% 3.13/1.67 % (29689)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_29473 for (2999ds/4Mi)
% 3.13/1.68 % (29690)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_29473 for (2999ds/27Mi)
% 3.13/1.68 % (29692)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_29473 for (2999ds/2Mi)
% 3.13/1.68 % (29691)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29473 for (2999ds/2Mi)
% 3.13/1.68 % (29693)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_29473 for (2999ds/275Mi)
% 3.13/1.68 % (29694)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29473 for (2999ds/18Mi)
% 3.13/1.68 % (29689)Instruction limit reached!
% 3.13/1.68 % (29689)------------------------------
% 3.13/1.68 % (29689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.68 % (29689)Termination reason: Unknown
% 3.13/1.68 % (29689)Termination phase: shuffling
% 3.13/1.68
% 3.13/1.68 % (29689)Memory used [KB]: 1791
% 3.13/1.68 % (29689)Time elapsed: 0.005 s
% 3.13/1.68 % (29689)Instructions burned: 5 (million)
% 3.13/1.68 % (29689)------------------------------
% 3.13/1.68 % (29689)------------------------------
% 3.13/1.68 % (29691)Instruction limit reached!
% 3.13/1.68 % (29691)------------------------------
% 3.13/1.68 % (29691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.68 % (29691)Termination reason: Unknown
% 3.13/1.68 % (29691)Termination phase: shuffling
% 3.13/1.68
% 3.13/1.68 % (29691)Memory used [KB]: 1791
% 3.13/1.68 % (29691)Time elapsed: 0.003 s
% 3.13/1.68 % (29691)Instructions burned: 2 (million)
% 3.13/1.68 % (29691)------------------------------
% 3.13/1.68 % (29691)------------------------------
% 3.13/1.68 % (29692)Instruction limit reached!
% 3.13/1.68 % (29692)------------------------------
% 3.13/1.68 % (29692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.68 % (29692)Termination reason: Unknown
% 3.13/1.68 % (29692)Termination phase: shuffling
% 3.13/1.68
% 3.13/1.68 % (29692)Memory used [KB]: 1791
% 3.13/1.68 % (29692)Time elapsed: 0.004 s
% 3.13/1.68 % (29692)Instructions burned: 2 (million)
% 3.13/1.68 % (29692)------------------------------
% 3.13/1.68 % (29692)------------------------------
% 3.13/1.69 % (29694)Instruction limit reached!
% 3.13/1.69 % (29694)------------------------------
% 3.13/1.69 % (29694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.69 % (29694)Termination reason: Unknown
% 3.13/1.69 % (29694)Termination phase: shuffling
% 3.13/1.69
% 3.13/1.69 % (29694)Memory used [KB]: 2046
% 3.13/1.69 % (29694)Time elapsed: 0.014 s
% 3.13/1.69 % (29694)Instructions burned: 19 (million)
% 3.13/1.69 % (29694)------------------------------
% 3.13/1.69 % (29694)------------------------------
% 3.13/1.69 % (29690)Instruction limit reached!
% 3.13/1.69 % (29690)------------------------------
% 3.13/1.69 % (29690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.69 % (29690)Termination reason: Unknown
% 3.13/1.69 % (29690)Termination phase: shuffling
% 3.13/1.69
% 3.13/1.69 % (29690)Memory used [KB]: 2302
% 3.13/1.69 % (29690)Time elapsed: 0.019 s
% 3.13/1.69 % (29690)Instructions burned: 27 (million)
% 3.13/1.69 % (29690)------------------------------
% 3.13/1.69 % (29690)------------------------------
% 3.13/1.69 % (29695)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_29473 for (2999ds/3Mi)
% 3.13/1.70 % (29696)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_29473 for (2999ds/37Mi)
% 3.13/1.70 % (29697)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_29473 for (2999ds/15Mi)
% 3.16/1.70 % (29695)Instruction limit reached!
% 3.16/1.70 % (29695)------------------------------
% 3.16/1.70 % (29695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.70 % (29695)Termination reason: Unknown
% 3.16/1.70 % (29695)Termination phase: shuffling
% 3.16/1.70
% 3.16/1.70 % (29695)Memory used [KB]: 1791
% 3.16/1.70 % (29695)Time elapsed: 0.004 s
% 3.16/1.70 % (29695)Instructions burned: 4 (million)
% 3.16/1.70 % (29695)------------------------------
% 3.16/1.70 % (29695)------------------------------
% 3.16/1.71 % (29697)Instruction limit reached!
% 3.16/1.71 % (29697)------------------------------
% 3.16/1.71 % (29697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.71 % (29697)Termination reason: Unknown
% 3.16/1.71 % (29697)Termination phase: shuffling
% 3.16/1.71
% 3.16/1.71 % (29697)Memory used [KB]: 2046
% 3.16/1.71 % (29697)Time elapsed: 0.012 s
% 3.16/1.71 % (29697)Instructions burned: 16 (million)
% 3.16/1.71 % (29697)------------------------------
% 3.16/1.71 % (29697)------------------------------
% 3.16/1.71 % (29700)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_29473 for (2999ds/7Mi)
% 3.16/1.71 % (29698)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_29473 for (2999ds/3Mi)
% 3.16/1.71 % (29699)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_29473 for (2999ds/1041Mi)
% 3.16/1.71 % (29698)Instruction limit reached!
% 3.16/1.71 % (29698)------------------------------
% 3.16/1.71 % (29698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.71 % (29698)Termination reason: Unknown
% 3.16/1.71 % (29698)Termination phase: shuffling
% 3.16/1.71
% 3.16/1.71 % (29698)Memory used [KB]: 1791
% 3.16/1.71 % (29698)Time elapsed: 0.004 s
% 3.16/1.71 % (29698)Instructions burned: 3 (million)
% 3.16/1.71 % (29698)------------------------------
% 3.16/1.71 % (29698)------------------------------
% 3.16/1.71 % (29700)Instruction limit reached!
% 3.16/1.71 % (29700)------------------------------
% 3.16/1.71 % (29700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.71 % (29700)Termination reason: Unknown
% 3.16/1.71 % (29700)Termination phase: shuffling
% 3.16/1.71
% 3.16/1.71 % (29700)Memory used [KB]: 1918
% 3.16/1.71 % (29700)Time elapsed: 0.004 s
% 3.16/1.71 % (29700)Instructions burned: 9 (million)
% 3.16/1.71 % (29700)------------------------------
% 3.16/1.71 % (29700)------------------------------
% 3.16/1.72 % (29696)Instruction limit reached!
% 3.16/1.72 % (29696)------------------------------
% 3.16/1.72 % (29696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.72 % (29696)Termination reason: Unknown
% 3.16/1.72 % (29696)Termination phase: shuffling
% 3.16/1.72
% 3.16/1.72 % (29696)Memory used [KB]: 2430
% 3.16/1.72 % (29696)Time elapsed: 0.022 s
% 3.16/1.72 % (29696)Instructions burned: 38 (million)
% 3.16/1.72 % (29696)------------------------------
% 3.16/1.72 % (29696)------------------------------
% 3.16/1.72 % (29703)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_29473 for (2999ds/3Mi)
% 3.16/1.72 % (29688)Instruction limit reached!
% 3.16/1.72 % (29688)------------------------------
% 3.16/1.72 % (29688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.72 % (29688)Termination reason: Unknown
% 3.16/1.72 % (29688)Termination phase: Property scanning
% 3.16/1.72
% 3.16/1.72 % (29688)Memory used [KB]: 3454
% 3.16/1.72 % (29688)Time elapsed: 0.052 s
% 3.16/1.72 % (29688)Instructions burned: 183 (million)
% 3.16/1.72 % (29688)------------------------------
% 3.16/1.72 % (29688)------------------------------
% 3.16/1.72 % (29693)Refutation not found, incomplete strategy
% 3.16/1.72 % (29693)------------------------------
% 3.16/1.72 % (29693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.72 % (29693)Termination reason: Refutation not found, incomplete strategy
% 3.16/1.72
% 3.16/1.72
% 3.16/1.72 % (29693)Memory used [KB]: 7036
% 3.16/1.72 % (29693)Time elapsed: 0.045 s
% 3.16/1.72 % (29693)Instructions burned: 74 (million)
% 3.16/1.72 % (29693)------------------------------
% 3.16/1.72 % (29693)------------------------------
% 3.16/1.72 % (29703)Instruction limit reached!
% 3.16/1.72 % (29703)------------------------------
% 3.16/1.72 % (29703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.72 % (29703)Termination reason: Unknown
% 3.16/1.72 % (29703)Termination phase: shuffling
% 3.16/1.72
% 3.16/1.72 % (29703)Memory used [KB]: 1791
% 3.16/1.72 % (29703)Time elapsed: 0.003 s
% 3.16/1.72 % (29703)Instructions burned: 5 (million)
% 3.16/1.72 % (29703)------------------------------
% 3.16/1.72 % (29703)------------------------------
% 3.16/1.72 % (29701)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_29473 for (2999ds/16Mi)
% 3.16/1.72 % (29702)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_29473 for (2999ds/3Mi)
% 3.16/1.72 % (29702)Instruction limit reached!
% 3.16/1.72 % (29702)------------------------------
% 3.16/1.72 % (29702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.72 % (29702)Termination reason: Unknown
% 3.16/1.72 % (29702)Termination phase: shuffling
% 3.16/1.72
% 3.16/1.72 % (29702)Memory used [KB]: 1791
% 3.16/1.72 % (29702)Time elapsed: 0.003 s
% 3.16/1.72 % (29702)Instructions burned: 5 (million)
% 3.16/1.72 % (29702)------------------------------
% 3.16/1.72 % (29702)------------------------------
% 3.16/1.73 % (29701)Instruction limit reached!
% 3.16/1.73 % (29701)------------------------------
% 3.16/1.73 % (29701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.73 % (29701)Termination reason: Unknown
% 3.16/1.73 % (29701)Termination phase: shuffling
% 3.16/1.73
% 3.16/1.73 % (29701)Memory used [KB]: 2174
% 3.16/1.73 % (29701)Time elapsed: 0.008 s
% 3.16/1.73 % (29701)Instructions burned: 16 (million)
% 3.16/1.73 % (29701)------------------------------
% 3.16/1.73 % (29701)------------------------------
% 3.16/1.73 % (29705)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_29473 for (2999ds/3Mi)
% 3.16/1.73 % (29706)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_29473 for (2999ds/4Mi)
% 3.16/1.73 % (29705)Instruction limit reached!
% 3.16/1.73 % (29705)------------------------------
% 3.16/1.73 % (29705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.73 % (29705)Termination reason: Unknown
% 3.16/1.73 % (29705)Termination phase: shuffling
% 3.16/1.73
% 3.16/1.73 % (29705)Memory used [KB]: 1791
% 3.16/1.73 % (29705)Time elapsed: 0.003 s
% 3.16/1.73 % (29705)Instructions burned: 6 (million)
% 3.16/1.73 % (29705)------------------------------
% 3.16/1.73 % (29705)------------------------------
% 3.16/1.73 % (29704)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_29473 for (2999ds/7Mi)
% 3.16/1.73 % (29706)Instruction limit reached!
% 3.16/1.73 % (29706)------------------------------
% 3.16/1.73 % (29706)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.73 % (29706)Termination reason: Unknown
% 3.16/1.73 % (29706)Termination phase: shuffling
% 3.16/1.73
% 3.16/1.73 % (29706)Memory used [KB]: 1791
% 3.16/1.73 % (29706)Time elapsed: 0.003 s
% 3.16/1.73 % (29706)Instructions burned: 6 (million)
% 3.16/1.73 % (29706)------------------------------
% 3.16/1.73 % (29706)------------------------------
% 3.16/1.73 % (29708)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_29473 for (2999ds/710Mi)
% 3.16/1.73 % (29704)Instruction limit reached!
% 3.16/1.73 % (29704)------------------------------
% 3.16/1.73 % (29704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.73 % (29704)Termination reason: Unknown
% 3.16/1.73 % (29704)Termination phase: shuffling
% 3.16/1.73
% 3.16/1.73 % (29704)Memory used [KB]: 1918
% 3.16/1.73 % (29704)Time elapsed: 0.006 s
% 3.16/1.73 % (29704)Instructions burned: 9 (million)
% 3.16/1.73 % (29704)------------------------------
% 3.16/1.73 % (29704)------------------------------
% 3.16/1.74 % (29709)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_29473 for (2998ds/6Mi)
% 3.16/1.74 % (29707)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_29473 for (2999ds/18Mi)
% 3.16/1.74 % (29709)Instruction limit reached!
% 3.16/1.74 % (29709)------------------------------
% 3.16/1.74 % (29709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.74 % (29709)Termination reason: Unknown
% 3.16/1.74 % (29709)Termination phase: shuffling
% 3.16/1.74
% 3.16/1.74 % (29709)Memory used [KB]: 1791
% 3.16/1.74 % (29709)Time elapsed: 0.003 s
% 3.16/1.74 % (29709)Instructions burned: 6 (million)
% 3.16/1.74 % (29709)------------------------------
% 3.16/1.74 % (29709)------------------------------
% 3.16/1.74 % (29710)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_29473 for (2998ds/902Mi)
% 3.16/1.74 % (29711)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_29473 for (2998ds/21Mi)
% 3.16/1.75 % (29712)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_29473 for (2998ds/5Mi)
% 3.16/1.75 % (29712)Instruction limit reached!
% 3.16/1.75 % (29712)------------------------------
% 3.16/1.75 % (29712)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.75 % (29712)Termination reason: Unknown
% 3.16/1.75 % (29712)Termination phase: shuffling
% 3.16/1.75
% 3.16/1.75 % (29712)Memory used [KB]: 1791
% 3.16/1.75 % (29712)Time elapsed: 0.003 s
% 3.16/1.75 % (29712)Instructions burned: 6 (million)
% 3.16/1.75 % (29712)------------------------------
% 3.16/1.75 % (29712)------------------------------
% 3.16/1.75 % (29713)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_29473 for (2998ds/6Mi)
% 3.16/1.75 % (29711)Instruction limit reached!
% 3.16/1.75 % (29711)------------------------------
% 3.16/1.75 % (29711)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.75 % (29711)Termination reason: Unknown
% 3.16/1.75 % (29711)Termination phase: shuffling
% 3.16/1.75
% 3.16/1.75 % (29711)Memory used [KB]: 2174
% 3.16/1.75 % (29711)Time elapsed: 0.008 s
% 3.16/1.75 % (29711)Instructions burned: 22 (million)
% 3.16/1.75 % (29711)------------------------------
% 3.16/1.75 % (29711)------------------------------
% 3.16/1.75 % (29707)Instruction limit reached!
% 3.16/1.75 % (29707)------------------------------
% 3.16/1.75 % (29707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.75 % (29707)Termination reason: Unknown
% 3.16/1.75 % (29707)Termination phase: shuffling
% 3.16/1.75
% 3.16/1.75 % (29707)Memory used [KB]: 2174
% 3.16/1.75 % (29707)Time elapsed: 0.013 s
% 3.16/1.75 % (29707)Instructions burned: 18 (million)
% 3.16/1.75 % (29707)------------------------------
% 3.16/1.75 % (29707)------------------------------
% 3.16/1.75 % (29713)Instruction limit reached!
% 3.16/1.75 % (29713)------------------------------
% 3.16/1.75 % (29713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.75 % (29713)Termination reason: Unknown
% 3.16/1.75 % (29713)Termination phase: shuffling
% 3.16/1.75
% 3.16/1.75 % (29713)Memory used [KB]: 1791
% 3.16/1.75 % (29713)Time elapsed: 0.003 s
% 3.16/1.75 % (29713)Instructions burned: 6 (million)
% 3.16/1.75 % (29713)------------------------------
% 3.16/1.75 % (29713)------------------------------
% 3.16/1.76 % (29715)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_29473 for (2998ds/779Mi)
% 3.16/1.76 % (29714)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_29473 for (2998ds/377Mi)
% 3.16/1.76 % (29717)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_29473 for (2998ds/879Mi)
% 3.16/1.77 % (29716)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_29473 for (2998ds/19Mi)
% 3.16/1.77 % (29716)Instruction limit reached!
% 3.16/1.77 % (29716)------------------------------
% 3.16/1.77 % (29716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.77 % (29716)Termination reason: Unknown
% 3.16/1.77 % (29716)Termination phase: shuffling
% 3.16/1.77
% 3.16/1.77 % (29716)Memory used [KB]: 2174
% 3.16/1.77 % (29716)Time elapsed: 0.010 s
% 3.16/1.77 % (29716)Instructions burned: 21 (million)
% 3.16/1.77 % (29716)------------------------------
% 3.16/1.77 % (29716)------------------------------
% 3.16/1.78 % (29718)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_29473 for (2998ds/17Mi)
% 3.16/1.79 % (29718)Instruction limit reached!
% 3.16/1.79 % (29718)------------------------------
% 3.16/1.79 % (29718)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.79 % (29718)Termination reason: Unknown
% 3.16/1.79 % (29718)Termination phase: shuffling
% 3.16/1.79
% 3.16/1.79 % (29718)Memory used [KB]: 2174
% 3.16/1.79 % (29718)Time elapsed: 0.008 s
% 3.16/1.79 % (29718)Instructions burned: 19 (million)
% 3.16/1.79 % (29718)------------------------------
% 3.16/1.79 % (29718)------------------------------
% 3.16/1.80 % (29719)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_29473 for (2998ds/3Mi)
% 3.16/1.80 % (29719)Instruction limit reached!
% 3.16/1.80 % (29719)------------------------------
% 3.16/1.80 % (29719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.80 % (29719)Termination reason: Unknown
% 3.16/1.80 % (29719)Termination phase: shuffling
% 3.16/1.80
% 3.16/1.80 % (29719)Memory used [KB]: 1791
% 3.16/1.80 % (29719)Time elapsed: 0.002 s
% 3.16/1.80 % (29719)Instructions burned: 3 (million)
% 3.16/1.80 % (29719)------------------------------
% 3.16/1.80 % (29719)------------------------------
% 3.16/1.81 % (29720)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_29473 for (2998ds/30Mi)
% 3.16/1.82 % (29720)Instruction limit reached!
% 3.16/1.82 % (29720)------------------------------
% 3.16/1.82 % (29720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.82 % (29720)Termination reason: Unknown
% 3.16/1.82 % (29720)Termination phase: shuffling
% 3.16/1.82
% 3.16/1.82 % (29720)Memory used [KB]: 2430
% 3.16/1.82 % (29720)Time elapsed: 0.013 s
% 3.16/1.82 % (29720)Instructions burned: 32 (million)
% 3.16/1.82 % (29720)------------------------------
% 3.16/1.82 % (29720)------------------------------
% 3.16/1.83 % (29721)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_29473 for (2998ds/127Mi)
% 3.16/1.87 % (29721)Instruction limit reached!
% 3.16/1.87 % (29721)------------------------------
% 3.16/1.87 % (29721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.87 % (29721)Termination reason: Unknown
% 3.16/1.87 % (29721)Termination phase: Property scanning
% 3.16/1.87
% 3.16/1.87 % (29721)Memory used [KB]: 3454
% 3.16/1.87 % (29721)Time elapsed: 0.041 s
% 3.16/1.87 % (29721)Instructions burned: 129 (million)
% 3.16/1.87 % (29721)------------------------------
% 3.16/1.87 % (29721)------------------------------
% 3.16/1.87 % (29714)Instruction limit reached!
% 3.16/1.87 % (29714)------------------------------
% 3.16/1.87 % (29714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.87 % (29714)Termination reason: Unknown
% 3.16/1.87 % (29714)Termination phase: Saturation
% 3.16/1.87
% 3.16/1.87 % (29714)Memory used [KB]: 9466
% 3.16/1.87 % (29714)Time elapsed: 0.118 s
% 3.16/1.87 % (29714)Instructions burned: 378 (million)
% 3.16/1.87 % (29714)------------------------------
% 3.16/1.87 % (29714)------------------------------
% 3.16/1.88 % (29722)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_29473 for (2997ds/100Mi)
% 3.16/1.89 % (29723)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_29473 for (2997ds/3Mi)
% 3.16/1.89 % (29723)Instruction limit reached!
% 3.16/1.89 % (29723)------------------------------
% 3.16/1.89 % (29723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.89 % (29723)Termination reason: Unknown
% 3.16/1.89 % (29723)Termination phase: shuffling
% 3.16/1.89
% 3.16/1.89 % (29723)Memory used [KB]: 1791
% 3.16/1.89 % (29723)Time elapsed: 0.002 s
% 3.16/1.89 % (29723)Instructions burned: 3 (million)
% 3.16/1.89 % (29723)------------------------------
% 3.16/1.89 % (29723)------------------------------
% 3.16/1.90 % (29724)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_29473 for (2997ds/20Mi)
% 3.16/1.90 % (29724)Instruction limit reached!
% 3.16/1.90 % (29724)------------------------------
% 3.16/1.90 % (29724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.90 % (29724)Termination reason: Unknown
% 3.16/1.90 % (29724)Termination phase: shuffling
% 3.16/1.90
% 3.16/1.90 % (29724)Memory used [KB]: 2046
% 3.16/1.90 % (29724)Time elapsed: 0.008 s
% 3.16/1.90 % (29724)Instructions burned: 20 (million)
% 3.16/1.90 % (29724)------------------------------
% 3.16/1.90 % (29724)------------------------------
% 3.16/1.91 % (29722)Instruction limit reached!
% 3.16/1.91 % (29722)------------------------------
% 3.16/1.91 % (29722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.91 % (29722)Termination reason: Unknown
% 3.16/1.91 % (29722)Termination phase: Property scanning
% 3.16/1.91
% 3.16/1.91 % (29722)Memory used [KB]: 3454
% 3.16/1.91 % (29722)Time elapsed: 0.030 s
% 3.16/1.91 % (29722)Instructions burned: 100 (million)
% 3.16/1.91 % (29722)------------------------------
% 3.16/1.91 % (29722)------------------------------
% 3.16/1.91 % (29725)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_29473 for (2997ds/86Mi)
% 3.16/1.92 % (29726)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_29473 for (2997ds/107Mi)
% 3.16/1.94 % (29725)Instruction limit reached!
% 3.16/1.94 % (29725)------------------------------
% 3.16/1.94 % (29725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.94 % (29725)Termination reason: Unknown
% 3.16/1.94 % (29725)Termination phase: Preprocessing 3
% 3.16/1.94
% 3.16/1.94 % (29725)Memory used [KB]: 2942
% 3.16/1.94 % (29725)Time elapsed: 0.029 s
% 3.16/1.94 % (29725)Instructions burned: 88 (million)
% 3.16/1.94 % (29725)------------------------------
% 3.16/1.94 % (29725)------------------------------
% 3.16/1.95 % (29727)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_29473 for (2996ds/39Mi)
% 3.16/1.96 % (29726)Instruction limit reached!
% 3.16/1.96 % (29726)------------------------------
% 3.16/1.96 % (29726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.96 % (29726)Termination reason: Unknown
% 3.16/1.96 % (29726)Termination phase: Property scanning
% 3.16/1.96
% 3.16/1.96 % (29726)Memory used [KB]: 2942
% 3.16/1.96 % (29726)Time elapsed: 0.034 s
% 3.16/1.96 % (29726)Instructions burned: 107 (million)
% 3.16/1.96 % (29726)------------------------------
% 3.16/1.96 % (29726)------------------------------
% 3.16/1.96 % (29727)Instruction limit reached!
% 3.16/1.96 % (29727)------------------------------
% 3.16/1.96 % (29727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.96 % (29727)Termination reason: Unknown
% 3.16/1.96 % (29727)Termination phase: shuffling
% 3.16/1.96
% 3.16/1.96 % (29727)Memory used [KB]: 2686
% 3.16/1.96 % (29727)Time elapsed: 0.014 s
% 3.16/1.96 % (29727)Instructions burned: 41 (million)
% 3.16/1.96 % (29727)------------------------------
% 3.16/1.96 % (29727)------------------------------
% 3.16/1.97 % (29728)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_29473 for (2996ds/448Mi)
% 3.16/1.97 % (29729)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_29473 for (2996ds/46Mi)
% 3.16/1.98 % (29708)Instruction limit reached!
% 3.16/1.98 % (29708)------------------------------
% 3.16/1.98 % (29708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.98 % (29708)Termination reason: Unknown
% 3.16/1.98 % (29708)Termination phase: Saturation
% 3.16/1.98
% 3.16/1.98 % (29708)Memory used [KB]: 7675
% 3.16/1.98 % (29708)Time elapsed: 0.244 s
% 3.16/1.98 % (29708)Instructions burned: 711 (million)
% 3.16/1.98 % (29708)------------------------------
% 3.16/1.98 % (29708)------------------------------
% 3.16/1.99 % (29730)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_29473 for (2996ds/98Mi)
% 3.16/1.99 % (29715)Instruction limit reached!
% 3.16/1.99 % (29715)------------------------------
% 3.16/1.99 % (29715)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.99 % (29715)Termination reason: Unknown
% 3.16/1.99 % (29715)Termination phase: Saturation
% 3.16/1.99
% 3.16/1.99 % (29715)Memory used [KB]: 9722
% 3.16/1.99 % (29715)Time elapsed: 0.233 s
% 3.16/1.99 % (29715)Instructions burned: 779 (million)
% 3.16/1.99 % (29715)------------------------------
% 3.16/1.99 % (29715)------------------------------
% 3.16/1.99 % (29729)Instruction limit reached!
% 3.16/1.99 % (29729)------------------------------
% 3.16/1.99 % (29729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/1.99 % (29729)Termination reason: Unknown
% 3.16/1.99 % (29729)Termination phase: Property scanning
% 3.16/1.99
% 3.16/1.99 % (29729)Memory used [KB]: 2430
% 3.16/1.99 % (29729)Time elapsed: 0.017 s
% 3.16/1.99 % (29729)Instructions burned: 48 (million)
% 3.16/1.99 % (29729)------------------------------
% 3.16/1.99 % (29729)------------------------------
% 3.16/2.00 % (29731)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_29473 for (2996ds/507Mi)
% 3.16/2.00 % (29732)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_29473 for (2996ds/149Mi)
% 3.16/2.00 % (29710)Instruction limit reached!
% 3.16/2.00 % (29710)------------------------------
% 3.16/2.00 % (29710)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.16/2.00 % (29710)Termination reason: Unknown
% 3.16/2.00 % (29710)Termination phase: Saturation
% 3.16/2.00
% 3.16/2.00 % (29710)Memory used [KB]: 11001
% 3.16/2.00 % (29710)Time elapsed: 0.266 s
% 3.16/2.00 % (29710)Instructions burned: 904 (million)
% 3.16/2.00 % (29710)------------------------------
% 3.16/2.00 % (29710)------------------------------
% 5.61/2.01 % (29733)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_29473 for (2996ds/39Mi)
% 5.61/2.02 % (29730)Instruction limit reached!
% 5.61/2.02 % (29730)------------------------------
% 5.61/2.02 % (29730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.61/2.02 % (29730)Termination reason: Unknown
% 5.61/2.02 % (29730)Termination phase: Property scanning
% 5.61/2.02
% 5.61/2.02 % (29730)Memory used [KB]: 3326
% 5.61/2.02 % (29730)Time elapsed: 0.030 s
% 5.61/2.02 % (29730)Instructions burned: 99 (million)
% 5.61/2.02 % (29730)------------------------------
% 5.61/2.02 % (29730)------------------------------
% 5.61/2.03 % (29733)Instruction limit reached!
% 5.61/2.03 % (29733)------------------------------
% 5.61/2.03 % (29733)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.61/2.03 % (29733)Termination reason: Unknown
% 5.61/2.03 % (29733)Termination phase: shuffling
% 5.61/2.03
% 5.61/2.03 % (29733)Memory used [KB]: 2430
% 5.61/2.03 % (29733)Time elapsed: 0.014 s
% 5.61/2.03 % (29733)Instructions burned: 39 (million)
% 5.61/2.03 % (29733)------------------------------
% 5.61/2.03 % (29733)------------------------------
% 5.61/2.03 % (29734)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_29473 for (2996ds/6Mi)
% 5.61/2.03 % (29734)Instruction limit reached!
% 5.61/2.03 % (29734)------------------------------
% 5.61/2.03 % (29734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.61/2.03 % (29734)Termination reason: Unknown
% 5.61/2.03 % (29734)Termination phase: shuffling
% 5.61/2.03
% 5.61/2.03 % (29734)Memory used [KB]: 1791
% 5.61/2.03 % (29734)Time elapsed: 0.003 s
% 5.61/2.03 % (29734)Instructions burned: 6 (million)
% 5.61/2.03 % (29734)------------------------------
% 5.61/2.03 % (29734)------------------------------
% 5.61/2.04 % (29735)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_29473 for (2996ds/1087Mi)
% 5.61/2.04 % (29717)Instruction limit reached!
% 5.61/2.04 % (29717)------------------------------
% 5.61/2.04 % (29717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.61/2.04 % (29717)Termination reason: Unknown
% 5.61/2.04 % (29717)Termination phase: Saturation
% 5.61/2.04
% 5.61/2.04 % (29717)Memory used [KB]: 7547
% 5.61/2.04 % (29717)Time elapsed: 0.279 s
% 5.61/2.04 % (29717)Instructions burned: 879 (million)
% 5.61/2.04 % (29717)------------------------------
% 5.61/2.04 % (29717)------------------------------
% 5.61/2.04 % (29736)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_29473 for (2995ds/47Mi)
% 5.61/2.05 % (29732)Instruction limit reached!
% 5.61/2.05 % (29732)------------------------------
% 5.61/2.05 % (29732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.61/2.05 % (29732)Termination reason: Unknown
% 5.61/2.05 % (29732)Termination phase: Property scanning
% 5.61/2.05
% 5.61/2.05 % (29732)Memory used [KB]: 3454
% 5.61/2.05 % (29732)Time elapsed: 0.047 s
% 5.61/2.05 % (29732)Instructions burned: 149 (million)
% 5.61/2.05 % (29732)------------------------------
% 5.61/2.05 % (29732)------------------------------
% 5.61/2.05 % (29737)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_29473 for (2995ds/44Mi)
% 5.61/2.05 % (29699)Instruction limit reached!
% 5.61/2.05 % (29699)------------------------------
% 5.61/2.05 % (29699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.61/2.05 % (29699)Termination reason: Unknown
% 5.61/2.05 % (29699)Termination phase: Saturation
% 5.61/2.05
% 5.61/2.05 % (29699)Memory used [KB]: 10490
% 5.61/2.05 % (29699)Time elapsed: 0.342 s
% 5.61/2.05 % (29699)Instructions burned: 1042 (million)
% 5.61/2.05 % (29699)------------------------------
% 5.61/2.05 % (29699)------------------------------
% 5.61/2.06 % (29736)Instruction limit reached!
% 5.61/2.06 % (29736)------------------------------
% 5.61/2.06 % (29736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.61/2.06 % (29736)Termination reason: Unknown
% 5.61/2.06 % (29736)Termination phase: Property scanning
% 5.61/2.06
% 5.61/2.06 % (29736)Memory used [KB]: 2430
% 5.61/2.06 % (29736)Time elapsed: 0.017 s
% 5.61/2.06 % (29736)Instructions burned: 48 (million)
% 5.61/2.06 % (29736)------------------------------
% 5.61/2.06 % (29736)------------------------------
% 5.61/2.06 % (29738)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_29473 for (2995ds/432Mi)
% 5.61/2.06 % (29737)Instruction limit reached!
% 5.61/2.06 % (29737)------------------------------
% 5.61/2.06 % (29737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.61/2.06 % (29737)Termination reason: Unknown
% 5.61/2.06 % (29737)Termination phase: shuffling
% 5.61/2.06
% 5.61/2.06 % (29737)Memory used [KB]: 2686
% 5.61/2.06 % (29737)Time elapsed: 0.014 s
% 5.61/2.06 % (29737)Instructions burned: 47 (million)
% 5.61/2.06 % (29737)------------------------------
% 5.61/2.06 % (29737)------------------------------
% 5.61/2.07 % (29740)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_29473 for (2995ds/31Mi)
% 5.61/2.07 % (29739)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_29473 for (2995ds/62Mi)
% 5.61/2.07 % (29741)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_29473 for (2995ds/96Mi)
% 5.61/2.08 % (29740)Instruction limit reached!
% 5.61/2.08 % (29740)------------------------------
% 5.61/2.08 % (29740)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.61/2.08 % (29740)Termination reason: Unknown
% 5.61/2.08 % (29740)Termination phase: shuffling
% 5.61/2.08
% 5.61/2.08 % (29740)Memory used [KB]: 2302
% 5.61/2.08 % (29740)Time elapsed: 0.012 s
% 5.61/2.08 % (29740)Instructions burned: 32 (million)
% 5.61/2.08 % (29740)------------------------------
% 5.61/2.08 % (29740)------------------------------
% 5.61/2.09 % (29742)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_29473 for (2995ds/453Mi)
% 5.61/2.10 % (29741)Instruction limit reached!
% 5.61/2.10 % (29741)------------------------------
% 5.61/2.10 % (29741)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.61/2.10 % (29741)Termination reason: Unknown
% 5.61/2.10 % (29741)Termination phase: Preprocessing 3
% 5.61/2.10
% 5.61/2.10 % (29741)Memory used [KB]: 3326
% 5.61/2.10 % (29741)Time elapsed: 0.030 s
% 5.61/2.10 % (29741)Instructions burned: 96 (million)
% 5.61/2.10 % (29741)------------------------------
% 5.61/2.10 % (29741)------------------------------
% 5.61/2.10 % (29739)Instruction limit reached!
% 5.61/2.10 % (29739)------------------------------
% 5.61/2.10 % (29739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.61/2.10 % (29739)Termination reason: Unknown
% 5.61/2.10 % (29739)Termination phase: shuffling
% 5.61/2.10
% 5.61/2.10 % (29739)Memory used [KB]: 2942
% 5.61/2.10 % (29739)Time elapsed: 0.035 s
% 5.61/2.10 % (29739)Instructions burned: 63 (million)
% 5.61/2.10 % (29739)------------------------------
% 5.61/2.10 % (29739)------------------------------
% 5.61/2.11 % (29743)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_29473 for (2995ds/71Mi)
% 5.61/2.11 % (29728)Instruction limit reached!
% 5.61/2.11 % (29728)------------------------------
% 5.61/2.11 % (29728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.61/2.11 % (29728)Termination reason: Unknown
% 5.61/2.11 % (29728)Termination phase: Saturation
% 5.61/2.11
% 5.61/2.11 % (29728)Memory used [KB]: 9210
% 5.61/2.11 % (29728)Time elapsed: 0.144 s
% 5.61/2.11 % (29728)Instructions burned: 449 (million)
% 5.61/2.11 % (29728)------------------------------
% 5.61/2.11 % (29728)------------------------------
% 6.15/2.11 % (29744)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_29473 for (2995ds/83Mi)
% 6.15/2.12 % (29745)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_29473 for (2995ds/11Mi)
% 6.15/2.12 % (29745)Instruction limit reached!
% 6.15/2.12 % (29745)------------------------------
% 6.15/2.12 % (29745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.15/2.12 % (29745)Termination reason: Unknown
% 6.15/2.12 % (29745)Termination phase: shuffling
% 6.15/2.12
% 6.15/2.12 % (29745)Memory used [KB]: 2046
% 6.15/2.12 % (29745)Time elapsed: 0.005 s
% 6.15/2.12 % (29745)Instructions burned: 13 (million)
% 6.15/2.12 % (29745)------------------------------
% 6.15/2.12 % (29745)------------------------------
% 6.15/2.13 % (29743)Instruction limit reached!
% 6.15/2.13 % (29743)------------------------------
% 6.15/2.13 % (29743)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.15/2.13 % (29743)Termination reason: Unknown
% 6.15/2.13 % (29743)Termination phase: Property scanning
% 6.15/2.13
% 6.15/2.13 % (29743)Memory used [KB]: 2686
% 6.15/2.13 % (29743)Time elapsed: 0.023 s
% 6.15/2.13 % (29743)Instructions burned: 71 (million)
% 6.15/2.13 % (29743)------------------------------
% 6.15/2.13 % (29743)------------------------------
% 6.15/2.13 % (29746)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_29473 for (2994ds/41Mi)
% 6.15/2.14 % (29747)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_29473 for (2994ds/6Mi)
% 6.15/2.14 % (29747)Instruction limit reached!
% 6.15/2.14 % (29747)------------------------------
% 6.15/2.14 % (29747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.15/2.14 % (29747)Termination reason: Unknown
% 6.15/2.14 % (29747)Termination phase: shuffling
% 6.15/2.14
% 6.15/2.14 % (29747)Memory used [KB]: 1791
% 6.15/2.14 % (29747)Time elapsed: 0.003 s
% 6.15/2.14 % (29747)Instructions burned: 6 (million)
% 6.15/2.14 % (29747)------------------------------
% 6.15/2.14 % (29747)------------------------------
% 6.15/2.14 % (29744)Instruction limit reached!
% 6.15/2.14 % (29744)------------------------------
% 6.15/2.14 % (29744)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.15/2.14 % (29744)Termination reason: Unknown
% 6.15/2.14 % (29744)Termination phase: Saturation
% 6.15/2.14
% 6.15/2.14 % (29744)Memory used [KB]: 2558
% 6.15/2.14 % (29744)Time elapsed: 0.029 s
% 6.15/2.14 % (29744)Instructions burned: 84 (million)
% 6.15/2.14 % (29744)------------------------------
% 6.15/2.14 % (29744)------------------------------
% 6.15/2.14 % (29746)Instruction limit reached!
% 6.15/2.14 % (29746)------------------------------
% 6.15/2.14 % (29746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.15/2.14 % (29746)Termination reason: Unknown
% 6.15/2.14 % (29746)Termination phase: shuffling
% 6.15/2.14
% 6.15/2.14 % (29746)Memory used [KB]: 2814
% 6.15/2.14 % (29746)Time elapsed: 0.013 s
% 6.15/2.14 % (29746)Instructions burned: 44 (million)
% 6.15/2.14 % (29746)------------------------------
% 6.15/2.14 % (29746)------------------------------
% 6.15/2.15 % (29748)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_29473 for (2994ds/150Mi)
% 6.15/2.15 % (29731)Instruction limit reached!
% 6.15/2.15 % (29731)------------------------------
% 6.15/2.15 % (29731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.15/2.15 % (29731)Termination reason: Unknown
% 6.15/2.15 % (29731)Termination phase: Saturation
% 6.15/2.15
% 6.15/2.15 % (29731)Memory used [KB]: 11001
% 6.15/2.15 % (29731)Time elapsed: 0.153 s
% 6.15/2.15 % (29731)Instructions burned: 509 (million)
% 6.15/2.15 % (29731)------------------------------
% 6.15/2.15 % (29731)------------------------------
% 6.15/2.15 % (29749)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_29473 for (2994ds/343Mi)
% 6.15/2.15 % (29750)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_29473 for (2994ds/109Mi)
% 6.15/2.16 % (29751)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_29473 for (2994ds/253Mi)
% 6.15/2.18 % (29738)Instruction limit reached!
% 6.15/2.18 % (29738)------------------------------
% 6.15/2.18 % (29738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.15/2.18 % (29738)Termination reason: Unknown
% 6.15/2.18 % (29738)Termination phase: Saturation
% 6.15/2.18
% 6.15/2.18 % (29738)Memory used [KB]: 4733
% 6.15/2.18 % (29738)Time elapsed: 0.123 s
% 6.15/2.18 % (29738)Instructions burned: 433 (million)
% 6.15/2.18 % (29738)------------------------------
% 6.15/2.18 % (29738)------------------------------
% 6.15/2.18 % (29751)Refutation not found, incomplete strategy
% 6.15/2.18 % (29751)------------------------------
% 6.15/2.18 % (29751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.15/2.18 % (29751)Termination reason: Refutation not found, incomplete strategy
% 6.15/2.18
% 6.15/2.18
% 6.15/2.18 % (29751)Memory used [KB]: 7036
% 6.15/2.18 % (29751)Time elapsed: 0.024 s
% 6.15/2.18 % (29751)Instructions burned: 75 (million)
% 6.15/2.18 % (29751)------------------------------
% 6.15/2.18 % (29751)------------------------------
% 6.15/2.19 % (29750)Instruction limit reached!
% 6.15/2.19 % (29750)------------------------------
% 6.15/2.19 % (29750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.15/2.19 % (29750)Termination reason: Unknown
% 6.15/2.19 % (29750)Termination phase: Preprocessing 3
% 6.15/2.19
% 6.15/2.19 % (29750)Memory used [KB]: 3326
% 6.15/2.19 % (29750)Time elapsed: 0.034 s
% 6.15/2.19 % (29750)Instructions burned: 110 (million)
% 6.15/2.19 % (29750)------------------------------
% 6.15/2.19 % (29750)------------------------------
% 6.15/2.19 % (29752)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_29473 for (2994ds/140Mi)
% 6.15/2.19 % (29753)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_29473 for (2994ds/614Mi)
% 6.15/2.19 % (29748)Instruction limit reached!
% 6.15/2.19 % (29748)------------------------------
% 6.15/2.19 % (29748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.15/2.19 % (29748)Termination reason: Unknown
% 6.15/2.19 % (29748)Termination phase: Property scanning
% 6.15/2.19
% 6.15/2.19 % (29748)Memory used [KB]: 3709
% 6.15/2.19 % (29748)Time elapsed: 0.045 s
% 6.15/2.19 % (29748)Instructions burned: 153 (million)
% 6.15/2.19 % (29748)------------------------------
% 6.15/2.19 % (29748)------------------------------
% 6.58/2.20 % (29754)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_29473 for (2994ds/202Mi)
% 6.58/2.20 % (29755)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_29473 for (2994ds/339Mi)
% 6.58/2.21 % (29742)Instruction limit reached!
% 6.58/2.21 % (29742)------------------------------
% 6.58/2.21 % (29742)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.58/2.21 % (29742)Termination reason: Unknown
% 6.58/2.21 % (29742)Termination phase: Saturation
% 6.58/2.21
% 6.58/2.21 % (29742)Memory used [KB]: 9083
% 6.58/2.21 % (29742)Time elapsed: 0.125 s
% 6.58/2.21 % (29742)Instructions burned: 455 (million)
% 6.58/2.21 % (29742)------------------------------
% 6.58/2.21 % (29742)------------------------------
% 6.58/2.22 % (29756)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_29473 for (2994ds/283Mi)
% 6.58/2.23 % (29752)Instruction limit reached!
% 6.58/2.23 % (29752)------------------------------
% 6.58/2.23 % (29752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.58/2.23 % (29752)Termination reason: Unknown
% 6.58/2.23 % (29752)Termination phase: Saturation
% 6.58/2.23
% 6.58/2.23 % (29752)Memory used [KB]: 7419
% 6.58/2.23 % (29752)Time elapsed: 0.045 s
% 6.58/2.23 % (29752)Instructions burned: 140 (million)
% 6.58/2.23 % (29752)------------------------------
% 6.58/2.23 % (29752)------------------------------
% 6.58/2.24 % (29757)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_29473 for (2993ds/134Mi)
% 6.58/2.26 % (29754)Instruction limit reached!
% 6.58/2.26 % (29754)------------------------------
% 6.58/2.26 % (29754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.58/2.26 % (29754)Termination reason: Unknown
% 6.58/2.26 % (29754)Termination phase: Saturation
% 6.58/2.26
% 6.58/2.26 % (29754)Memory used [KB]: 7675
% 6.58/2.26 % (29754)Time elapsed: 0.062 s
% 6.58/2.26 % (29754)Instructions burned: 204 (million)
% 6.58/2.26 % (29754)------------------------------
% 6.58/2.26 % (29754)------------------------------
% 6.58/2.27 % (29749)Instruction limit reached!
% 6.58/2.27 % (29749)------------------------------
% 6.58/2.27 % (29749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.58/2.27 % (29749)Termination reason: Unknown
% 6.58/2.27 % (29749)Termination phase: Saturation
% 6.58/2.27
% 6.58/2.27 % (29749)Memory used [KB]: 7675
% 6.58/2.27 % (29749)Time elapsed: 0.116 s
% 6.58/2.27 % (29749)Instructions burned: 343 (million)
% 6.58/2.27 % (29749)------------------------------
% 6.58/2.27 % (29749)------------------------------
% 6.58/2.27 % (29758)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_29473 for (2993ds/298Mi)
% 6.58/2.28 % (29759)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_29473 for (2993ds/192Mi)
% 6.58/2.28 % (29757)Instruction limit reached!
% 6.58/2.28 % (29757)------------------------------
% 6.58/2.28 % (29757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.58/2.28 % (29757)Termination reason: Unknown
% 6.58/2.28 % (29757)Termination phase: Property scanning
% 6.58/2.28
% 6.58/2.28 % (29757)Memory used [KB]: 3454
% 6.58/2.28 % (29757)Time elapsed: 0.040 s
% 6.58/2.28 % (29757)Instructions burned: 136 (million)
% 6.58/2.28 % (29757)------------------------------
% 6.58/2.28 % (29757)------------------------------
% 6.58/2.29 % (29760)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_29473 for (2993ds/258Mi)
% 6.58/2.29 % (29756)Instruction limit reached!
% 6.58/2.29 % (29756)------------------------------
% 6.58/2.29 % (29756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.58/2.29 % (29756)Termination reason: Unknown
% 6.58/2.29 % (29756)Termination phase: Saturation
% 6.58/2.29
% 6.58/2.29 % (29756)Memory used [KB]: 7931
% 6.58/2.29 % (29756)Time elapsed: 0.074 s
% 6.58/2.29 % (29756)Instructions burned: 284 (million)
% 6.58/2.29 % (29756)------------------------------
% 6.58/2.29 % (29756)------------------------------
% 7.09/2.30 % (29755)Instruction limit reached!
% 7.09/2.30 % (29755)------------------------------
% 7.09/2.30 % (29755)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.09/2.30 % (29755)Termination reason: Unknown
% 7.09/2.30 % (29755)Termination phase: Saturation
% 7.09/2.30
% 7.09/2.30 % (29755)Memory used [KB]: 8059
% 7.09/2.30 % (29755)Time elapsed: 0.097 s
% 7.09/2.30 % (29755)Instructions burned: 341 (million)
% 7.09/2.30 % (29755)------------------------------
% 7.09/2.30 % (29755)------------------------------
% 7.09/2.30 % (29761)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_29473 for (2993ds/90Mi)
% 7.09/2.31 % (29762)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_29473 for (2993ds/231Mi)
% 7.09/2.33 % (29760)First to succeed.
% 7.09/2.33 % (29760)Refutation found. Thanks to Tanya!
% 7.09/2.33 % SZS status Theorem for DTF2THF_29473
% 7.09/2.33 % SZS output start Proof for DTF2THF_29473
% 7.09/2.33 thf(type_def_5, type, list_P1467822637od_a_a: $tType).
% 7.09/2.33 thf(type_def_7, type, list_P601816365list_a: $tType).
% 7.09/2.33 thf(type_def_8, type, list_P1891567085od_a_a: $tType).
% 7.09/2.33 thf(type_def_9, type, list_a_nat: $tType).
% 7.09/2.33 thf(type_def_10, type, list_l1108175539od_a_a: $tType).
% 7.09/2.33 thf(type_def_11, type, list_list_a: $tType).
% 7.09/2.33 thf(type_def_12, type, list_a: $tType).
% 7.09/2.33 thf(type_def_13, type, a: $tType).
% 7.09/2.33 thf(type_def_14, type, nat: $tType).
% 7.09/2.33 thf(type_def_15, type, product_prod_a_a: $tType).
% 7.09/2.33 thf(type_def_16, type, set_Pr1948701895od_a_a: $tType).
% 7.09/2.33 thf(type_def_17, type, set_Pr800560199od_a_a: $tType).
% 7.09/2.33 thf(type_def_18, type, set_Product_prod_a_a: $tType).
% 7.09/2.33 thf(type_def_19, type, set_Pr1971762695list_a: $tType).
% 7.09/2.33 thf(type_def_20, type, set_Pr1940702919_a_nat: $tType).
% 7.09/2.33 thf(type_def_21, type, set_Pr753687879_a_nat: $tType).
% 7.09/2.33 thf(type_def_22, type, set_Pr1239640519od_a_a: $tType).
% 7.09/2.33 thf(type_def_23, type, set_Pr1742859527list_a: $tType).
% 7.09/2.33 thf(type_def_24, type, set_Pr1295299783od_a_a: $tType).
% 7.09/2.33 thf(type_def_25, type, set_Pr779272263od_a_a: $tType).
% 7.09/2.33 thf(type_def_26, type, product_prod_a_nat_a: $tType).
% 7.09/2.33 thf(type_def_27, type, list_P916011052_nat_a: $tType).
% 7.09/2.33 thf(type_def_28, type, produc657167928_a_a_a: $tType).
% 7.09/2.33 thf(type_def_29, type, list_P305489470_a_a_a: $tType).
% 7.09/2.33 thf(type_def_30, type, produc864062247list_a: $tType).
% 7.09/2.33 thf(type_def_31, type, produc664688895_a_nat: $tType).
% 7.09/2.33 thf(type_def_32, type, list_P1435957893_a_nat: $tType).
% 7.09/2.33 thf(type_def_33, type, produc1572603623od_a_a: $tType).
% 7.09/2.33 thf(type_def_34, type, produc1016684094_a_a_a: $tType).
% 7.09/2.33 thf(type_def_35, type, list_P319927492_a_a_a: $tType).
% 7.09/2.33 thf(type_def_36, type, product_prod_a_a_nat: $tType).
% 7.09/2.33 thf(type_def_37, type, list_P576104046_a_nat: $tType).
% 7.09/2.33 thf(type_def_38, type, produc1701253078od_a_a: $tType).
% 7.09/2.33 thf(type_def_39, type, list_P1175580892od_a_a: $tType).
% 7.09/2.33 thf(type_def_40, type, produc1921647824od_a_a: $tType).
% 7.09/2.33 thf(type_def_41, type, list_P1458844246od_a_a: $tType).
% 7.09/2.33 thf(type_def_42, type, set_li562223245od_a_a: $tType).
% 7.09/2.33 thf(type_def_43, type, set_a: $tType).
% 7.09/2.33 thf(type_def_44, type, produc821581462od_a_a: $tType).
% 7.09/2.33 thf(type_def_45, type, produc501911462od_a_a: $tType).
% 7.09/2.33 thf(type_def_46, type, produc1178641895_a_nat: $tType).
% 7.09/2.33 thf(type_def_47, type, produc1334933863_a_nat: $tType).
% 7.09/2.33 thf(type_def_48, type, produc657724903od_a_a: $tType).
% 7.09/2.33 thf(type_def_49, type, produc403652391list_a: $tType).
% 7.09/2.33 thf(type_def_50, type, produc205693799od_a_a: $tType).
% 7.09/2.33 thf(type_def_51, type, produc651658087od_a_a: $tType).
% 7.09/2.33 thf(type_def_52, type, pair_p125712459t_unit: $tType).
% 7.09/2.33 thf(type_def_53, type, produc1912141786_a_a_a: $tType).
% 7.09/2.33 thf(type_def_54, type, produc1990712039od_a_a: $tType).
% 7.09/2.33 thf(type_def_55, type, produc1197928545_a_a_a: $tType).
% 7.09/2.33 thf(type_def_56, type, set_Pr727105414od_a_a: $tType).
% 7.09/2.33 thf(type_def_57, type, set_Pr1525541400_a_a_a: $tType).
% 7.09/2.33 thf(type_def_58, type, set_Pr248149174od_a_a: $tType).
% 7.09/2.33 thf(type_def_59, type, set_Pr110478017_a_a_a: $tType).
% 7.09/2.33 thf(type_def_60, type, pair_p1891813445t_unit: $tType).
% 7.09/2.33 thf(func_def_0, type, set_Pr779272263od_a_a: $tType).
% 7.09/2.33 thf(func_def_1, type, produc205693799od_a_a: $tType).
% 7.09/2.33 thf(func_def_2, type, set_Pr1295299783od_a_a: $tType).
% 7.09/2.33 thf(func_def_3, type, produc1990712039od_a_a: $tType).
% 7.09/2.33 thf(func_def_4, type, produc1912141786_a_a_a: $tType).
% 7.09/2.33 thf(func_def_5, type, set_Pr727105414od_a_a: $tType).
% 7.09/2.33 thf(func_def_6, type, set_Pr1239640519od_a_a: $tType).
% 7.09/2.33 thf(func_def_7, type, produc501911462od_a_a: $tType).
% 7.09/2.33 thf(func_def_8, type, produc657724903od_a_a: $tType).
% 7.09/2.33 thf(func_def_9, type, produc821581462od_a_a: $tType).
% 7.09/2.33 thf(func_def_10, type, set_Pr800560199od_a_a: $tType).
% 7.09/2.33 thf(func_def_11, type, produc651658087od_a_a: $tType).
% 7.09/2.33 thf(func_def_12, type, set_Pr110478017_a_a_a: $tType).
% 7.09/2.33 thf(func_def_13, type, set_Pr753687879_a_nat: $tType).
% 7.09/2.33 thf(func_def_14, type, produc1197928545_a_a_a: $tType).
% 7.09/2.33 thf(func_def_15, type, list_P1891567085od_a_a: $tType).
% 7.09/2.33 thf(func_def_16, type, set_Pr1948701895od_a_a: $tType).
% 7.09/2.33 thf(func_def_17, type, set_Pr1742859527list_a: $tType).
% 7.09/2.33 thf(func_def_18, type, pair_p1891813445t_unit: $tType).
% 7.09/2.33 thf(func_def_19, type, produc1334933863_a_nat: $tType).
% 7.09/2.33 thf(func_def_20, type, list_P1435957893_a_nat: $tType).
% 7.09/2.33 thf(func_def_21, type, produc1572603623od_a_a: $tType).
% 7.09/2.33 thf(func_def_22, type, produc403652391list_a: $tType).
% 7.09/2.33 thf(func_def_23, type, list_P1175580892od_a_a: $tType).
% 7.09/2.33 thf(func_def_24, type, list_P305489470_a_a_a: $tType).
% 7.09/2.33 thf(func_def_25, type, set_Pr248149174od_a_a: $tType).
% 7.09/2.33 thf(func_def_26, type, set_Pr1525541400_a_a_a: $tType).
% 7.09/2.33 thf(func_def_27, type, pair_p125712459t_unit: $tType).
% 7.09/2.33 thf(func_def_28, type, set_Pr1940702919_a_nat: $tType).
% 7.09/2.33 thf(func_def_29, type, produc664688895_a_nat: $tType).
% 7.09/2.33 thf(func_def_30, type, produc1701253078od_a_a: $tType).
% 7.09/2.33 thf(func_def_31, type, produc657167928_a_a_a: $tType).
% 7.09/2.33 thf(func_def_32, type, list_P1458844246od_a_a: $tType).
% 7.09/2.33 thf(func_def_33, type, list_P319927492_a_a_a: $tType).
% 7.09/2.33 thf(func_def_34, type, list_P601816365list_a: $tType).
% 7.09/2.33 thf(func_def_35, type, set_Pr1971762695list_a: $tType).
% 7.09/2.33 thf(func_def_36, type, produc1178641895_a_nat: $tType).
% 7.09/2.33 thf(func_def_37, type, list_P576104046_a_nat: $tType).
% 7.09/2.33 thf(func_def_38, type, list_P916011052_nat_a: $tType).
% 7.09/2.33 thf(func_def_39, type, produc1921647824od_a_a: $tType).
% 7.09/2.33 thf(func_def_40, type, produc1016684094_a_a_a: $tType).
% 7.09/2.33 thf(func_def_41, type, produc864062247list_a: $tType).
% 7.09/2.33 thf(func_def_42, type, list_l1108175539od_a_a: $tType).
% 7.09/2.33 thf(func_def_43, type, set_li562223245od_a_a: $tType).
% 7.09/2.33 thf(func_def_44, type, product_prod_a_a_nat: $tType).
% 7.09/2.33 thf(func_def_45, type, product_prod_a_nat_a: $tType).
% 7.09/2.33 thf(func_def_46, type, list_P1467822637od_a_a: $tType).
% 7.09/2.33 thf(func_def_47, type, set_Product_prod_a_a: $tType).
% 7.09/2.33 thf(func_def_48, type, list_a_nat: $tType).
% 7.09/2.33 thf(func_def_49, type, product_prod_a_a: $tType).
% 7.09/2.33 thf(func_def_50, type, list_list_a: $tType).
% 7.09/2.33 thf(func_def_51, type, list_a: $tType).
% 7.09/2.33 thf(func_def_52, type, set_a: $tType).
% 7.09/2.33 thf(func_def_53, type, nat: $tType).
% 7.09/2.33 thf(func_def_54, type, a: $tType).
% 7.09/2.33 thf(func_def_55, type, if_lis321365491od_a_a: $o > list_P1467822637od_a_a > list_P1467822637od_a_a > list_P1467822637od_a_a).
% 7.09/2.33 thf(func_def_56, type, kurato292963650list_a: list_P601816365list_a > $o).
% 7.09/2.33 thf(func_def_57, type, kurato1404746725od_a_a: list_P1891567085od_a_a > $o).
% 7.09/2.33 thf(func_def_58, type, kurato1072996284sing_a: list_P1467822637od_a_a > $o).
% 7.09/2.33 thf(func_def_59, type, append_a_nat: list_a_nat > list_a_nat > list_a_nat).
% 7.09/2.33 thf(func_def_60, type, append2141280328od_a_a: list_l1108175539od_a_a > list_l1108175539od_a_a > list_l1108175539od_a_a).
% 7.09/2.33 thf(func_def_61, type, append_list_a: list_list_a > list_list_a > list_list_a).
% 7.09/2.33 thf(func_def_62, type, append750086082list_a: list_P601816365list_a > list_P601816365list_a > list_P601816365list_a).
% 7.09/2.33 thf(func_def_63, type, append864718978od_a_a: list_P1891567085od_a_a > list_P1891567085od_a_a > list_P1891567085od_a_a).
% 7.09/2.33 thf(func_def_64, type, append1574001858od_a_a: list_P1467822637od_a_a > list_P1467822637od_a_a > list_P1467822637od_a_a).
% 7.09/2.33 thf(func_def_65, type, append_a: list_a > list_a > list_a).
% 7.09/2.33 thf(func_def_66, type, bind_a1190333103od_a_a: list_a_nat > ((a > nat) > list_P1467822637od_a_a) > list_P1467822637od_a_a).
% 7.09/2.33 thf(func_def_67, type, bind_a_nat_a: list_a_nat > ((a > nat) > list_a) > list_a).
% 7.09/2.33 thf(func_def_68, type, bind_l618536897od_a_a: list_l1108175539od_a_a > (list_P1467822637od_a_a > list_P1467822637od_a_a) > list_P1467822637od_a_a).
% 7.09/2.33 thf(func_def_69, type, bind_l1307590552_a_a_a: list_l1108175539od_a_a > (list_P1467822637od_a_a > list_a) > list_a).
% 7.09/2.33 thf(func_def_70, type, bind_P240085581od_a_a: list_P1467822637od_a_a > (product_prod_a_a > list_l1108175539od_a_a) > list_l1108175539od_a_a).
% 7.09/2.33 thf(func_def_71, type, bind_P1783625031od_a_a: list_P1467822637od_a_a > (product_prod_a_a > list_P1467822637od_a_a) > list_P1467822637od_a_a).
% 7.09/2.33 thf(func_def_72, type, bind_P293964574_a_a_a: list_P1467822637od_a_a > (product_prod_a_a > list_a) > list_a).
% 7.09/2.33 thf(func_def_73, type, bind_a883992246od_a_a: list_a > (a > list_l1108175539od_a_a) > list_l1108175539od_a_a).
% 7.09/2.33 thf(func_def_74, type, bind_a1679112752od_a_a: list_a > (a > list_P1467822637od_a_a) > list_P1467822637od_a_a).
% 7.09/2.33 thf(func_def_75, type, bind_a_a: list_a > (a > list_a) > list_a).
% 7.09/2.33 thf(func_def_76, type, concat1878217064od_a_a: list_l1108175539od_a_a > list_P1467822637od_a_a).
% 7.09/2.33 thf(func_def_77, type, insert2123825731od_a_a: product_prod_a_a > list_P1467822637od_a_a > list_P1467822637od_a_a).
% 7.09/2.33 thf(func_def_78, type, lenlex2038501170od_a_a: set_Pr1948701895od_a_a > set_Pr800560199od_a_a).
% 7.09/2.33 thf(func_def_79, type, lenlex_a: set_Product_prod_a_a > set_Pr1971762695list_a).
% 7.09/2.33 thf(func_def_80, type, lex_Product_prod_a_a: set_Pr1948701895od_a_a > set_Pr800560199od_a_a).
% 7.09/2.33 thf(func_def_81, type, lex_a: set_Product_prod_a_a > set_Pr1971762695list_a).
% 7.09/2.33 thf(func_def_82, type, lexord_a_nat: set_Pr1940702919_a_nat > set_Pr753687879_a_nat).
% 7.09/2.33 thf(func_def_83, type, lexord1284731808od_a_a: set_Pr800560199od_a_a > set_Pr1239640519od_a_a).
% 7.09/2.33 thf(func_def_84, type, lexord_list_a: set_Pr1971762695list_a > set_Pr1742859527list_a).
% 7.09/2.33 thf(func_def_85, type, lexord931792858od_a_a: set_Pr1295299783od_a_a > set_Pr779272263od_a_a).
% 7.09/2.33 thf(func_def_86, type, lexord673907738od_a_a: set_Pr1948701895od_a_a > set_Pr800560199od_a_a).
% 7.09/2.33 thf(func_def_87, type, lexord_a: set_Product_prod_a_a > set_Pr1971762695list_a).
% 7.09/2.33 thf(func_def_88, type, cons_a_nat: (a > nat) > list_a_nat > list_a_nat).
% 7.09/2.33 thf(func_def_89, type, cons_l724116707od_a_a: list_P1467822637od_a_a > list_l1108175539od_a_a > list_l1108175539od_a_a).
% 7.09/2.33 thf(func_def_90, type, cons_list_a: list_a > list_list_a > list_list_a).
% 7.09/2.33 thf(func_def_91, type, cons_P896312284_nat_a: product_prod_a_nat_a > list_P916011052_nat_a > list_P916011052_nat_a).
% 7.09/2.33 thf(func_def_92, type, cons_P169173742_a_a_a: produc657167928_a_a_a > list_P305489470_a_a_a > list_P305489470_a_a_a).
% 7.09/2.33 thf(func_def_93, type, cons_P2080942813list_a: produc864062247list_a > list_P601816365list_a > list_P601816365list_a).
% 7.09/2.33 thf(func_def_94, type, cons_P659009461_a_nat: produc664688895_a_nat > list_P1435957893_a_nat > list_P1435957893_a_nat).
% 7.09/2.33 thf(func_def_95, type, cons_P1070399645od_a_a: produc1572603623od_a_a > list_P1891567085od_a_a > list_P1891567085od_a_a).
% 7.09/2.33 thf(func_def_96, type, cons_P86081012_a_a_a: produc1016684094_a_a_a > list_P319927492_a_a_a > list_P319927492_a_a_a).
% 7.09/2.33 thf(func_def_97, type, cons_P1915851550_a_nat: product_prod_a_a_nat > list_P576104046_a_nat > list_P576104046_a_nat).
% 7.09/2.33 thf(func_def_98, type, cons_P1213258892od_a_a: produc1701253078od_a_a > list_P1175580892od_a_a > list_P1175580892od_a_a).
% 7.09/2.33 thf(func_def_99, type, cons_P991044742od_a_a: produc1921647824od_a_a > list_P1458844246od_a_a > list_P1458844246od_a_a).
% 7.09/2.33 thf(func_def_100, type, cons_P1921020637od_a_a: product_prod_a_a > list_P1467822637od_a_a > list_P1467822637od_a_a).
% 7.09/2.33 thf(func_def_101, type, cons_a: a > list_a > list_a).
% 7.09/2.33 thf(func_def_102, type, nil_a_nat: list_a_nat).
% 7.09/2.33 thf(func_def_103, type, nil_li1885598003od_a_a: list_l1108175539od_a_a).
% 7.09/2.33 thf(func_def_104, type, nil_Pr1049924845od_a_a: list_P1891567085od_a_a).
% 7.09/2.33 thf(func_def_105, type, nil_Product_prod_a_a: list_P1467822637od_a_a).
% 7.09/2.33 thf(func_def_106, type, nil_a: list_a).
% 7.09/2.33 thf(func_def_107, type, set_li1284606018od_a_a: list_l1108175539od_a_a > set_li562223245od_a_a).
% 7.09/2.33 thf(func_def_108, type, set_Product_prod_a_a2: list_P1467822637od_a_a > set_Product_prod_a_a).
% 7.09/2.33 thf(func_def_109, type, set_a2: list_a > set_a).
% 7.09/2.33 thf(func_def_110, type, listrel1_a_nat: set_Pr1940702919_a_nat > set_Pr753687879_a_nat).
% 7.09/2.33 thf(func_def_111, type, listre651914124od_a_a: set_Pr800560199od_a_a > set_Pr1239640519od_a_a).
% 7.09/2.33 thf(func_def_112, type, listrel1_list_a: set_Pr1971762695list_a > set_Pr1742859527list_a).
% 7.09/2.33 thf(func_def_113, type, listre1832537542od_a_a: set_Pr1295299783od_a_a > set_Pr779272263od_a_a).
% 7.09/2.33 thf(func_def_114, type, listre944824838od_a_a: set_Pr1948701895od_a_a > set_Pr800560199od_a_a).
% 7.09/2.33 thf(func_def_115, type, listrel1_a: set_Product_prod_a_a > set_Pr1971762695list_a).
% 7.09/2.33 thf(func_def_116, type, listre2074280881od_a_a: set_Pr1948701895od_a_a > set_Pr800560199od_a_a).
% 7.09/2.33 thf(func_def_117, type, listrel_a_a: set_Product_prod_a_a > set_Pr1971762695list_a).
% 7.09/2.33 thf(func_def_118, type, maps_a836827497od_a_a: ((a > nat) > list_P1467822637od_a_a) > list_a_nat > list_P1467822637od_a_a).
% 7.09/2.33 thf(func_def_119, type, maps_a_nat_a: ((a > nat) > list_a) > list_a_nat > list_a).
% 7.09/2.33 thf(func_def_120, type, maps_l1117535867od_a_a: (list_P1467822637od_a_a > list_P1467822637od_a_a) > list_l1108175539od_a_a > list_P1467822637od_a_a).
% 7.09/2.33 thf(func_def_121, type, maps_l1091119186_a_a_a: (list_P1467822637od_a_a > list_a) > list_l1108175539od_a_a > list_a).
% 7.09/2.33 thf(func_def_122, type, maps_P739084551od_a_a: (product_prod_a_a > list_l1108175539od_a_a) > list_P1467822637od_a_a > list_l1108175539od_a_a).
% 7.09/2.33 thf(func_def_123, type, maps_P1529886977od_a_a: (product_prod_a_a > list_P1467822637od_a_a) > list_P1467822637od_a_a > list_P1467822637od_a_a).
% 7.09/2.33 thf(func_def_124, type, maps_P321755352_a_a_a: (product_prod_a_a > list_a) > list_P1467822637od_a_a > list_a).
% 7.09/2.33 thf(func_def_125, type, maps_a667520880od_a_a: (a > list_l1108175539od_a_a) > list_a > list_l1108175539od_a_a).
% 7.09/2.33 thf(func_def_126, type, maps_a1706903530od_a_a: (a > list_P1467822637od_a_a) > list_a > list_P1467822637od_a_a).
% 7.09/2.33 thf(func_def_127, type, maps_a_a: (a > list_a) > list_a > list_a).
% 7.09/2.33 thf(func_def_128, type, measures_a: list_a_nat > set_Product_prod_a_a).
% 7.09/2.33 thf(func_def_129, type, member_a_nat: list_a_nat > (a > nat) > $o).
% 7.09/2.33 thf(func_def_130, type, member261538120od_a_a: list_l1108175539od_a_a > list_P1467822637od_a_a > $o).
% 7.09/2.33 thf(func_def_131, type, member2070313346od_a_a: list_P1891567085od_a_a > produc1572603623od_a_a > $o).
% 7.09/2.33 thf(func_def_132, type, member1112491458od_a_a: list_P1467822637od_a_a > product_prod_a_a > $o).
% 7.09/2.33 thf(func_def_133, type, member_a: list_a > a > $o).
% 7.09/2.33 thf(func_def_134, type, subseq2115548028od_a_a: list_P1467822637od_a_a > list_l1108175539od_a_a).
% 7.09/2.33 thf(func_def_135, type, zip_a_nat_a: list_a_nat > list_a > list_P916011052_nat_a).
% 7.09/2.33 thf(func_def_136, type, zip_li245157064_a_a_a: list_l1108175539od_a_a > list_a > list_P305489470_a_a_a).
% 7.09/2.33 thf(func_def_137, type, zip_list_a_list_a: list_list_a > list_list_a > list_P601816365list_a).
% 7.09/2.33 thf(func_def_138, type, zip_Pr24086287_a_nat: list_P1467822637od_a_a > list_a_nat > list_P1435957893_a_nat).
% 7.09/2.33 thf(func_def_139, type, zip_Pr792472183od_a_a: list_P1467822637od_a_a > list_P1467822637od_a_a > list_P1891567085od_a_a).
% 7.09/2.33 thf(func_def_140, type, zip_Pr201224270_a_a_a: list_P1467822637od_a_a > list_a > list_P319927492_a_a_a).
% 7.09/2.33 thf(func_def_141, type, zip_a_a_nat: list_a > list_a_nat > list_P576104046_a_nat).
% 7.09/2.33 thf(func_def_142, type, zip_a_1969042406od_a_a: list_a > list_l1108175539od_a_a > list_P1175580892od_a_a).
% 7.09/2.33 thf(func_def_143, type, zip_a_1586372448od_a_a: list_a > list_P1467822637od_a_a > list_P1458844246od_a_a).
% 7.09/2.33 thf(func_def_144, type, zip_a_a: list_a > list_a > list_P1467822637od_a_a).
% 7.09/2.33 thf(func_def_145, type, size_s642698393od_a_a: list_P1467822637od_a_a > nat).
% 7.09/2.33 thf(func_def_146, type, size_size_list_a: list_a > nat).
% 7.09/2.33 thf(func_def_147, type, ord_less_nat: nat > nat > $o).
% 7.09/2.33 thf(func_def_148, type, pair_co_path_a: product_prod_a_a > a > list_P1467822637od_a_a > list_P1467822637od_a_a).
% 7.09/2.33 thf(func_def_149, type, pair_co_path_rel_a: produc821581462od_a_a > produc821581462od_a_a > $o).
% 7.09/2.33 thf(func_def_150, type, pair_p2140537249od_a_a: product_prod_a_a > list_P1891567085od_a_a > list_P1467822637od_a_a).
% 7.09/2.33 thf(func_def_151, type, pair_sd_path_a: product_prod_a_a > a > list_P1467822637od_a_a > list_P1467822637od_a_a).
% 7.09/2.33 thf(func_def_152, type, pair_sd_path_rel_a: produc821581462od_a_a > produc821581462od_a_a > $o).
% 7.09/2.33 thf(func_def_153, type, invers1007791577list_a: list_P1467822637od_a_a > a > a).
% 7.09/2.33 thf(func_def_154, type, invers214109608_rel_a: produc657167928_a_a_a > produc657167928_a_a_a > $o).
% 7.09/2.33 thf(func_def_155, type, list_permutes_a: list_P1467822637od_a_a > set_a > $o).
% 7.09/2.33 thf(func_def_156, type, permut1422637723list_a: list_P1467822637od_a_a > a > a).
% 7.09/2.33 thf(func_def_157, type, produc214132118od_a_a: (product_prod_a_a > product_prod_a_a > $o) > list_P1467822637od_a_a > produc501911462od_a_a).
% 7.09/2.33 thf(func_def_158, type, produc1569872215_a_nat: (a > nat) > (a > nat) > produc1178641895_a_nat).
% 7.09/2.33 thf(func_def_159, type, product_Pair_a_nat_a: (a > nat) > a > product_prod_a_nat_a).
% 7.09/2.33 thf(func_def_160, type, produc1430747863_a_nat: list_a_nat > list_a_nat > produc1334933863_a_nat).
% 7.09/2.33 thf(func_def_161, type, produc915218007od_a_a: list_l1108175539od_a_a > list_l1108175539od_a_a > produc657724903od_a_a).
% 7.09/2.33 thf(func_def_162, type, produc2583831list_a: list_list_a > list_list_a > produc403652391list_a).
% 7.09/2.33 thf(func_def_163, type, produc461662679od_a_a: list_P1891567085od_a_a > list_P1891567085od_a_a > produc205693799od_a_a).
% 7.09/2.33 thf(func_def_164, type, produc85179863od_a_a: list_P1467822637od_a_a > list_P1467822637od_a_a > produc651658087od_a_a).
% 7.09/2.33 thf(func_def_165, type, produc998622632_a_a_a: list_P1467822637od_a_a > a > produc657167928_a_a_a).
% 7.09/2.33 thf(func_def_166, type, produc1448356631list_a: list_a > list_a > produc864062247list_a).
% 7.09/2.33 thf(func_def_167, type, produc74075722_a_a_a: pair_p125712459t_unit > produc1016684094_a_a_a > produc1912141786_a_a_a).
% 7.09/2.33 thf(func_def_168, type, produc1935643479od_a_a: produc1572603623od_a_a > produc1572603623od_a_a > produc1990712039od_a_a).
% 7.09/2.33 thf(func_def_169, type, produc825466863_a_nat: product_prod_a_a > (a > nat) > produc664688895_a_nat).
% 7.09/2.33 thf(func_def_170, type, produc600870406od_a_a: product_prod_a_a > produc1701253078od_a_a > produc821581462od_a_a).
% 7.09/2.33 thf(func_def_171, type, produc1474507607od_a_a: product_prod_a_a > product_prod_a_a > produc1572603623od_a_a).
% 7.09/2.33 thf(func_def_172, type, produc2061588782_a_a_a: product_prod_a_a > a > produc1016684094_a_a_a).
% 7.09/2.33 thf(func_def_173, type, product_Pair_a_a_nat: a > (a > nat) > product_prod_a_a_nat).
% 7.09/2.33 thf(func_def_174, type, produc575024326od_a_a: a > list_P1467822637od_a_a > produc1701253078od_a_a).
% 7.09/2.33 thf(func_def_175, type, produc1440321489_a_a_a: a > produc657167928_a_a_a > produc1197928545_a_a_a).
% 7.09/2.33 thf(func_def_176, type, produc1299253312od_a_a: a > product_prod_a_a > produc1921647824od_a_a).
% 7.09/2.33 thf(func_def_177, type, product_Pair_a_a: a > a > product_prod_a_a).
% 7.09/2.33 thf(func_def_178, type, asym_a: set_Product_prod_a_a > $o).
% 7.09/2.33 thf(func_def_179, type, irrefl76447196od_a_a: set_Pr1948701895od_a_a > $o).
% 7.09/2.33 thf(func_def_180, type, irrefl_a: set_Product_prod_a_a > $o).
% 7.09/2.33 thf(func_def_181, type, collec1811041560od_a_a: (list_P1467822637od_a_a > $o) > set_li562223245od_a_a).
% 7.09/2.33 thf(func_def_182, type, collec1566074578od_a_a: (produc651658087od_a_a > $o) > set_Pr800560199od_a_a).
% 7.09/2.33 thf(func_def_183, type, collec656258194list_a: (produc864062247list_a > $o) > set_Pr1971762695list_a).
% 7.09/2.33 thf(func_def_184, type, collec645855634od_a_a: (product_prod_a_a > $o) > set_Product_prod_a_a).
% 7.09/2.33 thf(func_def_185, type, collect_a: (a > $o) > set_a).
% 7.09/2.33 thf(func_def_186, type, the_el1640649244od_a_a: set_Product_prod_a_a > product_prod_a_a).
% 7.09/2.33 thf(func_def_187, type, accp_P941981633_a_a_a: (produc657167928_a_a_a > produc657167928_a_a_a > $o) > produc657167928_a_a_a > $o).
% 7.09/2.33 thf(func_def_188, type, accp_P1029463583od_a_a: (produc821581462od_a_a > produc821581462od_a_a > $o) > produc821581462od_a_a > $o).
% 7.09/2.33 thf(func_def_189, type, member1578987478od_a_a: list_P1467822637od_a_a > set_li562223245od_a_a > $o).
% 7.09/2.33 thf(func_def_190, type, member372644687od_a_a: produc501911462od_a_a > set_Pr727105414od_a_a > $o).
% 7.09/2.33 thf(func_def_191, type, member125757712_a_nat: produc1178641895_a_nat > set_Pr1940702919_a_nat > $o).
% 7.09/2.33 thf(func_def_192, type, member688761744_a_nat: produc1334933863_a_nat > set_Pr753687879_a_nat > $o).
% 7.09/2.33 thf(func_def_193, type, member8108048od_a_a: produc657724903od_a_a > set_Pr1239640519od_a_a > $o).
% 7.09/2.33 thf(func_def_194, type, member888406864list_a: produc403652391list_a > set_Pr1742859527list_a > $o).
% 7.09/2.33 thf(func_def_195, type, member1254757008od_a_a: produc205693799od_a_a > set_Pr779272263od_a_a > $o).
% 7.09/2.33 thf(func_def_196, type, member1691432592od_a_a: produc651658087od_a_a > set_Pr800560199od_a_a > $o).
% 7.09/2.33 thf(func_def_197, type, member430654177_a_a_a: produc657167928_a_a_a > set_Pr1525541400_a_a_a > $o).
% 7.09/2.33 thf(func_def_198, type, member1250517072list_a: produc864062247list_a > set_Pr1971762695list_a > $o).
% 7.09/2.33 thf(func_def_199, type, member1899387664od_a_a: produc1990712039od_a_a > set_Pr1295299783od_a_a > $o).
% 7.09/2.33 thf(func_def_200, type, member2057358096od_a_a: produc1572603623od_a_a > set_Pr1948701895od_a_a > $o).
% 7.09/2.33 thf(func_def_201, type, member1474739327od_a_a: produc1701253078od_a_a > set_Pr248149174od_a_a > $o).
% 7.09/2.33 thf(func_def_202, type, member1904151562_a_a_a: produc1197928545_a_a_a > set_Pr110478017_a_a_a > $o).
% 7.09/2.33 thf(func_def_203, type, member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o).
% 7.09/2.33 thf(func_def_204, type, member_a2: a > set_a > $o).
% 7.09/2.33 thf(func_def_205, type, e: product_prod_a_a).
% 7.09/2.33 thf(func_def_206, type, es: list_P1467822637od_a_a).
% 7.09/2.33 thf(func_def_223, type, sK0: product_prod_a_a > a).
% 7.09/2.33 thf(func_def_224, type, sK1: product_prod_a_a > a).
% 7.09/2.33 thf(func_def_225, type, sK2: (product_prod_a_a > $o) > a).
% 7.09/2.33 thf(func_def_226, type, sK3: (product_prod_a_a > $o) > a).
% 7.09/2.33 thf(func_def_227, type, sK4: product_prod_a_a > a).
% 7.09/2.33 thf(func_def_228, type, sK5: product_prod_a_a > a).
% 7.09/2.33 thf(func_def_229, type, sK6: list_P1467822637od_a_a).
% 7.09/2.33 thf(func_def_230, type, sK7: a).
% 7.09/2.33 thf(func_def_231, type, sK8: a).
% 7.09/2.33 thf(func_def_232, type, sK9: list_P1467822637od_a_a).
% 7.09/2.33 thf(func_def_233, type, sK10: (product_prod_a_a > $o) > a).
% 7.09/2.33 thf(func_def_234, type, sK11: (product_prod_a_a > $o) > a).
% 7.09/2.33 thf(func_def_236, type, ph13: !>[X0: $tType]:(X0)).
% 7.09/2.33 thf(f960,plain,(
% 7.09/2.33 $false),
% 7.09/2.33 inference(equality_resolution,[status(thm)],[f906])).
% 7.09/2.33 thf(f906,plain,(
% 7.09/2.33 ( ! [X2 : a,X3 : a,X0 : product_prod_a_a,X1 : list_P1467822637od_a_a,X4 : list_P1467822637od_a_a] : (((cons_P1921020637od_a_a @ X0 @ (append1574001858od_a_a @ X1 @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ X2 @ X3) @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ X3 @ X2) @ X4)))) != (cons_P1921020637od_a_a @ e @ (append1574001858od_a_a @ sK6 @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ sK7 @ sK8) @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ sK8 @ sK7) @ sK9)))))) )),
% 7.09/2.33 inference(superposition,[status(thm)],[f897,f882])).
% 7.09/2.33 thf(f882,plain,(
% 7.09/2.33 ( ! [X2 : list_P1467822637od_a_a,X1 : list_P1467822637od_a_a,X4 : product_prod_a_a] : (((cons_P1921020637od_a_a @ X4 @ (append1574001858od_a_a @ X2 @ X1)) = (append1574001858od_a_a @ (cons_P1921020637od_a_a @ X4 @ X2) @ X1))) )),
% 7.09/2.33 inference(equality_resolution,[status(thm)],[f881])).
% 7.09/2.33 thf(f881,plain,(
% 7.09/2.33 ( ! [X2 : list_P1467822637od_a_a,X0 : list_P1467822637od_a_a,X1 : list_P1467822637od_a_a,X4 : product_prod_a_a] : (((cons_P1921020637od_a_a @ X4 @ (append1574001858od_a_a @ X2 @ X1)) = (append1574001858od_a_a @ X0 @ X1)) | ((cons_P1921020637od_a_a @ X4 @ X2) != X0)) )),
% 7.09/2.33 inference(equality_resolution,[status(thm)],[f871])).
% 7.09/2.33 thf(f871,plain,(
% 7.09/2.33 ( ! [X2 : list_P1467822637od_a_a,X3 : list_P1467822637od_a_a,X0 : list_P1467822637od_a_a,X1 : list_P1467822637od_a_a,X4 : product_prod_a_a] : (((append1574001858od_a_a @ X0 @ X1) = (cons_P1921020637od_a_a @ X4 @ X3)) | ((append1574001858od_a_a @ X2 @ X1) != X3) | ((cons_P1921020637od_a_a @ X4 @ X2) != X0)) )),
% 7.09/2.33 inference(cnf_transformation,[status(thm)],[f844])).
% 7.09/2.33 thf(f844,plain,(
% 7.09/2.33 ! [X0 : list_P1467822637od_a_a,X1 : list_P1467822637od_a_a,X2 : list_P1467822637od_a_a,X3 : list_P1467822637od_a_a,X4 : product_prod_a_a] : (((append1574001858od_a_a @ X0 @ X1) = (cons_P1921020637od_a_a @ X4 @ X3)) | ((append1574001858od_a_a @ X2 @ X1) != X3) | ((cons_P1921020637od_a_a @ X4 @ X2) != X0))),
% 7.09/2.33 inference(flattening,[status(thm)],[f843])).
% 7.09/2.33 thf(f843,plain,(
% 7.09/2.33 ! [X0 : list_P1467822637od_a_a,X1 : list_P1467822637od_a_a,X2 : list_P1467822637od_a_a,X3 : list_P1467822637od_a_a,X4 : product_prod_a_a] : ((((append1574001858od_a_a @ X0 @ X1) = (cons_P1921020637od_a_a @ X4 @ X3)) | ((append1574001858od_a_a @ X2 @ X1) != X3)) | ((cons_P1921020637od_a_a @ X4 @ X2) != X0))),
% 7.09/2.33 inference(ennf_transformation,[status(thm)],[f833])).
% 7.09/2.33 thf(f833,plain,(
% 7.09/2.33 ! [X0 : list_P1467822637od_a_a,X1 : list_P1467822637od_a_a,X2 : list_P1467822637od_a_a,X3 : list_P1467822637od_a_a,X4 : product_prod_a_a] : (((cons_P1921020637od_a_a @ X4 @ X2) = X0) => (((append1574001858od_a_a @ X2 @ X1) = X3) => ((append1574001858od_a_a @ X0 @ X1) = (cons_P1921020637od_a_a @ X4 @ X3))))),
% 7.09/2.33 inference(rectify,[status(thm)],[f42])).
% 7.09/2.33 thf(f42,axiom,(
% 7.09/2.33 ! [X9 : list_P1467822637od_a_a,X10 : list_P1467822637od_a_a,X22 : list_P1467822637od_a_a,X8 : list_P1467822637od_a_a,X21 : product_prod_a_a] : (((cons_P1921020637od_a_a @ X21 @ X22) = X9) => (((append1574001858od_a_a @ X22 @ X10) = X8) => ((append1574001858od_a_a @ X9 @ X10) = (cons_P1921020637od_a_a @ X21 @ X8))))),
% 7.09/2.33 file('/export/starexec/sandbox2/tmp/tmp.3Q2PF44D5Z/DTF2THF_29473.p',fact_41_Cons__eq__appendI)).
% 7.09/2.33 thf(f897,plain,(
% 7.09/2.33 ( ! [X2 : a,X3 : a,X1 : list_P1467822637od_a_a,X4 : list_P1467822637od_a_a] : (((append1574001858od_a_a @ X1 @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ X3 @ X2) @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ X2 @ X3) @ X4))) != (cons_P1921020637od_a_a @ e @ (append1574001858od_a_a @ sK6 @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ sK7 @ sK8) @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ sK8 @ sK7) @ sK9)))))) )),
% 7.09/2.33 inference(equality_proxy_clausification,[status(thm)],[f896])).
% 7.09/2.33 thf(f896,plain,(
% 7.09/2.33 ( ! [X2 : a,X3 : a,X1 : list_P1467822637od_a_a,X4 : list_P1467822637od_a_a] : ((((append1574001858od_a_a @ X1 @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ X3 @ X2) @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ X2 @ X3) @ X4))) = (cons_P1921020637od_a_a @ e @ (append1574001858od_a_a @ sK6 @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ sK7 @ sK8) @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ sK8 @ sK7) @ sK9))))) = $false)) )),
% 7.09/2.33 inference(not_proxy_clausification,[status(thm)],[f895])).
% 7.09/2.33 thf(f895,plain,(
% 7.09/2.33 ( ! [X2 : a,X3 : a,X1 : list_P1467822637od_a_a,X4 : list_P1467822637od_a_a] : (($true = (~ ((append1574001858od_a_a @ X1 @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ X3 @ X2) @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ X2 @ X3) @ X4))) = (cons_P1921020637od_a_a @ e @ (append1574001858od_a_a @ sK6 @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ sK7 @ sK8) @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ sK8 @ sK7) @ sK9)))))))) )),
% 7.09/2.33 inference(beta_eta_normalization,[status(thm)],[f894])).
% 7.09/2.33 thf(f894,plain,(
% 7.09/2.33 ( ! [X2 : a,X3 : a,X1 : list_P1467822637od_a_a,X4 : list_P1467822637od_a_a] : (($true = ((^[Y0 : list_P1467822637od_a_a]: (~ ((append1574001858od_a_a @ X1 @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ X3 @ X2) @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ X2 @ X3) @ Y0))) = (cons_P1921020637od_a_a @ e @ (append1574001858od_a_a @ sK6 @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ sK7 @ sK8) @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ sK8 @ sK7) @ sK9))))))) @ X4))) )),
% 7.09/2.33 inference(pi_clausification,[status(thm)],[f893])).
% 7.09/2.33 thf(f893,plain,(
% 7.09/2.33 ( ! [X2 : a,X3 : a,X1 : list_P1467822637od_a_a] : (($true = (!! @ list_P1467822637od_a_a @ (^[Y0 : list_P1467822637od_a_a]: (~ ((append1574001858od_a_a @ X1 @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ X3 @ X2) @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ X2 @ X3) @ Y0))) = (cons_P1921020637od_a_a @ e @ (append1574001858od_a_a @ sK6 @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ sK7 @ sK8) @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ sK8 @ sK7) @ sK9)))))))))) )),
% 7.09/2.33 inference(beta_eta_normalization,[status(thm)],[f892])).
% 7.09/2.33 thf(f892,plain,(
% 7.09/2.33 ( ! [X2 : a,X3 : a,X1 : list_P1467822637od_a_a] : (($true = ((^[Y0 : a]: (!! @ list_P1467822637od_a_a @ (^[Y1 : list_P1467822637od_a_a]: (~ ((append1574001858od_a_a @ X1 @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ Y0 @ X2) @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ X2 @ Y0) @ Y1))) = (cons_P1921020637od_a_a @ e @ (append1574001858od_a_a @ sK6 @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ sK7 @ sK8) @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ sK8 @ sK7) @ sK9))))))))) @ X3))) )),
% 7.09/2.33 inference(pi_clausification,[status(thm)],[f891])).
% 7.09/2.33 thf(f891,plain,(
% 7.09/2.33 ( ! [X2 : a,X1 : list_P1467822637od_a_a] : (($true = (!! @ a @ (^[Y0 : a]: (!! @ list_P1467822637od_a_a @ (^[Y1 : list_P1467822637od_a_a]: (~ ((append1574001858od_a_a @ X1 @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ Y0 @ X2) @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ X2 @ Y0) @ Y1))) = (cons_P1921020637od_a_a @ e @ (append1574001858od_a_a @ sK6 @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ sK7 @ sK8) @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ sK8 @ sK7) @ sK9)))))))))))) )),
% 7.09/2.33 inference(beta_eta_normalization,[status(thm)],[f890])).
% 7.09/2.33 thf(f890,plain,(
% 7.09/2.33 ( ! [X2 : a,X1 : list_P1467822637od_a_a] : (($true = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ list_P1467822637od_a_a @ (^[Y2 : list_P1467822637od_a_a]: (~ ((append1574001858od_a_a @ X1 @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ Y1 @ Y0) @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ Y0 @ Y1) @ Y2))) = (cons_P1921020637od_a_a @ e @ (append1574001858od_a_a @ sK6 @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ sK7 @ sK8) @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ sK8 @ sK7) @ sK9))))))))))) @ X2))) )),
% 7.09/2.33 inference(pi_clausification,[status(thm)],[f889])).
% 7.09/2.33 thf(f889,plain,(
% 7.09/2.33 ( ! [X1 : list_P1467822637od_a_a] : (($true = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ list_P1467822637od_a_a @ (^[Y2 : list_P1467822637od_a_a]: (~ ((append1574001858od_a_a @ X1 @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ Y1 @ Y0) @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ Y0 @ Y1) @ Y2))) = (cons_P1921020637od_a_a @ e @ (append1574001858od_a_a @ sK6 @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ sK7 @ sK8) @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ sK8 @ sK7) @ sK9)))))))))))))) )),
% 7.09/2.33 inference(beta_eta_normalization,[status(thm)],[f888])).
% 7.09/2.33 thf(f888,plain,(
% 7.09/2.33 ( ! [X1 : list_P1467822637od_a_a] : (($true = ((^[Y0 : list_P1467822637od_a_a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ list_P1467822637od_a_a @ (^[Y3 : list_P1467822637od_a_a]: (~ ((append1574001858od_a_a @ Y0 @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ Y2 @ Y1) @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ Y1 @ Y2) @ Y3))) = (cons_P1921020637od_a_a @ e @ (append1574001858od_a_a @ sK6 @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ sK7 @ sK8) @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ sK8 @ sK7) @ sK9))))))))))))) @ X1))) )),
% 7.09/2.33 inference(pi_clausification,[status(thm)],[f887])).
% 7.09/2.33 thf(f887,plain,(
% 7.09/2.33 ($true = (!! @ list_P1467822637od_a_a @ (^[Y0 : list_P1467822637od_a_a]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ list_P1467822637od_a_a @ (^[Y3 : list_P1467822637od_a_a]: (~ ((append1574001858od_a_a @ Y0 @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ Y2 @ Y1) @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ Y1 @ Y2) @ Y3))) = (cons_P1921020637od_a_a @ e @ (append1574001858od_a_a @ sK6 @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ sK7 @ sK8) @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ sK8 @ sK7) @ sK9)))))))))))))))),
% 7.09/2.33 inference(beta_eta_normalization,[status(thm)],[f879])).
% 7.09/2.33 thf(f879,plain,(
% 7.09/2.33 ($true = ((^[Y0 : list_P1467822637od_a_a]: (!! @ list_P1467822637od_a_a @ (^[Y1 : list_P1467822637od_a_a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ list_P1467822637od_a_a @ (^[Y4 : list_P1467822637od_a_a]: (~ ((append1574001858od_a_a @ Y1 @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ Y3 @ Y2) @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ Y2 @ Y3) @ Y4))) = Y0))))))))))) @ (cons_P1921020637od_a_a @ e @ (append1574001858od_a_a @ sK6 @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ sK7 @ sK8) @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ sK8 @ sK7) @ sK9))))))),
% 7.09/2.33 inference(definition_unfolding,[status(thm)],[f873,f874,f866])).
% 7.09/2.33 thf(f866,plain,(
% 7.09/2.33 (es = (append1574001858od_a_a @ sK6 @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ sK7 @ sK8) @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ sK8 @ sK7) @ sK9))))),
% 7.09/2.33 inference(cnf_transformation,[status(thm)],[f856])).
% 7.09/2.33 thf(f856,plain,(
% 7.09/2.33 (es = (append1574001858od_a_a @ sK6 @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ sK7 @ sK8) @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ sK8 @ sK7) @ sK9))))),
% 7.09/2.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9])],[f847,f855])).
% 7.09/2.33 thf(f855,plain,(
% 7.09/2.33 ? [X0 : list_P1467822637od_a_a,X1 : a,X2 : a,X3 : list_P1467822637od_a_a] : (es = (append1574001858od_a_a @ X0 @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ X1 @ X2) @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ X2 @ X1) @ X3)))) => (es = (append1574001858od_a_a @ sK6 @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ sK7 @ sK8) @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ sK8 @ sK7) @ sK9))))),
% 7.09/2.33 introduced(definition,[],[choice_axiom])).
% 7.09/2.33 thf(f847,plain,(
% 7.09/2.33 ? [X0 : list_P1467822637od_a_a,X1 : a,X2 : a,X3 : list_P1467822637od_a_a] : (es = (append1574001858od_a_a @ X0 @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ X1 @ X2) @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ X2 @ X1) @ X3))))),
% 7.09/2.33 inference(ennf_transformation,[status(thm)],[f830])).
% 7.09/2.33 thf(f830,plain,(
% 7.09/2.33 ~! [X0 : list_P1467822637od_a_a,X1 : a,X2 : a,X3 : list_P1467822637od_a_a] : (es != (append1574001858od_a_a @ X0 @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ X1 @ X2) @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ X2 @ X1) @ X3))))),
% 7.09/2.33 inference(rectify,[status(thm)],[f360])).
% 7.09/2.33 thf(f360,negated_conjecture,(
% 7.09/2.33 ~! [X63 : list_P1467822637od_a_a,X33 : a,X34 : a,X64 : list_P1467822637od_a_a] : (es != (append1574001858od_a_a @ X63 @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ X33 @ X34) @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ X34 @ X33) @ X64))))),
% 7.09/2.33 inference(negated_conjecture,[status(cth)],[f359])).
% 7.09/2.33 thf(f359,conjecture,(
% 7.09/2.33 ! [X63 : list_P1467822637od_a_a,X33 : a,X34 : a,X64 : list_P1467822637od_a_a] : (es != (append1574001858od_a_a @ X63 @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ X33 @ X34) @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ X34 @ X33) @ X64))))),
% 7.09/2.33 file('/export/starexec/sandbox2/tmp/tmp.3Q2PF44D5Z/DTF2THF_29473.p',conj_0)).
% 7.09/2.33 thf(f874,plain,(
% 7.09/2.33 (kurato1072996284sing_a = (^[Y0 : list_P1467822637od_a_a]: (!! @ list_P1467822637od_a_a @ (^[Y1 : list_P1467822637od_a_a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ list_P1467822637od_a_a @ (^[Y4 : list_P1467822637od_a_a]: (~ ((append1574001858od_a_a @ Y1 @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ Y3 @ Y2) @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ Y2 @ Y3) @ Y4))) = Y0))))))))))))),
% 7.09/2.33 inference(cnf_transformation,[status(thm)],[f611])).
% 7.09/2.33 thf(f611,plain,(
% 7.09/2.33 (kurato1072996284sing_a = (^[Y0 : list_P1467822637od_a_a]: (!! @ list_P1467822637od_a_a @ (^[Y1 : list_P1467822637od_a_a]: (!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (!! @ list_P1467822637od_a_a @ (^[Y4 : list_P1467822637od_a_a]: (~ ((append1574001858od_a_a @ Y1 @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ Y3 @ Y2) @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ Y2 @ Y3) @ Y4))) = Y0))))))))))))),
% 7.09/2.33 inference(fool_elimination,[status(thm)],[f610])).
% 7.09/2.33 thf(f610,plain,(
% 7.09/2.33 (kurato1072996284sing_a = (^[X0 : list_P1467822637od_a_a] : (! [X1 : list_P1467822637od_a_a,X2 : a,X3 : a,X4 : list_P1467822637od_a_a] : ((append1574001858od_a_a @ X4 @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ X2 @ X3) @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ X3 @ X2) @ X1))) != X0))))),
% 7.09/2.33 inference(rectify,[status(thm)],[f4])).
% 7.09/2.33 thf(f4,axiom,(
% 7.09/2.33 (kurato1072996284sing_a = (^[X0 : list_P1467822637od_a_a] : (! [X4 : list_P1467822637od_a_a,X2 : a,X3 : a,X1 : list_P1467822637od_a_a] : ((append1574001858od_a_a @ X1 @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ X2 @ X3) @ (cons_P1921020637od_a_a @ (product_Pair_a_a @ X3 @ X2) @ X4))) != X0))))),
% 7.09/2.33 file('/export/starexec/sandbox2/tmp/tmp.3Q2PF44D5Z/DTF2THF_29473.p',fact_3_progressing__def)).
% 7.09/2.33 thf(f873,plain,(
% 7.09/2.33 ((kurato1072996284sing_a @ (cons_P1921020637od_a_a @ e @ es)) = $true)),
% 7.09/2.33 inference(cnf_transformation,[status(thm)],[f521])).
% 7.09/2.33 thf(f521,plain,(
% 7.09/2.33 ((kurato1072996284sing_a @ (cons_P1921020637od_a_a @ e @ es)) = $true)),
% 7.09/2.33 inference(fool_elimination,[status(thm)],[f520])).
% 7.09/2.33 thf(f520,plain,(
% 7.09/2.33 (kurato1072996284sing_a @ (cons_P1921020637od_a_a @ e @ es))),
% 7.09/2.33 inference(rectify,[status(thm)],[f1])).
% 7.09/2.33 thf(f1,axiom,(
% 7.09/2.33 (kurato1072996284sing_a @ (cons_P1921020637od_a_a @ e @ es))),
% 7.09/2.33 file('/export/starexec/sandbox2/tmp/tmp.3Q2PF44D5Z/DTF2THF_29473.p',fact_0_assms)).
% 7.09/2.33 % SZS output end Proof for DTF2THF_29473
% 7.09/2.33 % (29760)------------------------------
% 7.09/2.33 % (29760)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.09/2.33 % (29760)Termination reason: Refutation
% 7.09/2.33
% 7.09/2.33 % (29760)Memory used [KB]: 7164
% 7.09/2.33 % (29760)Time elapsed: 0.037 s
% 7.09/2.33 % (29760)Instructions burned: 111 (million)
% 7.09/2.33 % (29760)------------------------------
% 7.09/2.33 % (29760)------------------------------
% 7.09/2.33 % (29687)Success in time 0.706 s
%------------------------------------------------------------------------------