%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ITP157^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:24:24 AM UTC 2026
% Result : Theorem 43.76s 7.66s
% Output : CNFRefutation 43.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 132
% Syntax : Number of formulae : 2222 ( 932 unt; 0 typ; 0 def)
% Number of atoms : 15498 (5692 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 32484 (4678 ~;4100 |; 75 &;23196 @)
% ( 0 <=>; 435 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Number of types : 31 ( 30 usr)
% Number of type conns : 1069 (1069 >; 0 *; 0 +; 0 <<)
% Number of symbols : 208 ( 205 usr; 13 con; 0-4 aty)
% Number of variables : 8771 (1023 ^;7730 !; 18 ?;8771 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_produc1016684094_a_a_a,type,
produc1016684094_a_a_a: $tType ).
thf(tp_produc1056976615od_a_a,type,
produc1056976615od_a_a: $tType ).
thf(tp_produc1120419623_a_a_a,type,
produc1120419623_a_a_a: $tType ).
thf(tp_produc1423126247od_a_a,type,
produc1423126247od_a_a: $tType ).
thf(tp_produc1546279079od_a_a,type,
produc1546279079od_a_a: $tType ).
thf(tp_produc1555800720od_a_a,type,
produc1555800720od_a_a: $tType ).
thf(tp_produc1572603623od_a_a,type,
produc1572603623od_a_a: $tType ).
thf(tp_produc1683075710_a_a_a,type,
produc1683075710_a_a_a: $tType ).
thf(tp_produc1921647824od_a_a,type,
produc1921647824od_a_a: $tType ).
thf(tp_produc1990712039od_a_a,type,
produc1990712039od_a_a: $tType ).
thf(tp_produc2010915495od_a_a,type,
produc2010915495od_a_a: $tType ).
thf(tp_produc47586087od_a_a,type,
produc47586087od_a_a: $tType ).
thf(tp_produc772425383od_a_a,type,
produc772425383od_a_a: $tType ).
thf(tp_product_prod_a_a,type,
product_prod_a_a: $tType ).
thf(tp_set_Pr1194146439od_a_a,type,
set_Pr1194146439od_a_a: $tType ).
thf(tp_set_Pr1295299783od_a_a,type,
set_Pr1295299783od_a_a: $tType ).
thf(tp_set_Pr1689873822_a_a_a,type,
set_Pr1689873822_a_a_a: $tType ).
thf(tp_set_Pr173461255od_a_a,type,
set_Pr173461255od_a_a: $tType ).
thf(tp_set_Pr1948701895od_a_a,type,
set_Pr1948701895od_a_a: $tType ).
thf(tp_set_Pr195866352od_a_a,type,
set_Pr195866352od_a_a: $tType ).
thf(tp_set_Pr2081559751od_a_a,type,
set_Pr2081559751od_a_a: $tType ).
thf(tp_set_Pr231806599od_a_a,type,
set_Pr231806599od_a_a: $tType ).
thf(tp_set_Pr532616391od_a_a,type,
set_Pr532616391od_a_a: $tType ).
thf(tp_set_Pr6137822_a_a_a,type,
set_Pr6137822_a_a_a: $tType ).
thf(tp_set_Pr660101255od_a_a,type,
set_Pr660101255od_a_a: $tType ).
thf(tp_set_Pr681306928od_a_a,type,
set_Pr681306928od_a_a: $tType ).
thf(tp_set_Pr729215751_a_a_a,type,
set_Pr729215751_a_a_a: $tType ).
thf(tp_set_Product_prod_a_a,type,
set_Product_prod_a_a: $tType ).
thf(tp_set_a,type,
set_a: $tType ).
thf(tp_b,type,
b: set_a ).
thf(tp_bNF_Gr1372473186od_a_a,type,
bNF_Gr1372473186od_a_a: set_Product_prod_a_a > ( product_prod_a_a > product_prod_a_a ) > set_Pr1948701895od_a_a ).
thf(tp_bNF_Gr1715025636od_a_a,type,
bNF_Gr1715025636od_a_a: set_a > ( a > product_prod_a_a ) > ( a > product_prod_a_a ) > set_Pr1948701895od_a_a ).
thf(tp_bNF_Gr1853143117_a_a_a,type,
bNF_Gr1853143117_a_a_a: set_Product_prod_a_a > ( product_prod_a_a > a ) > ( product_prod_a_a > a ) > set_Product_prod_a_a ).
thf(tp_bNF_Gr200450189od_a_a,type,
bNF_Gr200450189od_a_a: set_Product_prod_a_a > ( product_prod_a_a > product_prod_a_a ) > ( product_prod_a_a > product_prod_a_a ) > set_Pr1948701895od_a_a ).
thf(tp_bNF_Gr356189709_a_a_a,type,
bNF_Gr356189709_a_a_a: set_Pr1948701895od_a_a > ( produc1572603623od_a_a > a ) > ( produc1572603623od_a_a > a ) > set_Product_prod_a_a ).
thf(tp_bNF_Gr423046308_a_a_a,type,
bNF_Gr423046308_a_a_a: set_a > ( a > a ) > ( a > a ) > set_Product_prod_a_a ).
thf(tp_bNF_Gr533818957od_a_a,type,
bNF_Gr533818957od_a_a: set_Pr1948701895od_a_a > ( produc1572603623od_a_a > product_prod_a_a ) > ( produc1572603623od_a_a > product_prod_a_a ) > set_Pr1948701895od_a_a ).
thf(tp_bNF_Gr_a_a,type,
bNF_Gr_a_a: set_a > ( a > a ) > set_Product_prod_a_a ).
thf(tp_bot_bo1116205875od_a_a,type,
bot_bo1116205875od_a_a: set_Pr1948701895od_a_a ).
thf(tp_bot_bo2131659635od_a_a,type,
bot_bo2131659635od_a_a: set_Product_prod_a_a ).
thf(tp_bot_bot_set_a,type,
bot_bot_set_a: set_a ).
thf(tp_collec1635618130od_a_a,type,
collec1635618130od_a_a: ( produc1572603623od_a_a > $o ) > set_Pr1948701895od_a_a ).
thf(tp_collec645855634od_a_a,type,
collec645855634od_a_a: ( product_prod_a_a > $o ) > set_Product_prod_a_a ).
thf(tp_collect_a,type,
collect_a: ( a > $o ) > set_a ).
thf(tp_image_1105229276_a_a_a,type,
image_1105229276_a_a_a: ( produc1572603623od_a_a > a ) > set_Pr1948701895od_a_a > set_a ).
thf(tp_image_1725938350od_a_a,type,
image_1725938350od_a_a: ( a > product_prod_a_a ) > set_a > set_Product_prod_a_a ).
thf(tp_image_1763923566od_a_a,type,
image_1763923566od_a_a: ( a > produc1572603623od_a_a ) > set_a > set_Pr1948701895od_a_a ).
thf(tp_image_1765377413od_a_a,type,
image_1765377413od_a_a: ( product_prod_a_a > produc1572603623od_a_a ) > set_Product_prod_a_a > set_Pr1948701895od_a_a ).
thf(tp_image_236793797od_a_a,type,
image_236793797od_a_a: ( produc1572603623od_a_a > produc1572603623od_a_a ) > set_Pr1948701895od_a_a > set_Pr1948701895od_a_a ).
thf(tp_image_340790172_a_a_a,type,
image_340790172_a_a_a: ( product_prod_a_a > a ) > set_Product_prod_a_a > set_a ).
thf(tp_image_734753285od_a_a,type,
image_734753285od_a_a: ( produc1572603623od_a_a > product_prod_a_a ) > set_Pr1948701895od_a_a > set_Product_prod_a_a ).
thf(tp_image_794773445od_a_a,type,
image_794773445od_a_a: ( product_prod_a_a > product_prod_a_a ) > set_Product_prod_a_a > set_Product_prod_a_a ).
thf(tp_image_a_a,type,
image_a_a: ( a > a ) > set_a > set_a ).
thf(tp_lex_pr1321960536od_a_a,type,
lex_pr1321960536od_a_a: set_Product_prod_a_a > set_Pr1948701895od_a_a > set_Pr231806599od_a_a ).
thf(tp_lex_pr2084296006_a_a_a,type,
lex_pr2084296006_a_a_a: set_Pr1948701895od_a_a > set_Product_prod_a_a > set_Pr729215751_a_a_a ).
thf(tp_lex_pr942790511od_a_a,type,
lex_pr942790511od_a_a: set_Pr1948701895od_a_a > set_Pr1948701895od_a_a > set_Pr1295299783od_a_a ).
thf(tp_lex_prod_a_a,type,
lex_prod_a_a: set_Product_prod_a_a > set_Product_prod_a_a > set_Pr1948701895od_a_a ).
thf(tp_member122808528od_a_a,type,
member122808528od_a_a: produc772425383od_a_a > set_Pr1194146439od_a_a > $o ).
thf(tp_member1361298640od_a_a,type,
member1361298640od_a_a: produc2010915495od_a_a > set_Pr231806599od_a_a > $o ).
thf(tp_member1403138919_a_a_a,type,
member1403138919_a_a_a: produc1016684094_a_a_a > set_Pr1689873822_a_a_a > $o ).
thf(tp_member1424209616od_a_a,type,
member1424209616od_a_a: produc1546279079od_a_a > set_Pr660101255od_a_a > $o ).
thf(tp_member1545452880od_a_a,type,
member1545452880od_a_a: produc47586087od_a_a > set_Pr173461255od_a_a > $o ).
thf(tp_member160619001od_a_a,type,
member160619001od_a_a: produc1921647824od_a_a > set_Pr681306928od_a_a > $o ).
thf(tp_member180906768od_a_a,type,
member180906768od_a_a: produc1056976615od_a_a > set_Pr532616391od_a_a > $o ).
thf(tp_member1899387664od_a_a,type,
member1899387664od_a_a: produc1990712039od_a_a > set_Pr1295299783od_a_a > $o ).
thf(tp_member2057358096od_a_a,type,
member2057358096od_a_a: produc1572603623od_a_a > set_Pr1948701895od_a_a > $o ).
thf(tp_member448091577od_a_a,type,
member448091577od_a_a: produc1555800720od_a_a > set_Pr195866352od_a_a > $o ).
thf(tp_member449909584od_a_a,type,
member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
thf(tp_member470802768_a_a_a,type,
member470802768_a_a_a: produc1120419623_a_a_a > set_Pr729215751_a_a_a > $o ).
thf(tp_member547056400od_a_a,type,
member547056400od_a_a: produc1423126247od_a_a > set_Pr2081559751od_a_a > $o ).
thf(tp_member575366567_a_a_a,type,
member575366567_a_a_a: produc1683075710_a_a_a > set_Pr6137822_a_a_a > $o ).
thf(tp_member_a,type,
member_a: a > set_a > $o ).
thf(tp_minus_1034916142od_a_a,type,
minus_1034916142od_a_a: set_Pr1948701895od_a_a > set_Pr1948701895od_a_a > set_Pr1948701895od_a_a ).
thf(tp_minus_107310383_a_a_o,type,
minus_107310383_a_a_o: ( produc1572603623od_a_a > $o ) > ( produc1572603623od_a_a > $o ) > produc1572603623od_a_a > $o ).
thf(tp_minus_1507102574od_a_a,type,
minus_1507102574od_a_a: set_Product_prod_a_a > set_Product_prod_a_a > set_Product_prod_a_a ).
thf(tp_minus_1797478127_a_a_o,type,
minus_1797478127_a_a_o: ( product_prod_a_a > $o ) > ( product_prod_a_a > $o ) > product_prod_a_a > $o ).
thf(tp_minus_minus_a_o,type,
minus_minus_a_o: ( a > $o ) > ( a > $o ) > a > $o ).
thf(tp_minus_minus_set_a,type,
minus_minus_set_a: set_a > set_a > set_a ).
thf(tp_ord_le1347718902_a_a_o,type,
ord_le1347718902_a_a_o: ( product_prod_a_a > $o ) > ( product_prod_a_a > $o ) > $o ).
thf(tp_ord_le1525442358_a_a_o,type,
ord_le1525442358_a_a_o: ( produc1572603623od_a_a > $o ) > ( produc1572603623od_a_a > $o ) > $o ).
thf(tp_ord_le1824328871od_a_a,type,
ord_le1824328871od_a_a: set_Product_prod_a_a > set_Product_prod_a_a > $o ).
thf(tp_ord_le252190158_a_a_o,type,
ord_le252190158_a_a_o: ( product_prod_a_a > product_prod_a_a > $o ) > ( product_prod_a_a > product_prod_a_a > $o ) > $o ).
thf(tp_ord_le456379495od_a_a,type,
ord_le456379495od_a_a: set_Pr1948701895od_a_a > set_Pr1948701895od_a_a > $o ).
thf(tp_ord_less_eq_a_a_o,type,
ord_less_eq_a_a_o: ( a > a > $o ) > ( a > a > $o ) > $o ).
thf(tp_ord_less_eq_a_o,type,
ord_less_eq_a_o: ( a > $o ) > ( a > $o ) > $o ).
thf(tp_ord_less_eq_set_a,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(tp_order_359341630od_a_a,type,
order_359341630od_a_a: set_Product_prod_a_a > set_Pr1948701895od_a_a > $o ).
thf(tp_order_491428350od_a_a,type,
order_491428350od_a_a: set_Pr1948701895od_a_a > set_Pr1295299783od_a_a > $o ).
thf(tp_order_preorder_on_a,type,
order_preorder_on_a: set_a > set_Product_prod_a_a > $o ).
thf(tp_pr,type,
pr: set_Product_prod_a_a ).
thf(tp_prefer1292084992ence_a,type,
prefer1292084992ence_a: set_a > set_Product_prod_a_a > $o ).
thf(tp_prefer1338892073od_a_a,type,
prefer1338892073od_a_a: set_Product_prod_a_a > set_Pr1948701895od_a_a > $o ).
thf(tp_prefer1377343203od_a_a,type,
prefer1377343203od_a_a: produc772425383od_a_a > set_Pr1194146439od_a_a > set_Pr2081559751od_a_a > set_Pr1194146439od_a_a ).
thf(tp_prefer1409946857od_a_a,type,
prefer1409946857od_a_a: set_Pr1948701895od_a_a > set_Pr1295299783od_a_a > $o ).
thf(tp_prefer1498087410od_a_a,type,
prefer1498087410od_a_a: product_prod_a_a > set_Product_prod_a_a > set_Pr1948701895od_a_a > set_Product_prod_a_a ).
thf(tp_prefer161218362good_a,type,
prefer161218362good_a: a > set_a > set_Product_prod_a_a > set_a ).
thf(tp_prefer1676310729than_a,type,
prefer1676310729than_a: a > set_a > set_Product_prod_a_a > set_a ).
thf(tp_prefer1867335523od_a_a,type,
prefer1867335523od_a_a: produc1572603623od_a_a > set_Pr1948701895od_a_a > set_Pr1295299783od_a_a > set_Pr1948701895od_a_a ).
thf(tp_prefer1944486522_a_a_a,type,
prefer1944486522_a_a_a: produc1016684094_a_a_a > set_Pr1689873822_a_a_a > set_Pr729215751_a_a_a > set_Pr1689873822_a_a_a ).
thf(tp_prefer436369274d_as_a,type,
prefer436369274d_as_a: a > set_a > set_Product_prod_a_a > set_a ).
thf(tp_prefer445484748od_a_a,type,
prefer445484748od_a_a: produc1555800720od_a_a > set_Pr195866352od_a_a > set_Pr660101255od_a_a > set_Pr195866352od_a_a ).
thf(tp_prefer468349667od_a_a,type,
prefer468349667od_a_a: produc2010915495od_a_a > set_Pr231806599od_a_a > set_Pr532616391od_a_a > set_Pr231806599od_a_a ).
thf(tp_prefer477097315od_a_a,type,
prefer477097315od_a_a: product_prod_a_a > set_Product_prod_a_a > set_Pr1948701895od_a_a > set_Product_prod_a_a ).
thf(tp_prefer55414563od_a_a,type,
prefer55414563od_a_a: produc1572603623od_a_a > set_Pr1948701895od_a_a > set_Pr1295299783od_a_a > set_Pr1948701895od_a_a ).
thf(tp_prefer701966604od_a_a,type,
prefer701966604od_a_a: produc1921647824od_a_a > set_Pr681306928od_a_a > set_Pr231806599od_a_a > set_Pr681306928od_a_a ).
thf(tp_prefer74720675od_a_a,type,
prefer74720675od_a_a: product_prod_a_a > set_Product_prod_a_a > set_Pr1948701895od_a_a > set_Product_prod_a_a ).
thf(tp_prefer926864306od_a_a,type,
prefer926864306od_a_a: produc1572603623od_a_a > set_Pr1948701895od_a_a > set_Pr1295299783od_a_a > set_Pr1948701895od_a_a ).
thf(tp_produc1043497516od_a_a,type,
produc1043497516od_a_a: produc1921647824od_a_a > a ).
thf(tp_produc1055472197od_a_a,type,
produc1055472197od_a_a: produc772425383od_a_a > produc1572603623od_a_a ).
thf(tp_produc1095491584od_a_a,type,
produc1095491584od_a_a: a > produc1572603623od_a_a > produc1555800720od_a_a ).
thf(tp_produc1191685998od_a_a,type,
produc1191685998od_a_a: produc1921647824od_a_a > product_prod_a_a ).
thf(tp_produc1227942600od_a_a,type,
produc1227942600od_a_a: set_Product_prod_a_a > ( product_prod_a_a > set_Pr1948701895od_a_a ) > set_Pr1194146439od_a_a ).
thf(tp_produc1282482655_a_a_a,type,
produc1282482655_a_a_a: set_Product_prod_a_a > ( product_prod_a_a > set_a ) > set_Pr1689873822_a_a_a ).
thf(tp_produc1299253312od_a_a,type,
produc1299253312od_a_a: a > product_prod_a_a > produc1921647824od_a_a ).
thf(tp_produc1441227909od_a_a,type,
produc1441227909od_a_a: produc1990712039od_a_a > produc1572603623od_a_a ).
thf(tp_produc1460477704od_a_a,type,
produc1460477704od_a_a: set_Pr1948701895od_a_a > ( produc1572603623od_a_a > set_Pr1948701895od_a_a ) > set_Pr1295299783od_a_a ).
thf(tp_produc1474507607od_a_a,type,
produc1474507607od_a_a: product_prod_a_a > product_prod_a_a > produc1572603623od_a_a ).
thf(tp_produc1555606807od_a_a,type,
produc1555606807od_a_a: product_prod_a_a > produc1572603623od_a_a > produc772425383od_a_a ).
thf(tp_produc1573596055od_a_a,type,
produc1573596055od_a_a: produc1555800720od_a_a > produc1555800720od_a_a > produc1546279079od_a_a ).
thf(tp_produc1641853175od_a_a,type,
produc1641853175od_a_a: produc1572603623od_a_a > produc1572603623od_a_a ).
thf(tp_produc1775747843od_a_a,type,
produc1775747843od_a_a: produc772425383od_a_a > product_prod_a_a ).
thf(tp_produc1779756150od_a_a,type,
produc1779756150od_a_a: ( product_prod_a_a > product_prod_a_a ) > ( product_prod_a_a > product_prod_a_a ) > produc1572603623od_a_a > produc1572603623od_a_a ).
thf(tp_produc1805832986_a_a_a,type,
produc1805832986_a_a_a: produc1016684094_a_a_a > product_prod_a_a ).
thf(tp_produc1935643479od_a_a,type,
produc1935643479od_a_a: produc1572603623od_a_a > produc1572603623od_a_a > produc1990712039od_a_a ).
thf(tp_produc1954021468_a_a_a,type,
produc1954021468_a_a_a: produc1016684094_a_a_a > a ).
thf(tp_produc197318472od_a_a,type,
produc197318472od_a_a: set_Pr1948701895od_a_a > ( produc1572603623od_a_a > set_Product_prod_a_a ) > set_Pr173461255od_a_a ).
thf(tp_produc2012818120od_a_a,type,
produc2012818120od_a_a: ( a > product_prod_a_a ) > ( a > product_prod_a_a ) > product_prod_a_a > produc1572603623od_a_a ).
thf(tp_produc2019352922_a_a_a,type,
produc2019352922_a_a_a: produc1683075710_a_a_a > produc1572603623od_a_a ).
thf(tp_produc2054708503_a_a_a,type,
produc2054708503_a_a_a: produc1016684094_a_a_a > produc1016684094_a_a_a > produc1120419623_a_a_a ).
thf(tp_produc2061588782_a_a_a,type,
produc2061588782_a_a_a: product_prod_a_a > a > produc1016684094_a_a_a ).
thf(tp_produc2115494211od_a_a,type,
produc2115494211od_a_a: produc1572603623od_a_a > product_prod_a_a ).
thf(tp_produc24848069od_a_a,type,
produc24848069od_a_a: produc47586087od_a_a > product_prod_a_a ).
thf(tp_produc262335132_a_a_a,type,
produc262335132_a_a_a: produc1683075710_a_a_a > a ).
thf(tp_produc303632707od_a_a,type,
produc303632707od_a_a: produc1990712039od_a_a > produc1572603623od_a_a ).
thf(tp_produc304751368od_a_a,type,
produc304751368od_a_a: set_Product_prod_a_a > ( product_prod_a_a > set_Product_prod_a_a ) > set_Pr1948701895od_a_a ).
thf(tp_produc363290532_a_a_a,type,
produc363290532_a_a_a: ( product_prod_a_a > a ) > ( product_prod_a_a > a ) > produc1572603623od_a_a > product_prod_a_a ).
thf(tp_produc368344197od_a_a,type,
produc368344197od_a_a: produc1572603623od_a_a > product_prod_a_a ).
thf(tp_produc436797294_a_a_a,type,
produc436797294_a_a_a: produc1572603623od_a_a > a > produc1683075710_a_a_a ).
thf(tp_produc4724255_a_a_a,type,
produc4724255_a_a_a: set_Pr1948701895od_a_a > ( produc1572603623od_a_a > set_a ) > set_Pr6137822_a_a_a ).
thf(tp_produc520147185od_a_a,type,
produc520147185od_a_a: set_a > ( a > set_Product_prod_a_a ) > set_Pr681306928od_a_a ).
thf(tp_produc524982679od_a_a,type,
produc524982679od_a_a: produc1572603623od_a_a > product_prod_a_a > produc47586087od_a_a ).
thf(tp_produc530563564od_a_a,type,
produc530563564od_a_a: produc1555800720od_a_a > a ).
thf(tp_produc539587415od_a_a,type,
produc539587415od_a_a: produc2010915495od_a_a > produc2010915495od_a_a > produc1056976615od_a_a ).
thf(tp_produc563767703od_a_a,type,
produc563767703od_a_a: produc1921647824od_a_a > produc1921647824od_a_a > produc2010915495od_a_a ).
thf(tp_produc663418545od_a_a,type,
produc663418545od_a_a: set_a > ( a > set_Pr1948701895od_a_a ) > set_Pr195866352od_a_a ).
thf(tp_produc700022774_a_a_a,type,
produc700022774_a_a_a: ( a > a ) > ( a > a ) > product_prod_a_a > product_prod_a_a ).
thf(tp_produc745123715od_a_a,type,
produc745123715od_a_a: produc47586087od_a_a > produc1572603623od_a_a ).
thf(tp_produc852390743od_a_a,type,
produc852390743od_a_a: produc772425383od_a_a > produc772425383od_a_a > produc1423126247od_a_a ).
thf(tp_produc905674258od_a_a,type,
produc905674258od_a_a: set_Product_prod_a_a > set_Product_prod_a_a > set_Pr1948701895od_a_a ).
thf(tp_produc921029422od_a_a,type,
produc921029422od_a_a: produc1555800720od_a_a > produc1572603623od_a_a ).
thf(tp_produc94438221_a_a_o,type,
produc94438221_a_a_o: ( produc1572603623od_a_a > $o ) > product_prod_a_a > product_prod_a_a > $o ).
thf(tp_product_Pair_a_a,type,
product_Pair_a_a: a > a > product_prod_a_a ).
thf(tp_product_Sigma_a_a,type,
product_Sigma_a_a: set_a > ( a > set_a ) > set_Product_prod_a_a ).
thf(tp_product_curry_a_a_o,type,
product_curry_a_a_o: ( product_prod_a_a > $o ) > a > a > $o ).
thf(tp_product_fst_a_a,type,
product_fst_a_a: product_prod_a_a > a ).
thf(tp_product_product_a_a,type,
product_product_a_a: set_a > set_a > set_Product_prod_a_a ).
thf(tp_product_snd_a_a,type,
product_snd_a_a: product_prod_a_a > a ).
thf(tp_product_swap_a_a,type,
product_swap_a_a: product_prod_a_a > product_prod_a_a ).
thf(tp_sK10_SY795,type,
sK10_SY795: set_Product_prod_a_a > product_prod_a_a ).
thf(tp_sK11_SY834,type,
sK11_SY834: set_Product_prod_a_a > set_Product_prod_a_a > product_prod_a_a ).
thf(tp_sK12_SY533,type,
sK12_SY533: produc1572603623od_a_a > ( produc1572603623od_a_a > $o ) > product_prod_a_a ).
thf(tp_sK13_SY892,type,
sK13_SY892: set_a > set_Product_prod_a_a > a ).
thf(tp_sK14_SY915,type,
sK14_SY915: set_Product_prod_a_a > set_Product_prod_a_a > a ).
thf(tp_sK15_SY1150,type,
sK15_SY1150: produc1921647824od_a_a > a ).
thf(tp_sK16_SY1162,type,
sK16_SY1162: produc1572603623od_a_a > a ).
thf(tp_sK17_SY722,type,
sK17_SY722: product_prod_a_a > ( product_prod_a_a > $o ) > a ).
thf(tp_sK18_SY740,type,
sK18_SY740: product_prod_a_a > ( product_prod_a_a > $o ) > a ).
thf(tp_sK19_SY508,type,
sK19_SY508: set_Product_prod_a_a > product_prod_a_a ).
thf(tp_sK1_SX0,type,
sK1_SX0: product_prod_a_a ).
thf(tp_sK20_SY1042,type,
sK20_SY1042: set_Product_prod_a_a > ( product_prod_a_a > product_prod_a_a ) > set_Product_prod_a_a > product_prod_a_a ).
thf(tp_sK21_SY1043,type,
sK21_SY1043: set_Product_prod_a_a > ( a > product_prod_a_a ) > set_a > a ).
thf(tp_sK22_SY1177,type,
sK22_SY1177: produc1572603623od_a_a > ( produc1572603623od_a_a > $o ) > a ).
thf(tp_sK23_SY1063,type,
sK23_SY1063: set_Product_prod_a_a > ( produc1572603623od_a_a > product_prod_a_a ) > set_Pr1948701895od_a_a > produc1572603623od_a_a ).
thf(tp_sK24_SY1180,type,
sK24_SY1180: set_Product_prod_a_a > set_a > a ).
thf(tp_sK25_SY1182,type,
sK25_SY1182: set_Product_prod_a_a > set_Product_prod_a_a > a ).
thf(tp_sK26_SY1085,type,
sK26_SY1085: set_Pr1948701895od_a_a > ( product_prod_a_a > produc1572603623od_a_a ) > set_Product_prod_a_a > product_prod_a_a ).
thf(tp_sK27_SY1186,type,
sK27_SY1186: product_prod_a_a > ( product_prod_a_a > $o ) > a ).
thf(tp_sK28_SY1188,type,
sK28_SY1188: product_prod_a_a > ( product_prod_a_a > $o ) > a ).
thf(tp_sK29_SY1119,type,
sK29_SY1119: product_prod_a_a > a ).
thf(tp_sK2_SY638,type,
sK2_SY638: produc1921647824od_a_a > a ).
thf(tp_sK30_SY1133,type,
sK30_SY1133: set_a > ( product_prod_a_a > a ) > set_Product_prod_a_a > product_prod_a_a ).
thf(tp_sK31_SY1191,type,
sK31_SY1191: produc1572603623od_a_a > ( produc1572603623od_a_a > $o ) > a ).
thf(tp_sK32_SY1045,type,
sK32_SY1045: set_Product_prod_a_a > ( product_prod_a_a > produc1572603623od_a_a ) > produc1572603623od_a_a > product_prod_a_a ).
thf(tp_sK33_SY1047,type,
sK33_SY1047: set_Product_prod_a_a > ( product_prod_a_a > product_prod_a_a ) > product_prod_a_a > product_prod_a_a ).
thf(tp_sK34_SY1053,type,
sK34_SY1053: set_Pr1948701895od_a_a > ( produc1572603623od_a_a > product_prod_a_a ) > product_prod_a_a > produc1572603623od_a_a ).
thf(tp_sK35_SY1109,type,
sK35_SY1109: set_Product_prod_a_a > ( product_prod_a_a > a ) > a > product_prod_a_a ).
thf(tp_sK36_SY1121,type,
sK36_SY1121: produc1572603623od_a_a > ( product_prod_a_a > set_Product_prod_a_a ) > set_Product_prod_a_a > product_prod_a_a ).
thf(tp_sK37_SY1124,type,
sK37_SY1124: set_a > ( a > product_prod_a_a ) > product_prod_a_a > a ).
thf(tp_sK38_SY1129,type,
sK38_SY1129: product_prod_a_a > ( a > set_a ) > set_a > a ).
thf(tp_sK39_SV412,type,
sK39_SV412: set_Product_prod_a_a > set_Product_prod_a_a > a ).
thf(tp_sK3_SY691,type,
sK3_SY691: produc1572603623od_a_a > product_prod_a_a ).
thf(tp_sK40_SY1167,type,
sK40_SY1167: set_Product_prod_a_a > ( a > a ) > ( a > a ) > product_prod_a_a > a ).
thf(tp_sK41_SY1143,type,
sK41_SY1143: set_Product_prod_a_a > set_Product_prod_a_a > product_prod_a_a ).
thf(tp_sK42_SY1144,type,
sK42_SY1144: set_Product_prod_a_a > set_Product_prod_a_a > product_prod_a_a ).
thf(tp_sK43_SY1159,type,
sK43_SY1159: set_Product_prod_a_a > ( product_prod_a_a > $o ) > ( product_prod_a_a > $o ) > set_Product_prod_a_a > product_prod_a_a ).
thf(tp_sK44_SY1201,type,
sK44_SY1201: ( a > a ) > set_Product_prod_a_a > ( a > a ) > product_prod_a_a > a ).
thf(tp_sK45_SY1197,type,
sK45_SY1197: set_Product_prod_a_a > produc1572603623od_a_a > ( product_prod_a_a > set_Product_prod_a_a ) > product_prod_a_a ).
thf(tp_sK46_SY1198,type,
sK46_SY1198: set_a > product_prod_a_a > ( a > set_a ) > a ).
thf(tp_sK47_SV416,type,
sK47_SV416: set_Product_prod_a_a > set_Product_prod_a_a > a ).
thf(tp_sK48_SY1050,type,
sK48_SY1050: set_Product_prod_a_a > ( product_prod_a_a > $o ) > set_Product_prod_a_a > product_prod_a_a ).
thf(tp_sK49_SY894,type,
sK49_SY894: set_a > set_Product_prod_a_a > a ).
thf(tp_sK4_SY716,type,
sK4_SY716: product_prod_a_a > a ).
thf(tp_sK50_SY531,type,
sK50_SY531: set_Product_prod_a_a > product_prod_a_a ).
thf(tp_sK51_SY894,type,
sK51_SY894: set_a > set_Product_prod_a_a > a ).
thf(tp_sK52_SY1204,type,
sK52_SY1204: set_Product_prod_a_a > set_a > a ).
thf(tp_sK53_SY956,type,
sK53_SY956: a > product_prod_a_a > a ).
thf(tp_sK54_SY1024,type,
sK54_SY1024: a > product_prod_a_a > a ).
thf(tp_sK55_SY1209,type,
sK55_SY1209: set_Product_prod_a_a > set_a > a ).
thf(tp_sK56_SY531,type,
sK56_SY531: product_prod_a_a > set_Product_prod_a_a > product_prod_a_a ).
thf(tp_sK57_SY956,type,
sK57_SY956: a > a > product_prod_a_a > a ).
thf(tp_sK58_SY1024,type,
sK58_SY1024: a > a > product_prod_a_a > a ).
thf(tp_sK59_SY1155,type,
sK59_SY1155: set_a > set_Product_prod_a_a > a ).
thf(tp_sK5_SY749,type,
sK5_SY749: product_prod_a_a > a ).
thf(tp_sK60_SY1218,type,
sK60_SY1218: set_Product_prod_a_a > set_a > a ).
thf(tp_sK61_SY1157,type,
sK61_SY1157: set_a > set_Product_prod_a_a > a ).
thf(tp_sK62_SY1157,type,
sK62_SY1157: set_a > set_Product_prod_a_a > a ).
thf(tp_sK63_SY1227,type,
sK63_SY1227: set_Product_prod_a_a > set_a > a ).
thf(tp_sK64_SY1230,type,
sK64_SY1230: set_Product_prod_a_a > set_a > a ).
thf(tp_sK6_SY1075,type,
sK6_SY1075: produc1921647824od_a_a > a ).
thf(tp_sK7_SY1097,type,
sK7_SY1097: produc1572603623od_a_a > a ).
thf(tp_sK8_SY1108,type,
sK8_SY1108: product_prod_a_a > a ).
thf(tp_sK9_SY773,type,
sK9_SY773: set_Product_prod_a_a > product_prod_a_a ).
thf(tp_same_f1138477100od_a_a,type,
same_f1138477100od_a_a: ( product_prod_a_a > $o ) > ( product_prod_a_a > set_Pr1948701895od_a_a ) > set_Pr1295299783od_a_a ).
thf(tp_same_fst_a_a,type,
same_fst_a_a: ( a > $o ) > ( a > set_Product_prod_a_a ) > set_Pr1948701895od_a_a ).
thf(tp_top_to1483957574_a_a_o,type,
top_to1483957574_a_a_o: product_prod_a_a > $o ).
thf(tp_top_to2011536774_a_a_o,type,
top_to2011536774_a_a_o: produc1572603623od_a_a > $o ).
thf(tp_top_to398455383od_a_a,type,
top_to398455383od_a_a: set_Product_prod_a_a ).
thf(tp_top_to52711959od_a_a,type,
top_to52711959od_a_a: set_Pr1948701895od_a_a ).
thf(tp_top_to993969022_a_a_o,type,
top_to993969022_a_a_o: product_prod_a_a > product_prod_a_a > $o ).
thf(tp_top_top_a_a_o,type,
top_top_a_a_o: a > a > $o ).
thf(tp_top_top_a_o,type,
top_top_a_o: a > $o ).
thf(tp_top_top_set_a,type,
top_top_set_a: set_a ).
thf(tp_y,type,
y: a ).
thf(tp_z,type,
z: a ).
thf(3,axiom,
! [A: product_prod_a_a] :
~ ( member449909584od_a_a @ A @ bot_bo2131659635od_a_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_352_emptyE) ).
thf(6,axiom,
! [A4: set_Product_prod_a_a,A: product_prod_a_a] :
( ( A4 = bot_bo2131659635od_a_a )
=> ~ ( member449909584od_a_a @ A @ A4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_equals0D) ).
thf(9,axiom,
! [A4: set_Product_prod_a_a] :
( ! [Y3: product_prod_a_a] :
~ ( member449909584od_a_a @ Y3 @ A4 )
=> ( A4 = bot_bo2131659635od_a_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_equals0I) ).
thf(12,axiom,
! [A4: set_Product_prod_a_a] :
( ( ? [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ A4 ) )
= ( A4 != bot_bo2131659635od_a_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_ex__in__conv) ).
thf(15,axiom,
! [C2: product_prod_a_a] :
~ ( member449909584od_a_a @ C2 @ bot_bo2131659635od_a_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_empty__iff) ).
thf(18,axiom,
! [A4: set_Product_prod_a_a] :
( ( ! [X4: product_prod_a_a] :
~ ( member449909584od_a_a @ X4 @ A4 ) )
= ( A4 = bot_bo2131659635od_a_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_all__not__in__conv) ).
thf(20,axiom,
! [X: a,Fx: a,A4: set_a,F: a > a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Fx ) @ ( bNF_Gr_a_a @ A4 @ F ) )
=> ( ( F @ X )
= Fx ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_GrD2) ).
thf(21,axiom,
! [X: product_prod_a_a,Fx: product_prod_a_a,A4: set_Product_prod_a_a,F: product_prod_a_a > product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X @ Fx ) @ ( bNF_Gr1372473186od_a_a @ A4 @ F ) )
=> ( member449909584od_a_a @ X @ A4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_GrD1) ).
thf(22,axiom,
! [X: a,Fx: a,A4: set_a,F: a > a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Fx ) @ ( bNF_Gr_a_a @ A4 @ F ) )
=> ( member_a @ X @ A4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_GrD1) ).
thf(24,axiom,
! [R2: set_Product_prod_a_a,S3: set_Product_prod_a_a] :
( ( ord_less_eq_a_a_o
@ ^ [X4: a,Y4: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ R2 )
@ ^ [X4: a,Y4: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ S3 ) )
= ( ord_le1824328871od_a_a @ R2 @ S3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_pred__subset__eq2) ).
thf(27,axiom,
( ord_le1824328871od_a_a
= ( ^ [A6: set_Product_prod_a_a,B5: set_Product_prod_a_a] :
( ord_le1347718902_a_a_o
@ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ A6 )
@ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ B5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_less__eq__set__def) ).
thf(30,axiom,
! [R2: set_Product_prod_a_a,S3: set_Product_prod_a_a] :
( ( ord_le1347718902_a_a_o
@ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ R2 )
@ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ S3 ) )
= ( ord_le1824328871od_a_a @ R2 @ S3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_pred__subset__eq) ).
thf(33,axiom,
! [B: set_Product_prod_a_a,A4: set_Product_prod_a_a,Q: product_prod_a_a > $o,P2: product_prod_a_a > $o] :
( ( ord_le1824328871od_a_a @ B @ A4 )
=> ( ! [X3: product_prod_a_a] :
( ( member449909584od_a_a @ X3 @ B )
=> ( ( Q @ X3 )
=> ( P2 @ X3 ) ) )
=> ( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [X4: product_prod_a_a] :
( ( member449909584od_a_a @ X4 @ B )
& ( Q @ X4 ) ) )
@ ( collec645855634od_a_a
@ ^ [X4: product_prod_a_a] :
( ( member449909584od_a_a @ X4 @ A4 )
& ( P2 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_subset__CollectI) ).
thf(36,axiom,
! [B: set_Product_prod_a_a,A4: set_Product_prod_a_a,P2: product_prod_a_a > $o] :
( ( ord_le1824328871od_a_a @ B @ A4 )
=> ( ( ord_le1824328871od_a_a @ B
@ ( collec645855634od_a_a
@ ^ [X4: product_prod_a_a] :
( ( member449909584od_a_a @ X4 @ A4 )
& ( P2 @ X4 ) ) ) )
= ( ! [X4: product_prod_a_a] :
( ( member449909584od_a_a @ X4 @ B )
=> ( P2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_subset__Collect__iff) ).
thf(39,axiom,
! [A4: set_Product_prod_a_a,P2: product_prod_a_a > $o] :
( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [X4: product_prod_a_a] :
( ( member449909584od_a_a @ X4 @ A4 )
& ( P2 @ X4 ) ) )
@ A4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_Collect__subset) ).
thf(42,axiom,
! [X5: set_Product_prod_a_a,P2: product_prod_a_a > $o] :
( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [X4: product_prod_a_a] :
( ( member449909584od_a_a @ X4 @ X5 )
& ( P2 @ X4 ) ) )
@ X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_Collect__restrict) ).
thf(45,axiom,
! [X: product_prod_a_a,Z2: set_Product_prod_a_a,X5: set_Product_prod_a_a,P2: product_prod_a_a > $o] :
( ( member449909584od_a_a @ X @ Z2 )
=> ( ( ord_le1824328871od_a_a @ Z2
@ ( collec645855634od_a_a
@ ^ [X4: product_prod_a_a] :
( ( member449909584od_a_a @ X4 @ X5 )
& ( P2 @ X4 ) ) ) )
=> ( P2 @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_prop__restrict) ).
thf(48,axiom,
! [A4: set_Product_prod_a_a,B: set_Product_prod_a_a,X: product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A4 @ B )
=> ( ( member449909584od_a_a @ X @ A4 )
=> ( member449909584od_a_a @ X @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_in__mono) ).
thf(51,axiom,
! [A4: set_Product_prod_a_a,B: set_Product_prod_a_a,C2: product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A4 @ B )
=> ( ( member449909584od_a_a @ C2 @ A4 )
=> ( member449909584od_a_a @ C2 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_subsetD) ).
thf(54,axiom,
( ord_le1824328871od_a_a
= ( ^ [A6: set_Product_prod_a_a,B5: set_Product_prod_a_a] :
! [X4: product_prod_a_a] :
( ( member449909584od_a_a @ X4 @ A6 )
=> ( member449909584od_a_a @ X4 @ B5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_subset__eq) ).
thf(57,axiom,
( ord_le1824328871od_a_a
= ( ^ [A6: set_Product_prod_a_a,B5: set_Product_prod_a_a] :
! [T2: product_prod_a_a] :
( ( member449909584od_a_a @ T2 @ A6 )
=> ( member449909584od_a_a @ T2 @ B5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_subset__iff) ).
thf(59,axiom,
! [R: set_Product_prod_a_a,S: set_Product_prod_a_a] :
( ! [X3: a,Y3: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ S ) )
=> ( ord_le1824328871od_a_a @ R @ S ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_subrelI) ).
thf(62,axiom,
! [A4: set_Pr1948701895od_a_a,F: produc1572603623od_a_a > product_prod_a_a,B: set_Product_prod_a_a] :
( ! [X3: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ X3 @ A4 )
=> ( member449909584od_a_a @ ( F @ X3 ) @ B ) )
=> ( ord_le1824328871od_a_a @ ( image_734753285od_a_a @ F @ A4 ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_image__subsetI) ).
thf(65,axiom,
! [A4: set_a,F: a > product_prod_a_a,B: set_Product_prod_a_a] :
( ! [X3: a] :
( ( member_a @ X3 @ A4 )
=> ( member449909584od_a_a @ ( F @ X3 ) @ B ) )
=> ( ord_le1824328871od_a_a @ ( image_1725938350od_a_a @ F @ A4 ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_image__subsetI) ).
thf(66,axiom,
! [A4: set_Product_prod_a_a,F: product_prod_a_a > produc1572603623od_a_a,B: set_Pr1948701895od_a_a] :
( ! [X3: product_prod_a_a] :
( ( member449909584od_a_a @ X3 @ A4 )
=> ( member2057358096od_a_a @ ( F @ X3 ) @ B ) )
=> ( ord_le456379495od_a_a @ ( image_1765377413od_a_a @ F @ A4 ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_image__subsetI) ).
thf(67,axiom,
! [A4: set_Product_prod_a_a,F: product_prod_a_a > a,B: set_a] :
( ! [X3: product_prod_a_a] :
( ( member449909584od_a_a @ X3 @ A4 )
=> ( member_a @ ( F @ X3 ) @ B ) )
=> ( ord_less_eq_set_a @ ( image_340790172_a_a_a @ F @ A4 ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_image__subsetI) ).
thf(68,axiom,
! [A4: set_Product_prod_a_a,F: product_prod_a_a > product_prod_a_a,B: set_Product_prod_a_a] :
( ! [X3: product_prod_a_a] :
( ( member449909584od_a_a @ X3 @ A4 )
=> ( member449909584od_a_a @ ( F @ X3 ) @ B ) )
=> ( ord_le1824328871od_a_a @ ( image_794773445od_a_a @ F @ A4 ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_image__subsetI) ).
thf(71,axiom,
! [A4: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ! [X3: product_prod_a_a] :
( ( member449909584od_a_a @ X3 @ A4 )
=> ( member449909584od_a_a @ X3 @ B ) )
=> ( ord_le1824328871od_a_a @ A4 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_subsetI) ).
thf(73,axiom,
! [X: product_prod_a_a,A4: set_a,B: set_a] :
( ( member449909584od_a_a @ X @ ( product_product_a_a @ A4 @ B ) )
= ( member449909584od_a_a @ X
@ ( product_Sigma_a_a @ A4
@ ^ [Uu: a] : B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_member__product) ).
thf(83,axiom,
! [C2: produc1572603623od_a_a,A4: set_Product_prod_a_a,B: product_prod_a_a > set_Product_prod_a_a] :
( ( member2057358096od_a_a @ C2 @ ( produc304751368od_a_a @ A4 @ B ) )
=> ~ ! [X3: product_prod_a_a] :
( ( member449909584od_a_a @ X3 @ A4 )
=> ! [Y3: product_prod_a_a] :
( ( member449909584od_a_a @ Y3 @ ( B @ X3 ) )
=> ( C2
!= ( produc1474507607od_a_a @ X3 @ Y3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_SigmaE) ).
thf(84,axiom,
! [C2: product_prod_a_a,A4: set_a,B: a > set_a] :
( ( member449909584od_a_a @ C2 @ ( product_Sigma_a_a @ A4 @ B ) )
=> ~ ! [X3: a] :
( ( member_a @ X3 @ A4 )
=> ! [Y3: a] :
( ( member_a @ Y3 @ ( B @ X3 ) )
=> ( C2
!= ( product_Pair_a_a @ X3 @ Y3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_SigmaE) ).
thf(92,axiom,
! [A: product_prod_a_a,B2: product_prod_a_a,A4: set_Product_prod_a_a,B: product_prod_a_a > set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B2 ) @ ( produc304751368od_a_a @ A4 @ B ) )
=> ( member449909584od_a_a @ A @ A4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_SigmaD1) ).
thf(93,axiom,
! [A: a,B2: a,A4: set_a,B: a > set_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B2 ) @ ( product_Sigma_a_a @ A4 @ B ) )
=> ( member_a @ A @ A4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_SigmaD1) ).
thf(94,axiom,
! [A: product_prod_a_a,B2: product_prod_a_a,A4: set_Product_prod_a_a,B: product_prod_a_a > set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B2 ) @ ( produc304751368od_a_a @ A4 @ B ) )
=> ( member449909584od_a_a @ B2 @ ( B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_SigmaD2) ).
thf(95,axiom,
! [A: a,B2: a,A4: set_a,B: a > set_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B2 ) @ ( product_Sigma_a_a @ A4 @ B ) )
=> ( member_a @ B2 @ ( B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_SigmaD2) ).
thf(96,axiom,
! [A: product_prod_a_a,B2: product_prod_a_a,A4: set_Product_prod_a_a,B: product_prod_a_a > set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B2 ) @ ( produc304751368od_a_a @ A4 @ B ) )
=> ~ ( ( member449909584od_a_a @ A @ A4 )
=> ~ ( member449909584od_a_a @ B2 @ ( B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_SigmaE2) ).
thf(97,axiom,
! [A: a,B2: a,A4: set_a,B: a > set_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B2 ) @ ( product_Sigma_a_a @ A4 @ B ) )
=> ~ ( ( member_a @ A @ A4 )
=> ~ ( member_a @ B2 @ ( B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_SigmaE2) ).
thf(105,axiom,
! [A: product_prod_a_a,A4: set_Product_prod_a_a,B2: product_prod_a_a,B: product_prod_a_a > set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ A4 )
=> ( ( member449909584od_a_a @ B2 @ ( B @ A ) )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B2 ) @ ( produc304751368od_a_a @ A4 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_SigmaI) ).
thf(106,axiom,
! [A: a,A4: set_a,B2: a,B: a > set_a] :
( ( member_a @ A @ A4 )
=> ( ( member_a @ B2 @ ( B @ A ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B2 ) @ ( product_Sigma_a_a @ A4 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_SigmaI) ).
thf(114,axiom,
! [A: product_prod_a_a,B2: product_prod_a_a,A4: set_Product_prod_a_a,B: product_prod_a_a > set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B2 ) @ ( produc304751368od_a_a @ A4 @ B ) )
= ( ( member449909584od_a_a @ A @ A4 )
& ( member449909584od_a_a @ B2 @ ( B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_mem__Sigma__iff) ).
thf(115,axiom,
! [A: a,B2: a,A4: set_a,B: a > set_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B2 ) @ ( product_Sigma_a_a @ A4 @ B ) )
= ( ( member_a @ A @ A4 )
& ( member_a @ B2 @ ( B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_mem__Sigma__iff) ).
thf(123,axiom,
! [A: a,B2: a,A2: a,B3: a,R: set_Product_prod_a_a,S: set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ A @ B2 ) @ ( product_Pair_a_a @ A2 @ B3 ) ) @ ( lex_prod_a_a @ R @ S ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ A2 ) @ R )
| ( ( A = A2 )
& ( member449909584od_a_a @ ( product_Pair_a_a @ B2 @ B3 ) @ S ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_in__lex__prod) ).
thf(129,axiom,
! [B2: product_prod_a_a,F: product_prod_a_a > product_prod_a_a,X: product_prod_a_a,C2: product_prod_a_a,G: product_prod_a_a > product_prod_a_a,A4: set_Product_prod_a_a] :
( ( B2
= ( F @ X ) )
=> ( ( C2
= ( G @ X ) )
=> ( ( member449909584od_a_a @ X @ A4 )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ B2 @ C2 ) @ ( bNF_Gr200450189od_a_a @ A4 @ F @ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_image2__eqI) ).
thf(130,axiom,
! [B2: a,F: produc1572603623od_a_a > a,X: produc1572603623od_a_a,C2: a,G: produc1572603623od_a_a > a,A4: set_Pr1948701895od_a_a] :
( ( B2
= ( F @ X ) )
=> ( ( C2
= ( G @ X ) )
=> ( ( member2057358096od_a_a @ X @ A4 )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ B2 @ C2 ) @ ( bNF_Gr356189709_a_a_a @ A4 @ F @ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_image2__eqI) ).
thf(131,axiom,
! [B2: a,F: a > a,X: a,C2: a,G: a > a,A4: set_a] :
( ( B2
= ( F @ X ) )
=> ( ( C2
= ( G @ X ) )
=> ( ( member_a @ X @ A4 )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ B2 @ C2 ) @ ( bNF_Gr423046308_a_a_a @ A4 @ F @ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_image2__eqI) ).
thf(132,axiom,
! [B2: a,F: product_prod_a_a > a,X: product_prod_a_a,C2: a,G: product_prod_a_a > a,A4: set_Product_prod_a_a] :
( ( B2
= ( F @ X ) )
=> ( ( C2
= ( G @ X ) )
=> ( ( member449909584od_a_a @ X @ A4 )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ B2 @ C2 ) @ ( bNF_Gr1853143117_a_a_a @ A4 @ F @ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_image2__eqI) ).
thf(134,axiom,
! [P2: a > a > $o,Y: a,X: a] :
( ( P2 @ Y @ X )
=> ( P2 @ ( product_snd_a_a @ ( product_Pair_a_a @ X @ Y ) ) @ ( product_fst_a_a @ ( product_Pair_a_a @ X @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_exI__realizer) ).
thf(136,axiom,
! [P2: a > $o,P: a,Q: a > $o,Q2: a] :
( ( P2 @ P )
=> ( ( Q @ Q2 )
=> ( ( P2 @ ( product_fst_a_a @ ( product_Pair_a_a @ P @ Q2 ) ) )
& ( Q @ ( product_snd_a_a @ ( product_Pair_a_a @ P @ Q2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_conjI__realizer) ).
thf(138,axiom,
! [P2: a > a > $o,X: a,Y: a,A: product_prod_a_a] :
( ( P2 @ X @ Y )
=> ( ( A
= ( product_Pair_a_a @ X @ Y ) )
=> ( P2 @ ( product_fst_a_a @ A ) @ ( product_snd_a_a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_BNF__Greatest__Fixpoint_Osubst__Pair) ).
thf(140,axiom,
( product_swap_a_a
= ( ^ [P4: product_prod_a_a] : ( product_Pair_a_a @ ( product_snd_a_a @ P4 ) @ ( product_fst_a_a @ P4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_prod_Oswap__def) ).
thf(142,axiom,
! [Prod: product_prod_a_a] :
( Prod
= ( product_Pair_a_a @ ( product_fst_a_a @ Prod ) @ ( product_snd_a_a @ Prod ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_prod_Oexhaust__sel) ).
thf(144,axiom,
! [T: product_prod_a_a] :
( T
= ( product_Pair_a_a @ ( product_fst_a_a @ T ) @ ( product_snd_a_a @ T ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_surjective__pairing) ).
thf(146,axiom,
! [X1: a,X2: a] :
( ( product_snd_a_a @ ( product_Pair_a_a @ X1 @ X2 ) )
= X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_snd__conv) ).
thf(148,axiom,
! [X: a,Y: a,A: a] :
( ( ( product_snd_a_a @ ( product_Pair_a_a @ X @ Y ) )
= A )
=> ( Y = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_snd__eqD) ).
thf(150,axiom,
! [X: product_prod_a_a,Y: a,Z: a] :
( ( X
= ( product_Pair_a_a @ Y @ Z ) )
=> ( ( product_snd_a_a @ X )
= Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_sndI) ).
thf(152,axiom,
! [B2: a,P: product_prod_a_a] :
( ( B2
= ( product_snd_a_a @ P ) )
= ( ? [A5: a] :
( P
= ( product_Pair_a_a @ A5 @ B2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_eq__snd__iff) ).
thf(154,axiom,
! [Prod: product_prod_a_a] :
( ( product_Pair_a_a @ ( product_fst_a_a @ Prod ) @ ( product_snd_a_a @ Prod ) )
= Prod ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_prod_Ocollapse) ).
thf(156,axiom,
! [X: product_prod_a_a,Y: a,Z: a] :
( ( X
= ( product_Pair_a_a @ Y @ Z ) )
=> ( ( product_fst_a_a @ X )
= Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_fstI) ).
thf(158,axiom,
! [A: a,P: product_prod_a_a] :
( ( A
= ( product_fst_a_a @ P ) )
= ( ? [B6: a] :
( P
= ( product_Pair_a_a @ A @ B6 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_eq__fst__iff) ).
thf(160,axiom,
( top_top_a_a_o
= ( ^ [X4: a,Y4: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ top_to398455383od_a_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_top__empty__eq2) ).
thf(164,axiom,
! [C2: product_prod_a_a,F: a > a,G: a > a,R2: set_Product_prod_a_a] :
( ( member449909584od_a_a @ C2 @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ F @ G ) @ R2 ) )
=> ~ ! [X3: a,Y3: a] :
( ( C2
= ( product_Pair_a_a @ ( F @ X3 ) @ ( G @ Y3 ) ) )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_prod__fun__imageE) ).
thf(166,axiom,
! [X1: a,X2: a] :
( ( product_fst_a_a @ ( product_Pair_a_a @ X1 @ X2 ) )
= X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_fst__conv) ).
thf(168,axiom,
! [X: a,Y: a,A: a] :
( ( ( product_fst_a_a @ ( product_Pair_a_a @ X @ Y ) )
= A )
=> ( X = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_fst__eqD) ).
thf(171,axiom,
( top_to1483957574_a_a_o
= ( ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ top_to398455383od_a_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_top__empty__eq) ).
thf(175,axiom,
! [A: a,B2: a,R2: set_Product_prod_a_a,F: a > a,G: a > a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B2 ) @ R2 )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ ( F @ A ) @ ( G @ B2 ) ) @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ F @ G ) @ R2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_map__prod__imageI) ).
thf(177,axiom,
! [F: product_prod_a_a > a,G: product_prod_a_a > a,A: product_prod_a_a,B2: product_prod_a_a] :
( ( produc363290532_a_a_a @ F @ G @ ( produc1474507607od_a_a @ A @ B2 ) )
= ( product_Pair_a_a @ ( F @ A ) @ ( G @ B2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_map__prod__simp) ).
thf(178,axiom,
! [F: a > product_prod_a_a,G: a > product_prod_a_a,A: a,B2: a] :
( ( produc2012818120od_a_a @ F @ G @ ( product_Pair_a_a @ A @ B2 ) )
= ( produc1474507607od_a_a @ ( F @ A ) @ ( G @ B2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_map__prod__simp) ).
thf(179,axiom,
! [F: a > a,G: a > a,A: a,B2: a] :
( ( produc700022774_a_a_a @ F @ G @ ( product_Pair_a_a @ A @ B2 ) )
= ( product_Pair_a_a @ ( F @ A ) @ ( G @ B2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_map__prod__simp) ).
thf(181,axiom,
! [P2: a > $o,X: a,Y5: a,Y: a,R2: a > set_Product_prod_a_a] :
( ( P2 @ X )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y5 @ Y ) @ ( R2 @ X ) )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ X @ Y5 ) @ ( product_Pair_a_a @ X @ Y ) ) @ ( same_fst_a_a @ P2 @ R2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_same__fstI) ).
thf(184,axiom,
! [X: product_prod_a_a] : ( member449909584od_a_a @ X @ top_to398455383od_a_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_iso__tuple__UNIV__I) ).
thf(187,axiom,
! [A4: set_Product_prod_a_a] :
( ! [X3: product_prod_a_a] : ( member449909584od_a_a @ X3 @ A4 )
=> ( top_to398455383od_a_a = A4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_UNIV__eq__I) ).
thf(190,axiom,
? [X3: product_prod_a_a] : ( member449909584od_a_a @ X3 @ top_to398455383od_a_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_UNIV__witness) ).
thf(193,axiom,
! [X: product_prod_a_a] : ( member449909584od_a_a @ X @ top_to398455383od_a_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_UNIV__I) ).
thf(196,axiom,
( minus_1507102574od_a_a
= ( ^ [A6: set_Product_prod_a_a,B5: set_Product_prod_a_a] :
( collec645855634od_a_a
@ ^ [X4: product_prod_a_a] :
( ( member449909584od_a_a @ X4 @ A6 )
& ~ ( member449909584od_a_a @ X4 @ B5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_set__diff__eq) ).
thf(205,axiom,
! [F: product_prod_a_a > product_prod_a_a,A4: set_Product_prod_a_a,P2: product_prod_a_a > $o] :
( ( collec645855634od_a_a
@ ^ [X4: product_prod_a_a] :
( ( member449909584od_a_a @ X4 @ ( image_794773445od_a_a @ F @ A4 ) )
& ( P2 @ X4 ) ) )
= ( image_794773445od_a_a @ F
@ ( collec645855634od_a_a
@ ^ [X4: product_prod_a_a] :
( ( member449909584od_a_a @ X4 @ A4 )
& ( P2 @ ( F @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_Compr__image__eq) ).
thf(208,axiom,
! [B2: produc1572603623od_a_a,F: product_prod_a_a > produc1572603623od_a_a,A4: set_Product_prod_a_a] :
( ( member2057358096od_a_a @ B2 @ ( image_1765377413od_a_a @ F @ A4 ) )
=> ~ ! [X3: product_prod_a_a] :
( ( B2
= ( F @ X3 ) )
=> ~ ( member449909584od_a_a @ X3 @ A4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_imageE) ).
thf(211,axiom,
! [B2: a,F: product_prod_a_a > a,A4: set_Product_prod_a_a] :
( ( member_a @ B2 @ ( image_340790172_a_a_a @ F @ A4 ) )
=> ~ ! [X3: product_prod_a_a] :
( ( B2
= ( F @ X3 ) )
=> ~ ( member449909584od_a_a @ X3 @ A4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_imageE) ).
thf(212,axiom,
! [B2: product_prod_a_a,F: produc1572603623od_a_a > product_prod_a_a,A4: set_Pr1948701895od_a_a] :
( ( member449909584od_a_a @ B2 @ ( image_734753285od_a_a @ F @ A4 ) )
=> ~ ! [X3: produc1572603623od_a_a] :
( ( B2
= ( F @ X3 ) )
=> ~ ( member2057358096od_a_a @ X3 @ A4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_imageE) ).
thf(213,axiom,
! [B2: product_prod_a_a,F: a > product_prod_a_a,A4: set_a] :
( ( member449909584od_a_a @ B2 @ ( image_1725938350od_a_a @ F @ A4 ) )
=> ~ ! [X3: a] :
( ( B2
= ( F @ X3 ) )
=> ~ ( member_a @ X3 @ A4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_imageE) ).
thf(214,axiom,
! [B2: product_prod_a_a,F: product_prod_a_a > product_prod_a_a,A4: set_Product_prod_a_a] :
( ( member449909584od_a_a @ B2 @ ( image_794773445od_a_a @ F @ A4 ) )
=> ~ ! [X3: product_prod_a_a] :
( ( B2
= ( F @ X3 ) )
=> ~ ( member449909584od_a_a @ X3 @ A4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_imageE) ).
thf(217,axiom,
! [C2: product_prod_a_a,A4: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( member449909584od_a_a @ C2 @ ( minus_1507102574od_a_a @ A4 @ B ) )
=> ~ ( ( member449909584od_a_a @ C2 @ A4 )
=> ( member449909584od_a_a @ C2 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_DiffE) ).
thf(220,axiom,
! [C2: product_prod_a_a,A4: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( member449909584od_a_a @ C2 @ ( minus_1507102574od_a_a @ A4 @ B ) )
=> ( member449909584od_a_a @ C2 @ A4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_DiffD1) ).
thf(223,axiom,
! [C2: product_prod_a_a,A4: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( member449909584od_a_a @ C2 @ ( minus_1507102574od_a_a @ A4 @ B ) )
=> ~ ( member449909584od_a_a @ C2 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_DiffD2) ).
thf(226,axiom,
! [X: produc1572603623od_a_a,A4: set_Pr1948701895od_a_a,F: produc1572603623od_a_a > product_prod_a_a] :
( ( member2057358096od_a_a @ X @ A4 )
=> ( member449909584od_a_a @ ( F @ X ) @ ( image_734753285od_a_a @ F @ A4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_imageI) ).
thf(229,axiom,
! [X: a,A4: set_a,F: a > product_prod_a_a] :
( ( member_a @ X @ A4 )
=> ( member449909584od_a_a @ ( F @ X ) @ ( image_1725938350od_a_a @ F @ A4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_imageI) ).
thf(230,axiom,
! [X: product_prod_a_a,A4: set_Product_prod_a_a,F: product_prod_a_a > produc1572603623od_a_a] :
( ( member449909584od_a_a @ X @ A4 )
=> ( member2057358096od_a_a @ ( F @ X ) @ ( image_1765377413od_a_a @ F @ A4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_imageI) ).
thf(231,axiom,
! [X: product_prod_a_a,A4: set_Product_prod_a_a,F: product_prod_a_a > a] :
( ( member449909584od_a_a @ X @ A4 )
=> ( member_a @ ( F @ X ) @ ( image_340790172_a_a_a @ F @ A4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_imageI) ).
thf(232,axiom,
! [X: product_prod_a_a,A4: set_Product_prod_a_a,F: product_prod_a_a > product_prod_a_a] :
( ( member449909584od_a_a @ X @ A4 )
=> ( member449909584od_a_a @ ( F @ X ) @ ( image_794773445od_a_a @ F @ A4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_imageI) ).
thf(235,axiom,
! [X: produc1572603623od_a_a,A4: set_Pr1948701895od_a_a,B2: product_prod_a_a,F: produc1572603623od_a_a > product_prod_a_a] :
( ( member2057358096od_a_a @ X @ A4 )
=> ( ( B2
= ( F @ X ) )
=> ( member449909584od_a_a @ B2 @ ( image_734753285od_a_a @ F @ A4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_rev__image__eqI) ).
thf(238,axiom,
! [X: a,A4: set_a,B2: product_prod_a_a,F: a > product_prod_a_a] :
( ( member_a @ X @ A4 )
=> ( ( B2
= ( F @ X ) )
=> ( member449909584od_a_a @ B2 @ ( image_1725938350od_a_a @ F @ A4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_rev__image__eqI) ).
thf(239,axiom,
! [X: product_prod_a_a,A4: set_Product_prod_a_a,B2: produc1572603623od_a_a,F: product_prod_a_a > produc1572603623od_a_a] :
( ( member449909584od_a_a @ X @ A4 )
=> ( ( B2
= ( F @ X ) )
=> ( member2057358096od_a_a @ B2 @ ( image_1765377413od_a_a @ F @ A4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_rev__image__eqI) ).
thf(240,axiom,
! [X: product_prod_a_a,A4: set_Product_prod_a_a,B2: a,F: product_prod_a_a > a] :
( ( member449909584od_a_a @ X @ A4 )
=> ( ( B2
= ( F @ X ) )
=> ( member_a @ B2 @ ( image_340790172_a_a_a @ F @ A4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_rev__image__eqI) ).
thf(241,axiom,
! [X: product_prod_a_a,A4: set_Product_prod_a_a,B2: product_prod_a_a,F: product_prod_a_a > product_prod_a_a] :
( ( member449909584od_a_a @ X @ A4 )
=> ( ( B2
= ( F @ X ) )
=> ( member449909584od_a_a @ B2 @ ( image_794773445od_a_a @ F @ A4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_rev__image__eqI) ).
thf(244,axiom,
( minus_1507102574od_a_a
= ( ^ [A6: set_Product_prod_a_a,B5: set_Product_prod_a_a] :
( collec645855634od_a_a
@ ( minus_1797478127_a_a_o
@ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ A6 )
@ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ B5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_minus__set__def) ).
thf(247,axiom,
! [C2: product_prod_a_a,A4: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( member449909584od_a_a @ C2 @ ( minus_1507102574od_a_a @ A4 @ B ) )
= ( ( member449909584od_a_a @ C2 @ A4 )
& ~ ( member449909584od_a_a @ C2 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_Diff__iff) ).
thf(250,axiom,
! [B2: product_prod_a_a,F: produc1572603623od_a_a > product_prod_a_a,X: produc1572603623od_a_a,A4: set_Pr1948701895od_a_a] :
( ( B2
= ( F @ X ) )
=> ( ( member2057358096od_a_a @ X @ A4 )
=> ( member449909584od_a_a @ B2 @ ( image_734753285od_a_a @ F @ A4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_image__eqI) ).
thf(253,axiom,
! [B2: product_prod_a_a,F: a > product_prod_a_a,X: a,A4: set_a] :
( ( B2
= ( F @ X ) )
=> ( ( member_a @ X @ A4 )
=> ( member449909584od_a_a @ B2 @ ( image_1725938350od_a_a @ F @ A4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_image__eqI) ).
thf(254,axiom,
! [B2: produc1572603623od_a_a,F: product_prod_a_a > produc1572603623od_a_a,X: product_prod_a_a,A4: set_Product_prod_a_a] :
( ( B2
= ( F @ X ) )
=> ( ( member449909584od_a_a @ X @ A4 )
=> ( member2057358096od_a_a @ B2 @ ( image_1765377413od_a_a @ F @ A4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_image__eqI) ).
thf(255,axiom,
! [B2: a,F: product_prod_a_a > a,X: product_prod_a_a,A4: set_Product_prod_a_a] :
( ( B2
= ( F @ X ) )
=> ( ( member449909584od_a_a @ X @ A4 )
=> ( member_a @ B2 @ ( image_340790172_a_a_a @ F @ A4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_image__eqI) ).
thf(256,axiom,
! [B2: product_prod_a_a,F: product_prod_a_a > product_prod_a_a,X: product_prod_a_a,A4: set_Product_prod_a_a] :
( ( B2
= ( F @ X ) )
=> ( ( member449909584od_a_a @ X @ A4 )
=> ( member449909584od_a_a @ B2 @ ( image_794773445od_a_a @ F @ A4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_image__eqI) ).
thf(259,axiom,
! [C2: product_prod_a_a,A4: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( member449909584od_a_a @ C2 @ A4 )
=> ( ~ ( member449909584od_a_a @ C2 @ B )
=> ( member449909584od_a_a @ C2 @ ( minus_1507102574od_a_a @ A4 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_DiffI) ).
thf(262,axiom,
! [A4: set_Product_prod_a_a] :
( ( collec645855634od_a_a
@ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ A4 ) )
= A4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_Collect__mem__eq) ).
thf(265,axiom,
! [A: product_prod_a_a,P2: product_prod_a_a > $o] :
( ( member449909584od_a_a @ A @ ( collec645855634od_a_a @ P2 ) )
= ( P2 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_mem__Collect__eq) ).
thf(270,axiom,
! [Y: a,X: a,A4: set_Product_prod_a_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ ( image_794773445od_a_a @ product_swap_a_a @ A4 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ A4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_pair__in__swap__image) ).
thf(272,axiom,
! [Relation: set_Product_prod_a_a,Carrier: set_a] :
( ! [X3: a,Y3: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ Relation )
=> ( member_a @ X3 @ Carrier ) )
=> ( ! [X3: a,Y3: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ Relation )
=> ( member_a @ Y3 @ Carrier ) )
=> ( ( order_preorder_on_a @ Carrier @ Relation )
=> ( prefer1292084992ence_a @ Carrier @ Relation ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_preference_Ointro) ).
thf(275,axiom,
( prefer1292084992ence_a
= ( ^ [Carrier2: set_a,Relation2: set_Product_prod_a_a] :
( ! [X4: a,Y4: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ Relation2 )
=> ( member_a @ X4 @ Carrier2 ) )
& ! [X4: a,Y4: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ Relation2 )
=> ( member_a @ Y4 @ Carrier2 ) )
& ( order_preorder_on_a @ Carrier2 @ Relation2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_preference__def) ).
thf(278,axiom,
! [R2: set_Product_prod_a_a,S3: set_Product_prod_a_a] :
( ( ( ^ [X4: a,Y4: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ R2 ) )
= ( ^ [X4: a,Y4: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ S3 ) ) )
= ( R2 = S3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_pred__equals__eq2) ).
thf(280,axiom,
( prefer436369274d_as_a
= ( ^ [X4: a,B5: set_a,P3: set_Product_prod_a_a] :
( collect_a
@ ^ [Y4: a] :
( ( member_a @ Y4 @ B5 )
& ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ P3 )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Y4 @ X4 ) @ P3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_as__good__as__def) ).
thf(283,axiom,
( prefer1676310729than_a
= ( ^ [X4: a,B5: set_a,P3: set_Product_prod_a_a] :
( collect_a
@ ^ [Y4: a] :
( ( member_a @ Y4 @ B5 )
& ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ P3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_no__better__than__def) ).
thf(286,axiom,
! [F: product_prod_a_a > $o,A: a,B2: a] :
( ( product_curry_a_a_o @ F @ A @ B2 )
=> ( F @ ( product_Pair_a_a @ A @ B2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_curryE) ).
thf(288,axiom,
! [F: product_prod_a_a > $o,A: a,B2: a] :
( ( product_curry_a_a_o @ F @ A @ B2 )
=> ( F @ ( product_Pair_a_a @ A @ B2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_curryD) ).
thf(290,axiom,
! [X: a,Y: a] :
( ( product_swap_a_a @ ( product_Pair_a_a @ X @ Y ) )
= ( product_Pair_a_a @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_swap__simp) ).
thf(291,axiom,
! [Carrier: set_Product_prod_a_a,Relation: set_Pr1948701895od_a_a,X: product_prod_a_a,Y: product_prod_a_a] :
( ( prefer1338892073od_a_a @ Carrier @ Relation )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X @ Y ) @ Relation )
=> ( member449909584od_a_a @ X @ Carrier ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_preference_Onot__outside) ).
thf(292,axiom,
! [Carrier: set_a,Relation: set_Product_prod_a_a,X: a,Y: a] :
( ( prefer1292084992ence_a @ Carrier @ Relation )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ Relation )
=> ( member_a @ X @ Carrier ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_preference_Onot__outside) ).
thf(295,axiom,
! [Carrier: set_a,Relation: set_Product_prod_a_a,X: a,Y: a,Z: a] :
( ( prefer1292084992ence_a @ Carrier @ Relation )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ Relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ Relation ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ Z ) @ Relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Z @ Y ) @ Relation ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Z ) @ Relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Z @ X ) @ Relation ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_preference_Oindiff__trans) ).
thf(297,axiom,
! [F: product_prod_a_a > $o,A: a,B2: a] :
( ( F @ ( product_Pair_a_a @ A @ B2 ) )
=> ( product_curry_a_a_o @ F @ A @ B2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_curryI) ).
thf(299,axiom,
! [R: a,S: a,R2: set_Product_prod_a_a,S2: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ R @ S ) @ R2 )
=> ( ( S2 = S )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ R @ S2 ) @ R2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_ssubst__Pair__rhs) ).
thf(301,axiom,
( prefer161218362good_a
= ( ^ [X4: a,B5: set_a,P3: set_Product_prod_a_a] :
( collect_a
@ ^ [Y4: a] :
( ( member_a @ Y4 @ B5 )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Y4 @ X4 ) @ P3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_at__least__as__good__def) ).
thf(304,axiom,
! [Y: product_prod_a_a] :
~ ! [A3: a,B4: a] :
( Y
!= ( product_Pair_a_a @ A3 @ B4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_old_Oprod_Oexhaust) ).
thf(306,axiom,
! [P2: product_prod_a_a > $o,Prod: product_prod_a_a] :
( ! [A3: a,B4: a] : ( P2 @ ( product_Pair_a_a @ A3 @ B4 ) )
=> ( P2 @ Prod ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_old_Oprod_Oinducts) ).
thf(307,axiom,
! [P2: produc1572603623od_a_a > $o,X: produc1572603623od_a_a] :
( ! [A3: product_prod_a_a,B4: a,C: a] : ( P2 @ ( produc1474507607od_a_a @ A3 @ ( product_Pair_a_a @ B4 @ C ) ) )
=> ( P2 @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_prod__induct3) ).
thf(308,axiom,
! [Y: produc1572603623od_a_a] :
~ ! [A3: product_prod_a_a,B4: a,C: a] :
( Y
!= ( produc1474507607od_a_a @ A3 @ ( product_Pair_a_a @ B4 @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_prod__cases3) ).
thf(309,axiom,
! [Y: produc1921647824od_a_a] :
~ ! [A3: a,B4: a,C: a] :
( Y
!= ( produc1299253312od_a_a @ A3 @ ( product_Pair_a_a @ B4 @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_prod__cases3) ).
thf(312,axiom,
! [A: a,B2: a,A2: a,B3: a] :
( ( ( product_Pair_a_a @ A @ B2 )
= ( product_Pair_a_a @ A2 @ B3 ) )
=> ~ ( ( A = A2 )
=> ( B2 != B3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_Pair__inject) ).
thf(319,axiom,
! [P2: product_prod_a_a > $o,P: product_prod_a_a] :
( ! [A3: a,B4: a] : ( P2 @ ( product_Pair_a_a @ A3 @ B4 ) )
=> ( P2 @ P ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_prod__cases) ).
thf(326,axiom,
! [P: product_prod_a_a] :
? [X3: a,Y3: a] :
( P
= ( product_Pair_a_a @ X3 @ Y3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_surj__pair) ).
thf(333,axiom,
! [A: a,B2: a,A2: a,B3: a] :
( ( ( product_Pair_a_a @ A @ B2 )
= ( product_Pair_a_a @ A2 @ B3 ) )
= ( ( A = A2 )
& ( B2 = B3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_old_Oprod_Oinject) ).
thf(340,axiom,
! [X1: a,X2: a,Y1: a,Y2: a] :
( ( ( product_Pair_a_a @ X1 @ X2 )
= ( product_Pair_a_a @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X2 = Y2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_prod_Oinject) ).
thf(347,axiom,
! [X: a,Y: a,B: set_a,Pr: set_Product_prod_a_a] :
( ( member_a @ X @ ( prefer161218362good_a @ Y @ B @ Pr ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ Pr ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_at__lst__asgd__ge) ).
thf(348,axiom,
! [X: product_prod_a_a,Y: product_prod_a_a,B: set_Product_prod_a_a,Pr: set_Pr1948701895od_a_a] :
( ( member449909584od_a_a @ X @ ( prefer477097315od_a_a @ Y @ B @ Pr ) )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X @ Y ) @ Pr ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_at__lst__asgd__ge) ).
thf(355,axiom,
member_a @ z @ ( prefer161218362good_a @ y @ b @ pr ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms) ).
thf(356,conjecture,
member449909584od_a_a @ ( product_Pair_a_a @ z @ y ) @ pr,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(357,negated_conjecture,
( ( member449909584od_a_a @ ( product_Pair_a_a @ z @ y ) @ pr )
= $false ),
inference(negate_conjecture,[status(cth)],[356]) ).
thf(358,plain,
( ( member449909584od_a_a @ ( product_Pair_a_a @ z @ y ) @ pr )
= $false ),
inference(unfold_def,[status(thm)],[357]) ).
thf(359,plain,
( ( ! [A: product_prod_a_a] :
~ ( member449909584od_a_a @ A @ bot_bo2131659635od_a_a ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(360,plain,
( ( ! [A4: set_Product_prod_a_a,A: product_prod_a_a] :
( ( A4 = bot_bo2131659635od_a_a )
=> ~ ( member449909584od_a_a @ A @ A4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(361,plain,
( ( ! [A4: set_Product_prod_a_a] :
( ! [Y3: product_prod_a_a] :
~ ( member449909584od_a_a @ Y3 @ A4 )
=> ( A4 = bot_bo2131659635od_a_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(362,plain,
( ( ! [A4: set_Product_prod_a_a] :
( ( ? [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ A4 ) )
= ( A4 != bot_bo2131659635od_a_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(363,plain,
( ( ! [C2: product_prod_a_a] :
~ ( member449909584od_a_a @ C2 @ bot_bo2131659635od_a_a ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(364,plain,
( ( ! [A4: set_Product_prod_a_a] :
( ( ! [X4: product_prod_a_a] :
~ ( member449909584od_a_a @ X4 @ A4 ) )
= ( A4 = bot_bo2131659635od_a_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(365,plain,
( ( ! [X: a,Fx: a,A4: set_a,F: a > a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Fx ) @ ( bNF_Gr_a_a @ A4 @ F ) )
=> ( ( F @ X )
= Fx ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(366,plain,
( ( ! [X: product_prod_a_a,Fx: product_prod_a_a,A4: set_Product_prod_a_a,F: product_prod_a_a > product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X @ Fx ) @ ( bNF_Gr1372473186od_a_a @ A4 @ F ) )
=> ( member449909584od_a_a @ X @ A4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(367,plain,
( ( ! [X: a,Fx: a,A4: set_a,F: a > a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Fx ) @ ( bNF_Gr_a_a @ A4 @ F ) )
=> ( member_a @ X @ A4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(368,plain,
( ( ! [R2: set_Product_prod_a_a,S3: set_Product_prod_a_a] :
( ( ord_less_eq_a_a_o
@ ^ [X4: a,Y4: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ R2 )
@ ^ [X4: a,Y4: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ S3 ) )
= ( ord_le1824328871od_a_a @ R2 @ S3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(369,plain,
( ( ord_le1824328871od_a_a
= ( ^ [A6: set_Product_prod_a_a,B5: set_Product_prod_a_a] :
( ord_le1347718902_a_a_o
@ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ A6 )
@ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ B5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(370,plain,
( ( ! [R2: set_Product_prod_a_a,S3: set_Product_prod_a_a] :
( ( ord_le1347718902_a_a_o
@ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ R2 )
@ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ S3 ) )
= ( ord_le1824328871od_a_a @ R2 @ S3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(371,plain,
( ( ! [B: set_Product_prod_a_a,A4: set_Product_prod_a_a,Q: product_prod_a_a > $o,P2: product_prod_a_a > $o] :
( ( ord_le1824328871od_a_a @ B @ A4 )
=> ( ! [X3: product_prod_a_a] :
( ( member449909584od_a_a @ X3 @ B )
=> ( ( Q @ X3 )
=> ( P2 @ X3 ) ) )
=> ( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [X4: product_prod_a_a] :
( ( member449909584od_a_a @ X4 @ B )
& ( Q @ X4 ) ) )
@ ( collec645855634od_a_a
@ ^ [X4: product_prod_a_a] :
( ( member449909584od_a_a @ X4 @ A4 )
& ( P2 @ X4 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(372,plain,
( ( ! [B: set_Product_prod_a_a,A4: set_Product_prod_a_a,P2: product_prod_a_a > $o] :
( ( ord_le1824328871od_a_a @ B @ A4 )
=> ( ( ord_le1824328871od_a_a @ B
@ ( collec645855634od_a_a
@ ^ [X4: product_prod_a_a] :
( ( member449909584od_a_a @ X4 @ A4 )
& ( P2 @ X4 ) ) ) )
= ( ! [X4: product_prod_a_a] :
( ( member449909584od_a_a @ X4 @ B )
=> ( P2 @ X4 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(373,plain,
( ( ! [A4: set_Product_prod_a_a,P2: product_prod_a_a > $o] :
( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [X4: product_prod_a_a] :
( ( member449909584od_a_a @ X4 @ A4 )
& ( P2 @ X4 ) ) )
@ A4 ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(374,plain,
( ( ! [X5: set_Product_prod_a_a,P2: product_prod_a_a > $o] :
( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [X4: product_prod_a_a] :
( ( member449909584od_a_a @ X4 @ X5 )
& ( P2 @ X4 ) ) )
@ X5 ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(375,plain,
( ( ! [X: product_prod_a_a,Z2: set_Product_prod_a_a,X5: set_Product_prod_a_a,P2: product_prod_a_a > $o] :
( ( member449909584od_a_a @ X @ Z2 )
=> ( ( ord_le1824328871od_a_a @ Z2
@ ( collec645855634od_a_a
@ ^ [X4: product_prod_a_a] :
( ( member449909584od_a_a @ X4 @ X5 )
& ( P2 @ X4 ) ) ) )
=> ( P2 @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(376,plain,
( ( ! [A4: set_Product_prod_a_a,B: set_Product_prod_a_a,X: product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A4 @ B )
=> ( ( member449909584od_a_a @ X @ A4 )
=> ( member449909584od_a_a @ X @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(377,plain,
( ( ! [A4: set_Product_prod_a_a,B: set_Product_prod_a_a,C2: product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A4 @ B )
=> ( ( member449909584od_a_a @ C2 @ A4 )
=> ( member449909584od_a_a @ C2 @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(378,plain,
( ( ord_le1824328871od_a_a
= ( ^ [A6: set_Product_prod_a_a,B5: set_Product_prod_a_a] :
! [X4: product_prod_a_a] :
( ( member449909584od_a_a @ X4 @ A6 )
=> ( member449909584od_a_a @ X4 @ B5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(379,plain,
( ( ord_le1824328871od_a_a
= ( ^ [A6: set_Product_prod_a_a,B5: set_Product_prod_a_a] :
! [T2: product_prod_a_a] :
( ( member449909584od_a_a @ T2 @ A6 )
=> ( member449909584od_a_a @ T2 @ B5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(380,plain,
( ( ! [R: set_Product_prod_a_a,S: set_Product_prod_a_a] :
( ! [X3: a,Y3: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ S ) )
=> ( ord_le1824328871od_a_a @ R @ S ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(381,plain,
( ( ! [A4: set_Pr1948701895od_a_a,F: produc1572603623od_a_a > product_prod_a_a,B: set_Product_prod_a_a] :
( ! [X3: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ X3 @ A4 )
=> ( member449909584od_a_a @ ( F @ X3 ) @ B ) )
=> ( ord_le1824328871od_a_a @ ( image_734753285od_a_a @ F @ A4 ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(382,plain,
( ( ! [A4: set_a,F: a > product_prod_a_a,B: set_Product_prod_a_a] :
( ! [X3: a] :
( ( member_a @ X3 @ A4 )
=> ( member449909584od_a_a @ ( F @ X3 ) @ B ) )
=> ( ord_le1824328871od_a_a @ ( image_1725938350od_a_a @ F @ A4 ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(383,plain,
( ( ! [A4: set_Product_prod_a_a,F: product_prod_a_a > produc1572603623od_a_a,B: set_Pr1948701895od_a_a] :
( ! [X3: product_prod_a_a] :
( ( member449909584od_a_a @ X3 @ A4 )
=> ( member2057358096od_a_a @ ( F @ X3 ) @ B ) )
=> ( ord_le456379495od_a_a @ ( image_1765377413od_a_a @ F @ A4 ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(384,plain,
( ( ! [A4: set_Product_prod_a_a,F: product_prod_a_a > a,B: set_a] :
( ! [X3: product_prod_a_a] :
( ( member449909584od_a_a @ X3 @ A4 )
=> ( member_a @ ( F @ X3 ) @ B ) )
=> ( ord_less_eq_set_a @ ( image_340790172_a_a_a @ F @ A4 ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(385,plain,
( ( ! [A4: set_Product_prod_a_a,F: product_prod_a_a > product_prod_a_a,B: set_Product_prod_a_a] :
( ! [X3: product_prod_a_a] :
( ( member449909584od_a_a @ X3 @ A4 )
=> ( member449909584od_a_a @ ( F @ X3 ) @ B ) )
=> ( ord_le1824328871od_a_a @ ( image_794773445od_a_a @ F @ A4 ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(386,plain,
( ( ! [A4: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ! [X3: product_prod_a_a] :
( ( member449909584od_a_a @ X3 @ A4 )
=> ( member449909584od_a_a @ X3 @ B ) )
=> ( ord_le1824328871od_a_a @ A4 @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(387,plain,
( ( ! [X: product_prod_a_a,A4: set_a,B: set_a] :
( ( member449909584od_a_a @ X @ ( product_product_a_a @ A4 @ B ) )
= ( member449909584od_a_a @ X
@ ( product_Sigma_a_a @ A4
@ ^ [Uu: a] : B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(388,plain,
( ( ! [C2: produc1572603623od_a_a,A4: set_Product_prod_a_a,B: product_prod_a_a > set_Product_prod_a_a] :
( ( member2057358096od_a_a @ C2 @ ( produc304751368od_a_a @ A4 @ B ) )
=> ~ ! [X3: product_prod_a_a] :
( ( member449909584od_a_a @ X3 @ A4 )
=> ! [Y3: product_prod_a_a] :
( ( member449909584od_a_a @ Y3 @ ( B @ X3 ) )
=> ( C2
!= ( produc1474507607od_a_a @ X3 @ Y3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(389,plain,
( ( ! [C2: product_prod_a_a,A4: set_a,B: a > set_a] :
( ( member449909584od_a_a @ C2 @ ( product_Sigma_a_a @ A4 @ B ) )
=> ~ ! [X3: a] :
( ( member_a @ X3 @ A4 )
=> ! [Y3: a] :
( ( member_a @ Y3 @ ( B @ X3 ) )
=> ( C2
!= ( product_Pair_a_a @ X3 @ Y3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(390,plain,
( ( ! [A: product_prod_a_a,B2: product_prod_a_a,A4: set_Product_prod_a_a,B: product_prod_a_a > set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B2 ) @ ( produc304751368od_a_a @ A4 @ B ) )
=> ( member449909584od_a_a @ A @ A4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(391,plain,
( ( ! [A: a,B2: a,A4: set_a,B: a > set_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B2 ) @ ( product_Sigma_a_a @ A4 @ B ) )
=> ( member_a @ A @ A4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(392,plain,
( ( ! [A: product_prod_a_a,B2: product_prod_a_a,A4: set_Product_prod_a_a,B: product_prod_a_a > set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B2 ) @ ( produc304751368od_a_a @ A4 @ B ) )
=> ( member449909584od_a_a @ B2 @ ( B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(393,plain,
( ( ! [A: a,B2: a,A4: set_a,B: a > set_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B2 ) @ ( product_Sigma_a_a @ A4 @ B ) )
=> ( member_a @ B2 @ ( B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(394,plain,
( ( ! [A: product_prod_a_a,B2: product_prod_a_a,A4: set_Product_prod_a_a,B: product_prod_a_a > set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B2 ) @ ( produc304751368od_a_a @ A4 @ B ) )
=> ~ ( ( member449909584od_a_a @ A @ A4 )
=> ~ ( member449909584od_a_a @ B2 @ ( B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(395,plain,
( ( ! [A: a,B2: a,A4: set_a,B: a > set_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B2 ) @ ( product_Sigma_a_a @ A4 @ B ) )
=> ~ ( ( member_a @ A @ A4 )
=> ~ ( member_a @ B2 @ ( B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(396,plain,
( ( ! [A: product_prod_a_a,A4: set_Product_prod_a_a,B2: product_prod_a_a,B: product_prod_a_a > set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ A4 )
=> ( ( member449909584od_a_a @ B2 @ ( B @ A ) )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B2 ) @ ( produc304751368od_a_a @ A4 @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(397,plain,
( ( ! [A: a,A4: set_a,B2: a,B: a > set_a] :
( ( member_a @ A @ A4 )
=> ( ( member_a @ B2 @ ( B @ A ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B2 ) @ ( product_Sigma_a_a @ A4 @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(398,plain,
( ( ! [A: product_prod_a_a,B2: product_prod_a_a,A4: set_Product_prod_a_a,B: product_prod_a_a > set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B2 ) @ ( produc304751368od_a_a @ A4 @ B ) )
= ( ( member449909584od_a_a @ A @ A4 )
& ( member449909584od_a_a @ B2 @ ( B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(399,plain,
( ( ! [A: a,B2: a,A4: set_a,B: a > set_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B2 ) @ ( product_Sigma_a_a @ A4 @ B ) )
= ( ( member_a @ A @ A4 )
& ( member_a @ B2 @ ( B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(400,plain,
( ( ! [A: a,B2: a,A2: a,B3: a,R: set_Product_prod_a_a,S: set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ A @ B2 ) @ ( product_Pair_a_a @ A2 @ B3 ) ) @ ( lex_prod_a_a @ R @ S ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ A2 ) @ R )
| ( ( A = A2 )
& ( member449909584od_a_a @ ( product_Pair_a_a @ B2 @ B3 ) @ S ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(401,plain,
( ( ! [B2: product_prod_a_a,F: product_prod_a_a > product_prod_a_a,X: product_prod_a_a,C2: product_prod_a_a,G: product_prod_a_a > product_prod_a_a,A4: set_Product_prod_a_a] :
( ( B2
= ( F @ X ) )
=> ( ( C2
= ( G @ X ) )
=> ( ( member449909584od_a_a @ X @ A4 )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ B2 @ C2 ) @ ( bNF_Gr200450189od_a_a @ A4 @ F @ G ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(402,plain,
( ( ! [B2: a,F: produc1572603623od_a_a > a,X: produc1572603623od_a_a,C2: a,G: produc1572603623od_a_a > a,A4: set_Pr1948701895od_a_a] :
( ( B2
= ( F @ X ) )
=> ( ( C2
= ( G @ X ) )
=> ( ( member2057358096od_a_a @ X @ A4 )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ B2 @ C2 ) @ ( bNF_Gr356189709_a_a_a @ A4 @ F @ G ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(403,plain,
( ( ! [B2: a,F: a > a,X: a,C2: a,G: a > a,A4: set_a] :
( ( B2
= ( F @ X ) )
=> ( ( C2
= ( G @ X ) )
=> ( ( member_a @ X @ A4 )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ B2 @ C2 ) @ ( bNF_Gr423046308_a_a_a @ A4 @ F @ G ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(404,plain,
( ( ! [B2: a,F: product_prod_a_a > a,X: product_prod_a_a,C2: a,G: product_prod_a_a > a,A4: set_Product_prod_a_a] :
( ( B2
= ( F @ X ) )
=> ( ( C2
= ( G @ X ) )
=> ( ( member449909584od_a_a @ X @ A4 )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ B2 @ C2 ) @ ( bNF_Gr1853143117_a_a_a @ A4 @ F @ G ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(405,plain,
( ( ! [P2: a > a > $o,Y: a,X: a] :
( ( P2 @ Y @ X )
=> ( P2 @ ( product_snd_a_a @ ( product_Pair_a_a @ X @ Y ) ) @ ( product_fst_a_a @ ( product_Pair_a_a @ X @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(406,plain,
( ( ! [P2: a > $o,P: a,Q: a > $o,Q2: a] :
( ( P2 @ P )
=> ( ( Q @ Q2 )
=> ( ( P2 @ ( product_fst_a_a @ ( product_Pair_a_a @ P @ Q2 ) ) )
& ( Q @ ( product_snd_a_a @ ( product_Pair_a_a @ P @ Q2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(407,plain,
( ( ! [P2: a > a > $o,X: a,Y: a,A: product_prod_a_a] :
( ( P2 @ X @ Y )
=> ( ( A
= ( product_Pair_a_a @ X @ Y ) )
=> ( P2 @ ( product_fst_a_a @ A ) @ ( product_snd_a_a @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(408,plain,
( ( product_swap_a_a
= ( ^ [P4: product_prod_a_a] : ( product_Pair_a_a @ ( product_snd_a_a @ P4 ) @ ( product_fst_a_a @ P4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(409,plain,
( ( ! [Prod: product_prod_a_a] :
( Prod
= ( product_Pair_a_a @ ( product_fst_a_a @ Prod ) @ ( product_snd_a_a @ Prod ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(410,plain,
( ( ! [T: product_prod_a_a] :
( T
= ( product_Pair_a_a @ ( product_fst_a_a @ T ) @ ( product_snd_a_a @ T ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(411,plain,
( ( ! [X1: a,X2: a] :
( ( product_snd_a_a @ ( product_Pair_a_a @ X1 @ X2 ) )
= X2 ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(412,plain,
( ( ! [X: a,Y: a,A: a] :
( ( ( product_snd_a_a @ ( product_Pair_a_a @ X @ Y ) )
= A )
=> ( Y = A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(413,plain,
( ( ! [X: product_prod_a_a,Y: a,Z: a] :
( ( X
= ( product_Pair_a_a @ Y @ Z ) )
=> ( ( product_snd_a_a @ X )
= Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(414,plain,
( ( ! [B2: a,P: product_prod_a_a] :
( ( B2
= ( product_snd_a_a @ P ) )
= ( ? [A5: a] :
( P
= ( product_Pair_a_a @ A5 @ B2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(415,plain,
( ( ! [Prod: product_prod_a_a] :
( ( product_Pair_a_a @ ( product_fst_a_a @ Prod ) @ ( product_snd_a_a @ Prod ) )
= Prod ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(416,plain,
( ( ! [X: product_prod_a_a,Y: a,Z: a] :
( ( X
= ( product_Pair_a_a @ Y @ Z ) )
=> ( ( product_fst_a_a @ X )
= Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(417,plain,
( ( ! [A: a,P: product_prod_a_a] :
( ( A
= ( product_fst_a_a @ P ) )
= ( ? [B6: a] :
( P
= ( product_Pair_a_a @ A @ B6 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(418,plain,
( ( top_top_a_a_o
= ( ^ [X4: a,Y4: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ top_to398455383od_a_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(419,plain,
( ( ! [C2: product_prod_a_a,F: a > a,G: a > a,R2: set_Product_prod_a_a] :
( ( member449909584od_a_a @ C2 @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ F @ G ) @ R2 ) )
=> ~ ! [X3: a,Y3: a] :
( ( C2
= ( product_Pair_a_a @ ( F @ X3 ) @ ( G @ Y3 ) ) )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(420,plain,
( ( ! [X1: a,X2: a] :
( ( product_fst_a_a @ ( product_Pair_a_a @ X1 @ X2 ) )
= X1 ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(421,plain,
( ( ! [X: a,Y: a,A: a] :
( ( ( product_fst_a_a @ ( product_Pair_a_a @ X @ Y ) )
= A )
=> ( X = A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(422,plain,
( ( top_to1483957574_a_a_o
= ( ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ top_to398455383od_a_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(423,plain,
( ( ! [A: a,B2: a,R2: set_Product_prod_a_a,F: a > a,G: a > a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B2 ) @ R2 )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ ( F @ A ) @ ( G @ B2 ) ) @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ F @ G ) @ R2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[175]) ).
thf(424,plain,
( ( ! [F: product_prod_a_a > a,G: product_prod_a_a > a,A: product_prod_a_a,B2: product_prod_a_a] :
( ( produc363290532_a_a_a @ F @ G @ ( produc1474507607od_a_a @ A @ B2 ) )
= ( product_Pair_a_a @ ( F @ A ) @ ( G @ B2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[177]) ).
thf(425,plain,
( ( ! [F: a > product_prod_a_a,G: a > product_prod_a_a,A: a,B2: a] :
( ( produc2012818120od_a_a @ F @ G @ ( product_Pair_a_a @ A @ B2 ) )
= ( produc1474507607od_a_a @ ( F @ A ) @ ( G @ B2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(426,plain,
( ( ! [F: a > a,G: a > a,A: a,B2: a] :
( ( produc700022774_a_a_a @ F @ G @ ( product_Pair_a_a @ A @ B2 ) )
= ( product_Pair_a_a @ ( F @ A ) @ ( G @ B2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[179]) ).
thf(427,plain,
( ( ! [P2: a > $o,X: a,Y5: a,Y: a,R2: a > set_Product_prod_a_a] :
( ( P2 @ X )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y5 @ Y ) @ ( R2 @ X ) )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ X @ Y5 ) @ ( product_Pair_a_a @ X @ Y ) ) @ ( same_fst_a_a @ P2 @ R2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(428,plain,
( ( ! [X: product_prod_a_a] : ( member449909584od_a_a @ X @ top_to398455383od_a_a ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(429,plain,
( ( ! [A4: set_Product_prod_a_a] :
( ! [X3: product_prod_a_a] : ( member449909584od_a_a @ X3 @ A4 )
=> ( top_to398455383od_a_a = A4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(430,plain,
( ( ? [X3: product_prod_a_a] : ( member449909584od_a_a @ X3 @ top_to398455383od_a_a ) )
= $true ),
inference(unfold_def,[status(thm)],[190]) ).
thf(431,plain,
( ( ! [X: product_prod_a_a] : ( member449909584od_a_a @ X @ top_to398455383od_a_a ) )
= $true ),
inference(unfold_def,[status(thm)],[193]) ).
thf(432,plain,
( ( minus_1507102574od_a_a
= ( ^ [A6: set_Product_prod_a_a,B5: set_Product_prod_a_a] :
( collec645855634od_a_a
@ ^ [X4: product_prod_a_a] :
( ( member449909584od_a_a @ X4 @ A6 )
& ~ ( member449909584od_a_a @ X4 @ B5 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[196]) ).
thf(433,plain,
( ( ! [F: product_prod_a_a > product_prod_a_a,A4: set_Product_prod_a_a,P2: product_prod_a_a > $o] :
( ( collec645855634od_a_a
@ ^ [X4: product_prod_a_a] :
( ( member449909584od_a_a @ X4 @ ( image_794773445od_a_a @ F @ A4 ) )
& ( P2 @ X4 ) ) )
= ( image_794773445od_a_a @ F
@ ( collec645855634od_a_a
@ ^ [X4: product_prod_a_a] :
( ( member449909584od_a_a @ X4 @ A4 )
& ( P2 @ ( F @ X4 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[205]) ).
thf(434,plain,
( ( ! [B2: produc1572603623od_a_a,F: product_prod_a_a > produc1572603623od_a_a,A4: set_Product_prod_a_a] :
( ( member2057358096od_a_a @ B2 @ ( image_1765377413od_a_a @ F @ A4 ) )
=> ~ ! [X3: product_prod_a_a] :
( ( B2
= ( F @ X3 ) )
=> ~ ( member449909584od_a_a @ X3 @ A4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[208]) ).
thf(435,plain,
( ( ! [B2: a,F: product_prod_a_a > a,A4: set_Product_prod_a_a] :
( ( member_a @ B2 @ ( image_340790172_a_a_a @ F @ A4 ) )
=> ~ ! [X3: product_prod_a_a] :
( ( B2
= ( F @ X3 ) )
=> ~ ( member449909584od_a_a @ X3 @ A4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[211]) ).
thf(436,plain,
( ( ! [B2: product_prod_a_a,F: produc1572603623od_a_a > product_prod_a_a,A4: set_Pr1948701895od_a_a] :
( ( member449909584od_a_a @ B2 @ ( image_734753285od_a_a @ F @ A4 ) )
=> ~ ! [X3: produc1572603623od_a_a] :
( ( B2
= ( F @ X3 ) )
=> ~ ( member2057358096od_a_a @ X3 @ A4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[212]) ).
thf(437,plain,
( ( ! [B2: product_prod_a_a,F: a > product_prod_a_a,A4: set_a] :
( ( member449909584od_a_a @ B2 @ ( image_1725938350od_a_a @ F @ A4 ) )
=> ~ ! [X3: a] :
( ( B2
= ( F @ X3 ) )
=> ~ ( member_a @ X3 @ A4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[213]) ).
thf(438,plain,
( ( ! [B2: product_prod_a_a,F: product_prod_a_a > product_prod_a_a,A4: set_Product_prod_a_a] :
( ( member449909584od_a_a @ B2 @ ( image_794773445od_a_a @ F @ A4 ) )
=> ~ ! [X3: product_prod_a_a] :
( ( B2
= ( F @ X3 ) )
=> ~ ( member449909584od_a_a @ X3 @ A4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[214]) ).
thf(439,plain,
( ( ! [C2: product_prod_a_a,A4: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( member449909584od_a_a @ C2 @ ( minus_1507102574od_a_a @ A4 @ B ) )
=> ~ ( ( member449909584od_a_a @ C2 @ A4 )
=> ( member449909584od_a_a @ C2 @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[217]) ).
thf(440,plain,
( ( ! [C2: product_prod_a_a,A4: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( member449909584od_a_a @ C2 @ ( minus_1507102574od_a_a @ A4 @ B ) )
=> ( member449909584od_a_a @ C2 @ A4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[220]) ).
thf(441,plain,
( ( ! [C2: product_prod_a_a,A4: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( member449909584od_a_a @ C2 @ ( minus_1507102574od_a_a @ A4 @ B ) )
=> ~ ( member449909584od_a_a @ C2 @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[223]) ).
thf(442,plain,
( ( ! [X: produc1572603623od_a_a,A4: set_Pr1948701895od_a_a,F: produc1572603623od_a_a > product_prod_a_a] :
( ( member2057358096od_a_a @ X @ A4 )
=> ( member449909584od_a_a @ ( F @ X ) @ ( image_734753285od_a_a @ F @ A4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[226]) ).
thf(443,plain,
( ( ! [X: a,A4: set_a,F: a > product_prod_a_a] :
( ( member_a @ X @ A4 )
=> ( member449909584od_a_a @ ( F @ X ) @ ( image_1725938350od_a_a @ F @ A4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[229]) ).
thf(444,plain,
( ( ! [X: product_prod_a_a,A4: set_Product_prod_a_a,F: product_prod_a_a > produc1572603623od_a_a] :
( ( member449909584od_a_a @ X @ A4 )
=> ( member2057358096od_a_a @ ( F @ X ) @ ( image_1765377413od_a_a @ F @ A4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[230]) ).
thf(445,plain,
( ( ! [X: product_prod_a_a,A4: set_Product_prod_a_a,F: product_prod_a_a > a] :
( ( member449909584od_a_a @ X @ A4 )
=> ( member_a @ ( F @ X ) @ ( image_340790172_a_a_a @ F @ A4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[231]) ).
thf(446,plain,
( ( ! [X: product_prod_a_a,A4: set_Product_prod_a_a,F: product_prod_a_a > product_prod_a_a] :
( ( member449909584od_a_a @ X @ A4 )
=> ( member449909584od_a_a @ ( F @ X ) @ ( image_794773445od_a_a @ F @ A4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[232]) ).
thf(447,plain,
( ( ! [X: produc1572603623od_a_a,A4: set_Pr1948701895od_a_a,B2: product_prod_a_a,F: produc1572603623od_a_a > product_prod_a_a] :
( ( member2057358096od_a_a @ X @ A4 )
=> ( ( B2
= ( F @ X ) )
=> ( member449909584od_a_a @ B2 @ ( image_734753285od_a_a @ F @ A4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[235]) ).
thf(448,plain,
( ( ! [X: a,A4: set_a,B2: product_prod_a_a,F: a > product_prod_a_a] :
( ( member_a @ X @ A4 )
=> ( ( B2
= ( F @ X ) )
=> ( member449909584od_a_a @ B2 @ ( image_1725938350od_a_a @ F @ A4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(449,plain,
( ( ! [X: product_prod_a_a,A4: set_Product_prod_a_a,B2: produc1572603623od_a_a,F: product_prod_a_a > produc1572603623od_a_a] :
( ( member449909584od_a_a @ X @ A4 )
=> ( ( B2
= ( F @ X ) )
=> ( member2057358096od_a_a @ B2 @ ( image_1765377413od_a_a @ F @ A4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(450,plain,
( ( ! [X: product_prod_a_a,A4: set_Product_prod_a_a,B2: a,F: product_prod_a_a > a] :
( ( member449909584od_a_a @ X @ A4 )
=> ( ( B2
= ( F @ X ) )
=> ( member_a @ B2 @ ( image_340790172_a_a_a @ F @ A4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[240]) ).
thf(451,plain,
( ( ! [X: product_prod_a_a,A4: set_Product_prod_a_a,B2: product_prod_a_a,F: product_prod_a_a > product_prod_a_a] :
( ( member449909584od_a_a @ X @ A4 )
=> ( ( B2
= ( F @ X ) )
=> ( member449909584od_a_a @ B2 @ ( image_794773445od_a_a @ F @ A4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[241]) ).
thf(452,plain,
( ( minus_1507102574od_a_a
= ( ^ [A6: set_Product_prod_a_a,B5: set_Product_prod_a_a] :
( collec645855634od_a_a
@ ( minus_1797478127_a_a_o
@ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ A6 )
@ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ B5 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[244]) ).
thf(453,plain,
( ( ! [C2: product_prod_a_a,A4: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( member449909584od_a_a @ C2 @ ( minus_1507102574od_a_a @ A4 @ B ) )
= ( ( member449909584od_a_a @ C2 @ A4 )
& ~ ( member449909584od_a_a @ C2 @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(454,plain,
( ( ! [B2: product_prod_a_a,F: produc1572603623od_a_a > product_prod_a_a,X: produc1572603623od_a_a,A4: set_Pr1948701895od_a_a] :
( ( B2
= ( F @ X ) )
=> ( ( member2057358096od_a_a @ X @ A4 )
=> ( member449909584od_a_a @ B2 @ ( image_734753285od_a_a @ F @ A4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(455,plain,
( ( ! [B2: product_prod_a_a,F: a > product_prod_a_a,X: a,A4: set_a] :
( ( B2
= ( F @ X ) )
=> ( ( member_a @ X @ A4 )
=> ( member449909584od_a_a @ B2 @ ( image_1725938350od_a_a @ F @ A4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253]) ).
thf(456,plain,
( ( ! [B2: produc1572603623od_a_a,F: product_prod_a_a > produc1572603623od_a_a,X: product_prod_a_a,A4: set_Product_prod_a_a] :
( ( B2
= ( F @ X ) )
=> ( ( member449909584od_a_a @ X @ A4 )
=> ( member2057358096od_a_a @ B2 @ ( image_1765377413od_a_a @ F @ A4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(457,plain,
( ( ! [B2: a,F: product_prod_a_a > a,X: product_prod_a_a,A4: set_Product_prod_a_a] :
( ( B2
= ( F @ X ) )
=> ( ( member449909584od_a_a @ X @ A4 )
=> ( member_a @ B2 @ ( image_340790172_a_a_a @ F @ A4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[255]) ).
thf(458,plain,
( ( ! [B2: product_prod_a_a,F: product_prod_a_a > product_prod_a_a,X: product_prod_a_a,A4: set_Product_prod_a_a] :
( ( B2
= ( F @ X ) )
=> ( ( member449909584od_a_a @ X @ A4 )
=> ( member449909584od_a_a @ B2 @ ( image_794773445od_a_a @ F @ A4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[256]) ).
thf(459,plain,
( ( ! [C2: product_prod_a_a,A4: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( member449909584od_a_a @ C2 @ A4 )
=> ( ~ ( member449909584od_a_a @ C2 @ B )
=> ( member449909584od_a_a @ C2 @ ( minus_1507102574od_a_a @ A4 @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[259]) ).
thf(460,plain,
( ( ! [A4: set_Product_prod_a_a] :
( ( collec645855634od_a_a
@ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ A4 ) )
= A4 ) )
= $true ),
inference(unfold_def,[status(thm)],[262]) ).
thf(461,plain,
( ( ! [A: product_prod_a_a,P2: product_prod_a_a > $o] :
( ( member449909584od_a_a @ A @ ( collec645855634od_a_a @ P2 ) )
= ( P2 @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[265]) ).
thf(462,plain,
( ( ! [Y: a,X: a,A4: set_Product_prod_a_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ ( image_794773445od_a_a @ product_swap_a_a @ A4 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ A4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[270]) ).
thf(463,plain,
( ( ! [Relation: set_Product_prod_a_a,Carrier: set_a] :
( ! [X3: a,Y3: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ Relation )
=> ( member_a @ X3 @ Carrier ) )
=> ( ! [X3: a,Y3: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ Relation )
=> ( member_a @ Y3 @ Carrier ) )
=> ( ( order_preorder_on_a @ Carrier @ Relation )
=> ( prefer1292084992ence_a @ Carrier @ Relation ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[272]) ).
thf(464,plain,
( ( prefer1292084992ence_a
= ( ^ [Carrier2: set_a,Relation2: set_Product_prod_a_a] :
( ! [X4: a,Y4: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ Relation2 )
=> ( member_a @ X4 @ Carrier2 ) )
& ! [X4: a,Y4: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ Relation2 )
=> ( member_a @ Y4 @ Carrier2 ) )
& ( order_preorder_on_a @ Carrier2 @ Relation2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[275]) ).
thf(465,plain,
( ( ! [R2: set_Product_prod_a_a,S3: set_Product_prod_a_a] :
( ( ( ^ [X4: a,Y4: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ R2 ) )
= ( ^ [X4: a,Y4: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ S3 ) ) )
= ( R2 = S3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[278]) ).
thf(466,plain,
( ( prefer436369274d_as_a
= ( ^ [X4: a,B5: set_a,P3: set_Product_prod_a_a] :
( collect_a
@ ^ [Y4: a] :
( ( member_a @ Y4 @ B5 )
& ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ P3 )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Y4 @ X4 ) @ P3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[280]) ).
thf(467,plain,
( ( prefer1676310729than_a
= ( ^ [X4: a,B5: set_a,P3: set_Product_prod_a_a] :
( collect_a
@ ^ [Y4: a] :
( ( member_a @ Y4 @ B5 )
& ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ P3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[283]) ).
thf(468,plain,
( ( ! [F: product_prod_a_a > $o,A: a,B2: a] :
( ( product_curry_a_a_o @ F @ A @ B2 )
=> ( F @ ( product_Pair_a_a @ A @ B2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[286]) ).
thf(469,plain,
( ( ! [F: product_prod_a_a > $o,A: a,B2: a] :
( ( product_curry_a_a_o @ F @ A @ B2 )
=> ( F @ ( product_Pair_a_a @ A @ B2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(470,plain,
( ( ! [X: a,Y: a] :
( ( product_swap_a_a @ ( product_Pair_a_a @ X @ Y ) )
= ( product_Pair_a_a @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(471,plain,
( ( ! [Carrier: set_Product_prod_a_a,Relation: set_Pr1948701895od_a_a,X: product_prod_a_a,Y: product_prod_a_a] :
( ( prefer1338892073od_a_a @ Carrier @ Relation )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X @ Y ) @ Relation )
=> ( member449909584od_a_a @ X @ Carrier ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(472,plain,
( ( ! [Carrier: set_a,Relation: set_Product_prod_a_a,X: a,Y: a] :
( ( prefer1292084992ence_a @ Carrier @ Relation )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ Relation )
=> ( member_a @ X @ Carrier ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(473,plain,
( ( ! [Carrier: set_a,Relation: set_Product_prod_a_a,X: a,Y: a,Z: a] :
( ( prefer1292084992ence_a @ Carrier @ Relation )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ Relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ Relation ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ Z ) @ Relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Z @ Y ) @ Relation ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Z ) @ Relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Z @ X ) @ Relation ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295]) ).
thf(474,plain,
( ( ! [F: product_prod_a_a > $o,A: a,B2: a] :
( ( F @ ( product_Pair_a_a @ A @ B2 ) )
=> ( product_curry_a_a_o @ F @ A @ B2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(475,plain,
( ( ! [R: a,S: a,R2: set_Product_prod_a_a,S2: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ R @ S ) @ R2 )
=> ( ( S2 = S )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ R @ S2 ) @ R2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(476,plain,
( ( prefer161218362good_a
= ( ^ [X4: a,B5: set_a,P3: set_Product_prod_a_a] :
( collect_a
@ ^ [Y4: a] :
( ( member_a @ Y4 @ B5 )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Y4 @ X4 ) @ P3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(477,plain,
( ( ! [Y: product_prod_a_a] :
~ ! [A3: a,B4: a] :
( Y
!= ( product_Pair_a_a @ A3 @ B4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[304]) ).
thf(478,plain,
( ( ! [P2: product_prod_a_a > $o,Prod: product_prod_a_a] :
( ! [A3: a,B4: a] : ( P2 @ ( product_Pair_a_a @ A3 @ B4 ) )
=> ( P2 @ Prod ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(479,plain,
( ( ! [P2: produc1572603623od_a_a > $o,X: produc1572603623od_a_a] :
( ! [A3: product_prod_a_a,B4: a,C: a] : ( P2 @ ( produc1474507607od_a_a @ A3 @ ( product_Pair_a_a @ B4 @ C ) ) )
=> ( P2 @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(480,plain,
( ( ! [Y: produc1572603623od_a_a] :
~ ! [A3: product_prod_a_a,B4: a,C: a] :
( Y
!= ( produc1474507607od_a_a @ A3 @ ( product_Pair_a_a @ B4 @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[308]) ).
thf(481,plain,
( ( ! [Y: produc1921647824od_a_a] :
~ ! [A3: a,B4: a,C: a] :
( Y
!= ( produc1299253312od_a_a @ A3 @ ( product_Pair_a_a @ B4 @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[309]) ).
thf(482,plain,
( ( ! [A: a,B2: a,A2: a,B3: a] :
( ( ( product_Pair_a_a @ A @ B2 )
= ( product_Pair_a_a @ A2 @ B3 ) )
=> ~ ( ( A = A2 )
=> ( B2 != B3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312]) ).
thf(483,plain,
( ( ! [P2: product_prod_a_a > $o,P: product_prod_a_a] :
( ! [A3: a,B4: a] : ( P2 @ ( product_Pair_a_a @ A3 @ B4 ) )
=> ( P2 @ P ) ) )
= $true ),
inference(unfold_def,[status(thm)],[319]) ).
thf(484,plain,
( ( ! [P: product_prod_a_a] :
? [X3: a,Y3: a] :
( P
= ( product_Pair_a_a @ X3 @ Y3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[326]) ).
thf(485,plain,
( ( ! [A: a,B2: a,A2: a,B3: a] :
( ( ( product_Pair_a_a @ A @ B2 )
= ( product_Pair_a_a @ A2 @ B3 ) )
= ( ( A = A2 )
& ( B2 = B3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[333]) ).
thf(486,plain,
( ( ! [X1: a,X2: a,Y1: a,Y2: a] :
( ( ( product_Pair_a_a @ X1 @ X2 )
= ( product_Pair_a_a @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X2 = Y2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(487,plain,
( ( ! [X: a,Y: a,B: set_a,Pr: set_Product_prod_a_a] :
( ( member_a @ X @ ( prefer161218362good_a @ Y @ B @ Pr ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ Pr ) ) )
= $true ),
inference(unfold_def,[status(thm)],[347]) ).
thf(488,plain,
( ( ! [X: product_prod_a_a,Y: product_prod_a_a,B: set_Product_prod_a_a,Pr: set_Pr1948701895od_a_a] :
( ( member449909584od_a_a @ X @ ( prefer477097315od_a_a @ Y @ B @ Pr ) )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X @ Y ) @ Pr ) ) )
= $true ),
inference(unfold_def,[status(thm)],[348]) ).
thf(489,plain,
( ( member_a @ z @ ( prefer161218362good_a @ y @ b @ pr ) )
= $true ),
inference(unfold_def,[status(thm)],[355]) ).
thf(490,plain,
( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ z @ y ) @ pr ) )
= $true ),
inference(polarity_switch,[status(thm)],[358]) ).
thf(491,plain,
( ( member_a @ z @ ( prefer161218362good_a @ y @ b @ pr ) )
= $true ),
inference(copy,[status(thm)],[489]) ).
thf(492,plain,
( ( ! [X: product_prod_a_a,Y: product_prod_a_a,B: set_Product_prod_a_a,Pr: set_Pr1948701895od_a_a] :
( ( member449909584od_a_a @ X @ ( prefer477097315od_a_a @ Y @ B @ Pr ) )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X @ Y ) @ Pr ) ) )
= $true ),
inference(copy,[status(thm)],[488]) ).
thf(493,plain,
( ( ! [X: a,Y: a,B: set_a,Pr: set_Product_prod_a_a] :
( ( member_a @ X @ ( prefer161218362good_a @ Y @ B @ Pr ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ Pr ) ) )
= $true ),
inference(copy,[status(thm)],[487]) ).
thf(494,plain,
( ( ! [X1: a,X2: a,Y1: a,Y2: a] :
( ( ( product_Pair_a_a @ X1 @ X2 )
= ( product_Pair_a_a @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X2 = Y2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[486]) ).
thf(495,plain,
( ( ! [A: a,B2: a,A2: a,B3: a] :
( ( ( product_Pair_a_a @ A @ B2 )
= ( product_Pair_a_a @ A2 @ B3 ) )
= ( ( A = A2 )
& ( B2 = B3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[485]) ).
thf(496,plain,
( ( ! [P: product_prod_a_a] :
? [X3: a,Y3: a] :
( P
= ( product_Pair_a_a @ X3 @ Y3 ) ) )
= $true ),
inference(copy,[status(thm)],[484]) ).
thf(497,plain,
( ( ! [P2: product_prod_a_a > $o,P: product_prod_a_a] :
( ! [A3: a,B4: a] : ( P2 @ ( product_Pair_a_a @ A3 @ B4 ) )
=> ( P2 @ P ) ) )
= $true ),
inference(copy,[status(thm)],[483]) ).
thf(498,plain,
( ( ! [A: a,B2: a,A2: a,B3: a] :
( ( ( product_Pair_a_a @ A @ B2 )
= ( product_Pair_a_a @ A2 @ B3 ) )
=> ~ ( ( A = A2 )
=> ( B2 != B3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[482]) ).
thf(499,plain,
( ( ! [Y: produc1921647824od_a_a] :
~ ! [A3: a,B4: a,C: a] :
( Y
!= ( produc1299253312od_a_a @ A3 @ ( product_Pair_a_a @ B4 @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[481]) ).
thf(500,plain,
( ( ! [Y: produc1572603623od_a_a] :
~ ! [A3: product_prod_a_a,B4: a,C: a] :
( Y
!= ( produc1474507607od_a_a @ A3 @ ( product_Pair_a_a @ B4 @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[480]) ).
thf(501,plain,
( ( ! [P2: produc1572603623od_a_a > $o,X: produc1572603623od_a_a] :
( ! [A3: product_prod_a_a,B4: a,C: a] : ( P2 @ ( produc1474507607od_a_a @ A3 @ ( product_Pair_a_a @ B4 @ C ) ) )
=> ( P2 @ X ) ) )
= $true ),
inference(copy,[status(thm)],[479]) ).
thf(502,plain,
( ( ! [P2: product_prod_a_a > $o,Prod: product_prod_a_a] :
( ! [A3: a,B4: a] : ( P2 @ ( product_Pair_a_a @ A3 @ B4 ) )
=> ( P2 @ Prod ) ) )
= $true ),
inference(copy,[status(thm)],[478]) ).
thf(503,plain,
( ( ! [Y: product_prod_a_a] :
~ ! [A3: a,B4: a] :
( Y
!= ( product_Pair_a_a @ A3 @ B4 ) ) )
= $true ),
inference(copy,[status(thm)],[477]) ).
thf(504,plain,
( ( prefer161218362good_a
= ( ^ [X4: a,B5: set_a,P3: set_Product_prod_a_a] :
( collect_a
@ ^ [Y4: a] :
( ( member_a @ Y4 @ B5 )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Y4 @ X4 ) @ P3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[476]) ).
thf(505,plain,
( ( ! [R: a,S: a,R2: set_Product_prod_a_a,S2: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ R @ S ) @ R2 )
=> ( ( S2 = S )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ R @ S2 ) @ R2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[475]) ).
thf(506,plain,
( ( ! [F: product_prod_a_a > $o,A: a,B2: a] :
( ( F @ ( product_Pair_a_a @ A @ B2 ) )
=> ( product_curry_a_a_o @ F @ A @ B2 ) ) )
= $true ),
inference(copy,[status(thm)],[474]) ).
thf(507,plain,
( ( ! [Carrier: set_a,Relation: set_Product_prod_a_a,X: a,Y: a,Z: a] :
( ( prefer1292084992ence_a @ Carrier @ Relation )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ Relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ Relation ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ Z ) @ Relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Z @ Y ) @ Relation ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Z ) @ Relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Z @ X ) @ Relation ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[473]) ).
thf(508,plain,
( ( ! [Carrier: set_a,Relation: set_Product_prod_a_a,X: a,Y: a] :
( ( prefer1292084992ence_a @ Carrier @ Relation )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ Relation )
=> ( member_a @ X @ Carrier ) ) ) )
= $true ),
inference(copy,[status(thm)],[472]) ).
thf(509,plain,
( ( ! [Carrier: set_Product_prod_a_a,Relation: set_Pr1948701895od_a_a,X: product_prod_a_a,Y: product_prod_a_a] :
( ( prefer1338892073od_a_a @ Carrier @ Relation )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X @ Y ) @ Relation )
=> ( member449909584od_a_a @ X @ Carrier ) ) ) )
= $true ),
inference(copy,[status(thm)],[471]) ).
thf(510,plain,
( ( ! [X: a,Y: a] :
( ( product_swap_a_a @ ( product_Pair_a_a @ X @ Y ) )
= ( product_Pair_a_a @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[470]) ).
thf(511,plain,
( ( ! [F: product_prod_a_a > $o,A: a,B2: a] :
( ( product_curry_a_a_o @ F @ A @ B2 )
=> ( F @ ( product_Pair_a_a @ A @ B2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[469]) ).
thf(512,plain,
( ( ! [F: product_prod_a_a > $o,A: a,B2: a] :
( ( product_curry_a_a_o @ F @ A @ B2 )
=> ( F @ ( product_Pair_a_a @ A @ B2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[468]) ).
thf(513,plain,
( ( prefer1676310729than_a
= ( ^ [X4: a,B5: set_a,P3: set_Product_prod_a_a] :
( collect_a
@ ^ [Y4: a] :
( ( member_a @ Y4 @ B5 )
& ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ P3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[467]) ).
thf(514,plain,
( ( prefer436369274d_as_a
= ( ^ [X4: a,B5: set_a,P3: set_Product_prod_a_a] :
( collect_a
@ ^ [Y4: a] :
( ( member_a @ Y4 @ B5 )
& ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ P3 )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Y4 @ X4 ) @ P3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[466]) ).
thf(515,plain,
( ( ! [R2: set_Product_prod_a_a,S3: set_Product_prod_a_a] :
( ( ( ^ [X4: a,Y4: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ R2 ) )
= ( ^ [X4: a,Y4: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ S3 ) ) )
= ( R2 = S3 ) ) )
= $true ),
inference(copy,[status(thm)],[465]) ).
thf(516,plain,
( ( prefer1292084992ence_a
= ( ^ [Carrier2: set_a,Relation2: set_Product_prod_a_a] :
( ! [X4: a,Y4: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ Relation2 )
=> ( member_a @ X4 @ Carrier2 ) )
& ! [X4: a,Y4: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ Relation2 )
=> ( member_a @ Y4 @ Carrier2 ) )
& ( order_preorder_on_a @ Carrier2 @ Relation2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[464]) ).
thf(517,plain,
( ( ! [Relation: set_Product_prod_a_a,Carrier: set_a] :
( ! [X3: a,Y3: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ Relation )
=> ( member_a @ X3 @ Carrier ) )
=> ( ! [X3: a,Y3: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ Relation )
=> ( member_a @ Y3 @ Carrier ) )
=> ( ( order_preorder_on_a @ Carrier @ Relation )
=> ( prefer1292084992ence_a @ Carrier @ Relation ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[463]) ).
thf(518,plain,
( ( ! [Y: a,X: a,A4: set_Product_prod_a_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ ( image_794773445od_a_a @ product_swap_a_a @ A4 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ A4 ) ) )
= $true ),
inference(copy,[status(thm)],[462]) ).
thf(519,plain,
( ( ! [A: product_prod_a_a,P2: product_prod_a_a > $o] :
( ( member449909584od_a_a @ A @ ( collec645855634od_a_a @ P2 ) )
= ( P2 @ A ) ) )
= $true ),
inference(copy,[status(thm)],[461]) ).
thf(520,plain,
( ( ! [A4: set_Product_prod_a_a] :
( ( collec645855634od_a_a
@ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ A4 ) )
= A4 ) )
= $true ),
inference(copy,[status(thm)],[460]) ).
thf(521,plain,
( ( ! [C2: product_prod_a_a,A4: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( member449909584od_a_a @ C2 @ A4 )
=> ( ~ ( member449909584od_a_a @ C2 @ B )
=> ( member449909584od_a_a @ C2 @ ( minus_1507102574od_a_a @ A4 @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[459]) ).
thf(522,plain,
( ( ! [B2: product_prod_a_a,F: product_prod_a_a > product_prod_a_a,X: product_prod_a_a,A4: set_Product_prod_a_a] :
( ( B2
= ( F @ X ) )
=> ( ( member449909584od_a_a @ X @ A4 )
=> ( member449909584od_a_a @ B2 @ ( image_794773445od_a_a @ F @ A4 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[458]) ).
thf(523,plain,
( ( ! [B2: a,F: product_prod_a_a > a,X: product_prod_a_a,A4: set_Product_prod_a_a] :
( ( B2
= ( F @ X ) )
=> ( ( member449909584od_a_a @ X @ A4 )
=> ( member_a @ B2 @ ( image_340790172_a_a_a @ F @ A4 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[457]) ).
thf(524,plain,
( ( ! [B2: produc1572603623od_a_a,F: product_prod_a_a > produc1572603623od_a_a,X: product_prod_a_a,A4: set_Product_prod_a_a] :
( ( B2
= ( F @ X ) )
=> ( ( member449909584od_a_a @ X @ A4 )
=> ( member2057358096od_a_a @ B2 @ ( image_1765377413od_a_a @ F @ A4 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[456]) ).
thf(525,plain,
( ( ! [B2: product_prod_a_a,F: a > product_prod_a_a,X: a,A4: set_a] :
( ( B2
= ( F @ X ) )
=> ( ( member_a @ X @ A4 )
=> ( member449909584od_a_a @ B2 @ ( image_1725938350od_a_a @ F @ A4 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[455]) ).
thf(526,plain,
( ( ! [B2: product_prod_a_a,F: produc1572603623od_a_a > product_prod_a_a,X: produc1572603623od_a_a,A4: set_Pr1948701895od_a_a] :
( ( B2
= ( F @ X ) )
=> ( ( member2057358096od_a_a @ X @ A4 )
=> ( member449909584od_a_a @ B2 @ ( image_734753285od_a_a @ F @ A4 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[454]) ).
thf(527,plain,
( ( ! [C2: product_prod_a_a,A4: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( member449909584od_a_a @ C2 @ ( minus_1507102574od_a_a @ A4 @ B ) )
= ( ( member449909584od_a_a @ C2 @ A4 )
& ~ ( member449909584od_a_a @ C2 @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[453]) ).
thf(528,plain,
( ( minus_1507102574od_a_a
= ( ^ [A6: set_Product_prod_a_a,B5: set_Product_prod_a_a] :
( collec645855634od_a_a
@ ( minus_1797478127_a_a_o
@ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ A6 )
@ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ B5 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[452]) ).
thf(529,plain,
( ( ! [X: product_prod_a_a,A4: set_Product_prod_a_a,B2: product_prod_a_a,F: product_prod_a_a > product_prod_a_a] :
( ( member449909584od_a_a @ X @ A4 )
=> ( ( B2
= ( F @ X ) )
=> ( member449909584od_a_a @ B2 @ ( image_794773445od_a_a @ F @ A4 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[451]) ).
thf(530,plain,
( ( ! [X: product_prod_a_a,A4: set_Product_prod_a_a,B2: a,F: product_prod_a_a > a] :
( ( member449909584od_a_a @ X @ A4 )
=> ( ( B2
= ( F @ X ) )
=> ( member_a @ B2 @ ( image_340790172_a_a_a @ F @ A4 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[450]) ).
thf(531,plain,
( ( ! [X: product_prod_a_a,A4: set_Product_prod_a_a,B2: produc1572603623od_a_a,F: product_prod_a_a > produc1572603623od_a_a] :
( ( member449909584od_a_a @ X @ A4 )
=> ( ( B2
= ( F @ X ) )
=> ( member2057358096od_a_a @ B2 @ ( image_1765377413od_a_a @ F @ A4 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[449]) ).
thf(532,plain,
( ( ! [X: a,A4: set_a,B2: product_prod_a_a,F: a > product_prod_a_a] :
( ( member_a @ X @ A4 )
=> ( ( B2
= ( F @ X ) )
=> ( member449909584od_a_a @ B2 @ ( image_1725938350od_a_a @ F @ A4 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[448]) ).
thf(533,plain,
( ( ! [X: produc1572603623od_a_a,A4: set_Pr1948701895od_a_a,B2: product_prod_a_a,F: produc1572603623od_a_a > product_prod_a_a] :
( ( member2057358096od_a_a @ X @ A4 )
=> ( ( B2
= ( F @ X ) )
=> ( member449909584od_a_a @ B2 @ ( image_734753285od_a_a @ F @ A4 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[447]) ).
thf(534,plain,
( ( ! [X: product_prod_a_a,A4: set_Product_prod_a_a,F: product_prod_a_a > product_prod_a_a] :
( ( member449909584od_a_a @ X @ A4 )
=> ( member449909584od_a_a @ ( F @ X ) @ ( image_794773445od_a_a @ F @ A4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[446]) ).
thf(535,plain,
( ( ! [X: product_prod_a_a,A4: set_Product_prod_a_a,F: product_prod_a_a > a] :
( ( member449909584od_a_a @ X @ A4 )
=> ( member_a @ ( F @ X ) @ ( image_340790172_a_a_a @ F @ A4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[445]) ).
thf(536,plain,
( ( ! [X: product_prod_a_a,A4: set_Product_prod_a_a,F: product_prod_a_a > produc1572603623od_a_a] :
( ( member449909584od_a_a @ X @ A4 )
=> ( member2057358096od_a_a @ ( F @ X ) @ ( image_1765377413od_a_a @ F @ A4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[444]) ).
thf(537,plain,
( ( ! [X: a,A4: set_a,F: a > product_prod_a_a] :
( ( member_a @ X @ A4 )
=> ( member449909584od_a_a @ ( F @ X ) @ ( image_1725938350od_a_a @ F @ A4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[443]) ).
thf(538,plain,
( ( ! [X: produc1572603623od_a_a,A4: set_Pr1948701895od_a_a,F: produc1572603623od_a_a > product_prod_a_a] :
( ( member2057358096od_a_a @ X @ A4 )
=> ( member449909584od_a_a @ ( F @ X ) @ ( image_734753285od_a_a @ F @ A4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[442]) ).
thf(539,plain,
( ( ! [C2: product_prod_a_a,A4: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( member449909584od_a_a @ C2 @ ( minus_1507102574od_a_a @ A4 @ B ) )
=> ~ ( member449909584od_a_a @ C2 @ B ) ) )
= $true ),
inference(copy,[status(thm)],[441]) ).
thf(540,plain,
( ( ! [C2: product_prod_a_a,A4: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( member449909584od_a_a @ C2 @ ( minus_1507102574od_a_a @ A4 @ B ) )
=> ( member449909584od_a_a @ C2 @ A4 ) ) )
= $true ),
inference(copy,[status(thm)],[440]) ).
thf(541,plain,
( ( ! [C2: product_prod_a_a,A4: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( member449909584od_a_a @ C2 @ ( minus_1507102574od_a_a @ A4 @ B ) )
=> ~ ( ( member449909584od_a_a @ C2 @ A4 )
=> ( member449909584od_a_a @ C2 @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[439]) ).
thf(542,plain,
( ( ! [B2: product_prod_a_a,F: product_prod_a_a > product_prod_a_a,A4: set_Product_prod_a_a] :
( ( member449909584od_a_a @ B2 @ ( image_794773445od_a_a @ F @ A4 ) )
=> ~ ! [X3: product_prod_a_a] :
( ( B2
= ( F @ X3 ) )
=> ~ ( member449909584od_a_a @ X3 @ A4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[438]) ).
thf(543,plain,
( ( ! [B2: product_prod_a_a,F: a > product_prod_a_a,A4: set_a] :
( ( member449909584od_a_a @ B2 @ ( image_1725938350od_a_a @ F @ A4 ) )
=> ~ ! [X3: a] :
( ( B2
= ( F @ X3 ) )
=> ~ ( member_a @ X3 @ A4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[437]) ).
thf(544,plain,
( ( ! [B2: product_prod_a_a,F: produc1572603623od_a_a > product_prod_a_a,A4: set_Pr1948701895od_a_a] :
( ( member449909584od_a_a @ B2 @ ( image_734753285od_a_a @ F @ A4 ) )
=> ~ ! [X3: produc1572603623od_a_a] :
( ( B2
= ( F @ X3 ) )
=> ~ ( member2057358096od_a_a @ X3 @ A4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[436]) ).
thf(545,plain,
( ( ! [B2: a,F: product_prod_a_a > a,A4: set_Product_prod_a_a] :
( ( member_a @ B2 @ ( image_340790172_a_a_a @ F @ A4 ) )
=> ~ ! [X3: product_prod_a_a] :
( ( B2
= ( F @ X3 ) )
=> ~ ( member449909584od_a_a @ X3 @ A4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[435]) ).
thf(546,plain,
( ( ! [B2: produc1572603623od_a_a,F: product_prod_a_a > produc1572603623od_a_a,A4: set_Product_prod_a_a] :
( ( member2057358096od_a_a @ B2 @ ( image_1765377413od_a_a @ F @ A4 ) )
=> ~ ! [X3: product_prod_a_a] :
( ( B2
= ( F @ X3 ) )
=> ~ ( member449909584od_a_a @ X3 @ A4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[434]) ).
thf(547,plain,
( ( ! [F: product_prod_a_a > product_prod_a_a,A4: set_Product_prod_a_a,P2: product_prod_a_a > $o] :
( ( collec645855634od_a_a
@ ^ [X4: product_prod_a_a] :
( ( member449909584od_a_a @ X4 @ ( image_794773445od_a_a @ F @ A4 ) )
& ( P2 @ X4 ) ) )
= ( image_794773445od_a_a @ F
@ ( collec645855634od_a_a
@ ^ [X4: product_prod_a_a] :
( ( member449909584od_a_a @ X4 @ A4 )
& ( P2 @ ( F @ X4 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[433]) ).
thf(548,plain,
( ( minus_1507102574od_a_a
= ( ^ [A6: set_Product_prod_a_a,B5: set_Product_prod_a_a] :
( collec645855634od_a_a
@ ^ [X4: product_prod_a_a] :
( ( member449909584od_a_a @ X4 @ A6 )
& ~ ( member449909584od_a_a @ X4 @ B5 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[432]) ).
thf(549,plain,
( ( ! [X: product_prod_a_a] : ( member449909584od_a_a @ X @ top_to398455383od_a_a ) )
= $true ),
inference(copy,[status(thm)],[431]) ).
thf(550,plain,
( ( ? [X3: product_prod_a_a] : ( member449909584od_a_a @ X3 @ top_to398455383od_a_a ) )
= $true ),
inference(copy,[status(thm)],[430]) ).
thf(551,plain,
( ( ! [A4: set_Product_prod_a_a] :
( ! [X3: product_prod_a_a] : ( member449909584od_a_a @ X3 @ A4 )
=> ( top_to398455383od_a_a = A4 ) ) )
= $true ),
inference(copy,[status(thm)],[429]) ).
thf(552,plain,
( ( ! [X: product_prod_a_a] : ( member449909584od_a_a @ X @ top_to398455383od_a_a ) )
= $true ),
inference(copy,[status(thm)],[428]) ).
thf(553,plain,
( ( ! [P2: a > $o,X: a,Y5: a,Y: a,R2: a > set_Product_prod_a_a] :
( ( P2 @ X )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y5 @ Y ) @ ( R2 @ X ) )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ X @ Y5 ) @ ( product_Pair_a_a @ X @ Y ) ) @ ( same_fst_a_a @ P2 @ R2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[427]) ).
thf(554,plain,
( ( ! [F: a > a,G: a > a,A: a,B2: a] :
( ( produc700022774_a_a_a @ F @ G @ ( product_Pair_a_a @ A @ B2 ) )
= ( product_Pair_a_a @ ( F @ A ) @ ( G @ B2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[426]) ).
thf(555,plain,
( ( ! [F: a > product_prod_a_a,G: a > product_prod_a_a,A: a,B2: a] :
( ( produc2012818120od_a_a @ F @ G @ ( product_Pair_a_a @ A @ B2 ) )
= ( produc1474507607od_a_a @ ( F @ A ) @ ( G @ B2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[425]) ).
thf(556,plain,
( ( ! [F: product_prod_a_a > a,G: product_prod_a_a > a,A: product_prod_a_a,B2: product_prod_a_a] :
( ( produc363290532_a_a_a @ F @ G @ ( produc1474507607od_a_a @ A @ B2 ) )
= ( product_Pair_a_a @ ( F @ A ) @ ( G @ B2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[424]) ).
thf(557,plain,
( ( ! [A: a,B2: a,R2: set_Product_prod_a_a,F: a > a,G: a > a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B2 ) @ R2 )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ ( F @ A ) @ ( G @ B2 ) ) @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ F @ G ) @ R2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[423]) ).
thf(558,plain,
( ( top_to1483957574_a_a_o
= ( ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ top_to398455383od_a_a ) ) )
= $true ),
inference(copy,[status(thm)],[422]) ).
thf(559,plain,
( ( ! [X: a,Y: a,A: a] :
( ( ( product_fst_a_a @ ( product_Pair_a_a @ X @ Y ) )
= A )
=> ( X = A ) ) )
= $true ),
inference(copy,[status(thm)],[421]) ).
thf(560,plain,
( ( ! [X1: a,X2: a] :
( ( product_fst_a_a @ ( product_Pair_a_a @ X1 @ X2 ) )
= X1 ) )
= $true ),
inference(copy,[status(thm)],[420]) ).
thf(561,plain,
( ( ! [C2: product_prod_a_a,F: a > a,G: a > a,R2: set_Product_prod_a_a] :
( ( member449909584od_a_a @ C2 @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ F @ G ) @ R2 ) )
=> ~ ! [X3: a,Y3: a] :
( ( C2
= ( product_Pair_a_a @ ( F @ X3 ) @ ( G @ Y3 ) ) )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[419]) ).
thf(562,plain,
( ( top_top_a_a_o
= ( ^ [X4: a,Y4: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ top_to398455383od_a_a ) ) )
= $true ),
inference(copy,[status(thm)],[418]) ).
thf(563,plain,
( ( ! [A: a,P: product_prod_a_a] :
( ( A
= ( product_fst_a_a @ P ) )
= ( ? [B6: a] :
( P
= ( product_Pair_a_a @ A @ B6 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[417]) ).
thf(564,plain,
( ( ! [X: product_prod_a_a,Y: a,Z: a] :
( ( X
= ( product_Pair_a_a @ Y @ Z ) )
=> ( ( product_fst_a_a @ X )
= Y ) ) )
= $true ),
inference(copy,[status(thm)],[416]) ).
thf(565,plain,
( ( ! [Prod: product_prod_a_a] :
( ( product_Pair_a_a @ ( product_fst_a_a @ Prod ) @ ( product_snd_a_a @ Prod ) )
= Prod ) )
= $true ),
inference(copy,[status(thm)],[415]) ).
thf(566,plain,
( ( ! [B2: a,P: product_prod_a_a] :
( ( B2
= ( product_snd_a_a @ P ) )
= ( ? [A5: a] :
( P
= ( product_Pair_a_a @ A5 @ B2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[414]) ).
thf(567,plain,
( ( ! [X: product_prod_a_a,Y: a,Z: a] :
( ( X
= ( product_Pair_a_a @ Y @ Z ) )
=> ( ( product_snd_a_a @ X )
= Z ) ) )
= $true ),
inference(copy,[status(thm)],[413]) ).
thf(568,plain,
( ( ! [X: a,Y: a,A: a] :
( ( ( product_snd_a_a @ ( product_Pair_a_a @ X @ Y ) )
= A )
=> ( Y = A ) ) )
= $true ),
inference(copy,[status(thm)],[412]) ).
thf(569,plain,
( ( ! [X1: a,X2: a] :
( ( product_snd_a_a @ ( product_Pair_a_a @ X1 @ X2 ) )
= X2 ) )
= $true ),
inference(copy,[status(thm)],[411]) ).
thf(570,plain,
( ( ! [T: product_prod_a_a] :
( T
= ( product_Pair_a_a @ ( product_fst_a_a @ T ) @ ( product_snd_a_a @ T ) ) ) )
= $true ),
inference(copy,[status(thm)],[410]) ).
thf(571,plain,
( ( ! [Prod: product_prod_a_a] :
( Prod
= ( product_Pair_a_a @ ( product_fst_a_a @ Prod ) @ ( product_snd_a_a @ Prod ) ) ) )
= $true ),
inference(copy,[status(thm)],[409]) ).
thf(572,plain,
( ( product_swap_a_a
= ( ^ [P4: product_prod_a_a] : ( product_Pair_a_a @ ( product_snd_a_a @ P4 ) @ ( product_fst_a_a @ P4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[408]) ).
thf(573,plain,
( ( ! [P2: a > a > $o,X: a,Y: a,A: product_prod_a_a] :
( ( P2 @ X @ Y )
=> ( ( A
= ( product_Pair_a_a @ X @ Y ) )
=> ( P2 @ ( product_fst_a_a @ A ) @ ( product_snd_a_a @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[407]) ).
thf(574,plain,
( ( ! [P2: a > $o,P: a,Q: a > $o,Q2: a] :
( ( P2 @ P )
=> ( ( Q @ Q2 )
=> ( ( P2 @ ( product_fst_a_a @ ( product_Pair_a_a @ P @ Q2 ) ) )
& ( Q @ ( product_snd_a_a @ ( product_Pair_a_a @ P @ Q2 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[406]) ).
thf(575,plain,
( ( ! [P2: a > a > $o,Y: a,X: a] :
( ( P2 @ Y @ X )
=> ( P2 @ ( product_snd_a_a @ ( product_Pair_a_a @ X @ Y ) ) @ ( product_fst_a_a @ ( product_Pair_a_a @ X @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[405]) ).
thf(576,plain,
( ( ! [B2: a,F: product_prod_a_a > a,X: product_prod_a_a,C2: a,G: product_prod_a_a > a,A4: set_Product_prod_a_a] :
( ( B2
= ( F @ X ) )
=> ( ( C2
= ( G @ X ) )
=> ( ( member449909584od_a_a @ X @ A4 )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ B2 @ C2 ) @ ( bNF_Gr1853143117_a_a_a @ A4 @ F @ G ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[404]) ).
thf(577,plain,
( ( ! [B2: a,F: a > a,X: a,C2: a,G: a > a,A4: set_a] :
( ( B2
= ( F @ X ) )
=> ( ( C2
= ( G @ X ) )
=> ( ( member_a @ X @ A4 )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ B2 @ C2 ) @ ( bNF_Gr423046308_a_a_a @ A4 @ F @ G ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[403]) ).
thf(578,plain,
( ( ! [B2: a,F: produc1572603623od_a_a > a,X: produc1572603623od_a_a,C2: a,G: produc1572603623od_a_a > a,A4: set_Pr1948701895od_a_a] :
( ( B2
= ( F @ X ) )
=> ( ( C2
= ( G @ X ) )
=> ( ( member2057358096od_a_a @ X @ A4 )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ B2 @ C2 ) @ ( bNF_Gr356189709_a_a_a @ A4 @ F @ G ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[402]) ).
thf(579,plain,
( ( ! [B2: product_prod_a_a,F: product_prod_a_a > product_prod_a_a,X: product_prod_a_a,C2: product_prod_a_a,G: product_prod_a_a > product_prod_a_a,A4: set_Product_prod_a_a] :
( ( B2
= ( F @ X ) )
=> ( ( C2
= ( G @ X ) )
=> ( ( member449909584od_a_a @ X @ A4 )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ B2 @ C2 ) @ ( bNF_Gr200450189od_a_a @ A4 @ F @ G ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[401]) ).
thf(580,plain,
( ( ! [A: a,B2: a,A2: a,B3: a,R: set_Product_prod_a_a,S: set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ A @ B2 ) @ ( product_Pair_a_a @ A2 @ B3 ) ) @ ( lex_prod_a_a @ R @ S ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ A2 ) @ R )
| ( ( A = A2 )
& ( member449909584od_a_a @ ( product_Pair_a_a @ B2 @ B3 ) @ S ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[400]) ).
thf(581,plain,
( ( ! [A: a,B2: a,A4: set_a,B: a > set_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B2 ) @ ( product_Sigma_a_a @ A4 @ B ) )
= ( ( member_a @ A @ A4 )
& ( member_a @ B2 @ ( B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[399]) ).
thf(582,plain,
( ( ! [A: product_prod_a_a,B2: product_prod_a_a,A4: set_Product_prod_a_a,B: product_prod_a_a > set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B2 ) @ ( produc304751368od_a_a @ A4 @ B ) )
= ( ( member449909584od_a_a @ A @ A4 )
& ( member449909584od_a_a @ B2 @ ( B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[398]) ).
thf(583,plain,
( ( ! [A: a,A4: set_a,B2: a,B: a > set_a] :
( ( member_a @ A @ A4 )
=> ( ( member_a @ B2 @ ( B @ A ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B2 ) @ ( product_Sigma_a_a @ A4 @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[397]) ).
thf(584,plain,
( ( ! [A: product_prod_a_a,A4: set_Product_prod_a_a,B2: product_prod_a_a,B: product_prod_a_a > set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ A4 )
=> ( ( member449909584od_a_a @ B2 @ ( B @ A ) )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B2 ) @ ( produc304751368od_a_a @ A4 @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[396]) ).
thf(585,plain,
( ( ! [A: a,B2: a,A4: set_a,B: a > set_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B2 ) @ ( product_Sigma_a_a @ A4 @ B ) )
=> ~ ( ( member_a @ A @ A4 )
=> ~ ( member_a @ B2 @ ( B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[395]) ).
thf(586,plain,
( ( ! [A: product_prod_a_a,B2: product_prod_a_a,A4: set_Product_prod_a_a,B: product_prod_a_a > set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B2 ) @ ( produc304751368od_a_a @ A4 @ B ) )
=> ~ ( ( member449909584od_a_a @ A @ A4 )
=> ~ ( member449909584od_a_a @ B2 @ ( B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[394]) ).
thf(587,plain,
( ( ! [A: a,B2: a,A4: set_a,B: a > set_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B2 ) @ ( product_Sigma_a_a @ A4 @ B ) )
=> ( member_a @ B2 @ ( B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[393]) ).
thf(588,plain,
( ( ! [A: product_prod_a_a,B2: product_prod_a_a,A4: set_Product_prod_a_a,B: product_prod_a_a > set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B2 ) @ ( produc304751368od_a_a @ A4 @ B ) )
=> ( member449909584od_a_a @ B2 @ ( B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[392]) ).
thf(589,plain,
( ( ! [A: a,B2: a,A4: set_a,B: a > set_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B2 ) @ ( product_Sigma_a_a @ A4 @ B ) )
=> ( member_a @ A @ A4 ) ) )
= $true ),
inference(copy,[status(thm)],[391]) ).
thf(590,plain,
( ( ! [A: product_prod_a_a,B2: product_prod_a_a,A4: set_Product_prod_a_a,B: product_prod_a_a > set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B2 ) @ ( produc304751368od_a_a @ A4 @ B ) )
=> ( member449909584od_a_a @ A @ A4 ) ) )
= $true ),
inference(copy,[status(thm)],[390]) ).
thf(591,plain,
( ( ! [C2: product_prod_a_a,A4: set_a,B: a > set_a] :
( ( member449909584od_a_a @ C2 @ ( product_Sigma_a_a @ A4 @ B ) )
=> ~ ! [X3: a] :
( ( member_a @ X3 @ A4 )
=> ! [Y3: a] :
( ( member_a @ Y3 @ ( B @ X3 ) )
=> ( C2
!= ( product_Pair_a_a @ X3 @ Y3 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[389]) ).
thf(592,plain,
( ( ! [C2: produc1572603623od_a_a,A4: set_Product_prod_a_a,B: product_prod_a_a > set_Product_prod_a_a] :
( ( member2057358096od_a_a @ C2 @ ( produc304751368od_a_a @ A4 @ B ) )
=> ~ ! [X3: product_prod_a_a] :
( ( member449909584od_a_a @ X3 @ A4 )
=> ! [Y3: product_prod_a_a] :
( ( member449909584od_a_a @ Y3 @ ( B @ X3 ) )
=> ( C2
!= ( produc1474507607od_a_a @ X3 @ Y3 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[388]) ).
thf(593,plain,
( ( ! [X: product_prod_a_a,A4: set_a,B: set_a] :
( ( member449909584od_a_a @ X @ ( product_product_a_a @ A4 @ B ) )
= ( member449909584od_a_a @ X
@ ( product_Sigma_a_a @ A4
@ ^ [Uu: a] : B ) ) ) )
= $true ),
inference(copy,[status(thm)],[387]) ).
thf(594,plain,
( ( ! [A4: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ! [X3: product_prod_a_a] :
( ( member449909584od_a_a @ X3 @ A4 )
=> ( member449909584od_a_a @ X3 @ B ) )
=> ( ord_le1824328871od_a_a @ A4 @ B ) ) )
= $true ),
inference(copy,[status(thm)],[386]) ).
thf(595,plain,
( ( ! [A4: set_Product_prod_a_a,F: product_prod_a_a > product_prod_a_a,B: set_Product_prod_a_a] :
( ! [X3: product_prod_a_a] :
( ( member449909584od_a_a @ X3 @ A4 )
=> ( member449909584od_a_a @ ( F @ X3 ) @ B ) )
=> ( ord_le1824328871od_a_a @ ( image_794773445od_a_a @ F @ A4 ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[385]) ).
thf(596,plain,
( ( ! [A4: set_Product_prod_a_a,F: product_prod_a_a > a,B: set_a] :
( ! [X3: product_prod_a_a] :
( ( member449909584od_a_a @ X3 @ A4 )
=> ( member_a @ ( F @ X3 ) @ B ) )
=> ( ord_less_eq_set_a @ ( image_340790172_a_a_a @ F @ A4 ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[384]) ).
thf(597,plain,
( ( ! [A4: set_Product_prod_a_a,F: product_prod_a_a > produc1572603623od_a_a,B: set_Pr1948701895od_a_a] :
( ! [X3: product_prod_a_a] :
( ( member449909584od_a_a @ X3 @ A4 )
=> ( member2057358096od_a_a @ ( F @ X3 ) @ B ) )
=> ( ord_le456379495od_a_a @ ( image_1765377413od_a_a @ F @ A4 ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[383]) ).
thf(598,plain,
( ( ! [A4: set_a,F: a > product_prod_a_a,B: set_Product_prod_a_a] :
( ! [X3: a] :
( ( member_a @ X3 @ A4 )
=> ( member449909584od_a_a @ ( F @ X3 ) @ B ) )
=> ( ord_le1824328871od_a_a @ ( image_1725938350od_a_a @ F @ A4 ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[382]) ).
thf(599,plain,
( ( ! [A4: set_Pr1948701895od_a_a,F: produc1572603623od_a_a > product_prod_a_a,B: set_Product_prod_a_a] :
( ! [X3: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ X3 @ A4 )
=> ( member449909584od_a_a @ ( F @ X3 ) @ B ) )
=> ( ord_le1824328871od_a_a @ ( image_734753285od_a_a @ F @ A4 ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[381]) ).
thf(600,plain,
( ( ! [R: set_Product_prod_a_a,S: set_Product_prod_a_a] :
( ! [X3: a,Y3: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ S ) )
=> ( ord_le1824328871od_a_a @ R @ S ) ) )
= $true ),
inference(copy,[status(thm)],[380]) ).
thf(601,plain,
( ( ord_le1824328871od_a_a
= ( ^ [A6: set_Product_prod_a_a,B5: set_Product_prod_a_a] :
! [T2: product_prod_a_a] :
( ( member449909584od_a_a @ T2 @ A6 )
=> ( member449909584od_a_a @ T2 @ B5 ) ) ) )
= $true ),
inference(copy,[status(thm)],[379]) ).
thf(602,plain,
( ( ord_le1824328871od_a_a
= ( ^ [A6: set_Product_prod_a_a,B5: set_Product_prod_a_a] :
! [X4: product_prod_a_a] :
( ( member449909584od_a_a @ X4 @ A6 )
=> ( member449909584od_a_a @ X4 @ B5 ) ) ) )
= $true ),
inference(copy,[status(thm)],[378]) ).
thf(603,plain,
( ( ! [A4: set_Product_prod_a_a,B: set_Product_prod_a_a,C2: product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A4 @ B )
=> ( ( member449909584od_a_a @ C2 @ A4 )
=> ( member449909584od_a_a @ C2 @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[377]) ).
thf(604,plain,
( ( ! [A4: set_Product_prod_a_a,B: set_Product_prod_a_a,X: product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A4 @ B )
=> ( ( member449909584od_a_a @ X @ A4 )
=> ( member449909584od_a_a @ X @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[376]) ).
thf(605,plain,
( ( ! [X: product_prod_a_a,Z2: set_Product_prod_a_a,X5: set_Product_prod_a_a,P2: product_prod_a_a > $o] :
( ( member449909584od_a_a @ X @ Z2 )
=> ( ( ord_le1824328871od_a_a @ Z2
@ ( collec645855634od_a_a
@ ^ [X4: product_prod_a_a] :
( ( member449909584od_a_a @ X4 @ X5 )
& ( P2 @ X4 ) ) ) )
=> ( P2 @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[375]) ).
thf(606,plain,
( ( ! [X5: set_Product_prod_a_a,P2: product_prod_a_a > $o] :
( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [X4: product_prod_a_a] :
( ( member449909584od_a_a @ X4 @ X5 )
& ( P2 @ X4 ) ) )
@ X5 ) )
= $true ),
inference(copy,[status(thm)],[374]) ).
thf(607,plain,
( ( ! [A4: set_Product_prod_a_a,P2: product_prod_a_a > $o] :
( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [X4: product_prod_a_a] :
( ( member449909584od_a_a @ X4 @ A4 )
& ( P2 @ X4 ) ) )
@ A4 ) )
= $true ),
inference(copy,[status(thm)],[373]) ).
thf(608,plain,
( ( ! [B: set_Product_prod_a_a,A4: set_Product_prod_a_a,P2: product_prod_a_a > $o] :
( ( ord_le1824328871od_a_a @ B @ A4 )
=> ( ( ord_le1824328871od_a_a @ B
@ ( collec645855634od_a_a
@ ^ [X4: product_prod_a_a] :
( ( member449909584od_a_a @ X4 @ A4 )
& ( P2 @ X4 ) ) ) )
= ( ! [X4: product_prod_a_a] :
( ( member449909584od_a_a @ X4 @ B )
=> ( P2 @ X4 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[372]) ).
thf(609,plain,
( ( ! [B: set_Product_prod_a_a,A4: set_Product_prod_a_a,Q: product_prod_a_a > $o,P2: product_prod_a_a > $o] :
( ( ord_le1824328871od_a_a @ B @ A4 )
=> ( ! [X3: product_prod_a_a] :
( ( member449909584od_a_a @ X3 @ B )
=> ( ( Q @ X3 )
=> ( P2 @ X3 ) ) )
=> ( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [X4: product_prod_a_a] :
( ( member449909584od_a_a @ X4 @ B )
& ( Q @ X4 ) ) )
@ ( collec645855634od_a_a
@ ^ [X4: product_prod_a_a] :
( ( member449909584od_a_a @ X4 @ A4 )
& ( P2 @ X4 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(610,plain,
( ( ! [R2: set_Product_prod_a_a,S3: set_Product_prod_a_a] :
( ( ord_le1347718902_a_a_o
@ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ R2 )
@ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ S3 ) )
= ( ord_le1824328871od_a_a @ R2 @ S3 ) ) )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(611,plain,
( ( ord_le1824328871od_a_a
= ( ^ [A6: set_Product_prod_a_a,B5: set_Product_prod_a_a] :
( ord_le1347718902_a_a_o
@ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ A6 )
@ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ B5 ) ) ) )
= $true ),
inference(copy,[status(thm)],[369]) ).
thf(612,plain,
( ( ! [R2: set_Product_prod_a_a,S3: set_Product_prod_a_a] :
( ( ord_less_eq_a_a_o
@ ^ [X4: a,Y4: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ R2 )
@ ^ [X4: a,Y4: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ S3 ) )
= ( ord_le1824328871od_a_a @ R2 @ S3 ) ) )
= $true ),
inference(copy,[status(thm)],[368]) ).
thf(613,plain,
( ( ! [X: a,Fx: a,A4: set_a,F: a > a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Fx ) @ ( bNF_Gr_a_a @ A4 @ F ) )
=> ( member_a @ X @ A4 ) ) )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(614,plain,
( ( ! [X: product_prod_a_a,Fx: product_prod_a_a,A4: set_Product_prod_a_a,F: product_prod_a_a > product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X @ Fx ) @ ( bNF_Gr1372473186od_a_a @ A4 @ F ) )
=> ( member449909584od_a_a @ X @ A4 ) ) )
= $true ),
inference(copy,[status(thm)],[366]) ).
thf(615,plain,
( ( ! [X: a,Fx: a,A4: set_a,F: a > a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Fx ) @ ( bNF_Gr_a_a @ A4 @ F ) )
=> ( ( F @ X )
= Fx ) ) )
= $true ),
inference(copy,[status(thm)],[365]) ).
thf(616,plain,
( ( ! [A4: set_Product_prod_a_a] :
( ( ! [X4: product_prod_a_a] :
~ ( member449909584od_a_a @ X4 @ A4 ) )
= ( A4 = bot_bo2131659635od_a_a ) ) )
= $true ),
inference(copy,[status(thm)],[364]) ).
thf(617,plain,
( ( ! [C2: product_prod_a_a] :
~ ( member449909584od_a_a @ C2 @ bot_bo2131659635od_a_a ) )
= $true ),
inference(copy,[status(thm)],[363]) ).
thf(618,plain,
( ( ! [A4: set_Product_prod_a_a] :
( ( ? [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ A4 ) )
= ( A4 != bot_bo2131659635od_a_a ) ) )
= $true ),
inference(copy,[status(thm)],[362]) ).
thf(619,plain,
( ( ! [A4: set_Product_prod_a_a] :
( ! [Y3: product_prod_a_a] :
~ ( member449909584od_a_a @ Y3 @ A4 )
=> ( A4 = bot_bo2131659635od_a_a ) ) )
= $true ),
inference(copy,[status(thm)],[361]) ).
thf(620,plain,
( ( ! [A4: set_Product_prod_a_a,A: product_prod_a_a] :
( ( A4 = bot_bo2131659635od_a_a )
=> ~ ( member449909584od_a_a @ A @ A4 ) ) )
= $true ),
inference(copy,[status(thm)],[360]) ).
thf(621,plain,
( ( ! [A: product_prod_a_a] :
~ ( member449909584od_a_a @ A @ bot_bo2131659635od_a_a ) )
= $true ),
inference(copy,[status(thm)],[359]) ).
thf(622,plain,
( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ z @ y ) @ pr ) )
= $true ),
inference(copy,[status(thm)],[490]) ).
thf(623,plain,
( ( ! [SX0: set_Product_prod_a_a,SX1: product_prod_a_a] :
( ( SX0 != bot_bo2131659635od_a_a )
| ~ ( member449909584od_a_a @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[620]) ).
thf(624,plain,
( ( ! [SX0: set_Product_prod_a_a,SX1: set_Product_prod_a_a] :
( ~ ! [SX2: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SX2 @ SX0 )
| ( member449909584od_a_a @ SX2 @ SX1 ) )
| ( ord_le1824328871od_a_a @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[594]) ).
thf(625,plain,
( ( ! [SX0: produc1572603623od_a_a,SX1: product_prod_a_a > produc1572603623od_a_a,SX2: product_prod_a_a,SX3: set_Product_prod_a_a] :
( ( SX0
!= ( SX1 @ SX2 ) )
| ~ ( member449909584od_a_a @ SX2 @ SX3 )
| ( member2057358096od_a_a @ SX0 @ ( image_1765377413od_a_a @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[524]) ).
thf(626,plain,
( ( ! [SX0: a,SX1: a,SX2: a,SX3: a] :
( ( ( product_Pair_a_a @ SX0 @ SX1 )
= ( product_Pair_a_a @ SX2 @ SX3 ) )
= ( ~ ( ( SX0 != SX2 )
| ( SX1 != SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[494]) ).
thf(627,plain,
( ( ! [SX0: product_prod_a_a,SX1: set_Product_prod_a_a,SX2: produc1572603623od_a_a,SX3: product_prod_a_a > produc1572603623od_a_a] :
( ~ ( member449909584od_a_a @ SX0 @ SX1 )
| ( SX2
!= ( SX3 @ SX0 ) )
| ( member2057358096od_a_a @ SX2 @ ( image_1765377413od_a_a @ SX3 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[531]) ).
thf(628,plain,
( ( ! [SX0: set_Product_prod_a_a,SX1: product_prod_a_a > product_prod_a_a,SX2: set_Product_prod_a_a] :
( ~ ! [SX3: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SX3 @ SX0 )
| ( member449909584od_a_a @ ( SX1 @ SX3 ) @ SX2 ) )
| ( ord_le1824328871od_a_a @ ( image_794773445od_a_a @ SX1 @ SX0 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[595]) ).
thf(629,plain,
( ( ! [SX0: product_prod_a_a,SX1: set_Product_prod_a_a,SX2: set_Product_prod_a_a] :
( ( member449909584od_a_a @ SX0 @ ( minus_1507102574od_a_a @ SX1 @ SX2 ) )
= ( ~ ( ~ ( member449909584od_a_a @ SX0 @ SX1 )
| ~ ~ ( member449909584od_a_a @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[527]) ).
thf(630,plain,
( ( ! [SX0: set_a,SX1: a > product_prod_a_a,SX2: set_Product_prod_a_a] :
( ~ ! [SX3: a] :
( ~ ( member_a @ SX3 @ SX0 )
| ( member449909584od_a_a @ ( SX1 @ SX3 ) @ SX2 ) )
| ( ord_le1824328871od_a_a @ ( image_1725938350od_a_a @ SX1 @ SX0 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[598]) ).
thf(631,plain,
( ( ord_le1824328871od_a_a
= ( ^ [SX0: set_Product_prod_a_a,SX1: set_Product_prod_a_a] :
! [SX2: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SX2 @ SX0 )
| ( member449909584od_a_a @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[601]) ).
thf(632,plain,
( ( ! [SX0: set_Product_prod_a_a] :
( ( ~ ! [SX1: product_prod_a_a] :
~ ( member449909584od_a_a @ SX1 @ SX0 ) )
= ( SX0 != bot_bo2131659635od_a_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[618]) ).
thf(633,plain,
( ( ! [SX0: produc1572603623od_a_a > $o,SX1: produc1572603623od_a_a] :
( ~ ! [SX2: product_prod_a_a,SX3: a,SX4: a] : ( SX0 @ ( produc1474507607od_a_a @ SX2 @ ( product_Pair_a_a @ SX3 @ SX4 ) ) )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[501]) ).
thf(634,plain,
( ( ! [SX0: set_Product_prod_a_a,SX1: product_prod_a_a > $o] :
( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [SX2: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) ) )
@ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[607]) ).
thf(635,plain,
( ( ! [SX0: produc1572603623od_a_a,SX1: product_prod_a_a > produc1572603623od_a_a,SX2: set_Product_prod_a_a] :
( ~ ( member2057358096od_a_a @ SX0 @ ( image_1765377413od_a_a @ SX1 @ SX2 ) )
| ~ ! [SX3: product_prod_a_a] :
( ( SX0
!= ( SX1 @ SX3 ) )
| ~ ( member449909584od_a_a @ SX3 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[546]) ).
thf(636,plain,
( ( ! [SX0: product_prod_a_a,SX1: a > product_prod_a_a,SX2: a,SX3: set_a] :
( ( SX0
!= ( SX1 @ SX2 ) )
| ~ ( member_a @ SX2 @ SX3 )
| ( member449909584od_a_a @ SX0 @ ( image_1725938350od_a_a @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[525]) ).
thf(637,plain,
( ( ! [SX0: set_Product_prod_a_a,SX1: product_prod_a_a > $o] :
( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [SX2: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) ) )
@ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[606]) ).
thf(638,plain,
( ( ! [SX0: product_prod_a_a,SX1: product_prod_a_a > product_prod_a_a,SX2: set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ SX0 @ ( image_794773445od_a_a @ SX1 @ SX2 ) )
| ~ ! [SX3: product_prod_a_a] :
( ( SX0
!= ( SX1 @ SX3 ) )
| ~ ( member449909584od_a_a @ SX3 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[542]) ).
thf(639,plain,
( ( ord_le1824328871od_a_a
= ( ^ [SX0: set_Product_prod_a_a,SX1: set_Product_prod_a_a] :
! [SX2: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SX2 @ SX0 )
| ( member449909584od_a_a @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[602]) ).
thf(640,plain,
( ( ! [SX0: product_prod_a_a > $o,SX1: a,SX2: a] :
( ~ ( SX0 @ ( product_Pair_a_a @ SX1 @ SX2 ) )
| ( product_curry_a_a_o @ SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[506]) ).
thf(641,plain,
( ( ! [SX0: product_prod_a_a,SX1: set_Product_prod_a_a,SX2: set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ SX0 @ ( minus_1507102574od_a_a @ SX1 @ SX2 ) )
| ~ ( ~ ( member449909584od_a_a @ SX0 @ SX1 )
| ( member449909584od_a_a @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[541]) ).
thf(642,plain,
( ( ! [SX0: set_Product_prod_a_a,SX1: set_Product_prod_a_a,SX2: product_prod_a_a > $o] :
( ~ ( ord_le1824328871od_a_a @ SX0 @ SX1 )
| ( ( ord_le1824328871od_a_a @ SX0
@ ( collec645855634od_a_a
@ ^ [SX3: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SX3 @ SX1 )
| ~ ( SX2 @ SX3 ) ) ) )
= ( ! [SX3: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SX3 @ SX0 )
| ( SX2 @ SX3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[608]) ).
thf(643,plain,
( ( prefer161218362good_a
= ( ^ [SX0: a,SX1: set_a,SX2: set_Product_prod_a_a] :
( collect_a
@ ^ [SX3: a] :
~ ( ~ ( member_a @ SX3 @ SX1 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX0 ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[504]) ).
thf(644,plain,
( ( ! [SX0: product_prod_a_a,SX1: produc1572603623od_a_a > product_prod_a_a,SX2: set_Pr1948701895od_a_a] :
( ~ ( member449909584od_a_a @ SX0 @ ( image_734753285od_a_a @ SX1 @ SX2 ) )
| ~ ! [SX3: produc1572603623od_a_a] :
( ( SX0
!= ( SX1 @ SX3 ) )
| ~ ( member2057358096od_a_a @ SX3 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[544]) ).
thf(645,plain,
( ( ! [SX0: set_a,SX1: set_Product_prod_a_a,SX2: a,SX3: a] :
( ~ ( prefer1292084992ence_a @ SX0 @ SX1 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SX1 )
| ( member_a @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[508]) ).
thf(646,plain,
( ( ! [SX0: a,SX1: set_a,SX2: a > product_prod_a_a] :
( ~ ( member_a @ SX0 @ SX1 )
| ( member449909584od_a_a @ ( SX2 @ SX0 ) @ ( image_1725938350od_a_a @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[537]) ).
thf(647,plain,
( ( ! [SX0: a,SX1: set_a,SX2: product_prod_a_a,SX3: a > product_prod_a_a] :
( ~ ( member_a @ SX0 @ SX1 )
| ( SX2
!= ( SX3 @ SX0 ) )
| ( member449909584od_a_a @ SX2 @ ( image_1725938350od_a_a @ SX3 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[532]) ).
thf(648,plain,
( ( ! [SX0: a,SX1: a,SX2: set_a,SX3: a > set_a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX1 ) @ ( product_Sigma_a_a @ SX2 @ SX3 ) )
| ( member_a @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[589]) ).
thf(649,plain,
( ( ! [SX0: produc1572603623od_a_a,SX1: set_Pr1948701895od_a_a,SX2: product_prod_a_a,SX3: produc1572603623od_a_a > product_prod_a_a] :
( ~ ( member2057358096od_a_a @ SX0 @ SX1 )
| ( SX2
!= ( SX3 @ SX0 ) )
| ( member449909584od_a_a @ SX2 @ ( image_734753285od_a_a @ SX3 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[533]) ).
thf(650,plain,
( ( ! [SX0: produc1572603623od_a_a,SX1: set_Pr1948701895od_a_a,SX2: produc1572603623od_a_a > product_prod_a_a] :
( ~ ( member2057358096od_a_a @ SX0 @ SX1 )
| ( member449909584od_a_a @ ( SX2 @ SX0 ) @ ( image_734753285od_a_a @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[538]) ).
thf(651,plain,
( ( ! [SX0: product_prod_a_a > product_prod_a_a,SX1: set_Product_prod_a_a,SX2: product_prod_a_a > $o] :
( ( collec645855634od_a_a
@ ^ [SX3: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SX3 @ ( image_794773445od_a_a @ SX0 @ SX1 ) )
| ~ ( SX2 @ SX3 ) ) )
= ( image_794773445od_a_a @ SX0
@ ( collec645855634od_a_a
@ ^ [SX3: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SX3 @ SX1 )
| ~ ( SX2 @ ( SX0 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[547]) ).
thf(652,plain,
( ( ! [SX0: a,SX1: a,SX2: set_Product_prod_a_a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX1 ) @ SX2 )
| ( SX3 != SX1 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX3 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[505]) ).
thf(653,plain,
( ( ! [SX0: a,SX1: a,SX2: a,SX3: a] :
( ( ( product_Pair_a_a @ SX0 @ SX1 )
= ( product_Pair_a_a @ SX2 @ SX3 ) )
= ( ~ ( ( SX0 != SX2 )
| ( SX1 != SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[495]) ).
thf(654,plain,
( ( ! [SX0: product_prod_a_a,SX1: set_Product_prod_a_a,SX2: a,SX3: product_prod_a_a > a] :
( ~ ( member449909584od_a_a @ SX0 @ SX1 )
| ( SX2
!= ( SX3 @ SX0 ) )
| ( member_a @ SX2 @ ( image_340790172_a_a_a @ SX3 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[530]) ).
thf(655,plain,
( ( ! [SX0: set_Pr1948701895od_a_a,SX1: produc1572603623od_a_a > product_prod_a_a,SX2: set_Product_prod_a_a] :
( ~ ! [SX3: produc1572603623od_a_a] :
( ~ ( member2057358096od_a_a @ SX3 @ SX0 )
| ( member449909584od_a_a @ ( SX1 @ SX3 ) @ SX2 ) )
| ( ord_le1824328871od_a_a @ ( image_734753285od_a_a @ SX1 @ SX0 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[599]) ).
thf(656,plain,
( ( ! [SX0: set_Product_prod_a_a,SX1: set_a] :
( ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SX0 )
| ( member_a @ SX2 @ SX1 ) )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SX0 )
| ( member_a @ SX3 @ SX1 ) )
| ~ ( order_preorder_on_a @ SX1 @ SX0 )
| ( prefer1292084992ence_a @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[517]) ).
thf(657,plain,
( ( ! [SX0: set_a,SX1: set_Product_prod_a_a,SX2: a,SX3: a,SX4: a] :
( ~ ( prefer1292084992ence_a @ SX0 @ SX1 )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SX1 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SX1 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX4 ) @ SX1 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX4 @ SX3 ) @ SX1 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX4 ) @ SX1 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX4 @ SX2 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[507]) ).
thf(658,plain,
( ( ! [SX0: set_Product_prod_a_a,SX1: set_Pr1948701895od_a_a,SX2: product_prod_a_a,SX3: product_prod_a_a] :
( ~ ( prefer1338892073od_a_a @ SX0 @ SX1 )
| ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SX2 @ SX3 ) @ SX1 )
| ( member449909584od_a_a @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[509]) ).
thf(659,plain,
( ( ! [SX0: product_prod_a_a,SX1: product_prod_a_a,SX2: set_Product_prod_a_a,SX3: product_prod_a_a > set_Product_prod_a_a] :
( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SX0 @ SX1 ) @ ( produc304751368od_a_a @ SX2 @ SX3 ) )
| ( member449909584od_a_a @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[590]) ).
thf(660,plain,
( ( ! [SX0: a > a > $o,SX1: a,SX2: a,SX3: product_prod_a_a] :
( ~ ( SX0 @ SX1 @ SX2 )
| ( SX3
!= ( product_Pair_a_a @ SX1 @ SX2 ) )
| ( SX0 @ ( product_fst_a_a @ SX3 ) @ ( product_snd_a_a @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[573]) ).
thf(661,plain,
( ( ! [SX0: a,SX1: a > a,SX2: a,SX3: a,SX4: a > a,SX5: set_a] :
( ( SX0
!= ( SX1 @ SX2 ) )
| ( SX3
!= ( SX4 @ SX2 ) )
| ~ ( member_a @ SX2 @ SX5 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX3 ) @ ( bNF_Gr423046308_a_a_a @ SX5 @ SX1 @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[577]) ).
thf(662,plain,
( ( ! [SX0: a,SX1: set_a,SX2: a,SX3: a > set_a] :
( ~ ( member_a @ SX0 @ SX1 )
| ~ ( member_a @ SX2 @ ( SX3 @ SX0 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX2 ) @ ( product_Sigma_a_a @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[583]) ).
thf(663,plain,
( ( ! [SX0: a,SX1: a,SX2: a,SX3: a] :
( ( ( product_Pair_a_a @ SX0 @ SX1 )
!= ( product_Pair_a_a @ SX2 @ SX3 ) )
| ~ ( ( SX0 != SX2 )
| ( SX1 != SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[498]) ).
thf(664,plain,
( ( ! [SX0: product_prod_a_a,SX1: set_Product_prod_a_a,SX2: set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ SX0 @ ( minus_1507102574od_a_a @ SX1 @ SX2 ) )
| ( member449909584od_a_a @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[540]) ).
thf(665,plain,
( ( ! [SX0: product_prod_a_a,SX1: set_Product_prod_a_a,SX2: set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ SX0 @ ( minus_1507102574od_a_a @ SX1 @ SX2 ) )
| ~ ( member449909584od_a_a @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[539]) ).
thf(666,plain,
( ( ! [SX0: set_Product_prod_a_a,SX1: set_Product_prod_a_a] :
( ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SX0 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SX1 ) )
| ( ord_le1824328871od_a_a @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[600]) ).
thf(667,plain,
( ( ! [SX0: product_prod_a_a > $o,SX1: a,SX2: a] :
( ~ ( product_curry_a_a_o @ SX0 @ SX1 @ SX2 )
| ( SX0 @ ( product_Pair_a_a @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[511]) ).
thf(668,plain,
( ( ! [SX0: a,SX1: a,SX2: set_a,SX3: a > set_a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX1 ) @ ( product_Sigma_a_a @ SX2 @ SX3 ) )
| ( member_a @ SX1 @ ( SX3 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[587]) ).
thf(669,plain,
( ( ! [SX0: produc1921647824od_a_a] :
~ ! [SX1: a,SX2: a,SX3: a] :
( SX0
!= ( produc1299253312od_a_a @ SX1 @ ( product_Pair_a_a @ SX2 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[499]) ).
thf(670,plain,
( ( ! [SX0: a,SX1: a,SX2: set_a,SX3: a > a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX1 ) @ ( bNF_Gr_a_a @ SX2 @ SX3 ) )
| ( ( SX3 @ SX0 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[615]) ).
thf(671,plain,
( ( ! [SX0: a,SX1: a,SX2: set_a,SX3: a > set_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX1 ) @ ( product_Sigma_a_a @ SX2 @ SX3 ) )
= ( ~ ( ~ ( member_a @ SX0 @ SX2 )
| ~ ( member_a @ SX1 @ ( SX3 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[581]) ).
thf(672,plain,
( ( ! [SX0: product_prod_a_a,SX1: product_prod_a_a > product_prod_a_a,SX2: product_prod_a_a,SX3: product_prod_a_a,SX4: product_prod_a_a > product_prod_a_a,SX5: set_Product_prod_a_a] :
( ( SX0
!= ( SX1 @ SX2 ) )
| ( SX3
!= ( SX4 @ SX2 ) )
| ~ ( member449909584od_a_a @ SX2 @ SX5 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SX0 @ SX3 ) @ ( bNF_Gr200450189od_a_a @ SX5 @ SX1 @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[579]) ).
thf(673,plain,
( ( minus_1507102574od_a_a
= ( ^ [SX0: set_Product_prod_a_a,SX1: set_Product_prod_a_a] :
( collec645855634od_a_a
@ ^ [SX2: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SX2 @ SX0 )
| ~ ~ ( member449909584od_a_a @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[548]) ).
thf(674,plain,
( ( ! [SX0: set_Product_prod_a_a,SX1: set_Product_prod_a_a,SX2: product_prod_a_a] :
( ~ ( ord_le1824328871od_a_a @ SX0 @ SX1 )
| ~ ( member449909584od_a_a @ SX2 @ SX0 )
| ( member449909584od_a_a @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[604]) ).
thf(675,plain,
( ( ! [SX0: a,SX1: a,SX2: set_Product_prod_a_a,SX3: a > a,SX4: a > a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX1 ) @ SX2 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( SX3 @ SX0 ) @ ( SX4 @ SX1 ) ) @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SX3 @ SX4 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[557]) ).
thf(676,plain,
( ( ! [SX0: set_Product_prod_a_a,SX1: set_Product_prod_a_a,SX2: product_prod_a_a] :
( ~ ( ord_le1824328871od_a_a @ SX0 @ SX1 )
| ~ ( member449909584od_a_a @ SX2 @ SX0 )
| ( member449909584od_a_a @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[603]) ).
thf(677,plain,
( ( ! [SX0: set_Product_prod_a_a,SX1: product_prod_a_a > produc1572603623od_a_a,SX2: set_Pr1948701895od_a_a] :
( ~ ! [SX3: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SX3 @ SX0 )
| ( member2057358096od_a_a @ ( SX1 @ SX3 ) @ SX2 ) )
| ( ord_le456379495od_a_a @ ( image_1765377413od_a_a @ SX1 @ SX0 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[597]) ).
thf(678,plain,
( ( ! [SX0: product_prod_a_a,SX1: a,SX2: a] :
( ( SX0
!= ( product_Pair_a_a @ SX1 @ SX2 ) )
| ( ( product_snd_a_a @ SX0 )
= SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[567]) ).
thf(679,plain,
( ( prefer1292084992ence_a
= ( ^ [SX0: set_a,SX1: set_Product_prod_a_a] :
~ ( ~ ~ ( ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SX1 )
| ( member_a @ SX2 @ SX0 ) )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SX1 )
| ( member_a @ SX3 @ SX0 ) ) )
| ~ ( order_preorder_on_a @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[516]) ).
thf(680,plain,
( ( ! [SX0: product_prod_a_a,SX1: product_prod_a_a,SX2: set_Product_prod_a_a,SX3: product_prod_a_a > set_Product_prod_a_a] :
( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SX0 @ SX1 ) @ ( produc304751368od_a_a @ SX2 @ SX3 ) )
| ~ ( ~ ( member449909584od_a_a @ SX0 @ SX2 )
| ~ ( member449909584od_a_a @ SX1 @ ( SX3 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[586]) ).
thf(681,plain,
( ( ! [SX0: product_prod_a_a,SX1: set_Product_prod_a_a,SX2: product_prod_a_a > produc1572603623od_a_a] :
( ~ ( member449909584od_a_a @ SX0 @ SX1 )
| ( member2057358096od_a_a @ ( SX2 @ SX0 ) @ ( image_1765377413od_a_a @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[536]) ).
thf(682,plain,
( ( ! [SX0: product_prod_a_a,SX1: set_Product_prod_a_a,SX2: product_prod_a_a,SX3: product_prod_a_a > set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ SX0 @ SX1 )
| ~ ( member449909584od_a_a @ SX2 @ ( SX3 @ SX0 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SX0 @ SX2 ) @ ( produc304751368od_a_a @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[584]) ).
thf(683,plain,
( ( ! [SX0: a > a > $o,SX1: a,SX2: a] :
( ~ ( SX0 @ SX1 @ SX2 )
| ( SX0 @ ( product_snd_a_a @ ( product_Pair_a_a @ SX2 @ SX1 ) ) @ ( product_fst_a_a @ ( product_Pair_a_a @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[575]) ).
thf(684,plain,
( ( ! [SX0: set_Product_prod_a_a,SX1: set_Product_prod_a_a,SX2: product_prod_a_a > $o,SX3: product_prod_a_a > $o] :
( ~ ( ord_le1824328871od_a_a @ SX0 @ SX1 )
| ~ ! [SX4: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SX4 @ SX0 )
| ~ ( SX2 @ SX4 )
| ( SX3 @ SX4 ) )
| ( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [SX4: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SX4 @ SX0 )
| ~ ( SX2 @ SX4 ) ) )
@ ( collec645855634od_a_a
@ ^ [SX4: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SX4 @ SX1 )
| ~ ( SX3 @ SX4 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[609]) ).
thf(685,plain,
( ( ! [SX0: product_prod_a_a,SX1: product_prod_a_a,SX2: set_Product_prod_a_a,SX3: product_prod_a_a > set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SX0 @ SX1 ) @ ( produc304751368od_a_a @ SX2 @ SX3 ) )
= ( ~ ( ~ ( member449909584od_a_a @ SX0 @ SX2 )
| ~ ( member449909584od_a_a @ SX1 @ ( SX3 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[582]) ).
thf(686,plain,
( ( ! [SX0: produc1572603623od_a_a] :
~ ! [SX1: product_prod_a_a,SX2: a,SX3: a] :
( SX0
!= ( produc1474507607od_a_a @ SX1 @ ( product_Pair_a_a @ SX2 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[500]) ).
thf(687,plain,
( ( ! [SX0: a,SX1: product_prod_a_a] :
( ( SX0
= ( product_snd_a_a @ SX1 ) )
= ( ~ ! [SX2: a] :
( SX1
!= ( product_Pair_a_a @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[566]) ).
thf(688,plain,
( ( ! [SX0: product_prod_a_a,SX1: produc1572603623od_a_a > product_prod_a_a,SX2: produc1572603623od_a_a,SX3: set_Pr1948701895od_a_a] :
( ( SX0
!= ( SX1 @ SX2 ) )
| ~ ( member2057358096od_a_a @ SX2 @ SX3 )
| ( member449909584od_a_a @ SX0 @ ( image_734753285od_a_a @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[526]) ).
thf(689,plain,
( ( ! [SX0: a > $o,SX1: a,SX2: a > $o,SX3: a] :
( ~ ( SX0 @ SX1 )
| ~ ( SX2 @ SX3 )
| ~ ( ~ ( SX0 @ ( product_fst_a_a @ ( product_Pair_a_a @ SX1 @ SX3 ) ) )
| ~ ( SX2 @ ( product_snd_a_a @ ( product_Pair_a_a @ SX1 @ SX3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[574]) ).
thf(690,plain,
( ( ! [SX0: a,SX1: a,SX2: set_a,SX3: set_Product_prod_a_a] :
( ~ ( member_a @ SX0 @ ( prefer161218362good_a @ SX1 @ SX2 @ SX3 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX1 ) @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[493]) ).
thf(691,plain,
( ( ! [SX0: a,SX1: product_prod_a_a > a,SX2: product_prod_a_a,SX3: a,SX4: product_prod_a_a > a,SX5: set_Product_prod_a_a] :
( ( SX0
!= ( SX1 @ SX2 ) )
| ( SX3
!= ( SX4 @ SX2 ) )
| ~ ( member449909584od_a_a @ SX2 @ SX5 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX3 ) @ ( bNF_Gr1853143117_a_a_a @ SX5 @ SX1 @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[576]) ).
thf(692,plain,
( ( ! [SX0: product_prod_a_a,SX1: product_prod_a_a,SX2: set_Product_prod_a_a,SX3: product_prod_a_a > product_prod_a_a] :
( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SX0 @ SX1 ) @ ( bNF_Gr1372473186od_a_a @ SX2 @ SX3 ) )
| ( member449909584od_a_a @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[614]) ).
thf(693,plain,
( ( prefer436369274d_as_a
= ( ^ [SX0: a,SX1: set_a,SX2: set_Product_prod_a_a] :
( collect_a
@ ^ [SX3: a] :
~ ( ~ ~ ( ~ ( member_a @ SX3 @ SX1 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX3 ) @ SX2 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX0 ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[514]) ).
thf(694,plain,
( ( ! [SX0: product_prod_a_a] :
~ ! [SX1: a,SX2: a] :
( SX0
!= ( product_Pair_a_a @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[503]) ).
thf(695,plain,
( ( ! [SX0: a,SX1: product_prod_a_a > a,SX2: set_Product_prod_a_a] :
( ~ ( member_a @ SX0 @ ( image_340790172_a_a_a @ SX1 @ SX2 ) )
| ~ ! [SX3: product_prod_a_a] :
( ( SX0
!= ( SX1 @ SX3 ) )
| ~ ( member449909584od_a_a @ SX3 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[545]) ).
thf(696,plain,
( ( ! [SX0: product_prod_a_a > $o,SX1: product_prod_a_a] :
( ~ ! [SX2: a,SX3: a] : ( SX0 @ ( product_Pair_a_a @ SX2 @ SX3 ) )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[497]) ).
thf(697,plain,
( ( ! [SX0: product_prod_a_a,SX1: a > a,SX2: a > a,SX3: set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ SX0 @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SX1 @ SX2 ) @ SX3 ) )
| ~ ! [SX4: a,SX5: a] :
( ( SX0
!= ( product_Pair_a_a @ ( SX1 @ SX4 ) @ ( SX2 @ SX5 ) ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX4 @ SX5 ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[561]) ).
thf(698,plain,
( ( prefer1676310729than_a
= ( ^ [SX0: a,SX1: set_a,SX2: set_Product_prod_a_a] :
( collect_a
@ ^ [SX3: a] :
~ ( ~ ( member_a @ SX3 @ SX1 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX3 ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[513]) ).
thf(699,plain,
( ( ! [SX0: a,SX1: a,SX2: set_a,SX3: a > a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX1 ) @ ( bNF_Gr_a_a @ SX2 @ SX3 ) )
| ( member_a @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[613]) ).
thf(700,plain,
( ( ! [SX0: a > $o,SX1: a,SX2: a,SX3: a,SX4: a > set_Product_prod_a_a] :
( ~ ( SX0 @ SX1 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ ( SX4 @ SX1 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SX1 @ SX2 ) @ ( product_Pair_a_a @ SX1 @ SX3 ) ) @ ( same_fst_a_a @ SX0 @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[553]) ).
thf(701,plain,
( ( ! [SX0: product_prod_a_a > $o,SX1: product_prod_a_a] :
( ~ ! [SX2: a,SX3: a] : ( SX0 @ ( product_Pair_a_a @ SX2 @ SX3 ) )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[502]) ).
thf(702,plain,
( ( ! [SX0: a,SX1: product_prod_a_a > a,SX2: product_prod_a_a,SX3: set_Product_prod_a_a] :
( ( SX0
!= ( SX1 @ SX2 ) )
| ~ ( member449909584od_a_a @ SX2 @ SX3 )
| ( member_a @ SX0 @ ( image_340790172_a_a_a @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[523]) ).
thf(703,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ( ( product_snd_a_a @ ( product_Pair_a_a @ SX0 @ SX1 ) )
!= SX2 )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[568]) ).
thf(704,plain,
( ( ! [SX0: product_prod_a_a > $o,SX1: a,SX2: a] :
( ~ ( product_curry_a_a_o @ SX0 @ SX1 @ SX2 )
| ( SX0 @ ( product_Pair_a_a @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[512]) ).
thf(705,plain,
( ( ! [SX0: product_prod_a_a] :
~ ! [SX1: a] :
~ ~ ! [SX2: a] :
( SX0
!= ( product_Pair_a_a @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[496]) ).
thf(706,plain,
( ( ! [SX0: product_prod_a_a,SX1: product_prod_a_a > product_prod_a_a,SX2: product_prod_a_a,SX3: set_Product_prod_a_a] :
( ( SX0
!= ( SX1 @ SX2 ) )
| ~ ( member449909584od_a_a @ SX2 @ SX3 )
| ( member449909584od_a_a @ SX0 @ ( image_794773445od_a_a @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[522]) ).
thf(707,plain,
( ( ! [SX0: produc1572603623od_a_a,SX1: set_Product_prod_a_a,SX2: product_prod_a_a > set_Product_prod_a_a] :
( ~ ( member2057358096od_a_a @ SX0 @ ( produc304751368od_a_a @ SX1 @ SX2 ) )
| ~ ! [SX3: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SX3 @ SX1 )
| ! [SX4: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SX4 @ ( SX2 @ SX3 ) )
| ( SX0
!= ( produc1474507607od_a_a @ SX3 @ SX4 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[592]) ).
thf(708,plain,
( ( ! [SX0: product_prod_a_a,SX1: set_Product_prod_a_a,SX2: product_prod_a_a > a] :
( ~ ( member449909584od_a_a @ SX0 @ SX1 )
| ( member_a @ ( SX2 @ SX0 ) @ ( image_340790172_a_a_a @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[535]) ).
thf(709,plain,
( ( ! [SX0: product_prod_a_a,SX1: set_Product_prod_a_a,SX2: product_prod_a_a,SX3: product_prod_a_a > product_prod_a_a] :
( ~ ( member449909584od_a_a @ SX0 @ SX1 )
| ( SX2
!= ( SX3 @ SX0 ) )
| ( member449909584od_a_a @ SX2 @ ( image_794773445od_a_a @ SX3 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[529]) ).
thf(710,plain,
( ( ! [SX0: product_prod_a_a,SX1: a > product_prod_a_a,SX2: set_a] :
( ~ ( member449909584od_a_a @ SX0 @ ( image_1725938350od_a_a @ SX1 @ SX2 ) )
| ~ ! [SX3: a] :
( ( SX0
!= ( SX1 @ SX3 ) )
| ~ ( member_a @ SX3 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[543]) ).
thf(711,plain,
( ( ! [SX0: product_prod_a_a,SX1: set_Product_prod_a_a,SX2: product_prod_a_a > product_prod_a_a] :
( ~ ( member449909584od_a_a @ SX0 @ SX1 )
| ( member449909584od_a_a @ ( SX2 @ SX0 ) @ ( image_794773445od_a_a @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[534]) ).
thf(712,plain,
( ( ! [SX0: a,SX1: produc1572603623od_a_a > a,SX2: produc1572603623od_a_a,SX3: a,SX4: produc1572603623od_a_a > a,SX5: set_Pr1948701895od_a_a] :
( ( SX0
!= ( SX1 @ SX2 ) )
| ( SX3
!= ( SX4 @ SX2 ) )
| ~ ( member2057358096od_a_a @ SX2 @ SX5 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX3 ) @ ( bNF_Gr356189709_a_a_a @ SX5 @ SX1 @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[578]) ).
thf(713,plain,
( ( ! [SX0: set_Product_prod_a_a] :
( ~ ! [SX1: product_prod_a_a] : ( member449909584od_a_a @ SX1 @ SX0 )
| ( top_to398455383od_a_a = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[551]) ).
thf(714,plain,
( ( ! [SX0: product_prod_a_a,SX1: product_prod_a_a,SX2: set_Product_prod_a_a,SX3: set_Pr1948701895od_a_a] :
( ~ ( member449909584od_a_a @ SX0 @ ( prefer477097315od_a_a @ SX1 @ SX2 @ SX3 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SX0 @ SX1 ) @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[492]) ).
thf(715,plain,
( ( ! [SX0: product_prod_a_a,SX1: set_a,SX2: a > set_a] :
( ~ ( member449909584od_a_a @ SX0 @ ( product_Sigma_a_a @ SX1 @ SX2 ) )
| ~ ! [SX3: a] :
( ~ ( member_a @ SX3 @ SX1 )
| ! [SX4: a] :
( ~ ( member_a @ SX4 @ ( SX2 @ SX3 ) )
| ( SX0
!= ( product_Pair_a_a @ SX3 @ SX4 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[591]) ).
thf(716,plain,
( ( ! [SX0: product_prod_a_a,SX1: set_Product_prod_a_a,SX2: set_Product_prod_a_a,SX3: product_prod_a_a > $o] :
( ~ ( member449909584od_a_a @ SX0 @ SX1 )
| ~ ( ord_le1824328871od_a_a @ SX1
@ ( collec645855634od_a_a
@ ^ [SX4: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SX4 @ SX2 )
| ~ ( SX3 @ SX4 ) ) ) )
| ( SX3 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[605]) ).
thf(717,plain,
( ( ! [SX0: product_prod_a_a,SX1: a,SX2: a] :
( ( SX0
!= ( product_Pair_a_a @ SX1 @ SX2 ) )
| ( ( product_fst_a_a @ SX0 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[564]) ).
thf(718,plain,
( ( ! [SX0: set_Product_prod_a_a,SX1: product_prod_a_a > a,SX2: set_a] :
( ~ ! [SX3: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SX3 @ SX0 )
| ( member_a @ ( SX1 @ SX3 ) @ SX2 ) )
| ( ord_less_eq_set_a @ ( image_340790172_a_a_a @ SX1 @ SX0 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[596]) ).
thf(719,plain,
( ( ! [SX0: a,SX1: a,SX2: a,SX3: a,SX4: set_Product_prod_a_a,SX5: set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SX0 @ SX1 ) @ ( product_Pair_a_a @ SX2 @ SX3 ) ) @ ( lex_prod_a_a @ SX4 @ SX5 ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX2 ) @ SX4 )
| ~ ( ( SX0 != SX2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX1 @ SX3 ) @ SX5 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[580]) ).
thf(720,plain,
( ( ~ ! [SX0: product_prod_a_a] :
~ ( member449909584od_a_a @ SX0 @ top_to398455383od_a_a ) )
= $true ),
inference(unfold_def,[status(thm)],[550]) ).
thf(721,plain,
( ( ! [SX0: set_Product_prod_a_a] :
( ~ ! [SX1: product_prod_a_a] :
~ ( member449909584od_a_a @ SX1 @ SX0 )
| ( SX0 = bot_bo2131659635od_a_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[619]) ).
thf(722,plain,
( ( ! [SX0: a,SX1: product_prod_a_a] :
( ( SX0
= ( product_fst_a_a @ SX1 ) )
= ( ~ ! [SX2: a] :
( SX1
!= ( product_Pair_a_a @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[563]) ).
thf(723,plain,
( ( ! [SX0: product_prod_a_a,SX1: set_Product_prod_a_a,SX2: set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ SX0 @ SX1 )
| ~ ~ ( member449909584od_a_a @ SX0 @ SX2 )
| ( member449909584od_a_a @ SX0 @ ( minus_1507102574od_a_a @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[521]) ).
thf(724,plain,
( ( ! [SX0: a,SX1: a,SX2: set_a,SX3: a > set_a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX1 ) @ ( product_Sigma_a_a @ SX2 @ SX3 ) )
| ~ ( ~ ( member_a @ SX0 @ SX2 )
| ~ ( member_a @ SX1 @ ( SX3 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[585]) ).
thf(725,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ( ( product_fst_a_a @ ( product_Pair_a_a @ SX0 @ SX1 ) )
!= SX2 )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[559]) ).
thf(726,plain,
( ( ! [SX0: product_prod_a_a,SX1: product_prod_a_a,SX2: set_Product_prod_a_a,SX3: product_prod_a_a > set_Product_prod_a_a] :
( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SX0 @ SX1 ) @ ( produc304751368od_a_a @ SX2 @ SX3 ) )
| ( member449909584od_a_a @ SX1 @ ( SX3 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[588]) ).
thf(727,plain,
! [SV1: a] :
( ( ! [SY469: a] :
( ( product_swap_a_a @ ( product_Pair_a_a @ SV1 @ SY469 ) )
= ( product_Pair_a_a @ SY469 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(728,plain,
! [SV2: set_Product_prod_a_a] :
( ( ! [SY470: set_Product_prod_a_a] :
( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [X4: a,Y4: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ SY470 ) ) )
= ( SV2 = SY470 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(729,plain,
! [SV3: a] :
( ( ! [SY475: a,SY476: set_Product_prod_a_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ SV3 @ SY475 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SY476 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ SY475 @ SV3 ) @ SY476 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(730,plain,
! [SV4: product_prod_a_a] :
( ( ! [SY477: product_prod_a_a > $o] :
( ( member449909584od_a_a @ SV4 @ ( collec645855634od_a_a @ SY477 ) )
= ( SY477 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[519]) ).
thf(731,plain,
! [SV5: set_Product_prod_a_a] :
( ( ( collec645855634od_a_a
@ ^ [SY478: product_prod_a_a] : ( member449909584od_a_a @ SY478 @ SV5 ) )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(732,plain,
( ( ! [SV6: set_Product_prod_a_a] :
( ( minus_1507102574od_a_a @ SV6 )
= ( ^ [SY479: set_Product_prod_a_a] :
( collec645855634od_a_a
@ ( minus_1797478127_a_a_o
@ ^ [SY480: product_prod_a_a] : ( member449909584od_a_a @ SY480 @ SV6 )
@ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ SY479 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[528]) ).
thf(733,plain,
( ( minus_1507102574od_a_a
= ( ^ [A6: set_Product_prod_a_a,B5: set_Product_prod_a_a] :
( collec645855634od_a_a
@ ( minus_1797478127_a_a_o
@ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ A6 )
@ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ B5 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[528]) ).
thf(734,plain,
! [SV7: product_prod_a_a] :
( ( member449909584od_a_a @ SV7 @ top_to398455383od_a_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[549]) ).
thf(735,plain,
! [SV8: product_prod_a_a] :
( ( member449909584od_a_a @ SV8 @ top_to398455383od_a_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[552]) ).
thf(736,plain,
! [SV9: a > a] :
( ( ! [SY482: a > a,SY483: a,SY484: a] :
( ( produc700022774_a_a_a @ SV9 @ SY482 @ ( product_Pair_a_a @ SY483 @ SY484 ) )
= ( product_Pair_a_a @ ( SV9 @ SY483 ) @ ( SY482 @ SY484 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(737,plain,
! [SV10: a > product_prod_a_a] :
( ( ! [SY485: a > product_prod_a_a,SY486: a,SY487: a] :
( ( produc2012818120od_a_a @ SV10 @ SY485 @ ( product_Pair_a_a @ SY486 @ SY487 ) )
= ( produc1474507607od_a_a @ ( SV10 @ SY486 ) @ ( SY485 @ SY487 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[555]) ).
thf(738,plain,
! [SV11: product_prod_a_a > a] :
( ( ! [SY488: product_prod_a_a > a,SY489: product_prod_a_a,SY490: product_prod_a_a] :
( ( produc363290532_a_a_a @ SV11 @ SY488 @ ( produc1474507607od_a_a @ SY489 @ SY490 ) )
= ( product_Pair_a_a @ ( SV11 @ SY489 ) @ ( SY488 @ SY490 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(739,plain,
( ( ! [SV12: product_prod_a_a] :
( ( top_to1483957574_a_a_o @ SV12 )
= ( member449909584od_a_a @ SV12 @ top_to398455383od_a_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[558]) ).
thf(740,plain,
( ( top_to1483957574_a_a_o
= ( ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ top_to398455383od_a_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[558]) ).
thf(741,plain,
! [SV13: a] :
( ( ! [SY491: a] :
( ( product_fst_a_a @ ( product_Pair_a_a @ SV13 @ SY491 ) )
= SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(742,plain,
( ( ! [SV14: a] :
( ( top_top_a_a_o @ SV14 )
= ( ^ [SY492: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV14 @ SY492 ) @ top_to398455383od_a_a ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[562]) ).
thf(743,plain,
( ( top_top_a_a_o
= ( ^ [X4: a,Y4: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ top_to398455383od_a_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[562]) ).
thf(744,plain,
! [SV15: product_prod_a_a] :
( ( ( product_Pair_a_a @ ( product_fst_a_a @ SV15 ) @ ( product_snd_a_a @ SV15 ) )
= SV15 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(745,plain,
! [SV16: a] :
( ( ! [SY493: a] :
( ( product_snd_a_a @ ( product_Pair_a_a @ SV16 @ SY493 ) )
= SY493 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(746,plain,
! [SV17: product_prod_a_a] :
( ( SV17
= ( product_Pair_a_a @ ( product_fst_a_a @ SV17 ) @ ( product_snd_a_a @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(747,plain,
! [SV18: product_prod_a_a] :
( ( SV18
= ( product_Pair_a_a @ ( product_fst_a_a @ SV18 ) @ ( product_snd_a_a @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(748,plain,
( ( ! [SV19: product_prod_a_a] :
( ( product_swap_a_a @ SV19 )
= ( product_Pair_a_a @ ( product_snd_a_a @ SV19 ) @ ( product_fst_a_a @ SV19 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[572]) ).
thf(749,plain,
( ( product_swap_a_a
= ( ^ [P4: product_prod_a_a] : ( product_Pair_a_a @ ( product_snd_a_a @ P4 ) @ ( product_fst_a_a @ P4 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[572]) ).
thf(750,plain,
! [SV20: product_prod_a_a] :
( ( ! [SY494: set_a,SY495: set_a] :
( ( member449909584od_a_a @ SV20 @ ( product_product_a_a @ SY494 @ SY495 ) )
= ( member449909584od_a_a @ SV20
@ ( product_Sigma_a_a @ SY494
@ ^ [Uu: a] : SY495 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(751,plain,
! [SV21: set_Product_prod_a_a] :
( ( ! [SY497: set_Product_prod_a_a] :
( ( ord_le1347718902_a_a_o
@ ^ [SY498: product_prod_a_a] : ( member449909584od_a_a @ SY498 @ SV21 )
@ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ SY497 ) )
= ( ord_le1824328871od_a_a @ SV21 @ SY497 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(752,plain,
( ( ! [SV22: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ SV22 )
= ( ^ [SY500: set_Product_prod_a_a] :
( ord_le1347718902_a_a_o
@ ^ [SY501: product_prod_a_a] : ( member449909584od_a_a @ SY501 @ SV22 )
@ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ SY500 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[611]) ).
thf(753,plain,
( ( ord_le1824328871od_a_a
= ( ^ [A6: set_Product_prod_a_a,B5: set_Product_prod_a_a] :
( ord_le1347718902_a_a_o
@ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ A6 )
@ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ B5 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[611]) ).
thf(754,plain,
! [SV23: set_Product_prod_a_a] :
( ( ! [SY503: set_Product_prod_a_a] :
( ( ord_less_eq_a_a_o
@ ^ [SY504: a,SY505: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY504 @ SY505 ) @ SV23 )
@ ^ [X4: a,Y4: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ SY503 ) )
= ( ord_le1824328871od_a_a @ SV23 @ SY503 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(755,plain,
! [SV24: set_Product_prod_a_a] :
( ( ( ! [SY508: product_prod_a_a] :
~ ( member449909584od_a_a @ SY508 @ SV24 ) )
= ( SV24 = bot_bo2131659635od_a_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[616]) ).
thf(756,plain,
! [SV25: product_prod_a_a] :
( ( ~ ( member449909584od_a_a @ SV25 @ bot_bo2131659635od_a_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(757,plain,
! [SV26: product_prod_a_a] :
( ( ~ ( member449909584od_a_a @ SV26 @ bot_bo2131659635od_a_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(758,plain,
( ( member449909584od_a_a @ ( product_Pair_a_a @ z @ y ) @ pr )
= $false ),
inference(extcnf_not_pos,[status(thm)],[622]) ).
thf(759,plain,
! [SV27: set_Product_prod_a_a] :
( ( ! [SY509: product_prod_a_a] :
( ( SV27 != bot_bo2131659635od_a_a )
| ~ ( member449909584od_a_a @ SY509 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(760,plain,
! [SV28: set_Product_prod_a_a] :
( ( ! [SY510: set_Product_prod_a_a] :
( ~ ! [SY511: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY511 @ SV28 )
| ( member449909584od_a_a @ SY511 @ SY510 ) )
| ( ord_le1824328871od_a_a @ SV28 @ SY510 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(761,plain,
! [SV29: produc1572603623od_a_a] :
( ( ! [SY512: product_prod_a_a > produc1572603623od_a_a,SY513: product_prod_a_a,SY514: set_Product_prod_a_a] :
( ( SV29
!= ( SY512 @ SY513 ) )
| ~ ( member449909584od_a_a @ SY513 @ SY514 )
| ( member2057358096od_a_a @ SV29 @ ( image_1765377413od_a_a @ SY512 @ SY514 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(762,plain,
! [SV30: a] :
( ( ! [SY515: a,SY516: a,SY517: a] :
( ( ( product_Pair_a_a @ SV30 @ SY515 )
= ( product_Pair_a_a @ SY516 @ SY517 ) )
= ( ~ ( ( SV30 != SY516 )
| ( SY515 != SY517 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(763,plain,
! [SV31: product_prod_a_a] :
( ( ! [SY518: set_Product_prod_a_a,SY519: produc1572603623od_a_a,SY520: product_prod_a_a > produc1572603623od_a_a] :
( ~ ( member449909584od_a_a @ SV31 @ SY518 )
| ( SY519
!= ( SY520 @ SV31 ) )
| ( member2057358096od_a_a @ SY519 @ ( image_1765377413od_a_a @ SY520 @ SY518 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(764,plain,
! [SV32: set_Product_prod_a_a] :
( ( ! [SY521: product_prod_a_a > product_prod_a_a,SY522: set_Product_prod_a_a] :
( ~ ! [SY523: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY523 @ SV32 )
| ( member449909584od_a_a @ ( SY521 @ SY523 ) @ SY522 ) )
| ( ord_le1824328871od_a_a @ ( image_794773445od_a_a @ SY521 @ SV32 ) @ SY522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(765,plain,
! [SV33: product_prod_a_a] :
( ( ! [SY524: set_Product_prod_a_a,SY525: set_Product_prod_a_a] :
( ( member449909584od_a_a @ SV33 @ ( minus_1507102574od_a_a @ SY524 @ SY525 ) )
= ( ~ ( ~ ( member449909584od_a_a @ SV33 @ SY524 )
| ~ ~ ( member449909584od_a_a @ SV33 @ SY525 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(766,plain,
! [SV34: set_a] :
( ( ! [SY526: a > product_prod_a_a,SY527: set_Product_prod_a_a] :
( ~ ! [SY528: a] :
( ~ ( member_a @ SY528 @ SV34 )
| ( member449909584od_a_a @ ( SY526 @ SY528 ) @ SY527 ) )
| ( ord_le1824328871od_a_a @ ( image_1725938350od_a_a @ SY526 @ SV34 ) @ SY527 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(767,plain,
( ( ! [SV35: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ SV35 )
= ( ^ [SY529: set_Product_prod_a_a] :
! [SY530: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY530 @ SV35 )
| ( member449909584od_a_a @ SY530 @ SY529 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[631]) ).
thf(768,plain,
( ( ord_le1824328871od_a_a
= ( ^ [SX0: set_Product_prod_a_a,SX1: set_Product_prod_a_a] :
! [SX2: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SX2 @ SX0 )
| ( member449909584od_a_a @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[631]) ).
thf(769,plain,
! [SV36: set_Product_prod_a_a] :
( ( ( ~ ! [SY531: product_prod_a_a] :
~ ( member449909584od_a_a @ SY531 @ SV36 ) )
= ( SV36 != bot_bo2131659635od_a_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(770,plain,
! [SV37: produc1572603623od_a_a > $o] :
( ( ! [SY532: produc1572603623od_a_a] :
( ~ ! [SY533: product_prod_a_a,SY534: a,SY535: a] : ( SV37 @ ( produc1474507607od_a_a @ SY533 @ ( product_Pair_a_a @ SY534 @ SY535 ) ) )
| ( SV37 @ SY532 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(771,plain,
! [SV38: set_Product_prod_a_a] :
( ( ! [SY536: product_prod_a_a > $o] :
( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [SY537: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY537 @ SV38 )
| ~ ( SY536 @ SY537 ) ) )
@ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(772,plain,
! [SV39: produc1572603623od_a_a] :
( ( ! [SY538: product_prod_a_a > produc1572603623od_a_a,SY539: set_Product_prod_a_a] :
( ~ ( member2057358096od_a_a @ SV39 @ ( image_1765377413od_a_a @ SY538 @ SY539 ) )
| ~ ! [SY540: product_prod_a_a] :
( ( SV39
!= ( SY538 @ SY540 ) )
| ~ ( member449909584od_a_a @ SY540 @ SY539 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(773,plain,
! [SV40: product_prod_a_a] :
( ( ! [SY541: a > product_prod_a_a,SY542: a,SY543: set_a] :
( ( SV40
!= ( SY541 @ SY542 ) )
| ~ ( member_a @ SY542 @ SY543 )
| ( member449909584od_a_a @ SV40 @ ( image_1725938350od_a_a @ SY541 @ SY543 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(774,plain,
! [SV41: set_Product_prod_a_a] :
( ( ! [SY544: product_prod_a_a > $o] :
( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [SY545: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY545 @ SV41 )
| ~ ( SY544 @ SY545 ) ) )
@ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(775,plain,
! [SV42: product_prod_a_a] :
( ( ! [SY546: product_prod_a_a > product_prod_a_a,SY547: set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ SV42 @ ( image_794773445od_a_a @ SY546 @ SY547 ) )
| ~ ! [SY548: product_prod_a_a] :
( ( SV42
!= ( SY546 @ SY548 ) )
| ~ ( member449909584od_a_a @ SY548 @ SY547 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(776,plain,
( ( ! [SV43: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ SV43 )
= ( ^ [SY549: set_Product_prod_a_a] :
! [SY550: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY550 @ SV43 )
| ( member449909584od_a_a @ SY550 @ SY549 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[639]) ).
thf(777,plain,
( ( ord_le1824328871od_a_a
= ( ^ [SX0: set_Product_prod_a_a,SX1: set_Product_prod_a_a] :
! [SX2: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SX2 @ SX0 )
| ( member449909584od_a_a @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[639]) ).
thf(778,plain,
! [SV44: product_prod_a_a > $o] :
( ( ! [SY551: a,SY552: a] :
( ~ ( SV44 @ ( product_Pair_a_a @ SY551 @ SY552 ) )
| ( product_curry_a_a_o @ SV44 @ SY551 @ SY552 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(779,plain,
! [SV45: product_prod_a_a] :
( ( ! [SY553: set_Product_prod_a_a,SY554: set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ SV45 @ ( minus_1507102574od_a_a @ SY553 @ SY554 ) )
| ~ ( ~ ( member449909584od_a_a @ SV45 @ SY553 )
| ( member449909584od_a_a @ SV45 @ SY554 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(780,plain,
! [SV46: set_Product_prod_a_a] :
( ( ! [SY555: set_Product_prod_a_a,SY556: product_prod_a_a > $o] :
( ~ ( ord_le1824328871od_a_a @ SV46 @ SY555 )
| ( ( ord_le1824328871od_a_a @ SV46
@ ( collec645855634od_a_a
@ ^ [SX3: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SX3 @ SY555 )
| ~ ( SY556 @ SX3 ) ) ) )
= ( ! [SY558: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY558 @ SV46 )
| ( SY556 @ SY558 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(781,plain,
( ( ! [SV47: a] :
( ( prefer161218362good_a @ SV47 )
= ( ^ [SY559: set_a,SY560: set_Product_prod_a_a] :
( collect_a
@ ^ [SY561: a] :
~ ( ~ ( member_a @ SY561 @ SY559 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY561 @ SV47 ) @ SY560 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[643]) ).
thf(782,plain,
( ( prefer161218362good_a
= ( ^ [SX0: a,SX1: set_a,SX2: set_Product_prod_a_a] :
( collect_a
@ ^ [SX3: a] :
~ ( ~ ( member_a @ SX3 @ SX1 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX0 ) @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[643]) ).
thf(783,plain,
! [SV48: product_prod_a_a] :
( ( ! [SY562: produc1572603623od_a_a > product_prod_a_a,SY563: set_Pr1948701895od_a_a] :
( ~ ( member449909584od_a_a @ SV48 @ ( image_734753285od_a_a @ SY562 @ SY563 ) )
| ~ ! [SY564: produc1572603623od_a_a] :
( ( SV48
!= ( SY562 @ SY564 ) )
| ~ ( member2057358096od_a_a @ SY564 @ SY563 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(784,plain,
! [SV49: set_a] :
( ( ! [SY565: set_Product_prod_a_a,SY566: a,SY567: a] :
( ~ ( prefer1292084992ence_a @ SV49 @ SY565 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY566 @ SY567 ) @ SY565 )
| ( member_a @ SY566 @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(785,plain,
! [SV50: a] :
( ( ! [SY568: set_a,SY569: a > product_prod_a_a] :
( ~ ( member_a @ SV50 @ SY568 )
| ( member449909584od_a_a @ ( SY569 @ SV50 ) @ ( image_1725938350od_a_a @ SY569 @ SY568 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(786,plain,
! [SV51: a] :
( ( ! [SY570: set_a,SY571: product_prod_a_a,SY572: a > product_prod_a_a] :
( ~ ( member_a @ SV51 @ SY570 )
| ( SY571
!= ( SY572 @ SV51 ) )
| ( member449909584od_a_a @ SY571 @ ( image_1725938350od_a_a @ SY572 @ SY570 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(787,plain,
! [SV52: a] :
( ( ! [SY573: a,SY574: set_a,SY575: a > set_a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SY573 ) @ ( product_Sigma_a_a @ SY574 @ SY575 ) )
| ( member_a @ SV52 @ SY574 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(788,plain,
! [SV53: produc1572603623od_a_a] :
( ( ! [SY576: set_Pr1948701895od_a_a,SY577: product_prod_a_a,SY578: produc1572603623od_a_a > product_prod_a_a] :
( ~ ( member2057358096od_a_a @ SV53 @ SY576 )
| ( SY577
!= ( SY578 @ SV53 ) )
| ( member449909584od_a_a @ SY577 @ ( image_734753285od_a_a @ SY578 @ SY576 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(789,plain,
! [SV54: produc1572603623od_a_a] :
( ( ! [SY579: set_Pr1948701895od_a_a,SY580: produc1572603623od_a_a > product_prod_a_a] :
( ~ ( member2057358096od_a_a @ SV54 @ SY579 )
| ( member449909584od_a_a @ ( SY580 @ SV54 ) @ ( image_734753285od_a_a @ SY580 @ SY579 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(790,plain,
! [SV55: product_prod_a_a > product_prod_a_a] :
( ( ! [SY581: set_Product_prod_a_a,SY582: product_prod_a_a > $o] :
( ( collec645855634od_a_a
@ ^ [SY583: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY583 @ ( image_794773445od_a_a @ SV55 @ SY581 ) )
| ~ ( SY582 @ SY583 ) ) )
= ( image_794773445od_a_a @ SV55
@ ( collec645855634od_a_a
@ ^ [SY584: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY584 @ SY581 )
| ~ ( SY582 @ ( SV55 @ SY584 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(791,plain,
! [SV56: a] :
( ( ! [SY585: a,SY586: set_Product_prod_a_a,SY587: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV56 @ SY585 ) @ SY586 )
| ( SY587 != SY585 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV56 @ SY587 ) @ SY586 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[652]) ).
thf(792,plain,
! [SV57: a] :
( ( ! [SY588: a,SY589: a,SY590: a] :
( ( ( product_Pair_a_a @ SV57 @ SY588 )
= ( product_Pair_a_a @ SY589 @ SY590 ) )
= ( ~ ( ( SV57 != SY589 )
| ( SY588 != SY590 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(793,plain,
! [SV58: product_prod_a_a] :
( ( ! [SY591: set_Product_prod_a_a,SY592: a,SY593: product_prod_a_a > a] :
( ~ ( member449909584od_a_a @ SV58 @ SY591 )
| ( SY592
!= ( SY593 @ SV58 ) )
| ( member_a @ SY592 @ ( image_340790172_a_a_a @ SY593 @ SY591 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(794,plain,
! [SV59: set_Pr1948701895od_a_a] :
( ( ! [SY594: produc1572603623od_a_a > product_prod_a_a,SY595: set_Product_prod_a_a] :
( ~ ! [SY596: produc1572603623od_a_a] :
( ~ ( member2057358096od_a_a @ SY596 @ SV59 )
| ( member449909584od_a_a @ ( SY594 @ SY596 ) @ SY595 ) )
| ( ord_le1824328871od_a_a @ ( image_734753285od_a_a @ SY594 @ SV59 ) @ SY595 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(795,plain,
! [SV60: set_Product_prod_a_a] :
( ( ! [SY597: set_a] :
( ~ ! [SY598: a,SY599: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY598 @ SY599 ) @ SV60 )
| ( member_a @ SY598 @ SY597 ) )
| ~ ! [SY600: a,SY601: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY600 @ SY601 ) @ SV60 )
| ( member_a @ SY601 @ SY597 ) )
| ~ ( order_preorder_on_a @ SY597 @ SV60 )
| ( prefer1292084992ence_a @ SY597 @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(796,plain,
! [SV61: set_a] :
( ( ! [SY602: set_Product_prod_a_a,SY603: a,SY604: a,SY605: a] :
( ~ ( prefer1292084992ence_a @ SV61 @ SY602 )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY603 @ SY604 ) @ SY602 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY604 @ SY603 ) @ SY602 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY604 @ SY605 ) @ SY602 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY605 @ SY604 ) @ SY602 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY603 @ SY605 ) @ SY602 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY605 @ SY603 ) @ SY602 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(797,plain,
! [SV62: set_Product_prod_a_a] :
( ( ! [SY606: set_Pr1948701895od_a_a,SY607: product_prod_a_a,SY608: product_prod_a_a] :
( ~ ( prefer1338892073od_a_a @ SV62 @ SY606 )
| ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY607 @ SY608 ) @ SY606 )
| ( member449909584od_a_a @ SY607 @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(798,plain,
! [SV63: product_prod_a_a] :
( ( ! [SY609: product_prod_a_a,SY610: set_Product_prod_a_a,SY611: product_prod_a_a > set_Product_prod_a_a] :
( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV63 @ SY609 ) @ ( produc304751368od_a_a @ SY610 @ SY611 ) )
| ( member449909584od_a_a @ SV63 @ SY610 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(799,plain,
! [SV64: a > a > $o] :
( ( ! [SY612: a,SY613: a,SY614: product_prod_a_a] :
( ~ ( SV64 @ SY612 @ SY613 )
| ( SY614
!= ( product_Pair_a_a @ SY612 @ SY613 ) )
| ( SV64 @ ( product_fst_a_a @ SY614 ) @ ( product_snd_a_a @ SY614 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(800,plain,
! [SV65: a] :
( ( ! [SY615: a > a,SY616: a,SY617: a,SY618: a > a,SY619: set_a] :
( ( SV65
!= ( SY615 @ SY616 ) )
| ( SY617
!= ( SY618 @ SY616 ) )
| ~ ( member_a @ SY616 @ SY619 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV65 @ SY617 ) @ ( bNF_Gr423046308_a_a_a @ SY619 @ SY615 @ SY618 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(801,plain,
! [SV66: a] :
( ( ! [SY620: set_a,SY621: a,SY622: a > set_a] :
( ~ ( member_a @ SV66 @ SY620 )
| ~ ( member_a @ SY621 @ ( SY622 @ SV66 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV66 @ SY621 ) @ ( product_Sigma_a_a @ SY620 @ SY622 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(802,plain,
! [SV67: a] :
( ( ! [SY623: a,SY624: a,SY625: a] :
( ( ( product_Pair_a_a @ SV67 @ SY623 )
!= ( product_Pair_a_a @ SY624 @ SY625 ) )
| ~ ( ( SV67 != SY624 )
| ( SY623 != SY625 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(803,plain,
! [SV68: product_prod_a_a] :
( ( ! [SY626: set_Product_prod_a_a,SY627: set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ SV68 @ ( minus_1507102574od_a_a @ SY626 @ SY627 ) )
| ( member449909584od_a_a @ SV68 @ SY626 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(804,plain,
! [SV69: product_prod_a_a] :
( ( ! [SY628: set_Product_prod_a_a,SY629: set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ SV69 @ ( minus_1507102574od_a_a @ SY628 @ SY629 ) )
| ~ ( member449909584od_a_a @ SV69 @ SY629 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(805,plain,
! [SV70: set_Product_prod_a_a] :
( ( ! [SY630: set_Product_prod_a_a] :
( ~ ! [SY631: a,SY632: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY631 @ SY632 ) @ SV70 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY631 @ SY632 ) @ SY630 ) )
| ( ord_le1824328871od_a_a @ SV70 @ SY630 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(806,plain,
! [SV71: product_prod_a_a > $o] :
( ( ! [SY633: a,SY634: a] :
( ~ ( product_curry_a_a_o @ SV71 @ SY633 @ SY634 )
| ( SV71 @ ( product_Pair_a_a @ SY633 @ SY634 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(807,plain,
! [SV72: a] :
( ( ! [SY635: a,SY636: set_a,SY637: a > set_a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV72 @ SY635 ) @ ( product_Sigma_a_a @ SY636 @ SY637 ) )
| ( member_a @ SY635 @ ( SY637 @ SV72 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(808,plain,
! [SV73: produc1921647824od_a_a] :
( ( ~ ! [SY638: a,SY639: a,SY640: a] :
( SV73
!= ( produc1299253312od_a_a @ SY638 @ ( product_Pair_a_a @ SY639 @ SY640 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(809,plain,
! [SV74: a] :
( ( ! [SY641: a,SY642: set_a,SY643: a > a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV74 @ SY641 ) @ ( bNF_Gr_a_a @ SY642 @ SY643 ) )
| ( ( SY643 @ SV74 )
= SY641 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(810,plain,
! [SV75: a] :
( ( ! [SY644: a,SY645: set_a,SY646: a > set_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ SV75 @ SY644 ) @ ( product_Sigma_a_a @ SY645 @ SY646 ) )
= ( ~ ( ~ ( member_a @ SV75 @ SY645 )
| ~ ( member_a @ SY644 @ ( SY646 @ SV75 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(811,plain,
! [SV76: product_prod_a_a] :
( ( ! [SY647: product_prod_a_a > product_prod_a_a,SY648: product_prod_a_a,SY649: product_prod_a_a,SY650: product_prod_a_a > product_prod_a_a,SY651: set_Product_prod_a_a] :
( ( SV76
!= ( SY647 @ SY648 ) )
| ( SY649
!= ( SY650 @ SY648 ) )
| ~ ( member449909584od_a_a @ SY648 @ SY651 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV76 @ SY649 ) @ ( bNF_Gr200450189od_a_a @ SY651 @ SY647 @ SY650 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(812,plain,
( ( ! [SV77: set_Product_prod_a_a] :
( ( minus_1507102574od_a_a @ SV77 )
= ( ^ [SY652: set_Product_prod_a_a] :
( collec645855634od_a_a
@ ^ [SY653: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY653 @ SV77 )
| ~ ~ ( member449909584od_a_a @ SY653 @ SY652 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[673]) ).
thf(813,plain,
( ( minus_1507102574od_a_a
= ( ^ [SX0: set_Product_prod_a_a,SX1: set_Product_prod_a_a] :
( collec645855634od_a_a
@ ^ [SX2: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SX2 @ SX0 )
| ~ ~ ( member449909584od_a_a @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[673]) ).
thf(814,plain,
! [SV78: set_Product_prod_a_a] :
( ( ! [SY654: set_Product_prod_a_a,SY655: product_prod_a_a] :
( ~ ( ord_le1824328871od_a_a @ SV78 @ SY654 )
| ~ ( member449909584od_a_a @ SY655 @ SV78 )
| ( member449909584od_a_a @ SY655 @ SY654 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(815,plain,
! [SV79: a] :
( ( ! [SY656: a,SY657: set_Product_prod_a_a,SY658: a > a,SY659: a > a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV79 @ SY656 ) @ SY657 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( SY658 @ SV79 ) @ ( SY659 @ SY656 ) ) @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SY658 @ SY659 ) @ SY657 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(816,plain,
! [SV80: set_Product_prod_a_a] :
( ( ! [SY660: set_Product_prod_a_a,SY661: product_prod_a_a] :
( ~ ( ord_le1824328871od_a_a @ SV80 @ SY660 )
| ~ ( member449909584od_a_a @ SY661 @ SV80 )
| ( member449909584od_a_a @ SY661 @ SY660 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(817,plain,
! [SV81: set_Product_prod_a_a] :
( ( ! [SY662: product_prod_a_a > produc1572603623od_a_a,SY663: set_Pr1948701895od_a_a] :
( ~ ! [SY664: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY664 @ SV81 )
| ( member2057358096od_a_a @ ( SY662 @ SY664 ) @ SY663 ) )
| ( ord_le456379495od_a_a @ ( image_1765377413od_a_a @ SY662 @ SV81 ) @ SY663 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(818,plain,
! [SV82: product_prod_a_a] :
( ( ! [SY665: a,SY666: a] :
( ( SV82
!= ( product_Pair_a_a @ SY665 @ SY666 ) )
| ( ( product_snd_a_a @ SV82 )
= SY666 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(819,plain,
( ( ! [SV83: set_a] :
( ( prefer1292084992ence_a @ SV83 )
= ( ^ [SY667: set_Product_prod_a_a] :
~ ( ~ ~ ( ~ ! [SY668: a,SY669: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY668 @ SY669 ) @ SY667 )
| ( member_a @ SY668 @ SV83 ) )
| ~ ! [SY670: a,SY671: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY670 @ SY671 ) @ SY667 )
| ( member_a @ SY671 @ SV83 ) ) )
| ~ ( order_preorder_on_a @ SV83 @ SY667 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[679]) ).
thf(820,plain,
( ( prefer1292084992ence_a
= ( ^ [SX0: set_a,SX1: set_Product_prod_a_a] :
~ ( ~ ~ ( ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SX1 )
| ( member_a @ SX2 @ SX0 ) )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SX1 )
| ( member_a @ SX3 @ SX0 ) ) )
| ~ ( order_preorder_on_a @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[679]) ).
thf(821,plain,
! [SV84: product_prod_a_a] :
( ( ! [SY672: product_prod_a_a,SY673: set_Product_prod_a_a,SY674: product_prod_a_a > set_Product_prod_a_a] :
( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV84 @ SY672 ) @ ( produc304751368od_a_a @ SY673 @ SY674 ) )
| ~ ( ~ ( member449909584od_a_a @ SV84 @ SY673 )
| ~ ( member449909584od_a_a @ SY672 @ ( SY674 @ SV84 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(822,plain,
! [SV85: product_prod_a_a] :
( ( ! [SY675: set_Product_prod_a_a,SY676: product_prod_a_a > produc1572603623od_a_a] :
( ~ ( member449909584od_a_a @ SV85 @ SY675 )
| ( member2057358096od_a_a @ ( SY676 @ SV85 ) @ ( image_1765377413od_a_a @ SY676 @ SY675 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(823,plain,
! [SV86: product_prod_a_a] :
( ( ! [SY677: set_Product_prod_a_a,SY678: product_prod_a_a,SY679: product_prod_a_a > set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ SV86 @ SY677 )
| ~ ( member449909584od_a_a @ SY678 @ ( SY679 @ SV86 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV86 @ SY678 ) @ ( produc304751368od_a_a @ SY677 @ SY679 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(824,plain,
! [SV87: a > a > $o] :
( ( ! [SY680: a,SY681: a] :
( ~ ( SV87 @ SY680 @ SY681 )
| ( SV87 @ ( product_snd_a_a @ ( product_Pair_a_a @ SY681 @ SY680 ) ) @ ( product_fst_a_a @ ( product_Pair_a_a @ SY681 @ SY680 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(825,plain,
! [SV88: set_Product_prod_a_a] :
( ( ! [SY682: set_Product_prod_a_a,SY683: product_prod_a_a > $o,SY684: product_prod_a_a > $o] :
( ~ ( ord_le1824328871od_a_a @ SV88 @ SY682 )
| ~ ! [SY685: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY685 @ SV88 )
| ~ ( SY683 @ SY685 )
| ( SY684 @ SY685 ) )
| ( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [SY686: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY686 @ SV88 )
| ~ ( SY683 @ SY686 ) ) )
@ ( collec645855634od_a_a
@ ^ [SX4: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SX4 @ SY682 )
| ~ ( SY684 @ SX4 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(826,plain,
! [SV89: product_prod_a_a] :
( ( ! [SY688: product_prod_a_a,SY689: set_Product_prod_a_a,SY690: product_prod_a_a > set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV89 @ SY688 ) @ ( produc304751368od_a_a @ SY689 @ SY690 ) )
= ( ~ ( ~ ( member449909584od_a_a @ SV89 @ SY689 )
| ~ ( member449909584od_a_a @ SY688 @ ( SY690 @ SV89 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(827,plain,
! [SV90: produc1572603623od_a_a] :
( ( ~ ! [SY691: product_prod_a_a,SY692: a,SY693: a] :
( SV90
!= ( produc1474507607od_a_a @ SY691 @ ( product_Pair_a_a @ SY692 @ SY693 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(828,plain,
! [SV91: a] :
( ( ! [SY694: product_prod_a_a] :
( ( SV91
= ( product_snd_a_a @ SY694 ) )
= ( ~ ! [SY695: a] :
( SY694
!= ( product_Pair_a_a @ SY695 @ SV91 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(829,plain,
! [SV92: product_prod_a_a] :
( ( ! [SY696: produc1572603623od_a_a > product_prod_a_a,SY697: produc1572603623od_a_a,SY698: set_Pr1948701895od_a_a] :
( ( SV92
!= ( SY696 @ SY697 ) )
| ~ ( member2057358096od_a_a @ SY697 @ SY698 )
| ( member449909584od_a_a @ SV92 @ ( image_734753285od_a_a @ SY696 @ SY698 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(830,plain,
! [SV93: a > $o] :
( ( ! [SY699: a,SY700: a > $o,SY701: a] :
( ~ ( SV93 @ SY699 )
| ~ ( SY700 @ SY701 )
| ~ ( ~ ( SV93 @ ( product_fst_a_a @ ( product_Pair_a_a @ SY699 @ SY701 ) ) )
| ~ ( SY700 @ ( product_snd_a_a @ ( product_Pair_a_a @ SY699 @ SY701 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(831,plain,
! [SV94: a] :
( ( ! [SY702: a,SY703: set_a,SY704: set_Product_prod_a_a] :
( ~ ( member_a @ SV94 @ ( prefer161218362good_a @ SY702 @ SY703 @ SY704 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV94 @ SY702 ) @ SY704 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(832,plain,
! [SV95: a] :
( ( ! [SY705: product_prod_a_a > a,SY706: product_prod_a_a,SY707: a,SY708: product_prod_a_a > a,SY709: set_Product_prod_a_a] :
( ( SV95
!= ( SY705 @ SY706 ) )
| ( SY707
!= ( SY708 @ SY706 ) )
| ~ ( member449909584od_a_a @ SY706 @ SY709 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV95 @ SY707 ) @ ( bNF_Gr1853143117_a_a_a @ SY709 @ SY705 @ SY708 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[691]) ).
thf(833,plain,
! [SV96: product_prod_a_a] :
( ( ! [SY710: product_prod_a_a,SY711: set_Product_prod_a_a,SY712: product_prod_a_a > product_prod_a_a] :
( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV96 @ SY710 ) @ ( bNF_Gr1372473186od_a_a @ SY711 @ SY712 ) )
| ( member449909584od_a_a @ SV96 @ SY711 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(834,plain,
( ( ! [SV97: a] :
( ( prefer436369274d_as_a @ SV97 )
= ( ^ [SY713: set_a,SY714: set_Product_prod_a_a] :
( collect_a
@ ^ [SY715: a] :
~ ( ~ ~ ( ~ ( member_a @ SY715 @ SY713 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV97 @ SY715 ) @ SY714 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY715 @ SV97 ) @ SY714 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[693]) ).
thf(835,plain,
( ( prefer436369274d_as_a
= ( ^ [SX0: a,SX1: set_a,SX2: set_Product_prod_a_a] :
( collect_a
@ ^ [SX3: a] :
~ ( ~ ~ ( ~ ( member_a @ SX3 @ SX1 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX3 ) @ SX2 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX0 ) @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[693]) ).
thf(836,plain,
! [SV98: product_prod_a_a] :
( ( ~ ! [SY716: a,SY717: a] :
( SV98
!= ( product_Pair_a_a @ SY716 @ SY717 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(837,plain,
! [SV99: a] :
( ( ! [SY718: product_prod_a_a > a,SY719: set_Product_prod_a_a] :
( ~ ( member_a @ SV99 @ ( image_340790172_a_a_a @ SY718 @ SY719 ) )
| ~ ! [SY720: product_prod_a_a] :
( ( SV99
!= ( SY718 @ SY720 ) )
| ~ ( member449909584od_a_a @ SY720 @ SY719 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(838,plain,
! [SV100: product_prod_a_a > $o] :
( ( ! [SY721: product_prod_a_a] :
( ~ ! [SY722: a,SY723: a] : ( SV100 @ ( product_Pair_a_a @ SY722 @ SY723 ) )
| ( SV100 @ SY721 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(839,plain,
! [SV101: product_prod_a_a] :
( ( ! [SY724: a > a,SY725: a > a,SY726: set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ SV101 @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SY724 @ SY725 ) @ SY726 ) )
| ~ ! [SY727: a,SY728: a] :
( ( SV101
!= ( product_Pair_a_a @ ( SY724 @ SY727 ) @ ( SY725 @ SY728 ) ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY727 @ SY728 ) @ SY726 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(840,plain,
( ( ! [SV102: a] :
( ( prefer1676310729than_a @ SV102 )
= ( ^ [SY729: set_a,SY730: set_Product_prod_a_a] :
( collect_a
@ ^ [SY731: a] :
~ ( ~ ( member_a @ SY731 @ SY729 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV102 @ SY731 ) @ SY730 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[698]) ).
thf(841,plain,
( ( prefer1676310729than_a
= ( ^ [SX0: a,SX1: set_a,SX2: set_Product_prod_a_a] :
( collect_a
@ ^ [SX3: a] :
~ ( ~ ( member_a @ SX3 @ SX1 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX3 ) @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[698]) ).
thf(842,plain,
! [SV103: a] :
( ( ! [SY732: a,SY733: set_a,SY734: a > a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV103 @ SY732 ) @ ( bNF_Gr_a_a @ SY733 @ SY734 ) )
| ( member_a @ SV103 @ SY733 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(843,plain,
! [SV104: a > $o] :
( ( ! [SY735: a,SY736: a,SY737: a,SY738: a > set_Product_prod_a_a] :
( ~ ( SV104 @ SY735 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY736 @ SY737 ) @ ( SY738 @ SY735 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SY735 @ SY736 ) @ ( product_Pair_a_a @ SY735 @ SY737 ) ) @ ( same_fst_a_a @ SV104 @ SY738 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(844,plain,
! [SV105: product_prod_a_a > $o] :
( ( ! [SY739: product_prod_a_a] :
( ~ ! [SY740: a,SY741: a] : ( SV105 @ ( product_Pair_a_a @ SY740 @ SY741 ) )
| ( SV105 @ SY739 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(845,plain,
! [SV106: a] :
( ( ! [SY742: product_prod_a_a > a,SY743: product_prod_a_a,SY744: set_Product_prod_a_a] :
( ( SV106
!= ( SY742 @ SY743 ) )
| ~ ( member449909584od_a_a @ SY743 @ SY744 )
| ( member_a @ SV106 @ ( image_340790172_a_a_a @ SY742 @ SY744 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(846,plain,
! [SV107: a] :
( ( ! [SY745: a,SY746: a] :
( ( ( product_snd_a_a @ ( product_Pair_a_a @ SV107 @ SY745 ) )
!= SY746 )
| ( SY745 = SY746 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(847,plain,
! [SV108: product_prod_a_a > $o] :
( ( ! [SY747: a,SY748: a] :
( ~ ( product_curry_a_a_o @ SV108 @ SY747 @ SY748 )
| ( SV108 @ ( product_Pair_a_a @ SY747 @ SY748 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(848,plain,
! [SV109: product_prod_a_a] :
( ( ~ ! [SY749: a] :
~ ~ ! [SY750: a] :
( SV109
!= ( product_Pair_a_a @ SY749 @ SY750 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(849,plain,
! [SV110: product_prod_a_a] :
( ( ! [SY751: product_prod_a_a > product_prod_a_a,SY752: product_prod_a_a,SY753: set_Product_prod_a_a] :
( ( SV110
!= ( SY751 @ SY752 ) )
| ~ ( member449909584od_a_a @ SY752 @ SY753 )
| ( member449909584od_a_a @ SV110 @ ( image_794773445od_a_a @ SY751 @ SY753 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(850,plain,
! [SV111: produc1572603623od_a_a] :
( ( ! [SY754: set_Product_prod_a_a,SY755: product_prod_a_a > set_Product_prod_a_a] :
( ~ ( member2057358096od_a_a @ SV111 @ ( produc304751368od_a_a @ SY754 @ SY755 ) )
| ~ ! [SY756: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY756 @ SY754 )
| ! [SY757: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY757 @ ( SY755 @ SY756 ) )
| ( SV111
!= ( produc1474507607od_a_a @ SY756 @ SY757 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(851,plain,
! [SV112: product_prod_a_a] :
( ( ! [SY758: set_Product_prod_a_a,SY759: product_prod_a_a > a] :
( ~ ( member449909584od_a_a @ SV112 @ SY758 )
| ( member_a @ ( SY759 @ SV112 ) @ ( image_340790172_a_a_a @ SY759 @ SY758 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(852,plain,
! [SV113: product_prod_a_a] :
( ( ! [SY760: set_Product_prod_a_a,SY761: product_prod_a_a,SY762: product_prod_a_a > product_prod_a_a] :
( ~ ( member449909584od_a_a @ SV113 @ SY760 )
| ( SY761
!= ( SY762 @ SV113 ) )
| ( member449909584od_a_a @ SY761 @ ( image_794773445od_a_a @ SY762 @ SY760 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(853,plain,
! [SV114: product_prod_a_a] :
( ( ! [SY763: a > product_prod_a_a,SY764: set_a] :
( ~ ( member449909584od_a_a @ SV114 @ ( image_1725938350od_a_a @ SY763 @ SY764 ) )
| ~ ! [SY765: a] :
( ( SV114
!= ( SY763 @ SY765 ) )
| ~ ( member_a @ SY765 @ SY764 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(854,plain,
! [SV115: product_prod_a_a] :
( ( ! [SY766: set_Product_prod_a_a,SY767: product_prod_a_a > product_prod_a_a] :
( ~ ( member449909584od_a_a @ SV115 @ SY766 )
| ( member449909584od_a_a @ ( SY767 @ SV115 ) @ ( image_794773445od_a_a @ SY767 @ SY766 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[711]) ).
thf(855,plain,
! [SV116: a] :
( ( ! [SY768: produc1572603623od_a_a > a,SY769: produc1572603623od_a_a,SY770: a,SY771: produc1572603623od_a_a > a,SY772: set_Pr1948701895od_a_a] :
( ( SV116
!= ( SY768 @ SY769 ) )
| ( SY770
!= ( SY771 @ SY769 ) )
| ~ ( member2057358096od_a_a @ SY769 @ SY772 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV116 @ SY770 ) @ ( bNF_Gr356189709_a_a_a @ SY772 @ SY768 @ SY771 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[712]) ).
thf(856,plain,
! [SV117: set_Product_prod_a_a] :
( ( ~ ! [SY773: product_prod_a_a] : ( member449909584od_a_a @ SY773 @ SV117 )
| ( top_to398455383od_a_a = SV117 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(857,plain,
! [SV118: product_prod_a_a] :
( ( ! [SY774: product_prod_a_a,SY775: set_Product_prod_a_a,SY776: set_Pr1948701895od_a_a] :
( ~ ( member449909584od_a_a @ SV118 @ ( prefer477097315od_a_a @ SY774 @ SY775 @ SY776 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV118 @ SY774 ) @ SY776 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[714]) ).
thf(858,plain,
! [SV119: product_prod_a_a] :
( ( ! [SY777: set_a,SY778: a > set_a] :
( ~ ( member449909584od_a_a @ SV119 @ ( product_Sigma_a_a @ SY777 @ SY778 ) )
| ~ ! [SY779: a] :
( ~ ( member_a @ SY779 @ SY777 )
| ! [SY780: a] :
( ~ ( member_a @ SY780 @ ( SY778 @ SY779 ) )
| ( SV119
!= ( product_Pair_a_a @ SY779 @ SY780 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(859,plain,
! [SV120: product_prod_a_a] :
( ( ! [SY781: set_Product_prod_a_a,SY782: set_Product_prod_a_a,SY783: product_prod_a_a > $o] :
( ~ ( member449909584od_a_a @ SV120 @ SY781 )
| ~ ( ord_le1824328871od_a_a @ SY781
@ ( collec645855634od_a_a
@ ^ [SX4: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SX4 @ SY782 )
| ~ ( SY783 @ SX4 ) ) ) )
| ( SY783 @ SV120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[716]) ).
thf(860,plain,
! [SV121: product_prod_a_a] :
( ( ! [SY785: a,SY786: a] :
( ( SV121
!= ( product_Pair_a_a @ SY785 @ SY786 ) )
| ( ( product_fst_a_a @ SV121 )
= SY785 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(861,plain,
! [SV122: set_Product_prod_a_a] :
( ( ! [SY787: product_prod_a_a > a,SY788: set_a] :
( ~ ! [SY789: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY789 @ SV122 )
| ( member_a @ ( SY787 @ SY789 ) @ SY788 ) )
| ( ord_less_eq_set_a @ ( image_340790172_a_a_a @ SY787 @ SV122 ) @ SY788 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[718]) ).
thf(862,plain,
! [SV123: a] :
( ( ! [SY790: a,SY791: a,SY792: a,SY793: set_Product_prod_a_a,SY794: set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SY790 ) @ ( product_Pair_a_a @ SY791 @ SY792 ) ) @ ( lex_prod_a_a @ SY793 @ SY794 ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SY791 ) @ SY793 )
| ~ ( ( SV123 != SY791 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY790 @ SY792 ) @ SY794 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(863,plain,
( ( ! [SX0: product_prod_a_a] :
~ ( member449909584od_a_a @ SX0 @ top_to398455383od_a_a ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[720]) ).
thf(864,plain,
! [SV124: set_Product_prod_a_a] :
( ( ~ ! [SY795: product_prod_a_a] :
~ ( member449909584od_a_a @ SY795 @ SV124 )
| ( SV124 = bot_bo2131659635od_a_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(865,plain,
! [SV125: a] :
( ( ! [SY796: product_prod_a_a] :
( ( SV125
= ( product_fst_a_a @ SY796 ) )
= ( ~ ! [SY797: a] :
( SY796
!= ( product_Pair_a_a @ SV125 @ SY797 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(866,plain,
! [SV126: product_prod_a_a] :
( ( ! [SY798: set_Product_prod_a_a,SY799: set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ SV126 @ SY798 )
| ~ ~ ( member449909584od_a_a @ SV126 @ SY799 )
| ( member449909584od_a_a @ SV126 @ ( minus_1507102574od_a_a @ SY798 @ SY799 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(867,plain,
! [SV127: a] :
( ( ! [SY800: a,SY801: set_a,SY802: a > set_a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV127 @ SY800 ) @ ( product_Sigma_a_a @ SY801 @ SY802 ) )
| ~ ( ~ ( member_a @ SV127 @ SY801 )
| ~ ( member_a @ SY800 @ ( SY802 @ SV127 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(868,plain,
! [SV128: a] :
( ( ! [SY803: a,SY804: a] :
( ( ( product_fst_a_a @ ( product_Pair_a_a @ SV128 @ SY803 ) )
!= SY804 )
| ( SV128 = SY804 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(869,plain,
! [SV129: product_prod_a_a] :
( ( ! [SY805: product_prod_a_a,SY806: set_Product_prod_a_a,SY807: product_prod_a_a > set_Product_prod_a_a] :
( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV129 @ SY805 ) @ ( produc304751368od_a_a @ SY806 @ SY807 ) )
| ( member449909584od_a_a @ SY805 @ ( SY807 @ SV129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(870,plain,
! [SV130: a,SV1: a] :
( ( ( product_swap_a_a @ ( product_Pair_a_a @ SV1 @ SV130 ) )
= ( product_Pair_a_a @ SV130 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(871,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= ( SV2 = SV131 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(872,plain,
! [SV132: a,SV3: a] :
( ( ! [SY812: set_Product_prod_a_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ SV3 @ SV132 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SY812 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ SV132 @ SV3 ) @ SY812 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(873,plain,
! [SV133: product_prod_a_a > $o,SV4: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV4 @ ( collec645855634od_a_a @ SV133 ) )
= ( SV133 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(874,plain,
! [SV134: set_Product_prod_a_a] :
( ( ( minus_1507102574od_a_a @ SV134 )
= ( ^ [SY813: set_Product_prod_a_a] :
( collec645855634od_a_a
@ ( minus_1797478127_a_a_o
@ ^ [SY814: product_prod_a_a] : ( member449909584od_a_a @ SY814 @ SV134 )
@ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ SY813 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[732]) ).
thf(875,plain,
! [SV135: a > a,SV9: a > a] :
( ( ! [SY816: a,SY817: a] :
( ( produc700022774_a_a_a @ SV9 @ SV135 @ ( product_Pair_a_a @ SY816 @ SY817 ) )
= ( product_Pair_a_a @ ( SV9 @ SY816 ) @ ( SV135 @ SY817 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(876,plain,
! [SV136: a > product_prod_a_a,SV10: a > product_prod_a_a] :
( ( ! [SY818: a,SY819: a] :
( ( produc2012818120od_a_a @ SV10 @ SV136 @ ( product_Pair_a_a @ SY818 @ SY819 ) )
= ( produc1474507607od_a_a @ ( SV10 @ SY818 ) @ ( SV136 @ SY819 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(877,plain,
! [SV137: product_prod_a_a > a,SV11: product_prod_a_a > a] :
( ( ! [SY820: product_prod_a_a,SY821: product_prod_a_a] :
( ( produc363290532_a_a_a @ SV11 @ SV137 @ ( produc1474507607od_a_a @ SY820 @ SY821 ) )
= ( product_Pair_a_a @ ( SV11 @ SY820 ) @ ( SV137 @ SY821 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(878,plain,
! [SV138: product_prod_a_a] :
( ( ( top_to1483957574_a_a_o @ SV138 )
= ( member449909584od_a_a @ SV138 @ top_to398455383od_a_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(879,plain,
! [SV139: a,SV13: a] :
( ( ( product_fst_a_a @ ( product_Pair_a_a @ SV13 @ SV139 ) )
= SV13 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(880,plain,
! [SV140: a] :
( ( ( top_top_a_a_o @ SV140 )
= ( ^ [SY822: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV140 @ SY822 ) @ top_to398455383od_a_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(881,plain,
! [SV141: a,SV16: a] :
( ( ( product_snd_a_a @ ( product_Pair_a_a @ SV16 @ SV141 ) )
= SV141 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(882,plain,
! [SV142: product_prod_a_a] :
( ( ( product_swap_a_a @ SV142 )
= ( product_Pair_a_a @ ( product_snd_a_a @ SV142 ) @ ( product_fst_a_a @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(883,plain,
! [SV143: set_a,SV20: product_prod_a_a] :
( ( ! [SY823: set_a] :
( ( member449909584od_a_a @ SV20 @ ( product_product_a_a @ SV143 @ SY823 ) )
= ( member449909584od_a_a @ SV20
@ ( product_Sigma_a_a @ SV143
@ ^ [Uu: a] : SY823 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[750]) ).
thf(884,plain,
! [SV144: set_Product_prod_a_a,SV21: set_Product_prod_a_a] :
( ( ( ord_le1347718902_a_a_o
@ ^ [SY498: product_prod_a_a] : ( member449909584od_a_a @ SY498 @ SV21 )
@ ^ [SY826: product_prod_a_a] : ( member449909584od_a_a @ SY826 @ SV144 ) )
= ( ord_le1824328871od_a_a @ SV21 @ SV144 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(885,plain,
! [SV145: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV145 )
= ( ^ [SY827: set_Product_prod_a_a] :
( ord_le1347718902_a_a_o
@ ^ [SY828: product_prod_a_a] : ( member449909584od_a_a @ SY828 @ SV145 )
@ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ SY827 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[752]) ).
thf(886,plain,
! [SV146: set_Product_prod_a_a,SV23: set_Product_prod_a_a] :
( ( ( ord_less_eq_a_a_o
@ ^ [SY504: a,SY505: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY504 @ SY505 ) @ SV23 )
@ ^ [SY832: a,SY833: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY832 @ SY833 ) @ SV146 ) )
= ( ord_le1824328871od_a_a @ SV23 @ SV146 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(887,plain,
! [SV24: set_Product_prod_a_a] :
( ( ~ ( ! [SY508: product_prod_a_a] :
~ ( member449909584od_a_a @ SY508 @ SV24 )
| ( SV24 = bot_bo2131659635od_a_a ) )
| ~ ( ~ ! [SY508: product_prod_a_a] :
~ ( member449909584od_a_a @ SY508 @ SV24 )
| ( SV24 != bot_bo2131659635od_a_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[755]) ).
thf(888,plain,
! [SV24: set_Product_prod_a_a] :
( ( ( ! [SY508: product_prod_a_a] :
~ ( member449909584od_a_a @ SY508 @ SV24 ) )
= ( SV24 = bot_bo2131659635od_a_a ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[755]) ).
thf(889,plain,
! [SV25: product_prod_a_a] :
( ( member449909584od_a_a @ SV25 @ bot_bo2131659635od_a_a )
= $false ),
inference(extcnf_not_pos,[status(thm)],[756]) ).
thf(890,plain,
! [SV26: product_prod_a_a] :
( ( member449909584od_a_a @ SV26 @ bot_bo2131659635od_a_a )
= $false ),
inference(extcnf_not_pos,[status(thm)],[757]) ).
thf(891,plain,
! [SV147: product_prod_a_a,SV27: set_Product_prod_a_a] :
( ( ( SV27 != bot_bo2131659635od_a_a )
| ~ ( member449909584od_a_a @ SV147 @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(892,plain,
! [SV148: set_Product_prod_a_a,SV28: set_Product_prod_a_a] :
( ( ~ ! [SY834: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY834 @ SV28 )
| ( member449909584od_a_a @ SY834 @ SV148 ) )
| ( ord_le1824328871od_a_a @ SV28 @ SV148 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(893,plain,
! [SV149: product_prod_a_a > produc1572603623od_a_a,SV29: produc1572603623od_a_a] :
( ( ! [SY835: product_prod_a_a,SY836: set_Product_prod_a_a] :
( ( SV29
!= ( SV149 @ SY835 ) )
| ~ ( member449909584od_a_a @ SY835 @ SY836 )
| ( member2057358096od_a_a @ SV29 @ ( image_1765377413od_a_a @ SV149 @ SY836 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[761]) ).
thf(894,plain,
! [SV150: a,SV30: a] :
( ( ! [SY837: a,SY838: a] :
( ( ( product_Pair_a_a @ SV30 @ SV150 )
= ( product_Pair_a_a @ SY837 @ SY838 ) )
= ( ~ ( ( SV30 != SY837 )
| ( SV150 != SY838 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(895,plain,
! [SV151: set_Product_prod_a_a,SV31: product_prod_a_a] :
( ( ! [SY839: produc1572603623od_a_a,SY840: product_prod_a_a > produc1572603623od_a_a] :
( ~ ( member449909584od_a_a @ SV31 @ SV151 )
| ( SY839
!= ( SY840 @ SV31 ) )
| ( member2057358096od_a_a @ SY839 @ ( image_1765377413od_a_a @ SY840 @ SV151 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[763]) ).
thf(896,plain,
! [SV152: product_prod_a_a > product_prod_a_a,SV32: set_Product_prod_a_a] :
( ( ! [SY841: set_Product_prod_a_a] :
( ~ ! [SY842: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY842 @ SV32 )
| ( member449909584od_a_a @ ( SV152 @ SY842 ) @ SY841 ) )
| ( ord_le1824328871od_a_a @ ( image_794773445od_a_a @ SV152 @ SV32 ) @ SY841 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[764]) ).
thf(897,plain,
! [SV153: set_Product_prod_a_a,SV33: product_prod_a_a] :
( ( ! [SY843: set_Product_prod_a_a] :
( ( member449909584od_a_a @ SV33 @ ( minus_1507102574od_a_a @ SV153 @ SY843 ) )
= ( ~ ( ~ ( member449909584od_a_a @ SV33 @ SV153 )
| ~ ~ ( member449909584od_a_a @ SV33 @ SY843 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(898,plain,
! [SV154: a > product_prod_a_a,SV34: set_a] :
( ( ! [SY844: set_Product_prod_a_a] :
( ~ ! [SY845: a] :
( ~ ( member_a @ SY845 @ SV34 )
| ( member449909584od_a_a @ ( SV154 @ SY845 ) @ SY844 ) )
| ( ord_le1824328871od_a_a @ ( image_1725938350od_a_a @ SV154 @ SV34 ) @ SY844 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[766]) ).
thf(899,plain,
! [SV155: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV155 )
= ( ^ [SY846: set_Product_prod_a_a] :
! [SY847: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY847 @ SV155 )
| ( member449909584od_a_a @ SY847 @ SY846 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[767]) ).
thf(900,plain,
! [SV36: set_Product_prod_a_a] :
( ( ~ ( ~ ! [SY531: product_prod_a_a] :
~ ( member449909584od_a_a @ SY531 @ SV36 )
| ( SV36 != bot_bo2131659635od_a_a ) )
| ~ ( ~ ~ ! [SY531: product_prod_a_a] :
~ ( member449909584od_a_a @ SY531 @ SV36 )
| ~ ( ( SV36 != bot_bo2131659635od_a_a ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[769]) ).
thf(901,plain,
! [SV36: set_Product_prod_a_a] :
( ( ( ~ ! [SY531: product_prod_a_a] :
~ ( member449909584od_a_a @ SY531 @ SV36 ) )
= ( SV36 != bot_bo2131659635od_a_a ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[769]) ).
thf(902,plain,
! [SV156: produc1572603623od_a_a,SV37: produc1572603623od_a_a > $o] :
( ( ~ ! [SY533: product_prod_a_a,SY534: a,SY535: a] : ( SV37 @ ( produc1474507607od_a_a @ SY533 @ ( product_Pair_a_a @ SY534 @ SY535 ) ) )
| ( SV37 @ SV156 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(903,plain,
! [SV157: product_prod_a_a > $o,SV38: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [SY851: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY851 @ SV38 )
| ~ ( SV157 @ SY851 ) ) )
@ SV38 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(904,plain,
! [SV158: product_prod_a_a > produc1572603623od_a_a,SV39: produc1572603623od_a_a] :
( ( ! [SY852: set_Product_prod_a_a] :
( ~ ( member2057358096od_a_a @ SV39 @ ( image_1765377413od_a_a @ SV158 @ SY852 ) )
| ~ ! [SY853: product_prod_a_a] :
( ( SV39
!= ( SV158 @ SY853 ) )
| ~ ( member449909584od_a_a @ SY853 @ SY852 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(905,plain,
! [SV159: a > product_prod_a_a,SV40: product_prod_a_a] :
( ( ! [SY854: a,SY855: set_a] :
( ( SV40
!= ( SV159 @ SY854 ) )
| ~ ( member_a @ SY854 @ SY855 )
| ( member449909584od_a_a @ SV40 @ ( image_1725938350od_a_a @ SV159 @ SY855 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(906,plain,
! [SV160: product_prod_a_a > $o,SV41: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [SY856: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY856 @ SV41 )
| ~ ( SV160 @ SY856 ) ) )
@ SV41 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(907,plain,
! [SV161: product_prod_a_a > product_prod_a_a,SV42: product_prod_a_a] :
( ( ! [SY857: set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ SV42 @ ( image_794773445od_a_a @ SV161 @ SY857 ) )
| ~ ! [SY858: product_prod_a_a] :
( ( SV42
!= ( SV161 @ SY858 ) )
| ~ ( member449909584od_a_a @ SY858 @ SY857 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(908,plain,
! [SV162: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV162 )
= ( ^ [SY859: set_Product_prod_a_a] :
! [SY860: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY860 @ SV162 )
| ( member449909584od_a_a @ SY860 @ SY859 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[776]) ).
thf(909,plain,
! [SV163: a,SV44: product_prod_a_a > $o] :
( ( ! [SY861: a] :
( ~ ( SV44 @ ( product_Pair_a_a @ SV163 @ SY861 ) )
| ( product_curry_a_a_o @ SV44 @ SV163 @ SY861 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(910,plain,
! [SV164: set_Product_prod_a_a,SV45: product_prod_a_a] :
( ( ! [SY862: set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ SV45 @ ( minus_1507102574od_a_a @ SV164 @ SY862 ) )
| ~ ( ~ ( member449909584od_a_a @ SV45 @ SV164 )
| ( member449909584od_a_a @ SV45 @ SY862 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[779]) ).
thf(911,plain,
! [SV165: set_Product_prod_a_a,SV46: set_Product_prod_a_a] :
( ( ! [SY863: product_prod_a_a > $o] :
( ~ ( ord_le1824328871od_a_a @ SV46 @ SV165 )
| ( ( ord_le1824328871od_a_a @ SV46
@ ( collec645855634od_a_a
@ ^ [SY864: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY864 @ SV165 )
| ~ ( SY863 @ SY864 ) ) ) )
= ( ! [SY558: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY558 @ SV46 )
| ( SY863 @ SY558 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[780]) ).
thf(912,plain,
! [SV166: a] :
( ( ( prefer161218362good_a @ SV166 )
= ( ^ [SY866: set_a,SY867: set_Product_prod_a_a] :
( collect_a
@ ^ [SY868: a] :
~ ( ~ ( member_a @ SY868 @ SY866 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY868 @ SV166 ) @ SY867 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[781]) ).
thf(913,plain,
! [SV167: produc1572603623od_a_a > product_prod_a_a,SV48: product_prod_a_a] :
( ( ! [SY869: set_Pr1948701895od_a_a] :
( ~ ( member449909584od_a_a @ SV48 @ ( image_734753285od_a_a @ SV167 @ SY869 ) )
| ~ ! [SY870: produc1572603623od_a_a] :
( ( SV48
!= ( SV167 @ SY870 ) )
| ~ ( member2057358096od_a_a @ SY870 @ SY869 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(914,plain,
! [SV168: set_Product_prod_a_a,SV49: set_a] :
( ( ! [SY871: a,SY872: a] :
( ~ ( prefer1292084992ence_a @ SV49 @ SV168 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY871 @ SY872 ) @ SV168 )
| ( member_a @ SY871 @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[784]) ).
thf(915,plain,
! [SV169: set_a,SV50: a] :
( ( ! [SY873: a > product_prod_a_a] :
( ~ ( member_a @ SV50 @ SV169 )
| ( member449909584od_a_a @ ( SY873 @ SV50 ) @ ( image_1725938350od_a_a @ SY873 @ SV169 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(916,plain,
! [SV170: set_a,SV51: a] :
( ( ! [SY874: product_prod_a_a,SY875: a > product_prod_a_a] :
( ~ ( member_a @ SV51 @ SV170 )
| ( SY874
!= ( SY875 @ SV51 ) )
| ( member449909584od_a_a @ SY874 @ ( image_1725938350od_a_a @ SY875 @ SV170 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(917,plain,
! [SV171: a,SV52: a] :
( ( ! [SY876: set_a,SY877: a > set_a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV171 ) @ ( product_Sigma_a_a @ SY876 @ SY877 ) )
| ( member_a @ SV52 @ SY876 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(918,plain,
! [SV172: set_Pr1948701895od_a_a,SV53: produc1572603623od_a_a] :
( ( ! [SY878: product_prod_a_a,SY879: produc1572603623od_a_a > product_prod_a_a] :
( ~ ( member2057358096od_a_a @ SV53 @ SV172 )
| ( SY878
!= ( SY879 @ SV53 ) )
| ( member449909584od_a_a @ SY878 @ ( image_734753285od_a_a @ SY879 @ SV172 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[788]) ).
thf(919,plain,
! [SV173: set_Pr1948701895od_a_a,SV54: produc1572603623od_a_a] :
( ( ! [SY880: produc1572603623od_a_a > product_prod_a_a] :
( ~ ( member2057358096od_a_a @ SV54 @ SV173 )
| ( member449909584od_a_a @ ( SY880 @ SV54 ) @ ( image_734753285od_a_a @ SY880 @ SV173 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[789]) ).
thf(920,plain,
! [SV174: set_Product_prod_a_a,SV55: product_prod_a_a > product_prod_a_a] :
( ( ! [SY881: product_prod_a_a > $o] :
( ( collec645855634od_a_a
@ ^ [SY882: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY882 @ ( image_794773445od_a_a @ SV55 @ SV174 ) )
| ~ ( SY881 @ SY882 ) ) )
= ( image_794773445od_a_a @ SV55
@ ( collec645855634od_a_a
@ ^ [SY883: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY883 @ SV174 )
| ~ ( SY881 @ ( SV55 @ SY883 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(921,plain,
! [SV175: a,SV56: a] :
( ( ! [SY884: set_Product_prod_a_a,SY885: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV56 @ SV175 ) @ SY884 )
| ( SY885 != SV175 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV56 @ SY885 ) @ SY884 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(922,plain,
! [SV176: a,SV57: a] :
( ( ! [SY886: a,SY887: a] :
( ( ( product_Pair_a_a @ SV57 @ SV176 )
= ( product_Pair_a_a @ SY886 @ SY887 ) )
= ( ~ ( ( SV57 != SY886 )
| ( SV176 != SY887 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(923,plain,
! [SV177: set_Product_prod_a_a,SV58: product_prod_a_a] :
( ( ! [SY888: a,SY889: product_prod_a_a > a] :
( ~ ( member449909584od_a_a @ SV58 @ SV177 )
| ( SY888
!= ( SY889 @ SV58 ) )
| ( member_a @ SY888 @ ( image_340790172_a_a_a @ SY889 @ SV177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(924,plain,
! [SV178: produc1572603623od_a_a > product_prod_a_a,SV59: set_Pr1948701895od_a_a] :
( ( ! [SY890: set_Product_prod_a_a] :
( ~ ! [SY891: produc1572603623od_a_a] :
( ~ ( member2057358096od_a_a @ SY891 @ SV59 )
| ( member449909584od_a_a @ ( SV178 @ SY891 ) @ SY890 ) )
| ( ord_le1824328871od_a_a @ ( image_734753285od_a_a @ SV178 @ SV59 ) @ SY890 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(925,plain,
! [SV179: set_a,SV60: set_Product_prod_a_a] :
( ( ~ ! [SY892: a,SY893: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY892 @ SY893 ) @ SV60 )
| ( member_a @ SY892 @ SV179 ) )
| ~ ! [SY894: a,SY895: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY894 @ SY895 ) @ SV60 )
| ( member_a @ SY895 @ SV179 ) )
| ~ ( order_preorder_on_a @ SV179 @ SV60 )
| ( prefer1292084992ence_a @ SV179 @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[795]) ).
thf(926,plain,
! [SV180: set_Product_prod_a_a,SV61: set_a] :
( ( ! [SY896: a,SY897: a,SY898: a] :
( ~ ( prefer1292084992ence_a @ SV61 @ SV180 )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY896 @ SY897 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY897 @ SY896 ) @ SV180 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY897 @ SY898 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY898 @ SY897 ) @ SV180 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY896 @ SY898 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY898 @ SY896 ) @ SV180 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(927,plain,
! [SV181: set_Pr1948701895od_a_a,SV62: set_Product_prod_a_a] :
( ( ! [SY899: product_prod_a_a,SY900: product_prod_a_a] :
( ~ ( prefer1338892073od_a_a @ SV62 @ SV181 )
| ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY899 @ SY900 ) @ SV181 )
| ( member449909584od_a_a @ SY899 @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(928,plain,
! [SV182: product_prod_a_a,SV63: product_prod_a_a] :
( ( ! [SY901: set_Product_prod_a_a,SY902: product_prod_a_a > set_Product_prod_a_a] :
( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV63 @ SV182 ) @ ( produc304751368od_a_a @ SY901 @ SY902 ) )
| ( member449909584od_a_a @ SV63 @ SY901 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[798]) ).
thf(929,plain,
! [SV183: a,SV64: a > a > $o] :
( ( ! [SY903: a,SY904: product_prod_a_a] :
( ~ ( SV64 @ SV183 @ SY903 )
| ( SY904
!= ( product_Pair_a_a @ SV183 @ SY903 ) )
| ( SV64 @ ( product_fst_a_a @ SY904 ) @ ( product_snd_a_a @ SY904 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[799]) ).
thf(930,plain,
! [SV184: a > a,SV65: a] :
( ( ! [SY905: a,SY906: a,SY907: a > a,SY908: set_a] :
( ( SV65
!= ( SV184 @ SY905 ) )
| ( SY906
!= ( SY907 @ SY905 ) )
| ~ ( member_a @ SY905 @ SY908 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV65 @ SY906 ) @ ( bNF_Gr423046308_a_a_a @ SY908 @ SV184 @ SY907 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(931,plain,
! [SV185: set_a,SV66: a] :
( ( ! [SY909: a,SY910: a > set_a] :
( ~ ( member_a @ SV66 @ SV185 )
| ~ ( member_a @ SY909 @ ( SY910 @ SV66 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV66 @ SY909 ) @ ( product_Sigma_a_a @ SV185 @ SY910 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(932,plain,
! [SV186: a,SV67: a] :
( ( ! [SY911: a,SY912: a] :
( ( ( product_Pair_a_a @ SV67 @ SV186 )
!= ( product_Pair_a_a @ SY911 @ SY912 ) )
| ~ ( ( SV67 != SY911 )
| ( SV186 != SY912 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(933,plain,
! [SV187: set_Product_prod_a_a,SV68: product_prod_a_a] :
( ( ! [SY913: set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ SV68 @ ( minus_1507102574od_a_a @ SV187 @ SY913 ) )
| ( member449909584od_a_a @ SV68 @ SV187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(934,plain,
! [SV188: set_Product_prod_a_a,SV69: product_prod_a_a] :
( ( ! [SY914: set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ SV69 @ ( minus_1507102574od_a_a @ SV188 @ SY914 ) )
| ~ ( member449909584od_a_a @ SV69 @ SY914 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[804]) ).
thf(935,plain,
! [SV189: set_Product_prod_a_a,SV70: set_Product_prod_a_a] :
( ( ~ ! [SY915: a,SY916: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY915 @ SY916 ) @ SV70 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY915 @ SY916 ) @ SV189 ) )
| ( ord_le1824328871od_a_a @ SV70 @ SV189 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(936,plain,
! [SV190: a,SV71: product_prod_a_a > $o] :
( ( ! [SY917: a] :
( ~ ( product_curry_a_a_o @ SV71 @ SV190 @ SY917 )
| ( SV71 @ ( product_Pair_a_a @ SV190 @ SY917 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(937,plain,
! [SV191: a,SV72: a] :
( ( ! [SY918: set_a,SY919: a > set_a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV72 @ SV191 ) @ ( product_Sigma_a_a @ SY918 @ SY919 ) )
| ( member_a @ SV191 @ ( SY919 @ SV72 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(938,plain,
! [SV73: produc1921647824od_a_a] :
( ( ! [SY638: a,SY639: a,SY640: a] :
( SV73
!= ( produc1299253312od_a_a @ SY638 @ ( product_Pair_a_a @ SY639 @ SY640 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[808]) ).
thf(939,plain,
! [SV192: a,SV74: a] :
( ( ! [SY920: set_a,SY921: a > a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV74 @ SV192 ) @ ( bNF_Gr_a_a @ SY920 @ SY921 ) )
| ( ( SY921 @ SV74 )
= SV192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(940,plain,
! [SV193: a,SV75: a] :
( ( ! [SY922: set_a,SY923: a > set_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ SV75 @ SV193 ) @ ( product_Sigma_a_a @ SY922 @ SY923 ) )
= ( ~ ( ~ ( member_a @ SV75 @ SY922 )
| ~ ( member_a @ SV193 @ ( SY923 @ SV75 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(941,plain,
! [SV194: product_prod_a_a > product_prod_a_a,SV76: product_prod_a_a] :
( ( ! [SY924: product_prod_a_a,SY925: product_prod_a_a,SY926: product_prod_a_a > product_prod_a_a,SY927: set_Product_prod_a_a] :
( ( SV76
!= ( SV194 @ SY924 ) )
| ( SY925
!= ( SY926 @ SY924 ) )
| ~ ( member449909584od_a_a @ SY924 @ SY927 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV76 @ SY925 ) @ ( bNF_Gr200450189od_a_a @ SY927 @ SV194 @ SY926 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(942,plain,
! [SV195: set_Product_prod_a_a] :
( ( ( minus_1507102574od_a_a @ SV195 )
= ( ^ [SY928: set_Product_prod_a_a] :
( collec645855634od_a_a
@ ^ [SY929: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY929 @ SV195 )
| ~ ~ ( member449909584od_a_a @ SY929 @ SY928 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(943,plain,
! [SV196: set_Product_prod_a_a,SV78: set_Product_prod_a_a] :
( ( ! [SY930: product_prod_a_a] :
( ~ ( ord_le1824328871od_a_a @ SV78 @ SV196 )
| ~ ( member449909584od_a_a @ SY930 @ SV78 )
| ( member449909584od_a_a @ SY930 @ SV196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(944,plain,
! [SV197: a,SV79: a] :
( ( ! [SY931: set_Product_prod_a_a,SY932: a > a,SY933: a > a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV79 @ SV197 ) @ SY931 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( SY932 @ SV79 ) @ ( SY933 @ SV197 ) ) @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SY932 @ SY933 ) @ SY931 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(945,plain,
! [SV198: set_Product_prod_a_a,SV80: set_Product_prod_a_a] :
( ( ! [SY934: product_prod_a_a] :
( ~ ( ord_le1824328871od_a_a @ SV80 @ SV198 )
| ~ ( member449909584od_a_a @ SY934 @ SV80 )
| ( member449909584od_a_a @ SY934 @ SV198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(946,plain,
! [SV199: product_prod_a_a > produc1572603623od_a_a,SV81: set_Product_prod_a_a] :
( ( ! [SY935: set_Pr1948701895od_a_a] :
( ~ ! [SY936: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY936 @ SV81 )
| ( member2057358096od_a_a @ ( SV199 @ SY936 ) @ SY935 ) )
| ( ord_le456379495od_a_a @ ( image_1765377413od_a_a @ SV199 @ SV81 ) @ SY935 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(947,plain,
! [SV200: a,SV82: product_prod_a_a] :
( ( ! [SY937: a] :
( ( SV82
!= ( product_Pair_a_a @ SV200 @ SY937 ) )
| ( ( product_snd_a_a @ SV82 )
= SY937 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(948,plain,
! [SV201: set_a] :
( ( ( prefer1292084992ence_a @ SV201 )
= ( ^ [SY938: set_Product_prod_a_a] :
~ ( ~ ~ ( ~ ! [SY939: a,SY940: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY939 @ SY940 ) @ SY938 )
| ( member_a @ SY939 @ SV201 ) )
| ~ ! [SY941: a,SY942: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY941 @ SY942 ) @ SY938 )
| ( member_a @ SY942 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SY938 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(949,plain,
! [SV202: product_prod_a_a,SV84: product_prod_a_a] :
( ( ! [SY943: set_Product_prod_a_a,SY944: product_prod_a_a > set_Product_prod_a_a] :
( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV84 @ SV202 ) @ ( produc304751368od_a_a @ SY943 @ SY944 ) )
| ~ ( ~ ( member449909584od_a_a @ SV84 @ SY943 )
| ~ ( member449909584od_a_a @ SV202 @ ( SY944 @ SV84 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(950,plain,
! [SV203: set_Product_prod_a_a,SV85: product_prod_a_a] :
( ( ! [SY945: product_prod_a_a > produc1572603623od_a_a] :
( ~ ( member449909584od_a_a @ SV85 @ SV203 )
| ( member2057358096od_a_a @ ( SY945 @ SV85 ) @ ( image_1765377413od_a_a @ SY945 @ SV203 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(951,plain,
! [SV204: set_Product_prod_a_a,SV86: product_prod_a_a] :
( ( ! [SY946: product_prod_a_a,SY947: product_prod_a_a > set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ SV86 @ SV204 )
| ~ ( member449909584od_a_a @ SY946 @ ( SY947 @ SV86 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV86 @ SY946 ) @ ( produc304751368od_a_a @ SV204 @ SY947 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(952,plain,
! [SV205: a,SV87: a > a > $o] :
( ( ! [SY948: a] :
( ~ ( SV87 @ SV205 @ SY948 )
| ( SV87 @ ( product_snd_a_a @ ( product_Pair_a_a @ SY948 @ SV205 ) ) @ ( product_fst_a_a @ ( product_Pair_a_a @ SY948 @ SV205 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(953,plain,
! [SV206: set_Product_prod_a_a,SV88: set_Product_prod_a_a] :
( ( ! [SY949: product_prod_a_a > $o,SY950: product_prod_a_a > $o] :
( ~ ( ord_le1824328871od_a_a @ SV88 @ SV206 )
| ~ ! [SY685: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY685 @ SV88 )
| ~ ( SY949 @ SY685 )
| ( SY950 @ SY685 ) )
| ( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [SY686: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY686 @ SV88 )
| ~ ( SY949 @ SY686 ) ) )
@ ( collec645855634od_a_a
@ ^ [SY953: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY953 @ SV206 )
| ~ ( SY950 @ SY953 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(954,plain,
! [SV207: product_prod_a_a,SV89: product_prod_a_a] :
( ( ! [SY954: set_Product_prod_a_a,SY955: product_prod_a_a > set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV89 @ SV207 ) @ ( produc304751368od_a_a @ SY954 @ SY955 ) )
= ( ~ ( ~ ( member449909584od_a_a @ SV89 @ SY954 )
| ~ ( member449909584od_a_a @ SV207 @ ( SY955 @ SV89 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(955,plain,
! [SV90: produc1572603623od_a_a] :
( ( ! [SY691: product_prod_a_a,SY692: a,SY693: a] :
( SV90
!= ( produc1474507607od_a_a @ SY691 @ ( product_Pair_a_a @ SY692 @ SY693 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[827]) ).
thf(956,plain,
! [SV208: product_prod_a_a,SV91: a] :
( ( ( SV91
= ( product_snd_a_a @ SV208 ) )
= ( ~ ! [SY956: a] :
( SV208
!= ( product_Pair_a_a @ SY956 @ SV91 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(957,plain,
! [SV209: produc1572603623od_a_a > product_prod_a_a,SV92: product_prod_a_a] :
( ( ! [SY957: produc1572603623od_a_a,SY958: set_Pr1948701895od_a_a] :
( ( SV92
!= ( SV209 @ SY957 ) )
| ~ ( member2057358096od_a_a @ SY957 @ SY958 )
| ( member449909584od_a_a @ SV92 @ ( image_734753285od_a_a @ SV209 @ SY958 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(958,plain,
! [SV210: a,SV93: a > $o] :
( ( ! [SY959: a > $o,SY960: a] :
( ~ ( SV93 @ SV210 )
| ~ ( SY959 @ SY960 )
| ~ ( ~ ( SV93 @ ( product_fst_a_a @ ( product_Pair_a_a @ SV210 @ SY960 ) ) )
| ~ ( SY959 @ ( product_snd_a_a @ ( product_Pair_a_a @ SV210 @ SY960 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(959,plain,
! [SV211: a,SV94: a] :
( ( ! [SY961: set_a,SY962: set_Product_prod_a_a] :
( ~ ( member_a @ SV94 @ ( prefer161218362good_a @ SV211 @ SY961 @ SY962 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV94 @ SV211 ) @ SY962 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(960,plain,
! [SV212: product_prod_a_a > a,SV95: a] :
( ( ! [SY963: product_prod_a_a,SY964: a,SY965: product_prod_a_a > a,SY966: set_Product_prod_a_a] :
( ( SV95
!= ( SV212 @ SY963 ) )
| ( SY964
!= ( SY965 @ SY963 ) )
| ~ ( member449909584od_a_a @ SY963 @ SY966 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV95 @ SY964 ) @ ( bNF_Gr1853143117_a_a_a @ SY966 @ SV212 @ SY965 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(961,plain,
! [SV213: product_prod_a_a,SV96: product_prod_a_a] :
( ( ! [SY967: set_Product_prod_a_a,SY968: product_prod_a_a > product_prod_a_a] :
( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV96 @ SV213 ) @ ( bNF_Gr1372473186od_a_a @ SY967 @ SY968 ) )
| ( member449909584od_a_a @ SV96 @ SY967 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(962,plain,
! [SV214: a] :
( ( ( prefer436369274d_as_a @ SV214 )
= ( ^ [SY969: set_a,SY970: set_Product_prod_a_a] :
( collect_a
@ ^ [SY971: a] :
~ ( ~ ~ ( ~ ( member_a @ SY971 @ SY969 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV214 @ SY971 ) @ SY970 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY971 @ SV214 ) @ SY970 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(963,plain,
! [SV98: product_prod_a_a] :
( ( ! [SY716: a,SY717: a] :
( SV98
!= ( product_Pair_a_a @ SY716 @ SY717 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[836]) ).
thf(964,plain,
! [SV215: product_prod_a_a > a,SV99: a] :
( ( ! [SY972: set_Product_prod_a_a] :
( ~ ( member_a @ SV99 @ ( image_340790172_a_a_a @ SV215 @ SY972 ) )
| ~ ! [SY973: product_prod_a_a] :
( ( SV99
!= ( SV215 @ SY973 ) )
| ~ ( member449909584od_a_a @ SY973 @ SY972 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(965,plain,
! [SV216: product_prod_a_a,SV100: product_prod_a_a > $o] :
( ( ~ ! [SY722: a,SY723: a] : ( SV100 @ ( product_Pair_a_a @ SY722 @ SY723 ) )
| ( SV100 @ SV216 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(966,plain,
! [SV217: a > a,SV101: product_prod_a_a] :
( ( ! [SY976: a > a,SY977: set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ SV101 @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SV217 @ SY976 ) @ SY977 ) )
| ~ ! [SY978: a,SY979: a] :
( ( SV101
!= ( product_Pair_a_a @ ( SV217 @ SY978 ) @ ( SY976 @ SY979 ) ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY978 @ SY979 ) @ SY977 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[839]) ).
thf(967,plain,
! [SV218: a] :
( ( ( prefer1676310729than_a @ SV218 )
= ( ^ [SY980: set_a,SY981: set_Product_prod_a_a] :
( collect_a
@ ^ [SY982: a] :
~ ( ~ ( member_a @ SY982 @ SY980 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV218 @ SY982 ) @ SY981 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(968,plain,
! [SV219: a,SV103: a] :
( ( ! [SY983: set_a,SY984: a > a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV103 @ SV219 ) @ ( bNF_Gr_a_a @ SY983 @ SY984 ) )
| ( member_a @ SV103 @ SY983 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(969,plain,
! [SV220: a,SV104: a > $o] :
( ( ! [SY985: a,SY986: a,SY987: a > set_Product_prod_a_a] :
( ~ ( SV104 @ SV220 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY985 @ SY986 ) @ ( SY987 @ SV220 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV220 @ SY985 ) @ ( product_Pair_a_a @ SV220 @ SY986 ) ) @ ( same_fst_a_a @ SV104 @ SY987 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(970,plain,
! [SV221: product_prod_a_a,SV105: product_prod_a_a > $o] :
( ( ~ ! [SY740: a,SY741: a] : ( SV105 @ ( product_Pair_a_a @ SY740 @ SY741 ) )
| ( SV105 @ SV221 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(971,plain,
! [SV222: product_prod_a_a > a,SV106: a] :
( ( ! [SY990: product_prod_a_a,SY991: set_Product_prod_a_a] :
( ( SV106
!= ( SV222 @ SY990 ) )
| ~ ( member449909584od_a_a @ SY990 @ SY991 )
| ( member_a @ SV106 @ ( image_340790172_a_a_a @ SV222 @ SY991 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(972,plain,
! [SV223: a,SV107: a] :
( ( ! [SY992: a] :
( ( ( product_snd_a_a @ ( product_Pair_a_a @ SV107 @ SV223 ) )
!= SY992 )
| ( SV223 = SY992 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(973,plain,
! [SV224: a,SV108: product_prod_a_a > $o] :
( ( ! [SY993: a] :
( ~ ( product_curry_a_a_o @ SV108 @ SV224 @ SY993 )
| ( SV108 @ ( product_Pair_a_a @ SV224 @ SY993 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(974,plain,
! [SV109: product_prod_a_a] :
( ( ! [SY749: a] :
~ ~ ! [SY750: a] :
( SV109
!= ( product_Pair_a_a @ SY749 @ SY750 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[848]) ).
thf(975,plain,
! [SV225: product_prod_a_a > product_prod_a_a,SV110: product_prod_a_a] :
( ( ! [SY994: product_prod_a_a,SY995: set_Product_prod_a_a] :
( ( SV110
!= ( SV225 @ SY994 ) )
| ~ ( member449909584od_a_a @ SY994 @ SY995 )
| ( member449909584od_a_a @ SV110 @ ( image_794773445od_a_a @ SV225 @ SY995 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[849]) ).
thf(976,plain,
! [SV226: set_Product_prod_a_a,SV111: produc1572603623od_a_a] :
( ( ! [SY996: product_prod_a_a > set_Product_prod_a_a] :
( ~ ( member2057358096od_a_a @ SV111 @ ( produc304751368od_a_a @ SV226 @ SY996 ) )
| ~ ! [SY997: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY997 @ SV226 )
| ! [SY757: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY757 @ ( SY996 @ SY997 ) )
| ( SV111
!= ( produc1474507607od_a_a @ SY997 @ SY757 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(977,plain,
! [SV227: set_Product_prod_a_a,SV112: product_prod_a_a] :
( ( ! [SY999: product_prod_a_a > a] :
( ~ ( member449909584od_a_a @ SV112 @ SV227 )
| ( member_a @ ( SY999 @ SV112 ) @ ( image_340790172_a_a_a @ SY999 @ SV227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[851]) ).
thf(978,plain,
! [SV228: set_Product_prod_a_a,SV113: product_prod_a_a] :
( ( ! [SY1000: product_prod_a_a,SY1001: product_prod_a_a > product_prod_a_a] :
( ~ ( member449909584od_a_a @ SV113 @ SV228 )
| ( SY1000
!= ( SY1001 @ SV113 ) )
| ( member449909584od_a_a @ SY1000 @ ( image_794773445od_a_a @ SY1001 @ SV228 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(979,plain,
! [SV229: a > product_prod_a_a,SV114: product_prod_a_a] :
( ( ! [SY1002: set_a] :
( ~ ( member449909584od_a_a @ SV114 @ ( image_1725938350od_a_a @ SV229 @ SY1002 ) )
| ~ ! [SY1003: a] :
( ( SV114
!= ( SV229 @ SY1003 ) )
| ~ ( member_a @ SY1003 @ SY1002 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[853]) ).
thf(980,plain,
! [SV230: set_Product_prod_a_a,SV115: product_prod_a_a] :
( ( ! [SY1004: product_prod_a_a > product_prod_a_a] :
( ~ ( member449909584od_a_a @ SV115 @ SV230 )
| ( member449909584od_a_a @ ( SY1004 @ SV115 ) @ ( image_794773445od_a_a @ SY1004 @ SV230 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(981,plain,
! [SV231: produc1572603623od_a_a > a,SV116: a] :
( ( ! [SY1005: produc1572603623od_a_a,SY1006: a,SY1007: produc1572603623od_a_a > a,SY1008: set_Pr1948701895od_a_a] :
( ( SV116
!= ( SV231 @ SY1005 ) )
| ( SY1006
!= ( SY1007 @ SY1005 ) )
| ~ ( member2057358096od_a_a @ SY1005 @ SY1008 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV116 @ SY1006 ) @ ( bNF_Gr356189709_a_a_a @ SY1008 @ SV231 @ SY1007 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(982,plain,
! [SV117: set_Product_prod_a_a] :
( ( ( ~ ! [SY773: product_prod_a_a] : ( member449909584od_a_a @ SY773 @ SV117 ) )
= $true )
| ( ( top_to398455383od_a_a = SV117 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[856]) ).
thf(983,plain,
! [SV232: product_prod_a_a,SV118: product_prod_a_a] :
( ( ! [SY1009: set_Product_prod_a_a,SY1010: set_Pr1948701895od_a_a] :
( ~ ( member449909584od_a_a @ SV118 @ ( prefer477097315od_a_a @ SV232 @ SY1009 @ SY1010 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV118 @ SV232 ) @ SY1010 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(984,plain,
! [SV233: set_a,SV119: product_prod_a_a] :
( ( ! [SY1011: a > set_a] :
( ~ ( member449909584od_a_a @ SV119 @ ( product_Sigma_a_a @ SV233 @ SY1011 ) )
| ~ ! [SY1012: a] :
( ~ ( member_a @ SY1012 @ SV233 )
| ! [SY780: a] :
( ~ ( member_a @ SY780 @ ( SY1011 @ SY1012 ) )
| ( SV119
!= ( product_Pair_a_a @ SY1012 @ SY780 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(985,plain,
! [SV234: set_Product_prod_a_a,SV120: product_prod_a_a] :
( ( ! [SY1014: set_Product_prod_a_a,SY1015: product_prod_a_a > $o] :
( ~ ( member449909584od_a_a @ SV120 @ SV234 )
| ~ ( ord_le1824328871od_a_a @ SV234
@ ( collec645855634od_a_a
@ ^ [SX4: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SX4 @ SY1014 )
| ~ ( SY1015 @ SX4 ) ) ) )
| ( SY1015 @ SV120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(986,plain,
! [SV235: a,SV121: product_prod_a_a] :
( ( ! [SY1017: a] :
( ( SV121
!= ( product_Pair_a_a @ SV235 @ SY1017 ) )
| ( ( product_fst_a_a @ SV121 )
= SV235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(987,plain,
! [SV236: product_prod_a_a > a,SV122: set_Product_prod_a_a] :
( ( ! [SY1018: set_a] :
( ~ ! [SY1019: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1019 @ SV122 )
| ( member_a @ ( SV236 @ SY1019 ) @ SY1018 ) )
| ( ord_less_eq_set_a @ ( image_340790172_a_a_a @ SV236 @ SV122 ) @ SY1018 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(988,plain,
! [SV237: a,SV123: a] :
( ( ! [SY1020: a,SY1021: a,SY1022: set_Product_prod_a_a,SY1023: set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SY1020 @ SY1021 ) ) @ ( lex_prod_a_a @ SY1022 @ SY1023 ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SY1020 ) @ SY1022 )
| ~ ( ( SV123 != SY1020 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SY1021 ) @ SY1023 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(989,plain,
( ( ~ ( member449909584od_a_a @ sK1_SX0 @ top_to398455383od_a_a ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[863]) ).
thf(990,plain,
! [SV124: set_Product_prod_a_a] :
( ( ( ~ ! [SY795: product_prod_a_a] :
~ ( member449909584od_a_a @ SY795 @ SV124 ) )
= $true )
| ( ( SV124 = bot_bo2131659635od_a_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[864]) ).
thf(991,plain,
! [SV238: product_prod_a_a,SV125: a] :
( ( ( SV125
= ( product_fst_a_a @ SV238 ) )
= ( ~ ! [SY1024: a] :
( SV238
!= ( product_Pair_a_a @ SV125 @ SY1024 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(992,plain,
! [SV239: set_Product_prod_a_a,SV126: product_prod_a_a] :
( ( ! [SY1025: set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ SV126 @ SV239 )
| ~ ~ ( member449909584od_a_a @ SV126 @ SY1025 )
| ( member449909584od_a_a @ SV126 @ ( minus_1507102574od_a_a @ SV239 @ SY1025 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[866]) ).
thf(993,plain,
! [SV240: a,SV127: a] :
( ( ! [SY1026: set_a,SY1027: a > set_a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV127 @ SV240 ) @ ( product_Sigma_a_a @ SY1026 @ SY1027 ) )
| ~ ( ~ ( member_a @ SV127 @ SY1026 )
| ~ ( member_a @ SV240 @ ( SY1027 @ SV127 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[867]) ).
thf(994,plain,
! [SV241: a,SV128: a] :
( ( ! [SY1028: a] :
( ( ( product_fst_a_a @ ( product_Pair_a_a @ SV128 @ SV241 ) )
!= SY1028 )
| ( SV128 = SY1028 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(995,plain,
! [SV242: product_prod_a_a,SV129: product_prod_a_a] :
( ( ! [SY1029: set_Product_prod_a_a,SY1030: product_prod_a_a > set_Product_prod_a_a] :
( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV129 @ SV242 ) @ ( produc304751368od_a_a @ SY1029 @ SY1030 ) )
| ( member449909584od_a_a @ SV242 @ ( SY1030 @ SV129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[869]) ).
thf(996,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ~ ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
| ( SV2 = SV131 ) )
| ~ ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
!= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
| ( SV2 != SV131 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[871]) ).
thf(997,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= ( SV2 = SV131 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[871]) ).
thf(998,plain,
! [SV243: set_Product_prod_a_a,SV132: a,SV3: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV3 @ SV132 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV243 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ SV132 @ SV3 ) @ SV243 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[872]) ).
thf(999,plain,
! [SV133: product_prod_a_a > $o,SV4: product_prod_a_a] :
( ( ~ ( ( member449909584od_a_a @ SV4 @ ( collec645855634od_a_a @ SV133 ) )
| ( SV133 @ SV4 ) )
| ~ ( ~ ( member449909584od_a_a @ SV4 @ ( collec645855634od_a_a @ SV133 ) )
| ~ ( SV133 @ SV4 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[873]) ).
thf(1000,plain,
! [SV133: product_prod_a_a > $o,SV4: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV4 @ ( collec645855634od_a_a @ SV133 ) )
= ( SV133 @ SV4 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[873]) ).
thf(1001,plain,
! [SV134: set_Product_prod_a_a] :
( ( ! [SV244: set_Product_prod_a_a] :
( ( minus_1507102574od_a_a @ SV134 @ SV244 )
= ( collec645855634od_a_a
@ ( minus_1797478127_a_a_o
@ ^ [SY814: product_prod_a_a] : ( member449909584od_a_a @ SY814 @ SV134 )
@ ^ [SY1032: product_prod_a_a] : ( member449909584od_a_a @ SY1032 @ SV244 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[874]) ).
thf(1002,plain,
! [SV134: set_Product_prod_a_a] :
( ( ( minus_1507102574od_a_a @ SV134 )
= ( ^ [SY813: set_Product_prod_a_a] :
( collec645855634od_a_a
@ ( minus_1797478127_a_a_o
@ ^ [SY814: product_prod_a_a] : ( member449909584od_a_a @ SY814 @ SV134 )
@ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ SY813 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[874]) ).
thf(1003,plain,
! [SV245: a,SV135: a > a,SV9: a > a] :
( ( ! [SY1033: a] :
( ( produc700022774_a_a_a @ SV9 @ SV135 @ ( product_Pair_a_a @ SV245 @ SY1033 ) )
= ( product_Pair_a_a @ ( SV9 @ SV245 ) @ ( SV135 @ SY1033 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(1004,plain,
! [SV246: a,SV136: a > product_prod_a_a,SV10: a > product_prod_a_a] :
( ( ! [SY1034: a] :
( ( produc2012818120od_a_a @ SV10 @ SV136 @ ( product_Pair_a_a @ SV246 @ SY1034 ) )
= ( produc1474507607od_a_a @ ( SV10 @ SV246 ) @ ( SV136 @ SY1034 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[876]) ).
thf(1005,plain,
! [SV247: product_prod_a_a,SV137: product_prod_a_a > a,SV11: product_prod_a_a > a] :
( ( ! [SY1035: product_prod_a_a] :
( ( produc363290532_a_a_a @ SV11 @ SV137 @ ( produc1474507607od_a_a @ SV247 @ SY1035 ) )
= ( product_Pair_a_a @ ( SV11 @ SV247 ) @ ( SV137 @ SY1035 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[877]) ).
thf(1006,plain,
! [SV138: product_prod_a_a] :
( ( ~ ( ( top_to1483957574_a_a_o @ SV138 )
| ( member449909584od_a_a @ SV138 @ top_to398455383od_a_a ) )
| ~ ( ~ ( top_to1483957574_a_a_o @ SV138 )
| ~ ( member449909584od_a_a @ SV138 @ top_to398455383od_a_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[878]) ).
thf(1007,plain,
! [SV138: product_prod_a_a] :
( ( ( top_to1483957574_a_a_o @ SV138 )
= ( member449909584od_a_a @ SV138 @ top_to398455383od_a_a ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[878]) ).
thf(1008,plain,
! [SV140: a] :
( ( ! [SV248: a] :
( ( top_top_a_a_o @ SV140 @ SV248 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ SV140 @ SV248 ) @ top_to398455383od_a_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[880]) ).
thf(1009,plain,
! [SV140: a] :
( ( ( top_top_a_a_o @ SV140 )
= ( ^ [SY822: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV140 @ SY822 ) @ top_to398455383od_a_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[880]) ).
thf(1010,plain,
! [SV249: set_a,SV143: set_a,SV20: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV20 @ ( product_product_a_a @ SV143 @ SV249 ) )
= ( member449909584od_a_a @ SV20
@ ( product_Sigma_a_a @ SV143
@ ^ [SY1036: a] : SV249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(1011,plain,
! [SV144: set_Product_prod_a_a,SV21: set_Product_prod_a_a] :
( ( ~ ( ( ord_le1347718902_a_a_o
@ ^ [SY498: product_prod_a_a] : ( member449909584od_a_a @ SY498 @ SV21 )
@ ^ [SY826: product_prod_a_a] : ( member449909584od_a_a @ SY826 @ SV144 ) )
| ( ord_le1824328871od_a_a @ SV21 @ SV144 ) )
| ~ ( ~ ( ord_le1347718902_a_a_o
@ ^ [SY498: product_prod_a_a] : ( member449909584od_a_a @ SY498 @ SV21 )
@ ^ [SY826: product_prod_a_a] : ( member449909584od_a_a @ SY826 @ SV144 ) )
| ~ ( ord_le1824328871od_a_a @ SV21 @ SV144 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[884]) ).
thf(1012,plain,
! [SV144: set_Product_prod_a_a,SV21: set_Product_prod_a_a] :
( ( ( ord_le1347718902_a_a_o
@ ^ [SY498: product_prod_a_a] : ( member449909584od_a_a @ SY498 @ SV21 )
@ ^ [SY826: product_prod_a_a] : ( member449909584od_a_a @ SY826 @ SV144 ) )
= ( ord_le1824328871od_a_a @ SV21 @ SV144 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[884]) ).
thf(1013,plain,
! [SV145: set_Product_prod_a_a] :
( ( ! [SV250: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ SV145 @ SV250 )
= ( ord_le1347718902_a_a_o
@ ^ [SY828: product_prod_a_a] : ( member449909584od_a_a @ SY828 @ SV145 )
@ ^ [SY1038: product_prod_a_a] : ( member449909584od_a_a @ SY1038 @ SV250 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[885]) ).
thf(1014,plain,
! [SV145: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV145 )
= ( ^ [SY827: set_Product_prod_a_a] :
( ord_le1347718902_a_a_o
@ ^ [SY828: product_prod_a_a] : ( member449909584od_a_a @ SY828 @ SV145 )
@ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ SY827 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[885]) ).
thf(1015,plain,
! [SV146: set_Product_prod_a_a,SV23: set_Product_prod_a_a] :
( ( ~ ( ( ord_less_eq_a_a_o
@ ^ [SY504: a,SY505: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY504 @ SY505 ) @ SV23 )
@ ^ [SY832: a,SY833: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY832 @ SY833 ) @ SV146 ) )
| ( ord_le1824328871od_a_a @ SV23 @ SV146 ) )
| ~ ( ~ ( ord_less_eq_a_a_o
@ ^ [SY504: a,SY505: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY504 @ SY505 ) @ SV23 )
@ ^ [SY832: a,SY833: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY832 @ SY833 ) @ SV146 ) )
| ~ ( ord_le1824328871od_a_a @ SV23 @ SV146 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[886]) ).
thf(1016,plain,
! [SV146: set_Product_prod_a_a,SV23: set_Product_prod_a_a] :
( ( ( ord_less_eq_a_a_o
@ ^ [SY504: a,SY505: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY504 @ SY505 ) @ SV23 )
@ ^ [SY832: a,SY833: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY832 @ SY833 ) @ SV146 ) )
= ( ord_le1824328871od_a_a @ SV23 @ SV146 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[886]) ).
thf(1017,plain,
! [SV24: set_Product_prod_a_a] :
( ( ( ~ ( ! [SY508: product_prod_a_a] :
~ ( member449909584od_a_a @ SY508 @ SV24 )
| ( SV24 = bot_bo2131659635od_a_a ) ) )
= $true )
| ( ( ~ ( ~ ! [SY508: product_prod_a_a] :
~ ( member449909584od_a_a @ SY508 @ SV24 )
| ( SV24 != bot_bo2131659635od_a_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[887]) ).
thf(1018,plain,
! [SV147: product_prod_a_a,SV27: set_Product_prod_a_a] :
( ( ( SV27 != bot_bo2131659635od_a_a )
= $true )
| ( ( ~ ( member449909584od_a_a @ SV147 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[891]) ).
thf(1019,plain,
! [SV148: set_Product_prod_a_a,SV28: set_Product_prod_a_a] :
( ( ( ~ ! [SY834: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY834 @ SV28 )
| ( member449909584od_a_a @ SY834 @ SV148 ) ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV28 @ SV148 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[892]) ).
thf(1020,plain,
! [SV251: product_prod_a_a,SV149: product_prod_a_a > produc1572603623od_a_a,SV29: produc1572603623od_a_a] :
( ( ! [SY1039: set_Product_prod_a_a] :
( ( SV29
!= ( SV149 @ SV251 ) )
| ~ ( member449909584od_a_a @ SV251 @ SY1039 )
| ( member2057358096od_a_a @ SV29 @ ( image_1765377413od_a_a @ SV149 @ SY1039 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[893]) ).
thf(1021,plain,
! [SV252: a,SV150: a,SV30: a] :
( ( ! [SY1040: a] :
( ( ( product_Pair_a_a @ SV30 @ SV150 )
= ( product_Pair_a_a @ SV252 @ SY1040 ) )
= ( ~ ( ( SV30 != SV252 )
| ( SV150 != SY1040 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(1022,plain,
! [SV253: produc1572603623od_a_a,SV151: set_Product_prod_a_a,SV31: product_prod_a_a] :
( ( ! [SY1041: product_prod_a_a > produc1572603623od_a_a] :
( ~ ( member449909584od_a_a @ SV31 @ SV151 )
| ( SV253
!= ( SY1041 @ SV31 ) )
| ( member2057358096od_a_a @ SV253 @ ( image_1765377413od_a_a @ SY1041 @ SV151 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[895]) ).
thf(1023,plain,
! [SV254: set_Product_prod_a_a,SV152: product_prod_a_a > product_prod_a_a,SV32: set_Product_prod_a_a] :
( ( ~ ! [SY1042: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1042 @ SV32 )
| ( member449909584od_a_a @ ( SV152 @ SY1042 ) @ SV254 ) )
| ( ord_le1824328871od_a_a @ ( image_794773445od_a_a @ SV152 @ SV32 ) @ SV254 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(1024,plain,
! [SV255: set_Product_prod_a_a,SV153: set_Product_prod_a_a,SV33: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV33 @ ( minus_1507102574od_a_a @ SV153 @ SV255 ) )
= ( ~ ( ~ ( member449909584od_a_a @ SV33 @ SV153 )
| ~ ~ ( member449909584od_a_a @ SV33 @ SV255 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[897]) ).
thf(1025,plain,
! [SV256: set_Product_prod_a_a,SV154: a > product_prod_a_a,SV34: set_a] :
( ( ~ ! [SY1043: a] :
( ~ ( member_a @ SY1043 @ SV34 )
| ( member449909584od_a_a @ ( SV154 @ SY1043 ) @ SV256 ) )
| ( ord_le1824328871od_a_a @ ( image_1725938350od_a_a @ SV154 @ SV34 ) @ SV256 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[898]) ).
thf(1026,plain,
! [SV155: set_Product_prod_a_a] :
( ( ! [SV257: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ SV155 @ SV257 )
= ( ! [SY1044: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1044 @ SV155 )
| ( member449909584od_a_a @ SY1044 @ SV257 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[899]) ).
thf(1027,plain,
! [SV155: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV155 )
= ( ^ [SY846: set_Product_prod_a_a] :
! [SY847: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY847 @ SV155 )
| ( member449909584od_a_a @ SY847 @ SY846 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[899]) ).
thf(1028,plain,
! [SV36: set_Product_prod_a_a] :
( ( ( ~ ( ~ ! [SY531: product_prod_a_a] :
~ ( member449909584od_a_a @ SY531 @ SV36 )
| ( SV36 != bot_bo2131659635od_a_a ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY531: product_prod_a_a] :
~ ( member449909584od_a_a @ SY531 @ SV36 )
| ~ ( ( SV36 != bot_bo2131659635od_a_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[900]) ).
thf(1029,plain,
! [SV156: produc1572603623od_a_a,SV37: produc1572603623od_a_a > $o] :
( ( ( ~ ! [SY533: product_prod_a_a,SY534: a,SY535: a] : ( SV37 @ ( produc1474507607od_a_a @ SY533 @ ( product_Pair_a_a @ SY534 @ SY535 ) ) ) )
= $true )
| ( ( SV37 @ SV156 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[902]) ).
thf(1030,plain,
! [SV258: set_Product_prod_a_a,SV158: product_prod_a_a > produc1572603623od_a_a,SV39: produc1572603623od_a_a] :
( ( ~ ( member2057358096od_a_a @ SV39 @ ( image_1765377413od_a_a @ SV158 @ SV258 ) )
| ~ ! [SY1045: product_prod_a_a] :
( ( SV39
!= ( SV158 @ SY1045 ) )
| ~ ( member449909584od_a_a @ SY1045 @ SV258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[904]) ).
thf(1031,plain,
! [SV259: a,SV159: a > product_prod_a_a,SV40: product_prod_a_a] :
( ( ! [SY1046: set_a] :
( ( SV40
!= ( SV159 @ SV259 ) )
| ~ ( member_a @ SV259 @ SY1046 )
| ( member449909584od_a_a @ SV40 @ ( image_1725938350od_a_a @ SV159 @ SY1046 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[905]) ).
thf(1032,plain,
! [SV260: set_Product_prod_a_a,SV161: product_prod_a_a > product_prod_a_a,SV42: product_prod_a_a] :
( ( ~ ( member449909584od_a_a @ SV42 @ ( image_794773445od_a_a @ SV161 @ SV260 ) )
| ~ ! [SY1047: product_prod_a_a] :
( ( SV42
!= ( SV161 @ SY1047 ) )
| ~ ( member449909584od_a_a @ SY1047 @ SV260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[907]) ).
thf(1033,plain,
! [SV162: set_Product_prod_a_a] :
( ( ! [SV261: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ SV162 @ SV261 )
= ( ! [SY1048: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1048 @ SV162 )
| ( member449909584od_a_a @ SY1048 @ SV261 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[908]) ).
thf(1034,plain,
! [SV162: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV162 )
= ( ^ [SY859: set_Product_prod_a_a] :
! [SY860: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY860 @ SV162 )
| ( member449909584od_a_a @ SY860 @ SY859 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[908]) ).
thf(1035,plain,
! [SV262: a,SV163: a,SV44: product_prod_a_a > $o] :
( ( ~ ( SV44 @ ( product_Pair_a_a @ SV163 @ SV262 ) )
| ( product_curry_a_a_o @ SV44 @ SV163 @ SV262 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[909]) ).
thf(1036,plain,
! [SV263: set_Product_prod_a_a,SV164: set_Product_prod_a_a,SV45: product_prod_a_a] :
( ( ~ ( member449909584od_a_a @ SV45 @ ( minus_1507102574od_a_a @ SV164 @ SV263 ) )
| ~ ( ~ ( member449909584od_a_a @ SV45 @ SV164 )
| ( member449909584od_a_a @ SV45 @ SV263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[910]) ).
thf(1037,plain,
! [SV264: product_prod_a_a > $o,SV165: set_Product_prod_a_a,SV46: set_Product_prod_a_a] :
( ( ~ ( ord_le1824328871od_a_a @ SV46 @ SV165 )
| ( ( ord_le1824328871od_a_a @ SV46
@ ( collec645855634od_a_a
@ ^ [SY1049: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1049 @ SV165 )
| ~ ( SV264 @ SY1049 ) ) ) )
= ( ! [SY1050: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1050 @ SV46 )
| ( SV264 @ SY1050 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[911]) ).
thf(1038,plain,
! [SV166: a] :
( ( ! [SV265: set_a] :
( ( prefer161218362good_a @ SV166 @ SV265 )
= ( ^ [SY1051: set_Product_prod_a_a] :
( collect_a
@ ^ [SY1052: a] :
~ ( ~ ( member_a @ SY1052 @ SV265 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1052 @ SV166 ) @ SY1051 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[912]) ).
thf(1039,plain,
! [SV166: a] :
( ( ( prefer161218362good_a @ SV166 )
= ( ^ [SY866: set_a,SY867: set_Product_prod_a_a] :
( collect_a
@ ^ [SY868: a] :
~ ( ~ ( member_a @ SY868 @ SY866 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY868 @ SV166 ) @ SY867 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[912]) ).
thf(1040,plain,
! [SV266: set_Pr1948701895od_a_a,SV167: produc1572603623od_a_a > product_prod_a_a,SV48: product_prod_a_a] :
( ( ~ ( member449909584od_a_a @ SV48 @ ( image_734753285od_a_a @ SV167 @ SV266 ) )
| ~ ! [SY1053: produc1572603623od_a_a] :
( ( SV48
!= ( SV167 @ SY1053 ) )
| ~ ( member2057358096od_a_a @ SY1053 @ SV266 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[913]) ).
thf(1041,plain,
! [SV267: a,SV168: set_Product_prod_a_a,SV49: set_a] :
( ( ! [SY1054: a] :
( ~ ( prefer1292084992ence_a @ SV49 @ SV168 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV267 @ SY1054 ) @ SV168 )
| ( member_a @ SV267 @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[914]) ).
thf(1042,plain,
! [SV268: a > product_prod_a_a,SV169: set_a,SV50: a] :
( ( ~ ( member_a @ SV50 @ SV169 )
| ( member449909584od_a_a @ ( SV268 @ SV50 ) @ ( image_1725938350od_a_a @ SV268 @ SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(1043,plain,
! [SV269: product_prod_a_a,SV170: set_a,SV51: a] :
( ( ! [SY1055: a > product_prod_a_a] :
( ~ ( member_a @ SV51 @ SV170 )
| ( SV269
!= ( SY1055 @ SV51 ) )
| ( member449909584od_a_a @ SV269 @ ( image_1725938350od_a_a @ SY1055 @ SV170 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[916]) ).
thf(1044,plain,
! [SV270: set_a,SV171: a,SV52: a] :
( ( ! [SY1056: a > set_a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV171 ) @ ( product_Sigma_a_a @ SV270 @ SY1056 ) )
| ( member_a @ SV52 @ SV270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[917]) ).
thf(1045,plain,
! [SV271: product_prod_a_a,SV172: set_Pr1948701895od_a_a,SV53: produc1572603623od_a_a] :
( ( ! [SY1057: produc1572603623od_a_a > product_prod_a_a] :
( ~ ( member2057358096od_a_a @ SV53 @ SV172 )
| ( SV271
!= ( SY1057 @ SV53 ) )
| ( member449909584od_a_a @ SV271 @ ( image_734753285od_a_a @ SY1057 @ SV172 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[918]) ).
thf(1046,plain,
! [SV272: produc1572603623od_a_a > product_prod_a_a,SV173: set_Pr1948701895od_a_a,SV54: produc1572603623od_a_a] :
( ( ~ ( member2057358096od_a_a @ SV54 @ SV173 )
| ( member449909584od_a_a @ ( SV272 @ SV54 ) @ ( image_734753285od_a_a @ SV272 @ SV173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[919]) ).
thf(1047,plain,
! [SV273: product_prod_a_a > $o,SV174: set_Product_prod_a_a,SV55: product_prod_a_a > product_prod_a_a] :
( ( ( collec645855634od_a_a
@ ^ [SY1058: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1058 @ ( image_794773445od_a_a @ SV55 @ SV174 ) )
| ~ ( SV273 @ SY1058 ) ) )
= ( image_794773445od_a_a @ SV55
@ ( collec645855634od_a_a
@ ^ [SY1059: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1059 @ SV174 )
| ~ ( SV273 @ ( SV55 @ SY1059 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[920]) ).
thf(1048,plain,
! [SV274: set_Product_prod_a_a,SV175: a,SV56: a] :
( ( ! [SY1060: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV56 @ SV175 ) @ SV274 )
| ( SY1060 != SV175 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV56 @ SY1060 ) @ SV274 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[921]) ).
thf(1049,plain,
! [SV275: a,SV176: a,SV57: a] :
( ( ! [SY1061: a] :
( ( ( product_Pair_a_a @ SV57 @ SV176 )
= ( product_Pair_a_a @ SV275 @ SY1061 ) )
= ( ~ ( ( SV57 != SV275 )
| ( SV176 != SY1061 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[922]) ).
thf(1050,plain,
! [SV276: a,SV177: set_Product_prod_a_a,SV58: product_prod_a_a] :
( ( ! [SY1062: product_prod_a_a > a] :
( ~ ( member449909584od_a_a @ SV58 @ SV177 )
| ( SV276
!= ( SY1062 @ SV58 ) )
| ( member_a @ SV276 @ ( image_340790172_a_a_a @ SY1062 @ SV177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[923]) ).
thf(1051,plain,
! [SV277: set_Product_prod_a_a,SV178: produc1572603623od_a_a > product_prod_a_a,SV59: set_Pr1948701895od_a_a] :
( ( ~ ! [SY1063: produc1572603623od_a_a] :
( ~ ( member2057358096od_a_a @ SY1063 @ SV59 )
| ( member449909584od_a_a @ ( SV178 @ SY1063 ) @ SV277 ) )
| ( ord_le1824328871od_a_a @ ( image_734753285od_a_a @ SV178 @ SV59 ) @ SV277 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(1052,plain,
! [SV179: set_a,SV60: set_Product_prod_a_a] :
( ( ( ~ ! [SY892: a,SY893: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY892 @ SY893 ) @ SV60 )
| ( member_a @ SY892 @ SV179 ) ) )
= $true )
| ( ( ~ ! [SY894: a,SY895: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY894 @ SY895 ) @ SV60 )
| ( member_a @ SY895 @ SV179 ) )
| ~ ( order_preorder_on_a @ SV179 @ SV60 )
| ( prefer1292084992ence_a @ SV179 @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[925]) ).
thf(1053,plain,
! [SV278: a,SV180: set_Product_prod_a_a,SV61: set_a] :
( ( ! [SY1064: a,SY1065: a] :
( ~ ( prefer1292084992ence_a @ SV61 @ SV180 )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SY1064 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1064 @ SV278 ) @ SV180 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1064 @ SY1065 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1065 @ SY1064 ) @ SV180 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SY1065 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1065 @ SV278 ) @ SV180 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[926]) ).
thf(1054,plain,
! [SV279: product_prod_a_a,SV181: set_Pr1948701895od_a_a,SV62: set_Product_prod_a_a] :
( ( ! [SY1066: product_prod_a_a] :
( ~ ( prefer1338892073od_a_a @ SV62 @ SV181 )
| ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV279 @ SY1066 ) @ SV181 )
| ( member449909584od_a_a @ SV279 @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[927]) ).
thf(1055,plain,
! [SV280: set_Product_prod_a_a,SV182: product_prod_a_a,SV63: product_prod_a_a] :
( ( ! [SY1067: product_prod_a_a > set_Product_prod_a_a] :
( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV63 @ SV182 ) @ ( produc304751368od_a_a @ SV280 @ SY1067 ) )
| ( member449909584od_a_a @ SV63 @ SV280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[928]) ).
thf(1056,plain,
! [SV281: a,SV183: a,SV64: a > a > $o] :
( ( ! [SY1068: product_prod_a_a] :
( ~ ( SV64 @ SV183 @ SV281 )
| ( SY1068
!= ( product_Pair_a_a @ SV183 @ SV281 ) )
| ( SV64 @ ( product_fst_a_a @ SY1068 ) @ ( product_snd_a_a @ SY1068 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[929]) ).
thf(1057,plain,
! [SV282: a,SV184: a > a,SV65: a] :
( ( ! [SY1069: a,SY1070: a > a,SY1071: set_a] :
( ( SV65
!= ( SV184 @ SV282 ) )
| ( SY1069
!= ( SY1070 @ SV282 ) )
| ~ ( member_a @ SV282 @ SY1071 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV65 @ SY1069 ) @ ( bNF_Gr423046308_a_a_a @ SY1071 @ SV184 @ SY1070 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[930]) ).
thf(1058,plain,
! [SV283: a,SV185: set_a,SV66: a] :
( ( ! [SY1072: a > set_a] :
( ~ ( member_a @ SV66 @ SV185 )
| ~ ( member_a @ SV283 @ ( SY1072 @ SV66 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV66 @ SV283 ) @ ( product_Sigma_a_a @ SV185 @ SY1072 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(1059,plain,
! [SV284: a,SV186: a,SV67: a] :
( ( ! [SY1073: a] :
( ( ( product_Pair_a_a @ SV67 @ SV186 )
!= ( product_Pair_a_a @ SV284 @ SY1073 ) )
| ~ ( ( SV67 != SV284 )
| ( SV186 != SY1073 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[932]) ).
thf(1060,plain,
! [SV285: set_Product_prod_a_a,SV187: set_Product_prod_a_a,SV68: product_prod_a_a] :
( ( ~ ( member449909584od_a_a @ SV68 @ ( minus_1507102574od_a_a @ SV187 @ SV285 ) )
| ( member449909584od_a_a @ SV68 @ SV187 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[933]) ).
thf(1061,plain,
! [SV286: set_Product_prod_a_a,SV188: set_Product_prod_a_a,SV69: product_prod_a_a] :
( ( ~ ( member449909584od_a_a @ SV69 @ ( minus_1507102574od_a_a @ SV188 @ SV286 ) )
| ~ ( member449909584od_a_a @ SV69 @ SV286 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[934]) ).
thf(1062,plain,
! [SV189: set_Product_prod_a_a,SV70: set_Product_prod_a_a] :
( ( ( ~ ! [SY915: a,SY916: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY915 @ SY916 ) @ SV70 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY915 @ SY916 ) @ SV189 ) ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV70 @ SV189 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[935]) ).
thf(1063,plain,
! [SV287: a,SV190: a,SV71: product_prod_a_a > $o] :
( ( ~ ( product_curry_a_a_o @ SV71 @ SV190 @ SV287 )
| ( SV71 @ ( product_Pair_a_a @ SV190 @ SV287 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(1064,plain,
! [SV288: set_a,SV191: a,SV72: a] :
( ( ! [SY1074: a > set_a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV72 @ SV191 ) @ ( product_Sigma_a_a @ SV288 @ SY1074 ) )
| ( member_a @ SV191 @ ( SY1074 @ SV72 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[937]) ).
thf(1065,plain,
! [SV73: produc1921647824od_a_a] :
( ( ! [SY1075: a,SY1076: a] :
( SV73
!= ( produc1299253312od_a_a @ ( sK2_SY638 @ SV73 ) @ ( product_Pair_a_a @ SY1075 @ SY1076 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[938]) ).
thf(1066,plain,
! [SV289: set_a,SV192: a,SV74: a] :
( ( ! [SY1077: a > a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV74 @ SV192 ) @ ( bNF_Gr_a_a @ SV289 @ SY1077 ) )
| ( ( SY1077 @ SV74 )
= SV192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[939]) ).
thf(1067,plain,
! [SV290: set_a,SV193: a,SV75: a] :
( ( ! [SY1078: a > set_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ SV75 @ SV193 ) @ ( product_Sigma_a_a @ SV290 @ SY1078 ) )
= ( ~ ( ~ ( member_a @ SV75 @ SV290 )
| ~ ( member_a @ SV193 @ ( SY1078 @ SV75 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[940]) ).
thf(1068,plain,
! [SV291: product_prod_a_a,SV194: product_prod_a_a > product_prod_a_a,SV76: product_prod_a_a] :
( ( ! [SY1079: product_prod_a_a,SY1080: product_prod_a_a > product_prod_a_a,SY1081: set_Product_prod_a_a] :
( ( SV76
!= ( SV194 @ SV291 ) )
| ( SY1079
!= ( SY1080 @ SV291 ) )
| ~ ( member449909584od_a_a @ SV291 @ SY1081 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV76 @ SY1079 ) @ ( bNF_Gr200450189od_a_a @ SY1081 @ SV194 @ SY1080 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[941]) ).
thf(1069,plain,
! [SV195: set_Product_prod_a_a] :
( ( ! [SV292: set_Product_prod_a_a] :
( ( minus_1507102574od_a_a @ SV195 @ SV292 )
= ( collec645855634od_a_a
@ ^ [SY1082: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1082 @ SV195 )
| ~ ~ ( member449909584od_a_a @ SY1082 @ SV292 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[942]) ).
thf(1070,plain,
! [SV195: set_Product_prod_a_a] :
( ( ( minus_1507102574od_a_a @ SV195 )
= ( ^ [SY928: set_Product_prod_a_a] :
( collec645855634od_a_a
@ ^ [SY929: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY929 @ SV195 )
| ~ ~ ( member449909584od_a_a @ SY929 @ SY928 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[942]) ).
thf(1071,plain,
! [SV293: product_prod_a_a,SV196: set_Product_prod_a_a,SV78: set_Product_prod_a_a] :
( ( ~ ( ord_le1824328871od_a_a @ SV78 @ SV196 )
| ~ ( member449909584od_a_a @ SV293 @ SV78 )
| ( member449909584od_a_a @ SV293 @ SV196 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[943]) ).
thf(1072,plain,
! [SV294: set_Product_prod_a_a,SV197: a,SV79: a] :
( ( ! [SY1083: a > a,SY1084: a > a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV79 @ SV197 ) @ SV294 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( SY1083 @ SV79 ) @ ( SY1084 @ SV197 ) ) @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SY1083 @ SY1084 ) @ SV294 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[944]) ).
thf(1073,plain,
! [SV295: product_prod_a_a,SV198: set_Product_prod_a_a,SV80: set_Product_prod_a_a] :
( ( ~ ( ord_le1824328871od_a_a @ SV80 @ SV198 )
| ~ ( member449909584od_a_a @ SV295 @ SV80 )
| ( member449909584od_a_a @ SV295 @ SV198 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[945]) ).
thf(1074,plain,
! [SV296: set_Pr1948701895od_a_a,SV199: product_prod_a_a > produc1572603623od_a_a,SV81: set_Product_prod_a_a] :
( ( ~ ! [SY1085: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1085 @ SV81 )
| ( member2057358096od_a_a @ ( SV199 @ SY1085 ) @ SV296 ) )
| ( ord_le456379495od_a_a @ ( image_1765377413od_a_a @ SV199 @ SV81 ) @ SV296 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[946]) ).
thf(1075,plain,
! [SV297: a,SV200: a,SV82: product_prod_a_a] :
( ( ( SV82
!= ( product_Pair_a_a @ SV200 @ SV297 ) )
| ( ( product_snd_a_a @ SV82 )
= SV297 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[947]) ).
thf(1076,plain,
! [SV201: set_a] :
( ( ! [SV298: set_Product_prod_a_a] :
( ( prefer1292084992ence_a @ SV201 @ SV298 )
= ( ~ ( ~ ~ ( ~ ! [SY1086: a,SY1087: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1086 @ SY1087 ) @ SV298 )
| ( member_a @ SY1086 @ SV201 ) )
| ~ ! [SY1088: a,SY1089: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1088 @ SY1089 ) @ SV298 )
| ( member_a @ SY1089 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV298 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[948]) ).
thf(1077,plain,
! [SV201: set_a] :
( ( ( prefer1292084992ence_a @ SV201 )
= ( ^ [SY938: set_Product_prod_a_a] :
~ ( ~ ~ ( ~ ! [SY939: a,SY940: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY939 @ SY940 ) @ SY938 )
| ( member_a @ SY939 @ SV201 ) )
| ~ ! [SY941: a,SY942: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY941 @ SY942 ) @ SY938 )
| ( member_a @ SY942 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SY938 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[948]) ).
thf(1078,plain,
! [SV299: set_Product_prod_a_a,SV202: product_prod_a_a,SV84: product_prod_a_a] :
( ( ! [SY1090: product_prod_a_a > set_Product_prod_a_a] :
( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV84 @ SV202 ) @ ( produc304751368od_a_a @ SV299 @ SY1090 ) )
| ~ ( ~ ( member449909584od_a_a @ SV84 @ SV299 )
| ~ ( member449909584od_a_a @ SV202 @ ( SY1090 @ SV84 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[949]) ).
thf(1079,plain,
! [SV300: product_prod_a_a > produc1572603623od_a_a,SV203: set_Product_prod_a_a,SV85: product_prod_a_a] :
( ( ~ ( member449909584od_a_a @ SV85 @ SV203 )
| ( member2057358096od_a_a @ ( SV300 @ SV85 ) @ ( image_1765377413od_a_a @ SV300 @ SV203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[950]) ).
thf(1080,plain,
! [SV301: product_prod_a_a,SV204: set_Product_prod_a_a,SV86: product_prod_a_a] :
( ( ! [SY1091: product_prod_a_a > set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ SV86 @ SV204 )
| ~ ( member449909584od_a_a @ SV301 @ ( SY1091 @ SV86 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV86 @ SV301 ) @ ( produc304751368od_a_a @ SV204 @ SY1091 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[951]) ).
thf(1081,plain,
! [SV302: a,SV205: a,SV87: a > a > $o] :
( ( ~ ( SV87 @ SV205 @ SV302 )
| ( SV87 @ ( product_snd_a_a @ ( product_Pair_a_a @ SV302 @ SV205 ) ) @ ( product_fst_a_a @ ( product_Pair_a_a @ SV302 @ SV205 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(1082,plain,
! [SV303: product_prod_a_a > $o,SV206: set_Product_prod_a_a,SV88: set_Product_prod_a_a] :
( ( ! [SY1092: product_prod_a_a > $o] :
( ~ ( ord_le1824328871od_a_a @ SV88 @ SV206 )
| ~ ! [SY1093: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1093 @ SV88 )
| ~ ( SV303 @ SY1093 )
| ( SY1092 @ SY1093 ) )
| ( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [SY1094: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1094 @ SV88 )
| ~ ( SV303 @ SY1094 ) ) )
@ ( collec645855634od_a_a
@ ^ [SY953: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY953 @ SV206 )
| ~ ( SY1092 @ SY953 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(1083,plain,
! [SV304: set_Product_prod_a_a,SV207: product_prod_a_a,SV89: product_prod_a_a] :
( ( ! [SY1096: product_prod_a_a > set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV89 @ SV207 ) @ ( produc304751368od_a_a @ SV304 @ SY1096 ) )
= ( ~ ( ~ ( member449909584od_a_a @ SV89 @ SV304 )
| ~ ( member449909584od_a_a @ SV207 @ ( SY1096 @ SV89 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(1084,plain,
! [SV90: produc1572603623od_a_a] :
( ( ! [SY1097: a,SY1098: a] :
( SV90
!= ( produc1474507607od_a_a @ ( sK3_SY691 @ SV90 ) @ ( product_Pair_a_a @ SY1097 @ SY1098 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[955]) ).
thf(1085,plain,
! [SV208: product_prod_a_a,SV91: a] :
( ( ~ ( ( SV91
= ( product_snd_a_a @ SV208 ) )
| ~ ! [SY956: a] :
( SV208
!= ( product_Pair_a_a @ SY956 @ SV91 ) ) )
| ~ ( ( SV91
!= ( product_snd_a_a @ SV208 ) )
| ~ ~ ! [SY956: a] :
( SV208
!= ( product_Pair_a_a @ SY956 @ SV91 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[956]) ).
thf(1086,plain,
! [SV208: product_prod_a_a,SV91: a] :
( ( ( SV91
= ( product_snd_a_a @ SV208 ) )
= ( ~ ! [SY956: a] :
( SV208
!= ( product_Pair_a_a @ SY956 @ SV91 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[956]) ).
thf(1087,plain,
! [SV305: produc1572603623od_a_a,SV209: produc1572603623od_a_a > product_prod_a_a,SV92: product_prod_a_a] :
( ( ! [SY1099: set_Pr1948701895od_a_a] :
( ( SV92
!= ( SV209 @ SV305 ) )
| ~ ( member2057358096od_a_a @ SV305 @ SY1099 )
| ( member449909584od_a_a @ SV92 @ ( image_734753285od_a_a @ SV209 @ SY1099 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[957]) ).
thf(1088,plain,
! [SV306: a > $o,SV210: a,SV93: a > $o] :
( ( ! [SY1100: a] :
( ~ ( SV93 @ SV210 )
| ~ ( SV306 @ SY1100 )
| ~ ( ~ ( SV93 @ ( product_fst_a_a @ ( product_Pair_a_a @ SV210 @ SY1100 ) ) )
| ~ ( SV306 @ ( product_snd_a_a @ ( product_Pair_a_a @ SV210 @ SY1100 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(1089,plain,
! [SV307: set_a,SV211: a,SV94: a] :
( ( ! [SY1101: set_Product_prod_a_a] :
( ~ ( member_a @ SV94 @ ( prefer161218362good_a @ SV211 @ SV307 @ SY1101 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV94 @ SV211 ) @ SY1101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(1090,plain,
! [SV308: product_prod_a_a,SV212: product_prod_a_a > a,SV95: a] :
( ( ! [SY1102: a,SY1103: product_prod_a_a > a,SY1104: set_Product_prod_a_a] :
( ( SV95
!= ( SV212 @ SV308 ) )
| ( SY1102
!= ( SY1103 @ SV308 ) )
| ~ ( member449909584od_a_a @ SV308 @ SY1104 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV95 @ SY1102 ) @ ( bNF_Gr1853143117_a_a_a @ SY1104 @ SV212 @ SY1103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[960]) ).
thf(1091,plain,
! [SV309: set_Product_prod_a_a,SV213: product_prod_a_a,SV96: product_prod_a_a] :
( ( ! [SY1105: product_prod_a_a > product_prod_a_a] :
( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV96 @ SV213 ) @ ( bNF_Gr1372473186od_a_a @ SV309 @ SY1105 ) )
| ( member449909584od_a_a @ SV96 @ SV309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(1092,plain,
! [SV214: a] :
( ( ! [SV310: set_a] :
( ( prefer436369274d_as_a @ SV214 @ SV310 )
= ( ^ [SY1106: set_Product_prod_a_a] :
( collect_a
@ ^ [SY1107: a] :
~ ( ~ ~ ( ~ ( member_a @ SY1107 @ SV310 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV214 @ SY1107 ) @ SY1106 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1107 @ SV214 ) @ SY1106 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[962]) ).
thf(1093,plain,
! [SV214: a] :
( ( ( prefer436369274d_as_a @ SV214 )
= ( ^ [SY969: set_a,SY970: set_Product_prod_a_a] :
( collect_a
@ ^ [SY971: a] :
~ ( ~ ~ ( ~ ( member_a @ SY971 @ SY969 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV214 @ SY971 ) @ SY970 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY971 @ SV214 ) @ SY970 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[962]) ).
thf(1094,plain,
! [SV98: product_prod_a_a] :
( ( ! [SY1108: a] :
( SV98
!= ( product_Pair_a_a @ ( sK4_SY716 @ SV98 ) @ SY1108 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[963]) ).
thf(1095,plain,
! [SV311: set_Product_prod_a_a,SV215: product_prod_a_a > a,SV99: a] :
( ( ~ ( member_a @ SV99 @ ( image_340790172_a_a_a @ SV215 @ SV311 ) )
| ~ ! [SY1109: product_prod_a_a] :
( ( SV99
!= ( SV215 @ SY1109 ) )
| ~ ( member449909584od_a_a @ SY1109 @ SV311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[964]) ).
thf(1096,plain,
! [SV216: product_prod_a_a,SV100: product_prod_a_a > $o] :
( ( ( ~ ! [SY722: a,SY723: a] : ( SV100 @ ( product_Pair_a_a @ SY722 @ SY723 ) ) )
= $true )
| ( ( SV100 @ SV216 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[965]) ).
thf(1097,plain,
! [SV312: a > a,SV217: a > a,SV101: product_prod_a_a] :
( ( ! [SY1110: set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ SV101 @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SV217 @ SV312 ) @ SY1110 ) )
| ~ ! [SY1111: a,SY1112: a] :
( ( SV101
!= ( product_Pair_a_a @ ( SV217 @ SY1111 ) @ ( SV312 @ SY1112 ) ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1111 @ SY1112 ) @ SY1110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[966]) ).
thf(1098,plain,
! [SV218: a] :
( ( ! [SV313: set_a] :
( ( prefer1676310729than_a @ SV218 @ SV313 )
= ( ^ [SY1113: set_Product_prod_a_a] :
( collect_a
@ ^ [SY1114: a] :
~ ( ~ ( member_a @ SY1114 @ SV313 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV218 @ SY1114 ) @ SY1113 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[967]) ).
thf(1099,plain,
! [SV218: a] :
( ( ( prefer1676310729than_a @ SV218 )
= ( ^ [SY980: set_a,SY981: set_Product_prod_a_a] :
( collect_a
@ ^ [SY982: a] :
~ ( ~ ( member_a @ SY982 @ SY980 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV218 @ SY982 ) @ SY981 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[967]) ).
thf(1100,plain,
! [SV314: set_a,SV219: a,SV103: a] :
( ( ! [SY1115: a > a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV103 @ SV219 ) @ ( bNF_Gr_a_a @ SV314 @ SY1115 ) )
| ( member_a @ SV103 @ SV314 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(1101,plain,
! [SV315: a,SV220: a,SV104: a > $o] :
( ( ! [SY1116: a,SY1117: a > set_Product_prod_a_a] :
( ~ ( SV104 @ SV220 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV315 @ SY1116 ) @ ( SY1117 @ SV220 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV220 @ SV315 ) @ ( product_Pair_a_a @ SV220 @ SY1116 ) ) @ ( same_fst_a_a @ SV104 @ SY1117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1102,plain,
! [SV221: product_prod_a_a,SV105: product_prod_a_a > $o] :
( ( ( ~ ! [SY740: a,SY741: a] : ( SV105 @ ( product_Pair_a_a @ SY740 @ SY741 ) ) )
= $true )
| ( ( SV105 @ SV221 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[970]) ).
thf(1103,plain,
! [SV316: product_prod_a_a,SV222: product_prod_a_a > a,SV106: a] :
( ( ! [SY1118: set_Product_prod_a_a] :
( ( SV106
!= ( SV222 @ SV316 ) )
| ~ ( member449909584od_a_a @ SV316 @ SY1118 )
| ( member_a @ SV106 @ ( image_340790172_a_a_a @ SV222 @ SY1118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[971]) ).
thf(1104,plain,
! [SV317: a,SV223: a,SV107: a] :
( ( ( ( product_snd_a_a @ ( product_Pair_a_a @ SV107 @ SV223 ) )
!= SV317 )
| ( SV223 = SV317 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1105,plain,
! [SV318: a,SV224: a,SV108: product_prod_a_a > $o] :
( ( ~ ( product_curry_a_a_o @ SV108 @ SV224 @ SV318 )
| ( SV108 @ ( product_Pair_a_a @ SV224 @ SV318 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1106,plain,
! [SV109: product_prod_a_a] :
( ( ~ ~ ! [SY1119: a] :
( SV109
!= ( product_Pair_a_a @ ( sK5_SY749 @ SV109 ) @ SY1119 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[974]) ).
thf(1107,plain,
! [SV319: product_prod_a_a,SV225: product_prod_a_a > product_prod_a_a,SV110: product_prod_a_a] :
( ( ! [SY1120: set_Product_prod_a_a] :
( ( SV110
!= ( SV225 @ SV319 ) )
| ~ ( member449909584od_a_a @ SV319 @ SY1120 )
| ( member449909584od_a_a @ SV110 @ ( image_794773445od_a_a @ SV225 @ SY1120 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1108,plain,
! [SV320: product_prod_a_a > set_Product_prod_a_a,SV226: set_Product_prod_a_a,SV111: produc1572603623od_a_a] :
( ( ~ ( member2057358096od_a_a @ SV111 @ ( produc304751368od_a_a @ SV226 @ SV320 ) )
| ~ ! [SY1121: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1121 @ SV226 )
| ! [SY1122: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1122 @ ( SV320 @ SY1121 ) )
| ( SV111
!= ( produc1474507607od_a_a @ SY1121 @ SY1122 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1109,plain,
! [SV321: product_prod_a_a > a,SV227: set_Product_prod_a_a,SV112: product_prod_a_a] :
( ( ~ ( member449909584od_a_a @ SV112 @ SV227 )
| ( member_a @ ( SV321 @ SV112 ) @ ( image_340790172_a_a_a @ SV321 @ SV227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[977]) ).
thf(1110,plain,
! [SV322: product_prod_a_a,SV228: set_Product_prod_a_a,SV113: product_prod_a_a] :
( ( ! [SY1123: product_prod_a_a > product_prod_a_a] :
( ~ ( member449909584od_a_a @ SV113 @ SV228 )
| ( SV322
!= ( SY1123 @ SV113 ) )
| ( member449909584od_a_a @ SV322 @ ( image_794773445od_a_a @ SY1123 @ SV228 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[978]) ).
thf(1111,plain,
! [SV323: set_a,SV229: a > product_prod_a_a,SV114: product_prod_a_a] :
( ( ~ ( member449909584od_a_a @ SV114 @ ( image_1725938350od_a_a @ SV229 @ SV323 ) )
| ~ ! [SY1124: a] :
( ( SV114
!= ( SV229 @ SY1124 ) )
| ~ ( member_a @ SY1124 @ SV323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[979]) ).
thf(1112,plain,
! [SV324: product_prod_a_a > product_prod_a_a,SV230: set_Product_prod_a_a,SV115: product_prod_a_a] :
( ( ~ ( member449909584od_a_a @ SV115 @ SV230 )
| ( member449909584od_a_a @ ( SV324 @ SV115 ) @ ( image_794773445od_a_a @ SV324 @ SV230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[980]) ).
thf(1113,plain,
! [SV325: produc1572603623od_a_a,SV231: produc1572603623od_a_a > a,SV116: a] :
( ( ! [SY1125: a,SY1126: produc1572603623od_a_a > a,SY1127: set_Pr1948701895od_a_a] :
( ( SV116
!= ( SV231 @ SV325 ) )
| ( SY1125
!= ( SY1126 @ SV325 ) )
| ~ ( member2057358096od_a_a @ SV325 @ SY1127 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV116 @ SY1125 ) @ ( bNF_Gr356189709_a_a_a @ SY1127 @ SV231 @ SY1126 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[981]) ).
thf(1114,plain,
! [SV117: set_Product_prod_a_a] :
( ( ( ! [SY773: product_prod_a_a] : ( member449909584od_a_a @ SY773 @ SV117 ) )
= $false )
| ( ( top_to398455383od_a_a = SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[982]) ).
thf(1115,plain,
! [SV326: set_Product_prod_a_a,SV232: product_prod_a_a,SV118: product_prod_a_a] :
( ( ! [SY1128: set_Pr1948701895od_a_a] :
( ~ ( member449909584od_a_a @ SV118 @ ( prefer477097315od_a_a @ SV232 @ SV326 @ SY1128 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV118 @ SV232 ) @ SY1128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1116,plain,
! [SV327: a > set_a,SV233: set_a,SV119: product_prod_a_a] :
( ( ~ ( member449909584od_a_a @ SV119 @ ( product_Sigma_a_a @ SV233 @ SV327 ) )
| ~ ! [SY1129: a] :
( ~ ( member_a @ SY1129 @ SV233 )
| ! [SY1130: a] :
( ~ ( member_a @ SY1130 @ ( SV327 @ SY1129 ) )
| ( SV119
!= ( product_Pair_a_a @ SY1129 @ SY1130 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[984]) ).
thf(1117,plain,
! [SV328: set_Product_prod_a_a,SV234: set_Product_prod_a_a,SV120: product_prod_a_a] :
( ( ! [SY1131: product_prod_a_a > $o] :
( ~ ( member449909584od_a_a @ SV120 @ SV234 )
| ~ ( ord_le1824328871od_a_a @ SV234
@ ( collec645855634od_a_a
@ ^ [SY1132: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1132 @ SV328 )
| ~ ( SY1131 @ SY1132 ) ) ) )
| ( SY1131 @ SV120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[985]) ).
thf(1118,plain,
! [SV329: a,SV235: a,SV121: product_prod_a_a] :
( ( ( SV121
!= ( product_Pair_a_a @ SV235 @ SV329 ) )
| ( ( product_fst_a_a @ SV121 )
= SV235 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[986]) ).
thf(1119,plain,
! [SV330: set_a,SV236: product_prod_a_a > a,SV122: set_Product_prod_a_a] :
( ( ~ ! [SY1133: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1133 @ SV122 )
| ( member_a @ ( SV236 @ SY1133 ) @ SV330 ) )
| ( ord_less_eq_set_a @ ( image_340790172_a_a_a @ SV236 @ SV122 ) @ SV330 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[987]) ).
thf(1120,plain,
! [SV331: a,SV237: a,SV123: a] :
( ( ! [SY1134: a,SY1135: set_Product_prod_a_a,SY1136: set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SV331 @ SY1134 ) ) @ ( lex_prod_a_a @ SY1135 @ SY1136 ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SY1135 )
| ~ ( ( SV123 != SV331 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SY1134 ) @ SY1136 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1121,plain,
( ( member449909584od_a_a @ sK1_SX0 @ top_to398455383od_a_a )
= $true ),
inference(extcnf_not_neg,[status(thm)],[989]) ).
thf(1122,plain,
! [SV124: set_Product_prod_a_a] :
( ( ( ! [SY795: product_prod_a_a] :
~ ( member449909584od_a_a @ SY795 @ SV124 ) )
= $false )
| ( ( SV124 = bot_bo2131659635od_a_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[990]) ).
thf(1123,plain,
! [SV238: product_prod_a_a,SV125: a] :
( ( ~ ( ( SV125
= ( product_fst_a_a @ SV238 ) )
| ~ ! [SY1024: a] :
( SV238
!= ( product_Pair_a_a @ SV125 @ SY1024 ) ) )
| ~ ( ( SV125
!= ( product_fst_a_a @ SV238 ) )
| ~ ~ ! [SY1024: a] :
( SV238
!= ( product_Pair_a_a @ SV125 @ SY1024 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[991]) ).
thf(1124,plain,
! [SV238: product_prod_a_a,SV125: a] :
( ( ( SV125
= ( product_fst_a_a @ SV238 ) )
= ( ~ ! [SY1024: a] :
( SV238
!= ( product_Pair_a_a @ SV125 @ SY1024 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[991]) ).
thf(1125,plain,
! [SV332: set_Product_prod_a_a,SV239: set_Product_prod_a_a,SV126: product_prod_a_a] :
( ( ~ ( member449909584od_a_a @ SV126 @ SV239 )
| ~ ~ ( member449909584od_a_a @ SV126 @ SV332 )
| ( member449909584od_a_a @ SV126 @ ( minus_1507102574od_a_a @ SV239 @ SV332 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[992]) ).
thf(1126,plain,
! [SV333: set_a,SV240: a,SV127: a] :
( ( ! [SY1137: a > set_a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV127 @ SV240 ) @ ( product_Sigma_a_a @ SV333 @ SY1137 ) )
| ~ ( ~ ( member_a @ SV127 @ SV333 )
| ~ ( member_a @ SV240 @ ( SY1137 @ SV127 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[993]) ).
thf(1127,plain,
! [SV334: a,SV241: a,SV128: a] :
( ( ( ( product_fst_a_a @ ( product_Pair_a_a @ SV128 @ SV241 ) )
!= SV334 )
| ( SV128 = SV334 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[994]) ).
thf(1128,plain,
! [SV335: set_Product_prod_a_a,SV242: product_prod_a_a,SV129: product_prod_a_a] :
( ( ! [SY1138: product_prod_a_a > set_Product_prod_a_a] :
( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV129 @ SV242 ) @ ( produc304751368od_a_a @ SV335 @ SY1138 ) )
| ( member449909584od_a_a @ SV242 @ ( SY1138 @ SV129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[995]) ).
thf(1129,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( ~ ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
| ( SV2 = SV131 ) ) )
= $true )
| ( ( ~ ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
!= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
| ( SV2 != SV131 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[996]) ).
thf(1130,plain,
! [SV243: set_Product_prod_a_a,SV132: a,SV3: a] :
( ( ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV3 @ SV132 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV243 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV132 @ SV3 ) @ SV243 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV3 @ SV132 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV243 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV132 @ SV3 ) @ SV243 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[998]) ).
thf(1131,plain,
! [SV243: set_Product_prod_a_a,SV132: a,SV3: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV3 @ SV132 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV243 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ SV132 @ SV3 ) @ SV243 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[998]) ).
thf(1132,plain,
! [SV133: product_prod_a_a > $o,SV4: product_prod_a_a] :
( ( ( ~ ( ( member449909584od_a_a @ SV4 @ ( collec645855634od_a_a @ SV133 ) )
| ( SV133 @ SV4 ) ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ SV4 @ ( collec645855634od_a_a @ SV133 ) )
| ~ ( SV133 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[999]) ).
thf(1133,plain,
! [SV336: set_Product_prod_a_a,SV134: set_Product_prod_a_a] :
( ( ( minus_1507102574od_a_a @ SV134 @ SV336 )
= ( collec645855634od_a_a
@ ( minus_1797478127_a_a_o
@ ^ [SY814: product_prod_a_a] : ( member449909584od_a_a @ SY814 @ SV134 )
@ ^ [SY1140: product_prod_a_a] : ( member449909584od_a_a @ SY1140 @ SV336 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1001]) ).
thf(1134,plain,
! [SV337: a,SV245: a,SV135: a > a,SV9: a > a] :
( ( ( produc700022774_a_a_a @ SV9 @ SV135 @ ( product_Pair_a_a @ SV245 @ SV337 ) )
= ( product_Pair_a_a @ ( SV9 @ SV245 ) @ ( SV135 @ SV337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1003]) ).
thf(1135,plain,
! [SV338: a,SV246: a,SV136: a > product_prod_a_a,SV10: a > product_prod_a_a] :
( ( ( produc2012818120od_a_a @ SV10 @ SV136 @ ( product_Pair_a_a @ SV246 @ SV338 ) )
= ( produc1474507607od_a_a @ ( SV10 @ SV246 ) @ ( SV136 @ SV338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1136,plain,
! [SV339: product_prod_a_a,SV247: product_prod_a_a,SV137: product_prod_a_a > a,SV11: product_prod_a_a > a] :
( ( ( produc363290532_a_a_a @ SV11 @ SV137 @ ( produc1474507607od_a_a @ SV247 @ SV339 ) )
= ( product_Pair_a_a @ ( SV11 @ SV247 ) @ ( SV137 @ SV339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1137,plain,
! [SV138: product_prod_a_a] :
( ( ( ~ ( ( top_to1483957574_a_a_o @ SV138 )
| ( member449909584od_a_a @ SV138 @ top_to398455383od_a_a ) ) )
= $true )
| ( ( ~ ( ~ ( top_to1483957574_a_a_o @ SV138 )
| ~ ( member449909584od_a_a @ SV138 @ top_to398455383od_a_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1006]) ).
thf(1138,plain,
! [SV340: a,SV140: a] :
( ( ( top_top_a_a_o @ SV140 @ SV340 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ SV140 @ SV340 ) @ top_to398455383od_a_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1008]) ).
thf(1139,plain,
! [SV249: set_a,SV143: set_a,SV20: product_prod_a_a] :
( ( ~ ( ( member449909584od_a_a @ SV20 @ ( product_product_a_a @ SV143 @ SV249 ) )
| ( member449909584od_a_a @ SV20
@ ( product_Sigma_a_a @ SV143
@ ^ [SY1036: a] : SV249 ) ) )
| ~ ( ~ ( member449909584od_a_a @ SV20 @ ( product_product_a_a @ SV143 @ SV249 ) )
| ~ ( member449909584od_a_a @ SV20
@ ( product_Sigma_a_a @ SV143
@ ^ [SY1036: a] : SV249 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1010]) ).
thf(1140,plain,
! [SV249: set_a,SV143: set_a,SV20: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV20 @ ( product_product_a_a @ SV143 @ SV249 ) )
= ( member449909584od_a_a @ SV20
@ ( product_Sigma_a_a @ SV143
@ ^ [SY1036: a] : SV249 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1010]) ).
thf(1141,plain,
! [SV144: set_Product_prod_a_a,SV21: set_Product_prod_a_a] :
( ( ( ~ ( ( ord_le1347718902_a_a_o
@ ^ [SY498: product_prod_a_a] : ( member449909584od_a_a @ SY498 @ SV21 )
@ ^ [SY826: product_prod_a_a] : ( member449909584od_a_a @ SY826 @ SV144 ) )
| ( ord_le1824328871od_a_a @ SV21 @ SV144 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_le1347718902_a_a_o
@ ^ [SY498: product_prod_a_a] : ( member449909584od_a_a @ SY498 @ SV21 )
@ ^ [SY826: product_prod_a_a] : ( member449909584od_a_a @ SY826 @ SV144 ) )
| ~ ( ord_le1824328871od_a_a @ SV21 @ SV144 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1011]) ).
thf(1142,plain,
! [SV341: set_Product_prod_a_a,SV145: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV145 @ SV341 )
= ( ord_le1347718902_a_a_o
@ ^ [SY828: product_prod_a_a] : ( member449909584od_a_a @ SY828 @ SV145 )
@ ^ [SY1142: product_prod_a_a] : ( member449909584od_a_a @ SY1142 @ SV341 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1013]) ).
thf(1143,plain,
! [SV146: set_Product_prod_a_a,SV23: set_Product_prod_a_a] :
( ( ( ~ ( ( ord_less_eq_a_a_o
@ ^ [SY504: a,SY505: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY504 @ SY505 ) @ SV23 )
@ ^ [SY832: a,SY833: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY832 @ SY833 ) @ SV146 ) )
| ( ord_le1824328871od_a_a @ SV23 @ SV146 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_a_a_o
@ ^ [SY504: a,SY505: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY504 @ SY505 ) @ SV23 )
@ ^ [SY832: a,SY833: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY832 @ SY833 ) @ SV146 ) )
| ~ ( ord_le1824328871od_a_a @ SV23 @ SV146 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1015]) ).
thf(1144,plain,
! [SV24: set_Product_prod_a_a] :
( ( ( ! [SY508: product_prod_a_a] :
~ ( member449909584od_a_a @ SY508 @ SV24 )
| ( SV24 = bot_bo2131659635od_a_a ) )
= $false )
| ( ( ~ ( ~ ! [SY508: product_prod_a_a] :
~ ( member449909584od_a_a @ SY508 @ SV24 )
| ( SV24 != bot_bo2131659635od_a_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1017]) ).
thf(1145,plain,
! [SV147: product_prod_a_a,SV27: set_Product_prod_a_a] :
( ( ( SV27 = bot_bo2131659635od_a_a )
= $false )
| ( ( ~ ( member449909584od_a_a @ SV147 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1018]) ).
thf(1146,plain,
! [SV148: set_Product_prod_a_a,SV28: set_Product_prod_a_a] :
( ( ( ! [SY834: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY834 @ SV28 )
| ( member449909584od_a_a @ SY834 @ SV148 ) ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV28 @ SV148 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1019]) ).
thf(1147,plain,
! [SV342: set_Product_prod_a_a,SV251: product_prod_a_a,SV149: product_prod_a_a > produc1572603623od_a_a,SV29: produc1572603623od_a_a] :
( ( ( SV29
!= ( SV149 @ SV251 ) )
| ~ ( member449909584od_a_a @ SV251 @ SV342 )
| ( member2057358096od_a_a @ SV29 @ ( image_1765377413od_a_a @ SV149 @ SV342 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1020]) ).
thf(1148,plain,
! [SV343: a,SV252: a,SV150: a,SV30: a] :
( ( ( ( product_Pair_a_a @ SV30 @ SV150 )
= ( product_Pair_a_a @ SV252 @ SV343 ) )
= ( ~ ( ( SV30 != SV252 )
| ( SV150 != SV343 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1021]) ).
thf(1149,plain,
! [SV344: product_prod_a_a > produc1572603623od_a_a,SV253: produc1572603623od_a_a,SV151: set_Product_prod_a_a,SV31: product_prod_a_a] :
( ( ~ ( member449909584od_a_a @ SV31 @ SV151 )
| ( SV253
!= ( SV344 @ SV31 ) )
| ( member2057358096od_a_a @ SV253 @ ( image_1765377413od_a_a @ SV344 @ SV151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1022]) ).
thf(1150,plain,
! [SV254: set_Product_prod_a_a,SV152: product_prod_a_a > product_prod_a_a,SV32: set_Product_prod_a_a] :
( ( ( ~ ! [SY1042: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1042 @ SV32 )
| ( member449909584od_a_a @ ( SV152 @ SY1042 ) @ SV254 ) ) )
= $true )
| ( ( ord_le1824328871od_a_a @ ( image_794773445od_a_a @ SV152 @ SV32 ) @ SV254 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1023]) ).
thf(1151,plain,
! [SV255: set_Product_prod_a_a,SV153: set_Product_prod_a_a,SV33: product_prod_a_a] :
( ( ~ ( ( member449909584od_a_a @ SV33 @ ( minus_1507102574od_a_a @ SV153 @ SV255 ) )
| ~ ( ~ ( member449909584od_a_a @ SV33 @ SV153 )
| ~ ~ ( member449909584od_a_a @ SV33 @ SV255 ) ) )
| ~ ( ~ ( member449909584od_a_a @ SV33 @ ( minus_1507102574od_a_a @ SV153 @ SV255 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ SV33 @ SV153 )
| ~ ~ ( member449909584od_a_a @ SV33 @ SV255 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1024]) ).
thf(1152,plain,
! [SV255: set_Product_prod_a_a,SV153: set_Product_prod_a_a,SV33: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV33 @ ( minus_1507102574od_a_a @ SV153 @ SV255 ) )
= ( ~ ( ~ ( member449909584od_a_a @ SV33 @ SV153 )
| ~ ~ ( member449909584od_a_a @ SV33 @ SV255 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1024]) ).
thf(1153,plain,
! [SV256: set_Product_prod_a_a,SV154: a > product_prod_a_a,SV34: set_a] :
( ( ( ~ ! [SY1043: a] :
( ~ ( member_a @ SY1043 @ SV34 )
| ( member449909584od_a_a @ ( SV154 @ SY1043 ) @ SV256 ) ) )
= $true )
| ( ( ord_le1824328871od_a_a @ ( image_1725938350od_a_a @ SV154 @ SV34 ) @ SV256 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1025]) ).
thf(1154,plain,
! [SV345: set_Product_prod_a_a,SV155: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV155 @ SV345 )
= ( ! [SY1143: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1143 @ SV155 )
| ( member449909584od_a_a @ SY1143 @ SV345 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1026]) ).
thf(1155,plain,
! [SV36: set_Product_prod_a_a] :
( ( ( ~ ! [SY531: product_prod_a_a] :
~ ( member449909584od_a_a @ SY531 @ SV36 )
| ( SV36 != bot_bo2131659635od_a_a ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY531: product_prod_a_a] :
~ ( member449909584od_a_a @ SY531 @ SV36 )
| ~ ( ( SV36 != bot_bo2131659635od_a_a ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1028]) ).
thf(1156,plain,
! [SV156: produc1572603623od_a_a,SV37: produc1572603623od_a_a > $o] :
( ( ( ! [SY533: product_prod_a_a,SY534: a,SY535: a] : ( SV37 @ ( produc1474507607od_a_a @ SY533 @ ( product_Pair_a_a @ SY534 @ SY535 ) ) ) )
= $false )
| ( ( SV37 @ SV156 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1029]) ).
thf(1157,plain,
! [SV258: set_Product_prod_a_a,SV158: product_prod_a_a > produc1572603623od_a_a,SV39: produc1572603623od_a_a] :
( ( ( ~ ( member2057358096od_a_a @ SV39 @ ( image_1765377413od_a_a @ SV158 @ SV258 ) ) )
= $true )
| ( ( ~ ! [SY1045: product_prod_a_a] :
( ( SV39
!= ( SV158 @ SY1045 ) )
| ~ ( member449909584od_a_a @ SY1045 @ SV258 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1030]) ).
thf(1158,plain,
! [SV346: set_a,SV259: a,SV159: a > product_prod_a_a,SV40: product_prod_a_a] :
( ( ( SV40
!= ( SV159 @ SV259 ) )
| ~ ( member_a @ SV259 @ SV346 )
| ( member449909584od_a_a @ SV40 @ ( image_1725938350od_a_a @ SV159 @ SV346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1031]) ).
thf(1159,plain,
! [SV260: set_Product_prod_a_a,SV161: product_prod_a_a > product_prod_a_a,SV42: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV42 @ ( image_794773445od_a_a @ SV161 @ SV260 ) ) )
= $true )
| ( ( ~ ! [SY1047: product_prod_a_a] :
( ( SV42
!= ( SV161 @ SY1047 ) )
| ~ ( member449909584od_a_a @ SY1047 @ SV260 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1032]) ).
thf(1160,plain,
! [SV347: set_Product_prod_a_a,SV162: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV162 @ SV347 )
= ( ! [SY1144: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1144 @ SV162 )
| ( member449909584od_a_a @ SY1144 @ SV347 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1033]) ).
thf(1161,plain,
! [SV262: a,SV163: a,SV44: product_prod_a_a > $o] :
( ( ( ~ ( SV44 @ ( product_Pair_a_a @ SV163 @ SV262 ) ) )
= $true )
| ( ( product_curry_a_a_o @ SV44 @ SV163 @ SV262 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1035]) ).
thf(1162,plain,
! [SV263: set_Product_prod_a_a,SV164: set_Product_prod_a_a,SV45: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV45 @ ( minus_1507102574od_a_a @ SV164 @ SV263 ) ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ SV45 @ SV164 )
| ( member449909584od_a_a @ SV45 @ SV263 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1036]) ).
thf(1163,plain,
! [SV264: product_prod_a_a > $o,SV165: set_Product_prod_a_a,SV46: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV46 @ SV165 ) )
= $true )
| ( ( ( ord_le1824328871od_a_a @ SV46
@ ( collec645855634od_a_a
@ ^ [SY1049: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1049 @ SV165 )
| ~ ( SV264 @ SY1049 ) ) ) )
= ( ! [SY1050: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1050 @ SV46 )
| ( SV264 @ SY1050 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1037]) ).
thf(1164,plain,
! [SV348: set_a,SV166: a] :
( ( ( prefer161218362good_a @ SV166 @ SV348 )
= ( ^ [SY1145: set_Product_prod_a_a] :
( collect_a
@ ^ [SY1146: a] :
~ ( ~ ( member_a @ SY1146 @ SV348 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1146 @ SV166 ) @ SY1145 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1038]) ).
thf(1165,plain,
! [SV266: set_Pr1948701895od_a_a,SV167: produc1572603623od_a_a > product_prod_a_a,SV48: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV48 @ ( image_734753285od_a_a @ SV167 @ SV266 ) ) )
= $true )
| ( ( ~ ! [SY1053: produc1572603623od_a_a] :
( ( SV48
!= ( SV167 @ SY1053 ) )
| ~ ( member2057358096od_a_a @ SY1053 @ SV266 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1040]) ).
thf(1166,plain,
! [SV349: a,SV267: a,SV168: set_Product_prod_a_a,SV49: set_a] :
( ( ~ ( prefer1292084992ence_a @ SV49 @ SV168 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV267 @ SV349 ) @ SV168 )
| ( member_a @ SV267 @ SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1041]) ).
thf(1167,plain,
! [SV268: a > product_prod_a_a,SV169: set_a,SV50: a] :
( ( ( ~ ( member_a @ SV50 @ SV169 ) )
= $true )
| ( ( member449909584od_a_a @ ( SV268 @ SV50 ) @ ( image_1725938350od_a_a @ SV268 @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1042]) ).
thf(1168,plain,
! [SV350: a > product_prod_a_a,SV269: product_prod_a_a,SV170: set_a,SV51: a] :
( ( ~ ( member_a @ SV51 @ SV170 )
| ( SV269
!= ( SV350 @ SV51 ) )
| ( member449909584od_a_a @ SV269 @ ( image_1725938350od_a_a @ SV350 @ SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1043]) ).
thf(1169,plain,
! [SV351: a > set_a,SV270: set_a,SV171: a,SV52: a] :
( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV171 ) @ ( product_Sigma_a_a @ SV270 @ SV351 ) )
| ( member_a @ SV52 @ SV270 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1170,plain,
! [SV352: produc1572603623od_a_a > product_prod_a_a,SV271: product_prod_a_a,SV172: set_Pr1948701895od_a_a,SV53: produc1572603623od_a_a] :
( ( ~ ( member2057358096od_a_a @ SV53 @ SV172 )
| ( SV271
!= ( SV352 @ SV53 ) )
| ( member449909584od_a_a @ SV271 @ ( image_734753285od_a_a @ SV352 @ SV172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1045]) ).
thf(1171,plain,
! [SV272: produc1572603623od_a_a > product_prod_a_a,SV173: set_Pr1948701895od_a_a,SV54: produc1572603623od_a_a] :
( ( ( ~ ( member2057358096od_a_a @ SV54 @ SV173 ) )
= $true )
| ( ( member449909584od_a_a @ ( SV272 @ SV54 ) @ ( image_734753285od_a_a @ SV272 @ SV173 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1046]) ).
thf(1172,plain,
! [SV353: a,SV274: set_Product_prod_a_a,SV175: a,SV56: a] :
( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV56 @ SV175 ) @ SV274 )
| ( SV353 != SV175 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV56 @ SV353 ) @ SV274 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1048]) ).
thf(1173,plain,
! [SV354: a,SV275: a,SV176: a,SV57: a] :
( ( ( ( product_Pair_a_a @ SV57 @ SV176 )
= ( product_Pair_a_a @ SV275 @ SV354 ) )
= ( ~ ( ( SV57 != SV275 )
| ( SV176 != SV354 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1049]) ).
thf(1174,plain,
! [SV355: product_prod_a_a > a,SV276: a,SV177: set_Product_prod_a_a,SV58: product_prod_a_a] :
( ( ~ ( member449909584od_a_a @ SV58 @ SV177 )
| ( SV276
!= ( SV355 @ SV58 ) )
| ( member_a @ SV276 @ ( image_340790172_a_a_a @ SV355 @ SV177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1175,plain,
! [SV277: set_Product_prod_a_a,SV178: produc1572603623od_a_a > product_prod_a_a,SV59: set_Pr1948701895od_a_a] :
( ( ( ~ ! [SY1063: produc1572603623od_a_a] :
( ~ ( member2057358096od_a_a @ SY1063 @ SV59 )
| ( member449909584od_a_a @ ( SV178 @ SY1063 ) @ SV277 ) ) )
= $true )
| ( ( ord_le1824328871od_a_a @ ( image_734753285od_a_a @ SV178 @ SV59 ) @ SV277 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1051]) ).
thf(1176,plain,
! [SV179: set_a,SV60: set_Product_prod_a_a] :
( ( ( ! [SY892: a,SY893: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY892 @ SY893 ) @ SV60 )
| ( member_a @ SY892 @ SV179 ) ) )
= $false )
| ( ( ~ ! [SY894: a,SY895: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY894 @ SY895 ) @ SV60 )
| ( member_a @ SY895 @ SV179 ) )
| ~ ( order_preorder_on_a @ SV179 @ SV60 )
| ( prefer1292084992ence_a @ SV179 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1052]) ).
thf(1177,plain,
! [SV356: a,SV278: a,SV180: set_Product_prod_a_a,SV61: set_a] :
( ( ! [SY1147: a] :
( ~ ( prefer1292084992ence_a @ SV61 @ SV180 )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV356 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV278 ) @ SV180 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SY1147 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1147 @ SV356 ) @ SV180 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SY1147 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1147 @ SV278 ) @ SV180 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1053]) ).
thf(1178,plain,
! [SV357: product_prod_a_a,SV279: product_prod_a_a,SV181: set_Pr1948701895od_a_a,SV62: set_Product_prod_a_a] :
( ( ~ ( prefer1338892073od_a_a @ SV62 @ SV181 )
| ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV279 @ SV357 ) @ SV181 )
| ( member449909584od_a_a @ SV279 @ SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1054]) ).
thf(1179,plain,
! [SV358: product_prod_a_a > set_Product_prod_a_a,SV280: set_Product_prod_a_a,SV182: product_prod_a_a,SV63: product_prod_a_a] :
( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV63 @ SV182 ) @ ( produc304751368od_a_a @ SV280 @ SV358 ) )
| ( member449909584od_a_a @ SV63 @ SV280 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1055]) ).
thf(1180,plain,
! [SV359: product_prod_a_a,SV281: a,SV183: a,SV64: a > a > $o] :
( ( ~ ( SV64 @ SV183 @ SV281 )
| ( SV359
!= ( product_Pair_a_a @ SV183 @ SV281 ) )
| ( SV64 @ ( product_fst_a_a @ SV359 ) @ ( product_snd_a_a @ SV359 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1056]) ).
thf(1181,plain,
! [SV360: a,SV282: a,SV184: a > a,SV65: a] :
( ( ! [SY1148: a > a,SY1149: set_a] :
( ( SV65
!= ( SV184 @ SV282 ) )
| ( SV360
!= ( SY1148 @ SV282 ) )
| ~ ( member_a @ SV282 @ SY1149 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV65 @ SV360 ) @ ( bNF_Gr423046308_a_a_a @ SY1149 @ SV184 @ SY1148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1057]) ).
thf(1182,plain,
! [SV361: a > set_a,SV283: a,SV185: set_a,SV66: a] :
( ( ~ ( member_a @ SV66 @ SV185 )
| ~ ( member_a @ SV283 @ ( SV361 @ SV66 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV66 @ SV283 ) @ ( product_Sigma_a_a @ SV185 @ SV361 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1058]) ).
thf(1183,plain,
! [SV362: a,SV284: a,SV186: a,SV67: a] :
( ( ( ( product_Pair_a_a @ SV67 @ SV186 )
!= ( product_Pair_a_a @ SV284 @ SV362 ) )
| ~ ( ( SV67 != SV284 )
| ( SV186 != SV362 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1059]) ).
thf(1184,plain,
! [SV285: set_Product_prod_a_a,SV187: set_Product_prod_a_a,SV68: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV68 @ ( minus_1507102574od_a_a @ SV187 @ SV285 ) ) )
= $true )
| ( ( member449909584od_a_a @ SV68 @ SV187 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1060]) ).
thf(1185,plain,
! [SV286: set_Product_prod_a_a,SV188: set_Product_prod_a_a,SV69: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV69 @ ( minus_1507102574od_a_a @ SV188 @ SV286 ) ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ SV69 @ SV286 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1061]) ).
thf(1186,plain,
! [SV189: set_Product_prod_a_a,SV70: set_Product_prod_a_a] :
( ( ( ! [SY915: a,SY916: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY915 @ SY916 ) @ SV70 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY915 @ SY916 ) @ SV189 ) ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV70 @ SV189 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1062]) ).
thf(1187,plain,
! [SV287: a,SV190: a,SV71: product_prod_a_a > $o] :
( ( ( ~ ( product_curry_a_a_o @ SV71 @ SV190 @ SV287 ) )
= $true )
| ( ( SV71 @ ( product_Pair_a_a @ SV190 @ SV287 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1063]) ).
thf(1188,plain,
! [SV363: a > set_a,SV288: set_a,SV191: a,SV72: a] :
( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV72 @ SV191 ) @ ( product_Sigma_a_a @ SV288 @ SV363 ) )
| ( member_a @ SV191 @ ( SV363 @ SV72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1064]) ).
thf(1189,plain,
! [SV73: produc1921647824od_a_a] :
( ( ! [SY1150: a] :
( SV73
!= ( produc1299253312od_a_a @ ( sK2_SY638 @ SV73 ) @ ( product_Pair_a_a @ ( sK6_SY1075 @ SV73 ) @ SY1150 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1065]) ).
thf(1190,plain,
! [SV364: a > a,SV289: set_a,SV192: a,SV74: a] :
( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV74 @ SV192 ) @ ( bNF_Gr_a_a @ SV289 @ SV364 ) )
| ( ( SV364 @ SV74 )
= SV192 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1066]) ).
thf(1191,plain,
! [SV365: a > set_a,SV290: set_a,SV193: a,SV75: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV75 @ SV193 ) @ ( product_Sigma_a_a @ SV290 @ SV365 ) )
= ( ~ ( ~ ( member_a @ SV75 @ SV290 )
| ~ ( member_a @ SV193 @ ( SV365 @ SV75 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1067]) ).
thf(1192,plain,
! [SV366: product_prod_a_a,SV291: product_prod_a_a,SV194: product_prod_a_a > product_prod_a_a,SV76: product_prod_a_a] :
( ( ! [SY1151: product_prod_a_a > product_prod_a_a,SY1152: set_Product_prod_a_a] :
( ( SV76
!= ( SV194 @ SV291 ) )
| ( SV366
!= ( SY1151 @ SV291 ) )
| ~ ( member449909584od_a_a @ SV291 @ SY1152 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV76 @ SV366 ) @ ( bNF_Gr200450189od_a_a @ SY1152 @ SV194 @ SY1151 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1068]) ).
thf(1193,plain,
! [SV367: set_Product_prod_a_a,SV195: set_Product_prod_a_a] :
( ( ( minus_1507102574od_a_a @ SV195 @ SV367 )
= ( collec645855634od_a_a
@ ^ [SY1153: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1153 @ SV195 )
| ~ ~ ( member449909584od_a_a @ SY1153 @ SV367 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1069]) ).
thf(1194,plain,
! [SV293: product_prod_a_a,SV196: set_Product_prod_a_a,SV78: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV78 @ SV196 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ SV293 @ SV78 )
| ( member449909584od_a_a @ SV293 @ SV196 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1071]) ).
thf(1195,plain,
! [SV368: a > a,SV294: set_Product_prod_a_a,SV197: a,SV79: a] :
( ( ! [SY1154: a > a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV79 @ SV197 ) @ SV294 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV368 @ SV79 ) @ ( SY1154 @ SV197 ) ) @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SV368 @ SY1154 ) @ SV294 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1072]) ).
thf(1196,plain,
! [SV295: product_prod_a_a,SV198: set_Product_prod_a_a,SV80: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV80 @ SV198 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ SV295 @ SV80 )
| ( member449909584od_a_a @ SV295 @ SV198 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1073]) ).
thf(1197,plain,
! [SV296: set_Pr1948701895od_a_a,SV199: product_prod_a_a > produc1572603623od_a_a,SV81: set_Product_prod_a_a] :
( ( ( ~ ! [SY1085: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1085 @ SV81 )
| ( member2057358096od_a_a @ ( SV199 @ SY1085 ) @ SV296 ) ) )
= $true )
| ( ( ord_le456379495od_a_a @ ( image_1765377413od_a_a @ SV199 @ SV81 ) @ SV296 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1074]) ).
thf(1198,plain,
! [SV297: a,SV200: a,SV82: product_prod_a_a] :
( ( ( SV82
!= ( product_Pair_a_a @ SV200 @ SV297 ) )
= $true )
| ( ( ( product_snd_a_a @ SV82 )
= SV297 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1075]) ).
thf(1199,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( prefer1292084992ence_a @ SV201 @ SV369 )
= ( ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1076]) ).
thf(1200,plain,
! [SV370: product_prod_a_a > set_Product_prod_a_a,SV299: set_Product_prod_a_a,SV202: product_prod_a_a,SV84: product_prod_a_a] :
( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV84 @ SV202 ) @ ( produc304751368od_a_a @ SV299 @ SV370 ) )
| ~ ( ~ ( member449909584od_a_a @ SV84 @ SV299 )
| ~ ( member449909584od_a_a @ SV202 @ ( SV370 @ SV84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1078]) ).
thf(1201,plain,
! [SV300: product_prod_a_a > produc1572603623od_a_a,SV203: set_Product_prod_a_a,SV85: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV85 @ SV203 ) )
= $true )
| ( ( member2057358096od_a_a @ ( SV300 @ SV85 ) @ ( image_1765377413od_a_a @ SV300 @ SV203 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1079]) ).
thf(1202,plain,
! [SV371: product_prod_a_a > set_Product_prod_a_a,SV301: product_prod_a_a,SV204: set_Product_prod_a_a,SV86: product_prod_a_a] :
( ( ~ ( member449909584od_a_a @ SV86 @ SV204 )
| ~ ( member449909584od_a_a @ SV301 @ ( SV371 @ SV86 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV86 @ SV301 ) @ ( produc304751368od_a_a @ SV204 @ SV371 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1080]) ).
thf(1203,plain,
! [SV302: a,SV205: a,SV87: a > a > $o] :
( ( ( ~ ( SV87 @ SV205 @ SV302 ) )
= $true )
| ( ( SV87 @ ( product_snd_a_a @ ( product_Pair_a_a @ SV302 @ SV205 ) ) @ ( product_fst_a_a @ ( product_Pair_a_a @ SV302 @ SV205 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1081]) ).
thf(1204,plain,
! [SV372: product_prod_a_a > $o,SV303: product_prod_a_a > $o,SV206: set_Product_prod_a_a,SV88: set_Product_prod_a_a] :
( ( ~ ( ord_le1824328871od_a_a @ SV88 @ SV206 )
| ~ ! [SY1159: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1159 @ SV88 )
| ~ ( SV303 @ SY1159 )
| ( SV372 @ SY1159 ) )
| ( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [SY1094: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1094 @ SV88 )
| ~ ( SV303 @ SY1094 ) ) )
@ ( collec645855634od_a_a
@ ^ [SY1161: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1161 @ SV206 )
| ~ ( SV372 @ SY1161 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1082]) ).
thf(1205,plain,
! [SV373: product_prod_a_a > set_Product_prod_a_a,SV304: set_Product_prod_a_a,SV207: product_prod_a_a,SV89: product_prod_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV89 @ SV207 ) @ ( produc304751368od_a_a @ SV304 @ SV373 ) )
= ( ~ ( ~ ( member449909584od_a_a @ SV89 @ SV304 )
| ~ ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1083]) ).
thf(1206,plain,
! [SV90: produc1572603623od_a_a] :
( ( ! [SY1162: a] :
( SV90
!= ( produc1474507607od_a_a @ ( sK3_SY691 @ SV90 ) @ ( product_Pair_a_a @ ( sK7_SY1097 @ SV90 ) @ SY1162 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1084]) ).
thf(1207,plain,
! [SV208: product_prod_a_a,SV91: a] :
( ( ( ~ ( ( SV91
= ( product_snd_a_a @ SV208 ) )
| ~ ! [SY956: a] :
( SV208
!= ( product_Pair_a_a @ SY956 @ SV91 ) ) ) )
= $true )
| ( ( ~ ( ( SV91
!= ( product_snd_a_a @ SV208 ) )
| ~ ~ ! [SY956: a] :
( SV208
!= ( product_Pair_a_a @ SY956 @ SV91 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1085]) ).
thf(1208,plain,
! [SV374: set_Pr1948701895od_a_a,SV305: produc1572603623od_a_a,SV209: produc1572603623od_a_a > product_prod_a_a,SV92: product_prod_a_a] :
( ( ( SV92
!= ( SV209 @ SV305 ) )
| ~ ( member2057358096od_a_a @ SV305 @ SV374 )
| ( member449909584od_a_a @ SV92 @ ( image_734753285od_a_a @ SV209 @ SV374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1087]) ).
thf(1209,plain,
! [SV375: a,SV306: a > $o,SV210: a,SV93: a > $o] :
( ( ~ ( SV93 @ SV210 )
| ~ ( SV306 @ SV375 )
| ~ ( ~ ( SV93 @ ( product_fst_a_a @ ( product_Pair_a_a @ SV210 @ SV375 ) ) )
| ~ ( SV306 @ ( product_snd_a_a @ ( product_Pair_a_a @ SV210 @ SV375 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1088]) ).
thf(1210,plain,
! [SV376: set_Product_prod_a_a,SV307: set_a,SV211: a,SV94: a] :
( ( ~ ( member_a @ SV94 @ ( prefer161218362good_a @ SV211 @ SV307 @ SV376 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV94 @ SV211 ) @ SV376 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1089]) ).
thf(1211,plain,
! [SV377: a,SV308: product_prod_a_a,SV212: product_prod_a_a > a,SV95: a] :
( ( ! [SY1163: product_prod_a_a > a,SY1164: set_Product_prod_a_a] :
( ( SV95
!= ( SV212 @ SV308 ) )
| ( SV377
!= ( SY1163 @ SV308 ) )
| ~ ( member449909584od_a_a @ SV308 @ SY1164 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV95 @ SV377 ) @ ( bNF_Gr1853143117_a_a_a @ SY1164 @ SV212 @ SY1163 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1090]) ).
thf(1212,plain,
! [SV378: product_prod_a_a > product_prod_a_a,SV309: set_Product_prod_a_a,SV213: product_prod_a_a,SV96: product_prod_a_a] :
( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV96 @ SV213 ) @ ( bNF_Gr1372473186od_a_a @ SV309 @ SV378 ) )
| ( member449909584od_a_a @ SV96 @ SV309 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1091]) ).
thf(1213,plain,
! [SV379: set_a,SV214: a] :
( ( ( prefer436369274d_as_a @ SV214 @ SV379 )
= ( ^ [SY1165: set_Product_prod_a_a] :
( collect_a
@ ^ [SY1166: a] :
~ ( ~ ~ ( ~ ( member_a @ SY1166 @ SV379 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV214 @ SY1166 ) @ SY1165 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1166 @ SV214 ) @ SY1165 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1092]) ).
thf(1214,plain,
! [SV98: product_prod_a_a] :
( ( SV98
!= ( product_Pair_a_a @ ( sK4_SY716 @ SV98 ) @ ( sK8_SY1108 @ SV98 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1094]) ).
thf(1215,plain,
! [SV311: set_Product_prod_a_a,SV215: product_prod_a_a > a,SV99: a] :
( ( ( ~ ( member_a @ SV99 @ ( image_340790172_a_a_a @ SV215 @ SV311 ) ) )
= $true )
| ( ( ~ ! [SY1109: product_prod_a_a] :
( ( SV99
!= ( SV215 @ SY1109 ) )
| ~ ( member449909584od_a_a @ SY1109 @ SV311 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1095]) ).
thf(1216,plain,
! [SV216: product_prod_a_a,SV100: product_prod_a_a > $o] :
( ( ( ! [SY722: a,SY723: a] : ( SV100 @ ( product_Pair_a_a @ SY722 @ SY723 ) ) )
= $false )
| ( ( SV100 @ SV216 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1096]) ).
thf(1217,plain,
! [SV380: set_Product_prod_a_a,SV312: a > a,SV217: a > a,SV101: product_prod_a_a] :
( ( ~ ( member449909584od_a_a @ SV101 @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SV217 @ SV312 ) @ SV380 ) )
| ~ ! [SY1167: a,SY1168: a] :
( ( SV101
!= ( product_Pair_a_a @ ( SV217 @ SY1167 ) @ ( SV312 @ SY1168 ) ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1167 @ SY1168 ) @ SV380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1097]) ).
thf(1218,plain,
! [SV381: set_a,SV218: a] :
( ( ( prefer1676310729than_a @ SV218 @ SV381 )
= ( ^ [SY1169: set_Product_prod_a_a] :
( collect_a
@ ^ [SY1170: a] :
~ ( ~ ( member_a @ SY1170 @ SV381 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV218 @ SY1170 ) @ SY1169 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1098]) ).
thf(1219,plain,
! [SV382: a > a,SV314: set_a,SV219: a,SV103: a] :
( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV103 @ SV219 ) @ ( bNF_Gr_a_a @ SV314 @ SV382 ) )
| ( member_a @ SV103 @ SV314 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1100]) ).
thf(1220,plain,
! [SV383: a,SV315: a,SV220: a,SV104: a > $o] :
( ( ! [SY1171: a > set_Product_prod_a_a] :
( ~ ( SV104 @ SV220 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV315 @ SV383 ) @ ( SY1171 @ SV220 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV220 @ SV315 ) @ ( product_Pair_a_a @ SV220 @ SV383 ) ) @ ( same_fst_a_a @ SV104 @ SY1171 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1221,plain,
! [SV221: product_prod_a_a,SV105: product_prod_a_a > $o] :
( ( ( ! [SY740: a,SY741: a] : ( SV105 @ ( product_Pair_a_a @ SY740 @ SY741 ) ) )
= $false )
| ( ( SV105 @ SV221 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1102]) ).
thf(1222,plain,
! [SV384: set_Product_prod_a_a,SV316: product_prod_a_a,SV222: product_prod_a_a > a,SV106: a] :
( ( ( SV106
!= ( SV222 @ SV316 ) )
| ~ ( member449909584od_a_a @ SV316 @ SV384 )
| ( member_a @ SV106 @ ( image_340790172_a_a_a @ SV222 @ SV384 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1103]) ).
thf(1223,plain,
! [SV317: a,SV223: a,SV107: a] :
( ( ( ( product_snd_a_a @ ( product_Pair_a_a @ SV107 @ SV223 ) )
!= SV317 )
= $true )
| ( ( SV223 = SV317 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1104]) ).
thf(1224,plain,
! [SV318: a,SV224: a,SV108: product_prod_a_a > $o] :
( ( ( ~ ( product_curry_a_a_o @ SV108 @ SV224 @ SV318 ) )
= $true )
| ( ( SV108 @ ( product_Pair_a_a @ SV224 @ SV318 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1105]) ).
thf(1225,plain,
! [SV109: product_prod_a_a] :
( ( ~ ! [SY1119: a] :
( SV109
!= ( product_Pair_a_a @ ( sK5_SY749 @ SV109 ) @ SY1119 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1106]) ).
thf(1226,plain,
! [SV385: set_Product_prod_a_a,SV319: product_prod_a_a,SV225: product_prod_a_a > product_prod_a_a,SV110: product_prod_a_a] :
( ( ( SV110
!= ( SV225 @ SV319 ) )
| ~ ( member449909584od_a_a @ SV319 @ SV385 )
| ( member449909584od_a_a @ SV110 @ ( image_794773445od_a_a @ SV225 @ SV385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1107]) ).
thf(1227,plain,
! [SV320: product_prod_a_a > set_Product_prod_a_a,SV226: set_Product_prod_a_a,SV111: produc1572603623od_a_a] :
( ( ( ~ ( member2057358096od_a_a @ SV111 @ ( produc304751368od_a_a @ SV226 @ SV320 ) ) )
= $true )
| ( ( ~ ! [SY1121: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1121 @ SV226 )
| ! [SY1122: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1122 @ ( SV320 @ SY1121 ) )
| ( SV111
!= ( produc1474507607od_a_a @ SY1121 @ SY1122 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1108]) ).
thf(1228,plain,
! [SV321: product_prod_a_a > a,SV227: set_Product_prod_a_a,SV112: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV112 @ SV227 ) )
= $true )
| ( ( member_a @ ( SV321 @ SV112 ) @ ( image_340790172_a_a_a @ SV321 @ SV227 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1109]) ).
thf(1229,plain,
! [SV386: product_prod_a_a > product_prod_a_a,SV322: product_prod_a_a,SV228: set_Product_prod_a_a,SV113: product_prod_a_a] :
( ( ~ ( member449909584od_a_a @ SV113 @ SV228 )
| ( SV322
!= ( SV386 @ SV113 ) )
| ( member449909584od_a_a @ SV322 @ ( image_794773445od_a_a @ SV386 @ SV228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1110]) ).
thf(1230,plain,
! [SV323: set_a,SV229: a > product_prod_a_a,SV114: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV114 @ ( image_1725938350od_a_a @ SV229 @ SV323 ) ) )
= $true )
| ( ( ~ ! [SY1124: a] :
( ( SV114
!= ( SV229 @ SY1124 ) )
| ~ ( member_a @ SY1124 @ SV323 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1111]) ).
thf(1231,plain,
! [SV324: product_prod_a_a > product_prod_a_a,SV230: set_Product_prod_a_a,SV115: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV115 @ SV230 ) )
= $true )
| ( ( member449909584od_a_a @ ( SV324 @ SV115 ) @ ( image_794773445od_a_a @ SV324 @ SV230 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1112]) ).
thf(1232,plain,
! [SV387: a,SV325: produc1572603623od_a_a,SV231: produc1572603623od_a_a > a,SV116: a] :
( ( ! [SY1172: produc1572603623od_a_a > a,SY1173: set_Pr1948701895od_a_a] :
( ( SV116
!= ( SV231 @ SV325 ) )
| ( SV387
!= ( SY1172 @ SV325 ) )
| ~ ( member2057358096od_a_a @ SV325 @ SY1173 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV116 @ SV387 ) @ ( bNF_Gr356189709_a_a_a @ SY1173 @ SV231 @ SY1172 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1113]) ).
thf(1233,plain,
! [SV117: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( sK9_SY773 @ SV117 ) @ SV117 )
= $false )
| ( ( top_to398455383od_a_a = SV117 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1114]) ).
thf(1234,plain,
! [SV388: set_Pr1948701895od_a_a,SV326: set_Product_prod_a_a,SV232: product_prod_a_a,SV118: product_prod_a_a] :
( ( ~ ( member449909584od_a_a @ SV118 @ ( prefer477097315od_a_a @ SV232 @ SV326 @ SV388 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV118 @ SV232 ) @ SV388 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1115]) ).
thf(1235,plain,
! [SV327: a > set_a,SV233: set_a,SV119: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV119 @ ( product_Sigma_a_a @ SV233 @ SV327 ) ) )
= $true )
| ( ( ~ ! [SY1129: a] :
( ~ ( member_a @ SY1129 @ SV233 )
| ! [SY1130: a] :
( ~ ( member_a @ SY1130 @ ( SV327 @ SY1129 ) )
| ( SV119
!= ( product_Pair_a_a @ SY1129 @ SY1130 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1116]) ).
thf(1236,plain,
! [SV389: product_prod_a_a > $o,SV328: set_Product_prod_a_a,SV234: set_Product_prod_a_a,SV120: product_prod_a_a] :
( ( ~ ( member449909584od_a_a @ SV120 @ SV234 )
| ~ ( ord_le1824328871od_a_a @ SV234
@ ( collec645855634od_a_a
@ ^ [SY1174: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1174 @ SV328 )
| ~ ( SV389 @ SY1174 ) ) ) )
| ( SV389 @ SV120 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1117]) ).
thf(1237,plain,
! [SV329: a,SV235: a,SV121: product_prod_a_a] :
( ( ( SV121
!= ( product_Pair_a_a @ SV235 @ SV329 ) )
= $true )
| ( ( ( product_fst_a_a @ SV121 )
= SV235 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1118]) ).
thf(1238,plain,
! [SV330: set_a,SV236: product_prod_a_a > a,SV122: set_Product_prod_a_a] :
( ( ( ~ ! [SY1133: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1133 @ SV122 )
| ( member_a @ ( SV236 @ SY1133 ) @ SV330 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ ( image_340790172_a_a_a @ SV236 @ SV122 ) @ SV330 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1119]) ).
thf(1239,plain,
! [SV390: a,SV331: a,SV237: a,SV123: a] :
( ( ! [SY1175: set_Product_prod_a_a,SY1176: set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SV331 @ SV390 ) ) @ ( lex_prod_a_a @ SY1175 @ SY1176 ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SY1175 )
| ~ ( ( SV123 != SV331 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SY1176 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1120]) ).
thf(1240,plain,
! [SV124: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK10_SY795 @ SV124 ) @ SV124 ) )
= $false )
| ( ( SV124 = bot_bo2131659635od_a_a )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1122]) ).
thf(1241,plain,
! [SV238: product_prod_a_a,SV125: a] :
( ( ( ~ ( ( SV125
= ( product_fst_a_a @ SV238 ) )
| ~ ! [SY1024: a] :
( SV238
!= ( product_Pair_a_a @ SV125 @ SY1024 ) ) ) )
= $true )
| ( ( ~ ( ( SV125
!= ( product_fst_a_a @ SV238 ) )
| ~ ~ ! [SY1024: a] :
( SV238
!= ( product_Pair_a_a @ SV125 @ SY1024 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1123]) ).
thf(1242,plain,
! [SV332: set_Product_prod_a_a,SV239: set_Product_prod_a_a,SV126: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV126 @ SV239 ) )
= $true )
| ( ( ~ ~ ( member449909584od_a_a @ SV126 @ SV332 )
| ( member449909584od_a_a @ SV126 @ ( minus_1507102574od_a_a @ SV239 @ SV332 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1125]) ).
thf(1243,plain,
! [SV391: a > set_a,SV333: set_a,SV240: a,SV127: a] :
( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV127 @ SV240 ) @ ( product_Sigma_a_a @ SV333 @ SV391 ) )
| ~ ( ~ ( member_a @ SV127 @ SV333 )
| ~ ( member_a @ SV240 @ ( SV391 @ SV127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1126]) ).
thf(1244,plain,
! [SV334: a,SV241: a,SV128: a] :
( ( ( ( product_fst_a_a @ ( product_Pair_a_a @ SV128 @ SV241 ) )
!= SV334 )
= $true )
| ( ( SV128 = SV334 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1127]) ).
thf(1245,plain,
! [SV392: product_prod_a_a > set_Product_prod_a_a,SV335: set_Product_prod_a_a,SV242: product_prod_a_a,SV129: product_prod_a_a] :
( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV129 @ SV242 ) @ ( produc304751368od_a_a @ SV335 @ SV392 ) )
| ( member449909584od_a_a @ SV242 @ ( SV392 @ SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1128]) ).
thf(1246,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
| ( SV2 = SV131 ) )
= $false )
| ( ( ~ ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
!= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
| ( SV2 != SV131 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1129]) ).
thf(1247,plain,
! [SV243: set_Product_prod_a_a,SV132: a,SV3: a] :
( ( ( ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV3 @ SV132 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV243 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV132 @ SV3 ) @ SV243 ) ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV3 @ SV132 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV243 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV132 @ SV3 ) @ SV243 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1130]) ).
thf(1248,plain,
! [SV133: product_prod_a_a > $o,SV4: product_prod_a_a] :
( ( ( ( member449909584od_a_a @ SV4 @ ( collec645855634od_a_a @ SV133 ) )
| ( SV133 @ SV4 ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ SV4 @ ( collec645855634od_a_a @ SV133 ) )
| ~ ( SV133 @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1132]) ).
thf(1249,plain,
! [SV138: product_prod_a_a] :
( ( ( ( top_to1483957574_a_a_o @ SV138 )
| ( member449909584od_a_a @ SV138 @ top_to398455383od_a_a ) )
= $false )
| ( ( ~ ( ~ ( top_to1483957574_a_a_o @ SV138 )
| ~ ( member449909584od_a_a @ SV138 @ top_to398455383od_a_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1137]) ).
thf(1250,plain,
! [SV340: a,SV140: a] :
( ( ~ ( ( top_top_a_a_o @ SV140 @ SV340 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV140 @ SV340 ) @ top_to398455383od_a_a ) )
| ~ ( ~ ( top_top_a_a_o @ SV140 @ SV340 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV140 @ SV340 ) @ top_to398455383od_a_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1138]) ).
thf(1251,plain,
! [SV340: a,SV140: a] :
( ( ( top_top_a_a_o @ SV140 @ SV340 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ SV140 @ SV340 ) @ top_to398455383od_a_a ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1138]) ).
thf(1252,plain,
! [SV249: set_a,SV143: set_a,SV20: product_prod_a_a] :
( ( ( ~ ( ( member449909584od_a_a @ SV20 @ ( product_product_a_a @ SV143 @ SV249 ) )
| ( member449909584od_a_a @ SV20
@ ( product_Sigma_a_a @ SV143
@ ^ [SY1036: a] : SV249 ) ) ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ SV20 @ ( product_product_a_a @ SV143 @ SV249 ) )
| ~ ( member449909584od_a_a @ SV20
@ ( product_Sigma_a_a @ SV143
@ ^ [SY1036: a] : SV249 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1139]) ).
thf(1253,plain,
! [SV144: set_Product_prod_a_a,SV21: set_Product_prod_a_a] :
( ( ( ( ord_le1347718902_a_a_o
@ ^ [SY498: product_prod_a_a] : ( member449909584od_a_a @ SY498 @ SV21 )
@ ^ [SY826: product_prod_a_a] : ( member449909584od_a_a @ SY826 @ SV144 ) )
| ( ord_le1824328871od_a_a @ SV21 @ SV144 ) )
= $false )
| ( ( ~ ( ~ ( ord_le1347718902_a_a_o
@ ^ [SY498: product_prod_a_a] : ( member449909584od_a_a @ SY498 @ SV21 )
@ ^ [SY826: product_prod_a_a] : ( member449909584od_a_a @ SY826 @ SV144 ) )
| ~ ( ord_le1824328871od_a_a @ SV21 @ SV144 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1141]) ).
thf(1254,plain,
! [SV341: set_Product_prod_a_a,SV145: set_Product_prod_a_a] :
( ( ~ ( ( ord_le1824328871od_a_a @ SV145 @ SV341 )
| ( ord_le1347718902_a_a_o
@ ^ [SY828: product_prod_a_a] : ( member449909584od_a_a @ SY828 @ SV145 )
@ ^ [SY1142: product_prod_a_a] : ( member449909584od_a_a @ SY1142 @ SV341 ) ) )
| ~ ( ~ ( ord_le1824328871od_a_a @ SV145 @ SV341 )
| ~ ( ord_le1347718902_a_a_o
@ ^ [SY828: product_prod_a_a] : ( member449909584od_a_a @ SY828 @ SV145 )
@ ^ [SY1142: product_prod_a_a] : ( member449909584od_a_a @ SY1142 @ SV341 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1142]) ).
thf(1255,plain,
! [SV341: set_Product_prod_a_a,SV145: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV145 @ SV341 )
= ( ord_le1347718902_a_a_o
@ ^ [SY828: product_prod_a_a] : ( member449909584od_a_a @ SY828 @ SV145 )
@ ^ [SY1142: product_prod_a_a] : ( member449909584od_a_a @ SY1142 @ SV341 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1142]) ).
thf(1256,plain,
! [SV146: set_Product_prod_a_a,SV23: set_Product_prod_a_a] :
( ( ( ( ord_less_eq_a_a_o
@ ^ [SY504: a,SY505: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY504 @ SY505 ) @ SV23 )
@ ^ [SY832: a,SY833: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY832 @ SY833 ) @ SV146 ) )
| ( ord_le1824328871od_a_a @ SV23 @ SV146 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_a_a_o
@ ^ [SY504: a,SY505: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY504 @ SY505 ) @ SV23 )
@ ^ [SY832: a,SY833: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY832 @ SY833 ) @ SV146 ) )
| ~ ( ord_le1824328871od_a_a @ SV23 @ SV146 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1143]) ).
thf(1257,plain,
! [SV24: set_Product_prod_a_a] :
( ( ( ! [SY508: product_prod_a_a] :
~ ( member449909584od_a_a @ SY508 @ SV24 ) )
= $false )
| ( ( ~ ( ~ ! [SY508: product_prod_a_a] :
~ ( member449909584od_a_a @ SY508 @ SV24 )
| ( SV24 != bot_bo2131659635od_a_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1144]) ).
thf(1258,plain,
! [SV24: set_Product_prod_a_a] :
( ( ( SV24 = bot_bo2131659635od_a_a )
= $false )
| ( ( ~ ( ~ ! [SY508: product_prod_a_a] :
~ ( member449909584od_a_a @ SY508 @ SV24 )
| ( SV24 != bot_bo2131659635od_a_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1144]) ).
thf(1259,plain,
! [SV27: set_Product_prod_a_a,SV147: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV147 @ SV27 )
= $false )
| ( ( SV27 = bot_bo2131659635od_a_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1145]) ).
thf(1260,plain,
! [SV28: set_Product_prod_a_a,SV148: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK11_SY834 @ SV148 @ SV28 ) @ SV28 )
| ( member449909584od_a_a @ ( sK11_SY834 @ SV148 @ SV28 ) @ SV148 ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV28 @ SV148 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1146]) ).
thf(1261,plain,
! [SV342: set_Product_prod_a_a,SV251: product_prod_a_a,SV149: product_prod_a_a > produc1572603623od_a_a,SV29: produc1572603623od_a_a] :
( ( ( SV29
!= ( SV149 @ SV251 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ SV251 @ SV342 )
| ( member2057358096od_a_a @ SV29 @ ( image_1765377413od_a_a @ SV149 @ SV342 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1147]) ).
thf(1262,plain,
! [SV343: a,SV252: a,SV150: a,SV30: a] :
( ( ~ ( ( ( product_Pair_a_a @ SV30 @ SV150 )
= ( product_Pair_a_a @ SV252 @ SV343 ) )
| ~ ( ( SV30 != SV252 )
| ( SV150 != SV343 ) ) )
| ~ ( ( ( product_Pair_a_a @ SV30 @ SV150 )
!= ( product_Pair_a_a @ SV252 @ SV343 ) )
| ~ ~ ( ( SV30 != SV252 )
| ( SV150 != SV343 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1148]) ).
thf(1263,plain,
! [SV343: a,SV252: a,SV150: a,SV30: a] :
( ( ( ( product_Pair_a_a @ SV30 @ SV150 )
= ( product_Pair_a_a @ SV252 @ SV343 ) )
= ( ~ ( ( SV30 != SV252 )
| ( SV150 != SV343 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1148]) ).
thf(1264,plain,
! [SV344: product_prod_a_a > produc1572603623od_a_a,SV253: produc1572603623od_a_a,SV151: set_Product_prod_a_a,SV31: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV31 @ SV151 ) )
= $true )
| ( ( ( SV253
!= ( SV344 @ SV31 ) )
| ( member2057358096od_a_a @ SV253 @ ( image_1765377413od_a_a @ SV344 @ SV151 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1149]) ).
thf(1265,plain,
! [SV254: set_Product_prod_a_a,SV152: product_prod_a_a > product_prod_a_a,SV32: set_Product_prod_a_a] :
( ( ( ! [SY1042: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1042 @ SV32 )
| ( member449909584od_a_a @ ( SV152 @ SY1042 ) @ SV254 ) ) )
= $false )
| ( ( ord_le1824328871od_a_a @ ( image_794773445od_a_a @ SV152 @ SV32 ) @ SV254 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1150]) ).
thf(1266,plain,
! [SV255: set_Product_prod_a_a,SV153: set_Product_prod_a_a,SV33: product_prod_a_a] :
( ( ( ~ ( ( member449909584od_a_a @ SV33 @ ( minus_1507102574od_a_a @ SV153 @ SV255 ) )
| ~ ( ~ ( member449909584od_a_a @ SV33 @ SV153 )
| ~ ~ ( member449909584od_a_a @ SV33 @ SV255 ) ) ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ SV33 @ ( minus_1507102574od_a_a @ SV153 @ SV255 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ SV33 @ SV153 )
| ~ ~ ( member449909584od_a_a @ SV33 @ SV255 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1151]) ).
thf(1267,plain,
! [SV256: set_Product_prod_a_a,SV154: a > product_prod_a_a,SV34: set_a] :
( ( ( ! [SY1043: a] :
( ~ ( member_a @ SY1043 @ SV34 )
| ( member449909584od_a_a @ ( SV154 @ SY1043 ) @ SV256 ) ) )
= $false )
| ( ( ord_le1824328871od_a_a @ ( image_1725938350od_a_a @ SV154 @ SV34 ) @ SV256 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1153]) ).
thf(1268,plain,
! [SV345: set_Product_prod_a_a,SV155: set_Product_prod_a_a] :
( ( ~ ( ( ord_le1824328871od_a_a @ SV155 @ SV345 )
| ! [SY1143: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1143 @ SV155 )
| ( member449909584od_a_a @ SY1143 @ SV345 ) ) )
| ~ ( ~ ( ord_le1824328871od_a_a @ SV155 @ SV345 )
| ~ ! [SY1143: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1143 @ SV155 )
| ( member449909584od_a_a @ SY1143 @ SV345 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1154]) ).
thf(1269,plain,
! [SV345: set_Product_prod_a_a,SV155: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV155 @ SV345 )
= ( ! [SY1143: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1143 @ SV155 )
| ( member449909584od_a_a @ SY1143 @ SV345 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1154]) ).
thf(1270,plain,
! [SV36: set_Product_prod_a_a] :
( ( ( ~ ! [SY531: product_prod_a_a] :
~ ( member449909584od_a_a @ SY531 @ SV36 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY531: product_prod_a_a] :
~ ( member449909584od_a_a @ SY531 @ SV36 )
| ~ ( ( SV36 != bot_bo2131659635od_a_a ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1155]) ).
thf(1271,plain,
! [SV36: set_Product_prod_a_a] :
( ( ( SV36 != bot_bo2131659635od_a_a )
= $false )
| ( ( ~ ( ~ ~ ! [SY531: product_prod_a_a] :
~ ( member449909584od_a_a @ SY531 @ SV36 )
| ~ ( ( SV36 != bot_bo2131659635od_a_a ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1155]) ).
thf(1272,plain,
! [SV156: produc1572603623od_a_a,SV37: produc1572603623od_a_a > $o] :
( ( ( ! [SY1177: a,SY1178: a] : ( SV37 @ ( produc1474507607od_a_a @ ( sK12_SY533 @ SV156 @ SV37 ) @ ( product_Pair_a_a @ SY1177 @ SY1178 ) ) ) )
= $false )
| ( ( SV37 @ SV156 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1156]) ).
thf(1273,plain,
! [SV258: set_Product_prod_a_a,SV158: product_prod_a_a > produc1572603623od_a_a,SV39: produc1572603623od_a_a] :
( ( ( member2057358096od_a_a @ SV39 @ ( image_1765377413od_a_a @ SV158 @ SV258 ) )
= $false )
| ( ( ~ ! [SY1045: product_prod_a_a] :
( ( SV39
!= ( SV158 @ SY1045 ) )
| ~ ( member449909584od_a_a @ SY1045 @ SV258 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1157]) ).
thf(1274,plain,
! [SV346: set_a,SV259: a,SV159: a > product_prod_a_a,SV40: product_prod_a_a] :
( ( ( SV40
!= ( SV159 @ SV259 ) )
= $true )
| ( ( ~ ( member_a @ SV259 @ SV346 )
| ( member449909584od_a_a @ SV40 @ ( image_1725938350od_a_a @ SV159 @ SV346 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1158]) ).
thf(1275,plain,
! [SV260: set_Product_prod_a_a,SV161: product_prod_a_a > product_prod_a_a,SV42: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV42 @ ( image_794773445od_a_a @ SV161 @ SV260 ) )
= $false )
| ( ( ~ ! [SY1047: product_prod_a_a] :
( ( SV42
!= ( SV161 @ SY1047 ) )
| ~ ( member449909584od_a_a @ SY1047 @ SV260 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1159]) ).
thf(1276,plain,
! [SV347: set_Product_prod_a_a,SV162: set_Product_prod_a_a] :
( ( ~ ( ( ord_le1824328871od_a_a @ SV162 @ SV347 )
| ! [SY1144: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1144 @ SV162 )
| ( member449909584od_a_a @ SY1144 @ SV347 ) ) )
| ~ ( ~ ( ord_le1824328871od_a_a @ SV162 @ SV347 )
| ~ ! [SY1144: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1144 @ SV162 )
| ( member449909584od_a_a @ SY1144 @ SV347 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1160]) ).
thf(1277,plain,
! [SV347: set_Product_prod_a_a,SV162: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV162 @ SV347 )
= ( ! [SY1144: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1144 @ SV162 )
| ( member449909584od_a_a @ SY1144 @ SV347 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1160]) ).
thf(1278,plain,
! [SV262: a,SV163: a,SV44: product_prod_a_a > $o] :
( ( ( SV44 @ ( product_Pair_a_a @ SV163 @ SV262 ) )
= $false )
| ( ( product_curry_a_a_o @ SV44 @ SV163 @ SV262 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1161]) ).
thf(1279,plain,
! [SV263: set_Product_prod_a_a,SV164: set_Product_prod_a_a,SV45: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV45 @ ( minus_1507102574od_a_a @ SV164 @ SV263 ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ SV45 @ SV164 )
| ( member449909584od_a_a @ SV45 @ SV263 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1162]) ).
thf(1280,plain,
! [SV264: product_prod_a_a > $o,SV165: set_Product_prod_a_a,SV46: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV46 @ SV165 )
= $false )
| ( ( ( ord_le1824328871od_a_a @ SV46
@ ( collec645855634od_a_a
@ ^ [SY1049: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1049 @ SV165 )
| ~ ( SV264 @ SY1049 ) ) ) )
= ( ! [SY1050: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1050 @ SV46 )
| ( SV264 @ SY1050 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1163]) ).
thf(1281,plain,
! [SV348: set_a,SV166: a] :
( ( ! [SV393: set_Product_prod_a_a] :
( ( prefer161218362good_a @ SV166 @ SV348 @ SV393 )
= ( collect_a
@ ^ [SY1179: a] :
~ ( ~ ( member_a @ SY1179 @ SV348 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1179 @ SV166 ) @ SV393 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1164]) ).
thf(1282,plain,
! [SV348: set_a,SV166: a] :
( ( ( prefer161218362good_a @ SV166 @ SV348 )
= ( ^ [SY1145: set_Product_prod_a_a] :
( collect_a
@ ^ [SY1146: a] :
~ ( ~ ( member_a @ SY1146 @ SV348 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1146 @ SV166 ) @ SY1145 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1164]) ).
thf(1283,plain,
! [SV266: set_Pr1948701895od_a_a,SV167: produc1572603623od_a_a > product_prod_a_a,SV48: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV48 @ ( image_734753285od_a_a @ SV167 @ SV266 ) )
= $false )
| ( ( ~ ! [SY1053: produc1572603623od_a_a] :
( ( SV48
!= ( SV167 @ SY1053 ) )
| ~ ( member2057358096od_a_a @ SY1053 @ SV266 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1165]) ).
thf(1284,plain,
! [SV349: a,SV267: a,SV168: set_Product_prod_a_a,SV49: set_a] :
( ( ( ~ ( prefer1292084992ence_a @ SV49 @ SV168 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV267 @ SV349 ) @ SV168 )
| ( member_a @ SV267 @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1166]) ).
thf(1285,plain,
! [SV268: a > product_prod_a_a,SV169: set_a,SV50: a] :
( ( ( member_a @ SV50 @ SV169 )
= $false )
| ( ( member449909584od_a_a @ ( SV268 @ SV50 ) @ ( image_1725938350od_a_a @ SV268 @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1167]) ).
thf(1286,plain,
! [SV350: a > product_prod_a_a,SV269: product_prod_a_a,SV170: set_a,SV51: a] :
( ( ( ~ ( member_a @ SV51 @ SV170 ) )
= $true )
| ( ( ( SV269
!= ( SV350 @ SV51 ) )
| ( member449909584od_a_a @ SV269 @ ( image_1725938350od_a_a @ SV350 @ SV170 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1168]) ).
thf(1287,plain,
! [SV351: a > set_a,SV270: set_a,SV171: a,SV52: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV171 ) @ ( product_Sigma_a_a @ SV270 @ SV351 ) ) )
= $true )
| ( ( member_a @ SV52 @ SV270 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1169]) ).
thf(1288,plain,
! [SV352: produc1572603623od_a_a > product_prod_a_a,SV271: product_prod_a_a,SV172: set_Pr1948701895od_a_a,SV53: produc1572603623od_a_a] :
( ( ( ~ ( member2057358096od_a_a @ SV53 @ SV172 ) )
= $true )
| ( ( ( SV271
!= ( SV352 @ SV53 ) )
| ( member449909584od_a_a @ SV271 @ ( image_734753285od_a_a @ SV352 @ SV172 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1170]) ).
thf(1289,plain,
! [SV272: produc1572603623od_a_a > product_prod_a_a,SV173: set_Pr1948701895od_a_a,SV54: produc1572603623od_a_a] :
( ( ( member2057358096od_a_a @ SV54 @ SV173 )
= $false )
| ( ( member449909584od_a_a @ ( SV272 @ SV54 ) @ ( image_734753285od_a_a @ SV272 @ SV173 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1171]) ).
thf(1290,plain,
! [SV353: a,SV274: set_Product_prod_a_a,SV175: a,SV56: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV56 @ SV175 ) @ SV274 ) )
= $true )
| ( ( ( SV353 != SV175 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV56 @ SV353 ) @ SV274 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1172]) ).
thf(1291,plain,
! [SV354: a,SV275: a,SV176: a,SV57: a] :
( ( ~ ( ( ( product_Pair_a_a @ SV57 @ SV176 )
= ( product_Pair_a_a @ SV275 @ SV354 ) )
| ~ ( ( SV57 != SV275 )
| ( SV176 != SV354 ) ) )
| ~ ( ( ( product_Pair_a_a @ SV57 @ SV176 )
!= ( product_Pair_a_a @ SV275 @ SV354 ) )
| ~ ~ ( ( SV57 != SV275 )
| ( SV176 != SV354 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1173]) ).
thf(1292,plain,
! [SV354: a,SV275: a,SV176: a,SV57: a] :
( ( ( ( product_Pair_a_a @ SV57 @ SV176 )
= ( product_Pair_a_a @ SV275 @ SV354 ) )
= ( ~ ( ( SV57 != SV275 )
| ( SV176 != SV354 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1173]) ).
thf(1293,plain,
! [SV355: product_prod_a_a > a,SV276: a,SV177: set_Product_prod_a_a,SV58: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV58 @ SV177 ) )
= $true )
| ( ( ( SV276
!= ( SV355 @ SV58 ) )
| ( member_a @ SV276 @ ( image_340790172_a_a_a @ SV355 @ SV177 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1174]) ).
thf(1294,plain,
! [SV277: set_Product_prod_a_a,SV178: produc1572603623od_a_a > product_prod_a_a,SV59: set_Pr1948701895od_a_a] :
( ( ( ! [SY1063: produc1572603623od_a_a] :
( ~ ( member2057358096od_a_a @ SY1063 @ SV59 )
| ( member449909584od_a_a @ ( SV178 @ SY1063 ) @ SV277 ) ) )
= $false )
| ( ( ord_le1824328871od_a_a @ ( image_734753285od_a_a @ SV178 @ SV59 ) @ SV277 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1175]) ).
thf(1295,plain,
! [SV60: set_Product_prod_a_a,SV179: set_a] :
( ( ( ! [SY1180: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK13_SY892 @ SV179 @ SV60 ) @ SY1180 ) @ SV60 )
| ( member_a @ ( sK13_SY892 @ SV179 @ SV60 ) @ SV179 ) ) )
= $false )
| ( ( ~ ! [SY894: a,SY895: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY894 @ SY895 ) @ SV60 )
| ( member_a @ SY895 @ SV179 ) )
| ~ ( order_preorder_on_a @ SV179 @ SV60 )
| ( prefer1292084992ence_a @ SV179 @ SV60 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1176]) ).
thf(1296,plain,
! [SV394: a,SV356: a,SV278: a,SV180: set_Product_prod_a_a,SV61: set_a] :
( ( ~ ( prefer1292084992ence_a @ SV61 @ SV180 )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV356 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV278 ) @ SV180 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV394 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV356 ) @ SV180 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV394 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV278 ) @ SV180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1177]) ).
thf(1297,plain,
! [SV357: product_prod_a_a,SV279: product_prod_a_a,SV181: set_Pr1948701895od_a_a,SV62: set_Product_prod_a_a] :
( ( ( ~ ( prefer1338892073od_a_a @ SV62 @ SV181 ) )
= $true )
| ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV279 @ SV357 ) @ SV181 )
| ( member449909584od_a_a @ SV279 @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1178]) ).
thf(1298,plain,
! [SV358: product_prod_a_a > set_Product_prod_a_a,SV280: set_Product_prod_a_a,SV182: product_prod_a_a,SV63: product_prod_a_a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV63 @ SV182 ) @ ( produc304751368od_a_a @ SV280 @ SV358 ) ) )
= $true )
| ( ( member449909584od_a_a @ SV63 @ SV280 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1179]) ).
thf(1299,plain,
! [SV359: product_prod_a_a,SV281: a,SV183: a,SV64: a > a > $o] :
( ( ( ~ ( SV64 @ SV183 @ SV281 ) )
= $true )
| ( ( ( SV359
!= ( product_Pair_a_a @ SV183 @ SV281 ) )
| ( SV64 @ ( product_fst_a_a @ SV359 ) @ ( product_snd_a_a @ SV359 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1180]) ).
thf(1300,plain,
! [SV395: a > a,SV360: a,SV282: a,SV184: a > a,SV65: a] :
( ( ! [SY1181: set_a] :
( ( SV65
!= ( SV184 @ SV282 ) )
| ( SV360
!= ( SV395 @ SV282 ) )
| ~ ( member_a @ SV282 @ SY1181 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV65 @ SV360 ) @ ( bNF_Gr423046308_a_a_a @ SY1181 @ SV184 @ SV395 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1181]) ).
thf(1301,plain,
! [SV361: a > set_a,SV283: a,SV185: set_a,SV66: a] :
( ( ( ~ ( member_a @ SV66 @ SV185 ) )
= $true )
| ( ( ~ ( member_a @ SV283 @ ( SV361 @ SV66 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV66 @ SV283 ) @ ( product_Sigma_a_a @ SV185 @ SV361 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1182]) ).
thf(1302,plain,
! [SV362: a,SV284: a,SV186: a,SV67: a] :
( ( ( ( product_Pair_a_a @ SV67 @ SV186 )
!= ( product_Pair_a_a @ SV284 @ SV362 ) )
= $true )
| ( ( ~ ( ( SV67 != SV284 )
| ( SV186 != SV362 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1183]) ).
thf(1303,plain,
! [SV285: set_Product_prod_a_a,SV187: set_Product_prod_a_a,SV68: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV68 @ ( minus_1507102574od_a_a @ SV187 @ SV285 ) )
= $false )
| ( ( member449909584od_a_a @ SV68 @ SV187 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1184]) ).
thf(1304,plain,
! [SV286: set_Product_prod_a_a,SV188: set_Product_prod_a_a,SV69: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV69 @ ( minus_1507102574od_a_a @ SV188 @ SV286 ) )
= $false )
| ( ( ~ ( member449909584od_a_a @ SV69 @ SV286 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1185]) ).
thf(1305,plain,
! [SV70: set_Product_prod_a_a,SV189: set_Product_prod_a_a] :
( ( ( ! [SY1182: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK14_SY915 @ SV189 @ SV70 ) @ SY1182 ) @ SV70 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK14_SY915 @ SV189 @ SV70 ) @ SY1182 ) @ SV189 ) ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV70 @ SV189 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1186]) ).
thf(1306,plain,
! [SV287: a,SV190: a,SV71: product_prod_a_a > $o] :
( ( ( product_curry_a_a_o @ SV71 @ SV190 @ SV287 )
= $false )
| ( ( SV71 @ ( product_Pair_a_a @ SV190 @ SV287 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1187]) ).
thf(1307,plain,
! [SV363: a > set_a,SV288: set_a,SV191: a,SV72: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV72 @ SV191 ) @ ( product_Sigma_a_a @ SV288 @ SV363 ) ) )
= $true )
| ( ( member_a @ SV191 @ ( SV363 @ SV72 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1188]) ).
thf(1308,plain,
! [SV73: produc1921647824od_a_a] :
( ( SV73
!= ( produc1299253312od_a_a @ ( sK2_SY638 @ SV73 ) @ ( product_Pair_a_a @ ( sK6_SY1075 @ SV73 ) @ ( sK15_SY1150 @ SV73 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1189]) ).
thf(1309,plain,
! [SV364: a > a,SV289: set_a,SV192: a,SV74: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV74 @ SV192 ) @ ( bNF_Gr_a_a @ SV289 @ SV364 ) ) )
= $true )
| ( ( ( SV364 @ SV74 )
= SV192 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1190]) ).
thf(1310,plain,
! [SV365: a > set_a,SV290: set_a,SV193: a,SV75: a] :
( ( ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV75 @ SV193 ) @ ( product_Sigma_a_a @ SV290 @ SV365 ) )
| ~ ( ~ ( member_a @ SV75 @ SV290 )
| ~ ( member_a @ SV193 @ ( SV365 @ SV75 ) ) ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV75 @ SV193 ) @ ( product_Sigma_a_a @ SV290 @ SV365 ) )
| ~ ~ ( ~ ( member_a @ SV75 @ SV290 )
| ~ ( member_a @ SV193 @ ( SV365 @ SV75 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1191]) ).
thf(1311,plain,
! [SV365: a > set_a,SV290: set_a,SV193: a,SV75: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV75 @ SV193 ) @ ( product_Sigma_a_a @ SV290 @ SV365 ) )
= ( ~ ( ~ ( member_a @ SV75 @ SV290 )
| ~ ( member_a @ SV193 @ ( SV365 @ SV75 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1191]) ).
thf(1312,plain,
! [SV396: product_prod_a_a > product_prod_a_a,SV366: product_prod_a_a,SV291: product_prod_a_a,SV194: product_prod_a_a > product_prod_a_a,SV76: product_prod_a_a] :
( ( ! [SY1183: set_Product_prod_a_a] :
( ( SV76
!= ( SV194 @ SV291 ) )
| ( SV366
!= ( SV396 @ SV291 ) )
| ~ ( member449909584od_a_a @ SV291 @ SY1183 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV76 @ SV366 ) @ ( bNF_Gr200450189od_a_a @ SY1183 @ SV194 @ SV396 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1192]) ).
thf(1313,plain,
! [SV293: product_prod_a_a,SV196: set_Product_prod_a_a,SV78: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV78 @ SV196 )
= $false )
| ( ( ~ ( member449909584od_a_a @ SV293 @ SV78 )
| ( member449909584od_a_a @ SV293 @ SV196 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1194]) ).
thf(1314,plain,
! [SV397: a > a,SV368: a > a,SV294: set_Product_prod_a_a,SV197: a,SV79: a] :
( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV79 @ SV197 ) @ SV294 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV368 @ SV79 ) @ ( SV397 @ SV197 ) ) @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SV368 @ SV397 ) @ SV294 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1195]) ).
thf(1315,plain,
! [SV295: product_prod_a_a,SV198: set_Product_prod_a_a,SV80: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV80 @ SV198 )
= $false )
| ( ( ~ ( member449909584od_a_a @ SV295 @ SV80 )
| ( member449909584od_a_a @ SV295 @ SV198 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1196]) ).
thf(1316,plain,
! [SV296: set_Pr1948701895od_a_a,SV199: product_prod_a_a > produc1572603623od_a_a,SV81: set_Product_prod_a_a] :
( ( ( ! [SY1085: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1085 @ SV81 )
| ( member2057358096od_a_a @ ( SV199 @ SY1085 ) @ SV296 ) ) )
= $false )
| ( ( ord_le456379495od_a_a @ ( image_1765377413od_a_a @ SV199 @ SV81 ) @ SV296 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1197]) ).
thf(1317,plain,
! [SV297: a,SV200: a,SV82: product_prod_a_a] :
( ( ( SV82
= ( product_Pair_a_a @ SV200 @ SV297 ) )
= $false )
| ( ( ( product_snd_a_a @ SV82 )
= SV297 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1198]) ).
thf(1318,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ~ ( ( prefer1292084992ence_a @ SV201 @ SV369 )
| ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) )
| ~ ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 )
| ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1199]) ).
thf(1319,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( prefer1292084992ence_a @ SV201 @ SV369 )
= ( ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1199]) ).
thf(1320,plain,
! [SV370: product_prod_a_a > set_Product_prod_a_a,SV299: set_Product_prod_a_a,SV202: product_prod_a_a,SV84: product_prod_a_a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV84 @ SV202 ) @ ( produc304751368od_a_a @ SV299 @ SV370 ) ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ SV84 @ SV299 )
| ~ ( member449909584od_a_a @ SV202 @ ( SV370 @ SV84 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1200]) ).
thf(1321,plain,
! [SV300: product_prod_a_a > produc1572603623od_a_a,SV203: set_Product_prod_a_a,SV85: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV85 @ SV203 )
= $false )
| ( ( member2057358096od_a_a @ ( SV300 @ SV85 ) @ ( image_1765377413od_a_a @ SV300 @ SV203 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1201]) ).
thf(1322,plain,
! [SV371: product_prod_a_a > set_Product_prod_a_a,SV301: product_prod_a_a,SV204: set_Product_prod_a_a,SV86: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV86 @ SV204 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ SV301 @ ( SV371 @ SV86 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV86 @ SV301 ) @ ( produc304751368od_a_a @ SV204 @ SV371 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1202]) ).
thf(1323,plain,
! [SV302: a,SV205: a,SV87: a > a > $o] :
( ( ( SV87 @ SV205 @ SV302 )
= $false )
| ( ( SV87 @ ( product_snd_a_a @ ( product_Pair_a_a @ SV302 @ SV205 ) ) @ ( product_fst_a_a @ ( product_Pair_a_a @ SV302 @ SV205 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1203]) ).
thf(1324,plain,
! [SV372: product_prod_a_a > $o,SV303: product_prod_a_a > $o,SV206: set_Product_prod_a_a,SV88: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV88 @ SV206 ) )
= $true )
| ( ( ~ ! [SY1159: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1159 @ SV88 )
| ~ ( SV303 @ SY1159 )
| ( SV372 @ SY1159 ) )
| ( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [SY1094: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1094 @ SV88 )
| ~ ( SV303 @ SY1094 ) ) )
@ ( collec645855634od_a_a
@ ^ [SY1161: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1161 @ SV206 )
| ~ ( SV372 @ SY1161 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1204]) ).
thf(1325,plain,
! [SV373: product_prod_a_a > set_Product_prod_a_a,SV304: set_Product_prod_a_a,SV207: product_prod_a_a,SV89: product_prod_a_a] :
( ( ~ ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV89 @ SV207 ) @ ( produc304751368od_a_a @ SV304 @ SV373 ) )
| ~ ( ~ ( member449909584od_a_a @ SV89 @ SV304 )
| ~ ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) ) ) )
| ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV89 @ SV207 ) @ ( produc304751368od_a_a @ SV304 @ SV373 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ SV89 @ SV304 )
| ~ ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1205]) ).
thf(1326,plain,
! [SV373: product_prod_a_a > set_Product_prod_a_a,SV304: set_Product_prod_a_a,SV207: product_prod_a_a,SV89: product_prod_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV89 @ SV207 ) @ ( produc304751368od_a_a @ SV304 @ SV373 ) )
= ( ~ ( ~ ( member449909584od_a_a @ SV89 @ SV304 )
| ~ ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1205]) ).
thf(1327,plain,
! [SV90: produc1572603623od_a_a] :
( ( SV90
!= ( produc1474507607od_a_a @ ( sK3_SY691 @ SV90 ) @ ( product_Pair_a_a @ ( sK7_SY1097 @ SV90 ) @ ( sK16_SY1162 @ SV90 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1206]) ).
thf(1328,plain,
! [SV208: product_prod_a_a,SV91: a] :
( ( ( ( SV91
= ( product_snd_a_a @ SV208 ) )
| ~ ! [SY956: a] :
( SV208
!= ( product_Pair_a_a @ SY956 @ SV91 ) ) )
= $false )
| ( ( ~ ( ( SV91
!= ( product_snd_a_a @ SV208 ) )
| ~ ~ ! [SY956: a] :
( SV208
!= ( product_Pair_a_a @ SY956 @ SV91 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1207]) ).
thf(1329,plain,
! [SV374: set_Pr1948701895od_a_a,SV305: produc1572603623od_a_a,SV209: produc1572603623od_a_a > product_prod_a_a,SV92: product_prod_a_a] :
( ( ( SV92
!= ( SV209 @ SV305 ) )
= $true )
| ( ( ~ ( member2057358096od_a_a @ SV305 @ SV374 )
| ( member449909584od_a_a @ SV92 @ ( image_734753285od_a_a @ SV209 @ SV374 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1208]) ).
thf(1330,plain,
! [SV375: a,SV306: a > $o,SV210: a,SV93: a > $o] :
( ( ( ~ ( SV93 @ SV210 ) )
= $true )
| ( ( ~ ( SV306 @ SV375 )
| ~ ( ~ ( SV93 @ ( product_fst_a_a @ ( product_Pair_a_a @ SV210 @ SV375 ) ) )
| ~ ( SV306 @ ( product_snd_a_a @ ( product_Pair_a_a @ SV210 @ SV375 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1209]) ).
thf(1331,plain,
! [SV376: set_Product_prod_a_a,SV307: set_a,SV211: a,SV94: a] :
( ( ( ~ ( member_a @ SV94 @ ( prefer161218362good_a @ SV211 @ SV307 @ SV376 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV94 @ SV211 ) @ SV376 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1210]) ).
thf(1332,plain,
! [SV398: product_prod_a_a > a,SV377: a,SV308: product_prod_a_a,SV212: product_prod_a_a > a,SV95: a] :
( ( ! [SY1184: set_Product_prod_a_a] :
( ( SV95
!= ( SV212 @ SV308 ) )
| ( SV377
!= ( SV398 @ SV308 ) )
| ~ ( member449909584od_a_a @ SV308 @ SY1184 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV95 @ SV377 ) @ ( bNF_Gr1853143117_a_a_a @ SY1184 @ SV212 @ SV398 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1211]) ).
thf(1333,plain,
! [SV378: product_prod_a_a > product_prod_a_a,SV309: set_Product_prod_a_a,SV213: product_prod_a_a,SV96: product_prod_a_a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV96 @ SV213 ) @ ( bNF_Gr1372473186od_a_a @ SV309 @ SV378 ) ) )
= $true )
| ( ( member449909584od_a_a @ SV96 @ SV309 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1212]) ).
thf(1334,plain,
! [SV379: set_a,SV214: a] :
( ( ! [SV399: set_Product_prod_a_a] :
( ( prefer436369274d_as_a @ SV214 @ SV379 @ SV399 )
= ( collect_a
@ ^ [SY1185: a] :
~ ( ~ ~ ( ~ ( member_a @ SY1185 @ SV379 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV214 @ SY1185 ) @ SV399 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1185 @ SV214 ) @ SV399 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1213]) ).
thf(1335,plain,
! [SV379: set_a,SV214: a] :
( ( ( prefer436369274d_as_a @ SV214 @ SV379 )
= ( ^ [SY1165: set_Product_prod_a_a] :
( collect_a
@ ^ [SY1166: a] :
~ ( ~ ~ ( ~ ( member_a @ SY1166 @ SV379 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV214 @ SY1166 ) @ SY1165 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1166 @ SV214 ) @ SY1165 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1213]) ).
thf(1336,plain,
! [SV98: product_prod_a_a] :
( ( SV98
= ( product_Pair_a_a @ ( sK4_SY716 @ SV98 ) @ ( sK8_SY1108 @ SV98 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1214]) ).
thf(1337,plain,
! [SV311: set_Product_prod_a_a,SV215: product_prod_a_a > a,SV99: a] :
( ( ( member_a @ SV99 @ ( image_340790172_a_a_a @ SV215 @ SV311 ) )
= $false )
| ( ( ~ ! [SY1109: product_prod_a_a] :
( ( SV99
!= ( SV215 @ SY1109 ) )
| ~ ( member449909584od_a_a @ SY1109 @ SV311 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1215]) ).
thf(1338,plain,
! [SV216: product_prod_a_a,SV100: product_prod_a_a > $o] :
( ( ( ! [SY1186: a] : ( SV100 @ ( product_Pair_a_a @ ( sK17_SY722 @ SV216 @ SV100 ) @ SY1186 ) ) )
= $false )
| ( ( SV100 @ SV216 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1216]) ).
thf(1339,plain,
! [SV380: set_Product_prod_a_a,SV312: a > a,SV217: a > a,SV101: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV101 @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SV217 @ SV312 ) @ SV380 ) ) )
= $true )
| ( ( ~ ! [SY1167: a,SY1168: a] :
( ( SV101
!= ( product_Pair_a_a @ ( SV217 @ SY1167 ) @ ( SV312 @ SY1168 ) ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1167 @ SY1168 ) @ SV380 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1217]) ).
thf(1340,plain,
! [SV381: set_a,SV218: a] :
( ( ! [SV400: set_Product_prod_a_a] :
( ( prefer1676310729than_a @ SV218 @ SV381 @ SV400 )
= ( collect_a
@ ^ [SY1187: a] :
~ ( ~ ( member_a @ SY1187 @ SV381 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV218 @ SY1187 ) @ SV400 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1218]) ).
thf(1341,plain,
! [SV381: set_a,SV218: a] :
( ( ( prefer1676310729than_a @ SV218 @ SV381 )
= ( ^ [SY1169: set_Product_prod_a_a] :
( collect_a
@ ^ [SY1170: a] :
~ ( ~ ( member_a @ SY1170 @ SV381 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV218 @ SY1170 ) @ SY1169 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1218]) ).
thf(1342,plain,
! [SV382: a > a,SV314: set_a,SV219: a,SV103: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV103 @ SV219 ) @ ( bNF_Gr_a_a @ SV314 @ SV382 ) ) )
= $true )
| ( ( member_a @ SV103 @ SV314 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1219]) ).
thf(1343,plain,
! [SV401: a > set_Product_prod_a_a,SV383: a,SV315: a,SV220: a,SV104: a > $o] :
( ( ~ ( SV104 @ SV220 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV315 @ SV383 ) @ ( SV401 @ SV220 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV220 @ SV315 ) @ ( product_Pair_a_a @ SV220 @ SV383 ) ) @ ( same_fst_a_a @ SV104 @ SV401 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1220]) ).
thf(1344,plain,
! [SV221: product_prod_a_a,SV105: product_prod_a_a > $o] :
( ( ( ! [SY1188: a] : ( SV105 @ ( product_Pair_a_a @ ( sK18_SY740 @ SV221 @ SV105 ) @ SY1188 ) ) )
= $false )
| ( ( SV105 @ SV221 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1221]) ).
thf(1345,plain,
! [SV384: set_Product_prod_a_a,SV316: product_prod_a_a,SV222: product_prod_a_a > a,SV106: a] :
( ( ( SV106
!= ( SV222 @ SV316 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ SV316 @ SV384 )
| ( member_a @ SV106 @ ( image_340790172_a_a_a @ SV222 @ SV384 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1222]) ).
thf(1346,plain,
! [SV317: a,SV223: a,SV107: a] :
( ( ( ( product_snd_a_a @ ( product_Pair_a_a @ SV107 @ SV223 ) )
= SV317 )
= $false )
| ( ( SV223 = SV317 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1223]) ).
thf(1347,plain,
! [SV318: a,SV224: a,SV108: product_prod_a_a > $o] :
( ( ( product_curry_a_a_o @ SV108 @ SV224 @ SV318 )
= $false )
| ( ( SV108 @ ( product_Pair_a_a @ SV224 @ SV318 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1224]) ).
thf(1348,plain,
! [SV109: product_prod_a_a] :
( ( ! [SY1119: a] :
( SV109
!= ( product_Pair_a_a @ ( sK5_SY749 @ SV109 ) @ SY1119 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1225]) ).
thf(1349,plain,
! [SV385: set_Product_prod_a_a,SV319: product_prod_a_a,SV225: product_prod_a_a > product_prod_a_a,SV110: product_prod_a_a] :
( ( ( SV110
!= ( SV225 @ SV319 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ SV319 @ SV385 )
| ( member449909584od_a_a @ SV110 @ ( image_794773445od_a_a @ SV225 @ SV385 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1226]) ).
thf(1350,plain,
! [SV320: product_prod_a_a > set_Product_prod_a_a,SV226: set_Product_prod_a_a,SV111: produc1572603623od_a_a] :
( ( ( member2057358096od_a_a @ SV111 @ ( produc304751368od_a_a @ SV226 @ SV320 ) )
= $false )
| ( ( ~ ! [SY1121: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1121 @ SV226 )
| ! [SY1122: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1122 @ ( SV320 @ SY1121 ) )
| ( SV111
!= ( produc1474507607od_a_a @ SY1121 @ SY1122 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1227]) ).
thf(1351,plain,
! [SV321: product_prod_a_a > a,SV227: set_Product_prod_a_a,SV112: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV112 @ SV227 )
= $false )
| ( ( member_a @ ( SV321 @ SV112 ) @ ( image_340790172_a_a_a @ SV321 @ SV227 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1228]) ).
thf(1352,plain,
! [SV386: product_prod_a_a > product_prod_a_a,SV322: product_prod_a_a,SV228: set_Product_prod_a_a,SV113: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV113 @ SV228 ) )
= $true )
| ( ( ( SV322
!= ( SV386 @ SV113 ) )
| ( member449909584od_a_a @ SV322 @ ( image_794773445od_a_a @ SV386 @ SV228 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1229]) ).
thf(1353,plain,
! [SV323: set_a,SV229: a > product_prod_a_a,SV114: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV114 @ ( image_1725938350od_a_a @ SV229 @ SV323 ) )
= $false )
| ( ( ~ ! [SY1124: a] :
( ( SV114
!= ( SV229 @ SY1124 ) )
| ~ ( member_a @ SY1124 @ SV323 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1230]) ).
thf(1354,plain,
! [SV324: product_prod_a_a > product_prod_a_a,SV230: set_Product_prod_a_a,SV115: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV115 @ SV230 )
= $false )
| ( ( member449909584od_a_a @ ( SV324 @ SV115 ) @ ( image_794773445od_a_a @ SV324 @ SV230 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1231]) ).
thf(1355,plain,
! [SV402: produc1572603623od_a_a > a,SV387: a,SV325: produc1572603623od_a_a,SV231: produc1572603623od_a_a > a,SV116: a] :
( ( ! [SY1189: set_Pr1948701895od_a_a] :
( ( SV116
!= ( SV231 @ SV325 ) )
| ( SV387
!= ( SV402 @ SV325 ) )
| ~ ( member2057358096od_a_a @ SV325 @ SY1189 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV116 @ SV387 ) @ ( bNF_Gr356189709_a_a_a @ SY1189 @ SV231 @ SV402 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1232]) ).
thf(1356,plain,
! [SV388: set_Pr1948701895od_a_a,SV326: set_Product_prod_a_a,SV232: product_prod_a_a,SV118: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV118 @ ( prefer477097315od_a_a @ SV232 @ SV326 @ SV388 ) ) )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV118 @ SV232 ) @ SV388 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1234]) ).
thf(1357,plain,
! [SV327: a > set_a,SV233: set_a,SV119: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV119 @ ( product_Sigma_a_a @ SV233 @ SV327 ) )
= $false )
| ( ( ~ ! [SY1129: a] :
( ~ ( member_a @ SY1129 @ SV233 )
| ! [SY1130: a] :
( ~ ( member_a @ SY1130 @ ( SV327 @ SY1129 ) )
| ( SV119
!= ( product_Pair_a_a @ SY1129 @ SY1130 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1235]) ).
thf(1358,plain,
! [SV389: product_prod_a_a > $o,SV328: set_Product_prod_a_a,SV234: set_Product_prod_a_a,SV120: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV120 @ SV234 ) )
= $true )
| ( ( ~ ( ord_le1824328871od_a_a @ SV234
@ ( collec645855634od_a_a
@ ^ [SY1174: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1174 @ SV328 )
| ~ ( SV389 @ SY1174 ) ) ) )
| ( SV389 @ SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1236]) ).
thf(1359,plain,
! [SV329: a,SV235: a,SV121: product_prod_a_a] :
( ( ( SV121
= ( product_Pair_a_a @ SV235 @ SV329 ) )
= $false )
| ( ( ( product_fst_a_a @ SV121 )
= SV235 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1237]) ).
thf(1360,plain,
! [SV330: set_a,SV236: product_prod_a_a > a,SV122: set_Product_prod_a_a] :
( ( ( ! [SY1133: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1133 @ SV122 )
| ( member_a @ ( SV236 @ SY1133 ) @ SV330 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( image_340790172_a_a_a @ SV236 @ SV122 ) @ SV330 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1238]) ).
thf(1361,plain,
! [SV403: set_Product_prod_a_a,SV390: a,SV331: a,SV237: a,SV123: a] :
( ( ! [SY1190: set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SV331 @ SV390 ) ) @ ( lex_prod_a_a @ SV403 @ SY1190 ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
| ~ ( ( SV123 != SV331 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SY1190 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1239]) ).
thf(1362,plain,
! [SV124: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( sK10_SY795 @ SV124 ) @ SV124 )
= $true )
| ( ( SV124 = bot_bo2131659635od_a_a )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1240]) ).
thf(1363,plain,
! [SV238: product_prod_a_a,SV125: a] :
( ( ( ( SV125
= ( product_fst_a_a @ SV238 ) )
| ~ ! [SY1024: a] :
( SV238
!= ( product_Pair_a_a @ SV125 @ SY1024 ) ) )
= $false )
| ( ( ~ ( ( SV125
!= ( product_fst_a_a @ SV238 ) )
| ~ ~ ! [SY1024: a] :
( SV238
!= ( product_Pair_a_a @ SV125 @ SY1024 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1241]) ).
thf(1364,plain,
! [SV332: set_Product_prod_a_a,SV239: set_Product_prod_a_a,SV126: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV126 @ SV239 )
= $false )
| ( ( ~ ~ ( member449909584od_a_a @ SV126 @ SV332 )
| ( member449909584od_a_a @ SV126 @ ( minus_1507102574od_a_a @ SV239 @ SV332 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1242]) ).
thf(1365,plain,
! [SV391: a > set_a,SV333: set_a,SV240: a,SV127: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV127 @ SV240 ) @ ( product_Sigma_a_a @ SV333 @ SV391 ) ) )
= $true )
| ( ( ~ ( ~ ( member_a @ SV127 @ SV333 )
| ~ ( member_a @ SV240 @ ( SV391 @ SV127 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1243]) ).
thf(1366,plain,
! [SV334: a,SV241: a,SV128: a] :
( ( ( ( product_fst_a_a @ ( product_Pair_a_a @ SV128 @ SV241 ) )
= SV334 )
= $false )
| ( ( SV128 = SV334 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1244]) ).
thf(1367,plain,
! [SV392: product_prod_a_a > set_Product_prod_a_a,SV335: set_Product_prod_a_a,SV242: product_prod_a_a,SV129: product_prod_a_a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV129 @ SV242 ) @ ( produc304751368od_a_a @ SV335 @ SV392 ) ) )
= $true )
| ( ( member449909584od_a_a @ SV242 @ ( SV392 @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1245]) ).
thf(1368,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $false )
| ( ( ~ ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
!= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
| ( SV2 != SV131 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1246]) ).
thf(1369,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( SV2 = SV131 )
= $false )
| ( ( ~ ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
!= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
| ( SV2 != SV131 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1246]) ).
thf(1370,plain,
! [SV243: set_Product_prod_a_a,SV132: a,SV3: a] :
( ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV3 @ SV132 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV243 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV132 @ SV3 ) @ SV243 ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV3 @ SV132 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV243 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV132 @ SV3 ) @ SV243 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1247]) ).
thf(1371,plain,
! [SV133: product_prod_a_a > $o,SV4: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV4 @ ( collec645855634od_a_a @ SV133 ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ SV4 @ ( collec645855634od_a_a @ SV133 ) )
| ~ ( SV133 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1248]) ).
thf(1372,plain,
! [SV4: product_prod_a_a,SV133: product_prod_a_a > $o] :
( ( ( SV133 @ SV4 )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ SV4 @ ( collec645855634od_a_a @ SV133 ) )
| ~ ( SV133 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1248]) ).
thf(1373,plain,
! [SV138: product_prod_a_a] :
( ( ( top_to1483957574_a_a_o @ SV138 )
= $false )
| ( ( ~ ( ~ ( top_to1483957574_a_a_o @ SV138 )
| ~ ( member449909584od_a_a @ SV138 @ top_to398455383od_a_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1249]) ).
thf(1374,plain,
! [SV138: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV138 @ top_to398455383od_a_a )
= $false )
| ( ( ~ ( ~ ( top_to1483957574_a_a_o @ SV138 )
| ~ ( member449909584od_a_a @ SV138 @ top_to398455383od_a_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1249]) ).
thf(1375,plain,
! [SV340: a,SV140: a] :
( ( ( ~ ( ( top_top_a_a_o @ SV140 @ SV340 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV140 @ SV340 ) @ top_to398455383od_a_a ) ) )
= $true )
| ( ( ~ ( ~ ( top_top_a_a_o @ SV140 @ SV340 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV140 @ SV340 ) @ top_to398455383od_a_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1250]) ).
thf(1376,plain,
! [SV249: set_a,SV143: set_a,SV20: product_prod_a_a] :
( ( ( ( member449909584od_a_a @ SV20 @ ( product_product_a_a @ SV143 @ SV249 ) )
| ( member449909584od_a_a @ SV20
@ ( product_Sigma_a_a @ SV143
@ ^ [SY1036: a] : SV249 ) ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ SV20 @ ( product_product_a_a @ SV143 @ SV249 ) )
| ~ ( member449909584od_a_a @ SV20
@ ( product_Sigma_a_a @ SV143
@ ^ [SY1036: a] : SV249 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1252]) ).
thf(1377,plain,
! [SV144: set_Product_prod_a_a,SV21: set_Product_prod_a_a] :
( ( ( ord_le1347718902_a_a_o
@ ^ [SY498: product_prod_a_a] : ( member449909584od_a_a @ SY498 @ SV21 )
@ ^ [SY826: product_prod_a_a] : ( member449909584od_a_a @ SY826 @ SV144 ) )
= $false )
| ( ( ~ ( ~ ( ord_le1347718902_a_a_o
@ ^ [SY498: product_prod_a_a] : ( member449909584od_a_a @ SY498 @ SV21 )
@ ^ [SY826: product_prod_a_a] : ( member449909584od_a_a @ SY826 @ SV144 ) )
| ~ ( ord_le1824328871od_a_a @ SV21 @ SV144 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1253]) ).
thf(1378,plain,
! [SV144: set_Product_prod_a_a,SV21: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV21 @ SV144 )
= $false )
| ( ( ~ ( ~ ( ord_le1347718902_a_a_o
@ ^ [SY498: product_prod_a_a] : ( member449909584od_a_a @ SY498 @ SV21 )
@ ^ [SY826: product_prod_a_a] : ( member449909584od_a_a @ SY826 @ SV144 ) )
| ~ ( ord_le1824328871od_a_a @ SV21 @ SV144 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1253]) ).
thf(1379,plain,
! [SV341: set_Product_prod_a_a,SV145: set_Product_prod_a_a] :
( ( ( ~ ( ( ord_le1824328871od_a_a @ SV145 @ SV341 )
| ( ord_le1347718902_a_a_o
@ ^ [SY828: product_prod_a_a] : ( member449909584od_a_a @ SY828 @ SV145 )
@ ^ [SY1142: product_prod_a_a] : ( member449909584od_a_a @ SY1142 @ SV341 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV145 @ SV341 )
| ~ ( ord_le1347718902_a_a_o
@ ^ [SY828: product_prod_a_a] : ( member449909584od_a_a @ SY828 @ SV145 )
@ ^ [SY1142: product_prod_a_a] : ( member449909584od_a_a @ SY1142 @ SV341 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1254]) ).
thf(1380,plain,
! [SV146: set_Product_prod_a_a,SV23: set_Product_prod_a_a] :
( ( ( ord_less_eq_a_a_o
@ ^ [SY504: a,SY505: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY504 @ SY505 ) @ SV23 )
@ ^ [SY832: a,SY833: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY832 @ SY833 ) @ SV146 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_a_a_o
@ ^ [SY504: a,SY505: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY504 @ SY505 ) @ SV23 )
@ ^ [SY832: a,SY833: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY832 @ SY833 ) @ SV146 ) )
| ~ ( ord_le1824328871od_a_a @ SV23 @ SV146 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1256]) ).
thf(1381,plain,
! [SV146: set_Product_prod_a_a,SV23: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV23 @ SV146 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_a_a_o
@ ^ [SY504: a,SY505: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY504 @ SY505 ) @ SV23 )
@ ^ [SY832: a,SY833: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY832 @ SY833 ) @ SV146 ) )
| ~ ( ord_le1824328871od_a_a @ SV23 @ SV146 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1256]) ).
thf(1382,plain,
! [SV24: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK19_SY508 @ SV24 ) @ SV24 ) )
= $false )
| ( ( ~ ( ~ ! [SY508: product_prod_a_a] :
~ ( member449909584od_a_a @ SY508 @ SV24 )
| ( SV24 != bot_bo2131659635od_a_a ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1257]) ).
thf(1383,plain,
! [SV24: set_Product_prod_a_a] :
( ( ( ~ ! [SY508: product_prod_a_a] :
~ ( member449909584od_a_a @ SY508 @ SV24 )
| ( SV24 != bot_bo2131659635od_a_a ) )
= $false )
| ( ( SV24 = bot_bo2131659635od_a_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1258]) ).
thf(1384,plain,
! [SV28: set_Product_prod_a_a,SV148: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK11_SY834 @ SV148 @ SV28 ) @ SV28 ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV28 @ SV148 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1260]) ).
thf(1385,plain,
! [SV28: set_Product_prod_a_a,SV148: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( sK11_SY834 @ SV148 @ SV28 ) @ SV148 )
= $false )
| ( ( ord_le1824328871od_a_a @ SV28 @ SV148 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1260]) ).
thf(1386,plain,
! [SV342: set_Product_prod_a_a,SV251: product_prod_a_a,SV149: product_prod_a_a > produc1572603623od_a_a,SV29: produc1572603623od_a_a] :
( ( ( SV29
= ( SV149 @ SV251 ) )
= $false )
| ( ( ~ ( member449909584od_a_a @ SV251 @ SV342 )
| ( member2057358096od_a_a @ SV29 @ ( image_1765377413od_a_a @ SV149 @ SV342 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1261]) ).
thf(1387,plain,
! [SV343: a,SV252: a,SV150: a,SV30: a] :
( ( ( ~ ( ( ( product_Pair_a_a @ SV30 @ SV150 )
= ( product_Pair_a_a @ SV252 @ SV343 ) )
| ~ ( ( SV30 != SV252 )
| ( SV150 != SV343 ) ) ) )
= $true )
| ( ( ~ ( ( ( product_Pair_a_a @ SV30 @ SV150 )
!= ( product_Pair_a_a @ SV252 @ SV343 ) )
| ~ ~ ( ( SV30 != SV252 )
| ( SV150 != SV343 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1262]) ).
thf(1388,plain,
! [SV344: product_prod_a_a > produc1572603623od_a_a,SV253: produc1572603623od_a_a,SV151: set_Product_prod_a_a,SV31: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV31 @ SV151 )
= $false )
| ( ( ( SV253
!= ( SV344 @ SV31 ) )
| ( member2057358096od_a_a @ SV253 @ ( image_1765377413od_a_a @ SV344 @ SV151 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1264]) ).
thf(1389,plain,
! [SV32: set_Product_prod_a_a,SV152: product_prod_a_a > product_prod_a_a,SV254: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK20_SY1042 @ SV254 @ SV152 @ SV32 ) @ SV32 )
| ( member449909584od_a_a @ ( SV152 @ ( sK20_SY1042 @ SV254 @ SV152 @ SV32 ) ) @ SV254 ) )
= $false )
| ( ( ord_le1824328871od_a_a @ ( image_794773445od_a_a @ SV152 @ SV32 ) @ SV254 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1265]) ).
thf(1390,plain,
! [SV255: set_Product_prod_a_a,SV153: set_Product_prod_a_a,SV33: product_prod_a_a] :
( ( ( ( member449909584od_a_a @ SV33 @ ( minus_1507102574od_a_a @ SV153 @ SV255 ) )
| ~ ( ~ ( member449909584od_a_a @ SV33 @ SV153 )
| ~ ~ ( member449909584od_a_a @ SV33 @ SV255 ) ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ SV33 @ ( minus_1507102574od_a_a @ SV153 @ SV255 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ SV33 @ SV153 )
| ~ ~ ( member449909584od_a_a @ SV33 @ SV255 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1266]) ).
thf(1391,plain,
! [SV34: set_a,SV154: a > product_prod_a_a,SV256: set_Product_prod_a_a] :
( ( ( ~ ( member_a @ ( sK21_SY1043 @ SV256 @ SV154 @ SV34 ) @ SV34 )
| ( member449909584od_a_a @ ( SV154 @ ( sK21_SY1043 @ SV256 @ SV154 @ SV34 ) ) @ SV256 ) )
= $false )
| ( ( ord_le1824328871od_a_a @ ( image_1725938350od_a_a @ SV154 @ SV34 ) @ SV256 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1267]) ).
thf(1392,plain,
! [SV345: set_Product_prod_a_a,SV155: set_Product_prod_a_a] :
( ( ( ~ ( ( ord_le1824328871od_a_a @ SV155 @ SV345 )
| ! [SY1143: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1143 @ SV155 )
| ( member449909584od_a_a @ SY1143 @ SV345 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV155 @ SV345 )
| ~ ! [SY1143: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1143 @ SV155 )
| ( member449909584od_a_a @ SY1143 @ SV345 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1268]) ).
thf(1393,plain,
! [SV36: set_Product_prod_a_a] :
( ( ( ! [SY531: product_prod_a_a] :
~ ( member449909584od_a_a @ SY531 @ SV36 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY531: product_prod_a_a] :
~ ( member449909584od_a_a @ SY531 @ SV36 )
| ~ ( ( SV36 != bot_bo2131659635od_a_a ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1270]) ).
thf(1394,plain,
! [SV36: set_Product_prod_a_a] :
( ( ( SV36 = bot_bo2131659635od_a_a )
= $true )
| ( ( ~ ( ~ ~ ! [SY531: product_prod_a_a] :
~ ( member449909584od_a_a @ SY531 @ SV36 )
| ~ ( ( SV36 != bot_bo2131659635od_a_a ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1271]) ).
thf(1395,plain,
! [SV156: produc1572603623od_a_a,SV37: produc1572603623od_a_a > $o] :
( ( ( ! [SY1191: a] : ( SV37 @ ( produc1474507607od_a_a @ ( sK12_SY533 @ SV156 @ SV37 ) @ ( product_Pair_a_a @ ( sK22_SY1177 @ SV156 @ SV37 ) @ SY1191 ) ) ) )
= $false )
| ( ( SV37 @ SV156 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1272]) ).
thf(1396,plain,
! [SV258: set_Product_prod_a_a,SV158: product_prod_a_a > produc1572603623od_a_a,SV39: produc1572603623od_a_a] :
( ( ( ! [SY1045: product_prod_a_a] :
( ( SV39
!= ( SV158 @ SY1045 ) )
| ~ ( member449909584od_a_a @ SY1045 @ SV258 ) ) )
= $false )
| ( ( member2057358096od_a_a @ SV39 @ ( image_1765377413od_a_a @ SV158 @ SV258 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1273]) ).
thf(1397,plain,
! [SV346: set_a,SV259: a,SV159: a > product_prod_a_a,SV40: product_prod_a_a] :
( ( ( SV40
= ( SV159 @ SV259 ) )
= $false )
| ( ( ~ ( member_a @ SV259 @ SV346 )
| ( member449909584od_a_a @ SV40 @ ( image_1725938350od_a_a @ SV159 @ SV346 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1274]) ).
thf(1398,plain,
! [SV260: set_Product_prod_a_a,SV161: product_prod_a_a > product_prod_a_a,SV42: product_prod_a_a] :
( ( ( ! [SY1047: product_prod_a_a] :
( ( SV42
!= ( SV161 @ SY1047 ) )
| ~ ( member449909584od_a_a @ SY1047 @ SV260 ) ) )
= $false )
| ( ( member449909584od_a_a @ SV42 @ ( image_794773445od_a_a @ SV161 @ SV260 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1275]) ).
thf(1399,plain,
! [SV347: set_Product_prod_a_a,SV162: set_Product_prod_a_a] :
( ( ( ~ ( ( ord_le1824328871od_a_a @ SV162 @ SV347 )
| ! [SY1144: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1144 @ SV162 )
| ( member449909584od_a_a @ SY1144 @ SV347 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV162 @ SV347 )
| ~ ! [SY1144: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1144 @ SV162 )
| ( member449909584od_a_a @ SY1144 @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1276]) ).
thf(1400,plain,
! [SV263: set_Product_prod_a_a,SV164: set_Product_prod_a_a,SV45: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV45 @ SV164 )
| ( member449909584od_a_a @ SV45 @ SV263 ) )
= $false )
| ( ( member449909584od_a_a @ SV45 @ ( minus_1507102574od_a_a @ SV164 @ SV263 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1279]) ).
thf(1401,plain,
! [SV264: product_prod_a_a > $o,SV165: set_Product_prod_a_a,SV46: set_Product_prod_a_a] :
( ( ( ~ ( ( ord_le1824328871od_a_a @ SV46
@ ( collec645855634od_a_a
@ ^ [SY1049: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1049 @ SV165 )
| ~ ( SV264 @ SY1049 ) ) ) )
| ! [SY1050: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1050 @ SV46 )
| ( SV264 @ SY1050 ) ) )
| ~ ( ~ ( ord_le1824328871od_a_a @ SV46
@ ( collec645855634od_a_a
@ ^ [SY1049: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1049 @ SV165 )
| ~ ( SV264 @ SY1049 ) ) ) )
| ~ ! [SY1050: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1050 @ SV46 )
| ( SV264 @ SY1050 ) ) ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV46 @ SV165 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1280]) ).
thf(1402,plain,
! [SV264: product_prod_a_a > $o,SV165: set_Product_prod_a_a,SV46: set_Product_prod_a_a] :
( ( ( ( ord_le1824328871od_a_a @ SV46
@ ( collec645855634od_a_a
@ ^ [SY1049: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1049 @ SV165 )
| ~ ( SV264 @ SY1049 ) ) ) )
= ( ! [SY1050: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1050 @ SV46 )
| ( SV264 @ SY1050 ) ) ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV46 @ SV165 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1280]) ).
thf(1403,plain,
! [SV404: set_Product_prod_a_a,SV348: set_a,SV166: a] :
( ( ( prefer161218362good_a @ SV166 @ SV348 @ SV404 )
= ( collect_a
@ ^ [SY1192: a] :
~ ( ~ ( member_a @ SY1192 @ SV348 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1192 @ SV166 ) @ SV404 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1281]) ).
thf(1404,plain,
! [SV266: set_Pr1948701895od_a_a,SV167: produc1572603623od_a_a > product_prod_a_a,SV48: product_prod_a_a] :
( ( ( ! [SY1053: produc1572603623od_a_a] :
( ( SV48
!= ( SV167 @ SY1053 ) )
| ~ ( member2057358096od_a_a @ SY1053 @ SV266 ) ) )
= $false )
| ( ( member449909584od_a_a @ SV48 @ ( image_734753285od_a_a @ SV167 @ SV266 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1283]) ).
thf(1405,plain,
! [SV349: a,SV267: a,SV168: set_Product_prod_a_a,SV49: set_a] :
( ( ( prefer1292084992ence_a @ SV49 @ SV168 )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV267 @ SV349 ) @ SV168 )
| ( member_a @ SV267 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1284]) ).
thf(1406,plain,
! [SV350: a > product_prod_a_a,SV269: product_prod_a_a,SV170: set_a,SV51: a] :
( ( ( member_a @ SV51 @ SV170 )
= $false )
| ( ( ( SV269
!= ( SV350 @ SV51 ) )
| ( member449909584od_a_a @ SV269 @ ( image_1725938350od_a_a @ SV350 @ SV170 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1286]) ).
thf(1407,plain,
! [SV351: a > set_a,SV270: set_a,SV171: a,SV52: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV171 ) @ ( product_Sigma_a_a @ SV270 @ SV351 ) )
= $false )
| ( ( member_a @ SV52 @ SV270 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1287]) ).
thf(1408,plain,
! [SV352: produc1572603623od_a_a > product_prod_a_a,SV271: product_prod_a_a,SV172: set_Pr1948701895od_a_a,SV53: produc1572603623od_a_a] :
( ( ( member2057358096od_a_a @ SV53 @ SV172 )
= $false )
| ( ( ( SV271
!= ( SV352 @ SV53 ) )
| ( member449909584od_a_a @ SV271 @ ( image_734753285od_a_a @ SV352 @ SV172 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1288]) ).
thf(1409,plain,
! [SV353: a,SV274: set_Product_prod_a_a,SV175: a,SV56: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV56 @ SV175 ) @ SV274 )
= $false )
| ( ( ( SV353 != SV175 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV56 @ SV353 ) @ SV274 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1290]) ).
thf(1410,plain,
! [SV354: a,SV275: a,SV176: a,SV57: a] :
( ( ( ~ ( ( ( product_Pair_a_a @ SV57 @ SV176 )
= ( product_Pair_a_a @ SV275 @ SV354 ) )
| ~ ( ( SV57 != SV275 )
| ( SV176 != SV354 ) ) ) )
= $true )
| ( ( ~ ( ( ( product_Pair_a_a @ SV57 @ SV176 )
!= ( product_Pair_a_a @ SV275 @ SV354 ) )
| ~ ~ ( ( SV57 != SV275 )
| ( SV176 != SV354 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1291]) ).
thf(1411,plain,
! [SV355: product_prod_a_a > a,SV276: a,SV177: set_Product_prod_a_a,SV58: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV58 @ SV177 )
= $false )
| ( ( ( SV276
!= ( SV355 @ SV58 ) )
| ( member_a @ SV276 @ ( image_340790172_a_a_a @ SV355 @ SV177 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1293]) ).
thf(1412,plain,
! [SV59: set_Pr1948701895od_a_a,SV178: produc1572603623od_a_a > product_prod_a_a,SV277: set_Product_prod_a_a] :
( ( ( ~ ( member2057358096od_a_a @ ( sK23_SY1063 @ SV277 @ SV178 @ SV59 ) @ SV59 )
| ( member449909584od_a_a @ ( SV178 @ ( sK23_SY1063 @ SV277 @ SV178 @ SV59 ) ) @ SV277 ) )
= $false )
| ( ( ord_le1824328871od_a_a @ ( image_734753285od_a_a @ SV178 @ SV59 ) @ SV277 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1294]) ).
thf(1413,plain,
! [SV60: set_Product_prod_a_a,SV179: set_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK13_SY892 @ SV179 @ SV60 ) @ ( sK24_SY1180 @ SV60 @ SV179 ) ) @ SV60 )
| ( member_a @ ( sK13_SY892 @ SV179 @ SV60 ) @ SV179 ) )
= $false )
| ( ( ~ ! [SY894: a,SY895: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY894 @ SY895 ) @ SV60 )
| ( member_a @ SY895 @ SV179 ) )
| ~ ( order_preorder_on_a @ SV179 @ SV60 )
| ( prefer1292084992ence_a @ SV179 @ SV60 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1295]) ).
thf(1414,plain,
! [SV394: a,SV356: a,SV278: a,SV180: set_Product_prod_a_a,SV61: set_a] :
( ( ( ~ ( prefer1292084992ence_a @ SV61 @ SV180 ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV356 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV278 ) @ SV180 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV394 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV356 ) @ SV180 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV394 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV278 ) @ SV180 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1296]) ).
thf(1415,plain,
! [SV357: product_prod_a_a,SV279: product_prod_a_a,SV181: set_Pr1948701895od_a_a,SV62: set_Product_prod_a_a] :
( ( ( prefer1338892073od_a_a @ SV62 @ SV181 )
= $false )
| ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV279 @ SV357 ) @ SV181 )
| ( member449909584od_a_a @ SV279 @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1297]) ).
thf(1416,plain,
! [SV358: product_prod_a_a > set_Product_prod_a_a,SV280: set_Product_prod_a_a,SV182: product_prod_a_a,SV63: product_prod_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV63 @ SV182 ) @ ( produc304751368od_a_a @ SV280 @ SV358 ) )
= $false )
| ( ( member449909584od_a_a @ SV63 @ SV280 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1298]) ).
thf(1417,plain,
! [SV359: product_prod_a_a,SV281: a,SV183: a,SV64: a > a > $o] :
( ( ( SV64 @ SV183 @ SV281 )
= $false )
| ( ( ( SV359
!= ( product_Pair_a_a @ SV183 @ SV281 ) )
| ( SV64 @ ( product_fst_a_a @ SV359 ) @ ( product_snd_a_a @ SV359 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1299]) ).
thf(1418,plain,
! [SV405: set_a,SV395: a > a,SV360: a,SV282: a,SV184: a > a,SV65: a] :
( ( ( SV65
!= ( SV184 @ SV282 ) )
| ( SV360
!= ( SV395 @ SV282 ) )
| ~ ( member_a @ SV282 @ SV405 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV65 @ SV360 ) @ ( bNF_Gr423046308_a_a_a @ SV405 @ SV184 @ SV395 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1300]) ).
thf(1419,plain,
! [SV361: a > set_a,SV283: a,SV185: set_a,SV66: a] :
( ( ( member_a @ SV66 @ SV185 )
= $false )
| ( ( ~ ( member_a @ SV283 @ ( SV361 @ SV66 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV66 @ SV283 ) @ ( product_Sigma_a_a @ SV185 @ SV361 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1301]) ).
thf(1420,plain,
! [SV362: a,SV284: a,SV186: a,SV67: a] :
( ( ( ( product_Pair_a_a @ SV67 @ SV186 )
= ( product_Pair_a_a @ SV284 @ SV362 ) )
= $false )
| ( ( ~ ( ( SV67 != SV284 )
| ( SV186 != SV362 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1302]) ).
thf(1421,plain,
! [SV188: set_Product_prod_a_a,SV286: set_Product_prod_a_a,SV69: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV69 @ SV286 )
= $false )
| ( ( member449909584od_a_a @ SV69 @ ( minus_1507102574od_a_a @ SV188 @ SV286 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1304]) ).
thf(1422,plain,
! [SV70: set_Product_prod_a_a,SV189: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK14_SY915 @ SV189 @ SV70 ) @ ( sK25_SY1182 @ SV70 @ SV189 ) ) @ SV70 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK14_SY915 @ SV189 @ SV70 ) @ ( sK25_SY1182 @ SV70 @ SV189 ) ) @ SV189 ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV70 @ SV189 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1305]) ).
thf(1423,plain,
! [SV363: a > set_a,SV288: set_a,SV191: a,SV72: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV72 @ SV191 ) @ ( product_Sigma_a_a @ SV288 @ SV363 ) )
= $false )
| ( ( member_a @ SV191 @ ( SV363 @ SV72 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1307]) ).
thf(1424,plain,
! [SV73: produc1921647824od_a_a] :
( ( SV73
= ( produc1299253312od_a_a @ ( sK2_SY638 @ SV73 ) @ ( product_Pair_a_a @ ( sK6_SY1075 @ SV73 ) @ ( sK15_SY1150 @ SV73 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1308]) ).
thf(1425,plain,
! [SV364: a > a,SV289: set_a,SV192: a,SV74: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV74 @ SV192 ) @ ( bNF_Gr_a_a @ SV289 @ SV364 ) )
= $false )
| ( ( ( SV364 @ SV74 )
= SV192 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1309]) ).
thf(1426,plain,
! [SV365: a > set_a,SV290: set_a,SV193: a,SV75: a] :
( ( ( ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV75 @ SV193 ) @ ( product_Sigma_a_a @ SV290 @ SV365 ) )
| ~ ( ~ ( member_a @ SV75 @ SV290 )
| ~ ( member_a @ SV193 @ ( SV365 @ SV75 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV75 @ SV193 ) @ ( product_Sigma_a_a @ SV290 @ SV365 ) )
| ~ ~ ( ~ ( member_a @ SV75 @ SV290 )
| ~ ( member_a @ SV193 @ ( SV365 @ SV75 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1310]) ).
thf(1427,plain,
! [SV406: set_Product_prod_a_a,SV396: product_prod_a_a > product_prod_a_a,SV366: product_prod_a_a,SV291: product_prod_a_a,SV194: product_prod_a_a > product_prod_a_a,SV76: product_prod_a_a] :
( ( ( SV76
!= ( SV194 @ SV291 ) )
| ( SV366
!= ( SV396 @ SV291 ) )
| ~ ( member449909584od_a_a @ SV291 @ SV406 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV76 @ SV366 ) @ ( bNF_Gr200450189od_a_a @ SV406 @ SV194 @ SV396 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1312]) ).
thf(1428,plain,
! [SV196: set_Product_prod_a_a,SV78: set_Product_prod_a_a,SV293: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV293 @ SV78 ) )
= $true )
| ( ( member449909584od_a_a @ SV293 @ SV196 )
= $true )
| ( ( ord_le1824328871od_a_a @ SV78 @ SV196 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1313]) ).
thf(1429,plain,
! [SV397: a > a,SV368: a > a,SV294: set_Product_prod_a_a,SV197: a,SV79: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV79 @ SV197 ) @ SV294 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV368 @ SV79 ) @ ( SV397 @ SV197 ) ) @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SV368 @ SV397 ) @ SV294 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1314]) ).
thf(1430,plain,
! [SV198: set_Product_prod_a_a,SV80: set_Product_prod_a_a,SV295: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV295 @ SV80 ) )
= $true )
| ( ( member449909584od_a_a @ SV295 @ SV198 )
= $true )
| ( ( ord_le1824328871od_a_a @ SV80 @ SV198 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1315]) ).
thf(1431,plain,
! [SV81: set_Product_prod_a_a,SV199: product_prod_a_a > produc1572603623od_a_a,SV296: set_Pr1948701895od_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK26_SY1085 @ SV296 @ SV199 @ SV81 ) @ SV81 )
| ( member2057358096od_a_a @ ( SV199 @ ( sK26_SY1085 @ SV296 @ SV199 @ SV81 ) ) @ SV296 ) )
= $false )
| ( ( ord_le456379495od_a_a @ ( image_1765377413od_a_a @ SV199 @ SV81 ) @ SV296 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1316]) ).
thf(1432,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( ~ ( ( prefer1292084992ence_a @ SV201 @ SV369 )
| ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 )
| ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1318]) ).
thf(1433,plain,
! [SV370: product_prod_a_a > set_Product_prod_a_a,SV299: set_Product_prod_a_a,SV202: product_prod_a_a,SV84: product_prod_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV84 @ SV202 ) @ ( produc304751368od_a_a @ SV299 @ SV370 ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ SV84 @ SV299 )
| ~ ( member449909584od_a_a @ SV202 @ ( SV370 @ SV84 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1320]) ).
thf(1434,plain,
! [SV371: product_prod_a_a > set_Product_prod_a_a,SV301: product_prod_a_a,SV204: set_Product_prod_a_a,SV86: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV86 @ SV204 )
= $false )
| ( ( ~ ( member449909584od_a_a @ SV301 @ ( SV371 @ SV86 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV86 @ SV301 ) @ ( produc304751368od_a_a @ SV204 @ SV371 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1322]) ).
thf(1435,plain,
! [SV372: product_prod_a_a > $o,SV303: product_prod_a_a > $o,SV206: set_Product_prod_a_a,SV88: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV88 @ SV206 )
= $false )
| ( ( ~ ! [SY1159: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1159 @ SV88 )
| ~ ( SV303 @ SY1159 )
| ( SV372 @ SY1159 ) )
| ( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [SY1094: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1094 @ SV88 )
| ~ ( SV303 @ SY1094 ) ) )
@ ( collec645855634od_a_a
@ ^ [SY1161: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1161 @ SV206 )
| ~ ( SV372 @ SY1161 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1324]) ).
thf(1436,plain,
! [SV373: product_prod_a_a > set_Product_prod_a_a,SV304: set_Product_prod_a_a,SV207: product_prod_a_a,SV89: product_prod_a_a] :
( ( ( ~ ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV89 @ SV207 ) @ ( produc304751368od_a_a @ SV304 @ SV373 ) )
| ~ ( ~ ( member449909584od_a_a @ SV89 @ SV304 )
| ~ ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV89 @ SV207 ) @ ( produc304751368od_a_a @ SV304 @ SV373 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ SV89 @ SV304 )
| ~ ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1325]) ).
thf(1437,plain,
! [SV90: produc1572603623od_a_a] :
( ( SV90
= ( produc1474507607od_a_a @ ( sK3_SY691 @ SV90 ) @ ( product_Pair_a_a @ ( sK7_SY1097 @ SV90 ) @ ( sK16_SY1162 @ SV90 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1327]) ).
thf(1438,plain,
! [SV208: product_prod_a_a,SV91: a] :
( ( ( SV91
= ( product_snd_a_a @ SV208 ) )
= $false )
| ( ( ~ ( ( SV91
!= ( product_snd_a_a @ SV208 ) )
| ~ ~ ! [SY956: a] :
( SV208
!= ( product_Pair_a_a @ SY956 @ SV91 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1328]) ).
thf(1439,plain,
! [SV91: a,SV208: product_prod_a_a] :
( ( ( ~ ! [SY956: a] :
( SV208
!= ( product_Pair_a_a @ SY956 @ SV91 ) ) )
= $false )
| ( ( ~ ( ( SV91
!= ( product_snd_a_a @ SV208 ) )
| ~ ~ ! [SY956: a] :
( SV208
!= ( product_Pair_a_a @ SY956 @ SV91 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1328]) ).
thf(1440,plain,
! [SV374: set_Pr1948701895od_a_a,SV305: produc1572603623od_a_a,SV209: produc1572603623od_a_a > product_prod_a_a,SV92: product_prod_a_a] :
( ( ( SV92
= ( SV209 @ SV305 ) )
= $false )
| ( ( ~ ( member2057358096od_a_a @ SV305 @ SV374 )
| ( member449909584od_a_a @ SV92 @ ( image_734753285od_a_a @ SV209 @ SV374 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1329]) ).
thf(1441,plain,
! [SV375: a,SV306: a > $o,SV210: a,SV93: a > $o] :
( ( ( SV93 @ SV210 )
= $false )
| ( ( ~ ( SV306 @ SV375 )
| ~ ( ~ ( SV93 @ ( product_fst_a_a @ ( product_Pair_a_a @ SV210 @ SV375 ) ) )
| ~ ( SV306 @ ( product_snd_a_a @ ( product_Pair_a_a @ SV210 @ SV375 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1330]) ).
thf(1442,plain,
! [SV376: set_Product_prod_a_a,SV307: set_a,SV211: a,SV94: a] :
( ( ( member_a @ SV94 @ ( prefer161218362good_a @ SV211 @ SV307 @ SV376 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV94 @ SV211 ) @ SV376 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1331]) ).
thf(1443,plain,
! [SV407: set_Product_prod_a_a,SV398: product_prod_a_a > a,SV377: a,SV308: product_prod_a_a,SV212: product_prod_a_a > a,SV95: a] :
( ( ( SV95
!= ( SV212 @ SV308 ) )
| ( SV377
!= ( SV398 @ SV308 ) )
| ~ ( member449909584od_a_a @ SV308 @ SV407 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV95 @ SV377 ) @ ( bNF_Gr1853143117_a_a_a @ SV407 @ SV212 @ SV398 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1332]) ).
thf(1444,plain,
! [SV378: product_prod_a_a > product_prod_a_a,SV309: set_Product_prod_a_a,SV213: product_prod_a_a,SV96: product_prod_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV96 @ SV213 ) @ ( bNF_Gr1372473186od_a_a @ SV309 @ SV378 ) )
= $false )
| ( ( member449909584od_a_a @ SV96 @ SV309 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1333]) ).
thf(1445,plain,
! [SV408: set_Product_prod_a_a,SV379: set_a,SV214: a] :
( ( ( prefer436369274d_as_a @ SV214 @ SV379 @ SV408 )
= ( collect_a
@ ^ [SY1193: a] :
~ ( ~ ~ ( ~ ( member_a @ SY1193 @ SV379 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV214 @ SY1193 ) @ SV408 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1193 @ SV214 ) @ SV408 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1334]) ).
thf(1446,plain,
! [SV311: set_Product_prod_a_a,SV215: product_prod_a_a > a,SV99: a] :
( ( ( ! [SY1109: product_prod_a_a] :
( ( SV99
!= ( SV215 @ SY1109 ) )
| ~ ( member449909584od_a_a @ SY1109 @ SV311 ) ) )
= $false )
| ( ( member_a @ SV99 @ ( image_340790172_a_a_a @ SV215 @ SV311 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1337]) ).
thf(1447,plain,
! [SV216: product_prod_a_a,SV100: product_prod_a_a > $o] :
( ( ( SV100 @ ( product_Pair_a_a @ ( sK17_SY722 @ SV216 @ SV100 ) @ ( sK27_SY1186 @ SV216 @ SV100 ) ) )
= $false )
| ( ( SV100 @ SV216 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1338]) ).
thf(1448,plain,
! [SV380: set_Product_prod_a_a,SV312: a > a,SV217: a > a,SV101: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV101 @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SV217 @ SV312 ) @ SV380 ) )
= $false )
| ( ( ~ ! [SY1167: a,SY1168: a] :
( ( SV101
!= ( product_Pair_a_a @ ( SV217 @ SY1167 ) @ ( SV312 @ SY1168 ) ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1167 @ SY1168 ) @ SV380 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1339]) ).
thf(1449,plain,
! [SV409: set_Product_prod_a_a,SV381: set_a,SV218: a] :
( ( ( prefer1676310729than_a @ SV218 @ SV381 @ SV409 )
= ( collect_a
@ ^ [SY1194: a] :
~ ( ~ ( member_a @ SY1194 @ SV381 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV218 @ SY1194 ) @ SV409 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1340]) ).
thf(1450,plain,
! [SV382: a > a,SV314: set_a,SV219: a,SV103: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV103 @ SV219 ) @ ( bNF_Gr_a_a @ SV314 @ SV382 ) )
= $false )
| ( ( member_a @ SV103 @ SV314 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1342]) ).
thf(1451,plain,
! [SV401: a > set_Product_prod_a_a,SV383: a,SV315: a,SV220: a,SV104: a > $o] :
( ( ( ~ ( SV104 @ SV220 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV315 @ SV383 ) @ ( SV401 @ SV220 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV220 @ SV315 ) @ ( product_Pair_a_a @ SV220 @ SV383 ) ) @ ( same_fst_a_a @ SV104 @ SV401 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1343]) ).
thf(1452,plain,
! [SV221: product_prod_a_a,SV105: product_prod_a_a > $o] :
( ( ( SV105 @ ( product_Pair_a_a @ ( sK18_SY740 @ SV221 @ SV105 ) @ ( sK28_SY1188 @ SV221 @ SV105 ) ) )
= $false )
| ( ( SV105 @ SV221 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1344]) ).
thf(1453,plain,
! [SV384: set_Product_prod_a_a,SV316: product_prod_a_a,SV222: product_prod_a_a > a,SV106: a] :
( ( ( SV106
= ( SV222 @ SV316 ) )
= $false )
| ( ( ~ ( member449909584od_a_a @ SV316 @ SV384 )
| ( member_a @ SV106 @ ( image_340790172_a_a_a @ SV222 @ SV384 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1345]) ).
thf(1454,plain,
! [SV109: product_prod_a_a] :
( ( SV109
!= ( product_Pair_a_a @ ( sK5_SY749 @ SV109 ) @ ( sK29_SY1119 @ SV109 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1348]) ).
thf(1455,plain,
! [SV385: set_Product_prod_a_a,SV319: product_prod_a_a,SV225: product_prod_a_a > product_prod_a_a,SV110: product_prod_a_a] :
( ( ( SV110
= ( SV225 @ SV319 ) )
= $false )
| ( ( ~ ( member449909584od_a_a @ SV319 @ SV385 )
| ( member449909584od_a_a @ SV110 @ ( image_794773445od_a_a @ SV225 @ SV385 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1349]) ).
thf(1456,plain,
! [SV111: produc1572603623od_a_a,SV320: product_prod_a_a > set_Product_prod_a_a,SV226: set_Product_prod_a_a] :
( ( ( ! [SY1121: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1121 @ SV226 )
| ! [SY1122: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1122 @ ( SV320 @ SY1121 ) )
| ( SV111
!= ( produc1474507607od_a_a @ SY1121 @ SY1122 ) ) ) ) )
= $false )
| ( ( member2057358096od_a_a @ SV111 @ ( produc304751368od_a_a @ SV226 @ SV320 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1350]) ).
thf(1457,plain,
! [SV386: product_prod_a_a > product_prod_a_a,SV322: product_prod_a_a,SV228: set_Product_prod_a_a,SV113: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV113 @ SV228 )
= $false )
| ( ( ( SV322
!= ( SV386 @ SV113 ) )
| ( member449909584od_a_a @ SV322 @ ( image_794773445od_a_a @ SV386 @ SV228 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1352]) ).
thf(1458,plain,
! [SV323: set_a,SV229: a > product_prod_a_a,SV114: product_prod_a_a] :
( ( ( ! [SY1124: a] :
( ( SV114
!= ( SV229 @ SY1124 ) )
| ~ ( member_a @ SY1124 @ SV323 ) ) )
= $false )
| ( ( member449909584od_a_a @ SV114 @ ( image_1725938350od_a_a @ SV229 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1353]) ).
thf(1459,plain,
! [SV410: set_Pr1948701895od_a_a,SV402: produc1572603623od_a_a > a,SV387: a,SV325: produc1572603623od_a_a,SV231: produc1572603623od_a_a > a,SV116: a] :
( ( ( SV116
!= ( SV231 @ SV325 ) )
| ( SV387
!= ( SV402 @ SV325 ) )
| ~ ( member2057358096od_a_a @ SV325 @ SV410 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV116 @ SV387 ) @ ( bNF_Gr356189709_a_a_a @ SV410 @ SV231 @ SV402 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1355]) ).
thf(1460,plain,
! [SV388: set_Pr1948701895od_a_a,SV326: set_Product_prod_a_a,SV232: product_prod_a_a,SV118: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV118 @ ( prefer477097315od_a_a @ SV232 @ SV326 @ SV388 ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV118 @ SV232 ) @ SV388 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1356]) ).
thf(1461,plain,
! [SV119: product_prod_a_a,SV327: a > set_a,SV233: set_a] :
( ( ( ! [SY1129: a] :
( ~ ( member_a @ SY1129 @ SV233 )
| ! [SY1130: a] :
( ~ ( member_a @ SY1130 @ ( SV327 @ SY1129 ) )
| ( SV119
!= ( product_Pair_a_a @ SY1129 @ SY1130 ) ) ) ) )
= $false )
| ( ( member449909584od_a_a @ SV119 @ ( product_Sigma_a_a @ SV233 @ SV327 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1357]) ).
thf(1462,plain,
! [SV389: product_prod_a_a > $o,SV328: set_Product_prod_a_a,SV234: set_Product_prod_a_a,SV120: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV120 @ SV234 )
= $false )
| ( ( ~ ( ord_le1824328871od_a_a @ SV234
@ ( collec645855634od_a_a
@ ^ [SY1174: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1174 @ SV328 )
| ~ ( SV389 @ SY1174 ) ) ) )
| ( SV389 @ SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1358]) ).
thf(1463,plain,
! [SV122: set_Product_prod_a_a,SV236: product_prod_a_a > a,SV330: set_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK30_SY1133 @ SV330 @ SV236 @ SV122 ) @ SV122 )
| ( member_a @ ( SV236 @ ( sK30_SY1133 @ SV330 @ SV236 @ SV122 ) ) @ SV330 ) )
= $false )
| ( ( ord_less_eq_set_a @ ( image_340790172_a_a_a @ SV236 @ SV122 ) @ SV330 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1360]) ).
thf(1464,plain,
! [SV411: set_Product_prod_a_a,SV403: set_Product_prod_a_a,SV390: a,SV331: a,SV237: a,SV123: a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SV331 @ SV390 ) ) @ ( lex_prod_a_a @ SV403 @ SV411 ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
| ~ ( ( SV123 != SV331 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1361]) ).
thf(1465,plain,
! [SV238: product_prod_a_a,SV125: a] :
( ( ( SV125
= ( product_fst_a_a @ SV238 ) )
= $false )
| ( ( ~ ( ( SV125
!= ( product_fst_a_a @ SV238 ) )
| ~ ~ ! [SY1024: a] :
( SV238
!= ( product_Pair_a_a @ SV125 @ SY1024 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1363]) ).
thf(1466,plain,
! [SV125: a,SV238: product_prod_a_a] :
( ( ( ~ ! [SY1024: a] :
( SV238
!= ( product_Pair_a_a @ SV125 @ SY1024 ) ) )
= $false )
| ( ( ~ ( ( SV125
!= ( product_fst_a_a @ SV238 ) )
| ~ ~ ! [SY1024: a] :
( SV238
!= ( product_Pair_a_a @ SV125 @ SY1024 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1363]) ).
thf(1467,plain,
! [SV239: set_Product_prod_a_a,SV332: set_Product_prod_a_a,SV126: product_prod_a_a] :
( ( ( ~ ~ ( member449909584od_a_a @ SV126 @ SV332 ) )
= $true )
| ( ( member449909584od_a_a @ SV126 @ ( minus_1507102574od_a_a @ SV239 @ SV332 ) )
= $true )
| ( ( member449909584od_a_a @ SV126 @ SV239 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1364]) ).
thf(1468,plain,
! [SV391: a > set_a,SV333: set_a,SV240: a,SV127: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV127 @ SV240 ) @ ( product_Sigma_a_a @ SV333 @ SV391 ) )
= $false )
| ( ( ~ ( ~ ( member_a @ SV127 @ SV333 )
| ~ ( member_a @ SV240 @ ( SV391 @ SV127 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1365]) ).
thf(1469,plain,
! [SV392: product_prod_a_a > set_Product_prod_a_a,SV335: set_Product_prod_a_a,SV242: product_prod_a_a,SV129: product_prod_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV129 @ SV242 ) @ ( produc304751368od_a_a @ SV335 @ SV392 ) )
= $false )
| ( ( member449909584od_a_a @ SV242 @ ( SV392 @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1367]) ).
thf(1470,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( ! [SV412: a] :
( ( ^ [SY1195: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV412 @ SY1195 ) @ SV2 ) )
= ( ^ [SY1196: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV412 @ SY1196 ) @ SV131 ) ) ) )
= $false )
| ( ( ~ ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
!= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
| ( SV2 != SV131 ) ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[1368]) ).
thf(1471,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $false )
| ( ( ~ ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
!= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
| ( SV2 != SV131 ) ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[1368]) ).
thf(1472,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
!= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
| ( SV2 != SV131 ) )
= $false )
| ( ( SV2 = SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1369]) ).
thf(1473,plain,
! [SV243: set_Product_prod_a_a,SV132: a,SV3: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV3 @ SV132 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV243 ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV3 @ SV132 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV243 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV132 @ SV3 ) @ SV243 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1370]) ).
thf(1474,plain,
! [SV243: set_Product_prod_a_a,SV3: a,SV132: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV132 @ SV3 ) @ SV243 )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV3 @ SV132 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV243 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV132 @ SV3 ) @ SV243 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1370]) ).
thf(1475,plain,
! [SV133: product_prod_a_a > $o,SV4: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV4 @ ( collec645855634od_a_a @ SV133 ) )
| ~ ( SV133 @ SV4 ) )
= $false )
| ( ( member449909584od_a_a @ SV4 @ ( collec645855634od_a_a @ SV133 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1371]) ).
thf(1476,plain,
! [SV133: product_prod_a_a > $o,SV4: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV4 @ ( collec645855634od_a_a @ SV133 ) )
| ~ ( SV133 @ SV4 ) )
= $false )
| ( ( SV133 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1372]) ).
thf(1477,plain,
! [SV138: product_prod_a_a] :
( ( ( ~ ( top_to1483957574_a_a_o @ SV138 )
| ~ ( member449909584od_a_a @ SV138 @ top_to398455383od_a_a ) )
= $false )
| ( ( top_to1483957574_a_a_o @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1373]) ).
thf(1478,plain,
! [SV138: product_prod_a_a] :
( ( ( ~ ( top_to1483957574_a_a_o @ SV138 )
| ~ ( member449909584od_a_a @ SV138 @ top_to398455383od_a_a ) )
= $false )
| ( ( member449909584od_a_a @ SV138 @ top_to398455383od_a_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1374]) ).
thf(1479,plain,
! [SV340: a,SV140: a] :
( ( ( ( top_top_a_a_o @ SV140 @ SV340 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV140 @ SV340 ) @ top_to398455383od_a_a ) )
= $false )
| ( ( ~ ( ~ ( top_top_a_a_o @ SV140 @ SV340 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV140 @ SV340 ) @ top_to398455383od_a_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1375]) ).
thf(1480,plain,
! [SV249: set_a,SV143: set_a,SV20: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV20 @ ( product_product_a_a @ SV143 @ SV249 ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ SV20 @ ( product_product_a_a @ SV143 @ SV249 ) )
| ~ ( member449909584od_a_a @ SV20
@ ( product_Sigma_a_a @ SV143
@ ^ [SY1036: a] : SV249 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1376]) ).
thf(1481,plain,
! [SV249: set_a,SV143: set_a,SV20: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV20
@ ( product_Sigma_a_a @ SV143
@ ^ [SY1036: a] : SV249 ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ SV20 @ ( product_product_a_a @ SV143 @ SV249 ) )
| ~ ( member449909584od_a_a @ SV20
@ ( product_Sigma_a_a @ SV143
@ ^ [SY1036: a] : SV249 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1376]) ).
thf(1482,plain,
! [SV144: set_Product_prod_a_a,SV21: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1347718902_a_a_o
@ ^ [SY498: product_prod_a_a] : ( member449909584od_a_a @ SY498 @ SV21 )
@ ^ [SY826: product_prod_a_a] : ( member449909584od_a_a @ SY826 @ SV144 ) )
| ~ ( ord_le1824328871od_a_a @ SV21 @ SV144 ) )
= $false )
| ( ( ord_le1347718902_a_a_o
@ ^ [SY498: product_prod_a_a] : ( member449909584od_a_a @ SY498 @ SV21 )
@ ^ [SY826: product_prod_a_a] : ( member449909584od_a_a @ SY826 @ SV144 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1377]) ).
thf(1483,plain,
! [SV144: set_Product_prod_a_a,SV21: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1347718902_a_a_o
@ ^ [SY498: product_prod_a_a] : ( member449909584od_a_a @ SY498 @ SV21 )
@ ^ [SY826: product_prod_a_a] : ( member449909584od_a_a @ SY826 @ SV144 ) )
| ~ ( ord_le1824328871od_a_a @ SV21 @ SV144 ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV21 @ SV144 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1378]) ).
thf(1484,plain,
! [SV341: set_Product_prod_a_a,SV145: set_Product_prod_a_a] :
( ( ( ( ord_le1824328871od_a_a @ SV145 @ SV341 )
| ( ord_le1347718902_a_a_o
@ ^ [SY828: product_prod_a_a] : ( member449909584od_a_a @ SY828 @ SV145 )
@ ^ [SY1142: product_prod_a_a] : ( member449909584od_a_a @ SY1142 @ SV341 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV145 @ SV341 )
| ~ ( ord_le1347718902_a_a_o
@ ^ [SY828: product_prod_a_a] : ( member449909584od_a_a @ SY828 @ SV145 )
@ ^ [SY1142: product_prod_a_a] : ( member449909584od_a_a @ SY1142 @ SV341 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1379]) ).
thf(1485,plain,
! [SV146: set_Product_prod_a_a,SV23: set_Product_prod_a_a] :
( ( ( ~ ( ord_less_eq_a_a_o
@ ^ [SY504: a,SY505: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY504 @ SY505 ) @ SV23 )
@ ^ [SY832: a,SY833: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY832 @ SY833 ) @ SV146 ) )
| ~ ( ord_le1824328871od_a_a @ SV23 @ SV146 ) )
= $false )
| ( ( ord_less_eq_a_a_o
@ ^ [SY504: a,SY505: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY504 @ SY505 ) @ SV23 )
@ ^ [SY832: a,SY833: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY832 @ SY833 ) @ SV146 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1380]) ).
thf(1486,plain,
! [SV146: set_Product_prod_a_a,SV23: set_Product_prod_a_a] :
( ( ( ~ ( ord_less_eq_a_a_o
@ ^ [SY504: a,SY505: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY504 @ SY505 ) @ SV23 )
@ ^ [SY832: a,SY833: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY832 @ SY833 ) @ SV146 ) )
| ~ ( ord_le1824328871od_a_a @ SV23 @ SV146 ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV23 @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1381]) ).
thf(1487,plain,
! [SV24: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( sK19_SY508 @ SV24 ) @ SV24 )
= $true )
| ( ( ~ ( ~ ! [SY508: product_prod_a_a] :
~ ( member449909584od_a_a @ SY508 @ SV24 )
| ( SV24 != bot_bo2131659635od_a_a ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1382]) ).
thf(1488,plain,
! [SV24: set_Product_prod_a_a] :
( ( ( ~ ! [SY508: product_prod_a_a] :
~ ( member449909584od_a_a @ SY508 @ SV24 ) )
= $false )
| ( ( SV24 = bot_bo2131659635od_a_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1383]) ).
thf(1489,plain,
! [SV24: set_Product_prod_a_a] :
( ( ( SV24 != bot_bo2131659635od_a_a )
= $false )
| ( ( SV24 = bot_bo2131659635od_a_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1383]) ).
thf(1490,plain,
! [SV28: set_Product_prod_a_a,SV148: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( sK11_SY834 @ SV148 @ SV28 ) @ SV28 )
= $true )
| ( ( ord_le1824328871od_a_a @ SV28 @ SV148 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1384]) ).
thf(1491,plain,
! [SV149: product_prod_a_a > produc1572603623od_a_a,SV29: produc1572603623od_a_a,SV342: set_Product_prod_a_a,SV251: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV251 @ SV342 ) )
= $true )
| ( ( member2057358096od_a_a @ SV29 @ ( image_1765377413od_a_a @ SV149 @ SV342 ) )
= $true )
| ( ( SV29
= ( SV149 @ SV251 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1386]) ).
thf(1492,plain,
! [SV343: a,SV252: a,SV150: a,SV30: a] :
( ( ( ( ( product_Pair_a_a @ SV30 @ SV150 )
= ( product_Pair_a_a @ SV252 @ SV343 ) )
| ~ ( ( SV30 != SV252 )
| ( SV150 != SV343 ) ) )
= $false )
| ( ( ~ ( ( ( product_Pair_a_a @ SV30 @ SV150 )
!= ( product_Pair_a_a @ SV252 @ SV343 ) )
| ~ ~ ( ( SV30 != SV252 )
| ( SV150 != SV343 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1387]) ).
thf(1493,plain,
! [SV151: set_Product_prod_a_a,SV31: product_prod_a_a,SV344: product_prod_a_a > produc1572603623od_a_a,SV253: produc1572603623od_a_a] :
( ( ( SV253
!= ( SV344 @ SV31 ) )
= $true )
| ( ( member2057358096od_a_a @ SV253 @ ( image_1765377413od_a_a @ SV344 @ SV151 ) )
= $true )
| ( ( member449909584od_a_a @ SV31 @ SV151 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1388]) ).
thf(1494,plain,
! [SV32: set_Product_prod_a_a,SV152: product_prod_a_a > product_prod_a_a,SV254: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK20_SY1042 @ SV254 @ SV152 @ SV32 ) @ SV32 ) )
= $false )
| ( ( ord_le1824328871od_a_a @ ( image_794773445od_a_a @ SV152 @ SV32 ) @ SV254 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1389]) ).
thf(1495,plain,
! [SV32: set_Product_prod_a_a,SV254: set_Product_prod_a_a,SV152: product_prod_a_a > product_prod_a_a] :
( ( ( member449909584od_a_a @ ( SV152 @ ( sK20_SY1042 @ SV254 @ SV152 @ SV32 ) ) @ SV254 )
= $false )
| ( ( ord_le1824328871od_a_a @ ( image_794773445od_a_a @ SV152 @ SV32 ) @ SV254 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1389]) ).
thf(1496,plain,
! [SV255: set_Product_prod_a_a,SV153: set_Product_prod_a_a,SV33: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV33 @ ( minus_1507102574od_a_a @ SV153 @ SV255 ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ SV33 @ ( minus_1507102574od_a_a @ SV153 @ SV255 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ SV33 @ SV153 )
| ~ ~ ( member449909584od_a_a @ SV33 @ SV255 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1390]) ).
thf(1497,plain,
! [SV255: set_Product_prod_a_a,SV153: set_Product_prod_a_a,SV33: product_prod_a_a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ SV33 @ SV153 )
| ~ ~ ( member449909584od_a_a @ SV33 @ SV255 ) ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ SV33 @ ( minus_1507102574od_a_a @ SV153 @ SV255 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ SV33 @ SV153 )
| ~ ~ ( member449909584od_a_a @ SV33 @ SV255 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1390]) ).
thf(1498,plain,
! [SV34: set_a,SV154: a > product_prod_a_a,SV256: set_Product_prod_a_a] :
( ( ( ~ ( member_a @ ( sK21_SY1043 @ SV256 @ SV154 @ SV34 ) @ SV34 ) )
= $false )
| ( ( ord_le1824328871od_a_a @ ( image_1725938350od_a_a @ SV154 @ SV34 ) @ SV256 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1391]) ).
thf(1499,plain,
! [SV34: set_a,SV256: set_Product_prod_a_a,SV154: a > product_prod_a_a] :
( ( ( member449909584od_a_a @ ( SV154 @ ( sK21_SY1043 @ SV256 @ SV154 @ SV34 ) ) @ SV256 )
= $false )
| ( ( ord_le1824328871od_a_a @ ( image_1725938350od_a_a @ SV154 @ SV34 ) @ SV256 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1391]) ).
thf(1500,plain,
! [SV345: set_Product_prod_a_a,SV155: set_Product_prod_a_a] :
( ( ( ( ord_le1824328871od_a_a @ SV155 @ SV345 )
| ! [SY1143: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1143 @ SV155 )
| ( member449909584od_a_a @ SY1143 @ SV345 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV155 @ SV345 )
| ~ ! [SY1143: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1143 @ SV155 )
| ( member449909584od_a_a @ SY1143 @ SV345 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1392]) ).
thf(1501,plain,
! [SV36: set_Product_prod_a_a,SV413: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV413 @ SV36 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY531: product_prod_a_a] :
~ ( member449909584od_a_a @ SY531 @ SV36 )
| ~ ( ( SV36 != bot_bo2131659635od_a_a ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1393]) ).
thf(1502,plain,
! [SV36: set_Product_prod_a_a] :
( ( ( ~ ~ ! [SY531: product_prod_a_a] :
~ ( member449909584od_a_a @ SY531 @ SV36 )
| ~ ( ( SV36 != bot_bo2131659635od_a_a ) ) )
= $false )
| ( ( SV36 = bot_bo2131659635od_a_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1394]) ).
thf(1503,plain,
! [SV156: produc1572603623od_a_a,SV37: produc1572603623od_a_a > $o] :
( ( ( SV37 @ ( produc1474507607od_a_a @ ( sK12_SY533 @ SV156 @ SV37 ) @ ( product_Pair_a_a @ ( sK22_SY1177 @ SV156 @ SV37 ) @ ( sK31_SY1191 @ SV156 @ SV37 ) ) ) )
= $false )
| ( ( SV37 @ SV156 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1395]) ).
thf(1504,plain,
! [SV258: set_Product_prod_a_a,SV158: product_prod_a_a > produc1572603623od_a_a,SV39: produc1572603623od_a_a] :
( ( ( ( SV39
!= ( SV158 @ ( sK32_SY1045 @ SV258 @ SV158 @ SV39 ) ) )
| ~ ( member449909584od_a_a @ ( sK32_SY1045 @ SV258 @ SV158 @ SV39 ) @ SV258 ) )
= $false )
| ( ( member2057358096od_a_a @ SV39 @ ( image_1765377413od_a_a @ SV158 @ SV258 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1396]) ).
thf(1505,plain,
! [SV159: a > product_prod_a_a,SV40: product_prod_a_a,SV346: set_a,SV259: a] :
( ( ( ~ ( member_a @ SV259 @ SV346 ) )
= $true )
| ( ( member449909584od_a_a @ SV40 @ ( image_1725938350od_a_a @ SV159 @ SV346 ) )
= $true )
| ( ( SV40
= ( SV159 @ SV259 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1397]) ).
thf(1506,plain,
! [SV260: set_Product_prod_a_a,SV161: product_prod_a_a > product_prod_a_a,SV42: product_prod_a_a] :
( ( ( ( SV42
!= ( SV161 @ ( sK33_SY1047 @ SV260 @ SV161 @ SV42 ) ) )
| ~ ( member449909584od_a_a @ ( sK33_SY1047 @ SV260 @ SV161 @ SV42 ) @ SV260 ) )
= $false )
| ( ( member449909584od_a_a @ SV42 @ ( image_794773445od_a_a @ SV161 @ SV260 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1398]) ).
thf(1507,plain,
! [SV347: set_Product_prod_a_a,SV162: set_Product_prod_a_a] :
( ( ( ( ord_le1824328871od_a_a @ SV162 @ SV347 )
| ! [SY1144: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1144 @ SV162 )
| ( member449909584od_a_a @ SY1144 @ SV347 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV162 @ SV347 )
| ~ ! [SY1144: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1144 @ SV162 )
| ( member449909584od_a_a @ SY1144 @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1399]) ).
thf(1508,plain,
! [SV263: set_Product_prod_a_a,SV164: set_Product_prod_a_a,SV45: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV45 @ SV164 ) )
= $false )
| ( ( member449909584od_a_a @ SV45 @ ( minus_1507102574od_a_a @ SV164 @ SV263 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1400]) ).
thf(1509,plain,
! [SV164: set_Product_prod_a_a,SV263: set_Product_prod_a_a,SV45: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV45 @ SV263 )
= $false )
| ( ( member449909584od_a_a @ SV45 @ ( minus_1507102574od_a_a @ SV164 @ SV263 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1400]) ).
thf(1510,plain,
! [SV264: product_prod_a_a > $o,SV165: set_Product_prod_a_a,SV46: set_Product_prod_a_a] :
( ( ( ~ ( ( ord_le1824328871od_a_a @ SV46
@ ( collec645855634od_a_a
@ ^ [SY1049: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1049 @ SV165 )
| ~ ( SV264 @ SY1049 ) ) ) )
| ! [SY1050: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1050 @ SV46 )
| ( SV264 @ SY1050 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV46
@ ( collec645855634od_a_a
@ ^ [SY1049: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1049 @ SV165 )
| ~ ( SV264 @ SY1049 ) ) ) )
| ~ ! [SY1050: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1050 @ SV46 )
| ( SV264 @ SY1050 ) ) ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV46 @ SV165 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1401]) ).
thf(1511,plain,
! [SV266: set_Pr1948701895od_a_a,SV167: produc1572603623od_a_a > product_prod_a_a,SV48: product_prod_a_a] :
( ( ( ( SV48
!= ( SV167 @ ( sK34_SY1053 @ SV266 @ SV167 @ SV48 ) ) )
| ~ ( member2057358096od_a_a @ ( sK34_SY1053 @ SV266 @ SV167 @ SV48 ) @ SV266 ) )
= $false )
| ( ( member449909584od_a_a @ SV48 @ ( image_734753285od_a_a @ SV167 @ SV266 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1404]) ).
thf(1512,plain,
! [SV49: set_a,SV168: set_Product_prod_a_a,SV349: a,SV267: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV267 @ SV349 ) @ SV168 ) )
= $true )
| ( ( member_a @ SV267 @ SV49 )
= $true )
| ( ( prefer1292084992ence_a @ SV49 @ SV168 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1405]) ).
thf(1513,plain,
! [SV170: set_a,SV51: a,SV350: a > product_prod_a_a,SV269: product_prod_a_a] :
( ( ( SV269
!= ( SV350 @ SV51 ) )
= $true )
| ( ( member449909584od_a_a @ SV269 @ ( image_1725938350od_a_a @ SV350 @ SV170 ) )
= $true )
| ( ( member_a @ SV51 @ SV170 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1406]) ).
thf(1514,plain,
! [SV172: set_Pr1948701895od_a_a,SV53: produc1572603623od_a_a,SV352: produc1572603623od_a_a > product_prod_a_a,SV271: product_prod_a_a] :
( ( ( SV271
!= ( SV352 @ SV53 ) )
= $true )
| ( ( member449909584od_a_a @ SV271 @ ( image_734753285od_a_a @ SV352 @ SV172 ) )
= $true )
| ( ( member2057358096od_a_a @ SV53 @ SV172 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1408]) ).
thf(1515,plain,
! [SV274: set_Product_prod_a_a,SV56: a,SV175: a,SV353: a] :
( ( ( SV353 != SV175 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV56 @ SV353 ) @ SV274 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV56 @ SV175 ) @ SV274 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1409]) ).
thf(1516,plain,
! [SV354: a,SV275: a,SV176: a,SV57: a] :
( ( ( ( ( product_Pair_a_a @ SV57 @ SV176 )
= ( product_Pair_a_a @ SV275 @ SV354 ) )
| ~ ( ( SV57 != SV275 )
| ( SV176 != SV354 ) ) )
= $false )
| ( ( ~ ( ( ( product_Pair_a_a @ SV57 @ SV176 )
!= ( product_Pair_a_a @ SV275 @ SV354 ) )
| ~ ~ ( ( SV57 != SV275 )
| ( SV176 != SV354 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1410]) ).
thf(1517,plain,
! [SV177: set_Product_prod_a_a,SV58: product_prod_a_a,SV355: product_prod_a_a > a,SV276: a] :
( ( ( SV276
!= ( SV355 @ SV58 ) )
= $true )
| ( ( member_a @ SV276 @ ( image_340790172_a_a_a @ SV355 @ SV177 ) )
= $true )
| ( ( member449909584od_a_a @ SV58 @ SV177 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1411]) ).
thf(1518,plain,
! [SV59: set_Pr1948701895od_a_a,SV178: produc1572603623od_a_a > product_prod_a_a,SV277: set_Product_prod_a_a] :
( ( ( ~ ( member2057358096od_a_a @ ( sK23_SY1063 @ SV277 @ SV178 @ SV59 ) @ SV59 ) )
= $false )
| ( ( ord_le1824328871od_a_a @ ( image_734753285od_a_a @ SV178 @ SV59 ) @ SV277 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1412]) ).
thf(1519,plain,
! [SV59: set_Pr1948701895od_a_a,SV277: set_Product_prod_a_a,SV178: produc1572603623od_a_a > product_prod_a_a] :
( ( ( member449909584od_a_a @ ( SV178 @ ( sK23_SY1063 @ SV277 @ SV178 @ SV59 ) ) @ SV277 )
= $false )
| ( ( ord_le1824328871od_a_a @ ( image_734753285od_a_a @ SV178 @ SV59 ) @ SV277 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1412]) ).
thf(1520,plain,
! [SV60: set_Product_prod_a_a,SV179: set_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK13_SY892 @ SV179 @ SV60 ) @ ( sK24_SY1180 @ SV60 @ SV179 ) ) @ SV60 ) )
= $false )
| ( ( ~ ! [SY894: a,SY895: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY894 @ SY895 ) @ SV60 )
| ( member_a @ SY895 @ SV179 ) )
| ~ ( order_preorder_on_a @ SV179 @ SV60 )
| ( prefer1292084992ence_a @ SV179 @ SV60 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1413]) ).
thf(1521,plain,
! [SV60: set_Product_prod_a_a,SV179: set_a] :
( ( ( member_a @ ( sK13_SY892 @ SV179 @ SV60 ) @ SV179 )
= $false )
| ( ( ~ ! [SY894: a,SY895: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY894 @ SY895 ) @ SV60 )
| ( member_a @ SY895 @ SV179 ) )
| ~ ( order_preorder_on_a @ SV179 @ SV60 )
| ( prefer1292084992ence_a @ SV179 @ SV60 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1413]) ).
thf(1522,plain,
! [SV394: a,SV356: a,SV278: a,SV180: set_Product_prod_a_a,SV61: set_a] :
( ( ( prefer1292084992ence_a @ SV61 @ SV180 )
= $false )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV356 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV278 ) @ SV180 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV394 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV356 ) @ SV180 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV394 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV278 ) @ SV180 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1414]) ).
thf(1523,plain,
! [SV62: set_Product_prod_a_a,SV181: set_Pr1948701895od_a_a,SV357: product_prod_a_a,SV279: product_prod_a_a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV279 @ SV357 ) @ SV181 ) )
= $true )
| ( ( member449909584od_a_a @ SV279 @ SV62 )
= $true )
| ( ( prefer1338892073od_a_a @ SV62 @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1415]) ).
thf(1524,plain,
! [SV64: a > a > $o,SV281: a,SV183: a,SV359: product_prod_a_a] :
( ( ( SV359
!= ( product_Pair_a_a @ SV183 @ SV281 ) )
= $true )
| ( ( SV64 @ ( product_fst_a_a @ SV359 ) @ ( product_snd_a_a @ SV359 ) )
= $true )
| ( ( SV64 @ SV183 @ SV281 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1417]) ).
thf(1525,plain,
! [SV405: set_a,SV395: a > a,SV360: a,SV282: a,SV184: a > a,SV65: a] :
( ( ( SV65
!= ( SV184 @ SV282 ) )
= $true )
| ( ( ( SV360
!= ( SV395 @ SV282 ) )
| ~ ( member_a @ SV282 @ SV405 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV65 @ SV360 ) @ ( bNF_Gr423046308_a_a_a @ SV405 @ SV184 @ SV395 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1418]) ).
thf(1526,plain,
! [SV185: set_a,SV66: a,SV361: a > set_a,SV283: a] :
( ( ( ~ ( member_a @ SV283 @ ( SV361 @ SV66 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV66 @ SV283 ) @ ( product_Sigma_a_a @ SV185 @ SV361 ) )
= $true )
| ( ( member_a @ SV66 @ SV185 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1419]) ).
thf(1527,plain,
! [SV362: a,SV186: a,SV284: a,SV67: a] :
( ( ( ( SV67 != SV284 )
| ( SV186 != SV362 ) )
= $false )
| ( ( ( product_Pair_a_a @ SV67 @ SV186 )
= ( product_Pair_a_a @ SV284 @ SV362 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1420]) ).
thf(1528,plain,
! [SV70: set_Product_prod_a_a,SV189: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK14_SY915 @ SV189 @ SV70 ) @ ( sK25_SY1182 @ SV70 @ SV189 ) ) @ SV70 ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV70 @ SV189 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1422]) ).
thf(1529,plain,
! [SV70: set_Product_prod_a_a,SV189: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK14_SY915 @ SV189 @ SV70 ) @ ( sK25_SY1182 @ SV70 @ SV189 ) ) @ SV189 )
= $false )
| ( ( ord_le1824328871od_a_a @ SV70 @ SV189 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1422]) ).
thf(1530,plain,
! [SV365: a > set_a,SV290: set_a,SV193: a,SV75: a] :
( ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV75 @ SV193 ) @ ( product_Sigma_a_a @ SV290 @ SV365 ) )
| ~ ( ~ ( member_a @ SV75 @ SV290 )
| ~ ( member_a @ SV193 @ ( SV365 @ SV75 ) ) ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV75 @ SV193 ) @ ( product_Sigma_a_a @ SV290 @ SV365 ) )
| ~ ~ ( ~ ( member_a @ SV75 @ SV290 )
| ~ ( member_a @ SV193 @ ( SV365 @ SV75 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1426]) ).
thf(1531,plain,
! [SV406: set_Product_prod_a_a,SV396: product_prod_a_a > product_prod_a_a,SV366: product_prod_a_a,SV291: product_prod_a_a,SV194: product_prod_a_a > product_prod_a_a,SV76: product_prod_a_a] :
( ( ( SV76
!= ( SV194 @ SV291 ) )
= $true )
| ( ( ( SV366
!= ( SV396 @ SV291 ) )
| ~ ( member449909584od_a_a @ SV291 @ SV406 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV76 @ SV366 ) @ ( bNF_Gr200450189od_a_a @ SV406 @ SV194 @ SV396 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1427]) ).
thf(1532,plain,
! [SV196: set_Product_prod_a_a,SV78: set_Product_prod_a_a,SV293: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV293 @ SV78 )
= $false )
| ( ( member449909584od_a_a @ SV293 @ SV196 )
= $true )
| ( ( ord_le1824328871od_a_a @ SV78 @ SV196 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1428]) ).
thf(1533,plain,
! [SV397: a > a,SV368: a > a,SV294: set_Product_prod_a_a,SV197: a,SV79: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV79 @ SV197 ) @ SV294 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV368 @ SV79 ) @ ( SV397 @ SV197 ) ) @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SV368 @ SV397 ) @ SV294 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1429]) ).
thf(1534,plain,
! [SV198: set_Product_prod_a_a,SV80: set_Product_prod_a_a,SV295: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV295 @ SV80 )
= $false )
| ( ( member449909584od_a_a @ SV295 @ SV198 )
= $true )
| ( ( ord_le1824328871od_a_a @ SV80 @ SV198 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1430]) ).
thf(1535,plain,
! [SV81: set_Product_prod_a_a,SV199: product_prod_a_a > produc1572603623od_a_a,SV296: set_Pr1948701895od_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK26_SY1085 @ SV296 @ SV199 @ SV81 ) @ SV81 ) )
= $false )
| ( ( ord_le456379495od_a_a @ ( image_1765377413od_a_a @ SV199 @ SV81 ) @ SV296 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1431]) ).
thf(1536,plain,
! [SV81: set_Product_prod_a_a,SV296: set_Pr1948701895od_a_a,SV199: product_prod_a_a > produc1572603623od_a_a] :
( ( ( member2057358096od_a_a @ ( SV199 @ ( sK26_SY1085 @ SV296 @ SV199 @ SV81 ) ) @ SV296 )
= $false )
| ( ( ord_le456379495od_a_a @ ( image_1765377413od_a_a @ SV199 @ SV81 ) @ SV296 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1431]) ).
thf(1537,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( ( prefer1292084992ence_a @ SV201 @ SV369 )
| ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) )
= $false )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 )
| ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1432]) ).
thf(1538,plain,
! [SV370: product_prod_a_a > set_Product_prod_a_a,SV202: product_prod_a_a,SV299: set_Product_prod_a_a,SV84: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV84 @ SV299 )
| ~ ( member449909584od_a_a @ SV202 @ ( SV370 @ SV84 ) ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV84 @ SV202 ) @ ( produc304751368od_a_a @ SV299 @ SV370 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1433]) ).
thf(1539,plain,
! [SV204: set_Product_prod_a_a,SV86: product_prod_a_a,SV371: product_prod_a_a > set_Product_prod_a_a,SV301: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV301 @ ( SV371 @ SV86 ) ) )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV86 @ SV301 ) @ ( produc304751368od_a_a @ SV204 @ SV371 ) )
= $true )
| ( ( member449909584od_a_a @ SV86 @ SV204 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1434]) ).
thf(1540,plain,
! [SV206: set_Product_prod_a_a,SV372: product_prod_a_a > $o,SV303: product_prod_a_a > $o,SV88: set_Product_prod_a_a] :
( ( ( ~ ! [SY1159: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1159 @ SV88 )
| ~ ( SV303 @ SY1159 )
| ( SV372 @ SY1159 ) ) )
= $true )
| ( ( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [SY1094: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1094 @ SV88 )
| ~ ( SV303 @ SY1094 ) ) )
@ ( collec645855634od_a_a
@ ^ [SY1161: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1161 @ SV206 )
| ~ ( SV372 @ SY1161 ) ) ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV88 @ SV206 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1435]) ).
thf(1541,plain,
! [SV373: product_prod_a_a > set_Product_prod_a_a,SV304: set_Product_prod_a_a,SV207: product_prod_a_a,SV89: product_prod_a_a] :
( ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV89 @ SV207 ) @ ( produc304751368od_a_a @ SV304 @ SV373 ) )
| ~ ( ~ ( member449909584od_a_a @ SV89 @ SV304 )
| ~ ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) ) ) )
= $false )
| ( ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV89 @ SV207 ) @ ( produc304751368od_a_a @ SV304 @ SV373 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ SV89 @ SV304 )
| ~ ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1436]) ).
thf(1542,plain,
! [SV208: product_prod_a_a,SV91: a] :
( ( ( ( SV91
!= ( product_snd_a_a @ SV208 ) )
| ~ ~ ! [SY956: a] :
( SV208
!= ( product_Pair_a_a @ SY956 @ SV91 ) ) )
= $false )
| ( ( SV91
= ( product_snd_a_a @ SV208 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1438]) ).
thf(1543,plain,
! [SV91: a,SV208: product_prod_a_a] :
( ( ( ! [SY956: a] :
( SV208
!= ( product_Pair_a_a @ SY956 @ SV91 ) ) )
= $true )
| ( ( ~ ( ( SV91
!= ( product_snd_a_a @ SV208 ) )
| ~ ~ ! [SY956: a] :
( SV208
!= ( product_Pair_a_a @ SY956 @ SV91 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1439]) ).
thf(1544,plain,
! [SV209: produc1572603623od_a_a > product_prod_a_a,SV92: product_prod_a_a,SV374: set_Pr1948701895od_a_a,SV305: produc1572603623od_a_a] :
( ( ( ~ ( member2057358096od_a_a @ SV305 @ SV374 ) )
= $true )
| ( ( member449909584od_a_a @ SV92 @ ( image_734753285od_a_a @ SV209 @ SV374 ) )
= $true )
| ( ( SV92
= ( SV209 @ SV305 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1440]) ).
thf(1545,plain,
! [SV210: a,SV93: a > $o,SV375: a,SV306: a > $o] :
( ( ( ~ ( SV306 @ SV375 ) )
= $true )
| ( ( ~ ( ~ ( SV93 @ ( product_fst_a_a @ ( product_Pair_a_a @ SV210 @ SV375 ) ) )
| ~ ( SV306 @ ( product_snd_a_a @ ( product_Pair_a_a @ SV210 @ SV375 ) ) ) ) )
= $true )
| ( ( SV93 @ SV210 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1441]) ).
thf(1546,plain,
! [SV407: set_Product_prod_a_a,SV398: product_prod_a_a > a,SV377: a,SV308: product_prod_a_a,SV212: product_prod_a_a > a,SV95: a] :
( ( ( SV95
!= ( SV212 @ SV308 ) )
= $true )
| ( ( ( SV377
!= ( SV398 @ SV308 ) )
| ~ ( member449909584od_a_a @ SV308 @ SV407 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV95 @ SV377 ) @ ( bNF_Gr1853143117_a_a_a @ SV407 @ SV212 @ SV398 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1443]) ).
thf(1547,plain,
! [SV311: set_Product_prod_a_a,SV215: product_prod_a_a > a,SV99: a] :
( ( ( ( SV99
!= ( SV215 @ ( sK35_SY1109 @ SV311 @ SV215 @ SV99 ) ) )
| ~ ( member449909584od_a_a @ ( sK35_SY1109 @ SV311 @ SV215 @ SV99 ) @ SV311 ) )
= $false )
| ( ( member_a @ SV99 @ ( image_340790172_a_a_a @ SV215 @ SV311 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1446]) ).
thf(1548,plain,
! [SV380: set_Product_prod_a_a,SV312: a > a,SV217: a > a,SV101: product_prod_a_a] :
( ( ( ! [SY1167: a,SY1168: a] :
( ( SV101
!= ( product_Pair_a_a @ ( SV217 @ SY1167 ) @ ( SV312 @ SY1168 ) ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1167 @ SY1168 ) @ SV380 ) ) )
= $false )
| ( ( member449909584od_a_a @ SV101 @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SV217 @ SV312 ) @ SV380 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1448]) ).
thf(1549,plain,
! [SV401: a > set_Product_prod_a_a,SV383: a,SV315: a,SV220: a,SV104: a > $o] :
( ( ( SV104 @ SV220 )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV315 @ SV383 ) @ ( SV401 @ SV220 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV220 @ SV315 ) @ ( product_Pair_a_a @ SV220 @ SV383 ) ) @ ( same_fst_a_a @ SV104 @ SV401 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1451]) ).
thf(1550,plain,
! [SV222: product_prod_a_a > a,SV106: a,SV384: set_Product_prod_a_a,SV316: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV316 @ SV384 ) )
= $true )
| ( ( member_a @ SV106 @ ( image_340790172_a_a_a @ SV222 @ SV384 ) )
= $true )
| ( ( SV106
= ( SV222 @ SV316 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1453]) ).
thf(1551,plain,
! [SV109: product_prod_a_a] :
( ( SV109
= ( product_Pair_a_a @ ( sK5_SY749 @ SV109 ) @ ( sK29_SY1119 @ SV109 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1454]) ).
thf(1552,plain,
! [SV225: product_prod_a_a > product_prod_a_a,SV110: product_prod_a_a,SV385: set_Product_prod_a_a,SV319: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV319 @ SV385 ) )
= $true )
| ( ( member449909584od_a_a @ SV110 @ ( image_794773445od_a_a @ SV225 @ SV385 ) )
= $true )
| ( ( SV110
= ( SV225 @ SV319 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1455]) ).
thf(1553,plain,
! [SV226: set_Product_prod_a_a,SV320: product_prod_a_a > set_Product_prod_a_a,SV111: produc1572603623od_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK36_SY1121 @ SV111 @ SV320 @ SV226 ) @ SV226 )
| ! [SY1197: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1197 @ ( SV320 @ ( sK36_SY1121 @ SV111 @ SV320 @ SV226 ) ) )
| ( SV111
!= ( produc1474507607od_a_a @ ( sK36_SY1121 @ SV111 @ SV320 @ SV226 ) @ SY1197 ) ) ) )
= $false )
| ( ( member2057358096od_a_a @ SV111 @ ( produc304751368od_a_a @ SV226 @ SV320 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1456]) ).
thf(1554,plain,
! [SV228: set_Product_prod_a_a,SV113: product_prod_a_a,SV386: product_prod_a_a > product_prod_a_a,SV322: product_prod_a_a] :
( ( ( SV322
!= ( SV386 @ SV113 ) )
= $true )
| ( ( member449909584od_a_a @ SV322 @ ( image_794773445od_a_a @ SV386 @ SV228 ) )
= $true )
| ( ( member449909584od_a_a @ SV113 @ SV228 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1457]) ).
thf(1555,plain,
! [SV323: set_a,SV229: a > product_prod_a_a,SV114: product_prod_a_a] :
( ( ( ( SV114
!= ( SV229 @ ( sK37_SY1124 @ SV323 @ SV229 @ SV114 ) ) )
| ~ ( member_a @ ( sK37_SY1124 @ SV323 @ SV229 @ SV114 ) @ SV323 ) )
= $false )
| ( ( member449909584od_a_a @ SV114 @ ( image_1725938350od_a_a @ SV229 @ SV323 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1458]) ).
thf(1556,plain,
! [SV410: set_Pr1948701895od_a_a,SV402: produc1572603623od_a_a > a,SV387: a,SV325: produc1572603623od_a_a,SV231: produc1572603623od_a_a > a,SV116: a] :
( ( ( SV116
!= ( SV231 @ SV325 ) )
= $true )
| ( ( ( SV387
!= ( SV402 @ SV325 ) )
| ~ ( member2057358096od_a_a @ SV325 @ SV410 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV116 @ SV387 ) @ ( bNF_Gr356189709_a_a_a @ SV410 @ SV231 @ SV402 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1459]) ).
thf(1557,plain,
! [SV233: set_a,SV327: a > set_a,SV119: product_prod_a_a] :
( ( ( ~ ( member_a @ ( sK38_SY1129 @ SV119 @ SV327 @ SV233 ) @ SV233 )
| ! [SY1198: a] :
( ~ ( member_a @ SY1198 @ ( SV327 @ ( sK38_SY1129 @ SV119 @ SV327 @ SV233 ) ) )
| ( SV119
!= ( product_Pair_a_a @ ( sK38_SY1129 @ SV119 @ SV327 @ SV233 ) @ SY1198 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ SV119 @ ( product_Sigma_a_a @ SV233 @ SV327 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1461]) ).
thf(1558,plain,
! [SV120: product_prod_a_a,SV389: product_prod_a_a > $o,SV328: set_Product_prod_a_a,SV234: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV234
@ ( collec645855634od_a_a
@ ^ [SY1174: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1174 @ SV328 )
| ~ ( SV389 @ SY1174 ) ) ) ) )
= $true )
| ( ( SV389 @ SV120 )
= $true )
| ( ( member449909584od_a_a @ SV120 @ SV234 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1462]) ).
thf(1559,plain,
! [SV122: set_Product_prod_a_a,SV236: product_prod_a_a > a,SV330: set_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK30_SY1133 @ SV330 @ SV236 @ SV122 ) @ SV122 ) )
= $false )
| ( ( ord_less_eq_set_a @ ( image_340790172_a_a_a @ SV236 @ SV122 ) @ SV330 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1463]) ).
thf(1560,plain,
! [SV122: set_Product_prod_a_a,SV330: set_a,SV236: product_prod_a_a > a] :
( ( ( member_a @ ( SV236 @ ( sK30_SY1133 @ SV330 @ SV236 @ SV122 ) ) @ SV330 )
= $false )
| ( ( ord_less_eq_set_a @ ( image_340790172_a_a_a @ SV236 @ SV122 ) @ SV330 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1463]) ).
thf(1561,plain,
! [SV411: set_Product_prod_a_a,SV403: set_Product_prod_a_a,SV390: a,SV331: a,SV237: a,SV123: a] :
( ( ~ ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SV331 @ SV390 ) ) @ ( lex_prod_a_a @ SV403 @ SV411 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
| ~ ( ( SV123 != SV331 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 ) ) )
| ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SV331 @ SV390 ) ) @ ( lex_prod_a_a @ SV403 @ SV411 ) )
| ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
| ~ ( ( SV123 != SV331 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1464]) ).
thf(1562,plain,
! [SV411: set_Product_prod_a_a,SV403: set_Product_prod_a_a,SV390: a,SV331: a,SV237: a,SV123: a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SV331 @ SV390 ) ) @ ( lex_prod_a_a @ SV403 @ SV411 ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
| ~ ( ( SV123 != SV331 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1464]) ).
thf(1563,plain,
! [SV238: product_prod_a_a,SV125: a] :
( ( ( ( SV125
!= ( product_fst_a_a @ SV238 ) )
| ~ ~ ! [SY1024: a] :
( SV238
!= ( product_Pair_a_a @ SV125 @ SY1024 ) ) )
= $false )
| ( ( SV125
= ( product_fst_a_a @ SV238 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1465]) ).
thf(1564,plain,
! [SV125: a,SV238: product_prod_a_a] :
( ( ( ! [SY1024: a] :
( SV238
!= ( product_Pair_a_a @ SV125 @ SY1024 ) ) )
= $true )
| ( ( ~ ( ( SV125
!= ( product_fst_a_a @ SV238 ) )
| ~ ~ ! [SY1024: a] :
( SV238
!= ( product_Pair_a_a @ SV125 @ SY1024 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1466]) ).
thf(1565,plain,
! [SV239: set_Product_prod_a_a,SV332: set_Product_prod_a_a,SV126: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV126 @ SV332 ) )
= $false )
| ( ( member449909584od_a_a @ SV126 @ ( minus_1507102574od_a_a @ SV239 @ SV332 ) )
= $true )
| ( ( member449909584od_a_a @ SV126 @ SV239 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1467]) ).
thf(1566,plain,
! [SV391: a > set_a,SV240: a,SV333: set_a,SV127: a] :
( ( ( ~ ( member_a @ SV127 @ SV333 )
| ~ ( member_a @ SV240 @ ( SV391 @ SV127 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV127 @ SV240 ) @ ( product_Sigma_a_a @ SV333 @ SV391 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1468]) ).
thf(1567,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a] :
( ( ( ( ^ [SY1199: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1199 ) @ SV2 ) )
= ( ^ [SY1200: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1200 ) @ SV131 ) ) )
= $false )
| ( ( ~ ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
!= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
| ( SV2 != SV131 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1470]) ).
thf(1568,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
!= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
| ( SV2 != SV131 ) )
= $false )
| ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1471]) ).
thf(1569,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
!= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $false )
| ( ( SV2 = SV131 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1472]) ).
thf(1570,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( SV2 != SV131 )
= $false )
| ( ( SV2 = SV131 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1472]) ).
thf(1571,plain,
! [SV243: set_Product_prod_a_a,SV132: a,SV3: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV3 @ SV132 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV243 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV132 @ SV3 ) @ SV243 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV3 @ SV132 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV243 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1473]) ).
thf(1572,plain,
! [SV243: set_Product_prod_a_a,SV132: a,SV3: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV3 @ SV132 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV243 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV132 @ SV3 ) @ SV243 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV132 @ SV3 ) @ SV243 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1474]) ).
thf(1573,plain,
! [SV133: product_prod_a_a > $o,SV4: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV4 @ ( collec645855634od_a_a @ SV133 ) ) )
= $false )
| ( ( member449909584od_a_a @ SV4 @ ( collec645855634od_a_a @ SV133 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1475]) ).
thf(1574,plain,
! [SV4: product_prod_a_a,SV133: product_prod_a_a > $o] :
( ( ( ~ ( SV133 @ SV4 ) )
= $false )
| ( ( member449909584od_a_a @ SV4 @ ( collec645855634od_a_a @ SV133 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1475]) ).
thf(1575,plain,
! [SV133: product_prod_a_a > $o,SV4: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV4 @ ( collec645855634od_a_a @ SV133 ) ) )
= $false )
| ( ( SV133 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1476]) ).
thf(1576,plain,
! [SV4: product_prod_a_a,SV133: product_prod_a_a > $o] :
( ( ( ~ ( SV133 @ SV4 ) )
= $false )
| ( ( SV133 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1476]) ).
thf(1577,plain,
! [SV138: product_prod_a_a] :
( ( ( ~ ( top_to1483957574_a_a_o @ SV138 ) )
= $false )
| ( ( top_to1483957574_a_a_o @ SV138 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1477]) ).
thf(1578,plain,
! [SV138: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV138 @ top_to398455383od_a_a ) )
= $false )
| ( ( top_to1483957574_a_a_o @ SV138 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1477]) ).
thf(1579,plain,
! [SV138: product_prod_a_a] :
( ( ( ~ ( top_to1483957574_a_a_o @ SV138 ) )
= $false )
| ( ( member449909584od_a_a @ SV138 @ top_to398455383od_a_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1478]) ).
thf(1580,plain,
! [SV138: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV138 @ top_to398455383od_a_a ) )
= $false )
| ( ( member449909584od_a_a @ SV138 @ top_to398455383od_a_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1478]) ).
thf(1581,plain,
! [SV340: a,SV140: a] :
( ( ( top_top_a_a_o @ SV140 @ SV340 )
= $false )
| ( ( ~ ( ~ ( top_top_a_a_o @ SV140 @ SV340 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV140 @ SV340 ) @ top_to398455383od_a_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1479]) ).
thf(1582,plain,
! [SV340: a,SV140: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV140 @ SV340 ) @ top_to398455383od_a_a )
= $false )
| ( ( ~ ( ~ ( top_top_a_a_o @ SV140 @ SV340 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV140 @ SV340 ) @ top_to398455383od_a_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1479]) ).
thf(1583,plain,
! [SV249: set_a,SV143: set_a,SV20: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV20 @ ( product_product_a_a @ SV143 @ SV249 ) )
| ~ ( member449909584od_a_a @ SV20
@ ( product_Sigma_a_a @ SV143
@ ^ [SY1036: a] : SV249 ) ) )
= $false )
| ( ( member449909584od_a_a @ SV20 @ ( product_product_a_a @ SV143 @ SV249 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1480]) ).
thf(1584,plain,
! [SV249: set_a,SV143: set_a,SV20: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV20 @ ( product_product_a_a @ SV143 @ SV249 ) )
| ~ ( member449909584od_a_a @ SV20
@ ( product_Sigma_a_a @ SV143
@ ^ [SY1036: a] : SV249 ) ) )
= $false )
| ( ( member449909584od_a_a @ SV20
@ ( product_Sigma_a_a @ SV143
@ ^ [SY1036: a] : SV249 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1481]) ).
thf(1585,plain,
! [SV144: set_Product_prod_a_a,SV21: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1347718902_a_a_o
@ ^ [SY498: product_prod_a_a] : ( member449909584od_a_a @ SY498 @ SV21 )
@ ^ [SY826: product_prod_a_a] : ( member449909584od_a_a @ SY826 @ SV144 ) ) )
= $false )
| ( ( ord_le1347718902_a_a_o
@ ^ [SY498: product_prod_a_a] : ( member449909584od_a_a @ SY498 @ SV21 )
@ ^ [SY826: product_prod_a_a] : ( member449909584od_a_a @ SY826 @ SV144 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1482]) ).
thf(1586,plain,
! [SV144: set_Product_prod_a_a,SV21: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV21 @ SV144 ) )
= $false )
| ( ( ord_le1347718902_a_a_o
@ ^ [SY498: product_prod_a_a] : ( member449909584od_a_a @ SY498 @ SV21 )
@ ^ [SY826: product_prod_a_a] : ( member449909584od_a_a @ SY826 @ SV144 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1482]) ).
thf(1587,plain,
! [SV144: set_Product_prod_a_a,SV21: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1347718902_a_a_o
@ ^ [SY498: product_prod_a_a] : ( member449909584od_a_a @ SY498 @ SV21 )
@ ^ [SY826: product_prod_a_a] : ( member449909584od_a_a @ SY826 @ SV144 ) ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV21 @ SV144 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1483]) ).
thf(1588,plain,
! [SV144: set_Product_prod_a_a,SV21: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV21 @ SV144 ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV21 @ SV144 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1483]) ).
thf(1589,plain,
! [SV341: set_Product_prod_a_a,SV145: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV145 @ SV341 )
= $false )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV145 @ SV341 )
| ~ ( ord_le1347718902_a_a_o
@ ^ [SY828: product_prod_a_a] : ( member449909584od_a_a @ SY828 @ SV145 )
@ ^ [SY1142: product_prod_a_a] : ( member449909584od_a_a @ SY1142 @ SV341 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1484]) ).
thf(1590,plain,
! [SV341: set_Product_prod_a_a,SV145: set_Product_prod_a_a] :
( ( ( ord_le1347718902_a_a_o
@ ^ [SY828: product_prod_a_a] : ( member449909584od_a_a @ SY828 @ SV145 )
@ ^ [SY1142: product_prod_a_a] : ( member449909584od_a_a @ SY1142 @ SV341 ) )
= $false )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV145 @ SV341 )
| ~ ( ord_le1347718902_a_a_o
@ ^ [SY828: product_prod_a_a] : ( member449909584od_a_a @ SY828 @ SV145 )
@ ^ [SY1142: product_prod_a_a] : ( member449909584od_a_a @ SY1142 @ SV341 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1484]) ).
thf(1591,plain,
! [SV146: set_Product_prod_a_a,SV23: set_Product_prod_a_a] :
( ( ( ~ ( ord_less_eq_a_a_o
@ ^ [SY504: a,SY505: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY504 @ SY505 ) @ SV23 )
@ ^ [SY832: a,SY833: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY832 @ SY833 ) @ SV146 ) ) )
= $false )
| ( ( ord_less_eq_a_a_o
@ ^ [SY504: a,SY505: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY504 @ SY505 ) @ SV23 )
@ ^ [SY832: a,SY833: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY832 @ SY833 ) @ SV146 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1485]) ).
thf(1592,plain,
! [SV146: set_Product_prod_a_a,SV23: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV23 @ SV146 ) )
= $false )
| ( ( ord_less_eq_a_a_o
@ ^ [SY504: a,SY505: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY504 @ SY505 ) @ SV23 )
@ ^ [SY832: a,SY833: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY832 @ SY833 ) @ SV146 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1485]) ).
thf(1593,plain,
! [SV146: set_Product_prod_a_a,SV23: set_Product_prod_a_a] :
( ( ( ~ ( ord_less_eq_a_a_o
@ ^ [SY504: a,SY505: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY504 @ SY505 ) @ SV23 )
@ ^ [SY832: a,SY833: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY832 @ SY833 ) @ SV146 ) ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV23 @ SV146 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1486]) ).
thf(1594,plain,
! [SV146: set_Product_prod_a_a,SV23: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV23 @ SV146 ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV23 @ SV146 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1486]) ).
thf(1595,plain,
! [SV24: set_Product_prod_a_a] :
( ( ( ~ ! [SY508: product_prod_a_a] :
~ ( member449909584od_a_a @ SY508 @ SV24 )
| ( SV24 != bot_bo2131659635od_a_a ) )
= $false )
| ( ( member449909584od_a_a @ ( sK19_SY508 @ SV24 ) @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1487]) ).
thf(1596,plain,
! [SV24: set_Product_prod_a_a] :
( ( ( ! [SY508: product_prod_a_a] :
~ ( member449909584od_a_a @ SY508 @ SV24 ) )
= $true )
| ( ( SV24 = bot_bo2131659635od_a_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1488]) ).
thf(1597,plain,
! [SV24: set_Product_prod_a_a] :
( ( ( SV24 = bot_bo2131659635od_a_a )
= $true )
| ( ( SV24 = bot_bo2131659635od_a_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1489]) ).
thf(1598,plain,
! [SV149: product_prod_a_a > produc1572603623od_a_a,SV29: produc1572603623od_a_a,SV342: set_Product_prod_a_a,SV251: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV251 @ SV342 )
= $false )
| ( ( member2057358096od_a_a @ SV29 @ ( image_1765377413od_a_a @ SV149 @ SV342 ) )
= $true )
| ( ( SV29
= ( SV149 @ SV251 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1491]) ).
thf(1599,plain,
! [SV343: a,SV252: a,SV150: a,SV30: a] :
( ( ( ( product_Pair_a_a @ SV30 @ SV150 )
= ( product_Pair_a_a @ SV252 @ SV343 ) )
= $false )
| ( ( ~ ( ( ( product_Pair_a_a @ SV30 @ SV150 )
!= ( product_Pair_a_a @ SV252 @ SV343 ) )
| ~ ~ ( ( SV30 != SV252 )
| ( SV150 != SV343 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1492]) ).
thf(1600,plain,
! [SV343: a,SV150: a,SV252: a,SV30: a] :
( ( ( ~ ( ( SV30 != SV252 )
| ( SV150 != SV343 ) ) )
= $false )
| ( ( ~ ( ( ( product_Pair_a_a @ SV30 @ SV150 )
!= ( product_Pair_a_a @ SV252 @ SV343 ) )
| ~ ~ ( ( SV30 != SV252 )
| ( SV150 != SV343 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1492]) ).
thf(1601,plain,
! [SV151: set_Product_prod_a_a,SV31: product_prod_a_a,SV344: product_prod_a_a > produc1572603623od_a_a,SV253: produc1572603623od_a_a] :
( ( ( SV253
= ( SV344 @ SV31 ) )
= $false )
| ( ( member2057358096od_a_a @ SV253 @ ( image_1765377413od_a_a @ SV344 @ SV151 ) )
= $true )
| ( ( member449909584od_a_a @ SV31 @ SV151 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1493]) ).
thf(1602,plain,
! [SV32: set_Product_prod_a_a,SV152: product_prod_a_a > product_prod_a_a,SV254: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( sK20_SY1042 @ SV254 @ SV152 @ SV32 ) @ SV32 )
= $true )
| ( ( ord_le1824328871od_a_a @ ( image_794773445od_a_a @ SV152 @ SV32 ) @ SV254 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1494]) ).
thf(1603,plain,
! [SV255: set_Product_prod_a_a,SV153: set_Product_prod_a_a,SV33: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV33 @ ( minus_1507102574od_a_a @ SV153 @ SV255 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ SV33 @ SV153 )
| ~ ~ ( member449909584od_a_a @ SV33 @ SV255 ) ) )
= $false )
| ( ( member449909584od_a_a @ SV33 @ ( minus_1507102574od_a_a @ SV153 @ SV255 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1496]) ).
thf(1604,plain,
! [SV255: set_Product_prod_a_a,SV153: set_Product_prod_a_a,SV33: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV33 @ SV153 )
| ~ ~ ( member449909584od_a_a @ SV33 @ SV255 ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ SV33 @ ( minus_1507102574od_a_a @ SV153 @ SV255 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ SV33 @ SV153 )
| ~ ~ ( member449909584od_a_a @ SV33 @ SV255 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1497]) ).
thf(1605,plain,
! [SV34: set_a,SV154: a > product_prod_a_a,SV256: set_Product_prod_a_a] :
( ( ( member_a @ ( sK21_SY1043 @ SV256 @ SV154 @ SV34 ) @ SV34 )
= $true )
| ( ( ord_le1824328871od_a_a @ ( image_1725938350od_a_a @ SV154 @ SV34 ) @ SV256 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1498]) ).
thf(1606,plain,
! [SV345: set_Product_prod_a_a,SV155: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV155 @ SV345 )
= $false )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV155 @ SV345 )
| ~ ! [SY1143: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1143 @ SV155 )
| ( member449909584od_a_a @ SY1143 @ SV345 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1500]) ).
thf(1607,plain,
! [SV345: set_Product_prod_a_a,SV155: set_Product_prod_a_a] :
( ( ( ! [SY1143: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1143 @ SV155 )
| ( member449909584od_a_a @ SY1143 @ SV345 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV155 @ SV345 )
| ~ ! [SY1143: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1143 @ SV155 )
| ( member449909584od_a_a @ SY1143 @ SV345 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1500]) ).
thf(1608,plain,
! [SV36: set_Product_prod_a_a,SV413: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV413 @ SV36 )
= $false )
| ( ( ~ ( ~ ~ ! [SY531: product_prod_a_a] :
~ ( member449909584od_a_a @ SY531 @ SV36 )
| ~ ( ( SV36 != bot_bo2131659635od_a_a ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1501]) ).
thf(1609,plain,
! [SV36: set_Product_prod_a_a] :
( ( ( ~ ~ ! [SY531: product_prod_a_a] :
~ ( member449909584od_a_a @ SY531 @ SV36 ) )
= $false )
| ( ( SV36 = bot_bo2131659635od_a_a )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1502]) ).
thf(1610,plain,
! [SV36: set_Product_prod_a_a] :
( ( ( ~ ( ( SV36 != bot_bo2131659635od_a_a ) ) )
= $false )
| ( ( SV36 = bot_bo2131659635od_a_a )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1502]) ).
thf(1611,plain,
! [SV258: set_Product_prod_a_a,SV158: product_prod_a_a > produc1572603623od_a_a,SV39: produc1572603623od_a_a] :
( ( ( SV39
!= ( SV158 @ ( sK32_SY1045 @ SV258 @ SV158 @ SV39 ) ) )
= $false )
| ( ( member2057358096od_a_a @ SV39 @ ( image_1765377413od_a_a @ SV158 @ SV258 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1504]) ).
thf(1612,plain,
! [SV39: produc1572603623od_a_a,SV158: product_prod_a_a > produc1572603623od_a_a,SV258: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK32_SY1045 @ SV258 @ SV158 @ SV39 ) @ SV258 ) )
= $false )
| ( ( member2057358096od_a_a @ SV39 @ ( image_1765377413od_a_a @ SV158 @ SV258 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1504]) ).
thf(1613,plain,
! [SV159: a > product_prod_a_a,SV40: product_prod_a_a,SV346: set_a,SV259: a] :
( ( ( member_a @ SV259 @ SV346 )
= $false )
| ( ( member449909584od_a_a @ SV40 @ ( image_1725938350od_a_a @ SV159 @ SV346 ) )
= $true )
| ( ( SV40
= ( SV159 @ SV259 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1505]) ).
thf(1614,plain,
! [SV260: set_Product_prod_a_a,SV161: product_prod_a_a > product_prod_a_a,SV42: product_prod_a_a] :
( ( ( SV42
!= ( SV161 @ ( sK33_SY1047 @ SV260 @ SV161 @ SV42 ) ) )
= $false )
| ( ( member449909584od_a_a @ SV42 @ ( image_794773445od_a_a @ SV161 @ SV260 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1506]) ).
thf(1615,plain,
! [SV42: product_prod_a_a,SV161: product_prod_a_a > product_prod_a_a,SV260: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK33_SY1047 @ SV260 @ SV161 @ SV42 ) @ SV260 ) )
= $false )
| ( ( member449909584od_a_a @ SV42 @ ( image_794773445od_a_a @ SV161 @ SV260 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1506]) ).
thf(1616,plain,
! [SV347: set_Product_prod_a_a,SV162: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV162 @ SV347 )
= $false )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV162 @ SV347 )
| ~ ! [SY1144: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1144 @ SV162 )
| ( member449909584od_a_a @ SY1144 @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1507]) ).
thf(1617,plain,
! [SV347: set_Product_prod_a_a,SV162: set_Product_prod_a_a] :
( ( ( ! [SY1144: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1144 @ SV162 )
| ( member449909584od_a_a @ SY1144 @ SV347 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV162 @ SV347 )
| ~ ! [SY1144: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1144 @ SV162 )
| ( member449909584od_a_a @ SY1144 @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1507]) ).
thf(1618,plain,
! [SV263: set_Product_prod_a_a,SV164: set_Product_prod_a_a,SV45: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV45 @ SV164 )
= $true )
| ( ( member449909584od_a_a @ SV45 @ ( minus_1507102574od_a_a @ SV164 @ SV263 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1508]) ).
thf(1619,plain,
! [SV264: product_prod_a_a > $o,SV165: set_Product_prod_a_a,SV46: set_Product_prod_a_a] :
( ( ( ( ord_le1824328871od_a_a @ SV46
@ ( collec645855634od_a_a
@ ^ [SY1049: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1049 @ SV165 )
| ~ ( SV264 @ SY1049 ) ) ) )
| ! [SY1050: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1050 @ SV46 )
| ( SV264 @ SY1050 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV46
@ ( collec645855634od_a_a
@ ^ [SY1049: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1049 @ SV165 )
| ~ ( SV264 @ SY1049 ) ) ) )
| ~ ! [SY1050: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1050 @ SV46 )
| ( SV264 @ SY1050 ) ) ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV46 @ SV165 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1510]) ).
thf(1620,plain,
! [SV266: set_Pr1948701895od_a_a,SV167: produc1572603623od_a_a > product_prod_a_a,SV48: product_prod_a_a] :
( ( ( SV48
!= ( SV167 @ ( sK34_SY1053 @ SV266 @ SV167 @ SV48 ) ) )
= $false )
| ( ( member449909584od_a_a @ SV48 @ ( image_734753285od_a_a @ SV167 @ SV266 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1511]) ).
thf(1621,plain,
! [SV48: product_prod_a_a,SV167: produc1572603623od_a_a > product_prod_a_a,SV266: set_Pr1948701895od_a_a] :
( ( ( ~ ( member2057358096od_a_a @ ( sK34_SY1053 @ SV266 @ SV167 @ SV48 ) @ SV266 ) )
= $false )
| ( ( member449909584od_a_a @ SV48 @ ( image_734753285od_a_a @ SV167 @ SV266 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1511]) ).
thf(1622,plain,
! [SV49: set_a,SV168: set_Product_prod_a_a,SV349: a,SV267: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV267 @ SV349 ) @ SV168 )
= $false )
| ( ( member_a @ SV267 @ SV49 )
= $true )
| ( ( prefer1292084992ence_a @ SV49 @ SV168 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1512]) ).
thf(1623,plain,
! [SV170: set_a,SV51: a,SV350: a > product_prod_a_a,SV269: product_prod_a_a] :
( ( ( SV269
= ( SV350 @ SV51 ) )
= $false )
| ( ( member449909584od_a_a @ SV269 @ ( image_1725938350od_a_a @ SV350 @ SV170 ) )
= $true )
| ( ( member_a @ SV51 @ SV170 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1513]) ).
thf(1624,plain,
! [SV172: set_Pr1948701895od_a_a,SV53: produc1572603623od_a_a,SV352: produc1572603623od_a_a > product_prod_a_a,SV271: product_prod_a_a] :
( ( ( SV271
= ( SV352 @ SV53 ) )
= $false )
| ( ( member449909584od_a_a @ SV271 @ ( image_734753285od_a_a @ SV352 @ SV172 ) )
= $true )
| ( ( member2057358096od_a_a @ SV53 @ SV172 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1514]) ).
thf(1625,plain,
! [SV274: set_Product_prod_a_a,SV56: a,SV175: a,SV353: a] :
( ( ( SV353 = SV175 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV56 @ SV353 ) @ SV274 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV56 @ SV175 ) @ SV274 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1515]) ).
thf(1626,plain,
! [SV354: a,SV275: a,SV176: a,SV57: a] :
( ( ( ( product_Pair_a_a @ SV57 @ SV176 )
= ( product_Pair_a_a @ SV275 @ SV354 ) )
= $false )
| ( ( ~ ( ( ( product_Pair_a_a @ SV57 @ SV176 )
!= ( product_Pair_a_a @ SV275 @ SV354 ) )
| ~ ~ ( ( SV57 != SV275 )
| ( SV176 != SV354 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1516]) ).
thf(1627,plain,
! [SV354: a,SV176: a,SV275: a,SV57: a] :
( ( ( ~ ( ( SV57 != SV275 )
| ( SV176 != SV354 ) ) )
= $false )
| ( ( ~ ( ( ( product_Pair_a_a @ SV57 @ SV176 )
!= ( product_Pair_a_a @ SV275 @ SV354 ) )
| ~ ~ ( ( SV57 != SV275 )
| ( SV176 != SV354 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1516]) ).
thf(1628,plain,
! [SV177: set_Product_prod_a_a,SV58: product_prod_a_a,SV355: product_prod_a_a > a,SV276: a] :
( ( ( SV276
= ( SV355 @ SV58 ) )
= $false )
| ( ( member_a @ SV276 @ ( image_340790172_a_a_a @ SV355 @ SV177 ) )
= $true )
| ( ( member449909584od_a_a @ SV58 @ SV177 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1517]) ).
thf(1629,plain,
! [SV59: set_Pr1948701895od_a_a,SV178: produc1572603623od_a_a > product_prod_a_a,SV277: set_Product_prod_a_a] :
( ( ( member2057358096od_a_a @ ( sK23_SY1063 @ SV277 @ SV178 @ SV59 ) @ SV59 )
= $true )
| ( ( ord_le1824328871od_a_a @ ( image_734753285od_a_a @ SV178 @ SV59 ) @ SV277 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1518]) ).
thf(1630,plain,
! [SV60: set_Product_prod_a_a,SV179: set_a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK13_SY892 @ SV179 @ SV60 ) @ ( sK24_SY1180 @ SV60 @ SV179 ) ) @ SV60 )
= $true )
| ( ( ~ ! [SY894: a,SY895: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY894 @ SY895 ) @ SV60 )
| ( member_a @ SY895 @ SV179 ) )
| ~ ( order_preorder_on_a @ SV179 @ SV60 )
| ( prefer1292084992ence_a @ SV179 @ SV60 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1520]) ).
thf(1631,plain,
! [SV179: set_a,SV60: set_Product_prod_a_a] :
( ( ( ~ ! [SY894: a,SY895: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY894 @ SY895 ) @ SV60 )
| ( member_a @ SY895 @ SV179 ) ) )
= $true )
| ( ( ~ ( order_preorder_on_a @ SV179 @ SV60 )
| ( prefer1292084992ence_a @ SV179 @ SV60 ) )
= $true )
| ( ( member_a @ ( sK13_SY892 @ SV179 @ SV60 ) @ SV179 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1521]) ).
thf(1632,plain,
! [SV61: set_a,SV394: a,SV180: set_Product_prod_a_a,SV356: a,SV278: a] :
( ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV356 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV278 ) @ SV180 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV394 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV356 ) @ SV180 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV394 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV278 ) @ SV180 ) ) )
= $true )
| ( ( prefer1292084992ence_a @ SV61 @ SV180 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1522]) ).
thf(1633,plain,
! [SV62: set_Product_prod_a_a,SV181: set_Pr1948701895od_a_a,SV357: product_prod_a_a,SV279: product_prod_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV279 @ SV357 ) @ SV181 )
= $false )
| ( ( member449909584od_a_a @ SV279 @ SV62 )
= $true )
| ( ( prefer1338892073od_a_a @ SV62 @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1523]) ).
thf(1634,plain,
! [SV64: a > a > $o,SV281: a,SV183: a,SV359: product_prod_a_a] :
( ( ( SV359
= ( product_Pair_a_a @ SV183 @ SV281 ) )
= $false )
| ( ( SV64 @ ( product_fst_a_a @ SV359 ) @ ( product_snd_a_a @ SV359 ) )
= $true )
| ( ( SV64 @ SV183 @ SV281 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1524]) ).
thf(1635,plain,
! [SV405: set_a,SV395: a > a,SV360: a,SV282: a,SV184: a > a,SV65: a] :
( ( ( SV65
= ( SV184 @ SV282 ) )
= $false )
| ( ( ( SV360
!= ( SV395 @ SV282 ) )
| ~ ( member_a @ SV282 @ SV405 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV65 @ SV360 ) @ ( bNF_Gr423046308_a_a_a @ SV405 @ SV184 @ SV395 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1525]) ).
thf(1636,plain,
! [SV185: set_a,SV66: a,SV361: a > set_a,SV283: a] :
( ( ( member_a @ SV283 @ ( SV361 @ SV66 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV66 @ SV283 ) @ ( product_Sigma_a_a @ SV185 @ SV361 ) )
= $true )
| ( ( member_a @ SV66 @ SV185 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1526]) ).
thf(1637,plain,
! [SV362: a,SV186: a,SV284: a,SV67: a] :
( ( ( SV67 != SV284 )
= $false )
| ( ( ( product_Pair_a_a @ SV67 @ SV186 )
= ( product_Pair_a_a @ SV284 @ SV362 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1527]) ).
thf(1638,plain,
! [SV284: a,SV67: a,SV362: a,SV186: a] :
( ( ( SV186 != SV362 )
= $false )
| ( ( ( product_Pair_a_a @ SV67 @ SV186 )
= ( product_Pair_a_a @ SV284 @ SV362 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1527]) ).
thf(1639,plain,
! [SV70: set_Product_prod_a_a,SV189: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK14_SY915 @ SV189 @ SV70 ) @ ( sK25_SY1182 @ SV70 @ SV189 ) ) @ SV70 )
= $true )
| ( ( ord_le1824328871od_a_a @ SV70 @ SV189 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1528]) ).
thf(1640,plain,
! [SV365: a > set_a,SV290: set_a,SV193: a,SV75: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV75 @ SV193 ) @ ( product_Sigma_a_a @ SV290 @ SV365 ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV75 @ SV193 ) @ ( product_Sigma_a_a @ SV290 @ SV365 ) )
| ~ ~ ( ~ ( member_a @ SV75 @ SV290 )
| ~ ( member_a @ SV193 @ ( SV365 @ SV75 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1530]) ).
thf(1641,plain,
! [SV365: a > set_a,SV193: a,SV290: set_a,SV75: a] :
( ( ( ~ ( ~ ( member_a @ SV75 @ SV290 )
| ~ ( member_a @ SV193 @ ( SV365 @ SV75 ) ) ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV75 @ SV193 ) @ ( product_Sigma_a_a @ SV290 @ SV365 ) )
| ~ ~ ( ~ ( member_a @ SV75 @ SV290 )
| ~ ( member_a @ SV193 @ ( SV365 @ SV75 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1530]) ).
thf(1642,plain,
! [SV406: set_Product_prod_a_a,SV396: product_prod_a_a > product_prod_a_a,SV366: product_prod_a_a,SV291: product_prod_a_a,SV194: product_prod_a_a > product_prod_a_a,SV76: product_prod_a_a] :
( ( ( SV76
= ( SV194 @ SV291 ) )
= $false )
| ( ( ( SV366
!= ( SV396 @ SV291 ) )
| ~ ( member449909584od_a_a @ SV291 @ SV406 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV76 @ SV366 ) @ ( bNF_Gr200450189od_a_a @ SV406 @ SV194 @ SV396 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1531]) ).
thf(1643,plain,
! [SV81: set_Product_prod_a_a,SV199: product_prod_a_a > produc1572603623od_a_a,SV296: set_Pr1948701895od_a_a] :
( ( ( member449909584od_a_a @ ( sK26_SY1085 @ SV296 @ SV199 @ SV81 ) @ SV81 )
= $true )
| ( ( ord_le456379495od_a_a @ ( image_1765377413od_a_a @ SV199 @ SV81 ) @ SV296 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1535]) ).
thf(1644,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( prefer1292084992ence_a @ SV201 @ SV369 )
= $false )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 )
| ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1537]) ).
thf(1645,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) )
= $false )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 )
| ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1537]) ).
thf(1646,plain,
! [SV370: product_prod_a_a > set_Product_prod_a_a,SV202: product_prod_a_a,SV299: set_Product_prod_a_a,SV84: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV84 @ SV299 ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV84 @ SV202 ) @ ( produc304751368od_a_a @ SV299 @ SV370 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1538]) ).
thf(1647,plain,
! [SV299: set_Product_prod_a_a,SV84: product_prod_a_a,SV370: product_prod_a_a > set_Product_prod_a_a,SV202: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV202 @ ( SV370 @ SV84 ) ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV84 @ SV202 ) @ ( produc304751368od_a_a @ SV299 @ SV370 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1538]) ).
thf(1648,plain,
! [SV204: set_Product_prod_a_a,SV86: product_prod_a_a,SV371: product_prod_a_a > set_Product_prod_a_a,SV301: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV301 @ ( SV371 @ SV86 ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV86 @ SV301 ) @ ( produc304751368od_a_a @ SV204 @ SV371 ) )
= $true )
| ( ( member449909584od_a_a @ SV86 @ SV204 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1539]) ).
thf(1649,plain,
! [SV206: set_Product_prod_a_a,SV372: product_prod_a_a > $o,SV303: product_prod_a_a > $o,SV88: set_Product_prod_a_a] :
( ( ( ! [SY1159: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1159 @ SV88 )
| ~ ( SV303 @ SY1159 )
| ( SV372 @ SY1159 ) ) )
= $false )
| ( ( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [SY1094: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1094 @ SV88 )
| ~ ( SV303 @ SY1094 ) ) )
@ ( collec645855634od_a_a
@ ^ [SY1161: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1161 @ SV206 )
| ~ ( SV372 @ SY1161 ) ) ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV88 @ SV206 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1540]) ).
thf(1650,plain,
! [SV373: product_prod_a_a > set_Product_prod_a_a,SV304: set_Product_prod_a_a,SV207: product_prod_a_a,SV89: product_prod_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV89 @ SV207 ) @ ( produc304751368od_a_a @ SV304 @ SV373 ) )
= $false )
| ( ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV89 @ SV207 ) @ ( produc304751368od_a_a @ SV304 @ SV373 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ SV89 @ SV304 )
| ~ ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1541]) ).
thf(1651,plain,
! [SV373: product_prod_a_a > set_Product_prod_a_a,SV207: product_prod_a_a,SV304: set_Product_prod_a_a,SV89: product_prod_a_a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ SV89 @ SV304 )
| ~ ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) ) ) )
= $false )
| ( ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV89 @ SV207 ) @ ( produc304751368od_a_a @ SV304 @ SV373 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ SV89 @ SV304 )
| ~ ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1541]) ).
thf(1652,plain,
! [SV208: product_prod_a_a,SV91: a] :
( ( ( SV91
!= ( product_snd_a_a @ SV208 ) )
= $false )
| ( ( SV91
= ( product_snd_a_a @ SV208 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1542]) ).
thf(1653,plain,
! [SV91: a,SV208: product_prod_a_a] :
( ( ( ~ ~ ! [SY956: a] :
( SV208
!= ( product_Pair_a_a @ SY956 @ SV91 ) ) )
= $false )
| ( ( SV91
= ( product_snd_a_a @ SV208 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1542]) ).
thf(1654,plain,
! [SV91: a,SV414: a,SV208: product_prod_a_a] :
( ( ( SV208
!= ( product_Pair_a_a @ SV414 @ SV91 ) )
= $true )
| ( ( ~ ( ( SV91
!= ( product_snd_a_a @ SV208 ) )
| ~ ~ ! [SY956: a] :
( SV208
!= ( product_Pair_a_a @ SY956 @ SV91 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1543]) ).
thf(1655,plain,
! [SV209: produc1572603623od_a_a > product_prod_a_a,SV92: product_prod_a_a,SV374: set_Pr1948701895od_a_a,SV305: produc1572603623od_a_a] :
( ( ( member2057358096od_a_a @ SV305 @ SV374 )
= $false )
| ( ( member449909584od_a_a @ SV92 @ ( image_734753285od_a_a @ SV209 @ SV374 ) )
= $true )
| ( ( SV92
= ( SV209 @ SV305 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1544]) ).
thf(1656,plain,
! [SV210: a,SV93: a > $o,SV375: a,SV306: a > $o] :
( ( ( SV306 @ SV375 )
= $false )
| ( ( ~ ( ~ ( SV93 @ ( product_fst_a_a @ ( product_Pair_a_a @ SV210 @ SV375 ) ) )
| ~ ( SV306 @ ( product_snd_a_a @ ( product_Pair_a_a @ SV210 @ SV375 ) ) ) ) )
= $true )
| ( ( SV93 @ SV210 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1545]) ).
thf(1657,plain,
! [SV407: set_Product_prod_a_a,SV398: product_prod_a_a > a,SV377: a,SV308: product_prod_a_a,SV212: product_prod_a_a > a,SV95: a] :
( ( ( SV95
= ( SV212 @ SV308 ) )
= $false )
| ( ( ( SV377
!= ( SV398 @ SV308 ) )
| ~ ( member449909584od_a_a @ SV308 @ SV407 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV95 @ SV377 ) @ ( bNF_Gr1853143117_a_a_a @ SV407 @ SV212 @ SV398 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1546]) ).
thf(1658,plain,
! [SV311: set_Product_prod_a_a,SV215: product_prod_a_a > a,SV99: a] :
( ( ( SV99
!= ( SV215 @ ( sK35_SY1109 @ SV311 @ SV215 @ SV99 ) ) )
= $false )
| ( ( member_a @ SV99 @ ( image_340790172_a_a_a @ SV215 @ SV311 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1547]) ).
thf(1659,plain,
! [SV99: a,SV215: product_prod_a_a > a,SV311: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK35_SY1109 @ SV311 @ SV215 @ SV99 ) @ SV311 ) )
= $false )
| ( ( member_a @ SV99 @ ( image_340790172_a_a_a @ SV215 @ SV311 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1547]) ).
thf(1660,plain,
! [SV312: a > a,SV380: set_Product_prod_a_a,SV217: a > a,SV101: product_prod_a_a] :
( ( ( ! [SY1201: a] :
( ( SV101
!= ( product_Pair_a_a @ ( SV217 @ ( sK40_SY1167 @ SV380 @ SV312 @ SV217 @ SV101 ) ) @ ( SV312 @ SY1201 ) ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK40_SY1167 @ SV380 @ SV312 @ SV217 @ SV101 ) @ SY1201 ) @ SV380 ) ) )
= $false )
| ( ( member449909584od_a_a @ SV101 @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SV217 @ SV312 ) @ SV380 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1548]) ).
thf(1661,plain,
! [SV104: a > $o,SV220: a,SV401: a > set_Product_prod_a_a,SV383: a,SV315: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV315 @ SV383 ) @ ( SV401 @ SV220 ) ) )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV220 @ SV315 ) @ ( product_Pair_a_a @ SV220 @ SV383 ) ) @ ( same_fst_a_a @ SV104 @ SV401 ) )
= $true )
| ( ( SV104 @ SV220 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1549]) ).
thf(1662,plain,
! [SV222: product_prod_a_a > a,SV106: a,SV384: set_Product_prod_a_a,SV316: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV316 @ SV384 )
= $false )
| ( ( member_a @ SV106 @ ( image_340790172_a_a_a @ SV222 @ SV384 ) )
= $true )
| ( ( SV106
= ( SV222 @ SV316 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1550]) ).
thf(1663,plain,
! [SV225: product_prod_a_a > product_prod_a_a,SV110: product_prod_a_a,SV385: set_Product_prod_a_a,SV319: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV319 @ SV385 )
= $false )
| ( ( member449909584od_a_a @ SV110 @ ( image_794773445od_a_a @ SV225 @ SV385 ) )
= $true )
| ( ( SV110
= ( SV225 @ SV319 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1552]) ).
thf(1664,plain,
! [SV226: set_Product_prod_a_a,SV320: product_prod_a_a > set_Product_prod_a_a,SV111: produc1572603623od_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK36_SY1121 @ SV111 @ SV320 @ SV226 ) @ SV226 ) )
= $false )
| ( ( member2057358096od_a_a @ SV111 @ ( produc304751368od_a_a @ SV226 @ SV320 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1553]) ).
thf(1665,plain,
! [SV226: set_Product_prod_a_a,SV111: produc1572603623od_a_a,SV320: product_prod_a_a > set_Product_prod_a_a] :
( ( ( ! [SY1197: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1197 @ ( SV320 @ ( sK36_SY1121 @ SV111 @ SV320 @ SV226 ) ) )
| ( SV111
!= ( produc1474507607od_a_a @ ( sK36_SY1121 @ SV111 @ SV320 @ SV226 ) @ SY1197 ) ) ) )
= $false )
| ( ( member2057358096od_a_a @ SV111 @ ( produc304751368od_a_a @ SV226 @ SV320 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1553]) ).
thf(1666,plain,
! [SV228: set_Product_prod_a_a,SV113: product_prod_a_a,SV386: product_prod_a_a > product_prod_a_a,SV322: product_prod_a_a] :
( ( ( SV322
= ( SV386 @ SV113 ) )
= $false )
| ( ( member449909584od_a_a @ SV322 @ ( image_794773445od_a_a @ SV386 @ SV228 ) )
= $true )
| ( ( member449909584od_a_a @ SV113 @ SV228 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1554]) ).
thf(1667,plain,
! [SV323: set_a,SV229: a > product_prod_a_a,SV114: product_prod_a_a] :
( ( ( SV114
!= ( SV229 @ ( sK37_SY1124 @ SV323 @ SV229 @ SV114 ) ) )
= $false )
| ( ( member449909584od_a_a @ SV114 @ ( image_1725938350od_a_a @ SV229 @ SV323 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1555]) ).
thf(1668,plain,
! [SV114: product_prod_a_a,SV229: a > product_prod_a_a,SV323: set_a] :
( ( ( ~ ( member_a @ ( sK37_SY1124 @ SV323 @ SV229 @ SV114 ) @ SV323 ) )
= $false )
| ( ( member449909584od_a_a @ SV114 @ ( image_1725938350od_a_a @ SV229 @ SV323 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1555]) ).
thf(1669,plain,
! [SV410: set_Pr1948701895od_a_a,SV402: produc1572603623od_a_a > a,SV387: a,SV325: produc1572603623od_a_a,SV231: produc1572603623od_a_a > a,SV116: a] :
( ( ( SV116
= ( SV231 @ SV325 ) )
= $false )
| ( ( ( SV387
!= ( SV402 @ SV325 ) )
| ~ ( member2057358096od_a_a @ SV325 @ SV410 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV116 @ SV387 ) @ ( bNF_Gr356189709_a_a_a @ SV410 @ SV231 @ SV402 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1556]) ).
thf(1670,plain,
! [SV233: set_a,SV327: a > set_a,SV119: product_prod_a_a] :
( ( ( ~ ( member_a @ ( sK38_SY1129 @ SV119 @ SV327 @ SV233 ) @ SV233 ) )
= $false )
| ( ( member449909584od_a_a @ SV119 @ ( product_Sigma_a_a @ SV233 @ SV327 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1557]) ).
thf(1671,plain,
! [SV233: set_a,SV119: product_prod_a_a,SV327: a > set_a] :
( ( ( ! [SY1198: a] :
( ~ ( member_a @ SY1198 @ ( SV327 @ ( sK38_SY1129 @ SV119 @ SV327 @ SV233 ) ) )
| ( SV119
!= ( product_Pair_a_a @ ( sK38_SY1129 @ SV119 @ SV327 @ SV233 ) @ SY1198 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ SV119 @ ( product_Sigma_a_a @ SV233 @ SV327 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1557]) ).
thf(1672,plain,
! [SV120: product_prod_a_a,SV389: product_prod_a_a > $o,SV328: set_Product_prod_a_a,SV234: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV234
@ ( collec645855634od_a_a
@ ^ [SY1174: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1174 @ SV328 )
| ~ ( SV389 @ SY1174 ) ) ) )
= $false )
| ( ( SV389 @ SV120 )
= $true )
| ( ( member449909584od_a_a @ SV120 @ SV234 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1558]) ).
thf(1673,plain,
! [SV122: set_Product_prod_a_a,SV236: product_prod_a_a > a,SV330: set_a] :
( ( ( member449909584od_a_a @ ( sK30_SY1133 @ SV330 @ SV236 @ SV122 ) @ SV122 )
= $true )
| ( ( ord_less_eq_set_a @ ( image_340790172_a_a_a @ SV236 @ SV122 ) @ SV330 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1559]) ).
thf(1674,plain,
! [SV411: set_Product_prod_a_a,SV403: set_Product_prod_a_a,SV390: a,SV331: a,SV237: a,SV123: a] :
( ( ( ~ ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SV331 @ SV390 ) ) @ ( lex_prod_a_a @ SV403 @ SV411 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
| ~ ( ( SV123 != SV331 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 ) ) ) )
= $true )
| ( ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SV331 @ SV390 ) ) @ ( lex_prod_a_a @ SV403 @ SV411 ) )
| ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
| ~ ( ( SV123 != SV331 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1561]) ).
thf(1675,plain,
! [SV238: product_prod_a_a,SV125: a] :
( ( ( SV125
!= ( product_fst_a_a @ SV238 ) )
= $false )
| ( ( SV125
= ( product_fst_a_a @ SV238 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1563]) ).
thf(1676,plain,
! [SV125: a,SV238: product_prod_a_a] :
( ( ( ~ ~ ! [SY1024: a] :
( SV238
!= ( product_Pair_a_a @ SV125 @ SY1024 ) ) )
= $false )
| ( ( SV125
= ( product_fst_a_a @ SV238 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1563]) ).
thf(1677,plain,
! [SV415: a,SV125: a,SV238: product_prod_a_a] :
( ( ( SV238
!= ( product_Pair_a_a @ SV125 @ SV415 ) )
= $true )
| ( ( ~ ( ( SV125
!= ( product_fst_a_a @ SV238 ) )
| ~ ~ ! [SY1024: a] :
( SV238
!= ( product_Pair_a_a @ SV125 @ SY1024 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1564]) ).
thf(1678,plain,
! [SV239: set_Product_prod_a_a,SV332: set_Product_prod_a_a,SV126: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV126 @ SV332 )
= $true )
| ( ( member449909584od_a_a @ SV126 @ ( minus_1507102574od_a_a @ SV239 @ SV332 ) )
= $true )
| ( ( member449909584od_a_a @ SV126 @ SV239 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1565]) ).
thf(1679,plain,
! [SV391: a > set_a,SV240: a,SV333: set_a,SV127: a] :
( ( ( ~ ( member_a @ SV127 @ SV333 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV127 @ SV240 ) @ ( product_Sigma_a_a @ SV333 @ SV391 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1566]) ).
thf(1680,plain,
! [SV333: set_a,SV127: a,SV391: a > set_a,SV240: a] :
( ( ( ~ ( member_a @ SV240 @ ( SV391 @ SV127 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV127 @ SV240 ) @ ( product_Sigma_a_a @ SV333 @ SV391 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1566]) ).
thf(1681,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a] :
( ( ( ! [SV416: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SV416 ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SV416 ) @ SV131 ) ) )
= $false )
| ( ( ~ ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
!= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
| ( SV2 != SV131 ) ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[1567]) ).
thf(1682,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a] :
( ( ( ( ^ [SY1199: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1199 ) @ SV2 ) )
= ( ^ [SY1200: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1200 ) @ SV131 ) ) )
= $false )
| ( ( ~ ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
!= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
| ( SV2 != SV131 ) ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[1567]) ).
thf(1683,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
!= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $false )
| ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1568]) ).
thf(1684,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( SV2 != SV131 )
= $false )
| ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1568]) ).
thf(1685,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $true )
| ( ( SV2 = SV131 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1569]) ).
thf(1686,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( SV2 = SV131 )
= $true )
| ( ( SV2 = SV131 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1570]) ).
thf(1687,plain,
! [SV243: set_Product_prod_a_a,SV132: a,SV3: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV3 @ SV132 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV243 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV3 @ SV132 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV243 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1571]) ).
thf(1688,plain,
! [SV243: set_Product_prod_a_a,SV3: a,SV132: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV132 @ SV3 ) @ SV243 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV3 @ SV132 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV243 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1571]) ).
thf(1689,plain,
! [SV243: set_Product_prod_a_a,SV132: a,SV3: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV3 @ SV132 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV243 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV132 @ SV3 ) @ SV243 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1572]) ).
thf(1690,plain,
! [SV243: set_Product_prod_a_a,SV3: a,SV132: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV132 @ SV3 ) @ SV243 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV132 @ SV3 ) @ SV243 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1572]) ).
thf(1691,plain,
! [SV133: product_prod_a_a > $o,SV4: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV4 @ ( collec645855634od_a_a @ SV133 ) )
= $true )
| ( ( member449909584od_a_a @ SV4 @ ( collec645855634od_a_a @ SV133 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1573]) ).
thf(1692,plain,
! [SV4: product_prod_a_a,SV133: product_prod_a_a > $o] :
( ( ( SV133 @ SV4 )
= $true )
| ( ( member449909584od_a_a @ SV4 @ ( collec645855634od_a_a @ SV133 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1574]) ).
thf(1693,plain,
! [SV133: product_prod_a_a > $o,SV4: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV4 @ ( collec645855634od_a_a @ SV133 ) )
= $true )
| ( ( SV133 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1575]) ).
thf(1694,plain,
! [SV4: product_prod_a_a,SV133: product_prod_a_a > $o] :
( ( ( SV133 @ SV4 )
= $true )
| ( ( SV133 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1576]) ).
thf(1695,plain,
! [SV138: product_prod_a_a] :
( ( ( top_to1483957574_a_a_o @ SV138 )
= $true )
| ( ( top_to1483957574_a_a_o @ SV138 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1577]) ).
thf(1696,plain,
! [SV138: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV138 @ top_to398455383od_a_a )
= $true )
| ( ( top_to1483957574_a_a_o @ SV138 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1578]) ).
thf(1697,plain,
! [SV138: product_prod_a_a] :
( ( ( top_to1483957574_a_a_o @ SV138 )
= $true )
| ( ( member449909584od_a_a @ SV138 @ top_to398455383od_a_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1579]) ).
thf(1698,plain,
! [SV138: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV138 @ top_to398455383od_a_a )
= $true )
| ( ( member449909584od_a_a @ SV138 @ top_to398455383od_a_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1580]) ).
thf(1699,plain,
! [SV340: a,SV140: a] :
( ( ( ~ ( top_top_a_a_o @ SV140 @ SV340 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV140 @ SV340 ) @ top_to398455383od_a_a ) )
= $false )
| ( ( top_top_a_a_o @ SV140 @ SV340 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1581]) ).
thf(1700,plain,
! [SV340: a,SV140: a] :
( ( ( ~ ( top_top_a_a_o @ SV140 @ SV340 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV140 @ SV340 ) @ top_to398455383od_a_a ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV140 @ SV340 ) @ top_to398455383od_a_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1582]) ).
thf(1701,plain,
! [SV249: set_a,SV143: set_a,SV20: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV20 @ ( product_product_a_a @ SV143 @ SV249 ) ) )
= $false )
| ( ( member449909584od_a_a @ SV20 @ ( product_product_a_a @ SV143 @ SV249 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1583]) ).
thf(1702,plain,
! [SV249: set_a,SV143: set_a,SV20: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV20
@ ( product_Sigma_a_a @ SV143
@ ^ [SY1036: a] : SV249 ) ) )
= $false )
| ( ( member449909584od_a_a @ SV20 @ ( product_product_a_a @ SV143 @ SV249 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1583]) ).
thf(1703,plain,
! [SV249: set_a,SV143: set_a,SV20: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV20 @ ( product_product_a_a @ SV143 @ SV249 ) ) )
= $false )
| ( ( member449909584od_a_a @ SV20
@ ( product_Sigma_a_a @ SV143
@ ^ [SY1036: a] : SV249 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1584]) ).
thf(1704,plain,
! [SV249: set_a,SV143: set_a,SV20: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV20
@ ( product_Sigma_a_a @ SV143
@ ^ [SY1036: a] : SV249 ) ) )
= $false )
| ( ( member449909584od_a_a @ SV20
@ ( product_Sigma_a_a @ SV143
@ ^ [SY1036: a] : SV249 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1584]) ).
thf(1705,plain,
! [SV144: set_Product_prod_a_a,SV21: set_Product_prod_a_a] :
( ( ( ord_le1347718902_a_a_o
@ ^ [SY498: product_prod_a_a] : ( member449909584od_a_a @ SY498 @ SV21 )
@ ^ [SY826: product_prod_a_a] : ( member449909584od_a_a @ SY826 @ SV144 ) )
= $true )
| ( ( ord_le1347718902_a_a_o
@ ^ [SY498: product_prod_a_a] : ( member449909584od_a_a @ SY498 @ SV21 )
@ ^ [SY826: product_prod_a_a] : ( member449909584od_a_a @ SY826 @ SV144 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1585]) ).
thf(1706,plain,
! [SV144: set_Product_prod_a_a,SV21: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV21 @ SV144 )
= $true )
| ( ( ord_le1347718902_a_a_o
@ ^ [SY498: product_prod_a_a] : ( member449909584od_a_a @ SY498 @ SV21 )
@ ^ [SY826: product_prod_a_a] : ( member449909584od_a_a @ SY826 @ SV144 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1586]) ).
thf(1707,plain,
! [SV144: set_Product_prod_a_a,SV21: set_Product_prod_a_a] :
( ( ( ord_le1347718902_a_a_o
@ ^ [SY498: product_prod_a_a] : ( member449909584od_a_a @ SY498 @ SV21 )
@ ^ [SY826: product_prod_a_a] : ( member449909584od_a_a @ SY826 @ SV144 ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV21 @ SV144 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1587]) ).
thf(1708,plain,
! [SV144: set_Product_prod_a_a,SV21: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV21 @ SV144 )
= $true )
| ( ( ord_le1824328871od_a_a @ SV21 @ SV144 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1588]) ).
thf(1709,plain,
! [SV341: set_Product_prod_a_a,SV145: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV145 @ SV341 )
| ~ ( ord_le1347718902_a_a_o
@ ^ [SY828: product_prod_a_a] : ( member449909584od_a_a @ SY828 @ SV145 )
@ ^ [SY1142: product_prod_a_a] : ( member449909584od_a_a @ SY1142 @ SV341 ) ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV145 @ SV341 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1589]) ).
thf(1710,plain,
! [SV341: set_Product_prod_a_a,SV145: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV145 @ SV341 )
| ~ ( ord_le1347718902_a_a_o
@ ^ [SY828: product_prod_a_a] : ( member449909584od_a_a @ SY828 @ SV145 )
@ ^ [SY1142: product_prod_a_a] : ( member449909584od_a_a @ SY1142 @ SV341 ) ) )
= $false )
| ( ( ord_le1347718902_a_a_o
@ ^ [SY828: product_prod_a_a] : ( member449909584od_a_a @ SY828 @ SV145 )
@ ^ [SY1142: product_prod_a_a] : ( member449909584od_a_a @ SY1142 @ SV341 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1590]) ).
thf(1711,plain,
! [SV146: set_Product_prod_a_a,SV23: set_Product_prod_a_a] :
( ( ( ord_less_eq_a_a_o
@ ^ [SY504: a,SY505: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY504 @ SY505 ) @ SV23 )
@ ^ [SY832: a,SY833: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY832 @ SY833 ) @ SV146 ) )
= $true )
| ( ( ord_less_eq_a_a_o
@ ^ [SY504: a,SY505: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY504 @ SY505 ) @ SV23 )
@ ^ [SY832: a,SY833: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY832 @ SY833 ) @ SV146 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1591]) ).
thf(1712,plain,
! [SV146: set_Product_prod_a_a,SV23: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV23 @ SV146 )
= $true )
| ( ( ord_less_eq_a_a_o
@ ^ [SY504: a,SY505: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY504 @ SY505 ) @ SV23 )
@ ^ [SY832: a,SY833: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY832 @ SY833 ) @ SV146 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1592]) ).
thf(1713,plain,
! [SV146: set_Product_prod_a_a,SV23: set_Product_prod_a_a] :
( ( ( ord_less_eq_a_a_o
@ ^ [SY504: a,SY505: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY504 @ SY505 ) @ SV23 )
@ ^ [SY832: a,SY833: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY832 @ SY833 ) @ SV146 ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV23 @ SV146 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1593]) ).
thf(1714,plain,
! [SV146: set_Product_prod_a_a,SV23: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV23 @ SV146 )
= $true )
| ( ( ord_le1824328871od_a_a @ SV23 @ SV146 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1594]) ).
thf(1715,plain,
! [SV24: set_Product_prod_a_a] :
( ( ( ~ ! [SY508: product_prod_a_a] :
~ ( member449909584od_a_a @ SY508 @ SV24 ) )
= $false )
| ( ( member449909584od_a_a @ ( sK19_SY508 @ SV24 ) @ SV24 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1595]) ).
thf(1716,plain,
! [SV24: set_Product_prod_a_a] :
( ( ( SV24 != bot_bo2131659635od_a_a )
= $false )
| ( ( member449909584od_a_a @ ( sK19_SY508 @ SV24 ) @ SV24 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1595]) ).
thf(1717,plain,
! [SV24: set_Product_prod_a_a,SV417: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV417 @ SV24 ) )
= $true )
| ( ( SV24 = bot_bo2131659635od_a_a )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1596]) ).
thf(1718,plain,
! [SV343: a,SV252: a,SV150: a,SV30: a] :
( ( ( ( ( product_Pair_a_a @ SV30 @ SV150 )
!= ( product_Pair_a_a @ SV252 @ SV343 ) )
| ~ ~ ( ( SV30 != SV252 )
| ( SV150 != SV343 ) ) )
= $false )
| ( ( ( product_Pair_a_a @ SV30 @ SV150 )
= ( product_Pair_a_a @ SV252 @ SV343 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1599]) ).
thf(1719,plain,
! [SV343: a,SV150: a,SV252: a,SV30: a] :
( ( ( ( SV30 != SV252 )
| ( SV150 != SV343 ) )
= $true )
| ( ( ~ ( ( ( product_Pair_a_a @ SV30 @ SV150 )
!= ( product_Pair_a_a @ SV252 @ SV343 ) )
| ~ ~ ( ( SV30 != SV252 )
| ( SV150 != SV343 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1600]) ).
thf(1720,plain,
! [SV255: set_Product_prod_a_a,SV153: set_Product_prod_a_a,SV33: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV33 @ ( minus_1507102574od_a_a @ SV153 @ SV255 ) ) )
= $false )
| ( ( member449909584od_a_a @ SV33 @ ( minus_1507102574od_a_a @ SV153 @ SV255 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1603]) ).
thf(1721,plain,
! [SV255: set_Product_prod_a_a,SV153: set_Product_prod_a_a,SV33: product_prod_a_a] :
( ( ( ~ ~ ( ~ ( member449909584od_a_a @ SV33 @ SV153 )
| ~ ~ ( member449909584od_a_a @ SV33 @ SV255 ) ) )
= $false )
| ( ( member449909584od_a_a @ SV33 @ ( minus_1507102574od_a_a @ SV153 @ SV255 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1603]) ).
thf(1722,plain,
! [SV255: set_Product_prod_a_a,SV153: set_Product_prod_a_a,SV33: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV33 @ SV153 ) )
= $true )
| ( ( ~ ~ ( member449909584od_a_a @ SV33 @ SV255 ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ SV33 @ ( minus_1507102574od_a_a @ SV153 @ SV255 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ SV33 @ SV153 )
| ~ ~ ( member449909584od_a_a @ SV33 @ SV255 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1604]) ).
thf(1723,plain,
! [SV345: set_Product_prod_a_a,SV155: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV155 @ SV345 )
| ~ ! [SY1143: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1143 @ SV155 )
| ( member449909584od_a_a @ SY1143 @ SV345 ) ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV155 @ SV345 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1606]) ).
thf(1724,plain,
! [SV155: set_Product_prod_a_a,SV345: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK41_SY1143 @ SV345 @ SV155 ) @ SV155 )
| ( member449909584od_a_a @ ( sK41_SY1143 @ SV345 @ SV155 ) @ SV345 ) )
= $false )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV155 @ SV345 )
| ~ ! [SY1143: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1143 @ SV155 )
| ( member449909584od_a_a @ SY1143 @ SV345 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1607]) ).
thf(1725,plain,
! [SV413: product_prod_a_a,SV36: set_Product_prod_a_a] :
( ( ( ~ ~ ! [SY531: product_prod_a_a] :
~ ( member449909584od_a_a @ SY531 @ SV36 )
| ~ ( ( SV36 != bot_bo2131659635od_a_a ) ) )
= $false )
| ( ( member449909584od_a_a @ SV413 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1608]) ).
thf(1726,plain,
! [SV36: set_Product_prod_a_a] :
( ( ( ~ ! [SY531: product_prod_a_a] :
~ ( member449909584od_a_a @ SY531 @ SV36 ) )
= $true )
| ( ( SV36 = bot_bo2131659635od_a_a )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1609]) ).
thf(1727,plain,
! [SV36: set_Product_prod_a_a] :
( ( ( SV36 != bot_bo2131659635od_a_a )
= $true )
| ( ( SV36 = bot_bo2131659635od_a_a )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1610]) ).
thf(1728,plain,
! [SV258: set_Product_prod_a_a,SV158: product_prod_a_a > produc1572603623od_a_a,SV39: produc1572603623od_a_a] :
( ( ( SV39
= ( SV158 @ ( sK32_SY1045 @ SV258 @ SV158 @ SV39 ) ) )
= $true )
| ( ( member2057358096od_a_a @ SV39 @ ( image_1765377413od_a_a @ SV158 @ SV258 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1611]) ).
thf(1729,plain,
! [SV39: produc1572603623od_a_a,SV158: product_prod_a_a > produc1572603623od_a_a,SV258: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( sK32_SY1045 @ SV258 @ SV158 @ SV39 ) @ SV258 )
= $true )
| ( ( member2057358096od_a_a @ SV39 @ ( image_1765377413od_a_a @ SV158 @ SV258 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1612]) ).
thf(1730,plain,
! [SV260: set_Product_prod_a_a,SV161: product_prod_a_a > product_prod_a_a,SV42: product_prod_a_a] :
( ( ( SV42
= ( SV161 @ ( sK33_SY1047 @ SV260 @ SV161 @ SV42 ) ) )
= $true )
| ( ( member449909584od_a_a @ SV42 @ ( image_794773445od_a_a @ SV161 @ SV260 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1614]) ).
thf(1731,plain,
! [SV42: product_prod_a_a,SV161: product_prod_a_a > product_prod_a_a,SV260: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( sK33_SY1047 @ SV260 @ SV161 @ SV42 ) @ SV260 )
= $true )
| ( ( member449909584od_a_a @ SV42 @ ( image_794773445od_a_a @ SV161 @ SV260 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1615]) ).
thf(1732,plain,
! [SV347: set_Product_prod_a_a,SV162: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV162 @ SV347 )
| ~ ! [SY1144: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1144 @ SV162 )
| ( member449909584od_a_a @ SY1144 @ SV347 ) ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV162 @ SV347 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1616]) ).
thf(1733,plain,
! [SV162: set_Product_prod_a_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK42_SY1144 @ SV347 @ SV162 ) @ SV162 )
| ( member449909584od_a_a @ ( sK42_SY1144 @ SV347 @ SV162 ) @ SV347 ) )
= $false )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV162 @ SV347 )
| ~ ! [SY1144: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1144 @ SV162 )
| ( member449909584od_a_a @ SY1144 @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1617]) ).
thf(1734,plain,
! [SV264: product_prod_a_a > $o,SV165: set_Product_prod_a_a,SV46: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV46
@ ( collec645855634od_a_a
@ ^ [SY1049: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1049 @ SV165 )
| ~ ( SV264 @ SY1049 ) ) ) )
= $false )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV46
@ ( collec645855634od_a_a
@ ^ [SY1049: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1049 @ SV165 )
| ~ ( SV264 @ SY1049 ) ) ) )
| ~ ! [SY1050: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1050 @ SV46 )
| ( SV264 @ SY1050 ) ) ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV46 @ SV165 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1619]) ).
thf(1735,plain,
! [SV165: set_Product_prod_a_a,SV264: product_prod_a_a > $o,SV46: set_Product_prod_a_a] :
( ( ( ! [SY1050: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1050 @ SV46 )
| ( SV264 @ SY1050 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV46
@ ( collec645855634od_a_a
@ ^ [SY1049: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1049 @ SV165 )
| ~ ( SV264 @ SY1049 ) ) ) )
| ~ ! [SY1050: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1050 @ SV46 )
| ( SV264 @ SY1050 ) ) ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV46 @ SV165 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1619]) ).
thf(1736,plain,
! [SV266: set_Pr1948701895od_a_a,SV167: produc1572603623od_a_a > product_prod_a_a,SV48: product_prod_a_a] :
( ( ( SV48
= ( SV167 @ ( sK34_SY1053 @ SV266 @ SV167 @ SV48 ) ) )
= $true )
| ( ( member449909584od_a_a @ SV48 @ ( image_734753285od_a_a @ SV167 @ SV266 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1620]) ).
thf(1737,plain,
! [SV48: product_prod_a_a,SV167: produc1572603623od_a_a > product_prod_a_a,SV266: set_Pr1948701895od_a_a] :
( ( ( member2057358096od_a_a @ ( sK34_SY1053 @ SV266 @ SV167 @ SV48 ) @ SV266 )
= $true )
| ( ( member449909584od_a_a @ SV48 @ ( image_734753285od_a_a @ SV167 @ SV266 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1621]) ).
thf(1738,plain,
! [SV354: a,SV275: a,SV176: a,SV57: a] :
( ( ( ( ( product_Pair_a_a @ SV57 @ SV176 )
!= ( product_Pair_a_a @ SV275 @ SV354 ) )
| ~ ~ ( ( SV57 != SV275 )
| ( SV176 != SV354 ) ) )
= $false )
| ( ( ( product_Pair_a_a @ SV57 @ SV176 )
= ( product_Pair_a_a @ SV275 @ SV354 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1626]) ).
thf(1739,plain,
! [SV354: a,SV176: a,SV275: a,SV57: a] :
( ( ( ( SV57 != SV275 )
| ( SV176 != SV354 ) )
= $true )
| ( ( ~ ( ( ( product_Pair_a_a @ SV57 @ SV176 )
!= ( product_Pair_a_a @ SV275 @ SV354 ) )
| ~ ~ ( ( SV57 != SV275 )
| ( SV176 != SV354 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1627]) ).
thf(1740,plain,
! [SV179: set_a,SV60: set_Product_prod_a_a] :
( ( ( ~ ! [SY894: a,SY895: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY894 @ SY895 ) @ SV60 )
| ( member_a @ SY895 @ SV179 ) ) )
= $true )
| ( ( ~ ( order_preorder_on_a @ SV179 @ SV60 )
| ( prefer1292084992ence_a @ SV179 @ SV60 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK13_SY892 @ SV179 @ SV60 ) @ ( sK24_SY1180 @ SV60 @ SV179 ) ) @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1630]) ).
thf(1741,plain,
! [SV179: set_a,SV60: set_Product_prod_a_a] :
( ( ( ! [SY894: a,SY895: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY894 @ SY895 ) @ SV60 )
| ( member_a @ SY895 @ SV179 ) ) )
= $false )
| ( ( ~ ( order_preorder_on_a @ SV179 @ SV60 )
| ( prefer1292084992ence_a @ SV179 @ SV60 ) )
= $true )
| ( ( member_a @ ( sK13_SY892 @ SV179 @ SV60 ) @ SV179 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1631]) ).
thf(1742,plain,
! [SV61: set_a,SV394: a,SV180: set_Product_prod_a_a,SV356: a,SV278: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV356 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV278 ) @ SV180 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV394 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV356 ) @ SV180 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV394 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV278 ) @ SV180 ) ) )
= $true )
| ( ( prefer1292084992ence_a @ SV61 @ SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1632]) ).
thf(1743,plain,
! [SV184: a > a,SV65: a,SV405: set_a,SV282: a,SV395: a > a,SV360: a] :
( ( ( SV360
!= ( SV395 @ SV282 ) )
= $true )
| ( ( ~ ( member_a @ SV282 @ SV405 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV65 @ SV360 ) @ ( bNF_Gr423046308_a_a_a @ SV405 @ SV184 @ SV395 ) ) )
= $true )
| ( ( SV65
= ( SV184 @ SV282 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1635]) ).
thf(1744,plain,
! [SV362: a,SV186: a,SV284: a,SV67: a] :
( ( ( SV67 = SV284 )
= $true )
| ( ( ( product_Pair_a_a @ SV67 @ SV186 )
= ( product_Pair_a_a @ SV284 @ SV362 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1637]) ).
thf(1745,plain,
! [SV284: a,SV67: a,SV362: a,SV186: a] :
( ( ( SV186 = SV362 )
= $true )
| ( ( ( product_Pair_a_a @ SV67 @ SV186 )
= ( product_Pair_a_a @ SV284 @ SV362 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1638]) ).
thf(1746,plain,
! [SV365: a > set_a,SV290: set_a,SV193: a,SV75: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV75 @ SV193 ) @ ( product_Sigma_a_a @ SV290 @ SV365 ) )
| ~ ~ ( ~ ( member_a @ SV75 @ SV290 )
| ~ ( member_a @ SV193 @ ( SV365 @ SV75 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV75 @ SV193 ) @ ( product_Sigma_a_a @ SV290 @ SV365 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1640]) ).
thf(1747,plain,
! [SV365: a > set_a,SV193: a,SV290: set_a,SV75: a] :
( ( ( ~ ( member_a @ SV75 @ SV290 )
| ~ ( member_a @ SV193 @ ( SV365 @ SV75 ) ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV75 @ SV193 ) @ ( product_Sigma_a_a @ SV290 @ SV365 ) )
| ~ ~ ( ~ ( member_a @ SV75 @ SV290 )
| ~ ( member_a @ SV193 @ ( SV365 @ SV75 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1641]) ).
thf(1748,plain,
! [SV194: product_prod_a_a > product_prod_a_a,SV76: product_prod_a_a,SV406: set_Product_prod_a_a,SV291: product_prod_a_a,SV396: product_prod_a_a > product_prod_a_a,SV366: product_prod_a_a] :
( ( ( SV366
!= ( SV396 @ SV291 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ SV291 @ SV406 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV76 @ SV366 ) @ ( bNF_Gr200450189od_a_a @ SV406 @ SV194 @ SV396 ) ) )
= $true )
| ( ( SV76
= ( SV194 @ SV291 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1642]) ).
thf(1749,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 )
| ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) )
= $false )
| ( ( prefer1292084992ence_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1644]) ).
thf(1750,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 )
| ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1645]) ).
thf(1751,plain,
! [SV370: product_prod_a_a > set_Product_prod_a_a,SV202: product_prod_a_a,SV299: set_Product_prod_a_a,SV84: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV84 @ SV299 )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV84 @ SV202 ) @ ( produc304751368od_a_a @ SV299 @ SV370 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1646]) ).
thf(1752,plain,
! [SV299: set_Product_prod_a_a,SV84: product_prod_a_a,SV370: product_prod_a_a > set_Product_prod_a_a,SV202: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV202 @ ( SV370 @ SV84 ) )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV84 @ SV202 ) @ ( produc304751368od_a_a @ SV299 @ SV370 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1647]) ).
thf(1753,plain,
! [SV88: set_Product_prod_a_a,SV303: product_prod_a_a > $o,SV372: product_prod_a_a > $o,SV206: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK43_SY1159 @ SV206 @ SV372 @ SV303 @ SV88 ) @ SV88 )
| ~ ( SV303 @ ( sK43_SY1159 @ SV206 @ SV372 @ SV303 @ SV88 ) )
| ( SV372 @ ( sK43_SY1159 @ SV206 @ SV372 @ SV303 @ SV88 ) ) )
= $false )
| ( ( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [SY1094: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1094 @ SV88 )
| ~ ( SV303 @ SY1094 ) ) )
@ ( collec645855634od_a_a
@ ^ [SY1161: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1161 @ SV206 )
| ~ ( SV372 @ SY1161 ) ) ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV88 @ SV206 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1649]) ).
thf(1754,plain,
! [SV373: product_prod_a_a > set_Product_prod_a_a,SV304: set_Product_prod_a_a,SV207: product_prod_a_a,SV89: product_prod_a_a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV89 @ SV207 ) @ ( produc304751368od_a_a @ SV304 @ SV373 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ SV89 @ SV304 )
| ~ ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) ) ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV89 @ SV207 ) @ ( produc304751368od_a_a @ SV304 @ SV373 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1650]) ).
thf(1755,plain,
! [SV373: product_prod_a_a > set_Product_prod_a_a,SV207: product_prod_a_a,SV304: set_Product_prod_a_a,SV89: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV89 @ SV304 )
| ~ ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) ) )
= $true )
| ( ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV89 @ SV207 ) @ ( produc304751368od_a_a @ SV304 @ SV373 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ SV89 @ SV304 )
| ~ ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1651]) ).
thf(1756,plain,
! [SV208: product_prod_a_a,SV91: a] :
( ( ( SV91
= ( product_snd_a_a @ SV208 ) )
= $true )
| ( ( SV91
= ( product_snd_a_a @ SV208 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1652]) ).
thf(1757,plain,
! [SV91: a,SV208: product_prod_a_a] :
( ( ( ~ ! [SY956: a] :
( SV208
!= ( product_Pair_a_a @ SY956 @ SV91 ) ) )
= $true )
| ( ( SV91
= ( product_snd_a_a @ SV208 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1653]) ).
thf(1758,plain,
! [SV91: a,SV414: a,SV208: product_prod_a_a] :
( ( ( SV208
= ( product_Pair_a_a @ SV414 @ SV91 ) )
= $false )
| ( ( ~ ( ( SV91
!= ( product_snd_a_a @ SV208 ) )
| ~ ~ ! [SY956: a] :
( SV208
!= ( product_Pair_a_a @ SY956 @ SV91 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1654]) ).
thf(1759,plain,
! [SV306: a > $o,SV375: a,SV210: a,SV93: a > $o] :
( ( ( ~ ( SV93 @ ( product_fst_a_a @ ( product_Pair_a_a @ SV210 @ SV375 ) ) )
| ~ ( SV306 @ ( product_snd_a_a @ ( product_Pair_a_a @ SV210 @ SV375 ) ) ) )
= $false )
| ( ( SV306 @ SV375 )
= $false )
| ( ( SV93 @ SV210 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1656]) ).
thf(1760,plain,
! [SV212: product_prod_a_a > a,SV95: a,SV407: set_Product_prod_a_a,SV308: product_prod_a_a,SV398: product_prod_a_a > a,SV377: a] :
( ( ( SV377
!= ( SV398 @ SV308 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ SV308 @ SV407 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV95 @ SV377 ) @ ( bNF_Gr1853143117_a_a_a @ SV407 @ SV212 @ SV398 ) ) )
= $true )
| ( ( SV95
= ( SV212 @ SV308 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1657]) ).
thf(1761,plain,
! [SV311: set_Product_prod_a_a,SV215: product_prod_a_a > a,SV99: a] :
( ( ( SV99
= ( SV215 @ ( sK35_SY1109 @ SV311 @ SV215 @ SV99 ) ) )
= $true )
| ( ( member_a @ SV99 @ ( image_340790172_a_a_a @ SV215 @ SV311 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1658]) ).
thf(1762,plain,
! [SV99: a,SV215: product_prod_a_a > a,SV311: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( sK35_SY1109 @ SV311 @ SV215 @ SV99 ) @ SV311 )
= $true )
| ( ( member_a @ SV99 @ ( image_340790172_a_a_a @ SV215 @ SV311 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1659]) ).
thf(1763,plain,
! [SV312: a > a,SV380: set_Product_prod_a_a,SV217: a > a,SV101: product_prod_a_a] :
( ( ( ( SV101
!= ( product_Pair_a_a @ ( SV217 @ ( sK40_SY1167 @ SV380 @ SV312 @ SV217 @ SV101 ) ) @ ( SV312 @ ( sK44_SY1201 @ SV312 @ SV380 @ SV217 @ SV101 ) ) ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK40_SY1167 @ SV380 @ SV312 @ SV217 @ SV101 ) @ ( sK44_SY1201 @ SV312 @ SV380 @ SV217 @ SV101 ) ) @ SV380 ) )
= $false )
| ( ( member449909584od_a_a @ SV101 @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SV217 @ SV312 ) @ SV380 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1660]) ).
thf(1764,plain,
! [SV104: a > $o,SV220: a,SV401: a > set_Product_prod_a_a,SV383: a,SV315: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV315 @ SV383 ) @ ( SV401 @ SV220 ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV220 @ SV315 ) @ ( product_Pair_a_a @ SV220 @ SV383 ) ) @ ( same_fst_a_a @ SV104 @ SV401 ) )
= $true )
| ( ( SV104 @ SV220 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1661]) ).
thf(1765,plain,
! [SV226: set_Product_prod_a_a,SV320: product_prod_a_a > set_Product_prod_a_a,SV111: produc1572603623od_a_a] :
( ( ( member449909584od_a_a @ ( sK36_SY1121 @ SV111 @ SV320 @ SV226 ) @ SV226 )
= $true )
| ( ( member2057358096od_a_a @ SV111 @ ( produc304751368od_a_a @ SV226 @ SV320 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1664]) ).
thf(1766,plain,
! [SV320: product_prod_a_a > set_Product_prod_a_a,SV111: produc1572603623od_a_a,SV226: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK45_SY1197 @ SV226 @ SV111 @ SV320 ) @ ( SV320 @ ( sK36_SY1121 @ SV111 @ SV320 @ SV226 ) ) )
| ( SV111
!= ( produc1474507607od_a_a @ ( sK36_SY1121 @ SV111 @ SV320 @ SV226 ) @ ( sK45_SY1197 @ SV226 @ SV111 @ SV320 ) ) ) )
= $false )
| ( ( member2057358096od_a_a @ SV111 @ ( produc304751368od_a_a @ SV226 @ SV320 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1665]) ).
thf(1767,plain,
! [SV323: set_a,SV229: a > product_prod_a_a,SV114: product_prod_a_a] :
( ( ( SV114
= ( SV229 @ ( sK37_SY1124 @ SV323 @ SV229 @ SV114 ) ) )
= $true )
| ( ( member449909584od_a_a @ SV114 @ ( image_1725938350od_a_a @ SV229 @ SV323 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1667]) ).
thf(1768,plain,
! [SV114: product_prod_a_a,SV229: a > product_prod_a_a,SV323: set_a] :
( ( ( member_a @ ( sK37_SY1124 @ SV323 @ SV229 @ SV114 ) @ SV323 )
= $true )
| ( ( member449909584od_a_a @ SV114 @ ( image_1725938350od_a_a @ SV229 @ SV323 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1668]) ).
thf(1769,plain,
! [SV231: produc1572603623od_a_a > a,SV116: a,SV410: set_Pr1948701895od_a_a,SV325: produc1572603623od_a_a,SV402: produc1572603623od_a_a > a,SV387: a] :
( ( ( SV387
!= ( SV402 @ SV325 ) )
= $true )
| ( ( ~ ( member2057358096od_a_a @ SV325 @ SV410 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV116 @ SV387 ) @ ( bNF_Gr356189709_a_a_a @ SV410 @ SV231 @ SV402 ) ) )
= $true )
| ( ( SV116
= ( SV231 @ SV325 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1669]) ).
thf(1770,plain,
! [SV233: set_a,SV327: a > set_a,SV119: product_prod_a_a] :
( ( ( member_a @ ( sK38_SY1129 @ SV119 @ SV327 @ SV233 ) @ SV233 )
= $true )
| ( ( member449909584od_a_a @ SV119 @ ( product_Sigma_a_a @ SV233 @ SV327 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1670]) ).
thf(1771,plain,
! [SV327: a > set_a,SV119: product_prod_a_a,SV233: set_a] :
( ( ( ~ ( member_a @ ( sK46_SY1198 @ SV233 @ SV119 @ SV327 ) @ ( SV327 @ ( sK38_SY1129 @ SV119 @ SV327 @ SV233 ) ) )
| ( SV119
!= ( product_Pair_a_a @ ( sK38_SY1129 @ SV119 @ SV327 @ SV233 ) @ ( sK46_SY1198 @ SV233 @ SV119 @ SV327 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ SV119 @ ( product_Sigma_a_a @ SV233 @ SV327 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1671]) ).
thf(1772,plain,
! [SV411: set_Product_prod_a_a,SV403: set_Product_prod_a_a,SV390: a,SV331: a,SV237: a,SV123: a] :
( ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SV331 @ SV390 ) ) @ ( lex_prod_a_a @ SV403 @ SV411 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
| ~ ( ( SV123 != SV331 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 ) ) )
= $false )
| ( ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SV331 @ SV390 ) ) @ ( lex_prod_a_a @ SV403 @ SV411 ) )
| ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
| ~ ( ( SV123 != SV331 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1674]) ).
thf(1773,plain,
! [SV238: product_prod_a_a,SV125: a] :
( ( ( SV125
= ( product_fst_a_a @ SV238 ) )
= $true )
| ( ( SV125
= ( product_fst_a_a @ SV238 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1675]) ).
thf(1774,plain,
! [SV125: a,SV238: product_prod_a_a] :
( ( ( ~ ! [SY1024: a] :
( SV238
!= ( product_Pair_a_a @ SV125 @ SY1024 ) ) )
= $true )
| ( ( SV125
= ( product_fst_a_a @ SV238 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1676]) ).
thf(1775,plain,
! [SV415: a,SV125: a,SV238: product_prod_a_a] :
( ( ( SV238
= ( product_Pair_a_a @ SV125 @ SV415 ) )
= $false )
| ( ( ~ ( ( SV125
!= ( product_fst_a_a @ SV238 ) )
| ~ ~ ! [SY1024: a] :
( SV238
!= ( product_Pair_a_a @ SV125 @ SY1024 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1677]) ).
thf(1776,plain,
! [SV391: a > set_a,SV240: a,SV333: set_a,SV127: a] :
( ( ( member_a @ SV127 @ SV333 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV127 @ SV240 ) @ ( product_Sigma_a_a @ SV333 @ SV391 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1679]) ).
thf(1777,plain,
! [SV333: set_a,SV127: a,SV391: a > set_a,SV240: a] :
( ( ( member_a @ SV240 @ ( SV391 @ SV127 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV127 @ SV240 ) @ ( product_Sigma_a_a @ SV333 @ SV391 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1680]) ).
thf(1778,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a] :
( ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 ) )
= $false )
| ( ( ~ ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
!= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
| ( SV2 != SV131 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1681]) ).
thf(1779,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
!= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
| ( SV2 != SV131 ) )
= $false )
| ( ( ( ^ [SY1199: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1199 ) @ SV2 ) )
= ( ^ [SY1200: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1200 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1682]) ).
thf(1780,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $true )
| ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1683]) ).
thf(1781,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( SV2 = SV131 )
= $true )
| ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1684]) ).
thf(1782,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( ! [SV418: a] :
( ( ^ [SY1202: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV418 @ SY1202 ) @ SV2 ) )
= ( ^ [SY1203: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV418 @ SY1203 ) @ SV131 ) ) ) )
= $true )
| ( ( SV2 = SV131 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1685]) ).
thf(1783,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $true )
| ( ( SV2 = SV131 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1685]) ).
thf(1784,plain,
! [SV243: set_Product_prod_a_a,SV132: a,SV3: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV3 @ SV132 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV243 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV3 @ SV132 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV243 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1687]) ).
thf(1785,plain,
! [SV243: set_Product_prod_a_a,SV3: a,SV132: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV132 @ SV3 ) @ SV243 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV3 @ SV132 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV243 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1688]) ).
thf(1786,plain,
! [SV243: set_Product_prod_a_a,SV132: a,SV3: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV3 @ SV132 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV243 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV132 @ SV3 ) @ SV243 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1689]) ).
thf(1787,plain,
! [SV243: set_Product_prod_a_a,SV3: a,SV132: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV132 @ SV3 ) @ SV243 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV132 @ SV3 ) @ SV243 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1690]) ).
thf(1788,plain,
! [SV340: a,SV140: a] :
( ( ( ~ ( top_top_a_a_o @ SV140 @ SV340 ) )
= $false )
| ( ( top_top_a_a_o @ SV140 @ SV340 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1699]) ).
thf(1789,plain,
! [SV340: a,SV140: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV140 @ SV340 ) @ top_to398455383od_a_a ) )
= $false )
| ( ( top_top_a_a_o @ SV140 @ SV340 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1699]) ).
thf(1790,plain,
! [SV340: a,SV140: a] :
( ( ( ~ ( top_top_a_a_o @ SV140 @ SV340 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV140 @ SV340 ) @ top_to398455383od_a_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1700]) ).
thf(1791,plain,
! [SV340: a,SV140: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV140 @ SV340 ) @ top_to398455383od_a_a ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV140 @ SV340 ) @ top_to398455383od_a_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1700]) ).
thf(1792,plain,
! [SV249: set_a,SV143: set_a,SV20: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV20 @ ( product_product_a_a @ SV143 @ SV249 ) )
= $true )
| ( ( member449909584od_a_a @ SV20 @ ( product_product_a_a @ SV143 @ SV249 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1701]) ).
thf(1793,plain,
! [SV249: set_a,SV143: set_a,SV20: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV20
@ ( product_Sigma_a_a @ SV143
@ ^ [SY1036: a] : SV249 ) )
= $true )
| ( ( member449909584od_a_a @ SV20 @ ( product_product_a_a @ SV143 @ SV249 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1702]) ).
thf(1794,plain,
! [SV249: set_a,SV143: set_a,SV20: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV20 @ ( product_product_a_a @ SV143 @ SV249 ) )
= $true )
| ( ( member449909584od_a_a @ SV20
@ ( product_Sigma_a_a @ SV143
@ ^ [SY1036: a] : SV249 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1703]) ).
thf(1795,plain,
! [SV249: set_a,SV143: set_a,SV20: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV20
@ ( product_Sigma_a_a @ SV143
@ ^ [SY1036: a] : SV249 ) )
= $true )
| ( ( member449909584od_a_a @ SV20
@ ( product_Sigma_a_a @ SV143
@ ^ [SY1036: a] : SV249 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1704]) ).
thf(1796,plain,
! [SV341: set_Product_prod_a_a,SV145: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV145 @ SV341 ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV145 @ SV341 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1709]) ).
thf(1797,plain,
! [SV341: set_Product_prod_a_a,SV145: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1347718902_a_a_o
@ ^ [SY828: product_prod_a_a] : ( member449909584od_a_a @ SY828 @ SV145 )
@ ^ [SY1142: product_prod_a_a] : ( member449909584od_a_a @ SY1142 @ SV341 ) ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV145 @ SV341 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1709]) ).
thf(1798,plain,
! [SV341: set_Product_prod_a_a,SV145: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV145 @ SV341 ) )
= $false )
| ( ( ord_le1347718902_a_a_o
@ ^ [SY828: product_prod_a_a] : ( member449909584od_a_a @ SY828 @ SV145 )
@ ^ [SY1142: product_prod_a_a] : ( member449909584od_a_a @ SY1142 @ SV341 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1710]) ).
thf(1799,plain,
! [SV341: set_Product_prod_a_a,SV145: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1347718902_a_a_o
@ ^ [SY828: product_prod_a_a] : ( member449909584od_a_a @ SY828 @ SV145 )
@ ^ [SY1142: product_prod_a_a] : ( member449909584od_a_a @ SY1142 @ SV341 ) ) )
= $false )
| ( ( ord_le1347718902_a_a_o
@ ^ [SY828: product_prod_a_a] : ( member449909584od_a_a @ SY828 @ SV145 )
@ ^ [SY1142: product_prod_a_a] : ( member449909584od_a_a @ SY1142 @ SV341 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1710]) ).
thf(1800,plain,
! [SV24: set_Product_prod_a_a] :
( ( ( ! [SY508: product_prod_a_a] :
~ ( member449909584od_a_a @ SY508 @ SV24 ) )
= $true )
| ( ( member449909584od_a_a @ ( sK19_SY508 @ SV24 ) @ SV24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1715]) ).
thf(1801,plain,
! [SV24: set_Product_prod_a_a] :
( ( ( SV24 = bot_bo2131659635od_a_a )
= $true )
| ( ( member449909584od_a_a @ ( sK19_SY508 @ SV24 ) @ SV24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1716]) ).
thf(1802,plain,
! [SV24: set_Product_prod_a_a,SV417: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV417 @ SV24 )
= $false )
| ( ( SV24 = bot_bo2131659635od_a_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1717]) ).
thf(1803,plain,
! [SV343: a,SV252: a,SV150: a,SV30: a] :
( ( ( ( product_Pair_a_a @ SV30 @ SV150 )
!= ( product_Pair_a_a @ SV252 @ SV343 ) )
= $false )
| ( ( ( product_Pair_a_a @ SV30 @ SV150 )
= ( product_Pair_a_a @ SV252 @ SV343 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1718]) ).
thf(1804,plain,
! [SV343: a,SV150: a,SV252: a,SV30: a] :
( ( ( ~ ~ ( ( SV30 != SV252 )
| ( SV150 != SV343 ) ) )
= $false )
| ( ( ( product_Pair_a_a @ SV30 @ SV150 )
= ( product_Pair_a_a @ SV252 @ SV343 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1718]) ).
thf(1805,plain,
! [SV343: a,SV150: a,SV252: a,SV30: a] :
( ( ( SV30 != SV252 )
= $true )
| ( ( SV150 != SV343 )
= $true )
| ( ( ~ ( ( ( product_Pair_a_a @ SV30 @ SV150 )
!= ( product_Pair_a_a @ SV252 @ SV343 ) )
| ~ ~ ( ( SV30 != SV252 )
| ( SV150 != SV343 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1719]) ).
thf(1806,plain,
! [SV255: set_Product_prod_a_a,SV153: set_Product_prod_a_a,SV33: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV33 @ ( minus_1507102574od_a_a @ SV153 @ SV255 ) )
= $true )
| ( ( member449909584od_a_a @ SV33 @ ( minus_1507102574od_a_a @ SV153 @ SV255 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1720]) ).
thf(1807,plain,
! [SV255: set_Product_prod_a_a,SV153: set_Product_prod_a_a,SV33: product_prod_a_a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ SV33 @ SV153 )
| ~ ~ ( member449909584od_a_a @ SV33 @ SV255 ) ) )
= $true )
| ( ( member449909584od_a_a @ SV33 @ ( minus_1507102574od_a_a @ SV153 @ SV255 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1721]) ).
thf(1808,plain,
! [SV255: set_Product_prod_a_a,SV153: set_Product_prod_a_a,SV33: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV33 @ SV153 )
= $false )
| ( ( ~ ~ ( member449909584od_a_a @ SV33 @ SV255 ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ SV33 @ ( minus_1507102574od_a_a @ SV153 @ SV255 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ SV33 @ SV153 )
| ~ ~ ( member449909584od_a_a @ SV33 @ SV255 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1722]) ).
thf(1809,plain,
! [SV345: set_Product_prod_a_a,SV155: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV155 @ SV345 ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV155 @ SV345 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1723]) ).
thf(1810,plain,
! [SV345: set_Product_prod_a_a,SV155: set_Product_prod_a_a] :
( ( ( ~ ! [SY1143: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1143 @ SV155 )
| ( member449909584od_a_a @ SY1143 @ SV345 ) ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV155 @ SV345 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1723]) ).
thf(1811,plain,
! [SV155: set_Product_prod_a_a,SV345: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK41_SY1143 @ SV345 @ SV155 ) @ SV155 ) )
= $false )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV155 @ SV345 )
| ~ ! [SY1143: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1143 @ SV155 )
| ( member449909584od_a_a @ SY1143 @ SV345 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1724]) ).
thf(1812,plain,
! [SV155: set_Product_prod_a_a,SV345: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( sK41_SY1143 @ SV345 @ SV155 ) @ SV345 )
= $false )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV155 @ SV345 )
| ~ ! [SY1143: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1143 @ SV155 )
| ( member449909584od_a_a @ SY1143 @ SV345 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1724]) ).
thf(1813,plain,
! [SV413: product_prod_a_a,SV36: set_Product_prod_a_a] :
( ( ( ~ ~ ! [SY531: product_prod_a_a] :
~ ( member449909584od_a_a @ SY531 @ SV36 ) )
= $false )
| ( ( member449909584od_a_a @ SV413 @ SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1725]) ).
thf(1814,plain,
! [SV413: product_prod_a_a,SV36: set_Product_prod_a_a] :
( ( ( ~ ( ( SV36 != bot_bo2131659635od_a_a ) ) )
= $false )
| ( ( member449909584od_a_a @ SV413 @ SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1725]) ).
thf(1815,plain,
! [SV36: set_Product_prod_a_a] :
( ( ( ! [SY531: product_prod_a_a] :
~ ( member449909584od_a_a @ SY531 @ SV36 ) )
= $false )
| ( ( SV36 = bot_bo2131659635od_a_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1726]) ).
thf(1816,plain,
! [SV36: set_Product_prod_a_a] :
( ( ( SV36 = bot_bo2131659635od_a_a )
= $false )
| ( ( SV36 = bot_bo2131659635od_a_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1727]) ).
thf(1817,plain,
! [SV347: set_Product_prod_a_a,SV162: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV162 @ SV347 ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV162 @ SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1732]) ).
thf(1818,plain,
! [SV347: set_Product_prod_a_a,SV162: set_Product_prod_a_a] :
( ( ( ~ ! [SY1144: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1144 @ SV162 )
| ( member449909584od_a_a @ SY1144 @ SV347 ) ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV162 @ SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1732]) ).
thf(1819,plain,
! [SV162: set_Product_prod_a_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK42_SY1144 @ SV347 @ SV162 ) @ SV162 ) )
= $false )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV162 @ SV347 )
| ~ ! [SY1144: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1144 @ SV162 )
| ( member449909584od_a_a @ SY1144 @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1733]) ).
thf(1820,plain,
! [SV162: set_Product_prod_a_a,SV347: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( sK42_SY1144 @ SV347 @ SV162 ) @ SV347 )
= $false )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV162 @ SV347 )
| ~ ! [SY1144: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1144 @ SV162 )
| ( member449909584od_a_a @ SY1144 @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1733]) ).
thf(1821,plain,
! [SV264: product_prod_a_a > $o,SV165: set_Product_prod_a_a,SV46: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV46
@ ( collec645855634od_a_a
@ ^ [SY1049: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1049 @ SV165 )
| ~ ( SV264 @ SY1049 ) ) ) )
| ~ ! [SY1050: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1050 @ SV46 )
| ( SV264 @ SY1050 ) ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV46
@ ( collec645855634od_a_a
@ ^ [SY1049: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1049 @ SV165 )
| ~ ( SV264 @ SY1049 ) ) ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV46 @ SV165 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1734]) ).
thf(1822,plain,
! [SV46: set_Product_prod_a_a,SV264: product_prod_a_a > $o,SV165: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK48_SY1050 @ SV165 @ SV264 @ SV46 ) @ SV46 )
| ( SV264 @ ( sK48_SY1050 @ SV165 @ SV264 @ SV46 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV46
@ ( collec645855634od_a_a
@ ^ [SY1049: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1049 @ SV165 )
| ~ ( SV264 @ SY1049 ) ) ) )
| ~ ! [SY1050: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1050 @ SV46 )
| ( SV264 @ SY1050 ) ) ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV46 @ SV165 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1735]) ).
thf(1823,plain,
! [SV354: a,SV275: a,SV176: a,SV57: a] :
( ( ( ( product_Pair_a_a @ SV57 @ SV176 )
!= ( product_Pair_a_a @ SV275 @ SV354 ) )
= $false )
| ( ( ( product_Pair_a_a @ SV57 @ SV176 )
= ( product_Pair_a_a @ SV275 @ SV354 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1738]) ).
thf(1824,plain,
! [SV354: a,SV176: a,SV275: a,SV57: a] :
( ( ( ~ ~ ( ( SV57 != SV275 )
| ( SV176 != SV354 ) ) )
= $false )
| ( ( ( product_Pair_a_a @ SV57 @ SV176 )
= ( product_Pair_a_a @ SV275 @ SV354 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1738]) ).
thf(1825,plain,
! [SV354: a,SV176: a,SV275: a,SV57: a] :
( ( ( SV57 != SV275 )
= $true )
| ( ( SV176 != SV354 )
= $true )
| ( ( ~ ( ( ( product_Pair_a_a @ SV57 @ SV176 )
!= ( product_Pair_a_a @ SV275 @ SV354 ) )
| ~ ~ ( ( SV57 != SV275 )
| ( SV176 != SV354 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1739]) ).
thf(1826,plain,
! [SV179: set_a,SV60: set_Product_prod_a_a] :
( ( ( ! [SY894: a,SY895: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY894 @ SY895 ) @ SV60 )
| ( member_a @ SY895 @ SV179 ) ) )
= $false )
| ( ( ~ ( order_preorder_on_a @ SV179 @ SV60 )
| ( prefer1292084992ence_a @ SV179 @ SV60 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK13_SY892 @ SV179 @ SV60 ) @ ( sK24_SY1180 @ SV60 @ SV179 ) ) @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1740]) ).
thf(1827,plain,
! [SV60: set_Product_prod_a_a,SV179: set_a] :
( ( ( ! [SY1204: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK49_SY894 @ SV179 @ SV60 ) @ SY1204 ) @ SV60 )
| ( member_a @ SY1204 @ SV179 ) ) )
= $false )
| ( ( ~ ( order_preorder_on_a @ SV179 @ SV60 )
| ( prefer1292084992ence_a @ SV179 @ SV60 ) )
= $true )
| ( ( member_a @ ( sK13_SY892 @ SV179 @ SV60 ) @ SV179 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1741]) ).
thf(1828,plain,
! [SV61: set_a,SV394: a,SV180: set_Product_prod_a_a,SV356: a,SV278: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV356 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV278 ) @ SV180 ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV394 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV356 ) @ SV180 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV394 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV278 ) @ SV180 ) ) )
= $true )
| ( ( prefer1292084992ence_a @ SV61 @ SV180 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1742]) ).
thf(1829,plain,
! [SV184: a > a,SV65: a,SV405: set_a,SV282: a,SV395: a > a,SV360: a] :
( ( ( SV360
= ( SV395 @ SV282 ) )
= $false )
| ( ( ~ ( member_a @ SV282 @ SV405 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV65 @ SV360 ) @ ( bNF_Gr423046308_a_a_a @ SV405 @ SV184 @ SV395 ) ) )
= $true )
| ( ( SV65
= ( SV184 @ SV282 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1743]) ).
thf(1830,plain,
! [SV365: a > set_a,SV290: set_a,SV193: a,SV75: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV75 @ SV193 ) @ ( product_Sigma_a_a @ SV290 @ SV365 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV75 @ SV193 ) @ ( product_Sigma_a_a @ SV290 @ SV365 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1746]) ).
thf(1831,plain,
! [SV365: a > set_a,SV193: a,SV290: set_a,SV75: a] :
( ( ( ~ ~ ( ~ ( member_a @ SV75 @ SV290 )
| ~ ( member_a @ SV193 @ ( SV365 @ SV75 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV75 @ SV193 ) @ ( product_Sigma_a_a @ SV290 @ SV365 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1746]) ).
thf(1832,plain,
! [SV365: a > set_a,SV193: a,SV290: set_a,SV75: a] :
( ( ( ~ ( member_a @ SV75 @ SV290 ) )
= $true )
| ( ( ~ ( member_a @ SV193 @ ( SV365 @ SV75 ) ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV75 @ SV193 ) @ ( product_Sigma_a_a @ SV290 @ SV365 ) )
| ~ ~ ( ~ ( member_a @ SV75 @ SV290 )
| ~ ( member_a @ SV193 @ ( SV365 @ SV75 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1747]) ).
thf(1833,plain,
! [SV194: product_prod_a_a > product_prod_a_a,SV76: product_prod_a_a,SV406: set_Product_prod_a_a,SV291: product_prod_a_a,SV396: product_prod_a_a > product_prod_a_a,SV366: product_prod_a_a] :
( ( ( SV366
= ( SV396 @ SV291 ) )
= $false )
| ( ( ~ ( member449909584od_a_a @ SV291 @ SV406 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV76 @ SV366 ) @ ( bNF_Gr200450189od_a_a @ SV406 @ SV194 @ SV396 ) ) )
= $true )
| ( ( SV76
= ( SV194 @ SV291 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1748]) ).
thf(1834,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 ) )
= $false )
| ( ( prefer1292084992ence_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1749]) ).
thf(1835,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) )
= $false )
| ( ( prefer1292084992ence_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1749]) ).
thf(1836,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) ) )
= $true )
| ( ( ~ ( order_preorder_on_a @ SV201 @ SV369 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 )
| ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1750]) ).
thf(1837,plain,
! [SV88: set_Product_prod_a_a,SV303: product_prod_a_a > $o,SV372: product_prod_a_a > $o,SV206: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK43_SY1159 @ SV206 @ SV372 @ SV303 @ SV88 ) @ SV88 ) )
= $false )
| ( ( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [SY1094: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1094 @ SV88 )
| ~ ( SV303 @ SY1094 ) ) )
@ ( collec645855634od_a_a
@ ^ [SY1161: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1161 @ SV206 )
| ~ ( SV372 @ SY1161 ) ) ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV88 @ SV206 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1753]) ).
thf(1838,plain,
! [SV88: set_Product_prod_a_a,SV372: product_prod_a_a > $o,SV206: set_Product_prod_a_a,SV303: product_prod_a_a > $o] :
( ( ( ~ ( SV303 @ ( sK43_SY1159 @ SV206 @ SV372 @ SV303 @ SV88 ) )
| ( SV372 @ ( sK43_SY1159 @ SV206 @ SV372 @ SV303 @ SV88 ) ) )
= $false )
| ( ( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [SY1094: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1094 @ SV88 )
| ~ ( SV303 @ SY1094 ) ) )
@ ( collec645855634od_a_a
@ ^ [SY1161: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1161 @ SV206 )
| ~ ( SV372 @ SY1161 ) ) ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV88 @ SV206 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1753]) ).
thf(1839,plain,
! [SV373: product_prod_a_a > set_Product_prod_a_a,SV304: set_Product_prod_a_a,SV207: product_prod_a_a,SV89: product_prod_a_a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV89 @ SV207 ) @ ( produc304751368od_a_a @ SV304 @ SV373 ) ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV89 @ SV207 ) @ ( produc304751368od_a_a @ SV304 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1754]) ).
thf(1840,plain,
! [SV373: product_prod_a_a > set_Product_prod_a_a,SV207: product_prod_a_a,SV304: set_Product_prod_a_a,SV89: product_prod_a_a] :
( ( ( ~ ~ ( ~ ( member449909584od_a_a @ SV89 @ SV304 )
| ~ ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) ) ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV89 @ SV207 ) @ ( produc304751368od_a_a @ SV304 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1754]) ).
thf(1841,plain,
! [SV373: product_prod_a_a > set_Product_prod_a_a,SV207: product_prod_a_a,SV304: set_Product_prod_a_a,SV89: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV89 @ SV304 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) ) )
= $true )
| ( ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV89 @ SV207 ) @ ( produc304751368od_a_a @ SV304 @ SV373 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ SV89 @ SV304 )
| ~ ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1755]) ).
thf(1842,plain,
! [SV91: a,SV208: product_prod_a_a] :
( ( ( ! [SY956: a] :
( SV208
!= ( product_Pair_a_a @ SY956 @ SV91 ) ) )
= $false )
| ( ( SV91
= ( product_snd_a_a @ SV208 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1757]) ).
thf(1843,plain,
! [SV414: a,SV208: product_prod_a_a,SV91: a] :
( ( ( ( SV91
!= ( product_snd_a_a @ SV208 ) )
| ~ ~ ! [SY956: a] :
( SV208
!= ( product_Pair_a_a @ SY956 @ SV91 ) ) )
= $false )
| ( ( SV208
= ( product_Pair_a_a @ SV414 @ SV91 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1758]) ).
thf(1844,plain,
! [SV306: a > $o,SV375: a,SV210: a,SV93: a > $o] :
( ( ( ~ ( SV93 @ ( product_fst_a_a @ ( product_Pair_a_a @ SV210 @ SV375 ) ) ) )
= $false )
| ( ( SV306 @ SV375 )
= $false )
| ( ( SV93 @ SV210 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1759]) ).
thf(1845,plain,
! [SV93: a > $o,SV375: a,SV210: a,SV306: a > $o] :
( ( ( ~ ( SV306 @ ( product_snd_a_a @ ( product_Pair_a_a @ SV210 @ SV375 ) ) ) )
= $false )
| ( ( SV306 @ SV375 )
= $false )
| ( ( SV93 @ SV210 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1759]) ).
thf(1846,plain,
! [SV212: product_prod_a_a > a,SV95: a,SV407: set_Product_prod_a_a,SV308: product_prod_a_a,SV398: product_prod_a_a > a,SV377: a] :
( ( ( SV377
= ( SV398 @ SV308 ) )
= $false )
| ( ( ~ ( member449909584od_a_a @ SV308 @ SV407 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV95 @ SV377 ) @ ( bNF_Gr1853143117_a_a_a @ SV407 @ SV212 @ SV398 ) ) )
= $true )
| ( ( SV95
= ( SV212 @ SV308 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1760]) ).
thf(1847,plain,
! [SV312: a > a,SV380: set_Product_prod_a_a,SV217: a > a,SV101: product_prod_a_a] :
( ( ( SV101
!= ( product_Pair_a_a @ ( SV217 @ ( sK40_SY1167 @ SV380 @ SV312 @ SV217 @ SV101 ) ) @ ( SV312 @ ( sK44_SY1201 @ SV312 @ SV380 @ SV217 @ SV101 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ SV101 @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SV217 @ SV312 ) @ SV380 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1763]) ).
thf(1848,plain,
! [SV101: product_prod_a_a,SV217: a > a,SV312: a > a,SV380: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK40_SY1167 @ SV380 @ SV312 @ SV217 @ SV101 ) @ ( sK44_SY1201 @ SV312 @ SV380 @ SV217 @ SV101 ) ) @ SV380 ) )
= $false )
| ( ( member449909584od_a_a @ SV101 @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SV217 @ SV312 ) @ SV380 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1763]) ).
thf(1849,plain,
! [SV320: product_prod_a_a > set_Product_prod_a_a,SV111: produc1572603623od_a_a,SV226: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK45_SY1197 @ SV226 @ SV111 @ SV320 ) @ ( SV320 @ ( sK36_SY1121 @ SV111 @ SV320 @ SV226 ) ) ) )
= $false )
| ( ( member2057358096od_a_a @ SV111 @ ( produc304751368od_a_a @ SV226 @ SV320 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1766]) ).
thf(1850,plain,
! [SV226: set_Product_prod_a_a,SV320: product_prod_a_a > set_Product_prod_a_a,SV111: produc1572603623od_a_a] :
( ( ( SV111
!= ( produc1474507607od_a_a @ ( sK36_SY1121 @ SV111 @ SV320 @ SV226 ) @ ( sK45_SY1197 @ SV226 @ SV111 @ SV320 ) ) )
= $false )
| ( ( member2057358096od_a_a @ SV111 @ ( produc304751368od_a_a @ SV226 @ SV320 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1766]) ).
thf(1851,plain,
! [SV231: produc1572603623od_a_a > a,SV116: a,SV410: set_Pr1948701895od_a_a,SV325: produc1572603623od_a_a,SV402: produc1572603623od_a_a > a,SV387: a] :
( ( ( SV387
= ( SV402 @ SV325 ) )
= $false )
| ( ( ~ ( member2057358096od_a_a @ SV325 @ SV410 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV116 @ SV387 ) @ ( bNF_Gr356189709_a_a_a @ SV410 @ SV231 @ SV402 ) ) )
= $true )
| ( ( SV116
= ( SV231 @ SV325 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1769]) ).
thf(1852,plain,
! [SV327: a > set_a,SV119: product_prod_a_a,SV233: set_a] :
( ( ( ~ ( member_a @ ( sK46_SY1198 @ SV233 @ SV119 @ SV327 ) @ ( SV327 @ ( sK38_SY1129 @ SV119 @ SV327 @ SV233 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ SV119 @ ( product_Sigma_a_a @ SV233 @ SV327 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1771]) ).
thf(1853,plain,
! [SV233: set_a,SV327: a > set_a,SV119: product_prod_a_a] :
( ( ( SV119
!= ( product_Pair_a_a @ ( sK38_SY1129 @ SV119 @ SV327 @ SV233 ) @ ( sK46_SY1198 @ SV233 @ SV119 @ SV327 ) ) )
= $false )
| ( ( member449909584od_a_a @ SV119 @ ( product_Sigma_a_a @ SV233 @ SV327 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1771]) ).
thf(1854,plain,
! [SV411: set_Product_prod_a_a,SV403: set_Product_prod_a_a,SV390: a,SV331: a,SV237: a,SV123: a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SV331 @ SV390 ) ) @ ( lex_prod_a_a @ SV403 @ SV411 ) )
= $false )
| ( ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SV331 @ SV390 ) ) @ ( lex_prod_a_a @ SV403 @ SV411 ) )
| ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
| ~ ( ( SV123 != SV331 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1772]) ).
thf(1855,plain,
! [SV411: set_Product_prod_a_a,SV390: a,SV237: a,SV403: set_Product_prod_a_a,SV331: a,SV123: a] :
( ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
| ~ ( ( SV123 != SV331 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 ) ) )
= $false )
| ( ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SV331 @ SV390 ) ) @ ( lex_prod_a_a @ SV403 @ SV411 ) )
| ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
| ~ ( ( SV123 != SV331 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1772]) ).
thf(1856,plain,
! [SV125: a,SV238: product_prod_a_a] :
( ( ( ! [SY1024: a] :
( SV238
!= ( product_Pair_a_a @ SV125 @ SY1024 ) ) )
= $false )
| ( ( SV125
= ( product_fst_a_a @ SV238 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1774]) ).
thf(1857,plain,
! [SV415: a,SV238: product_prod_a_a,SV125: a] :
( ( ( ( SV125
!= ( product_fst_a_a @ SV238 ) )
| ~ ~ ! [SY1024: a] :
( SV238
!= ( product_Pair_a_a @ SV125 @ SY1024 ) ) )
= $false )
| ( ( SV238
= ( product_Pair_a_a @ SV125 @ SV415 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1775]) ).
thf(1858,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a] :
( ( ( ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 ) ) )
= $false )
| ( ( ~ ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
!= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
| ( SV2 != SV131 ) ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[1778]) ).
thf(1859,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a] :
( ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 ) )
= $false )
| ( ( ~ ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
!= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
| ( SV2 != SV131 ) ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[1778]) ).
thf(1860,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
!= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $false )
| ( ( ( ^ [SY1199: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1199 ) @ SV2 ) )
= ( ^ [SY1200: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1200 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1779]) ).
thf(1861,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( SV2 != SV131 )
= $false )
| ( ( ( ^ [SY1199: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1199 ) @ SV2 ) )
= ( ^ [SY1200: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1200 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1779]) ).
thf(1862,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( ! [SV419: a] :
( ( ^ [SY1205: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV419 @ SY1205 ) @ SV2 ) )
= ( ^ [SY1206: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV419 @ SY1206 ) @ SV131 ) ) ) )
= $true )
| ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1780]) ).
thf(1863,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $true )
| ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1780]) ).
thf(1864,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV420: a] :
( ( ( ( ^ [SY1207: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SY1207 ) @ SV2 ) )
= ( ^ [SY1208: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SY1208 ) @ SV131 ) ) )
= $true )
| ( ( SV2 = SV131 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1782]) ).
thf(1865,plain,
! [SV340: a,SV140: a] :
( ( ( top_top_a_a_o @ SV140 @ SV340 )
= $true )
| ( ( top_top_a_a_o @ SV140 @ SV340 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1788]) ).
thf(1866,plain,
! [SV340: a,SV140: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV140 @ SV340 ) @ top_to398455383od_a_a )
= $true )
| ( ( top_top_a_a_o @ SV140 @ SV340 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1789]) ).
thf(1867,plain,
! [SV340: a,SV140: a] :
( ( ( top_top_a_a_o @ SV140 @ SV340 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV140 @ SV340 ) @ top_to398455383od_a_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1790]) ).
thf(1868,plain,
! [SV340: a,SV140: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV140 @ SV340 ) @ top_to398455383od_a_a )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV140 @ SV340 ) @ top_to398455383od_a_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1791]) ).
thf(1869,plain,
! [SV341: set_Product_prod_a_a,SV145: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV145 @ SV341 )
= $true )
| ( ( ord_le1824328871od_a_a @ SV145 @ SV341 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1796]) ).
thf(1870,plain,
! [SV341: set_Product_prod_a_a,SV145: set_Product_prod_a_a] :
( ( ( ord_le1347718902_a_a_o
@ ^ [SY828: product_prod_a_a] : ( member449909584od_a_a @ SY828 @ SV145 )
@ ^ [SY1142: product_prod_a_a] : ( member449909584od_a_a @ SY1142 @ SV341 ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV145 @ SV341 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1797]) ).
thf(1871,plain,
! [SV341: set_Product_prod_a_a,SV145: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV145 @ SV341 )
= $true )
| ( ( ord_le1347718902_a_a_o
@ ^ [SY828: product_prod_a_a] : ( member449909584od_a_a @ SY828 @ SV145 )
@ ^ [SY1142: product_prod_a_a] : ( member449909584od_a_a @ SY1142 @ SV341 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1798]) ).
thf(1872,plain,
! [SV341: set_Product_prod_a_a,SV145: set_Product_prod_a_a] :
( ( ( ord_le1347718902_a_a_o
@ ^ [SY828: product_prod_a_a] : ( member449909584od_a_a @ SY828 @ SV145 )
@ ^ [SY1142: product_prod_a_a] : ( member449909584od_a_a @ SY1142 @ SV341 ) )
= $true )
| ( ( ord_le1347718902_a_a_o
@ ^ [SY828: product_prod_a_a] : ( member449909584od_a_a @ SY828 @ SV145 )
@ ^ [SY1142: product_prod_a_a] : ( member449909584od_a_a @ SY1142 @ SV341 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1799]) ).
thf(1873,plain,
! [SV24: set_Product_prod_a_a,SV421: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV421 @ SV24 ) )
= $true )
| ( ( member449909584od_a_a @ ( sK19_SY508 @ SV24 ) @ SV24 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1800]) ).
thf(1874,plain,
! [SV343: a,SV252: a,SV150: a,SV30: a] :
( ( ( ( product_Pair_a_a @ SV30 @ SV150 )
= ( product_Pair_a_a @ SV252 @ SV343 ) )
= $true )
| ( ( ( product_Pair_a_a @ SV30 @ SV150 )
= ( product_Pair_a_a @ SV252 @ SV343 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1803]) ).
thf(1875,plain,
! [SV343: a,SV150: a,SV252: a,SV30: a] :
( ( ( ~ ( ( SV30 != SV252 )
| ( SV150 != SV343 ) ) )
= $true )
| ( ( ( product_Pair_a_a @ SV30 @ SV150 )
= ( product_Pair_a_a @ SV252 @ SV343 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1804]) ).
thf(1876,plain,
! [SV343: a,SV150: a,SV252: a,SV30: a] :
( ( ( SV30 = SV252 )
= $false )
| ( ( SV150 != SV343 )
= $true )
| ( ( ~ ( ( ( product_Pair_a_a @ SV30 @ SV150 )
!= ( product_Pair_a_a @ SV252 @ SV343 ) )
| ~ ~ ( ( SV30 != SV252 )
| ( SV150 != SV343 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1805]) ).
thf(1877,plain,
! [SV255: set_Product_prod_a_a,SV153: set_Product_prod_a_a,SV33: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV33 @ SV153 )
| ~ ~ ( member449909584od_a_a @ SV33 @ SV255 ) )
= $false )
| ( ( member449909584od_a_a @ SV33 @ ( minus_1507102574od_a_a @ SV153 @ SV255 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1807]) ).
thf(1878,plain,
! [SV153: set_Product_prod_a_a,SV255: set_Product_prod_a_a,SV33: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV33 @ SV255 ) )
= $false )
| ( ( member449909584od_a_a @ SV33 @ SV153 )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ SV33 @ ( minus_1507102574od_a_a @ SV153 @ SV255 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ SV33 @ SV153 )
| ~ ~ ( member449909584od_a_a @ SV33 @ SV255 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1808]) ).
thf(1879,plain,
! [SV345: set_Product_prod_a_a,SV155: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV155 @ SV345 )
= $true )
| ( ( ord_le1824328871od_a_a @ SV155 @ SV345 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1809]) ).
thf(1880,plain,
! [SV345: set_Product_prod_a_a,SV155: set_Product_prod_a_a] :
( ( ( ! [SY1143: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1143 @ SV155 )
| ( member449909584od_a_a @ SY1143 @ SV345 ) ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV155 @ SV345 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1810]) ).
thf(1881,plain,
! [SV155: set_Product_prod_a_a,SV345: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( sK41_SY1143 @ SV345 @ SV155 ) @ SV155 )
= $true )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV155 @ SV345 )
| ~ ! [SY1143: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1143 @ SV155 )
| ( member449909584od_a_a @ SY1143 @ SV345 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1811]) ).
thf(1882,plain,
! [SV345: set_Product_prod_a_a,SV155: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV155 @ SV345 )
| ~ ! [SY1143: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1143 @ SV155 )
| ( member449909584od_a_a @ SY1143 @ SV345 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( sK41_SY1143 @ SV345 @ SV155 ) @ SV345 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1812]) ).
thf(1883,plain,
! [SV413: product_prod_a_a,SV36: set_Product_prod_a_a] :
( ( ( ~ ! [SY531: product_prod_a_a] :
~ ( member449909584od_a_a @ SY531 @ SV36 ) )
= $true )
| ( ( member449909584od_a_a @ SV413 @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1813]) ).
thf(1884,plain,
! [SV413: product_prod_a_a,SV36: set_Product_prod_a_a] :
( ( ( SV36 != bot_bo2131659635od_a_a )
= $true )
| ( ( member449909584od_a_a @ SV413 @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1814]) ).
thf(1885,plain,
! [SV36: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK50_SY531 @ SV36 ) @ SV36 ) )
= $false )
| ( ( SV36 = bot_bo2131659635od_a_a )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1815]) ).
thf(1886,plain,
! [SV347: set_Product_prod_a_a,SV162: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV162 @ SV347 )
= $true )
| ( ( ord_le1824328871od_a_a @ SV162 @ SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1817]) ).
thf(1887,plain,
! [SV347: set_Product_prod_a_a,SV162: set_Product_prod_a_a] :
( ( ( ! [SY1144: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1144 @ SV162 )
| ( member449909584od_a_a @ SY1144 @ SV347 ) ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV162 @ SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1818]) ).
thf(1888,plain,
! [SV162: set_Product_prod_a_a,SV347: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( sK42_SY1144 @ SV347 @ SV162 ) @ SV162 )
= $true )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV162 @ SV347 )
| ~ ! [SY1144: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1144 @ SV162 )
| ( member449909584od_a_a @ SY1144 @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1819]) ).
thf(1889,plain,
! [SV347: set_Product_prod_a_a,SV162: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV162 @ SV347 )
| ~ ! [SY1144: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1144 @ SV162 )
| ( member449909584od_a_a @ SY1144 @ SV347 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( sK42_SY1144 @ SV347 @ SV162 ) @ SV347 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1820]) ).
thf(1890,plain,
! [SV264: product_prod_a_a > $o,SV165: set_Product_prod_a_a,SV46: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV46
@ ( collec645855634od_a_a
@ ^ [SY1049: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1049 @ SV165 )
| ~ ( SV264 @ SY1049 ) ) ) ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV46
@ ( collec645855634od_a_a
@ ^ [SY1049: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1049 @ SV165 )
| ~ ( SV264 @ SY1049 ) ) ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV46 @ SV165 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1821]) ).
thf(1891,plain,
! [SV165: set_Product_prod_a_a,SV264: product_prod_a_a > $o,SV46: set_Product_prod_a_a] :
( ( ( ~ ! [SY1050: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1050 @ SV46 )
| ( SV264 @ SY1050 ) ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV46
@ ( collec645855634od_a_a
@ ^ [SY1049: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1049 @ SV165 )
| ~ ( SV264 @ SY1049 ) ) ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV46 @ SV165 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1821]) ).
thf(1892,plain,
! [SV46: set_Product_prod_a_a,SV264: product_prod_a_a > $o,SV165: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK48_SY1050 @ SV165 @ SV264 @ SV46 ) @ SV46 ) )
= $false )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV46
@ ( collec645855634od_a_a
@ ^ [SY1049: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1049 @ SV165 )
| ~ ( SV264 @ SY1049 ) ) ) )
| ~ ! [SY1050: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1050 @ SV46 )
| ( SV264 @ SY1050 ) ) ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV46 @ SV165 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1822]) ).
thf(1893,plain,
! [SV46: set_Product_prod_a_a,SV165: set_Product_prod_a_a,SV264: product_prod_a_a > $o] :
( ( ( SV264 @ ( sK48_SY1050 @ SV165 @ SV264 @ SV46 ) )
= $false )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV46
@ ( collec645855634od_a_a
@ ^ [SY1049: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1049 @ SV165 )
| ~ ( SV264 @ SY1049 ) ) ) )
| ~ ! [SY1050: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1050 @ SV46 )
| ( SV264 @ SY1050 ) ) ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV46 @ SV165 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1822]) ).
thf(1894,plain,
! [SV354: a,SV275: a,SV176: a,SV57: a] :
( ( ( ( product_Pair_a_a @ SV57 @ SV176 )
= ( product_Pair_a_a @ SV275 @ SV354 ) )
= $true )
| ( ( ( product_Pair_a_a @ SV57 @ SV176 )
= ( product_Pair_a_a @ SV275 @ SV354 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1823]) ).
thf(1895,plain,
! [SV354: a,SV176: a,SV275: a,SV57: a] :
( ( ( ~ ( ( SV57 != SV275 )
| ( SV176 != SV354 ) ) )
= $true )
| ( ( ( product_Pair_a_a @ SV57 @ SV176 )
= ( product_Pair_a_a @ SV275 @ SV354 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1824]) ).
thf(1896,plain,
! [SV354: a,SV176: a,SV275: a,SV57: a] :
( ( ( SV57 = SV275 )
= $false )
| ( ( SV176 != SV354 )
= $true )
| ( ( ~ ( ( ( product_Pair_a_a @ SV57 @ SV176 )
!= ( product_Pair_a_a @ SV275 @ SV354 ) )
| ~ ~ ( ( SV57 != SV275 )
| ( SV176 != SV354 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1825]) ).
thf(1897,plain,
! [SV60: set_Product_prod_a_a,SV179: set_a] :
( ( ( ! [SY1209: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK51_SY894 @ SV179 @ SV60 ) @ SY1209 ) @ SV60 )
| ( member_a @ SY1209 @ SV179 ) ) )
= $false )
| ( ( ~ ( order_preorder_on_a @ SV179 @ SV60 )
| ( prefer1292084992ence_a @ SV179 @ SV60 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK13_SY892 @ SV179 @ SV60 ) @ ( sK24_SY1180 @ SV60 @ SV179 ) ) @ SV60 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1826]) ).
thf(1898,plain,
! [SV60: set_Product_prod_a_a,SV179: set_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK49_SY894 @ SV179 @ SV60 ) @ ( sK52_SY1204 @ SV60 @ SV179 ) ) @ SV60 )
| ( member_a @ ( sK52_SY1204 @ SV60 @ SV179 ) @ SV179 ) )
= $false )
| ( ( ~ ( order_preorder_on_a @ SV179 @ SV60 )
| ( prefer1292084992ence_a @ SV179 @ SV60 ) )
= $true )
| ( ( member_a @ ( sK13_SY892 @ SV179 @ SV60 ) @ SV179 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1827]) ).
thf(1899,plain,
! [SV61: set_a,SV394: a,SV180: set_Product_prod_a_a,SV356: a,SV278: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV356 ) @ SV180 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV278 ) @ SV180 ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV394 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV356 ) @ SV180 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV394 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV278 ) @ SV180 ) ) )
= $true )
| ( ( prefer1292084992ence_a @ SV61 @ SV180 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1828]) ).
thf(1900,plain,
! [SV395: a > a,SV184: a > a,SV360: a,SV65: a,SV405: set_a,SV282: a] :
( ( ( ~ ( member_a @ SV282 @ SV405 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV65 @ SV360 ) @ ( bNF_Gr423046308_a_a_a @ SV405 @ SV184 @ SV395 ) )
= $true )
| ( ( SV360
= ( SV395 @ SV282 ) )
= $false )
| ( ( SV65
= ( SV184 @ SV282 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1829]) ).
thf(1901,plain,
! [SV365: a > set_a,SV290: set_a,SV193: a,SV75: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV75 @ SV193 ) @ ( product_Sigma_a_a @ SV290 @ SV365 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV75 @ SV193 ) @ ( product_Sigma_a_a @ SV290 @ SV365 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1830]) ).
thf(1902,plain,
! [SV365: a > set_a,SV193: a,SV290: set_a,SV75: a] :
( ( ( ~ ( ~ ( member_a @ SV75 @ SV290 )
| ~ ( member_a @ SV193 @ ( SV365 @ SV75 ) ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV75 @ SV193 ) @ ( product_Sigma_a_a @ SV290 @ SV365 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1831]) ).
thf(1903,plain,
! [SV365: a > set_a,SV193: a,SV290: set_a,SV75: a] :
( ( ( member_a @ SV75 @ SV290 )
= $false )
| ( ( ~ ( member_a @ SV193 @ ( SV365 @ SV75 ) ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV75 @ SV193 ) @ ( product_Sigma_a_a @ SV290 @ SV365 ) )
| ~ ~ ( ~ ( member_a @ SV75 @ SV290 )
| ~ ( member_a @ SV193 @ ( SV365 @ SV75 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1832]) ).
thf(1904,plain,
! [SV396: product_prod_a_a > product_prod_a_a,SV194: product_prod_a_a > product_prod_a_a,SV366: product_prod_a_a,SV76: product_prod_a_a,SV406: set_Product_prod_a_a,SV291: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV291 @ SV406 ) )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV76 @ SV366 ) @ ( bNF_Gr200450189od_a_a @ SV406 @ SV194 @ SV396 ) )
= $true )
| ( ( SV366
= ( SV396 @ SV291 ) )
= $false )
| ( ( SV76
= ( SV194 @ SV291 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1833]) ).
thf(1905,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( prefer1292084992ence_a @ SV201 @ SV369 )
= $true )
| ( ( prefer1292084992ence_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1834]) ).
thf(1906,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) )
= $true )
| ( ( prefer1292084992ence_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1835]) ).
thf(1907,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) ) )
= $false )
| ( ( ~ ( order_preorder_on_a @ SV201 @ SV369 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 )
| ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1836]) ).
thf(1908,plain,
! [SV88: set_Product_prod_a_a,SV303: product_prod_a_a > $o,SV372: product_prod_a_a > $o,SV206: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( sK43_SY1159 @ SV206 @ SV372 @ SV303 @ SV88 ) @ SV88 )
= $true )
| ( ( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [SY1094: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1094 @ SV88 )
| ~ ( SV303 @ SY1094 ) ) )
@ ( collec645855634od_a_a
@ ^ [SY1161: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1161 @ SV206 )
| ~ ( SV372 @ SY1161 ) ) ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV88 @ SV206 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1837]) ).
thf(1909,plain,
! [SV88: set_Product_prod_a_a,SV372: product_prod_a_a > $o,SV206: set_Product_prod_a_a,SV303: product_prod_a_a > $o] :
( ( ( ~ ( SV303 @ ( sK43_SY1159 @ SV206 @ SV372 @ SV303 @ SV88 ) ) )
= $false )
| ( ( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [SY1094: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1094 @ SV88 )
| ~ ( SV303 @ SY1094 ) ) )
@ ( collec645855634od_a_a
@ ^ [SY1161: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1161 @ SV206 )
| ~ ( SV372 @ SY1161 ) ) ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV88 @ SV206 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1838]) ).
thf(1910,plain,
! [SV88: set_Product_prod_a_a,SV303: product_prod_a_a > $o,SV206: set_Product_prod_a_a,SV372: product_prod_a_a > $o] :
( ( ( SV372 @ ( sK43_SY1159 @ SV206 @ SV372 @ SV303 @ SV88 ) )
= $false )
| ( ( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [SY1094: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1094 @ SV88 )
| ~ ( SV303 @ SY1094 ) ) )
@ ( collec645855634od_a_a
@ ^ [SY1161: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1161 @ SV206 )
| ~ ( SV372 @ SY1161 ) ) ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV88 @ SV206 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1838]) ).
thf(1911,plain,
! [SV373: product_prod_a_a > set_Product_prod_a_a,SV304: set_Product_prod_a_a,SV207: product_prod_a_a,SV89: product_prod_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV89 @ SV207 ) @ ( produc304751368od_a_a @ SV304 @ SV373 ) )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV89 @ SV207 ) @ ( produc304751368od_a_a @ SV304 @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1839]) ).
thf(1912,plain,
! [SV373: product_prod_a_a > set_Product_prod_a_a,SV207: product_prod_a_a,SV304: set_Product_prod_a_a,SV89: product_prod_a_a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ SV89 @ SV304 )
| ~ ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) ) ) )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV89 @ SV207 ) @ ( produc304751368od_a_a @ SV304 @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1840]) ).
thf(1913,plain,
! [SV373: product_prod_a_a > set_Product_prod_a_a,SV207: product_prod_a_a,SV304: set_Product_prod_a_a,SV89: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV89 @ SV304 )
= $false )
| ( ( ~ ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) ) )
= $true )
| ( ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV89 @ SV207 ) @ ( produc304751368od_a_a @ SV304 @ SV373 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ SV89 @ SV304 )
| ~ ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1841]) ).
thf(1914,plain,
! [SV91: a,SV208: product_prod_a_a] :
( ( ( SV208
!= ( product_Pair_a_a @ ( sK53_SY956 @ SV91 @ SV208 ) @ SV91 ) )
= $false )
| ( ( SV91
= ( product_snd_a_a @ SV208 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1842]) ).
thf(1915,plain,
! [SV414: a,SV208: product_prod_a_a,SV91: a] :
( ( ( SV91
!= ( product_snd_a_a @ SV208 ) )
= $false )
| ( ( SV208
= ( product_Pair_a_a @ SV414 @ SV91 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1843]) ).
thf(1916,plain,
! [SV414: a,SV91: a,SV208: product_prod_a_a] :
( ( ( ~ ~ ! [SY956: a] :
( SV208
!= ( product_Pair_a_a @ SY956 @ SV91 ) ) )
= $false )
| ( ( SV208
= ( product_Pair_a_a @ SV414 @ SV91 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1843]) ).
thf(1917,plain,
! [SV306: a > $o,SV375: a,SV210: a,SV93: a > $o] :
( ( ( SV93 @ ( product_fst_a_a @ ( product_Pair_a_a @ SV210 @ SV375 ) ) )
= $true )
| ( ( SV306 @ SV375 )
= $false )
| ( ( SV93 @ SV210 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1844]) ).
thf(1918,plain,
! [SV93: a > $o,SV375: a,SV210: a,SV306: a > $o] :
( ( ( SV306 @ ( product_snd_a_a @ ( product_Pair_a_a @ SV210 @ SV375 ) ) )
= $true )
| ( ( SV306 @ SV375 )
= $false )
| ( ( SV93 @ SV210 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1845]) ).
thf(1919,plain,
! [SV398: product_prod_a_a > a,SV212: product_prod_a_a > a,SV377: a,SV95: a,SV407: set_Product_prod_a_a,SV308: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV308 @ SV407 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV95 @ SV377 ) @ ( bNF_Gr1853143117_a_a_a @ SV407 @ SV212 @ SV398 ) )
= $true )
| ( ( SV377
= ( SV398 @ SV308 ) )
= $false )
| ( ( SV95
= ( SV212 @ SV308 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1846]) ).
thf(1920,plain,
! [SV312: a > a,SV380: set_Product_prod_a_a,SV217: a > a,SV101: product_prod_a_a] :
( ( ( SV101
= ( product_Pair_a_a @ ( SV217 @ ( sK40_SY1167 @ SV380 @ SV312 @ SV217 @ SV101 ) ) @ ( SV312 @ ( sK44_SY1201 @ SV312 @ SV380 @ SV217 @ SV101 ) ) ) )
= $true )
| ( ( member449909584od_a_a @ SV101 @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SV217 @ SV312 ) @ SV380 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1847]) ).
thf(1921,plain,
! [SV101: product_prod_a_a,SV217: a > a,SV312: a > a,SV380: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK40_SY1167 @ SV380 @ SV312 @ SV217 @ SV101 ) @ ( sK44_SY1201 @ SV312 @ SV380 @ SV217 @ SV101 ) ) @ SV380 )
= $true )
| ( ( member449909584od_a_a @ SV101 @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SV217 @ SV312 ) @ SV380 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1848]) ).
thf(1922,plain,
! [SV320: product_prod_a_a > set_Product_prod_a_a,SV111: produc1572603623od_a_a,SV226: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( sK45_SY1197 @ SV226 @ SV111 @ SV320 ) @ ( SV320 @ ( sK36_SY1121 @ SV111 @ SV320 @ SV226 ) ) )
= $true )
| ( ( member2057358096od_a_a @ SV111 @ ( produc304751368od_a_a @ SV226 @ SV320 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1849]) ).
thf(1923,plain,
! [SV226: set_Product_prod_a_a,SV320: product_prod_a_a > set_Product_prod_a_a,SV111: produc1572603623od_a_a] :
( ( ( SV111
= ( produc1474507607od_a_a @ ( sK36_SY1121 @ SV111 @ SV320 @ SV226 ) @ ( sK45_SY1197 @ SV226 @ SV111 @ SV320 ) ) )
= $true )
| ( ( member2057358096od_a_a @ SV111 @ ( produc304751368od_a_a @ SV226 @ SV320 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1850]) ).
thf(1924,plain,
! [SV402: produc1572603623od_a_a > a,SV231: produc1572603623od_a_a > a,SV387: a,SV116: a,SV410: set_Pr1948701895od_a_a,SV325: produc1572603623od_a_a] :
( ( ( ~ ( member2057358096od_a_a @ SV325 @ SV410 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV116 @ SV387 ) @ ( bNF_Gr356189709_a_a_a @ SV410 @ SV231 @ SV402 ) )
= $true )
| ( ( SV387
= ( SV402 @ SV325 ) )
= $false )
| ( ( SV116
= ( SV231 @ SV325 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1851]) ).
thf(1925,plain,
! [SV327: a > set_a,SV119: product_prod_a_a,SV233: set_a] :
( ( ( member_a @ ( sK46_SY1198 @ SV233 @ SV119 @ SV327 ) @ ( SV327 @ ( sK38_SY1129 @ SV119 @ SV327 @ SV233 ) ) )
= $true )
| ( ( member449909584od_a_a @ SV119 @ ( product_Sigma_a_a @ SV233 @ SV327 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1852]) ).
thf(1926,plain,
! [SV233: set_a,SV327: a > set_a,SV119: product_prod_a_a] :
( ( ( SV119
= ( product_Pair_a_a @ ( sK38_SY1129 @ SV119 @ SV327 @ SV233 ) @ ( sK46_SY1198 @ SV233 @ SV119 @ SV327 ) ) )
= $true )
| ( ( member449909584od_a_a @ SV119 @ ( product_Sigma_a_a @ SV233 @ SV327 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1853]) ).
thf(1927,plain,
! [SV411: set_Product_prod_a_a,SV403: set_Product_prod_a_a,SV390: a,SV331: a,SV237: a,SV123: a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SV331 @ SV390 ) ) @ ( lex_prod_a_a @ SV403 @ SV411 ) )
| ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
| ~ ( ( SV123 != SV331 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 ) ) ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SV331 @ SV390 ) ) @ ( lex_prod_a_a @ SV403 @ SV411 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1854]) ).
thf(1928,plain,
! [SV411: set_Product_prod_a_a,SV390: a,SV237: a,SV403: set_Product_prod_a_a,SV331: a,SV123: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
= $false )
| ( ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SV331 @ SV390 ) ) @ ( lex_prod_a_a @ SV403 @ SV411 ) )
| ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
| ~ ( ( SV123 != SV331 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1855]) ).
thf(1929,plain,
! [SV403: set_Product_prod_a_a,SV411: set_Product_prod_a_a,SV390: a,SV237: a,SV331: a,SV123: a] :
( ( ( ~ ( ( SV123 != SV331 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 ) ) )
= $false )
| ( ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SV331 @ SV390 ) ) @ ( lex_prod_a_a @ SV403 @ SV411 ) )
| ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
| ~ ( ( SV123 != SV331 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1855]) ).
thf(1930,plain,
! [SV125: a,SV238: product_prod_a_a] :
( ( ( SV238
!= ( product_Pair_a_a @ SV125 @ ( sK54_SY1024 @ SV125 @ SV238 ) ) )
= $false )
| ( ( SV125
= ( product_fst_a_a @ SV238 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1856]) ).
thf(1931,plain,
! [SV415: a,SV238: product_prod_a_a,SV125: a] :
( ( ( SV125
!= ( product_fst_a_a @ SV238 ) )
= $false )
| ( ( SV238
= ( product_Pair_a_a @ SV125 @ SV415 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1857]) ).
thf(1932,plain,
! [SV415: a,SV125: a,SV238: product_prod_a_a] :
( ( ( ~ ~ ! [SY1024: a] :
( SV238
!= ( product_Pair_a_a @ SV125 @ SY1024 ) ) )
= $false )
| ( ( SV238
= ( product_Pair_a_a @ SV125 @ SV415 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1857]) ).
thf(1933,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a] :
( ( ( ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 ) ) )
= $false )
| ( ( ~ ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
!= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
| ( SV2 != SV131 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1858]) ).
thf(1934,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 ) ) )
= $false )
| ( ( ~ ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
!= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
| ( SV2 != SV131 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1858]) ).
thf(1935,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
!= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
| ( SV2 != SV131 ) )
= $false )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1859]) ).
thf(1936,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $true )
| ( ( ( ^ [SY1199: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1199 ) @ SV2 ) )
= ( ^ [SY1200: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1200 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1860]) ).
thf(1937,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( SV2 = SV131 )
= $true )
| ( ( ( ^ [SY1199: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1199 ) @ SV2 ) )
= ( ^ [SY1200: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1200 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1861]) ).
thf(1938,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV422: a] :
( ( ( ( ^ [SY1210: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SY1210 ) @ SV2 ) )
= ( ^ [SY1211: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SY1211 ) @ SV131 ) ) )
= $true )
| ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1862]) ).
thf(1939,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV420: a] :
( ( ( ! [SV423: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV423 ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV423 ) @ SV131 ) ) )
= $true )
| ( ( SV2 = SV131 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1864]) ).
thf(1940,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV420: a] :
( ( ( ( ^ [SY1207: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SY1207 ) @ SV2 ) )
= ( ^ [SY1208: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SY1208 ) @ SV131 ) ) )
= $true )
| ( ( SV2 = SV131 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1864]) ).
thf(1941,plain,
! [SV24: set_Product_prod_a_a,SV421: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV421 @ SV24 )
= $false )
| ( ( member449909584od_a_a @ ( sK19_SY508 @ SV24 ) @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1873]) ).
thf(1942,plain,
! [SV343: a,SV150: a,SV252: a,SV30: a] :
( ( ( ( SV30 != SV252 )
| ( SV150 != SV343 ) )
= $false )
| ( ( ( product_Pair_a_a @ SV30 @ SV150 )
= ( product_Pair_a_a @ SV252 @ SV343 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1875]) ).
thf(1943,plain,
! [SV252: a,SV30: a,SV343: a,SV150: a] :
( ( ( SV150 = SV343 )
= $false )
| ( ( SV30 = SV252 )
= $false )
| ( ( ~ ( ( ( product_Pair_a_a @ SV30 @ SV150 )
!= ( product_Pair_a_a @ SV252 @ SV343 ) )
| ~ ~ ( ( SV30 != SV252 )
| ( SV150 != SV343 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1876]) ).
thf(1944,plain,
! [SV255: set_Product_prod_a_a,SV153: set_Product_prod_a_a,SV33: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV33 @ SV153 ) )
= $false )
| ( ( member449909584od_a_a @ SV33 @ ( minus_1507102574od_a_a @ SV153 @ SV255 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1877]) ).
thf(1945,plain,
! [SV153: set_Product_prod_a_a,SV255: set_Product_prod_a_a,SV33: product_prod_a_a] :
( ( ( ~ ~ ( member449909584od_a_a @ SV33 @ SV255 ) )
= $false )
| ( ( member449909584od_a_a @ SV33 @ ( minus_1507102574od_a_a @ SV153 @ SV255 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1877]) ).
thf(1946,plain,
! [SV153: set_Product_prod_a_a,SV255: set_Product_prod_a_a,SV33: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV33 @ SV255 )
= $true )
| ( ( member449909584od_a_a @ SV33 @ SV153 )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ SV33 @ ( minus_1507102574od_a_a @ SV153 @ SV255 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ SV33 @ SV153 )
| ~ ~ ( member449909584od_a_a @ SV33 @ SV255 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1878]) ).
thf(1947,plain,
! [SV345: set_Product_prod_a_a,SV155: set_Product_prod_a_a,SV424: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV424 @ SV155 )
| ( member449909584od_a_a @ SV424 @ SV345 ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV155 @ SV345 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1880]) ).
thf(1948,plain,
! [SV345: set_Product_prod_a_a,SV155: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV155 @ SV345 )
| ~ ! [SY1143: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1143 @ SV155 )
| ( member449909584od_a_a @ SY1143 @ SV345 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( sK41_SY1143 @ SV345 @ SV155 ) @ SV155 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1881]) ).
thf(1949,plain,
! [SV345: set_Product_prod_a_a,SV155: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV155 @ SV345 ) )
= $false )
| ( ( member449909584od_a_a @ ( sK41_SY1143 @ SV345 @ SV155 ) @ SV345 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1882]) ).
thf(1950,plain,
! [SV345: set_Product_prod_a_a,SV155: set_Product_prod_a_a] :
( ( ( ~ ! [SY1143: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1143 @ SV155 )
| ( member449909584od_a_a @ SY1143 @ SV345 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( sK41_SY1143 @ SV345 @ SV155 ) @ SV345 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1882]) ).
thf(1951,plain,
! [SV413: product_prod_a_a,SV36: set_Product_prod_a_a] :
( ( ( ! [SY531: product_prod_a_a] :
~ ( member449909584od_a_a @ SY531 @ SV36 ) )
= $false )
| ( ( member449909584od_a_a @ SV413 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1883]) ).
thf(1952,plain,
! [SV413: product_prod_a_a,SV36: set_Product_prod_a_a] :
( ( ( SV36 = bot_bo2131659635od_a_a )
= $false )
| ( ( member449909584od_a_a @ SV413 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1884]) ).
thf(1953,plain,
! [SV36: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( sK50_SY531 @ SV36 ) @ SV36 )
= $true )
| ( ( SV36 = bot_bo2131659635od_a_a )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1885]) ).
thf(1954,plain,
! [SV347: set_Product_prod_a_a,SV162: set_Product_prod_a_a,SV425: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV425 @ SV162 )
| ( member449909584od_a_a @ SV425 @ SV347 ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV162 @ SV347 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1887]) ).
thf(1955,plain,
! [SV347: set_Product_prod_a_a,SV162: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV162 @ SV347 )
| ~ ! [SY1144: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1144 @ SV162 )
| ( member449909584od_a_a @ SY1144 @ SV347 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( sK42_SY1144 @ SV347 @ SV162 ) @ SV162 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1888]) ).
thf(1956,plain,
! [SV347: set_Product_prod_a_a,SV162: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV162 @ SV347 ) )
= $false )
| ( ( member449909584od_a_a @ ( sK42_SY1144 @ SV347 @ SV162 ) @ SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1889]) ).
thf(1957,plain,
! [SV347: set_Product_prod_a_a,SV162: set_Product_prod_a_a] :
( ( ( ~ ! [SY1144: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1144 @ SV162 )
| ( member449909584od_a_a @ SY1144 @ SV347 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( sK42_SY1144 @ SV347 @ SV162 ) @ SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1889]) ).
thf(1958,plain,
! [SV264: product_prod_a_a > $o,SV165: set_Product_prod_a_a,SV46: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV46
@ ( collec645855634od_a_a
@ ^ [SY1049: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1049 @ SV165 )
| ~ ( SV264 @ SY1049 ) ) ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV46
@ ( collec645855634od_a_a
@ ^ [SY1049: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1049 @ SV165 )
| ~ ( SV264 @ SY1049 ) ) ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV46 @ SV165 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1890]) ).
thf(1959,plain,
! [SV165: set_Product_prod_a_a,SV264: product_prod_a_a > $o,SV46: set_Product_prod_a_a] :
( ( ( ! [SY1050: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1050 @ SV46 )
| ( SV264 @ SY1050 ) ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV46
@ ( collec645855634od_a_a
@ ^ [SY1049: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1049 @ SV165 )
| ~ ( SV264 @ SY1049 ) ) ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV46 @ SV165 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1891]) ).
thf(1960,plain,
! [SV46: set_Product_prod_a_a,SV264: product_prod_a_a > $o,SV165: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( sK48_SY1050 @ SV165 @ SV264 @ SV46 ) @ SV46 )
= $true )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV46
@ ( collec645855634od_a_a
@ ^ [SY1049: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1049 @ SV165 )
| ~ ( SV264 @ SY1049 ) ) ) )
| ~ ! [SY1050: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1050 @ SV46 )
| ( SV264 @ SY1050 ) ) ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV46 @ SV165 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1892]) ).
thf(1961,plain,
! [SV264: product_prod_a_a > $o,SV165: set_Product_prod_a_a,SV46: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV46
@ ( collec645855634od_a_a
@ ^ [SY1049: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1049 @ SV165 )
| ~ ( SV264 @ SY1049 ) ) ) )
| ~ ! [SY1050: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1050 @ SV46 )
| ( SV264 @ SY1050 ) ) )
= $false )
| ( ( SV264 @ ( sK48_SY1050 @ SV165 @ SV264 @ SV46 ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV46 @ SV165 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1893]) ).
thf(1962,plain,
! [SV354: a,SV176: a,SV275: a,SV57: a] :
( ( ( ( SV57 != SV275 )
| ( SV176 != SV354 ) )
= $false )
| ( ( ( product_Pair_a_a @ SV57 @ SV176 )
= ( product_Pair_a_a @ SV275 @ SV354 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1895]) ).
thf(1963,plain,
! [SV275: a,SV57: a,SV354: a,SV176: a] :
( ( ( SV176 = SV354 )
= $false )
| ( ( SV57 = SV275 )
= $false )
| ( ( ~ ( ( ( product_Pair_a_a @ SV57 @ SV176 )
!= ( product_Pair_a_a @ SV275 @ SV354 ) )
| ~ ~ ( ( SV57 != SV275 )
| ( SV176 != SV354 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1896]) ).
thf(1964,plain,
! [SV60: set_Product_prod_a_a,SV179: set_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK51_SY894 @ SV179 @ SV60 ) @ ( sK55_SY1209 @ SV60 @ SV179 ) ) @ SV60 )
| ( member_a @ ( sK55_SY1209 @ SV60 @ SV179 ) @ SV179 ) )
= $false )
| ( ( ~ ( order_preorder_on_a @ SV179 @ SV60 )
| ( prefer1292084992ence_a @ SV179 @ SV60 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK13_SY892 @ SV179 @ SV60 ) @ ( sK24_SY1180 @ SV60 @ SV179 ) ) @ SV60 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1897]) ).
thf(1965,plain,
! [SV60: set_Product_prod_a_a,SV179: set_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK49_SY894 @ SV179 @ SV60 ) @ ( sK52_SY1204 @ SV60 @ SV179 ) ) @ SV60 ) )
= $false )
| ( ( ~ ( order_preorder_on_a @ SV179 @ SV60 )
| ( prefer1292084992ence_a @ SV179 @ SV60 ) )
= $true )
| ( ( member_a @ ( sK13_SY892 @ SV179 @ SV60 ) @ SV179 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1898]) ).
thf(1966,plain,
! [SV179: set_a,SV60: set_Product_prod_a_a] :
( ( ( member_a @ ( sK52_SY1204 @ SV60 @ SV179 ) @ SV179 )
= $false )
| ( ( ~ ( order_preorder_on_a @ SV179 @ SV60 )
| ( prefer1292084992ence_a @ SV179 @ SV60 ) )
= $true )
| ( ( member_a @ ( sK13_SY892 @ SV179 @ SV60 ) @ SV179 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1898]) ).
thf(1967,plain,
! [SV61: set_a,SV394: a,SV180: set_Product_prod_a_a,SV356: a,SV278: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV356 ) @ SV180 )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV278 ) @ SV180 ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV394 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV356 ) @ SV180 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV394 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV278 ) @ SV180 ) ) )
= $true )
| ( ( prefer1292084992ence_a @ SV61 @ SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1899]) ).
thf(1968,plain,
! [SV395: a > a,SV184: a > a,SV360: a,SV65: a,SV405: set_a,SV282: a] :
( ( ( member_a @ SV282 @ SV405 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV65 @ SV360 ) @ ( bNF_Gr423046308_a_a_a @ SV405 @ SV184 @ SV395 ) )
= $true )
| ( ( SV360
= ( SV395 @ SV282 ) )
= $false )
| ( ( SV65
= ( SV184 @ SV282 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1900]) ).
thf(1969,plain,
! [SV365: a > set_a,SV193: a,SV290: set_a,SV75: a] :
( ( ( ~ ( member_a @ SV75 @ SV290 )
| ~ ( member_a @ SV193 @ ( SV365 @ SV75 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV75 @ SV193 ) @ ( product_Sigma_a_a @ SV290 @ SV365 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1902]) ).
thf(1970,plain,
! [SV290: set_a,SV75: a,SV365: a > set_a,SV193: a] :
( ( ( member_a @ SV193 @ ( SV365 @ SV75 ) )
= $false )
| ( ( member_a @ SV75 @ SV290 )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV75 @ SV193 ) @ ( product_Sigma_a_a @ SV290 @ SV365 ) )
| ~ ~ ( ~ ( member_a @ SV75 @ SV290 )
| ~ ( member_a @ SV193 @ ( SV365 @ SV75 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1903]) ).
thf(1971,plain,
! [SV396: product_prod_a_a > product_prod_a_a,SV194: product_prod_a_a > product_prod_a_a,SV366: product_prod_a_a,SV76: product_prod_a_a,SV406: set_Product_prod_a_a,SV291: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV291 @ SV406 )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV76 @ SV366 ) @ ( bNF_Gr200450189od_a_a @ SV406 @ SV194 @ SV396 ) )
= $true )
| ( ( SV366
= ( SV396 @ SV291 ) )
= $false )
| ( ( SV76
= ( SV194 @ SV291 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1904]) ).
thf(1972,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) )
= $false )
| ( ( prefer1292084992ence_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1906]) ).
thf(1973,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
= $true )
| ( ( ~ ( order_preorder_on_a @ SV201 @ SV369 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 )
| ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1907]) ).
thf(1974,plain,
! [SV88: set_Product_prod_a_a,SV372: product_prod_a_a > $o,SV206: set_Product_prod_a_a,SV303: product_prod_a_a > $o] :
( ( ( SV303 @ ( sK43_SY1159 @ SV206 @ SV372 @ SV303 @ SV88 ) )
= $true )
| ( ( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [SY1094: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1094 @ SV88 )
| ~ ( SV303 @ SY1094 ) ) )
@ ( collec645855634od_a_a
@ ^ [SY1161: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1161 @ SV206 )
| ~ ( SV372 @ SY1161 ) ) ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV88 @ SV206 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1909]) ).
thf(1975,plain,
! [SV373: product_prod_a_a > set_Product_prod_a_a,SV207: product_prod_a_a,SV304: set_Product_prod_a_a,SV89: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV89 @ SV304 )
| ~ ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV89 @ SV207 ) @ ( produc304751368od_a_a @ SV304 @ SV373 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1912]) ).
thf(1976,plain,
! [SV304: set_Product_prod_a_a,SV89: product_prod_a_a,SV373: product_prod_a_a > set_Product_prod_a_a,SV207: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) )
= $false )
| ( ( member449909584od_a_a @ SV89 @ SV304 )
= $false )
| ( ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV89 @ SV207 ) @ ( produc304751368od_a_a @ SV304 @ SV373 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ SV89 @ SV304 )
| ~ ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1913]) ).
thf(1977,plain,
! [SV91: a,SV208: product_prod_a_a] :
( ( ( SV208
= ( product_Pair_a_a @ ( sK53_SY956 @ SV91 @ SV208 ) @ SV91 ) )
= $true )
| ( ( SV91
= ( product_snd_a_a @ SV208 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1914]) ).
thf(1978,plain,
! [SV414: a,SV208: product_prod_a_a,SV91: a] :
( ( ( SV91
= ( product_snd_a_a @ SV208 ) )
= $true )
| ( ( SV208
= ( product_Pair_a_a @ SV414 @ SV91 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1915]) ).
thf(1979,plain,
! [SV414: a,SV91: a,SV208: product_prod_a_a] :
( ( ( ~ ! [SY956: a] :
( SV208
!= ( product_Pair_a_a @ SY956 @ SV91 ) ) )
= $true )
| ( ( SV208
= ( product_Pair_a_a @ SV414 @ SV91 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1916]) ).
thf(1980,plain,
! [SV398: product_prod_a_a > a,SV212: product_prod_a_a > a,SV377: a,SV95: a,SV407: set_Product_prod_a_a,SV308: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV308 @ SV407 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV95 @ SV377 ) @ ( bNF_Gr1853143117_a_a_a @ SV407 @ SV212 @ SV398 ) )
= $true )
| ( ( SV377
= ( SV398 @ SV308 ) )
= $false )
| ( ( SV95
= ( SV212 @ SV308 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1919]) ).
thf(1981,plain,
! [SV402: produc1572603623od_a_a > a,SV231: produc1572603623od_a_a > a,SV387: a,SV116: a,SV410: set_Pr1948701895od_a_a,SV325: produc1572603623od_a_a] :
( ( ( member2057358096od_a_a @ SV325 @ SV410 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV116 @ SV387 ) @ ( bNF_Gr356189709_a_a_a @ SV410 @ SV231 @ SV402 ) )
= $true )
| ( ( SV387
= ( SV402 @ SV325 ) )
= $false )
| ( ( SV116
= ( SV231 @ SV325 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1924]) ).
thf(1982,plain,
! [SV411: set_Product_prod_a_a,SV403: set_Product_prod_a_a,SV390: a,SV331: a,SV237: a,SV123: a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SV331 @ SV390 ) ) @ ( lex_prod_a_a @ SV403 @ SV411 ) ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SV331 @ SV390 ) ) @ ( lex_prod_a_a @ SV403 @ SV411 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1927]) ).
thf(1983,plain,
! [SV411: set_Product_prod_a_a,SV390: a,SV237: a,SV403: set_Product_prod_a_a,SV331: a,SV123: a] :
( ( ( ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
| ~ ( ( SV123 != SV331 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 ) ) ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SV331 @ SV390 ) ) @ ( lex_prod_a_a @ SV403 @ SV411 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1927]) ).
thf(1984,plain,
! [SV411: set_Product_prod_a_a,SV403: set_Product_prod_a_a,SV390: a,SV331: a,SV237: a,SV123: a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SV331 @ SV390 ) ) @ ( lex_prod_a_a @ SV403 @ SV411 ) )
| ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
| ~ ( ( SV123 != SV331 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1928]) ).
thf(1985,plain,
! [SV403: set_Product_prod_a_a,SV411: set_Product_prod_a_a,SV390: a,SV237: a,SV331: a,SV123: a] :
( ( ( ( SV123 != SV331 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 ) )
= $true )
| ( ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SV331 @ SV390 ) ) @ ( lex_prod_a_a @ SV403 @ SV411 ) )
| ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
| ~ ( ( SV123 != SV331 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1929]) ).
thf(1986,plain,
! [SV125: a,SV238: product_prod_a_a] :
( ( ( SV238
= ( product_Pair_a_a @ SV125 @ ( sK54_SY1024 @ SV125 @ SV238 ) ) )
= $true )
| ( ( SV125
= ( product_fst_a_a @ SV238 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1930]) ).
thf(1987,plain,
! [SV415: a,SV238: product_prod_a_a,SV125: a] :
( ( ( SV125
= ( product_fst_a_a @ SV238 ) )
= $true )
| ( ( SV238
= ( product_Pair_a_a @ SV125 @ SV415 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1931]) ).
thf(1988,plain,
! [SV415: a,SV125: a,SV238: product_prod_a_a] :
( ( ( ~ ! [SY1024: a] :
( SV238
!= ( product_Pair_a_a @ SV125 @ SY1024 ) ) )
= $true )
| ( ( SV238
= ( product_Pair_a_a @ SV125 @ SV415 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1932]) ).
thf(1989,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a] :
( ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 ) )
= $true )
| ( ( ~ ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
!= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
| ( SV2 != SV131 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1933]) ).
thf(1990,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 ) )
= $true )
| ( ( ~ ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
!= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
| ( SV2 != SV131 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1934]) ).
thf(1991,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
!= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $false )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1935]) ).
thf(1992,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( SV2 != SV131 )
= $false )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1935]) ).
thf(1993,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( ! [SV426: a] :
( ( ^ [SY1212: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV426 @ SY1212 ) @ SV2 ) )
= ( ^ [SY1213: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV426 @ SY1213 ) @ SV131 ) ) ) )
= $true )
| ( ( ( ^ [SY1199: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1199 ) @ SV2 ) )
= ( ^ [SY1200: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1200 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1936]) ).
thf(1994,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $true )
| ( ( ( ^ [SY1199: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1199 ) @ SV2 ) )
= ( ^ [SY1200: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1200 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1936]) ).
thf(1995,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV422: a] :
( ( ( ! [SV427: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV427 ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV427 ) @ SV131 ) ) )
= $true )
| ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1938]) ).
thf(1996,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV422: a] :
( ( ( ( ^ [SY1210: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SY1210 ) @ SV2 ) )
= ( ^ [SY1211: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SY1211 ) @ SV131 ) ) )
= $true )
| ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1938]) ).
thf(1997,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV428: a,SV420: a] :
( ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV131 ) )
= $true )
| ( ( SV2 = SV131 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1939]) ).
thf(1998,plain,
! [SV343: a,SV150: a,SV252: a,SV30: a] :
( ( ( SV30 != SV252 )
= $false )
| ( ( ( product_Pair_a_a @ SV30 @ SV150 )
= ( product_Pair_a_a @ SV252 @ SV343 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1942]) ).
thf(1999,plain,
! [SV252: a,SV30: a,SV343: a,SV150: a] :
( ( ( SV150 != SV343 )
= $false )
| ( ( ( product_Pair_a_a @ SV30 @ SV150 )
= ( product_Pair_a_a @ SV252 @ SV343 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1942]) ).
thf(2000,plain,
! [SV343: a,SV252: a,SV150: a,SV30: a] :
( ( ( ( ( product_Pair_a_a @ SV30 @ SV150 )
!= ( product_Pair_a_a @ SV252 @ SV343 ) )
| ~ ~ ( ( SV30 != SV252 )
| ( SV150 != SV343 ) ) )
= $false )
| ( ( SV30 = SV252 )
= $false )
| ( ( SV150 = SV343 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1943]) ).
thf(2001,plain,
! [SV255: set_Product_prod_a_a,SV153: set_Product_prod_a_a,SV33: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV33 @ SV153 )
= $true )
| ( ( member449909584od_a_a @ SV33 @ ( minus_1507102574od_a_a @ SV153 @ SV255 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1944]) ).
thf(2002,plain,
! [SV153: set_Product_prod_a_a,SV255: set_Product_prod_a_a,SV33: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV33 @ SV255 ) )
= $true )
| ( ( member449909584od_a_a @ SV33 @ ( minus_1507102574od_a_a @ SV153 @ SV255 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1945]) ).
thf(2003,plain,
! [SV255: set_Product_prod_a_a,SV153: set_Product_prod_a_a,SV33: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV33 @ ( minus_1507102574od_a_a @ SV153 @ SV255 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ SV33 @ SV153 )
| ~ ~ ( member449909584od_a_a @ SV33 @ SV255 ) ) )
= $false )
| ( ( member449909584od_a_a @ SV33 @ SV153 )
= $false )
| ( ( member449909584od_a_a @ SV33 @ SV255 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1946]) ).
thf(2004,plain,
! [SV345: set_Product_prod_a_a,SV155: set_Product_prod_a_a,SV424: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV424 @ SV155 ) )
= $true )
| ( ( member449909584od_a_a @ SV424 @ SV345 )
= $true )
| ( ( ord_le1824328871od_a_a @ SV155 @ SV345 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1947]) ).
thf(2005,plain,
! [SV345: set_Product_prod_a_a,SV155: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV155 @ SV345 ) )
= $false )
| ( ( member449909584od_a_a @ ( sK41_SY1143 @ SV345 @ SV155 ) @ SV155 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1948]) ).
thf(2006,plain,
! [SV345: set_Product_prod_a_a,SV155: set_Product_prod_a_a] :
( ( ( ~ ! [SY1143: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1143 @ SV155 )
| ( member449909584od_a_a @ SY1143 @ SV345 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( sK41_SY1143 @ SV345 @ SV155 ) @ SV155 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1948]) ).
thf(2007,plain,
! [SV345: set_Product_prod_a_a,SV155: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV155 @ SV345 )
= $true )
| ( ( member449909584od_a_a @ ( sK41_SY1143 @ SV345 @ SV155 ) @ SV345 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1949]) ).
thf(2008,plain,
! [SV345: set_Product_prod_a_a,SV155: set_Product_prod_a_a] :
( ( ( ! [SY1143: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1143 @ SV155 )
| ( member449909584od_a_a @ SY1143 @ SV345 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( sK41_SY1143 @ SV345 @ SV155 ) @ SV345 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1950]) ).
thf(2009,plain,
! [SV36: set_Product_prod_a_a,SV413: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK56_SY531 @ SV413 @ SV36 ) @ SV36 ) )
= $false )
| ( ( member449909584od_a_a @ SV413 @ SV36 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1951]) ).
thf(2010,plain,
! [SV347: set_Product_prod_a_a,SV162: set_Product_prod_a_a,SV425: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV425 @ SV162 ) )
= $true )
| ( ( member449909584od_a_a @ SV425 @ SV347 )
= $true )
| ( ( ord_le1824328871od_a_a @ SV162 @ SV347 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1954]) ).
thf(2011,plain,
! [SV347: set_Product_prod_a_a,SV162: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV162 @ SV347 ) )
= $false )
| ( ( member449909584od_a_a @ ( sK42_SY1144 @ SV347 @ SV162 ) @ SV162 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1955]) ).
thf(2012,plain,
! [SV347: set_Product_prod_a_a,SV162: set_Product_prod_a_a] :
( ( ( ~ ! [SY1144: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1144 @ SV162 )
| ( member449909584od_a_a @ SY1144 @ SV347 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( sK42_SY1144 @ SV347 @ SV162 ) @ SV162 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1955]) ).
thf(2013,plain,
! [SV347: set_Product_prod_a_a,SV162: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV162 @ SV347 )
= $true )
| ( ( member449909584od_a_a @ ( sK42_SY1144 @ SV347 @ SV162 ) @ SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1956]) ).
thf(2014,plain,
! [SV347: set_Product_prod_a_a,SV162: set_Product_prod_a_a] :
( ( ( ! [SY1144: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1144 @ SV162 )
| ( member449909584od_a_a @ SY1144 @ SV347 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( sK42_SY1144 @ SV347 @ SV162 ) @ SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1957]) ).
thf(2015,plain,
! [SV165: set_Product_prod_a_a,SV264: product_prod_a_a > $o,SV46: set_Product_prod_a_a,SV429: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV429 @ SV46 )
| ( SV264 @ SV429 ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV46
@ ( collec645855634od_a_a
@ ^ [SY1049: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1049 @ SV165 )
| ~ ( SV264 @ SY1049 ) ) ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV46 @ SV165 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1959]) ).
thf(2016,plain,
! [SV264: product_prod_a_a > $o,SV165: set_Product_prod_a_a,SV46: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV46
@ ( collec645855634od_a_a
@ ^ [SY1049: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1049 @ SV165 )
| ~ ( SV264 @ SY1049 ) ) ) )
| ~ ! [SY1050: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1050 @ SV46 )
| ( SV264 @ SY1050 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( sK48_SY1050 @ SV165 @ SV264 @ SV46 ) @ SV46 )
= $true )
| ( ( ord_le1824328871od_a_a @ SV46 @ SV165 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1960]) ).
thf(2017,plain,
! [SV264: product_prod_a_a > $o,SV165: set_Product_prod_a_a,SV46: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV46
@ ( collec645855634od_a_a
@ ^ [SY1049: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1049 @ SV165 )
| ~ ( SV264 @ SY1049 ) ) ) ) )
= $false )
| ( ( SV264 @ ( sK48_SY1050 @ SV165 @ SV264 @ SV46 ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV46 @ SV165 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1961]) ).
thf(2018,plain,
! [SV165: set_Product_prod_a_a,SV264: product_prod_a_a > $o,SV46: set_Product_prod_a_a] :
( ( ( ~ ! [SY1050: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1050 @ SV46 )
| ( SV264 @ SY1050 ) ) )
= $false )
| ( ( SV264 @ ( sK48_SY1050 @ SV165 @ SV264 @ SV46 ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV46 @ SV165 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1961]) ).
thf(2019,plain,
! [SV354: a,SV176: a,SV275: a,SV57: a] :
( ( ( SV57 != SV275 )
= $false )
| ( ( ( product_Pair_a_a @ SV57 @ SV176 )
= ( product_Pair_a_a @ SV275 @ SV354 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1962]) ).
thf(2020,plain,
! [SV275: a,SV57: a,SV354: a,SV176: a] :
( ( ( SV176 != SV354 )
= $false )
| ( ( ( product_Pair_a_a @ SV57 @ SV176 )
= ( product_Pair_a_a @ SV275 @ SV354 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1962]) ).
thf(2021,plain,
! [SV354: a,SV275: a,SV176: a,SV57: a] :
( ( ( ( ( product_Pair_a_a @ SV57 @ SV176 )
!= ( product_Pair_a_a @ SV275 @ SV354 ) )
| ~ ~ ( ( SV57 != SV275 )
| ( SV176 != SV354 ) ) )
= $false )
| ( ( SV57 = SV275 )
= $false )
| ( ( SV176 = SV354 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1963]) ).
thf(2022,plain,
! [SV60: set_Product_prod_a_a,SV179: set_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK51_SY894 @ SV179 @ SV60 ) @ ( sK55_SY1209 @ SV60 @ SV179 ) ) @ SV60 ) )
= $false )
| ( ( ~ ( order_preorder_on_a @ SV179 @ SV60 )
| ( prefer1292084992ence_a @ SV179 @ SV60 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK13_SY892 @ SV179 @ SV60 ) @ ( sK24_SY1180 @ SV60 @ SV179 ) ) @ SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1964]) ).
thf(2023,plain,
! [SV179: set_a,SV60: set_Product_prod_a_a] :
( ( ( member_a @ ( sK55_SY1209 @ SV60 @ SV179 ) @ SV179 )
= $false )
| ( ( ~ ( order_preorder_on_a @ SV179 @ SV60 )
| ( prefer1292084992ence_a @ SV179 @ SV60 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK13_SY892 @ SV179 @ SV60 ) @ ( sK24_SY1180 @ SV60 @ SV179 ) ) @ SV60 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1964]) ).
thf(2024,plain,
! [SV60: set_Product_prod_a_a,SV179: set_a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK49_SY894 @ SV179 @ SV60 ) @ ( sK52_SY1204 @ SV60 @ SV179 ) ) @ SV60 )
= $true )
| ( ( ~ ( order_preorder_on_a @ SV179 @ SV60 )
| ( prefer1292084992ence_a @ SV179 @ SV60 ) )
= $true )
| ( ( member_a @ ( sK13_SY892 @ SV179 @ SV60 ) @ SV179 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1965]) ).
thf(2025,plain,
! [SV60: set_Product_prod_a_a,SV179: set_a] :
( ( ( ~ ( order_preorder_on_a @ SV179 @ SV60 ) )
= $true )
| ( ( prefer1292084992ence_a @ SV179 @ SV60 )
= $true )
| ( ( member_a @ ( sK52_SY1204 @ SV60 @ SV179 ) @ SV179 )
= $false )
| ( ( member_a @ ( sK13_SY892 @ SV179 @ SV60 ) @ SV179 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1966]) ).
thf(2026,plain,
! [SV61: set_a,SV394: a,SV180: set_Product_prod_a_a,SV278: a,SV356: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV278 ) @ SV180 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV356 ) @ SV180 )
= $false )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV394 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV356 ) @ SV180 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV394 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV278 ) @ SV180 ) ) )
= $true )
| ( ( prefer1292084992ence_a @ SV61 @ SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1967]) ).
thf(2027,plain,
! [SV365: a > set_a,SV193: a,SV290: set_a,SV75: a] :
( ( ( ~ ( member_a @ SV75 @ SV290 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV75 @ SV193 ) @ ( product_Sigma_a_a @ SV290 @ SV365 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1969]) ).
thf(2028,plain,
! [SV290: set_a,SV75: a,SV365: a > set_a,SV193: a] :
( ( ( ~ ( member_a @ SV193 @ ( SV365 @ SV75 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV75 @ SV193 ) @ ( product_Sigma_a_a @ SV290 @ SV365 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1969]) ).
thf(2029,plain,
! [SV365: a > set_a,SV290: set_a,SV193: a,SV75: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV75 @ SV193 ) @ ( product_Sigma_a_a @ SV290 @ SV365 ) )
| ~ ~ ( ~ ( member_a @ SV75 @ SV290 )
| ~ ( member_a @ SV193 @ ( SV365 @ SV75 ) ) ) )
= $false )
| ( ( member_a @ SV75 @ SV290 )
= $false )
| ( ( member_a @ SV193 @ ( SV365 @ SV75 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1970]) ).
thf(2030,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) ) )
= $false )
| ( ( prefer1292084992ence_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1972]) ).
thf(2031,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( ~ ( order_preorder_on_a @ SV201 @ SV369 ) )
= $false )
| ( ( prefer1292084992ence_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1972]) ).
thf(2032,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) ) )
= $true )
| ( ( ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
= $true )
| ( ( ~ ( order_preorder_on_a @ SV201 @ SV369 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 )
| ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1973]) ).
thf(2033,plain,
! [SV373: product_prod_a_a > set_Product_prod_a_a,SV207: product_prod_a_a,SV304: set_Product_prod_a_a,SV89: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV89 @ SV304 ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV89 @ SV207 ) @ ( produc304751368od_a_a @ SV304 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1975]) ).
thf(2034,plain,
! [SV304: set_Product_prod_a_a,SV89: product_prod_a_a,SV373: product_prod_a_a > set_Product_prod_a_a,SV207: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV89 @ SV207 ) @ ( produc304751368od_a_a @ SV304 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1975]) ).
thf(2035,plain,
! [SV373: product_prod_a_a > set_Product_prod_a_a,SV304: set_Product_prod_a_a,SV207: product_prod_a_a,SV89: product_prod_a_a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV89 @ SV207 ) @ ( produc304751368od_a_a @ SV304 @ SV373 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ SV89 @ SV304 )
| ~ ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ SV89 @ SV304 )
= $false )
| ( ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1976]) ).
thf(2036,plain,
! [SV414: a,SV91: a,SV208: product_prod_a_a] :
( ( ( ! [SY956: a] :
( SV208
!= ( product_Pair_a_a @ SY956 @ SV91 ) ) )
= $false )
| ( ( SV208
= ( product_Pair_a_a @ SV414 @ SV91 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1979]) ).
thf(2037,plain,
! [SV411: set_Product_prod_a_a,SV403: set_Product_prod_a_a,SV390: a,SV331: a,SV237: a,SV123: a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SV331 @ SV390 ) ) @ ( lex_prod_a_a @ SV403 @ SV411 ) )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SV331 @ SV390 ) ) @ ( lex_prod_a_a @ SV403 @ SV411 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1982]) ).
thf(2038,plain,
! [SV411: set_Product_prod_a_a,SV390: a,SV237: a,SV403: set_Product_prod_a_a,SV331: a,SV123: a] :
( ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
| ~ ( ( SV123 != SV331 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 ) ) )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SV331 @ SV390 ) ) @ ( lex_prod_a_a @ SV403 @ SV411 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1983]) ).
thf(2039,plain,
! [SV411: set_Product_prod_a_a,SV403: set_Product_prod_a_a,SV390: a,SV331: a,SV237: a,SV123: a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SV331 @ SV390 ) ) @ ( lex_prod_a_a @ SV403 @ SV411 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1984]) ).
thf(2040,plain,
! [SV411: set_Product_prod_a_a,SV390: a,SV237: a,SV403: set_Product_prod_a_a,SV331: a,SV123: a] :
( ( ( ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
| ~ ( ( SV123 != SV331 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1984]) ).
thf(2041,plain,
! [SV403: set_Product_prod_a_a,SV411: set_Product_prod_a_a,SV390: a,SV237: a,SV331: a,SV123: a] :
( ( ( SV123 != SV331 )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 ) )
= $true )
| ( ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SV331 @ SV390 ) ) @ ( lex_prod_a_a @ SV403 @ SV411 ) )
| ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
| ~ ( ( SV123 != SV331 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1985]) ).
thf(2042,plain,
! [SV415: a,SV125: a,SV238: product_prod_a_a] :
( ( ( ! [SY1024: a] :
( SV238
!= ( product_Pair_a_a @ SV125 @ SY1024 ) ) )
= $false )
| ( ( SV238
= ( product_Pair_a_a @ SV125 @ SV415 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1988]) ).
thf(2043,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $true )
| ( ( ~ ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
!= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
| ( SV2 != SV131 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1989]) ).
thf(2044,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 ) )
= $true )
| ( ( ~ ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
!= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
| ( SV2 != SV131 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1990]) ).
thf(2045,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $true )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1991]) ).
thf(2046,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( SV2 = SV131 )
= $true )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1992]) ).
thf(2047,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV430: a] :
( ( ( ( ^ [SY1214: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SY1214 ) @ SV2 ) )
= ( ^ [SY1215: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SY1215 ) @ SV131 ) ) )
= $true )
| ( ( ( ^ [SY1199: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1199 ) @ SV2 ) )
= ( ^ [SY1200: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1200 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1993]) ).
thf(2048,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV431: a,SV422: a] :
( ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV131 ) )
= $true )
| ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1995]) ).
thf(2049,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV428: a,SV420: a] :
( ( ( ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV2 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV131 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV131 ) ) )
= $true )
| ( ( SV2 = SV131 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1997]) ).
thf(2050,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV428: a,SV420: a] :
( ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV131 ) )
= $true )
| ( ( SV2 = SV131 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1997]) ).
thf(2051,plain,
! [SV343: a,SV150: a,SV252: a,SV30: a] :
( ( ( SV30 = SV252 )
= $true )
| ( ( ( product_Pair_a_a @ SV30 @ SV150 )
= ( product_Pair_a_a @ SV252 @ SV343 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1998]) ).
thf(2052,plain,
! [SV252: a,SV30: a,SV343: a,SV150: a] :
( ( ( SV150 = SV343 )
= $true )
| ( ( ( product_Pair_a_a @ SV30 @ SV150 )
= ( product_Pair_a_a @ SV252 @ SV343 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1999]) ).
thf(2053,plain,
! [SV343: a,SV252: a,SV150: a,SV30: a] :
( ( ( ( product_Pair_a_a @ SV30 @ SV150 )
!= ( product_Pair_a_a @ SV252 @ SV343 ) )
= $false )
| ( ( SV30 = SV252 )
= $false )
| ( ( SV150 = SV343 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2000]) ).
thf(2054,plain,
! [SV343: a,SV150: a,SV252: a,SV30: a] :
( ( ( ~ ~ ( ( SV30 != SV252 )
| ( SV150 != SV343 ) ) )
= $false )
| ( ( SV30 = SV252 )
= $false )
| ( ( SV150 = SV343 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2000]) ).
thf(2055,plain,
! [SV153: set_Product_prod_a_a,SV255: set_Product_prod_a_a,SV33: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV33 @ SV255 )
= $false )
| ( ( member449909584od_a_a @ SV33 @ ( minus_1507102574od_a_a @ SV153 @ SV255 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2002]) ).
thf(2056,plain,
! [SV255: set_Product_prod_a_a,SV153: set_Product_prod_a_a,SV33: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV33 @ ( minus_1507102574od_a_a @ SV153 @ SV255 ) ) )
= $false )
| ( ( member449909584od_a_a @ SV33 @ SV153 )
= $false )
| ( ( member449909584od_a_a @ SV33 @ SV255 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2003]) ).
thf(2057,plain,
! [SV255: set_Product_prod_a_a,SV153: set_Product_prod_a_a,SV33: product_prod_a_a] :
( ( ( ~ ~ ( ~ ( member449909584od_a_a @ SV33 @ SV153 )
| ~ ~ ( member449909584od_a_a @ SV33 @ SV255 ) ) )
= $false )
| ( ( member449909584od_a_a @ SV33 @ SV153 )
= $false )
| ( ( member449909584od_a_a @ SV33 @ SV255 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2003]) ).
thf(2058,plain,
! [SV345: set_Product_prod_a_a,SV155: set_Product_prod_a_a,SV424: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV424 @ SV155 )
= $false )
| ( ( member449909584od_a_a @ SV424 @ SV345 )
= $true )
| ( ( ord_le1824328871od_a_a @ SV155 @ SV345 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2004]) ).
thf(2059,plain,
! [SV345: set_Product_prod_a_a,SV155: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV155 @ SV345 )
= $true )
| ( ( member449909584od_a_a @ ( sK41_SY1143 @ SV345 @ SV155 ) @ SV155 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2005]) ).
thf(2060,plain,
! [SV345: set_Product_prod_a_a,SV155: set_Product_prod_a_a] :
( ( ( ! [SY1143: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1143 @ SV155 )
| ( member449909584od_a_a @ SY1143 @ SV345 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( sK41_SY1143 @ SV345 @ SV155 ) @ SV155 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2006]) ).
thf(2061,plain,
! [SV345: set_Product_prod_a_a,SV155: set_Product_prod_a_a,SV432: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV432 @ SV155 )
| ( member449909584od_a_a @ SV432 @ SV345 ) )
= $true )
| ( ( member449909584od_a_a @ ( sK41_SY1143 @ SV345 @ SV155 ) @ SV345 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2008]) ).
thf(2062,plain,
! [SV36: set_Product_prod_a_a,SV413: product_prod_a_a] :
( ( ( member449909584od_a_a @ ( sK56_SY531 @ SV413 @ SV36 ) @ SV36 )
= $true )
| ( ( member449909584od_a_a @ SV413 @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2009]) ).
thf(2063,plain,
! [SV347: set_Product_prod_a_a,SV162: set_Product_prod_a_a,SV425: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV425 @ SV162 )
= $false )
| ( ( member449909584od_a_a @ SV425 @ SV347 )
= $true )
| ( ( ord_le1824328871od_a_a @ SV162 @ SV347 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2010]) ).
thf(2064,plain,
! [SV347: set_Product_prod_a_a,SV162: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV162 @ SV347 )
= $true )
| ( ( member449909584od_a_a @ ( sK42_SY1144 @ SV347 @ SV162 ) @ SV162 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2011]) ).
thf(2065,plain,
! [SV347: set_Product_prod_a_a,SV162: set_Product_prod_a_a] :
( ( ( ! [SY1144: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1144 @ SV162 )
| ( member449909584od_a_a @ SY1144 @ SV347 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( sK42_SY1144 @ SV347 @ SV162 ) @ SV162 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2012]) ).
thf(2066,plain,
! [SV347: set_Product_prod_a_a,SV162: set_Product_prod_a_a,SV433: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV433 @ SV162 )
| ( member449909584od_a_a @ SV433 @ SV347 ) )
= $true )
| ( ( member449909584od_a_a @ ( sK42_SY1144 @ SV347 @ SV162 ) @ SV347 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2014]) ).
thf(2067,plain,
! [SV165: set_Product_prod_a_a,SV264: product_prod_a_a > $o,SV46: set_Product_prod_a_a,SV429: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV429 @ SV46 ) )
= $true )
| ( ( SV264 @ SV429 )
= $true )
| ( ( ord_le1824328871od_a_a @ SV46
@ ( collec645855634od_a_a
@ ^ [SY1049: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1049 @ SV165 )
| ~ ( SV264 @ SY1049 ) ) ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV46 @ SV165 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2015]) ).
thf(2068,plain,
! [SV264: product_prod_a_a > $o,SV165: set_Product_prod_a_a,SV46: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV46
@ ( collec645855634od_a_a
@ ^ [SY1049: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1049 @ SV165 )
| ~ ( SV264 @ SY1049 ) ) ) ) )
= $false )
| ( ( member449909584od_a_a @ ( sK48_SY1050 @ SV165 @ SV264 @ SV46 ) @ SV46 )
= $true )
| ( ( ord_le1824328871od_a_a @ SV46 @ SV165 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2016]) ).
thf(2069,plain,
! [SV165: set_Product_prod_a_a,SV264: product_prod_a_a > $o,SV46: set_Product_prod_a_a] :
( ( ( ~ ! [SY1050: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1050 @ SV46 )
| ( SV264 @ SY1050 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( sK48_SY1050 @ SV165 @ SV264 @ SV46 ) @ SV46 )
= $true )
| ( ( ord_le1824328871od_a_a @ SV46 @ SV165 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2016]) ).
thf(2070,plain,
! [SV264: product_prod_a_a > $o,SV165: set_Product_prod_a_a,SV46: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV46
@ ( collec645855634od_a_a
@ ^ [SY1049: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1049 @ SV165 )
| ~ ( SV264 @ SY1049 ) ) ) )
= $true )
| ( ( SV264 @ ( sK48_SY1050 @ SV165 @ SV264 @ SV46 ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV46 @ SV165 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2017]) ).
thf(2071,plain,
! [SV165: set_Product_prod_a_a,SV264: product_prod_a_a > $o,SV46: set_Product_prod_a_a] :
( ( ( ! [SY1050: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1050 @ SV46 )
| ( SV264 @ SY1050 ) ) )
= $true )
| ( ( SV264 @ ( sK48_SY1050 @ SV165 @ SV264 @ SV46 ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV46 @ SV165 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2018]) ).
thf(2072,plain,
! [SV354: a,SV176: a,SV275: a,SV57: a] :
( ( ( SV57 = SV275 )
= $true )
| ( ( ( product_Pair_a_a @ SV57 @ SV176 )
= ( product_Pair_a_a @ SV275 @ SV354 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2019]) ).
thf(2073,plain,
! [SV275: a,SV57: a,SV354: a,SV176: a] :
( ( ( SV176 = SV354 )
= $true )
| ( ( ( product_Pair_a_a @ SV57 @ SV176 )
= ( product_Pair_a_a @ SV275 @ SV354 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2020]) ).
thf(2074,plain,
! [SV354: a,SV275: a,SV176: a,SV57: a] :
( ( ( ( product_Pair_a_a @ SV57 @ SV176 )
!= ( product_Pair_a_a @ SV275 @ SV354 ) )
= $false )
| ( ( SV57 = SV275 )
= $false )
| ( ( SV176 = SV354 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2021]) ).
thf(2075,plain,
! [SV354: a,SV176: a,SV275: a,SV57: a] :
( ( ( ~ ~ ( ( SV57 != SV275 )
| ( SV176 != SV354 ) ) )
= $false )
| ( ( SV57 = SV275 )
= $false )
| ( ( SV176 = SV354 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2021]) ).
thf(2076,plain,
! [SV60: set_Product_prod_a_a,SV179: set_a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK51_SY894 @ SV179 @ SV60 ) @ ( sK55_SY1209 @ SV60 @ SV179 ) ) @ SV60 )
= $true )
| ( ( ~ ( order_preorder_on_a @ SV179 @ SV60 )
| ( prefer1292084992ence_a @ SV179 @ SV60 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK13_SY892 @ SV179 @ SV60 ) @ ( sK24_SY1180 @ SV60 @ SV179 ) ) @ SV60 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2022]) ).
thf(2077,plain,
! [SV60: set_Product_prod_a_a,SV179: set_a] :
( ( ( ~ ( order_preorder_on_a @ SV179 @ SV60 ) )
= $true )
| ( ( prefer1292084992ence_a @ SV179 @ SV60 )
= $true )
| ( ( member_a @ ( sK55_SY1209 @ SV60 @ SV179 ) @ SV179 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK13_SY892 @ SV179 @ SV60 ) @ ( sK24_SY1180 @ SV60 @ SV179 ) ) @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2023]) ).
thf(2078,plain,
! [SV60: set_Product_prod_a_a,SV179: set_a] :
( ( ( ~ ( order_preorder_on_a @ SV179 @ SV60 ) )
= $true )
| ( ( prefer1292084992ence_a @ SV179 @ SV60 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK49_SY894 @ SV179 @ SV60 ) @ ( sK52_SY1204 @ SV60 @ SV179 ) ) @ SV60 )
= $true )
| ( ( member_a @ ( sK13_SY892 @ SV179 @ SV60 ) @ SV179 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2024]) ).
thf(2079,plain,
! [SV60: set_Product_prod_a_a,SV179: set_a] :
( ( ( order_preorder_on_a @ SV179 @ SV60 )
= $false )
| ( ( prefer1292084992ence_a @ SV179 @ SV60 )
= $true )
| ( ( member_a @ ( sK52_SY1204 @ SV60 @ SV179 ) @ SV179 )
= $false )
| ( ( member_a @ ( sK13_SY892 @ SV179 @ SV60 ) @ SV179 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2025]) ).
thf(2080,plain,
! [SV61: set_a,SV278: a,SV180: set_Product_prod_a_a,SV394: a,SV356: a] :
( ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV394 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV356 ) @ SV180 ) ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV394 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV278 ) @ SV180 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV356 ) @ SV180 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV278 ) @ SV180 )
= $false )
| ( ( prefer1292084992ence_a @ SV61 @ SV180 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2026]) ).
thf(2081,plain,
! [SV365: a > set_a,SV193: a,SV290: set_a,SV75: a] :
( ( ( member_a @ SV75 @ SV290 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV75 @ SV193 ) @ ( product_Sigma_a_a @ SV290 @ SV365 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2027]) ).
thf(2082,plain,
! [SV290: set_a,SV75: a,SV365: a > set_a,SV193: a] :
( ( ( member_a @ SV193 @ ( SV365 @ SV75 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV75 @ SV193 ) @ ( product_Sigma_a_a @ SV290 @ SV365 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2028]) ).
thf(2083,plain,
! [SV365: a > set_a,SV290: set_a,SV193: a,SV75: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV75 @ SV193 ) @ ( product_Sigma_a_a @ SV290 @ SV365 ) ) )
= $false )
| ( ( member_a @ SV75 @ SV290 )
= $false )
| ( ( member_a @ SV193 @ ( SV365 @ SV75 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2029]) ).
thf(2084,plain,
! [SV365: a > set_a,SV193: a,SV290: set_a,SV75: a] :
( ( ( ~ ~ ( ~ ( member_a @ SV75 @ SV290 )
| ~ ( member_a @ SV193 @ ( SV365 @ SV75 ) ) ) )
= $false )
| ( ( member_a @ SV75 @ SV290 )
= $false )
| ( ( member_a @ SV193 @ ( SV365 @ SV75 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2029]) ).
thf(2085,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) ) )
= $true )
| ( ( prefer1292084992ence_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2030]) ).
thf(2086,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( order_preorder_on_a @ SV201 @ SV369 )
= $true )
| ( ( prefer1292084992ence_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2031]) ).
thf(2087,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) ) )
= $false )
| ( ( ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
= $true )
| ( ( ~ ( order_preorder_on_a @ SV201 @ SV369 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 )
| ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2032]) ).
thf(2088,plain,
! [SV373: product_prod_a_a > set_Product_prod_a_a,SV207: product_prod_a_a,SV304: set_Product_prod_a_a,SV89: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV89 @ SV304 )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV89 @ SV207 ) @ ( produc304751368od_a_a @ SV304 @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2033]) ).
thf(2089,plain,
! [SV304: set_Product_prod_a_a,SV89: product_prod_a_a,SV373: product_prod_a_a > set_Product_prod_a_a,SV207: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV89 @ SV207 ) @ ( produc304751368od_a_a @ SV304 @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2034]) ).
thf(2090,plain,
! [SV373: product_prod_a_a > set_Product_prod_a_a,SV304: set_Product_prod_a_a,SV207: product_prod_a_a,SV89: product_prod_a_a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV89 @ SV207 ) @ ( produc304751368od_a_a @ SV304 @ SV373 ) ) )
= $false )
| ( ( member449909584od_a_a @ SV89 @ SV304 )
= $false )
| ( ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2035]) ).
thf(2091,plain,
! [SV373: product_prod_a_a > set_Product_prod_a_a,SV207: product_prod_a_a,SV304: set_Product_prod_a_a,SV89: product_prod_a_a] :
( ( ( ~ ~ ( ~ ( member449909584od_a_a @ SV89 @ SV304 )
| ~ ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ SV89 @ SV304 )
= $false )
| ( ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2035]) ).
thf(2092,plain,
! [SV91: a,SV414: a,SV208: product_prod_a_a] :
( ( ( SV208
!= ( product_Pair_a_a @ ( sK57_SY956 @ SV414 @ SV91 @ SV208 ) @ SV91 ) )
= $false )
| ( ( SV208
= ( product_Pair_a_a @ SV414 @ SV91 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2036]) ).
thf(2093,plain,
! [SV411: set_Product_prod_a_a,SV390: a,SV237: a,SV403: set_Product_prod_a_a,SV331: a,SV123: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
= $true )
| ( ( ~ ( ( SV123 != SV331 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 ) ) )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SV331 @ SV390 ) ) @ ( lex_prod_a_a @ SV403 @ SV411 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2038]) ).
thf(2094,plain,
! [SV411: set_Product_prod_a_a,SV403: set_Product_prod_a_a,SV390: a,SV331: a,SV237: a,SV123: a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SV331 @ SV390 ) ) @ ( lex_prod_a_a @ SV403 @ SV411 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2039]) ).
thf(2095,plain,
! [SV411: set_Product_prod_a_a,SV390: a,SV237: a,SV403: set_Product_prod_a_a,SV331: a,SV123: a] :
( ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
| ~ ( ( SV123 != SV331 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2040]) ).
thf(2096,plain,
! [SV403: set_Product_prod_a_a,SV411: set_Product_prod_a_a,SV390: a,SV237: a,SV331: a,SV123: a] :
( ( ( SV123 = SV331 )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 ) )
= $true )
| ( ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SV331 @ SV390 ) ) @ ( lex_prod_a_a @ SV403 @ SV411 ) )
| ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
| ~ ( ( SV123 != SV331 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2041]) ).
thf(2097,plain,
! [SV415: a,SV125: a,SV238: product_prod_a_a] :
( ( ( SV238
!= ( product_Pair_a_a @ SV125 @ ( sK58_SY1024 @ SV415 @ SV125 @ SV238 ) ) )
= $false )
| ( ( SV238
= ( product_Pair_a_a @ SV125 @ SV415 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2042]) ).
thf(2098,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
!= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
| ( SV2 != SV131 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2043]) ).
thf(2099,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 ) )
= $true )
| ( ( ~ ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
!= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
| ( SV2 != SV131 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2044]) ).
thf(2100,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( ! [SV434: a] :
( ( ^ [SY1216: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV434 @ SY1216 ) @ SV2 ) )
= ( ^ [SY1217: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV434 @ SY1217 ) @ SV131 ) ) ) )
= $true )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[2045]) ).
thf(2101,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $true )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[2045]) ).
thf(2102,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV430: a] :
( ( ( ! [SV435: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV435 ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV435 ) @ SV131 ) ) )
= $true )
| ( ( ( ^ [SY1199: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1199 ) @ SV2 ) )
= ( ^ [SY1200: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1200 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[2047]) ).
thf(2103,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV430: a] :
( ( ( ( ^ [SY1214: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SY1214 ) @ SV2 ) )
= ( ^ [SY1215: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SY1215 ) @ SV131 ) ) )
= $true )
| ( ( ( ^ [SY1199: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1199 ) @ SV2 ) )
= ( ^ [SY1200: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1200 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[2047]) ).
thf(2104,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV431: a,SV422: a] :
( ( ( ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV2 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV131 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV131 ) ) )
= $true )
| ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[2048]) ).
thf(2105,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV431: a,SV422: a] :
( ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV131 ) )
= $true )
| ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[2048]) ).
thf(2106,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV428: a,SV420: a] :
( ( ( ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV2 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV131 ) ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV131 ) ) )
= $true )
| ( ( SV2 = SV131 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2049]) ).
thf(2107,plain,
! [SV343: a,SV252: a,SV150: a,SV30: a] :
( ( ( ( product_Pair_a_a @ SV30 @ SV150 )
= ( product_Pair_a_a @ SV252 @ SV343 ) )
= $true )
| ( ( SV30 = SV252 )
= $false )
| ( ( SV150 = SV343 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2053]) ).
thf(2108,plain,
! [SV343: a,SV150: a,SV252: a,SV30: a] :
( ( ( ~ ( ( SV30 != SV252 )
| ( SV150 != SV343 ) ) )
= $true )
| ( ( SV30 = SV252 )
= $false )
| ( ( SV150 = SV343 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2054]) ).
thf(2109,plain,
! [SV255: set_Product_prod_a_a,SV153: set_Product_prod_a_a,SV33: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV33 @ ( minus_1507102574od_a_a @ SV153 @ SV255 ) )
= $true )
| ( ( member449909584od_a_a @ SV33 @ SV153 )
= $false )
| ( ( member449909584od_a_a @ SV33 @ SV255 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2056]) ).
thf(2110,plain,
! [SV255: set_Product_prod_a_a,SV153: set_Product_prod_a_a,SV33: product_prod_a_a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ SV33 @ SV153 )
| ~ ~ ( member449909584od_a_a @ SV33 @ SV255 ) ) )
= $true )
| ( ( member449909584od_a_a @ SV33 @ SV153 )
= $false )
| ( ( member449909584od_a_a @ SV33 @ SV255 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2057]) ).
thf(2111,plain,
! [SV345: set_Product_prod_a_a,SV155: set_Product_prod_a_a,SV436: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV436 @ SV155 )
| ( member449909584od_a_a @ SV436 @ SV345 ) )
= $true )
| ( ( member449909584od_a_a @ ( sK41_SY1143 @ SV345 @ SV155 ) @ SV155 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2060]) ).
thf(2112,plain,
! [SV345: set_Product_prod_a_a,SV155: set_Product_prod_a_a,SV432: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV432 @ SV155 ) )
= $true )
| ( ( member449909584od_a_a @ SV432 @ SV345 )
= $true )
| ( ( member449909584od_a_a @ ( sK41_SY1143 @ SV345 @ SV155 ) @ SV345 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2061]) ).
thf(2113,plain,
! [SV347: set_Product_prod_a_a,SV162: set_Product_prod_a_a,SV437: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV437 @ SV162 )
| ( member449909584od_a_a @ SV437 @ SV347 ) )
= $true )
| ( ( member449909584od_a_a @ ( sK42_SY1144 @ SV347 @ SV162 ) @ SV162 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2065]) ).
thf(2114,plain,
! [SV347: set_Product_prod_a_a,SV162: set_Product_prod_a_a,SV433: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV433 @ SV162 ) )
= $true )
| ( ( member449909584od_a_a @ SV433 @ SV347 )
= $true )
| ( ( member449909584od_a_a @ ( sK42_SY1144 @ SV347 @ SV162 ) @ SV347 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2066]) ).
thf(2115,plain,
! [SV165: set_Product_prod_a_a,SV264: product_prod_a_a > $o,SV46: set_Product_prod_a_a,SV429: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV429 @ SV46 )
= $false )
| ( ( SV264 @ SV429 )
= $true )
| ( ( ord_le1824328871od_a_a @ SV46
@ ( collec645855634od_a_a
@ ^ [SY1049: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1049 @ SV165 )
| ~ ( SV264 @ SY1049 ) ) ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV46 @ SV165 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2067]) ).
thf(2116,plain,
! [SV264: product_prod_a_a > $o,SV165: set_Product_prod_a_a,SV46: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV46
@ ( collec645855634od_a_a
@ ^ [SY1049: product_prod_a_a] :
~ ( ~ ( member449909584od_a_a @ SY1049 @ SV165 )
| ~ ( SV264 @ SY1049 ) ) ) )
= $true )
| ( ( member449909584od_a_a @ ( sK48_SY1050 @ SV165 @ SV264 @ SV46 ) @ SV46 )
= $true )
| ( ( ord_le1824328871od_a_a @ SV46 @ SV165 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2068]) ).
thf(2117,plain,
! [SV165: set_Product_prod_a_a,SV264: product_prod_a_a > $o,SV46: set_Product_prod_a_a] :
( ( ( ! [SY1050: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1050 @ SV46 )
| ( SV264 @ SY1050 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( sK48_SY1050 @ SV165 @ SV264 @ SV46 ) @ SV46 )
= $true )
| ( ( ord_le1824328871od_a_a @ SV46 @ SV165 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2069]) ).
thf(2118,plain,
! [SV165: set_Product_prod_a_a,SV264: product_prod_a_a > $o,SV46: set_Product_prod_a_a,SV438: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV438 @ SV46 )
| ( SV264 @ SV438 ) )
= $true )
| ( ( SV264 @ ( sK48_SY1050 @ SV165 @ SV264 @ SV46 ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV46 @ SV165 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2071]) ).
thf(2119,plain,
! [SV354: a,SV275: a,SV176: a,SV57: a] :
( ( ( ( product_Pair_a_a @ SV57 @ SV176 )
= ( product_Pair_a_a @ SV275 @ SV354 ) )
= $true )
| ( ( SV57 = SV275 )
= $false )
| ( ( SV176 = SV354 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2074]) ).
thf(2120,plain,
! [SV354: a,SV176: a,SV275: a,SV57: a] :
( ( ( ~ ( ( SV57 != SV275 )
| ( SV176 != SV354 ) ) )
= $true )
| ( ( SV57 = SV275 )
= $false )
| ( ( SV176 = SV354 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2075]) ).
thf(2121,plain,
! [SV60: set_Product_prod_a_a,SV179: set_a] :
( ( ( ~ ( order_preorder_on_a @ SV179 @ SV60 ) )
= $true )
| ( ( prefer1292084992ence_a @ SV179 @ SV60 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK51_SY894 @ SV179 @ SV60 ) @ ( sK55_SY1209 @ SV60 @ SV179 ) ) @ SV60 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK13_SY892 @ SV179 @ SV60 ) @ ( sK24_SY1180 @ SV60 @ SV179 ) ) @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2076]) ).
thf(2122,plain,
! [SV60: set_Product_prod_a_a,SV179: set_a] :
( ( ( order_preorder_on_a @ SV179 @ SV60 )
= $false )
| ( ( prefer1292084992ence_a @ SV179 @ SV60 )
= $true )
| ( ( member_a @ ( sK55_SY1209 @ SV60 @ SV179 ) @ SV179 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK13_SY892 @ SV179 @ SV60 ) @ ( sK24_SY1180 @ SV60 @ SV179 ) ) @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2077]) ).
thf(2123,plain,
! [SV60: set_Product_prod_a_a,SV179: set_a] :
( ( ( order_preorder_on_a @ SV179 @ SV60 )
= $false )
| ( ( prefer1292084992ence_a @ SV179 @ SV60 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK49_SY894 @ SV179 @ SV60 ) @ ( sK52_SY1204 @ SV60 @ SV179 ) ) @ SV60 )
= $true )
| ( ( member_a @ ( sK13_SY892 @ SV179 @ SV60 ) @ SV179 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2078]) ).
thf(2124,plain,
! [SV61: set_a,SV278: a,SV180: set_Product_prod_a_a,SV394: a,SV356: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV394 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV356 ) @ SV180 ) ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV394 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV278 ) @ SV180 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV356 ) @ SV180 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV278 ) @ SV180 )
= $false )
| ( ( prefer1292084992ence_a @ SV61 @ SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2080]) ).
thf(2125,plain,
! [SV365: a > set_a,SV290: set_a,SV193: a,SV75: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV75 @ SV193 ) @ ( product_Sigma_a_a @ SV290 @ SV365 ) )
= $true )
| ( ( member_a @ SV75 @ SV290 )
= $false )
| ( ( member_a @ SV193 @ ( SV365 @ SV75 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2083]) ).
thf(2126,plain,
! [SV365: a > set_a,SV193: a,SV290: set_a,SV75: a] :
( ( ( ~ ( ~ ( member_a @ SV75 @ SV290 )
| ~ ( member_a @ SV193 @ ( SV365 @ SV75 ) ) ) )
= $true )
| ( ( member_a @ SV75 @ SV290 )
= $false )
| ( ( member_a @ SV193 @ ( SV365 @ SV75 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2084]) ).
thf(2127,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
= $false )
| ( ( prefer1292084992ence_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2085]) ).
thf(2128,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( ! [SY1218: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SY1218 ) @ SV369 )
| ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 ) ) )
= $false )
| ( ( ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
= $true )
| ( ( ~ ( order_preorder_on_a @ SV201 @ SV369 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 )
| ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2087]) ).
thf(2129,plain,
! [SV373: product_prod_a_a > set_Product_prod_a_a,SV304: set_Product_prod_a_a,SV207: product_prod_a_a,SV89: product_prod_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV89 @ SV207 ) @ ( produc304751368od_a_a @ SV304 @ SV373 ) )
= $true )
| ( ( member449909584od_a_a @ SV89 @ SV304 )
= $false )
| ( ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2090]) ).
thf(2130,plain,
! [SV373: product_prod_a_a > set_Product_prod_a_a,SV207: product_prod_a_a,SV304: set_Product_prod_a_a,SV89: product_prod_a_a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ SV89 @ SV304 )
| ~ ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) ) ) )
= $true )
| ( ( member449909584od_a_a @ SV89 @ SV304 )
= $false )
| ( ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2091]) ).
thf(2131,plain,
! [SV91: a,SV414: a,SV208: product_prod_a_a] :
( ( ( SV208
= ( product_Pair_a_a @ ( sK57_SY956 @ SV414 @ SV91 @ SV208 ) @ SV91 ) )
= $true )
| ( ( SV208
= ( product_Pair_a_a @ SV414 @ SV91 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2092]) ).
thf(2132,plain,
! [SV403: set_Product_prod_a_a,SV411: set_Product_prod_a_a,SV390: a,SV237: a,SV331: a,SV123: a] :
( ( ( ( SV123 != SV331 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SV331 @ SV390 ) ) @ ( lex_prod_a_a @ SV403 @ SV411 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2093]) ).
thf(2133,plain,
! [SV411: set_Product_prod_a_a,SV390: a,SV237: a,SV403: set_Product_prod_a_a,SV331: a,SV123: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
= $true )
| ( ( ~ ( ( SV123 != SV331 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2095]) ).
thf(2134,plain,
! [SV403: set_Product_prod_a_a,SV331: a,SV123: a,SV411: set_Product_prod_a_a,SV390: a,SV237: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 )
= $false )
| ( ( SV123 = SV331 )
= $false )
| ( ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SV331 @ SV390 ) ) @ ( lex_prod_a_a @ SV403 @ SV411 ) )
| ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
| ~ ( ( SV123 != SV331 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2096]) ).
thf(2135,plain,
! [SV415: a,SV125: a,SV238: product_prod_a_a] :
( ( ( SV238
= ( product_Pair_a_a @ SV125 @ ( sK58_SY1024 @ SV415 @ SV125 @ SV238 ) ) )
= $true )
| ( ( SV238
= ( product_Pair_a_a @ SV125 @ SV415 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2097]) ).
thf(2136,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
!= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2098]) ).
thf(2137,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( SV2 != SV131 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2098]) ).
thf(2138,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $false )
| ( ( ~ ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
!= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
| ( SV2 != SV131 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2099]) ).
thf(2139,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV439: a] :
( ( ( ( ^ [SY1219: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SY1219 ) @ SV2 ) )
= ( ^ [SY1220: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SY1220 ) @ SV131 ) ) )
= $true )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2100]) ).
thf(2140,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV440: a,SV430: a] :
( ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV131 ) )
= $true )
| ( ( ( ^ [SY1199: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1199 ) @ SV2 ) )
= ( ^ [SY1200: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1200 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2102]) ).
thf(2141,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV431: a,SV422: a] :
( ( ( ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV2 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV131 ) ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV131 ) ) )
= $true )
| ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2104]) ).
thf(2142,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV428: a,SV420: a] :
( ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV2 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV131 ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV131 ) ) )
= $true )
| ( ( SV2 = SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2106]) ).
thf(2143,plain,
! [SV343: a,SV150: a,SV252: a,SV30: a] :
( ( ( ( SV30 != SV252 )
| ( SV150 != SV343 ) )
= $false )
| ( ( SV30 = SV252 )
= $false )
| ( ( SV150 = SV343 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2108]) ).
thf(2144,plain,
! [SV255: set_Product_prod_a_a,SV153: set_Product_prod_a_a,SV33: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV33 @ SV153 )
| ~ ~ ( member449909584od_a_a @ SV33 @ SV255 ) )
= $false )
| ( ( member449909584od_a_a @ SV33 @ SV153 )
= $false )
| ( ( member449909584od_a_a @ SV33 @ SV255 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2110]) ).
thf(2145,plain,
! [SV345: set_Product_prod_a_a,SV155: set_Product_prod_a_a,SV436: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV436 @ SV155 ) )
= $true )
| ( ( member449909584od_a_a @ SV436 @ SV345 )
= $true )
| ( ( member449909584od_a_a @ ( sK41_SY1143 @ SV345 @ SV155 ) @ SV155 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2111]) ).
thf(2146,plain,
! [SV345: set_Product_prod_a_a,SV155: set_Product_prod_a_a,SV432: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV432 @ SV155 )
= $false )
| ( ( member449909584od_a_a @ SV432 @ SV345 )
= $true )
| ( ( member449909584od_a_a @ ( sK41_SY1143 @ SV345 @ SV155 ) @ SV345 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2112]) ).
thf(2147,plain,
! [SV347: set_Product_prod_a_a,SV162: set_Product_prod_a_a,SV437: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV437 @ SV162 ) )
= $true )
| ( ( member449909584od_a_a @ SV437 @ SV347 )
= $true )
| ( ( member449909584od_a_a @ ( sK42_SY1144 @ SV347 @ SV162 ) @ SV162 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2113]) ).
thf(2148,plain,
! [SV347: set_Product_prod_a_a,SV162: set_Product_prod_a_a,SV433: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV433 @ SV162 )
= $false )
| ( ( member449909584od_a_a @ SV433 @ SV347 )
= $true )
| ( ( member449909584od_a_a @ ( sK42_SY1144 @ SV347 @ SV162 ) @ SV347 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2114]) ).
thf(2149,plain,
! [SV165: set_Product_prod_a_a,SV264: product_prod_a_a > $o,SV46: set_Product_prod_a_a,SV441: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV441 @ SV46 )
| ( SV264 @ SV441 ) )
= $true )
| ( ( member449909584od_a_a @ ( sK48_SY1050 @ SV165 @ SV264 @ SV46 ) @ SV46 )
= $true )
| ( ( ord_le1824328871od_a_a @ SV46 @ SV165 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2117]) ).
thf(2150,plain,
! [SV165: set_Product_prod_a_a,SV264: product_prod_a_a > $o,SV46: set_Product_prod_a_a,SV438: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV438 @ SV46 ) )
= $true )
| ( ( SV264 @ SV438 )
= $true )
| ( ( SV264 @ ( sK48_SY1050 @ SV165 @ SV264 @ SV46 ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV46 @ SV165 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2118]) ).
thf(2151,plain,
! [SV354: a,SV176: a,SV275: a,SV57: a] :
( ( ( ( SV57 != SV275 )
| ( SV176 != SV354 ) )
= $false )
| ( ( SV57 = SV275 )
= $false )
| ( ( SV176 = SV354 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2120]) ).
thf(2152,plain,
! [SV60: set_Product_prod_a_a,SV179: set_a] :
( ( ( order_preorder_on_a @ SV179 @ SV60 )
= $false )
| ( ( prefer1292084992ence_a @ SV179 @ SV60 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK51_SY894 @ SV179 @ SV60 ) @ ( sK55_SY1209 @ SV60 @ SV179 ) ) @ SV60 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK13_SY892 @ SV179 @ SV60 ) @ ( sK24_SY1180 @ SV60 @ SV179 ) ) @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2121]) ).
thf(2153,plain,
! [SV61: set_a,SV278: a,SV180: set_Product_prod_a_a,SV394: a,SV356: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV394 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV356 ) @ SV180 ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV394 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV278 ) @ SV180 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV356 ) @ SV180 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV278 ) @ SV180 )
= $false )
| ( ( prefer1292084992ence_a @ SV61 @ SV180 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2124]) ).
thf(2154,plain,
! [SV365: a > set_a,SV193: a,SV290: set_a,SV75: a] :
( ( ( ~ ( member_a @ SV75 @ SV290 )
| ~ ( member_a @ SV193 @ ( SV365 @ SV75 ) ) )
= $false )
| ( ( member_a @ SV75 @ SV290 )
= $false )
| ( ( member_a @ SV193 @ ( SV365 @ SV75 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2126]) ).
thf(2155,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) ) )
= $false )
| ( ( prefer1292084992ence_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2127]) ).
thf(2156,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
= $false )
| ( ( prefer1292084992ence_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2127]) ).
thf(2157,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
| ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 ) )
= $false )
| ( ( ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
= $true )
| ( ( ~ ( order_preorder_on_a @ SV201 @ SV369 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 )
| ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2128]) ).
thf(2158,plain,
! [SV373: product_prod_a_a > set_Product_prod_a_a,SV207: product_prod_a_a,SV304: set_Product_prod_a_a,SV89: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV89 @ SV304 )
| ~ ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) ) )
= $false )
| ( ( member449909584od_a_a @ SV89 @ SV304 )
= $false )
| ( ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2130]) ).
thf(2159,plain,
! [SV411: set_Product_prod_a_a,SV390: a,SV237: a,SV403: set_Product_prod_a_a,SV331: a,SV123: a] :
( ( ( SV123 != SV331 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SV331 @ SV390 ) ) @ ( lex_prod_a_a @ SV403 @ SV411 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2132]) ).
thf(2160,plain,
! [SV403: set_Product_prod_a_a,SV331: a,SV123: a,SV411: set_Product_prod_a_a,SV390: a,SV237: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SV331 @ SV390 ) ) @ ( lex_prod_a_a @ SV403 @ SV411 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2132]) ).
thf(2161,plain,
! [SV403: set_Product_prod_a_a,SV411: set_Product_prod_a_a,SV390: a,SV237: a,SV331: a,SV123: a] :
( ( ( ( SV123 != SV331 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2133]) ).
thf(2162,plain,
! [SV411: set_Product_prod_a_a,SV403: set_Product_prod_a_a,SV390: a,SV331: a,SV237: a,SV123: a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SV331 @ SV390 ) ) @ ( lex_prod_a_a @ SV403 @ SV411 ) )
| ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
| ~ ( ( SV123 != SV331 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 ) ) ) )
= $false )
| ( ( SV123 = SV331 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2134]) ).
thf(2163,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2136]) ).
thf(2164,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( SV2 = SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2137]) ).
thf(2165,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
!= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
| ( SV2 != SV131 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2138]) ).
thf(2166,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV439: a] :
( ( ( ! [SV442: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV442 ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV442 ) @ SV131 ) ) )
= $true )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[2139]) ).
thf(2167,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV439: a] :
( ( ( ( ^ [SY1219: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SY1219 ) @ SV2 ) )
= ( ^ [SY1220: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SY1220 ) @ SV131 ) ) )
= $true )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[2139]) ).
thf(2168,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV440: a,SV430: a] :
( ( ( ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV2 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV131 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV131 ) ) )
= $true )
| ( ( ( ^ [SY1199: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1199 ) @ SV2 ) )
= ( ^ [SY1200: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1200 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[2140]) ).
thf(2169,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV440: a,SV430: a] :
( ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV131 ) )
= $true )
| ( ( ( ^ [SY1199: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1199 ) @ SV2 ) )
= ( ^ [SY1200: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1200 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[2140]) ).
thf(2170,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV431: a,SV422: a] :
( ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV2 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV131 ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV131 ) ) )
= $true )
| ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2141]) ).
thf(2171,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV428: a,SV420: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV2 )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV131 ) ) )
= $true )
| ( ( SV2 = SV131 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2142]) ).
thf(2172,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a,SV428: a,SV420: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV131 )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV131 ) ) )
= $true )
| ( ( SV2 = SV131 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2142]) ).
thf(2173,plain,
! [SV343: a,SV150: a,SV252: a,SV30: a] :
( ( ( SV30 != SV252 )
= $false )
| ( ( SV30 = SV252 )
= $false )
| ( ( SV150 = SV343 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2143]) ).
thf(2174,plain,
! [SV252: a,SV30: a,SV343: a,SV150: a] :
( ( ( SV150 != SV343 )
= $false )
| ( ( SV30 = SV252 )
= $false )
| ( ( SV150 = SV343 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2143]) ).
thf(2175,plain,
! [SV255: set_Product_prod_a_a,SV153: set_Product_prod_a_a,SV33: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV33 @ SV153 ) )
= $false )
| ( ( member449909584od_a_a @ SV33 @ SV153 )
= $false )
| ( ( member449909584od_a_a @ SV33 @ SV255 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2144]) ).
thf(2176,plain,
! [SV153: set_Product_prod_a_a,SV255: set_Product_prod_a_a,SV33: product_prod_a_a] :
( ( ( ~ ~ ( member449909584od_a_a @ SV33 @ SV255 ) )
= $false )
| ( ( member449909584od_a_a @ SV33 @ SV153 )
= $false )
| ( ( member449909584od_a_a @ SV33 @ SV255 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2144]) ).
thf(2177,plain,
! [SV345: set_Product_prod_a_a,SV155: set_Product_prod_a_a,SV436: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV436 @ SV155 )
= $false )
| ( ( member449909584od_a_a @ SV436 @ SV345 )
= $true )
| ( ( member449909584od_a_a @ ( sK41_SY1143 @ SV345 @ SV155 ) @ SV155 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2145]) ).
thf(2178,plain,
! [SV347: set_Product_prod_a_a,SV162: set_Product_prod_a_a,SV437: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV437 @ SV162 )
= $false )
| ( ( member449909584od_a_a @ SV437 @ SV347 )
= $true )
| ( ( member449909584od_a_a @ ( sK42_SY1144 @ SV347 @ SV162 ) @ SV162 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2147]) ).
thf(2179,plain,
! [SV165: set_Product_prod_a_a,SV264: product_prod_a_a > $o,SV46: set_Product_prod_a_a,SV441: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV441 @ SV46 ) )
= $true )
| ( ( SV264 @ SV441 )
= $true )
| ( ( member449909584od_a_a @ ( sK48_SY1050 @ SV165 @ SV264 @ SV46 ) @ SV46 )
= $true )
| ( ( ord_le1824328871od_a_a @ SV46 @ SV165 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2149]) ).
thf(2180,plain,
! [SV165: set_Product_prod_a_a,SV264: product_prod_a_a > $o,SV46: set_Product_prod_a_a,SV438: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV438 @ SV46 )
= $false )
| ( ( SV264 @ SV438 )
= $true )
| ( ( SV264 @ ( sK48_SY1050 @ SV165 @ SV264 @ SV46 ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV46 @ SV165 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2150]) ).
thf(2181,plain,
! [SV354: a,SV176: a,SV275: a,SV57: a] :
( ( ( SV57 != SV275 )
= $false )
| ( ( SV57 = SV275 )
= $false )
| ( ( SV176 = SV354 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2151]) ).
thf(2182,plain,
! [SV275: a,SV57: a,SV354: a,SV176: a] :
( ( ( SV176 != SV354 )
= $false )
| ( ( SV57 = SV275 )
= $false )
| ( ( SV176 = SV354 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2151]) ).
thf(2183,plain,
! [SV61: set_a,SV278: a,SV180: set_Product_prod_a_a,SV394: a,SV356: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV394 ) @ SV180 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV356 ) @ SV180 ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV394 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV278 ) @ SV180 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV356 ) @ SV180 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV278 ) @ SV180 )
= $false )
| ( ( prefer1292084992ence_a @ SV61 @ SV180 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2153]) ).
thf(2184,plain,
! [SV365: a > set_a,SV193: a,SV290: set_a,SV75: a] :
( ( ( ~ ( member_a @ SV75 @ SV290 ) )
= $false )
| ( ( member_a @ SV75 @ SV290 )
= $false )
| ( ( member_a @ SV193 @ ( SV365 @ SV75 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2154]) ).
thf(2185,plain,
! [SV290: set_a,SV75: a,SV365: a > set_a,SV193: a] :
( ( ( ~ ( member_a @ SV193 @ ( SV365 @ SV75 ) ) )
= $false )
| ( ( member_a @ SV75 @ SV290 )
= $false )
| ( ( member_a @ SV193 @ ( SV365 @ SV75 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2154]) ).
thf(2186,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) ) )
= $true )
| ( ( prefer1292084992ence_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2155]) ).
thf(2187,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
= $true )
| ( ( prefer1292084992ence_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2156]) ).
thf(2188,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 ) )
= $false )
| ( ( ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
= $true )
| ( ( ~ ( order_preorder_on_a @ SV201 @ SV369 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 )
| ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2157]) ).
thf(2189,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
= $true )
| ( ( ~ ( order_preorder_on_a @ SV201 @ SV369 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 )
| ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2157]) ).
thf(2190,plain,
! [SV373: product_prod_a_a > set_Product_prod_a_a,SV207: product_prod_a_a,SV304: set_Product_prod_a_a,SV89: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV89 @ SV304 ) )
= $false )
| ( ( member449909584od_a_a @ SV89 @ SV304 )
= $false )
| ( ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2158]) ).
thf(2191,plain,
! [SV304: set_Product_prod_a_a,SV89: product_prod_a_a,SV373: product_prod_a_a > set_Product_prod_a_a,SV207: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) ) )
= $false )
| ( ( member449909584od_a_a @ SV89 @ SV304 )
= $false )
| ( ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2158]) ).
thf(2192,plain,
! [SV411: set_Product_prod_a_a,SV390: a,SV237: a,SV403: set_Product_prod_a_a,SV331: a,SV123: a] :
( ( ( SV123 = SV331 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SV331 @ SV390 ) ) @ ( lex_prod_a_a @ SV403 @ SV411 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2159]) ).
thf(2193,plain,
! [SV403: set_Product_prod_a_a,SV331: a,SV123: a,SV411: set_Product_prod_a_a,SV390: a,SV237: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SV331 @ SV390 ) ) @ ( lex_prod_a_a @ SV403 @ SV411 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2160]) ).
thf(2194,plain,
! [SV403: set_Product_prod_a_a,SV331: a,SV123: a] :
( ( ( SV123 != SV331 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2161]) ).
thf(2195,plain,
! [SV403: set_Product_prod_a_a,SV331: a,SV123: a,SV411: set_Product_prod_a_a,SV390: a,SV237: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2161]) ).
thf(2196,plain,
! [SV411: set_Product_prod_a_a,SV403: set_Product_prod_a_a,SV390: a,SV331: a,SV237: a,SV123: a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SV331 @ SV390 ) ) @ ( lex_prod_a_a @ SV403 @ SV411 ) ) )
= $false )
| ( ( SV123 = SV331 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2162]) ).
thf(2197,plain,
! [SV411: set_Product_prod_a_a,SV390: a,SV237: a,SV403: set_Product_prod_a_a,SV331: a,SV123: a] :
( ( ( ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
| ~ ( ( SV123 != SV331 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 ) ) ) )
= $false )
| ( ( SV123 = SV331 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2162]) ).
thf(2198,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( ! [SV443: a] :
( ( ^ [SY1221: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV443 @ SY1221 ) @ SV2 ) )
= ( ^ [SY1222: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV443 @ SY1222 ) @ SV131 ) ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[2163]) ).
thf(2199,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[2163]) ).
thf(2200,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
!= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2165]) ).
thf(2201,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( SV2 != SV131 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2165]) ).
thf(2202,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV444: a,SV439: a] :
( ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV131 ) )
= $true )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2166]) ).
thf(2203,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV440: a,SV430: a] :
( ( ( ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV2 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV131 ) ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV131 ) ) )
= $true )
| ( ( ( ^ [SY1199: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1199 ) @ SV2 ) )
= ( ^ [SY1200: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1200 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2168]) ).
thf(2204,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV431: a,SV422: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV2 )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV131 ) ) )
= $true )
| ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2170]) ).
thf(2205,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a,SV431: a,SV422: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV131 )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV131 ) ) )
= $true )
| ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2170]) ).
thf(2206,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV428: a,SV420: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV131 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV2 )
= $false )
| ( ( SV2 = SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2171]) ).
thf(2207,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV428: a,SV420: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV131 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV131 )
= $false )
| ( ( SV2 = SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2172]) ).
thf(2208,plain,
! [SV343: a,SV150: a,SV252: a,SV30: a] :
( ( ( SV30 = SV252 )
= $true )
| ( ( SV30 = SV252 )
= $false )
| ( ( SV150 = SV343 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2173]) ).
thf(2209,plain,
! [SV252: a,SV30: a,SV343: a,SV150: a] :
( ( ( SV150 = SV343 )
= $true )
| ( ( SV30 = SV252 )
= $false )
| ( ( SV150 = SV343 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2174]) ).
thf(2210,plain,
! [SV255: set_Product_prod_a_a,SV153: set_Product_prod_a_a,SV33: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV33 @ SV153 )
= $true )
| ( ( member449909584od_a_a @ SV33 @ SV153 )
= $false )
| ( ( member449909584od_a_a @ SV33 @ SV255 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2175]) ).
thf(2211,plain,
! [SV153: set_Product_prod_a_a,SV255: set_Product_prod_a_a,SV33: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV33 @ SV255 ) )
= $true )
| ( ( member449909584od_a_a @ SV33 @ SV153 )
= $false )
| ( ( member449909584od_a_a @ SV33 @ SV255 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2176]) ).
thf(2212,plain,
! [SV165: set_Product_prod_a_a,SV264: product_prod_a_a > $o,SV46: set_Product_prod_a_a,SV441: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV441 @ SV46 )
= $false )
| ( ( SV264 @ SV441 )
= $true )
| ( ( member449909584od_a_a @ ( sK48_SY1050 @ SV165 @ SV264 @ SV46 ) @ SV46 )
= $true )
| ( ( ord_le1824328871od_a_a @ SV46 @ SV165 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2179]) ).
thf(2213,plain,
! [SV354: a,SV176: a,SV275: a,SV57: a] :
( ( ( SV57 = SV275 )
= $true )
| ( ( SV57 = SV275 )
= $false )
| ( ( SV176 = SV354 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2181]) ).
thf(2214,plain,
! [SV275: a,SV57: a,SV354: a,SV176: a] :
( ( ( SV176 = SV354 )
= $true )
| ( ( SV57 = SV275 )
= $false )
| ( ( SV176 = SV354 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2182]) ).
thf(2215,plain,
! [SV61: set_a,SV278: a,SV180: set_Product_prod_a_a,SV394: a,SV356: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV394 ) @ SV180 )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV356 ) @ SV180 ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV394 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV278 ) @ SV180 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV356 ) @ SV180 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV278 ) @ SV180 )
= $false )
| ( ( prefer1292084992ence_a @ SV61 @ SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2183]) ).
thf(2216,plain,
! [SV365: a > set_a,SV193: a,SV290: set_a,SV75: a] :
( ( ( member_a @ SV75 @ SV290 )
= $true )
| ( ( member_a @ SV75 @ SV290 )
= $false )
| ( ( member_a @ SV193 @ ( SV365 @ SV75 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2184]) ).
thf(2217,plain,
! [SV290: set_a,SV75: a,SV365: a > set_a,SV193: a] :
( ( ( member_a @ SV193 @ ( SV365 @ SV75 ) )
= $true )
| ( ( member_a @ SV75 @ SV290 )
= $false )
| ( ( member_a @ SV193 @ ( SV365 @ SV75 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2185]) ).
thf(2218,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a,SV445: a] :
( ( ( ! [SY1223: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV445 @ SY1223 ) @ SV369 )
| ( member_a @ SV445 @ SV201 ) ) )
= $true )
| ( ( prefer1292084992ence_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2186]) ).
thf(2219,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a,SV446: a] :
( ( ( ! [SY1224: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV446 @ SY1224 ) @ SV369 )
| ( member_a @ SY1224 @ SV201 ) ) )
= $true )
| ( ( prefer1292084992ence_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2187]) ).
thf(2220,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
= $true )
| ( ( ~ ( order_preorder_on_a @ SV201 @ SV369 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 )
| ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2188]) ).
thf(2221,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
= $false )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( ~ ( order_preorder_on_a @ SV201 @ SV369 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 )
| ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2189]) ).
thf(2222,plain,
! [SV373: product_prod_a_a > set_Product_prod_a_a,SV207: product_prod_a_a,SV304: set_Product_prod_a_a,SV89: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV89 @ SV304 )
= $true )
| ( ( member449909584od_a_a @ SV89 @ SV304 )
= $false )
| ( ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2190]) ).
thf(2223,plain,
! [SV304: set_Product_prod_a_a,SV89: product_prod_a_a,SV373: product_prod_a_a > set_Product_prod_a_a,SV207: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) )
= $true )
| ( ( member449909584od_a_a @ SV89 @ SV304 )
= $false )
| ( ( member449909584od_a_a @ SV207 @ ( SV373 @ SV89 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2191]) ).
thf(2224,plain,
! [SV403: set_Product_prod_a_a,SV331: a,SV123: a] :
( ( ( SV123 = SV331 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2194]) ).
thf(2225,plain,
! [SV403: set_Product_prod_a_a,SV331: a,SV123: a,SV411: set_Product_prod_a_a,SV390: a,SV237: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2195]) ).
thf(2226,plain,
! [SV411: set_Product_prod_a_a,SV403: set_Product_prod_a_a,SV390: a,SV331: a,SV237: a,SV123: a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV123 @ SV237 ) @ ( product_Pair_a_a @ SV331 @ SV390 ) ) @ ( lex_prod_a_a @ SV403 @ SV411 ) )
= $true )
| ( ( SV123 = SV331 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2196]) ).
thf(2227,plain,
! [SV411: set_Product_prod_a_a,SV390: a,SV237: a,SV403: set_Product_prod_a_a,SV331: a,SV123: a] :
( ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
| ~ ( ( SV123 != SV331 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 ) ) )
= $true )
| ( ( SV123 = SV331 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2197]) ).
thf(2228,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV447: a] :
( ( ( ( ^ [SY1225: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SY1225 ) @ SV2 ) )
= ( ^ [SY1226: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SY1226 ) @ SV131 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2198]) ).
thf(2229,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2200]) ).
thf(2230,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( SV2 = SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2201]) ).
thf(2231,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV444: a,SV439: a] :
( ( ( ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV2 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV131 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV131 ) ) )
= $true )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[2202]) ).
thf(2232,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV444: a,SV439: a] :
( ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV131 ) )
= $true )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[2202]) ).
thf(2233,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV440: a,SV430: a] :
( ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV2 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV131 ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV131 ) ) )
= $true )
| ( ( ( ^ [SY1199: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1199 ) @ SV2 ) )
= ( ^ [SY1200: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1200 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2203]) ).
thf(2234,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV431: a,SV422: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV131 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV2 )
= $false )
| ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2204]) ).
thf(2235,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV431: a,SV422: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV131 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV131 )
= $false )
| ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2205]) ).
thf(2236,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV428: a,SV420: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV2 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV2 )
= $false )
| ( ( SV2 = SV131 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2206]) ).
thf(2237,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a,SV428: a,SV420: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV131 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV2 )
= $false )
| ( ( SV2 = SV131 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2206]) ).
thf(2238,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV428: a,SV420: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV2 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV131 )
= $false )
| ( ( SV2 = SV131 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2207]) ).
thf(2239,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a,SV428: a,SV420: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV131 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV131 )
= $false )
| ( ( SV2 = SV131 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2207]) ).
thf(2240,plain,
! [SV153: set_Product_prod_a_a,SV255: set_Product_prod_a_a,SV33: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV33 @ SV255 )
= $false )
| ( ( member449909584od_a_a @ SV33 @ SV153 )
= $false )
| ( ( member449909584od_a_a @ SV33 @ SV255 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2211]) ).
thf(2241,plain,
! [SV61: set_a,SV278: a,SV180: set_Product_prod_a_a,SV356: a,SV394: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV356 ) @ SV180 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV394 ) @ SV180 )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV394 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV278 ) @ SV180 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV356 ) @ SV180 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV278 ) @ SV180 )
= $false )
| ( ( prefer1292084992ence_a @ SV61 @ SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2215]) ).
thf(2242,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a,SV448: a,SV445: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV445 @ SV448 ) @ SV369 )
| ( member_a @ SV445 @ SV201 ) )
= $true )
| ( ( prefer1292084992ence_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2218]) ).
thf(2243,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a,SV449: a,SV446: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV446 @ SV449 ) @ SV369 )
| ( member_a @ SV449 @ SV201 ) )
= $true )
| ( ( prefer1292084992ence_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2219]) ).
thf(2244,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( ~ ( order_preorder_on_a @ SV201 @ SV369 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 )
| ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2220]) ).
thf(2245,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( ! [SY1227: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1157 @ SV201 @ SV369 ) @ SY1227 ) @ SV369 )
| ( member_a @ SY1227 @ SV201 ) ) )
= $false )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( ~ ( order_preorder_on_a @ SV201 @ SV369 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 )
| ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2221]) ).
thf(2246,plain,
! [SV411: set_Product_prod_a_a,SV390: a,SV237: a,SV403: set_Product_prod_a_a,SV331: a,SV123: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
= $true )
| ( ( ~ ( ( SV123 != SV331 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 ) ) )
= $true )
| ( ( SV123 = SV331 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2227]) ).
thf(2247,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV447: a] :
( ( ( ! [SV450: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV450 ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV450 ) @ SV131 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[2228]) ).
thf(2248,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV447: a] :
( ( ( ( ^ [SY1225: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SY1225 ) @ SV2 ) )
= ( ^ [SY1226: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SY1226 ) @ SV131 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[2228]) ).
thf(2249,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( ! [SV451: a] :
( ( ^ [SY1228: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV451 @ SY1228 ) @ SV2 ) )
= ( ^ [SY1229: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV451 @ SY1229 ) @ SV131 ) ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[2229]) ).
thf(2250,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a] :
( ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[2229]) ).
thf(2251,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV444: a,SV439: a] :
( ( ( ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV2 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV131 ) ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV131 ) ) )
= $true )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2231]) ).
thf(2252,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV440: a,SV430: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV2 )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV131 ) ) )
= $true )
| ( ( ( ^ [SY1199: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1199 ) @ SV2 ) )
= ( ^ [SY1200: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1200 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2233]) ).
thf(2253,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a,SV440: a,SV430: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV131 )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV131 ) ) )
= $true )
| ( ( ( ^ [SY1199: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1199 ) @ SV2 ) )
= ( ^ [SY1200: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1200 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2233]) ).
thf(2254,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV431: a,SV422: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV2 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV2 )
= $false )
| ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2234]) ).
thf(2255,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a,SV431: a,SV422: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV131 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV2 )
= $false )
| ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2234]) ).
thf(2256,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV431: a,SV422: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV2 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV131 )
= $false )
| ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2235]) ).
thf(2257,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a,SV431: a,SV422: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV131 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV131 )
= $false )
| ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2235]) ).
thf(2258,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV428: a,SV420: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV2 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV2 )
= $false )
| ( ( SV2 = SV131 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2236]) ).
thf(2259,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a,SV428: a,SV420: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV2 )
= $false )
| ( ( SV2 = SV131 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2237]) ).
thf(2260,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV428: a,SV420: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV2 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV131 )
= $false )
| ( ( SV2 = SV131 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2238]) ).
thf(2261,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a,SV428: a,SV420: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV428 ) @ SV131 )
= $false )
| ( ( SV2 = SV131 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2239]) ).
thf(2262,plain,
! [SV61: set_a,SV356: a,SV180: set_Product_prod_a_a,SV394: a,SV278: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV394 ) @ SV180 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV278 ) @ SV180 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV394 ) @ SV180 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV356 ) @ SV180 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV356 ) @ SV180 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV278 ) @ SV180 )
= $false )
| ( ( prefer1292084992ence_a @ SV61 @ SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2241]) ).
thf(2263,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a,SV448: a,SV445: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV445 @ SV448 ) @ SV369 ) )
= $true )
| ( ( member_a @ SV445 @ SV201 )
= $true )
| ( ( prefer1292084992ence_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2242]) ).
thf(2264,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a,SV449: a,SV446: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV446 @ SV449 ) @ SV369 ) )
= $true )
| ( ( member_a @ SV449 @ SV201 )
= $true )
| ( ( prefer1292084992ence_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2243]) ).
thf(2265,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( ! [SY1230: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK62_SY1157 @ SV201 @ SV369 ) @ SY1230 ) @ SV369 )
| ( member_a @ SY1230 @ SV201 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( ~ ( order_preorder_on_a @ SV201 @ SV369 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 )
| ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2244]) ).
thf(2266,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1157 @ SV201 @ SV369 ) @ ( sK63_SY1227 @ SV369 @ SV201 ) ) @ SV369 )
| ( member_a @ ( sK63_SY1227 @ SV369 @ SV201 ) @ SV201 ) )
= $false )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( ~ ( order_preorder_on_a @ SV201 @ SV369 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 )
| ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2245]) ).
thf(2267,plain,
! [SV403: set_Product_prod_a_a,SV411: set_Product_prod_a_a,SV390: a,SV237: a,SV331: a,SV123: a] :
( ( ( ( SV123 != SV331 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
= $true )
| ( ( SV123 = SV331 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2246]) ).
thf(2268,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV452: a,SV447: a] :
( ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV131 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2247]) ).
thf(2269,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV453: a] :
( ( ( ( ^ [SY1231: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SY1231 ) @ SV2 ) )
= ( ^ [SY1232: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SY1232 ) @ SV131 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2249]) ).
thf(2270,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV444: a,SV439: a] :
( ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV2 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV131 ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV131 ) ) )
= $true )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2251]) ).
thf(2271,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV440: a,SV430: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV131 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV2 )
= $false )
| ( ( ( ^ [SY1199: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1199 ) @ SV2 ) )
= ( ^ [SY1200: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1200 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2252]) ).
thf(2272,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV440: a,SV430: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV131 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV131 )
= $false )
| ( ( ( ^ [SY1199: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1199 ) @ SV2 ) )
= ( ^ [SY1200: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1200 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2253]) ).
thf(2273,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV431: a,SV422: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV2 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV2 )
= $false )
| ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2254]) ).
thf(2274,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a,SV431: a,SV422: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV2 )
= $false )
| ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2255]) ).
thf(2275,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV431: a,SV422: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV2 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV131 )
= $false )
| ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2256]) ).
thf(2276,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a,SV431: a,SV422: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV422 @ SV431 ) @ SV131 )
= $false )
| ( ( ( ^ [SY471: a,SY472: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY471 @ SY472 ) @ SV2 ) )
= ( ^ [SY810: a,SY811: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SY810 @ SY811 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2257]) ).
thf(2277,plain,
! [SV61: set_a,SV356: a,SV180: set_Product_prod_a_a,SV394: a,SV278: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV394 ) @ SV180 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV394 ) @ SV180 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV356 ) @ SV180 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV356 ) @ SV180 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV278 ) @ SV180 )
= $false )
| ( ( prefer1292084992ence_a @ SV61 @ SV180 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2262]) ).
thf(2278,plain,
! [SV61: set_a,SV356: a,SV180: set_Product_prod_a_a,SV278: a,SV394: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV278 ) @ SV180 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV394 ) @ SV180 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV356 ) @ SV180 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV356 ) @ SV180 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV278 ) @ SV180 )
= $false )
| ( ( prefer1292084992ence_a @ SV61 @ SV180 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2262]) ).
thf(2279,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a,SV448: a,SV445: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV445 @ SV448 ) @ SV369 )
= $false )
| ( ( member_a @ SV445 @ SV201 )
= $true )
| ( ( prefer1292084992ence_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2263]) ).
thf(2280,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a,SV449: a,SV446: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV446 @ SV449 ) @ SV369 )
= $false )
| ( ( member_a @ SV449 @ SV201 )
= $true )
| ( ( prefer1292084992ence_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2264]) ).
thf(2281,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK62_SY1157 @ SV201 @ SV369 ) @ ( sK64_SY1230 @ SV369 @ SV201 ) ) @ SV369 )
| ( member_a @ ( sK64_SY1230 @ SV369 @ SV201 ) @ SV201 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( ~ ( order_preorder_on_a @ SV201 @ SV369 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 )
| ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2265]) ).
thf(2282,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1157 @ SV201 @ SV369 ) @ ( sK63_SY1227 @ SV369 @ SV201 ) ) @ SV369 ) )
= $false )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( ~ ( order_preorder_on_a @ SV201 @ SV369 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 )
| ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2266]) ).
thf(2283,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( member_a @ ( sK63_SY1227 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( ~ ( order_preorder_on_a @ SV201 @ SV369 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 )
| ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2266]) ).
thf(2284,plain,
! [SV411: set_Product_prod_a_a,SV390: a,SV237: a,SV403: set_Product_prod_a_a,SV331: a,SV123: a] :
( ( ( SV123 != SV331 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
= $true )
| ( ( SV123 = SV331 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2267]) ).
thf(2285,plain,
! [SV403: set_Product_prod_a_a,SV331: a,SV123: a,SV411: set_Product_prod_a_a,SV390: a,SV237: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
= $true )
| ( ( SV123 = SV331 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2267]) ).
thf(2286,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV452: a,SV447: a] :
( ( ( ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV2 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV131 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV131 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[2268]) ).
thf(2287,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV452: a,SV447: a] :
( ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV131 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[2268]) ).
thf(2288,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV453: a] :
( ( ( ! [SV454: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV454 ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV454 ) @ SV131 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[2269]) ).
thf(2289,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV453: a] :
( ( ( ( ^ [SY1231: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SY1231 ) @ SV2 ) )
= ( ^ [SY1232: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SY1232 ) @ SV131 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[2269]) ).
thf(2290,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV444: a,SV439: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV2 )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV131 ) ) )
= $true )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2270]) ).
thf(2291,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a,SV444: a,SV439: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV131 )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV131 ) ) )
= $true )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2270]) ).
thf(2292,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV440: a,SV430: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV2 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV2 )
= $false )
| ( ( ( ^ [SY1199: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1199 ) @ SV2 ) )
= ( ^ [SY1200: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1200 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2271]) ).
thf(2293,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a,SV440: a,SV430: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV131 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV2 )
= $false )
| ( ( ( ^ [SY1199: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1199 ) @ SV2 ) )
= ( ^ [SY1200: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1200 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2271]) ).
thf(2294,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV440: a,SV430: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV2 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV131 )
= $false )
| ( ( ( ^ [SY1199: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1199 ) @ SV2 ) )
= ( ^ [SY1200: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1200 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2272]) ).
thf(2295,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a,SV440: a,SV430: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV131 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV131 )
= $false )
| ( ( ( ^ [SY1199: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1199 ) @ SV2 ) )
= ( ^ [SY1200: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1200 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2272]) ).
thf(2296,plain,
! [SV61: set_a,SV356: a,SV180: set_Product_prod_a_a,SV394: a,SV278: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV394 ) @ SV180 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV394 ) @ SV180 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV356 ) @ SV180 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV356 ) @ SV180 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV278 ) @ SV180 )
= $false )
| ( ( prefer1292084992ence_a @ SV61 @ SV180 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2277]) ).
thf(2297,plain,
! [SV61: set_a,SV356: a,SV180: set_Product_prod_a_a,SV278: a,SV394: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV278 ) @ SV180 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV394 ) @ SV180 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV356 ) @ SV180 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV356 ) @ SV180 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV356 @ SV278 ) @ SV180 )
= $false )
| ( ( prefer1292084992ence_a @ SV61 @ SV180 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2278]) ).
thf(2298,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK62_SY1157 @ SV201 @ SV369 ) @ ( sK64_SY1230 @ SV369 @ SV201 ) ) @ SV369 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( ~ ( order_preorder_on_a @ SV201 @ SV369 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 )
| ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2281]) ).
thf(2299,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( member_a @ ( sK64_SY1230 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( ~ ( order_preorder_on_a @ SV201 @ SV369 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 )
| ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2281]) ).
thf(2300,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1157 @ SV201 @ SV369 ) @ ( sK63_SY1227 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( ~ ( order_preorder_on_a @ SV201 @ SV369 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 )
| ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2282]) ).
thf(2301,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( member_a @ ( sK63_SY1227 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 )
| ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2283]) ).
thf(2302,plain,
! [SV411: set_Product_prod_a_a,SV390: a,SV237: a,SV403: set_Product_prod_a_a,SV331: a,SV123: a] :
( ( ( SV123 = SV331 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
= $true )
| ( ( SV123 = SV331 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2284]) ).
thf(2303,plain,
! [SV403: set_Product_prod_a_a,SV331: a,SV123: a,SV411: set_Product_prod_a_a,SV390: a,SV237: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV123 @ SV331 ) @ SV403 )
= $true )
| ( ( SV123 = SV331 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV237 @ SV390 ) @ SV411 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2285]) ).
thf(2304,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV452: a,SV447: a] :
( ( ( ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV2 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV131 ) ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV131 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2286]) ).
thf(2305,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV455: a,SV453: a] :
( ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV131 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2288]) ).
thf(2306,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV444: a,SV439: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV131 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV2 )
= $false )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2290]) ).
thf(2307,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV444: a,SV439: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV131 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV131 )
= $false )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2291]) ).
thf(2308,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV440: a,SV430: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV2 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV2 )
= $false )
| ( ( ( ^ [SY1199: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1199 ) @ SV2 ) )
= ( ^ [SY1200: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1200 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2292]) ).
thf(2309,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a,SV440: a,SV430: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV2 )
= $false )
| ( ( ( ^ [SY1199: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1199 ) @ SV2 ) )
= ( ^ [SY1200: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1200 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2293]) ).
thf(2310,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV440: a,SV430: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV2 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV131 )
= $false )
| ( ( ( ^ [SY1199: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1199 ) @ SV2 ) )
= ( ^ [SY1200: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1200 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2294]) ).
thf(2311,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a,SV440: a,SV430: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV440 ) @ SV131 )
= $false )
| ( ( ( ^ [SY1199: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1199 ) @ SV2 ) )
= ( ^ [SY1200: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ SY1200 ) @ SV131 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2295]) ).
thf(2312,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK62_SY1157 @ SV201 @ SV369 ) @ ( sK64_SY1230 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( ~ ( order_preorder_on_a @ SV201 @ SV369 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 )
| ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2298]) ).
thf(2313,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member_a @ ( sK64_SY1230 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 )
| ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2299]) ).
thf(2314,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1157 @ SV201 @ SV369 ) @ ( sK63_SY1227 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 )
| ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2300]) ).
thf(2315,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 )
| ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) )
= $false )
| ( ( member_a @ ( sK63_SY1227 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2301]) ).
thf(2316,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV452: a,SV447: a] :
( ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV2 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV131 ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV131 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2304]) ).
thf(2317,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV455: a,SV453: a] :
( ( ( ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV2 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV131 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV131 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[2305]) ).
thf(2318,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV455: a,SV453: a] :
( ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV131 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[2305]) ).
thf(2319,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV444: a,SV439: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV2 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV2 )
= $false )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2306]) ).
thf(2320,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a,SV444: a,SV439: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV131 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV2 )
= $false )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2306]) ).
thf(2321,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV444: a,SV439: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV2 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV131 )
= $false )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2307]) ).
thf(2322,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a,SV444: a,SV439: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV131 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV131 )
= $false )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2307]) ).
thf(2323,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK62_SY1157 @ SV201 @ SV369 ) @ ( sK64_SY1230 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 )
| ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2312]) ).
thf(2324,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 )
| ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) )
= $false )
| ( ( member_a @ ( sK64_SY1230 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2313]) ).
thf(2325,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 )
| ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1157 @ SV201 @ SV369 ) @ ( sK63_SY1227 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2314]) ).
thf(2326,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 ) )
= $false )
| ( ( member_a @ ( sK63_SY1227 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2315]) ).
thf(2327,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) )
= $false )
| ( ( member_a @ ( sK63_SY1227 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2315]) ).
thf(2328,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV452: a,SV447: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV2 )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV131 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2316]) ).
thf(2329,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a,SV452: a,SV447: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV131 )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV131 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2316]) ).
thf(2330,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV455: a,SV453: a] :
( ( ( ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV2 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV131 ) ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV131 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2317]) ).
thf(2331,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV444: a,SV439: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV2 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV2 )
= $false )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2319]) ).
thf(2332,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a,SV444: a,SV439: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV2 )
= $false )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2320]) ).
thf(2333,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV444: a,SV439: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV2 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV131 )
= $false )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2321]) ).
thf(2334,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a,SV444: a,SV439: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV439 @ SV444 ) @ SV131 )
= $false )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2322]) ).
thf(2335,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 )
| ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK62_SY1157 @ SV201 @ SV369 ) @ ( sK64_SY1230 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2323]) ).
thf(2336,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 ) )
= $false )
| ( ( member_a @ ( sK64_SY1230 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2324]) ).
thf(2337,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) )
= $false )
| ( ( member_a @ ( sK64_SY1230 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2324]) ).
thf(2338,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1157 @ SV201 @ SV369 ) @ ( sK63_SY1227 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2325]) ).
thf(2339,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1157 @ SV201 @ SV369 ) @ ( sK63_SY1227 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2325]) ).
thf(2340,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( prefer1292084992ence_a @ SV201 @ SV369 )
= $true )
| ( ( member_a @ ( sK63_SY1227 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2326]) ).
thf(2341,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) )
= $true )
| ( ( member_a @ ( sK63_SY1227 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2327]) ).
thf(2342,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV452: a,SV447: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV131 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV2 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2328]) ).
thf(2343,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV452: a,SV447: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV131 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV131 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2329]) ).
thf(2344,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV455: a,SV453: a] :
( ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV2 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV131 ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV131 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2330]) ).
thf(2345,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( ~ ( prefer1292084992ence_a @ SV201 @ SV369 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK62_SY1157 @ SV201 @ SV369 ) @ ( sK64_SY1230 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2335]) ).
thf(2346,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK62_SY1157 @ SV201 @ SV369 ) @ ( sK64_SY1230 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2335]) ).
thf(2347,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( prefer1292084992ence_a @ SV201 @ SV369 )
= $true )
| ( ( member_a @ ( sK64_SY1230 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2336]) ).
thf(2348,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) )
= $true )
| ( ( member_a @ ( sK64_SY1230 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2337]) ).
thf(2349,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( prefer1292084992ence_a @ SV201 @ SV369 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1157 @ SV201 @ SV369 ) @ ( sK63_SY1227 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2338]) ).
thf(2350,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1157 @ SV201 @ SV369 ) @ ( sK63_SY1227 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2339]) ).
thf(2351,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) )
= $false )
| ( ( member_a @ ( sK63_SY1227 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2341]) ).
thf(2352,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV452: a,SV447: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV2 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV2 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2342]) ).
thf(2353,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a,SV452: a,SV447: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV131 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV2 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2342]) ).
thf(2354,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV452: a,SV447: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV2 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV131 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2343]) ).
thf(2355,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a,SV452: a,SV447: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV131 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV131 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2343]) ).
thf(2356,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV455: a,SV453: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV2 )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV131 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2344]) ).
thf(2357,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a,SV455: a,SV453: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV131 )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV131 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2344]) ).
thf(2358,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( prefer1292084992ence_a @ SV201 @ SV369 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK62_SY1157 @ SV201 @ SV369 ) @ ( sK64_SY1230 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2345]) ).
thf(2359,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK62_SY1157 @ SV201 @ SV369 ) @ ( sK64_SY1230 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2346]) ).
thf(2360,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) )
= $false )
| ( ( member_a @ ( sK64_SY1230 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2348]) ).
thf(2361,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1157 @ SV201 @ SV369 ) @ ( sK63_SY1227 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2350]) ).
thf(2362,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) ) )
= $false )
| ( ( member_a @ ( sK63_SY1227 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2351]) ).
thf(2363,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( ~ ( order_preorder_on_a @ SV201 @ SV369 ) )
= $false )
| ( ( member_a @ ( sK63_SY1227 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2351]) ).
thf(2364,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV452: a,SV447: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV2 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV2 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2352]) ).
thf(2365,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a,SV452: a,SV447: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV2 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2353]) ).
thf(2366,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV452: a,SV447: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV2 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV131 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2354]) ).
thf(2367,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a,SV452: a,SV447: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV447 @ SV452 ) @ SV131 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2355]) ).
thf(2368,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV455: a,SV453: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV131 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV2 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2356]) ).
thf(2369,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV455: a,SV453: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV131 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV131 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2357]) ).
thf(2370,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
| ~ ( order_preorder_on_a @ SV201 @ SV369 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK62_SY1157 @ SV201 @ SV369 ) @ ( sK64_SY1230 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2359]) ).
thf(2371,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) ) )
= $false )
| ( ( member_a @ ( sK64_SY1230 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2360]) ).
thf(2372,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( ~ ( order_preorder_on_a @ SV201 @ SV369 ) )
= $false )
| ( ( member_a @ ( sK64_SY1230 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2360]) ).
thf(2373,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1157 @ SV201 @ SV369 ) @ ( sK63_SY1227 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2361]) ).
thf(2374,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( ~ ( order_preorder_on_a @ SV201 @ SV369 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1157 @ SV201 @ SV369 ) @ ( sK63_SY1227 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2361]) ).
thf(2375,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) ) )
= $true )
| ( ( member_a @ ( sK63_SY1227 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2362]) ).
thf(2376,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( order_preorder_on_a @ SV201 @ SV369 )
= $true )
| ( ( member_a @ ( sK63_SY1227 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2363]) ).
thf(2377,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV455: a,SV453: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV2 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV2 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2368]) ).
thf(2378,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a,SV455: a,SV453: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV131 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV2 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2368]) ).
thf(2379,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV455: a,SV453: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV2 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV131 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2369]) ).
thf(2380,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a,SV455: a,SV453: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV131 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV131 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2369]) ).
thf(2381,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK62_SY1157 @ SV201 @ SV369 ) @ ( sK64_SY1230 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2370]) ).
thf(2382,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( ~ ( order_preorder_on_a @ SV201 @ SV369 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK62_SY1157 @ SV201 @ SV369 ) @ ( sK64_SY1230 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2370]) ).
thf(2383,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) ) )
= $true )
| ( ( member_a @ ( sK64_SY1230 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2371]) ).
thf(2384,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( order_preorder_on_a @ SV201 @ SV369 )
= $true )
| ( ( member_a @ ( sK64_SY1230 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2372]) ).
thf(2385,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1157 @ SV201 @ SV369 ) @ ( sK63_SY1227 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2373]) ).
thf(2386,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( order_preorder_on_a @ SV201 @ SV369 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1157 @ SV201 @ SV369 ) @ ( sK63_SY1227 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2374]) ).
thf(2387,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
= $false )
| ( ( member_a @ ( sK63_SY1227 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2375]) ).
thf(2388,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV455: a,SV453: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV2 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV2 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2377]) ).
thf(2389,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a,SV455: a,SV453: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV2 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2378]) ).
thf(2390,plain,
! [SV131: set_Product_prod_a_a,SV2: set_Product_prod_a_a,SV455: a,SV453: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV2 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV131 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2379]) ).
thf(2391,plain,
! [SV2: set_Product_prod_a_a,SV131: set_Product_prod_a_a,SV455: a,SV453: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV131 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV453 @ SV455 ) @ SV131 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV2 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK39_SV412 @ SV131 @ SV2 ) @ ( sK47_SV416 @ SV2 @ SV131 ) ) @ SV131 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2380]) ).
thf(2392,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK62_SY1157 @ SV201 @ SV369 ) @ ( sK64_SY1230 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2381]) ).
thf(2393,plain,
! [SV369: set_Product_prod_a_a,SV201: set_a] :
( ( ( order_preorder_on_a @ SV201 @ SV369 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK62_SY1157 @ SV201 @ SV369 ) @ ( sK64_SY1230 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2382]) ).
thf(2394,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
= $false )
| ( ( member_a @ ( sK64_SY1230 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2383]) ).
thf(2395,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1157 @ SV201 @ SV369 ) @ ( sK63_SY1227 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2385]) ).
thf(2396,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) ) )
= $false )
| ( ( member_a @ ( sK63_SY1227 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2387]) ).
thf(2397,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
= $false )
| ( ( member_a @ ( sK63_SY1227 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2387]) ).
thf(2398,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) )
| ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK62_SY1157 @ SV201 @ SV369 ) @ ( sK64_SY1230 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2392]) ).
thf(2399,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) ) )
= $false )
| ( ( member_a @ ( sK64_SY1230 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2394]) ).
thf(2400,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
= $false )
| ( ( member_a @ ( sK64_SY1230 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2394]) ).
thf(2401,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1157 @ SV201 @ SV369 ) @ ( sK63_SY1227 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2395]) ).
thf(2402,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1157 @ SV201 @ SV369 ) @ ( sK63_SY1227 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2395]) ).
thf(2403,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) ) )
= $true )
| ( ( member_a @ ( sK63_SY1227 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2396]) ).
thf(2404,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
= $true )
| ( ( member_a @ ( sK63_SY1227 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2397]) ).
thf(2405,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK62_SY1157 @ SV201 @ SV369 ) @ ( sK64_SY1230 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2398]) ).
thf(2406,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK62_SY1157 @ SV201 @ SV369 ) @ ( sK64_SY1230 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2398]) ).
thf(2407,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) ) )
= $true )
| ( ( member_a @ ( sK64_SY1230 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2399]) ).
thf(2408,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
= $true )
| ( ( member_a @ ( sK64_SY1230 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2400]) ).
thf(2409,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1157 @ SV201 @ SV369 ) @ ( sK63_SY1227 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2401]) ).
thf(2410,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1157 @ SV201 @ SV369 ) @ ( sK63_SY1227 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2402]) ).
thf(2411,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a,SV456: a] :
( ( ( ! [SY1233: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV456 @ SY1233 ) @ SV369 )
| ( member_a @ SV456 @ SV201 ) ) )
= $true )
| ( ( member_a @ ( sK63_SY1227 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2403]) ).
thf(2412,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a,SV457: a] :
( ( ( ! [SY1234: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV457 @ SY1234 ) @ SV369 )
| ( member_a @ SY1234 @ SV201 ) ) )
= $true )
| ( ( member_a @ ( sK63_SY1227 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2404]) ).
thf(2413,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ! [SY1155: a,SY1156: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1155 @ SY1156 ) @ SV369 )
| ( member_a @ SY1155 @ SV201 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK62_SY1157 @ SV201 @ SV369 ) @ ( sK64_SY1230 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2405]) ).
thf(2414,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a] :
( ( ( ! [SY1157: a,SY1158: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1157 @ SY1158 ) @ SV369 )
| ( member_a @ SY1158 @ SV201 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK62_SY1157 @ SV201 @ SV369 ) @ ( sK64_SY1230 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2406]) ).
thf(2415,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a,SV458: a] :
( ( ( ! [SY1235: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV458 @ SY1235 ) @ SV369 )
| ( member_a @ SV458 @ SV201 ) ) )
= $true )
| ( ( member_a @ ( sK64_SY1230 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2407]) ).
thf(2416,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a,SV459: a] :
( ( ( ! [SY1236: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV459 @ SY1236 ) @ SV369 )
| ( member_a @ SY1236 @ SV201 ) ) )
= $true )
| ( ( member_a @ ( sK64_SY1230 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2408]) ).
thf(2417,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a,SV460: a] :
( ( ( ! [SY1237: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV460 @ SY1237 ) @ SV369 )
| ( member_a @ SV460 @ SV201 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1157 @ SV201 @ SV369 ) @ ( sK63_SY1227 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2409]) ).
thf(2418,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a,SV461: a] :
( ( ( ! [SY1238: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV461 @ SY1238 ) @ SV369 )
| ( member_a @ SY1238 @ SV201 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1157 @ SV201 @ SV369 ) @ ( sK63_SY1227 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2410]) ).
thf(2419,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a,SV462: a,SV456: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV456 @ SV462 ) @ SV369 )
| ( member_a @ SV456 @ SV201 ) )
= $true )
| ( ( member_a @ ( sK63_SY1227 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2411]) ).
thf(2420,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a,SV463: a,SV457: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV457 @ SV463 ) @ SV369 )
| ( member_a @ SV463 @ SV201 ) )
= $true )
| ( ( member_a @ ( sK63_SY1227 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2412]) ).
thf(2421,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a,SV464: a] :
( ( ( ! [SY1239: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV464 @ SY1239 ) @ SV369 )
| ( member_a @ SV464 @ SV201 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK62_SY1157 @ SV201 @ SV369 ) @ ( sK64_SY1230 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2413]) ).
thf(2422,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a,SV465: a] :
( ( ( ! [SY1240: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV465 @ SY1240 ) @ SV369 )
| ( member_a @ SY1240 @ SV201 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK62_SY1157 @ SV201 @ SV369 ) @ ( sK64_SY1230 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2414]) ).
thf(2423,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a,SV466: a,SV458: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV458 @ SV466 ) @ SV369 )
| ( member_a @ SV458 @ SV201 ) )
= $true )
| ( ( member_a @ ( sK64_SY1230 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2415]) ).
thf(2424,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a,SV467: a,SV459: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV459 @ SV467 ) @ SV369 )
| ( member_a @ SV467 @ SV201 ) )
= $true )
| ( ( member_a @ ( sK64_SY1230 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2416]) ).
thf(2425,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a,SV468: a,SV460: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV460 @ SV468 ) @ SV369 )
| ( member_a @ SV460 @ SV201 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1157 @ SV201 @ SV369 ) @ ( sK63_SY1227 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2417]) ).
thf(2426,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a,SV469: a,SV461: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV461 @ SV469 ) @ SV369 )
| ( member_a @ SV469 @ SV201 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1157 @ SV201 @ SV369 ) @ ( sK63_SY1227 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2418]) ).
thf(2427,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a,SV462: a,SV456: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV456 @ SV462 ) @ SV369 ) )
= $true )
| ( ( member_a @ SV456 @ SV201 )
= $true )
| ( ( member_a @ ( sK63_SY1227 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2419]) ).
thf(2428,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a,SV463: a,SV457: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV457 @ SV463 ) @ SV369 ) )
= $true )
| ( ( member_a @ SV463 @ SV201 )
= $true )
| ( ( member_a @ ( sK63_SY1227 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2420]) ).
thf(2429,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a,SV470: a,SV464: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV464 @ SV470 ) @ SV369 )
| ( member_a @ SV464 @ SV201 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK62_SY1157 @ SV201 @ SV369 ) @ ( sK64_SY1230 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2421]) ).
thf(2430,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a,SV471: a,SV465: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV465 @ SV471 ) @ SV369 )
| ( member_a @ SV471 @ SV201 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK62_SY1157 @ SV201 @ SV369 ) @ ( sK64_SY1230 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2422]) ).
thf(2431,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a,SV466: a,SV458: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV458 @ SV466 ) @ SV369 ) )
= $true )
| ( ( member_a @ SV458 @ SV201 )
= $true )
| ( ( member_a @ ( sK64_SY1230 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2423]) ).
thf(2432,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a,SV467: a,SV459: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV459 @ SV467 ) @ SV369 ) )
= $true )
| ( ( member_a @ SV467 @ SV201 )
= $true )
| ( ( member_a @ ( sK64_SY1230 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2424]) ).
thf(2433,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a,SV468: a,SV460: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV460 @ SV468 ) @ SV369 ) )
= $true )
| ( ( member_a @ SV460 @ SV201 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1157 @ SV201 @ SV369 ) @ ( sK63_SY1227 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2425]) ).
thf(2434,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a,SV469: a,SV461: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV461 @ SV469 ) @ SV369 ) )
= $true )
| ( ( member_a @ SV469 @ SV201 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1157 @ SV201 @ SV369 ) @ ( sK63_SY1227 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2426]) ).
thf(2435,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a,SV462: a,SV456: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV456 @ SV462 ) @ SV369 )
= $false )
| ( ( member_a @ SV456 @ SV201 )
= $true )
| ( ( member_a @ ( sK63_SY1227 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2427]) ).
thf(2436,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a,SV463: a,SV457: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV457 @ SV463 ) @ SV369 )
= $false )
| ( ( member_a @ SV463 @ SV201 )
= $true )
| ( ( member_a @ ( sK63_SY1227 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2428]) ).
thf(2437,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a,SV470: a,SV464: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV464 @ SV470 ) @ SV369 ) )
= $true )
| ( ( member_a @ SV464 @ SV201 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK62_SY1157 @ SV201 @ SV369 ) @ ( sK64_SY1230 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2429]) ).
thf(2438,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a,SV471: a,SV465: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV465 @ SV471 ) @ SV369 ) )
= $true )
| ( ( member_a @ SV471 @ SV201 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK62_SY1157 @ SV201 @ SV369 ) @ ( sK64_SY1230 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2430]) ).
thf(2439,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a,SV466: a,SV458: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV458 @ SV466 ) @ SV369 )
= $false )
| ( ( member_a @ SV458 @ SV201 )
= $true )
| ( ( member_a @ ( sK64_SY1230 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2431]) ).
thf(2440,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a,SV467: a,SV459: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV459 @ SV467 ) @ SV369 )
= $false )
| ( ( member_a @ SV467 @ SV201 )
= $true )
| ( ( member_a @ ( sK64_SY1230 @ SV369 @ SV201 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2432]) ).
thf(2441,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a,SV468: a,SV460: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV460 @ SV468 ) @ SV369 )
= $false )
| ( ( member_a @ SV460 @ SV201 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1157 @ SV201 @ SV369 ) @ ( sK63_SY1227 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2433]) ).
thf(2442,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a,SV469: a,SV461: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV461 @ SV469 ) @ SV369 )
= $false )
| ( ( member_a @ SV469 @ SV201 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1157 @ SV201 @ SV369 ) @ ( sK63_SY1227 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ SV201 )
= $false )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2434]) ).
thf(2443,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a,SV470: a,SV464: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV464 @ SV470 ) @ SV369 )
= $false )
| ( ( member_a @ SV464 @ SV201 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK62_SY1157 @ SV201 @ SV369 ) @ ( sK64_SY1230 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2437]) ).
thf(2444,plain,
! [SV201: set_a,SV369: set_Product_prod_a_a,SV471: a,SV465: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV465 @ SV471 ) @ SV369 )
= $false )
| ( ( member_a @ SV471 @ SV201 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK62_SY1157 @ SV201 @ SV369 ) @ ( sK64_SY1230 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK59_SY1155 @ SV201 @ SV369 ) @ ( sK60_SY1218 @ SV369 @ SV201 ) ) @ SV369 )
= $true )
| ( ( order_preorder_on_a @ SV201 @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2438]) ).
thf(2445,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[491,2444,2443,2442,2441,2440,2439,2436,2435,2393,2391,2390,2389,2388,2386,2384,2376,2367,2366,2365,2364,2358,2349,2347,2340,2334,2333,2332,2331,2318,2311,2310,2309,2308,2303,2302,2297,2296,2289,2287,2280,2279,2276,2275,2274,2273,2261,2260,2259,2258,2250,2248,2240,2232,2230,2226,2225,2224,2223,2222,2217,2216,2214,2213,2212,2210,2209,2208,2199,2193,2192,2180,2178,2177,2169,2167,2164,2152,2148,2146,2135,2131,2129,2125,2123,2122,2119,2116,2115,2109,2107,2105,2103,2101,2094,2089,2088,2086,2082,2081,2079,2073,2072,2070,2064,2063,2062,2059,2058,2055,2052,2051,2050,2046,2037,2013,2007,2001,1996,1994,1987,1986,1981,1980,1978,1977,1974,1971,1968,1958,1953,1952,1941,1940,1937,1926,1925,1923,1922,1921,1920,1918,1917,1911,1910,1908,1905,1901,1894,1886,1879,1874,1872,1871,1870,1869,1868,1867,1866,1865,1863,1816,1806,1802,1801,1795,1794,1793,1792,1787,1786,1785,1784,1783,1781,1777,1776,1773,1770,1768,1767,1765,1764,1762,1761,1756,1752,1751,1745,1744,1737,1736,1731,1730,1729,1728,1714,1713,1712,1711,1708,1707,1706,1705,1698,1697,1696,1695,1694,1693,1692,1691,1686,1678,1673,1672,1666,1663,1662,1655,1648,1643,1639,1636,1634,1633,1629,1628,1625,1624,1623,1622,1618,1613,1605,1602,1601,1598,1597,1562,1560,1551,1536,1534,1533,1532,1529,1519,1509,1503,1499,1495,1490,1469,1460,1452,1450,1449,1447,1445,1444,1442,1437,1425,1424,1423,1421,1416,1407,1403,1402,1385,1366,1362,1359,1354,1351,1347,1346,1341,1336,1335,1326,1323,1321,1319,1317,1311,1306,1303,1292,1289,1285,1282,1278,1277,1269,1263,1259,1255,1251,1233,1193,1152,1140,1136,1135,1134,1133,1131,1124,1121,1099,1093,1086,1077,1070,1047,1039,1034,1027,1016,1014,1012,1009,1007,1002,1000,997,906,903,901,890,889,888,882,881,879,870,841,835,820,813,782,777,768,758,753,749,747,746,744,743,740,735,734,733,731]) ).
thf(2446,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[2445]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP157^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.15 % Computer : n020.cluster.edu
% 0.09/0.15 % Model : x86_64 x86_64
% 0.09/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.15 % Memory : 8046.5625MB
% 0.09/0.15 % OS : Linux 6.8.0-71-generic
% 0.09/0.15 % CPULimit : 300
% 0.09/0.15 % WCLimit : 300
% 0.09/0.15 % DateTime : Tue Oct 6 11:19:36 UTC 2026
% 0.09/0.15 % CPUTime :
% 0.09/0.15 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 43.76/7.66 ..
% 43.76/7.66
% 43.76/7.66 No.of.Axioms: 131
% 43.76/7.66
% 43.76/7.66 Length.of.Defs: 0
% 43.76/7.66
% 43.76/7.66 Contains.Choice.Funs: false
% 43.76/7.66 ..............................................................................
% 43.76/7.66
% 43.76/7.66 ********************************
% 43.76/7.66 * All subproblems solved! *
% 43.76/7.66 ********************************
% 43.76/7.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:131,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:2445,loop_count:0,foatp_calls:1,translation:fof_full)
% 43.76/7.66
% 43.76/7.66 %**** Beginning of derivation protocol ****
% 43.76/7.66 % SZS output start CNFRefutation
% See solution above
% 43.76/7.69
% 43.76/7.69 %**** End of derivation protocol ****
% 43.76/7.69 %**** no. of clauses in derivation: 2222 ****
% 43.76/7.69 %**** clause counter: 2445 ****
% 43.76/7.69
% 43.76/7.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:131,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:2445,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------