%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ITP152^1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 10:24:21 AM UTC 2026
% Result : Theorem 159.73s 26.87s
% Output : CNFRefutation 26.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 130
% Syntax : Number of formulae : 2443 ( 857 unt; 0 typ; 0 def)
% Number of atoms : 19517 (6759 equ; 0 cnn)
% Maximal formula atoms : 7 ( 7 avg)
% Number of connectives : 43447 (6466 ~;6040 |; 81 &;30380 @)
% ( 0 <=>; 480 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Number of types : 23 ( 22 usr)
% Number of type conns : 857 ( 857 >; 0 *; 0 +; 0 <<)
% Number of symbols : 231 ( 228 usr; 10 con; 0-4 aty)
% Number of variables : 8916 ( 91 ^;8807 !; 18 ?;8916 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_multis1735859763od_a_a,type,
multis1735859763od_a_a: $tType ).
thf(tp_multis599418605od_a_a,type,
multis599418605od_a_a: $tType ).
thf(tp_multiset_a,type,
multiset_a: $tType ).
thf(tp_multiset_multiset_a,type,
multiset_multiset_a: $tType ).
thf(tp_produc1127127335iset_a,type,
produc1127127335iset_a: $tType ).
thf(tp_produc1572603623od_a_a,type,
produc1572603623od_a_a: $tType ).
thf(tp_produc1990712039od_a_a,type,
produc1990712039od_a_a: $tType ).
thf(tp_produc2061001575od_a_a,type,
produc2061001575od_a_a: $tType ).
thf(tp_produc558600423iset_a,type,
produc558600423iset_a: $tType ).
thf(tp_produc562496743od_a_a,type,
produc562496743od_a_a: $tType ).
thf(tp_product_prod_a_a,type,
product_prod_a_a: $tType ).
thf(tp_set_Pr1295299783od_a_a,type,
set_Pr1295299783od_a_a: $tType ).
thf(tp_set_Pr146455751iset_a,type,
set_Pr146455751iset_a: $tType ).
thf(tp_set_Pr158363655iset_a,type,
set_Pr158363655iset_a: $tType ).
thf(tp_set_Pr1821581383od_a_a,type,
set_Pr1821581383od_a_a: $tType ).
thf(tp_set_Pr1930443975od_a_a,type,
set_Pr1930443975od_a_a: $tType ).
thf(tp_set_Pr1948701895od_a_a,type,
set_Pr1948701895od_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_set_mu1281098573od_a_a,type,
set_mu1281098573od_a_a: $tType ).
thf(tp_set_multiset_a,type,
set_multiset_a: $tType ).
thf(tp_add_ms1725977093od_a_a,type,
add_ms1725977093od_a_a: product_prod_a_a > multis599418605od_a_a > multis599418605od_a_a ).
thf(tp_add_mset_a,type,
add_mset_a: a > multiset_a > multiset_a ).
thf(tp_asym_a,type,
asym_a: set_Product_prod_a_a > $o ).
thf(tp_carrier,type,
carrier: set_a ).
thf(tp_collec1104713362iset_a,type,
collec1104713362iset_a: ( produc1127127335iset_a > $o ) > set_Pr158363655iset_a ).
thf(tp_collec1635618130od_a_a,type,
collec1635618130od_a_a: ( produc1572603623od_a_a > $o ) > set_Pr1948701895od_a_a ).
thf(tp_collec1948052440od_a_a,type,
collec1948052440od_a_a: ( multis599418605od_a_a > $o ) > set_mu1281098573od_a_a ).
thf(tp_collec645855634od_a_a,type,
collec645855634od_a_a: ( product_prod_a_a > $o ) > set_Product_prod_a_a ).
thf(tp_collec8264402od_a_a,type,
collec8264402od_a_a: ( produc2061001575od_a_a > $o ) > set_Pr1821581383od_a_a ).
thf(tp_collect_a,type,
collect_a: ( a > $o ) > set_a ).
thf(tp_collect_multiset_a,type,
collect_multiset_a: ( multiset_a > $o ) > set_multiset_a ).
thf(tp_fold_m382157835iset_a,type,
fold_m382157835iset_a: ( multiset_a > multiset_a > multiset_a ) > multiset_a > multiset_multiset_a > multiset_a ).
thf(tp_fold_m773816523od_a_a,type,
fold_m773816523od_a_a: ( multis599418605od_a_a > multis599418605od_a_a > multis599418605od_a_a ) > multis599418605od_a_a > multis1735859763od_a_a > multis599418605od_a_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_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_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_inv_im15016955od_a_a,type,
inv_im15016955od_a_a: set_Product_prod_a_a > ( product_prod_a_a > a ) > set_Pr1948701895od_a_a ).
thf(tp_inv_im1681759523_a_a_a,type,
inv_im1681759523_a_a_a: set_Pr1821581383od_a_a > ( a > multis599418605od_a_a ) > set_Product_prod_a_a ).
thf(tp_inv_im1716587189od_a_a,type,
inv_im1716587189od_a_a: set_Pr158363655iset_a > ( product_prod_a_a > multiset_a ) > set_Pr1948701895od_a_a ).
thf(tp_inv_im184450735iset_a,type,
inv_im184450735iset_a: set_Pr1948701895od_a_a > ( multiset_a > product_prod_a_a ) > set_Pr158363655iset_a ).
thf(tp_inv_im343774418iset_a,type,
inv_im343774418iset_a: set_Pr158363655iset_a > ( multiset_a > multiset_a ) > set_Pr158363655iset_a ).
thf(tp_inv_im479034648iset_a,type,
inv_im479034648iset_a: set_Product_prod_a_a > ( multiset_a > a ) > set_Pr158363655iset_a ).
thf(tp_inv_im777352425_a_a_a,type,
inv_im777352425_a_a_a: set_Pr1948701895od_a_a > ( a > product_prod_a_a ) > set_Product_prod_a_a ).
thf(tp_inv_im941243329od_a_a,type,
inv_im941243329od_a_a: set_Product_prod_a_a > ( multis599418605od_a_a > a ) > set_Pr1821581383od_a_a ).
thf(tp_inv_im975322764et_a_a,type,
inv_im975322764et_a_a: set_Pr158363655iset_a > ( a > multiset_a ) > set_Product_prod_a_a ).
thf(tp_inv_image_a_a,type,
inv_image_a_a: set_Product_prod_a_a > ( a > a ) > set_Product_prod_a_a ).
thf(tp_irrefl1672195874od_a_a,type,
irrefl1672195874od_a_a: set_Pr1821581383od_a_a > $o ).
thf(tp_irrefl76447196od_a_a,type,
irrefl76447196od_a_a: set_Pr1948701895od_a_a > $o ).
thf(tp_irrefl_a,type,
irrefl_a: set_Product_prod_a_a > $o ).
thf(tp_irrefl_multiset_a,type,
irrefl_multiset_a: set_Pr158363655iset_a > $o ).
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_member1349055120od_a_a,type,
member1349055120od_a_a: produc2061001575od_a_a > set_Pr1821581383od_a_a > $o ).
thf(tp_member1755255446od_a_a,type,
member1755255446od_a_a: multis599418605od_a_a > set_mu1281098573od_a_a > $o ).
thf(tp_member1899387664od_a_a,type,
member1899387664od_a_a: produc1990712039od_a_a > set_Pr1295299783od_a_a > $o ).
thf(tp_member2007374608od_a_a,type,
member2007374608od_a_a: produc562496743od_a_a > set_Pr1930443975od_a_a > $o ).
thf(tp_member2057358096od_a_a,type,
member2057358096od_a_a: produc1572603623od_a_a > set_Pr1948701895od_a_a > $o ).
thf(tp_member340150864iset_a,type,
member340150864iset_a: produc1127127335iset_a > set_Pr158363655iset_a > $o ).
thf(tp_member449909584od_a_a,type,
member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
thf(tp_member567864080iset_a,type,
member567864080iset_a: produc558600423iset_a > set_Pr146455751iset_a > $o ).
thf(tp_member_a,type,
member_a: a > set_a > $o ).
thf(tp_member_multiset_a,type,
member_multiset_a: multiset_a > set_multiset_a > $o ).
thf(tp_minus_1257885652od_a_a,type,
minus_1257885652od_a_a: multis599418605od_a_a > multis599418605od_a_a > multis599418605od_a_a ).
thf(tp_minus_1649712171iset_a,type,
minus_1649712171iset_a: multiset_a > multiset_a > multiset_a ).
thf(tp_mult1_1719650714od_a_a,type,
mult1_1719650714od_a_a: set_Pr1948701895od_a_a > set_Pr1821581383od_a_a ).
thf(tp_mult1_a,type,
mult1_a: set_Product_prod_a_a > set_Pr158363655iset_a ).
thf(tp_mult_a,type,
mult_a: set_Product_prod_a_a > set_Pr158363655iset_a ).
thf(tp_multp_a,type,
multp_a: ( a > a > $o ) > multiset_a > multiset_a > $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_less_eq_set_a,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(tp_order_1040740996od_a_a,type,
order_1040740996od_a_a: set_mu1281098573od_a_a > set_Pr1821581383od_a_a > $o ).
thf(tp_order_1210379134od_a_a,type,
order_1210379134od_a_a: set_Pr1821581383od_a_a > set_Pr1930443975od_a_a > $o ).
thf(tp_order_1505515173od_a_a,type,
order_1505515173od_a_a: set_Product_prod_a_a > set_Pr1948701895od_a_a > $o ).
thf(tp_order_1558116988r_on_a,type,
order_1558116988r_on_a: set_a > set_Product_prod_a_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_750350043iset_a,type,
order_750350043iset_a: set_multiset_a > set_Pr158363655iset_a > $o ).
thf(tp_order_761691966iset_a,type,
order_761691966iset_a: set_Pr158363655iset_a > set_Pr146455751iset_a > $o ).
thf(tp_order_preorder_on_a,type,
order_preorder_on_a: set_a > set_Product_prod_a_a > $o ).
thf(tp_plus_p404985124od_a_a,type,
plus_p404985124od_a_a: multis599418605od_a_a > multis599418605od_a_a > multis599418605od_a_a ).
thf(tp_plus_plus_multiset_a,type,
plus_plus_multiset_a: multiset_a > multiset_a > multiset_a ).
thf(tp_prefer1064779160od_a_a,type,
prefer1064779160od_a_a: set_Product_prod_a_a > set_Pr1948701895od_a_a > $o ).
thf(tp_prefer1191731497od_a_a,type,
prefer1191731497od_a_a: multis599418605od_a_a > set_mu1281098573od_a_a > set_Pr1821581383od_a_a > set_mu1281098573od_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_prefer1340910575od_a_a,type,
prefer1340910575od_a_a: set_mu1281098573od_a_a > set_Pr1821581383od_a_a > $o ).
thf(tp_prefer1409946857od_a_a,type,
prefer1409946857od_a_a: set_Pr1948701895od_a_a > set_Pr1295299783od_a_a > $o ).
thf(tp_prefer1571048262iset_a,type,
prefer1571048262iset_a: set_multiset_a > set_Pr158363655iset_a > $o ).
thf(tp_prefer1608839465iset_a,type,
prefer1608839465iset_a: set_Pr158363655iset_a > set_Pr146455751iset_a > $o ).
thf(tp_prefer161218362good_a,type,
prefer161218362good_a: a > set_a > set_Product_prod_a_a > set_a ).
thf(tp_prefer1669415233od_a_a,type,
prefer1669415233od_a_a: set_mu1281098573od_a_a > set_Pr1821581383od_a_a > $o ).
thf(tp_prefer1779827352iset_a,type,
prefer1779827352iset_a: set_multiset_a > set_Pr158363655iset_a > $o ).
thf(tp_prefer1828051771od_a_a,type,
prefer1828051771od_a_a: set_Pr1948701895od_a_a > set_Pr1295299783od_a_a > $o ).
thf(tp_prefer2130004608iset_a,type,
prefer2130004608iset_a: multiset_a > set_multiset_a > set_Pr158363655iset_a > set_multiset_a ).
thf(tp_prefer273553257od_a_a,type,
prefer273553257od_a_a: set_Pr1821581383od_a_a > set_Pr1930443975od_a_a > $o ).
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_prefer580340847ioms_a,type,
prefer580340847ioms_a: set_a > set_Product_prod_a_a > $o ).
thf(tp_prefer619498851iset_a,type,
prefer619498851iset_a: produc1127127335iset_a > set_Pr158363655iset_a > set_Pr146455751iset_a > set_Pr158363655iset_a ).
thf(tp_prefer697821563od_a_a,type,
prefer697821563od_a_a: set_Product_prod_a_a > set_Pr1948701895od_a_a > $o ).
thf(tp_prefer719835986ence_a,type,
prefer719835986ence_a: set_a > set_Product_prod_a_a > $o ).
thf(tp_prefer737894307od_a_a,type,
prefer737894307od_a_a: produc2061001575od_a_a > set_Pr1821581383od_a_a > set_Pr1930443975od_a_a > set_Pr1821581383od_a_a ).
thf(tp_prefer841781627iset_a,type,
prefer841781627iset_a: set_Pr158363655iset_a > set_Pr146455751iset_a > $o ).
thf(tp_prefer933983163od_a_a,type,
prefer933983163od_a_a: set_Pr1821581383od_a_a > set_Pr1930443975od_a_a > $o ).
thf(tp_produc1093061851od_a_a,type,
produc1093061851od_a_a: ( a > a > set_Product_prod_a_a ) > product_prod_a_a > set_Product_prod_a_a ).
thf(tp_produc1121147169od_a_a,type,
produc1121147169od_a_a: ( a > a > set_mu1281098573od_a_a ) > product_prod_a_a > set_mu1281098573od_a_a ).
thf(tp_produc143372156od_a_a,type,
produc143372156od_a_a: ( product_prod_a_a > set_Product_prod_a_a ) > a > a > set_Product_prod_a_a ).
thf(tp_produc1474507607od_a_a,type,
produc1474507607od_a_a: product_prod_a_a > product_prod_a_a > produc1572603623od_a_a ).
thf(tp_produc1530159757et_a_o,type,
produc1530159757et_a_o: ( produc1127127335iset_a > $o ) > multiset_a > multiset_a > $o ).
thf(tp_produc1548936141_a_a_o,type,
produc1548936141_a_a_o: ( produc2061001575od_a_a > $o ) > multis599418605od_a_a > multis599418605od_a_a > $o ).
thf(tp_produc1641853175od_a_a,type,
produc1641853175od_a_a: produc1572603623od_a_a > produc1572603623od_a_a ).
thf(tp_produc1653225349od_a_a,type,
produc1653225349od_a_a: ( a > a > set_Product_prod_a_a ) > product_prod_a_a > set_Product_prod_a_a ).
thf(tp_produc1828150264iset_a,type,
produc1828150264iset_a: ( a > a > set_multiset_a ) > product_prod_a_a > set_multiset_a ).
thf(tp_produc1833107820_a_a_o,type,
produc1833107820_a_a_o: ( a > a > $o ) > product_prod_a_a > $o ).
thf(tp_produc1859144151od_a_a,type,
produc1859144151od_a_a: multis599418605od_a_a > multis599418605od_a_a > produc2061001575od_a_a ).
thf(tp_produc1898392407iset_a,type,
produc1898392407iset_a: produc1127127335iset_a > produc1127127335iset_a > produc558600423iset_a ).
thf(tp_produc1913956215od_a_a,type,
produc1913956215od_a_a: produc2061001575od_a_a > produc2061001575od_a_a ).
thf(tp_produc1935643479od_a_a,type,
produc1935643479od_a_a: produc1572603623od_a_a > produc1572603623od_a_a > produc1990712039od_a_a ).
thf(tp_produc2037245207iset_a,type,
produc2037245207iset_a: multiset_a > multiset_a > produc1127127335iset_a ).
thf(tp_produc2041367259od_a_a,type,
produc2041367259od_a_a: ( multiset_a > multiset_a > set_Product_prod_a_a ) > produc1127127335iset_a > set_Product_prod_a_a ).
thf(tp_produc429414904iset_a,type,
produc429414904iset_a: ( multiset_a > multiset_a > set_multiset_a ) > produc1127127335iset_a > set_multiset_a ).
thf(tp_produc506430135iset_a,type,
produc506430135iset_a: produc1127127335iset_a > produc1127127335iset_a ).
thf(tp_produc580150227_set_a,type,
produc580150227_set_a: ( product_prod_a_a > set_a ) > a > a > set_a ).
thf(tp_produc694541532_set_a,type,
produc694541532_set_a: ( a > a > set_a ) > product_prod_a_a > set_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_produc734625720iset_a,type,
produc734625720iset_a: ( product_prod_a_a > product_prod_a_a > set_multiset_a ) > produc1572603623od_a_a > set_multiset_a ).
thf(tp_produc747255346_set_a,type,
produc747255346_set_a: ( multiset_a > multiset_a > set_a ) > produc1127127335iset_a > set_a ).
thf(tp_produc748978966_a_a_o,type,
produc748978966_a_a_o: ( a > a > $o ) > product_prod_a_a > $o ).
thf(tp_produc869579762_set_a,type,
produc869579762_set_a: ( product_prod_a_a > product_prod_a_a > set_a ) > produc1572603623od_a_a > set_a ).
thf(tp_produc93594587iset_a,type,
produc93594587iset_a: ( a > a > set_Pr158363655iset_a ) > product_prod_a_a > set_Pr158363655iset_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_produc961951794_set_a,type,
produc961951794_set_a: ( a > a > set_a ) > product_prod_a_a > set_a ).
thf(tp_produc978545495od_a_a,type,
produc978545495od_a_a: produc2061001575od_a_a > produc2061001575od_a_a > produc562496743od_a_a ).
thf(tp_product_Pair_a_a,type,
product_Pair_a_a: a > a > 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_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_refl_o102522214od_a_a,type,
refl_o102522214od_a_a: set_Pr1821581383od_a_a > set_Pr1930443975od_a_a > $o ).
thf(tp_refl_o1298442278od_a_a,type,
refl_o1298442278od_a_a: set_Product_prod_a_a > set_Pr1948701895od_a_a > $o ).
thf(tp_refl_o1522155814iset_a,type,
refl_o1522155814iset_a: set_Pr158363655iset_a > set_Pr146455751iset_a > $o ).
thf(tp_refl_o198693862od_a_a,type,
refl_o198693862od_a_a: set_Pr1948701895od_a_a > set_Pr1295299783od_a_a > $o ).
thf(tp_refl_o581572716od_a_a,type,
refl_o581572716od_a_a: set_mu1281098573od_a_a > set_Pr1821581383od_a_a > $o ).
thf(tp_refl_on_a,type,
refl_on_a: set_a > set_Product_prod_a_a > $o ).
thf(tp_refl_on_multiset_a,type,
refl_on_multiset_a: set_multiset_a > set_Pr158363655iset_a > $o ).
thf(tp_relation,type,
relation: set_Product_prod_a_a ).
thf(tp_sK10_SY764,type,
sK10_SY764: set_Pr1948701895od_a_a > set_Product_prod_a_a > product_prod_a_a ).
thf(tp_sK11_SY775,type,
sK11_SY775: set_Product_prod_a_a > set_Product_prod_a_a > a ).
thf(tp_sK12_SY797,type,
sK12_SY797: set_Product_prod_a_a > set_a > a ).
thf(tp_sK13_SY572,type,
sK13_SY572: product_prod_a_a > ( product_prod_a_a > $o ) > a ).
thf(tp_sK14_SY1011,type,
sK14_SY1011: set_Product_prod_a_a > a ).
thf(tp_sK15_SY1012,type,
sK15_SY1012: set_Product_prod_a_a > a ).
thf(tp_sK16_SY1014,type,
sK16_SY1014: produc1572603623od_a_a > a ).
thf(tp_sK17_SY881,type,
sK17_SY881: set_a > set_Product_prod_a_a > a ).
thf(tp_sK18_SY682,type,
sK18_SY682: product_prod_a_a > ( product_prod_a_a > $o ) > a ).
thf(tp_sK19_SY1025,type,
sK19_SY1025: produc1572603623od_a_a > ( produc1572603623od_a_a > $o ) > a ).
thf(tp_sK1_SY535,type,
sK1_SY535: product_prod_a_a > a ).
thf(tp_sK20_SY1027,type,
sK20_SY1027: set_Product_prod_a_a > set_Pr1948701895od_a_a > product_prod_a_a ).
thf(tp_sK21_SY771,type,
sK21_SY771: product_prod_a_a > multis599418605od_a_a > multis599418605od_a_a ).
thf(tp_sK22_SY1028,type,
sK22_SY1028: set_Product_prod_a_a > set_Product_prod_a_a > a ).
thf(tp_sK23_SY945,type,
sK23_SY945: set_Product_prod_a_a > ( a > product_prod_a_a ) > set_a > a ).
thf(tp_sK24_SY1030,type,
sK24_SY1030: set_a > set_Product_prod_a_a > a ).
thf(tp_sK25_SY947,type,
sK25_SY947: product_prod_a_a > a ).
thf(tp_sK26_SY1032,type,
sK26_SY1032: product_prod_a_a > ( product_prod_a_a > $o ) > a ).
thf(tp_sK27_SY1033,type,
sK27_SY1033: set_Product_prod_a_a > a ).
thf(tp_sK28_SY969,type,
sK28_SY969: set_a > ( product_prod_a_a > a ) > set_Product_prod_a_a > product_prod_a_a ).
thf(tp_sK29_SY877,type,
sK29_SY877: product_prod_a_a > multis599418605od_a_a > multis599418605od_a_a ).
thf(tp_sK2_SY589,type,
sK2_SY589: produc1572603623od_a_a > product_prod_a_a ).
thf(tp_sK30_SY1034,type,
sK30_SY1034: set_Product_prod_a_a > set_a > a ).
thf(tp_sK31_SY1035,type,
sK31_SY1035: product_prod_a_a > ( product_prod_a_a > $o ) > a ).
thf(tp_sK32_SY989,type,
sK32_SY989: set_Product_prod_a_a > ( product_prod_a_a > product_prod_a_a ) > set_Product_prod_a_a > product_prod_a_a ).
thf(tp_sK33_SY708,type,
sK33_SY708: multis599418605od_a_a > product_prod_a_a ).
thf(tp_sK34_SY751,type,
sK34_SY751: set_Product_prod_a_a > a ).
thf(tp_sK35_SY1037,type,
sK35_SY1037: produc1572603623od_a_a > ( produc1572603623od_a_a > $o ) > a ).
thf(tp_sK36_SY772,type,
sK36_SY772: set_Product_prod_a_a > ( set_Product_prod_a_a > $o ) > set_Product_prod_a_a ).
thf(tp_sK37_SY828,type,
sK37_SY828: set_Product_prod_a_a > a ).
thf(tp_sK38_SY860,type,
sK38_SY860: set_Product_prod_a_a > a ).
thf(tp_sK39_SY976,type,
sK39_SY976: ( a > a > set_mu1281098573od_a_a ) > multis599418605od_a_a > product_prod_a_a > a ).
thf(tp_sK3_SY666,type,
sK3_SY666: product_prod_a_a > a ).
thf(tp_sK40_SY982,type,
sK40_SY982: ( a > a > set_multiset_a ) > multiset_a > product_prod_a_a > a ).
thf(tp_sK41_SY985,type,
sK41_SY985: ( a > a > set_a ) > a > product_prod_a_a > a ).
thf(tp_sK42_SY996,type,
sK42_SY996: ( a > a > set_Pr158363655iset_a ) > produc1127127335iset_a > product_prod_a_a > a ).
thf(tp_sK43_SY998,type,
sK43_SY998: ( multiset_a > multiset_a > set_Product_prod_a_a ) > product_prod_a_a > produc1127127335iset_a > multiset_a ).
thf(tp_sK44_SY1001,type,
sK44_SY1001: ( a > a > set_Product_prod_a_a ) > product_prod_a_a > product_prod_a_a > a ).
thf(tp_sK45_SY1009,type,
sK45_SY1009: set_Product_prod_a_a > ( a > a ) > ( a > a ) > product_prod_a_a > a ).
thf(tp_sK46_SY1040,type,
sK46_SY1040: set_Product_prod_a_a > a ).
thf(tp_sK47_SY1042,type,
sK47_SY1042: set_Product_prod_a_a > a ).
thf(tp_sK48_SY1043,type,
sK48_SY1043: multis599418605od_a_a > ( a > a > set_mu1281098573od_a_a ) > product_prod_a_a > a ).
thf(tp_sK49_SY1044,type,
sK49_SY1044: multiset_a > ( a > a > set_multiset_a ) > product_prod_a_a > a ).
thf(tp_sK4_SY574,type,
sK4_SY574: set_Product_prod_a_a > a ).
thf(tp_sK50_SY1045,type,
sK50_SY1045: a > ( a > a > set_a ) > product_prod_a_a > a ).
thf(tp_sK51_SY1046,type,
sK51_SY1046: produc1127127335iset_a > ( a > a > set_Pr158363655iset_a ) > product_prod_a_a > a ).
thf(tp_sK52_SY1047,type,
sK52_SY1047: product_prod_a_a > ( multiset_a > multiset_a > set_Product_prod_a_a ) > produc1127127335iset_a > multiset_a ).
thf(tp_sK53_SY1048,type,
sK53_SY1048: product_prod_a_a > ( a > a > set_Product_prod_a_a ) > product_prod_a_a > a ).
thf(tp_sK54_SY1005,type,
sK54_SY1005: set_Pr1948701895od_a_a > set_Product_prod_a_a > product_prod_a_a ).
thf(tp_sK55_SY1049,type,
sK55_SY1049: ( a > a ) > set_Product_prod_a_a > ( a > a ) > product_prod_a_a > a ).
thf(tp_sK56_SY1050,type,
sK56_SY1050: set_Product_prod_a_a > a ).
thf(tp_sK57_SY1017,type,
sK57_SY1017: set_Product_prod_a_a > set_a > a ).
thf(tp_sK58_SY883,type,
sK58_SY883: set_a > set_Product_prod_a_a > a ).
thf(tp_sK59_SY1053,type,
sK59_SY1053: set_Pr1948701895od_a_a > set_Product_prod_a_a > product_prod_a_a ).
thf(tp_sK5_SY581,type,
sK5_SY581: set_Product_prod_a_a > a ).
thf(tp_sK60_SY782,type,
sK60_SY782: a > product_prod_a_a > a ).
thf(tp_sK61_SY1054,type,
sK61_SY1054: set_Product_prod_a_a > set_a > a ).
thf(tp_sK62_SY857,type,
sK62_SY857: set_Product_prod_a_a > set_Product_prod_a_a ).
thf(tp_sK63_SY883,type,
sK63_SY883: set_a > set_Product_prod_a_a > a ).
thf(tp_sK64_SY1059,type,
sK64_SY1059: set_Product_prod_a_a > set_a > a ).
thf(tp_sK65_SY907,type,
sK65_SY907: a > product_prod_a_a > a ).
thf(tp_sK66_SY1063,type,
sK66_SY1063: set_Product_prod_a_a > set_a > a ).
thf(tp_sK67_SY782,type,
sK67_SY782: a > a > product_prod_a_a > a ).
thf(tp_sK68_SY1051,type,
sK68_SY1051: set_Product_prod_a_a > set_Product_prod_a_a > a ).
thf(tp_sK69_SY907,type,
sK69_SY907: a > a > product_prod_a_a > a ).
thf(tp_sK6_SY960,type,
sK6_SY960: produc1572603623od_a_a > a ).
thf(tp_sK70_SY1066,type,
sK70_SY1066: set_Product_prod_a_a > set_Product_prod_a_a > a ).
thf(tp_sK71_SY1020,type,
sK71_SY1020: set_a > set_Product_prod_a_a > a ).
thf(tp_sK72_SY1075,type,
sK72_SY1075: set_Product_prod_a_a > set_a > a ).
thf(tp_sK73_SY1022,type,
sK73_SY1022: set_a > set_Product_prod_a_a > a ).
thf(tp_sK74_SY1022,type,
sK74_SY1022: set_a > set_Product_prod_a_a > a ).
thf(tp_sK75_SY1092,type,
sK75_SY1092: set_Product_prod_a_a > set_a > a ).
thf(tp_sK76_SY1093,type,
sK76_SY1093: set_Product_prod_a_a > set_a > a ).
thf(tp_sK77_SY857,type,
sK77_SY857: set_Product_prod_a_a > set_Product_prod_a_a > set_Product_prod_a_a ).
thf(tp_sK78_SY857,type,
sK78_SY857: set_Product_prod_a_a > set_Product_prod_a_a > set_Product_prod_a_a ).
thf(tp_sK7_SY612,type,
sK7_SY612: set_Product_prod_a_a > a ).
thf(tp_sK8_SY984,type,
sK8_SY984: product_prod_a_a > a ).
thf(tp_sK9_SY474,type,
sK9_SY474: produc1572603623od_a_a > ( produc1572603623od_a_a > $o ) > product_prod_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_set_ms1818337124od_a_a,type,
set_ms1818337124od_a_a: multis599418605od_a_a > set_Product_prod_a_a ).
thf(tp_set_ms1869569194od_a_a,type,
set_ms1869569194od_a_a: multis1735859763od_a_a > set_mu1281098573od_a_a ).
thf(tp_set_mset_a,type,
set_mset_a: multiset_a > set_a ).
thf(tp_set_mset_multiset_a,type,
set_mset_multiset_a: multiset_multiset_a > set_multiset_a ).
thf(tp_top_to1483957574_a_a_o,type,
top_to1483957574_a_a_o: product_prod_a_a > $o ).
thf(tp_top_to398455383od_a_a,type,
top_to398455383od_a_a: set_Product_prod_a_a ).
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_total_1024184433od_a_a,type,
total_1024184433od_a_a: set_mu1281098573od_a_a > set_Pr1821581383od_a_a > $o ).
thf(tp_total_1170533099od_a_a,type,
total_1170533099od_a_a: set_Pr1821581383od_a_a > set_Pr1930443975od_a_a > $o ).
thf(tp_total_1340260971od_a_a,type,
total_1340260971od_a_a: set_Pr1948701895od_a_a > set_Pr1295299783od_a_a > $o ).
thf(tp_total_1490170027od_a_a,type,
total_1490170027od_a_a: set_Product_prod_a_a > set_Pr1948701895od_a_a > $o ).
thf(tp_total_313747627iset_a,type,
total_313747627iset_a: set_Pr158363655iset_a > set_Pr146455751iset_a > $o ).
thf(tp_total_on_a,type,
total_on_a: set_a > set_Product_prod_a_a > $o ).
thf(tp_total_on_multiset_a,type,
total_on_multiset_a: set_multiset_a > set_Pr158363655iset_a > $o ).
thf(tp_trans_1520871884od_a_a,type,
trans_1520871884od_a_a: set_Pr1821581383od_a_a > $o ).
thf(tp_trans_972827014od_a_a,type,
trans_972827014od_a_a: set_Pr1948701895od_a_a > $o ).
thf(tp_trans_a,type,
trans_a: set_Product_prod_a_a > $o ).
thf(tp_trans_multiset_a,type,
trans_multiset_a: set_Pr158363655iset_a > $o ).
thf(tp_x,type,
x: a ).
thf(tp_y,type,
y: a ).
thf(tp_zero_z160849828od_a_a,type,
zero_z160849828od_a_a: multis599418605od_a_a ).
thf(tp_zero_zero_multiset_a,type,
zero_zero_multiset_a: multiset_a ).
thf(17,axiom,
! [A: product_prod_a_a,M: multis599418605od_a_a,N: multis599418605od_a_a] :
( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ ( minus_1257885652od_a_a @ M @ N ) ) )
=> ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ M ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_in__diffD) ).
thf(23,axiom,
! [B: product_prod_a_a,A5: multis599418605od_a_a,M: multis599418605od_a_a] :
( ~ ( member449909584od_a_a @ B @ ( set_ms1818337124od_a_a @ A5 ) )
=> ( ( minus_1257885652od_a_a @ ( add_ms1725977093od_a_a @ B @ M ) @ A5 )
= ( add_ms1725977093od_a_a @ B @ ( minus_1257885652od_a_a @ M @ A5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_diff__add__mset__swap) ).
thf(33,axiom,
! [X: product_prod_a_a] : ( member449909584od_a_a @ X @ ( set_ms1818337124od_a_a @ ( add_ms1725977093od_a_a @ X @ zero_z160849828od_a_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_multi__member__last) ).
thf(35,axiom,
! [A5: multis599418605od_a_a] :
( ( A5 != zero_z160849828od_a_a )
=> ~ ! [X3: product_prod_a_a] :
~ ( member449909584od_a_a @ X3 @ ( set_ms1818337124od_a_a @ A5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_multiset__nonemptyE) ).
thf(39,axiom,
! [A: product_prod_a_a,A5: multis599418605od_a_a,B4: multis599418605od_a_a] :
( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ ( plus_p404985124od_a_a @ A5 @ B4 ) ) )
= ( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ A5 ) )
| ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ B4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_union__iff) ).
thf(41,axiom,
! [X: product_prod_a_a,M: multis599418605od_a_a,N: multis599418605od_a_a] :
( ( ( add_ms1725977093od_a_a @ X @ M )
= N )
=> ( member449909584od_a_a @ X @ ( set_ms1818337124od_a_a @ N ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_union__single__eq__member) ).
thf(43,axiom,
! [B: product_prod_a_a,B4: multis599418605od_a_a,C2: product_prod_a_a,C3: multis599418605od_a_a] :
( ( ( add_ms1725977093od_a_a @ B @ B4 )
= ( add_ms1725977093od_a_a @ C2 @ C3 ) )
=> ( ( B != C2 )
=> ( member449909584od_a_a @ C2 @ ( set_ms1818337124od_a_a @ B4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_insert__noteq__member) ).
thf(45,axiom,
! [X: product_prod_a_a,M: multis599418605od_a_a] :
( ( member449909584od_a_a @ X @ ( set_ms1818337124od_a_a @ M ) )
=> ? [A8: multis599418605od_a_a] :
( M
= ( add_ms1725977093od_a_a @ X @ A8 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_multi__member__split) ).
thf(47,axiom,
! [A: product_prod_a_a,A5: multis599418605od_a_a] :
( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ A5 ) )
=> ~ ! [B7: multis599418605od_a_a] :
( A5
!= ( add_ms1725977093od_a_a @ A @ B7 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_mset__add) ).
thf(55,axiom,
! [P2: a > $o,X: a,Y6: a,Y: a,R3: a > set_Product_prod_a_a] :
( ( P2 @ X )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y6 @ Y ) @ ( R3 @ X ) )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ X @ Y6 ) @ ( product_Pair_a_a @ X @ Y ) ) @ ( same_fst_a_a @ P2 @ R3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_same__fstI) ).
thf(56,axiom,
! [A5: set_Product_prod_a_a,F2: product_prod_a_a > product_prod_a_a,B4: set_Product_prod_a_a] :
( ! [X3: product_prod_a_a] :
( ( member449909584od_a_a @ X3 @ A5 )
=> ( member449909584od_a_a @ ( F2 @ X3 ) @ B4 ) )
=> ( ord_le1824328871od_a_a @ ( image_794773445od_a_a @ F2 @ A5 ) @ B4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_image__subsetI) ).
thf(57,axiom,
! [A5: set_Product_prod_a_a,F2: product_prod_a_a > a,B4: set_a] :
( ! [X3: product_prod_a_a] :
( ( member449909584od_a_a @ X3 @ A5 )
=> ( member_a @ ( F2 @ X3 ) @ B4 ) )
=> ( ord_less_eq_set_a @ ( image_340790172_a_a_a @ F2 @ A5 ) @ B4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_image__subsetI) ).
thf(58,axiom,
! [A5: set_a,F2: a > product_prod_a_a,B4: set_Product_prod_a_a] :
( ! [X3: a] :
( ( member_a @ X3 @ A5 )
=> ( member449909584od_a_a @ ( F2 @ X3 ) @ B4 ) )
=> ( ord_le1824328871od_a_a @ ( image_1725938350od_a_a @ F2 @ A5 ) @ B4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_image__subsetI) ).
thf(60,axiom,
! [R2: set_Product_prod_a_a,S: set_Product_prod_a_a] :
( ! [X3: a,Y3: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R2 )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ S ) )
=> ( ord_le1824328871od_a_a @ R2 @ S ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_subrelI) ).
thf(61,axiom,
! [A: a,P: product_prod_a_a] :
( ( A
= ( product_fst_a_a @ P ) )
= ( ? [B5: a] :
( P
= ( product_Pair_a_a @ A @ B5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_eq__fst__iff) ).
thf(62,axiom,
! [B: a,P: product_prod_a_a] :
( ( B
= ( product_snd_a_a @ P ) )
= ( ? [A6: a] :
( P
= ( product_Pair_a_a @ A6 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_eq__snd__iff) ).
thf(63,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/sandbox2/benchmark/theBenchmark.p',fact_292_fstI) ).
thf(64,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/sandbox2/benchmark/theBenchmark.p',fact_291_sndI) ).
thf(65,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/sandbox2/benchmark/theBenchmark.p',fact_290_BNF__Greatest__Fixpoint_Osubst__Pair) ).
thf(66,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/sandbox2/benchmark/theBenchmark.p',fact_289_conjI__realizer) ).
thf(67,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/sandbox2/benchmark/theBenchmark.p',fact_288_exI__realizer) ).
thf(68,axiom,
! [C2: product_prod_a_a,F2: a > a,G: a > a,R3: set_Product_prod_a_a] :
( ( member449909584od_a_a @ C2 @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ F2 @ G ) @ R3 ) )
=> ~ ! [X3: a,Y3: a] :
( ( C2
= ( product_Pair_a_a @ ( F2 @ X3 ) @ ( G @ Y3 ) ) )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_prod__fun__imageE) ).
thf(69,axiom,
( product_swap_a_a
= ( ^ [P3: product_prod_a_a] : ( product_Pair_a_a @ ( product_snd_a_a @ P3 ) @ ( product_fst_a_a @ P3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_prod_Oswap__def) ).
thf(70,axiom,
! [X: a,Y: a,A: a] :
( ( ( product_snd_a_a @ ( product_Pair_a_a @ X @ Y ) )
= A )
=> ( Y = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_snd__eqD) ).
thf(71,axiom,
! [X1: a,X22: a] :
( ( product_snd_a_a @ ( product_Pair_a_a @ X1 @ X22 ) )
= X22 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_snd__conv) ).
thf(72,axiom,
! [X: a,Y: a,A: a] :
( ( ( product_fst_a_a @ ( product_Pair_a_a @ X @ Y ) )
= A )
=> ( X = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_fst__eqD) ).
thf(73,axiom,
! [X1: a,X22: a] :
( ( product_fst_a_a @ ( product_Pair_a_a @ X1 @ X22 ) )
= X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_fst__conv) ).
thf(74,axiom,
! [T: product_prod_a_a] :
( T
= ( product_Pair_a_a @ ( product_fst_a_a @ T ) @ ( product_snd_a_a @ T ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_surjective__pairing) ).
thf(75,axiom,
! [Prod: product_prod_a_a] :
( Prod
= ( product_Pair_a_a @ ( product_fst_a_a @ Prod ) @ ( product_snd_a_a @ Prod ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_prod_Oexhaust__sel) ).
thf(77,axiom,
! [A: a,B: a,R3: set_Product_prod_a_a,F2: a > a,G: a > a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ R3 )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ ( F2 @ A ) @ ( G @ B ) ) @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ F2 @ G ) @ R3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_map__prod__imageI) ).
thf(78,axiom,
! [Prod: product_prod_a_a] :
( ( product_Pair_a_a @ ( product_fst_a_a @ Prod ) @ ( product_snd_a_a @ Prod ) )
= Prod ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_prod_Ocollapse) ).
thf(80,axiom,
! [A: a,B: a,A2: a,B2: a,R2: set_Product_prod_a_a,S: set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ A @ B ) @ ( product_Pair_a_a @ A2 @ B2 ) ) @ ( lex_prod_a_a @ R2 @ S ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ A2 ) @ R2 )
| ( ( A = A2 )
& ( member449909584od_a_a @ ( product_Pair_a_a @ B @ B2 ) @ S ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_in__lex__prod) ).
thf(81,axiom,
! [F2: a > a,G: a > a,A: a,B: a] :
( ( produc700022774_a_a_a @ F2 @ G @ ( product_Pair_a_a @ A @ B ) )
= ( product_Pair_a_a @ ( F2 @ A ) @ ( G @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_map__prod__simp) ).
thf(83,axiom,
( top_to1483957574_a_a_o
= ( ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ top_to398455383od_a_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_top__empty__eq) ).
thf(85,axiom,
! [X: product_prod_a_a,A5: set_Product_prod_a_a,B: product_prod_a_a,F2: product_prod_a_a > product_prod_a_a] :
( ( member449909584od_a_a @ X @ A5 )
=> ( ( B
= ( F2 @ X ) )
=> ( member449909584od_a_a @ B @ ( image_794773445od_a_a @ F2 @ A5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_rev__image__eqI) ).
thf(86,axiom,
! [X: product_prod_a_a,A5: set_Product_prod_a_a,B: a,F2: product_prod_a_a > a] :
( ( member449909584od_a_a @ X @ A5 )
=> ( ( B
= ( F2 @ X ) )
=> ( member_a @ B @ ( image_340790172_a_a_a @ F2 @ A5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_rev__image__eqI) ).
thf(87,axiom,
! [X: a,A5: set_a,B: product_prod_a_a,F2: a > product_prod_a_a] :
( ( member_a @ X @ A5 )
=> ( ( B
= ( F2 @ X ) )
=> ( member449909584od_a_a @ B @ ( image_1725938350od_a_a @ F2 @ A5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_rev__image__eqI) ).
thf(89,axiom,
! [X: product_prod_a_a,A5: set_Product_prod_a_a,F2: product_prod_a_a > product_prod_a_a] :
( ( member449909584od_a_a @ X @ A5 )
=> ( member449909584od_a_a @ ( F2 @ X ) @ ( image_794773445od_a_a @ F2 @ A5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_imageI) ).
thf(90,axiom,
! [X: product_prod_a_a,A5: set_Product_prod_a_a,F2: product_prod_a_a > a] :
( ( member449909584od_a_a @ X @ A5 )
=> ( member_a @ ( F2 @ X ) @ ( image_340790172_a_a_a @ F2 @ A5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_imageI) ).
thf(91,axiom,
! [X: a,A5: set_a,F2: a > product_prod_a_a] :
( ( member_a @ X @ A5 )
=> ( member449909584od_a_a @ ( F2 @ X ) @ ( image_1725938350od_a_a @ F2 @ A5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_imageI) ).
thf(95,axiom,
! [B: product_prod_a_a,F2: product_prod_a_a > product_prod_a_a,X: product_prod_a_a,A5: set_Product_prod_a_a] :
( ( B
= ( F2 @ X ) )
=> ( ( member449909584od_a_a @ X @ A5 )
=> ( member449909584od_a_a @ B @ ( image_794773445od_a_a @ F2 @ A5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_image__eqI) ).
thf(96,axiom,
! [B: a,F2: product_prod_a_a > a,X: product_prod_a_a,A5: set_Product_prod_a_a] :
( ( B
= ( F2 @ X ) )
=> ( ( member449909584od_a_a @ X @ A5 )
=> ( member_a @ B @ ( image_340790172_a_a_a @ F2 @ A5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_image__eqI) ).
thf(97,axiom,
! [B: product_prod_a_a,F2: a > product_prod_a_a,X: a,A5: set_a] :
( ( B
= ( F2 @ X ) )
=> ( ( member_a @ X @ A5 )
=> ( member449909584od_a_a @ B @ ( image_1725938350od_a_a @ F2 @ A5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_image__eqI) ).
thf(99,axiom,
! [R3: set_Product_prod_a_a,X: a,Y: a] :
( ( asym_a @ R3 )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ R3 )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ R3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_asymD) ).
thf(100,axiom,
( asym_a
= ( ^ [R5: set_Product_prod_a_a] :
! [X4: a,Y4: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ R5 )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y4 @ X4 ) @ R5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_asym__iff) ).
thf(101,axiom,
! [A: set_Product_prod_a_a] :
( ( asym_a @ A )
=> ! [A7: a,B6: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A7 @ B6 ) @ A )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B6 @ A7 ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_asym_Ocases) ).
thf(102,axiom,
( asym_a
= ( ^ [A6: set_Product_prod_a_a] :
? [R5: set_Product_prod_a_a] :
( ( A6 = R5 )
& ! [X4: a,Y4: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ R5 )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y4 @ X4 ) @ R5 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_asym_Osimps) ).
thf(103,axiom,
! [R3: set_Product_prod_a_a] :
( ! [A3: a,B3: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A3 @ B3 ) @ R3 )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B3 @ A3 ) @ R3 ) )
=> ( asym_a @ R3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_asym_Ointros) ).
thf(104,axiom,
! [X: set_Product_prod_a_a,P2: set_Product_prod_a_a > $o] :
( ( asym_a @ X )
=> ( ! [R4: set_Product_prod_a_a] :
( ! [A7: a,B6: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A7 @ B6 ) @ R4 )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B6 @ A7 ) @ R4 ) )
=> ( P2 @ R4 ) )
=> ( P2 @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_asym_Oinducts) ).
thf(106,axiom,
! [Y: a,X: a,A5: set_Product_prod_a_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ ( image_794773445od_a_a @ product_swap_a_a @ A5 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ A5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_pair__in__swap__image) ).
thf(108,axiom,
! [F2: product_prod_a_a > $o,A: a,B: a] :
( ( product_curry_a_a_o @ F2 @ A @ B )
=> ( F2 @ ( product_Pair_a_a @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_curryE) ).
thf(109,axiom,
! [F2: product_prod_a_a > $o,A: a,B: a] :
( ( product_curry_a_a_o @ F2 @ A @ B )
=> ( F2 @ ( product_Pair_a_a @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_curryD) ).
thf(112,axiom,
( irrefl_a
= ( ^ [R: set_Product_prod_a_a] :
! [A6: a] :
~ ( member449909584od_a_a @ ( product_Pair_a_a @ A6 @ A6 ) @ R ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_irrefl__def) ).
thf(116,axiom,
! [R3: set_Product_prod_a_a] :
( ! [A3: a] :
~ ( member449909584od_a_a @ ( product_Pair_a_a @ A3 @ A3 ) @ R3 )
=> ( irrefl_a @ R3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_irreflI) ).
thf(120,axiom,
! [F2: a > a > $o,X1: a,X22: a] :
( ( produc1833107820_a_a_o @ F2 @ ( product_Pair_a_a @ X1 @ X22 ) )
= ( F2 @ X1 @ X22 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_old_Oprod_Ocase) ).
thf(121,axiom,
! [F2: a > a > set_a,X1: a,X22: a] :
( ( produc961951794_set_a @ F2 @ ( product_Pair_a_a @ X1 @ X22 ) )
= ( F2 @ X1 @ X22 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_old_Oprod_Ocase) ).
thf(122,axiom,
! [F2: a > a > set_Product_prod_a_a,X1: a,X22: a] :
( ( produc1093061851od_a_a @ F2 @ ( product_Pair_a_a @ X1 @ X22 ) )
= ( F2 @ X1 @ X22 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_old_Oprod_Ocase) ).
thf(124,axiom,
! [Z: product_prod_a_a,C2: multiset_a > multiset_a > set_Product_prod_a_a,P: produc1127127335iset_a] :
( ( member449909584od_a_a @ Z @ ( produc2041367259od_a_a @ C2 @ P ) )
=> ~ ! [X3: multiset_a,Y3: multiset_a] :
( ( P
= ( produc2037245207iset_a @ X3 @ Y3 ) )
=> ~ ( member449909584od_a_a @ Z @ ( C2 @ X3 @ Y3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_mem__case__prodE) ).
thf(126,axiom,
! [Z: produc1127127335iset_a,C2: a > a > set_Pr158363655iset_a,P: product_prod_a_a] :
( ( member340150864iset_a @ Z @ ( produc93594587iset_a @ C2 @ P ) )
=> ~ ! [X3: a,Y3: a] :
( ( P
= ( product_Pair_a_a @ X3 @ Y3 ) )
=> ~ ( member340150864iset_a @ Z @ ( C2 @ X3 @ Y3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_mem__case__prodE) ).
thf(128,axiom,
! [Z: multis599418605od_a_a,C2: a > a > set_mu1281098573od_a_a,P: product_prod_a_a] :
( ( member1755255446od_a_a @ Z @ ( produc1121147169od_a_a @ C2 @ P ) )
=> ~ ! [X3: a,Y3: a] :
( ( P
= ( product_Pair_a_a @ X3 @ Y3 ) )
=> ~ ( member1755255446od_a_a @ Z @ ( C2 @ X3 @ Y3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_mem__case__prodE) ).
thf(130,axiom,
! [Z: multiset_a,C2: a > a > set_multiset_a,P: product_prod_a_a] :
( ( member_multiset_a @ Z @ ( produc1828150264iset_a @ C2 @ P ) )
=> ~ ! [X3: a,Y3: a] :
( ( P
= ( product_Pair_a_a @ X3 @ Y3 ) )
=> ~ ( member_multiset_a @ Z @ ( C2 @ X3 @ Y3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_mem__case__prodE) ).
thf(131,axiom,
! [Z: product_prod_a_a,C2: a > a > set_Product_prod_a_a,P: product_prod_a_a] :
( ( member449909584od_a_a @ Z @ ( produc1093061851od_a_a @ C2 @ P ) )
=> ~ ! [X3: a,Y3: a] :
( ( P
= ( product_Pair_a_a @ X3 @ Y3 ) )
=> ~ ( member449909584od_a_a @ Z @ ( C2 @ X3 @ Y3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_mem__case__prodE) ).
thf(132,axiom,
! [Z: a,C2: a > a > set_a,P: product_prod_a_a] :
( ( member_a @ Z @ ( produc961951794_set_a @ C2 @ P ) )
=> ~ ! [X3: a,Y3: a] :
( ( P
= ( product_Pair_a_a @ X3 @ Y3 ) )
=> ~ ( member_a @ Z @ ( C2 @ X3 @ Y3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_mem__case__prodE) ).
thf(143,axiom,
! [X: a,Y: a] :
( ( product_swap_a_a @ ( product_Pair_a_a @ X @ Y ) )
= ( product_Pair_a_a @ Y @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_swap__simp) ).
thf(149,axiom,
! [X: multis599418605od_a_a,Y: multis599418605od_a_a,R2: set_Product_prod_a_a,F2: multis599418605od_a_a > a] :
( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ X @ Y ) @ ( inv_im941243329od_a_a @ R2 @ F2 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( F2 @ X ) @ ( F2 @ Y ) ) @ R2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_in__inv__image) ).
thf(152,axiom,
! [X: a,Y: a,R2: set_Pr1821581383od_a_a,F2: a > multis599418605od_a_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ ( inv_im1681759523_a_a_a @ R2 @ F2 ) )
= ( member1349055120od_a_a @ ( produc1859144151od_a_a @ ( F2 @ X ) @ ( F2 @ Y ) ) @ R2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_in__inv__image) ).
thf(154,axiom,
! [X: product_prod_a_a,Y: product_prod_a_a,R2: set_Product_prod_a_a,F2: product_prod_a_a > a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X @ Y ) @ ( inv_im15016955od_a_a @ R2 @ F2 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( F2 @ X ) @ ( F2 @ Y ) ) @ R2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_in__inv__image) ).
thf(155,axiom,
! [X: a,Y: a,R2: set_Pr1948701895od_a_a,F2: a > product_prod_a_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ ( inv_im777352425_a_a_a @ R2 @ F2 ) )
= ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( F2 @ X ) @ ( F2 @ Y ) ) @ R2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_in__inv__image) ).
thf(156,axiom,
! [X: multiset_a,Y: multiset_a,R2: set_Product_prod_a_a,F2: multiset_a > a] :
( ( member340150864iset_a @ ( produc2037245207iset_a @ X @ Y ) @ ( inv_im479034648iset_a @ R2 @ F2 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( F2 @ X ) @ ( F2 @ Y ) ) @ R2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_in__inv__image) ).
thf(157,axiom,
! [X: a,Y: a,R2: set_Pr158363655iset_a,F2: a > multiset_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ ( inv_im975322764et_a_a @ R2 @ F2 ) )
= ( member340150864iset_a @ ( produc2037245207iset_a @ ( F2 @ X ) @ ( F2 @ Y ) ) @ R2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_in__inv__image) ).
thf(158,axiom,
! [X: a,Y: a,R2: set_Product_prod_a_a,F2: a > a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ ( inv_image_a_a @ R2 @ F2 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( F2 @ X ) @ ( F2 @ Y ) ) @ R2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_in__inv__image) ).
thf(159,axiom,
! [F2: product_prod_a_a > $o,A: a,B: a] :
( ( F2 @ ( product_Pair_a_a @ A @ B ) )
=> ( product_curry_a_a_o @ F2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_curryI) ).
thf(163,axiom,
( product_curry_a_a_o
= ( ^ [F: product_prod_a_a > $o,A6: a,B5: a] : ( F @ ( product_Pair_a_a @ A6 @ B5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_curry__conv) ).
thf(164,axiom,
! [Z: a,Y: a,B4: set_a,Pr: set_Product_prod_a_a] :
( ( member_a @ Z @ ( prefer161218362good_a @ Y @ B4 @ Pr ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ Z @ Y ) @ Pr ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_at__least__as__goodD) ).
thf(165,axiom,
! [Z: product_prod_a_a,Y: product_prod_a_a,B4: set_Product_prod_a_a,Pr: set_Pr1948701895od_a_a] :
( ( member449909584od_a_a @ Z @ ( prefer477097315od_a_a @ Y @ B4 @ Pr ) )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ Z @ Y ) @ Pr ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_at__least__as__goodD) ).
thf(171,axiom,
! [X: a,Y: a,B4: set_a,Pr: set_Product_prod_a_a] :
( ( member_a @ X @ ( prefer161218362good_a @ Y @ B4 @ Pr ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ Pr ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_at__lst__asgd__ge) ).
thf(172,axiom,
! [X: product_prod_a_a,Y: product_prod_a_a,B4: set_Product_prod_a_a,Pr: set_Pr1948701895od_a_a] :
( ( member449909584od_a_a @ X @ ( prefer477097315od_a_a @ Y @ B4 @ Pr ) )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X @ Y ) @ Pr ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_at__lst__asgd__ge) ).
thf(178,axiom,
! [R2: a,S: a,R3: set_Product_prod_a_a,S2: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ R2 @ S ) @ R3 )
=> ( ( S2 = S )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ R2 @ S2 ) @ R3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_ssubst__Pair__rhs) ).
thf(192,axiom,
! [R2: set_Product_prod_a_a,X: a,Y: a,Z: a] :
( ( trans_a @ R2 )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ R2 )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ Z ) @ R2 )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Z ) @ R2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_transE) ).
thf(196,axiom,
! [R2: set_Product_prod_a_a,X: a,Y: a,Z: a] :
( ( trans_a @ R2 )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ R2 )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ Z ) @ R2 )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Z ) @ R2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_transD) ).
thf(200,axiom,
! [R2: set_Product_prod_a_a] :
( ! [X3: a,Y3: a,Z3: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R2 )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y3 @ Z3 ) @ R2 )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Z3 ) @ R2 ) ) )
=> ( trans_a @ R2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_transI) ).
thf(204,axiom,
( trans_a
= ( ^ [R: set_Product_prod_a_a] :
! [X4: a,Y4: a,Z2: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ R )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y4 @ Z2 ) @ R )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Z2 ) @ R ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_trans__def) ).
thf(208,axiom,
! [A5: set_a,R2: set_Product_prod_a_a,A: a] :
( ( refl_on_a @ A5 @ R2 )
=> ( ( member_a @ A @ A5 )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ A ) @ R2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_refl__onD) ).
thf(209,axiom,
! [A5: set_Product_prod_a_a,R2: set_Pr1948701895od_a_a,A: product_prod_a_a] :
( ( refl_o1298442278od_a_a @ A5 @ R2 )
=> ( ( member449909584od_a_a @ A @ A5 )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ A ) @ R2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_refl__onD) ).
thf(215,axiom,
! [A5: set_a,R2: set_Product_prod_a_a,X: a,Y: a] :
( ( refl_on_a @ A5 @ R2 )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ R2 )
=> ( member_a @ X @ A5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_refl__onD1) ).
thf(216,axiom,
! [A5: set_Product_prod_a_a,R2: set_Pr1948701895od_a_a,X: product_prod_a_a,Y: product_prod_a_a] :
( ( refl_o1298442278od_a_a @ A5 @ R2 )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X @ Y ) @ R2 )
=> ( member449909584od_a_a @ X @ A5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_refl__onD1) ).
thf(222,axiom,
! [A5: set_a,R2: set_Product_prod_a_a,X: a,Y: a] :
( ( refl_on_a @ A5 @ R2 )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ R2 )
=> ( member_a @ Y @ A5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_refl__onD2) ).
thf(223,axiom,
! [A5: set_Product_prod_a_a,R2: set_Pr1948701895od_a_a,X: product_prod_a_a,Y: product_prod_a_a] :
( ( refl_o1298442278od_a_a @ A5 @ R2 )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X @ Y ) @ R2 )
=> ( member449909584od_a_a @ Y @ A5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_refl__onD2) ).
thf(231,axiom,
! [A5: set_Product_prod_a_a] :
( ( collec645855634od_a_a
@ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ A5 ) )
= A5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_Collect__mem__eq) ).
thf(238,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/sandbox2/benchmark/theBenchmark.p',fact_117_mem__Collect__eq) ).
thf(245,axiom,
! [A5: set_a,R2: set_Product_prod_a_a,A: a,B: a] :
( ( refl_on_a @ A5 @ R2 )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ R2 )
=> ( ( member_a @ A @ A5 )
& ( member_a @ B @ A5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_refl__on__domain) ).
thf(246,axiom,
! [A5: set_Product_prod_a_a,R2: set_Pr1948701895od_a_a,A: product_prod_a_a,B: product_prod_a_a] :
( ( refl_o1298442278od_a_a @ A5 @ R2 )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B ) @ R2 )
=> ( ( member449909584od_a_a @ A @ A5 )
& ( member449909584od_a_a @ B @ A5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_refl__on__domain) ).
thf(252,axiom,
! [A5: set_a,R2: set_Product_prod_a_a] :
( ! [X3: a,Y3: a] :
( ( member_a @ X3 @ A5 )
=> ( ( member_a @ Y3 @ A5 )
=> ( ( X3 != Y3 )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R2 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ Y3 @ X3 ) @ R2 ) ) ) ) )
=> ( total_on_a @ A5 @ R2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_total__onI) ).
thf(253,axiom,
! [A5: set_Product_prod_a_a,R2: set_Pr1948701895od_a_a] :
( ! [X3: product_prod_a_a,Y3: product_prod_a_a] :
( ( member449909584od_a_a @ X3 @ A5 )
=> ( ( member449909584od_a_a @ Y3 @ A5 )
=> ( ( X3 != Y3 )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X3 @ Y3 ) @ R2 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ Y3 @ X3 ) @ R2 ) ) ) ) )
=> ( total_1490170027od_a_a @ A5 @ R2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_total__onI) ).
thf(259,axiom,
( total_on_a
= ( ^ [A4: set_a,R: set_Product_prod_a_a] :
! [X4: a] :
( ( member_a @ X4 @ A4 )
=> ! [Y4: a] :
( ( member_a @ Y4 @ A4 )
=> ( ( X4 != Y4 )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ R )
| ( member449909584od_a_a @ ( product_Pair_a_a @ Y4 @ X4 ) @ R ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_total__on__def) ).
thf(260,axiom,
( total_1490170027od_a_a
= ( ^ [A4: set_Product_prod_a_a,R: set_Pr1948701895od_a_a] :
! [X4: product_prod_a_a] :
( ( member449909584od_a_a @ X4 @ A4 )
=> ! [Y4: product_prod_a_a] :
( ( member449909584od_a_a @ Y4 @ A4 )
=> ( ( X4 != Y4 )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X4 @ Y4 ) @ R )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ Y4 @ X4 ) @ R ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_total__on__def) ).
thf(265,axiom,
! [P2: produc1572603623od_a_a > $o,X: produc1572603623od_a_a] :
( ! [A3: product_prod_a_a,B3: a,C: a] : ( P2 @ ( produc1474507607od_a_a @ A3 @ ( product_Pair_a_a @ B3 @ C ) ) )
=> ( P2 @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_prod__induct3) ).
thf(266,axiom,
! [Y: product_prod_a_a] :
~ ! [A3: a,B3: a] :
( Y
!= ( product_Pair_a_a @ A3 @ B3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_old_Oprod_Oexhaust) ).
thf(270,axiom,
! [P2: product_prod_a_a > $o,Prod: product_prod_a_a] :
( ! [A3: a,B3: a] : ( P2 @ ( product_Pair_a_a @ A3 @ B3 ) )
=> ( P2 @ Prod ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_old_Oprod_Oinducts) ).
thf(274,axiom,
! [Carrier: set_a,Relation: set_Product_prod_a_a] :
( ( prefer719835986ence_a @ Carrier @ Relation )
=> ! [X2: a] :
( ( member_a @ X2 @ Carrier )
=> ! [Xa: a] :
( ( member_a @ Xa @ Carrier )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X2 @ Xa ) @ Relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ Xa @ X2 ) @ Relation ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_rational__preference_Ocompl) ).
thf(275,axiom,
! [Carrier: set_Product_prod_a_a,Relation: set_Pr1948701895od_a_a] :
( ( prefer697821563od_a_a @ Carrier @ Relation )
=> ! [X2: product_prod_a_a] :
( ( member449909584od_a_a @ X2 @ Carrier )
=> ! [Xa: product_prod_a_a] :
( ( member449909584od_a_a @ Xa @ Carrier )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X2 @ Xa ) @ Relation )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ Xa @ X2 ) @ Relation ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_rational__preference_Ocompl) ).
thf(278,axiom,
! [Carrier: set_a,Relation: set_Product_prod_a_a,X: a,Y: a,Z: a] :
( ( prefer719835986ence_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/sandbox2/benchmark/theBenchmark.p',fact_77_rational__preference_Ostrict__trans) ).
thf(282,axiom,
! [Carrier: set_a,Relation: set_Product_prod_a_a,X: a,Y: a] :
( ( prefer719835986ence_a @ Carrier @ Relation )
=> ( ( ( member_a @ X @ Carrier )
& ( member_a @ Y @ Carrier ) )
=> ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ Relation ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ Relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ Relation ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_rational__preference_Ostrict__not__refl__weak) ).
thf(283,axiom,
! [Carrier: set_Product_prod_a_a,Relation: set_Pr1948701895od_a_a,X: product_prod_a_a,Y: product_prod_a_a] :
( ( prefer697821563od_a_a @ Carrier @ Relation )
=> ( ( ( member449909584od_a_a @ X @ Carrier )
& ( member449909584od_a_a @ Y @ Carrier ) )
=> ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ Y @ X ) @ Relation ) )
= ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X @ Y ) @ Relation )
& ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ Y @ X ) @ Relation ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_rational__preference_Ostrict__not__refl__weak) ).
thf(289,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/sandbox2/benchmark/theBenchmark.p',fact_66_preference_Onot__outside) ).
thf(290,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/sandbox2/benchmark/theBenchmark.p',fact_65_preference_Onot__outside) ).
thf(296,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/sandbox2/benchmark/theBenchmark.p',fact_59_preference_Oindiff__trans) ).
thf(300,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/sandbox2/benchmark/theBenchmark.p',fact_55_preference__def) ).
thf(307,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/sandbox2/benchmark/theBenchmark.p',fact_48_preference_Ointro) ).
thf(324,axiom,
! [Y: produc1572603623od_a_a] :
~ ! [A3: product_prod_a_a,B3: a,C: a] :
( Y
!= ( produc1474507607od_a_a @ A3 @ ( product_Pair_a_a @ B3 @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_prod__cases3) ).
thf(325,axiom,
! [A: a,B: a,A2: a,B2: a] :
( ( ( product_Pair_a_a @ A @ B )
= ( product_Pair_a_a @ A2 @ B2 ) )
=> ~ ( ( A = A2 )
=> ( B != B2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_Pair__inject) ).
thf(329,axiom,
! [P2: product_prod_a_a > $o,P: product_prod_a_a] :
( ! [A3: a,B3: a] : ( P2 @ ( product_Pair_a_a @ A3 @ B3 ) )
=> ( P2 @ P ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_prod__cases) ).
thf(333,axiom,
! [P: product_prod_a_a] :
? [X3: a,Y3: a] :
( P
= ( product_Pair_a_a @ X3 @ Y3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_surj__pair) ).
thf(337,axiom,
trans_a @ relation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_transitivity) ).
thf(338,axiom,
! [A: a,B: a,A2: a,B2: a] :
( ( ( product_Pair_a_a @ A @ B )
= ( product_Pair_a_a @ A2 @ B2 ) )
= ( ( A = A2 )
& ( B = B2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_old_Oprod_Oinject) ).
thf(342,axiom,
! [X1: a,X22: a,Y1: a,Y2: a] :
( ( ( product_Pair_a_a @ X1 @ X22 )
= ( product_Pair_a_a @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X22 = Y2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_prod_Oinject) ).
thf(346,axiom,
refl_on_a @ carrier @ relation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_reflexivity) ).
thf(347,axiom,
total_on_a @ carrier @ relation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_total) ).
thf(348,axiom,
order_preorder_on_a @ carrier @ relation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_trans__refl) ).
thf(349,axiom,
prefer1292084992ence_a @ carrier @ relation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_preference__axioms) ).
thf(350,axiom,
! [X: a,Y: a] :
( ( ( member_a @ X @ carrier )
& ( member_a @ Y @ carrier ) )
=> ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ relation ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ relation ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_strict__not__refl__weak) ).
thf(351,axiom,
! [X: a,Y: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
=> ( member_a @ X @ carrier ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_not__outside) ).
thf(352,axiom,
! [X2: a] :
( ( member_a @ X2 @ carrier )
=> ! [Xa: a] :
( ( member_a @ Xa @ carrier )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X2 @ Xa ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ Xa @ X2 ) @ relation ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_compl) ).
thf(353,axiom,
prefer719835986ence_a @ carrier @ relation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_rational__preference__axioms) ).
thf(354,axiom,
! [X: a,Y: a,Z: a] :
( ( ( 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/sandbox2/benchmark/theBenchmark.p',fact_1_strict__trans) ).
thf(355,axiom,
! [X: a,Y: a,Z: a] :
( ( ( 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/sandbox2/benchmark/theBenchmark.p',fact_0_indiff__trans) ).
thf(356,axiom,
x != y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
thf(357,axiom,
member_a @ y @ carrier,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(358,axiom,
member_a @ x @ carrier,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(359,conjecture,
( ( member449909584od_a_a @ ( product_Pair_a_a @ x @ y ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ y @ x ) @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).
thf(360,negated_conjecture,
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ x @ y ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ y @ x ) @ relation ) )
= $false ),
inference(negate_conjecture,[status(cth)],[359]) ).
thf(361,plain,
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ x @ y ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ y @ x ) @ relation ) )
= $false ),
inference(unfold_def,[status(thm)],[360]) ).
thf(362,plain,
( ( ! [A: product_prod_a_a,M: multis599418605od_a_a,N: multis599418605od_a_a] :
( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ ( minus_1257885652od_a_a @ M @ N ) ) )
=> ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(363,plain,
( ( ! [B: product_prod_a_a,A5: multis599418605od_a_a,M: multis599418605od_a_a] :
( ~ ( member449909584od_a_a @ B @ ( set_ms1818337124od_a_a @ A5 ) )
=> ( ( minus_1257885652od_a_a @ ( add_ms1725977093od_a_a @ B @ M ) @ A5 )
= ( add_ms1725977093od_a_a @ B @ ( minus_1257885652od_a_a @ M @ A5 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(364,plain,
( ( ! [X: product_prod_a_a] : ( member449909584od_a_a @ X @ ( set_ms1818337124od_a_a @ ( add_ms1725977093od_a_a @ X @ zero_z160849828od_a_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(365,plain,
( ( ! [A5: multis599418605od_a_a] :
( ( A5 != zero_z160849828od_a_a )
=> ~ ! [X3: product_prod_a_a] :
~ ( member449909584od_a_a @ X3 @ ( set_ms1818337124od_a_a @ A5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(366,plain,
( ( ! [A: product_prod_a_a,A5: multis599418605od_a_a,B4: multis599418605od_a_a] :
( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ ( plus_p404985124od_a_a @ A5 @ B4 ) ) )
= ( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ A5 ) )
| ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ B4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(367,plain,
( ( ! [X: product_prod_a_a,M: multis599418605od_a_a,N: multis599418605od_a_a] :
( ( ( add_ms1725977093od_a_a @ X @ M )
= N )
=> ( member449909584od_a_a @ X @ ( set_ms1818337124od_a_a @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(368,plain,
( ( ! [B: product_prod_a_a,B4: multis599418605od_a_a,C2: product_prod_a_a,C3: multis599418605od_a_a] :
( ( ( add_ms1725977093od_a_a @ B @ B4 )
= ( add_ms1725977093od_a_a @ C2 @ C3 ) )
=> ( ( B != C2 )
=> ( member449909584od_a_a @ C2 @ ( set_ms1818337124od_a_a @ B4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(369,plain,
( ( ! [X: product_prod_a_a,M: multis599418605od_a_a] :
( ( member449909584od_a_a @ X @ ( set_ms1818337124od_a_a @ M ) )
=> ? [A8: multis599418605od_a_a] :
( M
= ( add_ms1725977093od_a_a @ X @ A8 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(370,plain,
( ( ! [A: product_prod_a_a,A5: multis599418605od_a_a] :
( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ A5 ) )
=> ~ ! [B7: multis599418605od_a_a] :
( A5
!= ( add_ms1725977093od_a_a @ A @ B7 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(371,plain,
( ( ! [P2: a > $o,X: a,Y6: a,Y: a,R3: a > set_Product_prod_a_a] :
( ( P2 @ X )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y6 @ Y ) @ ( R3 @ X ) )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ X @ Y6 ) @ ( product_Pair_a_a @ X @ Y ) ) @ ( same_fst_a_a @ P2 @ R3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(372,plain,
( ( ! [A5: set_Product_prod_a_a,F2: product_prod_a_a > product_prod_a_a,B4: set_Product_prod_a_a] :
( ! [X3: product_prod_a_a] :
( ( member449909584od_a_a @ X3 @ A5 )
=> ( member449909584od_a_a @ ( F2 @ X3 ) @ B4 ) )
=> ( ord_le1824328871od_a_a @ ( image_794773445od_a_a @ F2 @ A5 ) @ B4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(373,plain,
( ( ! [A5: set_Product_prod_a_a,F2: product_prod_a_a > a,B4: set_a] :
( ! [X3: product_prod_a_a] :
( ( member449909584od_a_a @ X3 @ A5 )
=> ( member_a @ ( F2 @ X3 ) @ B4 ) )
=> ( ord_less_eq_set_a @ ( image_340790172_a_a_a @ F2 @ A5 ) @ B4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(374,plain,
( ( ! [A5: set_a,F2: a > product_prod_a_a,B4: set_Product_prod_a_a] :
( ! [X3: a] :
( ( member_a @ X3 @ A5 )
=> ( member449909584od_a_a @ ( F2 @ X3 ) @ B4 ) )
=> ( ord_le1824328871od_a_a @ ( image_1725938350od_a_a @ F2 @ A5 ) @ B4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(375,plain,
( ( ! [R2: set_Product_prod_a_a,S: set_Product_prod_a_a] :
( ! [X3: a,Y3: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R2 )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ S ) )
=> ( ord_le1824328871od_a_a @ R2 @ S ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(376,plain,
( ( ! [A: a,P: product_prod_a_a] :
( ( A
= ( product_fst_a_a @ P ) )
= ( ? [B5: a] :
( P
= ( product_Pair_a_a @ A @ B5 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(377,plain,
( ( ! [B: a,P: product_prod_a_a] :
( ( B
= ( product_snd_a_a @ P ) )
= ( ? [A6: a] :
( P
= ( product_Pair_a_a @ A6 @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(378,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)],[63]) ).
thf(379,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)],[64]) ).
thf(380,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)],[65]) ).
thf(381,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)],[66]) ).
thf(382,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)],[67]) ).
thf(383,plain,
( ( ! [C2: product_prod_a_a,F2: a > a,G: a > a,R3: set_Product_prod_a_a] :
( ( member449909584od_a_a @ C2 @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ F2 @ G ) @ R3 ) )
=> ~ ! [X3: a,Y3: a] :
( ( C2
= ( product_Pair_a_a @ ( F2 @ X3 ) @ ( G @ Y3 ) ) )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(384,plain,
( ( product_swap_a_a
= ( ^ [P3: product_prod_a_a] : ( product_Pair_a_a @ ( product_snd_a_a @ P3 ) @ ( product_fst_a_a @ P3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(385,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)],[70]) ).
thf(386,plain,
( ( ! [X1: a,X22: a] :
( ( product_snd_a_a @ ( product_Pair_a_a @ X1 @ X22 ) )
= X22 ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(387,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)],[72]) ).
thf(388,plain,
( ( ! [X1: a,X22: a] :
( ( product_fst_a_a @ ( product_Pair_a_a @ X1 @ X22 ) )
= X1 ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(389,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)],[74]) ).
thf(390,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)],[75]) ).
thf(391,plain,
( ( ! [A: a,B: a,R3: set_Product_prod_a_a,F2: a > a,G: a > a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ R3 )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ ( F2 @ A ) @ ( G @ B ) ) @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ F2 @ G ) @ R3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(392,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)],[78]) ).
thf(393,plain,
( ( ! [A: a,B: a,A2: a,B2: a,R2: set_Product_prod_a_a,S: set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ A @ B ) @ ( product_Pair_a_a @ A2 @ B2 ) ) @ ( lex_prod_a_a @ R2 @ S ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ A2 ) @ R2 )
| ( ( A = A2 )
& ( member449909584od_a_a @ ( product_Pair_a_a @ B @ B2 ) @ S ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(394,plain,
( ( ! [F2: a > a,G: a > a,A: a,B: a] :
( ( produc700022774_a_a_a @ F2 @ G @ ( product_Pair_a_a @ A @ B ) )
= ( product_Pair_a_a @ ( F2 @ A ) @ ( G @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(395,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)],[83]) ).
thf(396,plain,
( ( ! [X: product_prod_a_a,A5: set_Product_prod_a_a,B: product_prod_a_a,F2: product_prod_a_a > product_prod_a_a] :
( ( member449909584od_a_a @ X @ A5 )
=> ( ( B
= ( F2 @ X ) )
=> ( member449909584od_a_a @ B @ ( image_794773445od_a_a @ F2 @ A5 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(397,plain,
( ( ! [X: product_prod_a_a,A5: set_Product_prod_a_a,B: a,F2: product_prod_a_a > a] :
( ( member449909584od_a_a @ X @ A5 )
=> ( ( B
= ( F2 @ X ) )
=> ( member_a @ B @ ( image_340790172_a_a_a @ F2 @ A5 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(398,plain,
( ( ! [X: a,A5: set_a,B: product_prod_a_a,F2: a > product_prod_a_a] :
( ( member_a @ X @ A5 )
=> ( ( B
= ( F2 @ X ) )
=> ( member449909584od_a_a @ B @ ( image_1725938350od_a_a @ F2 @ A5 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(399,plain,
( ( ! [X: product_prod_a_a,A5: set_Product_prod_a_a,F2: product_prod_a_a > product_prod_a_a] :
( ( member449909584od_a_a @ X @ A5 )
=> ( member449909584od_a_a @ ( F2 @ X ) @ ( image_794773445od_a_a @ F2 @ A5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(400,plain,
( ( ! [X: product_prod_a_a,A5: set_Product_prod_a_a,F2: product_prod_a_a > a] :
( ( member449909584od_a_a @ X @ A5 )
=> ( member_a @ ( F2 @ X ) @ ( image_340790172_a_a_a @ F2 @ A5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(401,plain,
( ( ! [X: a,A5: set_a,F2: a > product_prod_a_a] :
( ( member_a @ X @ A5 )
=> ( member449909584od_a_a @ ( F2 @ X ) @ ( image_1725938350od_a_a @ F2 @ A5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(402,plain,
( ( ! [B: product_prod_a_a,F2: product_prod_a_a > product_prod_a_a,X: product_prod_a_a,A5: set_Product_prod_a_a] :
( ( B
= ( F2 @ X ) )
=> ( ( member449909584od_a_a @ X @ A5 )
=> ( member449909584od_a_a @ B @ ( image_794773445od_a_a @ F2 @ A5 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(403,plain,
( ( ! [B: a,F2: product_prod_a_a > a,X: product_prod_a_a,A5: set_Product_prod_a_a] :
( ( B
= ( F2 @ X ) )
=> ( ( member449909584od_a_a @ X @ A5 )
=> ( member_a @ B @ ( image_340790172_a_a_a @ F2 @ A5 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(404,plain,
( ( ! [B: product_prod_a_a,F2: a > product_prod_a_a,X: a,A5: set_a] :
( ( B
= ( F2 @ X ) )
=> ( ( member_a @ X @ A5 )
=> ( member449909584od_a_a @ B @ ( image_1725938350od_a_a @ F2 @ A5 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(405,plain,
( ( ! [R3: set_Product_prod_a_a,X: a,Y: a] :
( ( asym_a @ R3 )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ R3 )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ R3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(406,plain,
( ( asym_a
= ( ^ [R5: set_Product_prod_a_a] :
! [X4: a,Y4: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ R5 )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y4 @ X4 ) @ R5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(407,plain,
( ( ! [A: set_Product_prod_a_a] :
( ( asym_a @ A )
=> ! [A7: a,B6: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A7 @ B6 ) @ A )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B6 @ A7 ) @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(408,plain,
( ( asym_a
= ( ^ [A6: set_Product_prod_a_a] :
? [R5: set_Product_prod_a_a] :
( ( A6 = R5 )
& ! [X4: a,Y4: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ R5 )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y4 @ X4 ) @ R5 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(409,plain,
( ( ! [R3: set_Product_prod_a_a] :
( ! [A3: a,B3: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A3 @ B3 ) @ R3 )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B3 @ A3 ) @ R3 ) )
=> ( asym_a @ R3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(410,plain,
( ( ! [X: set_Product_prod_a_a,P2: set_Product_prod_a_a > $o] :
( ( asym_a @ X )
=> ( ! [R4: set_Product_prod_a_a] :
( ! [A7: a,B6: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A7 @ B6 ) @ R4 )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B6 @ A7 ) @ R4 ) )
=> ( P2 @ R4 ) )
=> ( P2 @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(411,plain,
( ( ! [Y: a,X: a,A5: set_Product_prod_a_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ ( image_794773445od_a_a @ product_swap_a_a @ A5 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ A5 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(412,plain,
( ( ! [F2: product_prod_a_a > $o,A: a,B: a] :
( ( product_curry_a_a_o @ F2 @ A @ B )
=> ( F2 @ ( product_Pair_a_a @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(413,plain,
( ( ! [F2: product_prod_a_a > $o,A: a,B: a] :
( ( product_curry_a_a_o @ F2 @ A @ B )
=> ( F2 @ ( product_Pair_a_a @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(414,plain,
( ( irrefl_a
= ( ^ [R: set_Product_prod_a_a] :
! [A6: a] :
~ ( member449909584od_a_a @ ( product_Pair_a_a @ A6 @ A6 ) @ R ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(415,plain,
( ( ! [R3: set_Product_prod_a_a] :
( ! [A3: a] :
~ ( member449909584od_a_a @ ( product_Pair_a_a @ A3 @ A3 ) @ R3 )
=> ( irrefl_a @ R3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(416,plain,
( ( ! [F2: a > a > $o,X1: a,X22: a] :
( ( produc1833107820_a_a_o @ F2 @ ( product_Pair_a_a @ X1 @ X22 ) )
= ( F2 @ X1 @ X22 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(417,plain,
( ( ! [F2: a > a > set_a,X1: a,X22: a] :
( ( produc961951794_set_a @ F2 @ ( product_Pair_a_a @ X1 @ X22 ) )
= ( F2 @ X1 @ X22 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(418,plain,
( ( ! [F2: a > a > set_Product_prod_a_a,X1: a,X22: a] :
( ( produc1093061851od_a_a @ F2 @ ( product_Pair_a_a @ X1 @ X22 ) )
= ( F2 @ X1 @ X22 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(419,plain,
( ( ! [Z: product_prod_a_a,C2: multiset_a > multiset_a > set_Product_prod_a_a,P: produc1127127335iset_a] :
( ( member449909584od_a_a @ Z @ ( produc2041367259od_a_a @ C2 @ P ) )
=> ~ ! [X3: multiset_a,Y3: multiset_a] :
( ( P
= ( produc2037245207iset_a @ X3 @ Y3 ) )
=> ~ ( member449909584od_a_a @ Z @ ( C2 @ X3 @ Y3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(420,plain,
( ( ! [Z: produc1127127335iset_a,C2: a > a > set_Pr158363655iset_a,P: product_prod_a_a] :
( ( member340150864iset_a @ Z @ ( produc93594587iset_a @ C2 @ P ) )
=> ~ ! [X3: a,Y3: a] :
( ( P
= ( product_Pair_a_a @ X3 @ Y3 ) )
=> ~ ( member340150864iset_a @ Z @ ( C2 @ X3 @ Y3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(421,plain,
( ( ! [Z: multis599418605od_a_a,C2: a > a > set_mu1281098573od_a_a,P: product_prod_a_a] :
( ( member1755255446od_a_a @ Z @ ( produc1121147169od_a_a @ C2 @ P ) )
=> ~ ! [X3: a,Y3: a] :
( ( P
= ( product_Pair_a_a @ X3 @ Y3 ) )
=> ~ ( member1755255446od_a_a @ Z @ ( C2 @ X3 @ Y3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(422,plain,
( ( ! [Z: multiset_a,C2: a > a > set_multiset_a,P: product_prod_a_a] :
( ( member_multiset_a @ Z @ ( produc1828150264iset_a @ C2 @ P ) )
=> ~ ! [X3: a,Y3: a] :
( ( P
= ( product_Pair_a_a @ X3 @ Y3 ) )
=> ~ ( member_multiset_a @ Z @ ( C2 @ X3 @ Y3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(423,plain,
( ( ! [Z: product_prod_a_a,C2: a > a > set_Product_prod_a_a,P: product_prod_a_a] :
( ( member449909584od_a_a @ Z @ ( produc1093061851od_a_a @ C2 @ P ) )
=> ~ ! [X3: a,Y3: a] :
( ( P
= ( product_Pair_a_a @ X3 @ Y3 ) )
=> ~ ( member449909584od_a_a @ Z @ ( C2 @ X3 @ Y3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(424,plain,
( ( ! [Z: a,C2: a > a > set_a,P: product_prod_a_a] :
( ( member_a @ Z @ ( produc961951794_set_a @ C2 @ P ) )
=> ~ ! [X3: a,Y3: a] :
( ( P
= ( product_Pair_a_a @ X3 @ Y3 ) )
=> ~ ( member_a @ Z @ ( C2 @ X3 @ Y3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(425,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)],[143]) ).
thf(426,plain,
( ( ! [X: multis599418605od_a_a,Y: multis599418605od_a_a,R2: set_Product_prod_a_a,F2: multis599418605od_a_a > a] :
( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ X @ Y ) @ ( inv_im941243329od_a_a @ R2 @ F2 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( F2 @ X ) @ ( F2 @ Y ) ) @ R2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(427,plain,
( ( ! [X: a,Y: a,R2: set_Pr1821581383od_a_a,F2: a > multis599418605od_a_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ ( inv_im1681759523_a_a_a @ R2 @ F2 ) )
= ( member1349055120od_a_a @ ( produc1859144151od_a_a @ ( F2 @ X ) @ ( F2 @ Y ) ) @ R2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(428,plain,
( ( ! [X: product_prod_a_a,Y: product_prod_a_a,R2: set_Product_prod_a_a,F2: product_prod_a_a > a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X @ Y ) @ ( inv_im15016955od_a_a @ R2 @ F2 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( F2 @ X ) @ ( F2 @ Y ) ) @ R2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(429,plain,
( ( ! [X: a,Y: a,R2: set_Pr1948701895od_a_a,F2: a > product_prod_a_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ ( inv_im777352425_a_a_a @ R2 @ F2 ) )
= ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( F2 @ X ) @ ( F2 @ Y ) ) @ R2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(430,plain,
( ( ! [X: multiset_a,Y: multiset_a,R2: set_Product_prod_a_a,F2: multiset_a > a] :
( ( member340150864iset_a @ ( produc2037245207iset_a @ X @ Y ) @ ( inv_im479034648iset_a @ R2 @ F2 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( F2 @ X ) @ ( F2 @ Y ) ) @ R2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(431,plain,
( ( ! [X: a,Y: a,R2: set_Pr158363655iset_a,F2: a > multiset_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ ( inv_im975322764et_a_a @ R2 @ F2 ) )
= ( member340150864iset_a @ ( produc2037245207iset_a @ ( F2 @ X ) @ ( F2 @ Y ) ) @ R2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(432,plain,
( ( ! [X: a,Y: a,R2: set_Product_prod_a_a,F2: a > a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ ( inv_image_a_a @ R2 @ F2 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( F2 @ X ) @ ( F2 @ Y ) ) @ R2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(433,plain,
( ( ! [F2: product_prod_a_a > $o,A: a,B: a] :
( ( F2 @ ( product_Pair_a_a @ A @ B ) )
=> ( product_curry_a_a_o @ F2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(434,plain,
( ( product_curry_a_a_o
= ( ^ [F: product_prod_a_a > $o,A6: a,B5: a] : ( F @ ( product_Pair_a_a @ A6 @ B5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(435,plain,
( ( ! [Z: a,Y: a,B4: set_a,Pr: set_Product_prod_a_a] :
( ( member_a @ Z @ ( prefer161218362good_a @ Y @ B4 @ Pr ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ Z @ Y ) @ Pr ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(436,plain,
( ( ! [Z: product_prod_a_a,Y: product_prod_a_a,B4: set_Product_prod_a_a,Pr: set_Pr1948701895od_a_a] :
( ( member449909584od_a_a @ Z @ ( prefer477097315od_a_a @ Y @ B4 @ Pr ) )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ Z @ Y ) @ Pr ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(437,plain,
( ( ! [X: a,Y: a,B4: set_a,Pr: set_Product_prod_a_a] :
( ( member_a @ X @ ( prefer161218362good_a @ Y @ B4 @ Pr ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ Pr ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(438,plain,
( ( ! [X: product_prod_a_a,Y: product_prod_a_a,B4: set_Product_prod_a_a,Pr: set_Pr1948701895od_a_a] :
( ( member449909584od_a_a @ X @ ( prefer477097315od_a_a @ Y @ B4 @ Pr ) )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X @ Y ) @ Pr ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(439,plain,
( ( ! [R2: a,S: a,R3: set_Product_prod_a_a,S2: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ R2 @ S ) @ R3 )
=> ( ( S2 = S )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ R2 @ S2 ) @ R3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(440,plain,
( ( ! [R2: set_Product_prod_a_a,X: a,Y: a,Z: a] :
( ( trans_a @ R2 )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ R2 )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ Z ) @ R2 )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Z ) @ R2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(441,plain,
( ( ! [R2: set_Product_prod_a_a,X: a,Y: a,Z: a] :
( ( trans_a @ R2 )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ R2 )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ Z ) @ R2 )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Z ) @ R2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[196]) ).
thf(442,plain,
( ( ! [R2: set_Product_prod_a_a] :
( ! [X3: a,Y3: a,Z3: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R2 )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y3 @ Z3 ) @ R2 )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Z3 ) @ R2 ) ) )
=> ( trans_a @ R2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[200]) ).
thf(443,plain,
( ( trans_a
= ( ^ [R: set_Product_prod_a_a] :
! [X4: a,Y4: a,Z2: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ R )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y4 @ Z2 ) @ R )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Z2 ) @ R ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[204]) ).
thf(444,plain,
( ( ! [A5: set_a,R2: set_Product_prod_a_a,A: a] :
( ( refl_on_a @ A5 @ R2 )
=> ( ( member_a @ A @ A5 )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ A ) @ R2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[208]) ).
thf(445,plain,
( ( ! [A5: set_Product_prod_a_a,R2: set_Pr1948701895od_a_a,A: product_prod_a_a] :
( ( refl_o1298442278od_a_a @ A5 @ R2 )
=> ( ( member449909584od_a_a @ A @ A5 )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ A ) @ R2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(446,plain,
( ( ! [A5: set_a,R2: set_Product_prod_a_a,X: a,Y: a] :
( ( refl_on_a @ A5 @ R2 )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ R2 )
=> ( member_a @ X @ A5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[215]) ).
thf(447,plain,
( ( ! [A5: set_Product_prod_a_a,R2: set_Pr1948701895od_a_a,X: product_prod_a_a,Y: product_prod_a_a] :
( ( refl_o1298442278od_a_a @ A5 @ R2 )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X @ Y ) @ R2 )
=> ( member449909584od_a_a @ X @ A5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[216]) ).
thf(448,plain,
( ( ! [A5: set_a,R2: set_Product_prod_a_a,X: a,Y: a] :
( ( refl_on_a @ A5 @ R2 )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ R2 )
=> ( member_a @ Y @ A5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(449,plain,
( ( ! [A5: set_Product_prod_a_a,R2: set_Pr1948701895od_a_a,X: product_prod_a_a,Y: product_prod_a_a] :
( ( refl_o1298442278od_a_a @ A5 @ R2 )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X @ Y ) @ R2 )
=> ( member449909584od_a_a @ Y @ A5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[223]) ).
thf(450,plain,
( ( ! [A5: set_Product_prod_a_a] :
( ( collec645855634od_a_a
@ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ A5 ) )
= A5 ) )
= $true ),
inference(unfold_def,[status(thm)],[231]) ).
thf(451,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)],[238]) ).
thf(452,plain,
( ( ! [A5: set_a,R2: set_Product_prod_a_a,A: a,B: a] :
( ( refl_on_a @ A5 @ R2 )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ R2 )
=> ( ( member_a @ A @ A5 )
& ( member_a @ B @ A5 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[245]) ).
thf(453,plain,
( ( ! [A5: set_Product_prod_a_a,R2: set_Pr1948701895od_a_a,A: product_prod_a_a,B: product_prod_a_a] :
( ( refl_o1298442278od_a_a @ A5 @ R2 )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B ) @ R2 )
=> ( ( member449909584od_a_a @ A @ A5 )
& ( member449909584od_a_a @ B @ A5 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[246]) ).
thf(454,plain,
( ( ! [A5: set_a,R2: set_Product_prod_a_a] :
( ! [X3: a,Y3: a] :
( ( member_a @ X3 @ A5 )
=> ( ( member_a @ Y3 @ A5 )
=> ( ( X3 != Y3 )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R2 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ Y3 @ X3 ) @ R2 ) ) ) ) )
=> ( total_on_a @ A5 @ R2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[252]) ).
thf(455,plain,
( ( ! [A5: set_Product_prod_a_a,R2: set_Pr1948701895od_a_a] :
( ! [X3: product_prod_a_a,Y3: product_prod_a_a] :
( ( member449909584od_a_a @ X3 @ A5 )
=> ( ( member449909584od_a_a @ Y3 @ A5 )
=> ( ( X3 != Y3 )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X3 @ Y3 ) @ R2 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ Y3 @ X3 ) @ R2 ) ) ) ) )
=> ( total_1490170027od_a_a @ A5 @ R2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253]) ).
thf(456,plain,
( ( total_on_a
= ( ^ [A4: set_a,R: set_Product_prod_a_a] :
! [X4: a] :
( ( member_a @ X4 @ A4 )
=> ! [Y4: a] :
( ( member_a @ Y4 @ A4 )
=> ( ( X4 != Y4 )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ R )
| ( member449909584od_a_a @ ( product_Pair_a_a @ Y4 @ X4 ) @ R ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[259]) ).
thf(457,plain,
( ( total_1490170027od_a_a
= ( ^ [A4: set_Product_prod_a_a,R: set_Pr1948701895od_a_a] :
! [X4: product_prod_a_a] :
( ( member449909584od_a_a @ X4 @ A4 )
=> ! [Y4: product_prod_a_a] :
( ( member449909584od_a_a @ Y4 @ A4 )
=> ( ( X4 != Y4 )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X4 @ Y4 ) @ R )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ Y4 @ X4 ) @ R ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[260]) ).
thf(458,plain,
( ( ! [P2: produc1572603623od_a_a > $o,X: produc1572603623od_a_a] :
( ! [A3: product_prod_a_a,B3: a,C: a] : ( P2 @ ( produc1474507607od_a_a @ A3 @ ( product_Pair_a_a @ B3 @ C ) ) )
=> ( P2 @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[265]) ).
thf(459,plain,
( ( ! [Y: product_prod_a_a] :
~ ! [A3: a,B3: a] :
( Y
!= ( product_Pair_a_a @ A3 @ B3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[266]) ).
thf(460,plain,
( ( ! [P2: product_prod_a_a > $o,Prod: product_prod_a_a] :
( ! [A3: a,B3: a] : ( P2 @ ( product_Pair_a_a @ A3 @ B3 ) )
=> ( P2 @ Prod ) ) )
= $true ),
inference(unfold_def,[status(thm)],[270]) ).
thf(461,plain,
( ( ! [Carrier: set_a,Relation: set_Product_prod_a_a] :
( ( prefer719835986ence_a @ Carrier @ Relation )
=> ! [X2: a] :
( ( member_a @ X2 @ Carrier )
=> ! [Xa: a] :
( ( member_a @ Xa @ Carrier )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X2 @ Xa ) @ Relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ Xa @ X2 ) @ Relation ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[274]) ).
thf(462,plain,
( ( ! [Carrier: set_Product_prod_a_a,Relation: set_Pr1948701895od_a_a] :
( ( prefer697821563od_a_a @ Carrier @ Relation )
=> ! [X2: product_prod_a_a] :
( ( member449909584od_a_a @ X2 @ Carrier )
=> ! [Xa: product_prod_a_a] :
( ( member449909584od_a_a @ Xa @ Carrier )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X2 @ Xa ) @ Relation )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ Xa @ X2 ) @ Relation ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[275]) ).
thf(463,plain,
( ( ! [Carrier: set_a,Relation: set_Product_prod_a_a,X: a,Y: a,Z: a] :
( ( prefer719835986ence_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)],[278]) ).
thf(464,plain,
( ( ! [Carrier: set_a,Relation: set_Product_prod_a_a,X: a,Y: a] :
( ( prefer719835986ence_a @ Carrier @ Relation )
=> ( ( ( member_a @ X @ Carrier )
& ( member_a @ Y @ Carrier ) )
=> ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ Relation ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ Relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ Relation ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[282]) ).
thf(465,plain,
( ( ! [Carrier: set_Product_prod_a_a,Relation: set_Pr1948701895od_a_a,X: product_prod_a_a,Y: product_prod_a_a] :
( ( prefer697821563od_a_a @ Carrier @ Relation )
=> ( ( ( member449909584od_a_a @ X @ Carrier )
& ( member449909584od_a_a @ Y @ Carrier ) )
=> ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ Y @ X ) @ Relation ) )
= ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X @ Y ) @ Relation )
& ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ Y @ X ) @ Relation ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[283]) ).
thf(466,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)],[289]) ).
thf(467,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)],[290]) ).
thf(468,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)],[296]) ).
thf(469,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)],[300]) ).
thf(470,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)],[307]) ).
thf(471,plain,
( ( ! [Y: produc1572603623od_a_a] :
~ ! [A3: product_prod_a_a,B3: a,C: a] :
( Y
!= ( produc1474507607od_a_a @ A3 @ ( product_Pair_a_a @ B3 @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[324]) ).
thf(472,plain,
( ( ! [A: a,B: a,A2: a,B2: a] :
( ( ( product_Pair_a_a @ A @ B )
= ( product_Pair_a_a @ A2 @ B2 ) )
=> ~ ( ( A = A2 )
=> ( B != B2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[325]) ).
thf(473,plain,
( ( ! [P2: product_prod_a_a > $o,P: product_prod_a_a] :
( ! [A3: a,B3: a] : ( P2 @ ( product_Pair_a_a @ A3 @ B3 ) )
=> ( P2 @ P ) ) )
= $true ),
inference(unfold_def,[status(thm)],[329]) ).
thf(474,plain,
( ( ! [P: product_prod_a_a] :
? [X3: a,Y3: a] :
( P
= ( product_Pair_a_a @ X3 @ Y3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[333]) ).
thf(475,plain,
( ( trans_a @ relation )
= $true ),
inference(unfold_def,[status(thm)],[337]) ).
thf(476,plain,
( ( ! [A: a,B: a,A2: a,B2: a] :
( ( ( product_Pair_a_a @ A @ B )
= ( product_Pair_a_a @ A2 @ B2 ) )
= ( ( A = A2 )
& ( B = B2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[338]) ).
thf(477,plain,
( ( ! [X1: a,X22: a,Y1: a,Y2: a] :
( ( ( product_Pair_a_a @ X1 @ X22 )
= ( product_Pair_a_a @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X22 = Y2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(478,plain,
( ( refl_on_a @ carrier @ relation )
= $true ),
inference(unfold_def,[status(thm)],[346]) ).
thf(479,plain,
( ( total_on_a @ carrier @ relation )
= $true ),
inference(unfold_def,[status(thm)],[347]) ).
thf(480,plain,
( ( order_preorder_on_a @ carrier @ relation )
= $true ),
inference(unfold_def,[status(thm)],[348]) ).
thf(481,plain,
( ( prefer1292084992ence_a @ carrier @ relation )
= $true ),
inference(unfold_def,[status(thm)],[349]) ).
thf(482,plain,
( ( ! [X: a,Y: a] :
( ( ( member_a @ X @ carrier )
& ( member_a @ Y @ carrier ) )
=> ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ relation ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ relation ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[350]) ).
thf(483,plain,
( ( ! [X: a,Y: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
=> ( member_a @ X @ carrier ) ) )
= $true ),
inference(unfold_def,[status(thm)],[351]) ).
thf(484,plain,
( ( ! [X2: a] :
( ( member_a @ X2 @ carrier )
=> ! [Xa: a] :
( ( member_a @ Xa @ carrier )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X2 @ Xa ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ Xa @ X2 ) @ relation ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(485,plain,
( ( prefer719835986ence_a @ carrier @ relation )
= $true ),
inference(unfold_def,[status(thm)],[353]) ).
thf(486,plain,
( ( ! [X: a,Y: a,Z: a] :
( ( ( 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)],[354]) ).
thf(487,plain,
( ( ! [X: a,Y: a,Z: a] :
( ( ( 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)],[355]) ).
thf(488,plain,
( ( x != y )
= $true ),
inference(unfold_def,[status(thm)],[356]) ).
thf(489,plain,
( ( member_a @ y @ carrier )
= $true ),
inference(unfold_def,[status(thm)],[357]) ).
thf(490,plain,
( ( member_a @ x @ carrier )
= $true ),
inference(unfold_def,[status(thm)],[358]) ).
thf(491,plain,
( ( ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ x @ y ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ y @ x ) @ relation ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[361]) ).
thf(492,plain,
( ( member_a @ x @ carrier )
= $true ),
inference(copy,[status(thm)],[490]) ).
thf(493,plain,
( ( member_a @ y @ carrier )
= $true ),
inference(copy,[status(thm)],[489]) ).
thf(494,plain,
( ( x != y )
= $true ),
inference(copy,[status(thm)],[488]) ).
thf(495,plain,
( ( ! [X: a,Y: a,Z: a] :
( ( ( 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)],[487]) ).
thf(496,plain,
( ( ! [X: a,Y: a,Z: a] :
( ( ( 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)],[486]) ).
thf(497,plain,
( ( prefer719835986ence_a @ carrier @ relation )
= $true ),
inference(copy,[status(thm)],[485]) ).
thf(498,plain,
( ( ! [X2: a] :
( ( member_a @ X2 @ carrier )
=> ! [Xa: a] :
( ( member_a @ Xa @ carrier )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X2 @ Xa ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ Xa @ X2 ) @ relation ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[484]) ).
thf(499,plain,
( ( ! [X: a,Y: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
=> ( member_a @ X @ carrier ) ) )
= $true ),
inference(copy,[status(thm)],[483]) ).
thf(500,plain,
( ( ! [X: a,Y: a] :
( ( ( member_a @ X @ carrier )
& ( member_a @ Y @ carrier ) )
=> ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ relation ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ relation ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[482]) ).
thf(501,plain,
( ( prefer1292084992ence_a @ carrier @ relation )
= $true ),
inference(copy,[status(thm)],[481]) ).
thf(502,plain,
( ( order_preorder_on_a @ carrier @ relation )
= $true ),
inference(copy,[status(thm)],[480]) ).
thf(503,plain,
( ( total_on_a @ carrier @ relation )
= $true ),
inference(copy,[status(thm)],[479]) ).
thf(504,plain,
( ( refl_on_a @ carrier @ relation )
= $true ),
inference(copy,[status(thm)],[478]) ).
thf(505,plain,
( ( ! [X1: a,X22: a,Y1: a,Y2: a] :
( ( ( product_Pair_a_a @ X1 @ X22 )
= ( product_Pair_a_a @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X22 = Y2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[477]) ).
thf(506,plain,
( ( ! [A: a,B: a,A2: a,B2: a] :
( ( ( product_Pair_a_a @ A @ B )
= ( product_Pair_a_a @ A2 @ B2 ) )
= ( ( A = A2 )
& ( B = B2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[476]) ).
thf(507,plain,
( ( trans_a @ relation )
= $true ),
inference(copy,[status(thm)],[475]) ).
thf(508,plain,
( ( ! [P: product_prod_a_a] :
? [X3: a,Y3: a] :
( P
= ( product_Pair_a_a @ X3 @ Y3 ) ) )
= $true ),
inference(copy,[status(thm)],[474]) ).
thf(509,plain,
( ( ! [P2: product_prod_a_a > $o,P: product_prod_a_a] :
( ! [A3: a,B3: a] : ( P2 @ ( product_Pair_a_a @ A3 @ B3 ) )
=> ( P2 @ P ) ) )
= $true ),
inference(copy,[status(thm)],[473]) ).
thf(510,plain,
( ( ! [A: a,B: a,A2: a,B2: a] :
( ( ( product_Pair_a_a @ A @ B )
= ( product_Pair_a_a @ A2 @ B2 ) )
=> ~ ( ( A = A2 )
=> ( B != B2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[472]) ).
thf(511,plain,
( ( ! [Y: produc1572603623od_a_a] :
~ ! [A3: product_prod_a_a,B3: a,C: a] :
( Y
!= ( produc1474507607od_a_a @ A3 @ ( product_Pair_a_a @ B3 @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[471]) ).
thf(512,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)],[470]) ).
thf(513,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)],[469]) ).
thf(514,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)],[468]) ).
thf(515,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)],[467]) ).
thf(516,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)],[466]) ).
thf(517,plain,
( ( ! [Carrier: set_Product_prod_a_a,Relation: set_Pr1948701895od_a_a,X: product_prod_a_a,Y: product_prod_a_a] :
( ( prefer697821563od_a_a @ Carrier @ Relation )
=> ( ( ( member449909584od_a_a @ X @ Carrier )
& ( member449909584od_a_a @ Y @ Carrier ) )
=> ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ Y @ X ) @ Relation ) )
= ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X @ Y ) @ Relation )
& ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ Y @ X ) @ Relation ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[465]) ).
thf(518,plain,
( ( ! [Carrier: set_a,Relation: set_Product_prod_a_a,X: a,Y: a] :
( ( prefer719835986ence_a @ Carrier @ Relation )
=> ( ( ( member_a @ X @ Carrier )
& ( member_a @ Y @ Carrier ) )
=> ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ Relation ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ Relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ Relation ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[464]) ).
thf(519,plain,
( ( ! [Carrier: set_a,Relation: set_Product_prod_a_a,X: a,Y: a,Z: a] :
( ( prefer719835986ence_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)],[463]) ).
thf(520,plain,
( ( ! [Carrier: set_Product_prod_a_a,Relation: set_Pr1948701895od_a_a] :
( ( prefer697821563od_a_a @ Carrier @ Relation )
=> ! [X2: product_prod_a_a] :
( ( member449909584od_a_a @ X2 @ Carrier )
=> ! [Xa: product_prod_a_a] :
( ( member449909584od_a_a @ Xa @ Carrier )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X2 @ Xa ) @ Relation )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ Xa @ X2 ) @ Relation ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[462]) ).
thf(521,plain,
( ( ! [Carrier: set_a,Relation: set_Product_prod_a_a] :
( ( prefer719835986ence_a @ Carrier @ Relation )
=> ! [X2: a] :
( ( member_a @ X2 @ Carrier )
=> ! [Xa: a] :
( ( member_a @ Xa @ Carrier )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X2 @ Xa ) @ Relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ Xa @ X2 ) @ Relation ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[461]) ).
thf(522,plain,
( ( ! [P2: product_prod_a_a > $o,Prod: product_prod_a_a] :
( ! [A3: a,B3: a] : ( P2 @ ( product_Pair_a_a @ A3 @ B3 ) )
=> ( P2 @ Prod ) ) )
= $true ),
inference(copy,[status(thm)],[460]) ).
thf(523,plain,
( ( ! [Y: product_prod_a_a] :
~ ! [A3: a,B3: a] :
( Y
!= ( product_Pair_a_a @ A3 @ B3 ) ) )
= $true ),
inference(copy,[status(thm)],[459]) ).
thf(524,plain,
( ( ! [P2: produc1572603623od_a_a > $o,X: produc1572603623od_a_a] :
( ! [A3: product_prod_a_a,B3: a,C: a] : ( P2 @ ( produc1474507607od_a_a @ A3 @ ( product_Pair_a_a @ B3 @ C ) ) )
=> ( P2 @ X ) ) )
= $true ),
inference(copy,[status(thm)],[458]) ).
thf(525,plain,
( ( total_1490170027od_a_a
= ( ^ [A4: set_Product_prod_a_a,R: set_Pr1948701895od_a_a] :
! [X4: product_prod_a_a] :
( ( member449909584od_a_a @ X4 @ A4 )
=> ! [Y4: product_prod_a_a] :
( ( member449909584od_a_a @ Y4 @ A4 )
=> ( ( X4 != Y4 )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X4 @ Y4 ) @ R )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ Y4 @ X4 ) @ R ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[457]) ).
thf(526,plain,
( ( total_on_a
= ( ^ [A4: set_a,R: set_Product_prod_a_a] :
! [X4: a] :
( ( member_a @ X4 @ A4 )
=> ! [Y4: a] :
( ( member_a @ Y4 @ A4 )
=> ( ( X4 != Y4 )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ R )
| ( member449909584od_a_a @ ( product_Pair_a_a @ Y4 @ X4 ) @ R ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[456]) ).
thf(527,plain,
( ( ! [A5: set_Product_prod_a_a,R2: set_Pr1948701895od_a_a] :
( ! [X3: product_prod_a_a,Y3: product_prod_a_a] :
( ( member449909584od_a_a @ X3 @ A5 )
=> ( ( member449909584od_a_a @ Y3 @ A5 )
=> ( ( X3 != Y3 )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X3 @ Y3 ) @ R2 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ Y3 @ X3 ) @ R2 ) ) ) ) )
=> ( total_1490170027od_a_a @ A5 @ R2 ) ) )
= $true ),
inference(copy,[status(thm)],[455]) ).
thf(528,plain,
( ( ! [A5: set_a,R2: set_Product_prod_a_a] :
( ! [X3: a,Y3: a] :
( ( member_a @ X3 @ A5 )
=> ( ( member_a @ Y3 @ A5 )
=> ( ( X3 != Y3 )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R2 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ Y3 @ X3 ) @ R2 ) ) ) ) )
=> ( total_on_a @ A5 @ R2 ) ) )
= $true ),
inference(copy,[status(thm)],[454]) ).
thf(529,plain,
( ( ! [A5: set_Product_prod_a_a,R2: set_Pr1948701895od_a_a,A: product_prod_a_a,B: product_prod_a_a] :
( ( refl_o1298442278od_a_a @ A5 @ R2 )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B ) @ R2 )
=> ( ( member449909584od_a_a @ A @ A5 )
& ( member449909584od_a_a @ B @ A5 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[453]) ).
thf(530,plain,
( ( ! [A5: set_a,R2: set_Product_prod_a_a,A: a,B: a] :
( ( refl_on_a @ A5 @ R2 )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ R2 )
=> ( ( member_a @ A @ A5 )
& ( member_a @ B @ A5 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[452]) ).
thf(531,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)],[451]) ).
thf(532,plain,
( ( ! [A5: set_Product_prod_a_a] :
( ( collec645855634od_a_a
@ ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ A5 ) )
= A5 ) )
= $true ),
inference(copy,[status(thm)],[450]) ).
thf(533,plain,
( ( ! [A5: set_Product_prod_a_a,R2: set_Pr1948701895od_a_a,X: product_prod_a_a,Y: product_prod_a_a] :
( ( refl_o1298442278od_a_a @ A5 @ R2 )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X @ Y ) @ R2 )
=> ( member449909584od_a_a @ Y @ A5 ) ) ) )
= $true ),
inference(copy,[status(thm)],[449]) ).
thf(534,plain,
( ( ! [A5: set_a,R2: set_Product_prod_a_a,X: a,Y: a] :
( ( refl_on_a @ A5 @ R2 )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ R2 )
=> ( member_a @ Y @ A5 ) ) ) )
= $true ),
inference(copy,[status(thm)],[448]) ).
thf(535,plain,
( ( ! [A5: set_Product_prod_a_a,R2: set_Pr1948701895od_a_a,X: product_prod_a_a,Y: product_prod_a_a] :
( ( refl_o1298442278od_a_a @ A5 @ R2 )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X @ Y ) @ R2 )
=> ( member449909584od_a_a @ X @ A5 ) ) ) )
= $true ),
inference(copy,[status(thm)],[447]) ).
thf(536,plain,
( ( ! [A5: set_a,R2: set_Product_prod_a_a,X: a,Y: a] :
( ( refl_on_a @ A5 @ R2 )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ R2 )
=> ( member_a @ X @ A5 ) ) ) )
= $true ),
inference(copy,[status(thm)],[446]) ).
thf(537,plain,
( ( ! [A5: set_Product_prod_a_a,R2: set_Pr1948701895od_a_a,A: product_prod_a_a] :
( ( refl_o1298442278od_a_a @ A5 @ R2 )
=> ( ( member449909584od_a_a @ A @ A5 )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ A ) @ R2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[445]) ).
thf(538,plain,
( ( ! [A5: set_a,R2: set_Product_prod_a_a,A: a] :
( ( refl_on_a @ A5 @ R2 )
=> ( ( member_a @ A @ A5 )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ A ) @ R2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[444]) ).
thf(539,plain,
( ( trans_a
= ( ^ [R: set_Product_prod_a_a] :
! [X4: a,Y4: a,Z2: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ R )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y4 @ Z2 ) @ R )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Z2 ) @ R ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[443]) ).
thf(540,plain,
( ( ! [R2: set_Product_prod_a_a] :
( ! [X3: a,Y3: a,Z3: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R2 )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y3 @ Z3 ) @ R2 )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Z3 ) @ R2 ) ) )
=> ( trans_a @ R2 ) ) )
= $true ),
inference(copy,[status(thm)],[442]) ).
thf(541,plain,
( ( ! [R2: set_Product_prod_a_a,X: a,Y: a,Z: a] :
( ( trans_a @ R2 )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ R2 )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ Z ) @ R2 )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Z ) @ R2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[441]) ).
thf(542,plain,
( ( ! [R2: set_Product_prod_a_a,X: a,Y: a,Z: a] :
( ( trans_a @ R2 )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ R2 )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ Z ) @ R2 )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Z ) @ R2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[440]) ).
thf(543,plain,
( ( ! [R2: a,S: a,R3: set_Product_prod_a_a,S2: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ R2 @ S ) @ R3 )
=> ( ( S2 = S )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ R2 @ S2 ) @ R3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[439]) ).
thf(544,plain,
( ( ! [X: product_prod_a_a,Y: product_prod_a_a,B4: set_Product_prod_a_a,Pr: set_Pr1948701895od_a_a] :
( ( member449909584od_a_a @ X @ ( prefer477097315od_a_a @ Y @ B4 @ Pr ) )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X @ Y ) @ Pr ) ) )
= $true ),
inference(copy,[status(thm)],[438]) ).
thf(545,plain,
( ( ! [X: a,Y: a,B4: set_a,Pr: set_Product_prod_a_a] :
( ( member_a @ X @ ( prefer161218362good_a @ Y @ B4 @ Pr ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ Pr ) ) )
= $true ),
inference(copy,[status(thm)],[437]) ).
thf(546,plain,
( ( ! [Z: product_prod_a_a,Y: product_prod_a_a,B4: set_Product_prod_a_a,Pr: set_Pr1948701895od_a_a] :
( ( member449909584od_a_a @ Z @ ( prefer477097315od_a_a @ Y @ B4 @ Pr ) )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ Z @ Y ) @ Pr ) ) )
= $true ),
inference(copy,[status(thm)],[436]) ).
thf(547,plain,
( ( ! [Z: a,Y: a,B4: set_a,Pr: set_Product_prod_a_a] :
( ( member_a @ Z @ ( prefer161218362good_a @ Y @ B4 @ Pr ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ Z @ Y ) @ Pr ) ) )
= $true ),
inference(copy,[status(thm)],[435]) ).
thf(548,plain,
( ( product_curry_a_a_o
= ( ^ [F: product_prod_a_a > $o,A6: a,B5: a] : ( F @ ( product_Pair_a_a @ A6 @ B5 ) ) ) )
= $true ),
inference(copy,[status(thm)],[434]) ).
thf(549,plain,
( ( ! [F2: product_prod_a_a > $o,A: a,B: a] :
( ( F2 @ ( product_Pair_a_a @ A @ B ) )
=> ( product_curry_a_a_o @ F2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[433]) ).
thf(550,plain,
( ( ! [X: a,Y: a,R2: set_Product_prod_a_a,F2: a > a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ ( inv_image_a_a @ R2 @ F2 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( F2 @ X ) @ ( F2 @ Y ) ) @ R2 ) ) )
= $true ),
inference(copy,[status(thm)],[432]) ).
thf(551,plain,
( ( ! [X: a,Y: a,R2: set_Pr158363655iset_a,F2: a > multiset_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ ( inv_im975322764et_a_a @ R2 @ F2 ) )
= ( member340150864iset_a @ ( produc2037245207iset_a @ ( F2 @ X ) @ ( F2 @ Y ) ) @ R2 ) ) )
= $true ),
inference(copy,[status(thm)],[431]) ).
thf(552,plain,
( ( ! [X: multiset_a,Y: multiset_a,R2: set_Product_prod_a_a,F2: multiset_a > a] :
( ( member340150864iset_a @ ( produc2037245207iset_a @ X @ Y ) @ ( inv_im479034648iset_a @ R2 @ F2 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( F2 @ X ) @ ( F2 @ Y ) ) @ R2 ) ) )
= $true ),
inference(copy,[status(thm)],[430]) ).
thf(553,plain,
( ( ! [X: a,Y: a,R2: set_Pr1948701895od_a_a,F2: a > product_prod_a_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ ( inv_im777352425_a_a_a @ R2 @ F2 ) )
= ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( F2 @ X ) @ ( F2 @ Y ) ) @ R2 ) ) )
= $true ),
inference(copy,[status(thm)],[429]) ).
thf(554,plain,
( ( ! [X: product_prod_a_a,Y: product_prod_a_a,R2: set_Product_prod_a_a,F2: product_prod_a_a > a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ X @ Y ) @ ( inv_im15016955od_a_a @ R2 @ F2 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( F2 @ X ) @ ( F2 @ Y ) ) @ R2 ) ) )
= $true ),
inference(copy,[status(thm)],[428]) ).
thf(555,plain,
( ( ! [X: a,Y: a,R2: set_Pr1821581383od_a_a,F2: a > multis599418605od_a_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ ( inv_im1681759523_a_a_a @ R2 @ F2 ) )
= ( member1349055120od_a_a @ ( produc1859144151od_a_a @ ( F2 @ X ) @ ( F2 @ Y ) ) @ R2 ) ) )
= $true ),
inference(copy,[status(thm)],[427]) ).
thf(556,plain,
( ( ! [X: multis599418605od_a_a,Y: multis599418605od_a_a,R2: set_Product_prod_a_a,F2: multis599418605od_a_a > a] :
( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ X @ Y ) @ ( inv_im941243329od_a_a @ R2 @ F2 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( F2 @ X ) @ ( F2 @ Y ) ) @ R2 ) ) )
= $true ),
inference(copy,[status(thm)],[426]) ).
thf(557,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)],[425]) ).
thf(558,plain,
( ( ! [Z: a,C2: a > a > set_a,P: product_prod_a_a] :
( ( member_a @ Z @ ( produc961951794_set_a @ C2 @ P ) )
=> ~ ! [X3: a,Y3: a] :
( ( P
= ( product_Pair_a_a @ X3 @ Y3 ) )
=> ~ ( member_a @ Z @ ( C2 @ X3 @ Y3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[424]) ).
thf(559,plain,
( ( ! [Z: product_prod_a_a,C2: a > a > set_Product_prod_a_a,P: product_prod_a_a] :
( ( member449909584od_a_a @ Z @ ( produc1093061851od_a_a @ C2 @ P ) )
=> ~ ! [X3: a,Y3: a] :
( ( P
= ( product_Pair_a_a @ X3 @ Y3 ) )
=> ~ ( member449909584od_a_a @ Z @ ( C2 @ X3 @ Y3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[423]) ).
thf(560,plain,
( ( ! [Z: multiset_a,C2: a > a > set_multiset_a,P: product_prod_a_a] :
( ( member_multiset_a @ Z @ ( produc1828150264iset_a @ C2 @ P ) )
=> ~ ! [X3: a,Y3: a] :
( ( P
= ( product_Pair_a_a @ X3 @ Y3 ) )
=> ~ ( member_multiset_a @ Z @ ( C2 @ X3 @ Y3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[422]) ).
thf(561,plain,
( ( ! [Z: multis599418605od_a_a,C2: a > a > set_mu1281098573od_a_a,P: product_prod_a_a] :
( ( member1755255446od_a_a @ Z @ ( produc1121147169od_a_a @ C2 @ P ) )
=> ~ ! [X3: a,Y3: a] :
( ( P
= ( product_Pair_a_a @ X3 @ Y3 ) )
=> ~ ( member1755255446od_a_a @ Z @ ( C2 @ X3 @ Y3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[421]) ).
thf(562,plain,
( ( ! [Z: produc1127127335iset_a,C2: a > a > set_Pr158363655iset_a,P: product_prod_a_a] :
( ( member340150864iset_a @ Z @ ( produc93594587iset_a @ C2 @ P ) )
=> ~ ! [X3: a,Y3: a] :
( ( P
= ( product_Pair_a_a @ X3 @ Y3 ) )
=> ~ ( member340150864iset_a @ Z @ ( C2 @ X3 @ Y3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[420]) ).
thf(563,plain,
( ( ! [Z: product_prod_a_a,C2: multiset_a > multiset_a > set_Product_prod_a_a,P: produc1127127335iset_a] :
( ( member449909584od_a_a @ Z @ ( produc2041367259od_a_a @ C2 @ P ) )
=> ~ ! [X3: multiset_a,Y3: multiset_a] :
( ( P
= ( produc2037245207iset_a @ X3 @ Y3 ) )
=> ~ ( member449909584od_a_a @ Z @ ( C2 @ X3 @ Y3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[419]) ).
thf(564,plain,
( ( ! [F2: a > a > set_Product_prod_a_a,X1: a,X22: a] :
( ( produc1093061851od_a_a @ F2 @ ( product_Pair_a_a @ X1 @ X22 ) )
= ( F2 @ X1 @ X22 ) ) )
= $true ),
inference(copy,[status(thm)],[418]) ).
thf(565,plain,
( ( ! [F2: a > a > set_a,X1: a,X22: a] :
( ( produc961951794_set_a @ F2 @ ( product_Pair_a_a @ X1 @ X22 ) )
= ( F2 @ X1 @ X22 ) ) )
= $true ),
inference(copy,[status(thm)],[417]) ).
thf(566,plain,
( ( ! [F2: a > a > $o,X1: a,X22: a] :
( ( produc1833107820_a_a_o @ F2 @ ( product_Pair_a_a @ X1 @ X22 ) )
= ( F2 @ X1 @ X22 ) ) )
= $true ),
inference(copy,[status(thm)],[416]) ).
thf(567,plain,
( ( ! [R3: set_Product_prod_a_a] :
( ! [A3: a] :
~ ( member449909584od_a_a @ ( product_Pair_a_a @ A3 @ A3 ) @ R3 )
=> ( irrefl_a @ R3 ) ) )
= $true ),
inference(copy,[status(thm)],[415]) ).
thf(568,plain,
( ( irrefl_a
= ( ^ [R: set_Product_prod_a_a] :
! [A6: a] :
~ ( member449909584od_a_a @ ( product_Pair_a_a @ A6 @ A6 ) @ R ) ) )
= $true ),
inference(copy,[status(thm)],[414]) ).
thf(569,plain,
( ( ! [F2: product_prod_a_a > $o,A: a,B: a] :
( ( product_curry_a_a_o @ F2 @ A @ B )
=> ( F2 @ ( product_Pair_a_a @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[413]) ).
thf(570,plain,
( ( ! [F2: product_prod_a_a > $o,A: a,B: a] :
( ( product_curry_a_a_o @ F2 @ A @ B )
=> ( F2 @ ( product_Pair_a_a @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[412]) ).
thf(571,plain,
( ( ! [Y: a,X: a,A5: set_Product_prod_a_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ ( image_794773445od_a_a @ product_swap_a_a @ A5 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ A5 ) ) )
= $true ),
inference(copy,[status(thm)],[411]) ).
thf(572,plain,
( ( ! [X: set_Product_prod_a_a,P2: set_Product_prod_a_a > $o] :
( ( asym_a @ X )
=> ( ! [R4: set_Product_prod_a_a] :
( ! [A7: a,B6: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A7 @ B6 ) @ R4 )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B6 @ A7 ) @ R4 ) )
=> ( P2 @ R4 ) )
=> ( P2 @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[410]) ).
thf(573,plain,
( ( ! [R3: set_Product_prod_a_a] :
( ! [A3: a,B3: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A3 @ B3 ) @ R3 )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B3 @ A3 ) @ R3 ) )
=> ( asym_a @ R3 ) ) )
= $true ),
inference(copy,[status(thm)],[409]) ).
thf(574,plain,
( ( asym_a
= ( ^ [A6: set_Product_prod_a_a] :
? [R5: set_Product_prod_a_a] :
( ( A6 = R5 )
& ! [X4: a,Y4: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ R5 )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y4 @ X4 ) @ R5 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[408]) ).
thf(575,plain,
( ( ! [A: set_Product_prod_a_a] :
( ( asym_a @ A )
=> ! [A7: a,B6: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A7 @ B6 ) @ A )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B6 @ A7 ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[407]) ).
thf(576,plain,
( ( asym_a
= ( ^ [R5: set_Product_prod_a_a] :
! [X4: a,Y4: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ Y4 ) @ R5 )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y4 @ X4 ) @ R5 ) ) ) )
= $true ),
inference(copy,[status(thm)],[406]) ).
thf(577,plain,
( ( ! [R3: set_Product_prod_a_a,X: a,Y: a] :
( ( asym_a @ R3 )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ R3 )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ R3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[405]) ).
thf(578,plain,
( ( ! [B: product_prod_a_a,F2: a > product_prod_a_a,X: a,A5: set_a] :
( ( B
= ( F2 @ X ) )
=> ( ( member_a @ X @ A5 )
=> ( member449909584od_a_a @ B @ ( image_1725938350od_a_a @ F2 @ A5 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[404]) ).
thf(579,plain,
( ( ! [B: a,F2: product_prod_a_a > a,X: product_prod_a_a,A5: set_Product_prod_a_a] :
( ( B
= ( F2 @ X ) )
=> ( ( member449909584od_a_a @ X @ A5 )
=> ( member_a @ B @ ( image_340790172_a_a_a @ F2 @ A5 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[403]) ).
thf(580,plain,
( ( ! [B: product_prod_a_a,F2: product_prod_a_a > product_prod_a_a,X: product_prod_a_a,A5: set_Product_prod_a_a] :
( ( B
= ( F2 @ X ) )
=> ( ( member449909584od_a_a @ X @ A5 )
=> ( member449909584od_a_a @ B @ ( image_794773445od_a_a @ F2 @ A5 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[402]) ).
thf(581,plain,
( ( ! [X: a,A5: set_a,F2: a > product_prod_a_a] :
( ( member_a @ X @ A5 )
=> ( member449909584od_a_a @ ( F2 @ X ) @ ( image_1725938350od_a_a @ F2 @ A5 ) ) ) )
= $true ),
inference(copy,[status(thm)],[401]) ).
thf(582,plain,
( ( ! [X: product_prod_a_a,A5: set_Product_prod_a_a,F2: product_prod_a_a > a] :
( ( member449909584od_a_a @ X @ A5 )
=> ( member_a @ ( F2 @ X ) @ ( image_340790172_a_a_a @ F2 @ A5 ) ) ) )
= $true ),
inference(copy,[status(thm)],[400]) ).
thf(583,plain,
( ( ! [X: product_prod_a_a,A5: set_Product_prod_a_a,F2: product_prod_a_a > product_prod_a_a] :
( ( member449909584od_a_a @ X @ A5 )
=> ( member449909584od_a_a @ ( F2 @ X ) @ ( image_794773445od_a_a @ F2 @ A5 ) ) ) )
= $true ),
inference(copy,[status(thm)],[399]) ).
thf(584,plain,
( ( ! [X: a,A5: set_a,B: product_prod_a_a,F2: a > product_prod_a_a] :
( ( member_a @ X @ A5 )
=> ( ( B
= ( F2 @ X ) )
=> ( member449909584od_a_a @ B @ ( image_1725938350od_a_a @ F2 @ A5 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[398]) ).
thf(585,plain,
( ( ! [X: product_prod_a_a,A5: set_Product_prod_a_a,B: a,F2: product_prod_a_a > a] :
( ( member449909584od_a_a @ X @ A5 )
=> ( ( B
= ( F2 @ X ) )
=> ( member_a @ B @ ( image_340790172_a_a_a @ F2 @ A5 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[397]) ).
thf(586,plain,
( ( ! [X: product_prod_a_a,A5: set_Product_prod_a_a,B: product_prod_a_a,F2: product_prod_a_a > product_prod_a_a] :
( ( member449909584od_a_a @ X @ A5 )
=> ( ( B
= ( F2 @ X ) )
=> ( member449909584od_a_a @ B @ ( image_794773445od_a_a @ F2 @ A5 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[396]) ).
thf(587,plain,
( ( top_to1483957574_a_a_o
= ( ^ [X4: product_prod_a_a] : ( member449909584od_a_a @ X4 @ top_to398455383od_a_a ) ) )
= $true ),
inference(copy,[status(thm)],[395]) ).
thf(588,plain,
( ( ! [F2: a > a,G: a > a,A: a,B: a] :
( ( produc700022774_a_a_a @ F2 @ G @ ( product_Pair_a_a @ A @ B ) )
= ( product_Pair_a_a @ ( F2 @ A ) @ ( G @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[394]) ).
thf(589,plain,
( ( ! [A: a,B: a,A2: a,B2: a,R2: set_Product_prod_a_a,S: set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ A @ B ) @ ( product_Pair_a_a @ A2 @ B2 ) ) @ ( lex_prod_a_a @ R2 @ S ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ A2 ) @ R2 )
| ( ( A = A2 )
& ( member449909584od_a_a @ ( product_Pair_a_a @ B @ B2 ) @ S ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[393]) ).
thf(590,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)],[392]) ).
thf(591,plain,
( ( ! [A: a,B: a,R3: set_Product_prod_a_a,F2: a > a,G: a > a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ R3 )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ ( F2 @ A ) @ ( G @ B ) ) @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ F2 @ G ) @ R3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[391]) ).
thf(592,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)],[390]) ).
thf(593,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)],[389]) ).
thf(594,plain,
( ( ! [X1: a,X22: a] :
( ( product_fst_a_a @ ( product_Pair_a_a @ X1 @ X22 ) )
= X1 ) )
= $true ),
inference(copy,[status(thm)],[388]) ).
thf(595,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)],[387]) ).
thf(596,plain,
( ( ! [X1: a,X22: a] :
( ( product_snd_a_a @ ( product_Pair_a_a @ X1 @ X22 ) )
= X22 ) )
= $true ),
inference(copy,[status(thm)],[386]) ).
thf(597,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)],[385]) ).
thf(598,plain,
( ( product_swap_a_a
= ( ^ [P3: product_prod_a_a] : ( product_Pair_a_a @ ( product_snd_a_a @ P3 ) @ ( product_fst_a_a @ P3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[384]) ).
thf(599,plain,
( ( ! [C2: product_prod_a_a,F2: a > a,G: a > a,R3: set_Product_prod_a_a] :
( ( member449909584od_a_a @ C2 @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ F2 @ G ) @ R3 ) )
=> ~ ! [X3: a,Y3: a] :
( ( C2
= ( product_Pair_a_a @ ( F2 @ X3 ) @ ( G @ Y3 ) ) )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[383]) ).
thf(600,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)],[382]) ).
thf(601,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)],[381]) ).
thf(602,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)],[380]) ).
thf(603,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)],[379]) ).
thf(604,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)],[378]) ).
thf(605,plain,
( ( ! [B: a,P: product_prod_a_a] :
( ( B
= ( product_snd_a_a @ P ) )
= ( ? [A6: a] :
( P
= ( product_Pair_a_a @ A6 @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[377]) ).
thf(606,plain,
( ( ! [A: a,P: product_prod_a_a] :
( ( A
= ( product_fst_a_a @ P ) )
= ( ? [B5: a] :
( P
= ( product_Pair_a_a @ A @ B5 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[376]) ).
thf(607,plain,
( ( ! [R2: set_Product_prod_a_a,S: set_Product_prod_a_a] :
( ! [X3: a,Y3: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ R2 )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ Y3 ) @ S ) )
=> ( ord_le1824328871od_a_a @ R2 @ S ) ) )
= $true ),
inference(copy,[status(thm)],[375]) ).
thf(608,plain,
( ( ! [A5: set_a,F2: a > product_prod_a_a,B4: set_Product_prod_a_a] :
( ! [X3: a] :
( ( member_a @ X3 @ A5 )
=> ( member449909584od_a_a @ ( F2 @ X3 ) @ B4 ) )
=> ( ord_le1824328871od_a_a @ ( image_1725938350od_a_a @ F2 @ A5 ) @ B4 ) ) )
= $true ),
inference(copy,[status(thm)],[374]) ).
thf(609,plain,
( ( ! [A5: set_Product_prod_a_a,F2: product_prod_a_a > a,B4: set_a] :
( ! [X3: product_prod_a_a] :
( ( member449909584od_a_a @ X3 @ A5 )
=> ( member_a @ ( F2 @ X3 ) @ B4 ) )
=> ( ord_less_eq_set_a @ ( image_340790172_a_a_a @ F2 @ A5 ) @ B4 ) ) )
= $true ),
inference(copy,[status(thm)],[373]) ).
thf(610,plain,
( ( ! [A5: set_Product_prod_a_a,F2: product_prod_a_a > product_prod_a_a,B4: set_Product_prod_a_a] :
( ! [X3: product_prod_a_a] :
( ( member449909584od_a_a @ X3 @ A5 )
=> ( member449909584od_a_a @ ( F2 @ X3 ) @ B4 ) )
=> ( ord_le1824328871od_a_a @ ( image_794773445od_a_a @ F2 @ A5 ) @ B4 ) ) )
= $true ),
inference(copy,[status(thm)],[372]) ).
thf(611,plain,
( ( ! [P2: a > $o,X: a,Y6: a,Y: a,R3: a > set_Product_prod_a_a] :
( ( P2 @ X )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y6 @ Y ) @ ( R3 @ X ) )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ X @ Y6 ) @ ( product_Pair_a_a @ X @ Y ) ) @ ( same_fst_a_a @ P2 @ R3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(612,plain,
( ( ! [A: product_prod_a_a,A5: multis599418605od_a_a] :
( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ A5 ) )
=> ~ ! [B7: multis599418605od_a_a] :
( A5
!= ( add_ms1725977093od_a_a @ A @ B7 ) ) ) )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(613,plain,
( ( ! [X: product_prod_a_a,M: multis599418605od_a_a] :
( ( member449909584od_a_a @ X @ ( set_ms1818337124od_a_a @ M ) )
=> ? [A8: multis599418605od_a_a] :
( M
= ( add_ms1725977093od_a_a @ X @ A8 ) ) ) )
= $true ),
inference(copy,[status(thm)],[369]) ).
thf(614,plain,
( ( ! [B: product_prod_a_a,B4: multis599418605od_a_a,C2: product_prod_a_a,C3: multis599418605od_a_a] :
( ( ( add_ms1725977093od_a_a @ B @ B4 )
= ( add_ms1725977093od_a_a @ C2 @ C3 ) )
=> ( ( B != C2 )
=> ( member449909584od_a_a @ C2 @ ( set_ms1818337124od_a_a @ B4 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[368]) ).
thf(615,plain,
( ( ! [X: product_prod_a_a,M: multis599418605od_a_a,N: multis599418605od_a_a] :
( ( ( add_ms1725977093od_a_a @ X @ M )
= N )
=> ( member449909584od_a_a @ X @ ( set_ms1818337124od_a_a @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(616,plain,
( ( ! [A: product_prod_a_a,A5: multis599418605od_a_a,B4: multis599418605od_a_a] :
( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ ( plus_p404985124od_a_a @ A5 @ B4 ) ) )
= ( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ A5 ) )
| ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ B4 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[366]) ).
thf(617,plain,
( ( ! [A5: multis599418605od_a_a] :
( ( A5 != zero_z160849828od_a_a )
=> ~ ! [X3: product_prod_a_a] :
~ ( member449909584od_a_a @ X3 @ ( set_ms1818337124od_a_a @ A5 ) ) ) )
= $true ),
inference(copy,[status(thm)],[365]) ).
thf(618,plain,
( ( ! [X: product_prod_a_a] : ( member449909584od_a_a @ X @ ( set_ms1818337124od_a_a @ ( add_ms1725977093od_a_a @ X @ zero_z160849828od_a_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[364]) ).
thf(619,plain,
( ( ! [B: product_prod_a_a,A5: multis599418605od_a_a,M: multis599418605od_a_a] :
( ~ ( member449909584od_a_a @ B @ ( set_ms1818337124od_a_a @ A5 ) )
=> ( ( minus_1257885652od_a_a @ ( add_ms1725977093od_a_a @ B @ M ) @ A5 )
= ( add_ms1725977093od_a_a @ B @ ( minus_1257885652od_a_a @ M @ A5 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[363]) ).
thf(620,plain,
( ( ! [A: product_prod_a_a,M: multis599418605od_a_a,N: multis599418605od_a_a] :
( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ ( minus_1257885652od_a_a @ M @ N ) ) )
=> ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[362]) ).
thf(621,plain,
( ( ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ x @ y ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ y @ x ) @ relation ) ) )
= $true ),
inference(copy,[status(thm)],[491]) ).
thf(622,plain,
( ( ! [SX0: product_prod_a_a,SX1: multis599418605od_a_a,SX2: multis599418605od_a_a] :
( ~ ( member449909584od_a_a @ SX0 @ ( set_ms1818337124od_a_a @ ( minus_1257885652od_a_a @ SX1 @ SX2 ) ) )
| ( member449909584od_a_a @ SX0 @ ( set_ms1818337124od_a_a @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[620]) ).
thf(623,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)],[510]) ).
thf(624,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)],[524]) ).
thf(625,plain,
( ( x != y )
= $true ),
inference(unfold_def,[status(thm)],[494]) ).
thf(626,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)],[595]) ).
thf(627,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)],[549]) ).
thf(628,plain,
( ( ! [SX0: set_Product_prod_a_a,SX1: set_Pr1948701895od_a_a] :
( ~ ! [SX2: product_prod_a_a,SX3: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SX2 @ SX0 )
| ~ ( member449909584od_a_a @ SX3 @ SX0 )
| ~ ( ( SX2 != SX3 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SX2 @ SX3 ) @ SX1 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SX3 @ SX2 ) @ SX1 ) )
| ( total_1490170027od_a_a @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[527]) ).
thf(629,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)],[601]) ).
thf(630,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)],[611]) ).
thf(631,plain,
( ( ! [SX0: product_prod_a_a,SX1: multis599418605od_a_a] :
( ~ ( member449909584od_a_a @ SX0 @ ( set_ms1818337124od_a_a @ SX1 ) )
| ~ ! [SX2: multis599418605od_a_a] :
( SX1
!= ( add_ms1725977093od_a_a @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[612]) ).
thf(632,plain,
( ( ! [SX0: set_Product_prod_a_a,SX1: set_Product_prod_a_a > $o] :
( ~ ( asym_a @ SX0 )
| ~ ! [SX2: set_Product_prod_a_a] :
( ~ ! [SX3: a,SX4: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX4 ) @ SX2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX4 @ SX3 ) @ SX2 ) )
| ( SX1 @ SX2 ) )
| ( SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[572]) ).
thf(633,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)],[607]) ).
thf(634,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)],[546]) ).
thf(635,plain,
( ( total_1490170027od_a_a
= ( ^ [SX0: set_Product_prod_a_a,SX1: set_Pr1948701895od_a_a] :
! [SX2: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SX2 @ SX0 )
| ! [SX3: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SX3 @ SX0 )
| ~ ( ( SX2 != SX3 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SX2 @ SX3 ) @ SX1 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SX3 @ SX2 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[525]) ).
thf(636,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)],[606]) ).
thf(637,plain,
( ( ! [SX0: set_Product_prod_a_a,SX1: a,SX2: a,SX3: a] :
( ~ ( trans_a @ SX0 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX1 @ SX2 ) @ SX0 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SX0 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SX1 @ SX3 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[542]) ).
thf(638,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)],[515]) ).
thf(639,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)],[602]) ).
thf(640,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)],[506]) ).
thf(641,plain,
( ( ! [SX0: set_Product_prod_a_a,SX1: a,SX2: a,SX3: a] :
( ~ ( trans_a @ SX0 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX1 @ SX2 ) @ SX0 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SX0 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SX1 @ SX3 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[541]) ).
thf(642,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)],[608]) ).
thf(643,plain,
( ( ! [SX0: set_Product_prod_a_a,SX1: set_Pr1948701895od_a_a] :
( ~ ( prefer697821563od_a_a @ SX0 @ SX1 )
| ! [SX2: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SX2 @ SX0 )
| ! [SX3: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SX3 @ SX0 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SX2 @ SX3 ) @ SX1 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SX3 @ SX2 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[520]) ).
thf(644,plain,
( ( ! [SX0: set_a,SX1: set_Product_prod_a_a] :
( ~ ! [SX2: a,SX3: a] :
( ~ ( member_a @ SX2 @ SX0 )
| ~ ( member_a @ SX3 @ SX0 )
| ~ ( ( SX2 != SX3 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SX1 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SX1 ) )
| ( total_on_a @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[528]) ).
thf(645,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)],[544]) ).
thf(646,plain,
( ( ! [SX0: product_prod_a_a] :
~ ! [SX1: a] :
~ ~ ! [SX2: a] :
( SX0
!= ( product_Pair_a_a @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[508]) ).
thf(647,plain,
( ( ! [SX0: set_Product_prod_a_a,SX1: set_Pr1948701895od_a_a,SX2: product_prod_a_a] :
( ~ ( refl_o1298442278od_a_a @ SX0 @ SX1 )
| ~ ( member449909584od_a_a @ SX2 @ SX0 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SX2 @ SX2 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[537]) ).
thf(648,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)],[589]) ).
thf(649,plain,
( ( ! [SX0: set_Product_prod_a_a,SX1: set_Pr1948701895od_a_a,SX2: product_prod_a_a,SX3: product_prod_a_a] :
( ~ ( refl_o1298442278od_a_a @ SX0 @ SX1 )
| ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SX2 @ SX3 ) @ SX1 )
| ( member449909584od_a_a @ SX3 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[533]) ).
thf(650,plain,
( ( ! [SX0: set_a,SX1: set_Product_prod_a_a,SX2: a] :
( ~ ( refl_on_a @ SX0 @ SX1 )
| ~ ( member_a @ SX2 @ SX0 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX2 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[538]) ).
thf(651,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)],[547]) ).
thf(652,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)],[505]) ).
thf(653,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX1 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX1 @ SX0 ) @ relation ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX1 @ SX2 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX1 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX2 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX0 ) @ relation ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[495]) ).
thf(654,plain,
( ( ! [SX0: set_a,SX1: set_Product_prod_a_a,SX2: a,SX3: a] :
( ~ ( refl_on_a @ SX0 @ SX1 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SX1 )
| ~ ( ~ ( member_a @ SX2 @ SX0 )
| ~ ( member_a @ SX3 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[530]) ).
thf(655,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)],[599]) ).
thf(656,plain,
( ( ! [SX0: set_Product_prod_a_a,SX1: set_Pr1948701895od_a_a,SX2: product_prod_a_a,SX3: product_prod_a_a] :
( ~ ( prefer697821563od_a_a @ SX0 @ SX1 )
| ~ ~ ( ~ ( member449909584od_a_a @ SX2 @ SX0 )
| ~ ( member449909584od_a_a @ SX3 @ SX0 ) )
| ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SX3 @ SX2 ) @ SX1 ) )
= ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SX2 @ SX3 ) @ SX1 )
| ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SX3 @ SX2 ) @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[517]) ).
thf(657,plain,
( ( ! [SX0: set_a,SX1: set_Product_prod_a_a,SX2: a,SX3: a] :
( ~ ( prefer719835986ence_a @ SX0 @ SX1 )
| ~ ~ ( ~ ( member_a @ SX2 @ SX0 )
| ~ ( member_a @ SX3 @ SX0 ) )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SX1 ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SX1 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[518]) ).
thf(658,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)],[509]) ).
thf(659,plain,
( ( ! [SX0: set_Product_prod_a_a] :
( ~ ! [SX1: a,SX2: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX1 @ SX2 ) @ SX0 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX1 ) @ SX0 ) )
| ( asym_a @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[573]) ).
thf(660,plain,
( ( ! [SX0: set_Product_prod_a_a,SX1: a,SX2: a] :
( ~ ( asym_a @ SX0 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX1 @ SX2 ) @ SX0 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX1 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[577]) ).
thf(661,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)],[583]) ).
thf(662,plain,
( ( ! [SX0: a] :
( ~ ( member_a @ SX0 @ carrier )
| ! [SX1: a] :
( ~ ( member_a @ SX1 @ carrier )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX1 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SX1 @ SX0 ) @ relation ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[498]) ).
thf(663,plain,
( ( ! [SX0: set_Product_prod_a_a] :
( ~ ! [SX1: a,SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX1 @ SX2 ) @ SX0 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SX0 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SX1 @ SX3 ) @ SX0 ) )
| ( trans_a @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[540]) ).
thf(664,plain,
( ( trans_a
= ( ^ [SX0: set_Product_prod_a_a] :
! [SX1: a,SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX1 @ SX2 ) @ SX0 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SX0 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SX1 @ SX3 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[539]) ).
thf(665,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)],[600]) ).
thf(666,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)],[511]) ).
thf(667,plain,
( ( ! [SX0: a,SX1: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX1 ) @ relation )
| ( member_a @ SX0 @ carrier ) ) )
= $true ),
inference(unfold_def,[status(thm)],[499]) ).
thf(668,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)],[569]) ).
thf(669,plain,
( ( ! [SX0: product_prod_a_a,SX1: multis599418605od_a_a,SX2: multis599418605od_a_a] :
( ( ( add_ms1725977093od_a_a @ SX0 @ SX1 )
!= SX2 )
| ( member449909584od_a_a @ SX0 @ ( set_ms1818337124od_a_a @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[615]) ).
thf(670,plain,
( ( ! [SX0: set_a,SX1: set_Product_prod_a_a,SX2: a,SX3: a,SX4: a] :
( ~ ( prefer719835986ence_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)],[519]) ).
thf(671,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)],[581]) ).
thf(672,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)],[579]) ).
thf(673,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)],[604]) ).
thf(674,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)],[603]) ).
thf(675,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)],[597]) ).
thf(676,plain,
( ( ! [SX0: set_Product_prod_a_a] :
( ~ ! [SX1: a] :
~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX1 @ SX1 ) @ SX0 )
| ( irrefl_a @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[567]) ).
thf(677,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)],[516]) ).
thf(678,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)],[586]) ).
thf(679,plain,
( ( ! [SX0: set_a,SX1: set_Product_prod_a_a,SX2: a,SX3: a] :
( ~ ( refl_on_a @ SX0 @ SX1 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SX1 )
| ( member_a @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[536]) ).
thf(680,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)],[584]) ).
thf(681,plain,
( ( ! [SX0: set_Product_prod_a_a] :
( ~ ( asym_a @ SX0 )
| ! [SX1: a,SX2: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX1 @ SX2 ) @ SX0 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[575]) ).
thf(682,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)],[609]) ).
thf(683,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)],[582]) ).
thf(684,plain,
( ( ! [SX0: a,SX1: a] :
( ~ ~ ( ~ ( member_a @ SX0 @ carrier )
| ~ ( member_a @ SX1 @ carrier ) )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX1 @ SX0 ) @ relation ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX1 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX1 @ SX0 ) @ relation ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[500]) ).
thf(685,plain,
( ( total_on_a
= ( ^ [SX0: set_a,SX1: set_Product_prod_a_a] :
! [SX2: a] :
( ~ ( member_a @ SX2 @ SX0 )
| ! [SX3: a] :
( ~ ( member_a @ SX3 @ SX0 )
| ~ ( ( SX2 != SX3 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SX1 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[526]) ).
thf(686,plain,
( ( asym_a
= ( ^ [SX0: set_Product_prod_a_a] :
~ ! [SX1: set_Product_prod_a_a] :
~ ~ ( ( SX0 != SX1 )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SX1 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[574]) ).
thf(687,plain,
( ( asym_a
= ( ^ [SX0: set_Product_prod_a_a] :
! [SX1: a,SX2: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX1 @ SX2 ) @ SX0 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[576]) ).
thf(688,plain,
( ( ! [SX0: product_prod_a_a,SX1: multis599418605od_a_a,SX2: product_prod_a_a,SX3: multis599418605od_a_a] :
( ( ( add_ms1725977093od_a_a @ SX0 @ SX1 )
!= ( add_ms1725977093od_a_a @ SX2 @ SX3 ) )
| ~ ( ( SX0 != SX2 ) )
| ( member449909584od_a_a @ SX2 @ ( set_ms1818337124od_a_a @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[614]) ).
thf(689,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)],[514]) ).
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)],[545]) ).
thf(691,plain,
( ( ! [SX0: multis599418605od_a_a,SX1: a > a > set_mu1281098573od_a_a,SX2: product_prod_a_a] :
( ~ ( member1755255446od_a_a @ SX0 @ ( produc1121147169od_a_a @ SX1 @ SX2 ) )
| ~ ! [SX3: a,SX4: a] :
( ( SX2
!= ( product_Pair_a_a @ SX3 @ SX4 ) )
| ~ ( member1755255446od_a_a @ SX0 @ ( SX1 @ SX3 @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[561]) ).
thf(692,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)],[513]) ).
thf(693,plain,
( ( ! [SX0: product_prod_a_a,SX1: multis599418605od_a_a] :
( ~ ( member449909584od_a_a @ SX0 @ ( set_ms1818337124od_a_a @ SX1 ) )
| ~ ! [SX2: multis599418605od_a_a] :
( SX1
!= ( add_ms1725977093od_a_a @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[613]) ).
thf(694,plain,
( ( ! [SX0: multiset_a,SX1: a > a > set_multiset_a,SX2: product_prod_a_a] :
( ~ ( member_multiset_a @ SX0 @ ( produc1828150264iset_a @ SX1 @ SX2 ) )
| ~ ! [SX3: a,SX4: a] :
( ( SX2
!= ( product_Pair_a_a @ SX3 @ SX4 ) )
| ~ ( member_multiset_a @ SX0 @ ( SX1 @ SX3 @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[560]) ).
thf(695,plain,
( ( ! [SX0: product_prod_a_a] :
~ ! [SX1: a,SX2: a] :
( SX0
!= ( product_Pair_a_a @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[523]) ).
thf(696,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)],[512]) ).
thf(697,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX1 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX1 @ SX0 ) @ relation ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX1 @ SX2 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX1 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX2 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX0 ) @ relation ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[496]) ).
thf(698,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)],[570]) ).
thf(699,plain,
( ( ! [SX0: a,SX1: a > a > set_a,SX2: product_prod_a_a] :
( ~ ( member_a @ SX0 @ ( produc961951794_set_a @ SX1 @ SX2 ) )
| ~ ! [SX3: a,SX4: a] :
( ( SX2
!= ( product_Pair_a_a @ SX3 @ SX4 ) )
| ~ ( member_a @ SX0 @ ( SX1 @ SX3 @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[558]) ).
thf(700,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)],[522]) ).
thf(701,plain,
( ( ! [SX0: set_Product_prod_a_a,SX1: set_Pr1948701895od_a_a,SX2: product_prod_a_a,SX3: product_prod_a_a] :
( ~ ( refl_o1298442278od_a_a @ SX0 @ SX1 )
| ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SX2 @ SX3 ) @ SX1 )
| ( member449909584od_a_a @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[535]) ).
thf(702,plain,
( ( ! [SX0: set_Product_prod_a_a,SX1: set_Pr1948701895od_a_a,SX2: product_prod_a_a,SX3: product_prod_a_a] :
( ~ ( refl_o1298442278od_a_a @ SX0 @ SX1 )
| ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SX2 @ SX3 ) @ SX1 )
| ~ ( ~ ( member449909584od_a_a @ SX2 @ SX0 )
| ~ ( member449909584od_a_a @ SX3 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[529]) ).
thf(703,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)],[610]) ).
thf(704,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)],[543]) ).
thf(705,plain,
( ( ! [SX0: set_a,SX1: set_Product_prod_a_a,SX2: a,SX3: a] :
( ~ ( refl_on_a @ SX0 @ SX1 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SX1 )
| ( member_a @ SX3 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[534]) ).
thf(706,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)],[578]) ).
thf(707,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)],[591]) ).
thf(708,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)],[605]) ).
thf(709,plain,
( ( ! [SX0: multis599418605od_a_a] :
( ~ ( ( SX0 != zero_z160849828od_a_a ) )
| ~ ! [SX1: product_prod_a_a] :
~ ( member449909584od_a_a @ SX1 @ ( set_ms1818337124od_a_a @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[617]) ).
thf(710,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)],[580]) ).
thf(711,plain,
( ( ! [SX0: produc1127127335iset_a,SX1: a > a > set_Pr158363655iset_a,SX2: product_prod_a_a] :
( ~ ( member340150864iset_a @ SX0 @ ( produc93594587iset_a @ SX1 @ SX2 ) )
| ~ ! [SX3: a,SX4: a] :
( ( SX2
!= ( product_Pair_a_a @ SX3 @ SX4 ) )
| ~ ( member340150864iset_a @ SX0 @ ( SX1 @ SX3 @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[562]) ).
thf(712,plain,
( ( ! [SX0: product_prod_a_a,SX1: multis599418605od_a_a,SX2: multis599418605od_a_a] :
( ~ ~ ( member449909584od_a_a @ SX0 @ ( set_ms1818337124od_a_a @ SX1 ) )
| ( ( minus_1257885652od_a_a @ ( add_ms1725977093od_a_a @ SX0 @ SX2 ) @ SX1 )
= ( add_ms1725977093od_a_a @ SX0 @ ( minus_1257885652od_a_a @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[619]) ).
thf(713,plain,
( ( ! [SX0: product_prod_a_a,SX1: multiset_a > multiset_a > set_Product_prod_a_a,SX2: produc1127127335iset_a] :
( ~ ( member449909584od_a_a @ SX0 @ ( produc2041367259od_a_a @ SX1 @ SX2 ) )
| ~ ! [SX3: multiset_a,SX4: multiset_a] :
( ( SX2
!= ( produc2037245207iset_a @ SX3 @ SX4 ) )
| ~ ( member449909584od_a_a @ SX0 @ ( SX1 @ SX3 @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[563]) ).
thf(714,plain,
( ( ! [SX0: set_a,SX1: set_Product_prod_a_a] :
( ~ ( prefer719835986ence_a @ SX0 @ SX1 )
| ! [SX2: a] :
( ~ ( member_a @ SX2 @ SX0 )
| ! [SX3: a] :
( ~ ( member_a @ SX3 @ SX0 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SX1 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[521]) ).
thf(715,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)],[585]) ).
thf(716,plain,
( ( ! [SX0: product_prod_a_a,SX1: a > a > set_Product_prod_a_a,SX2: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SX0 @ ( produc1093061851od_a_a @ SX1 @ SX2 ) )
| ~ ! [SX3: a,SX4: a] :
( ( SX2
!= ( product_Pair_a_a @ SX3 @ SX4 ) )
| ~ ( member449909584od_a_a @ SX0 @ ( SX1 @ SX3 @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[559]) ).
thf(717,plain,
! [SV1: product_prod_a_a] :
( ( ! [SY426: product_prod_a_a > $o] :
( ( member449909584od_a_a @ SV1 @ ( collec645855634od_a_a @ SY426 ) )
= ( SY426 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(718,plain,
! [SV2: set_Product_prod_a_a] :
( ( ( collec645855634od_a_a
@ ^ [SY427: product_prod_a_a] : ( member449909584od_a_a @ SY427 @ SV2 ) )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(719,plain,
( ( ! [SV3: product_prod_a_a > $o] :
( ( product_curry_a_a_o @ SV3 )
= ( ^ [SY428: a,SY429: a] : ( SV3 @ ( product_Pair_a_a @ SY428 @ SY429 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[548]) ).
thf(720,plain,
( ( product_curry_a_a_o
= ( ^ [F: product_prod_a_a > $o,A6: a,B5: a] : ( F @ ( product_Pair_a_a @ A6 @ B5 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[548]) ).
thf(721,plain,
! [SV4: a] :
( ( ! [SY430: a,SY431: set_Product_prod_a_a,SY432: a > a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ SV4 @ SY430 ) @ ( inv_image_a_a @ SY431 @ SY432 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( SY432 @ SV4 ) @ ( SY432 @ SY430 ) ) @ SY431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(722,plain,
! [SV5: a] :
( ( ! [SY433: a,SY434: set_Pr158363655iset_a,SY435: a > multiset_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ SV5 @ SY433 ) @ ( inv_im975322764et_a_a @ SY434 @ SY435 ) )
= ( member340150864iset_a @ ( produc2037245207iset_a @ ( SY435 @ SV5 ) @ ( SY435 @ SY433 ) ) @ SY434 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(723,plain,
! [SV6: multiset_a] :
( ( ! [SY436: multiset_a,SY437: set_Product_prod_a_a,SY438: multiset_a > a] :
( ( member340150864iset_a @ ( produc2037245207iset_a @ SV6 @ SY436 ) @ ( inv_im479034648iset_a @ SY437 @ SY438 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( SY438 @ SV6 ) @ ( SY438 @ SY436 ) ) @ SY437 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[552]) ).
thf(724,plain,
! [SV7: a] :
( ( ! [SY439: a,SY440: set_Pr1948701895od_a_a,SY441: a > product_prod_a_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ SV7 @ SY439 ) @ ( inv_im777352425_a_a_a @ SY440 @ SY441 ) )
= ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( SY441 @ SV7 ) @ ( SY441 @ SY439 ) ) @ SY440 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(725,plain,
! [SV8: product_prod_a_a] :
( ( ! [SY442: product_prod_a_a,SY443: set_Product_prod_a_a,SY444: product_prod_a_a > a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV8 @ SY442 ) @ ( inv_im15016955od_a_a @ SY443 @ SY444 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( SY444 @ SV8 ) @ ( SY444 @ SY442 ) ) @ SY443 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(726,plain,
! [SV9: a] :
( ( ! [SY445: a,SY446: set_Pr1821581383od_a_a,SY447: a > multis599418605od_a_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SY445 ) @ ( inv_im1681759523_a_a_a @ SY446 @ SY447 ) )
= ( member1349055120od_a_a @ ( produc1859144151od_a_a @ ( SY447 @ SV9 ) @ ( SY447 @ SY445 ) ) @ SY446 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[555]) ).
thf(727,plain,
! [SV10: multis599418605od_a_a] :
( ( ! [SY448: multis599418605od_a_a,SY449: set_Product_prod_a_a,SY450: multis599418605od_a_a > a] :
( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ SV10 @ SY448 ) @ ( inv_im941243329od_a_a @ SY449 @ SY450 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( SY450 @ SV10 ) @ ( SY450 @ SY448 ) ) @ SY449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(728,plain,
! [SV11: a] :
( ( ! [SY451: a] :
( ( product_swap_a_a @ ( product_Pair_a_a @ SV11 @ SY451 ) )
= ( product_Pair_a_a @ SY451 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(729,plain,
! [SV12: a > a > set_Product_prod_a_a] :
( ( ! [SY452: a,SY453: a] :
( ( produc1093061851od_a_a @ SV12 @ ( product_Pair_a_a @ SY452 @ SY453 ) )
= ( SV12 @ SY452 @ SY453 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(730,plain,
! [SV13: a > a > set_a] :
( ( ! [SY454: a,SY455: a] :
( ( produc961951794_set_a @ SV13 @ ( product_Pair_a_a @ SY454 @ SY455 ) )
= ( SV13 @ SY454 @ SY455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(731,plain,
! [SV14: a > a > $o] :
( ( ! [SY456: a,SY457: a] :
( ( produc1833107820_a_a_o @ SV14 @ ( product_Pair_a_a @ SY456 @ SY457 ) )
= ( SV14 @ SY456 @ SY457 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(732,plain,
( ( ! [SV15: set_Product_prod_a_a] :
( ( irrefl_a @ SV15 )
= ( ! [SY458: a] :
~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY458 @ SY458 ) @ SV15 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[568]) ).
thf(733,plain,
( ( irrefl_a
= ( ^ [R: set_Product_prod_a_a] :
! [A6: a] :
~ ( member449909584od_a_a @ ( product_Pair_a_a @ A6 @ A6 ) @ R ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[568]) ).
thf(734,plain,
! [SV16: a] :
( ( ! [SY459: a,SY460: set_Product_prod_a_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ SV16 @ SY459 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SY460 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ SY459 @ SV16 ) @ SY460 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(735,plain,
( ( ! [SV17: product_prod_a_a] :
( ( top_to1483957574_a_a_o @ SV17 )
= ( member449909584od_a_a @ SV17 @ top_to398455383od_a_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[587]) ).
thf(736,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)],[587]) ).
thf(737,plain,
! [SV18: a > a] :
( ( ! [SY461: a > a,SY462: a,SY463: a] :
( ( produc700022774_a_a_a @ SV18 @ SY461 @ ( product_Pair_a_a @ SY462 @ SY463 ) )
= ( product_Pair_a_a @ ( SV18 @ SY462 ) @ ( SY461 @ SY463 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(738,plain,
! [SV19: product_prod_a_a] :
( ( ( product_Pair_a_a @ ( product_fst_a_a @ SV19 ) @ ( product_snd_a_a @ SV19 ) )
= SV19 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(739,plain,
! [SV20: product_prod_a_a] :
( ( SV20
= ( product_Pair_a_a @ ( product_fst_a_a @ SV20 ) @ ( product_snd_a_a @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(740,plain,
! [SV21: product_prod_a_a] :
( ( SV21
= ( product_Pair_a_a @ ( product_fst_a_a @ SV21 ) @ ( product_snd_a_a @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(741,plain,
! [SV22: a] :
( ( ! [SY464: a] :
( ( product_fst_a_a @ ( product_Pair_a_a @ SV22 @ SY464 ) )
= SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(742,plain,
! [SV23: a] :
( ( ! [SY465: a] :
( ( product_snd_a_a @ ( product_Pair_a_a @ SV23 @ SY465 ) )
= SY465 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(743,plain,
( ( ! [SV24: product_prod_a_a] :
( ( product_swap_a_a @ SV24 )
= ( product_Pair_a_a @ ( product_snd_a_a @ SV24 ) @ ( product_fst_a_a @ SV24 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[598]) ).
thf(744,plain,
( ( product_swap_a_a
= ( ^ [P3: product_prod_a_a] : ( product_Pair_a_a @ ( product_snd_a_a @ P3 ) @ ( product_fst_a_a @ P3 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[598]) ).
thf(745,plain,
! [SV25: product_prod_a_a] :
( ( ! [SY466: multis599418605od_a_a,SY467: multis599418605od_a_a] :
( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ ( plus_p404985124od_a_a @ SY466 @ SY467 ) ) )
= ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SY466 ) )
| ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SY467 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[616]) ).
thf(746,plain,
! [SV26: product_prod_a_a] :
( ( member449909584od_a_a @ SV26 @ ( set_ms1818337124od_a_a @ ( add_ms1725977093od_a_a @ SV26 @ zero_z160849828od_a_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(747,plain,
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ x @ y ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ y @ x ) @ relation ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[621]) ).
thf(748,plain,
! [SV27: product_prod_a_a] :
( ( ! [SY468: multis599418605od_a_a,SY469: multis599418605od_a_a] :
( ~ ( member449909584od_a_a @ SV27 @ ( set_ms1818337124od_a_a @ ( minus_1257885652od_a_a @ SY468 @ SY469 ) ) )
| ( member449909584od_a_a @ SV27 @ ( set_ms1818337124od_a_a @ SY468 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(749,plain,
! [SV28: a] :
( ( ! [SY470: a,SY471: a,SY472: a] :
( ( ( product_Pair_a_a @ SV28 @ SY470 )
!= ( product_Pair_a_a @ SY471 @ SY472 ) )
| ~ ( ( SV28 != SY471 )
| ( SY470 != SY472 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(750,plain,
! [SV29: produc1572603623od_a_a > $o] :
( ( ! [SY473: produc1572603623od_a_a] :
( ~ ! [SY474: product_prod_a_a,SY475: a,SY476: a] : ( SV29 @ ( produc1474507607od_a_a @ SY474 @ ( product_Pair_a_a @ SY475 @ SY476 ) ) )
| ( SV29 @ SY473 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(751,plain,
( ( x = y )
= $false ),
inference(extcnf_not_pos,[status(thm)],[625]) ).
thf(752,plain,
! [SV30: a] :
( ( ! [SY477: a,SY478: a] :
( ( ( product_fst_a_a @ ( product_Pair_a_a @ SV30 @ SY477 ) )
!= SY478 )
| ( SV30 = SY478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(753,plain,
! [SV31: product_prod_a_a > $o] :
( ( ! [SY479: a,SY480: a] :
( ~ ( SV31 @ ( product_Pair_a_a @ SY479 @ SY480 ) )
| ( product_curry_a_a_o @ SV31 @ SY479 @ SY480 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(754,plain,
! [SV32: set_Product_prod_a_a] :
( ( ! [SY481: set_Pr1948701895od_a_a] :
( ~ ! [SY482: product_prod_a_a,SY483: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY482 @ SV32 )
| ~ ( member449909584od_a_a @ SY483 @ SV32 )
| ~ ( ( SY482 != SY483 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY482 @ SY483 ) @ SY481 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY483 @ SY482 ) @ SY481 ) )
| ( total_1490170027od_a_a @ SV32 @ SY481 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(755,plain,
! [SV33: a > $o] :
( ( ! [SY484: a,SY485: a > $o,SY486: a] :
( ~ ( SV33 @ SY484 )
| ~ ( SY485 @ SY486 )
| ~ ( ~ ( SV33 @ ( product_fst_a_a @ ( product_Pair_a_a @ SY484 @ SY486 ) ) )
| ~ ( SY485 @ ( product_snd_a_a @ ( product_Pair_a_a @ SY484 @ SY486 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(756,plain,
! [SV34: a > $o] :
( ( ! [SY487: a,SY488: a,SY489: a,SY490: a > set_Product_prod_a_a] :
( ~ ( SV34 @ SY487 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY488 @ SY489 ) @ ( SY490 @ SY487 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SY487 @ SY488 ) @ ( product_Pair_a_a @ SY487 @ SY489 ) ) @ ( same_fst_a_a @ SV34 @ SY490 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(757,plain,
! [SV35: product_prod_a_a] :
( ( ! [SY491: multis599418605od_a_a] :
( ~ ( member449909584od_a_a @ SV35 @ ( set_ms1818337124od_a_a @ SY491 ) )
| ~ ! [SY492: multis599418605od_a_a] :
( SY491
!= ( add_ms1725977093od_a_a @ SV35 @ SY492 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(758,plain,
! [SV36: set_Product_prod_a_a] :
( ( ! [SY493: set_Product_prod_a_a > $o] :
( ~ ( asym_a @ SV36 )
| ~ ! [SX2: set_Product_prod_a_a] :
( ~ ! [SX3: a,SX4: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX4 ) @ SX2 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX4 @ SX3 ) @ SX2 ) )
| ( SY493 @ SX2 ) )
| ( SY493 @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(759,plain,
! [SV37: set_Product_prod_a_a] :
( ( ! [SY497: set_Product_prod_a_a] :
( ~ ! [SY498: a,SY499: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY498 @ SY499 ) @ SV37 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY498 @ SY499 ) @ SY497 ) )
| ( ord_le1824328871od_a_a @ SV37 @ SY497 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(760,plain,
! [SV38: product_prod_a_a] :
( ( ! [SY500: product_prod_a_a,SY501: set_Product_prod_a_a,SY502: set_Pr1948701895od_a_a] :
( ~ ( member449909584od_a_a @ SV38 @ ( prefer477097315od_a_a @ SY500 @ SY501 @ SY502 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV38 @ SY500 ) @ SY502 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(761,plain,
( ( ! [SV39: set_Product_prod_a_a] :
( ( total_1490170027od_a_a @ SV39 )
= ( ^ [SY503: set_Pr1948701895od_a_a] :
! [SY504: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY504 @ SV39 )
| ! [SY505: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY505 @ SV39 )
| ~ ( ( SY504 != SY505 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY504 @ SY505 ) @ SY503 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY505 @ SY504 ) @ SY503 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[635]) ).
thf(762,plain,
( ( total_1490170027od_a_a
= ( ^ [SX0: set_Product_prod_a_a,SX1: set_Pr1948701895od_a_a] :
! [SX2: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SX2 @ SX0 )
| ! [SX3: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SX3 @ SX0 )
| ~ ( ( SX2 != SX3 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SX2 @ SX3 ) @ SX1 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SX3 @ SX2 ) @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[635]) ).
thf(763,plain,
! [SV40: a] :
( ( ! [SY506: product_prod_a_a] :
( ( SV40
= ( product_fst_a_a @ SY506 ) )
= ( ~ ! [SY507: a] :
( SY506
!= ( product_Pair_a_a @ SV40 @ SY507 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(764,plain,
! [SV41: set_Product_prod_a_a] :
( ( ! [SY508: a,SY509: a,SY510: a] :
( ~ ( trans_a @ SV41 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY508 @ SY509 ) @ SV41 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY509 @ SY510 ) @ SV41 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY508 @ SY510 ) @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(765,plain,
! [SV42: set_Product_prod_a_a] :
( ( ! [SY511: set_Pr1948701895od_a_a,SY512: product_prod_a_a,SY513: product_prod_a_a] :
( ~ ( prefer1338892073od_a_a @ SV42 @ SY511 )
| ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY512 @ SY513 ) @ SY511 )
| ( member449909584od_a_a @ SY512 @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(766,plain,
! [SV43: a > a > $o] :
( ( ! [SY514: a,SY515: a,SY516: product_prod_a_a] :
( ~ ( SV43 @ SY514 @ SY515 )
| ( SY516
!= ( product_Pair_a_a @ SY514 @ SY515 ) )
| ( SV43 @ ( product_fst_a_a @ SY516 ) @ ( product_snd_a_a @ SY516 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(767,plain,
! [SV44: a] :
( ( ! [SY517: a,SY518: a,SY519: a] :
( ( ( product_Pair_a_a @ SV44 @ SY517 )
= ( product_Pair_a_a @ SY518 @ SY519 ) )
= ( ~ ( ( SV44 != SY518 )
| ( SY517 != SY519 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(768,plain,
! [SV45: set_Product_prod_a_a] :
( ( ! [SY520: a,SY521: a,SY522: a] :
( ~ ( trans_a @ SV45 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY520 @ SY521 ) @ SV45 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY521 @ SY522 ) @ SV45 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY520 @ SY522 ) @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(769,plain,
! [SV46: set_a] :
( ( ! [SY523: a > product_prod_a_a,SY524: set_Product_prod_a_a] :
( ~ ! [SY525: a] :
( ~ ( member_a @ SY525 @ SV46 )
| ( member449909584od_a_a @ ( SY523 @ SY525 ) @ SY524 ) )
| ( ord_le1824328871od_a_a @ ( image_1725938350od_a_a @ SY523 @ SV46 ) @ SY524 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(770,plain,
! [SV47: set_Product_prod_a_a] :
( ( ! [SY526: set_Pr1948701895od_a_a] :
( ~ ( prefer697821563od_a_a @ SV47 @ SY526 )
| ! [SY527: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY527 @ SV47 )
| ! [SY528: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY528 @ SV47 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY527 @ SY528 ) @ SY526 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY528 @ SY527 ) @ SY526 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(771,plain,
! [SV48: set_a] :
( ( ! [SY529: set_Product_prod_a_a] :
( ~ ! [SY530: a,SY531: a] :
( ~ ( member_a @ SY530 @ SV48 )
| ~ ( member_a @ SY531 @ SV48 )
| ~ ( ( SY530 != SY531 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY530 @ SY531 ) @ SY529 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY531 @ SY530 ) @ SY529 ) )
| ( total_on_a @ SV48 @ SY529 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(772,plain,
! [SV49: product_prod_a_a] :
( ( ! [SY532: product_prod_a_a,SY533: set_Product_prod_a_a,SY534: set_Pr1948701895od_a_a] :
( ~ ( member449909584od_a_a @ SV49 @ ( prefer477097315od_a_a @ SY532 @ SY533 @ SY534 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV49 @ SY532 ) @ SY534 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(773,plain,
! [SV50: product_prod_a_a] :
( ( ~ ! [SY535: a] :
~ ~ ! [SY536: a] :
( SV50
!= ( product_Pair_a_a @ SY535 @ SY536 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(774,plain,
! [SV51: set_Product_prod_a_a] :
( ( ! [SY537: set_Pr1948701895od_a_a,SY538: product_prod_a_a] :
( ~ ( refl_o1298442278od_a_a @ SV51 @ SY537 )
| ~ ( member449909584od_a_a @ SY538 @ SV51 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY538 @ SY538 ) @ SY537 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(775,plain,
! [SV52: a] :
( ( ! [SY539: a,SY540: a,SY541: a,SY542: set_Product_prod_a_a,SY543: set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SY539 ) @ ( product_Pair_a_a @ SY540 @ SY541 ) ) @ ( lex_prod_a_a @ SY542 @ SY543 ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SY540 ) @ SY542 )
| ~ ( ( SV52 != SY540 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY539 @ SY541 ) @ SY543 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(776,plain,
! [SV53: set_Product_prod_a_a] :
( ( ! [SY544: set_Pr1948701895od_a_a,SY545: product_prod_a_a,SY546: product_prod_a_a] :
( ~ ( refl_o1298442278od_a_a @ SV53 @ SY544 )
| ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY545 @ SY546 ) @ SY544 )
| ( member449909584od_a_a @ SY546 @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(777,plain,
! [SV54: set_a] :
( ( ! [SY547: set_Product_prod_a_a,SY548: a] :
( ~ ( refl_on_a @ SV54 @ SY547 )
| ~ ( member_a @ SY548 @ SV54 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY548 @ SY548 ) @ SY547 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(778,plain,
! [SV55: a] :
( ( ! [SY549: a,SY550: set_a,SY551: set_Product_prod_a_a] :
( ~ ( member_a @ SV55 @ ( prefer161218362good_a @ SY549 @ SY550 @ SY551 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV55 @ SY549 ) @ SY551 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(779,plain,
! [SV56: a] :
( ( ! [SY552: a,SY553: a,SY554: a] :
( ( ( product_Pair_a_a @ SV56 @ SY552 )
= ( product_Pair_a_a @ SY553 @ SY554 ) )
= ( ~ ( ( SV56 != SY553 )
| ( SY552 != SY554 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[652]) ).
thf(780,plain,
! [SV57: a] :
( ( ! [SY555: a,SY556: a] :
( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SY555 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY555 @ SV57 ) @ relation ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY555 @ SY556 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY556 @ SY555 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SY556 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY556 @ SV57 ) @ relation ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(781,plain,
! [SV58: set_a] :
( ( ! [SY557: set_Product_prod_a_a,SY558: a,SY559: a] :
( ~ ( refl_on_a @ SV58 @ SY557 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY558 @ SY559 ) @ SY557 )
| ~ ( ~ ( member_a @ SY558 @ SV58 )
| ~ ( member_a @ SY559 @ SV58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(782,plain,
! [SV59: product_prod_a_a] :
( ( ! [SY560: a > a,SY561: a > a,SY562: set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ SV59 @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SY560 @ SY561 ) @ SY562 ) )
| ~ ! [SY563: a,SY564: a] :
( ( SV59
!= ( product_Pair_a_a @ ( SY560 @ SY563 ) @ ( SY561 @ SY564 ) ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY563 @ SY564 ) @ SY562 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(783,plain,
! [SV60: set_Product_prod_a_a] :
( ( ! [SY565: set_Pr1948701895od_a_a,SY566: product_prod_a_a,SY567: product_prod_a_a] :
( ~ ( prefer697821563od_a_a @ SV60 @ SY565 )
| ~ ~ ( ~ ( member449909584od_a_a @ SY566 @ SV60 )
| ~ ( member449909584od_a_a @ SY567 @ SV60 ) )
| ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY567 @ SY566 ) @ SY565 ) )
= ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY566 @ SY567 ) @ SY565 )
| ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY567 @ SY566 ) @ SY565 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(784,plain,
! [SV61: set_a] :
( ( ! [SY568: set_Product_prod_a_a,SY569: a,SY570: a] :
( ~ ( prefer719835986ence_a @ SV61 @ SY568 )
| ~ ~ ( ~ ( member_a @ SY569 @ SV61 )
| ~ ( member_a @ SY570 @ SV61 ) )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY570 @ SY569 ) @ SY568 ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY569 @ SY570 ) @ SY568 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY570 @ SY569 ) @ SY568 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(785,plain,
! [SV62: product_prod_a_a > $o] :
( ( ! [SY571: product_prod_a_a] :
( ~ ! [SY572: a,SY573: a] : ( SV62 @ ( product_Pair_a_a @ SY572 @ SY573 ) )
| ( SV62 @ SY571 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(786,plain,
! [SV63: set_Product_prod_a_a] :
( ( ~ ! [SY574: a,SY575: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY574 @ SY575 ) @ SV63 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY575 @ SY574 ) @ SV63 ) )
| ( asym_a @ SV63 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(787,plain,
! [SV64: set_Product_prod_a_a] :
( ( ! [SY576: a,SY577: a] :
( ~ ( asym_a @ SV64 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY576 @ SY577 ) @ SV64 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY577 @ SY576 ) @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(788,plain,
! [SV65: product_prod_a_a] :
( ( ! [SY578: set_Product_prod_a_a,SY579: product_prod_a_a > product_prod_a_a] :
( ~ ( member449909584od_a_a @ SV65 @ SY578 )
| ( member449909584od_a_a @ ( SY579 @ SV65 ) @ ( image_794773445od_a_a @ SY579 @ SY578 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(789,plain,
! [SV66: a] :
( ( ~ ( member_a @ SV66 @ carrier )
| ! [SY580: a] :
( ~ ( member_a @ SY580 @ carrier )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV66 @ SY580 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY580 @ SV66 ) @ relation ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(790,plain,
! [SV67: set_Product_prod_a_a] :
( ( ~ ! [SY581: a,SY582: a,SY583: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY581 @ SY582 ) @ SV67 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY582 @ SY583 ) @ SV67 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY581 @ SY583 ) @ SV67 ) )
| ( trans_a @ SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(791,plain,
( ( ! [SV68: set_Product_prod_a_a] :
( ( trans_a @ SV68 )
= ( ! [SY584: a,SY585: a,SY586: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY584 @ SY585 ) @ SV68 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY585 @ SY586 ) @ SV68 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY584 @ SY586 ) @ SV68 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[664]) ).
thf(792,plain,
( ( trans_a
= ( ^ [SX0: set_Product_prod_a_a] :
! [SX1: a,SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX1 @ SX2 ) @ SX0 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SX0 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SX1 @ SX3 ) @ SX0 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[664]) ).
thf(793,plain,
! [SV69: a > a > $o] :
( ( ! [SY587: a,SY588: a] :
( ~ ( SV69 @ SY587 @ SY588 )
| ( SV69 @ ( product_snd_a_a @ ( product_Pair_a_a @ SY588 @ SY587 ) ) @ ( product_fst_a_a @ ( product_Pair_a_a @ SY588 @ SY587 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(794,plain,
! [SV70: produc1572603623od_a_a] :
( ( ~ ! [SY589: product_prod_a_a,SY590: a,SY591: a] :
( SV70
!= ( produc1474507607od_a_a @ SY589 @ ( product_Pair_a_a @ SY590 @ SY591 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(795,plain,
! [SV71: a] :
( ( ! [SY592: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SY592 ) @ relation )
| ( member_a @ SV71 @ carrier ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(796,plain,
! [SV72: product_prod_a_a > $o] :
( ( ! [SY593: a,SY594: a] :
( ~ ( product_curry_a_a_o @ SV72 @ SY593 @ SY594 )
| ( SV72 @ ( product_Pair_a_a @ SY593 @ SY594 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(797,plain,
! [SV73: product_prod_a_a] :
( ( ! [SY595: multis599418605od_a_a,SY596: multis599418605od_a_a] :
( ( ( add_ms1725977093od_a_a @ SV73 @ SY595 )
!= SY596 )
| ( member449909584od_a_a @ SV73 @ ( set_ms1818337124od_a_a @ SY596 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(798,plain,
! [SV74: set_a] :
( ( ! [SY597: set_Product_prod_a_a,SY598: a,SY599: a,SY600: a] :
( ~ ( prefer719835986ence_a @ SV74 @ SY597 )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY598 @ SY599 ) @ SY597 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY599 @ SY598 ) @ SY597 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY599 @ SY600 ) @ SY597 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY600 @ SY599 ) @ SY597 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY598 @ SY600 ) @ SY597 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY600 @ SY598 ) @ SY597 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(799,plain,
! [SV75: a] :
( ( ! [SY601: set_a,SY602: a > product_prod_a_a] :
( ~ ( member_a @ SV75 @ SY601 )
| ( member449909584od_a_a @ ( SY602 @ SV75 ) @ ( image_1725938350od_a_a @ SY602 @ SY601 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(800,plain,
! [SV76: a] :
( ( ! [SY603: product_prod_a_a > a,SY604: product_prod_a_a,SY605: set_Product_prod_a_a] :
( ( SV76
!= ( SY603 @ SY604 ) )
| ~ ( member449909584od_a_a @ SY604 @ SY605 )
| ( member_a @ SV76 @ ( image_340790172_a_a_a @ SY603 @ SY605 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(801,plain,
! [SV77: product_prod_a_a] :
( ( ! [SY606: a,SY607: a] :
( ( SV77
!= ( product_Pair_a_a @ SY606 @ SY607 ) )
| ( ( product_fst_a_a @ SV77 )
= SY606 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(802,plain,
! [SV78: product_prod_a_a] :
( ( ! [SY608: a,SY609: a] :
( ( SV78
!= ( product_Pair_a_a @ SY608 @ SY609 ) )
| ( ( product_snd_a_a @ SV78 )
= SY609 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(803,plain,
! [SV79: a] :
( ( ! [SY610: a,SY611: a] :
( ( ( product_snd_a_a @ ( product_Pair_a_a @ SV79 @ SY610 ) )
!= SY611 )
| ( SY610 = SY611 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(804,plain,
! [SV80: set_Product_prod_a_a] :
( ( ~ ! [SY612: a] :
~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY612 @ SY612 ) @ SV80 )
| ( irrefl_a @ SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(805,plain,
! [SV81: set_a] :
( ( ! [SY613: set_Product_prod_a_a,SY614: a,SY615: a] :
( ~ ( prefer1292084992ence_a @ SV81 @ SY613 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY614 @ SY615 ) @ SY613 )
| ( member_a @ SY614 @ SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(806,plain,
! [SV82: product_prod_a_a] :
( ( ! [SY616: set_Product_prod_a_a,SY617: product_prod_a_a,SY618: product_prod_a_a > product_prod_a_a] :
( ~ ( member449909584od_a_a @ SV82 @ SY616 )
| ( SY617
!= ( SY618 @ SV82 ) )
| ( member449909584od_a_a @ SY617 @ ( image_794773445od_a_a @ SY618 @ SY616 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(807,plain,
! [SV83: set_a] :
( ( ! [SY619: set_Product_prod_a_a,SY620: a,SY621: a] :
( ~ ( refl_on_a @ SV83 @ SY619 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY620 @ SY621 ) @ SY619 )
| ( member_a @ SY620 @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(808,plain,
! [SV84: a] :
( ( ! [SY622: set_a,SY623: product_prod_a_a,SY624: a > product_prod_a_a] :
( ~ ( member_a @ SV84 @ SY622 )
| ( SY623
!= ( SY624 @ SV84 ) )
| ( member449909584od_a_a @ SY623 @ ( image_1725938350od_a_a @ SY624 @ SY622 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(809,plain,
! [SV85: set_Product_prod_a_a] :
( ( ~ ( asym_a @ SV85 )
| ! [SY625: a,SY626: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY625 @ SY626 ) @ SV85 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY626 @ SY625 ) @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(810,plain,
! [SV86: set_Product_prod_a_a] :
( ( ! [SY627: product_prod_a_a > a,SY628: set_a] :
( ~ ! [SY629: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY629 @ SV86 )
| ( member_a @ ( SY627 @ SY629 ) @ SY628 ) )
| ( ord_less_eq_set_a @ ( image_340790172_a_a_a @ SY627 @ SV86 ) @ SY628 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(811,plain,
! [SV87: product_prod_a_a] :
( ( ! [SY630: set_Product_prod_a_a,SY631: product_prod_a_a > a] :
( ~ ( member449909584od_a_a @ SV87 @ SY630 )
| ( member_a @ ( SY631 @ SV87 ) @ ( image_340790172_a_a_a @ SY631 @ SY630 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(812,plain,
! [SV88: a] :
( ( ! [SY632: a] :
( ~ ~ ( ~ ( member_a @ SV88 @ carrier )
| ~ ( member_a @ SY632 @ carrier ) )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY632 @ SV88 ) @ relation ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SY632 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY632 @ SV88 ) @ relation ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(813,plain,
( ( ! [SV89: set_a] :
( ( total_on_a @ SV89 )
= ( ^ [SY633: set_Product_prod_a_a] :
! [SY634: a] :
( ~ ( member_a @ SY634 @ SV89 )
| ! [SY635: a] :
( ~ ( member_a @ SY635 @ SV89 )
| ~ ( ( SY634 != SY635 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY634 @ SY635 ) @ SY633 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY635 @ SY634 ) @ SY633 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[685]) ).
thf(814,plain,
( ( total_on_a
= ( ^ [SX0: set_a,SX1: set_Product_prod_a_a] :
! [SX2: a] :
( ~ ( member_a @ SX2 @ SX0 )
| ! [SX3: a] :
( ~ ( member_a @ SX3 @ SX0 )
| ~ ( ( SX2 != SX3 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SX1 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[685]) ).
thf(815,plain,
( ( ! [SV90: set_Product_prod_a_a] :
( ( asym_a @ SV90 )
= ( ~ ! [SY636: set_Product_prod_a_a] :
~ ~ ( ( SV90 != SY636 )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SY636 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SY636 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[686]) ).
thf(816,plain,
( ( asym_a
= ( ^ [SX0: set_Product_prod_a_a] :
~ ! [SX1: set_Product_prod_a_a] :
~ ~ ( ( SX0 != SX1 )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SX1 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[686]) ).
thf(817,plain,
( ( ! [SV91: set_Product_prod_a_a] :
( ( asym_a @ SV91 )
= ( ! [SY639: a,SY640: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY639 @ SY640 ) @ SV91 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY640 @ SY639 ) @ SV91 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[687]) ).
thf(818,plain,
( ( asym_a
= ( ^ [SX0: set_Product_prod_a_a] :
! [SX1: a,SX2: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX1 @ SX2 ) @ SX0 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[687]) ).
thf(819,plain,
! [SV92: product_prod_a_a] :
( ( ! [SY641: multis599418605od_a_a,SY642: product_prod_a_a,SY643: multis599418605od_a_a] :
( ( ( add_ms1725977093od_a_a @ SV92 @ SY641 )
!= ( add_ms1725977093od_a_a @ SY642 @ SY643 ) )
| ~ ( ( SV92 != SY642 ) )
| ( member449909584od_a_a @ SY642 @ ( set_ms1818337124od_a_a @ SY641 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(820,plain,
! [SV93: set_a] :
( ( ! [SY644: set_Product_prod_a_a,SY645: a,SY646: a,SY647: a] :
( ~ ( prefer1292084992ence_a @ SV93 @ SY644 )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY645 @ SY646 ) @ SY644 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY646 @ SY645 ) @ SY644 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY646 @ SY647 ) @ SY644 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY647 @ SY646 ) @ SY644 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY645 @ SY647 ) @ SY644 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY647 @ SY645 ) @ SY644 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(821,plain,
! [SV94: a] :
( ( ! [SY648: a,SY649: set_a,SY650: set_Product_prod_a_a] :
( ~ ( member_a @ SV94 @ ( prefer161218362good_a @ SY648 @ SY649 @ SY650 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV94 @ SY648 ) @ SY650 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(822,plain,
! [SV95: multis599418605od_a_a] :
( ( ! [SY651: a > a > set_mu1281098573od_a_a,SY652: product_prod_a_a] :
( ~ ( member1755255446od_a_a @ SV95 @ ( produc1121147169od_a_a @ SY651 @ SY652 ) )
| ~ ! [SY653: a,SY654: a] :
( ( SY652
!= ( product_Pair_a_a @ SY653 @ SY654 ) )
| ~ ( member1755255446od_a_a @ SV95 @ ( SY651 @ SY653 @ SY654 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[691]) ).
thf(823,plain,
( ( ! [SV96: set_a] :
( ( prefer1292084992ence_a @ SV96 )
= ( ^ [SY655: set_Product_prod_a_a] :
~ ( ~ ~ ( ~ ! [SY656: a,SY657: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY656 @ SY657 ) @ SY655 )
| ( member_a @ SY656 @ SV96 ) )
| ~ ! [SY658: a,SY659: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY658 @ SY659 ) @ SY655 )
| ( member_a @ SY659 @ SV96 ) ) )
| ~ ( order_preorder_on_a @ SV96 @ SY655 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[692]) ).
thf(824,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)],[692]) ).
thf(825,plain,
! [SV97: product_prod_a_a] :
( ( ! [SY660: multis599418605od_a_a] :
( ~ ( member449909584od_a_a @ SV97 @ ( set_ms1818337124od_a_a @ SY660 ) )
| ~ ! [SY661: multis599418605od_a_a] :
( SY660
!= ( add_ms1725977093od_a_a @ SV97 @ SY661 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(826,plain,
! [SV98: multiset_a] :
( ( ! [SY662: a > a > set_multiset_a,SY663: product_prod_a_a] :
( ~ ( member_multiset_a @ SV98 @ ( produc1828150264iset_a @ SY662 @ SY663 ) )
| ~ ! [SY664: a,SY665: a] :
( ( SY663
!= ( product_Pair_a_a @ SY664 @ SY665 ) )
| ~ ( member_multiset_a @ SV98 @ ( SY662 @ SY664 @ SY665 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(827,plain,
! [SV99: product_prod_a_a] :
( ( ~ ! [SY666: a,SY667: a] :
( SV99
!= ( product_Pair_a_a @ SY666 @ SY667 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(828,plain,
! [SV100: set_Product_prod_a_a] :
( ( ! [SY668: set_a] :
( ~ ! [SY669: a,SY670: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY669 @ SY670 ) @ SV100 )
| ( member_a @ SY669 @ SY668 ) )
| ~ ! [SY671: a,SY672: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY671 @ SY672 ) @ SV100 )
| ( member_a @ SY672 @ SY668 ) )
| ~ ( order_preorder_on_a @ SY668 @ SV100 )
| ( prefer1292084992ence_a @ SY668 @ SV100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(829,plain,
! [SV101: a] :
( ( ! [SY673: a,SY674: a] :
( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SY673 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY673 @ SV101 ) @ relation ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY673 @ SY674 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY674 @ SY673 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SY674 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY674 @ SV101 ) @ relation ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(830,plain,
! [SV102: product_prod_a_a > $o] :
( ( ! [SY675: a,SY676: a] :
( ~ ( product_curry_a_a_o @ SV102 @ SY675 @ SY676 )
| ( SV102 @ ( product_Pair_a_a @ SY675 @ SY676 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(831,plain,
! [SV103: a] :
( ( ! [SY677: a > a > set_a,SY678: product_prod_a_a] :
( ~ ( member_a @ SV103 @ ( produc961951794_set_a @ SY677 @ SY678 ) )
| ~ ! [SY679: a,SY680: a] :
( ( SY678
!= ( product_Pair_a_a @ SY679 @ SY680 ) )
| ~ ( member_a @ SV103 @ ( SY677 @ SY679 @ SY680 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(832,plain,
! [SV104: product_prod_a_a > $o] :
( ( ! [SY681: product_prod_a_a] :
( ~ ! [SY682: a,SY683: a] : ( SV104 @ ( product_Pair_a_a @ SY682 @ SY683 ) )
| ( SV104 @ SY681 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(833,plain,
! [SV105: set_Product_prod_a_a] :
( ( ! [SY684: set_Pr1948701895od_a_a,SY685: product_prod_a_a,SY686: product_prod_a_a] :
( ~ ( refl_o1298442278od_a_a @ SV105 @ SY684 )
| ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY685 @ SY686 ) @ SY684 )
| ( member449909584od_a_a @ SY685 @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(834,plain,
! [SV106: set_Product_prod_a_a] :
( ( ! [SY687: set_Pr1948701895od_a_a,SY688: product_prod_a_a,SY689: product_prod_a_a] :
( ~ ( refl_o1298442278od_a_a @ SV106 @ SY687 )
| ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY688 @ SY689 ) @ SY687 )
| ~ ( ~ ( member449909584od_a_a @ SY688 @ SV106 )
| ~ ( member449909584od_a_a @ SY689 @ SV106 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(835,plain,
! [SV107: set_Product_prod_a_a] :
( ( ! [SY690: product_prod_a_a > product_prod_a_a,SY691: set_Product_prod_a_a] :
( ~ ! [SY692: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY692 @ SV107 )
| ( member449909584od_a_a @ ( SY690 @ SY692 ) @ SY691 ) )
| ( ord_le1824328871od_a_a @ ( image_794773445od_a_a @ SY690 @ SV107 ) @ SY691 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(836,plain,
! [SV108: a] :
( ( ! [SY693: a,SY694: set_Product_prod_a_a,SY695: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV108 @ SY693 ) @ SY694 )
| ( SY695 != SY693 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV108 @ SY695 ) @ SY694 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(837,plain,
! [SV109: set_a] :
( ( ! [SY696: set_Product_prod_a_a,SY697: a,SY698: a] :
( ~ ( refl_on_a @ SV109 @ SY696 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY697 @ SY698 ) @ SY696 )
| ( member_a @ SY698 @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(838,plain,
! [SV110: product_prod_a_a] :
( ( ! [SY699: a > product_prod_a_a,SY700: a,SY701: set_a] :
( ( SV110
!= ( SY699 @ SY700 ) )
| ~ ( member_a @ SY700 @ SY701 )
| ( member449909584od_a_a @ SV110 @ ( image_1725938350od_a_a @ SY699 @ SY701 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(839,plain,
! [SV111: a] :
( ( ! [SY702: a,SY703: set_Product_prod_a_a,SY704: a > a,SY705: a > a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV111 @ SY702 ) @ SY703 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( SY704 @ SV111 ) @ ( SY705 @ SY702 ) ) @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SY704 @ SY705 ) @ SY703 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(840,plain,
! [SV112: a] :
( ( ! [SY706: product_prod_a_a] :
( ( SV112
= ( product_snd_a_a @ SY706 ) )
= ( ~ ! [SY707: a] :
( SY706
!= ( product_Pair_a_a @ SY707 @ SV112 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(841,plain,
! [SV113: multis599418605od_a_a] :
( ( ~ ( ( SV113 != zero_z160849828od_a_a ) )
| ~ ! [SY708: product_prod_a_a] :
~ ( member449909584od_a_a @ SY708 @ ( set_ms1818337124od_a_a @ SV113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(842,plain,
! [SV114: product_prod_a_a] :
( ( ! [SY709: product_prod_a_a > product_prod_a_a,SY710: product_prod_a_a,SY711: set_Product_prod_a_a] :
( ( SV114
!= ( SY709 @ SY710 ) )
| ~ ( member449909584od_a_a @ SY710 @ SY711 )
| ( member449909584od_a_a @ SV114 @ ( image_794773445od_a_a @ SY709 @ SY711 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(843,plain,
! [SV115: produc1127127335iset_a] :
( ( ! [SY712: a > a > set_Pr158363655iset_a,SY713: product_prod_a_a] :
( ~ ( member340150864iset_a @ SV115 @ ( produc93594587iset_a @ SY712 @ SY713 ) )
| ~ ! [SY714: a,SY715: a] :
( ( SY713
!= ( product_Pair_a_a @ SY714 @ SY715 ) )
| ~ ( member340150864iset_a @ SV115 @ ( SY712 @ SY714 @ SY715 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[711]) ).
thf(844,plain,
! [SV116: product_prod_a_a] :
( ( ! [SY716: multis599418605od_a_a,SY717: multis599418605od_a_a] :
( ~ ~ ( member449909584od_a_a @ SV116 @ ( set_ms1818337124od_a_a @ SY716 ) )
| ( ( minus_1257885652od_a_a @ ( add_ms1725977093od_a_a @ SV116 @ SY717 ) @ SY716 )
= ( add_ms1725977093od_a_a @ SV116 @ ( minus_1257885652od_a_a @ SY717 @ SY716 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[712]) ).
thf(845,plain,
! [SV117: product_prod_a_a] :
( ( ! [SY718: multiset_a > multiset_a > set_Product_prod_a_a,SY719: produc1127127335iset_a] :
( ~ ( member449909584od_a_a @ SV117 @ ( produc2041367259od_a_a @ SY718 @ SY719 ) )
| ~ ! [SY720: multiset_a,SY721: multiset_a] :
( ( SY719
!= ( produc2037245207iset_a @ SY720 @ SY721 ) )
| ~ ( member449909584od_a_a @ SV117 @ ( SY718 @ SY720 @ SY721 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(846,plain,
! [SV118: set_a] :
( ( ! [SY722: set_Product_prod_a_a] :
( ~ ( prefer719835986ence_a @ SV118 @ SY722 )
| ! [SY723: a] :
( ~ ( member_a @ SY723 @ SV118 )
| ! [SY724: a] :
( ~ ( member_a @ SY724 @ SV118 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY723 @ SY724 ) @ SY722 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY724 @ SY723 ) @ SY722 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[714]) ).
thf(847,plain,
! [SV119: product_prod_a_a] :
( ( ! [SY725: set_Product_prod_a_a,SY726: a,SY727: product_prod_a_a > a] :
( ~ ( member449909584od_a_a @ SV119 @ SY725 )
| ( SY726
!= ( SY727 @ SV119 ) )
| ( member_a @ SY726 @ ( image_340790172_a_a_a @ SY727 @ SY725 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(848,plain,
! [SV120: product_prod_a_a] :
( ( ! [SY728: a > a > set_Product_prod_a_a,SY729: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SV120 @ ( produc1093061851od_a_a @ SY728 @ SY729 ) )
| ~ ! [SY730: a,SY731: a] :
( ( SY729
!= ( product_Pair_a_a @ SY730 @ SY731 ) )
| ~ ( member449909584od_a_a @ SV120 @ ( SY728 @ SY730 @ SY731 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[716]) ).
thf(849,plain,
! [SV121: product_prod_a_a > $o,SV1: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV1 @ ( collec645855634od_a_a @ SV121 ) )
= ( SV121 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(850,plain,
! [SV122: product_prod_a_a > $o] :
( ( ( product_curry_a_a_o @ SV122 )
= ( ^ [SY732: a,SY733: a] : ( SV122 @ ( product_Pair_a_a @ SY732 @ SY733 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(851,plain,
! [SV123: a,SV4: a] :
( ( ! [SY734: set_Product_prod_a_a,SY735: a > a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ SV4 @ SV123 ) @ ( inv_image_a_a @ SY734 @ SY735 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( SY735 @ SV4 ) @ ( SY735 @ SV123 ) ) @ SY734 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(852,plain,
! [SV124: a,SV5: a] :
( ( ! [SY736: set_Pr158363655iset_a,SY737: a > multiset_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ SV5 @ SV124 ) @ ( inv_im975322764et_a_a @ SY736 @ SY737 ) )
= ( member340150864iset_a @ ( produc2037245207iset_a @ ( SY737 @ SV5 ) @ ( SY737 @ SV124 ) ) @ SY736 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(853,plain,
! [SV125: multiset_a,SV6: multiset_a] :
( ( ! [SY738: set_Product_prod_a_a,SY739: multiset_a > a] :
( ( member340150864iset_a @ ( produc2037245207iset_a @ SV6 @ SV125 ) @ ( inv_im479034648iset_a @ SY738 @ SY739 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( SY739 @ SV6 ) @ ( SY739 @ SV125 ) ) @ SY738 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(854,plain,
! [SV126: a,SV7: a] :
( ( ! [SY740: set_Pr1948701895od_a_a,SY741: a > product_prod_a_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ SV7 @ SV126 ) @ ( inv_im777352425_a_a_a @ SY740 @ SY741 ) )
= ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( SY741 @ SV7 ) @ ( SY741 @ SV126 ) ) @ SY740 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(855,plain,
! [SV127: product_prod_a_a,SV8: product_prod_a_a] :
( ( ! [SY742: set_Product_prod_a_a,SY743: product_prod_a_a > a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV8 @ SV127 ) @ ( inv_im15016955od_a_a @ SY742 @ SY743 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( SY743 @ SV8 ) @ ( SY743 @ SV127 ) ) @ SY742 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(856,plain,
! [SV128: a,SV9: a] :
( ( ! [SY744: set_Pr1821581383od_a_a,SY745: a > multis599418605od_a_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV128 ) @ ( inv_im1681759523_a_a_a @ SY744 @ SY745 ) )
= ( member1349055120od_a_a @ ( produc1859144151od_a_a @ ( SY745 @ SV9 ) @ ( SY745 @ SV128 ) ) @ SY744 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(857,plain,
! [SV129: multis599418605od_a_a,SV10: multis599418605od_a_a] :
( ( ! [SY746: set_Product_prod_a_a,SY747: multis599418605od_a_a > a] :
( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ SV10 @ SV129 ) @ ( inv_im941243329od_a_a @ SY746 @ SY747 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( SY747 @ SV10 ) @ ( SY747 @ SV129 ) ) @ SY746 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(858,plain,
! [SV130: a,SV11: a] :
( ( ( product_swap_a_a @ ( product_Pair_a_a @ SV11 @ SV130 ) )
= ( product_Pair_a_a @ SV130 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(859,plain,
! [SV131: a,SV12: a > a > set_Product_prod_a_a] :
( ( ! [SY748: a] :
( ( produc1093061851od_a_a @ SV12 @ ( product_Pair_a_a @ SV131 @ SY748 ) )
= ( SV12 @ SV131 @ SY748 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(860,plain,
! [SV132: a,SV13: a > a > set_a] :
( ( ! [SY749: a] :
( ( produc961951794_set_a @ SV13 @ ( product_Pair_a_a @ SV132 @ SY749 ) )
= ( SV13 @ SV132 @ SY749 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(861,plain,
! [SV133: a,SV14: a > a > $o] :
( ( ! [SY750: a] :
( ( produc1833107820_a_a_o @ SV14 @ ( product_Pair_a_a @ SV133 @ SY750 ) )
= ( SV14 @ SV133 @ SY750 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(862,plain,
! [SV134: set_Product_prod_a_a] :
( ( ( irrefl_a @ SV134 )
= ( ! [SY751: a] :
~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY751 @ SY751 ) @ SV134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[732]) ).
thf(863,plain,
! [SV135: a,SV16: a] :
( ( ! [SY752: set_Product_prod_a_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ SV16 @ SV135 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SY752 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ SV135 @ SV16 ) @ SY752 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(864,plain,
! [SV136: product_prod_a_a] :
( ( ( top_to1483957574_a_a_o @ SV136 )
= ( member449909584od_a_a @ SV136 @ top_to398455383od_a_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(865,plain,
! [SV137: a > a,SV18: a > a] :
( ( ! [SY753: a,SY754: a] :
( ( produc700022774_a_a_a @ SV18 @ SV137 @ ( product_Pair_a_a @ SY753 @ SY754 ) )
= ( product_Pair_a_a @ ( SV18 @ SY753 ) @ ( SV137 @ SY754 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(866,plain,
! [SV138: a,SV22: a] :
( ( ( product_fst_a_a @ ( product_Pair_a_a @ SV22 @ SV138 ) )
= SV22 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(867,plain,
! [SV139: a,SV23: a] :
( ( ( product_snd_a_a @ ( product_Pair_a_a @ SV23 @ SV139 ) )
= SV139 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(868,plain,
! [SV140: product_prod_a_a] :
( ( ( product_swap_a_a @ SV140 )
= ( product_Pair_a_a @ ( product_snd_a_a @ SV140 ) @ ( product_fst_a_a @ SV140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(869,plain,
! [SV141: multis599418605od_a_a,SV25: product_prod_a_a] :
( ( ! [SY755: multis599418605od_a_a] :
( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ ( plus_p404985124od_a_a @ SV141 @ SY755 ) ) )
= ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV141 ) )
| ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SY755 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(870,plain,
( ( member449909584od_a_a @ ( product_Pair_a_a @ x @ y ) @ relation )
= $false ),
inference(extcnf_or_neg,[status(thm)],[747]) ).
thf(871,plain,
( ( member449909584od_a_a @ ( product_Pair_a_a @ y @ x ) @ relation )
= $false ),
inference(extcnf_or_neg,[status(thm)],[747]) ).
thf(872,plain,
! [SV142: multis599418605od_a_a,SV27: product_prod_a_a] :
( ( ! [SY756: multis599418605od_a_a] :
( ~ ( member449909584od_a_a @ SV27 @ ( set_ms1818337124od_a_a @ ( minus_1257885652od_a_a @ SV142 @ SY756 ) ) )
| ( member449909584od_a_a @ SV27 @ ( set_ms1818337124od_a_a @ SV142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(873,plain,
! [SV143: a,SV28: a] :
( ( ! [SY757: a,SY758: a] :
( ( ( product_Pair_a_a @ SV28 @ SV143 )
!= ( product_Pair_a_a @ SY757 @ SY758 ) )
| ~ ( ( SV28 != SY757 )
| ( SV143 != SY758 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[749]) ).
thf(874,plain,
! [SV144: produc1572603623od_a_a,SV29: produc1572603623od_a_a > $o] :
( ( ~ ! [SY474: product_prod_a_a,SY475: a,SY476: a] : ( SV29 @ ( produc1474507607od_a_a @ SY474 @ ( product_Pair_a_a @ SY475 @ SY476 ) ) )
| ( SV29 @ SV144 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[750]) ).
thf(875,plain,
! [SV145: a,SV30: a] :
( ( ! [SY762: a] :
( ( ( product_fst_a_a @ ( product_Pair_a_a @ SV30 @ SV145 ) )
!= SY762 )
| ( SV30 = SY762 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[752]) ).
thf(876,plain,
! [SV146: a,SV31: product_prod_a_a > $o] :
( ( ! [SY763: a] :
( ~ ( SV31 @ ( product_Pair_a_a @ SV146 @ SY763 ) )
| ( product_curry_a_a_o @ SV31 @ SV146 @ SY763 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(877,plain,
! [SV147: set_Pr1948701895od_a_a,SV32: set_Product_prod_a_a] :
( ( ~ ! [SY764: product_prod_a_a,SY765: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY764 @ SV32 )
| ~ ( member449909584od_a_a @ SY765 @ SV32 )
| ~ ( ( SY764 != SY765 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY764 @ SY765 ) @ SV147 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY765 @ SY764 ) @ SV147 ) )
| ( total_1490170027od_a_a @ SV32 @ SV147 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(878,plain,
! [SV148: a,SV33: a > $o] :
( ( ! [SY766: a > $o,SY767: a] :
( ~ ( SV33 @ SV148 )
| ~ ( SY766 @ SY767 )
| ~ ( ~ ( SV33 @ ( product_fst_a_a @ ( product_Pair_a_a @ SV148 @ SY767 ) ) )
| ~ ( SY766 @ ( product_snd_a_a @ ( product_Pair_a_a @ SV148 @ SY767 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(879,plain,
! [SV149: a,SV34: a > $o] :
( ( ! [SY768: a,SY769: a,SY770: a > set_Product_prod_a_a] :
( ~ ( SV34 @ SV149 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY768 @ SY769 ) @ ( SY770 @ SV149 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV149 @ SY768 ) @ ( product_Pair_a_a @ SV149 @ SY769 ) ) @ ( same_fst_a_a @ SV34 @ SY770 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[756]) ).
thf(880,plain,
! [SV150: multis599418605od_a_a,SV35: product_prod_a_a] :
( ( ~ ( member449909584od_a_a @ SV35 @ ( set_ms1818337124od_a_a @ SV150 ) )
| ~ ! [SY771: multis599418605od_a_a] :
( SV150
!= ( add_ms1725977093od_a_a @ SV35 @ SY771 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(881,plain,
! [SV151: set_Product_prod_a_a > $o,SV36: set_Product_prod_a_a] :
( ( ~ ( asym_a @ SV36 )
| ~ ! [SY772: set_Product_prod_a_a] :
( ~ ! [SX3: a,SX4: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX4 ) @ SY772 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX4 @ SX3 ) @ SY772 ) )
| ( SV151 @ SY772 ) )
| ( SV151 @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(882,plain,
! [SV152: set_Product_prod_a_a,SV37: set_Product_prod_a_a] :
( ( ~ ! [SY775: a,SY776: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY775 @ SY776 ) @ SV37 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY775 @ SY776 ) @ SV152 ) )
| ( ord_le1824328871od_a_a @ SV37 @ SV152 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(883,plain,
! [SV153: product_prod_a_a,SV38: product_prod_a_a] :
( ( ! [SY777: set_Product_prod_a_a,SY778: set_Pr1948701895od_a_a] :
( ~ ( member449909584od_a_a @ SV38 @ ( prefer477097315od_a_a @ SV153 @ SY777 @ SY778 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV38 @ SV153 ) @ SY778 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(884,plain,
! [SV154: set_Product_prod_a_a] :
( ( ( total_1490170027od_a_a @ SV154 )
= ( ^ [SY779: set_Pr1948701895od_a_a] :
! [SY780: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY780 @ SV154 )
| ! [SY781: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY781 @ SV154 )
| ~ ( ( SY780 != SY781 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY780 @ SY781 ) @ SY779 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY781 @ SY780 ) @ SY779 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[761]) ).
thf(885,plain,
! [SV155: product_prod_a_a,SV40: a] :
( ( ( SV40
= ( product_fst_a_a @ SV155 ) )
= ( ~ ! [SY782: a] :
( SV155
!= ( product_Pair_a_a @ SV40 @ SY782 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[763]) ).
thf(886,plain,
! [SV156: a,SV41: set_Product_prod_a_a] :
( ( ! [SY783: a,SY784: a] :
( ~ ( trans_a @ SV41 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV156 @ SY783 ) @ SV41 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY783 @ SY784 ) @ SV41 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV156 @ SY784 ) @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[764]) ).
thf(887,plain,
! [SV157: set_Pr1948701895od_a_a,SV42: set_Product_prod_a_a] :
( ( ! [SY785: product_prod_a_a,SY786: product_prod_a_a] :
( ~ ( prefer1338892073od_a_a @ SV42 @ SV157 )
| ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY785 @ SY786 ) @ SV157 )
| ( member449909584od_a_a @ SY785 @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(888,plain,
! [SV158: a,SV43: a > a > $o] :
( ( ! [SY787: a,SY788: product_prod_a_a] :
( ~ ( SV43 @ SV158 @ SY787 )
| ( SY788
!= ( product_Pair_a_a @ SV158 @ SY787 ) )
| ( SV43 @ ( product_fst_a_a @ SY788 ) @ ( product_snd_a_a @ SY788 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[766]) ).
thf(889,plain,
! [SV159: a,SV44: a] :
( ( ! [SY789: a,SY790: a] :
( ( ( product_Pair_a_a @ SV44 @ SV159 )
= ( product_Pair_a_a @ SY789 @ SY790 ) )
= ( ~ ( ( SV44 != SY789 )
| ( SV159 != SY790 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[767]) ).
thf(890,plain,
! [SV160: a,SV45: set_Product_prod_a_a] :
( ( ! [SY791: a,SY792: a] :
( ~ ( trans_a @ SV45 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV160 @ SY791 ) @ SV45 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY791 @ SY792 ) @ SV45 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV160 @ SY792 ) @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(891,plain,
! [SV161: a > product_prod_a_a,SV46: set_a] :
( ( ! [SY793: set_Product_prod_a_a] :
( ~ ! [SY794: a] :
( ~ ( member_a @ SY794 @ SV46 )
| ( member449909584od_a_a @ ( SV161 @ SY794 ) @ SY793 ) )
| ( ord_le1824328871od_a_a @ ( image_1725938350od_a_a @ SV161 @ SV46 ) @ SY793 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(892,plain,
! [SV162: set_Pr1948701895od_a_a,SV47: set_Product_prod_a_a] :
( ( ~ ( prefer697821563od_a_a @ SV47 @ SV162 )
| ! [SY795: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY795 @ SV47 )
| ! [SY796: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY796 @ SV47 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY795 @ SY796 ) @ SV162 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY796 @ SY795 ) @ SV162 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(893,plain,
! [SV163: set_Product_prod_a_a,SV48: set_a] :
( ( ~ ! [SY797: a,SY798: a] :
( ~ ( member_a @ SY797 @ SV48 )
| ~ ( member_a @ SY798 @ SV48 )
| ~ ( ( SY797 != SY798 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY797 @ SY798 ) @ SV163 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY798 @ SY797 ) @ SV163 ) )
| ( total_on_a @ SV48 @ SV163 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(894,plain,
! [SV164: product_prod_a_a,SV49: product_prod_a_a] :
( ( ! [SY799: set_Product_prod_a_a,SY800: set_Pr1948701895od_a_a] :
( ~ ( member449909584od_a_a @ SV49 @ ( prefer477097315od_a_a @ SV164 @ SY799 @ SY800 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV49 @ SV164 ) @ SY800 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(895,plain,
! [SV50: product_prod_a_a] :
( ( ! [SY535: a] :
~ ~ ! [SY536: a] :
( SV50
!= ( product_Pair_a_a @ SY535 @ SY536 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[773]) ).
thf(896,plain,
! [SV165: set_Pr1948701895od_a_a,SV51: set_Product_prod_a_a] :
( ( ! [SY801: product_prod_a_a] :
( ~ ( refl_o1298442278od_a_a @ SV51 @ SV165 )
| ~ ( member449909584od_a_a @ SY801 @ SV51 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY801 @ SY801 ) @ SV165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(897,plain,
! [SV166: a,SV52: a] :
( ( ! [SY802: a,SY803: a,SY804: set_Product_prod_a_a,SY805: set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SY802 @ SY803 ) ) @ ( lex_prod_a_a @ SY804 @ SY805 ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SY802 ) @ SY804 )
| ~ ( ( SV52 != SY802 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SY803 ) @ SY805 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(898,plain,
! [SV167: set_Pr1948701895od_a_a,SV53: set_Product_prod_a_a] :
( ( ! [SY806: product_prod_a_a,SY807: product_prod_a_a] :
( ~ ( refl_o1298442278od_a_a @ SV53 @ SV167 )
| ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY806 @ SY807 ) @ SV167 )
| ( member449909584od_a_a @ SY807 @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[776]) ).
thf(899,plain,
! [SV168: set_Product_prod_a_a,SV54: set_a] :
( ( ! [SY808: a] :
( ~ ( refl_on_a @ SV54 @ SV168 )
| ~ ( member_a @ SY808 @ SV54 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY808 @ SY808 ) @ SV168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(900,plain,
! [SV169: a,SV55: a] :
( ( ! [SY809: set_a,SY810: set_Product_prod_a_a] :
( ~ ( member_a @ SV55 @ ( prefer161218362good_a @ SV169 @ SY809 @ SY810 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV55 @ SV169 ) @ SY810 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(901,plain,
! [SV170: a,SV56: a] :
( ( ! [SY811: a,SY812: a] :
( ( ( product_Pair_a_a @ SV56 @ SV170 )
= ( product_Pair_a_a @ SY811 @ SY812 ) )
= ( ~ ( ( SV56 != SY811 )
| ( SV170 != SY812 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[779]) ).
thf(902,plain,
! [SV171: a,SV57: a] :
( ( ! [SY813: a] :
( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV171 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV171 @ SV57 ) @ relation ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV171 @ SY813 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY813 @ SV171 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SY813 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY813 @ SV57 ) @ relation ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[780]) ).
thf(903,plain,
! [SV172: set_Product_prod_a_a,SV58: set_a] :
( ( ! [SY814: a,SY815: a] :
( ~ ( refl_on_a @ SV58 @ SV172 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY814 @ SY815 ) @ SV172 )
| ~ ( ~ ( member_a @ SY814 @ SV58 )
| ~ ( member_a @ SY815 @ SV58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[781]) ).
thf(904,plain,
! [SV173: a > a,SV59: product_prod_a_a] :
( ( ! [SY816: a > a,SY817: set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ SV59 @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SV173 @ SY816 ) @ SY817 ) )
| ~ ! [SY818: a,SY819: a] :
( ( SV59
!= ( product_Pair_a_a @ ( SV173 @ SY818 ) @ ( SY816 @ SY819 ) ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY818 @ SY819 ) @ SY817 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[782]) ).
thf(905,plain,
! [SV174: set_Pr1948701895od_a_a,SV60: set_Product_prod_a_a] :
( ( ! [SY820: product_prod_a_a,SY821: product_prod_a_a] :
( ~ ( prefer697821563od_a_a @ SV60 @ SV174 )
| ~ ~ ( ~ ( member449909584od_a_a @ SY820 @ SV60 )
| ~ ( member449909584od_a_a @ SY821 @ SV60 ) )
| ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY821 @ SY820 ) @ SV174 ) )
= ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY820 @ SY821 ) @ SV174 )
| ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY821 @ SY820 ) @ SV174 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(906,plain,
! [SV175: set_Product_prod_a_a,SV61: set_a] :
( ( ! [SY822: a,SY823: a] :
( ~ ( prefer719835986ence_a @ SV61 @ SV175 )
| ~ ~ ( ~ ( member_a @ SY822 @ SV61 )
| ~ ( member_a @ SY823 @ SV61 ) )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY823 @ SY822 ) @ SV175 ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY822 @ SY823 ) @ SV175 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY823 @ SY822 ) @ SV175 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[784]) ).
thf(907,plain,
! [SV176: product_prod_a_a,SV62: product_prod_a_a > $o] :
( ( ~ ! [SY572: a,SY573: a] : ( SV62 @ ( product_Pair_a_a @ SY572 @ SY573 ) )
| ( SV62 @ SV176 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(908,plain,
! [SV63: set_Product_prod_a_a] :
( ( ( ~ ! [SY574: a,SY575: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY574 @ SY575 ) @ SV63 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY575 @ SY574 ) @ SV63 ) ) )
= $true )
| ( ( asym_a @ SV63 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[786]) ).
thf(909,plain,
! [SV177: a,SV64: set_Product_prod_a_a] :
( ( ! [SY826: a] :
( ~ ( asym_a @ SV64 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV177 @ SY826 ) @ SV64 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY826 @ SV177 ) @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(910,plain,
! [SV178: set_Product_prod_a_a,SV65: product_prod_a_a] :
( ( ! [SY827: product_prod_a_a > product_prod_a_a] :
( ~ ( member449909584od_a_a @ SV65 @ SV178 )
| ( member449909584od_a_a @ ( SY827 @ SV65 ) @ ( image_794773445od_a_a @ SY827 @ SV178 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[788]) ).
thf(911,plain,
! [SV66: a] :
( ( ( ~ ( member_a @ SV66 @ carrier ) )
= $true )
| ( ( ! [SY580: a] :
( ~ ( member_a @ SY580 @ carrier )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV66 @ SY580 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY580 @ SV66 ) @ relation ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[789]) ).
thf(912,plain,
! [SV67: set_Product_prod_a_a] :
( ( ( ~ ! [SY581: a,SY582: a,SY583: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY581 @ SY582 ) @ SV67 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY582 @ SY583 ) @ SV67 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY581 @ SY583 ) @ SV67 ) ) )
= $true )
| ( ( trans_a @ SV67 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[790]) ).
thf(913,plain,
! [SV179: set_Product_prod_a_a] :
( ( ( trans_a @ SV179 )
= ( ! [SY828: a,SY829: a,SY830: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY829 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY829 @ SY830 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY830 ) @ SV179 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(914,plain,
! [SV180: a,SV69: a > a > $o] :
( ( ! [SY831: a] :
( ~ ( SV69 @ SV180 @ SY831 )
| ( SV69 @ ( product_snd_a_a @ ( product_Pair_a_a @ SY831 @ SV180 ) ) @ ( product_fst_a_a @ ( product_Pair_a_a @ SY831 @ SV180 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(915,plain,
! [SV70: produc1572603623od_a_a] :
( ( ! [SY589: product_prod_a_a,SY590: a,SY591: a] :
( SV70
!= ( produc1474507607od_a_a @ SY589 @ ( product_Pair_a_a @ SY590 @ SY591 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[794]) ).
thf(916,plain,
! [SV181: a,SV71: a] :
( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV181 ) @ relation )
| ( member_a @ SV71 @ carrier ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[795]) ).
thf(917,plain,
! [SV182: a,SV72: product_prod_a_a > $o] :
( ( ! [SY832: a] :
( ~ ( product_curry_a_a_o @ SV72 @ SV182 @ SY832 )
| ( SV72 @ ( product_Pair_a_a @ SV182 @ SY832 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(918,plain,
! [SV183: multis599418605od_a_a,SV73: product_prod_a_a] :
( ( ! [SY833: multis599418605od_a_a] :
( ( ( add_ms1725977093od_a_a @ SV73 @ SV183 )
!= SY833 )
| ( member449909584od_a_a @ SV73 @ ( set_ms1818337124od_a_a @ SY833 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(919,plain,
! [SV184: set_Product_prod_a_a,SV74: set_a] :
( ( ! [SY834: a,SY835: a,SY836: a] :
( ~ ( prefer719835986ence_a @ SV74 @ SV184 )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY834 @ SY835 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY835 @ SY834 ) @ SV184 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY835 @ SY836 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY836 @ SY835 ) @ SV184 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY834 @ SY836 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY836 @ SY834 ) @ SV184 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[798]) ).
thf(920,plain,
! [SV185: set_a,SV75: a] :
( ( ! [SY837: a > product_prod_a_a] :
( ~ ( member_a @ SV75 @ SV185 )
| ( member449909584od_a_a @ ( SY837 @ SV75 ) @ ( image_1725938350od_a_a @ SY837 @ SV185 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[799]) ).
thf(921,plain,
! [SV186: product_prod_a_a > a,SV76: a] :
( ( ! [SY838: product_prod_a_a,SY839: set_Product_prod_a_a] :
( ( SV76
!= ( SV186 @ SY838 ) )
| ~ ( member449909584od_a_a @ SY838 @ SY839 )
| ( member_a @ SV76 @ ( image_340790172_a_a_a @ SV186 @ SY839 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(922,plain,
! [SV187: a,SV77: product_prod_a_a] :
( ( ! [SY840: a] :
( ( SV77
!= ( product_Pair_a_a @ SV187 @ SY840 ) )
| ( ( product_fst_a_a @ SV77 )
= SV187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(923,plain,
! [SV188: a,SV78: product_prod_a_a] :
( ( ! [SY841: a] :
( ( SV78
!= ( product_Pair_a_a @ SV188 @ SY841 ) )
| ( ( product_snd_a_a @ SV78 )
= SY841 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(924,plain,
! [SV189: a,SV79: a] :
( ( ! [SY842: a] :
( ( ( product_snd_a_a @ ( product_Pair_a_a @ SV79 @ SV189 ) )
!= SY842 )
| ( SV189 = SY842 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(925,plain,
! [SV80: set_Product_prod_a_a] :
( ( ( ~ ! [SY612: a] :
~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY612 @ SY612 ) @ SV80 ) )
= $true )
| ( ( irrefl_a @ SV80 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[804]) ).
thf(926,plain,
! [SV190: set_Product_prod_a_a,SV81: set_a] :
( ( ! [SY843: a,SY844: a] :
( ~ ( prefer1292084992ence_a @ SV81 @ SV190 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY843 @ SY844 ) @ SV190 )
| ( member_a @ SY843 @ SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(927,plain,
! [SV191: set_Product_prod_a_a,SV82: product_prod_a_a] :
( ( ! [SY845: product_prod_a_a,SY846: product_prod_a_a > product_prod_a_a] :
( ~ ( member449909584od_a_a @ SV82 @ SV191 )
| ( SY845
!= ( SY846 @ SV82 ) )
| ( member449909584od_a_a @ SY845 @ ( image_794773445od_a_a @ SY846 @ SV191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(928,plain,
! [SV192: set_Product_prod_a_a,SV83: set_a] :
( ( ! [SY847: a,SY848: a] :
( ~ ( refl_on_a @ SV83 @ SV192 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY847 @ SY848 ) @ SV192 )
| ( member_a @ SY847 @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(929,plain,
! [SV193: set_a,SV84: a] :
( ( ! [SY849: product_prod_a_a,SY850: a > product_prod_a_a] :
( ~ ( member_a @ SV84 @ SV193 )
| ( SY849
!= ( SY850 @ SV84 ) )
| ( member449909584od_a_a @ SY849 @ ( image_1725938350od_a_a @ SY850 @ SV193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(930,plain,
! [SV85: set_Product_prod_a_a] :
( ( ( ~ ( asym_a @ SV85 ) )
= $true )
| ( ( ! [SY625: a,SY626: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY625 @ SY626 ) @ SV85 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY626 @ SY625 ) @ SV85 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[809]) ).
thf(931,plain,
! [SV194: product_prod_a_a > a,SV86: set_Product_prod_a_a] :
( ( ! [SY851: set_a] :
( ~ ! [SY852: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY852 @ SV86 )
| ( member_a @ ( SV194 @ SY852 ) @ SY851 ) )
| ( ord_less_eq_set_a @ ( image_340790172_a_a_a @ SV194 @ SV86 ) @ SY851 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(932,plain,
! [SV195: set_Product_prod_a_a,SV87: product_prod_a_a] :
( ( ! [SY853: product_prod_a_a > a] :
( ~ ( member449909584od_a_a @ SV87 @ SV195 )
| ( member_a @ ( SY853 @ SV87 ) @ ( image_340790172_a_a_a @ SY853 @ SV195 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(933,plain,
! [SV196: a,SV88: a] :
( ( ~ ~ ( ~ ( member_a @ SV88 @ carrier )
| ~ ( member_a @ SV196 @ carrier ) )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(934,plain,
! [SV197: set_a] :
( ( ( total_on_a @ SV197 )
= ( ^ [SY854: set_Product_prod_a_a] :
! [SY855: a] :
( ~ ( member_a @ SY855 @ SV197 )
| ! [SY856: a] :
( ~ ( member_a @ SY856 @ SV197 )
| ~ ( ( SY855 != SY856 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY855 @ SY856 ) @ SY854 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY856 @ SY855 ) @ SY854 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(935,plain,
! [SV198: set_Product_prod_a_a] :
( ( ( asym_a @ SV198 )
= ( ~ ! [SY857: set_Product_prod_a_a] :
~ ~ ( ( SV198 != SY857 )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SY857 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SY857 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(936,plain,
! [SV199: set_Product_prod_a_a] :
( ( ( asym_a @ SV199 )
= ( ! [SY860: a,SY861: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY860 @ SY861 ) @ SV199 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY861 @ SY860 ) @ SV199 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(937,plain,
! [SV200: multis599418605od_a_a,SV92: product_prod_a_a] :
( ( ! [SY862: product_prod_a_a,SY863: multis599418605od_a_a] :
( ( ( add_ms1725977093od_a_a @ SV92 @ SV200 )
!= ( add_ms1725977093od_a_a @ SY862 @ SY863 ) )
| ~ ( ( SV92 != SY862 ) )
| ( member449909584od_a_a @ SY862 @ ( set_ms1818337124od_a_a @ SV200 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(938,plain,
! [SV201: set_Product_prod_a_a,SV93: set_a] :
( ( ! [SY864: a,SY865: a,SY866: a] :
( ~ ( prefer1292084992ence_a @ SV93 @ SV201 )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY864 @ SY865 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY865 @ SY864 ) @ SV201 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY865 @ SY866 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY866 @ SY865 ) @ SV201 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY864 @ SY866 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY866 @ SY864 ) @ SV201 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(939,plain,
! [SV202: a,SV94: a] :
( ( ! [SY867: set_a,SY868: set_Product_prod_a_a] :
( ~ ( member_a @ SV94 @ ( prefer161218362good_a @ SV202 @ SY867 @ SY868 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV94 @ SV202 ) @ SY868 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(940,plain,
! [SV203: a > a > set_mu1281098573od_a_a,SV95: multis599418605od_a_a] :
( ( ! [SY869: product_prod_a_a] :
( ~ ( member1755255446od_a_a @ SV95 @ ( produc1121147169od_a_a @ SV203 @ SY869 ) )
| ~ ! [SY870: a,SY871: a] :
( ( SY869
!= ( product_Pair_a_a @ SY870 @ SY871 ) )
| ~ ( member1755255446od_a_a @ SV95 @ ( SV203 @ SY870 @ SY871 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(941,plain,
! [SV204: set_a] :
( ( ( prefer1292084992ence_a @ SV204 )
= ( ^ [SY872: set_Product_prod_a_a] :
~ ( ~ ~ ( ~ ! [SY873: a,SY874: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY873 @ SY874 ) @ SY872 )
| ( member_a @ SY873 @ SV204 ) )
| ~ ! [SY875: a,SY876: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY875 @ SY876 ) @ SY872 )
| ( member_a @ SY876 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SY872 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(942,plain,
! [SV205: multis599418605od_a_a,SV97: product_prod_a_a] :
( ( ~ ( member449909584od_a_a @ SV97 @ ( set_ms1818337124od_a_a @ SV205 ) )
| ~ ! [SY877: multis599418605od_a_a] :
( SV205
!= ( add_ms1725977093od_a_a @ SV97 @ SY877 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(943,plain,
! [SV206: a > a > set_multiset_a,SV98: multiset_a] :
( ( ! [SY878: product_prod_a_a] :
( ~ ( member_multiset_a @ SV98 @ ( produc1828150264iset_a @ SV206 @ SY878 ) )
| ~ ! [SY879: a,SY880: a] :
( ( SY878
!= ( product_Pair_a_a @ SY879 @ SY880 ) )
| ~ ( member_multiset_a @ SV98 @ ( SV206 @ SY879 @ SY880 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(944,plain,
! [SV99: product_prod_a_a] :
( ( ! [SY666: a,SY667: a] :
( SV99
!= ( product_Pair_a_a @ SY666 @ SY667 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[827]) ).
thf(945,plain,
! [SV207: set_a,SV100: set_Product_prod_a_a] :
( ( ~ ! [SY881: a,SY882: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY881 @ SY882 ) @ SV100 )
| ( member_a @ SY881 @ SV207 ) )
| ~ ! [SY883: a,SY884: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY883 @ SY884 ) @ SV100 )
| ( member_a @ SY884 @ SV207 ) )
| ~ ( order_preorder_on_a @ SV207 @ SV100 )
| ( prefer1292084992ence_a @ SV207 @ SV100 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(946,plain,
! [SV208: a,SV101: a] :
( ( ! [SY885: a] :
( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SV208 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV101 ) @ relation ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SY885 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY885 @ SV208 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SY885 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY885 @ SV101 ) @ relation ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(947,plain,
! [SV209: a,SV102: product_prod_a_a > $o] :
( ( ! [SY886: a] :
( ~ ( product_curry_a_a_o @ SV102 @ SV209 @ SY886 )
| ( SV102 @ ( product_Pair_a_a @ SV209 @ SY886 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(948,plain,
! [SV210: a > a > set_a,SV103: a] :
( ( ! [SY887: product_prod_a_a] :
( ~ ( member_a @ SV103 @ ( produc961951794_set_a @ SV210 @ SY887 ) )
| ~ ! [SY888: a,SY889: a] :
( ( SY887
!= ( product_Pair_a_a @ SY888 @ SY889 ) )
| ~ ( member_a @ SV103 @ ( SV210 @ SY888 @ SY889 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(949,plain,
! [SV211: product_prod_a_a,SV104: product_prod_a_a > $o] :
( ( ~ ! [SY682: a,SY683: a] : ( SV104 @ ( product_Pair_a_a @ SY682 @ SY683 ) )
| ( SV104 @ SV211 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(950,plain,
! [SV212: set_Pr1948701895od_a_a,SV105: set_Product_prod_a_a] :
( ( ! [SY892: product_prod_a_a,SY893: product_prod_a_a] :
( ~ ( refl_o1298442278od_a_a @ SV105 @ SV212 )
| ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY892 @ SY893 ) @ SV212 )
| ( member449909584od_a_a @ SY892 @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(951,plain,
! [SV213: set_Pr1948701895od_a_a,SV106: set_Product_prod_a_a] :
( ( ! [SY894: product_prod_a_a,SY895: product_prod_a_a] :
( ~ ( refl_o1298442278od_a_a @ SV106 @ SV213 )
| ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY894 @ SY895 ) @ SV213 )
| ~ ( ~ ( member449909584od_a_a @ SY894 @ SV106 )
| ~ ( member449909584od_a_a @ SY895 @ SV106 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(952,plain,
! [SV214: product_prod_a_a > product_prod_a_a,SV107: set_Product_prod_a_a] :
( ( ! [SY896: set_Product_prod_a_a] :
( ~ ! [SY897: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY897 @ SV107 )
| ( member449909584od_a_a @ ( SV214 @ SY897 ) @ SY896 ) )
| ( ord_le1824328871od_a_a @ ( image_794773445od_a_a @ SV214 @ SV107 ) @ SY896 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(953,plain,
! [SV215: a,SV108: a] :
( ( ! [SY898: set_Product_prod_a_a,SY899: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV108 @ SV215 ) @ SY898 )
| ( SY899 != SV215 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV108 @ SY899 ) @ SY898 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(954,plain,
! [SV216: set_Product_prod_a_a,SV109: set_a] :
( ( ! [SY900: a,SY901: a] :
( ~ ( refl_on_a @ SV109 @ SV216 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY900 @ SY901 ) @ SV216 )
| ( member_a @ SY901 @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(955,plain,
! [SV217: a > product_prod_a_a,SV110: product_prod_a_a] :
( ( ! [SY902: a,SY903: set_a] :
( ( SV110
!= ( SV217 @ SY902 ) )
| ~ ( member_a @ SY902 @ SY903 )
| ( member449909584od_a_a @ SV110 @ ( image_1725938350od_a_a @ SV217 @ SY903 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(956,plain,
! [SV218: a,SV111: a] :
( ( ! [SY904: set_Product_prod_a_a,SY905: a > a,SY906: a > a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV111 @ SV218 ) @ SY904 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( SY905 @ SV111 ) @ ( SY906 @ SV218 ) ) @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SY905 @ SY906 ) @ SY904 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[839]) ).
thf(957,plain,
! [SV219: product_prod_a_a,SV112: a] :
( ( ( SV112
= ( product_snd_a_a @ SV219 ) )
= ( ~ ! [SY907: a] :
( SV219
!= ( product_Pair_a_a @ SY907 @ SV112 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(958,plain,
! [SV113: multis599418605od_a_a] :
( ( ( ~ ( ( SV113 != zero_z160849828od_a_a ) ) )
= $true )
| ( ( ~ ! [SY708: product_prod_a_a] :
~ ( member449909584od_a_a @ SY708 @ ( set_ms1818337124od_a_a @ SV113 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[841]) ).
thf(959,plain,
! [SV220: product_prod_a_a > product_prod_a_a,SV114: product_prod_a_a] :
( ( ! [SY908: product_prod_a_a,SY909: set_Product_prod_a_a] :
( ( SV114
!= ( SV220 @ SY908 ) )
| ~ ( member449909584od_a_a @ SY908 @ SY909 )
| ( member449909584od_a_a @ SV114 @ ( image_794773445od_a_a @ SV220 @ SY909 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(960,plain,
! [SV221: a > a > set_Pr158363655iset_a,SV115: produc1127127335iset_a] :
( ( ! [SY910: product_prod_a_a] :
( ~ ( member340150864iset_a @ SV115 @ ( produc93594587iset_a @ SV221 @ SY910 ) )
| ~ ! [SY911: a,SY912: a] :
( ( SY910
!= ( product_Pair_a_a @ SY911 @ SY912 ) )
| ~ ( member340150864iset_a @ SV115 @ ( SV221 @ SY911 @ SY912 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(961,plain,
! [SV222: multis599418605od_a_a,SV116: product_prod_a_a] :
( ( ! [SY913: multis599418605od_a_a] :
( ~ ~ ( member449909584od_a_a @ SV116 @ ( set_ms1818337124od_a_a @ SV222 ) )
| ( ( minus_1257885652od_a_a @ ( add_ms1725977093od_a_a @ SV116 @ SY913 ) @ SV222 )
= ( add_ms1725977093od_a_a @ SV116 @ ( minus_1257885652od_a_a @ SY913 @ SV222 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(962,plain,
! [SV223: multiset_a > multiset_a > set_Product_prod_a_a,SV117: product_prod_a_a] :
( ( ! [SY914: produc1127127335iset_a] :
( ~ ( member449909584od_a_a @ SV117 @ ( produc2041367259od_a_a @ SV223 @ SY914 ) )
| ~ ! [SY915: multiset_a,SY916: multiset_a] :
( ( SY914
!= ( produc2037245207iset_a @ SY915 @ SY916 ) )
| ~ ( member449909584od_a_a @ SV117 @ ( SV223 @ SY915 @ SY916 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(963,plain,
! [SV224: set_Product_prod_a_a,SV118: set_a] :
( ( ~ ( prefer719835986ence_a @ SV118 @ SV224 )
| ! [SY917: a] :
( ~ ( member_a @ SY917 @ SV118 )
| ! [SY918: a] :
( ~ ( member_a @ SY918 @ SV118 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY917 @ SY918 ) @ SV224 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY918 @ SY917 ) @ SV224 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(964,plain,
! [SV225: set_Product_prod_a_a,SV119: product_prod_a_a] :
( ( ! [SY919: a,SY920: product_prod_a_a > a] :
( ~ ( member449909584od_a_a @ SV119 @ SV225 )
| ( SY919
!= ( SY920 @ SV119 ) )
| ( member_a @ SY919 @ ( image_340790172_a_a_a @ SY920 @ SV225 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(965,plain,
! [SV226: a > a > set_Product_prod_a_a,SV120: product_prod_a_a] :
( ( ! [SY921: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SV120 @ ( produc1093061851od_a_a @ SV226 @ SY921 ) )
| ~ ! [SY922: a,SY923: a] :
( ( SY921
!= ( product_Pair_a_a @ SY922 @ SY923 ) )
| ~ ( member449909584od_a_a @ SV120 @ ( SV226 @ SY922 @ SY923 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[848]) ).
thf(966,plain,
! [SV121: product_prod_a_a > $o,SV1: product_prod_a_a] :
( ( ~ ( ( member449909584od_a_a @ SV1 @ ( collec645855634od_a_a @ SV121 ) )
| ( SV121 @ SV1 ) )
| ~ ( ~ ( member449909584od_a_a @ SV1 @ ( collec645855634od_a_a @ SV121 ) )
| ~ ( SV121 @ SV1 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[849]) ).
thf(967,plain,
! [SV121: product_prod_a_a > $o,SV1: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV1 @ ( collec645855634od_a_a @ SV121 ) )
= ( SV121 @ SV1 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[849]) ).
thf(968,plain,
! [SV122: product_prod_a_a > $o] :
( ( ! [SV227: a] :
( ( product_curry_a_a_o @ SV122 @ SV227 )
= ( ^ [SY924: a] : ( SV122 @ ( product_Pair_a_a @ SV227 @ SY924 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[850]) ).
thf(969,plain,
! [SV122: product_prod_a_a > $o] :
( ( ( product_curry_a_a_o @ SV122 )
= ( ^ [SY732: a,SY733: a] : ( SV122 @ ( product_Pair_a_a @ SY732 @ SY733 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[850]) ).
thf(970,plain,
! [SV228: set_Product_prod_a_a,SV123: a,SV4: a] :
( ( ! [SY925: a > a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ SV4 @ SV123 ) @ ( inv_image_a_a @ SV228 @ SY925 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( SY925 @ SV4 ) @ ( SY925 @ SV123 ) ) @ SV228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[851]) ).
thf(971,plain,
! [SV229: set_Pr158363655iset_a,SV124: a,SV5: a] :
( ( ! [SY926: a > multiset_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ SV5 @ SV124 ) @ ( inv_im975322764et_a_a @ SV229 @ SY926 ) )
= ( member340150864iset_a @ ( produc2037245207iset_a @ ( SY926 @ SV5 ) @ ( SY926 @ SV124 ) ) @ SV229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(972,plain,
! [SV230: set_Product_prod_a_a,SV125: multiset_a,SV6: multiset_a] :
( ( ! [SY927: multiset_a > a] :
( ( member340150864iset_a @ ( produc2037245207iset_a @ SV6 @ SV125 ) @ ( inv_im479034648iset_a @ SV230 @ SY927 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( SY927 @ SV6 ) @ ( SY927 @ SV125 ) ) @ SV230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[853]) ).
thf(973,plain,
! [SV231: set_Pr1948701895od_a_a,SV126: a,SV7: a] :
( ( ! [SY928: a > product_prod_a_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ SV7 @ SV126 ) @ ( inv_im777352425_a_a_a @ SV231 @ SY928 ) )
= ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( SY928 @ SV7 ) @ ( SY928 @ SV126 ) ) @ SV231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(974,plain,
! [SV232: set_Product_prod_a_a,SV127: product_prod_a_a,SV8: product_prod_a_a] :
( ( ! [SY929: product_prod_a_a > a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV8 @ SV127 ) @ ( inv_im15016955od_a_a @ SV232 @ SY929 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( SY929 @ SV8 ) @ ( SY929 @ SV127 ) ) @ SV232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(975,plain,
! [SV233: set_Pr1821581383od_a_a,SV128: a,SV9: a] :
( ( ! [SY930: a > multis599418605od_a_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV128 ) @ ( inv_im1681759523_a_a_a @ SV233 @ SY930 ) )
= ( member1349055120od_a_a @ ( produc1859144151od_a_a @ ( SY930 @ SV9 ) @ ( SY930 @ SV128 ) ) @ SV233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(976,plain,
! [SV234: set_Product_prod_a_a,SV129: multis599418605od_a_a,SV10: multis599418605od_a_a] :
( ( ! [SY931: multis599418605od_a_a > a] :
( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ SV10 @ SV129 ) @ ( inv_im941243329od_a_a @ SV234 @ SY931 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( SY931 @ SV10 ) @ ( SY931 @ SV129 ) ) @ SV234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(977,plain,
! [SV235: a,SV131: a,SV12: a > a > set_Product_prod_a_a] :
( ( ( produc1093061851od_a_a @ SV12 @ ( product_Pair_a_a @ SV131 @ SV235 ) )
= ( SV12 @ SV131 @ SV235 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(978,plain,
! [SV236: a,SV132: a,SV13: a > a > set_a] :
( ( ( produc961951794_set_a @ SV13 @ ( product_Pair_a_a @ SV132 @ SV236 ) )
= ( SV13 @ SV132 @ SV236 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(979,plain,
! [SV237: a,SV133: a,SV14: a > a > $o] :
( ( ( produc1833107820_a_a_o @ SV14 @ ( product_Pair_a_a @ SV133 @ SV237 ) )
= ( SV14 @ SV133 @ SV237 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(980,plain,
! [SV134: set_Product_prod_a_a] :
( ( ~ ( ( irrefl_a @ SV134 )
| ! [SY751: a] :
~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY751 @ SY751 ) @ SV134 ) )
| ~ ( ~ ( irrefl_a @ SV134 )
| ~ ! [SY751: a] :
~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY751 @ SY751 ) @ SV134 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[862]) ).
thf(981,plain,
! [SV134: set_Product_prod_a_a] :
( ( ( irrefl_a @ SV134 )
= ( ! [SY751: a] :
~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY751 @ SY751 ) @ SV134 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[862]) ).
thf(982,plain,
! [SV238: set_Product_prod_a_a,SV135: a,SV16: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV16 @ SV135 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV238 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ SV135 @ SV16 ) @ SV238 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[863]) ).
thf(983,plain,
! [SV136: product_prod_a_a] :
( ( ~ ( ( top_to1483957574_a_a_o @ SV136 )
| ( member449909584od_a_a @ SV136 @ top_to398455383od_a_a ) )
| ~ ( ~ ( top_to1483957574_a_a_o @ SV136 )
| ~ ( member449909584od_a_a @ SV136 @ top_to398455383od_a_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[864]) ).
thf(984,plain,
! [SV136: product_prod_a_a] :
( ( ( top_to1483957574_a_a_o @ SV136 )
= ( member449909584od_a_a @ SV136 @ top_to398455383od_a_a ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[864]) ).
thf(985,plain,
! [SV239: a,SV137: a > a,SV18: a > a] :
( ( ! [SY932: a] :
( ( produc700022774_a_a_a @ SV18 @ SV137 @ ( product_Pair_a_a @ SV239 @ SY932 ) )
= ( product_Pair_a_a @ ( SV18 @ SV239 ) @ ( SV137 @ SY932 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(986,plain,
! [SV240: multis599418605od_a_a,SV141: multis599418605od_a_a,SV25: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ ( plus_p404985124od_a_a @ SV141 @ SV240 ) ) )
= ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV141 ) )
| ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV240 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[869]) ).
thf(987,plain,
! [SV241: multis599418605od_a_a,SV142: multis599418605od_a_a,SV27: product_prod_a_a] :
( ( ~ ( member449909584od_a_a @ SV27 @ ( set_ms1818337124od_a_a @ ( minus_1257885652od_a_a @ SV142 @ SV241 ) ) )
| ( member449909584od_a_a @ SV27 @ ( set_ms1818337124od_a_a @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[872]) ).
thf(988,plain,
! [SV242: a,SV143: a,SV28: a] :
( ( ! [SY933: a] :
( ( ( product_Pair_a_a @ SV28 @ SV143 )
!= ( product_Pair_a_a @ SV242 @ SY933 ) )
| ~ ( ( SV28 != SV242 )
| ( SV143 != SY933 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[873]) ).
thf(989,plain,
! [SV144: produc1572603623od_a_a,SV29: produc1572603623od_a_a > $o] :
( ( ( ~ ! [SY474: product_prod_a_a,SY475: a,SY476: a] : ( SV29 @ ( produc1474507607od_a_a @ SY474 @ ( product_Pair_a_a @ SY475 @ SY476 ) ) ) )
= $true )
| ( ( SV29 @ SV144 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[874]) ).
thf(990,plain,
! [SV243: a,SV145: a,SV30: a] :
( ( ( ( product_fst_a_a @ ( product_Pair_a_a @ SV30 @ SV145 ) )
!= SV243 )
| ( SV30 = SV243 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(991,plain,
! [SV244: a,SV146: a,SV31: product_prod_a_a > $o] :
( ( ~ ( SV31 @ ( product_Pair_a_a @ SV146 @ SV244 ) )
| ( product_curry_a_a_o @ SV31 @ SV146 @ SV244 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[876]) ).
thf(992,plain,
! [SV147: set_Pr1948701895od_a_a,SV32: set_Product_prod_a_a] :
( ( ( ~ ! [SY764: product_prod_a_a,SY765: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY764 @ SV32 )
| ~ ( member449909584od_a_a @ SY765 @ SV32 )
| ~ ( ( SY764 != SY765 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY764 @ SY765 ) @ SV147 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY765 @ SY764 ) @ SV147 ) ) )
= $true )
| ( ( total_1490170027od_a_a @ SV32 @ SV147 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[877]) ).
thf(993,plain,
! [SV245: a > $o,SV148: a,SV33: a > $o] :
( ( ! [SY934: a] :
( ~ ( SV33 @ SV148 )
| ~ ( SV245 @ SY934 )
| ~ ( ~ ( SV33 @ ( product_fst_a_a @ ( product_Pair_a_a @ SV148 @ SY934 ) ) )
| ~ ( SV245 @ ( product_snd_a_a @ ( product_Pair_a_a @ SV148 @ SY934 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[878]) ).
thf(994,plain,
! [SV246: a,SV149: a,SV34: a > $o] :
( ( ! [SY935: a,SY936: a > set_Product_prod_a_a] :
( ~ ( SV34 @ SV149 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV246 @ SY935 ) @ ( SY936 @ SV149 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV149 @ SV246 ) @ ( product_Pair_a_a @ SV149 @ SY935 ) ) @ ( same_fst_a_a @ SV34 @ SY936 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[879]) ).
thf(995,plain,
! [SV150: multis599418605od_a_a,SV35: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV35 @ ( set_ms1818337124od_a_a @ SV150 ) ) )
= $true )
| ( ( ~ ! [SY771: multis599418605od_a_a] :
( SV150
!= ( add_ms1725977093od_a_a @ SV35 @ SY771 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[880]) ).
thf(996,plain,
! [SV151: set_Product_prod_a_a > $o,SV36: set_Product_prod_a_a] :
( ( ( ~ ( asym_a @ SV36 ) )
= $true )
| ( ( ~ ! [SY772: set_Product_prod_a_a] :
( ~ ! [SX3: a,SX4: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX4 ) @ SY772 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX4 @ SX3 ) @ SY772 ) )
| ( SV151 @ SY772 ) )
| ( SV151 @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[881]) ).
thf(997,plain,
! [SV152: set_Product_prod_a_a,SV37: set_Product_prod_a_a] :
( ( ( ~ ! [SY775: a,SY776: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY775 @ SY776 ) @ SV37 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY775 @ SY776 ) @ SV152 ) ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV37 @ SV152 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[882]) ).
thf(998,plain,
! [SV247: set_Product_prod_a_a,SV153: product_prod_a_a,SV38: product_prod_a_a] :
( ( ! [SY937: set_Pr1948701895od_a_a] :
( ~ ( member449909584od_a_a @ SV38 @ ( prefer477097315od_a_a @ SV153 @ SV247 @ SY937 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV38 @ SV153 ) @ SY937 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(999,plain,
! [SV154: set_Product_prod_a_a] :
( ( ! [SV248: set_Pr1948701895od_a_a] :
( ( total_1490170027od_a_a @ SV154 @ SV248 )
= ( ! [SY938: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY938 @ SV154 )
| ! [SY939: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY939 @ SV154 )
| ~ ( ( SY938 != SY939 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY938 @ SY939 ) @ SV248 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY939 @ SY938 ) @ SV248 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[884]) ).
thf(1000,plain,
! [SV154: set_Product_prod_a_a] :
( ( ( total_1490170027od_a_a @ SV154 )
= ( ^ [SY779: set_Pr1948701895od_a_a] :
! [SY780: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY780 @ SV154 )
| ! [SY781: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY781 @ SV154 )
| ~ ( ( SY780 != SY781 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY780 @ SY781 ) @ SY779 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY781 @ SY780 ) @ SY779 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[884]) ).
thf(1001,plain,
! [SV155: product_prod_a_a,SV40: a] :
( ( ~ ( ( SV40
= ( product_fst_a_a @ SV155 ) )
| ~ ! [SY782: a] :
( SV155
!= ( product_Pair_a_a @ SV40 @ SY782 ) ) )
| ~ ( ( SV40
!= ( product_fst_a_a @ SV155 ) )
| ~ ~ ! [SY782: a] :
( SV155
!= ( product_Pair_a_a @ SV40 @ SY782 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[885]) ).
thf(1002,plain,
! [SV155: product_prod_a_a,SV40: a] :
( ( ( SV40
= ( product_fst_a_a @ SV155 ) )
= ( ~ ! [SY782: a] :
( SV155
!= ( product_Pair_a_a @ SV40 @ SY782 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[885]) ).
thf(1003,plain,
! [SV249: a,SV156: a,SV41: set_Product_prod_a_a] :
( ( ! [SY940: a] :
( ~ ( trans_a @ SV41 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV156 @ SV249 ) @ SV41 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV249 @ SY940 ) @ SV41 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV156 @ SY940 ) @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[886]) ).
thf(1004,plain,
! [SV250: product_prod_a_a,SV157: set_Pr1948701895od_a_a,SV42: set_Product_prod_a_a] :
( ( ! [SY941: product_prod_a_a] :
( ~ ( prefer1338892073od_a_a @ SV42 @ SV157 )
| ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV250 @ SY941 ) @ SV157 )
| ( member449909584od_a_a @ SV250 @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[887]) ).
thf(1005,plain,
! [SV251: a,SV158: a,SV43: a > a > $o] :
( ( ! [SY942: product_prod_a_a] :
( ~ ( SV43 @ SV158 @ SV251 )
| ( SY942
!= ( product_Pair_a_a @ SV158 @ SV251 ) )
| ( SV43 @ ( product_fst_a_a @ SY942 ) @ ( product_snd_a_a @ SY942 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[888]) ).
thf(1006,plain,
! [SV252: a,SV159: a,SV44: a] :
( ( ! [SY943: a] :
( ( ( product_Pair_a_a @ SV44 @ SV159 )
= ( product_Pair_a_a @ SV252 @ SY943 ) )
= ( ~ ( ( SV44 != SV252 )
| ( SV159 != SY943 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(1007,plain,
! [SV253: a,SV160: a,SV45: set_Product_prod_a_a] :
( ( ! [SY944: a] :
( ~ ( trans_a @ SV45 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV160 @ SV253 ) @ SV45 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV253 @ SY944 ) @ SV45 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV160 @ SY944 ) @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[890]) ).
thf(1008,plain,
! [SV254: set_Product_prod_a_a,SV161: a > product_prod_a_a,SV46: set_a] :
( ( ~ ! [SY945: a] :
( ~ ( member_a @ SY945 @ SV46 )
| ( member449909584od_a_a @ ( SV161 @ SY945 ) @ SV254 ) )
| ( ord_le1824328871od_a_a @ ( image_1725938350od_a_a @ SV161 @ SV46 ) @ SV254 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[891]) ).
thf(1009,plain,
! [SV162: set_Pr1948701895od_a_a,SV47: set_Product_prod_a_a] :
( ( ( ~ ( prefer697821563od_a_a @ SV47 @ SV162 ) )
= $true )
| ( ( ! [SY795: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY795 @ SV47 )
| ! [SY796: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY796 @ SV47 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY795 @ SY796 ) @ SV162 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY796 @ SY795 ) @ SV162 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[892]) ).
thf(1010,plain,
! [SV163: set_Product_prod_a_a,SV48: set_a] :
( ( ( ~ ! [SY797: a,SY798: a] :
( ~ ( member_a @ SY797 @ SV48 )
| ~ ( member_a @ SY798 @ SV48 )
| ~ ( ( SY797 != SY798 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY797 @ SY798 ) @ SV163 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY798 @ SY797 ) @ SV163 ) ) )
= $true )
| ( ( total_on_a @ SV48 @ SV163 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[893]) ).
thf(1011,plain,
! [SV255: set_Product_prod_a_a,SV164: product_prod_a_a,SV49: product_prod_a_a] :
( ( ! [SY946: set_Pr1948701895od_a_a] :
( ~ ( member449909584od_a_a @ SV49 @ ( prefer477097315od_a_a @ SV164 @ SV255 @ SY946 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV49 @ SV164 ) @ SY946 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(1012,plain,
! [SV50: product_prod_a_a] :
( ( ~ ~ ! [SY947: a] :
( SV50
!= ( product_Pair_a_a @ ( sK1_SY535 @ SV50 ) @ SY947 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[895]) ).
thf(1013,plain,
! [SV256: product_prod_a_a,SV165: set_Pr1948701895od_a_a,SV51: set_Product_prod_a_a] :
( ( ~ ( refl_o1298442278od_a_a @ SV51 @ SV165 )
| ~ ( member449909584od_a_a @ SV256 @ SV51 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV256 @ SV256 ) @ SV165 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(1014,plain,
! [SV257: a,SV166: a,SV52: a] :
( ( ! [SY948: a,SY949: set_Product_prod_a_a,SY950: set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SV257 @ SY948 ) ) @ ( lex_prod_a_a @ SY949 @ SY950 ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SY949 )
| ~ ( ( SV52 != SV257 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SY948 ) @ SY950 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[897]) ).
thf(1015,plain,
! [SV258: product_prod_a_a,SV167: set_Pr1948701895od_a_a,SV53: set_Product_prod_a_a] :
( ( ! [SY951: product_prod_a_a] :
( ~ ( refl_o1298442278od_a_a @ SV53 @ SV167 )
| ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV258 @ SY951 ) @ SV167 )
| ( member449909584od_a_a @ SY951 @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[898]) ).
thf(1016,plain,
! [SV259: a,SV168: set_Product_prod_a_a,SV54: set_a] :
( ( ~ ( refl_on_a @ SV54 @ SV168 )
| ~ ( member_a @ SV259 @ SV54 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV259 @ SV259 ) @ SV168 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[899]) ).
thf(1017,plain,
! [SV260: set_a,SV169: a,SV55: a] :
( ( ! [SY952: set_Product_prod_a_a] :
( ~ ( member_a @ SV55 @ ( prefer161218362good_a @ SV169 @ SV260 @ SY952 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV55 @ SV169 ) @ SY952 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[900]) ).
thf(1018,plain,
! [SV261: a,SV170: a,SV56: a] :
( ( ! [SY953: a] :
( ( ( product_Pair_a_a @ SV56 @ SV170 )
= ( product_Pair_a_a @ SV261 @ SY953 ) )
= ( ~ ( ( SV56 != SV261 )
| ( SV170 != SY953 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[901]) ).
thf(1019,plain,
! [SV262: a,SV171: a,SV57: a] :
( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV171 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV171 @ SV57 ) @ relation ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV171 @ SV262 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV262 @ SV171 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV262 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV262 @ SV57 ) @ relation ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[902]) ).
thf(1020,plain,
! [SV263: a,SV172: set_Product_prod_a_a,SV58: set_a] :
( ( ! [SY954: a] :
( ~ ( refl_on_a @ SV58 @ SV172 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV263 @ SY954 ) @ SV172 )
| ~ ( ~ ( member_a @ SV263 @ SV58 )
| ~ ( member_a @ SY954 @ SV58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[903]) ).
thf(1021,plain,
! [SV264: a > a,SV173: a > a,SV59: product_prod_a_a] :
( ( ! [SY955: set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ SV59 @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SV173 @ SV264 ) @ SY955 ) )
| ~ ! [SY956: a,SY957: a] :
( ( SV59
!= ( product_Pair_a_a @ ( SV173 @ SY956 ) @ ( SV264 @ SY957 ) ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY956 @ SY957 ) @ SY955 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[904]) ).
thf(1022,plain,
! [SV265: product_prod_a_a,SV174: set_Pr1948701895od_a_a,SV60: set_Product_prod_a_a] :
( ( ! [SY958: product_prod_a_a] :
( ~ ( prefer697821563od_a_a @ SV60 @ SV174 )
| ~ ~ ( ~ ( member449909584od_a_a @ SV265 @ SV60 )
| ~ ( member449909584od_a_a @ SY958 @ SV60 ) )
| ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY958 @ SV265 ) @ SV174 ) )
= ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SY958 ) @ SV174 )
| ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY958 @ SV265 ) @ SV174 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[905]) ).
thf(1023,plain,
! [SV266: a,SV175: set_Product_prod_a_a,SV61: set_a] :
( ( ! [SY959: a] :
( ~ ( prefer719835986ence_a @ SV61 @ SV175 )
| ~ ~ ( ~ ( member_a @ SV266 @ SV61 )
| ~ ( member_a @ SY959 @ SV61 ) )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY959 @ SV266 ) @ SV175 ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SY959 ) @ SV175 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY959 @ SV266 ) @ SV175 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[906]) ).
thf(1024,plain,
! [SV176: product_prod_a_a,SV62: product_prod_a_a > $o] :
( ( ( ~ ! [SY572: a,SY573: a] : ( SV62 @ ( product_Pair_a_a @ SY572 @ SY573 ) ) )
= $true )
| ( ( SV62 @ SV176 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[907]) ).
thf(1025,plain,
! [SV63: set_Product_prod_a_a] :
( ( ( ! [SY574: a,SY575: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY574 @ SY575 ) @ SV63 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY575 @ SY574 ) @ SV63 ) ) )
= $false )
| ( ( asym_a @ SV63 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[908]) ).
thf(1026,plain,
! [SV267: a,SV177: a,SV64: set_Product_prod_a_a] :
( ( ~ ( asym_a @ SV64 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV177 @ SV267 ) @ SV64 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV267 @ SV177 ) @ SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[909]) ).
thf(1027,plain,
! [SV268: product_prod_a_a > product_prod_a_a,SV178: set_Product_prod_a_a,SV65: product_prod_a_a] :
( ( ~ ( member449909584od_a_a @ SV65 @ SV178 )
| ( member449909584od_a_a @ ( SV268 @ SV65 ) @ ( image_794773445od_a_a @ SV268 @ SV178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[910]) ).
thf(1028,plain,
! [SV66: a] :
( ( ( member_a @ SV66 @ carrier )
= $false )
| ( ( ! [SY580: a] :
( ~ ( member_a @ SY580 @ carrier )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV66 @ SY580 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY580 @ SV66 ) @ relation ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[911]) ).
thf(1029,plain,
! [SV67: set_Product_prod_a_a] :
( ( ( ! [SY581: a,SY582: a,SY583: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY581 @ SY582 ) @ SV67 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY582 @ SY583 ) @ SV67 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY581 @ SY583 ) @ SV67 ) ) )
= $false )
| ( ( trans_a @ SV67 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[912]) ).
thf(1030,plain,
! [SV179: set_Product_prod_a_a] :
( ( ~ ( ( trans_a @ SV179 )
| ! [SY828: a,SY829: a,SY830: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY829 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY829 @ SY830 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY830 ) @ SV179 ) ) )
| ~ ( ~ ( trans_a @ SV179 )
| ~ ! [SY828: a,SY829: a,SY830: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY829 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY829 @ SY830 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY830 ) @ SV179 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[913]) ).
thf(1031,plain,
! [SV179: set_Product_prod_a_a] :
( ( ( trans_a @ SV179 )
= ( ! [SY828: a,SY829: a,SY830: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY829 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY829 @ SY830 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY830 ) @ SV179 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[913]) ).
thf(1032,plain,
! [SV269: a,SV180: a,SV69: a > a > $o] :
( ( ~ ( SV69 @ SV180 @ SV269 )
| ( SV69 @ ( product_snd_a_a @ ( product_Pair_a_a @ SV269 @ SV180 ) ) @ ( product_fst_a_a @ ( product_Pair_a_a @ SV269 @ SV180 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[914]) ).
thf(1033,plain,
! [SV70: produc1572603623od_a_a] :
( ( ! [SY960: a,SY961: a] :
( SV70
!= ( produc1474507607od_a_a @ ( sK2_SY589 @ SV70 ) @ ( product_Pair_a_a @ SY960 @ SY961 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[915]) ).
thf(1034,plain,
! [SV181: a,SV71: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV181 ) @ relation ) )
= $true )
| ( ( member_a @ SV71 @ carrier )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[916]) ).
thf(1035,plain,
! [SV270: a,SV182: a,SV72: product_prod_a_a > $o] :
( ( ~ ( product_curry_a_a_o @ SV72 @ SV182 @ SV270 )
| ( SV72 @ ( product_Pair_a_a @ SV182 @ SV270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[917]) ).
thf(1036,plain,
! [SV271: multis599418605od_a_a,SV183: multis599418605od_a_a,SV73: product_prod_a_a] :
( ( ( ( add_ms1725977093od_a_a @ SV73 @ SV183 )
!= SV271 )
| ( member449909584od_a_a @ SV73 @ ( set_ms1818337124od_a_a @ SV271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[918]) ).
thf(1037,plain,
! [SV272: a,SV184: set_Product_prod_a_a,SV74: set_a] :
( ( ! [SY962: a,SY963: a] :
( ~ ( prefer719835986ence_a @ SV74 @ SV184 )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SY962 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY962 @ SV272 ) @ SV184 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY962 @ SY963 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY963 @ SY962 ) @ SV184 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SY963 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY963 @ SV272 ) @ SV184 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[919]) ).
thf(1038,plain,
! [SV273: a > product_prod_a_a,SV185: set_a,SV75: a] :
( ( ~ ( member_a @ SV75 @ SV185 )
| ( member449909584od_a_a @ ( SV273 @ SV75 ) @ ( image_1725938350od_a_a @ SV273 @ SV185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[920]) ).
thf(1039,plain,
! [SV274: product_prod_a_a,SV186: product_prod_a_a > a,SV76: a] :
( ( ! [SY964: set_Product_prod_a_a] :
( ( SV76
!= ( SV186 @ SV274 ) )
| ~ ( member449909584od_a_a @ SV274 @ SY964 )
| ( member_a @ SV76 @ ( image_340790172_a_a_a @ SV186 @ SY964 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[921]) ).
thf(1040,plain,
! [SV275: a,SV187: a,SV77: product_prod_a_a] :
( ( ( SV77
!= ( product_Pair_a_a @ SV187 @ SV275 ) )
| ( ( product_fst_a_a @ SV77 )
= SV187 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[922]) ).
thf(1041,plain,
! [SV276: a,SV188: a,SV78: product_prod_a_a] :
( ( ( SV78
!= ( product_Pair_a_a @ SV188 @ SV276 ) )
| ( ( product_snd_a_a @ SV78 )
= SV276 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[923]) ).
thf(1042,plain,
! [SV277: a,SV189: a,SV79: a] :
( ( ( ( product_snd_a_a @ ( product_Pair_a_a @ SV79 @ SV189 ) )
!= SV277 )
| ( SV189 = SV277 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(1043,plain,
! [SV80: set_Product_prod_a_a] :
( ( ( ! [SY612: a] :
~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY612 @ SY612 ) @ SV80 ) )
= $false )
| ( ( irrefl_a @ SV80 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[925]) ).
thf(1044,plain,
! [SV278: a,SV190: set_Product_prod_a_a,SV81: set_a] :
( ( ! [SY965: a] :
( ~ ( prefer1292084992ence_a @ SV81 @ SV190 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SY965 ) @ SV190 )
| ( member_a @ SV278 @ SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[926]) ).
thf(1045,plain,
! [SV279: product_prod_a_a,SV191: set_Product_prod_a_a,SV82: product_prod_a_a] :
( ( ! [SY966: product_prod_a_a > product_prod_a_a] :
( ~ ( member449909584od_a_a @ SV82 @ SV191 )
| ( SV279
!= ( SY966 @ SV82 ) )
| ( member449909584od_a_a @ SV279 @ ( image_794773445od_a_a @ SY966 @ SV191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[927]) ).
thf(1046,plain,
! [SV280: a,SV192: set_Product_prod_a_a,SV83: set_a] :
( ( ! [SY967: a] :
( ~ ( refl_on_a @ SV83 @ SV192 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV280 @ SY967 ) @ SV192 )
| ( member_a @ SV280 @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[928]) ).
thf(1047,plain,
! [SV281: product_prod_a_a,SV193: set_a,SV84: a] :
( ( ! [SY968: a > product_prod_a_a] :
( ~ ( member_a @ SV84 @ SV193 )
| ( SV281
!= ( SY968 @ SV84 ) )
| ( member449909584od_a_a @ SV281 @ ( image_1725938350od_a_a @ SY968 @ SV193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[929]) ).
thf(1048,plain,
! [SV85: set_Product_prod_a_a] :
( ( ( asym_a @ SV85 )
= $false )
| ( ( ! [SY625: a,SY626: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY625 @ SY626 ) @ SV85 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY626 @ SY625 ) @ SV85 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[930]) ).
thf(1049,plain,
! [SV282: set_a,SV194: product_prod_a_a > a,SV86: set_Product_prod_a_a] :
( ( ~ ! [SY969: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY969 @ SV86 )
| ( member_a @ ( SV194 @ SY969 ) @ SV282 ) )
| ( ord_less_eq_set_a @ ( image_340790172_a_a_a @ SV194 @ SV86 ) @ SV282 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(1050,plain,
! [SV283: product_prod_a_a > a,SV195: set_Product_prod_a_a,SV87: product_prod_a_a] :
( ( ~ ( member449909584od_a_a @ SV87 @ SV195 )
| ( member_a @ ( SV283 @ SV87 ) @ ( image_340790172_a_a_a @ SV283 @ SV195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[932]) ).
thf(1051,plain,
! [SV196: a,SV88: a] :
( ( ( ~ ~ ( ~ ( member_a @ SV88 @ carrier )
| ~ ( member_a @ SV196 @ carrier ) ) )
= $true )
| ( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[933]) ).
thf(1052,plain,
! [SV197: set_a] :
( ( ! [SV284: set_Product_prod_a_a] :
( ( total_on_a @ SV197 @ SV284 )
= ( ! [SY970: a] :
( ~ ( member_a @ SY970 @ SV197 )
| ! [SY971: a] :
( ~ ( member_a @ SY971 @ SV197 )
| ~ ( ( SY970 != SY971 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY970 @ SY971 ) @ SV284 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY971 @ SY970 ) @ SV284 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[934]) ).
thf(1053,plain,
! [SV197: set_a] :
( ( ( total_on_a @ SV197 )
= ( ^ [SY854: set_Product_prod_a_a] :
! [SY855: a] :
( ~ ( member_a @ SY855 @ SV197 )
| ! [SY856: a] :
( ~ ( member_a @ SY856 @ SV197 )
| ~ ( ( SY855 != SY856 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY855 @ SY856 ) @ SY854 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY856 @ SY855 ) @ SY854 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[934]) ).
thf(1054,plain,
! [SV198: set_Product_prod_a_a] :
( ( ~ ( ( asym_a @ SV198 )
| ~ ! [SY857: set_Product_prod_a_a] :
~ ~ ( ( SV198 != SY857 )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SY857 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SY857 ) ) ) )
| ~ ( ~ ( asym_a @ SV198 )
| ~ ~ ! [SY857: set_Product_prod_a_a] :
~ ~ ( ( SV198 != SY857 )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SY857 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SY857 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[935]) ).
thf(1055,plain,
! [SV198: set_Product_prod_a_a] :
( ( ( asym_a @ SV198 )
= ( ~ ! [SY857: set_Product_prod_a_a] :
~ ~ ( ( SV198 != SY857 )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SY857 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SY857 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[935]) ).
thf(1056,plain,
! [SV199: set_Product_prod_a_a] :
( ( ~ ( ( asym_a @ SV199 )
| ! [SY860: a,SY861: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY860 @ SY861 ) @ SV199 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY861 @ SY860 ) @ SV199 ) ) )
| ~ ( ~ ( asym_a @ SV199 )
| ~ ! [SY860: a,SY861: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY860 @ SY861 ) @ SV199 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY861 @ SY860 ) @ SV199 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[936]) ).
thf(1057,plain,
! [SV199: set_Product_prod_a_a] :
( ( ( asym_a @ SV199 )
= ( ! [SY860: a,SY861: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY860 @ SY861 ) @ SV199 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY861 @ SY860 ) @ SV199 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[936]) ).
thf(1058,plain,
! [SV285: product_prod_a_a,SV200: multis599418605od_a_a,SV92: product_prod_a_a] :
( ( ! [SY972: multis599418605od_a_a] :
( ( ( add_ms1725977093od_a_a @ SV92 @ SV200 )
!= ( add_ms1725977093od_a_a @ SV285 @ SY972 ) )
| ~ ( ( SV92 != SV285 ) )
| ( member449909584od_a_a @ SV285 @ ( set_ms1818337124od_a_a @ SV200 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[937]) ).
thf(1059,plain,
! [SV286: a,SV201: set_Product_prod_a_a,SV93: set_a] :
( ( ! [SY973: a,SY974: a] :
( ~ ( prefer1292084992ence_a @ SV93 @ SV201 )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SY973 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY973 @ SV286 ) @ SV201 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY973 @ SY974 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY974 @ SY973 ) @ SV201 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SY974 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY974 @ SV286 ) @ SV201 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[938]) ).
thf(1060,plain,
! [SV287: set_a,SV202: a,SV94: a] :
( ( ! [SY975: set_Product_prod_a_a] :
( ~ ( member_a @ SV94 @ ( prefer161218362good_a @ SV202 @ SV287 @ SY975 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV94 @ SV202 ) @ SY975 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[939]) ).
thf(1061,plain,
! [SV288: product_prod_a_a,SV203: a > a > set_mu1281098573od_a_a,SV95: multis599418605od_a_a] :
( ( ~ ( member1755255446od_a_a @ SV95 @ ( produc1121147169od_a_a @ SV203 @ SV288 ) )
| ~ ! [SY976: a,SY977: a] :
( ( SV288
!= ( product_Pair_a_a @ SY976 @ SY977 ) )
| ~ ( member1755255446od_a_a @ SV95 @ ( SV203 @ SY976 @ SY977 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[940]) ).
thf(1062,plain,
! [SV204: set_a] :
( ( ! [SV289: set_Product_prod_a_a] :
( ( prefer1292084992ence_a @ SV204 @ SV289 )
= ( ~ ( ~ ~ ( ~ ! [SY978: a,SY979: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY978 @ SY979 ) @ SV289 )
| ( member_a @ SY978 @ SV204 ) )
| ~ ! [SY980: a,SY981: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY980 @ SY981 ) @ SV289 )
| ( member_a @ SY981 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV289 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[941]) ).
thf(1063,plain,
! [SV204: set_a] :
( ( ( prefer1292084992ence_a @ SV204 )
= ( ^ [SY872: set_Product_prod_a_a] :
~ ( ~ ~ ( ~ ! [SY873: a,SY874: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY873 @ SY874 ) @ SY872 )
| ( member_a @ SY873 @ SV204 ) )
| ~ ! [SY875: a,SY876: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY875 @ SY876 ) @ SY872 )
| ( member_a @ SY876 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SY872 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[941]) ).
thf(1064,plain,
! [SV205: multis599418605od_a_a,SV97: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV97 @ ( set_ms1818337124od_a_a @ SV205 ) ) )
= $true )
| ( ( ~ ! [SY877: multis599418605od_a_a] :
( SV205
!= ( add_ms1725977093od_a_a @ SV97 @ SY877 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[942]) ).
thf(1065,plain,
! [SV290: product_prod_a_a,SV206: a > a > set_multiset_a,SV98: multiset_a] :
( ( ~ ( member_multiset_a @ SV98 @ ( produc1828150264iset_a @ SV206 @ SV290 ) )
| ~ ! [SY982: a,SY983: a] :
( ( SV290
!= ( product_Pair_a_a @ SY982 @ SY983 ) )
| ~ ( member_multiset_a @ SV98 @ ( SV206 @ SY982 @ SY983 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[943]) ).
thf(1066,plain,
! [SV99: product_prod_a_a] :
( ( ! [SY984: a] :
( SV99
!= ( product_Pair_a_a @ ( sK3_SY666 @ SV99 ) @ SY984 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[944]) ).
thf(1067,plain,
! [SV207: set_a,SV100: set_Product_prod_a_a] :
( ( ( ~ ! [SY881: a,SY882: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY881 @ SY882 ) @ SV100 )
| ( member_a @ SY881 @ SV207 ) ) )
= $true )
| ( ( ~ ! [SY883: a,SY884: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY883 @ SY884 ) @ SV100 )
| ( member_a @ SY884 @ SV207 ) )
| ~ ( order_preorder_on_a @ SV207 @ SV100 )
| ( prefer1292084992ence_a @ SV207 @ SV100 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[945]) ).
thf(1068,plain,
! [SV291: a,SV208: a,SV101: a] :
( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SV208 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV101 ) @ relation ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV291 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV291 @ SV208 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SV291 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV291 @ SV101 ) @ relation ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[946]) ).
thf(1069,plain,
! [SV292: a,SV209: a,SV102: product_prod_a_a > $o] :
( ( ~ ( product_curry_a_a_o @ SV102 @ SV209 @ SV292 )
| ( SV102 @ ( product_Pair_a_a @ SV209 @ SV292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[947]) ).
thf(1070,plain,
! [SV293: product_prod_a_a,SV210: a > a > set_a,SV103: a] :
( ( ~ ( member_a @ SV103 @ ( produc961951794_set_a @ SV210 @ SV293 ) )
| ~ ! [SY985: a,SY986: a] :
( ( SV293
!= ( product_Pair_a_a @ SY985 @ SY986 ) )
| ~ ( member_a @ SV103 @ ( SV210 @ SY985 @ SY986 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(1071,plain,
! [SV211: product_prod_a_a,SV104: product_prod_a_a > $o] :
( ( ( ~ ! [SY682: a,SY683: a] : ( SV104 @ ( product_Pair_a_a @ SY682 @ SY683 ) ) )
= $true )
| ( ( SV104 @ SV211 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[949]) ).
thf(1072,plain,
! [SV294: product_prod_a_a,SV212: set_Pr1948701895od_a_a,SV105: set_Product_prod_a_a] :
( ( ! [SY987: product_prod_a_a] :
( ~ ( refl_o1298442278od_a_a @ SV105 @ SV212 )
| ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV294 @ SY987 ) @ SV212 )
| ( member449909584od_a_a @ SV294 @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[950]) ).
thf(1073,plain,
! [SV295: product_prod_a_a,SV213: set_Pr1948701895od_a_a,SV106: set_Product_prod_a_a] :
( ( ! [SY988: product_prod_a_a] :
( ~ ( refl_o1298442278od_a_a @ SV106 @ SV213 )
| ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV295 @ SY988 ) @ SV213 )
| ~ ( ~ ( member449909584od_a_a @ SV295 @ SV106 )
| ~ ( member449909584od_a_a @ SY988 @ SV106 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[951]) ).
thf(1074,plain,
! [SV296: set_Product_prod_a_a,SV214: product_prod_a_a > product_prod_a_a,SV107: set_Product_prod_a_a] :
( ( ~ ! [SY989: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY989 @ SV107 )
| ( member449909584od_a_a @ ( SV214 @ SY989 ) @ SV296 ) )
| ( ord_le1824328871od_a_a @ ( image_794773445od_a_a @ SV214 @ SV107 ) @ SV296 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(1075,plain,
! [SV297: set_Product_prod_a_a,SV215: a,SV108: a] :
( ( ! [SY990: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV108 @ SV215 ) @ SV297 )
| ( SY990 != SV215 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV108 @ SY990 ) @ SV297 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(1076,plain,
! [SV298: a,SV216: set_Product_prod_a_a,SV109: set_a] :
( ( ! [SY991: a] :
( ~ ( refl_on_a @ SV109 @ SV216 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV298 @ SY991 ) @ SV216 )
| ( member_a @ SY991 @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(1077,plain,
! [SV299: a,SV217: a > product_prod_a_a,SV110: product_prod_a_a] :
( ( ! [SY992: set_a] :
( ( SV110
!= ( SV217 @ SV299 ) )
| ~ ( member_a @ SV299 @ SY992 )
| ( member449909584od_a_a @ SV110 @ ( image_1725938350od_a_a @ SV217 @ SY992 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[955]) ).
thf(1078,plain,
! [SV300: set_Product_prod_a_a,SV218: a,SV111: a] :
( ( ! [SY993: a > a,SY994: a > a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV111 @ SV218 ) @ SV300 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( SY993 @ SV111 ) @ ( SY994 @ SV218 ) ) @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SY993 @ SY994 ) @ SV300 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[956]) ).
thf(1079,plain,
! [SV219: product_prod_a_a,SV112: a] :
( ( ~ ( ( SV112
= ( product_snd_a_a @ SV219 ) )
| ~ ! [SY907: a] :
( SV219
!= ( product_Pair_a_a @ SY907 @ SV112 ) ) )
| ~ ( ( SV112
!= ( product_snd_a_a @ SV219 ) )
| ~ ~ ! [SY907: a] :
( SV219
!= ( product_Pair_a_a @ SY907 @ SV112 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[957]) ).
thf(1080,plain,
! [SV219: product_prod_a_a,SV112: a] :
( ( ( SV112
= ( product_snd_a_a @ SV219 ) )
= ( ~ ! [SY907: a] :
( SV219
!= ( product_Pair_a_a @ SY907 @ SV112 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[957]) ).
thf(1081,plain,
! [SV113: multis599418605od_a_a] :
( ( ( SV113 != zero_z160849828od_a_a )
= $false )
| ( ( ~ ! [SY708: product_prod_a_a] :
~ ( member449909584od_a_a @ SY708 @ ( set_ms1818337124od_a_a @ SV113 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[958]) ).
thf(1082,plain,
! [SV301: product_prod_a_a,SV220: product_prod_a_a > product_prod_a_a,SV114: product_prod_a_a] :
( ( ! [SY995: set_Product_prod_a_a] :
( ( SV114
!= ( SV220 @ SV301 ) )
| ~ ( member449909584od_a_a @ SV301 @ SY995 )
| ( member449909584od_a_a @ SV114 @ ( image_794773445od_a_a @ SV220 @ SY995 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(1083,plain,
! [SV302: product_prod_a_a,SV221: a > a > set_Pr158363655iset_a,SV115: produc1127127335iset_a] :
( ( ~ ( member340150864iset_a @ SV115 @ ( produc93594587iset_a @ SV221 @ SV302 ) )
| ~ ! [SY996: a,SY997: a] :
( ( SV302
!= ( product_Pair_a_a @ SY996 @ SY997 ) )
| ~ ( member340150864iset_a @ SV115 @ ( SV221 @ SY996 @ SY997 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[960]) ).
thf(1084,plain,
! [SV303: multis599418605od_a_a,SV222: multis599418605od_a_a,SV116: product_prod_a_a] :
( ( ~ ~ ( member449909584od_a_a @ SV116 @ ( set_ms1818337124od_a_a @ SV222 ) )
| ( ( minus_1257885652od_a_a @ ( add_ms1725977093od_a_a @ SV116 @ SV303 ) @ SV222 )
= ( add_ms1725977093od_a_a @ SV116 @ ( minus_1257885652od_a_a @ SV303 @ SV222 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(1085,plain,
! [SV304: produc1127127335iset_a,SV223: multiset_a > multiset_a > set_Product_prod_a_a,SV117: product_prod_a_a] :
( ( ~ ( member449909584od_a_a @ SV117 @ ( produc2041367259od_a_a @ SV223 @ SV304 ) )
| ~ ! [SY998: multiset_a,SY999: multiset_a] :
( ( SV304
!= ( produc2037245207iset_a @ SY998 @ SY999 ) )
| ~ ( member449909584od_a_a @ SV117 @ ( SV223 @ SY998 @ SY999 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(1086,plain,
! [SV224: set_Product_prod_a_a,SV118: set_a] :
( ( ( ~ ( prefer719835986ence_a @ SV118 @ SV224 ) )
= $true )
| ( ( ! [SY917: a] :
( ~ ( member_a @ SY917 @ SV118 )
| ! [SY918: a] :
( ~ ( member_a @ SY918 @ SV118 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY917 @ SY918 ) @ SV224 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY918 @ SY917 ) @ SV224 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[963]) ).
thf(1087,plain,
! [SV305: a,SV225: set_Product_prod_a_a,SV119: product_prod_a_a] :
( ( ! [SY1000: product_prod_a_a > a] :
( ~ ( member449909584od_a_a @ SV119 @ SV225 )
| ( SV305
!= ( SY1000 @ SV119 ) )
| ( member_a @ SV305 @ ( image_340790172_a_a_a @ SY1000 @ SV225 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[964]) ).
thf(1088,plain,
! [SV306: product_prod_a_a,SV226: a > a > set_Product_prod_a_a,SV120: product_prod_a_a] :
( ( ~ ( member449909584od_a_a @ SV120 @ ( produc1093061851od_a_a @ SV226 @ SV306 ) )
| ~ ! [SY1001: a,SY1002: a] :
( ( SV306
!= ( product_Pair_a_a @ SY1001 @ SY1002 ) )
| ~ ( member449909584od_a_a @ SV120 @ ( SV226 @ SY1001 @ SY1002 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[965]) ).
thf(1089,plain,
! [SV121: product_prod_a_a > $o,SV1: product_prod_a_a] :
( ( ( ~ ( ( member449909584od_a_a @ SV1 @ ( collec645855634od_a_a @ SV121 ) )
| ( SV121 @ SV1 ) ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ SV1 @ ( collec645855634od_a_a @ SV121 ) )
| ~ ( SV121 @ SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[966]) ).
thf(1090,plain,
! [SV307: a,SV122: product_prod_a_a > $o] :
( ( ( product_curry_a_a_o @ SV122 @ SV307 )
= ( ^ [SY1003: a] : ( SV122 @ ( product_Pair_a_a @ SV307 @ SY1003 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(1091,plain,
! [SV308: a > a,SV228: set_Product_prod_a_a,SV123: a,SV4: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV4 @ SV123 ) @ ( inv_image_a_a @ SV228 @ SV308 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV308 @ SV4 ) @ ( SV308 @ SV123 ) ) @ SV228 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[970]) ).
thf(1092,plain,
! [SV309: a > multiset_a,SV229: set_Pr158363655iset_a,SV124: a,SV5: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV5 @ SV124 ) @ ( inv_im975322764et_a_a @ SV229 @ SV309 ) )
= ( member340150864iset_a @ ( produc2037245207iset_a @ ( SV309 @ SV5 ) @ ( SV309 @ SV124 ) ) @ SV229 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[971]) ).
thf(1093,plain,
! [SV310: multiset_a > a,SV230: set_Product_prod_a_a,SV125: multiset_a,SV6: multiset_a] :
( ( ( member340150864iset_a @ ( produc2037245207iset_a @ SV6 @ SV125 ) @ ( inv_im479034648iset_a @ SV230 @ SV310 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV310 @ SV6 ) @ ( SV310 @ SV125 ) ) @ SV230 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1094,plain,
! [SV311: a > product_prod_a_a,SV231: set_Pr1948701895od_a_a,SV126: a,SV7: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV7 @ SV126 ) @ ( inv_im777352425_a_a_a @ SV231 @ SV311 ) )
= ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( SV311 @ SV7 ) @ ( SV311 @ SV126 ) ) @ SV231 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1095,plain,
! [SV312: product_prod_a_a > a,SV232: set_Product_prod_a_a,SV127: product_prod_a_a,SV8: product_prod_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV8 @ SV127 ) @ ( inv_im15016955od_a_a @ SV232 @ SV312 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV312 @ SV8 ) @ ( SV312 @ SV127 ) ) @ SV232 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1096,plain,
! [SV313: a > multis599418605od_a_a,SV233: set_Pr1821581383od_a_a,SV128: a,SV9: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV128 ) @ ( inv_im1681759523_a_a_a @ SV233 @ SV313 ) )
= ( member1349055120od_a_a @ ( produc1859144151od_a_a @ ( SV313 @ SV9 ) @ ( SV313 @ SV128 ) ) @ SV233 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1097,plain,
! [SV314: multis599418605od_a_a > a,SV234: set_Product_prod_a_a,SV129: multis599418605od_a_a,SV10: multis599418605od_a_a] :
( ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ SV10 @ SV129 ) @ ( inv_im941243329od_a_a @ SV234 @ SV314 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV314 @ SV10 ) @ ( SV314 @ SV129 ) ) @ SV234 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1098,plain,
! [SV237: a,SV133: a,SV14: a > a > $o] :
( ( ~ ( ( produc1833107820_a_a_o @ SV14 @ ( product_Pair_a_a @ SV133 @ SV237 ) )
| ( SV14 @ SV133 @ SV237 ) )
| ~ ( ~ ( produc1833107820_a_a_o @ SV14 @ ( product_Pair_a_a @ SV133 @ SV237 ) )
| ~ ( SV14 @ SV133 @ SV237 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[979]) ).
thf(1099,plain,
! [SV237: a,SV133: a,SV14: a > a > $o] :
( ( ( produc1833107820_a_a_o @ SV14 @ ( product_Pair_a_a @ SV133 @ SV237 ) )
= ( SV14 @ SV133 @ SV237 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[979]) ).
thf(1100,plain,
! [SV134: set_Product_prod_a_a] :
( ( ( ~ ( ( irrefl_a @ SV134 )
| ! [SY751: a] :
~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY751 @ SY751 ) @ SV134 ) ) )
= $true )
| ( ( ~ ( ~ ( irrefl_a @ SV134 )
| ~ ! [SY751: a] :
~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY751 @ SY751 ) @ SV134 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[980]) ).
thf(1101,plain,
! [SV238: set_Product_prod_a_a,SV135: a,SV16: a] :
( ( ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV16 @ SV135 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV238 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV135 @ SV16 ) @ SV238 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV16 @ SV135 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV238 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV135 @ SV16 ) @ SV238 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[982]) ).
thf(1102,plain,
! [SV238: set_Product_prod_a_a,SV135: a,SV16: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV16 @ SV135 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV238 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ SV135 @ SV16 ) @ SV238 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[982]) ).
thf(1103,plain,
! [SV136: product_prod_a_a] :
( ( ( ~ ( ( top_to1483957574_a_a_o @ SV136 )
| ( member449909584od_a_a @ SV136 @ top_to398455383od_a_a ) ) )
= $true )
| ( ( ~ ( ~ ( top_to1483957574_a_a_o @ SV136 )
| ~ ( member449909584od_a_a @ SV136 @ top_to398455383od_a_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[983]) ).
thf(1104,plain,
! [SV315: a,SV239: a,SV137: a > a,SV18: a > a] :
( ( ( produc700022774_a_a_a @ SV18 @ SV137 @ ( product_Pair_a_a @ SV239 @ SV315 ) )
= ( product_Pair_a_a @ ( SV18 @ SV239 ) @ ( SV137 @ SV315 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[985]) ).
thf(1105,plain,
! [SV240: multis599418605od_a_a,SV141: multis599418605od_a_a,SV25: product_prod_a_a] :
( ( ~ ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ ( plus_p404985124od_a_a @ SV141 @ SV240 ) ) )
| ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV141 ) )
| ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV240 ) ) )
| ~ ( ~ ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ ( plus_p404985124od_a_a @ SV141 @ SV240 ) ) )
| ~ ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV141 ) )
| ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV240 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[986]) ).
thf(1106,plain,
! [SV240: multis599418605od_a_a,SV141: multis599418605od_a_a,SV25: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ ( plus_p404985124od_a_a @ SV141 @ SV240 ) ) )
= ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV141 ) )
| ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV240 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[986]) ).
thf(1107,plain,
! [SV241: multis599418605od_a_a,SV142: multis599418605od_a_a,SV27: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV27 @ ( set_ms1818337124od_a_a @ ( minus_1257885652od_a_a @ SV142 @ SV241 ) ) ) )
= $true )
| ( ( member449909584od_a_a @ SV27 @ ( set_ms1818337124od_a_a @ SV142 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[987]) ).
thf(1108,plain,
! [SV316: a,SV242: a,SV143: a,SV28: a] :
( ( ( ( product_Pair_a_a @ SV28 @ SV143 )
!= ( product_Pair_a_a @ SV242 @ SV316 ) )
| ~ ( ( SV28 != SV242 )
| ( SV143 != SV316 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1109,plain,
! [SV144: produc1572603623od_a_a,SV29: produc1572603623od_a_a > $o] :
( ( ( ! [SY474: product_prod_a_a,SY475: a,SY476: a] : ( SV29 @ ( produc1474507607od_a_a @ SY474 @ ( product_Pair_a_a @ SY475 @ SY476 ) ) ) )
= $false )
| ( ( SV29 @ SV144 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[989]) ).
thf(1110,plain,
! [SV243: a,SV145: a,SV30: a] :
( ( ( ( product_fst_a_a @ ( product_Pair_a_a @ SV30 @ SV145 ) )
!= SV243 )
= $true )
| ( ( SV30 = SV243 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[990]) ).
thf(1111,plain,
! [SV244: a,SV146: a,SV31: product_prod_a_a > $o] :
( ( ( ~ ( SV31 @ ( product_Pair_a_a @ SV146 @ SV244 ) ) )
= $true )
| ( ( product_curry_a_a_o @ SV31 @ SV146 @ SV244 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[991]) ).
thf(1112,plain,
! [SV147: set_Pr1948701895od_a_a,SV32: set_Product_prod_a_a] :
( ( ( ! [SY764: product_prod_a_a,SY765: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY764 @ SV32 )
| ~ ( member449909584od_a_a @ SY765 @ SV32 )
| ~ ( ( SY764 != SY765 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY764 @ SY765 ) @ SV147 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY765 @ SY764 ) @ SV147 ) ) )
= $false )
| ( ( total_1490170027od_a_a @ SV32 @ SV147 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[992]) ).
thf(1113,plain,
! [SV317: a,SV245: a > $o,SV148: a,SV33: a > $o] :
( ( ~ ( SV33 @ SV148 )
| ~ ( SV245 @ SV317 )
| ~ ( ~ ( SV33 @ ( product_fst_a_a @ ( product_Pair_a_a @ SV148 @ SV317 ) ) )
| ~ ( SV245 @ ( product_snd_a_a @ ( product_Pair_a_a @ SV148 @ SV317 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[993]) ).
thf(1114,plain,
! [SV318: a,SV246: a,SV149: a,SV34: a > $o] :
( ( ! [SY1004: a > set_Product_prod_a_a] :
( ~ ( SV34 @ SV149 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV246 @ SV318 ) @ ( SY1004 @ SV149 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV149 @ SV246 ) @ ( product_Pair_a_a @ SV149 @ SV318 ) ) @ ( same_fst_a_a @ SV34 @ SY1004 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[994]) ).
thf(1115,plain,
! [SV150: multis599418605od_a_a,SV35: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV35 @ ( set_ms1818337124od_a_a @ SV150 ) )
= $false )
| ( ( ~ ! [SY771: multis599418605od_a_a] :
( SV150
!= ( add_ms1725977093od_a_a @ SV35 @ SY771 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[995]) ).
thf(1116,plain,
! [SV151: set_Product_prod_a_a > $o,SV36: set_Product_prod_a_a] :
( ( ( asym_a @ SV36 )
= $false )
| ( ( ~ ! [SY772: set_Product_prod_a_a] :
( ~ ! [SX3: a,SX4: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX4 ) @ SY772 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX4 @ SX3 ) @ SY772 ) )
| ( SV151 @ SY772 ) )
| ( SV151 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[996]) ).
thf(1117,plain,
! [SV152: set_Product_prod_a_a,SV37: set_Product_prod_a_a] :
( ( ( ! [SY775: a,SY776: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY775 @ SY776 ) @ SV37 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY775 @ SY776 ) @ SV152 ) ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV37 @ SV152 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[997]) ).
thf(1118,plain,
! [SV319: set_Pr1948701895od_a_a,SV247: set_Product_prod_a_a,SV153: product_prod_a_a,SV38: product_prod_a_a] :
( ( ~ ( member449909584od_a_a @ SV38 @ ( prefer477097315od_a_a @ SV153 @ SV247 @ SV319 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV38 @ SV153 ) @ SV319 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[998]) ).
thf(1119,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a] :
( ( ( total_1490170027od_a_a @ SV154 @ SV320 )
= ( ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[999]) ).
thf(1120,plain,
! [SV155: product_prod_a_a,SV40: a] :
( ( ( ~ ( ( SV40
= ( product_fst_a_a @ SV155 ) )
| ~ ! [SY782: a] :
( SV155
!= ( product_Pair_a_a @ SV40 @ SY782 ) ) ) )
= $true )
| ( ( ~ ( ( SV40
!= ( product_fst_a_a @ SV155 ) )
| ~ ~ ! [SY782: a] :
( SV155
!= ( product_Pair_a_a @ SV40 @ SY782 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1001]) ).
thf(1121,plain,
! [SV321: a,SV249: a,SV156: a,SV41: set_Product_prod_a_a] :
( ( ~ ( trans_a @ SV41 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV156 @ SV249 ) @ SV41 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV249 @ SV321 ) @ SV41 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV156 @ SV321 ) @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1003]) ).
thf(1122,plain,
! [SV322: product_prod_a_a,SV250: product_prod_a_a,SV157: set_Pr1948701895od_a_a,SV42: set_Product_prod_a_a] :
( ( ~ ( prefer1338892073od_a_a @ SV42 @ SV157 )
| ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV250 @ SV322 ) @ SV157 )
| ( member449909584od_a_a @ SV250 @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1123,plain,
! [SV323: product_prod_a_a,SV251: a,SV158: a,SV43: a > a > $o] :
( ( ~ ( SV43 @ SV158 @ SV251 )
| ( SV323
!= ( product_Pair_a_a @ SV158 @ SV251 ) )
| ( SV43 @ ( product_fst_a_a @ SV323 ) @ ( product_snd_a_a @ SV323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1124,plain,
! [SV324: a,SV252: a,SV159: a,SV44: a] :
( ( ( ( product_Pair_a_a @ SV44 @ SV159 )
= ( product_Pair_a_a @ SV252 @ SV324 ) )
= ( ~ ( ( SV44 != SV252 )
| ( SV159 != SV324 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1006]) ).
thf(1125,plain,
! [SV325: a,SV253: a,SV160: a,SV45: set_Product_prod_a_a] :
( ( ~ ( trans_a @ SV45 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV160 @ SV253 ) @ SV45 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV253 @ SV325 ) @ SV45 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV160 @ SV325 ) @ SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1007]) ).
thf(1126,plain,
! [SV254: set_Product_prod_a_a,SV161: a > product_prod_a_a,SV46: set_a] :
( ( ( ~ ! [SY945: a] :
( ~ ( member_a @ SY945 @ SV46 )
| ( member449909584od_a_a @ ( SV161 @ SY945 ) @ SV254 ) ) )
= $true )
| ( ( ord_le1824328871od_a_a @ ( image_1725938350od_a_a @ SV161 @ SV46 ) @ SV254 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1008]) ).
thf(1127,plain,
! [SV162: set_Pr1948701895od_a_a,SV47: set_Product_prod_a_a] :
( ( ( prefer697821563od_a_a @ SV47 @ SV162 )
= $false )
| ( ( ! [SY795: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY795 @ SV47 )
| ! [SY796: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY796 @ SV47 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY795 @ SY796 ) @ SV162 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY796 @ SY795 ) @ SV162 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1009]) ).
thf(1128,plain,
! [SV163: set_Product_prod_a_a,SV48: set_a] :
( ( ( ! [SY797: a,SY798: a] :
( ~ ( member_a @ SY797 @ SV48 )
| ~ ( member_a @ SY798 @ SV48 )
| ~ ( ( SY797 != SY798 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY797 @ SY798 ) @ SV163 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY798 @ SY797 ) @ SV163 ) ) )
= $false )
| ( ( total_on_a @ SV48 @ SV163 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1010]) ).
thf(1129,plain,
! [SV326: set_Pr1948701895od_a_a,SV255: set_Product_prod_a_a,SV164: product_prod_a_a,SV49: product_prod_a_a] :
( ( ~ ( member449909584od_a_a @ SV49 @ ( prefer477097315od_a_a @ SV164 @ SV255 @ SV326 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV49 @ SV164 ) @ SV326 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1011]) ).
thf(1130,plain,
! [SV50: product_prod_a_a] :
( ( ~ ! [SY947: a] :
( SV50
!= ( product_Pair_a_a @ ( sK1_SY535 @ SV50 ) @ SY947 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1012]) ).
thf(1131,plain,
! [SV256: product_prod_a_a,SV165: set_Pr1948701895od_a_a,SV51: set_Product_prod_a_a] :
( ( ( ~ ( refl_o1298442278od_a_a @ SV51 @ SV165 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ SV256 @ SV51 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV256 @ SV256 ) @ SV165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1013]) ).
thf(1132,plain,
! [SV327: a,SV257: a,SV166: a,SV52: a] :
( ( ! [SY1007: set_Product_prod_a_a,SY1008: set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SV257 @ SV327 ) ) @ ( lex_prod_a_a @ SY1007 @ SY1008 ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SY1007 )
| ~ ( ( SV52 != SV257 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SY1008 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1014]) ).
thf(1133,plain,
! [SV328: product_prod_a_a,SV258: product_prod_a_a,SV167: set_Pr1948701895od_a_a,SV53: set_Product_prod_a_a] :
( ( ~ ( refl_o1298442278od_a_a @ SV53 @ SV167 )
| ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV258 @ SV328 ) @ SV167 )
| ( member449909584od_a_a @ SV328 @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1015]) ).
thf(1134,plain,
! [SV259: a,SV168: set_Product_prod_a_a,SV54: set_a] :
( ( ( ~ ( refl_on_a @ SV54 @ SV168 ) )
= $true )
| ( ( ~ ( member_a @ SV259 @ SV54 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV259 @ SV259 ) @ SV168 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1016]) ).
thf(1135,plain,
! [SV329: set_Product_prod_a_a,SV260: set_a,SV169: a,SV55: a] :
( ( ~ ( member_a @ SV55 @ ( prefer161218362good_a @ SV169 @ SV260 @ SV329 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV55 @ SV169 ) @ SV329 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1017]) ).
thf(1136,plain,
! [SV330: a,SV261: a,SV170: a,SV56: a] :
( ( ( ( product_Pair_a_a @ SV56 @ SV170 )
= ( product_Pair_a_a @ SV261 @ SV330 ) )
= ( ~ ( ( SV56 != SV261 )
| ( SV170 != SV330 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1018]) ).
thf(1137,plain,
! [SV262: a,SV171: a,SV57: a] :
( ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV171 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV171 @ SV57 ) @ relation ) ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV171 @ SV262 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV262 @ SV171 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV262 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV262 @ SV57 ) @ relation ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1019]) ).
thf(1138,plain,
! [SV331: a,SV263: a,SV172: set_Product_prod_a_a,SV58: set_a] :
( ( ~ ( refl_on_a @ SV58 @ SV172 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV263 @ SV331 ) @ SV172 )
| ~ ( ~ ( member_a @ SV263 @ SV58 )
| ~ ( member_a @ SV331 @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1020]) ).
thf(1139,plain,
! [SV332: set_Product_prod_a_a,SV264: a > a,SV173: a > a,SV59: product_prod_a_a] :
( ( ~ ( member449909584od_a_a @ SV59 @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SV173 @ SV264 ) @ SV332 ) )
| ~ ! [SY1009: a,SY1010: a] :
( ( SV59
!= ( product_Pair_a_a @ ( SV173 @ SY1009 ) @ ( SV264 @ SY1010 ) ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1009 @ SY1010 ) @ SV332 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1021]) ).
thf(1140,plain,
! [SV333: product_prod_a_a,SV265: product_prod_a_a,SV174: set_Pr1948701895od_a_a,SV60: set_Product_prod_a_a] :
( ( ~ ( prefer697821563od_a_a @ SV60 @ SV174 )
| ~ ~ ( ~ ( member449909584od_a_a @ SV265 @ SV60 )
| ~ ( member449909584od_a_a @ SV333 @ SV60 ) )
| ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) )
= ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
| ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1022]) ).
thf(1141,plain,
! [SV334: a,SV266: a,SV175: set_Product_prod_a_a,SV61: set_a] :
( ( ~ ( prefer719835986ence_a @ SV61 @ SV175 )
| ~ ~ ( ~ ( member_a @ SV266 @ SV61 )
| ~ ( member_a @ SV334 @ SV61 ) )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1023]) ).
thf(1142,plain,
! [SV176: product_prod_a_a,SV62: product_prod_a_a > $o] :
( ( ( ! [SY572: a,SY573: a] : ( SV62 @ ( product_Pair_a_a @ SY572 @ SY573 ) ) )
= $false )
| ( ( SV62 @ SV176 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1024]) ).
thf(1143,plain,
! [SV63: set_Product_prod_a_a] :
( ( ( ! [SY1011: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK4_SY574 @ SV63 ) @ SY1011 ) @ SV63 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1011 @ ( sK4_SY574 @ SV63 ) ) @ SV63 ) ) )
= $false )
| ( ( asym_a @ SV63 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1025]) ).
thf(1144,plain,
! [SV267: a,SV177: a,SV64: set_Product_prod_a_a] :
( ( ( ~ ( asym_a @ SV64 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV177 @ SV267 ) @ SV64 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV267 @ SV177 ) @ SV64 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1026]) ).
thf(1145,plain,
! [SV268: product_prod_a_a > product_prod_a_a,SV178: set_Product_prod_a_a,SV65: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV65 @ SV178 ) )
= $true )
| ( ( member449909584od_a_a @ ( SV268 @ SV65 ) @ ( image_794773445od_a_a @ SV268 @ SV178 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1027]) ).
thf(1146,plain,
! [SV66: a,SV335: a] :
( ( ( ~ ( member_a @ SV335 @ carrier )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV66 @ SV335 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV335 @ SV66 ) @ relation ) )
= $true )
| ( ( member_a @ SV66 @ carrier )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1147,plain,
! [SV67: set_Product_prod_a_a] :
( ( ( ! [SY1012: a,SY1013: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK5_SY581 @ SV67 ) @ SY1012 ) @ SV67 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1012 @ SY1013 ) @ SV67 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK5_SY581 @ SV67 ) @ SY1013 ) @ SV67 ) ) )
= $false )
| ( ( trans_a @ SV67 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1029]) ).
thf(1148,plain,
! [SV179: set_Product_prod_a_a] :
( ( ( ~ ( ( trans_a @ SV179 )
| ! [SY828: a,SY829: a,SY830: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY829 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY829 @ SY830 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY830 ) @ SV179 ) ) ) )
= $true )
| ( ( ~ ( ~ ( trans_a @ SV179 )
| ~ ! [SY828: a,SY829: a,SY830: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY829 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY829 @ SY830 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY830 ) @ SV179 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1030]) ).
thf(1149,plain,
! [SV269: a,SV180: a,SV69: a > a > $o] :
( ( ( ~ ( SV69 @ SV180 @ SV269 ) )
= $true )
| ( ( SV69 @ ( product_snd_a_a @ ( product_Pair_a_a @ SV269 @ SV180 ) ) @ ( product_fst_a_a @ ( product_Pair_a_a @ SV269 @ SV180 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1032]) ).
thf(1150,plain,
! [SV70: produc1572603623od_a_a] :
( ( ! [SY1014: a] :
( SV70
!= ( produc1474507607od_a_a @ ( sK2_SY589 @ SV70 ) @ ( product_Pair_a_a @ ( sK6_SY960 @ SV70 ) @ SY1014 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1033]) ).
thf(1151,plain,
! [SV181: a,SV71: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV71 @ SV181 ) @ relation )
= $false )
| ( ( member_a @ SV71 @ carrier )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1034]) ).
thf(1152,plain,
! [SV270: a,SV182: a,SV72: product_prod_a_a > $o] :
( ( ( ~ ( product_curry_a_a_o @ SV72 @ SV182 @ SV270 ) )
= $true )
| ( ( SV72 @ ( product_Pair_a_a @ SV182 @ SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1035]) ).
thf(1153,plain,
! [SV271: multis599418605od_a_a,SV183: multis599418605od_a_a,SV73: product_prod_a_a] :
( ( ( ( add_ms1725977093od_a_a @ SV73 @ SV183 )
!= SV271 )
= $true )
| ( ( member449909584od_a_a @ SV73 @ ( set_ms1818337124od_a_a @ SV271 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1036]) ).
thf(1154,plain,
! [SV336: a,SV272: a,SV184: set_Product_prod_a_a,SV74: set_a] :
( ( ! [SY1015: a] :
( ~ ( prefer719835986ence_a @ SV74 @ SV184 )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV336 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV272 ) @ SV184 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SY1015 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1015 @ SV336 ) @ SV184 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SY1015 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1015 @ SV272 ) @ SV184 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1037]) ).
thf(1155,plain,
! [SV273: a > product_prod_a_a,SV185: set_a,SV75: a] :
( ( ( ~ ( member_a @ SV75 @ SV185 ) )
= $true )
| ( ( member449909584od_a_a @ ( SV273 @ SV75 ) @ ( image_1725938350od_a_a @ SV273 @ SV185 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1038]) ).
thf(1156,plain,
! [SV337: set_Product_prod_a_a,SV274: product_prod_a_a,SV186: product_prod_a_a > a,SV76: a] :
( ( ( SV76
!= ( SV186 @ SV274 ) )
| ~ ( member449909584od_a_a @ SV274 @ SV337 )
| ( member_a @ SV76 @ ( image_340790172_a_a_a @ SV186 @ SV337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1039]) ).
thf(1157,plain,
! [SV275: a,SV187: a,SV77: product_prod_a_a] :
( ( ( SV77
!= ( product_Pair_a_a @ SV187 @ SV275 ) )
= $true )
| ( ( ( product_fst_a_a @ SV77 )
= SV187 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1040]) ).
thf(1158,plain,
! [SV276: a,SV188: a,SV78: product_prod_a_a] :
( ( ( SV78
!= ( product_Pair_a_a @ SV188 @ SV276 ) )
= $true )
| ( ( ( product_snd_a_a @ SV78 )
= SV276 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1041]) ).
thf(1159,plain,
! [SV277: a,SV189: a,SV79: a] :
( ( ( ( product_snd_a_a @ ( product_Pair_a_a @ SV79 @ SV189 ) )
!= SV277 )
= $true )
| ( ( SV189 = SV277 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1042]) ).
thf(1160,plain,
! [SV80: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK7_SY612 @ SV80 ) @ ( sK7_SY612 @ SV80 ) ) @ SV80 ) )
= $false )
| ( ( irrefl_a @ SV80 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1043]) ).
thf(1161,plain,
! [SV338: a,SV278: a,SV190: set_Product_prod_a_a,SV81: set_a] :
( ( ~ ( prefer1292084992ence_a @ SV81 @ SV190 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV338 ) @ SV190 )
| ( member_a @ SV278 @ SV81 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1162,plain,
! [SV339: product_prod_a_a > product_prod_a_a,SV279: product_prod_a_a,SV191: set_Product_prod_a_a,SV82: product_prod_a_a] :
( ( ~ ( member449909584od_a_a @ SV82 @ SV191 )
| ( SV279
!= ( SV339 @ SV82 ) )
| ( member449909584od_a_a @ SV279 @ ( image_794773445od_a_a @ SV339 @ SV191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1045]) ).
thf(1163,plain,
! [SV340: a,SV280: a,SV192: set_Product_prod_a_a,SV83: set_a] :
( ( ~ ( refl_on_a @ SV83 @ SV192 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV280 @ SV340 ) @ SV192 )
| ( member_a @ SV280 @ SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1046]) ).
thf(1164,plain,
! [SV341: a > product_prod_a_a,SV281: product_prod_a_a,SV193: set_a,SV84: a] :
( ( ~ ( member_a @ SV84 @ SV193 )
| ( SV281
!= ( SV341 @ SV84 ) )
| ( member449909584od_a_a @ SV281 @ ( image_1725938350od_a_a @ SV341 @ SV193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1047]) ).
thf(1165,plain,
! [SV85: set_Product_prod_a_a,SV342: a] :
( ( ( ! [SY1016: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV342 @ SY1016 ) @ SV85 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1016 @ SV342 ) @ SV85 ) ) )
= $true )
| ( ( asym_a @ SV85 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1048]) ).
thf(1166,plain,
! [SV282: set_a,SV194: product_prod_a_a > a,SV86: set_Product_prod_a_a] :
( ( ( ~ ! [SY969: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY969 @ SV86 )
| ( member_a @ ( SV194 @ SY969 ) @ SV282 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ ( image_340790172_a_a_a @ SV194 @ SV86 ) @ SV282 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1049]) ).
thf(1167,plain,
! [SV283: product_prod_a_a > a,SV195: set_Product_prod_a_a,SV87: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV87 @ SV195 ) )
= $true )
| ( ( member_a @ ( SV283 @ SV87 ) @ ( image_340790172_a_a_a @ SV283 @ SV195 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1050]) ).
thf(1168,plain,
! [SV196: a,SV88: a] :
( ( ( ~ ( ~ ( member_a @ SV88 @ carrier )
| ~ ( member_a @ SV196 @ carrier ) ) )
= $false )
| ( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1051]) ).
thf(1169,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a] :
( ( ( total_on_a @ SV197 @ SV343 )
= ( ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1052]) ).
thf(1170,plain,
! [SV198: set_Product_prod_a_a] :
( ( ( ~ ( ( asym_a @ SV198 )
| ~ ! [SY857: set_Product_prod_a_a] :
~ ~ ( ( SV198 != SY857 )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SY857 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SY857 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( asym_a @ SV198 )
| ~ ~ ! [SY857: set_Product_prod_a_a] :
~ ~ ( ( SV198 != SY857 )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SY857 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SY857 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1054]) ).
thf(1171,plain,
! [SV199: set_Product_prod_a_a] :
( ( ( ~ ( ( asym_a @ SV199 )
| ! [SY860: a,SY861: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY860 @ SY861 ) @ SV199 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY861 @ SY860 ) @ SV199 ) ) ) )
= $true )
| ( ( ~ ( ~ ( asym_a @ SV199 )
| ~ ! [SY860: a,SY861: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY860 @ SY861 ) @ SV199 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY861 @ SY860 ) @ SV199 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1056]) ).
thf(1172,plain,
! [SV344: multis599418605od_a_a,SV285: product_prod_a_a,SV200: multis599418605od_a_a,SV92: product_prod_a_a] :
( ( ( ( add_ms1725977093od_a_a @ SV92 @ SV200 )
!= ( add_ms1725977093od_a_a @ SV285 @ SV344 ) )
| ~ ( ( SV92 != SV285 ) )
| ( member449909584od_a_a @ SV285 @ ( set_ms1818337124od_a_a @ SV200 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1058]) ).
thf(1173,plain,
! [SV345: a,SV286: a,SV201: set_Product_prod_a_a,SV93: set_a] :
( ( ! [SY1019: a] :
( ~ ( prefer1292084992ence_a @ SV93 @ SV201 )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SV345 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV286 ) @ SV201 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SY1019 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1019 @ SV345 ) @ SV201 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SY1019 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1019 @ SV286 ) @ SV201 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1059]) ).
thf(1174,plain,
! [SV346: set_Product_prod_a_a,SV287: set_a,SV202: a,SV94: a] :
( ( ~ ( member_a @ SV94 @ ( prefer161218362good_a @ SV202 @ SV287 @ SV346 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV94 @ SV202 ) @ SV346 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1060]) ).
thf(1175,plain,
! [SV288: product_prod_a_a,SV203: a > a > set_mu1281098573od_a_a,SV95: multis599418605od_a_a] :
( ( ( ~ ( member1755255446od_a_a @ SV95 @ ( produc1121147169od_a_a @ SV203 @ SV288 ) ) )
= $true )
| ( ( ~ ! [SY976: a,SY977: a] :
( ( SV288
!= ( product_Pair_a_a @ SY976 @ SY977 ) )
| ~ ( member1755255446od_a_a @ SV95 @ ( SV203 @ SY976 @ SY977 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1061]) ).
thf(1176,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( prefer1292084992ence_a @ SV204 @ SV347 )
= ( ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1062]) ).
thf(1177,plain,
! [SV205: multis599418605od_a_a,SV97: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV97 @ ( set_ms1818337124od_a_a @ SV205 ) )
= $false )
| ( ( ~ ! [SY877: multis599418605od_a_a] :
( SV205
!= ( add_ms1725977093od_a_a @ SV97 @ SY877 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1064]) ).
thf(1178,plain,
! [SV290: product_prod_a_a,SV206: a > a > set_multiset_a,SV98: multiset_a] :
( ( ( ~ ( member_multiset_a @ SV98 @ ( produc1828150264iset_a @ SV206 @ SV290 ) ) )
= $true )
| ( ( ~ ! [SY982: a,SY983: a] :
( ( SV290
!= ( product_Pair_a_a @ SY982 @ SY983 ) )
| ~ ( member_multiset_a @ SV98 @ ( SV206 @ SY982 @ SY983 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1065]) ).
thf(1179,plain,
! [SV99: product_prod_a_a] :
( ( SV99
!= ( product_Pair_a_a @ ( sK3_SY666 @ SV99 ) @ ( sK8_SY984 @ SV99 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1066]) ).
thf(1180,plain,
! [SV207: set_a,SV100: set_Product_prod_a_a] :
( ( ( ! [SY881: a,SY882: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY881 @ SY882 ) @ SV100 )
| ( member_a @ SY881 @ SV207 ) ) )
= $false )
| ( ( ~ ! [SY883: a,SY884: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY883 @ SY884 ) @ SV100 )
| ( member_a @ SY884 @ SV207 ) )
| ~ ( order_preorder_on_a @ SV207 @ SV100 )
| ( prefer1292084992ence_a @ SV207 @ SV100 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1067]) ).
thf(1181,plain,
! [SV291: a,SV208: a,SV101: a] :
( ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SV208 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV101 ) @ relation ) ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV291 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV291 @ SV208 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SV291 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV291 @ SV101 ) @ relation ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1068]) ).
thf(1182,plain,
! [SV292: a,SV209: a,SV102: product_prod_a_a > $o] :
( ( ( ~ ( product_curry_a_a_o @ SV102 @ SV209 @ SV292 ) )
= $true )
| ( ( SV102 @ ( product_Pair_a_a @ SV209 @ SV292 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1069]) ).
thf(1183,plain,
! [SV293: product_prod_a_a,SV210: a > a > set_a,SV103: a] :
( ( ( ~ ( member_a @ SV103 @ ( produc961951794_set_a @ SV210 @ SV293 ) ) )
= $true )
| ( ( ~ ! [SY985: a,SY986: a] :
( ( SV293
!= ( product_Pair_a_a @ SY985 @ SY986 ) )
| ~ ( member_a @ SV103 @ ( SV210 @ SY985 @ SY986 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1070]) ).
thf(1184,plain,
! [SV211: product_prod_a_a,SV104: product_prod_a_a > $o] :
( ( ( ! [SY682: a,SY683: a] : ( SV104 @ ( product_Pair_a_a @ SY682 @ SY683 ) ) )
= $false )
| ( ( SV104 @ SV211 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1071]) ).
thf(1185,plain,
! [SV348: product_prod_a_a,SV294: product_prod_a_a,SV212: set_Pr1948701895od_a_a,SV105: set_Product_prod_a_a] :
( ( ~ ( refl_o1298442278od_a_a @ SV105 @ SV212 )
| ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV294 @ SV348 ) @ SV212 )
| ( member449909584od_a_a @ SV294 @ SV105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1072]) ).
thf(1186,plain,
! [SV349: product_prod_a_a,SV295: product_prod_a_a,SV213: set_Pr1948701895od_a_a,SV106: set_Product_prod_a_a] :
( ( ~ ( refl_o1298442278od_a_a @ SV106 @ SV213 )
| ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV295 @ SV349 ) @ SV213 )
| ~ ( ~ ( member449909584od_a_a @ SV295 @ SV106 )
| ~ ( member449909584od_a_a @ SV349 @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1073]) ).
thf(1187,plain,
! [SV296: set_Product_prod_a_a,SV214: product_prod_a_a > product_prod_a_a,SV107: set_Product_prod_a_a] :
( ( ( ~ ! [SY989: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY989 @ SV107 )
| ( member449909584od_a_a @ ( SV214 @ SY989 ) @ SV296 ) ) )
= $true )
| ( ( ord_le1824328871od_a_a @ ( image_794773445od_a_a @ SV214 @ SV107 ) @ SV296 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1074]) ).
thf(1188,plain,
! [SV350: a,SV297: set_Product_prod_a_a,SV215: a,SV108: a] :
( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV108 @ SV215 ) @ SV297 )
| ( SV350 != SV215 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV108 @ SV350 ) @ SV297 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1075]) ).
thf(1189,plain,
! [SV351: a,SV298: a,SV216: set_Product_prod_a_a,SV109: set_a] :
( ( ~ ( refl_on_a @ SV109 @ SV216 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV298 @ SV351 ) @ SV216 )
| ( member_a @ SV351 @ SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1076]) ).
thf(1190,plain,
! [SV352: set_a,SV299: a,SV217: a > product_prod_a_a,SV110: product_prod_a_a] :
( ( ( SV110
!= ( SV217 @ SV299 ) )
| ~ ( member_a @ SV299 @ SV352 )
| ( member449909584od_a_a @ SV110 @ ( image_1725938350od_a_a @ SV217 @ SV352 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1077]) ).
thf(1191,plain,
! [SV353: a > a,SV300: set_Product_prod_a_a,SV218: a,SV111: a] :
( ( ! [SY1024: a > a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV111 @ SV218 ) @ SV300 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV353 @ SV111 ) @ ( SY1024 @ SV218 ) ) @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SV353 @ SY1024 ) @ SV300 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1078]) ).
thf(1192,plain,
! [SV219: product_prod_a_a,SV112: a] :
( ( ( ~ ( ( SV112
= ( product_snd_a_a @ SV219 ) )
| ~ ! [SY907: a] :
( SV219
!= ( product_Pair_a_a @ SY907 @ SV112 ) ) ) )
= $true )
| ( ( ~ ( ( SV112
!= ( product_snd_a_a @ SV219 ) )
| ~ ~ ! [SY907: a] :
( SV219
!= ( product_Pair_a_a @ SY907 @ SV112 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1079]) ).
thf(1193,plain,
! [SV113: multis599418605od_a_a] :
( ( ( SV113 = zero_z160849828od_a_a )
= $true )
| ( ( ~ ! [SY708: product_prod_a_a] :
~ ( member449909584od_a_a @ SY708 @ ( set_ms1818337124od_a_a @ SV113 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1081]) ).
thf(1194,plain,
! [SV354: set_Product_prod_a_a,SV301: product_prod_a_a,SV220: product_prod_a_a > product_prod_a_a,SV114: product_prod_a_a] :
( ( ( SV114
!= ( SV220 @ SV301 ) )
| ~ ( member449909584od_a_a @ SV301 @ SV354 )
| ( member449909584od_a_a @ SV114 @ ( image_794773445od_a_a @ SV220 @ SV354 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1082]) ).
thf(1195,plain,
! [SV302: product_prod_a_a,SV221: a > a > set_Pr158363655iset_a,SV115: produc1127127335iset_a] :
( ( ( ~ ( member340150864iset_a @ SV115 @ ( produc93594587iset_a @ SV221 @ SV302 ) ) )
= $true )
| ( ( ~ ! [SY996: a,SY997: a] :
( ( SV302
!= ( product_Pair_a_a @ SY996 @ SY997 ) )
| ~ ( member340150864iset_a @ SV115 @ ( SV221 @ SY996 @ SY997 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1083]) ).
thf(1196,plain,
! [SV303: multis599418605od_a_a,SV222: multis599418605od_a_a,SV116: product_prod_a_a] :
( ( ( ~ ~ ( member449909584od_a_a @ SV116 @ ( set_ms1818337124od_a_a @ SV222 ) ) )
= $true )
| ( ( ( minus_1257885652od_a_a @ ( add_ms1725977093od_a_a @ SV116 @ SV303 ) @ SV222 )
= ( add_ms1725977093od_a_a @ SV116 @ ( minus_1257885652od_a_a @ SV303 @ SV222 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1084]) ).
thf(1197,plain,
! [SV304: produc1127127335iset_a,SV223: multiset_a > multiset_a > set_Product_prod_a_a,SV117: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV117 @ ( produc2041367259od_a_a @ SV223 @ SV304 ) ) )
= $true )
| ( ( ~ ! [SY998: multiset_a,SY999: multiset_a] :
( ( SV304
!= ( produc2037245207iset_a @ SY998 @ SY999 ) )
| ~ ( member449909584od_a_a @ SV117 @ ( SV223 @ SY998 @ SY999 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1085]) ).
thf(1198,plain,
! [SV224: set_Product_prod_a_a,SV118: set_a] :
( ( ( prefer719835986ence_a @ SV118 @ SV224 )
= $false )
| ( ( ! [SY917: a] :
( ~ ( member_a @ SY917 @ SV118 )
| ! [SY918: a] :
( ~ ( member_a @ SY918 @ SV118 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY917 @ SY918 ) @ SV224 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY918 @ SY917 ) @ SV224 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1086]) ).
thf(1199,plain,
! [SV355: product_prod_a_a > a,SV305: a,SV225: set_Product_prod_a_a,SV119: product_prod_a_a] :
( ( ~ ( member449909584od_a_a @ SV119 @ SV225 )
| ( SV305
!= ( SV355 @ SV119 ) )
| ( member_a @ SV305 @ ( image_340790172_a_a_a @ SV355 @ SV225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1087]) ).
thf(1200,plain,
! [SV306: product_prod_a_a,SV226: a > a > set_Product_prod_a_a,SV120: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV120 @ ( produc1093061851od_a_a @ SV226 @ SV306 ) ) )
= $true )
| ( ( ~ ! [SY1001: a,SY1002: a] :
( ( SV306
!= ( product_Pair_a_a @ SY1001 @ SY1002 ) )
| ~ ( member449909584od_a_a @ SV120 @ ( SV226 @ SY1001 @ SY1002 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1088]) ).
thf(1201,plain,
! [SV121: product_prod_a_a > $o,SV1: product_prod_a_a] :
( ( ( ( member449909584od_a_a @ SV1 @ ( collec645855634od_a_a @ SV121 ) )
| ( SV121 @ SV1 ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ SV1 @ ( collec645855634od_a_a @ SV121 ) )
| ~ ( SV121 @ SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1089]) ).
thf(1202,plain,
! [SV307: a,SV122: product_prod_a_a > $o] :
( ( ! [SV356: a] :
( ( product_curry_a_a_o @ SV122 @ SV307 @ SV356 )
= ( SV122 @ ( product_Pair_a_a @ SV307 @ SV356 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1090]) ).
thf(1203,plain,
! [SV307: a,SV122: product_prod_a_a > $o] :
( ( ( product_curry_a_a_o @ SV122 @ SV307 )
= ( ^ [SY1003: a] : ( SV122 @ ( product_Pair_a_a @ SV307 @ SY1003 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1090]) ).
thf(1204,plain,
! [SV308: a > a,SV228: set_Product_prod_a_a,SV123: a,SV4: a] :
( ( ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV4 @ SV123 ) @ ( inv_image_a_a @ SV228 @ SV308 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV308 @ SV4 ) @ ( SV308 @ SV123 ) ) @ SV228 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV4 @ SV123 ) @ ( inv_image_a_a @ SV228 @ SV308 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV308 @ SV4 ) @ ( SV308 @ SV123 ) ) @ SV228 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1091]) ).
thf(1205,plain,
! [SV308: a > a,SV228: set_Product_prod_a_a,SV123: a,SV4: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV4 @ SV123 ) @ ( inv_image_a_a @ SV228 @ SV308 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV308 @ SV4 ) @ ( SV308 @ SV123 ) ) @ SV228 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1091]) ).
thf(1206,plain,
! [SV309: a > multiset_a,SV229: set_Pr158363655iset_a,SV124: a,SV5: a] :
( ( ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV5 @ SV124 ) @ ( inv_im975322764et_a_a @ SV229 @ SV309 ) )
| ( member340150864iset_a @ ( produc2037245207iset_a @ ( SV309 @ SV5 ) @ ( SV309 @ SV124 ) ) @ SV229 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV5 @ SV124 ) @ ( inv_im975322764et_a_a @ SV229 @ SV309 ) )
| ~ ( member340150864iset_a @ ( produc2037245207iset_a @ ( SV309 @ SV5 ) @ ( SV309 @ SV124 ) ) @ SV229 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1092]) ).
thf(1207,plain,
! [SV309: a > multiset_a,SV229: set_Pr158363655iset_a,SV124: a,SV5: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV5 @ SV124 ) @ ( inv_im975322764et_a_a @ SV229 @ SV309 ) )
= ( member340150864iset_a @ ( produc2037245207iset_a @ ( SV309 @ SV5 ) @ ( SV309 @ SV124 ) ) @ SV229 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1092]) ).
thf(1208,plain,
! [SV310: multiset_a > a,SV230: set_Product_prod_a_a,SV125: multiset_a,SV6: multiset_a] :
( ( ~ ( ( member340150864iset_a @ ( produc2037245207iset_a @ SV6 @ SV125 ) @ ( inv_im479034648iset_a @ SV230 @ SV310 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV310 @ SV6 ) @ ( SV310 @ SV125 ) ) @ SV230 ) )
| ~ ( ~ ( member340150864iset_a @ ( produc2037245207iset_a @ SV6 @ SV125 ) @ ( inv_im479034648iset_a @ SV230 @ SV310 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV310 @ SV6 ) @ ( SV310 @ SV125 ) ) @ SV230 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1093]) ).
thf(1209,plain,
! [SV310: multiset_a > a,SV230: set_Product_prod_a_a,SV125: multiset_a,SV6: multiset_a] :
( ( ( member340150864iset_a @ ( produc2037245207iset_a @ SV6 @ SV125 ) @ ( inv_im479034648iset_a @ SV230 @ SV310 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV310 @ SV6 ) @ ( SV310 @ SV125 ) ) @ SV230 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1093]) ).
thf(1210,plain,
! [SV311: a > product_prod_a_a,SV231: set_Pr1948701895od_a_a,SV126: a,SV7: a] :
( ( ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV7 @ SV126 ) @ ( inv_im777352425_a_a_a @ SV231 @ SV311 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( SV311 @ SV7 ) @ ( SV311 @ SV126 ) ) @ SV231 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV7 @ SV126 ) @ ( inv_im777352425_a_a_a @ SV231 @ SV311 ) )
| ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( SV311 @ SV7 ) @ ( SV311 @ SV126 ) ) @ SV231 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1094]) ).
thf(1211,plain,
! [SV311: a > product_prod_a_a,SV231: set_Pr1948701895od_a_a,SV126: a,SV7: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV7 @ SV126 ) @ ( inv_im777352425_a_a_a @ SV231 @ SV311 ) )
= ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( SV311 @ SV7 ) @ ( SV311 @ SV126 ) ) @ SV231 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1094]) ).
thf(1212,plain,
! [SV312: product_prod_a_a > a,SV232: set_Product_prod_a_a,SV127: product_prod_a_a,SV8: product_prod_a_a] :
( ( ~ ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV8 @ SV127 ) @ ( inv_im15016955od_a_a @ SV232 @ SV312 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV312 @ SV8 ) @ ( SV312 @ SV127 ) ) @ SV232 ) )
| ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV8 @ SV127 ) @ ( inv_im15016955od_a_a @ SV232 @ SV312 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV312 @ SV8 ) @ ( SV312 @ SV127 ) ) @ SV232 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1095]) ).
thf(1213,plain,
! [SV312: product_prod_a_a > a,SV232: set_Product_prod_a_a,SV127: product_prod_a_a,SV8: product_prod_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV8 @ SV127 ) @ ( inv_im15016955od_a_a @ SV232 @ SV312 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV312 @ SV8 ) @ ( SV312 @ SV127 ) ) @ SV232 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1095]) ).
thf(1214,plain,
! [SV313: a > multis599418605od_a_a,SV233: set_Pr1821581383od_a_a,SV128: a,SV9: a] :
( ( ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV128 ) @ ( inv_im1681759523_a_a_a @ SV233 @ SV313 ) )
| ( member1349055120od_a_a @ ( produc1859144151od_a_a @ ( SV313 @ SV9 ) @ ( SV313 @ SV128 ) ) @ SV233 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV128 ) @ ( inv_im1681759523_a_a_a @ SV233 @ SV313 ) )
| ~ ( member1349055120od_a_a @ ( produc1859144151od_a_a @ ( SV313 @ SV9 ) @ ( SV313 @ SV128 ) ) @ SV233 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1096]) ).
thf(1215,plain,
! [SV313: a > multis599418605od_a_a,SV233: set_Pr1821581383od_a_a,SV128: a,SV9: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV128 ) @ ( inv_im1681759523_a_a_a @ SV233 @ SV313 ) )
= ( member1349055120od_a_a @ ( produc1859144151od_a_a @ ( SV313 @ SV9 ) @ ( SV313 @ SV128 ) ) @ SV233 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1096]) ).
thf(1216,plain,
! [SV314: multis599418605od_a_a > a,SV234: set_Product_prod_a_a,SV129: multis599418605od_a_a,SV10: multis599418605od_a_a] :
( ( ~ ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ SV10 @ SV129 ) @ ( inv_im941243329od_a_a @ SV234 @ SV314 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV314 @ SV10 ) @ ( SV314 @ SV129 ) ) @ SV234 ) )
| ~ ( ~ ( member1349055120od_a_a @ ( produc1859144151od_a_a @ SV10 @ SV129 ) @ ( inv_im941243329od_a_a @ SV234 @ SV314 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV314 @ SV10 ) @ ( SV314 @ SV129 ) ) @ SV234 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1097]) ).
thf(1217,plain,
! [SV314: multis599418605od_a_a > a,SV234: set_Product_prod_a_a,SV129: multis599418605od_a_a,SV10: multis599418605od_a_a] :
( ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ SV10 @ SV129 ) @ ( inv_im941243329od_a_a @ SV234 @ SV314 ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV314 @ SV10 ) @ ( SV314 @ SV129 ) ) @ SV234 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1097]) ).
thf(1218,plain,
! [SV237: a,SV133: a,SV14: a > a > $o] :
( ( ( ~ ( ( produc1833107820_a_a_o @ SV14 @ ( product_Pair_a_a @ SV133 @ SV237 ) )
| ( SV14 @ SV133 @ SV237 ) ) )
= $true )
| ( ( ~ ( ~ ( produc1833107820_a_a_o @ SV14 @ ( product_Pair_a_a @ SV133 @ SV237 ) )
| ~ ( SV14 @ SV133 @ SV237 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1098]) ).
thf(1219,plain,
! [SV134: set_Product_prod_a_a] :
( ( ( ( irrefl_a @ SV134 )
| ! [SY751: a] :
~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY751 @ SY751 ) @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( irrefl_a @ SV134 )
| ~ ! [SY751: a] :
~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY751 @ SY751 ) @ SV134 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1100]) ).
thf(1220,plain,
! [SV238: set_Product_prod_a_a,SV135: a,SV16: a] :
( ( ( ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV16 @ SV135 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV238 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV135 @ SV16 ) @ SV238 ) ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV16 @ SV135 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV238 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV135 @ SV16 ) @ SV238 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1101]) ).
thf(1221,plain,
! [SV136: product_prod_a_a] :
( ( ( ( top_to1483957574_a_a_o @ SV136 )
| ( member449909584od_a_a @ SV136 @ top_to398455383od_a_a ) )
= $false )
| ( ( ~ ( ~ ( top_to1483957574_a_a_o @ SV136 )
| ~ ( member449909584od_a_a @ SV136 @ top_to398455383od_a_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1103]) ).
thf(1222,plain,
! [SV240: multis599418605od_a_a,SV141: multis599418605od_a_a,SV25: product_prod_a_a] :
( ( ( ~ ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ ( plus_p404985124od_a_a @ SV141 @ SV240 ) ) )
| ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV141 ) )
| ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV240 ) ) ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ ( plus_p404985124od_a_a @ SV141 @ SV240 ) ) )
| ~ ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV141 ) )
| ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV240 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1105]) ).
thf(1223,plain,
! [SV241: multis599418605od_a_a,SV142: multis599418605od_a_a,SV27: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV27 @ ( set_ms1818337124od_a_a @ ( minus_1257885652od_a_a @ SV142 @ SV241 ) ) )
= $false )
| ( ( member449909584od_a_a @ SV27 @ ( set_ms1818337124od_a_a @ SV142 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1107]) ).
thf(1224,plain,
! [SV316: a,SV242: a,SV143: a,SV28: a] :
( ( ( ( product_Pair_a_a @ SV28 @ SV143 )
!= ( product_Pair_a_a @ SV242 @ SV316 ) )
= $true )
| ( ( ~ ( ( SV28 != SV242 )
| ( SV143 != SV316 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1108]) ).
thf(1225,plain,
! [SV144: produc1572603623od_a_a,SV29: produc1572603623od_a_a > $o] :
( ( ( ! [SY1025: a,SY1026: a] : ( SV29 @ ( produc1474507607od_a_a @ ( sK9_SY474 @ SV144 @ SV29 ) @ ( product_Pair_a_a @ SY1025 @ SY1026 ) ) ) )
= $false )
| ( ( SV29 @ SV144 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1109]) ).
thf(1226,plain,
! [SV243: a,SV145: a,SV30: a] :
( ( ( ( product_fst_a_a @ ( product_Pair_a_a @ SV30 @ SV145 ) )
= SV243 )
= $false )
| ( ( SV30 = SV243 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1110]) ).
thf(1227,plain,
! [SV244: a,SV146: a,SV31: product_prod_a_a > $o] :
( ( ( SV31 @ ( product_Pair_a_a @ SV146 @ SV244 ) )
= $false )
| ( ( product_curry_a_a_o @ SV31 @ SV146 @ SV244 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1111]) ).
thf(1228,plain,
! [SV32: set_Product_prod_a_a,SV147: set_Pr1948701895od_a_a] :
( ( ( ! [SY1027: product_prod_a_a] :
( ~ ( member449909584od_a_a @ ( sK10_SY764 @ SV147 @ SV32 ) @ SV32 )
| ~ ( member449909584od_a_a @ SY1027 @ SV32 )
| ~ ( ( ( sK10_SY764 @ SV147 @ SV32 )
!= SY1027 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK10_SY764 @ SV147 @ SV32 ) @ SY1027 ) @ SV147 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1027 @ ( sK10_SY764 @ SV147 @ SV32 ) ) @ SV147 ) ) )
= $false )
| ( ( total_1490170027od_a_a @ SV32 @ SV147 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1112]) ).
thf(1229,plain,
! [SV317: a,SV245: a > $o,SV148: a,SV33: a > $o] :
( ( ( ~ ( SV33 @ SV148 ) )
= $true )
| ( ( ~ ( SV245 @ SV317 )
| ~ ( ~ ( SV33 @ ( product_fst_a_a @ ( product_Pair_a_a @ SV148 @ SV317 ) ) )
| ~ ( SV245 @ ( product_snd_a_a @ ( product_Pair_a_a @ SV148 @ SV317 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1113]) ).
thf(1230,plain,
! [SV357: a > set_Product_prod_a_a,SV318: a,SV246: a,SV149: a,SV34: a > $o] :
( ( ~ ( SV34 @ SV149 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV246 @ SV318 ) @ ( SV357 @ SV149 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV149 @ SV246 ) @ ( product_Pair_a_a @ SV149 @ SV318 ) ) @ ( same_fst_a_a @ SV34 @ SV357 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1114]) ).
thf(1231,plain,
! [SV35: product_prod_a_a,SV150: multis599418605od_a_a] :
( ( ( ! [SY771: multis599418605od_a_a] :
( SV150
!= ( add_ms1725977093od_a_a @ SV35 @ SY771 ) ) )
= $false )
| ( ( member449909584od_a_a @ SV35 @ ( set_ms1818337124od_a_a @ SV150 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1115]) ).
thf(1232,plain,
! [SV36: set_Product_prod_a_a,SV151: set_Product_prod_a_a > $o] :
( ( ( ~ ! [SY772: set_Product_prod_a_a] :
( ~ ! [SX3: a,SX4: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX4 ) @ SY772 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX4 @ SX3 ) @ SY772 ) )
| ( SV151 @ SY772 ) ) )
= $true )
| ( ( SV151 @ SV36 )
= $true )
| ( ( asym_a @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1116]) ).
thf(1233,plain,
! [SV37: set_Product_prod_a_a,SV152: set_Product_prod_a_a] :
( ( ( ! [SY1028: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK11_SY775 @ SV152 @ SV37 ) @ SY1028 ) @ SV37 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK11_SY775 @ SV152 @ SV37 ) @ SY1028 ) @ SV152 ) ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV37 @ SV152 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1117]) ).
thf(1234,plain,
! [SV319: set_Pr1948701895od_a_a,SV247: set_Product_prod_a_a,SV153: product_prod_a_a,SV38: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV38 @ ( prefer477097315od_a_a @ SV153 @ SV247 @ SV319 ) ) )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV38 @ SV153 ) @ SV319 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1118]) ).
thf(1235,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a] :
( ( ~ ( ( total_1490170027od_a_a @ SV154 @ SV320 )
| ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) )
| ~ ( ~ ( total_1490170027od_a_a @ SV154 @ SV320 )
| ~ ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1119]) ).
thf(1236,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a] :
( ( ( total_1490170027od_a_a @ SV154 @ SV320 )
= ( ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1119]) ).
thf(1237,plain,
! [SV155: product_prod_a_a,SV40: a] :
( ( ( ( SV40
= ( product_fst_a_a @ SV155 ) )
| ~ ! [SY782: a] :
( SV155
!= ( product_Pair_a_a @ SV40 @ SY782 ) ) )
= $false )
| ( ( ~ ( ( SV40
!= ( product_fst_a_a @ SV155 ) )
| ~ ~ ! [SY782: a] :
( SV155
!= ( product_Pair_a_a @ SV40 @ SY782 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1120]) ).
thf(1238,plain,
! [SV321: a,SV249: a,SV156: a,SV41: set_Product_prod_a_a] :
( ( ( ~ ( trans_a @ SV41 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV156 @ SV249 ) @ SV41 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV249 @ SV321 ) @ SV41 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV156 @ SV321 ) @ SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1121]) ).
thf(1239,plain,
! [SV322: product_prod_a_a,SV250: product_prod_a_a,SV157: set_Pr1948701895od_a_a,SV42: set_Product_prod_a_a] :
( ( ( ~ ( prefer1338892073od_a_a @ SV42 @ SV157 ) )
= $true )
| ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV250 @ SV322 ) @ SV157 )
| ( member449909584od_a_a @ SV250 @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1122]) ).
thf(1240,plain,
! [SV323: product_prod_a_a,SV251: a,SV158: a,SV43: a > a > $o] :
( ( ( ~ ( SV43 @ SV158 @ SV251 ) )
= $true )
| ( ( ( SV323
!= ( product_Pair_a_a @ SV158 @ SV251 ) )
| ( SV43 @ ( product_fst_a_a @ SV323 ) @ ( product_snd_a_a @ SV323 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1123]) ).
thf(1241,plain,
! [SV324: a,SV252: a,SV159: a,SV44: a] :
( ( ~ ( ( ( product_Pair_a_a @ SV44 @ SV159 )
= ( product_Pair_a_a @ SV252 @ SV324 ) )
| ~ ( ( SV44 != SV252 )
| ( SV159 != SV324 ) ) )
| ~ ( ( ( product_Pair_a_a @ SV44 @ SV159 )
!= ( product_Pair_a_a @ SV252 @ SV324 ) )
| ~ ~ ( ( SV44 != SV252 )
| ( SV159 != SV324 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1124]) ).
thf(1242,plain,
! [SV324: a,SV252: a,SV159: a,SV44: a] :
( ( ( ( product_Pair_a_a @ SV44 @ SV159 )
= ( product_Pair_a_a @ SV252 @ SV324 ) )
= ( ~ ( ( SV44 != SV252 )
| ( SV159 != SV324 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1124]) ).
thf(1243,plain,
! [SV325: a,SV253: a,SV160: a,SV45: set_Product_prod_a_a] :
( ( ( ~ ( trans_a @ SV45 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV160 @ SV253 ) @ SV45 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV253 @ SV325 ) @ SV45 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV160 @ SV325 ) @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1125]) ).
thf(1244,plain,
! [SV254: set_Product_prod_a_a,SV161: a > product_prod_a_a,SV46: set_a] :
( ( ( ! [SY945: a] :
( ~ ( member_a @ SY945 @ SV46 )
| ( member449909584od_a_a @ ( SV161 @ SY945 ) @ SV254 ) ) )
= $false )
| ( ( ord_le1824328871od_a_a @ ( image_1725938350od_a_a @ SV161 @ SV46 ) @ SV254 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1126]) ).
thf(1245,plain,
! [SV162: set_Pr1948701895od_a_a,SV47: set_Product_prod_a_a,SV358: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV358 @ SV47 )
| ! [SY1029: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1029 @ SV47 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV358 @ SY1029 ) @ SV162 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1029 @ SV358 ) @ SV162 ) ) )
= $true )
| ( ( prefer697821563od_a_a @ SV47 @ SV162 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1127]) ).
thf(1246,plain,
! [SV48: set_a,SV163: set_Product_prod_a_a] :
( ( ( ! [SY1030: a] :
( ~ ( member_a @ ( sK12_SY797 @ SV163 @ SV48 ) @ SV48 )
| ~ ( member_a @ SY1030 @ SV48 )
| ~ ( ( ( sK12_SY797 @ SV163 @ SV48 )
!= SY1030 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK12_SY797 @ SV163 @ SV48 ) @ SY1030 ) @ SV163 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1030 @ ( sK12_SY797 @ SV163 @ SV48 ) ) @ SV163 ) ) )
= $false )
| ( ( total_on_a @ SV48 @ SV163 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1128]) ).
thf(1247,plain,
! [SV326: set_Pr1948701895od_a_a,SV255: set_Product_prod_a_a,SV164: product_prod_a_a,SV49: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV49 @ ( prefer477097315od_a_a @ SV164 @ SV255 @ SV326 ) ) )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV49 @ SV164 ) @ SV326 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1129]) ).
thf(1248,plain,
! [SV50: product_prod_a_a] :
( ( ! [SY947: a] :
( SV50
!= ( product_Pair_a_a @ ( sK1_SY535 @ SV50 ) @ SY947 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1130]) ).
thf(1249,plain,
! [SV256: product_prod_a_a,SV165: set_Pr1948701895od_a_a,SV51: set_Product_prod_a_a] :
( ( ( refl_o1298442278od_a_a @ SV51 @ SV165 )
= $false )
| ( ( ~ ( member449909584od_a_a @ SV256 @ SV51 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV256 @ SV256 ) @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1131]) ).
thf(1250,plain,
! [SV359: set_Product_prod_a_a,SV327: a,SV257: a,SV166: a,SV52: a] :
( ( ! [SY1031: set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SV257 @ SV327 ) ) @ ( lex_prod_a_a @ SV359 @ SY1031 ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
| ~ ( ( SV52 != SV257 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SY1031 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1132]) ).
thf(1251,plain,
! [SV328: product_prod_a_a,SV258: product_prod_a_a,SV167: set_Pr1948701895od_a_a,SV53: set_Product_prod_a_a] :
( ( ( ~ ( refl_o1298442278od_a_a @ SV53 @ SV167 ) )
= $true )
| ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV258 @ SV328 ) @ SV167 )
| ( member449909584od_a_a @ SV328 @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1133]) ).
thf(1252,plain,
! [SV259: a,SV168: set_Product_prod_a_a,SV54: set_a] :
( ( ( refl_on_a @ SV54 @ SV168 )
= $false )
| ( ( ~ ( member_a @ SV259 @ SV54 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV259 @ SV259 ) @ SV168 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1134]) ).
thf(1253,plain,
! [SV329: set_Product_prod_a_a,SV260: set_a,SV169: a,SV55: a] :
( ( ( ~ ( member_a @ SV55 @ ( prefer161218362good_a @ SV169 @ SV260 @ SV329 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV55 @ SV169 ) @ SV329 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1135]) ).
thf(1254,plain,
! [SV330: a,SV261: a,SV170: a,SV56: a] :
( ( ~ ( ( ( product_Pair_a_a @ SV56 @ SV170 )
= ( product_Pair_a_a @ SV261 @ SV330 ) )
| ~ ( ( SV56 != SV261 )
| ( SV170 != SV330 ) ) )
| ~ ( ( ( product_Pair_a_a @ SV56 @ SV170 )
!= ( product_Pair_a_a @ SV261 @ SV330 ) )
| ~ ~ ( ( SV56 != SV261 )
| ( SV170 != SV330 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1136]) ).
thf(1255,plain,
! [SV330: a,SV261: a,SV170: a,SV56: a] :
( ( ( ( product_Pair_a_a @ SV56 @ SV170 )
= ( product_Pair_a_a @ SV261 @ SV330 ) )
= ( ~ ( ( SV56 != SV261 )
| ( SV170 != SV330 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1136]) ).
thf(1256,plain,
! [SV262: a,SV171: a,SV57: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV171 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV171 @ SV57 ) @ relation ) ) )
= $false )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV171 @ SV262 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV262 @ SV171 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV262 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV262 @ SV57 ) @ relation ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1137]) ).
thf(1257,plain,
! [SV331: a,SV263: a,SV172: set_Product_prod_a_a,SV58: set_a] :
( ( ( ~ ( refl_on_a @ SV58 @ SV172 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV263 @ SV331 ) @ SV172 )
| ~ ( ~ ( member_a @ SV263 @ SV58 )
| ~ ( member_a @ SV331 @ SV58 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1138]) ).
thf(1258,plain,
! [SV332: set_Product_prod_a_a,SV264: a > a,SV173: a > a,SV59: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV59 @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SV173 @ SV264 ) @ SV332 ) ) )
= $true )
| ( ( ~ ! [SY1009: a,SY1010: a] :
( ( SV59
!= ( product_Pair_a_a @ ( SV173 @ SY1009 ) @ ( SV264 @ SY1010 ) ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1009 @ SY1010 ) @ SV332 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1139]) ).
thf(1259,plain,
! [SV333: product_prod_a_a,SV265: product_prod_a_a,SV174: set_Pr1948701895od_a_a,SV60: set_Product_prod_a_a] :
( ( ( ~ ( prefer697821563od_a_a @ SV60 @ SV174 ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ SV265 @ SV60 )
| ~ ( member449909584od_a_a @ SV333 @ SV60 ) )
| ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) )
= ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
| ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1140]) ).
thf(1260,plain,
! [SV334: a,SV266: a,SV175: set_Product_prod_a_a,SV61: set_a] :
( ( ( ~ ( prefer719835986ence_a @ SV61 @ SV175 ) )
= $true )
| ( ( ~ ~ ( ~ ( member_a @ SV266 @ SV61 )
| ~ ( member_a @ SV334 @ SV61 ) )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1141]) ).
thf(1261,plain,
! [SV176: product_prod_a_a,SV62: product_prod_a_a > $o] :
( ( ( ! [SY1032: a] : ( SV62 @ ( product_Pair_a_a @ ( sK13_SY572 @ SV176 @ SV62 ) @ SY1032 ) ) )
= $false )
| ( ( SV62 @ SV176 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1142]) ).
thf(1262,plain,
! [SV63: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK4_SY574 @ SV63 ) @ ( sK14_SY1011 @ SV63 ) ) @ SV63 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK14_SY1011 @ SV63 ) @ ( sK4_SY574 @ SV63 ) ) @ SV63 ) )
= $false )
| ( ( asym_a @ SV63 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1143]) ).
thf(1263,plain,
! [SV267: a,SV177: a,SV64: set_Product_prod_a_a] :
( ( ( asym_a @ SV64 )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV177 @ SV267 ) @ SV64 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV267 @ SV177 ) @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1144]) ).
thf(1264,plain,
! [SV268: product_prod_a_a > product_prod_a_a,SV178: set_Product_prod_a_a,SV65: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV65 @ SV178 )
= $false )
| ( ( member449909584od_a_a @ ( SV268 @ SV65 ) @ ( image_794773445od_a_a @ SV268 @ SV178 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1145]) ).
thf(1265,plain,
! [SV66: a,SV335: a] :
( ( ( ~ ( member_a @ SV335 @ carrier ) )
= $true )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV66 @ SV335 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV335 @ SV66 ) @ relation ) )
= $true )
| ( ( member_a @ SV66 @ carrier )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1146]) ).
thf(1266,plain,
! [SV67: set_Product_prod_a_a] :
( ( ( ! [SY1033: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK5_SY581 @ SV67 ) @ ( sK15_SY1012 @ SV67 ) ) @ SV67 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK15_SY1012 @ SV67 ) @ SY1033 ) @ SV67 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK5_SY581 @ SV67 ) @ SY1033 ) @ SV67 ) ) )
= $false )
| ( ( trans_a @ SV67 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1147]) ).
thf(1267,plain,
! [SV179: set_Product_prod_a_a] :
( ( ( ( trans_a @ SV179 )
| ! [SY828: a,SY829: a,SY830: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY829 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY829 @ SY830 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY830 ) @ SV179 ) ) )
= $false )
| ( ( ~ ( ~ ( trans_a @ SV179 )
| ~ ! [SY828: a,SY829: a,SY830: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY829 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY829 @ SY830 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY830 ) @ SV179 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1148]) ).
thf(1268,plain,
! [SV269: a,SV180: a,SV69: a > a > $o] :
( ( ( SV69 @ SV180 @ SV269 )
= $false )
| ( ( SV69 @ ( product_snd_a_a @ ( product_Pair_a_a @ SV269 @ SV180 ) ) @ ( product_fst_a_a @ ( product_Pair_a_a @ SV269 @ SV180 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1149]) ).
thf(1269,plain,
! [SV70: produc1572603623od_a_a] :
( ( SV70
!= ( produc1474507607od_a_a @ ( sK2_SY589 @ SV70 ) @ ( product_Pair_a_a @ ( sK6_SY960 @ SV70 ) @ ( sK16_SY1014 @ SV70 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1150]) ).
thf(1270,plain,
! [SV270: a,SV182: a,SV72: product_prod_a_a > $o] :
( ( ( product_curry_a_a_o @ SV72 @ SV182 @ SV270 )
= $false )
| ( ( SV72 @ ( product_Pair_a_a @ SV182 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1152]) ).
thf(1271,plain,
! [SV271: multis599418605od_a_a,SV183: multis599418605od_a_a,SV73: product_prod_a_a] :
( ( ( ( add_ms1725977093od_a_a @ SV73 @ SV183 )
= SV271 )
= $false )
| ( ( member449909584od_a_a @ SV73 @ ( set_ms1818337124od_a_a @ SV271 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1153]) ).
thf(1272,plain,
! [SV360: a,SV336: a,SV272: a,SV184: set_Product_prod_a_a,SV74: set_a] :
( ( ~ ( prefer719835986ence_a @ SV74 @ SV184 )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV336 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV272 ) @ SV184 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV360 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV336 ) @ SV184 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV360 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV272 ) @ SV184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1154]) ).
thf(1273,plain,
! [SV273: a > product_prod_a_a,SV185: set_a,SV75: a] :
( ( ( member_a @ SV75 @ SV185 )
= $false )
| ( ( member449909584od_a_a @ ( SV273 @ SV75 ) @ ( image_1725938350od_a_a @ SV273 @ SV185 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1155]) ).
thf(1274,plain,
! [SV337: set_Product_prod_a_a,SV274: product_prod_a_a,SV186: product_prod_a_a > a,SV76: a] :
( ( ( SV76
!= ( SV186 @ SV274 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ SV274 @ SV337 )
| ( member_a @ SV76 @ ( image_340790172_a_a_a @ SV186 @ SV337 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1156]) ).
thf(1275,plain,
! [SV275: a,SV187: a,SV77: product_prod_a_a] :
( ( ( SV77
= ( product_Pair_a_a @ SV187 @ SV275 ) )
= $false )
| ( ( ( product_fst_a_a @ SV77 )
= SV187 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1157]) ).
thf(1276,plain,
! [SV276: a,SV188: a,SV78: product_prod_a_a] :
( ( ( SV78
= ( product_Pair_a_a @ SV188 @ SV276 ) )
= $false )
| ( ( ( product_snd_a_a @ SV78 )
= SV276 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1158]) ).
thf(1277,plain,
! [SV277: a,SV189: a,SV79: a] :
( ( ( ( product_snd_a_a @ ( product_Pair_a_a @ SV79 @ SV189 ) )
= SV277 )
= $false )
| ( ( SV189 = SV277 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1159]) ).
thf(1278,plain,
! [SV80: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK7_SY612 @ SV80 ) @ ( sK7_SY612 @ SV80 ) ) @ SV80 )
= $true )
| ( ( irrefl_a @ SV80 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1160]) ).
thf(1279,plain,
! [SV338: a,SV278: a,SV190: set_Product_prod_a_a,SV81: set_a] :
( ( ( ~ ( prefer1292084992ence_a @ SV81 @ SV190 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV338 ) @ SV190 )
| ( member_a @ SV278 @ SV81 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1161]) ).
thf(1280,plain,
! [SV339: product_prod_a_a > product_prod_a_a,SV279: product_prod_a_a,SV191: set_Product_prod_a_a,SV82: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV82 @ SV191 ) )
= $true )
| ( ( ( SV279
!= ( SV339 @ SV82 ) )
| ( member449909584od_a_a @ SV279 @ ( image_794773445od_a_a @ SV339 @ SV191 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1162]) ).
thf(1281,plain,
! [SV340: a,SV280: a,SV192: set_Product_prod_a_a,SV83: set_a] :
( ( ( ~ ( refl_on_a @ SV83 @ SV192 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV280 @ SV340 ) @ SV192 )
| ( member_a @ SV280 @ SV83 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1163]) ).
thf(1282,plain,
! [SV341: a > product_prod_a_a,SV281: product_prod_a_a,SV193: set_a,SV84: a] :
( ( ( ~ ( member_a @ SV84 @ SV193 ) )
= $true )
| ( ( ( SV281
!= ( SV341 @ SV84 ) )
| ( member449909584od_a_a @ SV281 @ ( image_1725938350od_a_a @ SV341 @ SV193 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1164]) ).
thf(1283,plain,
! [SV85: set_Product_prod_a_a,SV361: a,SV342: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV342 @ SV361 ) @ SV85 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV361 @ SV342 ) @ SV85 ) )
= $true )
| ( ( asym_a @ SV85 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1165]) ).
thf(1284,plain,
! [SV282: set_a,SV194: product_prod_a_a > a,SV86: set_Product_prod_a_a] :
( ( ( ! [SY969: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY969 @ SV86 )
| ( member_a @ ( SV194 @ SY969 ) @ SV282 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( image_340790172_a_a_a @ SV194 @ SV86 ) @ SV282 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1166]) ).
thf(1285,plain,
! [SV283: product_prod_a_a > a,SV195: set_Product_prod_a_a,SV87: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV87 @ SV195 )
= $false )
| ( ( member_a @ ( SV283 @ SV87 ) @ ( image_340790172_a_a_a @ SV283 @ SV195 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1167]) ).
thf(1286,plain,
! [SV196: a,SV88: a] :
( ( ( ~ ( member_a @ SV88 @ carrier )
| ~ ( member_a @ SV196 @ carrier ) )
= $true )
| ( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1168]) ).
thf(1287,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a] :
( ( ~ ( ( total_on_a @ SV197 @ SV343 )
| ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) )
| ~ ( ~ ( total_on_a @ SV197 @ SV343 )
| ~ ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1169]) ).
thf(1288,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a] :
( ( ( total_on_a @ SV197 @ SV343 )
= ( ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1169]) ).
thf(1289,plain,
! [SV198: set_Product_prod_a_a] :
( ( ( ( asym_a @ SV198 )
| ~ ! [SY857: set_Product_prod_a_a] :
~ ~ ( ( SV198 != SY857 )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SY857 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SY857 ) ) ) )
= $false )
| ( ( ~ ( ~ ( asym_a @ SV198 )
| ~ ~ ! [SY857: set_Product_prod_a_a] :
~ ~ ( ( SV198 != SY857 )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SY857 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SY857 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1170]) ).
thf(1290,plain,
! [SV199: set_Product_prod_a_a] :
( ( ( ( asym_a @ SV199 )
| ! [SY860: a,SY861: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY860 @ SY861 ) @ SV199 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY861 @ SY860 ) @ SV199 ) ) )
= $false )
| ( ( ~ ( ~ ( asym_a @ SV199 )
| ~ ! [SY860: a,SY861: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY860 @ SY861 ) @ SV199 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY861 @ SY860 ) @ SV199 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1171]) ).
thf(1291,plain,
! [SV344: multis599418605od_a_a,SV285: product_prod_a_a,SV200: multis599418605od_a_a,SV92: product_prod_a_a] :
( ( ( ( add_ms1725977093od_a_a @ SV92 @ SV200 )
!= ( add_ms1725977093od_a_a @ SV285 @ SV344 ) )
= $true )
| ( ( ~ ( ( SV92 != SV285 ) )
| ( member449909584od_a_a @ SV285 @ ( set_ms1818337124od_a_a @ SV200 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1172]) ).
thf(1292,plain,
! [SV362: a,SV345: a,SV286: a,SV201: set_Product_prod_a_a,SV93: set_a] :
( ( ~ ( prefer1292084992ence_a @ SV93 @ SV201 )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SV345 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV286 ) @ SV201 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV362 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV362 @ SV345 ) @ SV201 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SV362 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV362 @ SV286 ) @ SV201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1173]) ).
thf(1293,plain,
! [SV346: set_Product_prod_a_a,SV287: set_a,SV202: a,SV94: a] :
( ( ( ~ ( member_a @ SV94 @ ( prefer161218362good_a @ SV202 @ SV287 @ SV346 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV94 @ SV202 ) @ SV346 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1174]) ).
thf(1294,plain,
! [SV288: product_prod_a_a,SV203: a > a > set_mu1281098573od_a_a,SV95: multis599418605od_a_a] :
( ( ( member1755255446od_a_a @ SV95 @ ( produc1121147169od_a_a @ SV203 @ SV288 ) )
= $false )
| ( ( ~ ! [SY976: a,SY977: a] :
( ( SV288
!= ( product_Pair_a_a @ SY976 @ SY977 ) )
| ~ ( member1755255446od_a_a @ SV95 @ ( SV203 @ SY976 @ SY977 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1175]) ).
thf(1295,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ~ ( ( prefer1292084992ence_a @ SV204 @ SV347 )
| ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) )
| ~ ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 )
| ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1176]) ).
thf(1296,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( prefer1292084992ence_a @ SV204 @ SV347 )
= ( ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1176]) ).
thf(1297,plain,
! [SV97: product_prod_a_a,SV205: multis599418605od_a_a] :
( ( ( ! [SY877: multis599418605od_a_a] :
( SV205
!= ( add_ms1725977093od_a_a @ SV97 @ SY877 ) ) )
= $false )
| ( ( member449909584od_a_a @ SV97 @ ( set_ms1818337124od_a_a @ SV205 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1177]) ).
thf(1298,plain,
! [SV290: product_prod_a_a,SV206: a > a > set_multiset_a,SV98: multiset_a] :
( ( ( member_multiset_a @ SV98 @ ( produc1828150264iset_a @ SV206 @ SV290 ) )
= $false )
| ( ( ~ ! [SY982: a,SY983: a] :
( ( SV290
!= ( product_Pair_a_a @ SY982 @ SY983 ) )
| ~ ( member_multiset_a @ SV98 @ ( SV206 @ SY982 @ SY983 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1178]) ).
thf(1299,plain,
! [SV99: product_prod_a_a] :
( ( SV99
= ( product_Pair_a_a @ ( sK3_SY666 @ SV99 ) @ ( sK8_SY984 @ SV99 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1179]) ).
thf(1300,plain,
! [SV100: set_Product_prod_a_a,SV207: set_a] :
( ( ( ! [SY1034: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK17_SY881 @ SV207 @ SV100 ) @ SY1034 ) @ SV100 )
| ( member_a @ ( sK17_SY881 @ SV207 @ SV100 ) @ SV207 ) ) )
= $false )
| ( ( ~ ! [SY883: a,SY884: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY883 @ SY884 ) @ SV100 )
| ( member_a @ SY884 @ SV207 ) )
| ~ ( order_preorder_on_a @ SV207 @ SV100 )
| ( prefer1292084992ence_a @ SV207 @ SV100 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1180]) ).
thf(1301,plain,
! [SV291: a,SV208: a,SV101: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SV208 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV101 ) @ relation ) ) )
= $false )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV291 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV291 @ SV208 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SV291 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV291 @ SV101 ) @ relation ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1181]) ).
thf(1302,plain,
! [SV292: a,SV209: a,SV102: product_prod_a_a > $o] :
( ( ( product_curry_a_a_o @ SV102 @ SV209 @ SV292 )
= $false )
| ( ( SV102 @ ( product_Pair_a_a @ SV209 @ SV292 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1182]) ).
thf(1303,plain,
! [SV293: product_prod_a_a,SV210: a > a > set_a,SV103: a] :
( ( ( member_a @ SV103 @ ( produc961951794_set_a @ SV210 @ SV293 ) )
= $false )
| ( ( ~ ! [SY985: a,SY986: a] :
( ( SV293
!= ( product_Pair_a_a @ SY985 @ SY986 ) )
| ~ ( member_a @ SV103 @ ( SV210 @ SY985 @ SY986 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1183]) ).
thf(1304,plain,
! [SV211: product_prod_a_a,SV104: product_prod_a_a > $o] :
( ( ( ! [SY1035: a] : ( SV104 @ ( product_Pair_a_a @ ( sK18_SY682 @ SV211 @ SV104 ) @ SY1035 ) ) )
= $false )
| ( ( SV104 @ SV211 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1184]) ).
thf(1305,plain,
! [SV348: product_prod_a_a,SV294: product_prod_a_a,SV212: set_Pr1948701895od_a_a,SV105: set_Product_prod_a_a] :
( ( ( ~ ( refl_o1298442278od_a_a @ SV105 @ SV212 ) )
= $true )
| ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV294 @ SV348 ) @ SV212 )
| ( member449909584od_a_a @ SV294 @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1185]) ).
thf(1306,plain,
! [SV349: product_prod_a_a,SV295: product_prod_a_a,SV213: set_Pr1948701895od_a_a,SV106: set_Product_prod_a_a] :
( ( ( ~ ( refl_o1298442278od_a_a @ SV106 @ SV213 ) )
= $true )
| ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV295 @ SV349 ) @ SV213 )
| ~ ( ~ ( member449909584od_a_a @ SV295 @ SV106 )
| ~ ( member449909584od_a_a @ SV349 @ SV106 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1186]) ).
thf(1307,plain,
! [SV296: set_Product_prod_a_a,SV214: product_prod_a_a > product_prod_a_a,SV107: set_Product_prod_a_a] :
( ( ( ! [SY989: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY989 @ SV107 )
| ( member449909584od_a_a @ ( SV214 @ SY989 ) @ SV296 ) ) )
= $false )
| ( ( ord_le1824328871od_a_a @ ( image_794773445od_a_a @ SV214 @ SV107 ) @ SV296 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1187]) ).
thf(1308,plain,
! [SV350: a,SV297: set_Product_prod_a_a,SV215: a,SV108: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV108 @ SV215 ) @ SV297 ) )
= $true )
| ( ( ( SV350 != SV215 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV108 @ SV350 ) @ SV297 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1188]) ).
thf(1309,plain,
! [SV351: a,SV298: a,SV216: set_Product_prod_a_a,SV109: set_a] :
( ( ( ~ ( refl_on_a @ SV109 @ SV216 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV298 @ SV351 ) @ SV216 )
| ( member_a @ SV351 @ SV109 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1189]) ).
thf(1310,plain,
! [SV352: set_a,SV299: a,SV217: a > product_prod_a_a,SV110: product_prod_a_a] :
( ( ( SV110
!= ( SV217 @ SV299 ) )
= $true )
| ( ( ~ ( member_a @ SV299 @ SV352 )
| ( member449909584od_a_a @ SV110 @ ( image_1725938350od_a_a @ SV217 @ SV352 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1190]) ).
thf(1311,plain,
! [SV363: a > a,SV353: a > a,SV300: set_Product_prod_a_a,SV218: a,SV111: a] :
( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV111 @ SV218 ) @ SV300 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV353 @ SV111 ) @ ( SV363 @ SV218 ) ) @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SV353 @ SV363 ) @ SV300 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1191]) ).
thf(1312,plain,
! [SV219: product_prod_a_a,SV112: a] :
( ( ( ( SV112
= ( product_snd_a_a @ SV219 ) )
| ~ ! [SY907: a] :
( SV219
!= ( product_Pair_a_a @ SY907 @ SV112 ) ) )
= $false )
| ( ( ~ ( ( SV112
!= ( product_snd_a_a @ SV219 ) )
| ~ ~ ! [SY907: a] :
( SV219
!= ( product_Pair_a_a @ SY907 @ SV112 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1192]) ).
thf(1313,plain,
! [SV113: multis599418605od_a_a] :
( ( ( ! [SY708: product_prod_a_a] :
~ ( member449909584od_a_a @ SY708 @ ( set_ms1818337124od_a_a @ SV113 ) ) )
= $false )
| ( ( SV113 = zero_z160849828od_a_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1193]) ).
thf(1314,plain,
! [SV354: set_Product_prod_a_a,SV301: product_prod_a_a,SV220: product_prod_a_a > product_prod_a_a,SV114: product_prod_a_a] :
( ( ( SV114
!= ( SV220 @ SV301 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ SV301 @ SV354 )
| ( member449909584od_a_a @ SV114 @ ( image_794773445od_a_a @ SV220 @ SV354 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1194]) ).
thf(1315,plain,
! [SV302: product_prod_a_a,SV221: a > a > set_Pr158363655iset_a,SV115: produc1127127335iset_a] :
( ( ( member340150864iset_a @ SV115 @ ( produc93594587iset_a @ SV221 @ SV302 ) )
= $false )
| ( ( ~ ! [SY996: a,SY997: a] :
( ( SV302
!= ( product_Pair_a_a @ SY996 @ SY997 ) )
| ~ ( member340150864iset_a @ SV115 @ ( SV221 @ SY996 @ SY997 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1195]) ).
thf(1316,plain,
! [SV303: multis599418605od_a_a,SV222: multis599418605od_a_a,SV116: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV116 @ ( set_ms1818337124od_a_a @ SV222 ) ) )
= $false )
| ( ( ( minus_1257885652od_a_a @ ( add_ms1725977093od_a_a @ SV116 @ SV303 ) @ SV222 )
= ( add_ms1725977093od_a_a @ SV116 @ ( minus_1257885652od_a_a @ SV303 @ SV222 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1196]) ).
thf(1317,plain,
! [SV304: produc1127127335iset_a,SV223: multiset_a > multiset_a > set_Product_prod_a_a,SV117: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV117 @ ( produc2041367259od_a_a @ SV223 @ SV304 ) )
= $false )
| ( ( ~ ! [SY998: multiset_a,SY999: multiset_a] :
( ( SV304
!= ( produc2037245207iset_a @ SY998 @ SY999 ) )
| ~ ( member449909584od_a_a @ SV117 @ ( SV223 @ SY998 @ SY999 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1197]) ).
thf(1318,plain,
! [SV224: set_Product_prod_a_a,SV118: set_a,SV364: a] :
( ( ( ~ ( member_a @ SV364 @ SV118 )
| ! [SY1036: a] :
( ~ ( member_a @ SY1036 @ SV118 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV364 @ SY1036 ) @ SV224 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1036 @ SV364 ) @ SV224 ) ) )
= $true )
| ( ( prefer719835986ence_a @ SV118 @ SV224 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1198]) ).
thf(1319,plain,
! [SV355: product_prod_a_a > a,SV305: a,SV225: set_Product_prod_a_a,SV119: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV119 @ SV225 ) )
= $true )
| ( ( ( SV305
!= ( SV355 @ SV119 ) )
| ( member_a @ SV305 @ ( image_340790172_a_a_a @ SV355 @ SV225 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1199]) ).
thf(1320,plain,
! [SV306: product_prod_a_a,SV226: a > a > set_Product_prod_a_a,SV120: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV120 @ ( produc1093061851od_a_a @ SV226 @ SV306 ) )
= $false )
| ( ( ~ ! [SY1001: a,SY1002: a] :
( ( SV306
!= ( product_Pair_a_a @ SY1001 @ SY1002 ) )
| ~ ( member449909584od_a_a @ SV120 @ ( SV226 @ SY1001 @ SY1002 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1200]) ).
thf(1321,plain,
! [SV121: product_prod_a_a > $o,SV1: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV1 @ ( collec645855634od_a_a @ SV121 ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ SV1 @ ( collec645855634od_a_a @ SV121 ) )
| ~ ( SV121 @ SV1 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1201]) ).
thf(1322,plain,
! [SV1: product_prod_a_a,SV121: product_prod_a_a > $o] :
( ( ( SV121 @ SV1 )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ SV1 @ ( collec645855634od_a_a @ SV121 ) )
| ~ ( SV121 @ SV1 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1201]) ).
thf(1323,plain,
! [SV365: a,SV307: a,SV122: product_prod_a_a > $o] :
( ( ( product_curry_a_a_o @ SV122 @ SV307 @ SV365 )
= ( SV122 @ ( product_Pair_a_a @ SV307 @ SV365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1202]) ).
thf(1324,plain,
! [SV308: a > a,SV228: set_Product_prod_a_a,SV123: a,SV4: a] :
( ( ( ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV4 @ SV123 ) @ ( inv_image_a_a @ SV228 @ SV308 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV308 @ SV4 ) @ ( SV308 @ SV123 ) ) @ SV228 ) ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV4 @ SV123 ) @ ( inv_image_a_a @ SV228 @ SV308 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV308 @ SV4 ) @ ( SV308 @ SV123 ) ) @ SV228 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1204]) ).
thf(1325,plain,
! [SV309: a > multiset_a,SV229: set_Pr158363655iset_a,SV124: a,SV5: a] :
( ( ( ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV5 @ SV124 ) @ ( inv_im975322764et_a_a @ SV229 @ SV309 ) )
| ( member340150864iset_a @ ( produc2037245207iset_a @ ( SV309 @ SV5 ) @ ( SV309 @ SV124 ) ) @ SV229 ) ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV5 @ SV124 ) @ ( inv_im975322764et_a_a @ SV229 @ SV309 ) )
| ~ ( member340150864iset_a @ ( produc2037245207iset_a @ ( SV309 @ SV5 ) @ ( SV309 @ SV124 ) ) @ SV229 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1206]) ).
thf(1326,plain,
! [SV310: multiset_a > a,SV230: set_Product_prod_a_a,SV125: multiset_a,SV6: multiset_a] :
( ( ( ~ ( ( member340150864iset_a @ ( produc2037245207iset_a @ SV6 @ SV125 ) @ ( inv_im479034648iset_a @ SV230 @ SV310 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV310 @ SV6 ) @ ( SV310 @ SV125 ) ) @ SV230 ) ) )
= $true )
| ( ( ~ ( ~ ( member340150864iset_a @ ( produc2037245207iset_a @ SV6 @ SV125 ) @ ( inv_im479034648iset_a @ SV230 @ SV310 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV310 @ SV6 ) @ ( SV310 @ SV125 ) ) @ SV230 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1208]) ).
thf(1327,plain,
! [SV311: a > product_prod_a_a,SV231: set_Pr1948701895od_a_a,SV126: a,SV7: a] :
( ( ( ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV7 @ SV126 ) @ ( inv_im777352425_a_a_a @ SV231 @ SV311 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( SV311 @ SV7 ) @ ( SV311 @ SV126 ) ) @ SV231 ) ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV7 @ SV126 ) @ ( inv_im777352425_a_a_a @ SV231 @ SV311 ) )
| ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( SV311 @ SV7 ) @ ( SV311 @ SV126 ) ) @ SV231 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1210]) ).
thf(1328,plain,
! [SV312: product_prod_a_a > a,SV232: set_Product_prod_a_a,SV127: product_prod_a_a,SV8: product_prod_a_a] :
( ( ( ~ ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV8 @ SV127 ) @ ( inv_im15016955od_a_a @ SV232 @ SV312 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV312 @ SV8 ) @ ( SV312 @ SV127 ) ) @ SV232 ) ) )
= $true )
| ( ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV8 @ SV127 ) @ ( inv_im15016955od_a_a @ SV232 @ SV312 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV312 @ SV8 ) @ ( SV312 @ SV127 ) ) @ SV232 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1212]) ).
thf(1329,plain,
! [SV313: a > multis599418605od_a_a,SV233: set_Pr1821581383od_a_a,SV128: a,SV9: a] :
( ( ( ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV128 ) @ ( inv_im1681759523_a_a_a @ SV233 @ SV313 ) )
| ( member1349055120od_a_a @ ( produc1859144151od_a_a @ ( SV313 @ SV9 ) @ ( SV313 @ SV128 ) ) @ SV233 ) ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV128 ) @ ( inv_im1681759523_a_a_a @ SV233 @ SV313 ) )
| ~ ( member1349055120od_a_a @ ( produc1859144151od_a_a @ ( SV313 @ SV9 ) @ ( SV313 @ SV128 ) ) @ SV233 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1214]) ).
thf(1330,plain,
! [SV314: multis599418605od_a_a > a,SV234: set_Product_prod_a_a,SV129: multis599418605od_a_a,SV10: multis599418605od_a_a] :
( ( ( ~ ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ SV10 @ SV129 ) @ ( inv_im941243329od_a_a @ SV234 @ SV314 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV314 @ SV10 ) @ ( SV314 @ SV129 ) ) @ SV234 ) ) )
= $true )
| ( ( ~ ( ~ ( member1349055120od_a_a @ ( produc1859144151od_a_a @ SV10 @ SV129 ) @ ( inv_im941243329od_a_a @ SV234 @ SV314 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV314 @ SV10 ) @ ( SV314 @ SV129 ) ) @ SV234 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1216]) ).
thf(1331,plain,
! [SV237: a,SV133: a,SV14: a > a > $o] :
( ( ( ( produc1833107820_a_a_o @ SV14 @ ( product_Pair_a_a @ SV133 @ SV237 ) )
| ( SV14 @ SV133 @ SV237 ) )
= $false )
| ( ( ~ ( ~ ( produc1833107820_a_a_o @ SV14 @ ( product_Pair_a_a @ SV133 @ SV237 ) )
| ~ ( SV14 @ SV133 @ SV237 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1218]) ).
thf(1332,plain,
! [SV134: set_Product_prod_a_a] :
( ( ( irrefl_a @ SV134 )
= $false )
| ( ( ~ ( ~ ( irrefl_a @ SV134 )
| ~ ! [SY751: a] :
~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY751 @ SY751 ) @ SV134 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1219]) ).
thf(1333,plain,
! [SV134: set_Product_prod_a_a] :
( ( ( ! [SY751: a] :
~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY751 @ SY751 ) @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( irrefl_a @ SV134 )
| ~ ! [SY751: a] :
~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY751 @ SY751 ) @ SV134 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1219]) ).
thf(1334,plain,
! [SV238: set_Product_prod_a_a,SV135: a,SV16: a] :
( ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV16 @ SV135 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV238 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV135 @ SV16 ) @ SV238 ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV16 @ SV135 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV238 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV135 @ SV16 ) @ SV238 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1220]) ).
thf(1335,plain,
! [SV136: product_prod_a_a] :
( ( ( top_to1483957574_a_a_o @ SV136 )
= $false )
| ( ( ~ ( ~ ( top_to1483957574_a_a_o @ SV136 )
| ~ ( member449909584od_a_a @ SV136 @ top_to398455383od_a_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1221]) ).
thf(1336,plain,
! [SV136: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV136 @ top_to398455383od_a_a )
= $false )
| ( ( ~ ( ~ ( top_to1483957574_a_a_o @ SV136 )
| ~ ( member449909584od_a_a @ SV136 @ top_to398455383od_a_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1221]) ).
thf(1337,plain,
! [SV240: multis599418605od_a_a,SV141: multis599418605od_a_a,SV25: product_prod_a_a] :
( ( ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ ( plus_p404985124od_a_a @ SV141 @ SV240 ) ) )
| ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV141 ) )
| ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV240 ) ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ ( plus_p404985124od_a_a @ SV141 @ SV240 ) ) )
| ~ ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV141 ) )
| ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV240 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1222]) ).
thf(1338,plain,
! [SV316: a,SV242: a,SV143: a,SV28: a] :
( ( ( ( product_Pair_a_a @ SV28 @ SV143 )
= ( product_Pair_a_a @ SV242 @ SV316 ) )
= $false )
| ( ( ~ ( ( SV28 != SV242 )
| ( SV143 != SV316 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1224]) ).
thf(1339,plain,
! [SV144: produc1572603623od_a_a,SV29: produc1572603623od_a_a > $o] :
( ( ( ! [SY1037: a] : ( SV29 @ ( produc1474507607od_a_a @ ( sK9_SY474 @ SV144 @ SV29 ) @ ( product_Pair_a_a @ ( sK19_SY1025 @ SV144 @ SV29 ) @ SY1037 ) ) ) )
= $false )
| ( ( SV29 @ SV144 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1225]) ).
thf(1340,plain,
! [SV32: set_Product_prod_a_a,SV147: set_Pr1948701895od_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK10_SY764 @ SV147 @ SV32 ) @ SV32 )
| ~ ( member449909584od_a_a @ ( sK20_SY1027 @ SV32 @ SV147 ) @ SV32 )
| ~ ( ( ( sK10_SY764 @ SV147 @ SV32 )
!= ( sK20_SY1027 @ SV32 @ SV147 ) ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK10_SY764 @ SV147 @ SV32 ) @ ( sK20_SY1027 @ SV32 @ SV147 ) ) @ SV147 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK20_SY1027 @ SV32 @ SV147 ) @ ( sK10_SY764 @ SV147 @ SV32 ) ) @ SV147 ) )
= $false )
| ( ( total_1490170027od_a_a @ SV32 @ SV147 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1228]) ).
thf(1341,plain,
! [SV317: a,SV245: a > $o,SV148: a,SV33: a > $o] :
( ( ( SV33 @ SV148 )
= $false )
| ( ( ~ ( SV245 @ SV317 )
| ~ ( ~ ( SV33 @ ( product_fst_a_a @ ( product_Pair_a_a @ SV148 @ SV317 ) ) )
| ~ ( SV245 @ ( product_snd_a_a @ ( product_Pair_a_a @ SV148 @ SV317 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1229]) ).
thf(1342,plain,
! [SV357: a > set_Product_prod_a_a,SV318: a,SV246: a,SV149: a,SV34: a > $o] :
( ( ( ~ ( SV34 @ SV149 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV246 @ SV318 ) @ ( SV357 @ SV149 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV149 @ SV246 ) @ ( product_Pair_a_a @ SV149 @ SV318 ) ) @ ( same_fst_a_a @ SV34 @ SV357 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1230]) ).
thf(1343,plain,
! [SV35: product_prod_a_a,SV150: multis599418605od_a_a] :
( ( ( SV150
!= ( add_ms1725977093od_a_a @ SV35 @ ( sK21_SY771 @ SV35 @ SV150 ) ) )
= $false )
| ( ( member449909584od_a_a @ SV35 @ ( set_ms1818337124od_a_a @ SV150 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1231]) ).
thf(1344,plain,
! [SV36: set_Product_prod_a_a,SV151: set_Product_prod_a_a > $o] :
( ( ( ! [SY772: set_Product_prod_a_a] :
( ~ ! [SX3: a,SX4: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX4 ) @ SY772 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX4 @ SX3 ) @ SY772 ) )
| ( SV151 @ SY772 ) ) )
= $false )
| ( ( SV151 @ SV36 )
= $true )
| ( ( asym_a @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1232]) ).
thf(1345,plain,
! [SV37: set_Product_prod_a_a,SV152: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK11_SY775 @ SV152 @ SV37 ) @ ( sK22_SY1028 @ SV37 @ SV152 ) ) @ SV37 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK11_SY775 @ SV152 @ SV37 ) @ ( sK22_SY1028 @ SV37 @ SV152 ) ) @ SV152 ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV37 @ SV152 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1233]) ).
thf(1346,plain,
! [SV319: set_Pr1948701895od_a_a,SV247: set_Product_prod_a_a,SV153: product_prod_a_a,SV38: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV38 @ ( prefer477097315od_a_a @ SV153 @ SV247 @ SV319 ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV38 @ SV153 ) @ SV319 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1234]) ).
thf(1347,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a] :
( ( ( ~ ( ( total_1490170027od_a_a @ SV154 @ SV320 )
| ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( total_1490170027od_a_a @ SV154 @ SV320 )
| ~ ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1235]) ).
thf(1348,plain,
! [SV155: product_prod_a_a,SV40: a] :
( ( ( SV40
= ( product_fst_a_a @ SV155 ) )
= $false )
| ( ( ~ ( ( SV40
!= ( product_fst_a_a @ SV155 ) )
| ~ ~ ! [SY782: a] :
( SV155
!= ( product_Pair_a_a @ SV40 @ SY782 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1237]) ).
thf(1349,plain,
! [SV40: a,SV155: product_prod_a_a] :
( ( ( ~ ! [SY782: a] :
( SV155
!= ( product_Pair_a_a @ SV40 @ SY782 ) ) )
= $false )
| ( ( ~ ( ( SV40
!= ( product_fst_a_a @ SV155 ) )
| ~ ~ ! [SY782: a] :
( SV155
!= ( product_Pair_a_a @ SV40 @ SY782 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1237]) ).
thf(1350,plain,
! [SV321: a,SV249: a,SV156: a,SV41: set_Product_prod_a_a] :
( ( ( trans_a @ SV41 )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV156 @ SV249 ) @ SV41 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV249 @ SV321 ) @ SV41 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV156 @ SV321 ) @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1238]) ).
thf(1351,plain,
! [SV322: product_prod_a_a,SV250: product_prod_a_a,SV157: set_Pr1948701895od_a_a,SV42: set_Product_prod_a_a] :
( ( ( prefer1338892073od_a_a @ SV42 @ SV157 )
= $false )
| ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV250 @ SV322 ) @ SV157 )
| ( member449909584od_a_a @ SV250 @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1239]) ).
thf(1352,plain,
! [SV323: product_prod_a_a,SV251: a,SV158: a,SV43: a > a > $o] :
( ( ( SV43 @ SV158 @ SV251 )
= $false )
| ( ( ( SV323
!= ( product_Pair_a_a @ SV158 @ SV251 ) )
| ( SV43 @ ( product_fst_a_a @ SV323 ) @ ( product_snd_a_a @ SV323 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1240]) ).
thf(1353,plain,
! [SV324: a,SV252: a,SV159: a,SV44: a] :
( ( ( ~ ( ( ( product_Pair_a_a @ SV44 @ SV159 )
= ( product_Pair_a_a @ SV252 @ SV324 ) )
| ~ ( ( SV44 != SV252 )
| ( SV159 != SV324 ) ) ) )
= $true )
| ( ( ~ ( ( ( product_Pair_a_a @ SV44 @ SV159 )
!= ( product_Pair_a_a @ SV252 @ SV324 ) )
| ~ ~ ( ( SV44 != SV252 )
| ( SV159 != SV324 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1241]) ).
thf(1354,plain,
! [SV325: a,SV253: a,SV160: a,SV45: set_Product_prod_a_a] :
( ( ( trans_a @ SV45 )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV160 @ SV253 ) @ SV45 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV253 @ SV325 ) @ SV45 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV160 @ SV325 ) @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1243]) ).
thf(1355,plain,
! [SV46: set_a,SV161: a > product_prod_a_a,SV254: set_Product_prod_a_a] :
( ( ( ~ ( member_a @ ( sK23_SY945 @ SV254 @ SV161 @ SV46 ) @ SV46 )
| ( member449909584od_a_a @ ( SV161 @ ( sK23_SY945 @ SV254 @ SV161 @ SV46 ) ) @ SV254 ) )
= $false )
| ( ( ord_le1824328871od_a_a @ ( image_1725938350od_a_a @ SV161 @ SV46 ) @ SV254 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1244]) ).
thf(1356,plain,
! [SV162: set_Pr1948701895od_a_a,SV47: set_Product_prod_a_a,SV358: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV358 @ SV47 ) )
= $true )
| ( ( ! [SY1029: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1029 @ SV47 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV358 @ SY1029 ) @ SV162 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1029 @ SV358 ) @ SV162 ) ) )
= $true )
| ( ( prefer697821563od_a_a @ SV47 @ SV162 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1245]) ).
thf(1357,plain,
! [SV48: set_a,SV163: set_Product_prod_a_a] :
( ( ( ~ ( member_a @ ( sK12_SY797 @ SV163 @ SV48 ) @ SV48 )
| ~ ( member_a @ ( sK24_SY1030 @ SV48 @ SV163 ) @ SV48 )
| ~ ( ( ( sK12_SY797 @ SV163 @ SV48 )
!= ( sK24_SY1030 @ SV48 @ SV163 ) ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK12_SY797 @ SV163 @ SV48 ) @ ( sK24_SY1030 @ SV48 @ SV163 ) ) @ SV163 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK24_SY1030 @ SV48 @ SV163 ) @ ( sK12_SY797 @ SV163 @ SV48 ) ) @ SV163 ) )
= $false )
| ( ( total_on_a @ SV48 @ SV163 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1246]) ).
thf(1358,plain,
! [SV326: set_Pr1948701895od_a_a,SV255: set_Product_prod_a_a,SV164: product_prod_a_a,SV49: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV49 @ ( prefer477097315od_a_a @ SV164 @ SV255 @ SV326 ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV49 @ SV164 ) @ SV326 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1247]) ).
thf(1359,plain,
! [SV50: product_prod_a_a] :
( ( SV50
!= ( product_Pair_a_a @ ( sK1_SY535 @ SV50 ) @ ( sK25_SY947 @ SV50 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1248]) ).
thf(1360,plain,
! [SV165: set_Pr1948701895od_a_a,SV51: set_Product_prod_a_a,SV256: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV256 @ SV51 ) )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV256 @ SV256 ) @ SV165 )
= $true )
| ( ( refl_o1298442278od_a_a @ SV51 @ SV165 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1249]) ).
thf(1361,plain,
! [SV366: set_Product_prod_a_a,SV359: set_Product_prod_a_a,SV327: a,SV257: a,SV166: a,SV52: a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SV257 @ SV327 ) ) @ ( lex_prod_a_a @ SV359 @ SV366 ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
| ~ ( ( SV52 != SV257 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1250]) ).
thf(1362,plain,
! [SV328: product_prod_a_a,SV258: product_prod_a_a,SV167: set_Pr1948701895od_a_a,SV53: set_Product_prod_a_a] :
( ( ( refl_o1298442278od_a_a @ SV53 @ SV167 )
= $false )
| ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV258 @ SV328 ) @ SV167 )
| ( member449909584od_a_a @ SV328 @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1251]) ).
thf(1363,plain,
! [SV168: set_Product_prod_a_a,SV54: set_a,SV259: a] :
( ( ( ~ ( member_a @ SV259 @ SV54 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV259 @ SV259 ) @ SV168 )
= $true )
| ( ( refl_on_a @ SV54 @ SV168 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1252]) ).
thf(1364,plain,
! [SV329: set_Product_prod_a_a,SV260: set_a,SV169: a,SV55: a] :
( ( ( member_a @ SV55 @ ( prefer161218362good_a @ SV169 @ SV260 @ SV329 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV55 @ SV169 ) @ SV329 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1253]) ).
thf(1365,plain,
! [SV330: a,SV261: a,SV170: a,SV56: a] :
( ( ( ~ ( ( ( product_Pair_a_a @ SV56 @ SV170 )
= ( product_Pair_a_a @ SV261 @ SV330 ) )
| ~ ( ( SV56 != SV261 )
| ( SV170 != SV330 ) ) ) )
= $true )
| ( ( ~ ( ( ( product_Pair_a_a @ SV56 @ SV170 )
!= ( product_Pair_a_a @ SV261 @ SV330 ) )
| ~ ~ ( ( SV56 != SV261 )
| ( SV170 != SV330 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1254]) ).
thf(1366,plain,
! [SV262: a,SV171: a,SV57: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV171 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV171 @ SV57 ) @ relation ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV171 @ SV262 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV262 @ SV171 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV262 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV262 @ SV57 ) @ relation ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1256]) ).
thf(1367,plain,
! [SV331: a,SV263: a,SV172: set_Product_prod_a_a,SV58: set_a] :
( ( ( refl_on_a @ SV58 @ SV172 )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV263 @ SV331 ) @ SV172 )
| ~ ( ~ ( member_a @ SV263 @ SV58 )
| ~ ( member_a @ SV331 @ SV58 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1257]) ).
thf(1368,plain,
! [SV332: set_Product_prod_a_a,SV264: a > a,SV173: a > a,SV59: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV59 @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SV173 @ SV264 ) @ SV332 ) )
= $false )
| ( ( ~ ! [SY1009: a,SY1010: a] :
( ( SV59
!= ( product_Pair_a_a @ ( SV173 @ SY1009 ) @ ( SV264 @ SY1010 ) ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1009 @ SY1010 ) @ SV332 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1258]) ).
thf(1369,plain,
! [SV333: product_prod_a_a,SV265: product_prod_a_a,SV174: set_Pr1948701895od_a_a,SV60: set_Product_prod_a_a] :
( ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ SV265 @ SV60 )
| ~ ( member449909584od_a_a @ SV333 @ SV60 ) )
| ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) )
= ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
| ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1259]) ).
thf(1370,plain,
! [SV334: a,SV266: a,SV175: set_Product_prod_a_a,SV61: set_a] :
( ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false )
| ( ( ~ ~ ( ~ ( member_a @ SV266 @ SV61 )
| ~ ( member_a @ SV334 @ SV61 ) )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1260]) ).
thf(1371,plain,
! [SV176: product_prod_a_a,SV62: product_prod_a_a > $o] :
( ( ( SV62 @ ( product_Pair_a_a @ ( sK13_SY572 @ SV176 @ SV62 ) @ ( sK26_SY1032 @ SV176 @ SV62 ) ) )
= $false )
| ( ( SV62 @ SV176 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1261]) ).
thf(1372,plain,
! [SV63: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK4_SY574 @ SV63 ) @ ( sK14_SY1011 @ SV63 ) ) @ SV63 ) )
= $false )
| ( ( asym_a @ SV63 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1262]) ).
thf(1373,plain,
! [SV63: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK14_SY1011 @ SV63 ) @ ( sK4_SY574 @ SV63 ) ) @ SV63 ) )
= $false )
| ( ( asym_a @ SV63 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1262]) ).
thf(1374,plain,
! [SV64: set_Product_prod_a_a,SV267: a,SV177: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV177 @ SV267 ) @ SV64 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV267 @ SV177 ) @ SV64 ) )
= $true )
| ( ( asym_a @ SV64 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1263]) ).
thf(1375,plain,
! [SV66: a,SV335: a] :
( ( ( member_a @ SV335 @ carrier )
= $false )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV66 @ SV335 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV335 @ SV66 ) @ relation ) )
= $true )
| ( ( member_a @ SV66 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1265]) ).
thf(1376,plain,
! [SV67: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK5_SY581 @ SV67 ) @ ( sK15_SY1012 @ SV67 ) ) @ SV67 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK15_SY1012 @ SV67 ) @ ( sK27_SY1033 @ SV67 ) ) @ SV67 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK5_SY581 @ SV67 ) @ ( sK27_SY1033 @ SV67 ) ) @ SV67 ) )
= $false )
| ( ( trans_a @ SV67 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1266]) ).
thf(1377,plain,
! [SV179: set_Product_prod_a_a] :
( ( ( trans_a @ SV179 )
= $false )
| ( ( ~ ( ~ ( trans_a @ SV179 )
| ~ ! [SY828: a,SY829: a,SY830: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY829 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY829 @ SY830 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY830 ) @ SV179 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1267]) ).
thf(1378,plain,
! [SV179: set_Product_prod_a_a] :
( ( ( ! [SY828: a,SY829: a,SY830: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY829 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY829 @ SY830 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY830 ) @ SV179 ) ) )
= $false )
| ( ( ~ ( ~ ( trans_a @ SV179 )
| ~ ! [SY828: a,SY829: a,SY830: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY829 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY829 @ SY830 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY830 ) @ SV179 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1267]) ).
thf(1379,plain,
! [SV70: produc1572603623od_a_a] :
( ( SV70
= ( produc1474507607od_a_a @ ( sK2_SY589 @ SV70 ) @ ( product_Pair_a_a @ ( sK6_SY960 @ SV70 ) @ ( sK16_SY1014 @ SV70 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1269]) ).
thf(1380,plain,
! [SV360: a,SV336: a,SV272: a,SV184: set_Product_prod_a_a,SV74: set_a] :
( ( ( ~ ( prefer719835986ence_a @ SV74 @ SV184 ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV336 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV272 ) @ SV184 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV360 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV336 ) @ SV184 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV360 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV272 ) @ SV184 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1272]) ).
thf(1381,plain,
! [SV337: set_Product_prod_a_a,SV274: product_prod_a_a,SV186: product_prod_a_a > a,SV76: a] :
( ( ( SV76
= ( SV186 @ SV274 ) )
= $false )
| ( ( ~ ( member449909584od_a_a @ SV274 @ SV337 )
| ( member_a @ SV76 @ ( image_340790172_a_a_a @ SV186 @ SV337 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1274]) ).
thf(1382,plain,
! [SV338: a,SV278: a,SV190: set_Product_prod_a_a,SV81: set_a] :
( ( ( prefer1292084992ence_a @ SV81 @ SV190 )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV338 ) @ SV190 )
| ( member_a @ SV278 @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1279]) ).
thf(1383,plain,
! [SV339: product_prod_a_a > product_prod_a_a,SV279: product_prod_a_a,SV191: set_Product_prod_a_a,SV82: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV82 @ SV191 )
= $false )
| ( ( ( SV279
!= ( SV339 @ SV82 ) )
| ( member449909584od_a_a @ SV279 @ ( image_794773445od_a_a @ SV339 @ SV191 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1280]) ).
thf(1384,plain,
! [SV340: a,SV280: a,SV192: set_Product_prod_a_a,SV83: set_a] :
( ( ( refl_on_a @ SV83 @ SV192 )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV280 @ SV340 ) @ SV192 )
| ( member_a @ SV280 @ SV83 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1281]) ).
thf(1385,plain,
! [SV341: a > product_prod_a_a,SV281: product_prod_a_a,SV193: set_a,SV84: a] :
( ( ( member_a @ SV84 @ SV193 )
= $false )
| ( ( ( SV281
!= ( SV341 @ SV84 ) )
| ( member449909584od_a_a @ SV281 @ ( image_1725938350od_a_a @ SV341 @ SV193 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1282]) ).
thf(1386,plain,
! [SV85: set_Product_prod_a_a,SV361: a,SV342: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV342 @ SV361 ) @ SV85 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV361 @ SV342 ) @ SV85 ) )
= $true )
| ( ( asym_a @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1283]) ).
thf(1387,plain,
! [SV86: set_Product_prod_a_a,SV194: product_prod_a_a > a,SV282: set_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK28_SY969 @ SV282 @ SV194 @ SV86 ) @ SV86 )
| ( member_a @ ( SV194 @ ( sK28_SY969 @ SV282 @ SV194 @ SV86 ) ) @ SV282 ) )
= $false )
| ( ( ord_less_eq_set_a @ ( image_340790172_a_a_a @ SV194 @ SV86 ) @ SV282 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1284]) ).
thf(1388,plain,
! [SV196: a,SV88: a] :
( ( ( ~ ( member_a @ SV88 @ carrier ) )
= $true )
| ( ( ~ ( member_a @ SV196 @ carrier ) )
= $true )
| ( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1286]) ).
thf(1389,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a] :
( ( ( ~ ( ( total_on_a @ SV197 @ SV343 )
| ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( total_on_a @ SV197 @ SV343 )
| ~ ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1287]) ).
thf(1390,plain,
! [SV198: set_Product_prod_a_a] :
( ( ( asym_a @ SV198 )
= $false )
| ( ( ~ ( ~ ( asym_a @ SV198 )
| ~ ~ ! [SY857: set_Product_prod_a_a] :
~ ~ ( ( SV198 != SY857 )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SY857 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SY857 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1289]) ).
thf(1391,plain,
! [SV198: set_Product_prod_a_a] :
( ( ( ~ ! [SY857: set_Product_prod_a_a] :
~ ~ ( ( SV198 != SY857 )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SY857 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SY857 ) ) ) )
= $false )
| ( ( ~ ( ~ ( asym_a @ SV198 )
| ~ ~ ! [SY857: set_Product_prod_a_a] :
~ ~ ( ( SV198 != SY857 )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SY857 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SY857 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1289]) ).
thf(1392,plain,
! [SV199: set_Product_prod_a_a] :
( ( ( asym_a @ SV199 )
= $false )
| ( ( ~ ( ~ ( asym_a @ SV199 )
| ~ ! [SY860: a,SY861: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY860 @ SY861 ) @ SV199 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY861 @ SY860 ) @ SV199 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1290]) ).
thf(1393,plain,
! [SV199: set_Product_prod_a_a] :
( ( ( ! [SY860: a,SY861: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY860 @ SY861 ) @ SV199 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY861 @ SY860 ) @ SV199 ) ) )
= $false )
| ( ( ~ ( ~ ( asym_a @ SV199 )
| ~ ! [SY860: a,SY861: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY860 @ SY861 ) @ SV199 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY861 @ SY860 ) @ SV199 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1290]) ).
thf(1394,plain,
! [SV344: multis599418605od_a_a,SV285: product_prod_a_a,SV200: multis599418605od_a_a,SV92: product_prod_a_a] :
( ( ( ( add_ms1725977093od_a_a @ SV92 @ SV200 )
= ( add_ms1725977093od_a_a @ SV285 @ SV344 ) )
= $false )
| ( ( ~ ( ( SV92 != SV285 ) )
| ( member449909584od_a_a @ SV285 @ ( set_ms1818337124od_a_a @ SV200 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1291]) ).
thf(1395,plain,
! [SV362: a,SV345: a,SV286: a,SV201: set_Product_prod_a_a,SV93: set_a] :
( ( ( ~ ( prefer1292084992ence_a @ SV93 @ SV201 ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SV345 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV286 ) @ SV201 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV362 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV362 @ SV345 ) @ SV201 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SV362 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV362 @ SV286 ) @ SV201 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1292]) ).
thf(1396,plain,
! [SV346: set_Product_prod_a_a,SV287: set_a,SV202: a,SV94: a] :
( ( ( member_a @ SV94 @ ( prefer161218362good_a @ SV202 @ SV287 @ SV346 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV94 @ SV202 ) @ SV346 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1293]) ).
thf(1397,plain,
! [SV203: a > a > set_mu1281098573od_a_a,SV95: multis599418605od_a_a,SV288: product_prod_a_a] :
( ( ( ! [SY976: a,SY977: a] :
( ( SV288
!= ( product_Pair_a_a @ SY976 @ SY977 ) )
| ~ ( member1755255446od_a_a @ SV95 @ ( SV203 @ SY976 @ SY977 ) ) ) )
= $false )
| ( ( member1755255446od_a_a @ SV95 @ ( produc1121147169od_a_a @ SV203 @ SV288 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1294]) ).
thf(1398,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( ~ ( ( prefer1292084992ence_a @ SV204 @ SV347 )
| ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 )
| ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1295]) ).
thf(1399,plain,
! [SV97: product_prod_a_a,SV205: multis599418605od_a_a] :
( ( ( SV205
!= ( add_ms1725977093od_a_a @ SV97 @ ( sK29_SY877 @ SV97 @ SV205 ) ) )
= $false )
| ( ( member449909584od_a_a @ SV97 @ ( set_ms1818337124od_a_a @ SV205 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1297]) ).
thf(1400,plain,
! [SV206: a > a > set_multiset_a,SV98: multiset_a,SV290: product_prod_a_a] :
( ( ( ! [SY982: a,SY983: a] :
( ( SV290
!= ( product_Pair_a_a @ SY982 @ SY983 ) )
| ~ ( member_multiset_a @ SV98 @ ( SV206 @ SY982 @ SY983 ) ) ) )
= $false )
| ( ( member_multiset_a @ SV98 @ ( produc1828150264iset_a @ SV206 @ SV290 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1298]) ).
thf(1401,plain,
! [SV100: set_Product_prod_a_a,SV207: set_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK17_SY881 @ SV207 @ SV100 ) @ ( sK30_SY1034 @ SV100 @ SV207 ) ) @ SV100 )
| ( member_a @ ( sK17_SY881 @ SV207 @ SV100 ) @ SV207 ) )
= $false )
| ( ( ~ ! [SY883: a,SY884: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY883 @ SY884 ) @ SV100 )
| ( member_a @ SY884 @ SV207 ) )
| ~ ( order_preorder_on_a @ SV207 @ SV100 )
| ( prefer1292084992ence_a @ SV207 @ SV100 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1300]) ).
thf(1402,plain,
! [SV291: a,SV208: a,SV101: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SV208 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV101 ) @ relation ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV291 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV291 @ SV208 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SV291 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV291 @ SV101 ) @ relation ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1301]) ).
thf(1403,plain,
! [SV210: a > a > set_a,SV103: a,SV293: product_prod_a_a] :
( ( ( ! [SY985: a,SY986: a] :
( ( SV293
!= ( product_Pair_a_a @ SY985 @ SY986 ) )
| ~ ( member_a @ SV103 @ ( SV210 @ SY985 @ SY986 ) ) ) )
= $false )
| ( ( member_a @ SV103 @ ( produc961951794_set_a @ SV210 @ SV293 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1303]) ).
thf(1404,plain,
! [SV211: product_prod_a_a,SV104: product_prod_a_a > $o] :
( ( ( SV104 @ ( product_Pair_a_a @ ( sK18_SY682 @ SV211 @ SV104 ) @ ( sK31_SY1035 @ SV211 @ SV104 ) ) )
= $false )
| ( ( SV104 @ SV211 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1304]) ).
thf(1405,plain,
! [SV348: product_prod_a_a,SV294: product_prod_a_a,SV212: set_Pr1948701895od_a_a,SV105: set_Product_prod_a_a] :
( ( ( refl_o1298442278od_a_a @ SV105 @ SV212 )
= $false )
| ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV294 @ SV348 ) @ SV212 )
| ( member449909584od_a_a @ SV294 @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1305]) ).
thf(1406,plain,
! [SV349: product_prod_a_a,SV295: product_prod_a_a,SV213: set_Pr1948701895od_a_a,SV106: set_Product_prod_a_a] :
( ( ( refl_o1298442278od_a_a @ SV106 @ SV213 )
= $false )
| ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV295 @ SV349 ) @ SV213 )
| ~ ( ~ ( member449909584od_a_a @ SV295 @ SV106 )
| ~ ( member449909584od_a_a @ SV349 @ SV106 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1306]) ).
thf(1407,plain,
! [SV107: set_Product_prod_a_a,SV214: product_prod_a_a > product_prod_a_a,SV296: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK32_SY989 @ SV296 @ SV214 @ SV107 ) @ SV107 )
| ( member449909584od_a_a @ ( SV214 @ ( sK32_SY989 @ SV296 @ SV214 @ SV107 ) ) @ SV296 ) )
= $false )
| ( ( ord_le1824328871od_a_a @ ( image_794773445od_a_a @ SV214 @ SV107 ) @ SV296 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1307]) ).
thf(1408,plain,
! [SV350: a,SV297: set_Product_prod_a_a,SV215: a,SV108: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV108 @ SV215 ) @ SV297 )
= $false )
| ( ( ( SV350 != SV215 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV108 @ SV350 ) @ SV297 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1308]) ).
thf(1409,plain,
! [SV351: a,SV298: a,SV216: set_Product_prod_a_a,SV109: set_a] :
( ( ( refl_on_a @ SV109 @ SV216 )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV298 @ SV351 ) @ SV216 )
| ( member_a @ SV351 @ SV109 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1309]) ).
thf(1410,plain,
! [SV352: set_a,SV299: a,SV217: a > product_prod_a_a,SV110: product_prod_a_a] :
( ( ( SV110
= ( SV217 @ SV299 ) )
= $false )
| ( ( ~ ( member_a @ SV299 @ SV352 )
| ( member449909584od_a_a @ SV110 @ ( image_1725938350od_a_a @ SV217 @ SV352 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1310]) ).
thf(1411,plain,
! [SV363: a > a,SV353: a > a,SV300: set_Product_prod_a_a,SV218: a,SV111: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV111 @ SV218 ) @ SV300 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV353 @ SV111 ) @ ( SV363 @ SV218 ) ) @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SV353 @ SV363 ) @ SV300 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1311]) ).
thf(1412,plain,
! [SV219: product_prod_a_a,SV112: a] :
( ( ( SV112
= ( product_snd_a_a @ SV219 ) )
= $false )
| ( ( ~ ( ( SV112
!= ( product_snd_a_a @ SV219 ) )
| ~ ~ ! [SY907: a] :
( SV219
!= ( product_Pair_a_a @ SY907 @ SV112 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1312]) ).
thf(1413,plain,
! [SV112: a,SV219: product_prod_a_a] :
( ( ( ~ ! [SY907: a] :
( SV219
!= ( product_Pair_a_a @ SY907 @ SV112 ) ) )
= $false )
| ( ( ~ ( ( SV112
!= ( product_snd_a_a @ SV219 ) )
| ~ ~ ! [SY907: a] :
( SV219
!= ( product_Pair_a_a @ SY907 @ SV112 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1312]) ).
thf(1414,plain,
! [SV113: multis599418605od_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK33_SY708 @ SV113 ) @ ( set_ms1818337124od_a_a @ SV113 ) ) )
= $false )
| ( ( SV113 = zero_z160849828od_a_a )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1313]) ).
thf(1415,plain,
! [SV354: set_Product_prod_a_a,SV301: product_prod_a_a,SV220: product_prod_a_a > product_prod_a_a,SV114: product_prod_a_a] :
( ( ( SV114
= ( SV220 @ SV301 ) )
= $false )
| ( ( ~ ( member449909584od_a_a @ SV301 @ SV354 )
| ( member449909584od_a_a @ SV114 @ ( image_794773445od_a_a @ SV220 @ SV354 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1314]) ).
thf(1416,plain,
! [SV221: a > a > set_Pr158363655iset_a,SV115: produc1127127335iset_a,SV302: product_prod_a_a] :
( ( ( ! [SY996: a,SY997: a] :
( ( SV302
!= ( product_Pair_a_a @ SY996 @ SY997 ) )
| ~ ( member340150864iset_a @ SV115 @ ( SV221 @ SY996 @ SY997 ) ) ) )
= $false )
| ( ( member340150864iset_a @ SV115 @ ( produc93594587iset_a @ SV221 @ SV302 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1315]) ).
thf(1417,plain,
! [SV303: multis599418605od_a_a,SV222: multis599418605od_a_a,SV116: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV116 @ ( set_ms1818337124od_a_a @ SV222 ) )
= $true )
| ( ( ( minus_1257885652od_a_a @ ( add_ms1725977093od_a_a @ SV116 @ SV303 ) @ SV222 )
= ( add_ms1725977093od_a_a @ SV116 @ ( minus_1257885652od_a_a @ SV303 @ SV222 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1316]) ).
thf(1418,plain,
! [SV223: multiset_a > multiset_a > set_Product_prod_a_a,SV117: product_prod_a_a,SV304: produc1127127335iset_a] :
( ( ( ! [SY998: multiset_a,SY999: multiset_a] :
( ( SV304
!= ( produc2037245207iset_a @ SY998 @ SY999 ) )
| ~ ( member449909584od_a_a @ SV117 @ ( SV223 @ SY998 @ SY999 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ SV117 @ ( produc2041367259od_a_a @ SV223 @ SV304 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1317]) ).
thf(1419,plain,
! [SV224: set_Product_prod_a_a,SV118: set_a,SV364: a] :
( ( ( ~ ( member_a @ SV364 @ SV118 ) )
= $true )
| ( ( ! [SY1036: a] :
( ~ ( member_a @ SY1036 @ SV118 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV364 @ SY1036 ) @ SV224 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1036 @ SV364 ) @ SV224 ) ) )
= $true )
| ( ( prefer719835986ence_a @ SV118 @ SV224 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1318]) ).
thf(1420,plain,
! [SV355: product_prod_a_a > a,SV305: a,SV225: set_Product_prod_a_a,SV119: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV119 @ SV225 )
= $false )
| ( ( ( SV305
!= ( SV355 @ SV119 ) )
| ( member_a @ SV305 @ ( image_340790172_a_a_a @ SV355 @ SV225 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1319]) ).
thf(1421,plain,
! [SV226: a > a > set_Product_prod_a_a,SV120: product_prod_a_a,SV306: product_prod_a_a] :
( ( ( ! [SY1001: a,SY1002: a] :
( ( SV306
!= ( product_Pair_a_a @ SY1001 @ SY1002 ) )
| ~ ( member449909584od_a_a @ SV120 @ ( SV226 @ SY1001 @ SY1002 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ SV120 @ ( produc1093061851od_a_a @ SV226 @ SV306 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1320]) ).
thf(1422,plain,
! [SV121: product_prod_a_a > $o,SV1: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV1 @ ( collec645855634od_a_a @ SV121 ) )
| ~ ( SV121 @ SV1 ) )
= $false )
| ( ( member449909584od_a_a @ SV1 @ ( collec645855634od_a_a @ SV121 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1321]) ).
thf(1423,plain,
! [SV121: product_prod_a_a > $o,SV1: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV1 @ ( collec645855634od_a_a @ SV121 ) )
| ~ ( SV121 @ SV1 ) )
= $false )
| ( ( SV121 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1322]) ).
thf(1424,plain,
! [SV365: a,SV307: a,SV122: product_prod_a_a > $o] :
( ( ~ ( ( product_curry_a_a_o @ SV122 @ SV307 @ SV365 )
| ( SV122 @ ( product_Pair_a_a @ SV307 @ SV365 ) ) )
| ~ ( ~ ( product_curry_a_a_o @ SV122 @ SV307 @ SV365 )
| ~ ( SV122 @ ( product_Pair_a_a @ SV307 @ SV365 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1323]) ).
thf(1425,plain,
! [SV365: a,SV307: a,SV122: product_prod_a_a > $o] :
( ( ( product_curry_a_a_o @ SV122 @ SV307 @ SV365 )
= ( SV122 @ ( product_Pair_a_a @ SV307 @ SV365 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1323]) ).
thf(1426,plain,
! [SV308: a > a,SV228: set_Product_prod_a_a,SV123: a,SV4: a] :
( ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV4 @ SV123 ) @ ( inv_image_a_a @ SV228 @ SV308 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV308 @ SV4 ) @ ( SV308 @ SV123 ) ) @ SV228 ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV4 @ SV123 ) @ ( inv_image_a_a @ SV228 @ SV308 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV308 @ SV4 ) @ ( SV308 @ SV123 ) ) @ SV228 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1324]) ).
thf(1427,plain,
! [SV309: a > multiset_a,SV229: set_Pr158363655iset_a,SV124: a,SV5: a] :
( ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV5 @ SV124 ) @ ( inv_im975322764et_a_a @ SV229 @ SV309 ) )
| ( member340150864iset_a @ ( produc2037245207iset_a @ ( SV309 @ SV5 ) @ ( SV309 @ SV124 ) ) @ SV229 ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV5 @ SV124 ) @ ( inv_im975322764et_a_a @ SV229 @ SV309 ) )
| ~ ( member340150864iset_a @ ( produc2037245207iset_a @ ( SV309 @ SV5 ) @ ( SV309 @ SV124 ) ) @ SV229 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1325]) ).
thf(1428,plain,
! [SV310: multiset_a > a,SV230: set_Product_prod_a_a,SV125: multiset_a,SV6: multiset_a] :
( ( ( ( member340150864iset_a @ ( produc2037245207iset_a @ SV6 @ SV125 ) @ ( inv_im479034648iset_a @ SV230 @ SV310 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV310 @ SV6 ) @ ( SV310 @ SV125 ) ) @ SV230 ) )
= $false )
| ( ( ~ ( ~ ( member340150864iset_a @ ( produc2037245207iset_a @ SV6 @ SV125 ) @ ( inv_im479034648iset_a @ SV230 @ SV310 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV310 @ SV6 ) @ ( SV310 @ SV125 ) ) @ SV230 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1326]) ).
thf(1429,plain,
! [SV311: a > product_prod_a_a,SV231: set_Pr1948701895od_a_a,SV126: a,SV7: a] :
( ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV7 @ SV126 ) @ ( inv_im777352425_a_a_a @ SV231 @ SV311 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( SV311 @ SV7 ) @ ( SV311 @ SV126 ) ) @ SV231 ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV7 @ SV126 ) @ ( inv_im777352425_a_a_a @ SV231 @ SV311 ) )
| ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( SV311 @ SV7 ) @ ( SV311 @ SV126 ) ) @ SV231 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1327]) ).
thf(1430,plain,
! [SV312: product_prod_a_a > a,SV232: set_Product_prod_a_a,SV127: product_prod_a_a,SV8: product_prod_a_a] :
( ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV8 @ SV127 ) @ ( inv_im15016955od_a_a @ SV232 @ SV312 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV312 @ SV8 ) @ ( SV312 @ SV127 ) ) @ SV232 ) )
= $false )
| ( ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV8 @ SV127 ) @ ( inv_im15016955od_a_a @ SV232 @ SV312 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV312 @ SV8 ) @ ( SV312 @ SV127 ) ) @ SV232 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1328]) ).
thf(1431,plain,
! [SV313: a > multis599418605od_a_a,SV233: set_Pr1821581383od_a_a,SV128: a,SV9: a] :
( ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV128 ) @ ( inv_im1681759523_a_a_a @ SV233 @ SV313 ) )
| ( member1349055120od_a_a @ ( produc1859144151od_a_a @ ( SV313 @ SV9 ) @ ( SV313 @ SV128 ) ) @ SV233 ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV128 ) @ ( inv_im1681759523_a_a_a @ SV233 @ SV313 ) )
| ~ ( member1349055120od_a_a @ ( produc1859144151od_a_a @ ( SV313 @ SV9 ) @ ( SV313 @ SV128 ) ) @ SV233 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1329]) ).
thf(1432,plain,
! [SV314: multis599418605od_a_a > a,SV234: set_Product_prod_a_a,SV129: multis599418605od_a_a,SV10: multis599418605od_a_a] :
( ( ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ SV10 @ SV129 ) @ ( inv_im941243329od_a_a @ SV234 @ SV314 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV314 @ SV10 ) @ ( SV314 @ SV129 ) ) @ SV234 ) )
= $false )
| ( ( ~ ( ~ ( member1349055120od_a_a @ ( produc1859144151od_a_a @ SV10 @ SV129 ) @ ( inv_im941243329od_a_a @ SV234 @ SV314 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV314 @ SV10 ) @ ( SV314 @ SV129 ) ) @ SV234 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1330]) ).
thf(1433,plain,
! [SV237: a,SV133: a,SV14: a > a > $o] :
( ( ( produc1833107820_a_a_o @ SV14 @ ( product_Pair_a_a @ SV133 @ SV237 ) )
= $false )
| ( ( ~ ( ~ ( produc1833107820_a_a_o @ SV14 @ ( product_Pair_a_a @ SV133 @ SV237 ) )
| ~ ( SV14 @ SV133 @ SV237 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1331]) ).
thf(1434,plain,
! [SV237: a,SV133: a,SV14: a > a > $o] :
( ( ( SV14 @ SV133 @ SV237 )
= $false )
| ( ( ~ ( ~ ( produc1833107820_a_a_o @ SV14 @ ( product_Pair_a_a @ SV133 @ SV237 ) )
| ~ ( SV14 @ SV133 @ SV237 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1331]) ).
thf(1435,plain,
! [SV134: set_Product_prod_a_a] :
( ( ( ~ ( irrefl_a @ SV134 )
| ~ ! [SY751: a] :
~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY751 @ SY751 ) @ SV134 ) )
= $false )
| ( ( irrefl_a @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1332]) ).
thf(1436,plain,
! [SV134: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK34_SY751 @ SV134 ) @ ( sK34_SY751 @ SV134 ) ) @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( irrefl_a @ SV134 )
| ~ ! [SY751: a] :
~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY751 @ SY751 ) @ SV134 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1333]) ).
thf(1437,plain,
! [SV238: set_Product_prod_a_a,SV135: a,SV16: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV16 @ SV135 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV238 ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV16 @ SV135 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV238 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV135 @ SV16 ) @ SV238 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1334]) ).
thf(1438,plain,
! [SV238: set_Product_prod_a_a,SV16: a,SV135: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV135 @ SV16 ) @ SV238 )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV16 @ SV135 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV238 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV135 @ SV16 ) @ SV238 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1334]) ).
thf(1439,plain,
! [SV136: product_prod_a_a] :
( ( ( ~ ( top_to1483957574_a_a_o @ SV136 )
| ~ ( member449909584od_a_a @ SV136 @ top_to398455383od_a_a ) )
= $false )
| ( ( top_to1483957574_a_a_o @ SV136 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1335]) ).
thf(1440,plain,
! [SV136: product_prod_a_a] :
( ( ( ~ ( top_to1483957574_a_a_o @ SV136 )
| ~ ( member449909584od_a_a @ SV136 @ top_to398455383od_a_a ) )
= $false )
| ( ( member449909584od_a_a @ SV136 @ top_to398455383od_a_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1336]) ).
thf(1441,plain,
! [SV240: multis599418605od_a_a,SV141: multis599418605od_a_a,SV25: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ ( plus_p404985124od_a_a @ SV141 @ SV240 ) ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ ( plus_p404985124od_a_a @ SV141 @ SV240 ) ) )
| ~ ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV141 ) )
| ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV240 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1337]) ).
thf(1442,plain,
! [SV240: multis599418605od_a_a,SV141: multis599418605od_a_a,SV25: product_prod_a_a] :
( ( ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV141 ) )
| ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV240 ) ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ ( plus_p404985124od_a_a @ SV141 @ SV240 ) ) )
| ~ ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV141 ) )
| ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV240 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1337]) ).
thf(1443,plain,
! [SV316: a,SV143: a,SV242: a,SV28: a] :
( ( ( ( SV28 != SV242 )
| ( SV143 != SV316 ) )
= $false )
| ( ( ( product_Pair_a_a @ SV28 @ SV143 )
= ( product_Pair_a_a @ SV242 @ SV316 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1338]) ).
thf(1444,plain,
! [SV144: produc1572603623od_a_a,SV29: produc1572603623od_a_a > $o] :
( ( ( SV29 @ ( produc1474507607od_a_a @ ( sK9_SY474 @ SV144 @ SV29 ) @ ( product_Pair_a_a @ ( sK19_SY1025 @ SV144 @ SV29 ) @ ( sK35_SY1037 @ SV144 @ SV29 ) ) ) )
= $false )
| ( ( SV29 @ SV144 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1339]) ).
thf(1445,plain,
! [SV32: set_Product_prod_a_a,SV147: set_Pr1948701895od_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK10_SY764 @ SV147 @ SV32 ) @ SV32 ) )
= $false )
| ( ( total_1490170027od_a_a @ SV32 @ SV147 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1340]) ).
thf(1446,plain,
! [SV147: set_Pr1948701895od_a_a,SV32: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK20_SY1027 @ SV32 @ SV147 ) @ SV32 )
| ~ ( ( ( sK10_SY764 @ SV147 @ SV32 )
!= ( sK20_SY1027 @ SV32 @ SV147 ) ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK10_SY764 @ SV147 @ SV32 ) @ ( sK20_SY1027 @ SV32 @ SV147 ) ) @ SV147 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK20_SY1027 @ SV32 @ SV147 ) @ ( sK10_SY764 @ SV147 @ SV32 ) ) @ SV147 ) )
= $false )
| ( ( total_1490170027od_a_a @ SV32 @ SV147 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1340]) ).
thf(1447,plain,
! [SV148: a,SV33: a > $o,SV317: a,SV245: a > $o] :
( ( ( ~ ( SV245 @ SV317 ) )
= $true )
| ( ( ~ ( ~ ( SV33 @ ( product_fst_a_a @ ( product_Pair_a_a @ SV148 @ SV317 ) ) )
| ~ ( SV245 @ ( product_snd_a_a @ ( product_Pair_a_a @ SV148 @ SV317 ) ) ) ) )
= $true )
| ( ( SV33 @ SV148 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1341]) ).
thf(1448,plain,
! [SV357: a > set_Product_prod_a_a,SV318: a,SV246: a,SV149: a,SV34: a > $o] :
( ( ( SV34 @ SV149 )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV246 @ SV318 ) @ ( SV357 @ SV149 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV149 @ SV246 ) @ ( product_Pair_a_a @ SV149 @ SV318 ) ) @ ( same_fst_a_a @ SV34 @ SV357 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1342]) ).
thf(1449,plain,
! [SV35: product_prod_a_a,SV150: multis599418605od_a_a] :
( ( ( SV150
= ( add_ms1725977093od_a_a @ SV35 @ ( sK21_SY771 @ SV35 @ SV150 ) ) )
= $true )
| ( ( member449909584od_a_a @ SV35 @ ( set_ms1818337124od_a_a @ SV150 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1343]) ).
thf(1450,plain,
! [SV151: set_Product_prod_a_a > $o,SV36: set_Product_prod_a_a] :
( ( ( ~ ! [SY1038: a,SY1039: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1038 @ SY1039 ) @ ( sK36_SY772 @ SV36 @ SV151 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1039 @ SY1038 ) @ ( sK36_SY772 @ SV36 @ SV151 ) ) )
| ( SV151 @ ( sK36_SY772 @ SV36 @ SV151 ) ) )
= $false )
| ( ( SV151 @ SV36 )
= $true )
| ( ( asym_a @ SV36 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1344]) ).
thf(1451,plain,
! [SV37: set_Product_prod_a_a,SV152: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK11_SY775 @ SV152 @ SV37 ) @ ( sK22_SY1028 @ SV37 @ SV152 ) ) @ SV37 ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV37 @ SV152 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1345]) ).
thf(1452,plain,
! [SV37: set_Product_prod_a_a,SV152: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK11_SY775 @ SV152 @ SV37 ) @ ( sK22_SY1028 @ SV37 @ SV152 ) ) @ SV152 )
= $false )
| ( ( ord_le1824328871od_a_a @ SV37 @ SV152 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1345]) ).
thf(1453,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a] :
( ( ( ( total_1490170027od_a_a @ SV154 @ SV320 )
| ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) )
= $false )
| ( ( ~ ( ~ ( total_1490170027od_a_a @ SV154 @ SV320 )
| ~ ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1347]) ).
thf(1454,plain,
! [SV155: product_prod_a_a,SV40: a] :
( ( ( ( SV40
!= ( product_fst_a_a @ SV155 ) )
| ~ ~ ! [SY782: a] :
( SV155
!= ( product_Pair_a_a @ SV40 @ SY782 ) ) )
= $false )
| ( ( SV40
= ( product_fst_a_a @ SV155 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1348]) ).
thf(1455,plain,
! [SV40: a,SV155: product_prod_a_a] :
( ( ( ! [SY782: a] :
( SV155
!= ( product_Pair_a_a @ SV40 @ SY782 ) ) )
= $true )
| ( ( ~ ( ( SV40
!= ( product_fst_a_a @ SV155 ) )
| ~ ~ ! [SY782: a] :
( SV155
!= ( product_Pair_a_a @ SV40 @ SY782 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1349]) ).
thf(1456,plain,
! [SV321: a,SV41: set_Product_prod_a_a,SV249: a,SV156: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV156 @ SV249 ) @ SV41 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV249 @ SV321 ) @ SV41 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV156 @ SV321 ) @ SV41 ) )
= $true )
| ( ( trans_a @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1350]) ).
thf(1457,plain,
! [SV42: set_Product_prod_a_a,SV157: set_Pr1948701895od_a_a,SV322: product_prod_a_a,SV250: product_prod_a_a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV250 @ SV322 ) @ SV157 ) )
= $true )
| ( ( member449909584od_a_a @ SV250 @ SV42 )
= $true )
| ( ( prefer1338892073od_a_a @ SV42 @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1351]) ).
thf(1458,plain,
! [SV43: a > a > $o,SV251: a,SV158: a,SV323: product_prod_a_a] :
( ( ( SV323
!= ( product_Pair_a_a @ SV158 @ SV251 ) )
= $true )
| ( ( SV43 @ ( product_fst_a_a @ SV323 ) @ ( product_snd_a_a @ SV323 ) )
= $true )
| ( ( SV43 @ SV158 @ SV251 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1352]) ).
thf(1459,plain,
! [SV324: a,SV252: a,SV159: a,SV44: a] :
( ( ( ( ( product_Pair_a_a @ SV44 @ SV159 )
= ( product_Pair_a_a @ SV252 @ SV324 ) )
| ~ ( ( SV44 != SV252 )
| ( SV159 != SV324 ) ) )
= $false )
| ( ( ~ ( ( ( product_Pair_a_a @ SV44 @ SV159 )
!= ( product_Pair_a_a @ SV252 @ SV324 ) )
| ~ ~ ( ( SV44 != SV252 )
| ( SV159 != SV324 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1353]) ).
thf(1460,plain,
! [SV325: a,SV45: set_Product_prod_a_a,SV253: a,SV160: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV160 @ SV253 ) @ SV45 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV253 @ SV325 ) @ SV45 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV160 @ SV325 ) @ SV45 ) )
= $true )
| ( ( trans_a @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1354]) ).
thf(1461,plain,
! [SV46: set_a,SV161: a > product_prod_a_a,SV254: set_Product_prod_a_a] :
( ( ( ~ ( member_a @ ( sK23_SY945 @ SV254 @ SV161 @ SV46 ) @ SV46 ) )
= $false )
| ( ( ord_le1824328871od_a_a @ ( image_1725938350od_a_a @ SV161 @ SV46 ) @ SV254 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1355]) ).
thf(1462,plain,
! [SV46: set_a,SV254: set_Product_prod_a_a,SV161: a > product_prod_a_a] :
( ( ( member449909584od_a_a @ ( SV161 @ ( sK23_SY945 @ SV254 @ SV161 @ SV46 ) ) @ SV254 )
= $false )
| ( ( ord_le1824328871od_a_a @ ( image_1725938350od_a_a @ SV161 @ SV46 ) @ SV254 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1355]) ).
thf(1463,plain,
! [SV162: set_Pr1948701895od_a_a,SV47: set_Product_prod_a_a,SV358: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV358 @ SV47 )
= $false )
| ( ( ! [SY1029: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1029 @ SV47 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV358 @ SY1029 ) @ SV162 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1029 @ SV358 ) @ SV162 ) ) )
= $true )
| ( ( prefer697821563od_a_a @ SV47 @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1356]) ).
thf(1464,plain,
! [SV48: set_a,SV163: set_Product_prod_a_a] :
( ( ( ~ ( member_a @ ( sK12_SY797 @ SV163 @ SV48 ) @ SV48 ) )
= $false )
| ( ( total_on_a @ SV48 @ SV163 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1357]) ).
thf(1465,plain,
! [SV163: set_Product_prod_a_a,SV48: set_a] :
( ( ( ~ ( member_a @ ( sK24_SY1030 @ SV48 @ SV163 ) @ SV48 )
| ~ ( ( ( sK12_SY797 @ SV163 @ SV48 )
!= ( sK24_SY1030 @ SV48 @ SV163 ) ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK12_SY797 @ SV163 @ SV48 ) @ ( sK24_SY1030 @ SV48 @ SV163 ) ) @ SV163 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK24_SY1030 @ SV48 @ SV163 ) @ ( sK12_SY797 @ SV163 @ SV48 ) ) @ SV163 ) )
= $false )
| ( ( total_on_a @ SV48 @ SV163 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1357]) ).
thf(1466,plain,
! [SV50: product_prod_a_a] :
( ( SV50
= ( product_Pair_a_a @ ( sK1_SY535 @ SV50 ) @ ( sK25_SY947 @ SV50 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1359]) ).
thf(1467,plain,
! [SV165: set_Pr1948701895od_a_a,SV51: set_Product_prod_a_a,SV256: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV256 @ SV51 )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV256 @ SV256 ) @ SV165 )
= $true )
| ( ( refl_o1298442278od_a_a @ SV51 @ SV165 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1360]) ).
thf(1468,plain,
! [SV366: set_Product_prod_a_a,SV359: set_Product_prod_a_a,SV327: a,SV257: a,SV166: a,SV52: a] :
( ( ~ ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SV257 @ SV327 ) ) @ ( lex_prod_a_a @ SV359 @ SV366 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
| ~ ( ( SV52 != SV257 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 ) ) )
| ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SV257 @ SV327 ) ) @ ( lex_prod_a_a @ SV359 @ SV366 ) )
| ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
| ~ ( ( SV52 != SV257 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1361]) ).
thf(1469,plain,
! [SV366: set_Product_prod_a_a,SV359: set_Product_prod_a_a,SV327: a,SV257: a,SV166: a,SV52: a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SV257 @ SV327 ) ) @ ( lex_prod_a_a @ SV359 @ SV366 ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
| ~ ( ( SV52 != SV257 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[1361]) ).
thf(1470,plain,
! [SV53: set_Product_prod_a_a,SV167: set_Pr1948701895od_a_a,SV328: product_prod_a_a,SV258: product_prod_a_a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV258 @ SV328 ) @ SV167 ) )
= $true )
| ( ( member449909584od_a_a @ SV328 @ SV53 )
= $true )
| ( ( refl_o1298442278od_a_a @ SV53 @ SV167 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1362]) ).
thf(1471,plain,
! [SV168: set_Product_prod_a_a,SV54: set_a,SV259: a] :
( ( ( member_a @ SV259 @ SV54 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV259 @ SV259 ) @ SV168 )
= $true )
| ( ( refl_on_a @ SV54 @ SV168 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1363]) ).
thf(1472,plain,
! [SV330: a,SV261: a,SV170: a,SV56: a] :
( ( ( ( ( product_Pair_a_a @ SV56 @ SV170 )
= ( product_Pair_a_a @ SV261 @ SV330 ) )
| ~ ( ( SV56 != SV261 )
| ( SV170 != SV330 ) ) )
= $false )
| ( ( ~ ( ( ( product_Pair_a_a @ SV56 @ SV170 )
!= ( product_Pair_a_a @ SV261 @ SV330 ) )
| ~ ~ ( ( SV56 != SV261 )
| ( SV170 != SV330 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1365]) ).
thf(1473,plain,
! [SV262: a,SV171: a,SV57: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV171 ) @ relation ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV171 @ SV57 ) @ relation ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV171 @ SV262 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV262 @ SV171 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV262 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV262 @ SV57 ) @ relation ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1366]) ).
thf(1474,plain,
! [SV58: set_a,SV172: set_Product_prod_a_a,SV331: a,SV263: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV263 @ SV331 ) @ SV172 ) )
= $true )
| ( ( ~ ( ~ ( member_a @ SV263 @ SV58 )
| ~ ( member_a @ SV331 @ SV58 ) ) )
= $true )
| ( ( refl_on_a @ SV58 @ SV172 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1367]) ).
thf(1475,plain,
! [SV332: set_Product_prod_a_a,SV264: a > a,SV173: a > a,SV59: product_prod_a_a] :
( ( ( ! [SY1009: a,SY1010: a] :
( ( SV59
!= ( product_Pair_a_a @ ( SV173 @ SY1009 ) @ ( SV264 @ SY1010 ) ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1009 @ SY1010 ) @ SV332 ) ) )
= $false )
| ( ( member449909584od_a_a @ SV59 @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SV173 @ SV264 ) @ SV332 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1368]) ).
thf(1476,plain,
! [SV174: set_Pr1948701895od_a_a,SV333: product_prod_a_a,SV60: set_Product_prod_a_a,SV265: product_prod_a_a] :
( ( ( ~ ~ ( ~ ( member449909584od_a_a @ SV265 @ SV60 )
| ~ ( member449909584od_a_a @ SV333 @ SV60 ) ) )
= $true )
| ( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) )
= ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
| ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) ) ) )
= $true )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1369]) ).
thf(1477,plain,
! [SV175: set_Product_prod_a_a,SV334: a,SV61: set_a,SV266: a] :
( ( ( ~ ~ ( ~ ( member_a @ SV266 @ SV61 )
| ~ ( member_a @ SV334 @ SV61 ) ) )
= $true )
| ( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) ) ) )
= $true )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1370]) ).
thf(1478,plain,
! [SV63: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK4_SY574 @ SV63 ) @ ( sK14_SY1011 @ SV63 ) ) @ SV63 )
= $true )
| ( ( asym_a @ SV63 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1372]) ).
thf(1479,plain,
! [SV63: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK14_SY1011 @ SV63 ) @ ( sK4_SY574 @ SV63 ) ) @ SV63 )
= $true )
| ( ( asym_a @ SV63 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1373]) ).
thf(1480,plain,
! [SV64: set_Product_prod_a_a,SV267: a,SV177: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV177 @ SV267 ) @ SV64 )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV267 @ SV177 ) @ SV64 ) )
= $true )
| ( ( asym_a @ SV64 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1374]) ).
thf(1481,plain,
! [SV335: a,SV66: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV66 @ SV335 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV335 @ SV66 ) @ relation )
= $true )
| ( ( member_a @ SV335 @ carrier )
= $false )
| ( ( member_a @ SV66 @ carrier )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1375]) ).
thf(1482,plain,
! [SV67: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK5_SY581 @ SV67 ) @ ( sK15_SY1012 @ SV67 ) ) @ SV67 ) )
= $false )
| ( ( trans_a @ SV67 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1376]) ).
thf(1483,plain,
! [SV67: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK15_SY1012 @ SV67 ) @ ( sK27_SY1033 @ SV67 ) ) @ SV67 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK5_SY581 @ SV67 ) @ ( sK27_SY1033 @ SV67 ) ) @ SV67 ) )
= $false )
| ( ( trans_a @ SV67 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1376]) ).
thf(1484,plain,
! [SV179: set_Product_prod_a_a] :
( ( ( ~ ( trans_a @ SV179 )
| ~ ! [SY828: a,SY829: a,SY830: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY829 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY829 @ SY830 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY830 ) @ SV179 ) ) )
= $false )
| ( ( trans_a @ SV179 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1377]) ).
thf(1485,plain,
! [SV179: set_Product_prod_a_a] :
( ( ( ! [SY1040: a,SY1041: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK37_SY828 @ SV179 ) @ SY1040 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1040 @ SY1041 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK37_SY828 @ SV179 ) @ SY1041 ) @ SV179 ) ) )
= $false )
| ( ( ~ ( ~ ( trans_a @ SV179 )
| ~ ! [SY828: a,SY829: a,SY830: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY829 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY829 @ SY830 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY830 ) @ SV179 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1378]) ).
thf(1486,plain,
! [SV360: a,SV336: a,SV272: a,SV184: set_Product_prod_a_a,SV74: set_a] :
( ( ( prefer719835986ence_a @ SV74 @ SV184 )
= $false )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV336 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV272 ) @ SV184 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV360 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV336 ) @ SV184 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV360 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV272 ) @ SV184 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1380]) ).
thf(1487,plain,
! [SV186: product_prod_a_a > a,SV76: a,SV337: set_Product_prod_a_a,SV274: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV274 @ SV337 ) )
= $true )
| ( ( member_a @ SV76 @ ( image_340790172_a_a_a @ SV186 @ SV337 ) )
= $true )
| ( ( SV76
= ( SV186 @ SV274 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1381]) ).
thf(1488,plain,
! [SV81: set_a,SV190: set_Product_prod_a_a,SV338: a,SV278: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV338 ) @ SV190 ) )
= $true )
| ( ( member_a @ SV278 @ SV81 )
= $true )
| ( ( prefer1292084992ence_a @ SV81 @ SV190 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1382]) ).
thf(1489,plain,
! [SV191: set_Product_prod_a_a,SV82: product_prod_a_a,SV339: product_prod_a_a > product_prod_a_a,SV279: product_prod_a_a] :
( ( ( SV279
!= ( SV339 @ SV82 ) )
= $true )
| ( ( member449909584od_a_a @ SV279 @ ( image_794773445od_a_a @ SV339 @ SV191 ) )
= $true )
| ( ( member449909584od_a_a @ SV82 @ SV191 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1383]) ).
thf(1490,plain,
! [SV83: set_a,SV192: set_Product_prod_a_a,SV340: a,SV280: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV280 @ SV340 ) @ SV192 ) )
= $true )
| ( ( member_a @ SV280 @ SV83 )
= $true )
| ( ( refl_on_a @ SV83 @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1384]) ).
thf(1491,plain,
! [SV193: set_a,SV84: a,SV341: a > product_prod_a_a,SV281: product_prod_a_a] :
( ( ( SV281
!= ( SV341 @ SV84 ) )
= $true )
| ( ( member449909584od_a_a @ SV281 @ ( image_1725938350od_a_a @ SV341 @ SV193 ) )
= $true )
| ( ( member_a @ SV84 @ SV193 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1385]) ).
thf(1492,plain,
! [SV85: set_Product_prod_a_a,SV361: a,SV342: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV342 @ SV361 ) @ SV85 )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV361 @ SV342 ) @ SV85 ) )
= $true )
| ( ( asym_a @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1386]) ).
thf(1493,plain,
! [SV86: set_Product_prod_a_a,SV194: product_prod_a_a > a,SV282: set_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK28_SY969 @ SV282 @ SV194 @ SV86 ) @ SV86 ) )
= $false )
| ( ( ord_less_eq_set_a @ ( image_340790172_a_a_a @ SV194 @ SV86 ) @ SV282 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1387]) ).
thf(1494,plain,
! [SV86: set_Product_prod_a_a,SV282: set_a,SV194: product_prod_a_a > a] :
( ( ( member_a @ ( SV194 @ ( sK28_SY969 @ SV282 @ SV194 @ SV86 ) ) @ SV282 )
= $false )
| ( ( ord_less_eq_set_a @ ( image_340790172_a_a_a @ SV194 @ SV86 ) @ SV282 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1387]) ).
thf(1495,plain,
! [SV196: a,SV88: a] :
( ( ( member_a @ SV88 @ carrier )
= $false )
| ( ( ~ ( member_a @ SV196 @ carrier ) )
= $true )
| ( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1388]) ).
thf(1496,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a] :
( ( ( ( total_on_a @ SV197 @ SV343 )
| ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) )
= $false )
| ( ( ~ ( ~ ( total_on_a @ SV197 @ SV343 )
| ~ ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1389]) ).
thf(1497,plain,
! [SV198: set_Product_prod_a_a] :
( ( ( ~ ( asym_a @ SV198 )
| ~ ~ ! [SY857: set_Product_prod_a_a] :
~ ~ ( ( SV198 != SY857 )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SY857 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SY857 ) ) ) )
= $false )
| ( ( asym_a @ SV198 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1390]) ).
thf(1498,plain,
! [SV198: set_Product_prod_a_a] :
( ( ( ! [SY857: set_Product_prod_a_a] :
~ ~ ( ( SV198 != SY857 )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SY857 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SY857 ) ) ) )
= $true )
| ( ( ~ ( ~ ( asym_a @ SV198 )
| ~ ~ ! [SY857: set_Product_prod_a_a] :
~ ~ ( ( SV198 != SY857 )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SY857 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SY857 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1391]) ).
thf(1499,plain,
! [SV199: set_Product_prod_a_a] :
( ( ( ~ ( asym_a @ SV199 )
| ~ ! [SY860: a,SY861: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY860 @ SY861 ) @ SV199 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY861 @ SY860 ) @ SV199 ) ) )
= $false )
| ( ( asym_a @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1392]) ).
thf(1500,plain,
! [SV199: set_Product_prod_a_a] :
( ( ( ! [SY1042: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK38_SY860 @ SV199 ) @ SY1042 ) @ SV199 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1042 @ ( sK38_SY860 @ SV199 ) ) @ SV199 ) ) )
= $false )
| ( ( ~ ( ~ ( asym_a @ SV199 )
| ~ ! [SY860: a,SY861: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY860 @ SY861 ) @ SV199 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY861 @ SY860 ) @ SV199 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1393]) ).
thf(1501,plain,
! [SV344: multis599418605od_a_a,SV200: multis599418605od_a_a,SV285: product_prod_a_a,SV92: product_prod_a_a] :
( ( ( ~ ( ( SV92 != SV285 ) ) )
= $true )
| ( ( member449909584od_a_a @ SV285 @ ( set_ms1818337124od_a_a @ SV200 ) )
= $true )
| ( ( ( add_ms1725977093od_a_a @ SV92 @ SV200 )
= ( add_ms1725977093od_a_a @ SV285 @ SV344 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1394]) ).
thf(1502,plain,
! [SV362: a,SV345: a,SV286: a,SV201: set_Product_prod_a_a,SV93: set_a] :
( ( ( prefer1292084992ence_a @ SV93 @ SV201 )
= $false )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SV345 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV286 ) @ SV201 ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV362 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV362 @ SV345 ) @ SV201 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SV362 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV362 @ SV286 ) @ SV201 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1395]) ).
thf(1503,plain,
! [SV95: multis599418605od_a_a,SV203: a > a > set_mu1281098573od_a_a,SV288: product_prod_a_a] :
( ( ( ! [SY1043: a] :
( ( SV288
!= ( product_Pair_a_a @ ( sK39_SY976 @ SV203 @ SV95 @ SV288 ) @ SY1043 ) )
| ~ ( member1755255446od_a_a @ SV95 @ ( SV203 @ ( sK39_SY976 @ SV203 @ SV95 @ SV288 ) @ SY1043 ) ) ) )
= $false )
| ( ( member1755255446od_a_a @ SV95 @ ( produc1121147169od_a_a @ SV203 @ SV288 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1397]) ).
thf(1504,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( ( prefer1292084992ence_a @ SV204 @ SV347 )
| ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) )
= $false )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 )
| ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1398]) ).
thf(1505,plain,
! [SV97: product_prod_a_a,SV205: multis599418605od_a_a] :
( ( ( SV205
= ( add_ms1725977093od_a_a @ SV97 @ ( sK29_SY877 @ SV97 @ SV205 ) ) )
= $true )
| ( ( member449909584od_a_a @ SV97 @ ( set_ms1818337124od_a_a @ SV205 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1399]) ).
thf(1506,plain,
! [SV98: multiset_a,SV206: a > a > set_multiset_a,SV290: product_prod_a_a] :
( ( ( ! [SY1044: a] :
( ( SV290
!= ( product_Pair_a_a @ ( sK40_SY982 @ SV206 @ SV98 @ SV290 ) @ SY1044 ) )
| ~ ( member_multiset_a @ SV98 @ ( SV206 @ ( sK40_SY982 @ SV206 @ SV98 @ SV290 ) @ SY1044 ) ) ) )
= $false )
| ( ( member_multiset_a @ SV98 @ ( produc1828150264iset_a @ SV206 @ SV290 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1400]) ).
thf(1507,plain,
! [SV100: set_Product_prod_a_a,SV207: set_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK17_SY881 @ SV207 @ SV100 ) @ ( sK30_SY1034 @ SV100 @ SV207 ) ) @ SV100 ) )
= $false )
| ( ( ~ ! [SY883: a,SY884: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY883 @ SY884 ) @ SV100 )
| ( member_a @ SY884 @ SV207 ) )
| ~ ( order_preorder_on_a @ SV207 @ SV100 )
| ( prefer1292084992ence_a @ SV207 @ SV100 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1401]) ).
thf(1508,plain,
! [SV100: set_Product_prod_a_a,SV207: set_a] :
( ( ( member_a @ ( sK17_SY881 @ SV207 @ SV100 ) @ SV207 )
= $false )
| ( ( ~ ! [SY883: a,SY884: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY883 @ SY884 ) @ SV100 )
| ( member_a @ SY884 @ SV207 ) )
| ~ ( order_preorder_on_a @ SV207 @ SV100 )
| ( prefer1292084992ence_a @ SV207 @ SV100 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1401]) ).
thf(1509,plain,
! [SV291: a,SV208: a,SV101: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SV208 ) @ relation ) )
= $true )
| ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV101 ) @ relation ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV291 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV291 @ SV208 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SV291 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV291 @ SV101 ) @ relation ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1402]) ).
thf(1510,plain,
! [SV103: a,SV210: a > a > set_a,SV293: product_prod_a_a] :
( ( ( ! [SY1045: a] :
( ( SV293
!= ( product_Pair_a_a @ ( sK41_SY985 @ SV210 @ SV103 @ SV293 ) @ SY1045 ) )
| ~ ( member_a @ SV103 @ ( SV210 @ ( sK41_SY985 @ SV210 @ SV103 @ SV293 ) @ SY1045 ) ) ) )
= $false )
| ( ( member_a @ SV103 @ ( produc961951794_set_a @ SV210 @ SV293 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1403]) ).
thf(1511,plain,
! [SV105: set_Product_prod_a_a,SV212: set_Pr1948701895od_a_a,SV348: product_prod_a_a,SV294: product_prod_a_a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV294 @ SV348 ) @ SV212 ) )
= $true )
| ( ( member449909584od_a_a @ SV294 @ SV105 )
= $true )
| ( ( refl_o1298442278od_a_a @ SV105 @ SV212 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1405]) ).
thf(1512,plain,
! [SV106: set_Product_prod_a_a,SV213: set_Pr1948701895od_a_a,SV349: product_prod_a_a,SV295: product_prod_a_a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV295 @ SV349 ) @ SV213 ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ SV295 @ SV106 )
| ~ ( member449909584od_a_a @ SV349 @ SV106 ) ) )
= $true )
| ( ( refl_o1298442278od_a_a @ SV106 @ SV213 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1406]) ).
thf(1513,plain,
! [SV107: set_Product_prod_a_a,SV214: product_prod_a_a > product_prod_a_a,SV296: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK32_SY989 @ SV296 @ SV214 @ SV107 ) @ SV107 ) )
= $false )
| ( ( ord_le1824328871od_a_a @ ( image_794773445od_a_a @ SV214 @ SV107 ) @ SV296 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1407]) ).
thf(1514,plain,
! [SV107: set_Product_prod_a_a,SV296: set_Product_prod_a_a,SV214: product_prod_a_a > product_prod_a_a] :
( ( ( member449909584od_a_a @ ( SV214 @ ( sK32_SY989 @ SV296 @ SV214 @ SV107 ) ) @ SV296 )
= $false )
| ( ( ord_le1824328871od_a_a @ ( image_794773445od_a_a @ SV214 @ SV107 ) @ SV296 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1407]) ).
thf(1515,plain,
! [SV297: set_Product_prod_a_a,SV108: a,SV215: a,SV350: a] :
( ( ( SV350 != SV215 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV108 @ SV350 ) @ SV297 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV108 @ SV215 ) @ SV297 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1408]) ).
thf(1516,plain,
! [SV109: set_a,SV216: set_Product_prod_a_a,SV351: a,SV298: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV298 @ SV351 ) @ SV216 ) )
= $true )
| ( ( member_a @ SV351 @ SV109 )
= $true )
| ( ( refl_on_a @ SV109 @ SV216 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1409]) ).
thf(1517,plain,
! [SV217: a > product_prod_a_a,SV110: product_prod_a_a,SV352: set_a,SV299: a] :
( ( ( ~ ( member_a @ SV299 @ SV352 ) )
= $true )
| ( ( member449909584od_a_a @ SV110 @ ( image_1725938350od_a_a @ SV217 @ SV352 ) )
= $true )
| ( ( SV110
= ( SV217 @ SV299 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1410]) ).
thf(1518,plain,
! [SV363: a > a,SV353: a > a,SV300: set_Product_prod_a_a,SV218: a,SV111: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV111 @ SV218 ) @ SV300 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV353 @ SV111 ) @ ( SV363 @ SV218 ) ) @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SV353 @ SV363 ) @ SV300 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1411]) ).
thf(1519,plain,
! [SV219: product_prod_a_a,SV112: a] :
( ( ( ( SV112
!= ( product_snd_a_a @ SV219 ) )
| ~ ~ ! [SY907: a] :
( SV219
!= ( product_Pair_a_a @ SY907 @ SV112 ) ) )
= $false )
| ( ( SV112
= ( product_snd_a_a @ SV219 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1412]) ).
thf(1520,plain,
! [SV112: a,SV219: product_prod_a_a] :
( ( ( ! [SY907: a] :
( SV219
!= ( product_Pair_a_a @ SY907 @ SV112 ) ) )
= $true )
| ( ( ~ ( ( SV112
!= ( product_snd_a_a @ SV219 ) )
| ~ ~ ! [SY907: a] :
( SV219
!= ( product_Pair_a_a @ SY907 @ SV112 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1413]) ).
thf(1521,plain,
! [SV113: multis599418605od_a_a] :
( ( ( member449909584od_a_a @ ( sK33_SY708 @ SV113 ) @ ( set_ms1818337124od_a_a @ SV113 ) )
= $true )
| ( ( SV113 = zero_z160849828od_a_a )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1414]) ).
thf(1522,plain,
! [SV220: product_prod_a_a > product_prod_a_a,SV114: product_prod_a_a,SV354: set_Product_prod_a_a,SV301: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV301 @ SV354 ) )
= $true )
| ( ( member449909584od_a_a @ SV114 @ ( image_794773445od_a_a @ SV220 @ SV354 ) )
= $true )
| ( ( SV114
= ( SV220 @ SV301 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1415]) ).
thf(1523,plain,
! [SV115: produc1127127335iset_a,SV221: a > a > set_Pr158363655iset_a,SV302: product_prod_a_a] :
( ( ( ! [SY1046: a] :
( ( SV302
!= ( product_Pair_a_a @ ( sK42_SY996 @ SV221 @ SV115 @ SV302 ) @ SY1046 ) )
| ~ ( member340150864iset_a @ SV115 @ ( SV221 @ ( sK42_SY996 @ SV221 @ SV115 @ SV302 ) @ SY1046 ) ) ) )
= $false )
| ( ( member340150864iset_a @ SV115 @ ( produc93594587iset_a @ SV221 @ SV302 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1416]) ).
thf(1524,plain,
! [SV117: product_prod_a_a,SV223: multiset_a > multiset_a > set_Product_prod_a_a,SV304: produc1127127335iset_a] :
( ( ( ! [SY1047: multiset_a] :
( ( SV304
!= ( produc2037245207iset_a @ ( sK43_SY998 @ SV223 @ SV117 @ SV304 ) @ SY1047 ) )
| ~ ( member449909584od_a_a @ SV117 @ ( SV223 @ ( sK43_SY998 @ SV223 @ SV117 @ SV304 ) @ SY1047 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ SV117 @ ( produc2041367259od_a_a @ SV223 @ SV304 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1418]) ).
thf(1525,plain,
! [SV224: set_Product_prod_a_a,SV118: set_a,SV364: a] :
( ( ( member_a @ SV364 @ SV118 )
= $false )
| ( ( ! [SY1036: a] :
( ~ ( member_a @ SY1036 @ SV118 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV364 @ SY1036 ) @ SV224 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1036 @ SV364 ) @ SV224 ) ) )
= $true )
| ( ( prefer719835986ence_a @ SV118 @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1419]) ).
thf(1526,plain,
! [SV225: set_Product_prod_a_a,SV119: product_prod_a_a,SV355: product_prod_a_a > a,SV305: a] :
( ( ( SV305
!= ( SV355 @ SV119 ) )
= $true )
| ( ( member_a @ SV305 @ ( image_340790172_a_a_a @ SV355 @ SV225 ) )
= $true )
| ( ( member449909584od_a_a @ SV119 @ SV225 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1420]) ).
thf(1527,plain,
! [SV120: product_prod_a_a,SV226: a > a > set_Product_prod_a_a,SV306: product_prod_a_a] :
( ( ( ! [SY1048: a] :
( ( SV306
!= ( product_Pair_a_a @ ( sK44_SY1001 @ SV226 @ SV120 @ SV306 ) @ SY1048 ) )
| ~ ( member449909584od_a_a @ SV120 @ ( SV226 @ ( sK44_SY1001 @ SV226 @ SV120 @ SV306 ) @ SY1048 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ SV120 @ ( produc1093061851od_a_a @ SV226 @ SV306 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1421]) ).
thf(1528,plain,
! [SV121: product_prod_a_a > $o,SV1: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV1 @ ( collec645855634od_a_a @ SV121 ) ) )
= $false )
| ( ( member449909584od_a_a @ SV1 @ ( collec645855634od_a_a @ SV121 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1422]) ).
thf(1529,plain,
! [SV1: product_prod_a_a,SV121: product_prod_a_a > $o] :
( ( ( ~ ( SV121 @ SV1 ) )
= $false )
| ( ( member449909584od_a_a @ SV1 @ ( collec645855634od_a_a @ SV121 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1422]) ).
thf(1530,plain,
! [SV121: product_prod_a_a > $o,SV1: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV1 @ ( collec645855634od_a_a @ SV121 ) ) )
= $false )
| ( ( SV121 @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1423]) ).
thf(1531,plain,
! [SV1: product_prod_a_a,SV121: product_prod_a_a > $o] :
( ( ( ~ ( SV121 @ SV1 ) )
= $false )
| ( ( SV121 @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1423]) ).
thf(1532,plain,
! [SV365: a,SV307: a,SV122: product_prod_a_a > $o] :
( ( ( ~ ( ( product_curry_a_a_o @ SV122 @ SV307 @ SV365 )
| ( SV122 @ ( product_Pair_a_a @ SV307 @ SV365 ) ) ) )
= $true )
| ( ( ~ ( ~ ( product_curry_a_a_o @ SV122 @ SV307 @ SV365 )
| ~ ( SV122 @ ( product_Pair_a_a @ SV307 @ SV365 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1424]) ).
thf(1533,plain,
! [SV308: a > a,SV228: set_Product_prod_a_a,SV123: a,SV4: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV4 @ SV123 ) @ ( inv_image_a_a @ SV228 @ SV308 ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV4 @ SV123 ) @ ( inv_image_a_a @ SV228 @ SV308 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV308 @ SV4 ) @ ( SV308 @ SV123 ) ) @ SV228 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1426]) ).
thf(1534,plain,
! [SV228: set_Product_prod_a_a,SV123: a,SV4: a,SV308: a > a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV308 @ SV4 ) @ ( SV308 @ SV123 ) ) @ SV228 )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV4 @ SV123 ) @ ( inv_image_a_a @ SV228 @ SV308 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV308 @ SV4 ) @ ( SV308 @ SV123 ) ) @ SV228 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1426]) ).
thf(1535,plain,
! [SV309: a > multiset_a,SV229: set_Pr158363655iset_a,SV124: a,SV5: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV5 @ SV124 ) @ ( inv_im975322764et_a_a @ SV229 @ SV309 ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV5 @ SV124 ) @ ( inv_im975322764et_a_a @ SV229 @ SV309 ) )
| ~ ( member340150864iset_a @ ( produc2037245207iset_a @ ( SV309 @ SV5 ) @ ( SV309 @ SV124 ) ) @ SV229 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1427]) ).
thf(1536,plain,
! [SV229: set_Pr158363655iset_a,SV124: a,SV5: a,SV309: a > multiset_a] :
( ( ( member340150864iset_a @ ( produc2037245207iset_a @ ( SV309 @ SV5 ) @ ( SV309 @ SV124 ) ) @ SV229 )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV5 @ SV124 ) @ ( inv_im975322764et_a_a @ SV229 @ SV309 ) )
| ~ ( member340150864iset_a @ ( produc2037245207iset_a @ ( SV309 @ SV5 ) @ ( SV309 @ SV124 ) ) @ SV229 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1427]) ).
thf(1537,plain,
! [SV310: multiset_a > a,SV230: set_Product_prod_a_a,SV125: multiset_a,SV6: multiset_a] :
( ( ( member340150864iset_a @ ( produc2037245207iset_a @ SV6 @ SV125 ) @ ( inv_im479034648iset_a @ SV230 @ SV310 ) )
= $false )
| ( ( ~ ( ~ ( member340150864iset_a @ ( produc2037245207iset_a @ SV6 @ SV125 ) @ ( inv_im479034648iset_a @ SV230 @ SV310 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV310 @ SV6 ) @ ( SV310 @ SV125 ) ) @ SV230 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1428]) ).
thf(1538,plain,
! [SV230: set_Product_prod_a_a,SV125: multiset_a,SV6: multiset_a,SV310: multiset_a > a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV310 @ SV6 ) @ ( SV310 @ SV125 ) ) @ SV230 )
= $false )
| ( ( ~ ( ~ ( member340150864iset_a @ ( produc2037245207iset_a @ SV6 @ SV125 ) @ ( inv_im479034648iset_a @ SV230 @ SV310 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV310 @ SV6 ) @ ( SV310 @ SV125 ) ) @ SV230 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1428]) ).
thf(1539,plain,
! [SV311: a > product_prod_a_a,SV231: set_Pr1948701895od_a_a,SV126: a,SV7: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV7 @ SV126 ) @ ( inv_im777352425_a_a_a @ SV231 @ SV311 ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV7 @ SV126 ) @ ( inv_im777352425_a_a_a @ SV231 @ SV311 ) )
| ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( SV311 @ SV7 ) @ ( SV311 @ SV126 ) ) @ SV231 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1429]) ).
thf(1540,plain,
! [SV231: set_Pr1948701895od_a_a,SV126: a,SV7: a,SV311: a > product_prod_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( SV311 @ SV7 ) @ ( SV311 @ SV126 ) ) @ SV231 )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV7 @ SV126 ) @ ( inv_im777352425_a_a_a @ SV231 @ SV311 ) )
| ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( SV311 @ SV7 ) @ ( SV311 @ SV126 ) ) @ SV231 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1429]) ).
thf(1541,plain,
! [SV312: product_prod_a_a > a,SV232: set_Product_prod_a_a,SV127: product_prod_a_a,SV8: product_prod_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV8 @ SV127 ) @ ( inv_im15016955od_a_a @ SV232 @ SV312 ) )
= $false )
| ( ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV8 @ SV127 ) @ ( inv_im15016955od_a_a @ SV232 @ SV312 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV312 @ SV8 ) @ ( SV312 @ SV127 ) ) @ SV232 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1430]) ).
thf(1542,plain,
! [SV232: set_Product_prod_a_a,SV127: product_prod_a_a,SV8: product_prod_a_a,SV312: product_prod_a_a > a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV312 @ SV8 ) @ ( SV312 @ SV127 ) ) @ SV232 )
= $false )
| ( ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV8 @ SV127 ) @ ( inv_im15016955od_a_a @ SV232 @ SV312 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV312 @ SV8 ) @ ( SV312 @ SV127 ) ) @ SV232 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1430]) ).
thf(1543,plain,
! [SV313: a > multis599418605od_a_a,SV233: set_Pr1821581383od_a_a,SV128: a,SV9: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV128 ) @ ( inv_im1681759523_a_a_a @ SV233 @ SV313 ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV128 ) @ ( inv_im1681759523_a_a_a @ SV233 @ SV313 ) )
| ~ ( member1349055120od_a_a @ ( produc1859144151od_a_a @ ( SV313 @ SV9 ) @ ( SV313 @ SV128 ) ) @ SV233 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1431]) ).
thf(1544,plain,
! [SV233: set_Pr1821581383od_a_a,SV128: a,SV9: a,SV313: a > multis599418605od_a_a] :
( ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ ( SV313 @ SV9 ) @ ( SV313 @ SV128 ) ) @ SV233 )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV128 ) @ ( inv_im1681759523_a_a_a @ SV233 @ SV313 ) )
| ~ ( member1349055120od_a_a @ ( produc1859144151od_a_a @ ( SV313 @ SV9 ) @ ( SV313 @ SV128 ) ) @ SV233 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1431]) ).
thf(1545,plain,
! [SV314: multis599418605od_a_a > a,SV234: set_Product_prod_a_a,SV129: multis599418605od_a_a,SV10: multis599418605od_a_a] :
( ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ SV10 @ SV129 ) @ ( inv_im941243329od_a_a @ SV234 @ SV314 ) )
= $false )
| ( ( ~ ( ~ ( member1349055120od_a_a @ ( produc1859144151od_a_a @ SV10 @ SV129 ) @ ( inv_im941243329od_a_a @ SV234 @ SV314 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV314 @ SV10 ) @ ( SV314 @ SV129 ) ) @ SV234 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1432]) ).
thf(1546,plain,
! [SV234: set_Product_prod_a_a,SV129: multis599418605od_a_a,SV10: multis599418605od_a_a,SV314: multis599418605od_a_a > a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV314 @ SV10 ) @ ( SV314 @ SV129 ) ) @ SV234 )
= $false )
| ( ( ~ ( ~ ( member1349055120od_a_a @ ( produc1859144151od_a_a @ SV10 @ SV129 ) @ ( inv_im941243329od_a_a @ SV234 @ SV314 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV314 @ SV10 ) @ ( SV314 @ SV129 ) ) @ SV234 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1432]) ).
thf(1547,plain,
! [SV237: a,SV133: a,SV14: a > a > $o] :
( ( ( ~ ( produc1833107820_a_a_o @ SV14 @ ( product_Pair_a_a @ SV133 @ SV237 ) )
| ~ ( SV14 @ SV133 @ SV237 ) )
= $false )
| ( ( produc1833107820_a_a_o @ SV14 @ ( product_Pair_a_a @ SV133 @ SV237 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1433]) ).
thf(1548,plain,
! [SV237: a,SV133: a,SV14: a > a > $o] :
( ( ( ~ ( produc1833107820_a_a_o @ SV14 @ ( product_Pair_a_a @ SV133 @ SV237 ) )
| ~ ( SV14 @ SV133 @ SV237 ) )
= $false )
| ( ( SV14 @ SV133 @ SV237 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1434]) ).
thf(1549,plain,
! [SV134: set_Product_prod_a_a] :
( ( ( ~ ( irrefl_a @ SV134 ) )
= $false )
| ( ( irrefl_a @ SV134 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1435]) ).
thf(1550,plain,
! [SV134: set_Product_prod_a_a] :
( ( ( ~ ! [SY751: a] :
~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY751 @ SY751 ) @ SV134 ) )
= $false )
| ( ( irrefl_a @ SV134 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1435]) ).
thf(1551,plain,
! [SV134: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK34_SY751 @ SV134 ) @ ( sK34_SY751 @ SV134 ) ) @ SV134 )
= $true )
| ( ( ~ ( ~ ( irrefl_a @ SV134 )
| ~ ! [SY751: a] :
~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY751 @ SY751 ) @ SV134 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1436]) ).
thf(1552,plain,
! [SV238: set_Product_prod_a_a,SV135: a,SV16: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV16 @ SV135 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV238 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV135 @ SV16 ) @ SV238 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV16 @ SV135 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV238 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1437]) ).
thf(1553,plain,
! [SV238: set_Product_prod_a_a,SV135: a,SV16: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV16 @ SV135 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV238 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV135 @ SV16 ) @ SV238 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV135 @ SV16 ) @ SV238 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1438]) ).
thf(1554,plain,
! [SV136: product_prod_a_a] :
( ( ( ~ ( top_to1483957574_a_a_o @ SV136 ) )
= $false )
| ( ( top_to1483957574_a_a_o @ SV136 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1439]) ).
thf(1555,plain,
! [SV136: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV136 @ top_to398455383od_a_a ) )
= $false )
| ( ( top_to1483957574_a_a_o @ SV136 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1439]) ).
thf(1556,plain,
! [SV136: product_prod_a_a] :
( ( ( ~ ( top_to1483957574_a_a_o @ SV136 ) )
= $false )
| ( ( member449909584od_a_a @ SV136 @ top_to398455383od_a_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1440]) ).
thf(1557,plain,
! [SV136: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV136 @ top_to398455383od_a_a ) )
= $false )
| ( ( member449909584od_a_a @ SV136 @ top_to398455383od_a_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1440]) ).
thf(1558,plain,
! [SV240: multis599418605od_a_a,SV141: multis599418605od_a_a,SV25: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ ( plus_p404985124od_a_a @ SV141 @ SV240 ) ) )
| ~ ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV141 ) )
| ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV240 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ ( plus_p404985124od_a_a @ SV141 @ SV240 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1441]) ).
thf(1559,plain,
! [SV240: multis599418605od_a_a,SV141: multis599418605od_a_a,SV25: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV141 ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ ( plus_p404985124od_a_a @ SV141 @ SV240 ) ) )
| ~ ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV141 ) )
| ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV240 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1442]) ).
thf(1560,plain,
! [SV141: multis599418605od_a_a,SV240: multis599418605od_a_a,SV25: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV240 ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ ( plus_p404985124od_a_a @ SV141 @ SV240 ) ) )
| ~ ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV141 ) )
| ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV240 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1442]) ).
thf(1561,plain,
! [SV316: a,SV143: a,SV242: a,SV28: a] :
( ( ( SV28 != SV242 )
= $false )
| ( ( ( product_Pair_a_a @ SV28 @ SV143 )
= ( product_Pair_a_a @ SV242 @ SV316 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1443]) ).
thf(1562,plain,
! [SV242: a,SV28: a,SV316: a,SV143: a] :
( ( ( SV143 != SV316 )
= $false )
| ( ( ( product_Pair_a_a @ SV28 @ SV143 )
= ( product_Pair_a_a @ SV242 @ SV316 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1443]) ).
thf(1563,plain,
! [SV32: set_Product_prod_a_a,SV147: set_Pr1948701895od_a_a] :
( ( ( member449909584od_a_a @ ( sK10_SY764 @ SV147 @ SV32 ) @ SV32 )
= $true )
| ( ( total_1490170027od_a_a @ SV32 @ SV147 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1445]) ).
thf(1564,plain,
! [SV147: set_Pr1948701895od_a_a,SV32: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK20_SY1027 @ SV32 @ SV147 ) @ SV32 ) )
= $false )
| ( ( total_1490170027od_a_a @ SV32 @ SV147 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1446]) ).
thf(1565,plain,
! [SV32: set_Product_prod_a_a,SV147: set_Pr1948701895od_a_a] :
( ( ( ~ ( ( ( sK10_SY764 @ SV147 @ SV32 )
!= ( sK20_SY1027 @ SV32 @ SV147 ) ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK10_SY764 @ SV147 @ SV32 ) @ ( sK20_SY1027 @ SV32 @ SV147 ) ) @ SV147 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK20_SY1027 @ SV32 @ SV147 ) @ ( sK10_SY764 @ SV147 @ SV32 ) ) @ SV147 ) )
= $false )
| ( ( total_1490170027od_a_a @ SV32 @ SV147 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1446]) ).
thf(1566,plain,
! [SV148: a,SV33: a > $o,SV317: a,SV245: a > $o] :
( ( ( SV245 @ SV317 )
= $false )
| ( ( ~ ( ~ ( SV33 @ ( product_fst_a_a @ ( product_Pair_a_a @ SV148 @ SV317 ) ) )
| ~ ( SV245 @ ( product_snd_a_a @ ( product_Pair_a_a @ SV148 @ SV317 ) ) ) ) )
= $true )
| ( ( SV33 @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1447]) ).
thf(1567,plain,
! [SV34: a > $o,SV149: a,SV357: a > set_Product_prod_a_a,SV318: a,SV246: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV246 @ SV318 ) @ ( SV357 @ SV149 ) ) )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV149 @ SV246 ) @ ( product_Pair_a_a @ SV149 @ SV318 ) ) @ ( same_fst_a_a @ SV34 @ SV357 ) )
= $true )
| ( ( SV34 @ SV149 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1448]) ).
thf(1568,plain,
! [SV151: set_Product_prod_a_a > $o,SV36: set_Product_prod_a_a] :
( ( ( ~ ! [SY1038: a,SY1039: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1038 @ SY1039 ) @ ( sK36_SY772 @ SV36 @ SV151 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1039 @ SY1038 ) @ ( sK36_SY772 @ SV36 @ SV151 ) ) ) )
= $false )
| ( ( SV151 @ SV36 )
= $true )
| ( ( asym_a @ SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1450]) ).
thf(1569,plain,
! [SV36: set_Product_prod_a_a,SV151: set_Product_prod_a_a > $o] :
( ( ( SV151 @ ( sK36_SY772 @ SV36 @ SV151 ) )
= $false )
| ( ( SV151 @ SV36 )
= $true )
| ( ( asym_a @ SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1450]) ).
thf(1570,plain,
! [SV37: set_Product_prod_a_a,SV152: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK11_SY775 @ SV152 @ SV37 ) @ ( sK22_SY1028 @ SV37 @ SV152 ) ) @ SV37 )
= $true )
| ( ( ord_le1824328871od_a_a @ SV37 @ SV152 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1451]) ).
thf(1571,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a] :
( ( ( total_1490170027od_a_a @ SV154 @ SV320 )
= $false )
| ( ( ~ ( ~ ( total_1490170027od_a_a @ SV154 @ SV320 )
| ~ ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1453]) ).
thf(1572,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a] :
( ( ( ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) )
= $false )
| ( ( ~ ( ~ ( total_1490170027od_a_a @ SV154 @ SV320 )
| ~ ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1453]) ).
thf(1573,plain,
! [SV155: product_prod_a_a,SV40: a] :
( ( ( SV40
!= ( product_fst_a_a @ SV155 ) )
= $false )
| ( ( SV40
= ( product_fst_a_a @ SV155 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1454]) ).
thf(1574,plain,
! [SV40: a,SV155: product_prod_a_a] :
( ( ( ~ ~ ! [SY782: a] :
( SV155
!= ( product_Pair_a_a @ SV40 @ SY782 ) ) )
= $false )
| ( ( SV40
= ( product_fst_a_a @ SV155 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1454]) ).
thf(1575,plain,
! [SV367: a,SV40: a,SV155: product_prod_a_a] :
( ( ( SV155
!= ( product_Pair_a_a @ SV40 @ SV367 ) )
= $true )
| ( ( ~ ( ( SV40
!= ( product_fst_a_a @ SV155 ) )
| ~ ~ ! [SY782: a] :
( SV155
!= ( product_Pair_a_a @ SV40 @ SY782 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1455]) ).
thf(1576,plain,
! [SV321: a,SV41: set_Product_prod_a_a,SV249: a,SV156: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV156 @ SV249 ) @ SV41 )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV249 @ SV321 ) @ SV41 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV156 @ SV321 ) @ SV41 ) )
= $true )
| ( ( trans_a @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1456]) ).
thf(1577,plain,
! [SV42: set_Product_prod_a_a,SV157: set_Pr1948701895od_a_a,SV322: product_prod_a_a,SV250: product_prod_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV250 @ SV322 ) @ SV157 )
= $false )
| ( ( member449909584od_a_a @ SV250 @ SV42 )
= $true )
| ( ( prefer1338892073od_a_a @ SV42 @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1457]) ).
thf(1578,plain,
! [SV43: a > a > $o,SV251: a,SV158: a,SV323: product_prod_a_a] :
( ( ( SV323
= ( product_Pair_a_a @ SV158 @ SV251 ) )
= $false )
| ( ( SV43 @ ( product_fst_a_a @ SV323 ) @ ( product_snd_a_a @ SV323 ) )
= $true )
| ( ( SV43 @ SV158 @ SV251 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1458]) ).
thf(1579,plain,
! [SV324: a,SV252: a,SV159: a,SV44: a] :
( ( ( ( product_Pair_a_a @ SV44 @ SV159 )
= ( product_Pair_a_a @ SV252 @ SV324 ) )
= $false )
| ( ( ~ ( ( ( product_Pair_a_a @ SV44 @ SV159 )
!= ( product_Pair_a_a @ SV252 @ SV324 ) )
| ~ ~ ( ( SV44 != SV252 )
| ( SV159 != SV324 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1459]) ).
thf(1580,plain,
! [SV324: a,SV159: a,SV252: a,SV44: a] :
( ( ( ~ ( ( SV44 != SV252 )
| ( SV159 != SV324 ) ) )
= $false )
| ( ( ~ ( ( ( product_Pair_a_a @ SV44 @ SV159 )
!= ( product_Pair_a_a @ SV252 @ SV324 ) )
| ~ ~ ( ( SV44 != SV252 )
| ( SV159 != SV324 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1459]) ).
thf(1581,plain,
! [SV325: a,SV45: set_Product_prod_a_a,SV253: a,SV160: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV160 @ SV253 ) @ SV45 )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV253 @ SV325 ) @ SV45 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV160 @ SV325 ) @ SV45 ) )
= $true )
| ( ( trans_a @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1460]) ).
thf(1582,plain,
! [SV46: set_a,SV161: a > product_prod_a_a,SV254: set_Product_prod_a_a] :
( ( ( member_a @ ( sK23_SY945 @ SV254 @ SV161 @ SV46 ) @ SV46 )
= $true )
| ( ( ord_le1824328871od_a_a @ ( image_1725938350od_a_a @ SV161 @ SV46 ) @ SV254 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1461]) ).
thf(1583,plain,
! [SV162: set_Pr1948701895od_a_a,SV358: product_prod_a_a,SV47: set_Product_prod_a_a,SV368: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV368 @ SV47 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV358 @ SV368 ) @ SV162 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV368 @ SV358 ) @ SV162 ) )
= $true )
| ( ( member449909584od_a_a @ SV358 @ SV47 )
= $false )
| ( ( prefer697821563od_a_a @ SV47 @ SV162 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1463]) ).
thf(1584,plain,
! [SV48: set_a,SV163: set_Product_prod_a_a] :
( ( ( member_a @ ( sK12_SY797 @ SV163 @ SV48 ) @ SV48 )
= $true )
| ( ( total_on_a @ SV48 @ SV163 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1464]) ).
thf(1585,plain,
! [SV163: set_Product_prod_a_a,SV48: set_a] :
( ( ( ~ ( member_a @ ( sK24_SY1030 @ SV48 @ SV163 ) @ SV48 ) )
= $false )
| ( ( total_on_a @ SV48 @ SV163 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1465]) ).
thf(1586,plain,
! [SV48: set_a,SV163: set_Product_prod_a_a] :
( ( ( ~ ( ( ( sK12_SY797 @ SV163 @ SV48 )
!= ( sK24_SY1030 @ SV48 @ SV163 ) ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK12_SY797 @ SV163 @ SV48 ) @ ( sK24_SY1030 @ SV48 @ SV163 ) ) @ SV163 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK24_SY1030 @ SV48 @ SV163 ) @ ( sK12_SY797 @ SV163 @ SV48 ) ) @ SV163 ) )
= $false )
| ( ( total_on_a @ SV48 @ SV163 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1465]) ).
thf(1587,plain,
! [SV366: set_Product_prod_a_a,SV359: set_Product_prod_a_a,SV327: a,SV257: a,SV166: a,SV52: a] :
( ( ( ~ ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SV257 @ SV327 ) ) @ ( lex_prod_a_a @ SV359 @ SV366 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
| ~ ( ( SV52 != SV257 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 ) ) ) )
= $true )
| ( ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SV257 @ SV327 ) ) @ ( lex_prod_a_a @ SV359 @ SV366 ) )
| ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
| ~ ( ( SV52 != SV257 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1468]) ).
thf(1588,plain,
! [SV53: set_Product_prod_a_a,SV167: set_Pr1948701895od_a_a,SV328: product_prod_a_a,SV258: product_prod_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV258 @ SV328 ) @ SV167 )
= $false )
| ( ( member449909584od_a_a @ SV328 @ SV53 )
= $true )
| ( ( refl_o1298442278od_a_a @ SV53 @ SV167 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1470]) ).
thf(1589,plain,
! [SV330: a,SV261: a,SV170: a,SV56: a] :
( ( ( ( product_Pair_a_a @ SV56 @ SV170 )
= ( product_Pair_a_a @ SV261 @ SV330 ) )
= $false )
| ( ( ~ ( ( ( product_Pair_a_a @ SV56 @ SV170 )
!= ( product_Pair_a_a @ SV261 @ SV330 ) )
| ~ ~ ( ( SV56 != SV261 )
| ( SV170 != SV330 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1472]) ).
thf(1590,plain,
! [SV330: a,SV170: a,SV261: a,SV56: a] :
( ( ( ~ ( ( SV56 != SV261 )
| ( SV170 != SV330 ) ) )
= $false )
| ( ( ~ ( ( ( product_Pair_a_a @ SV56 @ SV170 )
!= ( product_Pair_a_a @ SV261 @ SV330 ) )
| ~ ~ ( ( SV56 != SV261 )
| ( SV170 != SV330 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1472]) ).
thf(1591,plain,
! [SV262: a,SV171: a,SV57: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV171 ) @ relation )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV171 @ SV57 ) @ relation ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV171 @ SV262 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV262 @ SV171 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV262 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV262 @ SV57 ) @ relation ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1473]) ).
thf(1592,plain,
! [SV58: set_a,SV172: set_Product_prod_a_a,SV331: a,SV263: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV263 @ SV331 ) @ SV172 )
= $false )
| ( ( ~ ( ~ ( member_a @ SV263 @ SV58 )
| ~ ( member_a @ SV331 @ SV58 ) ) )
= $true )
| ( ( refl_on_a @ SV58 @ SV172 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1474]) ).
thf(1593,plain,
! [SV264: a > a,SV332: set_Product_prod_a_a,SV173: a > a,SV59: product_prod_a_a] :
( ( ( ! [SY1049: a] :
( ( SV59
!= ( product_Pair_a_a @ ( SV173 @ ( sK45_SY1009 @ SV332 @ SV264 @ SV173 @ SV59 ) ) @ ( SV264 @ SY1049 ) ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK45_SY1009 @ SV332 @ SV264 @ SV173 @ SV59 ) @ SY1049 ) @ SV332 ) ) )
= $false )
| ( ( member449909584od_a_a @ SV59 @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SV173 @ SV264 ) @ SV332 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1475]) ).
thf(1594,plain,
! [SV174: set_Pr1948701895od_a_a,SV333: product_prod_a_a,SV60: set_Product_prod_a_a,SV265: product_prod_a_a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ SV265 @ SV60 )
| ~ ( member449909584od_a_a @ SV333 @ SV60 ) ) )
= $false )
| ( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) )
= ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
| ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) ) ) )
= $true )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1476]) ).
thf(1595,plain,
! [SV175: set_Product_prod_a_a,SV334: a,SV61: set_a,SV266: a] :
( ( ( ~ ( ~ ( member_a @ SV266 @ SV61 )
| ~ ( member_a @ SV334 @ SV61 ) ) )
= $false )
| ( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) ) ) )
= $true )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1477]) ).
thf(1596,plain,
! [SV64: set_Product_prod_a_a,SV177: a,SV267: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV267 @ SV177 ) @ SV64 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV177 @ SV267 ) @ SV64 )
= $false )
| ( ( asym_a @ SV64 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1480]) ).
thf(1597,plain,
! [SV67: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK5_SY581 @ SV67 ) @ ( sK15_SY1012 @ SV67 ) ) @ SV67 )
= $true )
| ( ( trans_a @ SV67 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1482]) ).
thf(1598,plain,
! [SV67: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK15_SY1012 @ SV67 ) @ ( sK27_SY1033 @ SV67 ) ) @ SV67 ) )
= $false )
| ( ( trans_a @ SV67 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1483]) ).
thf(1599,plain,
! [SV67: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK5_SY581 @ SV67 ) @ ( sK27_SY1033 @ SV67 ) ) @ SV67 )
= $false )
| ( ( trans_a @ SV67 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1483]) ).
thf(1600,plain,
! [SV179: set_Product_prod_a_a] :
( ( ( ~ ( trans_a @ SV179 ) )
= $false )
| ( ( trans_a @ SV179 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1484]) ).
thf(1601,plain,
! [SV179: set_Product_prod_a_a] :
( ( ( ~ ! [SY828: a,SY829: a,SY830: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY829 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY829 @ SY830 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY830 ) @ SV179 ) ) )
= $false )
| ( ( trans_a @ SV179 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1484]) ).
thf(1602,plain,
! [SV179: set_Product_prod_a_a] :
( ( ( ! [SY1050: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK37_SY828 @ SV179 ) @ ( sK46_SY1040 @ SV179 ) ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK46_SY1040 @ SV179 ) @ SY1050 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK37_SY828 @ SV179 ) @ SY1050 ) @ SV179 ) ) )
= $false )
| ( ( ~ ( ~ ( trans_a @ SV179 )
| ~ ! [SY828: a,SY829: a,SY830: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY829 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY829 @ SY830 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY830 ) @ SV179 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1485]) ).
thf(1603,plain,
! [SV74: set_a,SV360: a,SV184: set_Product_prod_a_a,SV336: a,SV272: a] :
( ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV336 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV272 ) @ SV184 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV360 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV336 ) @ SV184 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV360 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV272 ) @ SV184 ) ) )
= $true )
| ( ( prefer719835986ence_a @ SV74 @ SV184 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1486]) ).
thf(1604,plain,
! [SV186: product_prod_a_a > a,SV76: a,SV337: set_Product_prod_a_a,SV274: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV274 @ SV337 )
= $false )
| ( ( member_a @ SV76 @ ( image_340790172_a_a_a @ SV186 @ SV337 ) )
= $true )
| ( ( SV76
= ( SV186 @ SV274 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1487]) ).
thf(1605,plain,
! [SV81: set_a,SV190: set_Product_prod_a_a,SV338: a,SV278: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV278 @ SV338 ) @ SV190 )
= $false )
| ( ( member_a @ SV278 @ SV81 )
= $true )
| ( ( prefer1292084992ence_a @ SV81 @ SV190 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1488]) ).
thf(1606,plain,
! [SV191: set_Product_prod_a_a,SV82: product_prod_a_a,SV339: product_prod_a_a > product_prod_a_a,SV279: product_prod_a_a] :
( ( ( SV279
= ( SV339 @ SV82 ) )
= $false )
| ( ( member449909584od_a_a @ SV279 @ ( image_794773445od_a_a @ SV339 @ SV191 ) )
= $true )
| ( ( member449909584od_a_a @ SV82 @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1489]) ).
thf(1607,plain,
! [SV83: set_a,SV192: set_Product_prod_a_a,SV340: a,SV280: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV280 @ SV340 ) @ SV192 )
= $false )
| ( ( member_a @ SV280 @ SV83 )
= $true )
| ( ( refl_on_a @ SV83 @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1490]) ).
thf(1608,plain,
! [SV193: set_a,SV84: a,SV341: a > product_prod_a_a,SV281: product_prod_a_a] :
( ( ( SV281
= ( SV341 @ SV84 ) )
= $false )
| ( ( member449909584od_a_a @ SV281 @ ( image_1725938350od_a_a @ SV341 @ SV193 ) )
= $true )
| ( ( member_a @ SV84 @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1491]) ).
thf(1609,plain,
! [SV85: set_Product_prod_a_a,SV342: a,SV361: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV361 @ SV342 ) @ SV85 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV342 @ SV361 ) @ SV85 )
= $false )
| ( ( asym_a @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1492]) ).
thf(1610,plain,
! [SV86: set_Product_prod_a_a,SV194: product_prod_a_a > a,SV282: set_a] :
( ( ( member449909584od_a_a @ ( sK28_SY969 @ SV282 @ SV194 @ SV86 ) @ SV86 )
= $true )
| ( ( ord_less_eq_set_a @ ( image_340790172_a_a_a @ SV194 @ SV86 ) @ SV282 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1493]) ).
thf(1611,plain,
! [SV88: a,SV196: a] :
( ( ( member_a @ SV196 @ carrier )
= $false )
| ( ( member_a @ SV88 @ carrier )
= $false )
| ( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1495]) ).
thf(1612,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a] :
( ( ( total_on_a @ SV197 @ SV343 )
= $false )
| ( ( ~ ( ~ ( total_on_a @ SV197 @ SV343 )
| ~ ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1496]) ).
thf(1613,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a] :
( ( ( ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) )
= $false )
| ( ( ~ ( ~ ( total_on_a @ SV197 @ SV343 )
| ~ ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1496]) ).
thf(1614,plain,
! [SV198: set_Product_prod_a_a] :
( ( ( ~ ( asym_a @ SV198 ) )
= $false )
| ( ( asym_a @ SV198 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1497]) ).
thf(1615,plain,
! [SV198: set_Product_prod_a_a] :
( ( ( ~ ~ ! [SY857: set_Product_prod_a_a] :
~ ~ ( ( SV198 != SY857 )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SY857 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SY857 ) ) ) )
= $false )
| ( ( asym_a @ SV198 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1497]) ).
thf(1616,plain,
! [SV369: set_Product_prod_a_a,SV198: set_Product_prod_a_a] :
( ( ( ~ ~ ( ( SV198 != SV369 )
| ~ ! [SY1051: a,SY1052: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1051 @ SY1052 ) @ SV369 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1052 @ SY1051 ) @ SV369 ) ) ) )
= $true )
| ( ( ~ ( ~ ( asym_a @ SV198 )
| ~ ~ ! [SY857: set_Product_prod_a_a] :
~ ~ ( ( SV198 != SY857 )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SY857 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SY857 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1498]) ).
thf(1617,plain,
! [SV199: set_Product_prod_a_a] :
( ( ( ~ ( asym_a @ SV199 ) )
= $false )
| ( ( asym_a @ SV199 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1499]) ).
thf(1618,plain,
! [SV199: set_Product_prod_a_a] :
( ( ( ~ ! [SY860: a,SY861: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY860 @ SY861 ) @ SV199 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY861 @ SY860 ) @ SV199 ) ) )
= $false )
| ( ( asym_a @ SV199 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1499]) ).
thf(1619,plain,
! [SV199: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK38_SY860 @ SV199 ) @ ( sK47_SY1042 @ SV199 ) ) @ SV199 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK47_SY1042 @ SV199 ) @ ( sK38_SY860 @ SV199 ) ) @ SV199 ) )
= $false )
| ( ( ~ ( ~ ( asym_a @ SV199 )
| ~ ! [SY860: a,SY861: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY860 @ SY861 ) @ SV199 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY861 @ SY860 ) @ SV199 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1500]) ).
thf(1620,plain,
! [SV344: multis599418605od_a_a,SV200: multis599418605od_a_a,SV285: product_prod_a_a,SV92: product_prod_a_a] :
( ( ( SV92 != SV285 )
= $false )
| ( ( member449909584od_a_a @ SV285 @ ( set_ms1818337124od_a_a @ SV200 ) )
= $true )
| ( ( ( add_ms1725977093od_a_a @ SV92 @ SV200 )
= ( add_ms1725977093od_a_a @ SV285 @ SV344 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1501]) ).
thf(1621,plain,
! [SV93: set_a,SV362: a,SV201: set_Product_prod_a_a,SV345: a,SV286: a] :
( ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SV345 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV286 ) @ SV201 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV362 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV362 @ SV345 ) @ SV201 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SV362 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV362 @ SV286 ) @ SV201 ) ) )
= $true )
| ( ( prefer1292084992ence_a @ SV93 @ SV201 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1502]) ).
thf(1622,plain,
! [SV95: multis599418605od_a_a,SV203: a > a > set_mu1281098573od_a_a,SV288: product_prod_a_a] :
( ( ( ( SV288
!= ( product_Pair_a_a @ ( sK39_SY976 @ SV203 @ SV95 @ SV288 ) @ ( sK48_SY1043 @ SV95 @ SV203 @ SV288 ) ) )
| ~ ( member1755255446od_a_a @ SV95 @ ( SV203 @ ( sK39_SY976 @ SV203 @ SV95 @ SV288 ) @ ( sK48_SY1043 @ SV95 @ SV203 @ SV288 ) ) ) )
= $false )
| ( ( member1755255446od_a_a @ SV95 @ ( produc1121147169od_a_a @ SV203 @ SV288 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1503]) ).
thf(1623,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( prefer1292084992ence_a @ SV204 @ SV347 )
= $false )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 )
| ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1504]) ).
thf(1624,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) )
= $false )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 )
| ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1504]) ).
thf(1625,plain,
! [SV98: multiset_a,SV206: a > a > set_multiset_a,SV290: product_prod_a_a] :
( ( ( ( SV290
!= ( product_Pair_a_a @ ( sK40_SY982 @ SV206 @ SV98 @ SV290 ) @ ( sK49_SY1044 @ SV98 @ SV206 @ SV290 ) ) )
| ~ ( member_multiset_a @ SV98 @ ( SV206 @ ( sK40_SY982 @ SV206 @ SV98 @ SV290 ) @ ( sK49_SY1044 @ SV98 @ SV206 @ SV290 ) ) ) )
= $false )
| ( ( member_multiset_a @ SV98 @ ( produc1828150264iset_a @ SV206 @ SV290 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1506]) ).
thf(1626,plain,
! [SV100: set_Product_prod_a_a,SV207: set_a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK17_SY881 @ SV207 @ SV100 ) @ ( sK30_SY1034 @ SV100 @ SV207 ) ) @ SV100 )
= $true )
| ( ( ~ ! [SY883: a,SY884: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY883 @ SY884 ) @ SV100 )
| ( member_a @ SY884 @ SV207 ) )
| ~ ( order_preorder_on_a @ SV207 @ SV100 )
| ( prefer1292084992ence_a @ SV207 @ SV100 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1507]) ).
thf(1627,plain,
! [SV207: set_a,SV100: set_Product_prod_a_a] :
( ( ( ~ ! [SY883: a,SY884: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY883 @ SY884 ) @ SV100 )
| ( member_a @ SY884 @ SV207 ) ) )
= $true )
| ( ( ~ ( order_preorder_on_a @ SV207 @ SV100 )
| ( prefer1292084992ence_a @ SV207 @ SV100 ) )
= $true )
| ( ( member_a @ ( sK17_SY881 @ SV207 @ SV100 ) @ SV207 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1508]) ).
thf(1628,plain,
! [SV291: a,SV208: a,SV101: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SV208 ) @ relation )
= $false )
| ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV101 ) @ relation ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV291 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV291 @ SV208 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SV291 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV291 @ SV101 ) @ relation ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1509]) ).
thf(1629,plain,
! [SV103: a,SV210: a > a > set_a,SV293: product_prod_a_a] :
( ( ( ( SV293
!= ( product_Pair_a_a @ ( sK41_SY985 @ SV210 @ SV103 @ SV293 ) @ ( sK50_SY1045 @ SV103 @ SV210 @ SV293 ) ) )
| ~ ( member_a @ SV103 @ ( SV210 @ ( sK41_SY985 @ SV210 @ SV103 @ SV293 ) @ ( sK50_SY1045 @ SV103 @ SV210 @ SV293 ) ) ) )
= $false )
| ( ( member_a @ SV103 @ ( produc961951794_set_a @ SV210 @ SV293 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1510]) ).
thf(1630,plain,
! [SV105: set_Product_prod_a_a,SV212: set_Pr1948701895od_a_a,SV348: product_prod_a_a,SV294: product_prod_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV294 @ SV348 ) @ SV212 )
= $false )
| ( ( member449909584od_a_a @ SV294 @ SV105 )
= $true )
| ( ( refl_o1298442278od_a_a @ SV105 @ SV212 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1511]) ).
thf(1631,plain,
! [SV106: set_Product_prod_a_a,SV213: set_Pr1948701895od_a_a,SV349: product_prod_a_a,SV295: product_prod_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV295 @ SV349 ) @ SV213 )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ SV295 @ SV106 )
| ~ ( member449909584od_a_a @ SV349 @ SV106 ) ) )
= $true )
| ( ( refl_o1298442278od_a_a @ SV106 @ SV213 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1512]) ).
thf(1632,plain,
! [SV107: set_Product_prod_a_a,SV214: product_prod_a_a > product_prod_a_a,SV296: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( sK32_SY989 @ SV296 @ SV214 @ SV107 ) @ SV107 )
= $true )
| ( ( ord_le1824328871od_a_a @ ( image_794773445od_a_a @ SV214 @ SV107 ) @ SV296 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1513]) ).
thf(1633,plain,
! [SV297: set_Product_prod_a_a,SV108: a,SV215: a,SV350: a] :
( ( ( SV350 = SV215 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV108 @ SV350 ) @ SV297 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV108 @ SV215 ) @ SV297 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1515]) ).
thf(1634,plain,
! [SV109: set_a,SV216: set_Product_prod_a_a,SV351: a,SV298: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV298 @ SV351 ) @ SV216 )
= $false )
| ( ( member_a @ SV351 @ SV109 )
= $true )
| ( ( refl_on_a @ SV109 @ SV216 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1516]) ).
thf(1635,plain,
! [SV217: a > product_prod_a_a,SV110: product_prod_a_a,SV352: set_a,SV299: a] :
( ( ( member_a @ SV299 @ SV352 )
= $false )
| ( ( member449909584od_a_a @ SV110 @ ( image_1725938350od_a_a @ SV217 @ SV352 ) )
= $true )
| ( ( SV110
= ( SV217 @ SV299 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1517]) ).
thf(1636,plain,
! [SV219: product_prod_a_a,SV112: a] :
( ( ( SV112
!= ( product_snd_a_a @ SV219 ) )
= $false )
| ( ( SV112
= ( product_snd_a_a @ SV219 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1519]) ).
thf(1637,plain,
! [SV112: a,SV219: product_prod_a_a] :
( ( ( ~ ~ ! [SY907: a] :
( SV219
!= ( product_Pair_a_a @ SY907 @ SV112 ) ) )
= $false )
| ( ( SV112
= ( product_snd_a_a @ SV219 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1519]) ).
thf(1638,plain,
! [SV112: a,SV370: a,SV219: product_prod_a_a] :
( ( ( SV219
!= ( product_Pair_a_a @ SV370 @ SV112 ) )
= $true )
| ( ( ~ ( ( SV112
!= ( product_snd_a_a @ SV219 ) )
| ~ ~ ! [SY907: a] :
( SV219
!= ( product_Pair_a_a @ SY907 @ SV112 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1520]) ).
thf(1639,plain,
! [SV220: product_prod_a_a > product_prod_a_a,SV114: product_prod_a_a,SV354: set_Product_prod_a_a,SV301: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV301 @ SV354 )
= $false )
| ( ( member449909584od_a_a @ SV114 @ ( image_794773445od_a_a @ SV220 @ SV354 ) )
= $true )
| ( ( SV114
= ( SV220 @ SV301 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1522]) ).
thf(1640,plain,
! [SV115: produc1127127335iset_a,SV221: a > a > set_Pr158363655iset_a,SV302: product_prod_a_a] :
( ( ( ( SV302
!= ( product_Pair_a_a @ ( sK42_SY996 @ SV221 @ SV115 @ SV302 ) @ ( sK51_SY1046 @ SV115 @ SV221 @ SV302 ) ) )
| ~ ( member340150864iset_a @ SV115 @ ( SV221 @ ( sK42_SY996 @ SV221 @ SV115 @ SV302 ) @ ( sK51_SY1046 @ SV115 @ SV221 @ SV302 ) ) ) )
= $false )
| ( ( member340150864iset_a @ SV115 @ ( produc93594587iset_a @ SV221 @ SV302 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1523]) ).
thf(1641,plain,
! [SV117: product_prod_a_a,SV223: multiset_a > multiset_a > set_Product_prod_a_a,SV304: produc1127127335iset_a] :
( ( ( ( SV304
!= ( produc2037245207iset_a @ ( sK43_SY998 @ SV223 @ SV117 @ SV304 ) @ ( sK52_SY1047 @ SV117 @ SV223 @ SV304 ) ) )
| ~ ( member449909584od_a_a @ SV117 @ ( SV223 @ ( sK43_SY998 @ SV223 @ SV117 @ SV304 ) @ ( sK52_SY1047 @ SV117 @ SV223 @ SV304 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ SV117 @ ( produc2041367259od_a_a @ SV223 @ SV304 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1524]) ).
thf(1642,plain,
! [SV224: set_Product_prod_a_a,SV364: a,SV118: set_a,SV371: a] :
( ( ( ~ ( member_a @ SV371 @ SV118 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV364 @ SV371 ) @ SV224 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV371 @ SV364 ) @ SV224 ) )
= $true )
| ( ( member_a @ SV364 @ SV118 )
= $false )
| ( ( prefer719835986ence_a @ SV118 @ SV224 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1525]) ).
thf(1643,plain,
! [SV225: set_Product_prod_a_a,SV119: product_prod_a_a,SV355: product_prod_a_a > a,SV305: a] :
( ( ( SV305
= ( SV355 @ SV119 ) )
= $false )
| ( ( member_a @ SV305 @ ( image_340790172_a_a_a @ SV355 @ SV225 ) )
= $true )
| ( ( member449909584od_a_a @ SV119 @ SV225 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1526]) ).
thf(1644,plain,
! [SV120: product_prod_a_a,SV226: a > a > set_Product_prod_a_a,SV306: product_prod_a_a] :
( ( ( ( SV306
!= ( product_Pair_a_a @ ( sK44_SY1001 @ SV226 @ SV120 @ SV306 ) @ ( sK53_SY1048 @ SV120 @ SV226 @ SV306 ) ) )
| ~ ( member449909584od_a_a @ SV120 @ ( SV226 @ ( sK44_SY1001 @ SV226 @ SV120 @ SV306 ) @ ( sK53_SY1048 @ SV120 @ SV226 @ SV306 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ SV120 @ ( produc1093061851od_a_a @ SV226 @ SV306 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1527]) ).
thf(1645,plain,
! [SV121: product_prod_a_a > $o,SV1: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV1 @ ( collec645855634od_a_a @ SV121 ) )
= $true )
| ( ( member449909584od_a_a @ SV1 @ ( collec645855634od_a_a @ SV121 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1528]) ).
thf(1646,plain,
! [SV1: product_prod_a_a,SV121: product_prod_a_a > $o] :
( ( ( SV121 @ SV1 )
= $true )
| ( ( member449909584od_a_a @ SV1 @ ( collec645855634od_a_a @ SV121 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1529]) ).
thf(1647,plain,
! [SV121: product_prod_a_a > $o,SV1: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV1 @ ( collec645855634od_a_a @ SV121 ) )
= $true )
| ( ( SV121 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1530]) ).
thf(1648,plain,
! [SV1: product_prod_a_a,SV121: product_prod_a_a > $o] :
( ( ( SV121 @ SV1 )
= $true )
| ( ( SV121 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1531]) ).
thf(1649,plain,
! [SV365: a,SV307: a,SV122: product_prod_a_a > $o] :
( ( ( ( product_curry_a_a_o @ SV122 @ SV307 @ SV365 )
| ( SV122 @ ( product_Pair_a_a @ SV307 @ SV365 ) ) )
= $false )
| ( ( ~ ( ~ ( product_curry_a_a_o @ SV122 @ SV307 @ SV365 )
| ~ ( SV122 @ ( product_Pair_a_a @ SV307 @ SV365 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1532]) ).
thf(1650,plain,
! [SV308: a > a,SV228: set_Product_prod_a_a,SV123: a,SV4: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV4 @ SV123 ) @ ( inv_image_a_a @ SV228 @ SV308 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV308 @ SV4 ) @ ( SV308 @ SV123 ) ) @ SV228 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV4 @ SV123 ) @ ( inv_image_a_a @ SV228 @ SV308 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1533]) ).
thf(1651,plain,
! [SV308: a > a,SV228: set_Product_prod_a_a,SV123: a,SV4: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV4 @ SV123 ) @ ( inv_image_a_a @ SV228 @ SV308 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV308 @ SV4 ) @ ( SV308 @ SV123 ) ) @ SV228 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV308 @ SV4 ) @ ( SV308 @ SV123 ) ) @ SV228 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1534]) ).
thf(1652,plain,
! [SV309: a > multiset_a,SV229: set_Pr158363655iset_a,SV124: a,SV5: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV5 @ SV124 ) @ ( inv_im975322764et_a_a @ SV229 @ SV309 ) )
| ~ ( member340150864iset_a @ ( produc2037245207iset_a @ ( SV309 @ SV5 ) @ ( SV309 @ SV124 ) ) @ SV229 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV5 @ SV124 ) @ ( inv_im975322764et_a_a @ SV229 @ SV309 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1535]) ).
thf(1653,plain,
! [SV309: a > multiset_a,SV229: set_Pr158363655iset_a,SV124: a,SV5: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV5 @ SV124 ) @ ( inv_im975322764et_a_a @ SV229 @ SV309 ) )
| ~ ( member340150864iset_a @ ( produc2037245207iset_a @ ( SV309 @ SV5 ) @ ( SV309 @ SV124 ) ) @ SV229 ) )
= $false )
| ( ( member340150864iset_a @ ( produc2037245207iset_a @ ( SV309 @ SV5 ) @ ( SV309 @ SV124 ) ) @ SV229 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1536]) ).
thf(1654,plain,
! [SV310: multiset_a > a,SV230: set_Product_prod_a_a,SV125: multiset_a,SV6: multiset_a] :
( ( ( ~ ( member340150864iset_a @ ( produc2037245207iset_a @ SV6 @ SV125 ) @ ( inv_im479034648iset_a @ SV230 @ SV310 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV310 @ SV6 ) @ ( SV310 @ SV125 ) ) @ SV230 ) )
= $false )
| ( ( member340150864iset_a @ ( produc2037245207iset_a @ SV6 @ SV125 ) @ ( inv_im479034648iset_a @ SV230 @ SV310 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1537]) ).
thf(1655,plain,
! [SV310: multiset_a > a,SV230: set_Product_prod_a_a,SV125: multiset_a,SV6: multiset_a] :
( ( ( ~ ( member340150864iset_a @ ( produc2037245207iset_a @ SV6 @ SV125 ) @ ( inv_im479034648iset_a @ SV230 @ SV310 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV310 @ SV6 ) @ ( SV310 @ SV125 ) ) @ SV230 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV310 @ SV6 ) @ ( SV310 @ SV125 ) ) @ SV230 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1538]) ).
thf(1656,plain,
! [SV311: a > product_prod_a_a,SV231: set_Pr1948701895od_a_a,SV126: a,SV7: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV7 @ SV126 ) @ ( inv_im777352425_a_a_a @ SV231 @ SV311 ) )
| ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( SV311 @ SV7 ) @ ( SV311 @ SV126 ) ) @ SV231 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV7 @ SV126 ) @ ( inv_im777352425_a_a_a @ SV231 @ SV311 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1539]) ).
thf(1657,plain,
! [SV311: a > product_prod_a_a,SV231: set_Pr1948701895od_a_a,SV126: a,SV7: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV7 @ SV126 ) @ ( inv_im777352425_a_a_a @ SV231 @ SV311 ) )
| ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( SV311 @ SV7 ) @ ( SV311 @ SV126 ) ) @ SV231 ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( SV311 @ SV7 ) @ ( SV311 @ SV126 ) ) @ SV231 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1540]) ).
thf(1658,plain,
! [SV312: product_prod_a_a > a,SV232: set_Product_prod_a_a,SV127: product_prod_a_a,SV8: product_prod_a_a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV8 @ SV127 ) @ ( inv_im15016955od_a_a @ SV232 @ SV312 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV312 @ SV8 ) @ ( SV312 @ SV127 ) ) @ SV232 ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV8 @ SV127 ) @ ( inv_im15016955od_a_a @ SV232 @ SV312 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1541]) ).
thf(1659,plain,
! [SV312: product_prod_a_a > a,SV232: set_Product_prod_a_a,SV127: product_prod_a_a,SV8: product_prod_a_a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV8 @ SV127 ) @ ( inv_im15016955od_a_a @ SV232 @ SV312 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV312 @ SV8 ) @ ( SV312 @ SV127 ) ) @ SV232 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV312 @ SV8 ) @ ( SV312 @ SV127 ) ) @ SV232 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1542]) ).
thf(1660,plain,
! [SV313: a > multis599418605od_a_a,SV233: set_Pr1821581383od_a_a,SV128: a,SV9: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV128 ) @ ( inv_im1681759523_a_a_a @ SV233 @ SV313 ) )
| ~ ( member1349055120od_a_a @ ( produc1859144151od_a_a @ ( SV313 @ SV9 ) @ ( SV313 @ SV128 ) ) @ SV233 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV128 ) @ ( inv_im1681759523_a_a_a @ SV233 @ SV313 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1543]) ).
thf(1661,plain,
! [SV313: a > multis599418605od_a_a,SV233: set_Pr1821581383od_a_a,SV128: a,SV9: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV128 ) @ ( inv_im1681759523_a_a_a @ SV233 @ SV313 ) )
| ~ ( member1349055120od_a_a @ ( produc1859144151od_a_a @ ( SV313 @ SV9 ) @ ( SV313 @ SV128 ) ) @ SV233 ) )
= $false )
| ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ ( SV313 @ SV9 ) @ ( SV313 @ SV128 ) ) @ SV233 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1544]) ).
thf(1662,plain,
! [SV314: multis599418605od_a_a > a,SV234: set_Product_prod_a_a,SV129: multis599418605od_a_a,SV10: multis599418605od_a_a] :
( ( ( ~ ( member1349055120od_a_a @ ( produc1859144151od_a_a @ SV10 @ SV129 ) @ ( inv_im941243329od_a_a @ SV234 @ SV314 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV314 @ SV10 ) @ ( SV314 @ SV129 ) ) @ SV234 ) )
= $false )
| ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ SV10 @ SV129 ) @ ( inv_im941243329od_a_a @ SV234 @ SV314 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1545]) ).
thf(1663,plain,
! [SV314: multis599418605od_a_a > a,SV234: set_Product_prod_a_a,SV129: multis599418605od_a_a,SV10: multis599418605od_a_a] :
( ( ( ~ ( member1349055120od_a_a @ ( produc1859144151od_a_a @ SV10 @ SV129 ) @ ( inv_im941243329od_a_a @ SV234 @ SV314 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV314 @ SV10 ) @ ( SV314 @ SV129 ) ) @ SV234 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV314 @ SV10 ) @ ( SV314 @ SV129 ) ) @ SV234 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1546]) ).
thf(1664,plain,
! [SV237: a,SV133: a,SV14: a > a > $o] :
( ( ( ~ ( produc1833107820_a_a_o @ SV14 @ ( product_Pair_a_a @ SV133 @ SV237 ) ) )
= $false )
| ( ( produc1833107820_a_a_o @ SV14 @ ( product_Pair_a_a @ SV133 @ SV237 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1547]) ).
thf(1665,plain,
! [SV237: a,SV133: a,SV14: a > a > $o] :
( ( ( ~ ( SV14 @ SV133 @ SV237 ) )
= $false )
| ( ( produc1833107820_a_a_o @ SV14 @ ( product_Pair_a_a @ SV133 @ SV237 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1547]) ).
thf(1666,plain,
! [SV237: a,SV133: a,SV14: a > a > $o] :
( ( ( ~ ( produc1833107820_a_a_o @ SV14 @ ( product_Pair_a_a @ SV133 @ SV237 ) ) )
= $false )
| ( ( SV14 @ SV133 @ SV237 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1548]) ).
thf(1667,plain,
! [SV237: a,SV133: a,SV14: a > a > $o] :
( ( ( ~ ( SV14 @ SV133 @ SV237 ) )
= $false )
| ( ( SV14 @ SV133 @ SV237 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1548]) ).
thf(1668,plain,
! [SV134: set_Product_prod_a_a] :
( ( ( irrefl_a @ SV134 )
= $true )
| ( ( irrefl_a @ SV134 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1549]) ).
thf(1669,plain,
! [SV134: set_Product_prod_a_a] :
( ( ( ! [SY751: a] :
~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY751 @ SY751 ) @ SV134 ) )
= $true )
| ( ( irrefl_a @ SV134 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1550]) ).
thf(1670,plain,
! [SV134: set_Product_prod_a_a] :
( ( ( ~ ( irrefl_a @ SV134 )
| ~ ! [SY751: a] :
~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY751 @ SY751 ) @ SV134 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK34_SY751 @ SV134 ) @ ( sK34_SY751 @ SV134 ) ) @ SV134 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1551]) ).
thf(1671,plain,
! [SV238: set_Product_prod_a_a,SV135: a,SV16: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV16 @ SV135 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV238 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV16 @ SV135 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV238 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1552]) ).
thf(1672,plain,
! [SV238: set_Product_prod_a_a,SV16: a,SV135: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV135 @ SV16 ) @ SV238 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV16 @ SV135 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV238 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1552]) ).
thf(1673,plain,
! [SV238: set_Product_prod_a_a,SV135: a,SV16: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV16 @ SV135 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV238 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV135 @ SV16 ) @ SV238 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1553]) ).
thf(1674,plain,
! [SV238: set_Product_prod_a_a,SV16: a,SV135: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV135 @ SV16 ) @ SV238 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV135 @ SV16 ) @ SV238 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1553]) ).
thf(1675,plain,
! [SV136: product_prod_a_a] :
( ( ( top_to1483957574_a_a_o @ SV136 )
= $true )
| ( ( top_to1483957574_a_a_o @ SV136 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1554]) ).
thf(1676,plain,
! [SV136: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV136 @ top_to398455383od_a_a )
= $true )
| ( ( top_to1483957574_a_a_o @ SV136 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1555]) ).
thf(1677,plain,
! [SV136: product_prod_a_a] :
( ( ( top_to1483957574_a_a_o @ SV136 )
= $true )
| ( ( member449909584od_a_a @ SV136 @ top_to398455383od_a_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1556]) ).
thf(1678,plain,
! [SV136: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV136 @ top_to398455383od_a_a )
= $true )
| ( ( member449909584od_a_a @ SV136 @ top_to398455383od_a_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1557]) ).
thf(1679,plain,
! [SV240: multis599418605od_a_a,SV141: multis599418605od_a_a,SV25: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ ( plus_p404985124od_a_a @ SV141 @ SV240 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ ( plus_p404985124od_a_a @ SV141 @ SV240 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1558]) ).
thf(1680,plain,
! [SV240: multis599418605od_a_a,SV141: multis599418605od_a_a,SV25: product_prod_a_a] :
( ( ( ~ ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV141 ) )
| ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV240 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ ( plus_p404985124od_a_a @ SV141 @ SV240 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1558]) ).
thf(1681,plain,
! [SV240: multis599418605od_a_a,SV141: multis599418605od_a_a,SV25: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ ( plus_p404985124od_a_a @ SV141 @ SV240 ) ) )
| ~ ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV141 ) )
| ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV240 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1559]) ).
thf(1682,plain,
! [SV240: multis599418605od_a_a,SV141: multis599418605od_a_a,SV25: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ ( plus_p404985124od_a_a @ SV141 @ SV240 ) ) )
| ~ ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV141 ) )
| ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV240 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV240 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1560]) ).
thf(1683,plain,
! [SV316: a,SV143: a,SV242: a,SV28: a] :
( ( ( SV28 = SV242 )
= $true )
| ( ( ( product_Pair_a_a @ SV28 @ SV143 )
= ( product_Pair_a_a @ SV242 @ SV316 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1561]) ).
thf(1684,plain,
! [SV242: a,SV28: a,SV316: a,SV143: a] :
( ( ( SV143 = SV316 )
= $true )
| ( ( ( product_Pair_a_a @ SV28 @ SV143 )
= ( product_Pair_a_a @ SV242 @ SV316 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1562]) ).
thf(1685,plain,
! [SV147: set_Pr1948701895od_a_a,SV32: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( sK20_SY1027 @ SV32 @ SV147 ) @ SV32 )
= $true )
| ( ( total_1490170027od_a_a @ SV32 @ SV147 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1564]) ).
thf(1686,plain,
! [SV32: set_Product_prod_a_a,SV147: set_Pr1948701895od_a_a] :
( ( ( ~ ( ( ( sK10_SY764 @ SV147 @ SV32 )
!= ( sK20_SY1027 @ SV32 @ SV147 ) ) ) )
= $false )
| ( ( total_1490170027od_a_a @ SV32 @ SV147 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1565]) ).
thf(1687,plain,
! [SV32: set_Product_prod_a_a,SV147: set_Pr1948701895od_a_a] :
( ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK10_SY764 @ SV147 @ SV32 ) @ ( sK20_SY1027 @ SV32 @ SV147 ) ) @ SV147 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK20_SY1027 @ SV32 @ SV147 ) @ ( sK10_SY764 @ SV147 @ SV32 ) ) @ SV147 ) )
= $false )
| ( ( total_1490170027od_a_a @ SV32 @ SV147 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1565]) ).
thf(1688,plain,
! [SV245: a > $o,SV317: a,SV148: a,SV33: a > $o] :
( ( ( ~ ( SV33 @ ( product_fst_a_a @ ( product_Pair_a_a @ SV148 @ SV317 ) ) )
| ~ ( SV245 @ ( product_snd_a_a @ ( product_Pair_a_a @ SV148 @ SV317 ) ) ) )
= $false )
| ( ( SV245 @ SV317 )
= $false )
| ( ( SV33 @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1566]) ).
thf(1689,plain,
! [SV34: a > $o,SV149: a,SV357: a > set_Product_prod_a_a,SV318: a,SV246: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV246 @ SV318 ) @ ( SV357 @ SV149 ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV149 @ SV246 ) @ ( product_Pair_a_a @ SV149 @ SV318 ) ) @ ( same_fst_a_a @ SV34 @ SV357 ) )
= $true )
| ( ( SV34 @ SV149 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1567]) ).
thf(1690,plain,
! [SV151: set_Product_prod_a_a > $o,SV36: set_Product_prod_a_a] :
( ( ( ! [SY1038: a,SY1039: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1038 @ SY1039 ) @ ( sK36_SY772 @ SV36 @ SV151 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1039 @ SY1038 ) @ ( sK36_SY772 @ SV36 @ SV151 ) ) ) )
= $true )
| ( ( SV151 @ SV36 )
= $true )
| ( ( asym_a @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1568]) ).
thf(1691,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a] :
( ( ( ~ ( total_1490170027od_a_a @ SV154 @ SV320 )
| ~ ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) )
= $false )
| ( ( total_1490170027od_a_a @ SV154 @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1571]) ).
thf(1692,plain,
! [SV154: set_Product_prod_a_a,SV320: set_Pr1948701895od_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK54_SY1005 @ SV320 @ SV154 ) @ SV154 )
| ! [SY1053: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1053 @ SV154 )
| ~ ( ( ( sK54_SY1005 @ SV320 @ SV154 )
!= SY1053 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK54_SY1005 @ SV320 @ SV154 ) @ SY1053 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1053 @ ( sK54_SY1005 @ SV320 @ SV154 ) ) @ SV320 ) ) )
= $false )
| ( ( ~ ( ~ ( total_1490170027od_a_a @ SV154 @ SV320 )
| ~ ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1572]) ).
thf(1693,plain,
! [SV155: product_prod_a_a,SV40: a] :
( ( ( SV40
= ( product_fst_a_a @ SV155 ) )
= $true )
| ( ( SV40
= ( product_fst_a_a @ SV155 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1573]) ).
thf(1694,plain,
! [SV40: a,SV155: product_prod_a_a] :
( ( ( ~ ! [SY782: a] :
( SV155
!= ( product_Pair_a_a @ SV40 @ SY782 ) ) )
= $true )
| ( ( SV40
= ( product_fst_a_a @ SV155 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1574]) ).
thf(1695,plain,
! [SV367: a,SV40: a,SV155: product_prod_a_a] :
( ( ( SV155
= ( product_Pair_a_a @ SV40 @ SV367 ) )
= $false )
| ( ( ~ ( ( SV40
!= ( product_fst_a_a @ SV155 ) )
| ~ ~ ! [SY782: a] :
( SV155
!= ( product_Pair_a_a @ SV40 @ SY782 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1575]) ).
thf(1696,plain,
! [SV156: a,SV41: set_Product_prod_a_a,SV321: a,SV249: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV249 @ SV321 ) @ SV41 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV156 @ SV321 ) @ SV41 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV156 @ SV249 ) @ SV41 )
= $false )
| ( ( trans_a @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1576]) ).
thf(1697,plain,
! [SV324: a,SV252: a,SV159: a,SV44: a] :
( ( ( ( ( product_Pair_a_a @ SV44 @ SV159 )
!= ( product_Pair_a_a @ SV252 @ SV324 ) )
| ~ ~ ( ( SV44 != SV252 )
| ( SV159 != SV324 ) ) )
= $false )
| ( ( ( product_Pair_a_a @ SV44 @ SV159 )
= ( product_Pair_a_a @ SV252 @ SV324 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1579]) ).
thf(1698,plain,
! [SV324: a,SV159: a,SV252: a,SV44: a] :
( ( ( ( SV44 != SV252 )
| ( SV159 != SV324 ) )
= $true )
| ( ( ~ ( ( ( product_Pair_a_a @ SV44 @ SV159 )
!= ( product_Pair_a_a @ SV252 @ SV324 ) )
| ~ ~ ( ( SV44 != SV252 )
| ( SV159 != SV324 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1580]) ).
thf(1699,plain,
! [SV160: a,SV45: set_Product_prod_a_a,SV325: a,SV253: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV253 @ SV325 ) @ SV45 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV160 @ SV325 ) @ SV45 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV160 @ SV253 ) @ SV45 )
= $false )
| ( ( trans_a @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1581]) ).
thf(1700,plain,
! [SV162: set_Pr1948701895od_a_a,SV358: product_prod_a_a,SV47: set_Product_prod_a_a,SV368: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV368 @ SV47 ) )
= $true )
| ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV358 @ SV368 ) @ SV162 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV368 @ SV358 ) @ SV162 ) )
= $true )
| ( ( member449909584od_a_a @ SV358 @ SV47 )
= $false )
| ( ( prefer697821563od_a_a @ SV47 @ SV162 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1583]) ).
thf(1701,plain,
! [SV163: set_Product_prod_a_a,SV48: set_a] :
( ( ( member_a @ ( sK24_SY1030 @ SV48 @ SV163 ) @ SV48 )
= $true )
| ( ( total_on_a @ SV48 @ SV163 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1585]) ).
thf(1702,plain,
! [SV48: set_a,SV163: set_Product_prod_a_a] :
( ( ( ~ ( ( ( sK12_SY797 @ SV163 @ SV48 )
!= ( sK24_SY1030 @ SV48 @ SV163 ) ) ) )
= $false )
| ( ( total_on_a @ SV48 @ SV163 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1586]) ).
thf(1703,plain,
! [SV48: set_a,SV163: set_Product_prod_a_a] :
( ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK12_SY797 @ SV163 @ SV48 ) @ ( sK24_SY1030 @ SV48 @ SV163 ) ) @ SV163 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK24_SY1030 @ SV48 @ SV163 ) @ ( sK12_SY797 @ SV163 @ SV48 ) ) @ SV163 ) )
= $false )
| ( ( total_on_a @ SV48 @ SV163 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1586]) ).
thf(1704,plain,
! [SV366: set_Product_prod_a_a,SV359: set_Product_prod_a_a,SV327: a,SV257: a,SV166: a,SV52: a] :
( ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SV257 @ SV327 ) ) @ ( lex_prod_a_a @ SV359 @ SV366 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
| ~ ( ( SV52 != SV257 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 ) ) )
= $false )
| ( ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SV257 @ SV327 ) ) @ ( lex_prod_a_a @ SV359 @ SV366 ) )
| ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
| ~ ( ( SV52 != SV257 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1587]) ).
thf(1705,plain,
! [SV330: a,SV261: a,SV170: a,SV56: a] :
( ( ( ( ( product_Pair_a_a @ SV56 @ SV170 )
!= ( product_Pair_a_a @ SV261 @ SV330 ) )
| ~ ~ ( ( SV56 != SV261 )
| ( SV170 != SV330 ) ) )
= $false )
| ( ( ( product_Pair_a_a @ SV56 @ SV170 )
= ( product_Pair_a_a @ SV261 @ SV330 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1589]) ).
thf(1706,plain,
! [SV330: a,SV170: a,SV261: a,SV56: a] :
( ( ( ( SV56 != SV261 )
| ( SV170 != SV330 ) )
= $true )
| ( ( ~ ( ( ( product_Pair_a_a @ SV56 @ SV170 )
!= ( product_Pair_a_a @ SV261 @ SV330 ) )
| ~ ~ ( ( SV56 != SV261 )
| ( SV170 != SV330 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1590]) ).
thf(1707,plain,
! [SV262: a,SV57: a,SV171: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV171 @ SV57 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV171 ) @ relation )
= $false )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV171 @ SV262 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV262 @ SV171 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV262 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV262 @ SV57 ) @ relation ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1591]) ).
thf(1708,plain,
! [SV172: set_Product_prod_a_a,SV331: a,SV58: set_a,SV263: a] :
( ( ( ~ ( member_a @ SV263 @ SV58 )
| ~ ( member_a @ SV331 @ SV58 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV263 @ SV331 ) @ SV172 )
= $false )
| ( ( refl_on_a @ SV58 @ SV172 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1592]) ).
thf(1709,plain,
! [SV264: a > a,SV332: set_Product_prod_a_a,SV173: a > a,SV59: product_prod_a_a] :
( ( ( ( SV59
!= ( product_Pair_a_a @ ( SV173 @ ( sK45_SY1009 @ SV332 @ SV264 @ SV173 @ SV59 ) ) @ ( SV264 @ ( sK55_SY1049 @ SV264 @ SV332 @ SV173 @ SV59 ) ) ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK45_SY1009 @ SV332 @ SV264 @ SV173 @ SV59 ) @ ( sK55_SY1049 @ SV264 @ SV332 @ SV173 @ SV59 ) ) @ SV332 ) )
= $false )
| ( ( member449909584od_a_a @ SV59 @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SV173 @ SV264 ) @ SV332 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1593]) ).
thf(1710,plain,
! [SV174: set_Pr1948701895od_a_a,SV333: product_prod_a_a,SV60: set_Product_prod_a_a,SV265: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV265 @ SV60 )
| ~ ( member449909584od_a_a @ SV333 @ SV60 ) )
= $true )
| ( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) )
= ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
| ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) ) ) )
= $true )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1594]) ).
thf(1711,plain,
! [SV175: set_Product_prod_a_a,SV334: a,SV61: set_a,SV266: a] :
( ( ( ~ ( member_a @ SV266 @ SV61 )
| ~ ( member_a @ SV334 @ SV61 ) )
= $true )
| ( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) ) ) )
= $true )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1595]) ).
thf(1712,plain,
! [SV67: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK15_SY1012 @ SV67 ) @ ( sK27_SY1033 @ SV67 ) ) @ SV67 )
= $true )
| ( ( trans_a @ SV67 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1598]) ).
thf(1713,plain,
! [SV179: set_Product_prod_a_a] :
( ( ( trans_a @ SV179 )
= $true )
| ( ( trans_a @ SV179 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1600]) ).
thf(1714,plain,
! [SV179: set_Product_prod_a_a] :
( ( ( ! [SY828: a,SY829: a,SY830: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY829 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY829 @ SY830 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY830 ) @ SV179 ) ) )
= $true )
| ( ( trans_a @ SV179 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1601]) ).
thf(1715,plain,
! [SV179: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK37_SY828 @ SV179 ) @ ( sK46_SY1040 @ SV179 ) ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK46_SY1040 @ SV179 ) @ ( sK56_SY1050 @ SV179 ) ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK37_SY828 @ SV179 ) @ ( sK56_SY1050 @ SV179 ) ) @ SV179 ) )
= $false )
| ( ( ~ ( ~ ( trans_a @ SV179 )
| ~ ! [SY828: a,SY829: a,SY830: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY829 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY829 @ SY830 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY830 ) @ SV179 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1602]) ).
thf(1716,plain,
! [SV74: set_a,SV360: a,SV184: set_Product_prod_a_a,SV336: a,SV272: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV336 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV272 ) @ SV184 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV360 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV336 ) @ SV184 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV360 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV272 ) @ SV184 ) ) )
= $true )
| ( ( prefer719835986ence_a @ SV74 @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1603]) ).
thf(1717,plain,
! [SV88: a,SV196: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) ) )
| ~ ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) ) ) )
= $true )
| ( ( member_a @ SV88 @ carrier )
= $false )
| ( ( member_a @ SV196 @ carrier )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1611]) ).
thf(1718,plain,
! [SV88: a,SV196: a] :
( ( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) ) ) )
= $true )
| ( ( member_a @ SV88 @ carrier )
= $false )
| ( ( member_a @ SV196 @ carrier )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1611]) ).
thf(1719,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a] :
( ( ( ~ ( total_on_a @ SV197 @ SV343 )
| ~ ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) )
= $false )
| ( ( total_on_a @ SV197 @ SV343 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1612]) ).
thf(1720,plain,
! [SV197: set_a,SV343: set_Product_prod_a_a] :
( ( ( ~ ( member_a @ ( sK57_SY1017 @ SV343 @ SV197 ) @ SV197 )
| ! [SY1054: a] :
( ~ ( member_a @ SY1054 @ SV197 )
| ~ ( ( ( sK57_SY1017 @ SV343 @ SV197 )
!= SY1054 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK57_SY1017 @ SV343 @ SV197 ) @ SY1054 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1054 @ ( sK57_SY1017 @ SV343 @ SV197 ) ) @ SV343 ) ) )
= $false )
| ( ( ~ ( ~ ( total_on_a @ SV197 @ SV343 )
| ~ ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1613]) ).
thf(1721,plain,
! [SV198: set_Product_prod_a_a] :
( ( ( asym_a @ SV198 )
= $true )
| ( ( asym_a @ SV198 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1614]) ).
thf(1722,plain,
! [SV198: set_Product_prod_a_a] :
( ( ( ~ ! [SY857: set_Product_prod_a_a] :
~ ~ ( ( SV198 != SY857 )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SY857 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SY857 ) ) ) )
= $true )
| ( ( asym_a @ SV198 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1615]) ).
thf(1723,plain,
! [SV369: set_Product_prod_a_a,SV198: set_Product_prod_a_a] :
( ( ( ~ ( ( SV198 != SV369 )
| ~ ! [SY1051: a,SY1052: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1051 @ SY1052 ) @ SV369 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1052 @ SY1051 ) @ SV369 ) ) ) )
= $false )
| ( ( ~ ( ~ ( asym_a @ SV198 )
| ~ ~ ! [SY857: set_Product_prod_a_a] :
~ ~ ( ( SV198 != SY857 )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SY857 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SY857 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1616]) ).
thf(1724,plain,
! [SV199: set_Product_prod_a_a] :
( ( ( asym_a @ SV199 )
= $true )
| ( ( asym_a @ SV199 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1617]) ).
thf(1725,plain,
! [SV199: set_Product_prod_a_a] :
( ( ( ! [SY860: a,SY861: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY860 @ SY861 ) @ SV199 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY861 @ SY860 ) @ SV199 ) ) )
= $true )
| ( ( asym_a @ SV199 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1618]) ).
thf(1726,plain,
! [SV199: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK38_SY860 @ SV199 ) @ ( sK47_SY1042 @ SV199 ) ) @ SV199 ) )
= $false )
| ( ( ~ ( ~ ( asym_a @ SV199 )
| ~ ! [SY860: a,SY861: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY860 @ SY861 ) @ SV199 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY861 @ SY860 ) @ SV199 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1619]) ).
thf(1727,plain,
! [SV199: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK47_SY1042 @ SV199 ) @ ( sK38_SY860 @ SV199 ) ) @ SV199 ) )
= $false )
| ( ( ~ ( ~ ( asym_a @ SV199 )
| ~ ! [SY860: a,SY861: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY860 @ SY861 ) @ SV199 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY861 @ SY860 ) @ SV199 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1619]) ).
thf(1728,plain,
! [SV344: multis599418605od_a_a,SV200: multis599418605od_a_a,SV285: product_prod_a_a,SV92: product_prod_a_a] :
( ( ( SV92 = SV285 )
= $true )
| ( ( member449909584od_a_a @ SV285 @ ( set_ms1818337124od_a_a @ SV200 ) )
= $true )
| ( ( ( add_ms1725977093od_a_a @ SV92 @ SV200 )
= ( add_ms1725977093od_a_a @ SV285 @ SV344 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1620]) ).
thf(1729,plain,
! [SV93: set_a,SV362: a,SV201: set_Product_prod_a_a,SV345: a,SV286: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SV345 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV286 ) @ SV201 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV362 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV362 @ SV345 ) @ SV201 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SV362 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV362 @ SV286 ) @ SV201 ) ) )
= $true )
| ( ( prefer1292084992ence_a @ SV93 @ SV201 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1621]) ).
thf(1730,plain,
! [SV95: multis599418605od_a_a,SV203: a > a > set_mu1281098573od_a_a,SV288: product_prod_a_a] :
( ( ( SV288
!= ( product_Pair_a_a @ ( sK39_SY976 @ SV203 @ SV95 @ SV288 ) @ ( sK48_SY1043 @ SV95 @ SV203 @ SV288 ) ) )
= $false )
| ( ( member1755255446od_a_a @ SV95 @ ( produc1121147169od_a_a @ SV203 @ SV288 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1622]) ).
thf(1731,plain,
! [SV288: product_prod_a_a,SV203: a > a > set_mu1281098573od_a_a,SV95: multis599418605od_a_a] :
( ( ( ~ ( member1755255446od_a_a @ SV95 @ ( SV203 @ ( sK39_SY976 @ SV203 @ SV95 @ SV288 ) @ ( sK48_SY1043 @ SV95 @ SV203 @ SV288 ) ) ) )
= $false )
| ( ( member1755255446od_a_a @ SV95 @ ( produc1121147169od_a_a @ SV203 @ SV288 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1622]) ).
thf(1732,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 )
| ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) )
= $false )
| ( ( prefer1292084992ence_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1623]) ).
thf(1733,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 )
| ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1624]) ).
thf(1734,plain,
! [SV98: multiset_a,SV206: a > a > set_multiset_a,SV290: product_prod_a_a] :
( ( ( SV290
!= ( product_Pair_a_a @ ( sK40_SY982 @ SV206 @ SV98 @ SV290 ) @ ( sK49_SY1044 @ SV98 @ SV206 @ SV290 ) ) )
= $false )
| ( ( member_multiset_a @ SV98 @ ( produc1828150264iset_a @ SV206 @ SV290 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1625]) ).
thf(1735,plain,
! [SV290: product_prod_a_a,SV206: a > a > set_multiset_a,SV98: multiset_a] :
( ( ( ~ ( member_multiset_a @ SV98 @ ( SV206 @ ( sK40_SY982 @ SV206 @ SV98 @ SV290 ) @ ( sK49_SY1044 @ SV98 @ SV206 @ SV290 ) ) ) )
= $false )
| ( ( member_multiset_a @ SV98 @ ( produc1828150264iset_a @ SV206 @ SV290 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1625]) ).
thf(1736,plain,
! [SV207: set_a,SV100: set_Product_prod_a_a] :
( ( ( ~ ! [SY883: a,SY884: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY883 @ SY884 ) @ SV100 )
| ( member_a @ SY884 @ SV207 ) ) )
= $true )
| ( ( ~ ( order_preorder_on_a @ SV207 @ SV100 )
| ( prefer1292084992ence_a @ SV207 @ SV100 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK17_SY881 @ SV207 @ SV100 ) @ ( sK30_SY1034 @ SV100 @ SV207 ) ) @ SV100 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1626]) ).
thf(1737,plain,
! [SV207: set_a,SV100: set_Product_prod_a_a] :
( ( ( ! [SY883: a,SY884: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY883 @ SY884 ) @ SV100 )
| ( member_a @ SY884 @ SV207 ) ) )
= $false )
| ( ( ~ ( order_preorder_on_a @ SV207 @ SV100 )
| ( prefer1292084992ence_a @ SV207 @ SV100 ) )
= $true )
| ( ( member_a @ ( sK17_SY881 @ SV207 @ SV100 ) @ SV207 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1627]) ).
thf(1738,plain,
! [SV291: a,SV101: a,SV208: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV101 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SV208 ) @ relation )
= $false )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV291 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV291 @ SV208 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SV291 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV291 @ SV101 ) @ relation ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1628]) ).
thf(1739,plain,
! [SV103: a,SV210: a > a > set_a,SV293: product_prod_a_a] :
( ( ( SV293
!= ( product_Pair_a_a @ ( sK41_SY985 @ SV210 @ SV103 @ SV293 ) @ ( sK50_SY1045 @ SV103 @ SV210 @ SV293 ) ) )
= $false )
| ( ( member_a @ SV103 @ ( produc961951794_set_a @ SV210 @ SV293 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1629]) ).
thf(1740,plain,
! [SV293: product_prod_a_a,SV210: a > a > set_a,SV103: a] :
( ( ( ~ ( member_a @ SV103 @ ( SV210 @ ( sK41_SY985 @ SV210 @ SV103 @ SV293 ) @ ( sK50_SY1045 @ SV103 @ SV210 @ SV293 ) ) ) )
= $false )
| ( ( member_a @ SV103 @ ( produc961951794_set_a @ SV210 @ SV293 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1629]) ).
thf(1741,plain,
! [SV213: set_Pr1948701895od_a_a,SV349: product_prod_a_a,SV106: set_Product_prod_a_a,SV295: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV295 @ SV106 )
| ~ ( member449909584od_a_a @ SV349 @ SV106 ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV295 @ SV349 ) @ SV213 )
= $false )
| ( ( refl_o1298442278od_a_a @ SV106 @ SV213 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1631]) ).
thf(1742,plain,
! [SV219: product_prod_a_a,SV112: a] :
( ( ( SV112
= ( product_snd_a_a @ SV219 ) )
= $true )
| ( ( SV112
= ( product_snd_a_a @ SV219 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1636]) ).
thf(1743,plain,
! [SV112: a,SV219: product_prod_a_a] :
( ( ( ~ ! [SY907: a] :
( SV219
!= ( product_Pair_a_a @ SY907 @ SV112 ) ) )
= $true )
| ( ( SV112
= ( product_snd_a_a @ SV219 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1637]) ).
thf(1744,plain,
! [SV112: a,SV370: a,SV219: product_prod_a_a] :
( ( ( SV219
= ( product_Pair_a_a @ SV370 @ SV112 ) )
= $false )
| ( ( ~ ( ( SV112
!= ( product_snd_a_a @ SV219 ) )
| ~ ~ ! [SY907: a] :
( SV219
!= ( product_Pair_a_a @ SY907 @ SV112 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1638]) ).
thf(1745,plain,
! [SV115: produc1127127335iset_a,SV221: a > a > set_Pr158363655iset_a,SV302: product_prod_a_a] :
( ( ( SV302
!= ( product_Pair_a_a @ ( sK42_SY996 @ SV221 @ SV115 @ SV302 ) @ ( sK51_SY1046 @ SV115 @ SV221 @ SV302 ) ) )
= $false )
| ( ( member340150864iset_a @ SV115 @ ( produc93594587iset_a @ SV221 @ SV302 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1640]) ).
thf(1746,plain,
! [SV302: product_prod_a_a,SV221: a > a > set_Pr158363655iset_a,SV115: produc1127127335iset_a] :
( ( ( ~ ( member340150864iset_a @ SV115 @ ( SV221 @ ( sK42_SY996 @ SV221 @ SV115 @ SV302 ) @ ( sK51_SY1046 @ SV115 @ SV221 @ SV302 ) ) ) )
= $false )
| ( ( member340150864iset_a @ SV115 @ ( produc93594587iset_a @ SV221 @ SV302 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1640]) ).
thf(1747,plain,
! [SV117: product_prod_a_a,SV223: multiset_a > multiset_a > set_Product_prod_a_a,SV304: produc1127127335iset_a] :
( ( ( SV304
!= ( produc2037245207iset_a @ ( sK43_SY998 @ SV223 @ SV117 @ SV304 ) @ ( sK52_SY1047 @ SV117 @ SV223 @ SV304 ) ) )
= $false )
| ( ( member449909584od_a_a @ SV117 @ ( produc2041367259od_a_a @ SV223 @ SV304 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1641]) ).
thf(1748,plain,
! [SV304: produc1127127335iset_a,SV223: multiset_a > multiset_a > set_Product_prod_a_a,SV117: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV117 @ ( SV223 @ ( sK43_SY998 @ SV223 @ SV117 @ SV304 ) @ ( sK52_SY1047 @ SV117 @ SV223 @ SV304 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ SV117 @ ( produc2041367259od_a_a @ SV223 @ SV304 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1641]) ).
thf(1749,plain,
! [SV224: set_Product_prod_a_a,SV364: a,SV118: set_a,SV371: a] :
( ( ( ~ ( member_a @ SV371 @ SV118 ) )
= $true )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV364 @ SV371 ) @ SV224 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV371 @ SV364 ) @ SV224 ) )
= $true )
| ( ( member_a @ SV364 @ SV118 )
= $false )
| ( ( prefer719835986ence_a @ SV118 @ SV224 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1642]) ).
thf(1750,plain,
! [SV120: product_prod_a_a,SV226: a > a > set_Product_prod_a_a,SV306: product_prod_a_a] :
( ( ( SV306
!= ( product_Pair_a_a @ ( sK44_SY1001 @ SV226 @ SV120 @ SV306 ) @ ( sK53_SY1048 @ SV120 @ SV226 @ SV306 ) ) )
= $false )
| ( ( member449909584od_a_a @ SV120 @ ( produc1093061851od_a_a @ SV226 @ SV306 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1644]) ).
thf(1751,plain,
! [SV306: product_prod_a_a,SV226: a > a > set_Product_prod_a_a,SV120: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV120 @ ( SV226 @ ( sK44_SY1001 @ SV226 @ SV120 @ SV306 ) @ ( sK53_SY1048 @ SV120 @ SV226 @ SV306 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ SV120 @ ( produc1093061851od_a_a @ SV226 @ SV306 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1644]) ).
thf(1752,plain,
! [SV365: a,SV307: a,SV122: product_prod_a_a > $o] :
( ( ( product_curry_a_a_o @ SV122 @ SV307 @ SV365 )
= $false )
| ( ( ~ ( ~ ( product_curry_a_a_o @ SV122 @ SV307 @ SV365 )
| ~ ( SV122 @ ( product_Pair_a_a @ SV307 @ SV365 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1649]) ).
thf(1753,plain,
! [SV365: a,SV307: a,SV122: product_prod_a_a > $o] :
( ( ( SV122 @ ( product_Pair_a_a @ SV307 @ SV365 ) )
= $false )
| ( ( ~ ( ~ ( product_curry_a_a_o @ SV122 @ SV307 @ SV365 )
| ~ ( SV122 @ ( product_Pair_a_a @ SV307 @ SV365 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1649]) ).
thf(1754,plain,
! [SV308: a > a,SV228: set_Product_prod_a_a,SV123: a,SV4: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV4 @ SV123 ) @ ( inv_image_a_a @ SV228 @ SV308 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV4 @ SV123 ) @ ( inv_image_a_a @ SV228 @ SV308 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1650]) ).
thf(1755,plain,
! [SV228: set_Product_prod_a_a,SV123: a,SV4: a,SV308: a > a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV308 @ SV4 ) @ ( SV308 @ SV123 ) ) @ SV228 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV4 @ SV123 ) @ ( inv_image_a_a @ SV228 @ SV308 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1650]) ).
thf(1756,plain,
! [SV308: a > a,SV228: set_Product_prod_a_a,SV123: a,SV4: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV4 @ SV123 ) @ ( inv_image_a_a @ SV228 @ SV308 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV308 @ SV4 ) @ ( SV308 @ SV123 ) ) @ SV228 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1651]) ).
thf(1757,plain,
! [SV228: set_Product_prod_a_a,SV123: a,SV4: a,SV308: a > a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV308 @ SV4 ) @ ( SV308 @ SV123 ) ) @ SV228 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV308 @ SV4 ) @ ( SV308 @ SV123 ) ) @ SV228 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1651]) ).
thf(1758,plain,
! [SV309: a > multiset_a,SV229: set_Pr158363655iset_a,SV124: a,SV5: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV5 @ SV124 ) @ ( inv_im975322764et_a_a @ SV229 @ SV309 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV5 @ SV124 ) @ ( inv_im975322764et_a_a @ SV229 @ SV309 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1652]) ).
thf(1759,plain,
! [SV229: set_Pr158363655iset_a,SV124: a,SV5: a,SV309: a > multiset_a] :
( ( ( ~ ( member340150864iset_a @ ( produc2037245207iset_a @ ( SV309 @ SV5 ) @ ( SV309 @ SV124 ) ) @ SV229 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV5 @ SV124 ) @ ( inv_im975322764et_a_a @ SV229 @ SV309 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1652]) ).
thf(1760,plain,
! [SV309: a > multiset_a,SV229: set_Pr158363655iset_a,SV124: a,SV5: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV5 @ SV124 ) @ ( inv_im975322764et_a_a @ SV229 @ SV309 ) ) )
= $false )
| ( ( member340150864iset_a @ ( produc2037245207iset_a @ ( SV309 @ SV5 ) @ ( SV309 @ SV124 ) ) @ SV229 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1653]) ).
thf(1761,plain,
! [SV229: set_Pr158363655iset_a,SV124: a,SV5: a,SV309: a > multiset_a] :
( ( ( ~ ( member340150864iset_a @ ( produc2037245207iset_a @ ( SV309 @ SV5 ) @ ( SV309 @ SV124 ) ) @ SV229 ) )
= $false )
| ( ( member340150864iset_a @ ( produc2037245207iset_a @ ( SV309 @ SV5 ) @ ( SV309 @ SV124 ) ) @ SV229 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1653]) ).
thf(1762,plain,
! [SV310: multiset_a > a,SV230: set_Product_prod_a_a,SV125: multiset_a,SV6: multiset_a] :
( ( ( ~ ( member340150864iset_a @ ( produc2037245207iset_a @ SV6 @ SV125 ) @ ( inv_im479034648iset_a @ SV230 @ SV310 ) ) )
= $false )
| ( ( member340150864iset_a @ ( produc2037245207iset_a @ SV6 @ SV125 ) @ ( inv_im479034648iset_a @ SV230 @ SV310 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1654]) ).
thf(1763,plain,
! [SV230: set_Product_prod_a_a,SV125: multiset_a,SV6: multiset_a,SV310: multiset_a > a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV310 @ SV6 ) @ ( SV310 @ SV125 ) ) @ SV230 ) )
= $false )
| ( ( member340150864iset_a @ ( produc2037245207iset_a @ SV6 @ SV125 ) @ ( inv_im479034648iset_a @ SV230 @ SV310 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1654]) ).
thf(1764,plain,
! [SV310: multiset_a > a,SV230: set_Product_prod_a_a,SV125: multiset_a,SV6: multiset_a] :
( ( ( ~ ( member340150864iset_a @ ( produc2037245207iset_a @ SV6 @ SV125 ) @ ( inv_im479034648iset_a @ SV230 @ SV310 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV310 @ SV6 ) @ ( SV310 @ SV125 ) ) @ SV230 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1655]) ).
thf(1765,plain,
! [SV230: set_Product_prod_a_a,SV125: multiset_a,SV6: multiset_a,SV310: multiset_a > a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV310 @ SV6 ) @ ( SV310 @ SV125 ) ) @ SV230 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV310 @ SV6 ) @ ( SV310 @ SV125 ) ) @ SV230 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1655]) ).
thf(1766,plain,
! [SV311: a > product_prod_a_a,SV231: set_Pr1948701895od_a_a,SV126: a,SV7: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV7 @ SV126 ) @ ( inv_im777352425_a_a_a @ SV231 @ SV311 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV7 @ SV126 ) @ ( inv_im777352425_a_a_a @ SV231 @ SV311 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1656]) ).
thf(1767,plain,
! [SV231: set_Pr1948701895od_a_a,SV126: a,SV7: a,SV311: a > product_prod_a_a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( SV311 @ SV7 ) @ ( SV311 @ SV126 ) ) @ SV231 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV7 @ SV126 ) @ ( inv_im777352425_a_a_a @ SV231 @ SV311 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1656]) ).
thf(1768,plain,
! [SV311: a > product_prod_a_a,SV231: set_Pr1948701895od_a_a,SV126: a,SV7: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV7 @ SV126 ) @ ( inv_im777352425_a_a_a @ SV231 @ SV311 ) ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( SV311 @ SV7 ) @ ( SV311 @ SV126 ) ) @ SV231 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1657]) ).
thf(1769,plain,
! [SV231: set_Pr1948701895od_a_a,SV126: a,SV7: a,SV311: a > product_prod_a_a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( SV311 @ SV7 ) @ ( SV311 @ SV126 ) ) @ SV231 ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( SV311 @ SV7 ) @ ( SV311 @ SV126 ) ) @ SV231 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1657]) ).
thf(1770,plain,
! [SV312: product_prod_a_a > a,SV232: set_Product_prod_a_a,SV127: product_prod_a_a,SV8: product_prod_a_a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV8 @ SV127 ) @ ( inv_im15016955od_a_a @ SV232 @ SV312 ) ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV8 @ SV127 ) @ ( inv_im15016955od_a_a @ SV232 @ SV312 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1658]) ).
thf(1771,plain,
! [SV232: set_Product_prod_a_a,SV127: product_prod_a_a,SV8: product_prod_a_a,SV312: product_prod_a_a > a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV312 @ SV8 ) @ ( SV312 @ SV127 ) ) @ SV232 ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV8 @ SV127 ) @ ( inv_im15016955od_a_a @ SV232 @ SV312 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1658]) ).
thf(1772,plain,
! [SV312: product_prod_a_a > a,SV232: set_Product_prod_a_a,SV127: product_prod_a_a,SV8: product_prod_a_a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV8 @ SV127 ) @ ( inv_im15016955od_a_a @ SV232 @ SV312 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV312 @ SV8 ) @ ( SV312 @ SV127 ) ) @ SV232 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1659]) ).
thf(1773,plain,
! [SV232: set_Product_prod_a_a,SV127: product_prod_a_a,SV8: product_prod_a_a,SV312: product_prod_a_a > a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV312 @ SV8 ) @ ( SV312 @ SV127 ) ) @ SV232 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV312 @ SV8 ) @ ( SV312 @ SV127 ) ) @ SV232 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1659]) ).
thf(1774,plain,
! [SV313: a > multis599418605od_a_a,SV233: set_Pr1821581383od_a_a,SV128: a,SV9: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV128 ) @ ( inv_im1681759523_a_a_a @ SV233 @ SV313 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV128 ) @ ( inv_im1681759523_a_a_a @ SV233 @ SV313 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1660]) ).
thf(1775,plain,
! [SV233: set_Pr1821581383od_a_a,SV128: a,SV9: a,SV313: a > multis599418605od_a_a] :
( ( ( ~ ( member1349055120od_a_a @ ( produc1859144151od_a_a @ ( SV313 @ SV9 ) @ ( SV313 @ SV128 ) ) @ SV233 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV128 ) @ ( inv_im1681759523_a_a_a @ SV233 @ SV313 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1660]) ).
thf(1776,plain,
! [SV313: a > multis599418605od_a_a,SV233: set_Pr1821581383od_a_a,SV128: a,SV9: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV128 ) @ ( inv_im1681759523_a_a_a @ SV233 @ SV313 ) ) )
= $false )
| ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ ( SV313 @ SV9 ) @ ( SV313 @ SV128 ) ) @ SV233 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1661]) ).
thf(1777,plain,
! [SV233: set_Pr1821581383od_a_a,SV128: a,SV9: a,SV313: a > multis599418605od_a_a] :
( ( ( ~ ( member1349055120od_a_a @ ( produc1859144151od_a_a @ ( SV313 @ SV9 ) @ ( SV313 @ SV128 ) ) @ SV233 ) )
= $false )
| ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ ( SV313 @ SV9 ) @ ( SV313 @ SV128 ) ) @ SV233 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1661]) ).
thf(1778,plain,
! [SV314: multis599418605od_a_a > a,SV234: set_Product_prod_a_a,SV129: multis599418605od_a_a,SV10: multis599418605od_a_a] :
( ( ( ~ ( member1349055120od_a_a @ ( produc1859144151od_a_a @ SV10 @ SV129 ) @ ( inv_im941243329od_a_a @ SV234 @ SV314 ) ) )
= $false )
| ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ SV10 @ SV129 ) @ ( inv_im941243329od_a_a @ SV234 @ SV314 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1662]) ).
thf(1779,plain,
! [SV234: set_Product_prod_a_a,SV129: multis599418605od_a_a,SV10: multis599418605od_a_a,SV314: multis599418605od_a_a > a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV314 @ SV10 ) @ ( SV314 @ SV129 ) ) @ SV234 ) )
= $false )
| ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ SV10 @ SV129 ) @ ( inv_im941243329od_a_a @ SV234 @ SV314 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1662]) ).
thf(1780,plain,
! [SV314: multis599418605od_a_a > a,SV234: set_Product_prod_a_a,SV129: multis599418605od_a_a,SV10: multis599418605od_a_a] :
( ( ( ~ ( member1349055120od_a_a @ ( produc1859144151od_a_a @ SV10 @ SV129 ) @ ( inv_im941243329od_a_a @ SV234 @ SV314 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV314 @ SV10 ) @ ( SV314 @ SV129 ) ) @ SV234 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1663]) ).
thf(1781,plain,
! [SV234: set_Product_prod_a_a,SV129: multis599418605od_a_a,SV10: multis599418605od_a_a,SV314: multis599418605od_a_a > a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV314 @ SV10 ) @ ( SV314 @ SV129 ) ) @ SV234 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV314 @ SV10 ) @ ( SV314 @ SV129 ) ) @ SV234 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1663]) ).
thf(1782,plain,
! [SV237: a,SV133: a,SV14: a > a > $o] :
( ( ( produc1833107820_a_a_o @ SV14 @ ( product_Pair_a_a @ SV133 @ SV237 ) )
= $true )
| ( ( produc1833107820_a_a_o @ SV14 @ ( product_Pair_a_a @ SV133 @ SV237 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1664]) ).
thf(1783,plain,
! [SV237: a,SV133: a,SV14: a > a > $o] :
( ( ( SV14 @ SV133 @ SV237 )
= $true )
| ( ( produc1833107820_a_a_o @ SV14 @ ( product_Pair_a_a @ SV133 @ SV237 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1665]) ).
thf(1784,plain,
! [SV237: a,SV133: a,SV14: a > a > $o] :
( ( ( produc1833107820_a_a_o @ SV14 @ ( product_Pair_a_a @ SV133 @ SV237 ) )
= $true )
| ( ( SV14 @ SV133 @ SV237 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1666]) ).
thf(1785,plain,
! [SV237: a,SV133: a,SV14: a > a > $o] :
( ( ( SV14 @ SV133 @ SV237 )
= $true )
| ( ( SV14 @ SV133 @ SV237 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1667]) ).
thf(1786,plain,
! [SV134: set_Product_prod_a_a,SV372: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV372 @ SV372 ) @ SV134 ) )
= $true )
| ( ( irrefl_a @ SV134 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1669]) ).
thf(1787,plain,
! [SV134: set_Product_prod_a_a] :
( ( ( ~ ( irrefl_a @ SV134 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK34_SY751 @ SV134 ) @ ( sK34_SY751 @ SV134 ) ) @ SV134 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1670]) ).
thf(1788,plain,
! [SV134: set_Product_prod_a_a] :
( ( ( ~ ! [SY751: a] :
~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY751 @ SY751 ) @ SV134 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK34_SY751 @ SV134 ) @ ( sK34_SY751 @ SV134 ) ) @ SV134 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1670]) ).
thf(1789,plain,
! [SV238: set_Product_prod_a_a,SV135: a,SV16: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV16 @ SV135 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV238 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV16 @ SV135 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV238 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1671]) ).
thf(1790,plain,
! [SV238: set_Product_prod_a_a,SV16: a,SV135: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV135 @ SV16 ) @ SV238 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV16 @ SV135 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV238 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1672]) ).
thf(1791,plain,
! [SV238: set_Product_prod_a_a,SV135: a,SV16: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV16 @ SV135 ) @ ( image_794773445od_a_a @ product_swap_a_a @ SV238 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV135 @ SV16 ) @ SV238 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1673]) ).
thf(1792,plain,
! [SV238: set_Product_prod_a_a,SV16: a,SV135: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV135 @ SV16 ) @ SV238 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV135 @ SV16 ) @ SV238 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1674]) ).
thf(1793,plain,
! [SV240: multis599418605od_a_a,SV141: multis599418605od_a_a,SV25: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ ( plus_p404985124od_a_a @ SV141 @ SV240 ) ) )
= $true )
| ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ ( plus_p404985124od_a_a @ SV141 @ SV240 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1679]) ).
thf(1794,plain,
! [SV240: multis599418605od_a_a,SV141: multis599418605od_a_a,SV25: product_prod_a_a] :
( ( ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV141 ) )
| ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV240 ) ) )
= $true )
| ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ ( plus_p404985124od_a_a @ SV141 @ SV240 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1680]) ).
thf(1795,plain,
! [SV240: multis599418605od_a_a,SV141: multis599418605od_a_a,SV25: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ ( plus_p404985124od_a_a @ SV141 @ SV240 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV141 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1681]) ).
thf(1796,plain,
! [SV240: multis599418605od_a_a,SV141: multis599418605od_a_a,SV25: product_prod_a_a] :
( ( ( ~ ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV141 ) )
| ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV240 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV141 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1681]) ).
thf(1797,plain,
! [SV240: multis599418605od_a_a,SV141: multis599418605od_a_a,SV25: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ ( plus_p404985124od_a_a @ SV141 @ SV240 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV240 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1682]) ).
thf(1798,plain,
! [SV240: multis599418605od_a_a,SV141: multis599418605od_a_a,SV25: product_prod_a_a] :
( ( ( ~ ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV141 ) )
| ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV240 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV240 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1682]) ).
thf(1799,plain,
! [SV32: set_Product_prod_a_a,SV147: set_Pr1948701895od_a_a] :
( ( ( ( sK10_SY764 @ SV147 @ SV32 )
!= ( sK20_SY1027 @ SV32 @ SV147 ) )
= $true )
| ( ( total_1490170027od_a_a @ SV32 @ SV147 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1686]) ).
thf(1800,plain,
! [SV32: set_Product_prod_a_a,SV147: set_Pr1948701895od_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK10_SY764 @ SV147 @ SV32 ) @ ( sK20_SY1027 @ SV32 @ SV147 ) ) @ SV147 )
= $false )
| ( ( total_1490170027od_a_a @ SV32 @ SV147 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1687]) ).
thf(1801,plain,
! [SV147: set_Pr1948701895od_a_a,SV32: set_Product_prod_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK20_SY1027 @ SV32 @ SV147 ) @ ( sK10_SY764 @ SV147 @ SV32 ) ) @ SV147 )
= $false )
| ( ( total_1490170027od_a_a @ SV32 @ SV147 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1687]) ).
thf(1802,plain,
! [SV245: a > $o,SV317: a,SV148: a,SV33: a > $o] :
( ( ( ~ ( SV33 @ ( product_fst_a_a @ ( product_Pair_a_a @ SV148 @ SV317 ) ) ) )
= $false )
| ( ( SV245 @ SV317 )
= $false )
| ( ( SV33 @ SV148 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1688]) ).
thf(1803,plain,
! [SV33: a > $o,SV317: a,SV148: a,SV245: a > $o] :
( ( ( ~ ( SV245 @ ( product_snd_a_a @ ( product_Pair_a_a @ SV148 @ SV317 ) ) ) )
= $false )
| ( ( SV245 @ SV317 )
= $false )
| ( ( SV33 @ SV148 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1688]) ).
thf(1804,plain,
! [SV151: set_Product_prod_a_a > $o,SV36: set_Product_prod_a_a,SV373: a] :
( ( ( ! [SY1055: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV373 @ SY1055 ) @ ( sK36_SY772 @ SV36 @ SV151 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1055 @ SV373 ) @ ( sK36_SY772 @ SV36 @ SV151 ) ) ) )
= $true )
| ( ( SV151 @ SV36 )
= $true )
| ( ( asym_a @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1690]) ).
thf(1805,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a] :
( ( ( ~ ( total_1490170027od_a_a @ SV154 @ SV320 ) )
= $false )
| ( ( total_1490170027od_a_a @ SV154 @ SV320 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1691]) ).
thf(1806,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a] :
( ( ( ~ ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) )
= $false )
| ( ( total_1490170027od_a_a @ SV154 @ SV320 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1691]) ).
thf(1807,plain,
! [SV154: set_Product_prod_a_a,SV320: set_Pr1948701895od_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK54_SY1005 @ SV320 @ SV154 ) @ SV154 ) )
= $false )
| ( ( ~ ( ~ ( total_1490170027od_a_a @ SV154 @ SV320 )
| ~ ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1692]) ).
thf(1808,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a] :
( ( ( ! [SY1053: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1053 @ SV154 )
| ~ ( ( ( sK54_SY1005 @ SV320 @ SV154 )
!= SY1053 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK54_SY1005 @ SV320 @ SV154 ) @ SY1053 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1053 @ ( sK54_SY1005 @ SV320 @ SV154 ) ) @ SV320 ) ) )
= $false )
| ( ( ~ ( ~ ( total_1490170027od_a_a @ SV154 @ SV320 )
| ~ ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1692]) ).
thf(1809,plain,
! [SV40: a,SV155: product_prod_a_a] :
( ( ( ! [SY782: a] :
( SV155
!= ( product_Pair_a_a @ SV40 @ SY782 ) ) )
= $false )
| ( ( SV40
= ( product_fst_a_a @ SV155 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1694]) ).
thf(1810,plain,
! [SV367: a,SV155: product_prod_a_a,SV40: a] :
( ( ( ( SV40
!= ( product_fst_a_a @ SV155 ) )
| ~ ~ ! [SY782: a] :
( SV155
!= ( product_Pair_a_a @ SV40 @ SY782 ) ) )
= $false )
| ( ( SV155
= ( product_Pair_a_a @ SV40 @ SV367 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1695]) ).
thf(1811,plain,
! [SV156: a,SV41: set_Product_prod_a_a,SV321: a,SV249: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV249 @ SV321 ) @ SV41 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV156 @ SV321 ) @ SV41 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV156 @ SV249 ) @ SV41 )
= $false )
| ( ( trans_a @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1696]) ).
thf(1812,plain,
! [SV324: a,SV252: a,SV159: a,SV44: a] :
( ( ( ( product_Pair_a_a @ SV44 @ SV159 )
!= ( product_Pair_a_a @ SV252 @ SV324 ) )
= $false )
| ( ( ( product_Pair_a_a @ SV44 @ SV159 )
= ( product_Pair_a_a @ SV252 @ SV324 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1697]) ).
thf(1813,plain,
! [SV324: a,SV159: a,SV252: a,SV44: a] :
( ( ( ~ ~ ( ( SV44 != SV252 )
| ( SV159 != SV324 ) ) )
= $false )
| ( ( ( product_Pair_a_a @ SV44 @ SV159 )
= ( product_Pair_a_a @ SV252 @ SV324 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1697]) ).
thf(1814,plain,
! [SV324: a,SV159: a,SV252: a,SV44: a] :
( ( ( SV44 != SV252 )
= $true )
| ( ( SV159 != SV324 )
= $true )
| ( ( ~ ( ( ( product_Pair_a_a @ SV44 @ SV159 )
!= ( product_Pair_a_a @ SV252 @ SV324 ) )
| ~ ~ ( ( SV44 != SV252 )
| ( SV159 != SV324 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1698]) ).
thf(1815,plain,
! [SV160: a,SV45: set_Product_prod_a_a,SV325: a,SV253: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV253 @ SV325 ) @ SV45 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV160 @ SV325 ) @ SV45 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV160 @ SV253 ) @ SV45 )
= $false )
| ( ( trans_a @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1699]) ).
thf(1816,plain,
! [SV162: set_Pr1948701895od_a_a,SV358: product_prod_a_a,SV47: set_Product_prod_a_a,SV368: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV368 @ SV47 )
= $false )
| ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV358 @ SV368 ) @ SV162 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV368 @ SV358 ) @ SV162 ) )
= $true )
| ( ( member449909584od_a_a @ SV358 @ SV47 )
= $false )
| ( ( prefer697821563od_a_a @ SV47 @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1700]) ).
thf(1817,plain,
! [SV48: set_a,SV163: set_Product_prod_a_a] :
( ( ( ( sK12_SY797 @ SV163 @ SV48 )
!= ( sK24_SY1030 @ SV48 @ SV163 ) )
= $true )
| ( ( total_on_a @ SV48 @ SV163 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1702]) ).
thf(1818,plain,
! [SV48: set_a,SV163: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK12_SY797 @ SV163 @ SV48 ) @ ( sK24_SY1030 @ SV48 @ SV163 ) ) @ SV163 )
= $false )
| ( ( total_on_a @ SV48 @ SV163 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1703]) ).
thf(1819,plain,
! [SV163: set_Product_prod_a_a,SV48: set_a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK24_SY1030 @ SV48 @ SV163 ) @ ( sK12_SY797 @ SV163 @ SV48 ) ) @ SV163 )
= $false )
| ( ( total_on_a @ SV48 @ SV163 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1703]) ).
thf(1820,plain,
! [SV366: set_Product_prod_a_a,SV359: set_Product_prod_a_a,SV327: a,SV257: a,SV166: a,SV52: a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SV257 @ SV327 ) ) @ ( lex_prod_a_a @ SV359 @ SV366 ) )
= $false )
| ( ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SV257 @ SV327 ) ) @ ( lex_prod_a_a @ SV359 @ SV366 ) )
| ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
| ~ ( ( SV52 != SV257 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1704]) ).
thf(1821,plain,
! [SV366: set_Product_prod_a_a,SV327: a,SV166: a,SV359: set_Product_prod_a_a,SV257: a,SV52: a] :
( ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
| ~ ( ( SV52 != SV257 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 ) ) )
= $false )
| ( ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SV257 @ SV327 ) ) @ ( lex_prod_a_a @ SV359 @ SV366 ) )
| ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
| ~ ( ( SV52 != SV257 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1704]) ).
thf(1822,plain,
! [SV330: a,SV261: a,SV170: a,SV56: a] :
( ( ( ( product_Pair_a_a @ SV56 @ SV170 )
!= ( product_Pair_a_a @ SV261 @ SV330 ) )
= $false )
| ( ( ( product_Pair_a_a @ SV56 @ SV170 )
= ( product_Pair_a_a @ SV261 @ SV330 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1705]) ).
thf(1823,plain,
! [SV330: a,SV170: a,SV261: a,SV56: a] :
( ( ( ~ ~ ( ( SV56 != SV261 )
| ( SV170 != SV330 ) ) )
= $false )
| ( ( ( product_Pair_a_a @ SV56 @ SV170 )
= ( product_Pair_a_a @ SV261 @ SV330 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1705]) ).
thf(1824,plain,
! [SV330: a,SV170: a,SV261: a,SV56: a] :
( ( ( SV56 != SV261 )
= $true )
| ( ( SV170 != SV330 )
= $true )
| ( ( ~ ( ( ( product_Pair_a_a @ SV56 @ SV170 )
!= ( product_Pair_a_a @ SV261 @ SV330 ) )
| ~ ~ ( ( SV56 != SV261 )
| ( SV170 != SV330 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1706]) ).
thf(1825,plain,
! [SV57: a,SV262: a,SV171: a] :
( ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV171 @ SV262 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV262 @ SV171 ) @ relation ) ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV262 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV262 @ SV57 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV171 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV171 @ SV57 ) @ relation )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1707]) ).
thf(1826,plain,
! [SV172: set_Product_prod_a_a,SV331: a,SV58: set_a,SV263: a] :
( ( ( ~ ( member_a @ SV263 @ SV58 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV263 @ SV331 ) @ SV172 )
= $false )
| ( ( refl_on_a @ SV58 @ SV172 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1708]) ).
thf(1827,plain,
! [SV172: set_Product_prod_a_a,SV263: a,SV58: set_a,SV331: a] :
( ( ( ~ ( member_a @ SV331 @ SV58 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV263 @ SV331 ) @ SV172 )
= $false )
| ( ( refl_on_a @ SV58 @ SV172 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1708]) ).
thf(1828,plain,
! [SV264: a > a,SV332: set_Product_prod_a_a,SV173: a > a,SV59: product_prod_a_a] :
( ( ( SV59
!= ( product_Pair_a_a @ ( SV173 @ ( sK45_SY1009 @ SV332 @ SV264 @ SV173 @ SV59 ) ) @ ( SV264 @ ( sK55_SY1049 @ SV264 @ SV332 @ SV173 @ SV59 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ SV59 @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SV173 @ SV264 ) @ SV332 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1709]) ).
thf(1829,plain,
! [SV59: product_prod_a_a,SV173: a > a,SV264: a > a,SV332: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK45_SY1009 @ SV332 @ SV264 @ SV173 @ SV59 ) @ ( sK55_SY1049 @ SV264 @ SV332 @ SV173 @ SV59 ) ) @ SV332 ) )
= $false )
| ( ( member449909584od_a_a @ SV59 @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SV173 @ SV264 ) @ SV332 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1709]) ).
thf(1830,plain,
! [SV174: set_Pr1948701895od_a_a,SV333: product_prod_a_a,SV60: set_Product_prod_a_a,SV265: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV265 @ SV60 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ SV333 @ SV60 ) )
= $true )
| ( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) )
= ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
| ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) ) ) )
= $true )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1710]) ).
thf(1831,plain,
! [SV175: set_Product_prod_a_a,SV334: a,SV61: set_a,SV266: a] :
( ( ( ~ ( member_a @ SV266 @ SV61 ) )
= $true )
| ( ( ~ ( member_a @ SV334 @ SV61 ) )
= $true )
| ( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) ) ) )
= $true )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1711]) ).
thf(1832,plain,
! [SV179: set_Product_prod_a_a,SV374: a] :
( ( ( ! [SY1056: a,SY1057: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV374 @ SY1056 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1056 @ SY1057 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV374 @ SY1057 ) @ SV179 ) ) )
= $true )
| ( ( trans_a @ SV179 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1714]) ).
thf(1833,plain,
! [SV179: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK37_SY828 @ SV179 ) @ ( sK46_SY1040 @ SV179 ) ) @ SV179 ) )
= $false )
| ( ( ~ ( ~ ( trans_a @ SV179 )
| ~ ! [SY828: a,SY829: a,SY830: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY829 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY829 @ SY830 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY830 ) @ SV179 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1715]) ).
thf(1834,plain,
! [SV179: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK46_SY1040 @ SV179 ) @ ( sK56_SY1050 @ SV179 ) ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK37_SY828 @ SV179 ) @ ( sK56_SY1050 @ SV179 ) ) @ SV179 ) )
= $false )
| ( ( ~ ( ~ ( trans_a @ SV179 )
| ~ ! [SY828: a,SY829: a,SY830: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY829 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY829 @ SY830 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY830 ) @ SV179 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1715]) ).
thf(1835,plain,
! [SV74: set_a,SV360: a,SV184: set_Product_prod_a_a,SV336: a,SV272: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV336 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV272 ) @ SV184 ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV360 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV336 ) @ SV184 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV360 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV272 ) @ SV184 ) ) )
= $true )
| ( ( prefer719835986ence_a @ SV74 @ SV184 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1716]) ).
thf(1836,plain,
! [SV88: a,SV196: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) ) ) )
= $true )
| ( ( member_a @ SV88 @ carrier )
= $false )
| ( ( member_a @ SV196 @ carrier )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1717]) ).
thf(1837,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a] :
( ( ( ~ ( total_on_a @ SV197 @ SV343 ) )
= $false )
| ( ( total_on_a @ SV197 @ SV343 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1719]) ).
thf(1838,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a] :
( ( ( ~ ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) )
= $false )
| ( ( total_on_a @ SV197 @ SV343 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1719]) ).
thf(1839,plain,
! [SV197: set_a,SV343: set_Product_prod_a_a] :
( ( ( ~ ( member_a @ ( sK57_SY1017 @ SV343 @ SV197 ) @ SV197 ) )
= $false )
| ( ( ~ ( ~ ( total_on_a @ SV197 @ SV343 )
| ~ ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1720]) ).
thf(1840,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a] :
( ( ( ! [SY1054: a] :
( ~ ( member_a @ SY1054 @ SV197 )
| ~ ( ( ( sK57_SY1017 @ SV343 @ SV197 )
!= SY1054 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK57_SY1017 @ SV343 @ SV197 ) @ SY1054 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1054 @ ( sK57_SY1017 @ SV343 @ SV197 ) ) @ SV343 ) ) )
= $false )
| ( ( ~ ( ~ ( total_on_a @ SV197 @ SV343 )
| ~ ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1720]) ).
thf(1841,plain,
! [SV198: set_Product_prod_a_a] :
( ( ( ! [SY857: set_Product_prod_a_a] :
~ ~ ( ( SV198 != SY857 )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SY857 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SY857 ) ) ) )
= $false )
| ( ( asym_a @ SV198 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1722]) ).
thf(1842,plain,
! [SV369: set_Product_prod_a_a,SV198: set_Product_prod_a_a] :
( ( ( ( SV198 != SV369 )
| ~ ! [SY1051: a,SY1052: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1051 @ SY1052 ) @ SV369 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1052 @ SY1051 ) @ SV369 ) ) )
= $true )
| ( ( ~ ( ~ ( asym_a @ SV198 )
| ~ ~ ! [SY857: set_Product_prod_a_a] :
~ ~ ( ( SV198 != SY857 )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SY857 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SY857 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1723]) ).
thf(1843,plain,
! [SV199: set_Product_prod_a_a,SV375: a] :
( ( ( ! [SY1058: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV375 @ SY1058 ) @ SV199 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1058 @ SV375 ) @ SV199 ) ) )
= $true )
| ( ( asym_a @ SV199 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1725]) ).
thf(1844,plain,
! [SV199: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK38_SY860 @ SV199 ) @ ( sK47_SY1042 @ SV199 ) ) @ SV199 )
= $true )
| ( ( ~ ( ~ ( asym_a @ SV199 )
| ~ ! [SY860: a,SY861: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY860 @ SY861 ) @ SV199 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY861 @ SY860 ) @ SV199 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1726]) ).
thf(1845,plain,
! [SV199: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK47_SY1042 @ SV199 ) @ ( sK38_SY860 @ SV199 ) ) @ SV199 )
= $true )
| ( ( ~ ( ~ ( asym_a @ SV199 )
| ~ ! [SY860: a,SY861: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY860 @ SY861 ) @ SV199 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY861 @ SY860 ) @ SV199 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1727]) ).
thf(1846,plain,
! [SV93: set_a,SV362: a,SV201: set_Product_prod_a_a,SV345: a,SV286: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SV345 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV286 ) @ SV201 ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV362 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV362 @ SV345 ) @ SV201 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SV362 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV362 @ SV286 ) @ SV201 ) ) )
= $true )
| ( ( prefer1292084992ence_a @ SV93 @ SV201 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1729]) ).
thf(1847,plain,
! [SV95: multis599418605od_a_a,SV203: a > a > set_mu1281098573od_a_a,SV288: product_prod_a_a] :
( ( ( SV288
= ( product_Pair_a_a @ ( sK39_SY976 @ SV203 @ SV95 @ SV288 ) @ ( sK48_SY1043 @ SV95 @ SV203 @ SV288 ) ) )
= $true )
| ( ( member1755255446od_a_a @ SV95 @ ( produc1121147169od_a_a @ SV203 @ SV288 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1730]) ).
thf(1848,plain,
! [SV288: product_prod_a_a,SV203: a > a > set_mu1281098573od_a_a,SV95: multis599418605od_a_a] :
( ( ( member1755255446od_a_a @ SV95 @ ( SV203 @ ( sK39_SY976 @ SV203 @ SV95 @ SV288 ) @ ( sK48_SY1043 @ SV95 @ SV203 @ SV288 ) ) )
= $true )
| ( ( member1755255446od_a_a @ SV95 @ ( produc1121147169od_a_a @ SV203 @ SV288 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1731]) ).
thf(1849,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 ) )
= $false )
| ( ( prefer1292084992ence_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1732]) ).
thf(1850,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) )
= $false )
| ( ( prefer1292084992ence_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1732]) ).
thf(1851,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) ) )
= $true )
| ( ( ~ ( order_preorder_on_a @ SV204 @ SV347 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 )
| ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1733]) ).
thf(1852,plain,
! [SV98: multiset_a,SV206: a > a > set_multiset_a,SV290: product_prod_a_a] :
( ( ( SV290
= ( product_Pair_a_a @ ( sK40_SY982 @ SV206 @ SV98 @ SV290 ) @ ( sK49_SY1044 @ SV98 @ SV206 @ SV290 ) ) )
= $true )
| ( ( member_multiset_a @ SV98 @ ( produc1828150264iset_a @ SV206 @ SV290 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1734]) ).
thf(1853,plain,
! [SV290: product_prod_a_a,SV206: a > a > set_multiset_a,SV98: multiset_a] :
( ( ( member_multiset_a @ SV98 @ ( SV206 @ ( sK40_SY982 @ SV206 @ SV98 @ SV290 ) @ ( sK49_SY1044 @ SV98 @ SV206 @ SV290 ) ) )
= $true )
| ( ( member_multiset_a @ SV98 @ ( produc1828150264iset_a @ SV206 @ SV290 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1735]) ).
thf(1854,plain,
! [SV207: set_a,SV100: set_Product_prod_a_a] :
( ( ( ! [SY883: a,SY884: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY883 @ SY884 ) @ SV100 )
| ( member_a @ SY884 @ SV207 ) ) )
= $false )
| ( ( ~ ( order_preorder_on_a @ SV207 @ SV100 )
| ( prefer1292084992ence_a @ SV207 @ SV100 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK17_SY881 @ SV207 @ SV100 ) @ ( sK30_SY1034 @ SV100 @ SV207 ) ) @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1736]) ).
thf(1855,plain,
! [SV100: set_Product_prod_a_a,SV207: set_a] :
( ( ( ! [SY1059: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK58_SY883 @ SV207 @ SV100 ) @ SY1059 ) @ SV100 )
| ( member_a @ SY1059 @ SV207 ) ) )
= $false )
| ( ( ~ ( order_preorder_on_a @ SV207 @ SV100 )
| ( prefer1292084992ence_a @ SV207 @ SV100 ) )
= $true )
| ( ( member_a @ ( sK17_SY881 @ SV207 @ SV100 ) @ SV207 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1737]) ).
thf(1856,plain,
! [SV291: a,SV101: a,SV208: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV101 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SV208 ) @ relation )
= $false )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV291 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV291 @ SV208 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SV291 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV291 @ SV101 ) @ relation ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1738]) ).
thf(1857,plain,
! [SV103: a,SV210: a > a > set_a,SV293: product_prod_a_a] :
( ( ( SV293
= ( product_Pair_a_a @ ( sK41_SY985 @ SV210 @ SV103 @ SV293 ) @ ( sK50_SY1045 @ SV103 @ SV210 @ SV293 ) ) )
= $true )
| ( ( member_a @ SV103 @ ( produc961951794_set_a @ SV210 @ SV293 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1739]) ).
thf(1858,plain,
! [SV293: product_prod_a_a,SV210: a > a > set_a,SV103: a] :
( ( ( member_a @ SV103 @ ( SV210 @ ( sK41_SY985 @ SV210 @ SV103 @ SV293 ) @ ( sK50_SY1045 @ SV103 @ SV210 @ SV293 ) ) )
= $true )
| ( ( member_a @ SV103 @ ( produc961951794_set_a @ SV210 @ SV293 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1740]) ).
thf(1859,plain,
! [SV213: set_Pr1948701895od_a_a,SV349: product_prod_a_a,SV106: set_Product_prod_a_a,SV295: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV295 @ SV106 ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV295 @ SV349 ) @ SV213 )
= $false )
| ( ( refl_o1298442278od_a_a @ SV106 @ SV213 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1741]) ).
thf(1860,plain,
! [SV213: set_Pr1948701895od_a_a,SV295: product_prod_a_a,SV106: set_Product_prod_a_a,SV349: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV349 @ SV106 ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV295 @ SV349 ) @ SV213 )
= $false )
| ( ( refl_o1298442278od_a_a @ SV106 @ SV213 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1741]) ).
thf(1861,plain,
! [SV112: a,SV219: product_prod_a_a] :
( ( ( ! [SY907: a] :
( SV219
!= ( product_Pair_a_a @ SY907 @ SV112 ) ) )
= $false )
| ( ( SV112
= ( product_snd_a_a @ SV219 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1743]) ).
thf(1862,plain,
! [SV370: a,SV219: product_prod_a_a,SV112: a] :
( ( ( ( SV112
!= ( product_snd_a_a @ SV219 ) )
| ~ ~ ! [SY907: a] :
( SV219
!= ( product_Pair_a_a @ SY907 @ SV112 ) ) )
= $false )
| ( ( SV219
= ( product_Pair_a_a @ SV370 @ SV112 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1744]) ).
thf(1863,plain,
! [SV115: produc1127127335iset_a,SV221: a > a > set_Pr158363655iset_a,SV302: product_prod_a_a] :
( ( ( SV302
= ( product_Pair_a_a @ ( sK42_SY996 @ SV221 @ SV115 @ SV302 ) @ ( sK51_SY1046 @ SV115 @ SV221 @ SV302 ) ) )
= $true )
| ( ( member340150864iset_a @ SV115 @ ( produc93594587iset_a @ SV221 @ SV302 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1745]) ).
thf(1864,plain,
! [SV302: product_prod_a_a,SV221: a > a > set_Pr158363655iset_a,SV115: produc1127127335iset_a] :
( ( ( member340150864iset_a @ SV115 @ ( SV221 @ ( sK42_SY996 @ SV221 @ SV115 @ SV302 ) @ ( sK51_SY1046 @ SV115 @ SV221 @ SV302 ) ) )
= $true )
| ( ( member340150864iset_a @ SV115 @ ( produc93594587iset_a @ SV221 @ SV302 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1746]) ).
thf(1865,plain,
! [SV117: product_prod_a_a,SV223: multiset_a > multiset_a > set_Product_prod_a_a,SV304: produc1127127335iset_a] :
( ( ( SV304
= ( produc2037245207iset_a @ ( sK43_SY998 @ SV223 @ SV117 @ SV304 ) @ ( sK52_SY1047 @ SV117 @ SV223 @ SV304 ) ) )
= $true )
| ( ( member449909584od_a_a @ SV117 @ ( produc2041367259od_a_a @ SV223 @ SV304 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1747]) ).
thf(1866,plain,
! [SV304: produc1127127335iset_a,SV223: multiset_a > multiset_a > set_Product_prod_a_a,SV117: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV117 @ ( SV223 @ ( sK43_SY998 @ SV223 @ SV117 @ SV304 ) @ ( sK52_SY1047 @ SV117 @ SV223 @ SV304 ) ) )
= $true )
| ( ( member449909584od_a_a @ SV117 @ ( produc2041367259od_a_a @ SV223 @ SV304 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1748]) ).
thf(1867,plain,
! [SV224: set_Product_prod_a_a,SV364: a,SV118: set_a,SV371: a] :
( ( ( member_a @ SV371 @ SV118 )
= $false )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV364 @ SV371 ) @ SV224 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV371 @ SV364 ) @ SV224 ) )
= $true )
| ( ( member_a @ SV364 @ SV118 )
= $false )
| ( ( prefer719835986ence_a @ SV118 @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1749]) ).
thf(1868,plain,
! [SV120: product_prod_a_a,SV226: a > a > set_Product_prod_a_a,SV306: product_prod_a_a] :
( ( ( SV306
= ( product_Pair_a_a @ ( sK44_SY1001 @ SV226 @ SV120 @ SV306 ) @ ( sK53_SY1048 @ SV120 @ SV226 @ SV306 ) ) )
= $true )
| ( ( member449909584od_a_a @ SV120 @ ( produc1093061851od_a_a @ SV226 @ SV306 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1750]) ).
thf(1869,plain,
! [SV306: product_prod_a_a,SV226: a > a > set_Product_prod_a_a,SV120: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV120 @ ( SV226 @ ( sK44_SY1001 @ SV226 @ SV120 @ SV306 ) @ ( sK53_SY1048 @ SV120 @ SV226 @ SV306 ) ) )
= $true )
| ( ( member449909584od_a_a @ SV120 @ ( produc1093061851od_a_a @ SV226 @ SV306 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1751]) ).
thf(1870,plain,
! [SV365: a,SV307: a,SV122: product_prod_a_a > $o] :
( ( ( ~ ( product_curry_a_a_o @ SV122 @ SV307 @ SV365 )
| ~ ( SV122 @ ( product_Pair_a_a @ SV307 @ SV365 ) ) )
= $false )
| ( ( product_curry_a_a_o @ SV122 @ SV307 @ SV365 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1752]) ).
thf(1871,plain,
! [SV365: a,SV307: a,SV122: product_prod_a_a > $o] :
( ( ( ~ ( product_curry_a_a_o @ SV122 @ SV307 @ SV365 )
| ~ ( SV122 @ ( product_Pair_a_a @ SV307 @ SV365 ) ) )
= $false )
| ( ( SV122 @ ( product_Pair_a_a @ SV307 @ SV365 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1753]) ).
thf(1872,plain,
! [SV308: a > a,SV228: set_Product_prod_a_a,SV123: a,SV4: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV4 @ SV123 ) @ ( inv_image_a_a @ SV228 @ SV308 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV4 @ SV123 ) @ ( inv_image_a_a @ SV228 @ SV308 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1754]) ).
thf(1873,plain,
! [SV228: set_Product_prod_a_a,SV123: a,SV4: a,SV308: a > a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV308 @ SV4 ) @ ( SV308 @ SV123 ) ) @ SV228 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV4 @ SV123 ) @ ( inv_image_a_a @ SV228 @ SV308 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1755]) ).
thf(1874,plain,
! [SV308: a > a,SV228: set_Product_prod_a_a,SV123: a,SV4: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV4 @ SV123 ) @ ( inv_image_a_a @ SV228 @ SV308 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV308 @ SV4 ) @ ( SV308 @ SV123 ) ) @ SV228 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1756]) ).
thf(1875,plain,
! [SV228: set_Product_prod_a_a,SV123: a,SV4: a,SV308: a > a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV308 @ SV4 ) @ ( SV308 @ SV123 ) ) @ SV228 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV308 @ SV4 ) @ ( SV308 @ SV123 ) ) @ SV228 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1757]) ).
thf(1876,plain,
! [SV309: a > multiset_a,SV229: set_Pr158363655iset_a,SV124: a,SV5: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV5 @ SV124 ) @ ( inv_im975322764et_a_a @ SV229 @ SV309 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV5 @ SV124 ) @ ( inv_im975322764et_a_a @ SV229 @ SV309 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1758]) ).
thf(1877,plain,
! [SV229: set_Pr158363655iset_a,SV124: a,SV5: a,SV309: a > multiset_a] :
( ( ( member340150864iset_a @ ( produc2037245207iset_a @ ( SV309 @ SV5 ) @ ( SV309 @ SV124 ) ) @ SV229 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV5 @ SV124 ) @ ( inv_im975322764et_a_a @ SV229 @ SV309 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1759]) ).
thf(1878,plain,
! [SV309: a > multiset_a,SV229: set_Pr158363655iset_a,SV124: a,SV5: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV5 @ SV124 ) @ ( inv_im975322764et_a_a @ SV229 @ SV309 ) )
= $true )
| ( ( member340150864iset_a @ ( produc2037245207iset_a @ ( SV309 @ SV5 ) @ ( SV309 @ SV124 ) ) @ SV229 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1760]) ).
thf(1879,plain,
! [SV229: set_Pr158363655iset_a,SV124: a,SV5: a,SV309: a > multiset_a] :
( ( ( member340150864iset_a @ ( produc2037245207iset_a @ ( SV309 @ SV5 ) @ ( SV309 @ SV124 ) ) @ SV229 )
= $true )
| ( ( member340150864iset_a @ ( produc2037245207iset_a @ ( SV309 @ SV5 ) @ ( SV309 @ SV124 ) ) @ SV229 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1761]) ).
thf(1880,plain,
! [SV310: multiset_a > a,SV230: set_Product_prod_a_a,SV125: multiset_a,SV6: multiset_a] :
( ( ( member340150864iset_a @ ( produc2037245207iset_a @ SV6 @ SV125 ) @ ( inv_im479034648iset_a @ SV230 @ SV310 ) )
= $true )
| ( ( member340150864iset_a @ ( produc2037245207iset_a @ SV6 @ SV125 ) @ ( inv_im479034648iset_a @ SV230 @ SV310 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1762]) ).
thf(1881,plain,
! [SV230: set_Product_prod_a_a,SV125: multiset_a,SV6: multiset_a,SV310: multiset_a > a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV310 @ SV6 ) @ ( SV310 @ SV125 ) ) @ SV230 )
= $true )
| ( ( member340150864iset_a @ ( produc2037245207iset_a @ SV6 @ SV125 ) @ ( inv_im479034648iset_a @ SV230 @ SV310 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1763]) ).
thf(1882,plain,
! [SV310: multiset_a > a,SV230: set_Product_prod_a_a,SV125: multiset_a,SV6: multiset_a] :
( ( ( member340150864iset_a @ ( produc2037245207iset_a @ SV6 @ SV125 ) @ ( inv_im479034648iset_a @ SV230 @ SV310 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV310 @ SV6 ) @ ( SV310 @ SV125 ) ) @ SV230 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1764]) ).
thf(1883,plain,
! [SV230: set_Product_prod_a_a,SV125: multiset_a,SV6: multiset_a,SV310: multiset_a > a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV310 @ SV6 ) @ ( SV310 @ SV125 ) ) @ SV230 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV310 @ SV6 ) @ ( SV310 @ SV125 ) ) @ SV230 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1765]) ).
thf(1884,plain,
! [SV311: a > product_prod_a_a,SV231: set_Pr1948701895od_a_a,SV126: a,SV7: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV7 @ SV126 ) @ ( inv_im777352425_a_a_a @ SV231 @ SV311 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV7 @ SV126 ) @ ( inv_im777352425_a_a_a @ SV231 @ SV311 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1766]) ).
thf(1885,plain,
! [SV231: set_Pr1948701895od_a_a,SV126: a,SV7: a,SV311: a > product_prod_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( SV311 @ SV7 ) @ ( SV311 @ SV126 ) ) @ SV231 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV7 @ SV126 ) @ ( inv_im777352425_a_a_a @ SV231 @ SV311 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1767]) ).
thf(1886,plain,
! [SV311: a > product_prod_a_a,SV231: set_Pr1948701895od_a_a,SV126: a,SV7: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV7 @ SV126 ) @ ( inv_im777352425_a_a_a @ SV231 @ SV311 ) )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( SV311 @ SV7 ) @ ( SV311 @ SV126 ) ) @ SV231 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1768]) ).
thf(1887,plain,
! [SV231: set_Pr1948701895od_a_a,SV126: a,SV7: a,SV311: a > product_prod_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( SV311 @ SV7 ) @ ( SV311 @ SV126 ) ) @ SV231 )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( SV311 @ SV7 ) @ ( SV311 @ SV126 ) ) @ SV231 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1769]) ).
thf(1888,plain,
! [SV312: product_prod_a_a > a,SV232: set_Product_prod_a_a,SV127: product_prod_a_a,SV8: product_prod_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV8 @ SV127 ) @ ( inv_im15016955od_a_a @ SV232 @ SV312 ) )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV8 @ SV127 ) @ ( inv_im15016955od_a_a @ SV232 @ SV312 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1770]) ).
thf(1889,plain,
! [SV232: set_Product_prod_a_a,SV127: product_prod_a_a,SV8: product_prod_a_a,SV312: product_prod_a_a > a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV312 @ SV8 ) @ ( SV312 @ SV127 ) ) @ SV232 )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV8 @ SV127 ) @ ( inv_im15016955od_a_a @ SV232 @ SV312 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1771]) ).
thf(1890,plain,
! [SV312: product_prod_a_a > a,SV232: set_Product_prod_a_a,SV127: product_prod_a_a,SV8: product_prod_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV8 @ SV127 ) @ ( inv_im15016955od_a_a @ SV232 @ SV312 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV312 @ SV8 ) @ ( SV312 @ SV127 ) ) @ SV232 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1772]) ).
thf(1891,plain,
! [SV232: set_Product_prod_a_a,SV127: product_prod_a_a,SV8: product_prod_a_a,SV312: product_prod_a_a > a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV312 @ SV8 ) @ ( SV312 @ SV127 ) ) @ SV232 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV312 @ SV8 ) @ ( SV312 @ SV127 ) ) @ SV232 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1773]) ).
thf(1892,plain,
! [SV313: a > multis599418605od_a_a,SV233: set_Pr1821581383od_a_a,SV128: a,SV9: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV128 ) @ ( inv_im1681759523_a_a_a @ SV233 @ SV313 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV128 ) @ ( inv_im1681759523_a_a_a @ SV233 @ SV313 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1774]) ).
thf(1893,plain,
! [SV233: set_Pr1821581383od_a_a,SV128: a,SV9: a,SV313: a > multis599418605od_a_a] :
( ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ ( SV313 @ SV9 ) @ ( SV313 @ SV128 ) ) @ SV233 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV128 ) @ ( inv_im1681759523_a_a_a @ SV233 @ SV313 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1775]) ).
thf(1894,plain,
! [SV313: a > multis599418605od_a_a,SV233: set_Pr1821581383od_a_a,SV128: a,SV9: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV9 @ SV128 ) @ ( inv_im1681759523_a_a_a @ SV233 @ SV313 ) )
= $true )
| ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ ( SV313 @ SV9 ) @ ( SV313 @ SV128 ) ) @ SV233 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1776]) ).
thf(1895,plain,
! [SV233: set_Pr1821581383od_a_a,SV128: a,SV9: a,SV313: a > multis599418605od_a_a] :
( ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ ( SV313 @ SV9 ) @ ( SV313 @ SV128 ) ) @ SV233 )
= $true )
| ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ ( SV313 @ SV9 ) @ ( SV313 @ SV128 ) ) @ SV233 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1777]) ).
thf(1896,plain,
! [SV314: multis599418605od_a_a > a,SV234: set_Product_prod_a_a,SV129: multis599418605od_a_a,SV10: multis599418605od_a_a] :
( ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ SV10 @ SV129 ) @ ( inv_im941243329od_a_a @ SV234 @ SV314 ) )
= $true )
| ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ SV10 @ SV129 ) @ ( inv_im941243329od_a_a @ SV234 @ SV314 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1778]) ).
thf(1897,plain,
! [SV234: set_Product_prod_a_a,SV129: multis599418605od_a_a,SV10: multis599418605od_a_a,SV314: multis599418605od_a_a > a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV314 @ SV10 ) @ ( SV314 @ SV129 ) ) @ SV234 )
= $true )
| ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ SV10 @ SV129 ) @ ( inv_im941243329od_a_a @ SV234 @ SV314 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1779]) ).
thf(1898,plain,
! [SV314: multis599418605od_a_a > a,SV234: set_Product_prod_a_a,SV129: multis599418605od_a_a,SV10: multis599418605od_a_a] :
( ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ SV10 @ SV129 ) @ ( inv_im941243329od_a_a @ SV234 @ SV314 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV314 @ SV10 ) @ ( SV314 @ SV129 ) ) @ SV234 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1780]) ).
thf(1899,plain,
! [SV234: set_Product_prod_a_a,SV129: multis599418605od_a_a,SV10: multis599418605od_a_a,SV314: multis599418605od_a_a > a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV314 @ SV10 ) @ ( SV314 @ SV129 ) ) @ SV234 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( SV314 @ SV10 ) @ ( SV314 @ SV129 ) ) @ SV234 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1781]) ).
thf(1900,plain,
! [SV134: set_Product_prod_a_a,SV372: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV372 @ SV372 ) @ SV134 )
= $false )
| ( ( irrefl_a @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1786]) ).
thf(1901,plain,
! [SV134: set_Product_prod_a_a] :
( ( ( irrefl_a @ SV134 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK34_SY751 @ SV134 ) @ ( sK34_SY751 @ SV134 ) ) @ SV134 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1787]) ).
thf(1902,plain,
! [SV134: set_Product_prod_a_a] :
( ( ( ! [SY751: a] :
~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY751 @ SY751 ) @ SV134 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK34_SY751 @ SV134 ) @ ( sK34_SY751 @ SV134 ) ) @ SV134 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1788]) ).
thf(1903,plain,
! [SV240: multis599418605od_a_a,SV141: multis599418605od_a_a,SV25: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV141 ) )
= $true )
| ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV240 ) )
= $true )
| ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ ( plus_p404985124od_a_a @ SV141 @ SV240 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1794]) ).
thf(1904,plain,
! [SV240: multis599418605od_a_a,SV141: multis599418605od_a_a,SV25: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ ( plus_p404985124od_a_a @ SV141 @ SV240 ) ) )
= $true )
| ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1795]) ).
thf(1905,plain,
! [SV240: multis599418605od_a_a,SV141: multis599418605od_a_a,SV25: product_prod_a_a] :
( ( ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV141 ) )
| ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV240 ) ) )
= $true )
| ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1796]) ).
thf(1906,plain,
! [SV240: multis599418605od_a_a,SV141: multis599418605od_a_a,SV25: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ ( plus_p404985124od_a_a @ SV141 @ SV240 ) ) )
= $true )
| ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV240 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1797]) ).
thf(1907,plain,
! [SV240: multis599418605od_a_a,SV141: multis599418605od_a_a,SV25: product_prod_a_a] :
( ( ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV141 ) )
| ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV240 ) ) )
= $true )
| ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV240 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1798]) ).
thf(1908,plain,
! [SV32: set_Product_prod_a_a,SV147: set_Pr1948701895od_a_a] :
( ( ( ( sK10_SY764 @ SV147 @ SV32 )
= ( sK20_SY1027 @ SV32 @ SV147 ) )
= $false )
| ( ( total_1490170027od_a_a @ SV32 @ SV147 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1799]) ).
thf(1909,plain,
! [SV245: a > $o,SV317: a,SV148: a,SV33: a > $o] :
( ( ( SV33 @ ( product_fst_a_a @ ( product_Pair_a_a @ SV148 @ SV317 ) ) )
= $true )
| ( ( SV245 @ SV317 )
= $false )
| ( ( SV33 @ SV148 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1802]) ).
thf(1910,plain,
! [SV33: a > $o,SV317: a,SV148: a,SV245: a > $o] :
( ( ( SV245 @ ( product_snd_a_a @ ( product_Pair_a_a @ SV148 @ SV317 ) ) )
= $true )
| ( ( SV245 @ SV317 )
= $false )
| ( ( SV33 @ SV148 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1803]) ).
thf(1911,plain,
! [SV151: set_Product_prod_a_a > $o,SV36: set_Product_prod_a_a,SV376: a,SV373: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV373 @ SV376 ) @ ( sK36_SY772 @ SV36 @ SV151 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV376 @ SV373 ) @ ( sK36_SY772 @ SV36 @ SV151 ) ) )
= $true )
| ( ( SV151 @ SV36 )
= $true )
| ( ( asym_a @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1804]) ).
thf(1912,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a] :
( ( ( total_1490170027od_a_a @ SV154 @ SV320 )
= $true )
| ( ( total_1490170027od_a_a @ SV154 @ SV320 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1805]) ).
thf(1913,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a] :
( ( ( ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) )
= $true )
| ( ( total_1490170027od_a_a @ SV154 @ SV320 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1806]) ).
thf(1914,plain,
! [SV154: set_Product_prod_a_a,SV320: set_Pr1948701895od_a_a] :
( ( ( member449909584od_a_a @ ( sK54_SY1005 @ SV320 @ SV154 ) @ SV154 )
= $true )
| ( ( ~ ( ~ ( total_1490170027od_a_a @ SV154 @ SV320 )
| ~ ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1807]) ).
thf(1915,plain,
! [SV154: set_Product_prod_a_a,SV320: set_Pr1948701895od_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK59_SY1053 @ SV320 @ SV154 ) @ SV154 )
| ~ ( ( ( sK54_SY1005 @ SV320 @ SV154 )
!= ( sK59_SY1053 @ SV320 @ SV154 ) ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK54_SY1005 @ SV320 @ SV154 ) @ ( sK59_SY1053 @ SV320 @ SV154 ) ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK59_SY1053 @ SV320 @ SV154 ) @ ( sK54_SY1005 @ SV320 @ SV154 ) ) @ SV320 ) )
= $false )
| ( ( ~ ( ~ ( total_1490170027od_a_a @ SV154 @ SV320 )
| ~ ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1808]) ).
thf(1916,plain,
! [SV40: a,SV155: product_prod_a_a] :
( ( ( SV155
!= ( product_Pair_a_a @ SV40 @ ( sK60_SY782 @ SV40 @ SV155 ) ) )
= $false )
| ( ( SV40
= ( product_fst_a_a @ SV155 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1809]) ).
thf(1917,plain,
! [SV367: a,SV155: product_prod_a_a,SV40: a] :
( ( ( SV40
!= ( product_fst_a_a @ SV155 ) )
= $false )
| ( ( SV155
= ( product_Pair_a_a @ SV40 @ SV367 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1810]) ).
thf(1918,plain,
! [SV367: a,SV40: a,SV155: product_prod_a_a] :
( ( ( ~ ~ ! [SY782: a] :
( SV155
!= ( product_Pair_a_a @ SV40 @ SY782 ) ) )
= $false )
| ( ( SV155
= ( product_Pair_a_a @ SV40 @ SV367 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1810]) ).
thf(1919,plain,
! [SV324: a,SV252: a,SV159: a,SV44: a] :
( ( ( ( product_Pair_a_a @ SV44 @ SV159 )
= ( product_Pair_a_a @ SV252 @ SV324 ) )
= $true )
| ( ( ( product_Pair_a_a @ SV44 @ SV159 )
= ( product_Pair_a_a @ SV252 @ SV324 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1812]) ).
thf(1920,plain,
! [SV324: a,SV159: a,SV252: a,SV44: a] :
( ( ( ~ ( ( SV44 != SV252 )
| ( SV159 != SV324 ) ) )
= $true )
| ( ( ( product_Pair_a_a @ SV44 @ SV159 )
= ( product_Pair_a_a @ SV252 @ SV324 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1813]) ).
thf(1921,plain,
! [SV324: a,SV159: a,SV252: a,SV44: a] :
( ( ( SV44 = SV252 )
= $false )
| ( ( SV159 != SV324 )
= $true )
| ( ( ~ ( ( ( product_Pair_a_a @ SV44 @ SV159 )
!= ( product_Pair_a_a @ SV252 @ SV324 ) )
| ~ ~ ( ( SV44 != SV252 )
| ( SV159 != SV324 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1814]) ).
thf(1922,plain,
! [SV47: set_Product_prod_a_a,SV162: set_Pr1948701895od_a_a,SV368: product_prod_a_a,SV358: product_prod_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV358 @ SV368 ) @ SV162 )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV368 @ SV358 ) @ SV162 )
= $true )
| ( ( member449909584od_a_a @ SV368 @ SV47 )
= $false )
| ( ( member449909584od_a_a @ SV358 @ SV47 )
= $false )
| ( ( prefer697821563od_a_a @ SV47 @ SV162 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1816]) ).
thf(1923,plain,
! [SV48: set_a,SV163: set_Product_prod_a_a] :
( ( ( ( sK12_SY797 @ SV163 @ SV48 )
= ( sK24_SY1030 @ SV48 @ SV163 ) )
= $false )
| ( ( total_on_a @ SV48 @ SV163 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1817]) ).
thf(1924,plain,
! [SV366: set_Product_prod_a_a,SV359: set_Product_prod_a_a,SV327: a,SV257: a,SV166: a,SV52: a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SV257 @ SV327 ) ) @ ( lex_prod_a_a @ SV359 @ SV366 ) )
| ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
| ~ ( ( SV52 != SV257 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 ) ) ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SV257 @ SV327 ) ) @ ( lex_prod_a_a @ SV359 @ SV366 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1820]) ).
thf(1925,plain,
! [SV366: set_Product_prod_a_a,SV327: a,SV166: a,SV359: set_Product_prod_a_a,SV257: a,SV52: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
= $false )
| ( ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SV257 @ SV327 ) ) @ ( lex_prod_a_a @ SV359 @ SV366 ) )
| ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
| ~ ( ( SV52 != SV257 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1821]) ).
thf(1926,plain,
! [SV359: set_Product_prod_a_a,SV366: set_Product_prod_a_a,SV327: a,SV166: a,SV257: a,SV52: a] :
( ( ( ~ ( ( SV52 != SV257 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 ) ) )
= $false )
| ( ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SV257 @ SV327 ) ) @ ( lex_prod_a_a @ SV359 @ SV366 ) )
| ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
| ~ ( ( SV52 != SV257 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1821]) ).
thf(1927,plain,
! [SV330: a,SV261: a,SV170: a,SV56: a] :
( ( ( ( product_Pair_a_a @ SV56 @ SV170 )
= ( product_Pair_a_a @ SV261 @ SV330 ) )
= $true )
| ( ( ( product_Pair_a_a @ SV56 @ SV170 )
= ( product_Pair_a_a @ SV261 @ SV330 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1822]) ).
thf(1928,plain,
! [SV330: a,SV170: a,SV261: a,SV56: a] :
( ( ( ~ ( ( SV56 != SV261 )
| ( SV170 != SV330 ) ) )
= $true )
| ( ( ( product_Pair_a_a @ SV56 @ SV170 )
= ( product_Pair_a_a @ SV261 @ SV330 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1823]) ).
thf(1929,plain,
! [SV330: a,SV170: a,SV261: a,SV56: a] :
( ( ( SV56 = SV261 )
= $false )
| ( ( SV170 != SV330 )
= $true )
| ( ( ~ ( ( ( product_Pair_a_a @ SV56 @ SV170 )
!= ( product_Pair_a_a @ SV261 @ SV330 ) )
| ~ ~ ( ( SV56 != SV261 )
| ( SV170 != SV330 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1824]) ).
thf(1930,plain,
! [SV57: a,SV262: a,SV171: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV171 @ SV262 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV262 @ SV171 ) @ relation ) ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV262 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV262 @ SV57 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV171 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV171 @ SV57 ) @ relation )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1825]) ).
thf(1931,plain,
! [SV172: set_Product_prod_a_a,SV331: a,SV58: set_a,SV263: a] :
( ( ( member_a @ SV263 @ SV58 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV263 @ SV331 ) @ SV172 )
= $false )
| ( ( refl_on_a @ SV58 @ SV172 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1826]) ).
thf(1932,plain,
! [SV172: set_Product_prod_a_a,SV263: a,SV58: set_a,SV331: a] :
( ( ( member_a @ SV331 @ SV58 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV263 @ SV331 ) @ SV172 )
= $false )
| ( ( refl_on_a @ SV58 @ SV172 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1827]) ).
thf(1933,plain,
! [SV264: a > a,SV332: set_Product_prod_a_a,SV173: a > a,SV59: product_prod_a_a] :
( ( ( SV59
= ( product_Pair_a_a @ ( SV173 @ ( sK45_SY1009 @ SV332 @ SV264 @ SV173 @ SV59 ) ) @ ( SV264 @ ( sK55_SY1049 @ SV264 @ SV332 @ SV173 @ SV59 ) ) ) )
= $true )
| ( ( member449909584od_a_a @ SV59 @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SV173 @ SV264 ) @ SV332 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1828]) ).
thf(1934,plain,
! [SV59: product_prod_a_a,SV173: a > a,SV264: a > a,SV332: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK45_SY1009 @ SV332 @ SV264 @ SV173 @ SV59 ) @ ( sK55_SY1049 @ SV264 @ SV332 @ SV173 @ SV59 ) ) @ SV332 )
= $true )
| ( ( member449909584od_a_a @ SV59 @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ SV173 @ SV264 ) @ SV332 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1829]) ).
thf(1935,plain,
! [SV174: set_Pr1948701895od_a_a,SV333: product_prod_a_a,SV60: set_Product_prod_a_a,SV265: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV265 @ SV60 )
= $false )
| ( ( ~ ( member449909584od_a_a @ SV333 @ SV60 ) )
= $true )
| ( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) )
= ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
| ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) ) ) )
= $true )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1830]) ).
thf(1936,plain,
! [SV175: set_Product_prod_a_a,SV334: a,SV61: set_a,SV266: a] :
( ( ( member_a @ SV266 @ SV61 )
= $false )
| ( ( ~ ( member_a @ SV334 @ SV61 ) )
= $true )
| ( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) ) ) )
= $true )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1831]) ).
thf(1937,plain,
! [SV179: set_Product_prod_a_a,SV377: a,SV374: a] :
( ( ( ! [SY1060: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV374 @ SV377 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV377 @ SY1060 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV374 @ SY1060 ) @ SV179 ) ) )
= $true )
| ( ( trans_a @ SV179 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1832]) ).
thf(1938,plain,
! [SV179: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK37_SY828 @ SV179 ) @ ( sK46_SY1040 @ SV179 ) ) @ SV179 )
= $true )
| ( ( ~ ( ~ ( trans_a @ SV179 )
| ~ ! [SY828: a,SY829: a,SY830: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY829 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY829 @ SY830 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY830 ) @ SV179 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1833]) ).
thf(1939,plain,
! [SV179: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK46_SY1040 @ SV179 ) @ ( sK56_SY1050 @ SV179 ) ) @ SV179 ) )
= $false )
| ( ( ~ ( ~ ( trans_a @ SV179 )
| ~ ! [SY828: a,SY829: a,SY830: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY829 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY829 @ SY830 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY830 ) @ SV179 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1834]) ).
thf(1940,plain,
! [SV179: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK37_SY828 @ SV179 ) @ ( sK56_SY1050 @ SV179 ) ) @ SV179 )
= $false )
| ( ( ~ ( ~ ( trans_a @ SV179 )
| ~ ! [SY828: a,SY829: a,SY830: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY829 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY829 @ SY830 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY830 ) @ SV179 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1834]) ).
thf(1941,plain,
! [SV74: set_a,SV360: a,SV184: set_Product_prod_a_a,SV336: a,SV272: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV336 ) @ SV184 ) )
= $true )
| ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV272 ) @ SV184 ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV360 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV336 ) @ SV184 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV360 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV272 ) @ SV184 ) ) )
= $true )
| ( ( prefer719835986ence_a @ SV74 @ SV184 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1835]) ).
thf(1942,plain,
! [SV88: a,SV196: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) ) )
= $false )
| ( ( ~ ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) ) ) )
= $true )
| ( ( member_a @ SV88 @ carrier )
= $false )
| ( ( member_a @ SV196 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1836]) ).
thf(1943,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a] :
( ( ( total_on_a @ SV197 @ SV343 )
= $true )
| ( ( total_on_a @ SV197 @ SV343 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1837]) ).
thf(1944,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a] :
( ( ( ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) )
= $true )
| ( ( total_on_a @ SV197 @ SV343 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1838]) ).
thf(1945,plain,
! [SV197: set_a,SV343: set_Product_prod_a_a] :
( ( ( member_a @ ( sK57_SY1017 @ SV343 @ SV197 ) @ SV197 )
= $true )
| ( ( ~ ( ~ ( total_on_a @ SV197 @ SV343 )
| ~ ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1839]) ).
thf(1946,plain,
! [SV197: set_a,SV343: set_Product_prod_a_a] :
( ( ( ~ ( member_a @ ( sK61_SY1054 @ SV343 @ SV197 ) @ SV197 )
| ~ ( ( ( sK57_SY1017 @ SV343 @ SV197 )
!= ( sK61_SY1054 @ SV343 @ SV197 ) ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK57_SY1017 @ SV343 @ SV197 ) @ ( sK61_SY1054 @ SV343 @ SV197 ) ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1054 @ SV343 @ SV197 ) @ ( sK57_SY1017 @ SV343 @ SV197 ) ) @ SV343 ) )
= $false )
| ( ( ~ ( ~ ( total_on_a @ SV197 @ SV343 )
| ~ ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1840]) ).
thf(1947,plain,
! [SV198: set_Product_prod_a_a] :
( ( ( ~ ~ ( ( SV198
!= ( sK62_SY857 @ SV198 ) )
| ~ ! [SY1061: a,SY1062: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1061 @ SY1062 ) @ ( sK62_SY857 @ SV198 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1062 @ SY1061 ) @ ( sK62_SY857 @ SV198 ) ) ) ) )
= $false )
| ( ( asym_a @ SV198 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1841]) ).
thf(1948,plain,
! [SV369: set_Product_prod_a_a,SV198: set_Product_prod_a_a] :
( ( ( SV198 != SV369 )
= $true )
| ( ( ~ ! [SY1051: a,SY1052: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1051 @ SY1052 ) @ SV369 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1052 @ SY1051 ) @ SV369 ) ) )
= $true )
| ( ( ~ ( ~ ( asym_a @ SV198 )
| ~ ~ ! [SY857: set_Product_prod_a_a] :
~ ~ ( ( SV198 != SY857 )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SY857 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SY857 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1842]) ).
thf(1949,plain,
! [SV199: set_Product_prod_a_a,SV378: a,SV375: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV375 @ SV378 ) @ SV199 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV378 @ SV375 ) @ SV199 ) )
= $true )
| ( ( asym_a @ SV199 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1843]) ).
thf(1950,plain,
! [SV199: set_Product_prod_a_a] :
( ( ( ~ ( asym_a @ SV199 )
| ~ ! [SY860: a,SY861: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY860 @ SY861 ) @ SV199 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY861 @ SY860 ) @ SV199 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK38_SY860 @ SV199 ) @ ( sK47_SY1042 @ SV199 ) ) @ SV199 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1844]) ).
thf(1951,plain,
! [SV199: set_Product_prod_a_a] :
( ( ( ~ ( asym_a @ SV199 )
| ~ ! [SY860: a,SY861: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY860 @ SY861 ) @ SV199 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY861 @ SY860 ) @ SV199 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK47_SY1042 @ SV199 ) @ ( sK38_SY860 @ SV199 ) ) @ SV199 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1845]) ).
thf(1952,plain,
! [SV93: set_a,SV362: a,SV201: set_Product_prod_a_a,SV345: a,SV286: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SV345 ) @ SV201 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV286 ) @ SV201 ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV362 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV362 @ SV345 ) @ SV201 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SV362 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV362 @ SV286 ) @ SV201 ) ) )
= $true )
| ( ( prefer1292084992ence_a @ SV93 @ SV201 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1846]) ).
thf(1953,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( prefer1292084992ence_a @ SV204 @ SV347 )
= $true )
| ( ( prefer1292084992ence_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1849]) ).
thf(1954,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) )
= $true )
| ( ( prefer1292084992ence_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1850]) ).
thf(1955,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) ) )
= $false )
| ( ( ~ ( order_preorder_on_a @ SV204 @ SV347 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 )
| ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1851]) ).
thf(1956,plain,
! [SV100: set_Product_prod_a_a,SV207: set_a] :
( ( ( ! [SY1063: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK63_SY883 @ SV207 @ SV100 ) @ SY1063 ) @ SV100 )
| ( member_a @ SY1063 @ SV207 ) ) )
= $false )
| ( ( ~ ( order_preorder_on_a @ SV207 @ SV100 )
| ( prefer1292084992ence_a @ SV207 @ SV100 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK17_SY881 @ SV207 @ SV100 ) @ ( sK30_SY1034 @ SV100 @ SV207 ) ) @ SV100 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1854]) ).
thf(1957,plain,
! [SV100: set_Product_prod_a_a,SV207: set_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK58_SY883 @ SV207 @ SV100 ) @ ( sK64_SY1059 @ SV100 @ SV207 ) ) @ SV100 )
| ( member_a @ ( sK64_SY1059 @ SV100 @ SV207 ) @ SV207 ) )
= $false )
| ( ( ~ ( order_preorder_on_a @ SV207 @ SV100 )
| ( prefer1292084992ence_a @ SV207 @ SV100 ) )
= $true )
| ( ( member_a @ ( sK17_SY881 @ SV207 @ SV100 ) @ SV207 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1855]) ).
thf(1958,plain,
! [SV101: a,SV291: a,SV208: a] :
( ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV291 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV291 @ SV208 ) @ relation ) ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SV291 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV291 @ SV101 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SV208 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV101 ) @ relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1856]) ).
thf(1959,plain,
! [SV213: set_Pr1948701895od_a_a,SV349: product_prod_a_a,SV106: set_Product_prod_a_a,SV295: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV295 @ SV106 )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV295 @ SV349 ) @ SV213 )
= $false )
| ( ( refl_o1298442278od_a_a @ SV106 @ SV213 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1859]) ).
thf(1960,plain,
! [SV213: set_Pr1948701895od_a_a,SV295: product_prod_a_a,SV106: set_Product_prod_a_a,SV349: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV349 @ SV106 )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV295 @ SV349 ) @ SV213 )
= $false )
| ( ( refl_o1298442278od_a_a @ SV106 @ SV213 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1860]) ).
thf(1961,plain,
! [SV112: a,SV219: product_prod_a_a] :
( ( ( SV219
!= ( product_Pair_a_a @ ( sK65_SY907 @ SV112 @ SV219 ) @ SV112 ) )
= $false )
| ( ( SV112
= ( product_snd_a_a @ SV219 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1861]) ).
thf(1962,plain,
! [SV370: a,SV219: product_prod_a_a,SV112: a] :
( ( ( SV112
!= ( product_snd_a_a @ SV219 ) )
= $false )
| ( ( SV219
= ( product_Pair_a_a @ SV370 @ SV112 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1862]) ).
thf(1963,plain,
! [SV370: a,SV112: a,SV219: product_prod_a_a] :
( ( ( ~ ~ ! [SY907: a] :
( SV219
!= ( product_Pair_a_a @ SY907 @ SV112 ) ) )
= $false )
| ( ( SV219
= ( product_Pair_a_a @ SV370 @ SV112 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1862]) ).
thf(1964,plain,
! [SV118: set_a,SV224: set_Product_prod_a_a,SV371: a,SV364: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV364 @ SV371 ) @ SV224 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV371 @ SV364 ) @ SV224 )
= $true )
| ( ( member_a @ SV371 @ SV118 )
= $false )
| ( ( member_a @ SV364 @ SV118 )
= $false )
| ( ( prefer719835986ence_a @ SV118 @ SV224 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1867]) ).
thf(1965,plain,
! [SV365: a,SV307: a,SV122: product_prod_a_a > $o] :
( ( ( ~ ( product_curry_a_a_o @ SV122 @ SV307 @ SV365 ) )
= $false )
| ( ( product_curry_a_a_o @ SV122 @ SV307 @ SV365 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1870]) ).
thf(1966,plain,
! [SV365: a,SV307: a,SV122: product_prod_a_a > $o] :
( ( ( ~ ( SV122 @ ( product_Pair_a_a @ SV307 @ SV365 ) ) )
= $false )
| ( ( product_curry_a_a_o @ SV122 @ SV307 @ SV365 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1870]) ).
thf(1967,plain,
! [SV365: a,SV307: a,SV122: product_prod_a_a > $o] :
( ( ( ~ ( product_curry_a_a_o @ SV122 @ SV307 @ SV365 ) )
= $false )
| ( ( SV122 @ ( product_Pair_a_a @ SV307 @ SV365 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1871]) ).
thf(1968,plain,
! [SV365: a,SV307: a,SV122: product_prod_a_a > $o] :
( ( ( ~ ( SV122 @ ( product_Pair_a_a @ SV307 @ SV365 ) ) )
= $false )
| ( ( SV122 @ ( product_Pair_a_a @ SV307 @ SV365 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1871]) ).
thf(1969,plain,
! [SV134: set_Product_prod_a_a,SV379: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV379 @ SV379 ) @ SV134 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK34_SY751 @ SV134 ) @ ( sK34_SY751 @ SV134 ) ) @ SV134 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1902]) ).
thf(1970,plain,
! [SV240: multis599418605od_a_a,SV141: multis599418605od_a_a,SV25: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV141 ) )
= $true )
| ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV240 ) )
= $true )
| ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV141 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1905]) ).
thf(1971,plain,
! [SV240: multis599418605od_a_a,SV141: multis599418605od_a_a,SV25: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV141 ) )
= $true )
| ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV240 ) )
= $true )
| ( ( member449909584od_a_a @ SV25 @ ( set_ms1818337124od_a_a @ SV240 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1907]) ).
thf(1972,plain,
! [SV151: set_Product_prod_a_a > $o,SV36: set_Product_prod_a_a,SV376: a,SV373: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV373 @ SV376 ) @ ( sK36_SY772 @ SV36 @ SV151 ) ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV376 @ SV373 ) @ ( sK36_SY772 @ SV36 @ SV151 ) ) )
= $true )
| ( ( SV151 @ SV36 )
= $true )
| ( ( asym_a @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1911]) ).
thf(1973,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a,SV380: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV380 @ SV154 )
| ! [SY1064: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1064 @ SV154 )
| ~ ( ( SV380 != SY1064 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV380 @ SY1064 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1064 @ SV380 ) @ SV320 ) ) )
= $true )
| ( ( total_1490170027od_a_a @ SV154 @ SV320 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1913]) ).
thf(1974,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a] :
( ( ( ~ ( total_1490170027od_a_a @ SV154 @ SV320 )
| ~ ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ ( sK54_SY1005 @ SV320 @ SV154 ) @ SV154 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1914]) ).
thf(1975,plain,
! [SV154: set_Product_prod_a_a,SV320: set_Pr1948701895od_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK59_SY1053 @ SV320 @ SV154 ) @ SV154 ) )
= $false )
| ( ( ~ ( ~ ( total_1490170027od_a_a @ SV154 @ SV320 )
| ~ ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1915]) ).
thf(1976,plain,
! [SV154: set_Product_prod_a_a,SV320: set_Pr1948701895od_a_a] :
( ( ( ~ ( ( ( sK54_SY1005 @ SV320 @ SV154 )
!= ( sK59_SY1053 @ SV320 @ SV154 ) ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK54_SY1005 @ SV320 @ SV154 ) @ ( sK59_SY1053 @ SV320 @ SV154 ) ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK59_SY1053 @ SV320 @ SV154 ) @ ( sK54_SY1005 @ SV320 @ SV154 ) ) @ SV320 ) )
= $false )
| ( ( ~ ( ~ ( total_1490170027od_a_a @ SV154 @ SV320 )
| ~ ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1915]) ).
thf(1977,plain,
! [SV40: a,SV155: product_prod_a_a] :
( ( ( SV155
= ( product_Pair_a_a @ SV40 @ ( sK60_SY782 @ SV40 @ SV155 ) ) )
= $true )
| ( ( SV40
= ( product_fst_a_a @ SV155 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1916]) ).
thf(1978,plain,
! [SV367: a,SV155: product_prod_a_a,SV40: a] :
( ( ( SV40
= ( product_fst_a_a @ SV155 ) )
= $true )
| ( ( SV155
= ( product_Pair_a_a @ SV40 @ SV367 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1917]) ).
thf(1979,plain,
! [SV367: a,SV40: a,SV155: product_prod_a_a] :
( ( ( ~ ! [SY782: a] :
( SV155
!= ( product_Pair_a_a @ SV40 @ SY782 ) ) )
= $true )
| ( ( SV155
= ( product_Pair_a_a @ SV40 @ SV367 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1918]) ).
thf(1980,plain,
! [SV324: a,SV159: a,SV252: a,SV44: a] :
( ( ( ( SV44 != SV252 )
| ( SV159 != SV324 ) )
= $false )
| ( ( ( product_Pair_a_a @ SV44 @ SV159 )
= ( product_Pair_a_a @ SV252 @ SV324 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1920]) ).
thf(1981,plain,
! [SV252: a,SV44: a,SV324: a,SV159: a] :
( ( ( SV159 = SV324 )
= $false )
| ( ( SV44 = SV252 )
= $false )
| ( ( ~ ( ( ( product_Pair_a_a @ SV44 @ SV159 )
!= ( product_Pair_a_a @ SV252 @ SV324 ) )
| ~ ~ ( ( SV44 != SV252 )
| ( SV159 != SV324 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1921]) ).
thf(1982,plain,
! [SV366: set_Product_prod_a_a,SV359: set_Product_prod_a_a,SV327: a,SV257: a,SV166: a,SV52: a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SV257 @ SV327 ) ) @ ( lex_prod_a_a @ SV359 @ SV366 ) ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SV257 @ SV327 ) ) @ ( lex_prod_a_a @ SV359 @ SV366 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1924]) ).
thf(1983,plain,
! [SV366: set_Product_prod_a_a,SV327: a,SV166: a,SV359: set_Product_prod_a_a,SV257: a,SV52: a] :
( ( ( ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
| ~ ( ( SV52 != SV257 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 ) ) ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SV257 @ SV327 ) ) @ ( lex_prod_a_a @ SV359 @ SV366 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1924]) ).
thf(1984,plain,
! [SV366: set_Product_prod_a_a,SV359: set_Product_prod_a_a,SV327: a,SV257: a,SV166: a,SV52: a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SV257 @ SV327 ) ) @ ( lex_prod_a_a @ SV359 @ SV366 ) )
| ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
| ~ ( ( SV52 != SV257 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1925]) ).
thf(1985,plain,
! [SV359: set_Product_prod_a_a,SV366: set_Product_prod_a_a,SV327: a,SV166: a,SV257: a,SV52: a] :
( ( ( ( SV52 != SV257 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 ) )
= $true )
| ( ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SV257 @ SV327 ) ) @ ( lex_prod_a_a @ SV359 @ SV366 ) )
| ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
| ~ ( ( SV52 != SV257 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1926]) ).
thf(1986,plain,
! [SV330: a,SV170: a,SV261: a,SV56: a] :
( ( ( ( SV56 != SV261 )
| ( SV170 != SV330 ) )
= $false )
| ( ( ( product_Pair_a_a @ SV56 @ SV170 )
= ( product_Pair_a_a @ SV261 @ SV330 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1928]) ).
thf(1987,plain,
! [SV261: a,SV56: a,SV330: a,SV170: a] :
( ( ( SV170 = SV330 )
= $false )
| ( ( SV56 = SV261 )
= $false )
| ( ( ~ ( ( ( product_Pair_a_a @ SV56 @ SV170 )
!= ( product_Pair_a_a @ SV261 @ SV330 ) )
| ~ ~ ( ( SV56 != SV261 )
| ( SV170 != SV330 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1929]) ).
thf(1988,plain,
! [SV57: a,SV262: a,SV171: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV171 @ SV262 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV262 @ SV171 ) @ relation ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV262 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV262 @ SV57 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV171 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV171 @ SV57 ) @ relation )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1930]) ).
thf(1989,plain,
! [SV174: set_Pr1948701895od_a_a,SV265: product_prod_a_a,SV60: set_Product_prod_a_a,SV333: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV333 @ SV60 )
= $false )
| ( ( member449909584od_a_a @ SV265 @ SV60 )
= $false )
| ( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) )
= ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
| ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) ) ) )
= $true )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1935]) ).
thf(1990,plain,
! [SV175: set_Product_prod_a_a,SV266: a,SV61: set_a,SV334: a] :
( ( ( member_a @ SV334 @ SV61 )
= $false )
| ( ( member_a @ SV266 @ SV61 )
= $false )
| ( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) ) ) )
= $true )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1936]) ).
thf(1991,plain,
! [SV381: a,SV179: set_Product_prod_a_a,SV377: a,SV374: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV374 @ SV377 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV377 @ SV381 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV374 @ SV381 ) @ SV179 ) )
= $true )
| ( ( trans_a @ SV179 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1937]) ).
thf(1992,plain,
! [SV179: set_Product_prod_a_a] :
( ( ( ~ ( trans_a @ SV179 )
| ~ ! [SY828: a,SY829: a,SY830: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY829 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY829 @ SY830 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY830 ) @ SV179 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK37_SY828 @ SV179 ) @ ( sK46_SY1040 @ SV179 ) ) @ SV179 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1938]) ).
thf(1993,plain,
! [SV179: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK46_SY1040 @ SV179 ) @ ( sK56_SY1050 @ SV179 ) ) @ SV179 )
= $true )
| ( ( ~ ( ~ ( trans_a @ SV179 )
| ~ ! [SY828: a,SY829: a,SY830: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY829 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY829 @ SY830 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY830 ) @ SV179 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1939]) ).
thf(1994,plain,
! [SV179: set_Product_prod_a_a] :
( ( ( ~ ( trans_a @ SV179 )
| ~ ! [SY828: a,SY829: a,SY830: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY829 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY829 @ SY830 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY830 ) @ SV179 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK37_SY828 @ SV179 ) @ ( sK56_SY1050 @ SV179 ) ) @ SV179 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1940]) ).
thf(1995,plain,
! [SV74: set_a,SV360: a,SV184: set_Product_prod_a_a,SV336: a,SV272: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV336 ) @ SV184 )
= $false )
| ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV272 ) @ SV184 ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV360 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV336 ) @ SV184 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV360 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV272 ) @ SV184 ) ) )
= $true )
| ( ( prefer719835986ence_a @ SV74 @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1941]) ).
thf(1996,plain,
! [SV88: a,SV196: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) )
= $false )
| ( ( ~ ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) ) ) )
= $true )
| ( ( member_a @ SV88 @ carrier )
= $false )
| ( ( member_a @ SV196 @ carrier )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1942]) ).
thf(1997,plain,
! [SV196: a,SV88: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) ) )
= $false )
| ( ( ~ ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) ) ) )
= $true )
| ( ( member_a @ SV88 @ carrier )
= $false )
| ( ( member_a @ SV196 @ carrier )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1942]) ).
thf(1998,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a,SV382: a] :
( ( ( ~ ( member_a @ SV382 @ SV197 )
| ! [SY1065: a] :
( ~ ( member_a @ SY1065 @ SV197 )
| ~ ( ( SV382 != SY1065 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV382 @ SY1065 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1065 @ SV382 ) @ SV343 ) ) )
= $true )
| ( ( total_on_a @ SV197 @ SV343 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1944]) ).
thf(1999,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a] :
( ( ( ~ ( total_on_a @ SV197 @ SV343 )
| ~ ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) )
= $false )
| ( ( member_a @ ( sK57_SY1017 @ SV343 @ SV197 ) @ SV197 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1945]) ).
thf(2000,plain,
! [SV197: set_a,SV343: set_Product_prod_a_a] :
( ( ( ~ ( member_a @ ( sK61_SY1054 @ SV343 @ SV197 ) @ SV197 ) )
= $false )
| ( ( ~ ( ~ ( total_on_a @ SV197 @ SV343 )
| ~ ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1946]) ).
thf(2001,plain,
! [SV197: set_a,SV343: set_Product_prod_a_a] :
( ( ( ~ ( ( ( sK57_SY1017 @ SV343 @ SV197 )
!= ( sK61_SY1054 @ SV343 @ SV197 ) ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK57_SY1017 @ SV343 @ SV197 ) @ ( sK61_SY1054 @ SV343 @ SV197 ) ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1054 @ SV343 @ SV197 ) @ ( sK57_SY1017 @ SV343 @ SV197 ) ) @ SV343 ) )
= $false )
| ( ( ~ ( ~ ( total_on_a @ SV197 @ SV343 )
| ~ ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1946]) ).
thf(2002,plain,
! [SV198: set_Product_prod_a_a] :
( ( ( ~ ( ( SV198
!= ( sK62_SY857 @ SV198 ) )
| ~ ! [SY1061: a,SY1062: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1061 @ SY1062 ) @ ( sK62_SY857 @ SV198 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1062 @ SY1061 ) @ ( sK62_SY857 @ SV198 ) ) ) ) )
= $true )
| ( ( asym_a @ SV198 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1947]) ).
thf(2003,plain,
! [SV369: set_Product_prod_a_a,SV198: set_Product_prod_a_a] :
( ( ( SV198 = SV369 )
= $false )
| ( ( ~ ! [SY1051: a,SY1052: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1051 @ SY1052 ) @ SV369 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1052 @ SY1051 ) @ SV369 ) ) )
= $true )
| ( ( ~ ( ~ ( asym_a @ SV198 )
| ~ ~ ! [SY857: set_Product_prod_a_a] :
~ ~ ( ( SV198 != SY857 )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SY857 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SY857 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1948]) ).
thf(2004,plain,
! [SV199: set_Product_prod_a_a,SV378: a,SV375: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV375 @ SV378 ) @ SV199 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV378 @ SV375 ) @ SV199 ) )
= $true )
| ( ( asym_a @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1949]) ).
thf(2005,plain,
! [SV199: set_Product_prod_a_a] :
( ( ( ~ ( asym_a @ SV199 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK38_SY860 @ SV199 ) @ ( sK47_SY1042 @ SV199 ) ) @ SV199 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1950]) ).
thf(2006,plain,
! [SV199: set_Product_prod_a_a] :
( ( ( ~ ! [SY860: a,SY861: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY860 @ SY861 ) @ SV199 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY861 @ SY860 ) @ SV199 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK38_SY860 @ SV199 ) @ ( sK47_SY1042 @ SV199 ) ) @ SV199 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1950]) ).
thf(2007,plain,
! [SV199: set_Product_prod_a_a] :
( ( ( ~ ( asym_a @ SV199 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK47_SY1042 @ SV199 ) @ ( sK38_SY860 @ SV199 ) ) @ SV199 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1951]) ).
thf(2008,plain,
! [SV199: set_Product_prod_a_a] :
( ( ( ~ ! [SY860: a,SY861: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY860 @ SY861 ) @ SV199 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY861 @ SY860 ) @ SV199 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK47_SY1042 @ SV199 ) @ ( sK38_SY860 @ SV199 ) ) @ SV199 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1951]) ).
thf(2009,plain,
! [SV93: set_a,SV362: a,SV201: set_Product_prod_a_a,SV345: a,SV286: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SV345 ) @ SV201 )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV286 ) @ SV201 ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV362 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV362 @ SV345 ) @ SV201 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SV362 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV362 @ SV286 ) @ SV201 ) ) )
= $true )
| ( ( prefer1292084992ence_a @ SV93 @ SV201 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1952]) ).
thf(2010,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) )
= $false )
| ( ( prefer1292084992ence_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1954]) ).
thf(2011,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
= $true )
| ( ( ~ ( order_preorder_on_a @ SV204 @ SV347 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 )
| ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1955]) ).
thf(2012,plain,
! [SV100: set_Product_prod_a_a,SV207: set_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK63_SY883 @ SV207 @ SV100 ) @ ( sK66_SY1063 @ SV100 @ SV207 ) ) @ SV100 )
| ( member_a @ ( sK66_SY1063 @ SV100 @ SV207 ) @ SV207 ) )
= $false )
| ( ( ~ ( order_preorder_on_a @ SV207 @ SV100 )
| ( prefer1292084992ence_a @ SV207 @ SV100 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK17_SY881 @ SV207 @ SV100 ) @ ( sK30_SY1034 @ SV100 @ SV207 ) ) @ SV100 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1956]) ).
thf(2013,plain,
! [SV100: set_Product_prod_a_a,SV207: set_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK58_SY883 @ SV207 @ SV100 ) @ ( sK64_SY1059 @ SV100 @ SV207 ) ) @ SV100 ) )
= $false )
| ( ( ~ ( order_preorder_on_a @ SV207 @ SV100 )
| ( prefer1292084992ence_a @ SV207 @ SV100 ) )
= $true )
| ( ( member_a @ ( sK17_SY881 @ SV207 @ SV100 ) @ SV207 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1957]) ).
thf(2014,plain,
! [SV207: set_a,SV100: set_Product_prod_a_a] :
( ( ( member_a @ ( sK64_SY1059 @ SV100 @ SV207 ) @ SV207 )
= $false )
| ( ( ~ ( order_preorder_on_a @ SV207 @ SV100 )
| ( prefer1292084992ence_a @ SV207 @ SV100 ) )
= $true )
| ( ( member_a @ ( sK17_SY881 @ SV207 @ SV100 ) @ SV207 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1957]) ).
thf(2015,plain,
! [SV101: a,SV291: a,SV208: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV291 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV291 @ SV208 ) @ relation ) ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SV291 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV291 @ SV101 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SV208 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV101 ) @ relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1958]) ).
thf(2016,plain,
! [SV112: a,SV219: product_prod_a_a] :
( ( ( SV219
= ( product_Pair_a_a @ ( sK65_SY907 @ SV112 @ SV219 ) @ SV112 ) )
= $true )
| ( ( SV112
= ( product_snd_a_a @ SV219 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1961]) ).
thf(2017,plain,
! [SV370: a,SV219: product_prod_a_a,SV112: a] :
( ( ( SV112
= ( product_snd_a_a @ SV219 ) )
= $true )
| ( ( SV219
= ( product_Pair_a_a @ SV370 @ SV112 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1962]) ).
thf(2018,plain,
! [SV370: a,SV112: a,SV219: product_prod_a_a] :
( ( ( ~ ! [SY907: a] :
( SV219
!= ( product_Pair_a_a @ SY907 @ SV112 ) ) )
= $true )
| ( ( SV219
= ( product_Pair_a_a @ SV370 @ SV112 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1963]) ).
thf(2019,plain,
! [SV365: a,SV307: a,SV122: product_prod_a_a > $o] :
( ( ( product_curry_a_a_o @ SV122 @ SV307 @ SV365 )
= $true )
| ( ( product_curry_a_a_o @ SV122 @ SV307 @ SV365 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1965]) ).
thf(2020,plain,
! [SV365: a,SV307: a,SV122: product_prod_a_a > $o] :
( ( ( SV122 @ ( product_Pair_a_a @ SV307 @ SV365 ) )
= $true )
| ( ( product_curry_a_a_o @ SV122 @ SV307 @ SV365 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1966]) ).
thf(2021,plain,
! [SV365: a,SV307: a,SV122: product_prod_a_a > $o] :
( ( ( product_curry_a_a_o @ SV122 @ SV307 @ SV365 )
= $true )
| ( ( SV122 @ ( product_Pair_a_a @ SV307 @ SV365 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1967]) ).
thf(2022,plain,
! [SV365: a,SV307: a,SV122: product_prod_a_a > $o] :
( ( ( SV122 @ ( product_Pair_a_a @ SV307 @ SV365 ) )
= $true )
| ( ( SV122 @ ( product_Pair_a_a @ SV307 @ SV365 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1968]) ).
thf(2023,plain,
! [SV134: set_Product_prod_a_a,SV379: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV379 @ SV379 ) @ SV134 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK34_SY751 @ SV134 ) @ ( sK34_SY751 @ SV134 ) ) @ SV134 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1969]) ).
thf(2024,plain,
! [SV151: set_Product_prod_a_a > $o,SV36: set_Product_prod_a_a,SV376: a,SV373: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV373 @ SV376 ) @ ( sK36_SY772 @ SV36 @ SV151 ) )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV376 @ SV373 ) @ ( sK36_SY772 @ SV36 @ SV151 ) ) )
= $true )
| ( ( SV151 @ SV36 )
= $true )
| ( ( asym_a @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1972]) ).
thf(2025,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a,SV380: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV380 @ SV154 ) )
= $true )
| ( ( ! [SY1064: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1064 @ SV154 )
| ~ ( ( SV380 != SY1064 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV380 @ SY1064 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1064 @ SV380 ) @ SV320 ) ) )
= $true )
| ( ( total_1490170027od_a_a @ SV154 @ SV320 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1973]) ).
thf(2026,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a] :
( ( ( ~ ( total_1490170027od_a_a @ SV154 @ SV320 ) )
= $false )
| ( ( member449909584od_a_a @ ( sK54_SY1005 @ SV320 @ SV154 ) @ SV154 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1974]) ).
thf(2027,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a] :
( ( ( ~ ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ ( sK54_SY1005 @ SV320 @ SV154 ) @ SV154 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1974]) ).
thf(2028,plain,
! [SV154: set_Product_prod_a_a,SV320: set_Pr1948701895od_a_a] :
( ( ( member449909584od_a_a @ ( sK59_SY1053 @ SV320 @ SV154 ) @ SV154 )
= $true )
| ( ( ~ ( ~ ( total_1490170027od_a_a @ SV154 @ SV320 )
| ~ ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1975]) ).
thf(2029,plain,
! [SV154: set_Product_prod_a_a,SV320: set_Pr1948701895od_a_a] :
( ( ( ~ ( ( ( sK54_SY1005 @ SV320 @ SV154 )
!= ( sK59_SY1053 @ SV320 @ SV154 ) ) ) )
= $false )
| ( ( ~ ( ~ ( total_1490170027od_a_a @ SV154 @ SV320 )
| ~ ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1976]) ).
thf(2030,plain,
! [SV154: set_Product_prod_a_a,SV320: set_Pr1948701895od_a_a] :
( ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK54_SY1005 @ SV320 @ SV154 ) @ ( sK59_SY1053 @ SV320 @ SV154 ) ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK59_SY1053 @ SV320 @ SV154 ) @ ( sK54_SY1005 @ SV320 @ SV154 ) ) @ SV320 ) )
= $false )
| ( ( ~ ( ~ ( total_1490170027od_a_a @ SV154 @ SV320 )
| ~ ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1976]) ).
thf(2031,plain,
! [SV367: a,SV40: a,SV155: product_prod_a_a] :
( ( ( ! [SY782: a] :
( SV155
!= ( product_Pair_a_a @ SV40 @ SY782 ) ) )
= $false )
| ( ( SV155
= ( product_Pair_a_a @ SV40 @ SV367 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1979]) ).
thf(2032,plain,
! [SV324: a,SV159: a,SV252: a,SV44: a] :
( ( ( SV44 != SV252 )
= $false )
| ( ( ( product_Pair_a_a @ SV44 @ SV159 )
= ( product_Pair_a_a @ SV252 @ SV324 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1980]) ).
thf(2033,plain,
! [SV252: a,SV44: a,SV324: a,SV159: a] :
( ( ( SV159 != SV324 )
= $false )
| ( ( ( product_Pair_a_a @ SV44 @ SV159 )
= ( product_Pair_a_a @ SV252 @ SV324 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1980]) ).
thf(2034,plain,
! [SV324: a,SV252: a,SV159: a,SV44: a] :
( ( ( ( ( product_Pair_a_a @ SV44 @ SV159 )
!= ( product_Pair_a_a @ SV252 @ SV324 ) )
| ~ ~ ( ( SV44 != SV252 )
| ( SV159 != SV324 ) ) )
= $false )
| ( ( SV44 = SV252 )
= $false )
| ( ( SV159 = SV324 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1981]) ).
thf(2035,plain,
! [SV366: set_Product_prod_a_a,SV359: set_Product_prod_a_a,SV327: a,SV257: a,SV166: a,SV52: a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SV257 @ SV327 ) ) @ ( lex_prod_a_a @ SV359 @ SV366 ) )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SV257 @ SV327 ) ) @ ( lex_prod_a_a @ SV359 @ SV366 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1982]) ).
thf(2036,plain,
! [SV366: set_Product_prod_a_a,SV327: a,SV166: a,SV359: set_Product_prod_a_a,SV257: a,SV52: a] :
( ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
| ~ ( ( SV52 != SV257 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 ) ) )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SV257 @ SV327 ) ) @ ( lex_prod_a_a @ SV359 @ SV366 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1983]) ).
thf(2037,plain,
! [SV366: set_Product_prod_a_a,SV359: set_Product_prod_a_a,SV327: a,SV257: a,SV166: a,SV52: a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SV257 @ SV327 ) ) @ ( lex_prod_a_a @ SV359 @ SV366 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1984]) ).
thf(2038,plain,
! [SV366: set_Product_prod_a_a,SV327: a,SV166: a,SV359: set_Product_prod_a_a,SV257: a,SV52: a] :
( ( ( ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
| ~ ( ( SV52 != SV257 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1984]) ).
thf(2039,plain,
! [SV359: set_Product_prod_a_a,SV366: set_Product_prod_a_a,SV327: a,SV166: a,SV257: a,SV52: a] :
( ( ( SV52 != SV257 )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 ) )
= $true )
| ( ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SV257 @ SV327 ) ) @ ( lex_prod_a_a @ SV359 @ SV366 ) )
| ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
| ~ ( ( SV52 != SV257 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1985]) ).
thf(2040,plain,
! [SV330: a,SV170: a,SV261: a,SV56: a] :
( ( ( SV56 != SV261 )
= $false )
| ( ( ( product_Pair_a_a @ SV56 @ SV170 )
= ( product_Pair_a_a @ SV261 @ SV330 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1986]) ).
thf(2041,plain,
! [SV261: a,SV56: a,SV330: a,SV170: a] :
( ( ( SV170 != SV330 )
= $false )
| ( ( ( product_Pair_a_a @ SV56 @ SV170 )
= ( product_Pair_a_a @ SV261 @ SV330 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1986]) ).
thf(2042,plain,
! [SV330: a,SV261: a,SV170: a,SV56: a] :
( ( ( ( ( product_Pair_a_a @ SV56 @ SV170 )
!= ( product_Pair_a_a @ SV261 @ SV330 ) )
| ~ ~ ( ( SV56 != SV261 )
| ( SV170 != SV330 ) ) )
= $false )
| ( ( SV56 = SV261 )
= $false )
| ( ( SV170 = SV330 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1987]) ).
thf(2043,plain,
! [SV57: a,SV262: a,SV171: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV171 @ SV262 ) @ relation ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV262 @ SV171 ) @ relation ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV262 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV262 @ SV57 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV171 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV171 @ SV57 ) @ relation )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1988]) ).
thf(2044,plain,
! [SV60: set_Product_prod_a_a,SV174: set_Pr1948701895od_a_a,SV265: product_prod_a_a,SV333: product_prod_a_a] :
( ( ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
| ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
| ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) ) )
| ~ ( ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
| ~ ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
| ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) ) ) )
= $true )
| ( ( member449909584od_a_a @ SV265 @ SV60 )
= $false )
| ( ( member449909584od_a_a @ SV333 @ SV60 )
= $false )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1989]) ).
thf(2045,plain,
! [SV60: set_Product_prod_a_a,SV174: set_Pr1948701895od_a_a,SV265: product_prod_a_a,SV333: product_prod_a_a] :
( ( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) )
= ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
| ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) ) ) )
= $true )
| ( ( member449909584od_a_a @ SV265 @ SV60 )
= $false )
| ( ( member449909584od_a_a @ SV333 @ SV60 )
= $false )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1989]) ).
thf(2046,plain,
! [SV61: set_a,SV175: set_Product_prod_a_a,SV266: a,SV334: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) ) )
| ~ ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) ) ) )
= $true )
| ( ( member_a @ SV266 @ SV61 )
= $false )
| ( ( member_a @ SV334 @ SV61 )
= $false )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1990]) ).
thf(2047,plain,
! [SV61: set_a,SV175: set_Product_prod_a_a,SV266: a,SV334: a] :
( ( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) )
= ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) ) ) )
= $true )
| ( ( member_a @ SV266 @ SV61 )
= $false )
| ( ( member_a @ SV334 @ SV61 )
= $false )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[1990]) ).
thf(2048,plain,
! [SV381: a,SV179: set_Product_prod_a_a,SV377: a,SV374: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV374 @ SV377 ) @ SV179 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV377 @ SV381 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV374 @ SV381 ) @ SV179 ) )
= $true )
| ( ( trans_a @ SV179 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1991]) ).
thf(2049,plain,
! [SV179: set_Product_prod_a_a] :
( ( ( ~ ( trans_a @ SV179 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK37_SY828 @ SV179 ) @ ( sK46_SY1040 @ SV179 ) ) @ SV179 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1992]) ).
thf(2050,plain,
! [SV179: set_Product_prod_a_a] :
( ( ( ~ ! [SY828: a,SY829: a,SY830: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY829 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY829 @ SY830 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY830 ) @ SV179 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK37_SY828 @ SV179 ) @ ( sK46_SY1040 @ SV179 ) ) @ SV179 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1992]) ).
thf(2051,plain,
! [SV179: set_Product_prod_a_a] :
( ( ( ~ ( trans_a @ SV179 )
| ~ ! [SY828: a,SY829: a,SY830: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY829 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY829 @ SY830 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY830 ) @ SV179 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK46_SY1040 @ SV179 ) @ ( sK56_SY1050 @ SV179 ) ) @ SV179 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1993]) ).
thf(2052,plain,
! [SV179: set_Product_prod_a_a] :
( ( ( ~ ( trans_a @ SV179 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK37_SY828 @ SV179 ) @ ( sK56_SY1050 @ SV179 ) ) @ SV179 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1994]) ).
thf(2053,plain,
! [SV179: set_Product_prod_a_a] :
( ( ( ~ ! [SY828: a,SY829: a,SY830: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY829 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY829 @ SY830 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY830 ) @ SV179 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK37_SY828 @ SV179 ) @ ( sK56_SY1050 @ SV179 ) ) @ SV179 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1994]) ).
thf(2054,plain,
! [SV74: set_a,SV360: a,SV184: set_Product_prod_a_a,SV272: a,SV336: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV272 ) @ SV184 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV336 ) @ SV184 )
= $false )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV360 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV336 ) @ SV184 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV360 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV272 ) @ SV184 ) ) )
= $true )
| ( ( prefer719835986ence_a @ SV74 @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1995]) ).
thf(2055,plain,
! [SV88: a,SV196: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
= $true )
| ( ( ~ ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) ) ) )
= $true )
| ( ( member_a @ SV88 @ carrier )
= $false )
| ( ( member_a @ SV196 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1996]) ).
thf(2056,plain,
! [SV196: a,SV88: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) )
= $true )
| ( ( ~ ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) ) ) )
= $true )
| ( ( member_a @ SV88 @ carrier )
= $false )
| ( ( member_a @ SV196 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1997]) ).
thf(2057,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a,SV382: a] :
( ( ( ~ ( member_a @ SV382 @ SV197 ) )
= $true )
| ( ( ! [SY1065: a] :
( ~ ( member_a @ SY1065 @ SV197 )
| ~ ( ( SV382 != SY1065 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV382 @ SY1065 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1065 @ SV382 ) @ SV343 ) ) )
= $true )
| ( ( total_on_a @ SV197 @ SV343 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1998]) ).
thf(2058,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a] :
( ( ( ~ ( total_on_a @ SV197 @ SV343 ) )
= $false )
| ( ( member_a @ ( sK57_SY1017 @ SV343 @ SV197 ) @ SV197 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1999]) ).
thf(2059,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a] :
( ( ( ~ ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) )
= $false )
| ( ( member_a @ ( sK57_SY1017 @ SV343 @ SV197 ) @ SV197 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1999]) ).
thf(2060,plain,
! [SV197: set_a,SV343: set_Product_prod_a_a] :
( ( ( member_a @ ( sK61_SY1054 @ SV343 @ SV197 ) @ SV197 )
= $true )
| ( ( ~ ( ~ ( total_on_a @ SV197 @ SV343 )
| ~ ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2000]) ).
thf(2061,plain,
! [SV197: set_a,SV343: set_Product_prod_a_a] :
( ( ( ~ ( ( ( sK57_SY1017 @ SV343 @ SV197 )
!= ( sK61_SY1054 @ SV343 @ SV197 ) ) ) )
= $false )
| ( ( ~ ( ~ ( total_on_a @ SV197 @ SV343 )
| ~ ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2001]) ).
thf(2062,plain,
! [SV197: set_a,SV343: set_Product_prod_a_a] :
( ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK57_SY1017 @ SV343 @ SV197 ) @ ( sK61_SY1054 @ SV343 @ SV197 ) ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1054 @ SV343 @ SV197 ) @ ( sK57_SY1017 @ SV343 @ SV197 ) ) @ SV343 ) )
= $false )
| ( ( ~ ( ~ ( total_on_a @ SV197 @ SV343 )
| ~ ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2001]) ).
thf(2063,plain,
! [SV198: set_Product_prod_a_a] :
( ( ( ( SV198
!= ( sK62_SY857 @ SV198 ) )
| ~ ! [SY1061: a,SY1062: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1061 @ SY1062 ) @ ( sK62_SY857 @ SV198 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1062 @ SY1061 ) @ ( sK62_SY857 @ SV198 ) ) ) )
= $false )
| ( ( asym_a @ SV198 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2002]) ).
thf(2064,plain,
! [SV198: set_Product_prod_a_a,SV369: set_Product_prod_a_a] :
( ( ( ! [SY1051: a,SY1052: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1051 @ SY1052 ) @ SV369 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1052 @ SY1051 ) @ SV369 ) ) )
= $false )
| ( ( SV198 = SV369 )
= $false )
| ( ( ~ ( ~ ( asym_a @ SV198 )
| ~ ~ ! [SY857: set_Product_prod_a_a] :
~ ~ ( ( SV198 != SY857 )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SY857 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SY857 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2003]) ).
thf(2065,plain,
! [SV199: set_Product_prod_a_a,SV378: a,SV375: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV375 @ SV378 ) @ SV199 )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV378 @ SV375 ) @ SV199 ) )
= $true )
| ( ( asym_a @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2004]) ).
thf(2066,plain,
! [SV199: set_Product_prod_a_a] :
( ( ( asym_a @ SV199 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK38_SY860 @ SV199 ) @ ( sK47_SY1042 @ SV199 ) ) @ SV199 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2005]) ).
thf(2067,plain,
! [SV199: set_Product_prod_a_a] :
( ( ( ! [SY860: a,SY861: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY860 @ SY861 ) @ SV199 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY861 @ SY860 ) @ SV199 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK38_SY860 @ SV199 ) @ ( sK47_SY1042 @ SV199 ) ) @ SV199 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2006]) ).
thf(2068,plain,
! [SV199: set_Product_prod_a_a] :
( ( ( asym_a @ SV199 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK47_SY1042 @ SV199 ) @ ( sK38_SY860 @ SV199 ) ) @ SV199 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2007]) ).
thf(2069,plain,
! [SV199: set_Product_prod_a_a] :
( ( ( ! [SY860: a,SY861: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY860 @ SY861 ) @ SV199 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY861 @ SY860 ) @ SV199 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK47_SY1042 @ SV199 ) @ ( sK38_SY860 @ SV199 ) ) @ SV199 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2008]) ).
thf(2070,plain,
! [SV93: set_a,SV362: a,SV201: set_Product_prod_a_a,SV286: a,SV345: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV286 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SV345 ) @ SV201 )
= $false )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV362 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV362 @ SV345 ) @ SV201 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SV362 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV362 @ SV286 ) @ SV201 ) ) )
= $true )
| ( ( prefer1292084992ence_a @ SV93 @ SV201 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2009]) ).
thf(2071,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) ) )
= $false )
| ( ( prefer1292084992ence_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2010]) ).
thf(2072,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( ~ ( order_preorder_on_a @ SV204 @ SV347 ) )
= $false )
| ( ( prefer1292084992ence_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2010]) ).
thf(2073,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) ) )
= $true )
| ( ( ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
= $true )
| ( ( ~ ( order_preorder_on_a @ SV204 @ SV347 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 )
| ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2011]) ).
thf(2074,plain,
! [SV100: set_Product_prod_a_a,SV207: set_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK63_SY883 @ SV207 @ SV100 ) @ ( sK66_SY1063 @ SV100 @ SV207 ) ) @ SV100 ) )
= $false )
| ( ( ~ ( order_preorder_on_a @ SV207 @ SV100 )
| ( prefer1292084992ence_a @ SV207 @ SV100 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK17_SY881 @ SV207 @ SV100 ) @ ( sK30_SY1034 @ SV100 @ SV207 ) ) @ SV100 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2012]) ).
thf(2075,plain,
! [SV207: set_a,SV100: set_Product_prod_a_a] :
( ( ( member_a @ ( sK66_SY1063 @ SV100 @ SV207 ) @ SV207 )
= $false )
| ( ( ~ ( order_preorder_on_a @ SV207 @ SV100 )
| ( prefer1292084992ence_a @ SV207 @ SV100 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK17_SY881 @ SV207 @ SV100 ) @ ( sK30_SY1034 @ SV100 @ SV207 ) ) @ SV100 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2012]) ).
thf(2076,plain,
! [SV100: set_Product_prod_a_a,SV207: set_a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK58_SY883 @ SV207 @ SV100 ) @ ( sK64_SY1059 @ SV100 @ SV207 ) ) @ SV100 )
= $true )
| ( ( ~ ( order_preorder_on_a @ SV207 @ SV100 )
| ( prefer1292084992ence_a @ SV207 @ SV100 ) )
= $true )
| ( ( member_a @ ( sK17_SY881 @ SV207 @ SV100 ) @ SV207 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2013]) ).
thf(2077,plain,
! [SV100: set_Product_prod_a_a,SV207: set_a] :
( ( ( ~ ( order_preorder_on_a @ SV207 @ SV100 ) )
= $true )
| ( ( prefer1292084992ence_a @ SV207 @ SV100 )
= $true )
| ( ( member_a @ ( sK64_SY1059 @ SV100 @ SV207 ) @ SV207 )
= $false )
| ( ( member_a @ ( sK17_SY881 @ SV207 @ SV100 ) @ SV207 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2014]) ).
thf(2078,plain,
! [SV101: a,SV291: a,SV208: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV291 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV291 @ SV208 ) @ relation ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SV291 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV291 @ SV101 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SV208 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV101 ) @ relation )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2015]) ).
thf(2079,plain,
! [SV370: a,SV112: a,SV219: product_prod_a_a] :
( ( ( ! [SY907: a] :
( SV219
!= ( product_Pair_a_a @ SY907 @ SV112 ) ) )
= $false )
| ( ( SV219
= ( product_Pair_a_a @ SV370 @ SV112 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2018]) ).
thf(2080,plain,
! [SV151: set_Product_prod_a_a > $o,SV36: set_Product_prod_a_a,SV373: a,SV376: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV376 @ SV373 ) @ ( sK36_SY772 @ SV36 @ SV151 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV373 @ SV376 ) @ ( sK36_SY772 @ SV36 @ SV151 ) )
= $false )
| ( ( SV151 @ SV36 )
= $true )
| ( ( asym_a @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2024]) ).
thf(2081,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a,SV380: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV380 @ SV154 )
= $false )
| ( ( ! [SY1064: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1064 @ SV154 )
| ~ ( ( SV380 != SY1064 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV380 @ SY1064 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1064 @ SV380 ) @ SV320 ) ) )
= $true )
| ( ( total_1490170027od_a_a @ SV154 @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2025]) ).
thf(2082,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a] :
( ( ( total_1490170027od_a_a @ SV154 @ SV320 )
= $true )
| ( ( member449909584od_a_a @ ( sK54_SY1005 @ SV320 @ SV154 ) @ SV154 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2026]) ).
thf(2083,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a] :
( ( ( ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) )
= $true )
| ( ( member449909584od_a_a @ ( sK54_SY1005 @ SV320 @ SV154 ) @ SV154 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2027]) ).
thf(2084,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a] :
( ( ( ~ ( total_1490170027od_a_a @ SV154 @ SV320 )
| ~ ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ ( sK59_SY1053 @ SV320 @ SV154 ) @ SV154 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2028]) ).
thf(2085,plain,
! [SV154: set_Product_prod_a_a,SV320: set_Pr1948701895od_a_a] :
( ( ( ( sK54_SY1005 @ SV320 @ SV154 )
!= ( sK59_SY1053 @ SV320 @ SV154 ) )
= $true )
| ( ( ~ ( ~ ( total_1490170027od_a_a @ SV154 @ SV320 )
| ~ ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2029]) ).
thf(2086,plain,
! [SV154: set_Product_prod_a_a,SV320: set_Pr1948701895od_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK54_SY1005 @ SV320 @ SV154 ) @ ( sK59_SY1053 @ SV320 @ SV154 ) ) @ SV320 )
= $false )
| ( ( ~ ( ~ ( total_1490170027od_a_a @ SV154 @ SV320 )
| ~ ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2030]) ).
thf(2087,plain,
! [SV154: set_Product_prod_a_a,SV320: set_Pr1948701895od_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK59_SY1053 @ SV320 @ SV154 ) @ ( sK54_SY1005 @ SV320 @ SV154 ) ) @ SV320 )
= $false )
| ( ( ~ ( ~ ( total_1490170027od_a_a @ SV154 @ SV320 )
| ~ ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2030]) ).
thf(2088,plain,
! [SV367: a,SV40: a,SV155: product_prod_a_a] :
( ( ( SV155
!= ( product_Pair_a_a @ SV40 @ ( sK67_SY782 @ SV367 @ SV40 @ SV155 ) ) )
= $false )
| ( ( SV155
= ( product_Pair_a_a @ SV40 @ SV367 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2031]) ).
thf(2089,plain,
! [SV324: a,SV159: a,SV252: a,SV44: a] :
( ( ( SV44 = SV252 )
= $true )
| ( ( ( product_Pair_a_a @ SV44 @ SV159 )
= ( product_Pair_a_a @ SV252 @ SV324 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2032]) ).
thf(2090,plain,
! [SV252: a,SV44: a,SV324: a,SV159: a] :
( ( ( SV159 = SV324 )
= $true )
| ( ( ( product_Pair_a_a @ SV44 @ SV159 )
= ( product_Pair_a_a @ SV252 @ SV324 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2033]) ).
thf(2091,plain,
! [SV324: a,SV252: a,SV159: a,SV44: a] :
( ( ( ( product_Pair_a_a @ SV44 @ SV159 )
!= ( product_Pair_a_a @ SV252 @ SV324 ) )
= $false )
| ( ( SV44 = SV252 )
= $false )
| ( ( SV159 = SV324 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2034]) ).
thf(2092,plain,
! [SV324: a,SV159: a,SV252: a,SV44: a] :
( ( ( ~ ~ ( ( SV44 != SV252 )
| ( SV159 != SV324 ) ) )
= $false )
| ( ( SV44 = SV252 )
= $false )
| ( ( SV159 = SV324 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2034]) ).
thf(2093,plain,
! [SV366: set_Product_prod_a_a,SV327: a,SV166: a,SV359: set_Product_prod_a_a,SV257: a,SV52: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
= $true )
| ( ( ~ ( ( SV52 != SV257 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 ) ) )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SV257 @ SV327 ) ) @ ( lex_prod_a_a @ SV359 @ SV366 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2036]) ).
thf(2094,plain,
! [SV366: set_Product_prod_a_a,SV359: set_Product_prod_a_a,SV327: a,SV257: a,SV166: a,SV52: a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SV257 @ SV327 ) ) @ ( lex_prod_a_a @ SV359 @ SV366 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2037]) ).
thf(2095,plain,
! [SV366: set_Product_prod_a_a,SV327: a,SV166: a,SV359: set_Product_prod_a_a,SV257: a,SV52: a] :
( ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
| ~ ( ( SV52 != SV257 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2038]) ).
thf(2096,plain,
! [SV359: set_Product_prod_a_a,SV366: set_Product_prod_a_a,SV327: a,SV166: a,SV257: a,SV52: a] :
( ( ( SV52 = SV257 )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 ) )
= $true )
| ( ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SV257 @ SV327 ) ) @ ( lex_prod_a_a @ SV359 @ SV366 ) )
| ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
| ~ ( ( SV52 != SV257 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2039]) ).
thf(2097,plain,
! [SV330: a,SV170: a,SV261: a,SV56: a] :
( ( ( SV56 = SV261 )
= $true )
| ( ( ( product_Pair_a_a @ SV56 @ SV170 )
= ( product_Pair_a_a @ SV261 @ SV330 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2040]) ).
thf(2098,plain,
! [SV261: a,SV56: a,SV330: a,SV170: a] :
( ( ( SV170 = SV330 )
= $true )
| ( ( ( product_Pair_a_a @ SV56 @ SV170 )
= ( product_Pair_a_a @ SV261 @ SV330 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2041]) ).
thf(2099,plain,
! [SV330: a,SV261: a,SV170: a,SV56: a] :
( ( ( ( product_Pair_a_a @ SV56 @ SV170 )
!= ( product_Pair_a_a @ SV261 @ SV330 ) )
= $false )
| ( ( SV56 = SV261 )
= $false )
| ( ( SV170 = SV330 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2042]) ).
thf(2100,plain,
! [SV330: a,SV170: a,SV261: a,SV56: a] :
( ( ( ~ ~ ( ( SV56 != SV261 )
| ( SV170 != SV330 ) ) )
= $false )
| ( ( SV56 = SV261 )
= $false )
| ( ( SV170 = SV330 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2042]) ).
thf(2101,plain,
! [SV57: a,SV262: a,SV171: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV171 @ SV262 ) @ relation )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV262 @ SV171 ) @ relation ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV262 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV262 @ SV57 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV171 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV171 @ SV57 ) @ relation )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2043]) ).
thf(2102,plain,
! [SV60: set_Product_prod_a_a,SV174: set_Pr1948701895od_a_a,SV265: product_prod_a_a,SV333: product_prod_a_a] :
( ( ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
| ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
| ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
| ~ ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
| ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) ) ) )
= $true )
| ( ( member449909584od_a_a @ SV265 @ SV60 )
= $false )
| ( ( member449909584od_a_a @ SV333 @ SV60 )
= $false )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2044]) ).
thf(2103,plain,
! [SV61: set_a,SV175: set_Product_prod_a_a,SV266: a,SV334: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) ) ) )
= $true )
| ( ( member_a @ SV266 @ SV61 )
= $false )
| ( ( member_a @ SV334 @ SV61 )
= $false )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2046]) ).
thf(2104,plain,
! [SV381: a,SV179: set_Product_prod_a_a,SV377: a,SV374: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV374 @ SV377 ) @ SV179 )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV377 @ SV381 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV374 @ SV381 ) @ SV179 ) )
= $true )
| ( ( trans_a @ SV179 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2048]) ).
thf(2105,plain,
! [SV179: set_Product_prod_a_a] :
( ( ( trans_a @ SV179 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK37_SY828 @ SV179 ) @ ( sK46_SY1040 @ SV179 ) ) @ SV179 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2049]) ).
thf(2106,plain,
! [SV179: set_Product_prod_a_a] :
( ( ( ! [SY828: a,SY829: a,SY830: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY829 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY829 @ SY830 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY830 ) @ SV179 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK37_SY828 @ SV179 ) @ ( sK46_SY1040 @ SV179 ) ) @ SV179 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2050]) ).
thf(2107,plain,
! [SV179: set_Product_prod_a_a] :
( ( ( ~ ( trans_a @ SV179 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK46_SY1040 @ SV179 ) @ ( sK56_SY1050 @ SV179 ) ) @ SV179 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2051]) ).
thf(2108,plain,
! [SV179: set_Product_prod_a_a] :
( ( ( ~ ! [SY828: a,SY829: a,SY830: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY829 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY829 @ SY830 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY830 ) @ SV179 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK46_SY1040 @ SV179 ) @ ( sK56_SY1050 @ SV179 ) ) @ SV179 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2051]) ).
thf(2109,plain,
! [SV179: set_Product_prod_a_a] :
( ( ( trans_a @ SV179 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK37_SY828 @ SV179 ) @ ( sK56_SY1050 @ SV179 ) ) @ SV179 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2052]) ).
thf(2110,plain,
! [SV179: set_Product_prod_a_a] :
( ( ( ! [SY828: a,SY829: a,SY830: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY829 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY829 @ SY830 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY830 ) @ SV179 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK37_SY828 @ SV179 ) @ ( sK56_SY1050 @ SV179 ) ) @ SV179 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2053]) ).
thf(2111,plain,
! [SV74: set_a,SV360: a,SV184: set_Product_prod_a_a,SV272: a,SV336: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV272 ) @ SV184 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV336 ) @ SV184 )
= $false )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV360 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV336 ) @ SV184 ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV360 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV272 ) @ SV184 ) ) )
= $true )
| ( ( prefer719835986ence_a @ SV74 @ SV184 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2054]) ).
thf(2112,plain,
! [SV88: a,SV196: a] :
( ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
= $true )
| ( ( member_a @ SV88 @ carrier )
= $false )
| ( ( member_a @ SV196 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2055]) ).
thf(2113,plain,
! [SV196: a,SV88: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation ) )
= $true )
| ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) )
= $true )
| ( ( ~ ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) ) ) )
= $true )
| ( ( member_a @ SV88 @ carrier )
= $false )
| ( ( member_a @ SV196 @ carrier )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2056]) ).
thf(2114,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a,SV382: a] :
( ( ( member_a @ SV382 @ SV197 )
= $false )
| ( ( ! [SY1065: a] :
( ~ ( member_a @ SY1065 @ SV197 )
| ~ ( ( SV382 != SY1065 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV382 @ SY1065 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1065 @ SV382 ) @ SV343 ) ) )
= $true )
| ( ( total_on_a @ SV197 @ SV343 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2057]) ).
thf(2115,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a] :
( ( ( total_on_a @ SV197 @ SV343 )
= $true )
| ( ( member_a @ ( sK57_SY1017 @ SV343 @ SV197 ) @ SV197 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2058]) ).
thf(2116,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a] :
( ( ( ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) )
= $true )
| ( ( member_a @ ( sK57_SY1017 @ SV343 @ SV197 ) @ SV197 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2059]) ).
thf(2117,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a] :
( ( ( ~ ( total_on_a @ SV197 @ SV343 )
| ~ ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) )
= $false )
| ( ( member_a @ ( sK61_SY1054 @ SV343 @ SV197 ) @ SV197 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2060]) ).
thf(2118,plain,
! [SV197: set_a,SV343: set_Product_prod_a_a] :
( ( ( ( sK57_SY1017 @ SV343 @ SV197 )
!= ( sK61_SY1054 @ SV343 @ SV197 ) )
= $true )
| ( ( ~ ( ~ ( total_on_a @ SV197 @ SV343 )
| ~ ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2061]) ).
thf(2119,plain,
! [SV197: set_a,SV343: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK57_SY1017 @ SV343 @ SV197 ) @ ( sK61_SY1054 @ SV343 @ SV197 ) ) @ SV343 )
= $false )
| ( ( ~ ( ~ ( total_on_a @ SV197 @ SV343 )
| ~ ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2062]) ).
thf(2120,plain,
! [SV197: set_a,SV343: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1054 @ SV343 @ SV197 ) @ ( sK57_SY1017 @ SV343 @ SV197 ) ) @ SV343 )
= $false )
| ( ( ~ ( ~ ( total_on_a @ SV197 @ SV343 )
| ~ ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2062]) ).
thf(2121,plain,
! [SV198: set_Product_prod_a_a] :
( ( ( SV198
!= ( sK62_SY857 @ SV198 ) )
= $false )
| ( ( asym_a @ SV198 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2063]) ).
thf(2122,plain,
! [SV198: set_Product_prod_a_a] :
( ( ( ~ ! [SY1061: a,SY1062: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1061 @ SY1062 ) @ ( sK62_SY857 @ SV198 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1062 @ SY1061 ) @ ( sK62_SY857 @ SV198 ) ) ) )
= $false )
| ( ( asym_a @ SV198 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2063]) ).
thf(2123,plain,
! [SV369: set_Product_prod_a_a,SV198: set_Product_prod_a_a] :
( ( ( ! [SY1066: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK68_SY1051 @ SV198 @ SV369 ) @ SY1066 ) @ SV369 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1066 @ ( sK68_SY1051 @ SV198 @ SV369 ) ) @ SV369 ) ) )
= $false )
| ( ( SV198 = SV369 )
= $false )
| ( ( ~ ( ~ ( asym_a @ SV198 )
| ~ ~ ! [SY857: set_Product_prod_a_a] :
~ ~ ( ( SV198 != SY857 )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SY857 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SY857 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2064]) ).
thf(2124,plain,
! [SV199: set_Product_prod_a_a,SV375: a,SV378: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV378 @ SV375 ) @ SV199 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV375 @ SV378 ) @ SV199 )
= $false )
| ( ( asym_a @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2065]) ).
thf(2125,plain,
! [SV199: set_Product_prod_a_a,SV383: a] :
( ( ( ! [SY1067: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV383 @ SY1067 ) @ SV199 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1067 @ SV383 ) @ SV199 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK38_SY860 @ SV199 ) @ ( sK47_SY1042 @ SV199 ) ) @ SV199 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2067]) ).
thf(2126,plain,
! [SV199: set_Product_prod_a_a,SV384: a] :
( ( ( ! [SY1068: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV384 @ SY1068 ) @ SV199 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1068 @ SV384 ) @ SV199 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK47_SY1042 @ SV199 ) @ ( sK38_SY860 @ SV199 ) ) @ SV199 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2069]) ).
thf(2127,plain,
! [SV93: set_a,SV286: a,SV201: set_Product_prod_a_a,SV362: a,SV345: a] :
( ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV362 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV362 @ SV345 ) @ SV201 ) ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SV362 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV362 @ SV286 ) @ SV201 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SV345 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV286 ) @ SV201 )
= $false )
| ( ( prefer1292084992ence_a @ SV93 @ SV201 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2070]) ).
thf(2128,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) ) )
= $true )
| ( ( prefer1292084992ence_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2071]) ).
thf(2129,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( order_preorder_on_a @ SV204 @ SV347 )
= $true )
| ( ( prefer1292084992ence_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2072]) ).
thf(2130,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) ) )
= $false )
| ( ( ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
= $true )
| ( ( ~ ( order_preorder_on_a @ SV204 @ SV347 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 )
| ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2073]) ).
thf(2131,plain,
! [SV100: set_Product_prod_a_a,SV207: set_a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK63_SY883 @ SV207 @ SV100 ) @ ( sK66_SY1063 @ SV100 @ SV207 ) ) @ SV100 )
= $true )
| ( ( ~ ( order_preorder_on_a @ SV207 @ SV100 )
| ( prefer1292084992ence_a @ SV207 @ SV100 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK17_SY881 @ SV207 @ SV100 ) @ ( sK30_SY1034 @ SV100 @ SV207 ) ) @ SV100 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2074]) ).
thf(2132,plain,
! [SV100: set_Product_prod_a_a,SV207: set_a] :
( ( ( ~ ( order_preorder_on_a @ SV207 @ SV100 ) )
= $true )
| ( ( prefer1292084992ence_a @ SV207 @ SV100 )
= $true )
| ( ( member_a @ ( sK66_SY1063 @ SV100 @ SV207 ) @ SV207 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK17_SY881 @ SV207 @ SV100 ) @ ( sK30_SY1034 @ SV100 @ SV207 ) ) @ SV100 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2075]) ).
thf(2133,plain,
! [SV100: set_Product_prod_a_a,SV207: set_a] :
( ( ( ~ ( order_preorder_on_a @ SV207 @ SV100 ) )
= $true )
| ( ( prefer1292084992ence_a @ SV207 @ SV100 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK58_SY883 @ SV207 @ SV100 ) @ ( sK64_SY1059 @ SV100 @ SV207 ) ) @ SV100 )
= $true )
| ( ( member_a @ ( sK17_SY881 @ SV207 @ SV100 ) @ SV207 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2076]) ).
thf(2134,plain,
! [SV100: set_Product_prod_a_a,SV207: set_a] :
( ( ( order_preorder_on_a @ SV207 @ SV100 )
= $false )
| ( ( prefer1292084992ence_a @ SV207 @ SV100 )
= $true )
| ( ( member_a @ ( sK64_SY1059 @ SV100 @ SV207 ) @ SV207 )
= $false )
| ( ( member_a @ ( sK17_SY881 @ SV207 @ SV100 ) @ SV207 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2077]) ).
thf(2135,plain,
! [SV101: a,SV291: a,SV208: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV291 ) @ relation ) )
= $true )
| ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV291 @ SV208 ) @ relation ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SV291 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV291 @ SV101 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SV208 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV101 ) @ relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2078]) ).
thf(2136,plain,
! [SV112: a,SV370: a,SV219: product_prod_a_a] :
( ( ( SV219
!= ( product_Pair_a_a @ ( sK69_SY907 @ SV370 @ SV112 @ SV219 ) @ SV112 ) )
= $false )
| ( ( SV219
= ( product_Pair_a_a @ SV370 @ SV112 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2079]) ).
thf(2137,plain,
! [SV320: set_Pr1948701895od_a_a,SV380: product_prod_a_a,SV154: set_Product_prod_a_a,SV385: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV385 @ SV154 )
| ~ ( ( SV380 != SV385 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV380 @ SV385 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV385 @ SV380 ) @ SV320 ) )
= $true )
| ( ( member449909584od_a_a @ SV380 @ SV154 )
= $false )
| ( ( total_1490170027od_a_a @ SV154 @ SV320 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2081]) ).
thf(2138,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a,SV386: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV386 @ SV154 )
| ! [SY1069: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1069 @ SV154 )
| ~ ( ( SV386 != SY1069 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV386 @ SY1069 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1069 @ SV386 ) @ SV320 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( sK54_SY1005 @ SV320 @ SV154 ) @ SV154 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2083]) ).
thf(2139,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a] :
( ( ( ~ ( total_1490170027od_a_a @ SV154 @ SV320 ) )
= $false )
| ( ( member449909584od_a_a @ ( sK59_SY1053 @ SV320 @ SV154 ) @ SV154 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2084]) ).
thf(2140,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a] :
( ( ( ~ ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ ( sK59_SY1053 @ SV320 @ SV154 ) @ SV154 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2084]) ).
thf(2141,plain,
! [SV154: set_Product_prod_a_a,SV320: set_Pr1948701895od_a_a] :
( ( ( ( sK54_SY1005 @ SV320 @ SV154 )
= ( sK59_SY1053 @ SV320 @ SV154 ) )
= $false )
| ( ( ~ ( ~ ( total_1490170027od_a_a @ SV154 @ SV320 )
| ~ ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2085]) ).
thf(2142,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a] :
( ( ( ~ ( total_1490170027od_a_a @ SV154 @ SV320 )
| ~ ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK54_SY1005 @ SV320 @ SV154 ) @ ( sK59_SY1053 @ SV320 @ SV154 ) ) @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2086]) ).
thf(2143,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a] :
( ( ( ~ ( total_1490170027od_a_a @ SV154 @ SV320 )
| ~ ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK59_SY1053 @ SV320 @ SV154 ) @ ( sK54_SY1005 @ SV320 @ SV154 ) ) @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2087]) ).
thf(2144,plain,
! [SV367: a,SV40: a,SV155: product_prod_a_a] :
( ( ( SV155
= ( product_Pair_a_a @ SV40 @ ( sK67_SY782 @ SV367 @ SV40 @ SV155 ) ) )
= $true )
| ( ( SV155
= ( product_Pair_a_a @ SV40 @ SV367 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2088]) ).
thf(2145,plain,
! [SV324: a,SV252: a,SV159: a,SV44: a] :
( ( ( ( product_Pair_a_a @ SV44 @ SV159 )
= ( product_Pair_a_a @ SV252 @ SV324 ) )
= $true )
| ( ( SV44 = SV252 )
= $false )
| ( ( SV159 = SV324 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2091]) ).
thf(2146,plain,
! [SV324: a,SV159: a,SV252: a,SV44: a] :
( ( ( ~ ( ( SV44 != SV252 )
| ( SV159 != SV324 ) ) )
= $true )
| ( ( SV44 = SV252 )
= $false )
| ( ( SV159 = SV324 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2092]) ).
thf(2147,plain,
! [SV359: set_Product_prod_a_a,SV366: set_Product_prod_a_a,SV327: a,SV166: a,SV257: a,SV52: a] :
( ( ( ( SV52 != SV257 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SV257 @ SV327 ) ) @ ( lex_prod_a_a @ SV359 @ SV366 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2093]) ).
thf(2148,plain,
! [SV366: set_Product_prod_a_a,SV327: a,SV166: a,SV359: set_Product_prod_a_a,SV257: a,SV52: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
= $true )
| ( ( ~ ( ( SV52 != SV257 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2095]) ).
thf(2149,plain,
! [SV359: set_Product_prod_a_a,SV257: a,SV52: a,SV366: set_Product_prod_a_a,SV327: a,SV166: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 )
= $false )
| ( ( SV52 = SV257 )
= $false )
| ( ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SV257 @ SV327 ) ) @ ( lex_prod_a_a @ SV359 @ SV366 ) )
| ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
| ~ ( ( SV52 != SV257 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2096]) ).
thf(2150,plain,
! [SV330: a,SV261: a,SV170: a,SV56: a] :
( ( ( ( product_Pair_a_a @ SV56 @ SV170 )
= ( product_Pair_a_a @ SV261 @ SV330 ) )
= $true )
| ( ( SV56 = SV261 )
= $false )
| ( ( SV170 = SV330 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2099]) ).
thf(2151,plain,
! [SV330: a,SV170: a,SV261: a,SV56: a] :
( ( ( ~ ( ( SV56 != SV261 )
| ( SV170 != SV330 ) ) )
= $true )
| ( ( SV56 = SV261 )
= $false )
| ( ( SV170 = SV330 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2100]) ).
thf(2152,plain,
! [SV57: a,SV171: a,SV262: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV262 @ SV171 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV171 @ SV262 ) @ relation )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV262 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV262 @ SV57 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV171 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV171 @ SV57 ) @ relation )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2101]) ).
thf(2153,plain,
! [SV60: set_Product_prod_a_a,SV174: set_Pr1948701895od_a_a,SV265: product_prod_a_a,SV333: product_prod_a_a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
| ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
| ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
| ~ ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
| ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) ) ) )
= $true )
| ( ( member449909584od_a_a @ SV265 @ SV60 )
= $false )
| ( ( member449909584od_a_a @ SV333 @ SV60 )
= $false )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2102]) ).
thf(2154,plain,
! [SV61: set_a,SV175: set_Product_prod_a_a,SV266: a,SV334: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) ) ) )
= $true )
| ( ( member_a @ SV266 @ SV61 )
= $false )
| ( ( member_a @ SV334 @ SV61 )
= $false )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2103]) ).
thf(2155,plain,
! [SV374: a,SV179: set_Product_prod_a_a,SV381: a,SV377: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV377 @ SV381 ) @ SV179 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV374 @ SV381 ) @ SV179 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV374 @ SV377 ) @ SV179 )
= $false )
| ( ( trans_a @ SV179 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2104]) ).
thf(2156,plain,
! [SV179: set_Product_prod_a_a,SV387: a] :
( ( ( ! [SY1070: a,SY1071: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV387 @ SY1070 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1070 @ SY1071 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV387 @ SY1071 ) @ SV179 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK37_SY828 @ SV179 ) @ ( sK46_SY1040 @ SV179 ) ) @ SV179 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2106]) ).
thf(2157,plain,
! [SV179: set_Product_prod_a_a] :
( ( ( trans_a @ SV179 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK46_SY1040 @ SV179 ) @ ( sK56_SY1050 @ SV179 ) ) @ SV179 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2107]) ).
thf(2158,plain,
! [SV179: set_Product_prod_a_a] :
( ( ( ! [SY828: a,SY829: a,SY830: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY829 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY829 @ SY830 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY828 @ SY830 ) @ SV179 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK46_SY1040 @ SV179 ) @ ( sK56_SY1050 @ SV179 ) ) @ SV179 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2108]) ).
thf(2159,plain,
! [SV179: set_Product_prod_a_a,SV388: a] :
( ( ( ! [SY1072: a,SY1073: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV388 @ SY1072 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1072 @ SY1073 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV388 @ SY1073 ) @ SV179 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK37_SY828 @ SV179 ) @ ( sK56_SY1050 @ SV179 ) ) @ SV179 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2110]) ).
thf(2160,plain,
! [SV74: set_a,SV272: a,SV184: set_Product_prod_a_a,SV360: a,SV336: a] :
( ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV360 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV336 ) @ SV184 ) ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV360 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV272 ) @ SV184 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV336 ) @ SV184 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV272 ) @ SV184 )
= $true )
| ( ( prefer719835986ence_a @ SV74 @ SV184 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2111]) ).
thf(2161,plain,
! [SV88: a,SV196: a] :
( ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
= $true )
| ( ( member_a @ SV88 @ carrier )
= $false )
| ( ( member_a @ SV196 @ carrier )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2112]) ).
thf(2162,plain,
! [SV196: a,SV88: a] :
( ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
= $true )
| ( ( member_a @ SV88 @ carrier )
= $false )
| ( ( member_a @ SV196 @ carrier )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2112]) ).
thf(2163,plain,
! [SV196: a,SV88: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
= $false )
| ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) )
= $true )
| ( ( ~ ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) ) ) )
= $true )
| ( ( member_a @ SV88 @ carrier )
= $false )
| ( ( member_a @ SV196 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2113]) ).
thf(2164,plain,
! [SV343: set_Product_prod_a_a,SV382: a,SV197: set_a,SV389: a] :
( ( ( ~ ( member_a @ SV389 @ SV197 )
| ~ ( ( SV382 != SV389 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV382 @ SV389 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV389 @ SV382 ) @ SV343 ) )
= $true )
| ( ( member_a @ SV382 @ SV197 )
= $false )
| ( ( total_on_a @ SV197 @ SV343 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2114]) ).
thf(2165,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a,SV390: a] :
( ( ( ~ ( member_a @ SV390 @ SV197 )
| ! [SY1074: a] :
( ~ ( member_a @ SY1074 @ SV197 )
| ~ ( ( SV390 != SY1074 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV390 @ SY1074 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1074 @ SV390 ) @ SV343 ) ) )
= $true )
| ( ( member_a @ ( sK57_SY1017 @ SV343 @ SV197 ) @ SV197 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2116]) ).
thf(2166,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a] :
( ( ( ~ ( total_on_a @ SV197 @ SV343 ) )
= $false )
| ( ( member_a @ ( sK61_SY1054 @ SV343 @ SV197 ) @ SV197 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2117]) ).
thf(2167,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a] :
( ( ( ~ ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) )
= $false )
| ( ( member_a @ ( sK61_SY1054 @ SV343 @ SV197 ) @ SV197 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2117]) ).
thf(2168,plain,
! [SV197: set_a,SV343: set_Product_prod_a_a] :
( ( ( ( sK57_SY1017 @ SV343 @ SV197 )
= ( sK61_SY1054 @ SV343 @ SV197 ) )
= $false )
| ( ( ~ ( ~ ( total_on_a @ SV197 @ SV343 )
| ~ ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2118]) ).
thf(2169,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a] :
( ( ( ~ ( total_on_a @ SV197 @ SV343 )
| ~ ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK57_SY1017 @ SV343 @ SV197 ) @ ( sK61_SY1054 @ SV343 @ SV197 ) ) @ SV343 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2119]) ).
thf(2170,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a] :
( ( ( ~ ( total_on_a @ SV197 @ SV343 )
| ~ ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1054 @ SV343 @ SV197 ) @ ( sK57_SY1017 @ SV343 @ SV197 ) ) @ SV343 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2120]) ).
thf(2171,plain,
! [SV198: set_Product_prod_a_a] :
( ( ( SV198
= ( sK62_SY857 @ SV198 ) )
= $true )
| ( ( asym_a @ SV198 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2121]) ).
thf(2172,plain,
! [SV198: set_Product_prod_a_a] :
( ( ( ! [SY1061: a,SY1062: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1061 @ SY1062 ) @ ( sK62_SY857 @ SV198 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1062 @ SY1061 ) @ ( sK62_SY857 @ SV198 ) ) ) )
= $true )
| ( ( asym_a @ SV198 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2122]) ).
thf(2173,plain,
! [SV369: set_Product_prod_a_a,SV198: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK68_SY1051 @ SV198 @ SV369 ) @ ( sK70_SY1066 @ SV369 @ SV198 ) ) @ SV369 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK70_SY1066 @ SV369 @ SV198 ) @ ( sK68_SY1051 @ SV198 @ SV369 ) ) @ SV369 ) )
= $false )
| ( ( SV198 = SV369 )
= $false )
| ( ( ~ ( ~ ( asym_a @ SV198 )
| ~ ~ ! [SY857: set_Product_prod_a_a] :
~ ~ ( ( SV198 != SY857 )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SY857 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SY857 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2123]) ).
thf(2174,plain,
! [SV199: set_Product_prod_a_a,SV391: a,SV383: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV383 @ SV391 ) @ SV199 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV391 @ SV383 ) @ SV199 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK38_SY860 @ SV199 ) @ ( sK47_SY1042 @ SV199 ) ) @ SV199 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2125]) ).
thf(2175,plain,
! [SV199: set_Product_prod_a_a,SV392: a,SV384: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV384 @ SV392 ) @ SV199 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV392 @ SV384 ) @ SV199 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK47_SY1042 @ SV199 ) @ ( sK38_SY860 @ SV199 ) ) @ SV199 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2126]) ).
thf(2176,plain,
! [SV93: set_a,SV286: a,SV201: set_Product_prod_a_a,SV362: a,SV345: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV362 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV362 @ SV345 ) @ SV201 ) ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SV362 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV362 @ SV286 ) @ SV201 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SV345 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV286 ) @ SV201 )
= $false )
| ( ( prefer1292084992ence_a @ SV93 @ SV201 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2127]) ).
thf(2177,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
= $false )
| ( ( prefer1292084992ence_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2128]) ).
thf(2178,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( ! [SY1075: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SY1075 ) @ SV347 )
| ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 ) ) )
= $false )
| ( ( ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
= $true )
| ( ( ~ ( order_preorder_on_a @ SV204 @ SV347 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 )
| ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2130]) ).
thf(2179,plain,
! [SV100: set_Product_prod_a_a,SV207: set_a] :
( ( ( ~ ( order_preorder_on_a @ SV207 @ SV100 ) )
= $true )
| ( ( prefer1292084992ence_a @ SV207 @ SV100 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK63_SY883 @ SV207 @ SV100 ) @ ( sK66_SY1063 @ SV100 @ SV207 ) ) @ SV100 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK17_SY881 @ SV207 @ SV100 ) @ ( sK30_SY1034 @ SV100 @ SV207 ) ) @ SV100 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2131]) ).
thf(2180,plain,
! [SV100: set_Product_prod_a_a,SV207: set_a] :
( ( ( order_preorder_on_a @ SV207 @ SV100 )
= $false )
| ( ( prefer1292084992ence_a @ SV207 @ SV100 )
= $true )
| ( ( member_a @ ( sK66_SY1063 @ SV100 @ SV207 ) @ SV207 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK17_SY881 @ SV207 @ SV100 ) @ ( sK30_SY1034 @ SV100 @ SV207 ) ) @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2132]) ).
thf(2181,plain,
! [SV100: set_Product_prod_a_a,SV207: set_a] :
( ( ( order_preorder_on_a @ SV207 @ SV100 )
= $false )
| ( ( prefer1292084992ence_a @ SV207 @ SV100 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK58_SY883 @ SV207 @ SV100 ) @ ( sK64_SY1059 @ SV100 @ SV207 ) ) @ SV100 )
= $true )
| ( ( member_a @ ( sK17_SY881 @ SV207 @ SV100 ) @ SV207 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2133]) ).
thf(2182,plain,
! [SV101: a,SV291: a,SV208: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV291 ) @ relation )
= $false )
| ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV291 @ SV208 ) @ relation ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SV291 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV291 @ SV101 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SV208 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV101 ) @ relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2135]) ).
thf(2183,plain,
! [SV112: a,SV370: a,SV219: product_prod_a_a] :
( ( ( SV219
= ( product_Pair_a_a @ ( sK69_SY907 @ SV370 @ SV112 @ SV219 ) @ SV112 ) )
= $true )
| ( ( SV219
= ( product_Pair_a_a @ SV370 @ SV112 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2136]) ).
thf(2184,plain,
! [SV320: set_Pr1948701895od_a_a,SV380: product_prod_a_a,SV154: set_Product_prod_a_a,SV385: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV385 @ SV154 ) )
= $true )
| ( ( ~ ( ( SV380 != SV385 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV380 @ SV385 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV385 @ SV380 ) @ SV320 ) )
= $true )
| ( ( member449909584od_a_a @ SV380 @ SV154 )
= $false )
| ( ( total_1490170027od_a_a @ SV154 @ SV320 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2137]) ).
thf(2185,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a,SV386: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV386 @ SV154 ) )
= $true )
| ( ( ! [SY1069: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1069 @ SV154 )
| ~ ( ( SV386 != SY1069 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV386 @ SY1069 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1069 @ SV386 ) @ SV320 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( sK54_SY1005 @ SV320 @ SV154 ) @ SV154 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2138]) ).
thf(2186,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a] :
( ( ( total_1490170027od_a_a @ SV154 @ SV320 )
= $true )
| ( ( member449909584od_a_a @ ( sK59_SY1053 @ SV320 @ SV154 ) @ SV154 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2139]) ).
thf(2187,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a] :
( ( ( ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) )
= $true )
| ( ( member449909584od_a_a @ ( sK59_SY1053 @ SV320 @ SV154 ) @ SV154 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2140]) ).
thf(2188,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a] :
( ( ( ~ ( total_1490170027od_a_a @ SV154 @ SV320 )
| ~ ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) )
= $false )
| ( ( ( sK54_SY1005 @ SV320 @ SV154 )
= ( sK59_SY1053 @ SV320 @ SV154 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2141]) ).
thf(2189,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a] :
( ( ( ~ ( total_1490170027od_a_a @ SV154 @ SV320 ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK54_SY1005 @ SV320 @ SV154 ) @ ( sK59_SY1053 @ SV320 @ SV154 ) ) @ SV320 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2142]) ).
thf(2190,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a] :
( ( ( ~ ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK54_SY1005 @ SV320 @ SV154 ) @ ( sK59_SY1053 @ SV320 @ SV154 ) ) @ SV320 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2142]) ).
thf(2191,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a] :
( ( ( ~ ( total_1490170027od_a_a @ SV154 @ SV320 ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK59_SY1053 @ SV320 @ SV154 ) @ ( sK54_SY1005 @ SV320 @ SV154 ) ) @ SV320 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2143]) ).
thf(2192,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a] :
( ( ( ~ ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK59_SY1053 @ SV320 @ SV154 ) @ ( sK54_SY1005 @ SV320 @ SV154 ) ) @ SV320 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2143]) ).
thf(2193,plain,
! [SV324: a,SV159: a,SV252: a,SV44: a] :
( ( ( ( SV44 != SV252 )
| ( SV159 != SV324 ) )
= $false )
| ( ( SV44 = SV252 )
= $false )
| ( ( SV159 = SV324 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2146]) ).
thf(2194,plain,
! [SV366: set_Product_prod_a_a,SV327: a,SV166: a,SV359: set_Product_prod_a_a,SV257: a,SV52: a] :
( ( ( SV52 != SV257 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SV257 @ SV327 ) ) @ ( lex_prod_a_a @ SV359 @ SV366 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2147]) ).
thf(2195,plain,
! [SV359: set_Product_prod_a_a,SV257: a,SV52: a,SV366: set_Product_prod_a_a,SV327: a,SV166: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SV257 @ SV327 ) ) @ ( lex_prod_a_a @ SV359 @ SV366 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2147]) ).
thf(2196,plain,
! [SV359: set_Product_prod_a_a,SV366: set_Product_prod_a_a,SV327: a,SV166: a,SV257: a,SV52: a] :
( ( ( ( SV52 != SV257 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2148]) ).
thf(2197,plain,
! [SV366: set_Product_prod_a_a,SV359: set_Product_prod_a_a,SV327: a,SV257: a,SV166: a,SV52: a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SV257 @ SV327 ) ) @ ( lex_prod_a_a @ SV359 @ SV366 ) )
| ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
| ~ ( ( SV52 != SV257 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 ) ) ) )
= $false )
| ( ( SV52 = SV257 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2149]) ).
thf(2198,plain,
! [SV330: a,SV170: a,SV261: a,SV56: a] :
( ( ( ( SV56 != SV261 )
| ( SV170 != SV330 ) )
= $false )
| ( ( SV56 = SV261 )
= $false )
| ( ( SV170 = SV330 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2151]) ).
thf(2199,plain,
! [SV171: a,SV262: a,SV57: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV262 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV262 @ SV57 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV171 @ SV262 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV262 @ SV171 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV171 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV171 @ SV57 ) @ relation )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2152]) ).
thf(2200,plain,
! [SV60: set_Product_prod_a_a,SV174: set_Pr1948701895od_a_a,SV265: product_prod_a_a,SV333: product_prod_a_a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) )
= $false )
| ( ( ~ ( ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
| ~ ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
| ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) ) ) )
= $true )
| ( ( member449909584od_a_a @ SV265 @ SV60 )
= $false )
| ( ( member449909584od_a_a @ SV333 @ SV60 )
= $false )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2153]) ).
thf(2201,plain,
! [SV60: set_Product_prod_a_a,SV174: set_Pr1948701895od_a_a,SV333: product_prod_a_a,SV265: product_prod_a_a] :
( ( ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
| ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
| ~ ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
| ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) ) ) )
= $true )
| ( ( member449909584od_a_a @ SV265 @ SV60 )
= $false )
| ( ( member449909584od_a_a @ SV333 @ SV60 )
= $false )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2153]) ).
thf(2202,plain,
! [SV61: set_a,SV175: set_Product_prod_a_a,SV266: a,SV334: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) )
= $false )
| ( ( ~ ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) ) ) )
= $true )
| ( ( member_a @ SV266 @ SV61 )
= $false )
| ( ( member_a @ SV334 @ SV61 )
= $false )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2154]) ).
thf(2203,plain,
! [SV61: set_a,SV175: set_Product_prod_a_a,SV334: a,SV266: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) ) ) )
= $true )
| ( ( member_a @ SV266 @ SV61 )
= $false )
| ( ( member_a @ SV334 @ SV61 )
= $false )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2154]) ).
thf(2204,plain,
! [SV374: a,SV179: set_Product_prod_a_a,SV381: a,SV377: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV377 @ SV381 ) @ SV179 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV374 @ SV381 ) @ SV179 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV374 @ SV377 ) @ SV179 )
= $false )
| ( ( trans_a @ SV179 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2155]) ).
thf(2205,plain,
! [SV179: set_Product_prod_a_a,SV393: a,SV387: a] :
( ( ( ! [SY1076: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV387 @ SV393 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV393 @ SY1076 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV387 @ SY1076 ) @ SV179 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK37_SY828 @ SV179 ) @ ( sK46_SY1040 @ SV179 ) ) @ SV179 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2156]) ).
thf(2206,plain,
! [SV179: set_Product_prod_a_a,SV394: a] :
( ( ( ! [SY1077: a,SY1078: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SY1077 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1077 @ SY1078 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SY1078 ) @ SV179 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK46_SY1040 @ SV179 ) @ ( sK56_SY1050 @ SV179 ) ) @ SV179 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2158]) ).
thf(2207,plain,
! [SV179: set_Product_prod_a_a,SV395: a,SV388: a] :
( ( ( ! [SY1079: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV388 @ SV395 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV395 @ SY1079 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV388 @ SY1079 ) @ SV179 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK37_SY828 @ SV179 ) @ ( sK56_SY1050 @ SV179 ) ) @ SV179 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2159]) ).
thf(2208,plain,
! [SV74: set_a,SV272: a,SV184: set_Product_prod_a_a,SV360: a,SV336: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV360 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV336 ) @ SV184 ) ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV360 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV272 ) @ SV184 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV336 ) @ SV184 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV272 ) @ SV184 )
= $true )
| ( ( prefer719835986ence_a @ SV74 @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2160]) ).
thf(2209,plain,
! [SV88: a,SV196: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
= $true )
| ( ( member_a @ SV88 @ carrier )
= $false )
| ( ( member_a @ SV196 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2161]) ).
thf(2210,plain,
! [SV196: a,SV88: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
= $true )
| ( ( member_a @ SV88 @ carrier )
= $false )
| ( ( member_a @ SV196 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2162]) ).
thf(2211,plain,
! [SV88: a,SV196: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
= $false )
| ( ( ~ ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) ) ) )
= $true )
| ( ( member_a @ SV88 @ carrier )
= $false )
| ( ( member_a @ SV196 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2163]) ).
thf(2212,plain,
! [SV343: set_Product_prod_a_a,SV382: a,SV197: set_a,SV389: a] :
( ( ( ~ ( member_a @ SV389 @ SV197 ) )
= $true )
| ( ( ~ ( ( SV382 != SV389 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV382 @ SV389 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV389 @ SV382 ) @ SV343 ) )
= $true )
| ( ( member_a @ SV382 @ SV197 )
= $false )
| ( ( total_on_a @ SV197 @ SV343 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2164]) ).
thf(2213,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a,SV390: a] :
( ( ( ~ ( member_a @ SV390 @ SV197 ) )
= $true )
| ( ( ! [SY1074: a] :
( ~ ( member_a @ SY1074 @ SV197 )
| ~ ( ( SV390 != SY1074 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV390 @ SY1074 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1074 @ SV390 ) @ SV343 ) ) )
= $true )
| ( ( member_a @ ( sK57_SY1017 @ SV343 @ SV197 ) @ SV197 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2165]) ).
thf(2214,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a] :
( ( ( total_on_a @ SV197 @ SV343 )
= $true )
| ( ( member_a @ ( sK61_SY1054 @ SV343 @ SV197 ) @ SV197 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2166]) ).
thf(2215,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a] :
( ( ( ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) )
= $true )
| ( ( member_a @ ( sK61_SY1054 @ SV343 @ SV197 ) @ SV197 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2167]) ).
thf(2216,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a] :
( ( ( ~ ( total_on_a @ SV197 @ SV343 )
| ~ ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) )
= $false )
| ( ( ( sK57_SY1017 @ SV343 @ SV197 )
= ( sK61_SY1054 @ SV343 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2168]) ).
thf(2217,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a] :
( ( ( ~ ( total_on_a @ SV197 @ SV343 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK57_SY1017 @ SV343 @ SV197 ) @ ( sK61_SY1054 @ SV343 @ SV197 ) ) @ SV343 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2169]) ).
thf(2218,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a] :
( ( ( ~ ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK57_SY1017 @ SV343 @ SV197 ) @ ( sK61_SY1054 @ SV343 @ SV197 ) ) @ SV343 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2169]) ).
thf(2219,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a] :
( ( ( ~ ( total_on_a @ SV197 @ SV343 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1054 @ SV343 @ SV197 ) @ ( sK57_SY1017 @ SV343 @ SV197 ) ) @ SV343 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2170]) ).
thf(2220,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a] :
( ( ( ~ ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1054 @ SV343 @ SV197 ) @ ( sK57_SY1017 @ SV343 @ SV197 ) ) @ SV343 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2170]) ).
thf(2221,plain,
! [SV198: set_Product_prod_a_a,SV396: a] :
( ( ( ! [SY1080: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV396 @ SY1080 ) @ ( sK62_SY857 @ SV198 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1080 @ SV396 ) @ ( sK62_SY857 @ SV198 ) ) ) )
= $true )
| ( ( asym_a @ SV198 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2172]) ).
thf(2222,plain,
! [SV369: set_Product_prod_a_a,SV198: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK68_SY1051 @ SV198 @ SV369 ) @ ( sK70_SY1066 @ SV369 @ SV198 ) ) @ SV369 ) )
= $false )
| ( ( SV198 = SV369 )
= $false )
| ( ( ~ ( ~ ( asym_a @ SV198 )
| ~ ~ ! [SY857: set_Product_prod_a_a] :
~ ~ ( ( SV198 != SY857 )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SY857 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SY857 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2173]) ).
thf(2223,plain,
! [SV198: set_Product_prod_a_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK70_SY1066 @ SV369 @ SV198 ) @ ( sK68_SY1051 @ SV198 @ SV369 ) ) @ SV369 ) )
= $false )
| ( ( SV198 = SV369 )
= $false )
| ( ( ~ ( ~ ( asym_a @ SV198 )
| ~ ~ ! [SY857: set_Product_prod_a_a] :
~ ~ ( ( SV198 != SY857 )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SY857 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SY857 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2173]) ).
thf(2224,plain,
! [SV199: set_Product_prod_a_a,SV391: a,SV383: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV383 @ SV391 ) @ SV199 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV391 @ SV383 ) @ SV199 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK38_SY860 @ SV199 ) @ ( sK47_SY1042 @ SV199 ) ) @ SV199 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2174]) ).
thf(2225,plain,
! [SV199: set_Product_prod_a_a,SV392: a,SV384: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV384 @ SV392 ) @ SV199 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV392 @ SV384 ) @ SV199 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK47_SY1042 @ SV199 ) @ ( sK38_SY860 @ SV199 ) ) @ SV199 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2175]) ).
thf(2226,plain,
! [SV93: set_a,SV286: a,SV201: set_Product_prod_a_a,SV362: a,SV345: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV362 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV362 @ SV345 ) @ SV201 ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SV362 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV362 @ SV286 ) @ SV201 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SV345 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV286 ) @ SV201 )
= $false )
| ( ( prefer1292084992ence_a @ SV93 @ SV201 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2176]) ).
thf(2227,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) ) )
= $false )
| ( ( prefer1292084992ence_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2177]) ).
thf(2228,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
= $false )
| ( ( prefer1292084992ence_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2177]) ).
thf(2229,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
| ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 ) )
= $false )
| ( ( ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
= $true )
| ( ( ~ ( order_preorder_on_a @ SV204 @ SV347 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 )
| ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2178]) ).
thf(2230,plain,
! [SV100: set_Product_prod_a_a,SV207: set_a] :
( ( ( order_preorder_on_a @ SV207 @ SV100 )
= $false )
| ( ( prefer1292084992ence_a @ SV207 @ SV100 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK63_SY883 @ SV207 @ SV100 ) @ ( sK66_SY1063 @ SV100 @ SV207 ) ) @ SV100 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK17_SY881 @ SV207 @ SV100 ) @ ( sK30_SY1034 @ SV100 @ SV207 ) ) @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2179]) ).
thf(2231,plain,
! [SV101: a,SV208: a,SV291: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV291 @ SV208 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV291 ) @ relation )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SV291 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV291 @ SV101 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SV208 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV101 ) @ relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2182]) ).
thf(2232,plain,
! [SV320: set_Pr1948701895od_a_a,SV380: product_prod_a_a,SV154: set_Product_prod_a_a,SV385: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV385 @ SV154 )
= $false )
| ( ( ~ ( ( SV380 != SV385 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV380 @ SV385 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV385 @ SV380 ) @ SV320 ) )
= $true )
| ( ( member449909584od_a_a @ SV380 @ SV154 )
= $false )
| ( ( total_1490170027od_a_a @ SV154 @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2184]) ).
thf(2233,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a,SV386: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV386 @ SV154 )
= $false )
| ( ( ! [SY1069: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1069 @ SV154 )
| ~ ( ( SV386 != SY1069 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV386 @ SY1069 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1069 @ SV386 ) @ SV320 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( sK54_SY1005 @ SV320 @ SV154 ) @ SV154 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2185]) ).
thf(2234,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a,SV397: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV397 @ SV154 )
| ! [SY1081: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1081 @ SV154 )
| ~ ( ( SV397 != SY1081 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV397 @ SY1081 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1081 @ SV397 ) @ SV320 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( sK59_SY1053 @ SV320 @ SV154 ) @ SV154 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2187]) ).
thf(2235,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a] :
( ( ( ~ ( total_1490170027od_a_a @ SV154 @ SV320 ) )
= $false )
| ( ( ( sK54_SY1005 @ SV320 @ SV154 )
= ( sK59_SY1053 @ SV320 @ SV154 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2188]) ).
thf(2236,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a] :
( ( ( ~ ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) )
= $false )
| ( ( ( sK54_SY1005 @ SV320 @ SV154 )
= ( sK59_SY1053 @ SV320 @ SV154 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2188]) ).
thf(2237,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a] :
( ( ( total_1490170027od_a_a @ SV154 @ SV320 )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK54_SY1005 @ SV320 @ SV154 ) @ ( sK59_SY1053 @ SV320 @ SV154 ) ) @ SV320 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2189]) ).
thf(2238,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a] :
( ( ( ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK54_SY1005 @ SV320 @ SV154 ) @ ( sK59_SY1053 @ SV320 @ SV154 ) ) @ SV320 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2190]) ).
thf(2239,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a] :
( ( ( total_1490170027od_a_a @ SV154 @ SV320 )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK59_SY1053 @ SV320 @ SV154 ) @ ( sK54_SY1005 @ SV320 @ SV154 ) ) @ SV320 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2191]) ).
thf(2240,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a] :
( ( ( ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK59_SY1053 @ SV320 @ SV154 ) @ ( sK54_SY1005 @ SV320 @ SV154 ) ) @ SV320 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2192]) ).
thf(2241,plain,
! [SV324: a,SV159: a,SV252: a,SV44: a] :
( ( ( SV44 != SV252 )
= $false )
| ( ( SV44 = SV252 )
= $false )
| ( ( SV159 = SV324 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2193]) ).
thf(2242,plain,
! [SV252: a,SV44: a,SV324: a,SV159: a] :
( ( ( SV159 != SV324 )
= $false )
| ( ( SV44 = SV252 )
= $false )
| ( ( SV159 = SV324 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2193]) ).
thf(2243,plain,
! [SV366: set_Product_prod_a_a,SV327: a,SV166: a,SV359: set_Product_prod_a_a,SV257: a,SV52: a] :
( ( ( SV52 = SV257 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SV257 @ SV327 ) ) @ ( lex_prod_a_a @ SV359 @ SV366 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2194]) ).
thf(2244,plain,
! [SV359: set_Product_prod_a_a,SV257: a,SV52: a,SV366: set_Product_prod_a_a,SV327: a,SV166: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SV257 @ SV327 ) ) @ ( lex_prod_a_a @ SV359 @ SV366 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2195]) ).
thf(2245,plain,
! [SV359: set_Product_prod_a_a,SV257: a,SV52: a] :
( ( ( SV52 != SV257 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2196]) ).
thf(2246,plain,
! [SV359: set_Product_prod_a_a,SV257: a,SV52: a,SV366: set_Product_prod_a_a,SV327: a,SV166: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2196]) ).
thf(2247,plain,
! [SV366: set_Product_prod_a_a,SV359: set_Product_prod_a_a,SV327: a,SV257: a,SV166: a,SV52: a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SV257 @ SV327 ) ) @ ( lex_prod_a_a @ SV359 @ SV366 ) ) )
= $false )
| ( ( SV52 = SV257 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2197]) ).
thf(2248,plain,
! [SV366: set_Product_prod_a_a,SV327: a,SV166: a,SV359: set_Product_prod_a_a,SV257: a,SV52: a] :
( ( ( ~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
| ~ ( ( SV52 != SV257 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 ) ) ) )
= $false )
| ( ( SV52 = SV257 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2197]) ).
thf(2249,plain,
! [SV330: a,SV170: a,SV261: a,SV56: a] :
( ( ( SV56 != SV261 )
= $false )
| ( ( SV56 = SV261 )
= $false )
| ( ( SV170 = SV330 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2198]) ).
thf(2250,plain,
! [SV261: a,SV56: a,SV330: a,SV170: a] :
( ( ( SV170 != SV330 )
= $false )
| ( ( SV56 = SV261 )
= $false )
| ( ( SV170 = SV330 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2198]) ).
thf(2251,plain,
! [SV171: a,SV262: a,SV57: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV262 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV171 @ SV262 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV262 @ SV171 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV171 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV171 @ SV57 ) @ relation )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2199]) ).
thf(2252,plain,
! [SV171: a,SV57: a,SV262: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV262 @ SV57 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV171 @ SV262 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV262 @ SV171 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV171 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV171 @ SV57 ) @ relation )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2199]) ).
thf(2253,plain,
! [SV60: set_Product_prod_a_a,SV174: set_Pr1948701895od_a_a,SV265: product_prod_a_a,SV333: product_prod_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
= $true )
| ( ( ~ ( ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
| ~ ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
| ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) ) ) )
= $true )
| ( ( member449909584od_a_a @ SV265 @ SV60 )
= $false )
| ( ( member449909584od_a_a @ SV333 @ SV60 )
= $false )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2200]) ).
thf(2254,plain,
! [SV60: set_Product_prod_a_a,SV174: set_Pr1948701895od_a_a,SV333: product_prod_a_a,SV265: product_prod_a_a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
| ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) )
= $true )
| ( ( ~ ( ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
| ~ ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
| ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) ) ) )
= $true )
| ( ( member449909584od_a_a @ SV265 @ SV60 )
= $false )
| ( ( member449909584od_a_a @ SV333 @ SV60 )
= $false )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2201]) ).
thf(2255,plain,
! [SV61: set_a,SV175: set_Product_prod_a_a,SV266: a,SV334: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
= $true )
| ( ( ~ ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) ) ) )
= $true )
| ( ( member_a @ SV266 @ SV61 )
= $false )
| ( ( member_a @ SV334 @ SV61 )
= $false )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2202]) ).
thf(2256,plain,
! [SV61: set_a,SV175: set_Product_prod_a_a,SV334: a,SV266: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) )
= $true )
| ( ( ~ ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) ) ) )
= $true )
| ( ( member_a @ SV266 @ SV61 )
= $false )
| ( ( member_a @ SV334 @ SV61 )
= $false )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2203]) ).
thf(2257,plain,
! [SV398: a,SV179: set_Product_prod_a_a,SV393: a,SV387: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV387 @ SV393 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV393 @ SV398 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV387 @ SV398 ) @ SV179 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK37_SY828 @ SV179 ) @ ( sK46_SY1040 @ SV179 ) ) @ SV179 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2205]) ).
thf(2258,plain,
! [SV179: set_Product_prod_a_a,SV399: a,SV394: a] :
( ( ( ! [SY1082: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV399 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV399 @ SY1082 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SY1082 ) @ SV179 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK46_SY1040 @ SV179 ) @ ( sK56_SY1050 @ SV179 ) ) @ SV179 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2206]) ).
thf(2259,plain,
! [SV400: a,SV179: set_Product_prod_a_a,SV395: a,SV388: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV388 @ SV395 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV395 @ SV400 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV388 @ SV400 ) @ SV179 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK37_SY828 @ SV179 ) @ ( sK56_SY1050 @ SV179 ) ) @ SV179 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2207]) ).
thf(2260,plain,
! [SV74: set_a,SV272: a,SV184: set_Product_prod_a_a,SV360: a,SV336: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV360 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV336 ) @ SV184 ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV360 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV272 ) @ SV184 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV336 ) @ SV184 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV272 ) @ SV184 )
= $true )
| ( ( prefer719835986ence_a @ SV74 @ SV184 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2208]) ).
thf(2261,plain,
! [SV88: a,SV196: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
= $true )
| ( ( member_a @ SV88 @ carrier )
= $false )
| ( ( member_a @ SV196 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2209]) ).
thf(2262,plain,
! [SV196: a,SV88: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
= $true )
| ( ( member_a @ SV88 @ carrier )
= $false )
| ( ( member_a @ SV196 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2210]) ).
thf(2263,plain,
! [SV88: a,SV196: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
= $false )
| ( ( ~ ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) ) ) )
= $true )
| ( ( member_a @ SV88 @ carrier )
= $false )
| ( ( member_a @ SV196 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2211]) ).
thf(2264,plain,
! [SV343: set_Product_prod_a_a,SV382: a,SV197: set_a,SV389: a] :
( ( ( member_a @ SV389 @ SV197 )
= $false )
| ( ( ~ ( ( SV382 != SV389 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV382 @ SV389 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV389 @ SV382 ) @ SV343 ) )
= $true )
| ( ( member_a @ SV382 @ SV197 )
= $false )
| ( ( total_on_a @ SV197 @ SV343 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2212]) ).
thf(2265,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a,SV390: a] :
( ( ( member_a @ SV390 @ SV197 )
= $false )
| ( ( ! [SY1074: a] :
( ~ ( member_a @ SY1074 @ SV197 )
| ~ ( ( SV390 != SY1074 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV390 @ SY1074 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1074 @ SV390 ) @ SV343 ) ) )
= $true )
| ( ( member_a @ ( sK57_SY1017 @ SV343 @ SV197 ) @ SV197 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2213]) ).
thf(2266,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a,SV401: a] :
( ( ( ~ ( member_a @ SV401 @ SV197 )
| ! [SY1083: a] :
( ~ ( member_a @ SY1083 @ SV197 )
| ~ ( ( SV401 != SY1083 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV401 @ SY1083 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1083 @ SV401 ) @ SV343 ) ) )
= $true )
| ( ( member_a @ ( sK61_SY1054 @ SV343 @ SV197 ) @ SV197 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2215]) ).
thf(2267,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a] :
( ( ( ~ ( total_on_a @ SV197 @ SV343 ) )
= $false )
| ( ( ( sK57_SY1017 @ SV343 @ SV197 )
= ( sK61_SY1054 @ SV343 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2216]) ).
thf(2268,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a] :
( ( ( ~ ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) )
= $false )
| ( ( ( sK57_SY1017 @ SV343 @ SV197 )
= ( sK61_SY1054 @ SV343 @ SV197 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2216]) ).
thf(2269,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a] :
( ( ( total_on_a @ SV197 @ SV343 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK57_SY1017 @ SV343 @ SV197 ) @ ( sK61_SY1054 @ SV343 @ SV197 ) ) @ SV343 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2217]) ).
thf(2270,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a] :
( ( ( ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK57_SY1017 @ SV343 @ SV197 ) @ ( sK61_SY1054 @ SV343 @ SV197 ) ) @ SV343 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2218]) ).
thf(2271,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a] :
( ( ( total_on_a @ SV197 @ SV343 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1054 @ SV343 @ SV197 ) @ ( sK57_SY1017 @ SV343 @ SV197 ) ) @ SV343 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2219]) ).
thf(2272,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a] :
( ( ( ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1054 @ SV343 @ SV197 ) @ ( sK57_SY1017 @ SV343 @ SV197 ) ) @ SV343 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2220]) ).
thf(2273,plain,
! [SV198: set_Product_prod_a_a,SV402: a,SV396: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV396 @ SV402 ) @ ( sK62_SY857 @ SV198 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV402 @ SV396 ) @ ( sK62_SY857 @ SV198 ) ) )
= $true )
| ( ( asym_a @ SV198 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2221]) ).
thf(2274,plain,
! [SV369: set_Product_prod_a_a,SV198: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK68_SY1051 @ SV198 @ SV369 ) @ ( sK70_SY1066 @ SV369 @ SV198 ) ) @ SV369 )
= $true )
| ( ( SV198 = SV369 )
= $false )
| ( ( ~ ( ~ ( asym_a @ SV198 )
| ~ ~ ! [SY857: set_Product_prod_a_a] :
~ ~ ( ( SV198 != SY857 )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SY857 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SY857 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2222]) ).
thf(2275,plain,
! [SV198: set_Product_prod_a_a,SV369: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK70_SY1066 @ SV369 @ SV198 ) @ ( sK68_SY1051 @ SV198 @ SV369 ) ) @ SV369 )
= $true )
| ( ( SV198 = SV369 )
= $false )
| ( ( ~ ( ~ ( asym_a @ SV198 )
| ~ ~ ! [SY857: set_Product_prod_a_a] :
~ ~ ( ( SV198 != SY857 )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SY857 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SY857 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2223]) ).
thf(2276,plain,
! [SV199: set_Product_prod_a_a,SV391: a,SV383: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV383 @ SV391 ) @ SV199 )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV391 @ SV383 ) @ SV199 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK38_SY860 @ SV199 ) @ ( sK47_SY1042 @ SV199 ) ) @ SV199 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2224]) ).
thf(2277,plain,
! [SV199: set_Product_prod_a_a,SV392: a,SV384: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV384 @ SV392 ) @ SV199 )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV392 @ SV384 ) @ SV199 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK47_SY1042 @ SV199 ) @ ( sK38_SY860 @ SV199 ) ) @ SV199 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2225]) ).
thf(2278,plain,
! [SV93: set_a,SV286: a,SV201: set_Product_prod_a_a,SV362: a,SV345: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV362 ) @ SV201 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV362 @ SV345 ) @ SV201 ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SV362 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV362 @ SV286 ) @ SV201 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SV345 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV286 ) @ SV201 )
= $false )
| ( ( prefer1292084992ence_a @ SV93 @ SV201 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2226]) ).
thf(2279,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) ) )
= $true )
| ( ( prefer1292084992ence_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2227]) ).
thf(2280,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
= $true )
| ( ( prefer1292084992ence_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2228]) ).
thf(2281,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 ) )
= $false )
| ( ( ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
= $true )
| ( ( ~ ( order_preorder_on_a @ SV204 @ SV347 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 )
| ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2229]) ).
thf(2282,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
= $true )
| ( ( ~ ( order_preorder_on_a @ SV204 @ SV347 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 )
| ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2229]) ).
thf(2283,plain,
! [SV101: a,SV208: a,SV291: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV291 @ SV208 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV291 ) @ relation )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SV291 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV291 @ SV101 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SV208 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV101 ) @ relation )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2231]) ).
thf(2284,plain,
! [SV154: set_Product_prod_a_a,SV320: set_Pr1948701895od_a_a,SV385: product_prod_a_a,SV380: product_prod_a_a] :
( ( ( ~ ( ( SV380 != SV385 ) ) )
= $true )
| ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV380 @ SV385 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV385 @ SV380 ) @ SV320 ) )
= $true )
| ( ( member449909584od_a_a @ SV385 @ SV154 )
= $false )
| ( ( member449909584od_a_a @ SV380 @ SV154 )
= $false )
| ( ( total_1490170027od_a_a @ SV154 @ SV320 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2232]) ).
thf(2285,plain,
! [SV320: set_Pr1948701895od_a_a,SV386: product_prod_a_a,SV154: set_Product_prod_a_a,SV403: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV403 @ SV154 )
| ~ ( ( SV386 != SV403 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV386 @ SV403 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV403 @ SV386 ) @ SV320 ) )
= $true )
| ( ( member449909584od_a_a @ SV386 @ SV154 )
= $false )
| ( ( member449909584od_a_a @ ( sK54_SY1005 @ SV320 @ SV154 ) @ SV154 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2233]) ).
thf(2286,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a,SV397: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV397 @ SV154 ) )
= $true )
| ( ( ! [SY1081: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1081 @ SV154 )
| ~ ( ( SV397 != SY1081 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV397 @ SY1081 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1081 @ SV397 ) @ SV320 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( sK59_SY1053 @ SV320 @ SV154 ) @ SV154 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2234]) ).
thf(2287,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a] :
( ( ( total_1490170027od_a_a @ SV154 @ SV320 )
= $true )
| ( ( ( sK54_SY1005 @ SV320 @ SV154 )
= ( sK59_SY1053 @ SV320 @ SV154 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2235]) ).
thf(2288,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a] :
( ( ( ! [SY1005: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1005 @ SV154 )
| ! [SY1006: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1006 @ SV154 )
| ~ ( ( SY1005 != SY1006 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1005 @ SY1006 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1006 @ SY1005 ) @ SV320 ) ) ) )
= $true )
| ( ( ( sK54_SY1005 @ SV320 @ SV154 )
= ( sK59_SY1053 @ SV320 @ SV154 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2236]) ).
thf(2289,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a,SV404: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV404 @ SV154 )
| ! [SY1084: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1084 @ SV154 )
| ~ ( ( SV404 != SY1084 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV404 @ SY1084 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1084 @ SV404 ) @ SV320 ) ) )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK54_SY1005 @ SV320 @ SV154 ) @ ( sK59_SY1053 @ SV320 @ SV154 ) ) @ SV320 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2238]) ).
thf(2290,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a,SV405: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV405 @ SV154 )
| ! [SY1085: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1085 @ SV154 )
| ~ ( ( SV405 != SY1085 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV405 @ SY1085 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1085 @ SV405 ) @ SV320 ) ) )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK59_SY1053 @ SV320 @ SV154 ) @ ( sK54_SY1005 @ SV320 @ SV154 ) ) @ SV320 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2240]) ).
thf(2291,plain,
! [SV324: a,SV159: a,SV252: a,SV44: a] :
( ( ( SV44 = SV252 )
= $true )
| ( ( SV44 = SV252 )
= $false )
| ( ( SV159 = SV324 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2241]) ).
thf(2292,plain,
! [SV252: a,SV44: a,SV324: a,SV159: a] :
( ( ( SV159 = SV324 )
= $true )
| ( ( SV44 = SV252 )
= $false )
| ( ( SV159 = SV324 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2242]) ).
thf(2293,plain,
! [SV359: set_Product_prod_a_a,SV257: a,SV52: a] :
( ( ( SV52 = SV257 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2245]) ).
thf(2294,plain,
! [SV359: set_Product_prod_a_a,SV257: a,SV52: a,SV366: set_Product_prod_a_a,SV327: a,SV166: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2246]) ).
thf(2295,plain,
! [SV366: set_Product_prod_a_a,SV359: set_Product_prod_a_a,SV327: a,SV257: a,SV166: a,SV52: a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ SV52 @ SV166 ) @ ( product_Pair_a_a @ SV257 @ SV327 ) ) @ ( lex_prod_a_a @ SV359 @ SV366 ) )
= $true )
| ( ( SV52 = SV257 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2247]) ).
thf(2296,plain,
! [SV366: set_Product_prod_a_a,SV327: a,SV166: a,SV359: set_Product_prod_a_a,SV257: a,SV52: a] :
( ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
| ~ ( ( SV52 != SV257 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 ) ) )
= $true )
| ( ( SV52 = SV257 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2248]) ).
thf(2297,plain,
! [SV330: a,SV170: a,SV261: a,SV56: a] :
( ( ( SV56 = SV261 )
= $true )
| ( ( SV56 = SV261 )
= $false )
| ( ( SV170 = SV330 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2249]) ).
thf(2298,plain,
! [SV261: a,SV56: a,SV330: a,SV170: a] :
( ( ( SV170 = SV330 )
= $true )
| ( ( SV56 = SV261 )
= $false )
| ( ( SV170 = SV330 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2250]) ).
thf(2299,plain,
! [SV171: a,SV262: a,SV57: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV262 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV171 @ SV262 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV262 @ SV171 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV171 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV171 @ SV57 ) @ relation )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2251]) ).
thf(2300,plain,
! [SV171: a,SV57: a,SV262: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV262 @ SV57 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV171 @ SV262 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV262 @ SV171 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV171 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV171 @ SV57 ) @ relation )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2252]) ).
thf(2301,plain,
! [SV60: set_Product_prod_a_a,SV174: set_Pr1948701895od_a_a,SV265: product_prod_a_a,SV333: product_prod_a_a] :
( ( ( ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
| ~ ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
| ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
= $true )
| ( ( member449909584od_a_a @ SV265 @ SV60 )
= $false )
| ( ( member449909584od_a_a @ SV333 @ SV60 )
= $false )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2253]) ).
thf(2302,plain,
! [SV60: set_Product_prod_a_a,SV174: set_Pr1948701895od_a_a,SV333: product_prod_a_a,SV265: product_prod_a_a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 ) )
= $true )
| ( ( ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) )
= $true )
| ( ( ~ ( ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
| ~ ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
| ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) ) ) )
= $true )
| ( ( member449909584od_a_a @ SV265 @ SV60 )
= $false )
| ( ( member449909584od_a_a @ SV333 @ SV60 )
= $false )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2254]) ).
thf(2303,plain,
! [SV61: set_a,SV175: set_Product_prod_a_a,SV266: a,SV334: a] :
( ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
= $true )
| ( ( member_a @ SV266 @ SV61 )
= $false )
| ( ( member_a @ SV334 @ SV61 )
= $false )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2255]) ).
thf(2304,plain,
! [SV61: set_a,SV175: set_Product_prod_a_a,SV334: a,SV266: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 ) )
= $true )
| ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) )
= $true )
| ( ( ~ ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) ) ) )
= $true )
| ( ( member_a @ SV266 @ SV61 )
= $false )
| ( ( member_a @ SV334 @ SV61 )
= $false )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2256]) ).
thf(2305,plain,
! [SV398: a,SV179: set_Product_prod_a_a,SV393: a,SV387: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV387 @ SV393 ) @ SV179 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV393 @ SV398 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV387 @ SV398 ) @ SV179 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK37_SY828 @ SV179 ) @ ( sK46_SY1040 @ SV179 ) ) @ SV179 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2257]) ).
thf(2306,plain,
! [SV406: a,SV179: set_Product_prod_a_a,SV399: a,SV394: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV399 ) @ SV179 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV399 @ SV406 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV406 ) @ SV179 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK46_SY1040 @ SV179 ) @ ( sK56_SY1050 @ SV179 ) ) @ SV179 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2258]) ).
thf(2307,plain,
! [SV400: a,SV179: set_Product_prod_a_a,SV395: a,SV388: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV388 @ SV395 ) @ SV179 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV395 @ SV400 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV388 @ SV400 ) @ SV179 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK37_SY828 @ SV179 ) @ ( sK56_SY1050 @ SV179 ) ) @ SV179 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2259]) ).
thf(2308,plain,
! [SV74: set_a,SV272: a,SV184: set_Product_prod_a_a,SV360: a,SV336: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV360 ) @ SV184 ) )
= $true )
| ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV336 ) @ SV184 ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV360 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV272 ) @ SV184 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV336 ) @ SV184 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV272 ) @ SV184 )
= $true )
| ( ( prefer719835986ence_a @ SV74 @ SV184 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2260]) ).
thf(2309,plain,
! [SV196: a,SV88: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
= $true )
| ( ( member_a @ SV88 @ carrier )
= $false )
| ( ( member_a @ SV196 @ carrier )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2262]) ).
thf(2310,plain,
! [SV88: a,SV196: a] :
( ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
= $true )
| ( ( member_a @ SV88 @ carrier )
= $false )
| ( ( member_a @ SV196 @ carrier )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2262]) ).
thf(2311,plain,
! [SV88: a,SV196: a] :
( ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
= $true )
| ( ( member_a @ SV88 @ carrier )
= $false )
| ( ( member_a @ SV196 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2263]) ).
thf(2312,plain,
! [SV197: set_a,SV343: set_Product_prod_a_a,SV389: a,SV382: a] :
( ( ( ~ ( ( SV382 != SV389 ) ) )
= $true )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV382 @ SV389 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV389 @ SV382 ) @ SV343 ) )
= $true )
| ( ( member_a @ SV389 @ SV197 )
= $false )
| ( ( member_a @ SV382 @ SV197 )
= $false )
| ( ( total_on_a @ SV197 @ SV343 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2264]) ).
thf(2313,plain,
! [SV343: set_Product_prod_a_a,SV390: a,SV197: set_a,SV407: a] :
( ( ( ~ ( member_a @ SV407 @ SV197 )
| ~ ( ( SV390 != SV407 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV390 @ SV407 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV407 @ SV390 ) @ SV343 ) )
= $true )
| ( ( member_a @ SV390 @ SV197 )
= $false )
| ( ( member_a @ ( sK57_SY1017 @ SV343 @ SV197 ) @ SV197 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2265]) ).
thf(2314,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a,SV401: a] :
( ( ( ~ ( member_a @ SV401 @ SV197 ) )
= $true )
| ( ( ! [SY1083: a] :
( ~ ( member_a @ SY1083 @ SV197 )
| ~ ( ( SV401 != SY1083 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV401 @ SY1083 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1083 @ SV401 ) @ SV343 ) ) )
= $true )
| ( ( member_a @ ( sK61_SY1054 @ SV343 @ SV197 ) @ SV197 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2266]) ).
thf(2315,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a] :
( ( ( total_on_a @ SV197 @ SV343 )
= $true )
| ( ( ( sK57_SY1017 @ SV343 @ SV197 )
= ( sK61_SY1054 @ SV343 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2267]) ).
thf(2316,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a] :
( ( ( ! [SY1017: a] :
( ~ ( member_a @ SY1017 @ SV197 )
| ! [SY1018: a] :
( ~ ( member_a @ SY1018 @ SV197 )
| ~ ( ( SY1017 != SY1018 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1017 @ SY1018 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1018 @ SY1017 ) @ SV343 ) ) ) )
= $true )
| ( ( ( sK57_SY1017 @ SV343 @ SV197 )
= ( sK61_SY1054 @ SV343 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2268]) ).
thf(2317,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a,SV408: a] :
( ( ( ~ ( member_a @ SV408 @ SV197 )
| ! [SY1086: a] :
( ~ ( member_a @ SY1086 @ SV197 )
| ~ ( ( SV408 != SY1086 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV408 @ SY1086 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1086 @ SV408 ) @ SV343 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK57_SY1017 @ SV343 @ SV197 ) @ ( sK61_SY1054 @ SV343 @ SV197 ) ) @ SV343 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2270]) ).
thf(2318,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a,SV409: a] :
( ( ( ~ ( member_a @ SV409 @ SV197 )
| ! [SY1087: a] :
( ~ ( member_a @ SY1087 @ SV197 )
| ~ ( ( SV409 != SY1087 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV409 @ SY1087 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1087 @ SV409 ) @ SV343 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1054 @ SV343 @ SV197 ) @ ( sK57_SY1017 @ SV343 @ SV197 ) ) @ SV343 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2272]) ).
thf(2319,plain,
! [SV198: set_Product_prod_a_a,SV402: a,SV396: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV396 @ SV402 ) @ ( sK62_SY857 @ SV198 ) ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV402 @ SV396 ) @ ( sK62_SY857 @ SV198 ) ) )
= $true )
| ( ( asym_a @ SV198 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2273]) ).
thf(2320,plain,
! [SV369: set_Product_prod_a_a,SV198: set_Product_prod_a_a] :
( ( ( ~ ( asym_a @ SV198 )
| ~ ~ ! [SY857: set_Product_prod_a_a] :
~ ~ ( ( SV198 != SY857 )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SY857 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SY857 ) ) ) )
= $false )
| ( ( SV198 = SV369 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK68_SY1051 @ SV198 @ SV369 ) @ ( sK70_SY1066 @ SV369 @ SV198 ) ) @ SV369 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2274]) ).
thf(2321,plain,
! [SV369: set_Product_prod_a_a,SV198: set_Product_prod_a_a] :
( ( ( ~ ( asym_a @ SV198 )
| ~ ~ ! [SY857: set_Product_prod_a_a] :
~ ~ ( ( SV198 != SY857 )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SY857 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SY857 ) ) ) )
= $false )
| ( ( SV198 = SV369 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK70_SY1066 @ SV369 @ SV198 ) @ ( sK68_SY1051 @ SV198 @ SV369 ) ) @ SV369 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2275]) ).
thf(2322,plain,
! [SV199: set_Product_prod_a_a,SV383: a,SV391: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV391 @ SV383 ) @ SV199 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV383 @ SV391 ) @ SV199 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK38_SY860 @ SV199 ) @ ( sK47_SY1042 @ SV199 ) ) @ SV199 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2276]) ).
thf(2323,plain,
! [SV199: set_Product_prod_a_a,SV384: a,SV392: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV392 @ SV384 ) @ SV199 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV384 @ SV392 ) @ SV199 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK47_SY1042 @ SV199 ) @ ( sK38_SY860 @ SV199 ) ) @ SV199 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2277]) ).
thf(2324,plain,
! [SV93: set_a,SV286: a,SV201: set_Product_prod_a_a,SV362: a,SV345: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV362 ) @ SV201 )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV362 @ SV345 ) @ SV201 ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SV362 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV362 @ SV286 ) @ SV201 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SV345 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV286 ) @ SV201 )
= $false )
| ( ( prefer1292084992ence_a @ SV93 @ SV201 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2278]) ).
thf(2325,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a,SV410: a] :
( ( ( ! [SY1088: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV410 @ SY1088 ) @ SV347 )
| ( member_a @ SV410 @ SV204 ) ) )
= $true )
| ( ( prefer1292084992ence_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2279]) ).
thf(2326,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a,SV411: a] :
( ( ( ! [SY1089: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV411 @ SY1089 ) @ SV347 )
| ( member_a @ SY1089 @ SV204 ) ) )
= $true )
| ( ( prefer1292084992ence_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2280]) ).
thf(2327,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
= $true )
| ( ( ~ ( order_preorder_on_a @ SV204 @ SV347 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 )
| ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2281]) ).
thf(2328,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
= $false )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( ~ ( order_preorder_on_a @ SV204 @ SV347 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 )
| ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2282]) ).
thf(2329,plain,
! [SV208: a,SV291: a,SV101: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SV291 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV291 @ SV101 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV291 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV291 @ SV208 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SV208 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV101 ) @ relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2283]) ).
thf(2330,plain,
! [SV154: set_Product_prod_a_a,SV320: set_Pr1948701895od_a_a,SV385: product_prod_a_a,SV380: product_prod_a_a] :
( ( ( SV380 != SV385 )
= $false )
| ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV380 @ SV385 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV385 @ SV380 ) @ SV320 ) )
= $true )
| ( ( member449909584od_a_a @ SV385 @ SV154 )
= $false )
| ( ( member449909584od_a_a @ SV380 @ SV154 )
= $false )
| ( ( total_1490170027od_a_a @ SV154 @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2284]) ).
thf(2331,plain,
! [SV320: set_Pr1948701895od_a_a,SV386: product_prod_a_a,SV154: set_Product_prod_a_a,SV403: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV403 @ SV154 ) )
= $true )
| ( ( ~ ( ( SV386 != SV403 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV386 @ SV403 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV403 @ SV386 ) @ SV320 ) )
= $true )
| ( ( member449909584od_a_a @ SV386 @ SV154 )
= $false )
| ( ( member449909584od_a_a @ ( sK54_SY1005 @ SV320 @ SV154 ) @ SV154 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2285]) ).
thf(2332,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a,SV397: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV397 @ SV154 )
= $false )
| ( ( ! [SY1081: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1081 @ SV154 )
| ~ ( ( SV397 != SY1081 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV397 @ SY1081 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1081 @ SV397 ) @ SV320 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( sK59_SY1053 @ SV320 @ SV154 ) @ SV154 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2286]) ).
thf(2333,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a,SV412: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV412 @ SV154 )
| ! [SY1090: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1090 @ SV154 )
| ~ ( ( SV412 != SY1090 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV412 @ SY1090 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1090 @ SV412 ) @ SV320 ) ) )
= $true )
| ( ( ( sK54_SY1005 @ SV320 @ SV154 )
= ( sK59_SY1053 @ SV320 @ SV154 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2288]) ).
thf(2334,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a,SV404: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV404 @ SV154 ) )
= $true )
| ( ( ! [SY1084: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1084 @ SV154 )
| ~ ( ( SV404 != SY1084 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV404 @ SY1084 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1084 @ SV404 ) @ SV320 ) ) )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK54_SY1005 @ SV320 @ SV154 ) @ ( sK59_SY1053 @ SV320 @ SV154 ) ) @ SV320 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2289]) ).
thf(2335,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a,SV405: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV405 @ SV154 ) )
= $true )
| ( ( ! [SY1085: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1085 @ SV154 )
| ~ ( ( SV405 != SY1085 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV405 @ SY1085 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1085 @ SV405 ) @ SV320 ) ) )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK59_SY1053 @ SV320 @ SV154 ) @ ( sK54_SY1005 @ SV320 @ SV154 ) ) @ SV320 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2290]) ).
thf(2336,plain,
! [SV366: set_Product_prod_a_a,SV327: a,SV166: a,SV359: set_Product_prod_a_a,SV257: a,SV52: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
= $true )
| ( ( ~ ( ( SV52 != SV257 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 ) ) )
= $true )
| ( ( SV52 = SV257 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2296]) ).
thf(2337,plain,
! [SV60: set_Product_prod_a_a,SV174: set_Pr1948701895od_a_a,SV265: product_prod_a_a,SV333: product_prod_a_a] :
( ( ( ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
= $true )
| ( ( member449909584od_a_a @ SV265 @ SV60 )
= $false )
| ( ( member449909584od_a_a @ SV333 @ SV60 )
= $false )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2301]) ).
thf(2338,plain,
! [SV60: set_Product_prod_a_a,SV174: set_Pr1948701895od_a_a,SV333: product_prod_a_a,SV265: product_prod_a_a] :
( ( ( ~ ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
| ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
= $true )
| ( ( member449909584od_a_a @ SV265 @ SV60 )
= $false )
| ( ( member449909584od_a_a @ SV333 @ SV60 )
= $false )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2301]) ).
thf(2339,plain,
! [SV60: set_Product_prod_a_a,SV174: set_Pr1948701895od_a_a,SV333: product_prod_a_a,SV265: product_prod_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
= $false )
| ( ( ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) )
= $true )
| ( ( ~ ( ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
| ~ ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
| ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) ) ) )
= $true )
| ( ( member449909584od_a_a @ SV265 @ SV60 )
= $false )
| ( ( member449909584od_a_a @ SV333 @ SV60 )
= $false )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2302]) ).
thf(2340,plain,
! [SV61: set_a,SV175: set_Product_prod_a_a,SV266: a,SV334: a] :
( ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
= $true )
| ( ( member_a @ SV266 @ SV61 )
= $false )
| ( ( member_a @ SV334 @ SV61 )
= $false )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2303]) ).
thf(2341,plain,
! [SV61: set_a,SV175: set_Product_prod_a_a,SV334: a,SV266: a] :
( ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
= $true )
| ( ( member_a @ SV266 @ SV61 )
= $false )
| ( ( member_a @ SV334 @ SV61 )
= $false )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2303]) ).
thf(2342,plain,
! [SV61: set_a,SV175: set_Product_prod_a_a,SV334: a,SV266: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
= $false )
| ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) )
= $true )
| ( ( ~ ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) ) ) )
= $true )
| ( ( member_a @ SV266 @ SV61 )
= $false )
| ( ( member_a @ SV334 @ SV61 )
= $false )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2304]) ).
thf(2343,plain,
! [SV398: a,SV179: set_Product_prod_a_a,SV393: a,SV387: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV387 @ SV393 ) @ SV179 )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV393 @ SV398 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV387 @ SV398 ) @ SV179 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK37_SY828 @ SV179 ) @ ( sK46_SY1040 @ SV179 ) ) @ SV179 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2305]) ).
thf(2344,plain,
! [SV406: a,SV179: set_Product_prod_a_a,SV399: a,SV394: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV399 ) @ SV179 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV399 @ SV406 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV406 ) @ SV179 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK46_SY1040 @ SV179 ) @ ( sK56_SY1050 @ SV179 ) ) @ SV179 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2306]) ).
thf(2345,plain,
! [SV400: a,SV179: set_Product_prod_a_a,SV395: a,SV388: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV388 @ SV395 ) @ SV179 )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV395 @ SV400 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV388 @ SV400 ) @ SV179 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK37_SY828 @ SV179 ) @ ( sK56_SY1050 @ SV179 ) ) @ SV179 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2307]) ).
thf(2346,plain,
! [SV74: set_a,SV272: a,SV184: set_Product_prod_a_a,SV360: a,SV336: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV360 ) @ SV184 )
= $false )
| ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV336 ) @ SV184 ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV360 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV272 ) @ SV184 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV336 ) @ SV184 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV272 ) @ SV184 )
= $true )
| ( ( prefer719835986ence_a @ SV74 @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2308]) ).
thf(2347,plain,
! [SV196: a,SV88: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
= $true )
| ( ( member_a @ SV88 @ carrier )
= $false )
| ( ( member_a @ SV196 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2309]) ).
thf(2348,plain,
! [SV88: a,SV196: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
= $true )
| ( ( member_a @ SV88 @ carrier )
= $false )
| ( ( member_a @ SV196 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2310]) ).
thf(2349,plain,
! [SV88: a,SV196: a] :
( ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
= $true )
| ( ( member_a @ SV88 @ carrier )
= $false )
| ( ( member_a @ SV196 @ carrier )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2311]) ).
thf(2350,plain,
! [SV196: a,SV88: a] :
( ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
= $true )
| ( ( member_a @ SV88 @ carrier )
= $false )
| ( ( member_a @ SV196 @ carrier )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2311]) ).
thf(2351,plain,
! [SV197: set_a,SV343: set_Product_prod_a_a,SV389: a,SV382: a] :
( ( ( SV382 != SV389 )
= $false )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV382 @ SV389 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV389 @ SV382 ) @ SV343 ) )
= $true )
| ( ( member_a @ SV389 @ SV197 )
= $false )
| ( ( member_a @ SV382 @ SV197 )
= $false )
| ( ( total_on_a @ SV197 @ SV343 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2312]) ).
thf(2352,plain,
! [SV343: set_Product_prod_a_a,SV390: a,SV197: set_a,SV407: a] :
( ( ( ~ ( member_a @ SV407 @ SV197 ) )
= $true )
| ( ( ~ ( ( SV390 != SV407 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV390 @ SV407 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV407 @ SV390 ) @ SV343 ) )
= $true )
| ( ( member_a @ SV390 @ SV197 )
= $false )
| ( ( member_a @ ( sK57_SY1017 @ SV343 @ SV197 ) @ SV197 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2313]) ).
thf(2353,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a,SV401: a] :
( ( ( member_a @ SV401 @ SV197 )
= $false )
| ( ( ! [SY1083: a] :
( ~ ( member_a @ SY1083 @ SV197 )
| ~ ( ( SV401 != SY1083 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV401 @ SY1083 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1083 @ SV401 ) @ SV343 ) ) )
= $true )
| ( ( member_a @ ( sK61_SY1054 @ SV343 @ SV197 ) @ SV197 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2314]) ).
thf(2354,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a,SV413: a] :
( ( ( ~ ( member_a @ SV413 @ SV197 )
| ! [SY1091: a] :
( ~ ( member_a @ SY1091 @ SV197 )
| ~ ( ( SV413 != SY1091 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV413 @ SY1091 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1091 @ SV413 ) @ SV343 ) ) )
= $true )
| ( ( ( sK57_SY1017 @ SV343 @ SV197 )
= ( sK61_SY1054 @ SV343 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2316]) ).
thf(2355,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a,SV408: a] :
( ( ( ~ ( member_a @ SV408 @ SV197 ) )
= $true )
| ( ( ! [SY1086: a] :
( ~ ( member_a @ SY1086 @ SV197 )
| ~ ( ( SV408 != SY1086 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV408 @ SY1086 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1086 @ SV408 ) @ SV343 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK57_SY1017 @ SV343 @ SV197 ) @ ( sK61_SY1054 @ SV343 @ SV197 ) ) @ SV343 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2317]) ).
thf(2356,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a,SV409: a] :
( ( ( ~ ( member_a @ SV409 @ SV197 ) )
= $true )
| ( ( ! [SY1087: a] :
( ~ ( member_a @ SY1087 @ SV197 )
| ~ ( ( SV409 != SY1087 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV409 @ SY1087 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1087 @ SV409 ) @ SV343 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1054 @ SV343 @ SV197 ) @ ( sK57_SY1017 @ SV343 @ SV197 ) ) @ SV343 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2318]) ).
thf(2357,plain,
! [SV198: set_Product_prod_a_a,SV402: a,SV396: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV396 @ SV402 ) @ ( sK62_SY857 @ SV198 ) )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV402 @ SV396 ) @ ( sK62_SY857 @ SV198 ) ) )
= $true )
| ( ( asym_a @ SV198 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2319]) ).
thf(2358,plain,
! [SV369: set_Product_prod_a_a,SV198: set_Product_prod_a_a] :
( ( ( ~ ( asym_a @ SV198 ) )
= $false )
| ( ( SV198 = SV369 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK68_SY1051 @ SV198 @ SV369 ) @ ( sK70_SY1066 @ SV369 @ SV198 ) ) @ SV369 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2320]) ).
thf(2359,plain,
! [SV369: set_Product_prod_a_a,SV198: set_Product_prod_a_a] :
( ( ( ~ ~ ! [SY857: set_Product_prod_a_a] :
~ ~ ( ( SV198 != SY857 )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SY857 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SY857 ) ) ) )
= $false )
| ( ( SV198 = SV369 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK68_SY1051 @ SV198 @ SV369 ) @ ( sK70_SY1066 @ SV369 @ SV198 ) ) @ SV369 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2320]) ).
thf(2360,plain,
! [SV369: set_Product_prod_a_a,SV198: set_Product_prod_a_a] :
( ( ( ~ ( asym_a @ SV198 ) )
= $false )
| ( ( SV198 = SV369 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK70_SY1066 @ SV369 @ SV198 ) @ ( sK68_SY1051 @ SV198 @ SV369 ) ) @ SV369 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2321]) ).
thf(2361,plain,
! [SV369: set_Product_prod_a_a,SV198: set_Product_prod_a_a] :
( ( ( ~ ~ ! [SY857: set_Product_prod_a_a] :
~ ~ ( ( SV198 != SY857 )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SY857 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SY857 ) ) ) )
= $false )
| ( ( SV198 = SV369 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK70_SY1066 @ SV369 @ SV198 ) @ ( sK68_SY1051 @ SV198 @ SV369 ) ) @ SV369 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2321]) ).
thf(2362,plain,
! [SV93: set_a,SV286: a,SV201: set_Product_prod_a_a,SV345: a,SV362: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV362 @ SV345 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV362 ) @ SV201 )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SV362 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV362 @ SV286 ) @ SV201 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SV345 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV286 ) @ SV201 )
= $false )
| ( ( prefer1292084992ence_a @ SV93 @ SV201 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2324]) ).
thf(2363,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a,SV414: a,SV410: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV410 @ SV414 ) @ SV347 )
| ( member_a @ SV410 @ SV204 ) )
= $true )
| ( ( prefer1292084992ence_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2325]) ).
thf(2364,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a,SV415: a,SV411: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV411 @ SV415 ) @ SV347 )
| ( member_a @ SV415 @ SV204 ) )
= $true )
| ( ( prefer1292084992ence_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2326]) ).
thf(2365,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( ~ ( order_preorder_on_a @ SV204 @ SV347 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 )
| ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2327]) ).
thf(2366,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( ! [SY1092: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK73_SY1022 @ SV204 @ SV347 ) @ SY1092 ) @ SV347 )
| ( member_a @ SY1092 @ SV204 ) ) )
= $false )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( ~ ( order_preorder_on_a @ SV204 @ SV347 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 )
| ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2328]) ).
thf(2367,plain,
! [SV208: a,SV291: a,SV101: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SV291 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV291 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV291 @ SV208 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SV208 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV101 ) @ relation )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2329]) ).
thf(2368,plain,
! [SV208: a,SV101: a,SV291: a] :
( ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV291 @ SV101 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV291 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV291 @ SV208 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SV208 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV101 ) @ relation )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2329]) ).
thf(2369,plain,
! [SV154: set_Product_prod_a_a,SV320: set_Pr1948701895od_a_a,SV385: product_prod_a_a,SV380: product_prod_a_a] :
( ( ( SV380 = SV385 )
= $true )
| ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV380 @ SV385 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV385 @ SV380 ) @ SV320 ) )
= $true )
| ( ( member449909584od_a_a @ SV385 @ SV154 )
= $false )
| ( ( member449909584od_a_a @ SV380 @ SV154 )
= $false )
| ( ( total_1490170027od_a_a @ SV154 @ SV320 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2330]) ).
thf(2370,plain,
! [SV320: set_Pr1948701895od_a_a,SV386: product_prod_a_a,SV154: set_Product_prod_a_a,SV403: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV403 @ SV154 )
= $false )
| ( ( ~ ( ( SV386 != SV403 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV386 @ SV403 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV403 @ SV386 ) @ SV320 ) )
= $true )
| ( ( member449909584od_a_a @ SV386 @ SV154 )
= $false )
| ( ( member449909584od_a_a @ ( sK54_SY1005 @ SV320 @ SV154 ) @ SV154 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2331]) ).
thf(2371,plain,
! [SV320: set_Pr1948701895od_a_a,SV397: product_prod_a_a,SV154: set_Product_prod_a_a,SV416: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV416 @ SV154 )
| ~ ( ( SV397 != SV416 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV397 @ SV416 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV416 @ SV397 ) @ SV320 ) )
= $true )
| ( ( member449909584od_a_a @ SV397 @ SV154 )
= $false )
| ( ( member449909584od_a_a @ ( sK59_SY1053 @ SV320 @ SV154 ) @ SV154 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2332]) ).
thf(2372,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a,SV412: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV412 @ SV154 ) )
= $true )
| ( ( ! [SY1090: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1090 @ SV154 )
| ~ ( ( SV412 != SY1090 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV412 @ SY1090 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1090 @ SV412 ) @ SV320 ) ) )
= $true )
| ( ( ( sK54_SY1005 @ SV320 @ SV154 )
= ( sK59_SY1053 @ SV320 @ SV154 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2333]) ).
thf(2373,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a,SV404: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV404 @ SV154 )
= $false )
| ( ( ! [SY1084: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1084 @ SV154 )
| ~ ( ( SV404 != SY1084 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV404 @ SY1084 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1084 @ SV404 ) @ SV320 ) ) )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK54_SY1005 @ SV320 @ SV154 ) @ ( sK59_SY1053 @ SV320 @ SV154 ) ) @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2334]) ).
thf(2374,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a,SV405: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV405 @ SV154 )
= $false )
| ( ( ! [SY1085: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1085 @ SV154 )
| ~ ( ( SV405 != SY1085 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV405 @ SY1085 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1085 @ SV405 ) @ SV320 ) ) )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK59_SY1053 @ SV320 @ SV154 ) @ ( sK54_SY1005 @ SV320 @ SV154 ) ) @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2335]) ).
thf(2375,plain,
! [SV359: set_Product_prod_a_a,SV366: set_Product_prod_a_a,SV327: a,SV166: a,SV257: a,SV52: a] :
( ( ( ( SV52 != SV257 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
= $true )
| ( ( SV52 = SV257 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2336]) ).
thf(2376,plain,
! [SV60: set_Product_prod_a_a,SV174: set_Pr1948701895od_a_a,SV265: product_prod_a_a,SV333: product_prod_a_a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
= $true )
| ( ( member449909584od_a_a @ SV265 @ SV60 )
= $false )
| ( ( member449909584od_a_a @ SV333 @ SV60 )
= $false )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2337]) ).
thf(2377,plain,
! [SV60: set_Product_prod_a_a,SV174: set_Pr1948701895od_a_a,SV333: product_prod_a_a,SV265: product_prod_a_a] :
( ( ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
| ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) ) )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
= $true )
| ( ( member449909584od_a_a @ SV265 @ SV60 )
= $false )
| ( ( member449909584od_a_a @ SV333 @ SV60 )
= $false )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2338]) ).
thf(2378,plain,
! [SV60: set_Product_prod_a_a,SV174: set_Pr1948701895od_a_a,SV265: product_prod_a_a,SV333: product_prod_a_a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
= $false )
| ( ( ~ ( ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
| ~ ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
| ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) ) ) )
= $true )
| ( ( member449909584od_a_a @ SV265 @ SV60 )
= $false )
| ( ( member449909584od_a_a @ SV333 @ SV60 )
= $false )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2339]) ).
thf(2379,plain,
! [SV61: set_a,SV175: set_Product_prod_a_a,SV266: a,SV334: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
= $true )
| ( ( member_a @ SV266 @ SV61 )
= $false )
| ( ( member_a @ SV334 @ SV61 )
= $false )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2340]) ).
thf(2380,plain,
! [SV61: set_a,SV175: set_Product_prod_a_a,SV334: a,SV266: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
= $true )
| ( ( member_a @ SV266 @ SV61 )
= $false )
| ( ( member_a @ SV334 @ SV61 )
= $false )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2341]) ).
thf(2381,plain,
! [SV61: set_a,SV175: set_Product_prod_a_a,SV266: a,SV334: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
= $false )
| ( ( ~ ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) ) ) )
= $true )
| ( ( member_a @ SV266 @ SV61 )
= $false )
| ( ( member_a @ SV334 @ SV61 )
= $false )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2342]) ).
thf(2382,plain,
! [SV387: a,SV179: set_Product_prod_a_a,SV398: a,SV393: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV393 @ SV398 ) @ SV179 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV387 @ SV398 ) @ SV179 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV387 @ SV393 ) @ SV179 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK37_SY828 @ SV179 ) @ ( sK46_SY1040 @ SV179 ) ) @ SV179 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2343]) ).
thf(2383,plain,
! [SV406: a,SV179: set_Product_prod_a_a,SV399: a,SV394: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV399 ) @ SV179 )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV399 @ SV406 ) @ SV179 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV406 ) @ SV179 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK46_SY1040 @ SV179 ) @ ( sK56_SY1050 @ SV179 ) ) @ SV179 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2344]) ).
thf(2384,plain,
! [SV388: a,SV179: set_Product_prod_a_a,SV400: a,SV395: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV395 @ SV400 ) @ SV179 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV388 @ SV400 ) @ SV179 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV388 @ SV395 ) @ SV179 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK37_SY828 @ SV179 ) @ ( sK56_SY1050 @ SV179 ) ) @ SV179 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2345]) ).
thf(2385,plain,
! [SV74: set_a,SV272: a,SV184: set_Product_prod_a_a,SV336: a,SV360: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV336 ) @ SV184 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV360 ) @ SV184 )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV360 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV272 ) @ SV184 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV336 ) @ SV184 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV272 ) @ SV184 )
= $true )
| ( ( prefer719835986ence_a @ SV74 @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2346]) ).
thf(2386,plain,
! [SV88: a,SV196: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
= $true )
| ( ( member_a @ SV88 @ carrier )
= $false )
| ( ( member_a @ SV196 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2348]) ).
thf(2387,plain,
! [SV88: a,SV196: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
= $true )
| ( ( member_a @ SV88 @ carrier )
= $false )
| ( ( member_a @ SV196 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2349]) ).
thf(2388,plain,
! [SV196: a,SV88: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
= $true )
| ( ( member_a @ SV88 @ carrier )
= $false )
| ( ( member_a @ SV196 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2350]) ).
thf(2389,plain,
! [SV197: set_a,SV343: set_Product_prod_a_a,SV389: a,SV382: a] :
( ( ( SV382 = SV389 )
= $true )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV382 @ SV389 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV389 @ SV382 ) @ SV343 ) )
= $true )
| ( ( member_a @ SV389 @ SV197 )
= $false )
| ( ( member_a @ SV382 @ SV197 )
= $false )
| ( ( total_on_a @ SV197 @ SV343 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2351]) ).
thf(2390,plain,
! [SV343: set_Product_prod_a_a,SV390: a,SV197: set_a,SV407: a] :
( ( ( member_a @ SV407 @ SV197 )
= $false )
| ( ( ~ ( ( SV390 != SV407 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV390 @ SV407 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV407 @ SV390 ) @ SV343 ) )
= $true )
| ( ( member_a @ SV390 @ SV197 )
= $false )
| ( ( member_a @ ( sK57_SY1017 @ SV343 @ SV197 ) @ SV197 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2352]) ).
thf(2391,plain,
! [SV343: set_Product_prod_a_a,SV401: a,SV197: set_a,SV417: a] :
( ( ( ~ ( member_a @ SV417 @ SV197 )
| ~ ( ( SV401 != SV417 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV401 @ SV417 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV417 @ SV401 ) @ SV343 ) )
= $true )
| ( ( member_a @ SV401 @ SV197 )
= $false )
| ( ( member_a @ ( sK61_SY1054 @ SV343 @ SV197 ) @ SV197 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2353]) ).
thf(2392,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a,SV413: a] :
( ( ( ~ ( member_a @ SV413 @ SV197 ) )
= $true )
| ( ( ! [SY1091: a] :
( ~ ( member_a @ SY1091 @ SV197 )
| ~ ( ( SV413 != SY1091 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV413 @ SY1091 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1091 @ SV413 ) @ SV343 ) ) )
= $true )
| ( ( ( sK57_SY1017 @ SV343 @ SV197 )
= ( sK61_SY1054 @ SV343 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2354]) ).
thf(2393,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a,SV408: a] :
( ( ( member_a @ SV408 @ SV197 )
= $false )
| ( ( ! [SY1086: a] :
( ~ ( member_a @ SY1086 @ SV197 )
| ~ ( ( SV408 != SY1086 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV408 @ SY1086 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1086 @ SV408 ) @ SV343 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK57_SY1017 @ SV343 @ SV197 ) @ ( sK61_SY1054 @ SV343 @ SV197 ) ) @ SV343 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2355]) ).
thf(2394,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a,SV409: a] :
( ( ( member_a @ SV409 @ SV197 )
= $false )
| ( ( ! [SY1087: a] :
( ~ ( member_a @ SY1087 @ SV197 )
| ~ ( ( SV409 != SY1087 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV409 @ SY1087 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1087 @ SV409 ) @ SV343 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1054 @ SV343 @ SV197 ) @ ( sK57_SY1017 @ SV343 @ SV197 ) ) @ SV343 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2356]) ).
thf(2395,plain,
! [SV198: set_Product_prod_a_a,SV396: a,SV402: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV402 @ SV396 ) @ ( sK62_SY857 @ SV198 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV396 @ SV402 ) @ ( sK62_SY857 @ SV198 ) )
= $false )
| ( ( asym_a @ SV198 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2357]) ).
thf(2396,plain,
! [SV369: set_Product_prod_a_a,SV198: set_Product_prod_a_a] :
( ( ( asym_a @ SV198 )
= $true )
| ( ( SV198 = SV369 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK68_SY1051 @ SV198 @ SV369 ) @ ( sK70_SY1066 @ SV369 @ SV198 ) ) @ SV369 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2358]) ).
thf(2397,plain,
! [SV369: set_Product_prod_a_a,SV198: set_Product_prod_a_a] :
( ( ( ~ ! [SY857: set_Product_prod_a_a] :
~ ~ ( ( SV198 != SY857 )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SY857 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SY857 ) ) ) )
= $true )
| ( ( SV198 = SV369 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK68_SY1051 @ SV198 @ SV369 ) @ ( sK70_SY1066 @ SV369 @ SV198 ) ) @ SV369 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2359]) ).
thf(2398,plain,
! [SV369: set_Product_prod_a_a,SV198: set_Product_prod_a_a] :
( ( ( asym_a @ SV198 )
= $true )
| ( ( SV198 = SV369 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK70_SY1066 @ SV369 @ SV198 ) @ ( sK68_SY1051 @ SV198 @ SV369 ) ) @ SV369 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2360]) ).
thf(2399,plain,
! [SV369: set_Product_prod_a_a,SV198: set_Product_prod_a_a] :
( ( ( ~ ! [SY857: set_Product_prod_a_a] :
~ ~ ( ( SV198 != SY857 )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SY857 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SY857 ) ) ) )
= $true )
| ( ( SV198 = SV369 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK70_SY1066 @ SV369 @ SV198 ) @ ( sK68_SY1051 @ SV198 @ SV369 ) ) @ SV369 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2361]) ).
thf(2400,plain,
! [SV93: set_a,SV345: a,SV201: set_Product_prod_a_a,SV362: a,SV286: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SV362 ) @ SV201 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV362 @ SV286 ) @ SV201 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV362 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV362 @ SV345 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SV345 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV286 ) @ SV201 )
= $false )
| ( ( prefer1292084992ence_a @ SV93 @ SV201 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2362]) ).
thf(2401,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a,SV414: a,SV410: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV410 @ SV414 ) @ SV347 ) )
= $true )
| ( ( member_a @ SV410 @ SV204 )
= $true )
| ( ( prefer1292084992ence_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2363]) ).
thf(2402,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a,SV415: a,SV411: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV411 @ SV415 ) @ SV347 ) )
= $true )
| ( ( member_a @ SV415 @ SV204 )
= $true )
| ( ( prefer1292084992ence_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2364]) ).
thf(2403,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( ! [SY1093: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK74_SY1022 @ SV204 @ SV347 ) @ SY1093 ) @ SV347 )
| ( member_a @ SY1093 @ SV204 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( ~ ( order_preorder_on_a @ SV204 @ SV347 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 )
| ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2365]) ).
thf(2404,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK73_SY1022 @ SV204 @ SV347 ) @ ( sK75_SY1092 @ SV347 @ SV204 ) ) @ SV347 )
| ( member_a @ ( sK75_SY1092 @ SV347 @ SV204 ) @ SV204 ) )
= $false )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( ~ ( order_preorder_on_a @ SV204 @ SV347 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 )
| ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2366]) ).
thf(2405,plain,
! [SV208: a,SV291: a,SV101: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SV291 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV291 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV291 @ SV208 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SV208 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV101 ) @ relation )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2367]) ).
thf(2406,plain,
! [SV208: a,SV101: a,SV291: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV291 @ SV101 ) @ relation ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV291 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV291 @ SV208 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SV208 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV101 ) @ relation )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2368]) ).
thf(2407,plain,
! [SV154: set_Product_prod_a_a,SV320: set_Pr1948701895od_a_a,SV385: product_prod_a_a,SV380: product_prod_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV380 @ SV385 ) @ SV320 )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV385 @ SV380 ) @ SV320 )
= $true )
| ( ( SV380 = SV385 )
= $true )
| ( ( member449909584od_a_a @ SV385 @ SV154 )
= $false )
| ( ( member449909584od_a_a @ SV380 @ SV154 )
= $false )
| ( ( total_1490170027od_a_a @ SV154 @ SV320 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2369]) ).
thf(2408,plain,
! [SV154: set_Product_prod_a_a,SV320: set_Pr1948701895od_a_a,SV403: product_prod_a_a,SV386: product_prod_a_a] :
( ( ( ~ ( ( SV386 != SV403 ) ) )
= $true )
| ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV386 @ SV403 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV403 @ SV386 ) @ SV320 ) )
= $true )
| ( ( member449909584od_a_a @ SV403 @ SV154 )
= $false )
| ( ( member449909584od_a_a @ SV386 @ SV154 )
= $false )
| ( ( member449909584od_a_a @ ( sK54_SY1005 @ SV320 @ SV154 ) @ SV154 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2370]) ).
thf(2409,plain,
! [SV320: set_Pr1948701895od_a_a,SV397: product_prod_a_a,SV154: set_Product_prod_a_a,SV416: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV416 @ SV154 ) )
= $true )
| ( ( ~ ( ( SV397 != SV416 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV397 @ SV416 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV416 @ SV397 ) @ SV320 ) )
= $true )
| ( ( member449909584od_a_a @ SV397 @ SV154 )
= $false )
| ( ( member449909584od_a_a @ ( sK59_SY1053 @ SV320 @ SV154 ) @ SV154 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2371]) ).
thf(2410,plain,
! [SV320: set_Pr1948701895od_a_a,SV154: set_Product_prod_a_a,SV412: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV412 @ SV154 )
= $false )
| ( ( ! [SY1090: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY1090 @ SV154 )
| ~ ( ( SV412 != SY1090 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV412 @ SY1090 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SY1090 @ SV412 ) @ SV320 ) ) )
= $true )
| ( ( ( sK54_SY1005 @ SV320 @ SV154 )
= ( sK59_SY1053 @ SV320 @ SV154 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2372]) ).
thf(2411,plain,
! [SV320: set_Pr1948701895od_a_a,SV404: product_prod_a_a,SV154: set_Product_prod_a_a,SV418: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV418 @ SV154 )
| ~ ( ( SV404 != SV418 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV404 @ SV418 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV418 @ SV404 ) @ SV320 ) )
= $true )
| ( ( member449909584od_a_a @ SV404 @ SV154 )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK54_SY1005 @ SV320 @ SV154 ) @ ( sK59_SY1053 @ SV320 @ SV154 ) ) @ SV320 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2373]) ).
thf(2412,plain,
! [SV320: set_Pr1948701895od_a_a,SV405: product_prod_a_a,SV154: set_Product_prod_a_a,SV419: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV419 @ SV154 )
| ~ ( ( SV405 != SV419 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV405 @ SV419 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV419 @ SV405 ) @ SV320 ) )
= $true )
| ( ( member449909584od_a_a @ SV405 @ SV154 )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK59_SY1053 @ SV320 @ SV154 ) @ ( sK54_SY1005 @ SV320 @ SV154 ) ) @ SV320 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2374]) ).
thf(2413,plain,
! [SV366: set_Product_prod_a_a,SV327: a,SV166: a,SV359: set_Product_prod_a_a,SV257: a,SV52: a] :
( ( ( SV52 != SV257 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
= $true )
| ( ( SV52 = SV257 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2375]) ).
thf(2414,plain,
! [SV359: set_Product_prod_a_a,SV257: a,SV52: a,SV366: set_Product_prod_a_a,SV327: a,SV166: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
= $true )
| ( ( SV52 = SV257 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2375]) ).
thf(2415,plain,
! [SV60: set_Product_prod_a_a,SV174: set_Pr1948701895od_a_a,SV265: product_prod_a_a,SV333: product_prod_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
= $true )
| ( ( member449909584od_a_a @ SV265 @ SV60 )
= $false )
| ( ( member449909584od_a_a @ SV333 @ SV60 )
= $false )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2376]) ).
thf(2416,plain,
! [SV60: set_Product_prod_a_a,SV174: set_Pr1948701895od_a_a,SV333: product_prod_a_a,SV265: product_prod_a_a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
| ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
= $true )
| ( ( member449909584od_a_a @ SV265 @ SV60 )
= $false )
| ( ( member449909584od_a_a @ SV333 @ SV60 )
= $false )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2377]) ).
thf(2417,plain,
! [SV60: set_Product_prod_a_a,SV174: set_Pr1948701895od_a_a,SV265: product_prod_a_a,SV333: product_prod_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
= $false )
| ( ( ~ ( ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
| ~ ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
| ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) ) ) )
= $true )
| ( ( member449909584od_a_a @ SV265 @ SV60 )
= $false )
| ( ( member449909584od_a_a @ SV333 @ SV60 )
= $false )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2378]) ).
thf(2418,plain,
! [SV61: set_a,SV175: set_Product_prod_a_a,SV266: a,SV334: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
= $true )
| ( ( member_a @ SV266 @ SV61 )
= $false )
| ( ( member_a @ SV334 @ SV61 )
= $false )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2379]) ).
thf(2419,plain,
! [SV61: set_a,SV175: set_Product_prod_a_a,SV334: a,SV266: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
= $true )
| ( ( member_a @ SV266 @ SV61 )
= $false )
| ( ( member_a @ SV334 @ SV61 )
= $false )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2380]) ).
thf(2420,plain,
! [SV61: set_a,SV175: set_Product_prod_a_a,SV266: a,SV334: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
= $false )
| ( ( ~ ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) ) ) )
= $true )
| ( ( member_a @ SV266 @ SV61 )
= $false )
| ( ( member_a @ SV334 @ SV61 )
= $false )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2381]) ).
thf(2421,plain,
! [SV387: a,SV179: set_Product_prod_a_a,SV398: a,SV393: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV393 @ SV398 ) @ SV179 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV387 @ SV398 ) @ SV179 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV387 @ SV393 ) @ SV179 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK37_SY828 @ SV179 ) @ ( sK46_SY1040 @ SV179 ) ) @ SV179 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2382]) ).
thf(2422,plain,
! [SV394: a,SV179: set_Product_prod_a_a,SV406: a,SV399: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV399 @ SV406 ) @ SV179 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV406 ) @ SV179 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV399 ) @ SV179 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK46_SY1040 @ SV179 ) @ ( sK56_SY1050 @ SV179 ) ) @ SV179 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2383]) ).
thf(2423,plain,
! [SV388: a,SV179: set_Product_prod_a_a,SV400: a,SV395: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV395 @ SV400 ) @ SV179 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV388 @ SV400 ) @ SV179 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV388 @ SV395 ) @ SV179 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK37_SY828 @ SV179 ) @ ( sK56_SY1050 @ SV179 ) ) @ SV179 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2384]) ).
thf(2424,plain,
! [SV74: set_a,SV272: a,SV184: set_Product_prod_a_a,SV336: a,SV360: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV336 ) @ SV184 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV360 ) @ SV184 )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV360 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV272 ) @ SV184 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV336 ) @ SV184 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV272 ) @ SV184 )
= $true )
| ( ( prefer719835986ence_a @ SV74 @ SV184 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2385]) ).
thf(2425,plain,
! [SV88: a,SV196: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
= $true )
| ( ( member_a @ SV88 @ carrier )
= $false )
| ( ( member_a @ SV196 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2387]) ).
thf(2426,plain,
! [SV196: a,SV88: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
= $true )
| ( ( member_a @ SV88 @ carrier )
= $false )
| ( ( member_a @ SV196 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2388]) ).
thf(2427,plain,
! [SV197: set_a,SV343: set_Product_prod_a_a,SV389: a,SV382: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV382 @ SV389 ) @ SV343 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV389 @ SV382 ) @ SV343 )
= $true )
| ( ( SV382 = SV389 )
= $true )
| ( ( member_a @ SV389 @ SV197 )
= $false )
| ( ( member_a @ SV382 @ SV197 )
= $false )
| ( ( total_on_a @ SV197 @ SV343 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2389]) ).
thf(2428,plain,
! [SV197: set_a,SV343: set_Product_prod_a_a,SV407: a,SV390: a] :
( ( ( ~ ( ( SV390 != SV407 ) ) )
= $true )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV390 @ SV407 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV407 @ SV390 ) @ SV343 ) )
= $true )
| ( ( member_a @ SV407 @ SV197 )
= $false )
| ( ( member_a @ SV390 @ SV197 )
= $false )
| ( ( member_a @ ( sK57_SY1017 @ SV343 @ SV197 ) @ SV197 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2390]) ).
thf(2429,plain,
! [SV343: set_Product_prod_a_a,SV401: a,SV197: set_a,SV417: a] :
( ( ( ~ ( member_a @ SV417 @ SV197 ) )
= $true )
| ( ( ~ ( ( SV401 != SV417 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV401 @ SV417 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV417 @ SV401 ) @ SV343 ) )
= $true )
| ( ( member_a @ SV401 @ SV197 )
= $false )
| ( ( member_a @ ( sK61_SY1054 @ SV343 @ SV197 ) @ SV197 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2391]) ).
thf(2430,plain,
! [SV343: set_Product_prod_a_a,SV197: set_a,SV413: a] :
( ( ( member_a @ SV413 @ SV197 )
= $false )
| ( ( ! [SY1091: a] :
( ~ ( member_a @ SY1091 @ SV197 )
| ~ ( ( SV413 != SY1091 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV413 @ SY1091 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY1091 @ SV413 ) @ SV343 ) ) )
= $true )
| ( ( ( sK57_SY1017 @ SV343 @ SV197 )
= ( sK61_SY1054 @ SV343 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2392]) ).
thf(2431,plain,
! [SV343: set_Product_prod_a_a,SV408: a,SV197: set_a,SV420: a] :
( ( ( ~ ( member_a @ SV420 @ SV197 )
| ~ ( ( SV408 != SV420 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV408 @ SV420 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV408 ) @ SV343 ) )
= $true )
| ( ( member_a @ SV408 @ SV197 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK57_SY1017 @ SV343 @ SV197 ) @ ( sK61_SY1054 @ SV343 @ SV197 ) ) @ SV343 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2393]) ).
thf(2432,plain,
! [SV343: set_Product_prod_a_a,SV409: a,SV197: set_a,SV421: a] :
( ( ( ~ ( member_a @ SV421 @ SV197 )
| ~ ( ( SV409 != SV421 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV409 @ SV421 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV421 @ SV409 ) @ SV343 ) )
= $true )
| ( ( member_a @ SV409 @ SV197 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1054 @ SV343 @ SV197 ) @ ( sK57_SY1017 @ SV343 @ SV197 ) ) @ SV343 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2394]) ).
thf(2433,plain,
! [SV369: set_Product_prod_a_a,SV198: set_Product_prod_a_a] :
( ( ( ! [SY857: set_Product_prod_a_a] :
~ ~ ( ( SV198 != SY857 )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SY857 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SY857 ) ) ) )
= $false )
| ( ( SV198 = SV369 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK68_SY1051 @ SV198 @ SV369 ) @ ( sK70_SY1066 @ SV369 @ SV198 ) ) @ SV369 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2397]) ).
thf(2434,plain,
! [SV369: set_Product_prod_a_a,SV198: set_Product_prod_a_a] :
( ( ( ! [SY857: set_Product_prod_a_a] :
~ ~ ( ( SV198 != SY857 )
| ~ ! [SX2: a,SX3: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX3 ) @ SY857 )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX3 @ SX2 ) @ SY857 ) ) ) )
= $false )
| ( ( SV198 = SV369 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK70_SY1066 @ SV369 @ SV198 ) @ ( sK68_SY1051 @ SV198 @ SV369 ) ) @ SV369 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2399]) ).
thf(2435,plain,
! [SV93: set_a,SV345: a,SV201: set_Product_prod_a_a,SV362: a,SV286: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SV362 ) @ SV201 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV362 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV362 @ SV345 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SV345 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV286 ) @ SV201 )
= $false )
| ( ( prefer1292084992ence_a @ SV93 @ SV201 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2400]) ).
thf(2436,plain,
! [SV93: set_a,SV345: a,SV201: set_Product_prod_a_a,SV286: a,SV362: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV362 @ SV286 ) @ SV201 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV362 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV362 @ SV345 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SV345 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV286 ) @ SV201 )
= $false )
| ( ( prefer1292084992ence_a @ SV93 @ SV201 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2400]) ).
thf(2437,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a,SV414: a,SV410: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV410 @ SV414 ) @ SV347 )
= $false )
| ( ( member_a @ SV410 @ SV204 )
= $true )
| ( ( prefer1292084992ence_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2401]) ).
thf(2438,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a,SV415: a,SV411: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV411 @ SV415 ) @ SV347 )
= $false )
| ( ( member_a @ SV415 @ SV204 )
= $true )
| ( ( prefer1292084992ence_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2402]) ).
thf(2439,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK74_SY1022 @ SV204 @ SV347 ) @ ( sK76_SY1093 @ SV347 @ SV204 ) ) @ SV347 )
| ( member_a @ ( sK76_SY1093 @ SV347 @ SV204 ) @ SV204 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( ~ ( order_preorder_on_a @ SV204 @ SV347 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 )
| ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2403]) ).
thf(2440,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK73_SY1022 @ SV204 @ SV347 ) @ ( sK75_SY1092 @ SV347 @ SV204 ) ) @ SV347 ) )
= $false )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( ~ ( order_preorder_on_a @ SV204 @ SV347 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 )
| ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2404]) ).
thf(2441,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( member_a @ ( sK75_SY1092 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( ~ ( order_preorder_on_a @ SV204 @ SV347 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 )
| ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2404]) ).
thf(2442,plain,
! [SV208: a,SV101: a,SV291: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV291 @ SV101 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV291 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV291 @ SV208 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV101 @ SV208 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV208 @ SV101 ) @ relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2406]) ).
thf(2443,plain,
! [SV154: set_Product_prod_a_a,SV320: set_Pr1948701895od_a_a,SV403: product_prod_a_a,SV386: product_prod_a_a] :
( ( ( SV386 != SV403 )
= $false )
| ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV386 @ SV403 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV403 @ SV386 ) @ SV320 ) )
= $true )
| ( ( member449909584od_a_a @ SV403 @ SV154 )
= $false )
| ( ( member449909584od_a_a @ SV386 @ SV154 )
= $false )
| ( ( member449909584od_a_a @ ( sK54_SY1005 @ SV320 @ SV154 ) @ SV154 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2408]) ).
thf(2444,plain,
! [SV320: set_Pr1948701895od_a_a,SV397: product_prod_a_a,SV154: set_Product_prod_a_a,SV416: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV416 @ SV154 )
= $false )
| ( ( ~ ( ( SV397 != SV416 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV397 @ SV416 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV416 @ SV397 ) @ SV320 ) )
= $true )
| ( ( member449909584od_a_a @ SV397 @ SV154 )
= $false )
| ( ( member449909584od_a_a @ ( sK59_SY1053 @ SV320 @ SV154 ) @ SV154 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2409]) ).
thf(2445,plain,
! [SV320: set_Pr1948701895od_a_a,SV412: product_prod_a_a,SV154: set_Product_prod_a_a,SV422: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV422 @ SV154 )
| ~ ( ( SV412 != SV422 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV412 @ SV422 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV422 @ SV412 ) @ SV320 ) )
= $true )
| ( ( member449909584od_a_a @ SV412 @ SV154 )
= $false )
| ( ( ( sK54_SY1005 @ SV320 @ SV154 )
= ( sK59_SY1053 @ SV320 @ SV154 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2410]) ).
thf(2446,plain,
! [SV320: set_Pr1948701895od_a_a,SV404: product_prod_a_a,SV154: set_Product_prod_a_a,SV418: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV418 @ SV154 ) )
= $true )
| ( ( ~ ( ( SV404 != SV418 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV404 @ SV418 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV418 @ SV404 ) @ SV320 ) )
= $true )
| ( ( member449909584od_a_a @ SV404 @ SV154 )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK54_SY1005 @ SV320 @ SV154 ) @ ( sK59_SY1053 @ SV320 @ SV154 ) ) @ SV320 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2411]) ).
thf(2447,plain,
! [SV320: set_Pr1948701895od_a_a,SV405: product_prod_a_a,SV154: set_Product_prod_a_a,SV419: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV419 @ SV154 ) )
= $true )
| ( ( ~ ( ( SV405 != SV419 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV405 @ SV419 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV419 @ SV405 ) @ SV320 ) )
= $true )
| ( ( member449909584od_a_a @ SV405 @ SV154 )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK59_SY1053 @ SV320 @ SV154 ) @ ( sK54_SY1005 @ SV320 @ SV154 ) ) @ SV320 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2412]) ).
thf(2448,plain,
! [SV366: set_Product_prod_a_a,SV327: a,SV166: a,SV359: set_Product_prod_a_a,SV257: a,SV52: a] :
( ( ( SV52 = SV257 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
= $true )
| ( ( SV52 = SV257 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2413]) ).
thf(2449,plain,
! [SV359: set_Product_prod_a_a,SV257: a,SV52: a,SV366: set_Product_prod_a_a,SV327: a,SV166: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV52 @ SV257 ) @ SV359 )
= $true )
| ( ( SV52 = SV257 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV166 @ SV327 ) @ SV366 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2414]) ).
thf(2450,plain,
! [SV60: set_Product_prod_a_a,SV174: set_Pr1948701895od_a_a,SV333: product_prod_a_a,SV265: product_prod_a_a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
= $true )
| ( ( member449909584od_a_a @ SV265 @ SV60 )
= $false )
| ( ( member449909584od_a_a @ SV333 @ SV60 )
= $false )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2416]) ).
thf(2451,plain,
! [SV60: set_Product_prod_a_a,SV174: set_Pr1948701895od_a_a,SV265: product_prod_a_a,SV333: product_prod_a_a] :
( ( ( ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
= $true )
| ( ( member449909584od_a_a @ SV265 @ SV60 )
= $false )
| ( ( member449909584od_a_a @ SV333 @ SV60 )
= $false )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2416]) ).
thf(2452,plain,
! [SV60: set_Product_prod_a_a,SV174: set_Pr1948701895od_a_a,SV265: product_prod_a_a,SV333: product_prod_a_a] :
( ( ( ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
| ~ ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
| ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
= $true )
| ( ( member449909584od_a_a @ SV265 @ SV60 )
= $false )
| ( ( member449909584od_a_a @ SV333 @ SV60 )
= $false )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2417]) ).
thf(2453,plain,
! [SV61: set_a,SV175: set_Product_prod_a_a,SV334: a,SV266: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
= $true )
| ( ( member_a @ SV266 @ SV61 )
= $false )
| ( ( member_a @ SV334 @ SV61 )
= $false )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2419]) ).
thf(2454,plain,
! [SV61: set_a,SV175: set_Product_prod_a_a,SV266: a,SV334: a] :
( ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
= $true )
| ( ( member_a @ SV266 @ SV61 )
= $false )
| ( ( member_a @ SV334 @ SV61 )
= $false )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2419]) ).
thf(2455,plain,
! [SV61: set_a,SV175: set_Product_prod_a_a,SV266: a,SV334: a] :
( ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
= $true )
| ( ( member_a @ SV266 @ SV61 )
= $false )
| ( ( member_a @ SV334 @ SV61 )
= $false )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2420]) ).
thf(2456,plain,
! [SV394: a,SV179: set_Product_prod_a_a,SV406: a,SV399: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV399 @ SV406 ) @ SV179 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV406 ) @ SV179 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV394 @ SV399 ) @ SV179 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK46_SY1040 @ SV179 ) @ ( sK56_SY1050 @ SV179 ) ) @ SV179 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2422]) ).
thf(2457,plain,
! [SV74: set_a,SV336: a,SV184: set_Product_prod_a_a,SV360: a,SV272: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV360 ) @ SV184 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV272 ) @ SV184 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV360 ) @ SV184 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV336 ) @ SV184 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV336 ) @ SV184 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV272 ) @ SV184 )
= $true )
| ( ( prefer719835986ence_a @ SV74 @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2424]) ).
thf(2458,plain,
! [SV196: a,SV88: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
= $true )
| ( ( member_a @ SV88 @ carrier )
= $false )
| ( ( member_a @ SV196 @ carrier )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2426]) ).
thf(2459,plain,
! [SV88: a,SV196: a] :
( ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
= $true )
| ( ( member_a @ SV88 @ carrier )
= $false )
| ( ( member_a @ SV196 @ carrier )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2426]) ).
thf(2460,plain,
! [SV197: set_a,SV343: set_Product_prod_a_a,SV407: a,SV390: a] :
( ( ( SV390 != SV407 )
= $false )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV390 @ SV407 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV407 @ SV390 ) @ SV343 ) )
= $true )
| ( ( member_a @ SV407 @ SV197 )
= $false )
| ( ( member_a @ SV390 @ SV197 )
= $false )
| ( ( member_a @ ( sK57_SY1017 @ SV343 @ SV197 ) @ SV197 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2428]) ).
thf(2461,plain,
! [SV343: set_Product_prod_a_a,SV401: a,SV197: set_a,SV417: a] :
( ( ( member_a @ SV417 @ SV197 )
= $false )
| ( ( ~ ( ( SV401 != SV417 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV401 @ SV417 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV417 @ SV401 ) @ SV343 ) )
= $true )
| ( ( member_a @ SV401 @ SV197 )
= $false )
| ( ( member_a @ ( sK61_SY1054 @ SV343 @ SV197 ) @ SV197 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2429]) ).
thf(2462,plain,
! [SV343: set_Product_prod_a_a,SV413: a,SV197: set_a,SV423: a] :
( ( ( ~ ( member_a @ SV423 @ SV197 )
| ~ ( ( SV413 != SV423 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV413 @ SV423 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV423 @ SV413 ) @ SV343 ) )
= $true )
| ( ( member_a @ SV413 @ SV197 )
= $false )
| ( ( ( sK57_SY1017 @ SV343 @ SV197 )
= ( sK61_SY1054 @ SV343 @ SV197 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2430]) ).
thf(2463,plain,
! [SV343: set_Product_prod_a_a,SV408: a,SV197: set_a,SV420: a] :
( ( ( ~ ( member_a @ SV420 @ SV197 ) )
= $true )
| ( ( ~ ( ( SV408 != SV420 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV408 @ SV420 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV408 ) @ SV343 ) )
= $true )
| ( ( member_a @ SV408 @ SV197 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK57_SY1017 @ SV343 @ SV197 ) @ ( sK61_SY1054 @ SV343 @ SV197 ) ) @ SV343 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2431]) ).
thf(2464,plain,
! [SV343: set_Product_prod_a_a,SV409: a,SV197: set_a,SV421: a] :
( ( ( ~ ( member_a @ SV421 @ SV197 ) )
= $true )
| ( ( ~ ( ( SV409 != SV421 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV409 @ SV421 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV421 @ SV409 ) @ SV343 ) )
= $true )
| ( ( member_a @ SV409 @ SV197 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1054 @ SV343 @ SV197 ) @ ( sK57_SY1017 @ SV343 @ SV197 ) ) @ SV343 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2432]) ).
thf(2465,plain,
! [SV369: set_Product_prod_a_a,SV198: set_Product_prod_a_a] :
( ( ( ~ ~ ( ( SV198
!= ( sK77_SY857 @ SV369 @ SV198 ) )
| ~ ! [SY1094: a,SY1095: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1094 @ SY1095 ) @ ( sK77_SY857 @ SV369 @ SV198 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1095 @ SY1094 ) @ ( sK77_SY857 @ SV369 @ SV198 ) ) ) ) )
= $false )
| ( ( SV198 = SV369 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK68_SY1051 @ SV198 @ SV369 ) @ ( sK70_SY1066 @ SV369 @ SV198 ) ) @ SV369 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2433]) ).
thf(2466,plain,
! [SV369: set_Product_prod_a_a,SV198: set_Product_prod_a_a] :
( ( ( ~ ~ ( ( SV198
!= ( sK78_SY857 @ SV369 @ SV198 ) )
| ~ ! [SY1096: a,SY1097: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1096 @ SY1097 ) @ ( sK78_SY857 @ SV369 @ SV198 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1097 @ SY1096 ) @ ( sK78_SY857 @ SV369 @ SV198 ) ) ) ) )
= $false )
| ( ( SV198 = SV369 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK70_SY1066 @ SV369 @ SV198 ) @ ( sK68_SY1051 @ SV198 @ SV369 ) ) @ SV369 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2434]) ).
thf(2467,plain,
! [SV93: set_a,SV345: a,SV201: set_Product_prod_a_a,SV362: a,SV286: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SV362 ) @ SV201 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV362 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV362 @ SV345 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SV345 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV286 ) @ SV201 )
= $false )
| ( ( prefer1292084992ence_a @ SV93 @ SV201 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2435]) ).
thf(2468,plain,
! [SV93: set_a,SV345: a,SV201: set_Product_prod_a_a,SV286: a,SV362: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV362 @ SV286 ) @ SV201 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV362 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV362 @ SV345 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV286 @ SV345 ) @ SV201 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV345 @ SV286 ) @ SV201 )
= $false )
| ( ( prefer1292084992ence_a @ SV93 @ SV201 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2436]) ).
thf(2469,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK74_SY1022 @ SV204 @ SV347 ) @ ( sK76_SY1093 @ SV347 @ SV204 ) ) @ SV347 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( ~ ( order_preorder_on_a @ SV204 @ SV347 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 )
| ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2439]) ).
thf(2470,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( member_a @ ( sK76_SY1093 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( ~ ( order_preorder_on_a @ SV204 @ SV347 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 )
| ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2439]) ).
thf(2471,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK73_SY1022 @ SV204 @ SV347 ) @ ( sK75_SY1092 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( ~ ( order_preorder_on_a @ SV204 @ SV347 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 )
| ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2440]) ).
thf(2472,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( member_a @ ( sK75_SY1092 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 )
| ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2441]) ).
thf(2473,plain,
! [SV154: set_Product_prod_a_a,SV320: set_Pr1948701895od_a_a,SV403: product_prod_a_a,SV386: product_prod_a_a] :
( ( ( SV386 = SV403 )
= $true )
| ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV386 @ SV403 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV403 @ SV386 ) @ SV320 ) )
= $true )
| ( ( member449909584od_a_a @ SV403 @ SV154 )
= $false )
| ( ( member449909584od_a_a @ SV386 @ SV154 )
= $false )
| ( ( member449909584od_a_a @ ( sK54_SY1005 @ SV320 @ SV154 ) @ SV154 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2443]) ).
thf(2474,plain,
! [SV154: set_Product_prod_a_a,SV320: set_Pr1948701895od_a_a,SV416: product_prod_a_a,SV397: product_prod_a_a] :
( ( ( ~ ( ( SV397 != SV416 ) ) )
= $true )
| ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV397 @ SV416 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV416 @ SV397 ) @ SV320 ) )
= $true )
| ( ( member449909584od_a_a @ SV416 @ SV154 )
= $false )
| ( ( member449909584od_a_a @ SV397 @ SV154 )
= $false )
| ( ( member449909584od_a_a @ ( sK59_SY1053 @ SV320 @ SV154 ) @ SV154 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2444]) ).
thf(2475,plain,
! [SV320: set_Pr1948701895od_a_a,SV412: product_prod_a_a,SV154: set_Product_prod_a_a,SV422: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV422 @ SV154 ) )
= $true )
| ( ( ~ ( ( SV412 != SV422 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV412 @ SV422 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV422 @ SV412 ) @ SV320 ) )
= $true )
| ( ( member449909584od_a_a @ SV412 @ SV154 )
= $false )
| ( ( ( sK54_SY1005 @ SV320 @ SV154 )
= ( sK59_SY1053 @ SV320 @ SV154 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2445]) ).
thf(2476,plain,
! [SV320: set_Pr1948701895od_a_a,SV404: product_prod_a_a,SV154: set_Product_prod_a_a,SV418: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV418 @ SV154 )
= $false )
| ( ( ~ ( ( SV404 != SV418 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV404 @ SV418 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV418 @ SV404 ) @ SV320 ) )
= $true )
| ( ( member449909584od_a_a @ SV404 @ SV154 )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK54_SY1005 @ SV320 @ SV154 ) @ ( sK59_SY1053 @ SV320 @ SV154 ) ) @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2446]) ).
thf(2477,plain,
! [SV320: set_Pr1948701895od_a_a,SV405: product_prod_a_a,SV154: set_Product_prod_a_a,SV419: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV419 @ SV154 )
= $false )
| ( ( ~ ( ( SV405 != SV419 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV405 @ SV419 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV419 @ SV405 ) @ SV320 ) )
= $true )
| ( ( member449909584od_a_a @ SV405 @ SV154 )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK59_SY1053 @ SV320 @ SV154 ) @ ( sK54_SY1005 @ SV320 @ SV154 ) ) @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2447]) ).
thf(2478,plain,
! [SV60: set_Product_prod_a_a,SV174: set_Pr1948701895od_a_a,SV333: product_prod_a_a,SV265: product_prod_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
= $true )
| ( ( member449909584od_a_a @ SV265 @ SV60 )
= $false )
| ( ( member449909584od_a_a @ SV333 @ SV60 )
= $false )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2450]) ).
thf(2479,plain,
! [SV60: set_Product_prod_a_a,SV174: set_Pr1948701895od_a_a,SV265: product_prod_a_a,SV333: product_prod_a_a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
= $true )
| ( ( member449909584od_a_a @ SV265 @ SV60 )
= $false )
| ( ( member449909584od_a_a @ SV333 @ SV60 )
= $false )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2451]) ).
thf(2480,plain,
! [SV60: set_Product_prod_a_a,SV174: set_Pr1948701895od_a_a,SV265: product_prod_a_a,SV333: product_prod_a_a] :
( ( ( ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
= $true )
| ( ( member449909584od_a_a @ SV265 @ SV60 )
= $false )
| ( ( member449909584od_a_a @ SV333 @ SV60 )
= $false )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2452]) ).
thf(2481,plain,
! [SV60: set_Product_prod_a_a,SV174: set_Pr1948701895od_a_a,SV333: product_prod_a_a,SV265: product_prod_a_a] :
( ( ( ~ ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
| ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
= $true )
| ( ( member449909584od_a_a @ SV265 @ SV60 )
= $false )
| ( ( member449909584od_a_a @ SV333 @ SV60 )
= $false )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2452]) ).
thf(2482,plain,
! [SV61: set_a,SV175: set_Product_prod_a_a,SV334: a,SV266: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
= $true )
| ( ( member_a @ SV266 @ SV61 )
= $false )
| ( ( member_a @ SV334 @ SV61 )
= $false )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2453]) ).
thf(2483,plain,
! [SV61: set_a,SV175: set_Product_prod_a_a,SV266: a,SV334: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
= $true )
| ( ( member_a @ SV266 @ SV61 )
= $false )
| ( ( member_a @ SV334 @ SV61 )
= $false )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2454]) ).
thf(2484,plain,
! [SV61: set_a,SV175: set_Product_prod_a_a,SV266: a,SV334: a] :
( ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
= $true )
| ( ( member_a @ SV266 @ SV61 )
= $false )
| ( ( member_a @ SV334 @ SV61 )
= $false )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2455]) ).
thf(2485,plain,
! [SV61: set_a,SV175: set_Product_prod_a_a,SV334: a,SV266: a] :
( ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
= $true )
| ( ( member_a @ SV266 @ SV61 )
= $false )
| ( ( member_a @ SV334 @ SV61 )
= $false )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2455]) ).
thf(2486,plain,
! [SV74: set_a,SV336: a,SV184: set_Product_prod_a_a,SV360: a,SV272: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV360 ) @ SV184 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV360 ) @ SV184 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV336 ) @ SV184 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV336 ) @ SV184 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV272 ) @ SV184 )
= $true )
| ( ( prefer719835986ence_a @ SV74 @ SV184 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2457]) ).
thf(2487,plain,
! [SV74: set_a,SV336: a,SV184: set_Product_prod_a_a,SV272: a,SV360: a] :
( ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV272 ) @ SV184 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV360 ) @ SV184 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV336 ) @ SV184 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV336 ) @ SV184 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV272 ) @ SV184 )
= $true )
| ( ( prefer719835986ence_a @ SV74 @ SV184 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2457]) ).
thf(2488,plain,
! [SV196: a,SV88: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
= $true )
| ( ( member_a @ SV88 @ carrier )
= $false )
| ( ( member_a @ SV196 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2458]) ).
thf(2489,plain,
! [SV88: a,SV196: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
= $true )
| ( ( member_a @ SV88 @ carrier )
= $false )
| ( ( member_a @ SV196 @ carrier )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2459]) ).
thf(2490,plain,
! [SV197: set_a,SV343: set_Product_prod_a_a,SV407: a,SV390: a] :
( ( ( SV390 = SV407 )
= $true )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV390 @ SV407 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV407 @ SV390 ) @ SV343 ) )
= $true )
| ( ( member_a @ SV407 @ SV197 )
= $false )
| ( ( member_a @ SV390 @ SV197 )
= $false )
| ( ( member_a @ ( sK57_SY1017 @ SV343 @ SV197 ) @ SV197 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2460]) ).
thf(2491,plain,
! [SV197: set_a,SV343: set_Product_prod_a_a,SV417: a,SV401: a] :
( ( ( ~ ( ( SV401 != SV417 ) ) )
= $true )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV401 @ SV417 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV417 @ SV401 ) @ SV343 ) )
= $true )
| ( ( member_a @ SV417 @ SV197 )
= $false )
| ( ( member_a @ SV401 @ SV197 )
= $false )
| ( ( member_a @ ( sK61_SY1054 @ SV343 @ SV197 ) @ SV197 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2461]) ).
thf(2492,plain,
! [SV343: set_Product_prod_a_a,SV413: a,SV197: set_a,SV423: a] :
( ( ( ~ ( member_a @ SV423 @ SV197 ) )
= $true )
| ( ( ~ ( ( SV413 != SV423 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV413 @ SV423 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV423 @ SV413 ) @ SV343 ) )
= $true )
| ( ( member_a @ SV413 @ SV197 )
= $false )
| ( ( ( sK57_SY1017 @ SV343 @ SV197 )
= ( sK61_SY1054 @ SV343 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2462]) ).
thf(2493,plain,
! [SV343: set_Product_prod_a_a,SV408: a,SV197: set_a,SV420: a] :
( ( ( member_a @ SV420 @ SV197 )
= $false )
| ( ( ~ ( ( SV408 != SV420 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV408 @ SV420 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV408 ) @ SV343 ) )
= $true )
| ( ( member_a @ SV408 @ SV197 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK57_SY1017 @ SV343 @ SV197 ) @ ( sK61_SY1054 @ SV343 @ SV197 ) ) @ SV343 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2463]) ).
thf(2494,plain,
! [SV343: set_Product_prod_a_a,SV409: a,SV197: set_a,SV421: a] :
( ( ( member_a @ SV421 @ SV197 )
= $false )
| ( ( ~ ( ( SV409 != SV421 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV409 @ SV421 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV421 @ SV409 ) @ SV343 ) )
= $true )
| ( ( member_a @ SV409 @ SV197 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1054 @ SV343 @ SV197 ) @ ( sK57_SY1017 @ SV343 @ SV197 ) ) @ SV343 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2464]) ).
thf(2495,plain,
! [SV369: set_Product_prod_a_a,SV198: set_Product_prod_a_a] :
( ( ( ~ ( ( SV198
!= ( sK77_SY857 @ SV369 @ SV198 ) )
| ~ ! [SY1094: a,SY1095: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1094 @ SY1095 ) @ ( sK77_SY857 @ SV369 @ SV198 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1095 @ SY1094 ) @ ( sK77_SY857 @ SV369 @ SV198 ) ) ) ) )
= $true )
| ( ( SV198 = SV369 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK68_SY1051 @ SV198 @ SV369 ) @ ( sK70_SY1066 @ SV369 @ SV198 ) ) @ SV369 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2465]) ).
thf(2496,plain,
! [SV369: set_Product_prod_a_a,SV198: set_Product_prod_a_a] :
( ( ( ~ ( ( SV198
!= ( sK78_SY857 @ SV369 @ SV198 ) )
| ~ ! [SY1096: a,SY1097: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1096 @ SY1097 ) @ ( sK78_SY857 @ SV369 @ SV198 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1097 @ SY1096 ) @ ( sK78_SY857 @ SV369 @ SV198 ) ) ) ) )
= $true )
| ( ( SV198 = SV369 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK70_SY1066 @ SV369 @ SV198 ) @ ( sK68_SY1051 @ SV198 @ SV369 ) ) @ SV369 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2466]) ).
thf(2497,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK74_SY1022 @ SV204 @ SV347 ) @ ( sK76_SY1093 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( ~ ( order_preorder_on_a @ SV204 @ SV347 ) )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 )
| ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2469]) ).
thf(2498,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member_a @ ( sK76_SY1093 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 )
| ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2470]) ).
thf(2499,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK73_SY1022 @ SV204 @ SV347 ) @ ( sK75_SY1092 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 )
| ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2471]) ).
thf(2500,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 )
| ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) )
= $false )
| ( ( member_a @ ( sK75_SY1092 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2472]) ).
thf(2501,plain,
! [SV154: set_Product_prod_a_a,SV320: set_Pr1948701895od_a_a,SV403: product_prod_a_a,SV386: product_prod_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV386 @ SV403 ) @ SV320 )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV403 @ SV386 ) @ SV320 )
= $true )
| ( ( SV386 = SV403 )
= $true )
| ( ( member449909584od_a_a @ SV403 @ SV154 )
= $false )
| ( ( member449909584od_a_a @ SV386 @ SV154 )
= $false )
| ( ( member449909584od_a_a @ ( sK54_SY1005 @ SV320 @ SV154 ) @ SV154 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2473]) ).
thf(2502,plain,
! [SV154: set_Product_prod_a_a,SV320: set_Pr1948701895od_a_a,SV416: product_prod_a_a,SV397: product_prod_a_a] :
( ( ( SV397 != SV416 )
= $false )
| ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV397 @ SV416 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV416 @ SV397 ) @ SV320 ) )
= $true )
| ( ( member449909584od_a_a @ SV416 @ SV154 )
= $false )
| ( ( member449909584od_a_a @ SV397 @ SV154 )
= $false )
| ( ( member449909584od_a_a @ ( sK59_SY1053 @ SV320 @ SV154 ) @ SV154 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2474]) ).
thf(2503,plain,
! [SV320: set_Pr1948701895od_a_a,SV412: product_prod_a_a,SV154: set_Product_prod_a_a,SV422: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV422 @ SV154 )
= $false )
| ( ( ~ ( ( SV412 != SV422 ) )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV412 @ SV422 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV422 @ SV412 ) @ SV320 ) )
= $true )
| ( ( member449909584od_a_a @ SV412 @ SV154 )
= $false )
| ( ( ( sK54_SY1005 @ SV320 @ SV154 )
= ( sK59_SY1053 @ SV320 @ SV154 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2475]) ).
thf(2504,plain,
! [SV154: set_Product_prod_a_a,SV320: set_Pr1948701895od_a_a,SV418: product_prod_a_a,SV404: product_prod_a_a] :
( ( ( ~ ( ( SV404 != SV418 ) ) )
= $true )
| ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV404 @ SV418 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV418 @ SV404 ) @ SV320 ) )
= $true )
| ( ( member449909584od_a_a @ SV418 @ SV154 )
= $false )
| ( ( member449909584od_a_a @ SV404 @ SV154 )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK54_SY1005 @ SV320 @ SV154 ) @ ( sK59_SY1053 @ SV320 @ SV154 ) ) @ SV320 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2476]) ).
thf(2505,plain,
! [SV154: set_Product_prod_a_a,SV320: set_Pr1948701895od_a_a,SV419: product_prod_a_a,SV405: product_prod_a_a] :
( ( ( ~ ( ( SV405 != SV419 ) ) )
= $true )
| ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV405 @ SV419 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV419 @ SV405 ) @ SV320 ) )
= $true )
| ( ( member449909584od_a_a @ SV419 @ SV154 )
= $false )
| ( ( member449909584od_a_a @ SV405 @ SV154 )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK59_SY1053 @ SV320 @ SV154 ) @ ( sK54_SY1005 @ SV320 @ SV154 ) ) @ SV320 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2477]) ).
thf(2506,plain,
! [SV60: set_Product_prod_a_a,SV174: set_Pr1948701895od_a_a,SV265: product_prod_a_a,SV333: product_prod_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
= $true )
| ( ( member449909584od_a_a @ SV265 @ SV60 )
= $false )
| ( ( member449909584od_a_a @ SV333 @ SV60 )
= $false )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2479]) ).
thf(2507,plain,
! [SV60: set_Product_prod_a_a,SV174: set_Pr1948701895od_a_a,SV265: product_prod_a_a,SV333: product_prod_a_a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
= $true )
| ( ( member449909584od_a_a @ SV265 @ SV60 )
= $false )
| ( ( member449909584od_a_a @ SV333 @ SV60 )
= $false )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2480]) ).
thf(2508,plain,
! [SV60: set_Product_prod_a_a,SV174: set_Pr1948701895od_a_a,SV333: product_prod_a_a,SV265: product_prod_a_a] :
( ( ( ~ ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
| ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) ) )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
= $true )
| ( ( member449909584od_a_a @ SV265 @ SV60 )
= $false )
| ( ( member449909584od_a_a @ SV333 @ SV60 )
= $false )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2481]) ).
thf(2509,plain,
! [SV61: set_a,SV175: set_Product_prod_a_a,SV266: a,SV334: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
= $true )
| ( ( member_a @ SV266 @ SV61 )
= $false )
| ( ( member_a @ SV334 @ SV61 )
= $false )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2483]) ).
thf(2510,plain,
! [SV61: set_a,SV175: set_Product_prod_a_a,SV266: a,SV334: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
= $true )
| ( ( member_a @ SV266 @ SV61 )
= $false )
| ( ( member_a @ SV334 @ SV61 )
= $false )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2484]) ).
thf(2511,plain,
! [SV61: set_a,SV175: set_Product_prod_a_a,SV334: a,SV266: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
= $true )
| ( ( member_a @ SV266 @ SV61 )
= $false )
| ( ( member_a @ SV334 @ SV61 )
= $false )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2485]) ).
thf(2512,plain,
! [SV74: set_a,SV336: a,SV184: set_Product_prod_a_a,SV360: a,SV272: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV360 ) @ SV184 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV360 ) @ SV184 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV336 ) @ SV184 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV336 ) @ SV184 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV272 ) @ SV184 )
= $true )
| ( ( prefer719835986ence_a @ SV74 @ SV184 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2486]) ).
thf(2513,plain,
! [SV74: set_a,SV336: a,SV184: set_Product_prod_a_a,SV272: a,SV360: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV272 ) @ SV184 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV360 ) @ SV184 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV336 ) @ SV184 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV336 ) @ SV184 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV272 ) @ SV184 )
= $true )
| ( ( prefer719835986ence_a @ SV74 @ SV184 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2487]) ).
thf(2514,plain,
! [SV88: a,SV196: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV88 @ SV196 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV196 @ SV88 ) @ relation )
= $true )
| ( ( member_a @ SV88 @ carrier )
= $false )
| ( ( member_a @ SV196 @ carrier )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2489]) ).
thf(2515,plain,
! [SV197: set_a,SV343: set_Product_prod_a_a,SV407: a,SV390: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV390 @ SV407 ) @ SV343 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV407 @ SV390 ) @ SV343 )
= $true )
| ( ( SV390 = SV407 )
= $true )
| ( ( member_a @ SV407 @ SV197 )
= $false )
| ( ( member_a @ SV390 @ SV197 )
= $false )
| ( ( member_a @ ( sK57_SY1017 @ SV343 @ SV197 ) @ SV197 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2490]) ).
thf(2516,plain,
! [SV197: set_a,SV343: set_Product_prod_a_a,SV417: a,SV401: a] :
( ( ( SV401 != SV417 )
= $false )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV401 @ SV417 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV417 @ SV401 ) @ SV343 ) )
= $true )
| ( ( member_a @ SV417 @ SV197 )
= $false )
| ( ( member_a @ SV401 @ SV197 )
= $false )
| ( ( member_a @ ( sK61_SY1054 @ SV343 @ SV197 ) @ SV197 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2491]) ).
thf(2517,plain,
! [SV343: set_Product_prod_a_a,SV413: a,SV197: set_a,SV423: a] :
( ( ( member_a @ SV423 @ SV197 )
= $false )
| ( ( ~ ( ( SV413 != SV423 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV413 @ SV423 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV423 @ SV413 ) @ SV343 ) )
= $true )
| ( ( member_a @ SV413 @ SV197 )
= $false )
| ( ( ( sK57_SY1017 @ SV343 @ SV197 )
= ( sK61_SY1054 @ SV343 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2492]) ).
thf(2518,plain,
! [SV197: set_a,SV343: set_Product_prod_a_a,SV420: a,SV408: a] :
( ( ( ~ ( ( SV408 != SV420 ) ) )
= $true )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV408 @ SV420 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV408 ) @ SV343 ) )
= $true )
| ( ( member_a @ SV420 @ SV197 )
= $false )
| ( ( member_a @ SV408 @ SV197 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK57_SY1017 @ SV343 @ SV197 ) @ ( sK61_SY1054 @ SV343 @ SV197 ) ) @ SV343 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2493]) ).
thf(2519,plain,
! [SV197: set_a,SV343: set_Product_prod_a_a,SV421: a,SV409: a] :
( ( ( ~ ( ( SV409 != SV421 ) ) )
= $true )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV409 @ SV421 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV421 @ SV409 ) @ SV343 ) )
= $true )
| ( ( member_a @ SV421 @ SV197 )
= $false )
| ( ( member_a @ SV409 @ SV197 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1054 @ SV343 @ SV197 ) @ ( sK57_SY1017 @ SV343 @ SV197 ) ) @ SV343 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2494]) ).
thf(2520,plain,
! [SV369: set_Product_prod_a_a,SV198: set_Product_prod_a_a] :
( ( ( ( SV198
!= ( sK77_SY857 @ SV369 @ SV198 ) )
| ~ ! [SY1094: a,SY1095: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1094 @ SY1095 ) @ ( sK77_SY857 @ SV369 @ SV198 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1095 @ SY1094 ) @ ( sK77_SY857 @ SV369 @ SV198 ) ) ) )
= $false )
| ( ( SV198 = SV369 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK68_SY1051 @ SV198 @ SV369 ) @ ( sK70_SY1066 @ SV369 @ SV198 ) ) @ SV369 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2495]) ).
thf(2521,plain,
! [SV369: set_Product_prod_a_a,SV198: set_Product_prod_a_a] :
( ( ( ( SV198
!= ( sK78_SY857 @ SV369 @ SV198 ) )
| ~ ! [SY1096: a,SY1097: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1096 @ SY1097 ) @ ( sK78_SY857 @ SV369 @ SV198 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1097 @ SY1096 ) @ ( sK78_SY857 @ SV369 @ SV198 ) ) ) )
= $false )
| ( ( SV198 = SV369 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK70_SY1066 @ SV369 @ SV198 ) @ ( sK68_SY1051 @ SV198 @ SV369 ) ) @ SV369 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2496]) ).
thf(2522,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK74_SY1022 @ SV204 @ SV347 ) @ ( sK76_SY1093 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( ~ ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 )
| ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2497]) ).
thf(2523,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 )
| ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) )
= $false )
| ( ( member_a @ ( sK76_SY1093 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2498]) ).
thf(2524,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 )
| ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK73_SY1022 @ SV204 @ SV347 ) @ ( sK75_SY1092 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2499]) ).
thf(2525,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 ) )
= $false )
| ( ( member_a @ ( sK75_SY1092 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2500]) ).
thf(2526,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) )
= $false )
| ( ( member_a @ ( sK75_SY1092 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2500]) ).
thf(2527,plain,
! [SV154: set_Product_prod_a_a,SV320: set_Pr1948701895od_a_a,SV416: product_prod_a_a,SV397: product_prod_a_a] :
( ( ( SV397 = SV416 )
= $true )
| ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV397 @ SV416 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV416 @ SV397 ) @ SV320 ) )
= $true )
| ( ( member449909584od_a_a @ SV416 @ SV154 )
= $false )
| ( ( member449909584od_a_a @ SV397 @ SV154 )
= $false )
| ( ( member449909584od_a_a @ ( sK59_SY1053 @ SV320 @ SV154 ) @ SV154 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2502]) ).
thf(2528,plain,
! [SV154: set_Product_prod_a_a,SV320: set_Pr1948701895od_a_a,SV422: product_prod_a_a,SV412: product_prod_a_a] :
( ( ( ~ ( ( SV412 != SV422 ) ) )
= $true )
| ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV412 @ SV422 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV422 @ SV412 ) @ SV320 ) )
= $true )
| ( ( member449909584od_a_a @ SV422 @ SV154 )
= $false )
| ( ( member449909584od_a_a @ SV412 @ SV154 )
= $false )
| ( ( ( sK54_SY1005 @ SV320 @ SV154 )
= ( sK59_SY1053 @ SV320 @ SV154 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2503]) ).
thf(2529,plain,
! [SV154: set_Product_prod_a_a,SV320: set_Pr1948701895od_a_a,SV418: product_prod_a_a,SV404: product_prod_a_a] :
( ( ( SV404 != SV418 )
= $false )
| ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV404 @ SV418 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV418 @ SV404 ) @ SV320 ) )
= $true )
| ( ( member449909584od_a_a @ SV418 @ SV154 )
= $false )
| ( ( member449909584od_a_a @ SV404 @ SV154 )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK54_SY1005 @ SV320 @ SV154 ) @ ( sK59_SY1053 @ SV320 @ SV154 ) ) @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2504]) ).
thf(2530,plain,
! [SV154: set_Product_prod_a_a,SV320: set_Pr1948701895od_a_a,SV419: product_prod_a_a,SV405: product_prod_a_a] :
( ( ( SV405 != SV419 )
= $false )
| ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV405 @ SV419 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV419 @ SV405 ) @ SV320 ) )
= $true )
| ( ( member449909584od_a_a @ SV419 @ SV154 )
= $false )
| ( ( member449909584od_a_a @ SV405 @ SV154 )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK59_SY1053 @ SV320 @ SV154 ) @ ( sK54_SY1005 @ SV320 @ SV154 ) ) @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2505]) ).
thf(2531,plain,
! [SV60: set_Product_prod_a_a,SV174: set_Pr1948701895od_a_a,SV265: product_prod_a_a,SV333: product_prod_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
= $true )
| ( ( member449909584od_a_a @ SV265 @ SV60 )
= $false )
| ( ( member449909584od_a_a @ SV333 @ SV60 )
= $false )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2507]) ).
thf(2532,plain,
! [SV60: set_Product_prod_a_a,SV174: set_Pr1948701895od_a_a,SV333: product_prod_a_a,SV265: product_prod_a_a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
| ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
= $true )
| ( ( member449909584od_a_a @ SV265 @ SV60 )
= $false )
| ( ( member449909584od_a_a @ SV333 @ SV60 )
= $false )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2508]) ).
thf(2533,plain,
! [SV61: set_a,SV175: set_Product_prod_a_a,SV266: a,SV334: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
= $true )
| ( ( member_a @ SV266 @ SV61 )
= $false )
| ( ( member_a @ SV334 @ SV61 )
= $false )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2510]) ).
thf(2534,plain,
! [SV61: set_a,SV175: set_Product_prod_a_a,SV334: a,SV266: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
= $true )
| ( ( member_a @ SV266 @ SV61 )
= $false )
| ( ( member_a @ SV334 @ SV61 )
= $false )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2511]) ).
thf(2535,plain,
! [SV74: set_a,SV336: a,SV184: set_Product_prod_a_a,SV272: a,SV360: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV272 ) @ SV184 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV360 ) @ SV184 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV360 @ SV336 ) @ SV184 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV272 @ SV336 ) @ SV184 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV336 @ SV272 ) @ SV184 )
= $true )
| ( ( prefer719835986ence_a @ SV74 @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2513]) ).
thf(2536,plain,
! [SV197: set_a,SV343: set_Product_prod_a_a,SV417: a,SV401: a] :
( ( ( SV401 = SV417 )
= $true )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV401 @ SV417 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV417 @ SV401 ) @ SV343 ) )
= $true )
| ( ( member_a @ SV417 @ SV197 )
= $false )
| ( ( member_a @ SV401 @ SV197 )
= $false )
| ( ( member_a @ ( sK61_SY1054 @ SV343 @ SV197 ) @ SV197 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2516]) ).
thf(2537,plain,
! [SV197: set_a,SV343: set_Product_prod_a_a,SV423: a,SV413: a] :
( ( ( ~ ( ( SV413 != SV423 ) ) )
= $true )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV413 @ SV423 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV423 @ SV413 ) @ SV343 ) )
= $true )
| ( ( member_a @ SV423 @ SV197 )
= $false )
| ( ( member_a @ SV413 @ SV197 )
= $false )
| ( ( ( sK57_SY1017 @ SV343 @ SV197 )
= ( sK61_SY1054 @ SV343 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2517]) ).
thf(2538,plain,
! [SV197: set_a,SV343: set_Product_prod_a_a,SV420: a,SV408: a] :
( ( ( SV408 != SV420 )
= $false )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV408 @ SV420 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV408 ) @ SV343 ) )
= $true )
| ( ( member_a @ SV420 @ SV197 )
= $false )
| ( ( member_a @ SV408 @ SV197 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK57_SY1017 @ SV343 @ SV197 ) @ ( sK61_SY1054 @ SV343 @ SV197 ) ) @ SV343 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2518]) ).
thf(2539,plain,
! [SV197: set_a,SV343: set_Product_prod_a_a,SV421: a,SV409: a] :
( ( ( SV409 != SV421 )
= $false )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV409 @ SV421 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV421 @ SV409 ) @ SV343 ) )
= $true )
| ( ( member_a @ SV421 @ SV197 )
= $false )
| ( ( member_a @ SV409 @ SV197 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1054 @ SV343 @ SV197 ) @ ( sK57_SY1017 @ SV343 @ SV197 ) ) @ SV343 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2519]) ).
thf(2540,plain,
! [SV369: set_Product_prod_a_a,SV198: set_Product_prod_a_a] :
( ( ( SV198
!= ( sK77_SY857 @ SV369 @ SV198 ) )
= $false )
| ( ( SV198 = SV369 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK68_SY1051 @ SV198 @ SV369 ) @ ( sK70_SY1066 @ SV369 @ SV198 ) ) @ SV369 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2520]) ).
thf(2541,plain,
! [SV198: set_Product_prod_a_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ! [SY1094: a,SY1095: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1094 @ SY1095 ) @ ( sK77_SY857 @ SV369 @ SV198 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1095 @ SY1094 ) @ ( sK77_SY857 @ SV369 @ SV198 ) ) ) )
= $false )
| ( ( SV198 = SV369 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK68_SY1051 @ SV198 @ SV369 ) @ ( sK70_SY1066 @ SV369 @ SV198 ) ) @ SV369 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2520]) ).
thf(2542,plain,
! [SV369: set_Product_prod_a_a,SV198: set_Product_prod_a_a] :
( ( ( SV198
!= ( sK78_SY857 @ SV369 @ SV198 ) )
= $false )
| ( ( SV198 = SV369 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK70_SY1066 @ SV369 @ SV198 ) @ ( sK68_SY1051 @ SV198 @ SV369 ) ) @ SV369 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2521]) ).
thf(2543,plain,
! [SV198: set_Product_prod_a_a,SV369: set_Product_prod_a_a] :
( ( ( ~ ! [SY1096: a,SY1097: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1096 @ SY1097 ) @ ( sK78_SY857 @ SV369 @ SV198 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1097 @ SY1096 ) @ ( sK78_SY857 @ SV369 @ SV198 ) ) ) )
= $false )
| ( ( SV198 = SV369 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK70_SY1066 @ SV369 @ SV198 ) @ ( sK68_SY1051 @ SV198 @ SV369 ) ) @ SV369 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2521]) ).
thf(2544,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 )
| ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK74_SY1022 @ SV204 @ SV347 ) @ ( sK76_SY1093 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2522]) ).
thf(2545,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 ) )
= $false )
| ( ( member_a @ ( sK76_SY1093 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2523]) ).
thf(2546,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) )
= $false )
| ( ( member_a @ ( sK76_SY1093 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2523]) ).
thf(2547,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK73_SY1022 @ SV204 @ SV347 ) @ ( sK75_SY1092 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2524]) ).
thf(2548,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK73_SY1022 @ SV204 @ SV347 ) @ ( sK75_SY1092 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2524]) ).
thf(2549,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( prefer1292084992ence_a @ SV204 @ SV347 )
= $true )
| ( ( member_a @ ( sK75_SY1092 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2525]) ).
thf(2550,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) )
= $true )
| ( ( member_a @ ( sK75_SY1092 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2526]) ).
thf(2551,plain,
! [SV154: set_Product_prod_a_a,SV320: set_Pr1948701895od_a_a,SV416: product_prod_a_a,SV397: product_prod_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV397 @ SV416 ) @ SV320 )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV416 @ SV397 ) @ SV320 )
= $true )
| ( ( SV397 = SV416 )
= $true )
| ( ( member449909584od_a_a @ SV416 @ SV154 )
= $false )
| ( ( member449909584od_a_a @ SV397 @ SV154 )
= $false )
| ( ( member449909584od_a_a @ ( sK59_SY1053 @ SV320 @ SV154 ) @ SV154 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2527]) ).
thf(2552,plain,
! [SV154: set_Product_prod_a_a,SV320: set_Pr1948701895od_a_a,SV422: product_prod_a_a,SV412: product_prod_a_a] :
( ( ( SV412 != SV422 )
= $false )
| ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV412 @ SV422 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV422 @ SV412 ) @ SV320 ) )
= $true )
| ( ( member449909584od_a_a @ SV422 @ SV154 )
= $false )
| ( ( member449909584od_a_a @ SV412 @ SV154 )
= $false )
| ( ( ( sK54_SY1005 @ SV320 @ SV154 )
= ( sK59_SY1053 @ SV320 @ SV154 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2528]) ).
thf(2553,plain,
! [SV154: set_Product_prod_a_a,SV320: set_Pr1948701895od_a_a,SV418: product_prod_a_a,SV404: product_prod_a_a] :
( ( ( SV404 = SV418 )
= $true )
| ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV404 @ SV418 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV418 @ SV404 ) @ SV320 ) )
= $true )
| ( ( member449909584od_a_a @ SV418 @ SV154 )
= $false )
| ( ( member449909584od_a_a @ SV404 @ SV154 )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK54_SY1005 @ SV320 @ SV154 ) @ ( sK59_SY1053 @ SV320 @ SV154 ) ) @ SV320 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2529]) ).
thf(2554,plain,
! [SV154: set_Product_prod_a_a,SV320: set_Pr1948701895od_a_a,SV419: product_prod_a_a,SV405: product_prod_a_a] :
( ( ( SV405 = SV419 )
= $true )
| ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV405 @ SV419 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV419 @ SV405 ) @ SV320 ) )
= $true )
| ( ( member449909584od_a_a @ SV419 @ SV154 )
= $false )
| ( ( member449909584od_a_a @ SV405 @ SV154 )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK59_SY1053 @ SV320 @ SV154 ) @ ( sK54_SY1005 @ SV320 @ SV154 ) ) @ SV320 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2530]) ).
thf(2555,plain,
! [SV60: set_Product_prod_a_a,SV174: set_Pr1948701895od_a_a,SV333: product_prod_a_a,SV265: product_prod_a_a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
= $true )
| ( ( member449909584od_a_a @ SV265 @ SV60 )
= $false )
| ( ( member449909584od_a_a @ SV333 @ SV60 )
= $false )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2532]) ).
thf(2556,plain,
! [SV60: set_Product_prod_a_a,SV174: set_Pr1948701895od_a_a,SV265: product_prod_a_a,SV333: product_prod_a_a] :
( ( ( ~ ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
= $true )
| ( ( member449909584od_a_a @ SV265 @ SV60 )
= $false )
| ( ( member449909584od_a_a @ SV333 @ SV60 )
= $false )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2532]) ).
thf(2557,plain,
! [SV61: set_a,SV175: set_Product_prod_a_a,SV334: a,SV266: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
= $true )
| ( ( member_a @ SV266 @ SV61 )
= $false )
| ( ( member_a @ SV334 @ SV61 )
= $false )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2534]) ).
thf(2558,plain,
! [SV61: set_a,SV175: set_Product_prod_a_a,SV266: a,SV334: a] :
( ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
= $true )
| ( ( member_a @ SV266 @ SV61 )
= $false )
| ( ( member_a @ SV334 @ SV61 )
= $false )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2534]) ).
thf(2559,plain,
! [SV197: set_a,SV343: set_Product_prod_a_a,SV417: a,SV401: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV401 @ SV417 ) @ SV343 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV417 @ SV401 ) @ SV343 )
= $true )
| ( ( SV401 = SV417 )
= $true )
| ( ( member_a @ SV417 @ SV197 )
= $false )
| ( ( member_a @ SV401 @ SV197 )
= $false )
| ( ( member_a @ ( sK61_SY1054 @ SV343 @ SV197 ) @ SV197 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2536]) ).
thf(2560,plain,
! [SV197: set_a,SV343: set_Product_prod_a_a,SV423: a,SV413: a] :
( ( ( SV413 != SV423 )
= $false )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV413 @ SV423 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV423 @ SV413 ) @ SV343 ) )
= $true )
| ( ( member_a @ SV423 @ SV197 )
= $false )
| ( ( member_a @ SV413 @ SV197 )
= $false )
| ( ( ( sK57_SY1017 @ SV343 @ SV197 )
= ( sK61_SY1054 @ SV343 @ SV197 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2537]) ).
thf(2561,plain,
! [SV197: set_a,SV343: set_Product_prod_a_a,SV420: a,SV408: a] :
( ( ( SV408 = SV420 )
= $true )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV408 @ SV420 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV408 ) @ SV343 ) )
= $true )
| ( ( member_a @ SV420 @ SV197 )
= $false )
| ( ( member_a @ SV408 @ SV197 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK57_SY1017 @ SV343 @ SV197 ) @ ( sK61_SY1054 @ SV343 @ SV197 ) ) @ SV343 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2538]) ).
thf(2562,plain,
! [SV197: set_a,SV343: set_Product_prod_a_a,SV421: a,SV409: a] :
( ( ( SV409 = SV421 )
= $true )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV409 @ SV421 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV421 @ SV409 ) @ SV343 ) )
= $true )
| ( ( member_a @ SV421 @ SV197 )
= $false )
| ( ( member_a @ SV409 @ SV197 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1054 @ SV343 @ SV197 ) @ ( sK57_SY1017 @ SV343 @ SV197 ) ) @ SV343 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2539]) ).
thf(2563,plain,
! [SV369: set_Product_prod_a_a,SV198: set_Product_prod_a_a] :
( ( ( SV198
= ( sK77_SY857 @ SV369 @ SV198 ) )
= $true )
| ( ( SV198 = SV369 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK68_SY1051 @ SV198 @ SV369 ) @ ( sK70_SY1066 @ SV369 @ SV198 ) ) @ SV369 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2540]) ).
thf(2564,plain,
! [SV198: set_Product_prod_a_a,SV369: set_Product_prod_a_a] :
( ( ( ! [SY1094: a,SY1095: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1094 @ SY1095 ) @ ( sK77_SY857 @ SV369 @ SV198 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1095 @ SY1094 ) @ ( sK77_SY857 @ SV369 @ SV198 ) ) ) )
= $true )
| ( ( SV198 = SV369 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK68_SY1051 @ SV198 @ SV369 ) @ ( sK70_SY1066 @ SV369 @ SV198 ) ) @ SV369 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2541]) ).
thf(2565,plain,
! [SV369: set_Product_prod_a_a,SV198: set_Product_prod_a_a] :
( ( ( SV198
= ( sK78_SY857 @ SV369 @ SV198 ) )
= $true )
| ( ( SV198 = SV369 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK70_SY1066 @ SV369 @ SV198 ) @ ( sK68_SY1051 @ SV198 @ SV369 ) ) @ SV369 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2542]) ).
thf(2566,plain,
! [SV198: set_Product_prod_a_a,SV369: set_Product_prod_a_a] :
( ( ( ! [SY1096: a,SY1097: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1096 @ SY1097 ) @ ( sK78_SY857 @ SV369 @ SV198 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1097 @ SY1096 ) @ ( sK78_SY857 @ SV369 @ SV198 ) ) ) )
= $true )
| ( ( SV198 = SV369 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK70_SY1066 @ SV369 @ SV198 ) @ ( sK68_SY1051 @ SV198 @ SV369 ) ) @ SV369 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2543]) ).
thf(2567,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( ~ ( prefer1292084992ence_a @ SV204 @ SV347 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK74_SY1022 @ SV204 @ SV347 ) @ ( sK76_SY1093 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2544]) ).
thf(2568,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK74_SY1022 @ SV204 @ SV347 ) @ ( sK76_SY1093 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2544]) ).
thf(2569,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( prefer1292084992ence_a @ SV204 @ SV347 )
= $true )
| ( ( member_a @ ( sK76_SY1093 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2545]) ).
thf(2570,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) )
= $true )
| ( ( member_a @ ( sK76_SY1093 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2546]) ).
thf(2571,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( prefer1292084992ence_a @ SV204 @ SV347 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK73_SY1022 @ SV204 @ SV347 ) @ ( sK75_SY1092 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2547]) ).
thf(2572,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK73_SY1022 @ SV204 @ SV347 ) @ ( sK75_SY1092 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2548]) ).
thf(2573,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) )
= $false )
| ( ( member_a @ ( sK75_SY1092 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2550]) ).
thf(2574,plain,
! [SV154: set_Product_prod_a_a,SV320: set_Pr1948701895od_a_a,SV422: product_prod_a_a,SV412: product_prod_a_a] :
( ( ( SV412 = SV422 )
= $true )
| ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV412 @ SV422 ) @ SV320 )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV422 @ SV412 ) @ SV320 ) )
= $true )
| ( ( member449909584od_a_a @ SV422 @ SV154 )
= $false )
| ( ( member449909584od_a_a @ SV412 @ SV154 )
= $false )
| ( ( ( sK54_SY1005 @ SV320 @ SV154 )
= ( sK59_SY1053 @ SV320 @ SV154 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2552]) ).
thf(2575,plain,
! [SV154: set_Product_prod_a_a,SV320: set_Pr1948701895od_a_a,SV418: product_prod_a_a,SV404: product_prod_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV404 @ SV418 ) @ SV320 )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV418 @ SV404 ) @ SV320 )
= $true )
| ( ( SV404 = SV418 )
= $true )
| ( ( member449909584od_a_a @ SV418 @ SV154 )
= $false )
| ( ( member449909584od_a_a @ SV404 @ SV154 )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK54_SY1005 @ SV320 @ SV154 ) @ ( sK59_SY1053 @ SV320 @ SV154 ) ) @ SV320 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2553]) ).
thf(2576,plain,
! [SV154: set_Product_prod_a_a,SV320: set_Pr1948701895od_a_a,SV419: product_prod_a_a,SV405: product_prod_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV405 @ SV419 ) @ SV320 )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV419 @ SV405 ) @ SV320 )
= $true )
| ( ( SV405 = SV419 )
= $true )
| ( ( member449909584od_a_a @ SV419 @ SV154 )
= $false )
| ( ( member449909584od_a_a @ SV405 @ SV154 )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( sK59_SY1053 @ SV320 @ SV154 ) @ ( sK54_SY1005 @ SV320 @ SV154 ) ) @ SV320 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2554]) ).
thf(2577,plain,
! [SV60: set_Product_prod_a_a,SV174: set_Pr1948701895od_a_a,SV333: product_prod_a_a,SV265: product_prod_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
= $true )
| ( ( member449909584od_a_a @ SV265 @ SV60 )
= $false )
| ( ( member449909584od_a_a @ SV333 @ SV60 )
= $false )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2555]) ).
thf(2578,plain,
! [SV60: set_Product_prod_a_a,SV174: set_Pr1948701895od_a_a,SV265: product_prod_a_a,SV333: product_prod_a_a] :
( ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 ) )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
= $true )
| ( ( member449909584od_a_a @ SV265 @ SV60 )
= $false )
| ( ( member449909584od_a_a @ SV333 @ SV60 )
= $false )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2556]) ).
thf(2579,plain,
! [SV61: set_a,SV175: set_Product_prod_a_a,SV334: a,SV266: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
= $true )
| ( ( member_a @ SV266 @ SV61 )
= $false )
| ( ( member_a @ SV334 @ SV61 )
= $false )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2557]) ).
thf(2580,plain,
! [SV61: set_a,SV175: set_Product_prod_a_a,SV266: a,SV334: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
= $true )
| ( ( member_a @ SV266 @ SV61 )
= $false )
| ( ( member_a @ SV334 @ SV61 )
= $false )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2558]) ).
thf(2581,plain,
! [SV197: set_a,SV343: set_Product_prod_a_a,SV423: a,SV413: a] :
( ( ( SV413 = SV423 )
= $true )
| ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV413 @ SV423 ) @ SV343 )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV423 @ SV413 ) @ SV343 ) )
= $true )
| ( ( member_a @ SV423 @ SV197 )
= $false )
| ( ( member_a @ SV413 @ SV197 )
= $false )
| ( ( ( sK57_SY1017 @ SV343 @ SV197 )
= ( sK61_SY1054 @ SV343 @ SV197 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2560]) ).
thf(2582,plain,
! [SV197: set_a,SV343: set_Product_prod_a_a,SV420: a,SV408: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV408 @ SV420 ) @ SV343 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV420 @ SV408 ) @ SV343 )
= $true )
| ( ( SV408 = SV420 )
= $true )
| ( ( member_a @ SV420 @ SV197 )
= $false )
| ( ( member_a @ SV408 @ SV197 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK57_SY1017 @ SV343 @ SV197 ) @ ( sK61_SY1054 @ SV343 @ SV197 ) ) @ SV343 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2561]) ).
thf(2583,plain,
! [SV197: set_a,SV343: set_Product_prod_a_a,SV421: a,SV409: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV409 @ SV421 ) @ SV343 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV421 @ SV409 ) @ SV343 )
= $true )
| ( ( SV409 = SV421 )
= $true )
| ( ( member_a @ SV421 @ SV197 )
= $false )
| ( ( member_a @ SV409 @ SV197 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK61_SY1054 @ SV343 @ SV197 ) @ ( sK57_SY1017 @ SV343 @ SV197 ) ) @ SV343 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2562]) ).
thf(2584,plain,
! [SV198: set_Product_prod_a_a,SV369: set_Product_prod_a_a,SV424: a] :
( ( ( ! [SY1098: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV424 @ SY1098 ) @ ( sK77_SY857 @ SV369 @ SV198 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1098 @ SV424 ) @ ( sK77_SY857 @ SV369 @ SV198 ) ) ) )
= $true )
| ( ( SV198 = SV369 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK68_SY1051 @ SV198 @ SV369 ) @ ( sK70_SY1066 @ SV369 @ SV198 ) ) @ SV369 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2564]) ).
thf(2585,plain,
! [SV198: set_Product_prod_a_a,SV369: set_Product_prod_a_a,SV425: a] :
( ( ( ! [SY1099: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV425 @ SY1099 ) @ ( sK78_SY857 @ SV369 @ SV198 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1099 @ SV425 ) @ ( sK78_SY857 @ SV369 @ SV198 ) ) ) )
= $true )
| ( ( SV198 = SV369 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK70_SY1066 @ SV369 @ SV198 ) @ ( sK68_SY1051 @ SV198 @ SV369 ) ) @ SV369 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2566]) ).
thf(2586,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( prefer1292084992ence_a @ SV204 @ SV347 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK74_SY1022 @ SV204 @ SV347 ) @ ( sK76_SY1093 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2567]) ).
thf(2587,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK74_SY1022 @ SV204 @ SV347 ) @ ( sK76_SY1093 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2568]) ).
thf(2588,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) )
= $false )
| ( ( member_a @ ( sK76_SY1093 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2570]) ).
thf(2589,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK73_SY1022 @ SV204 @ SV347 ) @ ( sK75_SY1092 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2572]) ).
thf(2590,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) ) )
= $false )
| ( ( member_a @ ( sK75_SY1092 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2573]) ).
thf(2591,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( ~ ( order_preorder_on_a @ SV204 @ SV347 ) )
= $false )
| ( ( member_a @ ( sK75_SY1092 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2573]) ).
thf(2592,plain,
! [SV154: set_Product_prod_a_a,SV320: set_Pr1948701895od_a_a,SV422: product_prod_a_a,SV412: product_prod_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV412 @ SV422 ) @ SV320 )
= $true )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV422 @ SV412 ) @ SV320 )
= $true )
| ( ( SV412 = SV422 )
= $true )
| ( ( member449909584od_a_a @ SV422 @ SV154 )
= $false )
| ( ( member449909584od_a_a @ SV412 @ SV154 )
= $false )
| ( ( ( sK54_SY1005 @ SV320 @ SV154 )
= ( sK59_SY1053 @ SV320 @ SV154 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2574]) ).
thf(2593,plain,
! [SV60: set_Product_prod_a_a,SV174: set_Pr1948701895od_a_a,SV265: product_prod_a_a,SV333: product_prod_a_a] :
( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV265 @ SV333 ) @ SV174 )
= $false )
| ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ SV333 @ SV265 ) @ SV174 )
= $true )
| ( ( member449909584od_a_a @ SV265 @ SV60 )
= $false )
| ( ( member449909584od_a_a @ SV333 @ SV60 )
= $false )
| ( ( prefer697821563od_a_a @ SV60 @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2578]) ).
thf(2594,plain,
! [SV61: set_a,SV175: set_Product_prod_a_a,SV266: a,SV334: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV266 @ SV334 ) @ SV175 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV334 @ SV266 ) @ SV175 )
= $true )
| ( ( member_a @ SV266 @ SV61 )
= $false )
| ( ( member_a @ SV334 @ SV61 )
= $false )
| ( ( prefer719835986ence_a @ SV61 @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2580]) ).
thf(2595,plain,
! [SV197: set_a,SV343: set_Product_prod_a_a,SV423: a,SV413: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV413 @ SV423 ) @ SV343 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV423 @ SV413 ) @ SV343 )
= $true )
| ( ( SV413 = SV423 )
= $true )
| ( ( member_a @ SV423 @ SV197 )
= $false )
| ( ( member_a @ SV413 @ SV197 )
= $false )
| ( ( ( sK57_SY1017 @ SV343 @ SV197 )
= ( sK61_SY1054 @ SV343 @ SV197 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2581]) ).
thf(2596,plain,
! [SV198: set_Product_prod_a_a,SV369: set_Product_prod_a_a,SV426: a,SV424: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV424 @ SV426 ) @ ( sK77_SY857 @ SV369 @ SV198 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV426 @ SV424 ) @ ( sK77_SY857 @ SV369 @ SV198 ) ) )
= $true )
| ( ( SV198 = SV369 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK68_SY1051 @ SV198 @ SV369 ) @ ( sK70_SY1066 @ SV369 @ SV198 ) ) @ SV369 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2584]) ).
thf(2597,plain,
! [SV198: set_Product_prod_a_a,SV369: set_Product_prod_a_a,SV427: a,SV425: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV425 @ SV427 ) @ ( sK78_SY857 @ SV369 @ SV198 ) )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV427 @ SV425 ) @ ( sK78_SY857 @ SV369 @ SV198 ) ) )
= $true )
| ( ( SV198 = SV369 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK70_SY1066 @ SV369 @ SV198 ) @ ( sK68_SY1051 @ SV198 @ SV369 ) ) @ SV369 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2585]) ).
thf(2598,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
| ~ ( order_preorder_on_a @ SV204 @ SV347 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK74_SY1022 @ SV204 @ SV347 ) @ ( sK76_SY1093 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2587]) ).
thf(2599,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) ) )
= $false )
| ( ( member_a @ ( sK76_SY1093 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2588]) ).
thf(2600,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( ~ ( order_preorder_on_a @ SV204 @ SV347 ) )
= $false )
| ( ( member_a @ ( sK76_SY1093 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2588]) ).
thf(2601,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK73_SY1022 @ SV204 @ SV347 ) @ ( sK75_SY1092 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2589]) ).
thf(2602,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( ~ ( order_preorder_on_a @ SV204 @ SV347 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK73_SY1022 @ SV204 @ SV347 ) @ ( sK75_SY1092 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2589]) ).
thf(2603,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) ) )
= $true )
| ( ( member_a @ ( sK75_SY1092 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2590]) ).
thf(2604,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( order_preorder_on_a @ SV204 @ SV347 )
= $true )
| ( ( member_a @ ( sK75_SY1092 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2591]) ).
thf(2605,plain,
! [SV198: set_Product_prod_a_a,SV369: set_Product_prod_a_a,SV426: a,SV424: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV424 @ SV426 ) @ ( sK77_SY857 @ SV369 @ SV198 ) ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV426 @ SV424 ) @ ( sK77_SY857 @ SV369 @ SV198 ) ) )
= $true )
| ( ( SV198 = SV369 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK68_SY1051 @ SV198 @ SV369 ) @ ( sK70_SY1066 @ SV369 @ SV198 ) ) @ SV369 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2596]) ).
thf(2606,plain,
! [SV198: set_Product_prod_a_a,SV369: set_Product_prod_a_a,SV427: a,SV425: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV425 @ SV427 ) @ ( sK78_SY857 @ SV369 @ SV198 ) ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV427 @ SV425 ) @ ( sK78_SY857 @ SV369 @ SV198 ) ) )
= $true )
| ( ( SV198 = SV369 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK70_SY1066 @ SV369 @ SV198 ) @ ( sK68_SY1051 @ SV198 @ SV369 ) ) @ SV369 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2597]) ).
thf(2607,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK74_SY1022 @ SV204 @ SV347 ) @ ( sK76_SY1093 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2598]) ).
thf(2608,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( ~ ( order_preorder_on_a @ SV204 @ SV347 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK74_SY1022 @ SV204 @ SV347 ) @ ( sK76_SY1093 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2598]) ).
thf(2609,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) ) )
= $true )
| ( ( member_a @ ( sK76_SY1093 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2599]) ).
thf(2610,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( order_preorder_on_a @ SV204 @ SV347 )
= $true )
| ( ( member_a @ ( sK76_SY1093 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2600]) ).
thf(2611,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK73_SY1022 @ SV204 @ SV347 ) @ ( sK75_SY1092 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2601]) ).
thf(2612,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( order_preorder_on_a @ SV204 @ SV347 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK73_SY1022 @ SV204 @ SV347 ) @ ( sK75_SY1092 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2602]) ).
thf(2613,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
= $false )
| ( ( member_a @ ( sK75_SY1092 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2603]) ).
thf(2614,plain,
! [SV198: set_Product_prod_a_a,SV369: set_Product_prod_a_a,SV426: a,SV424: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV424 @ SV426 ) @ ( sK77_SY857 @ SV369 @ SV198 ) )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV426 @ SV424 ) @ ( sK77_SY857 @ SV369 @ SV198 ) ) )
= $true )
| ( ( SV198 = SV369 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK68_SY1051 @ SV198 @ SV369 ) @ ( sK70_SY1066 @ SV369 @ SV198 ) ) @ SV369 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2605]) ).
thf(2615,plain,
! [SV198: set_Product_prod_a_a,SV369: set_Product_prod_a_a,SV427: a,SV425: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV425 @ SV427 ) @ ( sK78_SY857 @ SV369 @ SV198 ) )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV427 @ SV425 ) @ ( sK78_SY857 @ SV369 @ SV198 ) ) )
= $true )
| ( ( SV198 = SV369 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK70_SY1066 @ SV369 @ SV198 ) @ ( sK68_SY1051 @ SV198 @ SV369 ) ) @ SV369 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2606]) ).
thf(2616,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK74_SY1022 @ SV204 @ SV347 ) @ ( sK76_SY1093 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2607]) ).
thf(2617,plain,
! [SV347: set_Product_prod_a_a,SV204: set_a] :
( ( ( order_preorder_on_a @ SV204 @ SV347 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK74_SY1022 @ SV204 @ SV347 ) @ ( sK76_SY1093 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2608]) ).
thf(2618,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
= $false )
| ( ( member_a @ ( sK76_SY1093 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2609]) ).
thf(2619,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK73_SY1022 @ SV204 @ SV347 ) @ ( sK75_SY1092 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2611]) ).
thf(2620,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) ) )
= $false )
| ( ( member_a @ ( sK75_SY1092 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2613]) ).
thf(2621,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
= $false )
| ( ( member_a @ ( sK75_SY1092 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2613]) ).
thf(2622,plain,
! [SV198: set_Product_prod_a_a,SV369: set_Product_prod_a_a,SV424: a,SV426: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV426 @ SV424 ) @ ( sK77_SY857 @ SV369 @ SV198 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV424 @ SV426 ) @ ( sK77_SY857 @ SV369 @ SV198 ) )
= $false )
| ( ( SV198 = SV369 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK68_SY1051 @ SV198 @ SV369 ) @ ( sK70_SY1066 @ SV369 @ SV198 ) ) @ SV369 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2614]) ).
thf(2623,plain,
! [SV198: set_Product_prod_a_a,SV369: set_Product_prod_a_a,SV425: a,SV427: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV427 @ SV425 ) @ ( sK78_SY857 @ SV369 @ SV198 ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV425 @ SV427 ) @ ( sK78_SY857 @ SV369 @ SV198 ) )
= $false )
| ( ( SV198 = SV369 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK70_SY1066 @ SV369 @ SV198 ) @ ( sK68_SY1051 @ SV198 @ SV369 ) ) @ SV369 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2615]) ).
thf(2624,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) )
| ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK74_SY1022 @ SV204 @ SV347 ) @ ( sK76_SY1093 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2616]) ).
thf(2625,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) ) )
= $false )
| ( ( member_a @ ( sK76_SY1093 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2618]) ).
thf(2626,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
= $false )
| ( ( member_a @ ( sK76_SY1093 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2618]) ).
thf(2627,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK73_SY1022 @ SV204 @ SV347 ) @ ( sK75_SY1092 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2619]) ).
thf(2628,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK73_SY1022 @ SV204 @ SV347 ) @ ( sK75_SY1092 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2619]) ).
thf(2629,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) ) )
= $true )
| ( ( member_a @ ( sK75_SY1092 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2620]) ).
thf(2630,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
= $true )
| ( ( member_a @ ( sK75_SY1092 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2621]) ).
thf(2631,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK74_SY1022 @ SV204 @ SV347 ) @ ( sK76_SY1093 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2624]) ).
thf(2632,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ~ ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK74_SY1022 @ SV204 @ SV347 ) @ ( sK76_SY1093 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2624]) ).
thf(2633,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) ) )
= $true )
| ( ( member_a @ ( sK76_SY1093 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2625]) ).
thf(2634,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
= $true )
| ( ( member_a @ ( sK76_SY1093 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2626]) ).
thf(2635,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK73_SY1022 @ SV204 @ SV347 ) @ ( sK75_SY1092 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2627]) ).
thf(2636,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK73_SY1022 @ SV204 @ SV347 ) @ ( sK75_SY1092 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2628]) ).
thf(2637,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a,SV428: a] :
( ( ( ! [SY1100: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV428 @ SY1100 ) @ SV347 )
| ( member_a @ SV428 @ SV204 ) ) )
= $true )
| ( ( member_a @ ( sK75_SY1092 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2629]) ).
thf(2638,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a,SV429: a] :
( ( ( ! [SY1101: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV429 @ SY1101 ) @ SV347 )
| ( member_a @ SY1101 @ SV204 ) ) )
= $true )
| ( ( member_a @ ( sK75_SY1092 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2630]) ).
thf(2639,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ! [SY1020: a,SY1021: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1020 @ SY1021 ) @ SV347 )
| ( member_a @ SY1020 @ SV204 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK74_SY1022 @ SV204 @ SV347 ) @ ( sK76_SY1093 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2631]) ).
thf(2640,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a] :
( ( ( ! [SY1022: a,SY1023: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY1022 @ SY1023 ) @ SV347 )
| ( member_a @ SY1023 @ SV204 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK74_SY1022 @ SV204 @ SV347 ) @ ( sK76_SY1093 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2632]) ).
thf(2641,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a,SV430: a] :
( ( ( ! [SY1102: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SY1102 ) @ SV347 )
| ( member_a @ SV430 @ SV204 ) ) )
= $true )
| ( ( member_a @ ( sK76_SY1093 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2633]) ).
thf(2642,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a,SV431: a] :
( ( ( ! [SY1103: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV431 @ SY1103 ) @ SV347 )
| ( member_a @ SY1103 @ SV204 ) ) )
= $true )
| ( ( member_a @ ( sK76_SY1093 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2634]) ).
thf(2643,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a,SV432: a] :
( ( ( ! [SY1104: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV432 @ SY1104 ) @ SV347 )
| ( member_a @ SV432 @ SV204 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK73_SY1022 @ SV204 @ SV347 ) @ ( sK75_SY1092 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2635]) ).
thf(2644,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a,SV433: a] :
( ( ( ! [SY1105: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV433 @ SY1105 ) @ SV347 )
| ( member_a @ SY1105 @ SV204 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK73_SY1022 @ SV204 @ SV347 ) @ ( sK75_SY1092 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2636]) ).
thf(2645,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a,SV434: a,SV428: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV428 @ SV434 ) @ SV347 )
| ( member_a @ SV428 @ SV204 ) )
= $true )
| ( ( member_a @ ( sK75_SY1092 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2637]) ).
thf(2646,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a,SV435: a,SV429: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV429 @ SV435 ) @ SV347 )
| ( member_a @ SV435 @ SV204 ) )
= $true )
| ( ( member_a @ ( sK75_SY1092 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2638]) ).
thf(2647,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a,SV436: a] :
( ( ( ! [SY1106: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV436 @ SY1106 ) @ SV347 )
| ( member_a @ SV436 @ SV204 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK74_SY1022 @ SV204 @ SV347 ) @ ( sK76_SY1093 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2639]) ).
thf(2648,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a,SV437: a] :
( ( ( ! [SY1107: a] :
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV437 @ SY1107 ) @ SV347 )
| ( member_a @ SY1107 @ SV204 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK74_SY1022 @ SV204 @ SV347 ) @ ( sK76_SY1093 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2640]) ).
thf(2649,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a,SV438: a,SV430: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV438 ) @ SV347 )
| ( member_a @ SV430 @ SV204 ) )
= $true )
| ( ( member_a @ ( sK76_SY1093 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2641]) ).
thf(2650,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a,SV439: a,SV431: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV431 @ SV439 ) @ SV347 )
| ( member_a @ SV439 @ SV204 ) )
= $true )
| ( ( member_a @ ( sK76_SY1093 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2642]) ).
thf(2651,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a,SV440: a,SV432: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV432 @ SV440 ) @ SV347 )
| ( member_a @ SV432 @ SV204 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK73_SY1022 @ SV204 @ SV347 ) @ ( sK75_SY1092 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2643]) ).
thf(2652,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a,SV441: a,SV433: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV433 @ SV441 ) @ SV347 )
| ( member_a @ SV441 @ SV204 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK73_SY1022 @ SV204 @ SV347 ) @ ( sK75_SY1092 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2644]) ).
thf(2653,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a,SV434: a,SV428: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV428 @ SV434 ) @ SV347 ) )
= $true )
| ( ( member_a @ SV428 @ SV204 )
= $true )
| ( ( member_a @ ( sK75_SY1092 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2645]) ).
thf(2654,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a,SV435: a,SV429: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV429 @ SV435 ) @ SV347 ) )
= $true )
| ( ( member_a @ SV435 @ SV204 )
= $true )
| ( ( member_a @ ( sK75_SY1092 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2646]) ).
thf(2655,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a,SV442: a,SV436: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV436 @ SV442 ) @ SV347 )
| ( member_a @ SV436 @ SV204 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK74_SY1022 @ SV204 @ SV347 ) @ ( sK76_SY1093 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2647]) ).
thf(2656,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a,SV443: a,SV437: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV437 @ SV443 ) @ SV347 )
| ( member_a @ SV443 @ SV204 ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK74_SY1022 @ SV204 @ SV347 ) @ ( sK76_SY1093 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2648]) ).
thf(2657,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a,SV438: a,SV430: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV438 ) @ SV347 ) )
= $true )
| ( ( member_a @ SV430 @ SV204 )
= $true )
| ( ( member_a @ ( sK76_SY1093 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2649]) ).
thf(2658,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a,SV439: a,SV431: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV431 @ SV439 ) @ SV347 ) )
= $true )
| ( ( member_a @ SV439 @ SV204 )
= $true )
| ( ( member_a @ ( sK76_SY1093 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2650]) ).
thf(2659,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a,SV440: a,SV432: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV432 @ SV440 ) @ SV347 ) )
= $true )
| ( ( member_a @ SV432 @ SV204 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK73_SY1022 @ SV204 @ SV347 ) @ ( sK75_SY1092 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2651]) ).
thf(2660,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a,SV441: a,SV433: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV433 @ SV441 ) @ SV347 ) )
= $true )
| ( ( member_a @ SV441 @ SV204 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK73_SY1022 @ SV204 @ SV347 ) @ ( sK75_SY1092 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2652]) ).
thf(2661,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a,SV434: a,SV428: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV428 @ SV434 ) @ SV347 )
= $false )
| ( ( member_a @ SV428 @ SV204 )
= $true )
| ( ( member_a @ ( sK75_SY1092 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2653]) ).
thf(2662,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a,SV435: a,SV429: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV429 @ SV435 ) @ SV347 )
= $false )
| ( ( member_a @ SV435 @ SV204 )
= $true )
| ( ( member_a @ ( sK75_SY1092 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2654]) ).
thf(2663,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a,SV442: a,SV436: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV436 @ SV442 ) @ SV347 ) )
= $true )
| ( ( member_a @ SV436 @ SV204 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK74_SY1022 @ SV204 @ SV347 ) @ ( sK76_SY1093 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2655]) ).
thf(2664,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a,SV443: a,SV437: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV437 @ SV443 ) @ SV347 ) )
= $true )
| ( ( member_a @ SV443 @ SV204 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK74_SY1022 @ SV204 @ SV347 ) @ ( sK76_SY1093 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2656]) ).
thf(2665,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a,SV438: a,SV430: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV430 @ SV438 ) @ SV347 )
= $false )
| ( ( member_a @ SV430 @ SV204 )
= $true )
| ( ( member_a @ ( sK76_SY1093 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2657]) ).
thf(2666,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a,SV439: a,SV431: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV431 @ SV439 ) @ SV347 )
= $false )
| ( ( member_a @ SV439 @ SV204 )
= $true )
| ( ( member_a @ ( sK76_SY1093 @ SV347 @ SV204 ) @ SV204 )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2658]) ).
thf(2667,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a,SV440: a,SV432: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV432 @ SV440 ) @ SV347 )
= $false )
| ( ( member_a @ SV432 @ SV204 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK73_SY1022 @ SV204 @ SV347 ) @ ( sK75_SY1092 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2659]) ).
thf(2668,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a,SV441: a,SV433: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV433 @ SV441 ) @ SV347 )
= $false )
| ( ( member_a @ SV441 @ SV204 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK73_SY1022 @ SV204 @ SV347 ) @ ( sK75_SY1092 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ SV204 )
= $false )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2660]) ).
thf(2669,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a,SV442: a,SV436: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV436 @ SV442 ) @ SV347 )
= $false )
| ( ( member_a @ SV436 @ SV204 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK74_SY1022 @ SV204 @ SV347 ) @ ( sK76_SY1093 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2663]) ).
thf(2670,plain,
! [SV204: set_a,SV347: set_Product_prod_a_a,SV443: a,SV437: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV437 @ SV443 ) @ SV347 )
= $false )
| ( ( member_a @ SV443 @ SV204 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK74_SY1022 @ SV204 @ SV347 ) @ ( sK76_SY1093 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( sK71_SY1020 @ SV204 @ SV347 ) @ ( sK72_SY1075 @ SV347 @ SV204 ) ) @ SV347 )
= $true )
| ( ( order_preorder_on_a @ SV204 @ SV347 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2664]) ).
thf(2671,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[492,2670,2669,2668,2667,2666,2665,2662,2661,2623,2622,2617,2612,2610,2604,2595,2594,2593,2592,2586,2583,2582,2579,2577,2576,2575,2571,2569,2565,2563,2559,2551,2549,2535,2533,2531,2515,2514,2512,2509,2506,2501,2488,2482,2478,2468,2467,2456,2449,2448,2442,2438,2437,2427,2425,2423,2421,2418,2415,2407,2405,2398,2396,2395,2386,2347,2323,2322,2315,2300,2299,2298,2297,2295,2294,2293,2292,2291,2287,2271,2269,2261,2244,2243,2239,2237,2230,2214,2204,2186,2183,2181,2180,2171,2157,2150,2145,2144,2134,2129,2124,2115,2109,2105,2098,2097,2094,2090,2089,2082,2080,2068,2066,2047,2045,2035,2023,2022,2021,2020,2019,2017,2016,1978,1977,1971,1970,1964,1960,1959,1953,1943,1934,1933,1932,1931,1927,1923,1922,1919,1912,1910,1909,1908,1906,1904,1903,1901,1900,1899,1898,1897,1896,1895,1894,1893,1892,1891,1890,1889,1888,1887,1886,1885,1884,1883,1882,1881,1880,1879,1878,1877,1876,1875,1874,1873,1872,1869,1868,1866,1865,1864,1863,1858,1857,1853,1852,1848,1847,1819,1818,1815,1811,1801,1800,1793,1792,1791,1790,1789,1785,1784,1783,1782,1742,1728,1724,1721,1718,1713,1712,1701,1693,1689,1685,1684,1683,1678,1677,1676,1675,1668,1648,1647,1646,1645,1643,1639,1635,1634,1633,1632,1630,1610,1609,1608,1607,1606,1605,1604,1599,1597,1596,1588,1584,1582,1578,1577,1570,1569,1563,1521,1518,1514,1505,1494,1481,1479,1478,1471,1469,1467,1466,1462,1452,1449,1444,1425,1417,1404,1396,1379,1371,1364,1358,1346,1302,1299,1296,1288,1285,1278,1277,1276,1275,1273,1271,1270,1268,1264,1255,1242,1236,1227,1226,1223,1217,1215,1213,1211,1209,1207,1205,1203,1151,1106,1104,1102,1099,1080,1063,1057,1055,1053,1031,1002,1000,984,981,978,977,969,967,871,870,868,867,866,858,824,818,816,814,792,762,751,746,744,740,739,738,736,733,720,718,507,504,503,502,501,497,493]) ).
thf(2672,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[2671]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP152^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.16 % Computer : n017.cluster.edu
% 0.12/0.16 % Model : x86_64 x86_64
% 0.12/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.16 % Memory : 8046.5625MB
% 0.12/0.16 % OS : Linux 6.8.0-71-generic
% 0.12/0.16 % CPULimit : 300
% 0.12/0.16 % WCLimit : 300
% 0.12/0.16 % DateTime : Tue Oct 6 11:14:15 UTC 2026
% 0.12/0.17 % CPUTime :
% 0.12/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 159.73/26.87 ..
% 159.73/26.87
% 159.73/26.87 No.of.Axioms: 129
% 159.73/26.87
% 159.73/26.87 Length.of.Defs: 0
% 159.73/26.87
% 159.73/26.87 Contains.Choice.Funs: false
% 159.73/26.87 ...................................................................................
% 159.73/26.87
% 159.73/26.87 ********************************
% 159.73/26.87 * All subproblems solved! *
% 159.73/26.87 ********************************
% 159.73/26.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:129,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:2671,loop_count:0,foatp_calls:1,translation:fof_full)
% 159.73/26.87
% 159.73/26.87 %**** Beginning of derivation protocol ****
% 159.73/26.87 % SZS output start CNFRefutation
% See solution above
% 26.86/26.90
% 26.86/26.90 %**** End of derivation protocol ****
% 26.86/26.90 %**** no. of clauses in derivation: 2443 ****
% 26.86/26.90 %**** clause counter: 2671 ****
% 26.86/26.90
% 26.86/26.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:129,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:2671,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------