%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ITP154^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 10:24:23 AM UTC 2026
% Result : Theorem 8.26s 1.70s
% Output : CNFRefutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 62
% Syntax : Number of formulae : 903 ( 369 unt; 0 typ; 0 def)
% Number of atoms : 5959 (2135 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 9758 (1652 ~;1695 |; 18 &;6162 @)
% ( 0 <=>; 231 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 25 ( 24 usr)
% Number of type conns : 272 ( 272 >; 0 *; 0 +; 0 <<)
% Number of symbols : 125 ( 122 usr; 14 con; 0-4 aty)
% Number of variables : 2460 ( 130 ^;2330 !; 0 ?;2460 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_produc1083127431_set_a,type,
produc1083127431_set_a: $tType ).
thf(tp_produc1299534078_set_a,type,
produc1299534078_set_a: $tType ).
thf(tp_produc1472671646_set_a,type,
produc1472671646_set_a: $tType ).
thf(tp_produc1572603623od_a_a,type,
produc1572603623od_a_a: $tType ).
thf(tp_produc1691597095_set_a,type,
produc1691597095_set_a: $tType ).
thf(tp_produc1990712039od_a_a,type,
produc1990712039od_a_a: $tType ).
thf(tp_produc270245360od_a_a,type,
produc270245360od_a_a: $tType ).
thf(tp_produc275558334_set_a,type,
produc275558334_set_a: $tType ).
thf(tp_produc304417648_set_a,type,
produc304417648_set_a: $tType ).
thf(tp_produc376942416od_a_a,type,
produc376942416od_a_a: $tType ).
thf(tp_produc386552094_set_a,type,
produc386552094_set_a: $tType ).
thf(tp_produc398359056_set_a,type,
produc398359056_set_a: $tType ).
thf(tp_produc407913767_set_a,type,
produc407913767_set_a: $tType ).
thf(tp_produc522143687_set_a,type,
produc522143687_set_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_Pr1948701895od_a_a,type,
set_Pr1948701895od_a_a: $tType ).
thf(tp_set_Pr2045688071_set_a,type,
set_Pr2045688071_set_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_se1596668135od_a_a,type,
set_se1596668135od_a_a: $tType ).
thf(tp_set_set_a,type,
set_set_a: $tType ).
thf(tp_set_set_set_a,type,
set_set_set_a: $tType ).
thf(tp_bNF_Ca850758276_set_a,type,
bNF_Ca850758276_set_a: set_Product_prod_a_a > ( a > set_a ) > $o ).
thf(tp_bot_bo1116205875od_a_a,type,
bot_bo1116205875od_a_a: set_Pr1948701895od_a_a ).
thf(tp_bot_bo1264989578_set_a,type,
bot_bo1264989578_set_a: set_set_set_a ).
thf(tp_bot_bo1293121322_a_a_o,type,
bot_bo1293121322_a_a_o: product_prod_a_a > $o ).
thf(tp_bot_bo1424703315od_a_a,type,
bot_bo1424703315od_a_a: set_se1596668135od_a_a ).
thf(tp_bot_bo1519632275_set_a,type,
bot_bo1519632275_set_a: produc1691597095_set_a ).
thf(tp_bot_bo2131659635od_a_a,type,
bot_bo2131659635od_a_a: set_Product_prod_a_a ).
thf(tp_bot_bo671027059_set_a,type,
bot_bo671027059_set_a: set_Pr2045688071_set_a ).
thf(tp_bot_bot_a_o,type,
bot_bot_a_o: a > $o ).
thf(tp_bot_bot_set_a,type,
bot_bot_set_a: set_a ).
thf(tp_bot_bot_set_set_a,type,
bot_bot_set_set_a: set_set_a ).
thf(tp_carrier,type,
carrier: set_a ).
thf(tp_collec1635618130od_a_a,type,
collec1635618130od_a_a: ( produc1572603623od_a_a > $o ) > set_Pr1948701895od_a_a ).
thf(tp_collec645855634od_a_a,type,
collec645855634od_a_a: ( product_prod_a_a > $o ) > set_Product_prod_a_a ).
thf(tp_collect_a,type,
collect_a: ( a > $o ) > set_a ).
thf(tp_collect_set_a,type,
collect_set_a: ( set_a > $o ) > set_set_a ).
thf(tp_finite1145471536od_a_a,type,
finite1145471536od_a_a: set_se1596668135od_a_a > $o ).
thf(tp_finite1606323175_set_a,type,
finite1606323175_set_a: set_set_set_a > $o ).
thf(tp_finite179568208od_a_a,type,
finite179568208od_a_a: set_Product_prod_a_a > $o ).
thf(tp_finite283787856_set_a,type,
finite283787856_set_a: set_Pr2045688071_set_a > $o ).
thf(tp_finite_finite_a,type,
finite_finite_a: set_a > $o ).
thf(tp_finite_finite_set_a,type,
finite_finite_set_a: set_set_a > $o ).
thf(tp_id_on_1182990020od_a_a,type,
id_on_1182990020od_a_a: set_Product_prod_a_a > set_Pr1948701895od_a_a ).
thf(tp_id_on_a,type,
id_on_a: set_a > set_Product_prod_a_a ).
thf(tp_inf_in920712437od_a_a,type,
inf_in920712437od_a_a: set_Product_prod_a_a > set_Product_prod_a_a > set_Product_prod_a_a ).
thf(tp_inf_inf_set_a,type,
inf_inf_set_a: set_a > set_a > set_a ).
thf(tp_is_empty_a,type,
is_empty_a: set_a > $o ).
thf(tp_lattic1600076923_set_a,type,
lattic1600076923_set_a: set_set_a > set_a ).
thf(tp_lattic501550101_set_a,type,
lattic501550101_set_a: set_set_a > set_a ).
thf(tp_member1838126896od_a_a,type,
member1838126896od_a_a: set_Product_prod_a_a > set_se1596668135od_a_a > $o ).
thf(tp_member1899387664od_a_a,type,
member1899387664od_a_a: produc1990712039od_a_a > set_Pr1295299783od_a_a > $o ).
thf(tp_member2057358096od_a_a,type,
member2057358096od_a_a: produc1572603623od_a_a > set_Pr1948701895od_a_a > $o ).
thf(tp_member449909584od_a_a,type,
member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
thf(tp_member593450832_set_a,type,
member593450832_set_a: produc1691597095_set_a > set_Pr2045688071_set_a > $o ).
thf(tp_member_a,type,
member_a: a > set_a > $o ).
thf(tp_member_set_a,type,
member_set_a: set_a > set_set_a > $o ).
thf(tp_member_set_set_a,type,
member_set_set_a: set_set_a > set_set_set_a > $o ).
thf(tp_ord_le1138266544_set_a,type,
ord_le1138266544_set_a: produc398359056_set_a > produc398359056_set_a > $o ).
thf(tp_ord_le1201700711_set_a,type,
ord_le1201700711_set_a: produc522143687_set_a > produc522143687_set_a > $o ).
thf(tp_ord_le1729087294_set_a,type,
ord_le1729087294_set_a: produc1472671646_set_a > produc1472671646_set_a > $o ).
thf(tp_ord_le1762684455_set_a,type,
ord_le1762684455_set_a: produc1083127431_set_a > produc1083127431_set_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_le2039441566_set_a,type,
ord_le2039441566_set_a: produc1299534078_set_a > produc1299534078_set_a > $o ).
thf(tp_ord_le2095302494_set_a,type,
ord_le2095302494_set_a: produc275558334_set_a > produc275558334_set_a > $o ).
thf(tp_ord_le318720350_set_a,type,
ord_le318720350_set_a: set_set_a > set_set_a > $o ).
thf(tp_ord_le456379495od_a_a,type,
ord_le456379495od_a_a: set_Pr1948701895od_a_a > set_Pr1948701895od_a_a > $o ).
thf(tp_ord_le486764743_set_a,type,
ord_le486764743_set_a: produc1691597095_set_a > produc1691597095_set_a > $o ).
thf(tp_ord_le49202928od_a_a,type,
ord_le49202928od_a_a: produc376942416od_a_a > produc376942416od_a_a > $o ).
thf(tp_ord_le526661008od_a_a,type,
ord_le526661008od_a_a: produc270245360od_a_a > produc270245360od_a_a > $o ).
thf(tp_ord_le560833296_set_a,type,
ord_le560833296_set_a: produc304417648_set_a > produc304417648_set_a > $o ).
thf(tp_ord_le642967742_set_a,type,
ord_le642967742_set_a: produc386552094_set_a > produc386552094_set_a > $o ).
thf(tp_ord_le723713223_set_a,type,
ord_le723713223_set_a: produc407913767_set_a > produc407913767_set_a > $o ).
thf(tp_ord_less_eq_set_a,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(tp_order_359341630od_a_a,type,
order_359341630od_a_a: set_Product_prod_a_a > set_Pr1948701895od_a_a > $o ).
thf(tp_order_491428350od_a_a,type,
order_491428350od_a_a: set_Pr1948701895od_a_a > set_Pr1295299783od_a_a > $o ).
thf(tp_order_816746613_set_a,type,
order_816746613_set_a: set_set_a > set_Pr2045688071_set_a > $o ).
thf(tp_order_Greatest_set_a,type,
order_Greatest_set_a: ( set_a > $o ) > set_a ).
thf(tp_order_preorder_on_a,type,
order_preorder_on_a: set_a > set_Product_prod_a_a > $o ).
thf(tp_order_under_a,type,
order_under_a: set_Product_prod_a_a > a > set_a ).
thf(tp_prefer1203288218_set_a,type,
prefer1203288218_set_a: set_a > set_set_a > set_Pr2045688071_set_a > set_set_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_prefer1409946857od_a_a,type,
prefer1409946857od_a_a: set_Pr1948701895od_a_a > set_Pr1295299783od_a_a > $o ).
thf(tp_prefer1498087410od_a_a,type,
prefer1498087410od_a_a: product_prod_a_a > set_Product_prod_a_a > set_Pr1948701895od_a_a > set_Product_prod_a_a ).
thf(tp_prefer161218362good_a,type,
prefer161218362good_a: a > set_a > set_Product_prod_a_a > set_a ).
thf(tp_prefer1671525929_set_a,type,
prefer1671525929_set_a: set_a > set_set_a > set_Pr2045688071_set_a > set_set_a ).
thf(tp_prefer1676310729than_a,type,
prefer1676310729than_a: a > set_a > set_Product_prod_a_a > set_a ).
thf(tp_prefer1710114912_set_a,type,
prefer1710114912_set_a: set_set_a > set_Pr2045688071_set_a > $o ).
thf(tp_prefer1828051771od_a_a,type,
prefer1828051771od_a_a: set_Pr1948701895od_a_a > set_Pr1295299783od_a_a > $o ).
thf(tp_prefer1867335523od_a_a,type,
prefer1867335523od_a_a: produc1572603623od_a_a > set_Pr1948701895od_a_a > set_Pr1295299783od_a_a > set_Pr1948701895od_a_a ).
thf(tp_prefer270414042_set_a,type,
prefer270414042_set_a: set_a > set_set_a > set_Pr2045688071_set_a > set_set_a ).
thf(tp_prefer436369274d_as_a,type,
prefer436369274d_as_a: a > set_a > set_Product_prod_a_a > set_a ).
thf(tp_prefer477097315od_a_a,type,
prefer477097315od_a_a: product_prod_a_a > set_Product_prod_a_a > set_Pr1948701895od_a_a > set_Product_prod_a_a ).
thf(tp_prefer484977842_set_a,type,
prefer484977842_set_a: set_set_a > set_Pr2045688071_set_a > $o ).
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_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_prefer74720675od_a_a,type,
prefer74720675od_a_a: product_prod_a_a > set_Product_prod_a_a > set_Pr1948701895od_a_a > set_Product_prod_a_a ).
thf(tp_prefer926864306od_a_a,type,
prefer926864306od_a_a: produc1572603623od_a_a > set_Pr1948701895od_a_a > set_Pr1295299783od_a_a > set_Pr1948701895od_a_a ).
thf(tp_produc1397177024od_a_a,type,
produc1397177024od_a_a: set_a > set_Product_prod_a_a > produc376942416od_a_a ).
thf(tp_produc1474507607od_a_a,type,
produc1474507607od_a_a: product_prod_a_a > product_prod_a_a > produc1572603623od_a_a ).
thf(tp_produc1560024183_set_a,type,
produc1560024183_set_a: set_a > set_set_a > produc1083127431_set_a ).
thf(tp_produc1599887374_set_a,type,
produc1599887374_set_a: set_Product_prod_a_a > set_set_a > produc386552094_set_a ).
thf(tp_produc1618062688od_a_a,type,
produc1618062688od_a_a: set_set_a > set_Product_prod_a_a > produc270245360od_a_a ).
thf(tp_produc1719072398_set_a,type,
produc1719072398_set_a: produc1691597095_set_a > set_a > produc1472671646_set_a ).
thf(tp_produc1928581911_set_a,type,
produc1928581911_set_a: set_a > set_a > produc1691597095_set_a ).
thf(tp_produc1935643479od_a_a,type,
produc1935643479od_a_a: produc1572603623od_a_a > produc1572603623od_a_a > produc1990712039od_a_a ).
thf(tp_produc194376366_set_a,type,
produc194376366_set_a: set_Product_prod_a_a > set_a > produc275558334_set_a ).
thf(tp_produc2102896407_set_a,type,
produc2102896407_set_a: set_set_a > set_set_a > produc407913767_set_a ).
thf(tp_produc272677600_set_a,type,
produc272677600_set_a: set_a > produc1691597095_set_a > produc304417648_set_a ).
thf(tp_produc32105911_set_a,type,
produc32105911_set_a: set_set_a > set_a > produc522143687_set_a ).
thf(tp_produc759028718_set_a,type,
produc759028718_set_a: produc1691597095_set_a > set_set_a > produc1299534078_set_a ).
thf(tp_produc760262016_set_a,type,
produc760262016_set_a: set_set_a > produc1691597095_set_a > produc398359056_set_a ).
thf(tp_product_Pair_a_a,type,
product_Pair_a_a: a > a > product_prod_a_a ).
thf(tp_refl_o1298442278od_a_a,type,
refl_o1298442278od_a_a: set_Product_prod_a_a > set_Pr1948701895od_a_a > $o ).
thf(tp_refl_on_a,type,
refl_on_a: set_a > set_Product_prod_a_a > $o ).
thf(tp_relation,type,
relation: set_Product_prod_a_a ).
thf(tp_sK10_SY273,type,
sK10_SY273: set_a > set_a > set_a > ( set_a > set_a ) > set_a ).
thf(tp_sK11_SY304,type,
sK11_SY304: set_a > set_a > set_a > ( set_a > set_a ) > set_a ).
thf(tp_sK12_SY289,type,
sK12_SY289: set_a > ( set_a > $o ) > ( set_a > $o ) > set_a ).
thf(tp_sK13_SY317,type,
sK13_SY317: ( set_a > set_a ) > set_a > set_a > set_a > set_a ).
thf(tp_sK14_SY318,type,
sK14_SY318: ( set_a > set_a ) > set_a > set_a > set_a > set_a ).
thf(tp_sK15_SY319,type,
sK15_SY319: ( set_a > set_a ) > set_a > set_a > set_a > set_a ).
thf(tp_sK16_SY320,type,
sK16_SY320: ( set_a > set_a ) > set_a > set_a > set_a > set_a ).
thf(tp_sK17_SY289,type,
sK17_SY289: set_a > ( set_a > $o ) > ( set_a > $o ) > set_a ).
thf(tp_sK1_SY266,type,
sK1_SY266: set_a > set_a > a ).
thf(tp_sK2_SY277,type,
sK2_SY277: ( a > $o ) > ( a > $o ) > a ).
thf(tp_sK3_SY242,type,
sK3_SY242: set_a > ( set_a > $o ) > set_a ).
thf(tp_sK4_SY269,type,
sK4_SY269: ( a > $o ) > ( a > $o ) > a ).
thf(tp_sK5_SY244,type,
sK5_SY244: ( set_a > $o ) > set_a > ( set_a > $o ) > set_a ).
thf(tp_sK6_SY309,type,
sK6_SY309: set_a > set_a > a ).
thf(tp_sK7_SY316,type,
sK7_SY316: set_a > set_a > a ).
thf(tp_sK8_SY249,type,
sK8_SY249: set_a > set_a > set_a > ( set_a > set_a ) > set_a ).
thf(tp_sK9_SY296,type,
sK9_SY296: set_a > set_a > set_a > ( set_a > set_a ) > set_a ).
thf(tp_sup_su615935707od_a_a,type,
sup_su615935707od_a_a: set_Product_prod_a_a > set_Product_prod_a_a > set_Product_prod_a_a ).
thf(tp_sup_sup_set_a,type,
sup_sup_set_a: set_a > set_a > set_a ).
thf(tp_total_1490170027od_a_a,type,
total_1490170027od_a_a: set_Product_prod_a_a > set_Pr1948701895od_a_a > $o ).
thf(tp_total_on_a,type,
total_on_a: set_a > set_Product_prod_a_a > $o ).
thf(tp_trans_a,type,
trans_a: set_Product_prod_a_a > $o ).
thf(tp_x,type,
x: a ).
thf(tp_y,type,
y: a ).
thf(3,axiom,
! [C2: set_a,A: set_a,B2: set_a] :
( ( ord_less_eq_set_a @ C2 @ A )
=> ( ( ord_less_eq_set_a @ C2 @ B2 )
=> ( ord_less_eq_set_a @ C2 @ ( inf_inf_set_a @ A @ B2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_Int__greatest) ).
thf(4,axiom,
! [A: set_a,B2: set_a] :
( ( ord_less_eq_set_a @ A @ B2 )
=> ( ( inf_inf_set_a @ A @ B2 )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_Int__absorb2) ).
thf(5,axiom,
! [B2: set_a,A: set_a] :
( ( ord_less_eq_set_a @ B2 @ A )
=> ( ( inf_inf_set_a @ A @ B2 )
= B2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_Int__absorb1) ).
thf(6,axiom,
! [A: set_a,B2: set_a] : ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ B2 ) @ B2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_Int__lower2) ).
thf(7,axiom,
! [A: set_a,B2: set_a] : ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ B2 ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_Int__lower1) ).
thf(8,axiom,
! [A: set_a,C2: set_a,B2: set_a,D2: set_a] :
( ( ord_less_eq_set_a @ A @ C2 )
=> ( ( ord_less_eq_set_a @ B2 @ D2 )
=> ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ B2 ) @ ( inf_inf_set_a @ C2 @ D2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_Int__mono) ).
thf(18,axiom,
! [A: set_a,B2: set_a,C2: set_a] :
( ( ord_less_eq_set_a @ ( sup_sup_set_a @ A @ B2 ) @ C2 )
= ( ( ord_less_eq_set_a @ A @ C2 )
& ( ord_less_eq_set_a @ B2 @ C2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_Un__subset__iff) ).
thf(19,axiom,
! [C2: set_a,A: set_a,B2: set_a] :
( ( ord_less_eq_set_a @ C2 @ ( inf_inf_set_a @ A @ B2 ) )
= ( ( ord_less_eq_set_a @ C2 @ A )
& ( ord_less_eq_set_a @ C2 @ B2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_Int__subset__iff) ).
thf(32,axiom,
! [P: set_a > $o,X: set_a,Q: set_a > $o] :
( ( P @ X )
=> ( ! [Y3: set_a] :
( ( P @ Y3 )
=> ( ord_less_eq_set_a @ Y3 @ X ) )
=> ( ! [X4: set_a] :
( ( P @ X4 )
=> ( ! [Y6: set_a] :
( ( P @ Y6 )
=> ( ord_less_eq_set_a @ Y6 @ X4 ) )
=> ( Q @ X4 ) ) )
=> ( Q @ ( order_Greatest_set_a @ P ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_GreatestI2__order) ).
thf(33,axiom,
! [P: set_a > $o,X: set_a] :
( ( P @ X )
=> ( ! [Y3: set_a] :
( ( P @ Y3 )
=> ( ord_less_eq_set_a @ Y3 @ X ) )
=> ( ( order_Greatest_set_a @ P )
= X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_Greatest__equality) ).
thf(55,axiom,
trans_a @ relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_transitivity) ).
thf(76,axiom,
! [A2: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_bot_Oextremum) ).
thf(77,axiom,
! [A2: set_a] :
( ( ord_less_eq_set_a @ A2 @ bot_bot_set_a )
= ( A2 = bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_bot_Oextremum__unique) ).
thf(78,axiom,
! [A2: set_a] :
( ( ord_less_eq_set_a @ A2 @ bot_bot_set_a )
=> ( A2 = bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_bot_Oextremum__uniqueI) ).
thf(85,axiom,
! [A2: set_a,F: set_a > set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A2 @ ( F @ B ) )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ! [X4: set_a,Y3: set_a] :
( ( ord_less_eq_set_a @ X4 @ Y3 )
=> ( ord_less_eq_set_a @ ( F @ X4 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_set_a @ A2 @ ( F @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_order__subst1) ).
thf(86,axiom,
! [A2: set_a,B: set_a,F: set_a > set_a,C: set_a] :
( ( ord_less_eq_set_a @ A2 @ B )
=> ( ( ord_less_eq_set_a @ ( F @ B ) @ C )
=> ( ! [X4: set_a,Y3: set_a] :
( ( ord_less_eq_set_a @ X4 @ Y3 )
=> ( ord_less_eq_set_a @ ( F @ X4 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_set_a @ ( F @ A2 ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_order__subst2) ).
thf(87,axiom,
! [A2: set_a,F: set_a > set_a,B: set_a,C: set_a] :
( ( A2
= ( F @ B ) )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ! [X4: set_a,Y3: set_a] :
( ( ord_less_eq_set_a @ X4 @ Y3 )
=> ( ord_less_eq_set_a @ ( F @ X4 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_set_a @ A2 @ ( F @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_ord__eq__le__subst) ).
thf(88,axiom,
! [A2: set_a,B: set_a,F: set_a > set_a,C: set_a] :
( ( ord_less_eq_set_a @ A2 @ B )
=> ( ( ( F @ B )
= C )
=> ( ! [X4: set_a,Y3: set_a] :
( ( ord_less_eq_set_a @ X4 @ Y3 )
=> ( ord_less_eq_set_a @ ( F @ X4 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_set_a @ ( F @ A2 ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_ord__le__eq__subst) ).
thf(89,axiom,
( ( ^ [Y4: set_a,Z2: set_a] : ( Y4 = Z2 ) )
= ( ^ [X3: set_a,Y2: set_a] :
( ( ord_less_eq_set_a @ X3 @ Y2 )
& ( ord_less_eq_set_a @ Y2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_eq__iff) ).
thf(90,axiom,
! [X: set_a,Y: set_a] :
( ( ord_less_eq_set_a @ X @ Y )
=> ( ( ord_less_eq_set_a @ Y @ X )
=> ( X = Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_antisym) ).
thf(91,axiom,
! [X: set_a,Y: set_a] :
( ( X = Y )
=> ( ord_less_eq_set_a @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_eq__refl) ).
thf(92,axiom,
! [A2: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A2 @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A2 @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_order_Otrans) ).
thf(93,axiom,
! [Y: set_a,X: set_a] :
( ( ord_less_eq_set_a @ Y @ X )
=> ( ( ord_less_eq_set_a @ X @ Y )
= ( X = Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_antisym__conv) ).
thf(94,axiom,
( ( ^ [Y4: set_a,Z2: set_a] : ( Y4 = Z2 ) )
= ( ^ [A5: set_a,B5: set_a] :
( ( ord_less_eq_set_a @ A5 @ B5 )
& ( ord_less_eq_set_a @ B5 @ A5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_order__class_Oorder_Oeq__iff) ).
thf(95,axiom,
! [A2: set_a,B: set_a,C: set_a] :
( ( A2 = B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A2 @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_ord__eq__le__trans) ).
thf(96,axiom,
! [A2: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A2 @ B )
=> ( ( B = C )
=> ( ord_less_eq_set_a @ A2 @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_ord__le__eq__trans) ).
thf(97,axiom,
! [A2: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A2 @ B )
=> ( ( ord_less_eq_set_a @ B @ A2 )
=> ( A2 = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_order__class_Oorder_Oantisym) ).
thf(98,axiom,
! [X: set_a,Y: set_a,Z: set_a] :
( ( ord_less_eq_set_a @ X @ Y )
=> ( ( ord_less_eq_set_a @ Y @ Z )
=> ( ord_less_eq_set_a @ X @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_order__trans) ).
thf(99,axiom,
! [A2: set_a] : ( ord_less_eq_set_a @ A2 @ A2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_dual__order_Orefl) ).
thf(100,axiom,
! [B: set_a,A2: set_a,C: set_a] :
( ( ord_less_eq_set_a @ B @ A2 )
=> ( ( ord_less_eq_set_a @ C @ B )
=> ( ord_less_eq_set_a @ C @ A2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_dual__order_Otrans) ).
thf(101,axiom,
( ( ^ [Y4: set_a,Z2: set_a] : ( Y4 = Z2 ) )
= ( ^ [A5: set_a,B5: set_a] :
( ( ord_less_eq_set_a @ B5 @ A5 )
& ( ord_less_eq_set_a @ A5 @ B5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_dual__order_Oeq__iff) ).
thf(102,axiom,
! [B: set_a,A2: set_a] :
( ( ord_less_eq_set_a @ B @ A2 )
=> ( ( ord_less_eq_set_a @ A2 @ B )
=> ( A2 = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_dual__order_Oantisym) ).
thf(111,axiom,
! [X: set_a] : ( ord_less_eq_set_a @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_order__refl) ).
thf(114,axiom,
! [B2: set_a,A: set_a] :
( ( finite_finite_a @ B2 )
=> ( ( ord_less_eq_set_a @ A @ B2 )
=> ( finite_finite_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_rev__finite__subset) ).
thf(115,axiom,
! [S: set_a,T2: set_a] :
( ( ord_less_eq_set_a @ S @ T2 )
=> ( ~ ( finite_finite_a @ S )
=> ~ ( finite_finite_a @ T2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_infinite__super) ).
thf(116,axiom,
! [A: set_a,B2: set_a] :
( ( ord_less_eq_set_a @ A @ B2 )
=> ( ( finite_finite_a @ B2 )
=> ( finite_finite_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_finite__subset) ).
thf(147,axiom,
! [P: a > $o,Q: a > $o] :
( ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) )
= ( ! [X3: a] :
( ( P @ X3 )
=> ( Q @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_Collect__mono__iff) ).
thf(150,axiom,
( ( ^ [Y4: set_a,Z2: set_a] : ( Y4 = Z2 ) )
= ( ^ [A3: set_a,B3: set_a] :
( ( ord_less_eq_set_a @ A3 @ B3 )
& ( ord_less_eq_set_a @ B3 @ A3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_set__eq__subset) ).
thf(153,axiom,
! [A: set_a,B2: set_a,C2: set_a] :
( ( ord_less_eq_set_a @ A @ B2 )
=> ( ( ord_less_eq_set_a @ B2 @ C2 )
=> ( ord_less_eq_set_a @ A @ C2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_subset__trans) ).
thf(156,axiom,
! [P: a > $o,Q: a > $o] :
( ! [X4: a] :
( ( P @ X4 )
=> ( Q @ X4 ) )
=> ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_Collect__mono) ).
thf(159,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_subset__refl) ).
thf(162,axiom,
( ord_less_eq_set_a
= ( ^ [A3: set_a,B3: set_a] :
! [T: a] :
( ( member_a @ T @ A3 )
=> ( member_a @ T @ B3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_subset__iff) ).
thf(166,axiom,
! [A: set_a,B2: set_a] :
( ( A = B2 )
=> ( ord_less_eq_set_a @ B2 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_equalityD2) ).
thf(169,axiom,
! [A: set_a,B2: set_a] :
( ( A = B2 )
=> ( ord_less_eq_set_a @ A @ B2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_equalityD1) ).
thf(172,axiom,
( ord_less_eq_set_a
= ( ^ [A3: set_a,B3: set_a] :
! [X3: a] :
( ( member_a @ X3 @ A3 )
=> ( member_a @ X3 @ B3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_subset__eq) ).
thf(176,axiom,
! [A: set_a,B2: set_a] :
( ( A = B2 )
=> ~ ( ( ord_less_eq_set_a @ A @ B2 )
=> ~ ( ord_less_eq_set_a @ B2 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_equalityE) ).
thf(179,axiom,
! [A: set_a,B2: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B2 )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_subsetD) ).
thf(183,axiom,
! [A: set_a,B2: set_a,X: a] :
( ( ord_less_eq_set_a @ A @ B2 )
=> ( ( member_a @ X @ A )
=> ( member_a @ X @ B2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_in__mono) ).
thf(211,axiom,
! [A: set_a,B2: set_a] :
( ( ord_less_eq_set_a @ A @ B2 )
=> ( ( ord_less_eq_set_a @ B2 @ A )
=> ( A = B2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_subset__antisym) ).
thf(214,axiom,
! [A: set_a,B2: set_a] :
( ! [X4: a] :
( ( member_a @ X4 @ A )
=> ( member_a @ X4 @ B2 ) )
=> ( ord_less_eq_set_a @ A @ B2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_subsetI) ).
thf(262,axiom,
! [A: set_a] :
( ( ord_less_eq_set_a @ A @ bot_bot_set_a )
= ( A = bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_subset__empty) ).
thf(265,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_empty__subsetI) ).
thf(271,axiom,
! [Carrier: set_a,Relation: set_Product_prod_a_a,Y: a,X: a] :
( ( prefer719835986ence_a @ Carrier @ Relation )
=> ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ Y @ Carrier @ Relation ) @ ( prefer1676310729than_a @ X @ Carrier @ Relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X @ Carrier @ Relation ) @ ( prefer1676310729than_a @ Y @ Carrier @ Relation ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_rational__preference_Onbt__nest) ).
thf(342,axiom,
refl_on_a @ carrier @ relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_reflexivity) ).
thf(344,axiom,
total_on_a @ carrier @ relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_total) ).
thf(348,axiom,
order_preorder_on_a @ carrier @ relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_trans__refl) ).
thf(349,axiom,
prefer1292084992ence_a @ carrier @ relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_preference__axioms) ).
thf(350,axiom,
finite_finite_a @ carrier,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_assms_I1_J) ).
thf(351,axiom,
! [Y: a,X: a] :
( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ Y @ carrier @ relation ) @ ( prefer1676310729than_a @ X @ carrier @ relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X @ carrier @ relation ) @ ( prefer1676310729than_a @ Y @ carrier @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_nbt__nest) ).
thf(352,axiom,
prefer719835986ence_a @ carrier @ relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_rational__preference__axioms) ).
thf(353,axiom,
member_a @ x @ carrier,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_assms_I2_J) ).
thf(355,conjecture,
( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ x @ carrier @ relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ x @ carrier @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(356,negated_conjecture,
( ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ x @ carrier @ relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ x @ carrier @ relation ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[355]) ).
thf(357,plain,
( ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ x @ carrier @ relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ x @ carrier @ relation ) ) )
= $false ),
inference(unfold_def,[status(thm)],[356]) ).
thf(358,plain,
( ( ! [C2: set_a,A: set_a,B2: set_a] :
( ( ord_less_eq_set_a @ C2 @ A )
=> ( ( ord_less_eq_set_a @ C2 @ B2 )
=> ( ord_less_eq_set_a @ C2 @ ( inf_inf_set_a @ A @ B2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(359,plain,
( ( ! [A: set_a,B2: set_a] :
( ( ord_less_eq_set_a @ A @ B2 )
=> ( ( inf_inf_set_a @ A @ B2 )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(360,plain,
( ( ! [B2: set_a,A: set_a] :
( ( ord_less_eq_set_a @ B2 @ A )
=> ( ( inf_inf_set_a @ A @ B2 )
= B2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(361,plain,
( ( ! [A: set_a,B2: set_a] : ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ B2 ) @ B2 ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(362,plain,
( ( ! [A: set_a,B2: set_a] : ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ B2 ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(363,plain,
( ( ! [A: set_a,C2: set_a,B2: set_a,D2: set_a] :
( ( ord_less_eq_set_a @ A @ C2 )
=> ( ( ord_less_eq_set_a @ B2 @ D2 )
=> ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ B2 ) @ ( inf_inf_set_a @ C2 @ D2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(364,plain,
( ( ! [A: set_a,B2: set_a,C2: set_a] :
( ( ord_less_eq_set_a @ ( sup_sup_set_a @ A @ B2 ) @ C2 )
= ( ( ord_less_eq_set_a @ A @ C2 )
& ( ord_less_eq_set_a @ B2 @ C2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(365,plain,
( ( ! [C2: set_a,A: set_a,B2: set_a] :
( ( ord_less_eq_set_a @ C2 @ ( inf_inf_set_a @ A @ B2 ) )
= ( ( ord_less_eq_set_a @ C2 @ A )
& ( ord_less_eq_set_a @ C2 @ B2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(366,plain,
( ( ! [P: set_a > $o,X: set_a,Q: set_a > $o] :
( ( P @ X )
=> ( ! [Y3: set_a] :
( ( P @ Y3 )
=> ( ord_less_eq_set_a @ Y3 @ X ) )
=> ( ! [X4: set_a] :
( ( P @ X4 )
=> ( ! [Y6: set_a] :
( ( P @ Y6 )
=> ( ord_less_eq_set_a @ Y6 @ X4 ) )
=> ( Q @ X4 ) ) )
=> ( Q @ ( order_Greatest_set_a @ P ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(367,plain,
( ( ! [P: set_a > $o,X: set_a] :
( ( P @ X )
=> ( ! [Y3: set_a] :
( ( P @ Y3 )
=> ( ord_less_eq_set_a @ Y3 @ X ) )
=> ( ( order_Greatest_set_a @ P )
= X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(368,plain,
( ( trans_a @ relation )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(369,plain,
( ( ! [A2: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A2 ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(370,plain,
( ( ! [A2: set_a] :
( ( ord_less_eq_set_a @ A2 @ bot_bot_set_a )
= ( A2 = bot_bot_set_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(371,plain,
( ( ! [A2: set_a] :
( ( ord_less_eq_set_a @ A2 @ bot_bot_set_a )
=> ( A2 = bot_bot_set_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(372,plain,
( ( ! [A2: set_a,F: set_a > set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A2 @ ( F @ B ) )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ! [X4: set_a,Y3: set_a] :
( ( ord_less_eq_set_a @ X4 @ Y3 )
=> ( ord_less_eq_set_a @ ( F @ X4 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_set_a @ A2 @ ( F @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(373,plain,
( ( ! [A2: set_a,B: set_a,F: set_a > set_a,C: set_a] :
( ( ord_less_eq_set_a @ A2 @ B )
=> ( ( ord_less_eq_set_a @ ( F @ B ) @ C )
=> ( ! [X4: set_a,Y3: set_a] :
( ( ord_less_eq_set_a @ X4 @ Y3 )
=> ( ord_less_eq_set_a @ ( F @ X4 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_set_a @ ( F @ A2 ) @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(374,plain,
( ( ! [A2: set_a,F: set_a > set_a,B: set_a,C: set_a] :
( ( A2
= ( F @ B ) )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ! [X4: set_a,Y3: set_a] :
( ( ord_less_eq_set_a @ X4 @ Y3 )
=> ( ord_less_eq_set_a @ ( F @ X4 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_set_a @ A2 @ ( F @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(375,plain,
( ( ! [A2: set_a,B: set_a,F: set_a > set_a,C: set_a] :
( ( ord_less_eq_set_a @ A2 @ B )
=> ( ( ( F @ B )
= C )
=> ( ! [X4: set_a,Y3: set_a] :
( ( ord_less_eq_set_a @ X4 @ Y3 )
=> ( ord_less_eq_set_a @ ( F @ X4 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_set_a @ ( F @ A2 ) @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(376,plain,
( ( ( ^ [Y4: set_a,Z2: set_a] : ( Y4 = Z2 ) )
= ( ^ [X3: set_a,Y2: set_a] :
( ( ord_less_eq_set_a @ X3 @ Y2 )
& ( ord_less_eq_set_a @ Y2 @ X3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(377,plain,
( ( ! [X: set_a,Y: set_a] :
( ( ord_less_eq_set_a @ X @ Y )
=> ( ( ord_less_eq_set_a @ Y @ X )
=> ( X = Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(378,plain,
( ( ! [X: set_a,Y: set_a] :
( ( X = Y )
=> ( ord_less_eq_set_a @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(379,plain,
( ( ! [A2: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A2 @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A2 @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(380,plain,
( ( ! [Y: set_a,X: set_a] :
( ( ord_less_eq_set_a @ Y @ X )
=> ( ( ord_less_eq_set_a @ X @ Y )
= ( X = Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(381,plain,
( ( ( ^ [Y4: set_a,Z2: set_a] : ( Y4 = Z2 ) )
= ( ^ [A5: set_a,B5: set_a] :
( ( ord_less_eq_set_a @ A5 @ B5 )
& ( ord_less_eq_set_a @ B5 @ A5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(382,plain,
( ( ! [A2: set_a,B: set_a,C: set_a] :
( ( A2 = B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A2 @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(383,plain,
( ( ! [A2: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A2 @ B )
=> ( ( B = C )
=> ( ord_less_eq_set_a @ A2 @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(384,plain,
( ( ! [A2: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A2 @ B )
=> ( ( ord_less_eq_set_a @ B @ A2 )
=> ( A2 = B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(385,plain,
( ( ! [X: set_a,Y: set_a,Z: set_a] :
( ( ord_less_eq_set_a @ X @ Y )
=> ( ( ord_less_eq_set_a @ Y @ Z )
=> ( ord_less_eq_set_a @ X @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(386,plain,
( ( ! [A2: set_a] : ( ord_less_eq_set_a @ A2 @ A2 ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(387,plain,
( ( ! [B: set_a,A2: set_a,C: set_a] :
( ( ord_less_eq_set_a @ B @ A2 )
=> ( ( ord_less_eq_set_a @ C @ B )
=> ( ord_less_eq_set_a @ C @ A2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(388,plain,
( ( ( ^ [Y4: set_a,Z2: set_a] : ( Y4 = Z2 ) )
= ( ^ [A5: set_a,B5: set_a] :
( ( ord_less_eq_set_a @ B5 @ A5 )
& ( ord_less_eq_set_a @ A5 @ B5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(389,plain,
( ( ! [B: set_a,A2: set_a] :
( ( ord_less_eq_set_a @ B @ A2 )
=> ( ( ord_less_eq_set_a @ A2 @ B )
=> ( A2 = B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(390,plain,
( ( ! [X: set_a] : ( ord_less_eq_set_a @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(391,plain,
( ( ! [B2: set_a,A: set_a] :
( ( finite_finite_a @ B2 )
=> ( ( ord_less_eq_set_a @ A @ B2 )
=> ( finite_finite_a @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(392,plain,
( ( ! [S: set_a,T2: set_a] :
( ( ord_less_eq_set_a @ S @ T2 )
=> ( ~ ( finite_finite_a @ S )
=> ~ ( finite_finite_a @ T2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(393,plain,
( ( ! [A: set_a,B2: set_a] :
( ( ord_less_eq_set_a @ A @ B2 )
=> ( ( finite_finite_a @ B2 )
=> ( finite_finite_a @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(394,plain,
( ( ! [P: a > $o,Q: a > $o] :
( ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) )
= ( ! [X3: a] :
( ( P @ X3 )
=> ( Q @ X3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(395,plain,
( ( ( ^ [Y4: set_a,Z2: set_a] : ( Y4 = Z2 ) )
= ( ^ [A3: set_a,B3: set_a] :
( ( ord_less_eq_set_a @ A3 @ B3 )
& ( ord_less_eq_set_a @ B3 @ A3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(396,plain,
( ( ! [A: set_a,B2: set_a,C2: set_a] :
( ( ord_less_eq_set_a @ A @ B2 )
=> ( ( ord_less_eq_set_a @ B2 @ C2 )
=> ( ord_less_eq_set_a @ A @ C2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(397,plain,
( ( ! [P: a > $o,Q: a > $o] :
( ! [X4: a] :
( ( P @ X4 )
=> ( Q @ X4 ) )
=> ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(398,plain,
( ( ! [A: set_a] : ( ord_less_eq_set_a @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(399,plain,
( ( ord_less_eq_set_a
= ( ^ [A3: set_a,B3: set_a] :
! [T: a] :
( ( member_a @ T @ A3 )
=> ( member_a @ T @ B3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(400,plain,
( ( ! [A: set_a,B2: set_a] :
( ( A = B2 )
=> ( ord_less_eq_set_a @ B2 @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(401,plain,
( ( ! [A: set_a,B2: set_a] :
( ( A = B2 )
=> ( ord_less_eq_set_a @ A @ B2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(402,plain,
( ( ord_less_eq_set_a
= ( ^ [A3: set_a,B3: set_a] :
! [X3: a] :
( ( member_a @ X3 @ A3 )
=> ( member_a @ X3 @ B3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(403,plain,
( ( ! [A: set_a,B2: set_a] :
( ( A = B2 )
=> ~ ( ( ord_less_eq_set_a @ A @ B2 )
=> ~ ( ord_less_eq_set_a @ B2 @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(404,plain,
( ( ! [A: set_a,B2: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B2 )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[179]) ).
thf(405,plain,
( ( ! [A: set_a,B2: set_a,X: a] :
( ( ord_less_eq_set_a @ A @ B2 )
=> ( ( member_a @ X @ A )
=> ( member_a @ X @ B2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[183]) ).
thf(406,plain,
( ( ! [A: set_a,B2: set_a] :
( ( ord_less_eq_set_a @ A @ B2 )
=> ( ( ord_less_eq_set_a @ B2 @ A )
=> ( A = B2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[211]) ).
thf(407,plain,
( ( ! [A: set_a,B2: set_a] :
( ! [X4: a] :
( ( member_a @ X4 @ A )
=> ( member_a @ X4 @ B2 ) )
=> ( ord_less_eq_set_a @ A @ B2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[214]) ).
thf(408,plain,
( ( ! [A: set_a] :
( ( ord_less_eq_set_a @ A @ bot_bot_set_a )
= ( A = bot_bot_set_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[262]) ).
thf(409,plain,
( ( ! [A: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[265]) ).
thf(410,plain,
( ( ! [Carrier: set_a,Relation: set_Product_prod_a_a,Y: a,X: a] :
( ( prefer719835986ence_a @ Carrier @ Relation )
=> ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ Y @ Carrier @ Relation ) @ ( prefer1676310729than_a @ X @ Carrier @ Relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X @ Carrier @ Relation ) @ ( prefer1676310729than_a @ Y @ Carrier @ Relation ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[271]) ).
thf(411,plain,
( ( refl_on_a @ carrier @ relation )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(412,plain,
( ( total_on_a @ carrier @ relation )
= $true ),
inference(unfold_def,[status(thm)],[344]) ).
thf(413,plain,
( ( order_preorder_on_a @ carrier @ relation )
= $true ),
inference(unfold_def,[status(thm)],[348]) ).
thf(414,plain,
( ( prefer1292084992ence_a @ carrier @ relation )
= $true ),
inference(unfold_def,[status(thm)],[349]) ).
thf(415,plain,
( ( finite_finite_a @ carrier )
= $true ),
inference(unfold_def,[status(thm)],[350]) ).
thf(416,plain,
( ( ! [Y: a,X: a] :
( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ Y @ carrier @ relation ) @ ( prefer1676310729than_a @ X @ carrier @ relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X @ carrier @ relation ) @ ( prefer1676310729than_a @ Y @ carrier @ relation ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[351]) ).
thf(417,plain,
( ( prefer719835986ence_a @ carrier @ relation )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(418,plain,
( ( member_a @ x @ carrier )
= $true ),
inference(unfold_def,[status(thm)],[353]) ).
thf(419,plain,
( ( ~ ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ x @ carrier @ relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ x @ carrier @ relation ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[357]) ).
thf(420,plain,
( ( member_a @ x @ carrier )
= $true ),
inference(copy,[status(thm)],[418]) ).
thf(421,plain,
( ( prefer719835986ence_a @ carrier @ relation )
= $true ),
inference(copy,[status(thm)],[417]) ).
thf(422,plain,
( ( ! [Y: a,X: a] :
( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ Y @ carrier @ relation ) @ ( prefer1676310729than_a @ X @ carrier @ relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X @ carrier @ relation ) @ ( prefer1676310729than_a @ Y @ carrier @ relation ) ) ) )
= $true ),
inference(copy,[status(thm)],[416]) ).
thf(423,plain,
( ( finite_finite_a @ carrier )
= $true ),
inference(copy,[status(thm)],[415]) ).
thf(424,plain,
( ( prefer1292084992ence_a @ carrier @ relation )
= $true ),
inference(copy,[status(thm)],[414]) ).
thf(425,plain,
( ( order_preorder_on_a @ carrier @ relation )
= $true ),
inference(copy,[status(thm)],[413]) ).
thf(426,plain,
( ( total_on_a @ carrier @ relation )
= $true ),
inference(copy,[status(thm)],[412]) ).
thf(427,plain,
( ( refl_on_a @ carrier @ relation )
= $true ),
inference(copy,[status(thm)],[411]) ).
thf(428,plain,
( ( ! [Carrier: set_a,Relation: set_Product_prod_a_a,Y: a,X: a] :
( ( prefer719835986ence_a @ Carrier @ Relation )
=> ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ Y @ Carrier @ Relation ) @ ( prefer1676310729than_a @ X @ Carrier @ Relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X @ Carrier @ Relation ) @ ( prefer1676310729than_a @ Y @ Carrier @ Relation ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[410]) ).
thf(429,plain,
( ( ! [A: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A ) )
= $true ),
inference(copy,[status(thm)],[409]) ).
thf(430,plain,
( ( ! [A: set_a] :
( ( ord_less_eq_set_a @ A @ bot_bot_set_a )
= ( A = bot_bot_set_a ) ) )
= $true ),
inference(copy,[status(thm)],[408]) ).
thf(431,plain,
( ( ! [A: set_a,B2: set_a] :
( ! [X4: a] :
( ( member_a @ X4 @ A )
=> ( member_a @ X4 @ B2 ) )
=> ( ord_less_eq_set_a @ A @ B2 ) ) )
= $true ),
inference(copy,[status(thm)],[407]) ).
thf(432,plain,
( ( ! [A: set_a,B2: set_a] :
( ( ord_less_eq_set_a @ A @ B2 )
=> ( ( ord_less_eq_set_a @ B2 @ A )
=> ( A = B2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[406]) ).
thf(433,plain,
( ( ! [A: set_a,B2: set_a,X: a] :
( ( ord_less_eq_set_a @ A @ B2 )
=> ( ( member_a @ X @ A )
=> ( member_a @ X @ B2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[405]) ).
thf(434,plain,
( ( ! [A: set_a,B2: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B2 )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[404]) ).
thf(435,plain,
( ( ! [A: set_a,B2: set_a] :
( ( A = B2 )
=> ~ ( ( ord_less_eq_set_a @ A @ B2 )
=> ~ ( ord_less_eq_set_a @ B2 @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[403]) ).
thf(436,plain,
( ( ord_less_eq_set_a
= ( ^ [A3: set_a,B3: set_a] :
! [X3: a] :
( ( member_a @ X3 @ A3 )
=> ( member_a @ X3 @ B3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[402]) ).
thf(437,plain,
( ( ! [A: set_a,B2: set_a] :
( ( A = B2 )
=> ( ord_less_eq_set_a @ A @ B2 ) ) )
= $true ),
inference(copy,[status(thm)],[401]) ).
thf(438,plain,
( ( ! [A: set_a,B2: set_a] :
( ( A = B2 )
=> ( ord_less_eq_set_a @ B2 @ A ) ) )
= $true ),
inference(copy,[status(thm)],[400]) ).
thf(439,plain,
( ( ord_less_eq_set_a
= ( ^ [A3: set_a,B3: set_a] :
! [T: a] :
( ( member_a @ T @ A3 )
=> ( member_a @ T @ B3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[399]) ).
thf(440,plain,
( ( ! [A: set_a] : ( ord_less_eq_set_a @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[398]) ).
thf(441,plain,
( ( ! [P: a > $o,Q: a > $o] :
( ! [X4: a] :
( ( P @ X4 )
=> ( Q @ X4 ) )
=> ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) ) ) )
= $true ),
inference(copy,[status(thm)],[397]) ).
thf(442,plain,
( ( ! [A: set_a,B2: set_a,C2: set_a] :
( ( ord_less_eq_set_a @ A @ B2 )
=> ( ( ord_less_eq_set_a @ B2 @ C2 )
=> ( ord_less_eq_set_a @ A @ C2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[396]) ).
thf(443,plain,
( ( ( ^ [Y4: set_a,Z2: set_a] : ( Y4 = Z2 ) )
= ( ^ [A3: set_a,B3: set_a] :
( ( ord_less_eq_set_a @ A3 @ B3 )
& ( ord_less_eq_set_a @ B3 @ A3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[395]) ).
thf(444,plain,
( ( ! [P: a > $o,Q: a > $o] :
( ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) )
= ( ! [X3: a] :
( ( P @ X3 )
=> ( Q @ X3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[394]) ).
thf(445,plain,
( ( ! [A: set_a,B2: set_a] :
( ( ord_less_eq_set_a @ A @ B2 )
=> ( ( finite_finite_a @ B2 )
=> ( finite_finite_a @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[393]) ).
thf(446,plain,
( ( ! [S: set_a,T2: set_a] :
( ( ord_less_eq_set_a @ S @ T2 )
=> ( ~ ( finite_finite_a @ S )
=> ~ ( finite_finite_a @ T2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[392]) ).
thf(447,plain,
( ( ! [B2: set_a,A: set_a] :
( ( finite_finite_a @ B2 )
=> ( ( ord_less_eq_set_a @ A @ B2 )
=> ( finite_finite_a @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[391]) ).
thf(448,plain,
( ( ! [X: set_a] : ( ord_less_eq_set_a @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[390]) ).
thf(449,plain,
( ( ! [B: set_a,A2: set_a] :
( ( ord_less_eq_set_a @ B @ A2 )
=> ( ( ord_less_eq_set_a @ A2 @ B )
=> ( A2 = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[389]) ).
thf(450,plain,
( ( ( ^ [Y4: set_a,Z2: set_a] : ( Y4 = Z2 ) )
= ( ^ [A5: set_a,B5: set_a] :
( ( ord_less_eq_set_a @ B5 @ A5 )
& ( ord_less_eq_set_a @ A5 @ B5 ) ) ) )
= $true ),
inference(copy,[status(thm)],[388]) ).
thf(451,plain,
( ( ! [B: set_a,A2: set_a,C: set_a] :
( ( ord_less_eq_set_a @ B @ A2 )
=> ( ( ord_less_eq_set_a @ C @ B )
=> ( ord_less_eq_set_a @ C @ A2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[387]) ).
thf(452,plain,
( ( ! [A2: set_a] : ( ord_less_eq_set_a @ A2 @ A2 ) )
= $true ),
inference(copy,[status(thm)],[386]) ).
thf(453,plain,
( ( ! [X: set_a,Y: set_a,Z: set_a] :
( ( ord_less_eq_set_a @ X @ Y )
=> ( ( ord_less_eq_set_a @ Y @ Z )
=> ( ord_less_eq_set_a @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[385]) ).
thf(454,plain,
( ( ! [A2: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A2 @ B )
=> ( ( ord_less_eq_set_a @ B @ A2 )
=> ( A2 = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[384]) ).
thf(455,plain,
( ( ! [A2: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A2 @ B )
=> ( ( B = C )
=> ( ord_less_eq_set_a @ A2 @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[383]) ).
thf(456,plain,
( ( ! [A2: set_a,B: set_a,C: set_a] :
( ( A2 = B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A2 @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[382]) ).
thf(457,plain,
( ( ( ^ [Y4: set_a,Z2: set_a] : ( Y4 = Z2 ) )
= ( ^ [A5: set_a,B5: set_a] :
( ( ord_less_eq_set_a @ A5 @ B5 )
& ( ord_less_eq_set_a @ B5 @ A5 ) ) ) )
= $true ),
inference(copy,[status(thm)],[381]) ).
thf(458,plain,
( ( ! [Y: set_a,X: set_a] :
( ( ord_less_eq_set_a @ Y @ X )
=> ( ( ord_less_eq_set_a @ X @ Y )
= ( X = Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[380]) ).
thf(459,plain,
( ( ! [A2: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A2 @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A2 @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[379]) ).
thf(460,plain,
( ( ! [X: set_a,Y: set_a] :
( ( X = Y )
=> ( ord_less_eq_set_a @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[378]) ).
thf(461,plain,
( ( ! [X: set_a,Y: set_a] :
( ( ord_less_eq_set_a @ X @ Y )
=> ( ( ord_less_eq_set_a @ Y @ X )
=> ( X = Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[377]) ).
thf(462,plain,
( ( ( ^ [Y4: set_a,Z2: set_a] : ( Y4 = Z2 ) )
= ( ^ [X3: set_a,Y2: set_a] :
( ( ord_less_eq_set_a @ X3 @ Y2 )
& ( ord_less_eq_set_a @ Y2 @ X3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[376]) ).
thf(463,plain,
( ( ! [A2: set_a,B: set_a,F: set_a > set_a,C: set_a] :
( ( ord_less_eq_set_a @ A2 @ B )
=> ( ( ( F @ B )
= C )
=> ( ! [X4: set_a,Y3: set_a] :
( ( ord_less_eq_set_a @ X4 @ Y3 )
=> ( ord_less_eq_set_a @ ( F @ X4 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_set_a @ ( F @ A2 ) @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[375]) ).
thf(464,plain,
( ( ! [A2: set_a,F: set_a > set_a,B: set_a,C: set_a] :
( ( A2
= ( F @ B ) )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ! [X4: set_a,Y3: set_a] :
( ( ord_less_eq_set_a @ X4 @ Y3 )
=> ( ord_less_eq_set_a @ ( F @ X4 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_set_a @ A2 @ ( F @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[374]) ).
thf(465,plain,
( ( ! [A2: set_a,B: set_a,F: set_a > set_a,C: set_a] :
( ( ord_less_eq_set_a @ A2 @ B )
=> ( ( ord_less_eq_set_a @ ( F @ B ) @ C )
=> ( ! [X4: set_a,Y3: set_a] :
( ( ord_less_eq_set_a @ X4 @ Y3 )
=> ( ord_less_eq_set_a @ ( F @ X4 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_set_a @ ( F @ A2 ) @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[373]) ).
thf(466,plain,
( ( ! [A2: set_a,F: set_a > set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A2 @ ( F @ B ) )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ! [X4: set_a,Y3: set_a] :
( ( ord_less_eq_set_a @ X4 @ Y3 )
=> ( ord_less_eq_set_a @ ( F @ X4 ) @ ( F @ Y3 ) ) )
=> ( ord_less_eq_set_a @ A2 @ ( F @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[372]) ).
thf(467,plain,
( ( ! [A2: set_a] :
( ( ord_less_eq_set_a @ A2 @ bot_bot_set_a )
=> ( A2 = bot_bot_set_a ) ) )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(468,plain,
( ( ! [A2: set_a] :
( ( ord_less_eq_set_a @ A2 @ bot_bot_set_a )
= ( A2 = bot_bot_set_a ) ) )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(469,plain,
( ( ! [A2: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A2 ) )
= $true ),
inference(copy,[status(thm)],[369]) ).
thf(470,plain,
( ( trans_a @ relation )
= $true ),
inference(copy,[status(thm)],[368]) ).
thf(471,plain,
( ( ! [P: set_a > $o,X: set_a] :
( ( P @ X )
=> ( ! [Y3: set_a] :
( ( P @ Y3 )
=> ( ord_less_eq_set_a @ Y3 @ X ) )
=> ( ( order_Greatest_set_a @ P )
= X ) ) ) )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(472,plain,
( ( ! [P: set_a > $o,X: set_a,Q: set_a > $o] :
( ( P @ X )
=> ( ! [Y3: set_a] :
( ( P @ Y3 )
=> ( ord_less_eq_set_a @ Y3 @ X ) )
=> ( ! [X4: set_a] :
( ( P @ X4 )
=> ( ! [Y6: set_a] :
( ( P @ Y6 )
=> ( ord_less_eq_set_a @ Y6 @ X4 ) )
=> ( Q @ X4 ) ) )
=> ( Q @ ( order_Greatest_set_a @ P ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[366]) ).
thf(473,plain,
( ( ! [C2: set_a,A: set_a,B2: set_a] :
( ( ord_less_eq_set_a @ C2 @ ( inf_inf_set_a @ A @ B2 ) )
= ( ( ord_less_eq_set_a @ C2 @ A )
& ( ord_less_eq_set_a @ C2 @ B2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[365]) ).
thf(474,plain,
( ( ! [A: set_a,B2: set_a,C2: set_a] :
( ( ord_less_eq_set_a @ ( sup_sup_set_a @ A @ B2 ) @ C2 )
= ( ( ord_less_eq_set_a @ A @ C2 )
& ( ord_less_eq_set_a @ B2 @ C2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[364]) ).
thf(475,plain,
( ( ! [A: set_a,C2: set_a,B2: set_a,D2: set_a] :
( ( ord_less_eq_set_a @ A @ C2 )
=> ( ( ord_less_eq_set_a @ B2 @ D2 )
=> ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ B2 ) @ ( inf_inf_set_a @ C2 @ D2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[363]) ).
thf(476,plain,
( ( ! [A: set_a,B2: set_a] : ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ B2 ) @ A ) )
= $true ),
inference(copy,[status(thm)],[362]) ).
thf(477,plain,
( ( ! [A: set_a,B2: set_a] : ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ B2 ) @ B2 ) )
= $true ),
inference(copy,[status(thm)],[361]) ).
thf(478,plain,
( ( ! [B2: set_a,A: set_a] :
( ( ord_less_eq_set_a @ B2 @ A )
=> ( ( inf_inf_set_a @ A @ B2 )
= B2 ) ) )
= $true ),
inference(copy,[status(thm)],[360]) ).
thf(479,plain,
( ( ! [A: set_a,B2: set_a] :
( ( ord_less_eq_set_a @ A @ B2 )
=> ( ( inf_inf_set_a @ A @ B2 )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[359]) ).
thf(480,plain,
( ( ! [C2: set_a,A: set_a,B2: set_a] :
( ( ord_less_eq_set_a @ C2 @ A )
=> ( ( ord_less_eq_set_a @ C2 @ B2 )
=> ( ord_less_eq_set_a @ C2 @ ( inf_inf_set_a @ A @ B2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[358]) ).
thf(481,plain,
( ( ~ ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ x @ carrier @ relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ x @ carrier @ relation ) ) ) )
= $true ),
inference(copy,[status(thm)],[419]) ).
thf(482,plain,
( ( ! [SX0: set_a,SX1: set_a,SX2: set_a] :
( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_a @ SX2 @ SX0 )
| ( ord_less_eq_set_a @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[451]) ).
thf(483,plain,
( ( ! [SX0: set_a,SX1: set_a,SX2: set_a] :
( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ( SX1 != SX2 )
| ( ord_less_eq_set_a @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[455]) ).
thf(484,plain,
( ( ! [SX0: set_a,SX1: set_a,SX2: set_a] :
( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_a @ SX1 @ SX2 )
| ( ord_less_eq_set_a @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[442]) ).
thf(485,plain,
( ( ( ^ [SX0: set_a,SX1: set_a] : ( SX0 = SX1 ) )
= ( ^ [SX0: set_a,SX1: set_a] :
~ ( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_a @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[462]) ).
thf(486,plain,
( ( ! [SX0: set_a > $o,SX1: set_a] :
( ~ ( SX0 @ SX1 )
| ~ ! [SX2: set_a] :
( ~ ( SX0 @ SX2 )
| ( ord_less_eq_set_a @ SX2 @ SX1 ) )
| ( ( order_Greatest_set_a @ SX0 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[471]) ).
thf(487,plain,
( ( ! [SX0: set_a > $o,SX1: set_a,SX2: set_a > $o] :
( ~ ( SX0 @ SX1 )
| ~ ! [SX3: set_a] :
( ~ ( SX0 @ SX3 )
| ( ord_less_eq_set_a @ SX3 @ SX1 ) )
| ~ ! [SX3: set_a] :
( ~ ( SX0 @ SX3 )
| ~ ! [SX4: set_a] :
( ~ ( SX0 @ SX4 )
| ( ord_less_eq_set_a @ SX4 @ SX3 ) )
| ( SX2 @ SX3 ) )
| ( SX2 @ ( order_Greatest_set_a @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[472]) ).
thf(488,plain,
( ( ! [SX0: set_a] :
( ~ ( ord_less_eq_set_a @ SX0 @ bot_bot_set_a )
| ( SX0 = bot_bot_set_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[467]) ).
thf(489,plain,
( ( ! [SX0: set_a,SX1: set_a] :
( ( SX0 != SX1 )
| ( ord_less_eq_set_a @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[438]) ).
thf(490,plain,
( ( ! [SX0: set_a,SX1: set_a > set_a,SX2: set_a,SX3: set_a] :
( ~ ( ord_less_eq_set_a @ SX0 @ ( SX1 @ SX2 ) )
| ~ ( ord_less_eq_set_a @ SX2 @ SX3 )
| ~ ! [SX4: set_a,SX5: set_a] :
( ~ ( ord_less_eq_set_a @ SX4 @ SX5 )
| ( ord_less_eq_set_a @ ( SX1 @ SX4 ) @ ( SX1 @ SX5 ) ) )
| ( ord_less_eq_set_a @ SX0 @ ( SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[466]) ).
thf(491,plain,
( ( ! [SX0: set_a,SX1: set_a] :
( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( finite_finite_a @ SX1 )
| ( finite_finite_a @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[445]) ).
thf(492,plain,
( ( ! [SX0: set_a,SX1: set_a,SX2: set_a] :
( ( ord_less_eq_set_a @ SX0 @ ( inf_inf_set_a @ SX1 @ SX2 ) )
= ( ~ ( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_a @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[473]) ).
thf(493,plain,
( ( ( ^ [SX0: set_a,SX1: set_a] : ( SX0 = SX1 ) )
= ( ^ [SX0: set_a,SX1: set_a] :
~ ( ~ ( ord_less_eq_set_a @ SX1 @ SX0 )
| ~ ( ord_less_eq_set_a @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[450]) ).
thf(494,plain,
( ( ( ^ [SX0: set_a,SX1: set_a] : ( SX0 = SX1 ) )
= ( ^ [SX0: set_a,SX1: set_a] :
~ ( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_a @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[443]) ).
thf(495,plain,
( ( ord_less_eq_set_a
= ( ^ [SX0: set_a,SX1: set_a] :
! [SX2: a] :
( ~ ( member_a @ SX2 @ SX0 )
| ( member_a @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[436]) ).
thf(496,plain,
( ( ! [SX0: set_a,SX1: set_a] :
( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ( ( inf_inf_set_a @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[479]) ).
thf(497,plain,
( ( ! [SX0: set_a,SX1: set_a,SX2: set_a] :
( ( SX0 != SX1 )
| ~ ( ord_less_eq_set_a @ SX1 @ SX2 )
| ( ord_less_eq_set_a @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[456]) ).
thf(498,plain,
( ( ! [SX0: set_a,SX1: set_a] :
( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_a @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[454]) ).
thf(499,plain,
( ( ! [SX0: set_a,SX1: set_a,SX2: set_a > set_a,SX3: set_a] :
( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ( ( SX2 @ SX1 )
!= SX3 )
| ~ ! [SX4: set_a,SX5: set_a] :
( ~ ( ord_less_eq_set_a @ SX4 @ SX5 )
| ( ord_less_eq_set_a @ ( SX2 @ SX4 ) @ ( SX2 @ SX5 ) ) )
| ( ord_less_eq_set_a @ ( SX2 @ SX0 ) @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[463]) ).
thf(500,plain,
( ( ! [SX0: set_a,SX1: set_a] :
( ( SX0 != SX1 )
| ~ ( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_a @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[435]) ).
thf(501,plain,
( ( ! [SX0: set_a,SX1: set_a,SX2: set_a] :
( ( ord_less_eq_set_a @ ( sup_sup_set_a @ SX0 @ SX1 ) @ SX2 )
= ( ~ ( ~ ( ord_less_eq_set_a @ SX0 @ SX2 )
| ~ ( ord_less_eq_set_a @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[474]) ).
thf(502,plain,
( ( ! [SX0: set_a,SX1: set_a,SX2: set_a,SX3: set_a] :
( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_a @ SX2 @ SX3 )
| ( ord_less_eq_set_a @ ( inf_inf_set_a @ SX0 @ SX2 ) @ ( inf_inf_set_a @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[475]) ).
thf(503,plain,
( ( ! [SX0: set_a,SX1: set_a] :
( ~ ! [SX2: a] :
( ~ ( member_a @ SX2 @ SX0 )
| ( member_a @ SX2 @ SX1 ) )
| ( ord_less_eq_set_a @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[431]) ).
thf(504,plain,
( ( ! [SX0: set_a,SX1: set_Product_prod_a_a,SX2: a,SX3: a] :
( ~ ( prefer719835986ence_a @ SX0 @ SX1 )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SX2 @ SX0 @ SX1 ) @ ( prefer1676310729than_a @ SX3 @ SX0 @ SX1 ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SX3 @ SX0 @ SX1 ) @ ( prefer1676310729than_a @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[428]) ).
thf(505,plain,
( ( ! [SX0: set_a,SX1: set_a] :
( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ( ( inf_inf_set_a @ SX1 @ SX0 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[478]) ).
thf(506,plain,
( ( ! [SX0: a > $o,SX1: a > $o] :
( ( ord_less_eq_set_a @ ( collect_a @ SX0 ) @ ( collect_a @ SX1 ) )
= ( ! [SX2: a] :
( ~ ( SX0 @ SX2 )
| ( SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[444]) ).
thf(507,plain,
( ( ! [SX0: set_a,SX1: set_a,SX2: set_a] :
( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_a @ SX1 @ SX2 )
| ( ord_less_eq_set_a @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[453]) ).
thf(508,plain,
( ( ! [SX0: set_a,SX1: set_a > set_a,SX2: set_a,SX3: set_a] :
( ( SX0
!= ( SX1 @ SX2 ) )
| ~ ( ord_less_eq_set_a @ SX2 @ SX3 )
| ~ ! [SX4: set_a,SX5: set_a] :
( ~ ( ord_less_eq_set_a @ SX4 @ SX5 )
| ( ord_less_eq_set_a @ ( SX1 @ SX4 ) @ ( SX1 @ SX5 ) ) )
| ( ord_less_eq_set_a @ SX0 @ ( SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[464]) ).
thf(509,plain,
( ( ! [SX0: set_a,SX1: set_a] :
( ~ ( finite_finite_a @ SX0 )
| ~ ( ord_less_eq_set_a @ SX1 @ SX0 )
| ( finite_finite_a @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[447]) ).
thf(510,plain,
( ( ! [SX0: set_a,SX1: set_a] :
( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_a @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[461]) ).
thf(511,plain,
( ( ( ^ [SX0: set_a,SX1: set_a] : ( SX0 = SX1 ) )
= ( ^ [SX0: set_a,SX1: set_a] :
~ ( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_a @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[457]) ).
thf(512,plain,
( ( ! [SX0: set_a,SX1: set_a] :
( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ~ ( finite_finite_a @ SX0 )
| ~ ( finite_finite_a @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[446]) ).
thf(513,plain,
( ( ! [SX0: a > $o,SX1: a > $o] :
( ~ ! [SX2: a] :
( ~ ( SX0 @ SX2 )
| ( SX1 @ SX2 ) )
| ( ord_less_eq_set_a @ ( collect_a @ SX0 ) @ ( collect_a @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[441]) ).
thf(514,plain,
( ( ! [SX0: set_a,SX1: set_a] :
( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ( ( ord_less_eq_set_a @ SX1 @ SX0 )
= ( SX1 = SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[458]) ).
thf(515,plain,
( ( ! [SX0: set_a,SX1: set_a,SX2: set_a] :
( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_a @ SX0 @ SX2 )
| ( ord_less_eq_set_a @ SX0 @ ( inf_inf_set_a @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[480]) ).
thf(516,plain,
( ( ! [SX0: set_a,SX1: set_a] :
( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_a @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[432]) ).
thf(517,plain,
( ( ! [SX0: set_a,SX1: set_a] :
( ( SX0 != SX1 )
| ( ord_less_eq_set_a @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[460]) ).
thf(518,plain,
( ( ! [SX0: set_a,SX1: set_a,SX2: a] :
( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( member_a @ SX2 @ SX0 )
| ( member_a @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[434]) ).
thf(519,plain,
( ( ! [SX0: set_a,SX1: set_a,SX2: a] :
( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( member_a @ SX2 @ SX0 )
| ( member_a @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[433]) ).
thf(520,plain,
( ( ! [SX0: set_a,SX1: set_a] :
( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_a @ SX1 @ SX0 )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[449]) ).
thf(521,plain,
( ( ! [SX0: set_a,SX1: set_a] :
( ( SX0 != SX1 )
| ( ord_less_eq_set_a @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[437]) ).
thf(522,plain,
( ( ! [SX0: set_a,SX1: set_a,SX2: set_a > set_a,SX3: set_a] :
( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_a @ ( SX2 @ SX1 ) @ SX3 )
| ~ ! [SX4: set_a,SX5: set_a] :
( ~ ( ord_less_eq_set_a @ SX4 @ SX5 )
| ( ord_less_eq_set_a @ ( SX2 @ SX4 ) @ ( SX2 @ SX5 ) ) )
| ( ord_less_eq_set_a @ ( SX2 @ SX0 ) @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[465]) ).
thf(523,plain,
( ( ord_less_eq_set_a
= ( ^ [SX0: set_a,SX1: set_a] :
! [SX2: a] :
( ~ ( member_a @ SX2 @ SX0 )
| ( member_a @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[439]) ).
thf(524,plain,
( ( ! [SX0: set_a,SX1: set_a,SX2: set_a] :
( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_a @ SX1 @ SX2 )
| ( ord_less_eq_set_a @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[459]) ).
thf(525,plain,
! [SV1: a] :
( ( ! [SY147: a] :
( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV1 @ carrier @ relation ) @ ( prefer1676310729than_a @ SY147 @ carrier @ relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SY147 @ carrier @ relation ) @ ( prefer1676310729than_a @ SV1 @ carrier @ relation ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(526,plain,
! [SV2: set_a] :
( ( ord_less_eq_set_a @ bot_bot_set_a @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(527,plain,
! [SV3: set_a] :
( ( ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a )
= ( SV3 = bot_bot_set_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(528,plain,
! [SV4: set_a] :
( ( ord_less_eq_set_a @ SV4 @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(529,plain,
! [SV5: set_a] :
( ( ord_less_eq_set_a @ SV5 @ SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(530,plain,
! [SV6: set_a] :
( ( ord_less_eq_set_a @ SV6 @ SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(531,plain,
! [SV7: set_a] :
( ( ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a )
= ( SV7 = bot_bot_set_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(532,plain,
! [SV8: set_a] :
( ( ord_less_eq_set_a @ bot_bot_set_a @ SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(533,plain,
! [SV9: set_a] :
( ( ! [SY148: set_a] : ( ord_less_eq_set_a @ ( inf_inf_set_a @ SV9 @ SY148 ) @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[476]) ).
thf(534,plain,
! [SV10: set_a] :
( ( ! [SY149: set_a] : ( ord_less_eq_set_a @ ( inf_inf_set_a @ SV10 @ SY149 ) @ SY149 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(535,plain,
( ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ x @ carrier @ relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ x @ carrier @ relation ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[481]) ).
thf(536,plain,
! [SV11: set_a] :
( ( ! [SY150: set_a,SY151: set_a] :
( ~ ( ord_less_eq_set_a @ SV11 @ SY150 )
| ~ ( ord_less_eq_set_a @ SY151 @ SV11 )
| ( ord_less_eq_set_a @ SY151 @ SY150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(537,plain,
! [SV12: set_a] :
( ( ! [SY152: set_a,SY153: set_a] :
( ~ ( ord_less_eq_set_a @ SV12 @ SY152 )
| ( SY152 != SY153 )
| ( ord_less_eq_set_a @ SV12 @ SY153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(538,plain,
! [SV13: set_a] :
( ( ! [SY154: set_a,SY155: set_a] :
( ~ ( ord_less_eq_set_a @ SV13 @ SY154 )
| ~ ( ord_less_eq_set_a @ SY154 @ SY155 )
| ( ord_less_eq_set_a @ SV13 @ SY155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(539,plain,
( ( ! [SV14: set_a] :
( ( ^ [SY156: set_a] : ( SV14 = SY156 ) )
= ( ^ [SY157: set_a] :
~ ( ~ ( ord_less_eq_set_a @ SV14 @ SY157 )
| ~ ( ord_less_eq_set_a @ SY157 @ SV14 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[485]) ).
thf(540,plain,
( ( ( ^ [SX0: set_a,SX1: set_a] : ( SX0 = SX1 ) )
= ( ^ [SX0: set_a,SX1: set_a] :
~ ( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_a @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[485]) ).
thf(541,plain,
! [SV15: set_a > $o] :
( ( ! [SY158: set_a] :
( ~ ( SV15 @ SY158 )
| ~ ! [SY159: set_a] :
( ~ ( SV15 @ SY159 )
| ( ord_less_eq_set_a @ SY159 @ SY158 ) )
| ( ( order_Greatest_set_a @ SV15 )
= SY158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(542,plain,
! [SV16: set_a > $o] :
( ( ! [SY160: set_a,SY161: set_a > $o] :
( ~ ( SV16 @ SY160 )
| ~ ! [SY162: set_a] :
( ~ ( SV16 @ SY162 )
| ( ord_less_eq_set_a @ SY162 @ SY160 ) )
| ~ ! [SY163: set_a] :
( ~ ( SV16 @ SY163 )
| ~ ! [SY164: set_a] :
( ~ ( SV16 @ SY164 )
| ( ord_less_eq_set_a @ SY164 @ SY163 ) )
| ( SY161 @ SY163 ) )
| ( SY161 @ ( order_Greatest_set_a @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(543,plain,
! [SV17: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV17 @ bot_bot_set_a )
| ( SV17 = bot_bot_set_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(544,plain,
! [SV18: set_a] :
( ( ! [SY165: set_a] :
( ( SV18 != SY165 )
| ( ord_less_eq_set_a @ SY165 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(545,plain,
! [SV19: set_a] :
( ( ! [SY166: set_a > set_a,SY167: set_a,SY168: set_a] :
( ~ ( ord_less_eq_set_a @ SV19 @ ( SY166 @ SY167 ) )
| ~ ( ord_less_eq_set_a @ SY167 @ SY168 )
| ~ ! [SX4: set_a,SX5: set_a] :
( ~ ( ord_less_eq_set_a @ SX4 @ SX5 )
| ( ord_less_eq_set_a @ ( SY166 @ SX4 ) @ ( SY166 @ SX5 ) ) )
| ( ord_less_eq_set_a @ SV19 @ ( SY166 @ SY168 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(546,plain,
! [SV20: set_a] :
( ( ! [SY171: set_a] :
( ~ ( ord_less_eq_set_a @ SV20 @ SY171 )
| ~ ( finite_finite_a @ SY171 )
| ( finite_finite_a @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(547,plain,
! [SV21: set_a] :
( ( ! [SY172: set_a,SY173: set_a] :
( ( ord_less_eq_set_a @ SV21 @ ( inf_inf_set_a @ SY172 @ SY173 ) )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV21 @ SY172 )
| ~ ( ord_less_eq_set_a @ SV21 @ SY173 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(548,plain,
( ( ! [SV22: set_a] :
( ( ^ [SY174: set_a] : ( SV22 = SY174 ) )
= ( ^ [SY175: set_a] :
~ ( ~ ( ord_less_eq_set_a @ SY175 @ SV22 )
| ~ ( ord_less_eq_set_a @ SV22 @ SY175 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[493]) ).
thf(549,plain,
( ( ( ^ [SX0: set_a,SX1: set_a] : ( SX0 = SX1 ) )
= ( ^ [SX0: set_a,SX1: set_a] :
~ ( ~ ( ord_less_eq_set_a @ SX1 @ SX0 )
| ~ ( ord_less_eq_set_a @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[493]) ).
thf(550,plain,
( ( ! [SV23: set_a] :
( ( ^ [SY176: set_a] : ( SV23 = SY176 ) )
= ( ^ [SY177: set_a] :
~ ( ~ ( ord_less_eq_set_a @ SV23 @ SY177 )
| ~ ( ord_less_eq_set_a @ SY177 @ SV23 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[494]) ).
thf(551,plain,
( ( ( ^ [SX0: set_a,SX1: set_a] : ( SX0 = SX1 ) )
= ( ^ [SX0: set_a,SX1: set_a] :
~ ( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_a @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[494]) ).
thf(552,plain,
( ( ! [SV24: set_a] :
( ( ord_less_eq_set_a @ SV24 )
= ( ^ [SY178: set_a] :
! [SY179: a] :
( ~ ( member_a @ SY179 @ SV24 )
| ( member_a @ SY179 @ SY178 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[495]) ).
thf(553,plain,
( ( ord_less_eq_set_a
= ( ^ [SX0: set_a,SX1: set_a] :
! [SX2: a] :
( ~ ( member_a @ SX2 @ SX0 )
| ( member_a @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[495]) ).
thf(554,plain,
! [SV25: set_a] :
( ( ! [SY180: set_a] :
( ~ ( ord_less_eq_set_a @ SV25 @ SY180 )
| ( ( inf_inf_set_a @ SV25 @ SY180 )
= SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(555,plain,
! [SV26: set_a] :
( ( ! [SY181: set_a,SY182: set_a] :
( ( SV26 != SY181 )
| ~ ( ord_less_eq_set_a @ SY181 @ SY182 )
| ( ord_less_eq_set_a @ SV26 @ SY182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(556,plain,
! [SV27: set_a] :
( ( ! [SY183: set_a] :
( ~ ( ord_less_eq_set_a @ SV27 @ SY183 )
| ~ ( ord_less_eq_set_a @ SY183 @ SV27 )
| ( SV27 = SY183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(557,plain,
! [SV28: set_a] :
( ( ! [SY184: set_a,SY185: set_a > set_a,SY186: set_a] :
( ~ ( ord_less_eq_set_a @ SV28 @ SY184 )
| ( ( SY185 @ SY184 )
!= SY186 )
| ~ ! [SX4: set_a,SX5: set_a] :
( ~ ( ord_less_eq_set_a @ SX4 @ SX5 )
| ( ord_less_eq_set_a @ ( SY185 @ SX4 ) @ ( SY185 @ SX5 ) ) )
| ( ord_less_eq_set_a @ ( SY185 @ SV28 ) @ SY186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(558,plain,
! [SV29: set_a] :
( ( ! [SY189: set_a] :
( ( SV29 != SY189 )
| ~ ( ~ ( ord_less_eq_set_a @ SV29 @ SY189 )
| ~ ( ord_less_eq_set_a @ SY189 @ SV29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[500]) ).
thf(559,plain,
! [SV30: set_a] :
( ( ! [SY190: set_a,SY191: set_a] :
( ( ord_less_eq_set_a @ ( sup_sup_set_a @ SV30 @ SY190 ) @ SY191 )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV30 @ SY191 )
| ~ ( ord_less_eq_set_a @ SY190 @ SY191 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(560,plain,
! [SV31: set_a] :
( ( ! [SY192: set_a,SY193: set_a,SY194: set_a] :
( ~ ( ord_less_eq_set_a @ SV31 @ SY192 )
| ~ ( ord_less_eq_set_a @ SY193 @ SY194 )
| ( ord_less_eq_set_a @ ( inf_inf_set_a @ SV31 @ SY193 ) @ ( inf_inf_set_a @ SY192 @ SY194 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(561,plain,
! [SV32: set_a] :
( ( ! [SY195: set_a] :
( ~ ! [SY196: a] :
( ~ ( member_a @ SY196 @ SV32 )
| ( member_a @ SY196 @ SY195 ) )
| ( ord_less_eq_set_a @ SV32 @ SY195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(562,plain,
! [SV33: set_a] :
( ( ! [SY197: set_Product_prod_a_a,SY198: a,SY199: a] :
( ~ ( prefer719835986ence_a @ SV33 @ SY197 )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SY198 @ SV33 @ SY197 ) @ ( prefer1676310729than_a @ SY199 @ SV33 @ SY197 ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SY199 @ SV33 @ SY197 ) @ ( prefer1676310729than_a @ SY198 @ SV33 @ SY197 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(563,plain,
! [SV34: set_a] :
( ( ! [SY200: set_a] :
( ~ ( ord_less_eq_set_a @ SV34 @ SY200 )
| ( ( inf_inf_set_a @ SY200 @ SV34 )
= SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(564,plain,
! [SV35: a > $o] :
( ( ! [SY201: a > $o] :
( ( ord_less_eq_set_a @ ( collect_a @ SV35 ) @ ( collect_a @ SY201 ) )
= ( ! [SY202: a] :
( ~ ( SV35 @ SY202 )
| ( SY201 @ SY202 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(565,plain,
! [SV36: set_a] :
( ( ! [SY203: set_a,SY204: set_a] :
( ~ ( ord_less_eq_set_a @ SV36 @ SY203 )
| ~ ( ord_less_eq_set_a @ SY203 @ SY204 )
| ( ord_less_eq_set_a @ SV36 @ SY204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(566,plain,
! [SV37: set_a] :
( ( ! [SY205: set_a > set_a,SY206: set_a,SY207: set_a] :
( ( SV37
!= ( SY205 @ SY206 ) )
| ~ ( ord_less_eq_set_a @ SY206 @ SY207 )
| ~ ! [SX4: set_a,SX5: set_a] :
( ~ ( ord_less_eq_set_a @ SX4 @ SX5 )
| ( ord_less_eq_set_a @ ( SY205 @ SX4 ) @ ( SY205 @ SX5 ) ) )
| ( ord_less_eq_set_a @ SV37 @ ( SY205 @ SY207 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(567,plain,
! [SV38: set_a] :
( ( ! [SY210: set_a] :
( ~ ( finite_finite_a @ SV38 )
| ~ ( ord_less_eq_set_a @ SY210 @ SV38 )
| ( finite_finite_a @ SY210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(568,plain,
! [SV39: set_a] :
( ( ! [SY211: set_a] :
( ~ ( ord_less_eq_set_a @ SV39 @ SY211 )
| ~ ( ord_less_eq_set_a @ SY211 @ SV39 )
| ( SV39 = SY211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(569,plain,
( ( ! [SV40: set_a] :
( ( ^ [SY212: set_a] : ( SV40 = SY212 ) )
= ( ^ [SY213: set_a] :
~ ( ~ ( ord_less_eq_set_a @ SV40 @ SY213 )
| ~ ( ord_less_eq_set_a @ SY213 @ SV40 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[511]) ).
thf(570,plain,
( ( ( ^ [SX0: set_a,SX1: set_a] : ( SX0 = SX1 ) )
= ( ^ [SX0: set_a,SX1: set_a] :
~ ( ~ ( ord_less_eq_set_a @ SX0 @ SX1 )
| ~ ( ord_less_eq_set_a @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[511]) ).
thf(571,plain,
! [SV41: set_a] :
( ( ! [SY214: set_a] :
( ~ ( ord_less_eq_set_a @ SV41 @ SY214 )
| ~ ~ ( finite_finite_a @ SV41 )
| ~ ( finite_finite_a @ SY214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(572,plain,
! [SV42: a > $o] :
( ( ! [SY215: a > $o] :
( ~ ! [SY216: a] :
( ~ ( SV42 @ SY216 )
| ( SY215 @ SY216 ) )
| ( ord_less_eq_set_a @ ( collect_a @ SV42 ) @ ( collect_a @ SY215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(573,plain,
! [SV43: set_a] :
( ( ! [SY217: set_a] :
( ~ ( ord_less_eq_set_a @ SV43 @ SY217 )
| ( ( ord_less_eq_set_a @ SY217 @ SV43 )
= ( SY217 = SV43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(574,plain,
! [SV44: set_a] :
( ( ! [SY218: set_a,SY219: set_a] :
( ~ ( ord_less_eq_set_a @ SV44 @ SY218 )
| ~ ( ord_less_eq_set_a @ SV44 @ SY219 )
| ( ord_less_eq_set_a @ SV44 @ ( inf_inf_set_a @ SY218 @ SY219 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(575,plain,
! [SV45: set_a] :
( ( ! [SY220: set_a] :
( ~ ( ord_less_eq_set_a @ SV45 @ SY220 )
| ~ ( ord_less_eq_set_a @ SY220 @ SV45 )
| ( SV45 = SY220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(576,plain,
! [SV46: set_a] :
( ( ! [SY221: set_a] :
( ( SV46 != SY221 )
| ( ord_less_eq_set_a @ SV46 @ SY221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(577,plain,
! [SV47: set_a] :
( ( ! [SY222: set_a,SY223: a] :
( ~ ( ord_less_eq_set_a @ SV47 @ SY222 )
| ~ ( member_a @ SY223 @ SV47 )
| ( member_a @ SY223 @ SY222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(578,plain,
! [SV48: set_a] :
( ( ! [SY224: set_a,SY225: a] :
( ~ ( ord_less_eq_set_a @ SV48 @ SY224 )
| ~ ( member_a @ SY225 @ SV48 )
| ( member_a @ SY225 @ SY224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[519]) ).
thf(579,plain,
! [SV49: set_a] :
( ( ! [SY226: set_a] :
( ~ ( ord_less_eq_set_a @ SV49 @ SY226 )
| ~ ( ord_less_eq_set_a @ SY226 @ SV49 )
| ( SY226 = SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(580,plain,
! [SV50: set_a] :
( ( ! [SY227: set_a] :
( ( SV50 != SY227 )
| ( ord_less_eq_set_a @ SV50 @ SY227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(581,plain,
! [SV51: set_a] :
( ( ! [SY228: set_a,SY229: set_a > set_a,SY230: set_a] :
( ~ ( ord_less_eq_set_a @ SV51 @ SY228 )
| ~ ( ord_less_eq_set_a @ ( SY229 @ SY228 ) @ SY230 )
| ~ ! [SX4: set_a,SX5: set_a] :
( ~ ( ord_less_eq_set_a @ SX4 @ SX5 )
| ( ord_less_eq_set_a @ ( SY229 @ SX4 ) @ ( SY229 @ SX5 ) ) )
| ( ord_less_eq_set_a @ ( SY229 @ SV51 ) @ SY230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[522]) ).
thf(582,plain,
( ( ! [SV52: set_a] :
( ( ord_less_eq_set_a @ SV52 )
= ( ^ [SY233: set_a] :
! [SY234: a] :
( ~ ( member_a @ SY234 @ SV52 )
| ( member_a @ SY234 @ SY233 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[523]) ).
thf(583,plain,
( ( ord_less_eq_set_a
= ( ^ [SX0: set_a,SX1: set_a] :
! [SX2: a] :
( ~ ( member_a @ SX2 @ SX0 )
| ( member_a @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[523]) ).
thf(584,plain,
! [SV53: set_a] :
( ( ! [SY235: set_a,SY236: set_a] :
( ~ ( ord_less_eq_set_a @ SV53 @ SY235 )
| ~ ( ord_less_eq_set_a @ SY235 @ SY236 )
| ( ord_less_eq_set_a @ SV53 @ SY236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(585,plain,
! [SV54: a,SV1: a] :
( ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV1 @ carrier @ relation ) @ ( prefer1676310729than_a @ SV54 @ carrier @ relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV54 @ carrier @ relation ) @ ( prefer1676310729than_a @ SV1 @ carrier @ relation ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(586,plain,
! [SV3: set_a] :
( ( ~ ( ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a )
| ( SV3 = bot_bot_set_a ) )
| ~ ( ~ ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a )
| ( SV3 != bot_bot_set_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[527]) ).
thf(587,plain,
! [SV3: set_a] :
( ( ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a )
= ( SV3 = bot_bot_set_a ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[527]) ).
thf(588,plain,
! [SV7: set_a] :
( ( ~ ( ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a )
| ( SV7 = bot_bot_set_a ) )
| ~ ( ~ ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a )
| ( SV7 != bot_bot_set_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[531]) ).
thf(589,plain,
! [SV7: set_a] :
( ( ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a )
= ( SV7 = bot_bot_set_a ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[531]) ).
thf(590,plain,
! [SV55: set_a,SV9: set_a] :
( ( ord_less_eq_set_a @ ( inf_inf_set_a @ SV9 @ SV55 ) @ SV9 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(591,plain,
! [SV56: set_a,SV10: set_a] :
( ( ord_less_eq_set_a @ ( inf_inf_set_a @ SV10 @ SV56 ) @ SV56 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(592,plain,
( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ x @ carrier @ relation ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[535]) ).
thf(593,plain,
( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ x @ carrier @ relation ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[535]) ).
thf(594,plain,
! [SV57: set_a,SV11: set_a] :
( ( ! [SY237: set_a] :
( ~ ( ord_less_eq_set_a @ SV11 @ SV57 )
| ~ ( ord_less_eq_set_a @ SY237 @ SV11 )
| ( ord_less_eq_set_a @ SY237 @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(595,plain,
! [SV58: set_a,SV12: set_a] :
( ( ! [SY238: set_a] :
( ~ ( ord_less_eq_set_a @ SV12 @ SV58 )
| ( SV58 != SY238 )
| ( ord_less_eq_set_a @ SV12 @ SY238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(596,plain,
! [SV59: set_a,SV13: set_a] :
( ( ! [SY239: set_a] :
( ~ ( ord_less_eq_set_a @ SV13 @ SV59 )
| ~ ( ord_less_eq_set_a @ SV59 @ SY239 )
| ( ord_less_eq_set_a @ SV13 @ SY239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(597,plain,
! [SV60: set_a] :
( ( ( ^ [SY240: set_a] : ( SV60 = SY240 ) )
= ( ^ [SY241: set_a] :
~ ( ~ ( ord_less_eq_set_a @ SV60 @ SY241 )
| ~ ( ord_less_eq_set_a @ SY241 @ SV60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(598,plain,
! [SV61: set_a,SV15: set_a > $o] :
( ( ~ ( SV15 @ SV61 )
| ~ ! [SY242: set_a] :
( ~ ( SV15 @ SY242 )
| ( ord_less_eq_set_a @ SY242 @ SV61 ) )
| ( ( order_Greatest_set_a @ SV15 )
= SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(599,plain,
! [SV62: set_a,SV16: set_a > $o] :
( ( ! [SY243: set_a > $o] :
( ~ ( SV16 @ SV62 )
| ~ ! [SY244: set_a] :
( ~ ( SV16 @ SY244 )
| ( ord_less_eq_set_a @ SY244 @ SV62 ) )
| ~ ! [SY163: set_a] :
( ~ ( SV16 @ SY163 )
| ~ ! [SY164: set_a] :
( ~ ( SV16 @ SY164 )
| ( ord_less_eq_set_a @ SY164 @ SY163 ) )
| ( SY243 @ SY163 ) )
| ( SY243 @ ( order_Greatest_set_a @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(600,plain,
! [SV17: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV17 @ bot_bot_set_a ) )
= $true )
| ( ( SV17 = bot_bot_set_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[543]) ).
thf(601,plain,
! [SV63: set_a,SV18: set_a] :
( ( ( SV18 != SV63 )
| ( ord_less_eq_set_a @ SV63 @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[544]) ).
thf(602,plain,
! [SV64: set_a > set_a,SV19: set_a] :
( ( ! [SY247: set_a,SY248: set_a] :
( ~ ( ord_less_eq_set_a @ SV19 @ ( SV64 @ SY247 ) )
| ~ ( ord_less_eq_set_a @ SY247 @ SY248 )
| ~ ! [SY249: set_a,SY250: set_a] :
( ~ ( ord_less_eq_set_a @ SY249 @ SY250 )
| ( ord_less_eq_set_a @ ( SV64 @ SY249 ) @ ( SV64 @ SY250 ) ) )
| ( ord_less_eq_set_a @ SV19 @ ( SV64 @ SY248 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(603,plain,
! [SV65: set_a,SV20: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV20 @ SV65 )
| ~ ( finite_finite_a @ SV65 )
| ( finite_finite_a @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(604,plain,
! [SV66: set_a,SV21: set_a] :
( ( ! [SY251: set_a] :
( ( ord_less_eq_set_a @ SV21 @ ( inf_inf_set_a @ SV66 @ SY251 ) )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV21 @ SV66 )
| ~ ( ord_less_eq_set_a @ SV21 @ SY251 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(605,plain,
! [SV67: set_a] :
( ( ( ^ [SY252: set_a] : ( SV67 = SY252 ) )
= ( ^ [SY253: set_a] :
~ ( ~ ( ord_less_eq_set_a @ SY253 @ SV67 )
| ~ ( ord_less_eq_set_a @ SV67 @ SY253 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[548]) ).
thf(606,plain,
! [SV68: set_a] :
( ( ( ^ [SY254: set_a] : ( SV68 = SY254 ) )
= ( ^ [SY255: set_a] :
~ ( ~ ( ord_less_eq_set_a @ SV68 @ SY255 )
| ~ ( ord_less_eq_set_a @ SY255 @ SV68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(607,plain,
! [SV69: set_a] :
( ( ( ord_less_eq_set_a @ SV69 )
= ( ^ [SY256: set_a] :
! [SY257: a] :
( ~ ( member_a @ SY257 @ SV69 )
| ( member_a @ SY257 @ SY256 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[552]) ).
thf(608,plain,
! [SV70: set_a,SV25: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV25 @ SV70 )
| ( ( inf_inf_set_a @ SV25 @ SV70 )
= SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(609,plain,
! [SV71: set_a,SV26: set_a] :
( ( ! [SY258: set_a] :
( ( SV26 != SV71 )
| ~ ( ord_less_eq_set_a @ SV71 @ SY258 )
| ( ord_less_eq_set_a @ SV26 @ SY258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[555]) ).
thf(610,plain,
! [SV72: set_a,SV27: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV27 @ SV72 )
| ~ ( ord_less_eq_set_a @ SV72 @ SV27 )
| ( SV27 = SV72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(611,plain,
! [SV73: set_a,SV28: set_a] :
( ( ! [SY259: set_a > set_a,SY260: set_a] :
( ~ ( ord_less_eq_set_a @ SV28 @ SV73 )
| ( ( SY259 @ SV73 )
!= SY260 )
| ~ ! [SX4: set_a,SX5: set_a] :
( ~ ( ord_less_eq_set_a @ SX4 @ SX5 )
| ( ord_less_eq_set_a @ ( SY259 @ SX4 ) @ ( SY259 @ SX5 ) ) )
| ( ord_less_eq_set_a @ ( SY259 @ SV28 ) @ SY260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(612,plain,
! [SV74: set_a,SV29: set_a] :
( ( ( SV29 != SV74 )
| ~ ( ~ ( ord_less_eq_set_a @ SV29 @ SV74 )
| ~ ( ord_less_eq_set_a @ SV74 @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(613,plain,
! [SV75: set_a,SV30: set_a] :
( ( ! [SY263: set_a] :
( ( ord_less_eq_set_a @ ( sup_sup_set_a @ SV30 @ SV75 ) @ SY263 )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV30 @ SY263 )
| ~ ( ord_less_eq_set_a @ SV75 @ SY263 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(614,plain,
! [SV76: set_a,SV31: set_a] :
( ( ! [SY264: set_a,SY265: set_a] :
( ~ ( ord_less_eq_set_a @ SV31 @ SV76 )
| ~ ( ord_less_eq_set_a @ SY264 @ SY265 )
| ( ord_less_eq_set_a @ ( inf_inf_set_a @ SV31 @ SY264 ) @ ( inf_inf_set_a @ SV76 @ SY265 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(615,plain,
! [SV77: set_a,SV32: set_a] :
( ( ~ ! [SY266: a] :
( ~ ( member_a @ SY266 @ SV32 )
| ( member_a @ SY266 @ SV77 ) )
| ( ord_less_eq_set_a @ SV32 @ SV77 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(616,plain,
! [SV78: set_Product_prod_a_a,SV33: set_a] :
( ( ! [SY267: a,SY268: a] :
( ~ ( prefer719835986ence_a @ SV33 @ SV78 )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SY267 @ SV33 @ SV78 ) @ ( prefer1676310729than_a @ SY268 @ SV33 @ SV78 ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SY268 @ SV33 @ SV78 ) @ ( prefer1676310729than_a @ SY267 @ SV33 @ SV78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(617,plain,
! [SV79: set_a,SV34: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV34 @ SV79 )
| ( ( inf_inf_set_a @ SV79 @ SV34 )
= SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(618,plain,
! [SV80: a > $o,SV35: a > $o] :
( ( ( ord_less_eq_set_a @ ( collect_a @ SV35 ) @ ( collect_a @ SV80 ) )
= ( ! [SY269: a] :
( ~ ( SV35 @ SY269 )
| ( SV80 @ SY269 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(619,plain,
! [SV81: set_a,SV36: set_a] :
( ( ! [SY270: set_a] :
( ~ ( ord_less_eq_set_a @ SV36 @ SV81 )
| ~ ( ord_less_eq_set_a @ SV81 @ SY270 )
| ( ord_less_eq_set_a @ SV36 @ SY270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(620,plain,
! [SV82: set_a > set_a,SV37: set_a] :
( ( ! [SY271: set_a,SY272: set_a] :
( ( SV37
!= ( SV82 @ SY271 ) )
| ~ ( ord_less_eq_set_a @ SY271 @ SY272 )
| ~ ! [SY273: set_a,SY274: set_a] :
( ~ ( ord_less_eq_set_a @ SY273 @ SY274 )
| ( ord_less_eq_set_a @ ( SV82 @ SY273 ) @ ( SV82 @ SY274 ) ) )
| ( ord_less_eq_set_a @ SV37 @ ( SV82 @ SY272 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(621,plain,
! [SV83: set_a,SV38: set_a] :
( ( ~ ( finite_finite_a @ SV38 )
| ~ ( ord_less_eq_set_a @ SV83 @ SV38 )
| ( finite_finite_a @ SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(622,plain,
! [SV84: set_a,SV39: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV39 @ SV84 )
| ~ ( ord_less_eq_set_a @ SV84 @ SV39 )
| ( SV39 = SV84 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(623,plain,
! [SV85: set_a] :
( ( ( ^ [SY275: set_a] : ( SV85 = SY275 ) )
= ( ^ [SY276: set_a] :
~ ( ~ ( ord_less_eq_set_a @ SV85 @ SY276 )
| ~ ( ord_less_eq_set_a @ SY276 @ SV85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(624,plain,
! [SV86: set_a,SV41: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV41 @ SV86 )
| ~ ~ ( finite_finite_a @ SV41 )
| ~ ( finite_finite_a @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(625,plain,
! [SV87: a > $o,SV42: a > $o] :
( ( ~ ! [SY277: a] :
( ~ ( SV42 @ SY277 )
| ( SV87 @ SY277 ) )
| ( ord_less_eq_set_a @ ( collect_a @ SV42 ) @ ( collect_a @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(626,plain,
! [SV88: set_a,SV43: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV43 @ SV88 )
| ( ( ord_less_eq_set_a @ SV88 @ SV43 )
= ( SV88 = SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(627,plain,
! [SV89: set_a,SV44: set_a] :
( ( ! [SY278: set_a] :
( ~ ( ord_less_eq_set_a @ SV44 @ SV89 )
| ~ ( ord_less_eq_set_a @ SV44 @ SY278 )
| ( ord_less_eq_set_a @ SV44 @ ( inf_inf_set_a @ SV89 @ SY278 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(628,plain,
! [SV90: set_a,SV45: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV45 @ SV90 )
| ~ ( ord_less_eq_set_a @ SV90 @ SV45 )
| ( SV45 = SV90 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(629,plain,
! [SV91: set_a,SV46: set_a] :
( ( ( SV46 != SV91 )
| ( ord_less_eq_set_a @ SV46 @ SV91 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(630,plain,
! [SV92: set_a,SV47: set_a] :
( ( ! [SY279: a] :
( ~ ( ord_less_eq_set_a @ SV47 @ SV92 )
| ~ ( member_a @ SY279 @ SV47 )
| ( member_a @ SY279 @ SV92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(631,plain,
! [SV93: set_a,SV48: set_a] :
( ( ! [SY280: a] :
( ~ ( ord_less_eq_set_a @ SV48 @ SV93 )
| ~ ( member_a @ SY280 @ SV48 )
| ( member_a @ SY280 @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(632,plain,
! [SV94: set_a,SV49: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV49 @ SV94 )
| ~ ( ord_less_eq_set_a @ SV94 @ SV49 )
| ( SV94 = SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[579]) ).
thf(633,plain,
! [SV95: set_a,SV50: set_a] :
( ( ( SV50 != SV95 )
| ( ord_less_eq_set_a @ SV50 @ SV95 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(634,plain,
! [SV96: set_a,SV51: set_a] :
( ( ! [SY281: set_a > set_a,SY282: set_a] :
( ~ ( ord_less_eq_set_a @ SV51 @ SV96 )
| ~ ( ord_less_eq_set_a @ ( SY281 @ SV96 ) @ SY282 )
| ~ ! [SX4: set_a,SX5: set_a] :
( ~ ( ord_less_eq_set_a @ SX4 @ SX5 )
| ( ord_less_eq_set_a @ ( SY281 @ SX4 ) @ ( SY281 @ SX5 ) ) )
| ( ord_less_eq_set_a @ ( SY281 @ SV51 ) @ SY282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(635,plain,
! [SV97: set_a] :
( ( ( ord_less_eq_set_a @ SV97 )
= ( ^ [SY285: set_a] :
! [SY286: a] :
( ~ ( member_a @ SY286 @ SV97 )
| ( member_a @ SY286 @ SY285 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(636,plain,
! [SV98: set_a,SV53: set_a] :
( ( ! [SY287: set_a] :
( ~ ( ord_less_eq_set_a @ SV53 @ SV98 )
| ~ ( ord_less_eq_set_a @ SV98 @ SY287 )
| ( ord_less_eq_set_a @ SV53 @ SY287 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(637,plain,
! [SV54: a,SV1: a] :
( ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV1 @ carrier @ relation ) @ ( prefer1676310729than_a @ SV54 @ carrier @ relation ) )
= $true )
| ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV54 @ carrier @ relation ) @ ( prefer1676310729than_a @ SV1 @ carrier @ relation ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[585]) ).
thf(638,plain,
! [SV3: set_a] :
( ( ( ~ ( ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a )
| ( SV3 = bot_bot_set_a ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a )
| ( SV3 != bot_bot_set_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[586]) ).
thf(639,plain,
! [SV7: set_a] :
( ( ( ~ ( ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a )
| ( SV7 = bot_bot_set_a ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a )
| ( SV7 != bot_bot_set_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[588]) ).
thf(640,plain,
! [SV99: set_a,SV57: set_a,SV11: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV11 @ SV57 )
| ~ ( ord_less_eq_set_a @ SV99 @ SV11 )
| ( ord_less_eq_set_a @ SV99 @ SV57 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(641,plain,
! [SV100: set_a,SV58: set_a,SV12: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV12 @ SV58 )
| ( SV58 != SV100 )
| ( ord_less_eq_set_a @ SV12 @ SV100 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(642,plain,
! [SV101: set_a,SV59: set_a,SV13: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV13 @ SV59 )
| ~ ( ord_less_eq_set_a @ SV59 @ SV101 )
| ( ord_less_eq_set_a @ SV13 @ SV101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(643,plain,
! [SV60: set_a] :
( ( ! [SV102: set_a] :
( ( SV60 = SV102 )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV60 @ SV102 )
| ~ ( ord_less_eq_set_a @ SV102 @ SV60 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[597]) ).
thf(644,plain,
! [SV60: set_a] :
( ( ( ^ [SY240: set_a] : ( SV60 = SY240 ) )
= ( ^ [SY241: set_a] :
~ ( ~ ( ord_less_eq_set_a @ SV60 @ SY241 )
| ~ ( ord_less_eq_set_a @ SY241 @ SV60 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[597]) ).
thf(645,plain,
! [SV61: set_a,SV15: set_a > $o] :
( ( ( ~ ( SV15 @ SV61 ) )
= $true )
| ( ( ~ ! [SY242: set_a] :
( ~ ( SV15 @ SY242 )
| ( ord_less_eq_set_a @ SY242 @ SV61 ) )
| ( ( order_Greatest_set_a @ SV15 )
= SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[598]) ).
thf(646,plain,
! [SV103: set_a > $o,SV62: set_a,SV16: set_a > $o] :
( ( ~ ( SV16 @ SV62 )
| ~ ! [SY244: set_a] :
( ~ ( SV16 @ SY244 )
| ( ord_less_eq_set_a @ SY244 @ SV62 ) )
| ~ ! [SY289: set_a] :
( ~ ( SV16 @ SY289 )
| ~ ! [SY164: set_a] :
( ~ ( SV16 @ SY164 )
| ( ord_less_eq_set_a @ SY164 @ SY289 ) )
| ( SV103 @ SY289 ) )
| ( SV103 @ ( order_Greatest_set_a @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(647,plain,
! [SV17: set_a] :
( ( ( ord_less_eq_set_a @ SV17 @ bot_bot_set_a )
= $false )
| ( ( SV17 = bot_bot_set_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[600]) ).
thf(648,plain,
! [SV63: set_a,SV18: set_a] :
( ( ( SV18 != SV63 )
= $true )
| ( ( ord_less_eq_set_a @ SV63 @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[601]) ).
thf(649,plain,
! [SV104: set_a,SV64: set_a > set_a,SV19: set_a] :
( ( ! [SY291: set_a] :
( ~ ( ord_less_eq_set_a @ SV19 @ ( SV64 @ SV104 ) )
| ~ ( ord_less_eq_set_a @ SV104 @ SY291 )
| ~ ! [SY249: set_a,SY250: set_a] :
( ~ ( ord_less_eq_set_a @ SY249 @ SY250 )
| ( ord_less_eq_set_a @ ( SV64 @ SY249 ) @ ( SV64 @ SY250 ) ) )
| ( ord_less_eq_set_a @ SV19 @ ( SV64 @ SY291 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(650,plain,
! [SV65: set_a,SV20: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV20 @ SV65 ) )
= $true )
| ( ( ~ ( finite_finite_a @ SV65 )
| ( finite_finite_a @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[603]) ).
thf(651,plain,
! [SV105: set_a,SV66: set_a,SV21: set_a] :
( ( ( ord_less_eq_set_a @ SV21 @ ( inf_inf_set_a @ SV66 @ SV105 ) )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV21 @ SV66 )
| ~ ( ord_less_eq_set_a @ SV21 @ SV105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(652,plain,
! [SV67: set_a] :
( ( ! [SV106: set_a] :
( ( SV67 = SV106 )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV106 @ SV67 )
| ~ ( ord_less_eq_set_a @ SV67 @ SV106 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[605]) ).
thf(653,plain,
! [SV67: set_a] :
( ( ( ^ [SY252: set_a] : ( SV67 = SY252 ) )
= ( ^ [SY253: set_a] :
~ ( ~ ( ord_less_eq_set_a @ SY253 @ SV67 )
| ~ ( ord_less_eq_set_a @ SV67 @ SY253 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[605]) ).
thf(654,plain,
! [SV68: set_a] :
( ( ! [SV107: set_a] :
( ( SV68 = SV107 )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV68 @ SV107 )
| ~ ( ord_less_eq_set_a @ SV107 @ SV68 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[606]) ).
thf(655,plain,
! [SV68: set_a] :
( ( ( ^ [SY254: set_a] : ( SV68 = SY254 ) )
= ( ^ [SY255: set_a] :
~ ( ~ ( ord_less_eq_set_a @ SV68 @ SY255 )
| ~ ( ord_less_eq_set_a @ SY255 @ SV68 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[606]) ).
thf(656,plain,
! [SV69: set_a] :
( ( ! [SV108: set_a] :
( ( ord_less_eq_set_a @ SV69 @ SV108 )
= ( ! [SY294: a] :
( ~ ( member_a @ SY294 @ SV69 )
| ( member_a @ SY294 @ SV108 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[607]) ).
thf(657,plain,
! [SV69: set_a] :
( ( ( ord_less_eq_set_a @ SV69 )
= ( ^ [SY256: set_a] :
! [SY257: a] :
( ~ ( member_a @ SY257 @ SV69 )
| ( member_a @ SY257 @ SY256 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[607]) ).
thf(658,plain,
! [SV70: set_a,SV25: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV25 @ SV70 ) )
= $true )
| ( ( ( inf_inf_set_a @ SV25 @ SV70 )
= SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[608]) ).
thf(659,plain,
! [SV109: set_a,SV71: set_a,SV26: set_a] :
( ( ( SV26 != SV71 )
| ~ ( ord_less_eq_set_a @ SV71 @ SV109 )
| ( ord_less_eq_set_a @ SV26 @ SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(660,plain,
! [SV72: set_a,SV27: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV27 @ SV72 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV72 @ SV27 )
| ( SV27 = SV72 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[610]) ).
thf(661,plain,
! [SV110: set_a > set_a,SV73: set_a,SV28: set_a] :
( ( ! [SY295: set_a] :
( ~ ( ord_less_eq_set_a @ SV28 @ SV73 )
| ( ( SV110 @ SV73 )
!= SY295 )
| ~ ! [SY296: set_a,SY297: set_a] :
( ~ ( ord_less_eq_set_a @ SY296 @ SY297 )
| ( ord_less_eq_set_a @ ( SV110 @ SY296 ) @ ( SV110 @ SY297 ) ) )
| ( ord_less_eq_set_a @ ( SV110 @ SV28 ) @ SY295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(662,plain,
! [SV74: set_a,SV29: set_a] :
( ( ( SV29 != SV74 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV29 @ SV74 )
| ~ ( ord_less_eq_set_a @ SV74 @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[612]) ).
thf(663,plain,
! [SV111: set_a,SV75: set_a,SV30: set_a] :
( ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ SV30 @ SV75 ) @ SV111 )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV30 @ SV111 )
| ~ ( ord_less_eq_set_a @ SV75 @ SV111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(664,plain,
! [SV112: set_a,SV76: set_a,SV31: set_a] :
( ( ! [SY298: set_a] :
( ~ ( ord_less_eq_set_a @ SV31 @ SV76 )
| ~ ( ord_less_eq_set_a @ SV112 @ SY298 )
| ( ord_less_eq_set_a @ ( inf_inf_set_a @ SV31 @ SV112 ) @ ( inf_inf_set_a @ SV76 @ SY298 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(665,plain,
! [SV77: set_a,SV32: set_a] :
( ( ( ~ ! [SY266: a] :
( ~ ( member_a @ SY266 @ SV32 )
| ( member_a @ SY266 @ SV77 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV32 @ SV77 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[615]) ).
thf(666,plain,
! [SV113: a,SV78: set_Product_prod_a_a,SV33: set_a] :
( ( ! [SY299: a] :
( ~ ( prefer719835986ence_a @ SV33 @ SV78 )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV113 @ SV33 @ SV78 ) @ ( prefer1676310729than_a @ SY299 @ SV33 @ SV78 ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SY299 @ SV33 @ SV78 ) @ ( prefer1676310729than_a @ SV113 @ SV33 @ SV78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[616]) ).
thf(667,plain,
! [SV79: set_a,SV34: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV34 @ SV79 ) )
= $true )
| ( ( ( inf_inf_set_a @ SV79 @ SV34 )
= SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[617]) ).
thf(668,plain,
! [SV80: a > $o,SV35: a > $o] :
( ( ~ ( ( ord_less_eq_set_a @ ( collect_a @ SV35 ) @ ( collect_a @ SV80 ) )
| ! [SY269: a] :
( ~ ( SV35 @ SY269 )
| ( SV80 @ SY269 ) ) )
| ~ ( ~ ( ord_less_eq_set_a @ ( collect_a @ SV35 ) @ ( collect_a @ SV80 ) )
| ~ ! [SY269: a] :
( ~ ( SV35 @ SY269 )
| ( SV80 @ SY269 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[618]) ).
thf(669,plain,
! [SV80: a > $o,SV35: a > $o] :
( ( ( ord_less_eq_set_a @ ( collect_a @ SV35 ) @ ( collect_a @ SV80 ) )
= ( ! [SY269: a] :
( ~ ( SV35 @ SY269 )
| ( SV80 @ SY269 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[618]) ).
thf(670,plain,
! [SV114: set_a,SV81: set_a,SV36: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV36 @ SV81 )
| ~ ( ord_less_eq_set_a @ SV81 @ SV114 )
| ( ord_less_eq_set_a @ SV36 @ SV114 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(671,plain,
! [SV115: set_a,SV82: set_a > set_a,SV37: set_a] :
( ( ! [SY300: set_a] :
( ( SV37
!= ( SV82 @ SV115 ) )
| ~ ( ord_less_eq_set_a @ SV115 @ SY300 )
| ~ ! [SY273: set_a,SY274: set_a] :
( ~ ( ord_less_eq_set_a @ SY273 @ SY274 )
| ( ord_less_eq_set_a @ ( SV82 @ SY273 ) @ ( SV82 @ SY274 ) ) )
| ( ord_less_eq_set_a @ SV37 @ ( SV82 @ SY300 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(672,plain,
! [SV83: set_a,SV38: set_a] :
( ( ( ~ ( finite_finite_a @ SV38 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV83 @ SV38 )
| ( finite_finite_a @ SV83 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[621]) ).
thf(673,plain,
! [SV84: set_a,SV39: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV39 @ SV84 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV84 @ SV39 )
| ( SV39 = SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[622]) ).
thf(674,plain,
! [SV85: set_a] :
( ( ! [SV116: set_a] :
( ( SV85 = SV116 )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV85 @ SV116 )
| ~ ( ord_less_eq_set_a @ SV116 @ SV85 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[623]) ).
thf(675,plain,
! [SV85: set_a] :
( ( ( ^ [SY275: set_a] : ( SV85 = SY275 ) )
= ( ^ [SY276: set_a] :
~ ( ~ ( ord_less_eq_set_a @ SV85 @ SY276 )
| ~ ( ord_less_eq_set_a @ SY276 @ SV85 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[623]) ).
thf(676,plain,
! [SV86: set_a,SV41: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV41 @ SV86 ) )
= $true )
| ( ( ~ ~ ( finite_finite_a @ SV41 )
| ~ ( finite_finite_a @ SV86 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[624]) ).
thf(677,plain,
! [SV87: a > $o,SV42: a > $o] :
( ( ( ~ ! [SY277: a] :
( ~ ( SV42 @ SY277 )
| ( SV87 @ SY277 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ ( collect_a @ SV42 ) @ ( collect_a @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[625]) ).
thf(678,plain,
! [SV88: set_a,SV43: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV43 @ SV88 ) )
= $true )
| ( ( ( ord_less_eq_set_a @ SV88 @ SV43 )
= ( SV88 = SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[626]) ).
thf(679,plain,
! [SV117: set_a,SV89: set_a,SV44: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV44 @ SV89 )
| ~ ( ord_less_eq_set_a @ SV44 @ SV117 )
| ( ord_less_eq_set_a @ SV44 @ ( inf_inf_set_a @ SV89 @ SV117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(680,plain,
! [SV90: set_a,SV45: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV45 @ SV90 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV90 @ SV45 )
| ( SV45 = SV90 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[628]) ).
thf(681,plain,
! [SV91: set_a,SV46: set_a] :
( ( ( SV46 != SV91 )
= $true )
| ( ( ord_less_eq_set_a @ SV46 @ SV91 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[629]) ).
thf(682,plain,
! [SV118: a,SV92: set_a,SV47: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV47 @ SV92 )
| ~ ( member_a @ SV118 @ SV47 )
| ( member_a @ SV118 @ SV92 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(683,plain,
! [SV119: a,SV93: set_a,SV48: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV48 @ SV93 )
| ~ ( member_a @ SV119 @ SV48 )
| ( member_a @ SV119 @ SV93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(684,plain,
! [SV94: set_a,SV49: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV49 @ SV94 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV94 @ SV49 )
| ( SV94 = SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[632]) ).
thf(685,plain,
! [SV95: set_a,SV50: set_a] :
( ( ( SV50 != SV95 )
= $true )
| ( ( ord_less_eq_set_a @ SV50 @ SV95 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[633]) ).
thf(686,plain,
! [SV120: set_a > set_a,SV96: set_a,SV51: set_a] :
( ( ! [SY303: set_a] :
( ~ ( ord_less_eq_set_a @ SV51 @ SV96 )
| ~ ( ord_less_eq_set_a @ ( SV120 @ SV96 ) @ SY303 )
| ~ ! [SY304: set_a,SY305: set_a] :
( ~ ( ord_less_eq_set_a @ SY304 @ SY305 )
| ( ord_less_eq_set_a @ ( SV120 @ SY304 ) @ ( SV120 @ SY305 ) ) )
| ( ord_less_eq_set_a @ ( SV120 @ SV51 ) @ SY303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(687,plain,
! [SV97: set_a] :
( ( ! [SV121: set_a] :
( ( ord_less_eq_set_a @ SV97 @ SV121 )
= ( ! [SY306: a] :
( ~ ( member_a @ SY306 @ SV97 )
| ( member_a @ SY306 @ SV121 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[635]) ).
thf(688,plain,
! [SV97: set_a] :
( ( ( ord_less_eq_set_a @ SV97 )
= ( ^ [SY285: set_a] :
! [SY286: a] :
( ~ ( member_a @ SY286 @ SV97 )
| ( member_a @ SY286 @ SY285 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[635]) ).
thf(689,plain,
! [SV122: set_a,SV98: set_a,SV53: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV53 @ SV98 )
| ~ ( ord_less_eq_set_a @ SV98 @ SV122 )
| ( ord_less_eq_set_a @ SV53 @ SV122 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(690,plain,
! [SV3: set_a] :
( ( ( ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a )
| ( SV3 = bot_bot_set_a ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a )
| ( SV3 != bot_bot_set_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[638]) ).
thf(691,plain,
! [SV7: set_a] :
( ( ( ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a )
| ( SV7 = bot_bot_set_a ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a )
| ( SV7 != bot_bot_set_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[639]) ).
thf(692,plain,
! [SV99: set_a,SV57: set_a,SV11: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV11 @ SV57 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV99 @ SV11 )
| ( ord_less_eq_set_a @ SV99 @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[640]) ).
thf(693,plain,
! [SV100: set_a,SV58: set_a,SV12: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV12 @ SV58 ) )
= $true )
| ( ( ( SV58 != SV100 )
| ( ord_less_eq_set_a @ SV12 @ SV100 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[641]) ).
thf(694,plain,
! [SV101: set_a,SV59: set_a,SV13: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV13 @ SV59 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV59 @ SV101 )
| ( ord_less_eq_set_a @ SV13 @ SV101 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[642]) ).
thf(695,plain,
! [SV123: set_a,SV60: set_a] :
( ( ( SV60 = SV123 )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV60 @ SV123 )
| ~ ( ord_less_eq_set_a @ SV123 @ SV60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(696,plain,
! [SV61: set_a,SV15: set_a > $o] :
( ( ( SV15 @ SV61 )
= $false )
| ( ( ~ ! [SY242: set_a] :
( ~ ( SV15 @ SY242 )
| ( ord_less_eq_set_a @ SY242 @ SV61 ) )
| ( ( order_Greatest_set_a @ SV15 )
= SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[645]) ).
thf(697,plain,
! [SV103: set_a > $o,SV62: set_a,SV16: set_a > $o] :
( ( ( ~ ( SV16 @ SV62 ) )
= $true )
| ( ( ~ ! [SY244: set_a] :
( ~ ( SV16 @ SY244 )
| ( ord_less_eq_set_a @ SY244 @ SV62 ) )
| ~ ! [SY289: set_a] :
( ~ ( SV16 @ SY289 )
| ~ ! [SY164: set_a] :
( ~ ( SV16 @ SY164 )
| ( ord_less_eq_set_a @ SY164 @ SY289 ) )
| ( SV103 @ SY289 ) )
| ( SV103 @ ( order_Greatest_set_a @ SV16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[646]) ).
thf(698,plain,
! [SV63: set_a,SV18: set_a] :
( ( ( SV18 = SV63 )
= $false )
| ( ( ord_less_eq_set_a @ SV63 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[648]) ).
thf(699,plain,
! [SV124: set_a,SV104: set_a,SV64: set_a > set_a,SV19: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV19 @ ( SV64 @ SV104 ) )
| ~ ( ord_less_eq_set_a @ SV104 @ SV124 )
| ~ ! [SY249: set_a,SY250: set_a] :
( ~ ( ord_less_eq_set_a @ SY249 @ SY250 )
| ( ord_less_eq_set_a @ ( SV64 @ SY249 ) @ ( SV64 @ SY250 ) ) )
| ( ord_less_eq_set_a @ SV19 @ ( SV64 @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(700,plain,
! [SV65: set_a,SV20: set_a] :
( ( ( ord_less_eq_set_a @ SV20 @ SV65 )
= $false )
| ( ( ~ ( finite_finite_a @ SV65 )
| ( finite_finite_a @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[650]) ).
thf(701,plain,
! [SV105: set_a,SV66: set_a,SV21: set_a] :
( ( ~ ( ( ord_less_eq_set_a @ SV21 @ ( inf_inf_set_a @ SV66 @ SV105 ) )
| ~ ( ~ ( ord_less_eq_set_a @ SV21 @ SV66 )
| ~ ( ord_less_eq_set_a @ SV21 @ SV105 ) ) )
| ~ ( ~ ( ord_less_eq_set_a @ SV21 @ ( inf_inf_set_a @ SV66 @ SV105 ) )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV21 @ SV66 )
| ~ ( ord_less_eq_set_a @ SV21 @ SV105 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[651]) ).
thf(702,plain,
! [SV105: set_a,SV66: set_a,SV21: set_a] :
( ( ( ord_less_eq_set_a @ SV21 @ ( inf_inf_set_a @ SV66 @ SV105 ) )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV21 @ SV66 )
| ~ ( ord_less_eq_set_a @ SV21 @ SV105 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[651]) ).
thf(703,plain,
! [SV125: set_a,SV67: set_a] :
( ( ( SV67 = SV125 )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV125 @ SV67 )
| ~ ( ord_less_eq_set_a @ SV67 @ SV125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[652]) ).
thf(704,plain,
! [SV126: set_a,SV68: set_a] :
( ( ( SV68 = SV126 )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV68 @ SV126 )
| ~ ( ord_less_eq_set_a @ SV126 @ SV68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(705,plain,
! [SV127: set_a,SV69: set_a] :
( ( ( ord_less_eq_set_a @ SV69 @ SV127 )
= ( ! [SY309: a] :
( ~ ( member_a @ SY309 @ SV69 )
| ( member_a @ SY309 @ SV127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(706,plain,
! [SV70: set_a,SV25: set_a] :
( ( ( ord_less_eq_set_a @ SV25 @ SV70 )
= $false )
| ( ( ( inf_inf_set_a @ SV25 @ SV70 )
= SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[658]) ).
thf(707,plain,
! [SV109: set_a,SV71: set_a,SV26: set_a] :
( ( ( SV26 != SV71 )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV71 @ SV109 )
| ( ord_less_eq_set_a @ SV26 @ SV109 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[659]) ).
thf(708,plain,
! [SV72: set_a,SV27: set_a] :
( ( ( ord_less_eq_set_a @ SV27 @ SV72 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV72 @ SV27 )
| ( SV27 = SV72 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[660]) ).
thf(709,plain,
! [SV128: set_a,SV110: set_a > set_a,SV73: set_a,SV28: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV28 @ SV73 )
| ( ( SV110 @ SV73 )
!= SV128 )
| ~ ! [SY296: set_a,SY297: set_a] :
( ~ ( ord_less_eq_set_a @ SY296 @ SY297 )
| ( ord_less_eq_set_a @ ( SV110 @ SY296 ) @ ( SV110 @ SY297 ) ) )
| ( ord_less_eq_set_a @ ( SV110 @ SV28 ) @ SV128 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(710,plain,
! [SV74: set_a,SV29: set_a] :
( ( ( SV29 = SV74 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV29 @ SV74 )
| ~ ( ord_less_eq_set_a @ SV74 @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[662]) ).
thf(711,plain,
! [SV111: set_a,SV75: set_a,SV30: set_a] :
( ( ~ ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ SV30 @ SV75 ) @ SV111 )
| ~ ( ~ ( ord_less_eq_set_a @ SV30 @ SV111 )
| ~ ( ord_less_eq_set_a @ SV75 @ SV111 ) ) )
| ~ ( ~ ( ord_less_eq_set_a @ ( sup_sup_set_a @ SV30 @ SV75 ) @ SV111 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV30 @ SV111 )
| ~ ( ord_less_eq_set_a @ SV75 @ SV111 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[663]) ).
thf(712,plain,
! [SV111: set_a,SV75: set_a,SV30: set_a] :
( ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ SV30 @ SV75 ) @ SV111 )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV30 @ SV111 )
| ~ ( ord_less_eq_set_a @ SV75 @ SV111 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[663]) ).
thf(713,plain,
! [SV129: set_a,SV112: set_a,SV76: set_a,SV31: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV31 @ SV76 )
| ~ ( ord_less_eq_set_a @ SV112 @ SV129 )
| ( ord_less_eq_set_a @ ( inf_inf_set_a @ SV31 @ SV112 ) @ ( inf_inf_set_a @ SV76 @ SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(714,plain,
! [SV77: set_a,SV32: set_a] :
( ( ( ! [SY266: a] :
( ~ ( member_a @ SY266 @ SV32 )
| ( member_a @ SY266 @ SV77 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV32 @ SV77 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[665]) ).
thf(715,plain,
! [SV130: a,SV113: a,SV78: set_Product_prod_a_a,SV33: set_a] :
( ( ~ ( prefer719835986ence_a @ SV33 @ SV78 )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV113 @ SV33 @ SV78 ) @ ( prefer1676310729than_a @ SV130 @ SV33 @ SV78 ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV130 @ SV33 @ SV78 ) @ ( prefer1676310729than_a @ SV113 @ SV33 @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(716,plain,
! [SV79: set_a,SV34: set_a] :
( ( ( ord_less_eq_set_a @ SV34 @ SV79 )
= $false )
| ( ( ( inf_inf_set_a @ SV79 @ SV34 )
= SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[667]) ).
thf(717,plain,
! [SV80: a > $o,SV35: a > $o] :
( ( ( ~ ( ( ord_less_eq_set_a @ ( collect_a @ SV35 ) @ ( collect_a @ SV80 ) )
| ! [SY269: a] :
( ~ ( SV35 @ SY269 )
| ( SV80 @ SY269 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ ( collect_a @ SV35 ) @ ( collect_a @ SV80 ) )
| ~ ! [SY269: a] :
( ~ ( SV35 @ SY269 )
| ( SV80 @ SY269 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[668]) ).
thf(718,plain,
! [SV114: set_a,SV81: set_a,SV36: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV36 @ SV81 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV81 @ SV114 )
| ( ord_less_eq_set_a @ SV36 @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[670]) ).
thf(719,plain,
! [SV131: set_a,SV115: set_a,SV82: set_a > set_a,SV37: set_a] :
( ( ( SV37
!= ( SV82 @ SV115 ) )
| ~ ( ord_less_eq_set_a @ SV115 @ SV131 )
| ~ ! [SY273: set_a,SY274: set_a] :
( ~ ( ord_less_eq_set_a @ SY273 @ SY274 )
| ( ord_less_eq_set_a @ ( SV82 @ SY273 ) @ ( SV82 @ SY274 ) ) )
| ( ord_less_eq_set_a @ SV37 @ ( SV82 @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(720,plain,
! [SV83: set_a,SV38: set_a] :
( ( ( finite_finite_a @ SV38 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV83 @ SV38 )
| ( finite_finite_a @ SV83 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[672]) ).
thf(721,plain,
! [SV84: set_a,SV39: set_a] :
( ( ( ord_less_eq_set_a @ SV39 @ SV84 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV84 @ SV39 )
| ( SV39 = SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[673]) ).
thf(722,plain,
! [SV132: set_a,SV85: set_a] :
( ( ( SV85 = SV132 )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV85 @ SV132 )
| ~ ( ord_less_eq_set_a @ SV132 @ SV85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(723,plain,
! [SV86: set_a,SV41: set_a] :
( ( ( ord_less_eq_set_a @ SV41 @ SV86 )
= $false )
| ( ( ~ ~ ( finite_finite_a @ SV41 )
| ~ ( finite_finite_a @ SV86 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[676]) ).
thf(724,plain,
! [SV87: a > $o,SV42: a > $o] :
( ( ( ! [SY277: a] :
( ~ ( SV42 @ SY277 )
| ( SV87 @ SY277 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( collect_a @ SV42 ) @ ( collect_a @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[677]) ).
thf(725,plain,
! [SV88: set_a,SV43: set_a] :
( ( ( ord_less_eq_set_a @ SV43 @ SV88 )
= $false )
| ( ( ( ord_less_eq_set_a @ SV88 @ SV43 )
= ( SV88 = SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[678]) ).
thf(726,plain,
! [SV117: set_a,SV89: set_a,SV44: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV44 @ SV89 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV44 @ SV117 )
| ( ord_less_eq_set_a @ SV44 @ ( inf_inf_set_a @ SV89 @ SV117 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[679]) ).
thf(727,plain,
! [SV90: set_a,SV45: set_a] :
( ( ( ord_less_eq_set_a @ SV45 @ SV90 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV90 @ SV45 )
| ( SV45 = SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[680]) ).
thf(728,plain,
! [SV91: set_a,SV46: set_a] :
( ( ( SV46 = SV91 )
= $false )
| ( ( ord_less_eq_set_a @ SV46 @ SV91 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[681]) ).
thf(729,plain,
! [SV118: a,SV92: set_a,SV47: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV47 @ SV92 ) )
= $true )
| ( ( ~ ( member_a @ SV118 @ SV47 )
| ( member_a @ SV118 @ SV92 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[682]) ).
thf(730,plain,
! [SV119: a,SV93: set_a,SV48: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV48 @ SV93 ) )
= $true )
| ( ( ~ ( member_a @ SV119 @ SV48 )
| ( member_a @ SV119 @ SV93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[683]) ).
thf(731,plain,
! [SV94: set_a,SV49: set_a] :
( ( ( ord_less_eq_set_a @ SV49 @ SV94 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV94 @ SV49 )
| ( SV94 = SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[684]) ).
thf(732,plain,
! [SV95: set_a,SV50: set_a] :
( ( ( SV50 = SV95 )
= $false )
| ( ( ord_less_eq_set_a @ SV50 @ SV95 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[685]) ).
thf(733,plain,
! [SV133: set_a,SV120: set_a > set_a,SV96: set_a,SV51: set_a] :
( ( ~ ( ord_less_eq_set_a @ SV51 @ SV96 )
| ~ ( ord_less_eq_set_a @ ( SV120 @ SV96 ) @ SV133 )
| ~ ! [SY304: set_a,SY305: set_a] :
( ~ ( ord_less_eq_set_a @ SY304 @ SY305 )
| ( ord_less_eq_set_a @ ( SV120 @ SY304 ) @ ( SV120 @ SY305 ) ) )
| ( ord_less_eq_set_a @ ( SV120 @ SV51 ) @ SV133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(734,plain,
! [SV134: set_a,SV97: set_a] :
( ( ( ord_less_eq_set_a @ SV97 @ SV134 )
= ( ! [SY316: a] :
( ~ ( member_a @ SY316 @ SV97 )
| ( member_a @ SY316 @ SV134 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(735,plain,
! [SV122: set_a,SV98: set_a,SV53: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV53 @ SV98 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV98 @ SV122 )
| ( ord_less_eq_set_a @ SV53 @ SV122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[689]) ).
thf(736,plain,
! [SV3: set_a] :
( ( ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a )
| ( SV3 != bot_bot_set_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[690]) ).
thf(737,plain,
! [SV3: set_a] :
( ( ( SV3 = bot_bot_set_a )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a )
| ( SV3 != bot_bot_set_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[690]) ).
thf(738,plain,
! [SV7: set_a] :
( ( ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a )
| ( SV7 != bot_bot_set_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[691]) ).
thf(739,plain,
! [SV7: set_a] :
( ( ( SV7 = bot_bot_set_a )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a )
| ( SV7 != bot_bot_set_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[691]) ).
thf(740,plain,
! [SV99: set_a,SV57: set_a,SV11: set_a] :
( ( ( ord_less_eq_set_a @ SV11 @ SV57 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV99 @ SV11 )
| ( ord_less_eq_set_a @ SV99 @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[692]) ).
thf(741,plain,
! [SV100: set_a,SV58: set_a,SV12: set_a] :
( ( ( ord_less_eq_set_a @ SV12 @ SV58 )
= $false )
| ( ( ( SV58 != SV100 )
| ( ord_less_eq_set_a @ SV12 @ SV100 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[693]) ).
thf(742,plain,
! [SV101: set_a,SV59: set_a,SV13: set_a] :
( ( ( ord_less_eq_set_a @ SV13 @ SV59 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV59 @ SV101 )
| ( ord_less_eq_set_a @ SV13 @ SV101 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[694]) ).
thf(743,plain,
! [SV123: set_a,SV60: set_a] :
( ( ~ ( ( SV60 = SV123 )
| ~ ( ~ ( ord_less_eq_set_a @ SV60 @ SV123 )
| ~ ( ord_less_eq_set_a @ SV123 @ SV60 ) ) )
| ~ ( ( SV60 != SV123 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV60 @ SV123 )
| ~ ( ord_less_eq_set_a @ SV123 @ SV60 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[695]) ).
thf(744,plain,
! [SV123: set_a,SV60: set_a] :
( ( ( SV60 = SV123 )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV60 @ SV123 )
| ~ ( ord_less_eq_set_a @ SV123 @ SV60 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[695]) ).
thf(745,plain,
! [SV61: set_a,SV15: set_a > $o] :
( ( ( ~ ! [SY242: set_a] :
( ~ ( SV15 @ SY242 )
| ( ord_less_eq_set_a @ SY242 @ SV61 ) ) )
= $true )
| ( ( ( order_Greatest_set_a @ SV15 )
= SV61 )
= $true )
| ( ( SV15 @ SV61 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[696]) ).
thf(746,plain,
! [SV103: set_a > $o,SV62: set_a,SV16: set_a > $o] :
( ( ( SV16 @ SV62 )
= $false )
| ( ( ~ ! [SY244: set_a] :
( ~ ( SV16 @ SY244 )
| ( ord_less_eq_set_a @ SY244 @ SV62 ) )
| ~ ! [SY289: set_a] :
( ~ ( SV16 @ SY289 )
| ~ ! [SY164: set_a] :
( ~ ( SV16 @ SY164 )
| ( ord_less_eq_set_a @ SY164 @ SY289 ) )
| ( SV103 @ SY289 ) )
| ( SV103 @ ( order_Greatest_set_a @ SV16 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[697]) ).
thf(747,plain,
! [SV124: set_a,SV104: set_a,SV64: set_a > set_a,SV19: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV19 @ ( SV64 @ SV104 ) ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV104 @ SV124 )
| ~ ! [SY249: set_a,SY250: set_a] :
( ~ ( ord_less_eq_set_a @ SY249 @ SY250 )
| ( ord_less_eq_set_a @ ( SV64 @ SY249 ) @ ( SV64 @ SY250 ) ) )
| ( ord_less_eq_set_a @ SV19 @ ( SV64 @ SV124 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[699]) ).
thf(748,plain,
! [SV20: set_a,SV65: set_a] :
( ( ( ~ ( finite_finite_a @ SV65 ) )
= $true )
| ( ( finite_finite_a @ SV20 )
= $true )
| ( ( ord_less_eq_set_a @ SV20 @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[700]) ).
thf(749,plain,
! [SV105: set_a,SV66: set_a,SV21: set_a] :
( ( ( ~ ( ( ord_less_eq_set_a @ SV21 @ ( inf_inf_set_a @ SV66 @ SV105 ) )
| ~ ( ~ ( ord_less_eq_set_a @ SV21 @ SV66 )
| ~ ( ord_less_eq_set_a @ SV21 @ SV105 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV21 @ ( inf_inf_set_a @ SV66 @ SV105 ) )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV21 @ SV66 )
| ~ ( ord_less_eq_set_a @ SV21 @ SV105 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[701]) ).
thf(750,plain,
! [SV125: set_a,SV67: set_a] :
( ( ~ ( ( SV67 = SV125 )
| ~ ( ~ ( ord_less_eq_set_a @ SV125 @ SV67 )
| ~ ( ord_less_eq_set_a @ SV67 @ SV125 ) ) )
| ~ ( ( SV67 != SV125 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV125 @ SV67 )
| ~ ( ord_less_eq_set_a @ SV67 @ SV125 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[703]) ).
thf(751,plain,
! [SV125: set_a,SV67: set_a] :
( ( ( SV67 = SV125 )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV125 @ SV67 )
| ~ ( ord_less_eq_set_a @ SV67 @ SV125 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[703]) ).
thf(752,plain,
! [SV126: set_a,SV68: set_a] :
( ( ~ ( ( SV68 = SV126 )
| ~ ( ~ ( ord_less_eq_set_a @ SV68 @ SV126 )
| ~ ( ord_less_eq_set_a @ SV126 @ SV68 ) ) )
| ~ ( ( SV68 != SV126 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV68 @ SV126 )
| ~ ( ord_less_eq_set_a @ SV126 @ SV68 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[704]) ).
thf(753,plain,
! [SV126: set_a,SV68: set_a] :
( ( ( SV68 = SV126 )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV68 @ SV126 )
| ~ ( ord_less_eq_set_a @ SV126 @ SV68 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[704]) ).
thf(754,plain,
! [SV127: set_a,SV69: set_a] :
( ( ~ ( ( ord_less_eq_set_a @ SV69 @ SV127 )
| ! [SY309: a] :
( ~ ( member_a @ SY309 @ SV69 )
| ( member_a @ SY309 @ SV127 ) ) )
| ~ ( ~ ( ord_less_eq_set_a @ SV69 @ SV127 )
| ~ ! [SY309: a] :
( ~ ( member_a @ SY309 @ SV69 )
| ( member_a @ SY309 @ SV127 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[705]) ).
thf(755,plain,
! [SV127: set_a,SV69: set_a] :
( ( ( ord_less_eq_set_a @ SV69 @ SV127 )
= ( ! [SY309: a] :
( ~ ( member_a @ SY309 @ SV69 )
| ( member_a @ SY309 @ SV127 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[705]) ).
thf(756,plain,
! [SV109: set_a,SV71: set_a,SV26: set_a] :
( ( ( SV26 = SV71 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV71 @ SV109 )
| ( ord_less_eq_set_a @ SV26 @ SV109 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[707]) ).
thf(757,plain,
! [SV27: set_a,SV72: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV72 @ SV27 ) )
= $true )
| ( ( SV27 = SV72 )
= $true )
| ( ( ord_less_eq_set_a @ SV27 @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[708]) ).
thf(758,plain,
! [SV128: set_a,SV110: set_a > set_a,SV73: set_a,SV28: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV28 @ SV73 ) )
= $true )
| ( ( ( ( SV110 @ SV73 )
!= SV128 )
| ~ ! [SY296: set_a,SY297: set_a] :
( ~ ( ord_less_eq_set_a @ SY296 @ SY297 )
| ( ord_less_eq_set_a @ ( SV110 @ SY296 ) @ ( SV110 @ SY297 ) ) )
| ( ord_less_eq_set_a @ ( SV110 @ SV28 ) @ SV128 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[709]) ).
thf(759,plain,
! [SV74: set_a,SV29: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV29 @ SV74 )
| ~ ( ord_less_eq_set_a @ SV74 @ SV29 ) )
= $false )
| ( ( SV29 = SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[710]) ).
thf(760,plain,
! [SV111: set_a,SV75: set_a,SV30: set_a] :
( ( ( ~ ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ SV30 @ SV75 ) @ SV111 )
| ~ ( ~ ( ord_less_eq_set_a @ SV30 @ SV111 )
| ~ ( ord_less_eq_set_a @ SV75 @ SV111 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ ( sup_sup_set_a @ SV30 @ SV75 ) @ SV111 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV30 @ SV111 )
| ~ ( ord_less_eq_set_a @ SV75 @ SV111 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[711]) ).
thf(761,plain,
! [SV129: set_a,SV112: set_a,SV76: set_a,SV31: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV31 @ SV76 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV112 @ SV129 )
| ( ord_less_eq_set_a @ ( inf_inf_set_a @ SV31 @ SV112 ) @ ( inf_inf_set_a @ SV76 @ SV129 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[713]) ).
thf(762,plain,
! [SV32: set_a,SV77: set_a] :
( ( ( ~ ( member_a @ ( sK1_SY266 @ SV77 @ SV32 ) @ SV32 )
| ( member_a @ ( sK1_SY266 @ SV77 @ SV32 ) @ SV77 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV32 @ SV77 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[714]) ).
thf(763,plain,
! [SV130: a,SV113: a,SV78: set_Product_prod_a_a,SV33: set_a] :
( ( ( ~ ( prefer719835986ence_a @ SV33 @ SV78 ) )
= $true )
| ( ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV113 @ SV33 @ SV78 ) @ ( prefer1676310729than_a @ SV130 @ SV33 @ SV78 ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV130 @ SV33 @ SV78 ) @ ( prefer1676310729than_a @ SV113 @ SV33 @ SV78 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[715]) ).
thf(764,plain,
! [SV80: a > $o,SV35: a > $o] :
( ( ( ( ord_less_eq_set_a @ ( collect_a @ SV35 ) @ ( collect_a @ SV80 ) )
| ! [SY269: a] :
( ~ ( SV35 @ SY269 )
| ( SV80 @ SY269 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ ( collect_a @ SV35 ) @ ( collect_a @ SV80 ) )
| ~ ! [SY269: a] :
( ~ ( SV35 @ SY269 )
| ( SV80 @ SY269 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[717]) ).
thf(765,plain,
! [SV114: set_a,SV81: set_a,SV36: set_a] :
( ( ( ord_less_eq_set_a @ SV36 @ SV81 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV81 @ SV114 )
| ( ord_less_eq_set_a @ SV36 @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[718]) ).
thf(766,plain,
! [SV131: set_a,SV115: set_a,SV82: set_a > set_a,SV37: set_a] :
( ( ( SV37
!= ( SV82 @ SV115 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV115 @ SV131 )
| ~ ! [SY273: set_a,SY274: set_a] :
( ~ ( ord_less_eq_set_a @ SY273 @ SY274 )
| ( ord_less_eq_set_a @ ( SV82 @ SY273 ) @ ( SV82 @ SY274 ) ) )
| ( ord_less_eq_set_a @ SV37 @ ( SV82 @ SV131 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[719]) ).
thf(767,plain,
! [SV38: set_a,SV83: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV83 @ SV38 ) )
= $true )
| ( ( finite_finite_a @ SV83 )
= $true )
| ( ( finite_finite_a @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[720]) ).
thf(768,plain,
! [SV39: set_a,SV84: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV84 @ SV39 ) )
= $true )
| ( ( SV39 = SV84 )
= $true )
| ( ( ord_less_eq_set_a @ SV39 @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[721]) ).
thf(769,plain,
! [SV132: set_a,SV85: set_a] :
( ( ~ ( ( SV85 = SV132 )
| ~ ( ~ ( ord_less_eq_set_a @ SV85 @ SV132 )
| ~ ( ord_less_eq_set_a @ SV132 @ SV85 ) ) )
| ~ ( ( SV85 != SV132 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV85 @ SV132 )
| ~ ( ord_less_eq_set_a @ SV132 @ SV85 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[722]) ).
thf(770,plain,
! [SV132: set_a,SV85: set_a] :
( ( ( SV85 = SV132 )
= ( ~ ( ~ ( ord_less_eq_set_a @ SV85 @ SV132 )
| ~ ( ord_less_eq_set_a @ SV132 @ SV85 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[722]) ).
thf(771,plain,
! [SV86: set_a,SV41: set_a] :
( ( ( ~ ~ ( finite_finite_a @ SV41 ) )
= $true )
| ( ( ~ ( finite_finite_a @ SV86 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV41 @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[723]) ).
thf(772,plain,
! [SV87: a > $o,SV42: a > $o] :
( ( ( ~ ( SV42 @ ( sK2_SY277 @ SV87 @ SV42 ) )
| ( SV87 @ ( sK2_SY277 @ SV87 @ SV42 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( collect_a @ SV42 ) @ ( collect_a @ SV87 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[724]) ).
thf(773,plain,
! [SV43: set_a,SV88: set_a] :
( ( ( ~ ( ( ord_less_eq_set_a @ SV88 @ SV43 )
| ( SV88 = SV43 ) )
| ~ ( ~ ( ord_less_eq_set_a @ SV88 @ SV43 )
| ( SV88 != SV43 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV43 @ SV88 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[725]) ).
thf(774,plain,
! [SV43: set_a,SV88: set_a] :
( ( ( ( ord_less_eq_set_a @ SV88 @ SV43 )
= ( SV88 = SV43 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV43 @ SV88 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[725]) ).
thf(775,plain,
! [SV117: set_a,SV89: set_a,SV44: set_a] :
( ( ( ord_less_eq_set_a @ SV44 @ SV89 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV44 @ SV117 )
| ( ord_less_eq_set_a @ SV44 @ ( inf_inf_set_a @ SV89 @ SV117 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[726]) ).
thf(776,plain,
! [SV45: set_a,SV90: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV90 @ SV45 ) )
= $true )
| ( ( SV45 = SV90 )
= $true )
| ( ( ord_less_eq_set_a @ SV45 @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[727]) ).
thf(777,plain,
! [SV118: a,SV92: set_a,SV47: set_a] :
( ( ( ord_less_eq_set_a @ SV47 @ SV92 )
= $false )
| ( ( ~ ( member_a @ SV118 @ SV47 )
| ( member_a @ SV118 @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[729]) ).
thf(778,plain,
! [SV119: a,SV93: set_a,SV48: set_a] :
( ( ( ord_less_eq_set_a @ SV48 @ SV93 )
= $false )
| ( ( ~ ( member_a @ SV119 @ SV48 )
| ( member_a @ SV119 @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[730]) ).
thf(779,plain,
! [SV49: set_a,SV94: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV94 @ SV49 ) )
= $true )
| ( ( SV94 = SV49 )
= $true )
| ( ( ord_less_eq_set_a @ SV49 @ SV94 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[731]) ).
thf(780,plain,
! [SV133: set_a,SV120: set_a > set_a,SV96: set_a,SV51: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV51 @ SV96 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ ( SV120 @ SV96 ) @ SV133 )
| ~ ! [SY304: set_a,SY305: set_a] :
( ~ ( ord_less_eq_set_a @ SY304 @ SY305 )
| ( ord_less_eq_set_a @ ( SV120 @ SY304 ) @ ( SV120 @ SY305 ) ) )
| ( ord_less_eq_set_a @ ( SV120 @ SV51 ) @ SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[733]) ).
thf(781,plain,
! [SV134: set_a,SV97: set_a] :
( ( ~ ( ( ord_less_eq_set_a @ SV97 @ SV134 )
| ! [SY316: a] :
( ~ ( member_a @ SY316 @ SV97 )
| ( member_a @ SY316 @ SV134 ) ) )
| ~ ( ~ ( ord_less_eq_set_a @ SV97 @ SV134 )
| ~ ! [SY316: a] :
( ~ ( member_a @ SY316 @ SV97 )
| ( member_a @ SY316 @ SV134 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[734]) ).
thf(782,plain,
! [SV134: set_a,SV97: set_a] :
( ( ( ord_less_eq_set_a @ SV97 @ SV134 )
= ( ! [SY316: a] :
( ~ ( member_a @ SY316 @ SV97 )
| ( member_a @ SY316 @ SV134 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[734]) ).
thf(783,plain,
! [SV122: set_a,SV98: set_a,SV53: set_a] :
( ( ( ord_less_eq_set_a @ SV53 @ SV98 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV98 @ SV122 )
| ( ord_less_eq_set_a @ SV53 @ SV122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[735]) ).
thf(784,plain,
! [SV3: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a )
| ( SV3 != bot_bot_set_a ) )
= $false )
| ( ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[736]) ).
thf(785,plain,
! [SV3: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a )
| ( SV3 != bot_bot_set_a ) )
= $false )
| ( ( SV3 = bot_bot_set_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[737]) ).
thf(786,plain,
! [SV7: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a )
| ( SV7 != bot_bot_set_a ) )
= $false )
| ( ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[738]) ).
thf(787,plain,
! [SV7: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a )
| ( SV7 != bot_bot_set_a ) )
= $false )
| ( ( SV7 = bot_bot_set_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[739]) ).
thf(788,plain,
! [SV57: set_a,SV11: set_a,SV99: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV99 @ SV11 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV99 @ SV57 )
= $true )
| ( ( ord_less_eq_set_a @ SV11 @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[740]) ).
thf(789,plain,
! [SV12: set_a,SV100: set_a,SV58: set_a] :
( ( ( SV58 != SV100 )
= $true )
| ( ( ord_less_eq_set_a @ SV12 @ SV100 )
= $true )
| ( ( ord_less_eq_set_a @ SV12 @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[741]) ).
thf(790,plain,
! [SV13: set_a,SV101: set_a,SV59: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV59 @ SV101 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV13 @ SV101 )
= $true )
| ( ( ord_less_eq_set_a @ SV13 @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[742]) ).
thf(791,plain,
! [SV123: set_a,SV60: set_a] :
( ( ( ~ ( ( SV60 = SV123 )
| ~ ( ~ ( ord_less_eq_set_a @ SV60 @ SV123 )
| ~ ( ord_less_eq_set_a @ SV123 @ SV60 ) ) ) )
= $true )
| ( ( ~ ( ( SV60 != SV123 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV60 @ SV123 )
| ~ ( ord_less_eq_set_a @ SV123 @ SV60 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[743]) ).
thf(792,plain,
! [SV61: set_a,SV15: set_a > $o] :
( ( ( ! [SY242: set_a] :
( ~ ( SV15 @ SY242 )
| ( ord_less_eq_set_a @ SY242 @ SV61 ) ) )
= $false )
| ( ( ( order_Greatest_set_a @ SV15 )
= SV61 )
= $true )
| ( ( SV15 @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[745]) ).
thf(793,plain,
! [SV103: set_a > $o,SV62: set_a,SV16: set_a > $o] :
( ( ( ~ ! [SY244: set_a] :
( ~ ( SV16 @ SY244 )
| ( ord_less_eq_set_a @ SY244 @ SV62 ) ) )
= $true )
| ( ( ~ ! [SY289: set_a] :
( ~ ( SV16 @ SY289 )
| ~ ! [SY164: set_a] :
( ~ ( SV16 @ SY164 )
| ( ord_less_eq_set_a @ SY164 @ SY289 ) )
| ( SV103 @ SY289 ) )
| ( SV103 @ ( order_Greatest_set_a @ SV16 ) ) )
= $true )
| ( ( SV16 @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[746]) ).
thf(794,plain,
! [SV124: set_a,SV104: set_a,SV64: set_a > set_a,SV19: set_a] :
( ( ( ord_less_eq_set_a @ SV19 @ ( SV64 @ SV104 ) )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV104 @ SV124 )
| ~ ! [SY249: set_a,SY250: set_a] :
( ~ ( ord_less_eq_set_a @ SY249 @ SY250 )
| ( ord_less_eq_set_a @ ( SV64 @ SY249 ) @ ( SV64 @ SY250 ) ) )
| ( ord_less_eq_set_a @ SV19 @ ( SV64 @ SV124 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[747]) ).
thf(795,plain,
! [SV20: set_a,SV65: set_a] :
( ( ( finite_finite_a @ SV65 )
= $false )
| ( ( finite_finite_a @ SV20 )
= $true )
| ( ( ord_less_eq_set_a @ SV20 @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[748]) ).
thf(796,plain,
! [SV105: set_a,SV66: set_a,SV21: set_a] :
( ( ( ( ord_less_eq_set_a @ SV21 @ ( inf_inf_set_a @ SV66 @ SV105 ) )
| ~ ( ~ ( ord_less_eq_set_a @ SV21 @ SV66 )
| ~ ( ord_less_eq_set_a @ SV21 @ SV105 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV21 @ ( inf_inf_set_a @ SV66 @ SV105 ) )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV21 @ SV66 )
| ~ ( ord_less_eq_set_a @ SV21 @ SV105 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[749]) ).
thf(797,plain,
! [SV125: set_a,SV67: set_a] :
( ( ( ~ ( ( SV67 = SV125 )
| ~ ( ~ ( ord_less_eq_set_a @ SV125 @ SV67 )
| ~ ( ord_less_eq_set_a @ SV67 @ SV125 ) ) ) )
= $true )
| ( ( ~ ( ( SV67 != SV125 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV125 @ SV67 )
| ~ ( ord_less_eq_set_a @ SV67 @ SV125 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[750]) ).
thf(798,plain,
! [SV126: set_a,SV68: set_a] :
( ( ( ~ ( ( SV68 = SV126 )
| ~ ( ~ ( ord_less_eq_set_a @ SV68 @ SV126 )
| ~ ( ord_less_eq_set_a @ SV126 @ SV68 ) ) ) )
= $true )
| ( ( ~ ( ( SV68 != SV126 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV68 @ SV126 )
| ~ ( ord_less_eq_set_a @ SV126 @ SV68 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[752]) ).
thf(799,plain,
! [SV127: set_a,SV69: set_a] :
( ( ( ~ ( ( ord_less_eq_set_a @ SV69 @ SV127 )
| ! [SY309: a] :
( ~ ( member_a @ SY309 @ SV69 )
| ( member_a @ SY309 @ SV127 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV69 @ SV127 )
| ~ ! [SY309: a] :
( ~ ( member_a @ SY309 @ SV69 )
| ( member_a @ SY309 @ SV127 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[754]) ).
thf(800,plain,
! [SV26: set_a,SV109: set_a,SV71: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV71 @ SV109 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV26 @ SV109 )
= $true )
| ( ( SV26 = SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[756]) ).
thf(801,plain,
! [SV27: set_a,SV72: set_a] :
( ( ( ord_less_eq_set_a @ SV72 @ SV27 )
= $false )
| ( ( SV27 = SV72 )
= $true )
| ( ( ord_less_eq_set_a @ SV27 @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[757]) ).
thf(802,plain,
! [SV128: set_a,SV110: set_a > set_a,SV73: set_a,SV28: set_a] :
( ( ( ord_less_eq_set_a @ SV28 @ SV73 )
= $false )
| ( ( ( ( SV110 @ SV73 )
!= SV128 )
| ~ ! [SY296: set_a,SY297: set_a] :
( ~ ( ord_less_eq_set_a @ SY296 @ SY297 )
| ( ord_less_eq_set_a @ ( SV110 @ SY296 ) @ ( SV110 @ SY297 ) ) )
| ( ord_less_eq_set_a @ ( SV110 @ SV28 ) @ SV128 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[758]) ).
thf(803,plain,
! [SV74: set_a,SV29: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV29 @ SV74 ) )
= $false )
| ( ( SV29 = SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[759]) ).
thf(804,plain,
! [SV29: set_a,SV74: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV74 @ SV29 ) )
= $false )
| ( ( SV29 = SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[759]) ).
thf(805,plain,
! [SV111: set_a,SV75: set_a,SV30: set_a] :
( ( ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ SV30 @ SV75 ) @ SV111 )
| ~ ( ~ ( ord_less_eq_set_a @ SV30 @ SV111 )
| ~ ( ord_less_eq_set_a @ SV75 @ SV111 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ ( sup_sup_set_a @ SV30 @ SV75 ) @ SV111 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV30 @ SV111 )
| ~ ( ord_less_eq_set_a @ SV75 @ SV111 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[760]) ).
thf(806,plain,
! [SV129: set_a,SV112: set_a,SV76: set_a,SV31: set_a] :
( ( ( ord_less_eq_set_a @ SV31 @ SV76 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV112 @ SV129 )
| ( ord_less_eq_set_a @ ( inf_inf_set_a @ SV31 @ SV112 ) @ ( inf_inf_set_a @ SV76 @ SV129 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[761]) ).
thf(807,plain,
! [SV32: set_a,SV77: set_a] :
( ( ( ~ ( member_a @ ( sK1_SY266 @ SV77 @ SV32 ) @ SV32 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV32 @ SV77 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[762]) ).
thf(808,plain,
! [SV32: set_a,SV77: set_a] :
( ( ( member_a @ ( sK1_SY266 @ SV77 @ SV32 ) @ SV77 )
= $false )
| ( ( ord_less_eq_set_a @ SV32 @ SV77 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[762]) ).
thf(809,plain,
! [SV130: a,SV113: a,SV78: set_Product_prod_a_a,SV33: set_a] :
( ( ( prefer719835986ence_a @ SV33 @ SV78 )
= $false )
| ( ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV113 @ SV33 @ SV78 ) @ ( prefer1676310729than_a @ SV130 @ SV33 @ SV78 ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV130 @ SV33 @ SV78 ) @ ( prefer1676310729than_a @ SV113 @ SV33 @ SV78 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[763]) ).
thf(810,plain,
! [SV80: a > $o,SV35: a > $o] :
( ( ( ord_less_eq_set_a @ ( collect_a @ SV35 ) @ ( collect_a @ SV80 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ ( collect_a @ SV35 ) @ ( collect_a @ SV80 ) )
| ~ ! [SY269: a] :
( ~ ( SV35 @ SY269 )
| ( SV80 @ SY269 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[764]) ).
thf(811,plain,
! [SV80: a > $o,SV35: a > $o] :
( ( ( ! [SY269: a] :
( ~ ( SV35 @ SY269 )
| ( SV80 @ SY269 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ ( collect_a @ SV35 ) @ ( collect_a @ SV80 ) )
| ~ ! [SY269: a] :
( ~ ( SV35 @ SY269 )
| ( SV80 @ SY269 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[764]) ).
thf(812,plain,
! [SV36: set_a,SV114: set_a,SV81: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV81 @ SV114 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV36 @ SV114 )
= $true )
| ( ( ord_less_eq_set_a @ SV36 @ SV81 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[765]) ).
thf(813,plain,
! [SV131: set_a,SV115: set_a,SV82: set_a > set_a,SV37: set_a] :
( ( ( SV37
= ( SV82 @ SV115 ) )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV115 @ SV131 )
| ~ ! [SY273: set_a,SY274: set_a] :
( ~ ( ord_less_eq_set_a @ SY273 @ SY274 )
| ( ord_less_eq_set_a @ ( SV82 @ SY273 ) @ ( SV82 @ SY274 ) ) )
| ( ord_less_eq_set_a @ SV37 @ ( SV82 @ SV131 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[766]) ).
thf(814,plain,
! [SV38: set_a,SV83: set_a] :
( ( ( ord_less_eq_set_a @ SV83 @ SV38 )
= $false )
| ( ( finite_finite_a @ SV83 )
= $true )
| ( ( finite_finite_a @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[767]) ).
thf(815,plain,
! [SV39: set_a,SV84: set_a] :
( ( ( ord_less_eq_set_a @ SV84 @ SV39 )
= $false )
| ( ( SV39 = SV84 )
= $true )
| ( ( ord_less_eq_set_a @ SV39 @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[768]) ).
thf(816,plain,
! [SV132: set_a,SV85: set_a] :
( ( ( ~ ( ( SV85 = SV132 )
| ~ ( ~ ( ord_less_eq_set_a @ SV85 @ SV132 )
| ~ ( ord_less_eq_set_a @ SV132 @ SV85 ) ) ) )
= $true )
| ( ( ~ ( ( SV85 != SV132 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV85 @ SV132 )
| ~ ( ord_less_eq_set_a @ SV132 @ SV85 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[769]) ).
thf(817,plain,
! [SV86: set_a,SV41: set_a] :
( ( ( ~ ( finite_finite_a @ SV41 ) )
= $false )
| ( ( ~ ( finite_finite_a @ SV86 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV41 @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[771]) ).
thf(818,plain,
! [SV87: a > $o,SV42: a > $o] :
( ( ( ~ ( SV42 @ ( sK2_SY277 @ SV87 @ SV42 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( collect_a @ SV42 ) @ ( collect_a @ SV87 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[772]) ).
thf(819,plain,
! [SV42: a > $o,SV87: a > $o] :
( ( ( SV87 @ ( sK2_SY277 @ SV87 @ SV42 ) )
= $false )
| ( ( ord_less_eq_set_a @ ( collect_a @ SV42 ) @ ( collect_a @ SV87 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[772]) ).
thf(820,plain,
! [SV43: set_a,SV88: set_a] :
( ( ( ~ ( ( ord_less_eq_set_a @ SV88 @ SV43 )
| ( SV88 = SV43 ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV88 @ SV43 )
| ( SV88 != SV43 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV43 @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[773]) ).
thf(821,plain,
! [SV89: set_a,SV117: set_a,SV44: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV44 @ SV117 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV44 @ ( inf_inf_set_a @ SV89 @ SV117 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV44 @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[775]) ).
thf(822,plain,
! [SV45: set_a,SV90: set_a] :
( ( ( ord_less_eq_set_a @ SV90 @ SV45 )
= $false )
| ( ( SV45 = SV90 )
= $true )
| ( ( ord_less_eq_set_a @ SV45 @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[776]) ).
thf(823,plain,
! [SV92: set_a,SV47: set_a,SV118: a] :
( ( ( ~ ( member_a @ SV118 @ SV47 ) )
= $true )
| ( ( member_a @ SV118 @ SV92 )
= $true )
| ( ( ord_less_eq_set_a @ SV47 @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[777]) ).
thf(824,plain,
! [SV93: set_a,SV48: set_a,SV119: a] :
( ( ( ~ ( member_a @ SV119 @ SV48 ) )
= $true )
| ( ( member_a @ SV119 @ SV93 )
= $true )
| ( ( ord_less_eq_set_a @ SV48 @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[778]) ).
thf(825,plain,
! [SV49: set_a,SV94: set_a] :
( ( ( ord_less_eq_set_a @ SV94 @ SV49 )
= $false )
| ( ( SV94 = SV49 )
= $true )
| ( ( ord_less_eq_set_a @ SV49 @ SV94 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[779]) ).
thf(826,plain,
! [SV133: set_a,SV120: set_a > set_a,SV96: set_a,SV51: set_a] :
( ( ( ord_less_eq_set_a @ SV51 @ SV96 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ ( SV120 @ SV96 ) @ SV133 )
| ~ ! [SY304: set_a,SY305: set_a] :
( ~ ( ord_less_eq_set_a @ SY304 @ SY305 )
| ( ord_less_eq_set_a @ ( SV120 @ SY304 ) @ ( SV120 @ SY305 ) ) )
| ( ord_less_eq_set_a @ ( SV120 @ SV51 ) @ SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[780]) ).
thf(827,plain,
! [SV134: set_a,SV97: set_a] :
( ( ( ~ ( ( ord_less_eq_set_a @ SV97 @ SV134 )
| ! [SY316: a] :
( ~ ( member_a @ SY316 @ SV97 )
| ( member_a @ SY316 @ SV134 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV97 @ SV134 )
| ~ ! [SY316: a] :
( ~ ( member_a @ SY316 @ SV97 )
| ( member_a @ SY316 @ SV134 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[781]) ).
thf(828,plain,
! [SV53: set_a,SV122: set_a,SV98: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV98 @ SV122 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV53 @ SV122 )
= $true )
| ( ( ord_less_eq_set_a @ SV53 @ SV98 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[783]) ).
thf(829,plain,
! [SV3: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a ) )
= $false )
| ( ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[784]) ).
thf(830,plain,
! [SV3: set_a] :
( ( ( SV3 != bot_bot_set_a )
= $false )
| ( ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[784]) ).
thf(831,plain,
! [SV3: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a ) )
= $false )
| ( ( SV3 = bot_bot_set_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[785]) ).
thf(832,plain,
! [SV3: set_a] :
( ( ( SV3 != bot_bot_set_a )
= $false )
| ( ( SV3 = bot_bot_set_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[785]) ).
thf(833,plain,
! [SV7: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a ) )
= $false )
| ( ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[786]) ).
thf(834,plain,
! [SV7: set_a] :
( ( ( SV7 != bot_bot_set_a )
= $false )
| ( ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[786]) ).
thf(835,plain,
! [SV7: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a ) )
= $false )
| ( ( SV7 = bot_bot_set_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[787]) ).
thf(836,plain,
! [SV7: set_a] :
( ( ( SV7 != bot_bot_set_a )
= $false )
| ( ( SV7 = bot_bot_set_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[787]) ).
thf(837,plain,
! [SV57: set_a,SV11: set_a,SV99: set_a] :
( ( ( ord_less_eq_set_a @ SV99 @ SV11 )
= $false )
| ( ( ord_less_eq_set_a @ SV99 @ SV57 )
= $true )
| ( ( ord_less_eq_set_a @ SV11 @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[788]) ).
thf(838,plain,
! [SV12: set_a,SV100: set_a,SV58: set_a] :
( ( ( SV58 = SV100 )
= $false )
| ( ( ord_less_eq_set_a @ SV12 @ SV100 )
= $true )
| ( ( ord_less_eq_set_a @ SV12 @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[789]) ).
thf(839,plain,
! [SV13: set_a,SV101: set_a,SV59: set_a] :
( ( ( ord_less_eq_set_a @ SV59 @ SV101 )
= $false )
| ( ( ord_less_eq_set_a @ SV13 @ SV101 )
= $true )
| ( ( ord_less_eq_set_a @ SV13 @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[790]) ).
thf(840,plain,
! [SV123: set_a,SV60: set_a] :
( ( ( ( SV60 = SV123 )
| ~ ( ~ ( ord_less_eq_set_a @ SV60 @ SV123 )
| ~ ( ord_less_eq_set_a @ SV123 @ SV60 ) ) )
= $false )
| ( ( ~ ( ( SV60 != SV123 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV60 @ SV123 )
| ~ ( ord_less_eq_set_a @ SV123 @ SV60 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[791]) ).
thf(841,plain,
! [SV61: set_a,SV15: set_a > $o] :
( ( ( ~ ( SV15 @ ( sK3_SY242 @ SV61 @ SV15 ) )
| ( ord_less_eq_set_a @ ( sK3_SY242 @ SV61 @ SV15 ) @ SV61 ) )
= $false )
| ( ( ( order_Greatest_set_a @ SV15 )
= SV61 )
= $true )
| ( ( SV15 @ SV61 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[792]) ).
thf(842,plain,
! [SV103: set_a > $o,SV62: set_a,SV16: set_a > $o] :
( ( ( ! [SY244: set_a] :
( ~ ( SV16 @ SY244 )
| ( ord_less_eq_set_a @ SY244 @ SV62 ) ) )
= $false )
| ( ( ~ ! [SY289: set_a] :
( ~ ( SV16 @ SY289 )
| ~ ! [SY164: set_a] :
( ~ ( SV16 @ SY164 )
| ( ord_less_eq_set_a @ SY164 @ SY289 ) )
| ( SV103 @ SY289 ) )
| ( SV103 @ ( order_Greatest_set_a @ SV16 ) ) )
= $true )
| ( ( SV16 @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[793]) ).
thf(843,plain,
! [SV19: set_a,SV64: set_a > set_a,SV124: set_a,SV104: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV104 @ SV124 ) )
= $true )
| ( ( ~ ! [SY249: set_a,SY250: set_a] :
( ~ ( ord_less_eq_set_a @ SY249 @ SY250 )
| ( ord_less_eq_set_a @ ( SV64 @ SY249 ) @ ( SV64 @ SY250 ) ) )
| ( ord_less_eq_set_a @ SV19 @ ( SV64 @ SV124 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV19 @ ( SV64 @ SV104 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[794]) ).
thf(844,plain,
! [SV105: set_a,SV66: set_a,SV21: set_a] :
( ( ( ord_less_eq_set_a @ SV21 @ ( inf_inf_set_a @ SV66 @ SV105 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV21 @ ( inf_inf_set_a @ SV66 @ SV105 ) )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV21 @ SV66 )
| ~ ( ord_less_eq_set_a @ SV21 @ SV105 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[796]) ).
thf(845,plain,
! [SV105: set_a,SV66: set_a,SV21: set_a] :
( ( ( ~ ( ~ ( ord_less_eq_set_a @ SV21 @ SV66 )
| ~ ( ord_less_eq_set_a @ SV21 @ SV105 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV21 @ ( inf_inf_set_a @ SV66 @ SV105 ) )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV21 @ SV66 )
| ~ ( ord_less_eq_set_a @ SV21 @ SV105 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[796]) ).
thf(846,plain,
! [SV125: set_a,SV67: set_a] :
( ( ( ( SV67 = SV125 )
| ~ ( ~ ( ord_less_eq_set_a @ SV125 @ SV67 )
| ~ ( ord_less_eq_set_a @ SV67 @ SV125 ) ) )
= $false )
| ( ( ~ ( ( SV67 != SV125 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV125 @ SV67 )
| ~ ( ord_less_eq_set_a @ SV67 @ SV125 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[797]) ).
thf(847,plain,
! [SV126: set_a,SV68: set_a] :
( ( ( ( SV68 = SV126 )
| ~ ( ~ ( ord_less_eq_set_a @ SV68 @ SV126 )
| ~ ( ord_less_eq_set_a @ SV126 @ SV68 ) ) )
= $false )
| ( ( ~ ( ( SV68 != SV126 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV68 @ SV126 )
| ~ ( ord_less_eq_set_a @ SV126 @ SV68 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[798]) ).
thf(848,plain,
! [SV127: set_a,SV69: set_a] :
( ( ( ( ord_less_eq_set_a @ SV69 @ SV127 )
| ! [SY309: a] :
( ~ ( member_a @ SY309 @ SV69 )
| ( member_a @ SY309 @ SV127 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV69 @ SV127 )
| ~ ! [SY309: a] :
( ~ ( member_a @ SY309 @ SV69 )
| ( member_a @ SY309 @ SV127 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[799]) ).
thf(849,plain,
! [SV26: set_a,SV109: set_a,SV71: set_a] :
( ( ( ord_less_eq_set_a @ SV71 @ SV109 )
= $false )
| ( ( ord_less_eq_set_a @ SV26 @ SV109 )
= $true )
| ( ( SV26 = SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[800]) ).
thf(850,plain,
! [SV28: set_a,SV128: set_a,SV73: set_a,SV110: set_a > set_a] :
( ( ( ( SV110 @ SV73 )
!= SV128 )
= $true )
| ( ( ~ ! [SY296: set_a,SY297: set_a] :
( ~ ( ord_less_eq_set_a @ SY296 @ SY297 )
| ( ord_less_eq_set_a @ ( SV110 @ SY296 ) @ ( SV110 @ SY297 ) ) )
| ( ord_less_eq_set_a @ ( SV110 @ SV28 ) @ SV128 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV28 @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[802]) ).
thf(851,plain,
! [SV74: set_a,SV29: set_a] :
( ( ( ord_less_eq_set_a @ SV29 @ SV74 )
= $true )
| ( ( SV29 = SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[803]) ).
thf(852,plain,
! [SV29: set_a,SV74: set_a] :
( ( ( ord_less_eq_set_a @ SV74 @ SV29 )
= $true )
| ( ( SV29 = SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[804]) ).
thf(853,plain,
! [SV111: set_a,SV75: set_a,SV30: set_a] :
( ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ SV30 @ SV75 ) @ SV111 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ ( sup_sup_set_a @ SV30 @ SV75 ) @ SV111 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV30 @ SV111 )
| ~ ( ord_less_eq_set_a @ SV75 @ SV111 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[805]) ).
thf(854,plain,
! [SV75: set_a,SV111: set_a,SV30: set_a] :
( ( ( ~ ( ~ ( ord_less_eq_set_a @ SV30 @ SV111 )
| ~ ( ord_less_eq_set_a @ SV75 @ SV111 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ ( sup_sup_set_a @ SV30 @ SV75 ) @ SV111 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV30 @ SV111 )
| ~ ( ord_less_eq_set_a @ SV75 @ SV111 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[805]) ).
thf(855,plain,
! [SV76: set_a,SV31: set_a,SV129: set_a,SV112: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV112 @ SV129 ) )
= $true )
| ( ( ord_less_eq_set_a @ ( inf_inf_set_a @ SV31 @ SV112 ) @ ( inf_inf_set_a @ SV76 @ SV129 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV31 @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[806]) ).
thf(856,plain,
! [SV32: set_a,SV77: set_a] :
( ( ( member_a @ ( sK1_SY266 @ SV77 @ SV32 ) @ SV32 )
= $true )
| ( ( ord_less_eq_set_a @ SV32 @ SV77 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[807]) ).
thf(857,plain,
! [SV130: a,SV78: set_Product_prod_a_a,SV33: set_a,SV113: a] :
( ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV113 @ SV33 @ SV78 ) @ ( prefer1676310729than_a @ SV130 @ SV33 @ SV78 ) )
= $true )
| ( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ SV130 @ SV33 @ SV78 ) @ ( prefer1676310729than_a @ SV113 @ SV33 @ SV78 ) )
= $true )
| ( ( prefer719835986ence_a @ SV33 @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[809]) ).
thf(858,plain,
! [SV80: a > $o,SV35: a > $o] :
( ( ( ~ ( ord_less_eq_set_a @ ( collect_a @ SV35 ) @ ( collect_a @ SV80 ) )
| ~ ! [SY269: a] :
( ~ ( SV35 @ SY269 )
| ( SV80 @ SY269 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( collect_a @ SV35 ) @ ( collect_a @ SV80 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[810]) ).
thf(859,plain,
! [SV80: a > $o,SV35: a > $o] :
( ( ( ~ ( SV35 @ ( sK4_SY269 @ SV80 @ SV35 ) )
| ( SV80 @ ( sK4_SY269 @ SV80 @ SV35 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ ( collect_a @ SV35 ) @ ( collect_a @ SV80 ) )
| ~ ! [SY269: a] :
( ~ ( SV35 @ SY269 )
| ( SV80 @ SY269 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[811]) ).
thf(860,plain,
! [SV36: set_a,SV114: set_a,SV81: set_a] :
( ( ( ord_less_eq_set_a @ SV81 @ SV114 )
= $false )
| ( ( ord_less_eq_set_a @ SV36 @ SV114 )
= $true )
| ( ( ord_less_eq_set_a @ SV36 @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[812]) ).
thf(861,plain,
! [SV37: set_a,SV82: set_a > set_a,SV131: set_a,SV115: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV115 @ SV131 ) )
= $true )
| ( ( ~ ! [SY273: set_a,SY274: set_a] :
( ~ ( ord_less_eq_set_a @ SY273 @ SY274 )
| ( ord_less_eq_set_a @ ( SV82 @ SY273 ) @ ( SV82 @ SY274 ) ) )
| ( ord_less_eq_set_a @ SV37 @ ( SV82 @ SV131 ) ) )
= $true )
| ( ( SV37
= ( SV82 @ SV115 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[813]) ).
thf(862,plain,
! [SV132: set_a,SV85: set_a] :
( ( ( ( SV85 = SV132 )
| ~ ( ~ ( ord_less_eq_set_a @ SV85 @ SV132 )
| ~ ( ord_less_eq_set_a @ SV132 @ SV85 ) ) )
= $false )
| ( ( ~ ( ( SV85 != SV132 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV85 @ SV132 )
| ~ ( ord_less_eq_set_a @ SV132 @ SV85 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[816]) ).
thf(863,plain,
! [SV86: set_a,SV41: set_a] :
( ( ( finite_finite_a @ SV41 )
= $true )
| ( ( ~ ( finite_finite_a @ SV86 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV41 @ SV86 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[817]) ).
thf(864,plain,
! [SV87: a > $o,SV42: a > $o] :
( ( ( SV42 @ ( sK2_SY277 @ SV87 @ SV42 ) )
= $true )
| ( ( ord_less_eq_set_a @ ( collect_a @ SV42 ) @ ( collect_a @ SV87 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[818]) ).
thf(865,plain,
! [SV43: set_a,SV88: set_a] :
( ( ( ( ord_less_eq_set_a @ SV88 @ SV43 )
| ( SV88 = SV43 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV88 @ SV43 )
| ( SV88 != SV43 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV43 @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[820]) ).
thf(866,plain,
! [SV89: set_a,SV117: set_a,SV44: set_a] :
( ( ( ord_less_eq_set_a @ SV44 @ SV117 )
= $false )
| ( ( ord_less_eq_set_a @ SV44 @ ( inf_inf_set_a @ SV89 @ SV117 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV44 @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[821]) ).
thf(867,plain,
! [SV92: set_a,SV47: set_a,SV118: a] :
( ( ( member_a @ SV118 @ SV47 )
= $false )
| ( ( member_a @ SV118 @ SV92 )
= $true )
| ( ( ord_less_eq_set_a @ SV47 @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[823]) ).
thf(868,plain,
! [SV93: set_a,SV48: set_a,SV119: a] :
( ( ( member_a @ SV119 @ SV48 )
= $false )
| ( ( member_a @ SV119 @ SV93 )
= $true )
| ( ( ord_less_eq_set_a @ SV48 @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[824]) ).
thf(869,plain,
! [SV51: set_a,SV133: set_a,SV96: set_a,SV120: set_a > set_a] :
( ( ( ~ ( ord_less_eq_set_a @ ( SV120 @ SV96 ) @ SV133 ) )
= $true )
| ( ( ~ ! [SY304: set_a,SY305: set_a] :
( ~ ( ord_less_eq_set_a @ SY304 @ SY305 )
| ( ord_less_eq_set_a @ ( SV120 @ SY304 ) @ ( SV120 @ SY305 ) ) )
| ( ord_less_eq_set_a @ ( SV120 @ SV51 ) @ SV133 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV51 @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[826]) ).
thf(870,plain,
! [SV134: set_a,SV97: set_a] :
( ( ( ( ord_less_eq_set_a @ SV97 @ SV134 )
| ! [SY316: a] :
( ~ ( member_a @ SY316 @ SV97 )
| ( member_a @ SY316 @ SV134 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV97 @ SV134 )
| ~ ! [SY316: a] :
( ~ ( member_a @ SY316 @ SV97 )
| ( member_a @ SY316 @ SV134 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[827]) ).
thf(871,plain,
! [SV53: set_a,SV122: set_a,SV98: set_a] :
( ( ( ord_less_eq_set_a @ SV98 @ SV122 )
= $false )
| ( ( ord_less_eq_set_a @ SV53 @ SV122 )
= $true )
| ( ( ord_less_eq_set_a @ SV53 @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[828]) ).
thf(872,plain,
! [SV3: set_a] :
( ( ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[829]) ).
thf(873,plain,
! [SV3: set_a] :
( ( ( SV3 = bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[830]) ).
thf(874,plain,
! [SV3: set_a] :
( ( ( ord_less_eq_set_a @ SV3 @ bot_bot_set_a )
= $true )
| ( ( SV3 = bot_bot_set_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[831]) ).
thf(875,plain,
! [SV3: set_a] :
( ( ( SV3 = bot_bot_set_a )
= $true )
| ( ( SV3 = bot_bot_set_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[832]) ).
thf(876,plain,
! [SV7: set_a] :
( ( ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[833]) ).
thf(877,plain,
! [SV7: set_a] :
( ( ( SV7 = bot_bot_set_a )
= $true )
| ( ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[834]) ).
thf(878,plain,
! [SV7: set_a] :
( ( ( ord_less_eq_set_a @ SV7 @ bot_bot_set_a )
= $true )
| ( ( SV7 = bot_bot_set_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[835]) ).
thf(879,plain,
! [SV7: set_a] :
( ( ( SV7 = bot_bot_set_a )
= $true )
| ( ( SV7 = bot_bot_set_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[836]) ).
thf(880,plain,
! [SV123: set_a,SV60: set_a] :
( ( ( SV60 = SV123 )
= $false )
| ( ( ~ ( ( SV60 != SV123 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV60 @ SV123 )
| ~ ( ord_less_eq_set_a @ SV123 @ SV60 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[840]) ).
thf(881,plain,
! [SV123: set_a,SV60: set_a] :
( ( ( ~ ( ~ ( ord_less_eq_set_a @ SV60 @ SV123 )
| ~ ( ord_less_eq_set_a @ SV123 @ SV60 ) ) )
= $false )
| ( ( ~ ( ( SV60 != SV123 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV60 @ SV123 )
| ~ ( ord_less_eq_set_a @ SV123 @ SV60 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[840]) ).
thf(882,plain,
! [SV61: set_a,SV15: set_a > $o] :
( ( ( ~ ( SV15 @ ( sK3_SY242 @ SV61 @ SV15 ) ) )
= $false )
| ( ( ( order_Greatest_set_a @ SV15 )
= SV61 )
= $true )
| ( ( SV15 @ SV61 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[841]) ).
thf(883,plain,
! [SV15: set_a > $o,SV61: set_a] :
( ( ( ord_less_eq_set_a @ ( sK3_SY242 @ SV61 @ SV15 ) @ SV61 )
= $false )
| ( ( ( order_Greatest_set_a @ SV15 )
= SV61 )
= $true )
| ( ( SV15 @ SV61 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[841]) ).
thf(884,plain,
! [SV62: set_a,SV103: set_a > $o,SV16: set_a > $o] :
( ( ( ~ ( SV16 @ ( sK5_SY244 @ SV103 @ SV62 @ SV16 ) )
| ( ord_less_eq_set_a @ ( sK5_SY244 @ SV103 @ SV62 @ SV16 ) @ SV62 ) )
= $false )
| ( ( ~ ! [SY289: set_a] :
( ~ ( SV16 @ SY289 )
| ~ ! [SY164: set_a] :
( ~ ( SV16 @ SY164 )
| ( ord_less_eq_set_a @ SY164 @ SY289 ) )
| ( SV103 @ SY289 ) )
| ( SV103 @ ( order_Greatest_set_a @ SV16 ) ) )
= $true )
| ( ( SV16 @ SV62 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[842]) ).
thf(885,plain,
! [SV19: set_a,SV64: set_a > set_a,SV124: set_a,SV104: set_a] :
( ( ( ord_less_eq_set_a @ SV104 @ SV124 )
= $false )
| ( ( ~ ! [SY249: set_a,SY250: set_a] :
( ~ ( ord_less_eq_set_a @ SY249 @ SY250 )
| ( ord_less_eq_set_a @ ( SV64 @ SY249 ) @ ( SV64 @ SY250 ) ) )
| ( ord_less_eq_set_a @ SV19 @ ( SV64 @ SV124 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV19 @ ( SV64 @ SV104 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[843]) ).
thf(886,plain,
! [SV105: set_a,SV66: set_a,SV21: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV21 @ ( inf_inf_set_a @ SV66 @ SV105 ) )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV21 @ SV66 )
| ~ ( ord_less_eq_set_a @ SV21 @ SV105 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV21 @ ( inf_inf_set_a @ SV66 @ SV105 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[844]) ).
thf(887,plain,
! [SV105: set_a,SV66: set_a,SV21: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV21 @ SV66 )
| ~ ( ord_less_eq_set_a @ SV21 @ SV105 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV21 @ ( inf_inf_set_a @ SV66 @ SV105 ) )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV21 @ SV66 )
| ~ ( ord_less_eq_set_a @ SV21 @ SV105 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[845]) ).
thf(888,plain,
! [SV125: set_a,SV67: set_a] :
( ( ( SV67 = SV125 )
= $false )
| ( ( ~ ( ( SV67 != SV125 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV125 @ SV67 )
| ~ ( ord_less_eq_set_a @ SV67 @ SV125 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[846]) ).
thf(889,plain,
! [SV67: set_a,SV125: set_a] :
( ( ( ~ ( ~ ( ord_less_eq_set_a @ SV125 @ SV67 )
| ~ ( ord_less_eq_set_a @ SV67 @ SV125 ) ) )
= $false )
| ( ( ~ ( ( SV67 != SV125 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV125 @ SV67 )
| ~ ( ord_less_eq_set_a @ SV67 @ SV125 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[846]) ).
thf(890,plain,
! [SV126: set_a,SV68: set_a] :
( ( ( SV68 = SV126 )
= $false )
| ( ( ~ ( ( SV68 != SV126 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV68 @ SV126 )
| ~ ( ord_less_eq_set_a @ SV126 @ SV68 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[847]) ).
thf(891,plain,
! [SV126: set_a,SV68: set_a] :
( ( ( ~ ( ~ ( ord_less_eq_set_a @ SV68 @ SV126 )
| ~ ( ord_less_eq_set_a @ SV126 @ SV68 ) ) )
= $false )
| ( ( ~ ( ( SV68 != SV126 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV68 @ SV126 )
| ~ ( ord_less_eq_set_a @ SV126 @ SV68 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[847]) ).
thf(892,plain,
! [SV127: set_a,SV69: set_a] :
( ( ( ord_less_eq_set_a @ SV69 @ SV127 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV69 @ SV127 )
| ~ ! [SY309: a] :
( ~ ( member_a @ SY309 @ SV69 )
| ( member_a @ SY309 @ SV127 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[848]) ).
thf(893,plain,
! [SV127: set_a,SV69: set_a] :
( ( ( ! [SY309: a] :
( ~ ( member_a @ SY309 @ SV69 )
| ( member_a @ SY309 @ SV127 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV69 @ SV127 )
| ~ ! [SY309: a] :
( ~ ( member_a @ SY309 @ SV69 )
| ( member_a @ SY309 @ SV127 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[848]) ).
thf(894,plain,
! [SV28: set_a,SV128: set_a,SV73: set_a,SV110: set_a > set_a] :
( ( ( ( SV110 @ SV73 )
= SV128 )
= $false )
| ( ( ~ ! [SY296: set_a,SY297: set_a] :
( ~ ( ord_less_eq_set_a @ SY296 @ SY297 )
| ( ord_less_eq_set_a @ ( SV110 @ SY296 ) @ ( SV110 @ SY297 ) ) )
| ( ord_less_eq_set_a @ ( SV110 @ SV28 ) @ SV128 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV28 @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[850]) ).
thf(895,plain,
! [SV111: set_a,SV75: set_a,SV30: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ ( sup_sup_set_a @ SV30 @ SV75 ) @ SV111 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV30 @ SV111 )
| ~ ( ord_less_eq_set_a @ SV75 @ SV111 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ SV30 @ SV75 ) @ SV111 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[853]) ).
thf(896,plain,
! [SV75: set_a,SV111: set_a,SV30: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV30 @ SV111 )
| ~ ( ord_less_eq_set_a @ SV75 @ SV111 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ ( sup_sup_set_a @ SV30 @ SV75 ) @ SV111 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV30 @ SV111 )
| ~ ( ord_less_eq_set_a @ SV75 @ SV111 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[854]) ).
thf(897,plain,
! [SV76: set_a,SV31: set_a,SV129: set_a,SV112: set_a] :
( ( ( ord_less_eq_set_a @ SV112 @ SV129 )
= $false )
| ( ( ord_less_eq_set_a @ ( inf_inf_set_a @ SV31 @ SV112 ) @ ( inf_inf_set_a @ SV76 @ SV129 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV31 @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[855]) ).
thf(898,plain,
! [SV80: a > $o,SV35: a > $o] :
( ( ( ~ ( ord_less_eq_set_a @ ( collect_a @ SV35 ) @ ( collect_a @ SV80 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( collect_a @ SV35 ) @ ( collect_a @ SV80 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[858]) ).
thf(899,plain,
! [SV80: a > $o,SV35: a > $o] :
( ( ( ~ ! [SY269: a] :
( ~ ( SV35 @ SY269 )
| ( SV80 @ SY269 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( collect_a @ SV35 ) @ ( collect_a @ SV80 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[858]) ).
thf(900,plain,
! [SV80: a > $o,SV35: a > $o] :
( ( ( ~ ( SV35 @ ( sK4_SY269 @ SV80 @ SV35 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ ( collect_a @ SV35 ) @ ( collect_a @ SV80 ) )
| ~ ! [SY269: a] :
( ~ ( SV35 @ SY269 )
| ( SV80 @ SY269 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[859]) ).
thf(901,plain,
! [SV35: a > $o,SV80: a > $o] :
( ( ( SV80 @ ( sK4_SY269 @ SV80 @ SV35 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ ( collect_a @ SV35 ) @ ( collect_a @ SV80 ) )
| ~ ! [SY269: a] :
( ~ ( SV35 @ SY269 )
| ( SV80 @ SY269 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[859]) ).
thf(902,plain,
! [SV37: set_a,SV82: set_a > set_a,SV131: set_a,SV115: set_a] :
( ( ( ord_less_eq_set_a @ SV115 @ SV131 )
= $false )
| ( ( ~ ! [SY273: set_a,SY274: set_a] :
( ~ ( ord_less_eq_set_a @ SY273 @ SY274 )
| ( ord_less_eq_set_a @ ( SV82 @ SY273 ) @ ( SV82 @ SY274 ) ) )
| ( ord_less_eq_set_a @ SV37 @ ( SV82 @ SV131 ) ) )
= $true )
| ( ( SV37
= ( SV82 @ SV115 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[861]) ).
thf(903,plain,
! [SV132: set_a,SV85: set_a] :
( ( ( SV85 = SV132 )
= $false )
| ( ( ~ ( ( SV85 != SV132 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV85 @ SV132 )
| ~ ( ord_less_eq_set_a @ SV132 @ SV85 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[862]) ).
thf(904,plain,
! [SV132: set_a,SV85: set_a] :
( ( ( ~ ( ~ ( ord_less_eq_set_a @ SV85 @ SV132 )
| ~ ( ord_less_eq_set_a @ SV132 @ SV85 ) ) )
= $false )
| ( ( ~ ( ( SV85 != SV132 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV85 @ SV132 )
| ~ ( ord_less_eq_set_a @ SV132 @ SV85 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[862]) ).
thf(905,plain,
! [SV41: set_a,SV86: set_a] :
( ( ( finite_finite_a @ SV86 )
= $false )
| ( ( finite_finite_a @ SV41 )
= $true )
| ( ( ord_less_eq_set_a @ SV41 @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[863]) ).
thf(906,plain,
! [SV43: set_a,SV88: set_a] :
( ( ( ord_less_eq_set_a @ SV88 @ SV43 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV88 @ SV43 )
| ( SV88 != SV43 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV43 @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[865]) ).
thf(907,plain,
! [SV43: set_a,SV88: set_a] :
( ( ( SV88 = SV43 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV88 @ SV43 )
| ( SV88 != SV43 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV43 @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[865]) ).
thf(908,plain,
! [SV51: set_a,SV133: set_a,SV96: set_a,SV120: set_a > set_a] :
( ( ( ord_less_eq_set_a @ ( SV120 @ SV96 ) @ SV133 )
= $false )
| ( ( ~ ! [SY304: set_a,SY305: set_a] :
( ~ ( ord_less_eq_set_a @ SY304 @ SY305 )
| ( ord_less_eq_set_a @ ( SV120 @ SY304 ) @ ( SV120 @ SY305 ) ) )
| ( ord_less_eq_set_a @ ( SV120 @ SV51 ) @ SV133 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV51 @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[869]) ).
thf(909,plain,
! [SV134: set_a,SV97: set_a] :
( ( ( ord_less_eq_set_a @ SV97 @ SV134 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV97 @ SV134 )
| ~ ! [SY316: a] :
( ~ ( member_a @ SY316 @ SV97 )
| ( member_a @ SY316 @ SV134 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[870]) ).
thf(910,plain,
! [SV134: set_a,SV97: set_a] :
( ( ( ! [SY316: a] :
( ~ ( member_a @ SY316 @ SV97 )
| ( member_a @ SY316 @ SV134 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV97 @ SV134 )
| ~ ! [SY316: a] :
( ~ ( member_a @ SY316 @ SV97 )
| ( member_a @ SY316 @ SV134 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[870]) ).
thf(911,plain,
! [SV123: set_a,SV60: set_a] :
( ( ( ( SV60 != SV123 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV60 @ SV123 )
| ~ ( ord_less_eq_set_a @ SV123 @ SV60 ) ) )
= $false )
| ( ( SV60 = SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[880]) ).
thf(912,plain,
! [SV123: set_a,SV60: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV60 @ SV123 )
| ~ ( ord_less_eq_set_a @ SV123 @ SV60 ) )
= $true )
| ( ( ~ ( ( SV60 != SV123 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV60 @ SV123 )
| ~ ( ord_less_eq_set_a @ SV123 @ SV60 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[881]) ).
thf(913,plain,
! [SV61: set_a,SV15: set_a > $o] :
( ( ( SV15 @ ( sK3_SY242 @ SV61 @ SV15 ) )
= $true )
| ( ( ( order_Greatest_set_a @ SV15 )
= SV61 )
= $true )
| ( ( SV15 @ SV61 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[882]) ).
thf(914,plain,
! [SV62: set_a,SV103: set_a > $o,SV16: set_a > $o] :
( ( ( ~ ( SV16 @ ( sK5_SY244 @ SV103 @ SV62 @ SV16 ) ) )
= $false )
| ( ( ~ ! [SY289: set_a] :
( ~ ( SV16 @ SY289 )
| ~ ! [SY164: set_a] :
( ~ ( SV16 @ SY164 )
| ( ord_less_eq_set_a @ SY164 @ SY289 ) )
| ( SV103 @ SY289 ) )
| ( SV103 @ ( order_Greatest_set_a @ SV16 ) ) )
= $true )
| ( ( SV16 @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[884]) ).
thf(915,plain,
! [SV16: set_a > $o,SV62: set_a,SV103: set_a > $o] :
( ( ( ord_less_eq_set_a @ ( sK5_SY244 @ SV103 @ SV62 @ SV16 ) @ SV62 )
= $false )
| ( ( ~ ! [SY289: set_a] :
( ~ ( SV16 @ SY289 )
| ~ ! [SY164: set_a] :
( ~ ( SV16 @ SY164 )
| ( ord_less_eq_set_a @ SY164 @ SY289 ) )
| ( SV103 @ SY289 ) )
| ( SV103 @ ( order_Greatest_set_a @ SV16 ) ) )
= $true )
| ( ( SV16 @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[884]) ).
thf(916,plain,
! [SV104: set_a,SV124: set_a,SV19: set_a,SV64: set_a > set_a] :
( ( ( ~ ! [SY249: set_a,SY250: set_a] :
( ~ ( ord_less_eq_set_a @ SY249 @ SY250 )
| ( ord_less_eq_set_a @ ( SV64 @ SY249 ) @ ( SV64 @ SY250 ) ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV19 @ ( SV64 @ SV124 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV104 @ SV124 )
= $false )
| ( ( ord_less_eq_set_a @ SV19 @ ( SV64 @ SV104 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[885]) ).
thf(917,plain,
! [SV105: set_a,SV66: set_a,SV21: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV21 @ ( inf_inf_set_a @ SV66 @ SV105 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV21 @ ( inf_inf_set_a @ SV66 @ SV105 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[886]) ).
thf(918,plain,
! [SV105: set_a,SV66: set_a,SV21: set_a] :
( ( ( ~ ~ ( ~ ( ord_less_eq_set_a @ SV21 @ SV66 )
| ~ ( ord_less_eq_set_a @ SV21 @ SV105 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV21 @ ( inf_inf_set_a @ SV66 @ SV105 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[886]) ).
thf(919,plain,
! [SV105: set_a,SV66: set_a,SV21: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV21 @ SV66 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV21 @ SV105 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV21 @ ( inf_inf_set_a @ SV66 @ SV105 ) )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV21 @ SV66 )
| ~ ( ord_less_eq_set_a @ SV21 @ SV105 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[887]) ).
thf(920,plain,
! [SV125: set_a,SV67: set_a] :
( ( ( ( SV67 != SV125 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV125 @ SV67 )
| ~ ( ord_less_eq_set_a @ SV67 @ SV125 ) ) )
= $false )
| ( ( SV67 = SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[888]) ).
thf(921,plain,
! [SV67: set_a,SV125: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV125 @ SV67 )
| ~ ( ord_less_eq_set_a @ SV67 @ SV125 ) )
= $true )
| ( ( ~ ( ( SV67 != SV125 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV125 @ SV67 )
| ~ ( ord_less_eq_set_a @ SV67 @ SV125 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[889]) ).
thf(922,plain,
! [SV126: set_a,SV68: set_a] :
( ( ( ( SV68 != SV126 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV68 @ SV126 )
| ~ ( ord_less_eq_set_a @ SV126 @ SV68 ) ) )
= $false )
| ( ( SV68 = SV126 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[890]) ).
thf(923,plain,
! [SV126: set_a,SV68: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV68 @ SV126 )
| ~ ( ord_less_eq_set_a @ SV126 @ SV68 ) )
= $true )
| ( ( ~ ( ( SV68 != SV126 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV68 @ SV126 )
| ~ ( ord_less_eq_set_a @ SV126 @ SV68 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[891]) ).
thf(924,plain,
! [SV127: set_a,SV69: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV69 @ SV127 )
| ~ ! [SY309: a] :
( ~ ( member_a @ SY309 @ SV69 )
| ( member_a @ SY309 @ SV127 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV69 @ SV127 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[892]) ).
thf(925,plain,
! [SV69: set_a,SV127: set_a] :
( ( ( ~ ( member_a @ ( sK6_SY309 @ SV127 @ SV69 ) @ SV69 )
| ( member_a @ ( sK6_SY309 @ SV127 @ SV69 ) @ SV127 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV69 @ SV127 )
| ~ ! [SY309: a] :
( ~ ( member_a @ SY309 @ SV69 )
| ( member_a @ SY309 @ SV127 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[893]) ).
thf(926,plain,
! [SV73: set_a,SV128: set_a,SV28: set_a,SV110: set_a > set_a] :
( ( ( ~ ! [SY296: set_a,SY297: set_a] :
( ~ ( ord_less_eq_set_a @ SY296 @ SY297 )
| ( ord_less_eq_set_a @ ( SV110 @ SY296 ) @ ( SV110 @ SY297 ) ) ) )
= $true )
| ( ( ord_less_eq_set_a @ ( SV110 @ SV28 ) @ SV128 )
= $true )
| ( ( ( SV110 @ SV73 )
= SV128 )
= $false )
| ( ( ord_less_eq_set_a @ SV28 @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[894]) ).
thf(927,plain,
! [SV111: set_a,SV75: set_a,SV30: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ ( sup_sup_set_a @ SV30 @ SV75 ) @ SV111 ) )
= $false )
| ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ SV30 @ SV75 ) @ SV111 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[895]) ).
thf(928,plain,
! [SV75: set_a,SV111: set_a,SV30: set_a] :
( ( ( ~ ~ ( ~ ( ord_less_eq_set_a @ SV30 @ SV111 )
| ~ ( ord_less_eq_set_a @ SV75 @ SV111 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ SV30 @ SV75 ) @ SV111 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[895]) ).
thf(929,plain,
! [SV75: set_a,SV111: set_a,SV30: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV30 @ SV111 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV75 @ SV111 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ ( sup_sup_set_a @ SV30 @ SV75 ) @ SV111 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV30 @ SV111 )
| ~ ( ord_less_eq_set_a @ SV75 @ SV111 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[896]) ).
thf(930,plain,
! [SV80: a > $o,SV35: a > $o] :
( ( ( ord_less_eq_set_a @ ( collect_a @ SV35 ) @ ( collect_a @ SV80 ) )
= $true )
| ( ( ord_less_eq_set_a @ ( collect_a @ SV35 ) @ ( collect_a @ SV80 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[898]) ).
thf(931,plain,
! [SV80: a > $o,SV35: a > $o] :
( ( ( ! [SY269: a] :
( ~ ( SV35 @ SY269 )
| ( SV80 @ SY269 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ ( collect_a @ SV35 ) @ ( collect_a @ SV80 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[899]) ).
thf(932,plain,
! [SV80: a > $o,SV35: a > $o] :
( ( ( SV35 @ ( sK4_SY269 @ SV80 @ SV35 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ ( collect_a @ SV35 ) @ ( collect_a @ SV80 ) )
| ~ ! [SY269: a] :
( ~ ( SV35 @ SY269 )
| ( SV80 @ SY269 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[900]) ).
thf(933,plain,
! [SV80: a > $o,SV35: a > $o] :
( ( ( ~ ( ord_less_eq_set_a @ ( collect_a @ SV35 ) @ ( collect_a @ SV80 ) )
| ~ ! [SY269: a] :
( ~ ( SV35 @ SY269 )
| ( SV80 @ SY269 ) ) )
= $false )
| ( ( SV80 @ ( sK4_SY269 @ SV80 @ SV35 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[901]) ).
thf(934,plain,
! [SV115: set_a,SV131: set_a,SV37: set_a,SV82: set_a > set_a] :
( ( ( ~ ! [SY273: set_a,SY274: set_a] :
( ~ ( ord_less_eq_set_a @ SY273 @ SY274 )
| ( ord_less_eq_set_a @ ( SV82 @ SY273 ) @ ( SV82 @ SY274 ) ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV37 @ ( SV82 @ SV131 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV115 @ SV131 )
= $false )
| ( ( SV37
= ( SV82 @ SV115 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[902]) ).
thf(935,plain,
! [SV132: set_a,SV85: set_a] :
( ( ( ( SV85 != SV132 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV85 @ SV132 )
| ~ ( ord_less_eq_set_a @ SV132 @ SV85 ) ) )
= $false )
| ( ( SV85 = SV132 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[903]) ).
thf(936,plain,
! [SV132: set_a,SV85: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV85 @ SV132 )
| ~ ( ord_less_eq_set_a @ SV132 @ SV85 ) )
= $true )
| ( ( ~ ( ( SV85 != SV132 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV85 @ SV132 )
| ~ ( ord_less_eq_set_a @ SV132 @ SV85 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[904]) ).
thf(937,plain,
! [SV43: set_a,SV88: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV88 @ SV43 )
| ( SV88 != SV43 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV88 @ SV43 )
= $false )
| ( ( ord_less_eq_set_a @ SV43 @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[906]) ).
thf(938,plain,
! [SV43: set_a,SV88: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV88 @ SV43 )
| ( SV88 != SV43 ) )
= $false )
| ( ( SV88 = SV43 )
= $false )
| ( ( ord_less_eq_set_a @ SV43 @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[907]) ).
thf(939,plain,
! [SV96: set_a,SV133: set_a,SV51: set_a,SV120: set_a > set_a] :
( ( ( ~ ! [SY304: set_a,SY305: set_a] :
( ~ ( ord_less_eq_set_a @ SY304 @ SY305 )
| ( ord_less_eq_set_a @ ( SV120 @ SY304 ) @ ( SV120 @ SY305 ) ) ) )
= $true )
| ( ( ord_less_eq_set_a @ ( SV120 @ SV51 ) @ SV133 )
= $true )
| ( ( ord_less_eq_set_a @ ( SV120 @ SV96 ) @ SV133 )
= $false )
| ( ( ord_less_eq_set_a @ SV51 @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[908]) ).
thf(940,plain,
! [SV134: set_a,SV97: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV97 @ SV134 )
| ~ ! [SY316: a] :
( ~ ( member_a @ SY316 @ SV97 )
| ( member_a @ SY316 @ SV134 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV97 @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[909]) ).
thf(941,plain,
! [SV97: set_a,SV134: set_a] :
( ( ( ~ ( member_a @ ( sK7_SY316 @ SV134 @ SV97 ) @ SV97 )
| ( member_a @ ( sK7_SY316 @ SV134 @ SV97 ) @ SV134 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV97 @ SV134 )
| ~ ! [SY316: a] :
( ~ ( member_a @ SY316 @ SV97 )
| ( member_a @ SY316 @ SV134 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[910]) ).
thf(942,plain,
! [SV123: set_a,SV60: set_a] :
( ( ( SV60 != SV123 )
= $false )
| ( ( SV60 = SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[911]) ).
thf(943,plain,
! [SV123: set_a,SV60: set_a] :
( ( ( ~ ~ ( ~ ( ord_less_eq_set_a @ SV60 @ SV123 )
| ~ ( ord_less_eq_set_a @ SV123 @ SV60 ) ) )
= $false )
| ( ( SV60 = SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[911]) ).
thf(944,plain,
! [SV123: set_a,SV60: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV60 @ SV123 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV123 @ SV60 ) )
= $true )
| ( ( ~ ( ( SV60 != SV123 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV60 @ SV123 )
| ~ ( ord_less_eq_set_a @ SV123 @ SV60 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[912]) ).
thf(945,plain,
! [SV62: set_a,SV103: set_a > $o,SV16: set_a > $o] :
( ( ( SV16 @ ( sK5_SY244 @ SV103 @ SV62 @ SV16 ) )
= $true )
| ( ( ~ ! [SY289: set_a] :
( ~ ( SV16 @ SY289 )
| ~ ! [SY164: set_a] :
( ~ ( SV16 @ SY164 )
| ( ord_less_eq_set_a @ SY164 @ SY289 ) )
| ( SV103 @ SY289 ) )
| ( SV103 @ ( order_Greatest_set_a @ SV16 ) ) )
= $true )
| ( ( SV16 @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[914]) ).
thf(946,plain,
! [SV62: set_a,SV103: set_a > $o,SV16: set_a > $o] :
( ( ( ~ ! [SY289: set_a] :
( ~ ( SV16 @ SY289 )
| ~ ! [SY164: set_a] :
( ~ ( SV16 @ SY164 )
| ( ord_less_eq_set_a @ SY164 @ SY289 ) )
| ( SV103 @ SY289 ) ) )
= $true )
| ( ( SV103 @ ( order_Greatest_set_a @ SV16 ) )
= $true )
| ( ( ord_less_eq_set_a @ ( sK5_SY244 @ SV103 @ SV62 @ SV16 ) @ SV62 )
= $false )
| ( ( SV16 @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[915]) ).
thf(947,plain,
! [SV104: set_a,SV124: set_a,SV19: set_a,SV64: set_a > set_a] :
( ( ( ! [SY249: set_a,SY250: set_a] :
( ~ ( ord_less_eq_set_a @ SY249 @ SY250 )
| ( ord_less_eq_set_a @ ( SV64 @ SY249 ) @ ( SV64 @ SY250 ) ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV19 @ ( SV64 @ SV124 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV104 @ SV124 )
= $false )
| ( ( ord_less_eq_set_a @ SV19 @ ( SV64 @ SV104 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[916]) ).
thf(948,plain,
! [SV105: set_a,SV66: set_a,SV21: set_a] :
( ( ( ord_less_eq_set_a @ SV21 @ ( inf_inf_set_a @ SV66 @ SV105 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV21 @ ( inf_inf_set_a @ SV66 @ SV105 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[917]) ).
thf(949,plain,
! [SV105: set_a,SV66: set_a,SV21: set_a] :
( ( ( ~ ( ~ ( ord_less_eq_set_a @ SV21 @ SV66 )
| ~ ( ord_less_eq_set_a @ SV21 @ SV105 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV21 @ ( inf_inf_set_a @ SV66 @ SV105 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[918]) ).
thf(950,plain,
! [SV105: set_a,SV66: set_a,SV21: set_a] :
( ( ( ord_less_eq_set_a @ SV21 @ SV66 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV21 @ SV105 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV21 @ ( inf_inf_set_a @ SV66 @ SV105 ) )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV21 @ SV66 )
| ~ ( ord_less_eq_set_a @ SV21 @ SV105 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[919]) ).
thf(951,plain,
! [SV125: set_a,SV67: set_a] :
( ( ( SV67 != SV125 )
= $false )
| ( ( SV67 = SV125 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[920]) ).
thf(952,plain,
! [SV67: set_a,SV125: set_a] :
( ( ( ~ ~ ( ~ ( ord_less_eq_set_a @ SV125 @ SV67 )
| ~ ( ord_less_eq_set_a @ SV67 @ SV125 ) ) )
= $false )
| ( ( SV67 = SV125 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[920]) ).
thf(953,plain,
! [SV67: set_a,SV125: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV125 @ SV67 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV67 @ SV125 ) )
= $true )
| ( ( ~ ( ( SV67 != SV125 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV125 @ SV67 )
| ~ ( ord_less_eq_set_a @ SV67 @ SV125 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[921]) ).
thf(954,plain,
! [SV126: set_a,SV68: set_a] :
( ( ( SV68 != SV126 )
= $false )
| ( ( SV68 = SV126 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[922]) ).
thf(955,plain,
! [SV126: set_a,SV68: set_a] :
( ( ( ~ ~ ( ~ ( ord_less_eq_set_a @ SV68 @ SV126 )
| ~ ( ord_less_eq_set_a @ SV126 @ SV68 ) ) )
= $false )
| ( ( SV68 = SV126 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[922]) ).
thf(956,plain,
! [SV126: set_a,SV68: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV68 @ SV126 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV126 @ SV68 ) )
= $true )
| ( ( ~ ( ( SV68 != SV126 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV68 @ SV126 )
| ~ ( ord_less_eq_set_a @ SV126 @ SV68 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[923]) ).
thf(957,plain,
! [SV127: set_a,SV69: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV69 @ SV127 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV69 @ SV127 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[924]) ).
thf(958,plain,
! [SV127: set_a,SV69: set_a] :
( ( ( ~ ! [SY309: a] :
( ~ ( member_a @ SY309 @ SV69 )
| ( member_a @ SY309 @ SV127 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV69 @ SV127 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[924]) ).
thf(959,plain,
! [SV69: set_a,SV127: set_a] :
( ( ( ~ ( member_a @ ( sK6_SY309 @ SV127 @ SV69 ) @ SV69 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV69 @ SV127 )
| ~ ! [SY309: a] :
( ~ ( member_a @ SY309 @ SV69 )
| ( member_a @ SY309 @ SV127 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[925]) ).
thf(960,plain,
! [SV69: set_a,SV127: set_a] :
( ( ( member_a @ ( sK6_SY309 @ SV127 @ SV69 ) @ SV127 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV69 @ SV127 )
| ~ ! [SY309: a] :
( ~ ( member_a @ SY309 @ SV69 )
| ( member_a @ SY309 @ SV127 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[925]) ).
thf(961,plain,
! [SV73: set_a,SV128: set_a,SV28: set_a,SV110: set_a > set_a] :
( ( ( ! [SY296: set_a,SY297: set_a] :
( ~ ( ord_less_eq_set_a @ SY296 @ SY297 )
| ( ord_less_eq_set_a @ ( SV110 @ SY296 ) @ ( SV110 @ SY297 ) ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( SV110 @ SV28 ) @ SV128 )
= $true )
| ( ( ( SV110 @ SV73 )
= SV128 )
= $false )
| ( ( ord_less_eq_set_a @ SV28 @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[926]) ).
thf(962,plain,
! [SV111: set_a,SV75: set_a,SV30: set_a] :
( ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ SV30 @ SV75 ) @ SV111 )
= $true )
| ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ SV30 @ SV75 ) @ SV111 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[927]) ).
thf(963,plain,
! [SV75: set_a,SV111: set_a,SV30: set_a] :
( ( ( ~ ( ~ ( ord_less_eq_set_a @ SV30 @ SV111 )
| ~ ( ord_less_eq_set_a @ SV75 @ SV111 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ SV30 @ SV75 ) @ SV111 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[928]) ).
thf(964,plain,
! [SV75: set_a,SV111: set_a,SV30: set_a] :
( ( ( ord_less_eq_set_a @ SV30 @ SV111 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV75 @ SV111 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ ( sup_sup_set_a @ SV30 @ SV75 ) @ SV111 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV30 @ SV111 )
| ~ ( ord_less_eq_set_a @ SV75 @ SV111 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[929]) ).
thf(965,plain,
! [SV80: a > $o,SV135: a,SV35: a > $o] :
( ( ( ~ ( SV35 @ SV135 )
| ( SV80 @ SV135 ) )
= $true )
| ( ( ord_less_eq_set_a @ ( collect_a @ SV35 ) @ ( collect_a @ SV80 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(966,plain,
! [SV80: a > $o,SV35: a > $o] :
( ( ( ~ ( ord_less_eq_set_a @ ( collect_a @ SV35 ) @ ( collect_a @ SV80 ) )
| ~ ! [SY269: a] :
( ~ ( SV35 @ SY269 )
| ( SV80 @ SY269 ) ) )
= $false )
| ( ( SV35 @ ( sK4_SY269 @ SV80 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[932]) ).
thf(967,plain,
! [SV80: a > $o,SV35: a > $o] :
( ( ( ~ ( ord_less_eq_set_a @ ( collect_a @ SV35 ) @ ( collect_a @ SV80 ) ) )
= $false )
| ( ( SV80 @ ( sK4_SY269 @ SV80 @ SV35 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[933]) ).
thf(968,plain,
! [SV80: a > $o,SV35: a > $o] :
( ( ( ~ ! [SY269: a] :
( ~ ( SV35 @ SY269 )
| ( SV80 @ SY269 ) ) )
= $false )
| ( ( SV80 @ ( sK4_SY269 @ SV80 @ SV35 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[933]) ).
thf(969,plain,
! [SV115: set_a,SV131: set_a,SV37: set_a,SV82: set_a > set_a] :
( ( ( ! [SY273: set_a,SY274: set_a] :
( ~ ( ord_less_eq_set_a @ SY273 @ SY274 )
| ( ord_less_eq_set_a @ ( SV82 @ SY273 ) @ ( SV82 @ SY274 ) ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV37 @ ( SV82 @ SV131 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV115 @ SV131 )
= $false )
| ( ( SV37
= ( SV82 @ SV115 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[934]) ).
thf(970,plain,
! [SV132: set_a,SV85: set_a] :
( ( ( SV85 != SV132 )
= $false )
| ( ( SV85 = SV132 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[935]) ).
thf(971,plain,
! [SV132: set_a,SV85: set_a] :
( ( ( ~ ~ ( ~ ( ord_less_eq_set_a @ SV85 @ SV132 )
| ~ ( ord_less_eq_set_a @ SV132 @ SV85 ) ) )
= $false )
| ( ( SV85 = SV132 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[935]) ).
thf(972,plain,
! [SV132: set_a,SV85: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV85 @ SV132 ) )
= $true )
| ( ( ~ ( ord_less_eq_set_a @ SV132 @ SV85 ) )
= $true )
| ( ( ~ ( ( SV85 != SV132 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV85 @ SV132 )
| ~ ( ord_less_eq_set_a @ SV132 @ SV85 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[936]) ).
thf(973,plain,
! [SV43: set_a,SV88: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV88 @ SV43 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV88 @ SV43 )
= $false )
| ( ( ord_less_eq_set_a @ SV43 @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[937]) ).
thf(974,plain,
! [SV43: set_a,SV88: set_a] :
( ( ( SV88 != SV43 )
= $false )
| ( ( ord_less_eq_set_a @ SV88 @ SV43 )
= $false )
| ( ( ord_less_eq_set_a @ SV43 @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[937]) ).
thf(975,plain,
! [SV43: set_a,SV88: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV88 @ SV43 ) )
= $false )
| ( ( SV88 = SV43 )
= $false )
| ( ( ord_less_eq_set_a @ SV43 @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[938]) ).
thf(976,plain,
! [SV43: set_a,SV88: set_a] :
( ( ( SV88 != SV43 )
= $false )
| ( ( SV88 = SV43 )
= $false )
| ( ( ord_less_eq_set_a @ SV43 @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[938]) ).
thf(977,plain,
! [SV96: set_a,SV133: set_a,SV51: set_a,SV120: set_a > set_a] :
( ( ( ! [SY304: set_a,SY305: set_a] :
( ~ ( ord_less_eq_set_a @ SY304 @ SY305 )
| ( ord_less_eq_set_a @ ( SV120 @ SY304 ) @ ( SV120 @ SY305 ) ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( SV120 @ SV51 ) @ SV133 )
= $true )
| ( ( ord_less_eq_set_a @ ( SV120 @ SV96 ) @ SV133 )
= $false )
| ( ( ord_less_eq_set_a @ SV51 @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[939]) ).
thf(978,plain,
! [SV134: set_a,SV97: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV97 @ SV134 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV97 @ SV134 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[940]) ).
thf(979,plain,
! [SV134: set_a,SV97: set_a] :
( ( ( ~ ! [SY316: a] :
( ~ ( member_a @ SY316 @ SV97 )
| ( member_a @ SY316 @ SV134 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV97 @ SV134 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[940]) ).
thf(980,plain,
! [SV97: set_a,SV134: set_a] :
( ( ( ~ ( member_a @ ( sK7_SY316 @ SV134 @ SV97 ) @ SV97 ) )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV97 @ SV134 )
| ~ ! [SY316: a] :
( ~ ( member_a @ SY316 @ SV97 )
| ( member_a @ SY316 @ SV134 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[941]) ).
thf(981,plain,
! [SV97: set_a,SV134: set_a] :
( ( ( member_a @ ( sK7_SY316 @ SV134 @ SV97 ) @ SV134 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV97 @ SV134 )
| ~ ! [SY316: a] :
( ~ ( member_a @ SY316 @ SV97 )
| ( member_a @ SY316 @ SV134 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[941]) ).
thf(982,plain,
! [SV123: set_a,SV60: set_a] :
( ( ( SV60 = SV123 )
= $true )
| ( ( SV60 = SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[942]) ).
thf(983,plain,
! [SV123: set_a,SV60: set_a] :
( ( ( ~ ( ~ ( ord_less_eq_set_a @ SV60 @ SV123 )
| ~ ( ord_less_eq_set_a @ SV123 @ SV60 ) ) )
= $true )
| ( ( SV60 = SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[943]) ).
thf(984,plain,
! [SV123: set_a,SV60: set_a] :
( ( ( ord_less_eq_set_a @ SV60 @ SV123 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV123 @ SV60 ) )
= $true )
| ( ( ~ ( ( SV60 != SV123 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV60 @ SV123 )
| ~ ( ord_less_eq_set_a @ SV123 @ SV60 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[944]) ).
thf(985,plain,
! [SV62: set_a,SV103: set_a > $o,SV16: set_a > $o] :
( ( ( ~ ! [SY289: set_a] :
( ~ ( SV16 @ SY289 )
| ~ ! [SY164: set_a] :
( ~ ( SV16 @ SY164 )
| ( ord_less_eq_set_a @ SY164 @ SY289 ) )
| ( SV103 @ SY289 ) ) )
= $true )
| ( ( SV103 @ ( order_Greatest_set_a @ SV16 ) )
= $true )
| ( ( SV16 @ ( sK5_SY244 @ SV103 @ SV62 @ SV16 ) )
= $true )
| ( ( SV16 @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[945]) ).
thf(986,plain,
! [SV62: set_a,SV103: set_a > $o,SV16: set_a > $o] :
( ( ( ! [SY289: set_a] :
( ~ ( SV16 @ SY289 )
| ~ ! [SY164: set_a] :
( ~ ( SV16 @ SY164 )
| ( ord_less_eq_set_a @ SY164 @ SY289 ) )
| ( SV103 @ SY289 ) ) )
= $false )
| ( ( SV103 @ ( order_Greatest_set_a @ SV16 ) )
= $true )
| ( ( ord_less_eq_set_a @ ( sK5_SY244 @ SV103 @ SV62 @ SV16 ) @ SV62 )
= $false )
| ( ( SV16 @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[946]) ).
thf(987,plain,
! [SV64: set_a > set_a,SV19: set_a,SV124: set_a,SV104: set_a] :
( ( ( ! [SY317: set_a] :
( ~ ( ord_less_eq_set_a @ ( sK8_SY249 @ SV104 @ SV124 @ SV19 @ SV64 ) @ SY317 )
| ( ord_less_eq_set_a @ ( SV64 @ ( sK8_SY249 @ SV104 @ SV124 @ SV19 @ SV64 ) ) @ ( SV64 @ SY317 ) ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV19 @ ( SV64 @ SV124 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV104 @ SV124 )
= $false )
| ( ( ord_less_eq_set_a @ SV19 @ ( SV64 @ SV104 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[947]) ).
thf(988,plain,
! [SV105: set_a,SV66: set_a,SV21: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV21 @ SV66 )
| ~ ( ord_less_eq_set_a @ SV21 @ SV105 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV21 @ ( inf_inf_set_a @ SV66 @ SV105 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[949]) ).
thf(989,plain,
! [SV66: set_a,SV105: set_a,SV21: set_a] :
( ( ( ord_less_eq_set_a @ SV21 @ SV105 )
= $false )
| ( ( ord_less_eq_set_a @ SV21 @ SV66 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV21 @ ( inf_inf_set_a @ SV66 @ SV105 ) )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV21 @ SV66 )
| ~ ( ord_less_eq_set_a @ SV21 @ SV105 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[950]) ).
thf(990,plain,
! [SV125: set_a,SV67: set_a] :
( ( ( SV67 = SV125 )
= $true )
| ( ( SV67 = SV125 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[951]) ).
thf(991,plain,
! [SV67: set_a,SV125: set_a] :
( ( ( ~ ( ~ ( ord_less_eq_set_a @ SV125 @ SV67 )
| ~ ( ord_less_eq_set_a @ SV67 @ SV125 ) ) )
= $true )
| ( ( SV67 = SV125 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[952]) ).
thf(992,plain,
! [SV67: set_a,SV125: set_a] :
( ( ( ord_less_eq_set_a @ SV125 @ SV67 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV67 @ SV125 ) )
= $true )
| ( ( ~ ( ( SV67 != SV125 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV125 @ SV67 )
| ~ ( ord_less_eq_set_a @ SV67 @ SV125 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[953]) ).
thf(993,plain,
! [SV126: set_a,SV68: set_a] :
( ( ( SV68 = SV126 )
= $true )
| ( ( SV68 = SV126 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[954]) ).
thf(994,plain,
! [SV126: set_a,SV68: set_a] :
( ( ( ~ ( ~ ( ord_less_eq_set_a @ SV68 @ SV126 )
| ~ ( ord_less_eq_set_a @ SV126 @ SV68 ) ) )
= $true )
| ( ( SV68 = SV126 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[955]) ).
thf(995,plain,
! [SV126: set_a,SV68: set_a] :
( ( ( ord_less_eq_set_a @ SV68 @ SV126 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV126 @ SV68 ) )
= $true )
| ( ( ~ ( ( SV68 != SV126 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV68 @ SV126 )
| ~ ( ord_less_eq_set_a @ SV126 @ SV68 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[956]) ).
thf(996,plain,
! [SV127: set_a,SV69: set_a] :
( ( ( ord_less_eq_set_a @ SV69 @ SV127 )
= $true )
| ( ( ord_less_eq_set_a @ SV69 @ SV127 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[957]) ).
thf(997,plain,
! [SV127: set_a,SV69: set_a] :
( ( ( ! [SY309: a] :
( ~ ( member_a @ SY309 @ SV69 )
| ( member_a @ SY309 @ SV127 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV69 @ SV127 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[958]) ).
thf(998,plain,
! [SV69: set_a,SV127: set_a] :
( ( ( member_a @ ( sK6_SY309 @ SV127 @ SV69 ) @ SV69 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV69 @ SV127 )
| ~ ! [SY309: a] :
( ~ ( member_a @ SY309 @ SV69 )
| ( member_a @ SY309 @ SV127 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[959]) ).
thf(999,plain,
! [SV127: set_a,SV69: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV69 @ SV127 )
| ~ ! [SY309: a] :
( ~ ( member_a @ SY309 @ SV69 )
| ( member_a @ SY309 @ SV127 ) ) )
= $false )
| ( ( member_a @ ( sK6_SY309 @ SV127 @ SV69 ) @ SV127 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[960]) ).
thf(1000,plain,
! [SV110: set_a > set_a,SV28: set_a,SV128: set_a,SV73: set_a] :
( ( ( ! [SY318: set_a] :
( ~ ( ord_less_eq_set_a @ ( sK9_SY296 @ SV73 @ SV128 @ SV28 @ SV110 ) @ SY318 )
| ( ord_less_eq_set_a @ ( SV110 @ ( sK9_SY296 @ SV73 @ SV128 @ SV28 @ SV110 ) ) @ ( SV110 @ SY318 ) ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( SV110 @ SV28 ) @ SV128 )
= $true )
| ( ( ( SV110 @ SV73 )
= SV128 )
= $false )
| ( ( ord_less_eq_set_a @ SV28 @ SV73 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[961]) ).
thf(1001,plain,
! [SV75: set_a,SV111: set_a,SV30: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV30 @ SV111 )
| ~ ( ord_less_eq_set_a @ SV75 @ SV111 ) )
= $false )
| ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ SV30 @ SV75 ) @ SV111 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[963]) ).
thf(1002,plain,
! [SV30: set_a,SV111: set_a,SV75: set_a] :
( ( ( ord_less_eq_set_a @ SV75 @ SV111 )
= $false )
| ( ( ord_less_eq_set_a @ SV30 @ SV111 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ ( sup_sup_set_a @ SV30 @ SV75 ) @ SV111 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV30 @ SV111 )
| ~ ( ord_less_eq_set_a @ SV75 @ SV111 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[964]) ).
thf(1003,plain,
! [SV80: a > $o,SV135: a,SV35: a > $o] :
( ( ( ~ ( SV35 @ SV135 ) )
= $true )
| ( ( SV80 @ SV135 )
= $true )
| ( ( ord_less_eq_set_a @ ( collect_a @ SV35 ) @ ( collect_a @ SV80 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[965]) ).
thf(1004,plain,
! [SV80: a > $o,SV35: a > $o] :
( ( ( ~ ( ord_less_eq_set_a @ ( collect_a @ SV35 ) @ ( collect_a @ SV80 ) ) )
= $false )
| ( ( SV35 @ ( sK4_SY269 @ SV80 @ SV35 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[966]) ).
thf(1005,plain,
! [SV80: a > $o,SV35: a > $o] :
( ( ( ~ ! [SY269: a] :
( ~ ( SV35 @ SY269 )
| ( SV80 @ SY269 ) ) )
= $false )
| ( ( SV35 @ ( sK4_SY269 @ SV80 @ SV35 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[966]) ).
thf(1006,plain,
! [SV80: a > $o,SV35: a > $o] :
( ( ( ord_less_eq_set_a @ ( collect_a @ SV35 ) @ ( collect_a @ SV80 ) )
= $true )
| ( ( SV80 @ ( sK4_SY269 @ SV80 @ SV35 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[967]) ).
thf(1007,plain,
! [SV80: a > $o,SV35: a > $o] :
( ( ( ! [SY269: a] :
( ~ ( SV35 @ SY269 )
| ( SV80 @ SY269 ) ) )
= $true )
| ( ( SV80 @ ( sK4_SY269 @ SV80 @ SV35 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[968]) ).
thf(1008,plain,
! [SV82: set_a > set_a,SV37: set_a,SV131: set_a,SV115: set_a] :
( ( ( ! [SY319: set_a] :
( ~ ( ord_less_eq_set_a @ ( sK10_SY273 @ SV115 @ SV131 @ SV37 @ SV82 ) @ SY319 )
| ( ord_less_eq_set_a @ ( SV82 @ ( sK10_SY273 @ SV115 @ SV131 @ SV37 @ SV82 ) ) @ ( SV82 @ SY319 ) ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV37 @ ( SV82 @ SV131 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV115 @ SV131 )
= $false )
| ( ( SV37
= ( SV82 @ SV115 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[969]) ).
thf(1009,plain,
! [SV132: set_a,SV85: set_a] :
( ( ( SV85 = SV132 )
= $true )
| ( ( SV85 = SV132 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[970]) ).
thf(1010,plain,
! [SV132: set_a,SV85: set_a] :
( ( ( ~ ( ~ ( ord_less_eq_set_a @ SV85 @ SV132 )
| ~ ( ord_less_eq_set_a @ SV132 @ SV85 ) ) )
= $true )
| ( ( SV85 = SV132 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[971]) ).
thf(1011,plain,
! [SV132: set_a,SV85: set_a] :
( ( ( ord_less_eq_set_a @ SV85 @ SV132 )
= $false )
| ( ( ~ ( ord_less_eq_set_a @ SV132 @ SV85 ) )
= $true )
| ( ( ~ ( ( SV85 != SV132 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV85 @ SV132 )
| ~ ( ord_less_eq_set_a @ SV132 @ SV85 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[972]) ).
thf(1012,plain,
! [SV43: set_a,SV88: set_a] :
( ( ( ord_less_eq_set_a @ SV88 @ SV43 )
= $true )
| ( ( ord_less_eq_set_a @ SV88 @ SV43 )
= $false )
| ( ( ord_less_eq_set_a @ SV43 @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[973]) ).
thf(1013,plain,
! [SV43: set_a,SV88: set_a] :
( ( ( SV88 = SV43 )
= $true )
| ( ( ord_less_eq_set_a @ SV88 @ SV43 )
= $false )
| ( ( ord_less_eq_set_a @ SV43 @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[974]) ).
thf(1014,plain,
! [SV43: set_a,SV88: set_a] :
( ( ( ord_less_eq_set_a @ SV88 @ SV43 )
= $true )
| ( ( SV88 = SV43 )
= $false )
| ( ( ord_less_eq_set_a @ SV43 @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[975]) ).
thf(1015,plain,
! [SV43: set_a,SV88: set_a] :
( ( ( SV88 = SV43 )
= $true )
| ( ( SV88 = SV43 )
= $false )
| ( ( ord_less_eq_set_a @ SV43 @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[976]) ).
thf(1016,plain,
! [SV120: set_a > set_a,SV51: set_a,SV133: set_a,SV96: set_a] :
( ( ( ! [SY320: set_a] :
( ~ ( ord_less_eq_set_a @ ( sK11_SY304 @ SV96 @ SV133 @ SV51 @ SV120 ) @ SY320 )
| ( ord_less_eq_set_a @ ( SV120 @ ( sK11_SY304 @ SV96 @ SV133 @ SV51 @ SV120 ) ) @ ( SV120 @ SY320 ) ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( SV120 @ SV51 ) @ SV133 )
= $true )
| ( ( ord_less_eq_set_a @ ( SV120 @ SV96 ) @ SV133 )
= $false )
| ( ( ord_less_eq_set_a @ SV51 @ SV96 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[977]) ).
thf(1017,plain,
! [SV134: set_a,SV97: set_a] :
( ( ( ord_less_eq_set_a @ SV97 @ SV134 )
= $true )
| ( ( ord_less_eq_set_a @ SV97 @ SV134 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[978]) ).
thf(1018,plain,
! [SV134: set_a,SV97: set_a] :
( ( ( ! [SY316: a] :
( ~ ( member_a @ SY316 @ SV97 )
| ( member_a @ SY316 @ SV134 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV97 @ SV134 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[979]) ).
thf(1019,plain,
! [SV97: set_a,SV134: set_a] :
( ( ( member_a @ ( sK7_SY316 @ SV134 @ SV97 ) @ SV97 )
= $true )
| ( ( ~ ( ~ ( ord_less_eq_set_a @ SV97 @ SV134 )
| ~ ! [SY316: a] :
( ~ ( member_a @ SY316 @ SV97 )
| ( member_a @ SY316 @ SV134 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[980]) ).
thf(1020,plain,
! [SV134: set_a,SV97: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV97 @ SV134 )
| ~ ! [SY316: a] :
( ~ ( member_a @ SY316 @ SV97 )
| ( member_a @ SY316 @ SV134 ) ) )
= $false )
| ( ( member_a @ ( sK7_SY316 @ SV134 @ SV97 ) @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[981]) ).
thf(1021,plain,
! [SV123: set_a,SV60: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV60 @ SV123 )
| ~ ( ord_less_eq_set_a @ SV123 @ SV60 ) )
= $false )
| ( ( SV60 = SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[983]) ).
thf(1022,plain,
! [SV60: set_a,SV123: set_a] :
( ( ( ord_less_eq_set_a @ SV123 @ SV60 )
= $false )
| ( ( ord_less_eq_set_a @ SV60 @ SV123 )
= $false )
| ( ( ~ ( ( SV60 != SV123 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV60 @ SV123 )
| ~ ( ord_less_eq_set_a @ SV123 @ SV60 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[984]) ).
thf(1023,plain,
! [SV62: set_a,SV103: set_a > $o,SV16: set_a > $o] :
( ( ( ! [SY289: set_a] :
( ~ ( SV16 @ SY289 )
| ~ ! [SY164: set_a] :
( ~ ( SV16 @ SY164 )
| ( ord_less_eq_set_a @ SY164 @ SY289 ) )
| ( SV103 @ SY289 ) ) )
= $false )
| ( ( SV103 @ ( order_Greatest_set_a @ SV16 ) )
= $true )
| ( ( SV16 @ ( sK5_SY244 @ SV103 @ SV62 @ SV16 ) )
= $true )
| ( ( SV16 @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[985]) ).
thf(1024,plain,
! [SV103: set_a > $o,SV62: set_a,SV16: set_a > $o] :
( ( ( ~ ( SV16 @ ( sK12_SY289 @ SV62 @ SV103 @ SV16 ) )
| ~ ! [SY321: set_a] :
( ~ ( SV16 @ SY321 )
| ( ord_less_eq_set_a @ SY321 @ ( sK12_SY289 @ SV62 @ SV103 @ SV16 ) ) )
| ( SV103 @ ( sK12_SY289 @ SV62 @ SV103 @ SV16 ) ) )
= $false )
| ( ( SV103 @ ( order_Greatest_set_a @ SV16 ) )
= $true )
| ( ( ord_less_eq_set_a @ ( sK5_SY244 @ SV103 @ SV62 @ SV16 ) @ SV62 )
= $false )
| ( ( SV16 @ SV62 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[986]) ).
thf(1025,plain,
! [SV64: set_a > set_a,SV19: set_a,SV124: set_a,SV104: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ ( sK8_SY249 @ SV104 @ SV124 @ SV19 @ SV64 ) @ ( sK13_SY317 @ SV64 @ SV19 @ SV124 @ SV104 ) )
| ( ord_less_eq_set_a @ ( SV64 @ ( sK8_SY249 @ SV104 @ SV124 @ SV19 @ SV64 ) ) @ ( SV64 @ ( sK13_SY317 @ SV64 @ SV19 @ SV124 @ SV104 ) ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV19 @ ( SV64 @ SV124 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV104 @ SV124 )
= $false )
| ( ( ord_less_eq_set_a @ SV19 @ ( SV64 @ SV104 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[987]) ).
thf(1026,plain,
! [SV105: set_a,SV66: set_a,SV21: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV21 @ SV66 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV21 @ ( inf_inf_set_a @ SV66 @ SV105 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[988]) ).
thf(1027,plain,
! [SV66: set_a,SV105: set_a,SV21: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV21 @ SV105 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV21 @ ( inf_inf_set_a @ SV66 @ SV105 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[988]) ).
thf(1028,plain,
! [SV105: set_a,SV66: set_a,SV21: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV21 @ ( inf_inf_set_a @ SV66 @ SV105 ) )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV21 @ SV66 )
| ~ ( ord_less_eq_set_a @ SV21 @ SV105 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV21 @ SV66 )
= $false )
| ( ( ord_less_eq_set_a @ SV21 @ SV105 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[989]) ).
thf(1029,plain,
! [SV67: set_a,SV125: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV125 @ SV67 )
| ~ ( ord_less_eq_set_a @ SV67 @ SV125 ) )
= $false )
| ( ( SV67 = SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[991]) ).
thf(1030,plain,
! [SV125: set_a,SV67: set_a] :
( ( ( ord_less_eq_set_a @ SV67 @ SV125 )
= $false )
| ( ( ord_less_eq_set_a @ SV125 @ SV67 )
= $false )
| ( ( ~ ( ( SV67 != SV125 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV125 @ SV67 )
| ~ ( ord_less_eq_set_a @ SV67 @ SV125 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[992]) ).
thf(1031,plain,
! [SV126: set_a,SV68: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV68 @ SV126 )
| ~ ( ord_less_eq_set_a @ SV126 @ SV68 ) )
= $false )
| ( ( SV68 = SV126 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[994]) ).
thf(1032,plain,
! [SV68: set_a,SV126: set_a] :
( ( ( ord_less_eq_set_a @ SV126 @ SV68 )
= $false )
| ( ( ord_less_eq_set_a @ SV68 @ SV126 )
= $false )
| ( ( ~ ( ( SV68 != SV126 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV68 @ SV126 )
| ~ ( ord_less_eq_set_a @ SV126 @ SV68 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[995]) ).
thf(1033,plain,
! [SV127: set_a,SV69: set_a,SV136: a] :
( ( ( ~ ( member_a @ SV136 @ SV69 )
| ( member_a @ SV136 @ SV127 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV69 @ SV127 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[997]) ).
thf(1034,plain,
! [SV127: set_a,SV69: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV69 @ SV127 )
| ~ ! [SY309: a] :
( ~ ( member_a @ SY309 @ SV69 )
| ( member_a @ SY309 @ SV127 ) ) )
= $false )
| ( ( member_a @ ( sK6_SY309 @ SV127 @ SV69 ) @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[998]) ).
thf(1035,plain,
! [SV127: set_a,SV69: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV69 @ SV127 ) )
= $false )
| ( ( member_a @ ( sK6_SY309 @ SV127 @ SV69 ) @ SV127 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[999]) ).
thf(1036,plain,
! [SV127: set_a,SV69: set_a] :
( ( ( ~ ! [SY309: a] :
( ~ ( member_a @ SY309 @ SV69 )
| ( member_a @ SY309 @ SV127 ) ) )
= $false )
| ( ( member_a @ ( sK6_SY309 @ SV127 @ SV69 ) @ SV127 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[999]) ).
thf(1037,plain,
! [SV110: set_a > set_a,SV28: set_a,SV128: set_a,SV73: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ ( sK9_SY296 @ SV73 @ SV128 @ SV28 @ SV110 ) @ ( sK14_SY318 @ SV110 @ SV28 @ SV128 @ SV73 ) )
| ( ord_less_eq_set_a @ ( SV110 @ ( sK9_SY296 @ SV73 @ SV128 @ SV28 @ SV110 ) ) @ ( SV110 @ ( sK14_SY318 @ SV110 @ SV28 @ SV128 @ SV73 ) ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( SV110 @ SV28 ) @ SV128 )
= $true )
| ( ( ( SV110 @ SV73 )
= SV128 )
= $false )
| ( ( ord_less_eq_set_a @ SV28 @ SV73 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1000]) ).
thf(1038,plain,
! [SV75: set_a,SV111: set_a,SV30: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV30 @ SV111 ) )
= $false )
| ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ SV30 @ SV75 ) @ SV111 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1001]) ).
thf(1039,plain,
! [SV30: set_a,SV111: set_a,SV75: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV75 @ SV111 ) )
= $false )
| ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ SV30 @ SV75 ) @ SV111 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1001]) ).
thf(1040,plain,
! [SV111: set_a,SV75: set_a,SV30: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ ( sup_sup_set_a @ SV30 @ SV75 ) @ SV111 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV30 @ SV111 )
| ~ ( ord_less_eq_set_a @ SV75 @ SV111 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV30 @ SV111 )
= $false )
| ( ( ord_less_eq_set_a @ SV75 @ SV111 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1002]) ).
thf(1041,plain,
! [SV80: a > $o,SV135: a,SV35: a > $o] :
( ( ( SV35 @ SV135 )
= $false )
| ( ( SV80 @ SV135 )
= $true )
| ( ( ord_less_eq_set_a @ ( collect_a @ SV35 ) @ ( collect_a @ SV80 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1003]) ).
thf(1042,plain,
! [SV80: a > $o,SV35: a > $o] :
( ( ( ord_less_eq_set_a @ ( collect_a @ SV35 ) @ ( collect_a @ SV80 ) )
= $true )
| ( ( SV35 @ ( sK4_SY269 @ SV80 @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1004]) ).
thf(1043,plain,
! [SV80: a > $o,SV35: a > $o] :
( ( ( ! [SY269: a] :
( ~ ( SV35 @ SY269 )
| ( SV80 @ SY269 ) ) )
= $true )
| ( ( SV35 @ ( sK4_SY269 @ SV80 @ SV35 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1005]) ).
thf(1044,plain,
! [SV80: a > $o,SV137: a,SV35: a > $o] :
( ( ( ~ ( SV35 @ SV137 )
| ( SV80 @ SV137 ) )
= $true )
| ( ( SV80 @ ( sK4_SY269 @ SV80 @ SV35 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1007]) ).
thf(1045,plain,
! [SV82: set_a > set_a,SV37: set_a,SV131: set_a,SV115: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ ( sK10_SY273 @ SV115 @ SV131 @ SV37 @ SV82 ) @ ( sK15_SY319 @ SV82 @ SV37 @ SV131 @ SV115 ) )
| ( ord_less_eq_set_a @ ( SV82 @ ( sK10_SY273 @ SV115 @ SV131 @ SV37 @ SV82 ) ) @ ( SV82 @ ( sK15_SY319 @ SV82 @ SV37 @ SV131 @ SV115 ) ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV37 @ ( SV82 @ SV131 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV115 @ SV131 )
= $false )
| ( ( SV37
= ( SV82 @ SV115 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1008]) ).
thf(1046,plain,
! [SV132: set_a,SV85: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV85 @ SV132 )
| ~ ( ord_less_eq_set_a @ SV132 @ SV85 ) )
= $false )
| ( ( SV85 = SV132 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1010]) ).
thf(1047,plain,
! [SV85: set_a,SV132: set_a] :
( ( ( ord_less_eq_set_a @ SV132 @ SV85 )
= $false )
| ( ( ord_less_eq_set_a @ SV85 @ SV132 )
= $false )
| ( ( ~ ( ( SV85 != SV132 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV85 @ SV132 )
| ~ ( ord_less_eq_set_a @ SV132 @ SV85 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1011]) ).
thf(1048,plain,
! [SV120: set_a > set_a,SV51: set_a,SV133: set_a,SV96: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ ( sK11_SY304 @ SV96 @ SV133 @ SV51 @ SV120 ) @ ( sK16_SY320 @ SV120 @ SV51 @ SV133 @ SV96 ) )
| ( ord_less_eq_set_a @ ( SV120 @ ( sK11_SY304 @ SV96 @ SV133 @ SV51 @ SV120 ) ) @ ( SV120 @ ( sK16_SY320 @ SV120 @ SV51 @ SV133 @ SV96 ) ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( SV120 @ SV51 ) @ SV133 )
= $true )
| ( ( ord_less_eq_set_a @ ( SV120 @ SV96 ) @ SV133 )
= $false )
| ( ( ord_less_eq_set_a @ SV51 @ SV96 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1016]) ).
thf(1049,plain,
! [SV134: set_a,SV97: set_a,SV138: a] :
( ( ( ~ ( member_a @ SV138 @ SV97 )
| ( member_a @ SV138 @ SV134 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV97 @ SV134 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1018]) ).
thf(1050,plain,
! [SV134: set_a,SV97: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV97 @ SV134 )
| ~ ! [SY316: a] :
( ~ ( member_a @ SY316 @ SV97 )
| ( member_a @ SY316 @ SV134 ) ) )
= $false )
| ( ( member_a @ ( sK7_SY316 @ SV134 @ SV97 ) @ SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1019]) ).
thf(1051,plain,
! [SV134: set_a,SV97: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV97 @ SV134 ) )
= $false )
| ( ( member_a @ ( sK7_SY316 @ SV134 @ SV97 ) @ SV134 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1020]) ).
thf(1052,plain,
! [SV134: set_a,SV97: set_a] :
( ( ( ~ ! [SY316: a] :
( ~ ( member_a @ SY316 @ SV97 )
| ( member_a @ SY316 @ SV134 ) ) )
= $false )
| ( ( member_a @ ( sK7_SY316 @ SV134 @ SV97 ) @ SV134 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1020]) ).
thf(1053,plain,
! [SV123: set_a,SV60: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV60 @ SV123 ) )
= $false )
| ( ( SV60 = SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1021]) ).
thf(1054,plain,
! [SV60: set_a,SV123: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV123 @ SV60 ) )
= $false )
| ( ( SV60 = SV123 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1021]) ).
thf(1055,plain,
! [SV123: set_a,SV60: set_a] :
( ( ( ( SV60 != SV123 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV60 @ SV123 )
| ~ ( ord_less_eq_set_a @ SV123 @ SV60 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV60 @ SV123 )
= $false )
| ( ( ord_less_eq_set_a @ SV123 @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1022]) ).
thf(1056,plain,
! [SV103: set_a > $o,SV62: set_a,SV16: set_a > $o] :
( ( ( ~ ( SV16 @ ( sK17_SY289 @ SV62 @ SV103 @ SV16 ) )
| ~ ! [SY322: set_a] :
( ~ ( SV16 @ SY322 )
| ( ord_less_eq_set_a @ SY322 @ ( sK17_SY289 @ SV62 @ SV103 @ SV16 ) ) )
| ( SV103 @ ( sK17_SY289 @ SV62 @ SV103 @ SV16 ) ) )
= $false )
| ( ( SV103 @ ( order_Greatest_set_a @ SV16 ) )
= $true )
| ( ( SV16 @ ( sK5_SY244 @ SV103 @ SV62 @ SV16 ) )
= $true )
| ( ( SV16 @ SV62 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1023]) ).
thf(1057,plain,
! [SV103: set_a > $o,SV62: set_a,SV16: set_a > $o] :
( ( ( ~ ( SV16 @ ( sK12_SY289 @ SV62 @ SV103 @ SV16 ) ) )
= $false )
| ( ( SV103 @ ( order_Greatest_set_a @ SV16 ) )
= $true )
| ( ( ord_less_eq_set_a @ ( sK5_SY244 @ SV103 @ SV62 @ SV16 ) @ SV62 )
= $false )
| ( ( SV16 @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1024]) ).
thf(1058,plain,
! [SV103: set_a > $o,SV62: set_a,SV16: set_a > $o] :
( ( ( ~ ! [SY321: set_a] :
( ~ ( SV16 @ SY321 )
| ( ord_less_eq_set_a @ SY321 @ ( sK12_SY289 @ SV62 @ SV103 @ SV16 ) ) )
| ( SV103 @ ( sK12_SY289 @ SV62 @ SV103 @ SV16 ) ) )
= $false )
| ( ( SV103 @ ( order_Greatest_set_a @ SV16 ) )
= $true )
| ( ( ord_less_eq_set_a @ ( sK5_SY244 @ SV103 @ SV62 @ SV16 ) @ SV62 )
= $false )
| ( ( SV16 @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1024]) ).
thf(1059,plain,
! [SV64: set_a > set_a,SV19: set_a,SV124: set_a,SV104: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ ( sK8_SY249 @ SV104 @ SV124 @ SV19 @ SV64 ) @ ( sK13_SY317 @ SV64 @ SV19 @ SV124 @ SV104 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV19 @ ( SV64 @ SV124 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV104 @ SV124 )
= $false )
| ( ( ord_less_eq_set_a @ SV19 @ ( SV64 @ SV104 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1025]) ).
thf(1060,plain,
! [SV19: set_a,SV124: set_a,SV104: set_a,SV64: set_a > set_a] :
( ( ( ord_less_eq_set_a @ ( SV64 @ ( sK8_SY249 @ SV104 @ SV124 @ SV19 @ SV64 ) ) @ ( SV64 @ ( sK13_SY317 @ SV64 @ SV19 @ SV124 @ SV104 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV19 @ ( SV64 @ SV124 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV104 @ SV124 )
= $false )
| ( ( ord_less_eq_set_a @ SV19 @ ( SV64 @ SV104 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1025]) ).
thf(1061,plain,
! [SV105: set_a,SV66: set_a,SV21: set_a] :
( ( ( ord_less_eq_set_a @ SV21 @ SV66 )
= $true )
| ( ( ord_less_eq_set_a @ SV21 @ ( inf_inf_set_a @ SV66 @ SV105 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1026]) ).
thf(1062,plain,
! [SV66: set_a,SV105: set_a,SV21: set_a] :
( ( ( ord_less_eq_set_a @ SV21 @ SV105 )
= $true )
| ( ( ord_less_eq_set_a @ SV21 @ ( inf_inf_set_a @ SV66 @ SV105 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1027]) ).
thf(1063,plain,
! [SV105: set_a,SV66: set_a,SV21: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV21 @ ( inf_inf_set_a @ SV66 @ SV105 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV21 @ SV66 )
= $false )
| ( ( ord_less_eq_set_a @ SV21 @ SV105 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1028]) ).
thf(1064,plain,
! [SV105: set_a,SV66: set_a,SV21: set_a] :
( ( ( ~ ~ ( ~ ( ord_less_eq_set_a @ SV21 @ SV66 )
| ~ ( ord_less_eq_set_a @ SV21 @ SV105 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV21 @ SV66 )
= $false )
| ( ( ord_less_eq_set_a @ SV21 @ SV105 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1028]) ).
thf(1065,plain,
! [SV67: set_a,SV125: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV125 @ SV67 ) )
= $false )
| ( ( SV67 = SV125 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1029]) ).
thf(1066,plain,
! [SV125: set_a,SV67: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV67 @ SV125 ) )
= $false )
| ( ( SV67 = SV125 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1029]) ).
thf(1067,plain,
! [SV125: set_a,SV67: set_a] :
( ( ( ( SV67 != SV125 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV125 @ SV67 )
| ~ ( ord_less_eq_set_a @ SV67 @ SV125 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV125 @ SV67 )
= $false )
| ( ( ord_less_eq_set_a @ SV67 @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1030]) ).
thf(1068,plain,
! [SV126: set_a,SV68: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV68 @ SV126 ) )
= $false )
| ( ( SV68 = SV126 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1031]) ).
thf(1069,plain,
! [SV68: set_a,SV126: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV126 @ SV68 ) )
= $false )
| ( ( SV68 = SV126 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1031]) ).
thf(1070,plain,
! [SV126: set_a,SV68: set_a] :
( ( ( ( SV68 != SV126 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV68 @ SV126 )
| ~ ( ord_less_eq_set_a @ SV126 @ SV68 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV68 @ SV126 )
= $false )
| ( ( ord_less_eq_set_a @ SV126 @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1032]) ).
thf(1071,plain,
! [SV127: set_a,SV69: set_a,SV136: a] :
( ( ( ~ ( member_a @ SV136 @ SV69 ) )
= $true )
| ( ( member_a @ SV136 @ SV127 )
= $true )
| ( ( ord_less_eq_set_a @ SV69 @ SV127 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1033]) ).
thf(1072,plain,
! [SV127: set_a,SV69: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV69 @ SV127 ) )
= $false )
| ( ( member_a @ ( sK6_SY309 @ SV127 @ SV69 ) @ SV69 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1034]) ).
thf(1073,plain,
! [SV127: set_a,SV69: set_a] :
( ( ( ~ ! [SY309: a] :
( ~ ( member_a @ SY309 @ SV69 )
| ( member_a @ SY309 @ SV127 ) ) )
= $false )
| ( ( member_a @ ( sK6_SY309 @ SV127 @ SV69 ) @ SV69 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1034]) ).
thf(1074,plain,
! [SV127: set_a,SV69: set_a] :
( ( ( ord_less_eq_set_a @ SV69 @ SV127 )
= $true )
| ( ( member_a @ ( sK6_SY309 @ SV127 @ SV69 ) @ SV127 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1035]) ).
thf(1075,plain,
! [SV127: set_a,SV69: set_a] :
( ( ( ! [SY309: a] :
( ~ ( member_a @ SY309 @ SV69 )
| ( member_a @ SY309 @ SV127 ) ) )
= $true )
| ( ( member_a @ ( sK6_SY309 @ SV127 @ SV69 ) @ SV127 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1036]) ).
thf(1076,plain,
! [SV110: set_a > set_a,SV28: set_a,SV128: set_a,SV73: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ ( sK9_SY296 @ SV73 @ SV128 @ SV28 @ SV110 ) @ ( sK14_SY318 @ SV110 @ SV28 @ SV128 @ SV73 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( SV110 @ SV28 ) @ SV128 )
= $true )
| ( ( ( SV110 @ SV73 )
= SV128 )
= $false )
| ( ( ord_less_eq_set_a @ SV28 @ SV73 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1037]) ).
thf(1077,plain,
! [SV28: set_a,SV128: set_a,SV73: set_a,SV110: set_a > set_a] :
( ( ( ord_less_eq_set_a @ ( SV110 @ ( sK9_SY296 @ SV73 @ SV128 @ SV28 @ SV110 ) ) @ ( SV110 @ ( sK14_SY318 @ SV110 @ SV28 @ SV128 @ SV73 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( SV110 @ SV28 ) @ SV128 )
= $true )
| ( ( ( SV110 @ SV73 )
= SV128 )
= $false )
| ( ( ord_less_eq_set_a @ SV28 @ SV73 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1037]) ).
thf(1078,plain,
! [SV75: set_a,SV111: set_a,SV30: set_a] :
( ( ( ord_less_eq_set_a @ SV30 @ SV111 )
= $true )
| ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ SV30 @ SV75 ) @ SV111 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1038]) ).
thf(1079,plain,
! [SV30: set_a,SV111: set_a,SV75: set_a] :
( ( ( ord_less_eq_set_a @ SV75 @ SV111 )
= $true )
| ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ SV30 @ SV75 ) @ SV111 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1039]) ).
thf(1080,plain,
! [SV111: set_a,SV75: set_a,SV30: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ ( sup_sup_set_a @ SV30 @ SV75 ) @ SV111 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV30 @ SV111 )
= $false )
| ( ( ord_less_eq_set_a @ SV75 @ SV111 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1040]) ).
thf(1081,plain,
! [SV75: set_a,SV111: set_a,SV30: set_a] :
( ( ( ~ ~ ( ~ ( ord_less_eq_set_a @ SV30 @ SV111 )
| ~ ( ord_less_eq_set_a @ SV75 @ SV111 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV30 @ SV111 )
= $false )
| ( ( ord_less_eq_set_a @ SV75 @ SV111 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1040]) ).
thf(1082,plain,
! [SV80: a > $o,SV139: a,SV35: a > $o] :
( ( ( ~ ( SV35 @ SV139 )
| ( SV80 @ SV139 ) )
= $true )
| ( ( SV35 @ ( sK4_SY269 @ SV80 @ SV35 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1043]) ).
thf(1083,plain,
! [SV80: a > $o,SV137: a,SV35: a > $o] :
( ( ( ~ ( SV35 @ SV137 ) )
= $true )
| ( ( SV80 @ SV137 )
= $true )
| ( ( SV80 @ ( sK4_SY269 @ SV80 @ SV35 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1044]) ).
thf(1084,plain,
! [SV82: set_a > set_a,SV37: set_a,SV131: set_a,SV115: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ ( sK10_SY273 @ SV115 @ SV131 @ SV37 @ SV82 ) @ ( sK15_SY319 @ SV82 @ SV37 @ SV131 @ SV115 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV37 @ ( SV82 @ SV131 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV115 @ SV131 )
= $false )
| ( ( SV37
= ( SV82 @ SV115 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1045]) ).
thf(1085,plain,
! [SV37: set_a,SV131: set_a,SV115: set_a,SV82: set_a > set_a] :
( ( ( ord_less_eq_set_a @ ( SV82 @ ( sK10_SY273 @ SV115 @ SV131 @ SV37 @ SV82 ) ) @ ( SV82 @ ( sK15_SY319 @ SV82 @ SV37 @ SV131 @ SV115 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV37 @ ( SV82 @ SV131 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV115 @ SV131 )
= $false )
| ( ( SV37
= ( SV82 @ SV115 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1045]) ).
thf(1086,plain,
! [SV132: set_a,SV85: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV85 @ SV132 ) )
= $false )
| ( ( SV85 = SV132 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1046]) ).
thf(1087,plain,
! [SV85: set_a,SV132: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV132 @ SV85 ) )
= $false )
| ( ( SV85 = SV132 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1046]) ).
thf(1088,plain,
! [SV132: set_a,SV85: set_a] :
( ( ( ( SV85 != SV132 )
| ~ ~ ( ~ ( ord_less_eq_set_a @ SV85 @ SV132 )
| ~ ( ord_less_eq_set_a @ SV132 @ SV85 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV85 @ SV132 )
= $false )
| ( ( ord_less_eq_set_a @ SV132 @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1047]) ).
thf(1089,plain,
! [SV120: set_a > set_a,SV51: set_a,SV133: set_a,SV96: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ ( sK11_SY304 @ SV96 @ SV133 @ SV51 @ SV120 ) @ ( sK16_SY320 @ SV120 @ SV51 @ SV133 @ SV96 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( SV120 @ SV51 ) @ SV133 )
= $true )
| ( ( ord_less_eq_set_a @ ( SV120 @ SV96 ) @ SV133 )
= $false )
| ( ( ord_less_eq_set_a @ SV51 @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1048]) ).
thf(1090,plain,
! [SV51: set_a,SV133: set_a,SV96: set_a,SV120: set_a > set_a] :
( ( ( ord_less_eq_set_a @ ( SV120 @ ( sK11_SY304 @ SV96 @ SV133 @ SV51 @ SV120 ) ) @ ( SV120 @ ( sK16_SY320 @ SV120 @ SV51 @ SV133 @ SV96 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ ( SV120 @ SV51 ) @ SV133 )
= $true )
| ( ( ord_less_eq_set_a @ ( SV120 @ SV96 ) @ SV133 )
= $false )
| ( ( ord_less_eq_set_a @ SV51 @ SV96 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1048]) ).
thf(1091,plain,
! [SV134: set_a,SV97: set_a,SV138: a] :
( ( ( ~ ( member_a @ SV138 @ SV97 ) )
= $true )
| ( ( member_a @ SV138 @ SV134 )
= $true )
| ( ( ord_less_eq_set_a @ SV97 @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1049]) ).
thf(1092,plain,
! [SV134: set_a,SV97: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV97 @ SV134 ) )
= $false )
| ( ( member_a @ ( sK7_SY316 @ SV134 @ SV97 ) @ SV97 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1050]) ).
thf(1093,plain,
! [SV134: set_a,SV97: set_a] :
( ( ( ~ ! [SY316: a] :
( ~ ( member_a @ SY316 @ SV97 )
| ( member_a @ SY316 @ SV134 ) ) )
= $false )
| ( ( member_a @ ( sK7_SY316 @ SV134 @ SV97 ) @ SV97 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1050]) ).
thf(1094,plain,
! [SV134: set_a,SV97: set_a] :
( ( ( ord_less_eq_set_a @ SV97 @ SV134 )
= $true )
| ( ( member_a @ ( sK7_SY316 @ SV134 @ SV97 ) @ SV134 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1051]) ).
thf(1095,plain,
! [SV134: set_a,SV97: set_a] :
( ( ( ! [SY316: a] :
( ~ ( member_a @ SY316 @ SV97 )
| ( member_a @ SY316 @ SV134 ) ) )
= $true )
| ( ( member_a @ ( sK7_SY316 @ SV134 @ SV97 ) @ SV134 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1052]) ).
thf(1096,plain,
! [SV123: set_a,SV60: set_a] :
( ( ( ord_less_eq_set_a @ SV60 @ SV123 )
= $true )
| ( ( SV60 = SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1053]) ).
thf(1097,plain,
! [SV60: set_a,SV123: set_a] :
( ( ( ord_less_eq_set_a @ SV123 @ SV60 )
= $true )
| ( ( SV60 = SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1054]) ).
thf(1098,plain,
! [SV123: set_a,SV60: set_a] :
( ( ( SV60 != SV123 )
= $false )
| ( ( ord_less_eq_set_a @ SV60 @ SV123 )
= $false )
| ( ( ord_less_eq_set_a @ SV123 @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1055]) ).
thf(1099,plain,
! [SV123: set_a,SV60: set_a] :
( ( ( ~ ~ ( ~ ( ord_less_eq_set_a @ SV60 @ SV123 )
| ~ ( ord_less_eq_set_a @ SV123 @ SV60 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV60 @ SV123 )
= $false )
| ( ( ord_less_eq_set_a @ SV123 @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1055]) ).
thf(1100,plain,
! [SV103: set_a > $o,SV62: set_a,SV16: set_a > $o] :
( ( ( ~ ( SV16 @ ( sK17_SY289 @ SV62 @ SV103 @ SV16 ) ) )
= $false )
| ( ( SV103 @ ( order_Greatest_set_a @ SV16 ) )
= $true )
| ( ( SV16 @ ( sK5_SY244 @ SV103 @ SV62 @ SV16 ) )
= $true )
| ( ( SV16 @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1056]) ).
thf(1101,plain,
! [SV103: set_a > $o,SV62: set_a,SV16: set_a > $o] :
( ( ( ~ ! [SY322: set_a] :
( ~ ( SV16 @ SY322 )
| ( ord_less_eq_set_a @ SY322 @ ( sK17_SY289 @ SV62 @ SV103 @ SV16 ) ) )
| ( SV103 @ ( sK17_SY289 @ SV62 @ SV103 @ SV16 ) ) )
= $false )
| ( ( SV103 @ ( order_Greatest_set_a @ SV16 ) )
= $true )
| ( ( SV16 @ ( sK5_SY244 @ SV103 @ SV62 @ SV16 ) )
= $true )
| ( ( SV16 @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1056]) ).
thf(1102,plain,
! [SV103: set_a > $o,SV62: set_a,SV16: set_a > $o] :
( ( ( SV16 @ ( sK12_SY289 @ SV62 @ SV103 @ SV16 ) )
= $true )
| ( ( SV103 @ ( order_Greatest_set_a @ SV16 ) )
= $true )
| ( ( ord_less_eq_set_a @ ( sK5_SY244 @ SV103 @ SV62 @ SV16 ) @ SV62 )
= $false )
| ( ( SV16 @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1057]) ).
thf(1103,plain,
! [SV103: set_a > $o,SV62: set_a,SV16: set_a > $o] :
( ( ( ~ ! [SY321: set_a] :
( ~ ( SV16 @ SY321 )
| ( ord_less_eq_set_a @ SY321 @ ( sK12_SY289 @ SV62 @ SV103 @ SV16 ) ) ) )
= $false )
| ( ( SV103 @ ( order_Greatest_set_a @ SV16 ) )
= $true )
| ( ( ord_less_eq_set_a @ ( sK5_SY244 @ SV103 @ SV62 @ SV16 ) @ SV62 )
= $false )
| ( ( SV16 @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1058]) ).
thf(1104,plain,
! [SV16: set_a > $o,SV62: set_a,SV103: set_a > $o] :
( ( ( SV103 @ ( sK12_SY289 @ SV62 @ SV103 @ SV16 ) )
= $false )
| ( ( SV103 @ ( order_Greatest_set_a @ SV16 ) )
= $true )
| ( ( ord_less_eq_set_a @ ( sK5_SY244 @ SV103 @ SV62 @ SV16 ) @ SV62 )
= $false )
| ( ( SV16 @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1058]) ).
thf(1105,plain,
! [SV64: set_a > set_a,SV19: set_a,SV124: set_a,SV104: set_a] :
( ( ( ord_less_eq_set_a @ ( sK8_SY249 @ SV104 @ SV124 @ SV19 @ SV64 ) @ ( sK13_SY317 @ SV64 @ SV19 @ SV124 @ SV104 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV19 @ ( SV64 @ SV124 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV104 @ SV124 )
= $false )
| ( ( ord_less_eq_set_a @ SV19 @ ( SV64 @ SV104 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1059]) ).
thf(1106,plain,
! [SV105: set_a,SV66: set_a,SV21: set_a] :
( ( ( ord_less_eq_set_a @ SV21 @ ( inf_inf_set_a @ SV66 @ SV105 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV21 @ SV66 )
= $false )
| ( ( ord_less_eq_set_a @ SV21 @ SV105 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1063]) ).
thf(1107,plain,
! [SV105: set_a,SV66: set_a,SV21: set_a] :
( ( ( ~ ( ~ ( ord_less_eq_set_a @ SV21 @ SV66 )
| ~ ( ord_less_eq_set_a @ SV21 @ SV105 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV21 @ SV66 )
= $false )
| ( ( ord_less_eq_set_a @ SV21 @ SV105 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1064]) ).
thf(1108,plain,
! [SV67: set_a,SV125: set_a] :
( ( ( ord_less_eq_set_a @ SV125 @ SV67 )
= $true )
| ( ( SV67 = SV125 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1065]) ).
thf(1109,plain,
! [SV125: set_a,SV67: set_a] :
( ( ( ord_less_eq_set_a @ SV67 @ SV125 )
= $true )
| ( ( SV67 = SV125 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1066]) ).
thf(1110,plain,
! [SV125: set_a,SV67: set_a] :
( ( ( SV67 != SV125 )
= $false )
| ( ( ord_less_eq_set_a @ SV125 @ SV67 )
= $false )
| ( ( ord_less_eq_set_a @ SV67 @ SV125 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1067]) ).
thf(1111,plain,
! [SV67: set_a,SV125: set_a] :
( ( ( ~ ~ ( ~ ( ord_less_eq_set_a @ SV125 @ SV67 )
| ~ ( ord_less_eq_set_a @ SV67 @ SV125 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV125 @ SV67 )
= $false )
| ( ( ord_less_eq_set_a @ SV67 @ SV125 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1067]) ).
thf(1112,plain,
! [SV126: set_a,SV68: set_a] :
( ( ( ord_less_eq_set_a @ SV68 @ SV126 )
= $true )
| ( ( SV68 = SV126 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1068]) ).
thf(1113,plain,
! [SV68: set_a,SV126: set_a] :
( ( ( ord_less_eq_set_a @ SV126 @ SV68 )
= $true )
| ( ( SV68 = SV126 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1069]) ).
thf(1114,plain,
! [SV126: set_a,SV68: set_a] :
( ( ( SV68 != SV126 )
= $false )
| ( ( ord_less_eq_set_a @ SV68 @ SV126 )
= $false )
| ( ( ord_less_eq_set_a @ SV126 @ SV68 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1070]) ).
thf(1115,plain,
! [SV126: set_a,SV68: set_a] :
( ( ( ~ ~ ( ~ ( ord_less_eq_set_a @ SV68 @ SV126 )
| ~ ( ord_less_eq_set_a @ SV126 @ SV68 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV68 @ SV126 )
= $false )
| ( ( ord_less_eq_set_a @ SV126 @ SV68 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1070]) ).
thf(1116,plain,
! [SV127: set_a,SV69: set_a,SV136: a] :
( ( ( member_a @ SV136 @ SV69 )
= $false )
| ( ( member_a @ SV136 @ SV127 )
= $true )
| ( ( ord_less_eq_set_a @ SV69 @ SV127 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1071]) ).
thf(1117,plain,
! [SV127: set_a,SV69: set_a] :
( ( ( ord_less_eq_set_a @ SV69 @ SV127 )
= $true )
| ( ( member_a @ ( sK6_SY309 @ SV127 @ SV69 ) @ SV69 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1072]) ).
thf(1118,plain,
! [SV127: set_a,SV69: set_a] :
( ( ( ! [SY309: a] :
( ~ ( member_a @ SY309 @ SV69 )
| ( member_a @ SY309 @ SV127 ) ) )
= $true )
| ( ( member_a @ ( sK6_SY309 @ SV127 @ SV69 ) @ SV69 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1073]) ).
thf(1119,plain,
! [SV127: set_a,SV69: set_a,SV140: a] :
( ( ( ~ ( member_a @ SV140 @ SV69 )
| ( member_a @ SV140 @ SV127 ) )
= $true )
| ( ( member_a @ ( sK6_SY309 @ SV127 @ SV69 ) @ SV127 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1075]) ).
thf(1120,plain,
! [SV110: set_a > set_a,SV28: set_a,SV128: set_a,SV73: set_a] :
( ( ( ord_less_eq_set_a @ ( sK9_SY296 @ SV73 @ SV128 @ SV28 @ SV110 ) @ ( sK14_SY318 @ SV110 @ SV28 @ SV128 @ SV73 ) )
= $true )
| ( ( ord_less_eq_set_a @ ( SV110 @ SV28 ) @ SV128 )
= $true )
| ( ( ( SV110 @ SV73 )
= SV128 )
= $false )
| ( ( ord_less_eq_set_a @ SV28 @ SV73 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1076]) ).
thf(1121,plain,
! [SV111: set_a,SV75: set_a,SV30: set_a] :
( ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ SV30 @ SV75 ) @ SV111 )
= $true )
| ( ( ord_less_eq_set_a @ SV30 @ SV111 )
= $false )
| ( ( ord_less_eq_set_a @ SV75 @ SV111 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1080]) ).
thf(1122,plain,
! [SV75: set_a,SV111: set_a,SV30: set_a] :
( ( ( ~ ( ~ ( ord_less_eq_set_a @ SV30 @ SV111 )
| ~ ( ord_less_eq_set_a @ SV75 @ SV111 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV30 @ SV111 )
= $false )
| ( ( ord_less_eq_set_a @ SV75 @ SV111 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1081]) ).
thf(1123,plain,
! [SV80: a > $o,SV139: a,SV35: a > $o] :
( ( ( ~ ( SV35 @ SV139 ) )
= $true )
| ( ( SV80 @ SV139 )
= $true )
| ( ( SV35 @ ( sK4_SY269 @ SV80 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1082]) ).
thf(1124,plain,
! [SV80: a > $o,SV137: a,SV35: a > $o] :
( ( ( SV35 @ SV137 )
= $false )
| ( ( SV80 @ SV137 )
= $true )
| ( ( SV80 @ ( sK4_SY269 @ SV80 @ SV35 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1083]) ).
thf(1125,plain,
! [SV82: set_a > set_a,SV37: set_a,SV131: set_a,SV115: set_a] :
( ( ( ord_less_eq_set_a @ ( sK10_SY273 @ SV115 @ SV131 @ SV37 @ SV82 ) @ ( sK15_SY319 @ SV82 @ SV37 @ SV131 @ SV115 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV37 @ ( SV82 @ SV131 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV115 @ SV131 )
= $false )
| ( ( SV37
= ( SV82 @ SV115 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1084]) ).
thf(1126,plain,
! [SV132: set_a,SV85: set_a] :
( ( ( ord_less_eq_set_a @ SV85 @ SV132 )
= $true )
| ( ( SV85 = SV132 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1086]) ).
thf(1127,plain,
! [SV85: set_a,SV132: set_a] :
( ( ( ord_less_eq_set_a @ SV132 @ SV85 )
= $true )
| ( ( SV85 = SV132 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1087]) ).
thf(1128,plain,
! [SV132: set_a,SV85: set_a] :
( ( ( SV85 != SV132 )
= $false )
| ( ( ord_less_eq_set_a @ SV85 @ SV132 )
= $false )
| ( ( ord_less_eq_set_a @ SV132 @ SV85 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1088]) ).
thf(1129,plain,
! [SV132: set_a,SV85: set_a] :
( ( ( ~ ~ ( ~ ( ord_less_eq_set_a @ SV85 @ SV132 )
| ~ ( ord_less_eq_set_a @ SV132 @ SV85 ) ) )
= $false )
| ( ( ord_less_eq_set_a @ SV85 @ SV132 )
= $false )
| ( ( ord_less_eq_set_a @ SV132 @ SV85 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1088]) ).
thf(1130,plain,
! [SV120: set_a > set_a,SV51: set_a,SV133: set_a,SV96: set_a] :
( ( ( ord_less_eq_set_a @ ( sK11_SY304 @ SV96 @ SV133 @ SV51 @ SV120 ) @ ( sK16_SY320 @ SV120 @ SV51 @ SV133 @ SV96 ) )
= $true )
| ( ( ord_less_eq_set_a @ ( SV120 @ SV51 ) @ SV133 )
= $true )
| ( ( ord_less_eq_set_a @ ( SV120 @ SV96 ) @ SV133 )
= $false )
| ( ( ord_less_eq_set_a @ SV51 @ SV96 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1089]) ).
thf(1131,plain,
! [SV134: set_a,SV97: set_a,SV138: a] :
( ( ( member_a @ SV138 @ SV97 )
= $false )
| ( ( member_a @ SV138 @ SV134 )
= $true )
| ( ( ord_less_eq_set_a @ SV97 @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1091]) ).
thf(1132,plain,
! [SV134: set_a,SV97: set_a] :
( ( ( ord_less_eq_set_a @ SV97 @ SV134 )
= $true )
| ( ( member_a @ ( sK7_SY316 @ SV134 @ SV97 ) @ SV97 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1092]) ).
thf(1133,plain,
! [SV134: set_a,SV97: set_a] :
( ( ( ! [SY316: a] :
( ~ ( member_a @ SY316 @ SV97 )
| ( member_a @ SY316 @ SV134 ) ) )
= $true )
| ( ( member_a @ ( sK7_SY316 @ SV134 @ SV97 ) @ SV97 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1093]) ).
thf(1134,plain,
! [SV134: set_a,SV97: set_a,SV141: a] :
( ( ( ~ ( member_a @ SV141 @ SV97 )
| ( member_a @ SV141 @ SV134 ) )
= $true )
| ( ( member_a @ ( sK7_SY316 @ SV134 @ SV97 ) @ SV134 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1095]) ).
thf(1135,plain,
! [SV123: set_a,SV60: set_a] :
( ( ( SV60 = SV123 )
= $true )
| ( ( ord_less_eq_set_a @ SV60 @ SV123 )
= $false )
| ( ( ord_less_eq_set_a @ SV123 @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1098]) ).
thf(1136,plain,
! [SV123: set_a,SV60: set_a] :
( ( ( ~ ( ~ ( ord_less_eq_set_a @ SV60 @ SV123 )
| ~ ( ord_less_eq_set_a @ SV123 @ SV60 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV60 @ SV123 )
= $false )
| ( ( ord_less_eq_set_a @ SV123 @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1099]) ).
thf(1137,plain,
! [SV103: set_a > $o,SV62: set_a,SV16: set_a > $o] :
( ( ( SV16 @ ( sK17_SY289 @ SV62 @ SV103 @ SV16 ) )
= $true )
| ( ( SV103 @ ( order_Greatest_set_a @ SV16 ) )
= $true )
| ( ( SV16 @ ( sK5_SY244 @ SV103 @ SV62 @ SV16 ) )
= $true )
| ( ( SV16 @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1100]) ).
thf(1138,plain,
! [SV103: set_a > $o,SV62: set_a,SV16: set_a > $o] :
( ( ( ~ ! [SY322: set_a] :
( ~ ( SV16 @ SY322 )
| ( ord_less_eq_set_a @ SY322 @ ( sK17_SY289 @ SV62 @ SV103 @ SV16 ) ) ) )
= $false )
| ( ( SV103 @ ( order_Greatest_set_a @ SV16 ) )
= $true )
| ( ( SV16 @ ( sK5_SY244 @ SV103 @ SV62 @ SV16 ) )
= $true )
| ( ( SV16 @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1101]) ).
thf(1139,plain,
! [SV16: set_a > $o,SV62: set_a,SV103: set_a > $o] :
( ( ( SV103 @ ( sK17_SY289 @ SV62 @ SV103 @ SV16 ) )
= $false )
| ( ( SV103 @ ( order_Greatest_set_a @ SV16 ) )
= $true )
| ( ( SV16 @ ( sK5_SY244 @ SV103 @ SV62 @ SV16 ) )
= $true )
| ( ( SV16 @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1101]) ).
thf(1140,plain,
! [SV103: set_a > $o,SV62: set_a,SV16: set_a > $o] :
( ( ( ! [SY321: set_a] :
( ~ ( SV16 @ SY321 )
| ( ord_less_eq_set_a @ SY321 @ ( sK12_SY289 @ SV62 @ SV103 @ SV16 ) ) ) )
= $true )
| ( ( SV103 @ ( order_Greatest_set_a @ SV16 ) )
= $true )
| ( ( ord_less_eq_set_a @ ( sK5_SY244 @ SV103 @ SV62 @ SV16 ) @ SV62 )
= $false )
| ( ( SV16 @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1103]) ).
thf(1141,plain,
! [SV105: set_a,SV66: set_a,SV21: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV21 @ SV66 )
| ~ ( ord_less_eq_set_a @ SV21 @ SV105 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV21 @ SV66 )
= $false )
| ( ( ord_less_eq_set_a @ SV21 @ SV105 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1107]) ).
thf(1142,plain,
! [SV125: set_a,SV67: set_a] :
( ( ( SV67 = SV125 )
= $true )
| ( ( ord_less_eq_set_a @ SV125 @ SV67 )
= $false )
| ( ( ord_less_eq_set_a @ SV67 @ SV125 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1110]) ).
thf(1143,plain,
! [SV67: set_a,SV125: set_a] :
( ( ( ~ ( ~ ( ord_less_eq_set_a @ SV125 @ SV67 )
| ~ ( ord_less_eq_set_a @ SV67 @ SV125 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV125 @ SV67 )
= $false )
| ( ( ord_less_eq_set_a @ SV67 @ SV125 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1111]) ).
thf(1144,plain,
! [SV126: set_a,SV68: set_a] :
( ( ( SV68 = SV126 )
= $true )
| ( ( ord_less_eq_set_a @ SV68 @ SV126 )
= $false )
| ( ( ord_less_eq_set_a @ SV126 @ SV68 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1114]) ).
thf(1145,plain,
! [SV126: set_a,SV68: set_a] :
( ( ( ~ ( ~ ( ord_less_eq_set_a @ SV68 @ SV126 )
| ~ ( ord_less_eq_set_a @ SV126 @ SV68 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV68 @ SV126 )
= $false )
| ( ( ord_less_eq_set_a @ SV126 @ SV68 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1115]) ).
thf(1146,plain,
! [SV127: set_a,SV69: set_a,SV142: a] :
( ( ( ~ ( member_a @ SV142 @ SV69 )
| ( member_a @ SV142 @ SV127 ) )
= $true )
| ( ( member_a @ ( sK6_SY309 @ SV127 @ SV69 ) @ SV69 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1118]) ).
thf(1147,plain,
! [SV127: set_a,SV69: set_a,SV140: a] :
( ( ( ~ ( member_a @ SV140 @ SV69 ) )
= $true )
| ( ( member_a @ SV140 @ SV127 )
= $true )
| ( ( member_a @ ( sK6_SY309 @ SV127 @ SV69 ) @ SV127 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1119]) ).
thf(1148,plain,
! [SV75: set_a,SV111: set_a,SV30: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV30 @ SV111 )
| ~ ( ord_less_eq_set_a @ SV75 @ SV111 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV30 @ SV111 )
= $false )
| ( ( ord_less_eq_set_a @ SV75 @ SV111 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1122]) ).
thf(1149,plain,
! [SV80: a > $o,SV139: a,SV35: a > $o] :
( ( ( SV35 @ SV139 )
= $false )
| ( ( SV80 @ SV139 )
= $true )
| ( ( SV35 @ ( sK4_SY269 @ SV80 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1123]) ).
thf(1150,plain,
! [SV132: set_a,SV85: set_a] :
( ( ( SV85 = SV132 )
= $true )
| ( ( ord_less_eq_set_a @ SV85 @ SV132 )
= $false )
| ( ( ord_less_eq_set_a @ SV132 @ SV85 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1128]) ).
thf(1151,plain,
! [SV132: set_a,SV85: set_a] :
( ( ( ~ ( ~ ( ord_less_eq_set_a @ SV85 @ SV132 )
| ~ ( ord_less_eq_set_a @ SV132 @ SV85 ) ) )
= $true )
| ( ( ord_less_eq_set_a @ SV85 @ SV132 )
= $false )
| ( ( ord_less_eq_set_a @ SV132 @ SV85 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1129]) ).
thf(1152,plain,
! [SV134: set_a,SV97: set_a,SV143: a] :
( ( ( ~ ( member_a @ SV143 @ SV97 )
| ( member_a @ SV143 @ SV134 ) )
= $true )
| ( ( member_a @ ( sK7_SY316 @ SV134 @ SV97 ) @ SV97 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1133]) ).
thf(1153,plain,
! [SV134: set_a,SV97: set_a,SV141: a] :
( ( ( ~ ( member_a @ SV141 @ SV97 ) )
= $true )
| ( ( member_a @ SV141 @ SV134 )
= $true )
| ( ( member_a @ ( sK7_SY316 @ SV134 @ SV97 ) @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1134]) ).
thf(1154,plain,
! [SV123: set_a,SV60: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV60 @ SV123 )
| ~ ( ord_less_eq_set_a @ SV123 @ SV60 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV60 @ SV123 )
= $false )
| ( ( ord_less_eq_set_a @ SV123 @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1136]) ).
thf(1155,plain,
! [SV103: set_a > $o,SV62: set_a,SV16: set_a > $o] :
( ( ( ! [SY322: set_a] :
( ~ ( SV16 @ SY322 )
| ( ord_less_eq_set_a @ SY322 @ ( sK17_SY289 @ SV62 @ SV103 @ SV16 ) ) ) )
= $true )
| ( ( SV103 @ ( order_Greatest_set_a @ SV16 ) )
= $true )
| ( ( SV16 @ ( sK5_SY244 @ SV103 @ SV62 @ SV16 ) )
= $true )
| ( ( SV16 @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1138]) ).
thf(1156,plain,
! [SV103: set_a > $o,SV62: set_a,SV144: set_a,SV16: set_a > $o] :
( ( ( ~ ( SV16 @ SV144 )
| ( ord_less_eq_set_a @ SV144 @ ( sK12_SY289 @ SV62 @ SV103 @ SV16 ) ) )
= $true )
| ( ( SV103 @ ( order_Greatest_set_a @ SV16 ) )
= $true )
| ( ( ord_less_eq_set_a @ ( sK5_SY244 @ SV103 @ SV62 @ SV16 ) @ SV62 )
= $false )
| ( ( SV16 @ SV62 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1157,plain,
! [SV105: set_a,SV66: set_a,SV21: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV21 @ SV66 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV21 @ SV66 )
= $false )
| ( ( ord_less_eq_set_a @ SV21 @ SV105 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1141]) ).
thf(1158,plain,
! [SV66: set_a,SV105: set_a,SV21: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV21 @ SV105 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV21 @ SV66 )
= $false )
| ( ( ord_less_eq_set_a @ SV21 @ SV105 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1141]) ).
thf(1159,plain,
! [SV67: set_a,SV125: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV125 @ SV67 )
| ~ ( ord_less_eq_set_a @ SV67 @ SV125 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV125 @ SV67 )
= $false )
| ( ( ord_less_eq_set_a @ SV67 @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1143]) ).
thf(1160,plain,
! [SV126: set_a,SV68: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV68 @ SV126 )
| ~ ( ord_less_eq_set_a @ SV126 @ SV68 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV68 @ SV126 )
= $false )
| ( ( ord_less_eq_set_a @ SV126 @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1145]) ).
thf(1161,plain,
! [SV127: set_a,SV69: set_a,SV142: a] :
( ( ( ~ ( member_a @ SV142 @ SV69 ) )
= $true )
| ( ( member_a @ SV142 @ SV127 )
= $true )
| ( ( member_a @ ( sK6_SY309 @ SV127 @ SV69 ) @ SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1146]) ).
thf(1162,plain,
! [SV127: set_a,SV69: set_a,SV140: a] :
( ( ( member_a @ SV140 @ SV69 )
= $false )
| ( ( member_a @ SV140 @ SV127 )
= $true )
| ( ( member_a @ ( sK6_SY309 @ SV127 @ SV69 ) @ SV127 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1147]) ).
thf(1163,plain,
! [SV75: set_a,SV111: set_a,SV30: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV30 @ SV111 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV30 @ SV111 )
= $false )
| ( ( ord_less_eq_set_a @ SV75 @ SV111 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1148]) ).
thf(1164,plain,
! [SV30: set_a,SV111: set_a,SV75: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV75 @ SV111 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV30 @ SV111 )
= $false )
| ( ( ord_less_eq_set_a @ SV75 @ SV111 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1148]) ).
thf(1165,plain,
! [SV132: set_a,SV85: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV85 @ SV132 )
| ~ ( ord_less_eq_set_a @ SV132 @ SV85 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV85 @ SV132 )
= $false )
| ( ( ord_less_eq_set_a @ SV132 @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1151]) ).
thf(1166,plain,
! [SV134: set_a,SV97: set_a,SV143: a] :
( ( ( ~ ( member_a @ SV143 @ SV97 ) )
= $true )
| ( ( member_a @ SV143 @ SV134 )
= $true )
| ( ( member_a @ ( sK7_SY316 @ SV134 @ SV97 ) @ SV97 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1152]) ).
thf(1167,plain,
! [SV134: set_a,SV97: set_a,SV141: a] :
( ( ( member_a @ SV141 @ SV97 )
= $false )
| ( ( member_a @ SV141 @ SV134 )
= $true )
| ( ( member_a @ ( sK7_SY316 @ SV134 @ SV97 ) @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1153]) ).
thf(1168,plain,
! [SV123: set_a,SV60: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV60 @ SV123 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV60 @ SV123 )
= $false )
| ( ( ord_less_eq_set_a @ SV123 @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1154]) ).
thf(1169,plain,
! [SV60: set_a,SV123: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV123 @ SV60 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV60 @ SV123 )
= $false )
| ( ( ord_less_eq_set_a @ SV123 @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1154]) ).
thf(1170,plain,
! [SV103: set_a > $o,SV62: set_a,SV145: set_a,SV16: set_a > $o] :
( ( ( ~ ( SV16 @ SV145 )
| ( ord_less_eq_set_a @ SV145 @ ( sK17_SY289 @ SV62 @ SV103 @ SV16 ) ) )
= $true )
| ( ( SV103 @ ( order_Greatest_set_a @ SV16 ) )
= $true )
| ( ( SV16 @ ( sK5_SY244 @ SV103 @ SV62 @ SV16 ) )
= $true )
| ( ( SV16 @ SV62 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1155]) ).
thf(1171,plain,
! [SV103: set_a > $o,SV62: set_a,SV144: set_a,SV16: set_a > $o] :
( ( ( ~ ( SV16 @ SV144 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV144 @ ( sK12_SY289 @ SV62 @ SV103 @ SV16 ) )
= $true )
| ( ( SV103 @ ( order_Greatest_set_a @ SV16 ) )
= $true )
| ( ( ord_less_eq_set_a @ ( sK5_SY244 @ SV103 @ SV62 @ SV16 ) @ SV62 )
= $false )
| ( ( SV16 @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1156]) ).
thf(1172,plain,
! [SV105: set_a,SV66: set_a,SV21: set_a] :
( ( ( ord_less_eq_set_a @ SV21 @ SV66 )
= $true )
| ( ( ord_less_eq_set_a @ SV21 @ SV66 )
= $false )
| ( ( ord_less_eq_set_a @ SV21 @ SV105 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1157]) ).
thf(1173,plain,
! [SV66: set_a,SV105: set_a,SV21: set_a] :
( ( ( ord_less_eq_set_a @ SV21 @ SV105 )
= $true )
| ( ( ord_less_eq_set_a @ SV21 @ SV66 )
= $false )
| ( ( ord_less_eq_set_a @ SV21 @ SV105 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1158]) ).
thf(1174,plain,
! [SV67: set_a,SV125: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV125 @ SV67 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV125 @ SV67 )
= $false )
| ( ( ord_less_eq_set_a @ SV67 @ SV125 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1159]) ).
thf(1175,plain,
! [SV125: set_a,SV67: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV67 @ SV125 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV125 @ SV67 )
= $false )
| ( ( ord_less_eq_set_a @ SV67 @ SV125 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1159]) ).
thf(1176,plain,
! [SV126: set_a,SV68: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV68 @ SV126 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV68 @ SV126 )
= $false )
| ( ( ord_less_eq_set_a @ SV126 @ SV68 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1160]) ).
thf(1177,plain,
! [SV68: set_a,SV126: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV126 @ SV68 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV68 @ SV126 )
= $false )
| ( ( ord_less_eq_set_a @ SV126 @ SV68 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1160]) ).
thf(1178,plain,
! [SV127: set_a,SV69: set_a,SV142: a] :
( ( ( member_a @ SV142 @ SV69 )
= $false )
| ( ( member_a @ SV142 @ SV127 )
= $true )
| ( ( member_a @ ( sK6_SY309 @ SV127 @ SV69 ) @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1161]) ).
thf(1179,plain,
! [SV75: set_a,SV111: set_a,SV30: set_a] :
( ( ( ord_less_eq_set_a @ SV30 @ SV111 )
= $true )
| ( ( ord_less_eq_set_a @ SV30 @ SV111 )
= $false )
| ( ( ord_less_eq_set_a @ SV75 @ SV111 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1163]) ).
thf(1180,plain,
! [SV30: set_a,SV111: set_a,SV75: set_a] :
( ( ( ord_less_eq_set_a @ SV75 @ SV111 )
= $true )
| ( ( ord_less_eq_set_a @ SV30 @ SV111 )
= $false )
| ( ( ord_less_eq_set_a @ SV75 @ SV111 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1164]) ).
thf(1181,plain,
! [SV132: set_a,SV85: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV85 @ SV132 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV85 @ SV132 )
= $false )
| ( ( ord_less_eq_set_a @ SV132 @ SV85 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1165]) ).
thf(1182,plain,
! [SV85: set_a,SV132: set_a] :
( ( ( ~ ( ord_less_eq_set_a @ SV132 @ SV85 ) )
= $false )
| ( ( ord_less_eq_set_a @ SV85 @ SV132 )
= $false )
| ( ( ord_less_eq_set_a @ SV132 @ SV85 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1165]) ).
thf(1183,plain,
! [SV134: set_a,SV97: set_a,SV143: a] :
( ( ( member_a @ SV143 @ SV97 )
= $false )
| ( ( member_a @ SV143 @ SV134 )
= $true )
| ( ( member_a @ ( sK7_SY316 @ SV134 @ SV97 ) @ SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1166]) ).
thf(1184,plain,
! [SV123: set_a,SV60: set_a] :
( ( ( ord_less_eq_set_a @ SV60 @ SV123 )
= $true )
| ( ( ord_less_eq_set_a @ SV60 @ SV123 )
= $false )
| ( ( ord_less_eq_set_a @ SV123 @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1168]) ).
thf(1185,plain,
! [SV60: set_a,SV123: set_a] :
( ( ( ord_less_eq_set_a @ SV123 @ SV60 )
= $true )
| ( ( ord_less_eq_set_a @ SV60 @ SV123 )
= $false )
| ( ( ord_less_eq_set_a @ SV123 @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1169]) ).
thf(1186,plain,
! [SV103: set_a > $o,SV62: set_a,SV145: set_a,SV16: set_a > $o] :
( ( ( ~ ( SV16 @ SV145 ) )
= $true )
| ( ( ord_less_eq_set_a @ SV145 @ ( sK17_SY289 @ SV62 @ SV103 @ SV16 ) )
= $true )
| ( ( SV103 @ ( order_Greatest_set_a @ SV16 ) )
= $true )
| ( ( SV16 @ ( sK5_SY244 @ SV103 @ SV62 @ SV16 ) )
= $true )
| ( ( SV16 @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1170]) ).
thf(1187,plain,
! [SV103: set_a > $o,SV62: set_a,SV144: set_a,SV16: set_a > $o] :
( ( ( SV16 @ SV144 )
= $false )
| ( ( ord_less_eq_set_a @ SV144 @ ( sK12_SY289 @ SV62 @ SV103 @ SV16 ) )
= $true )
| ( ( SV103 @ ( order_Greatest_set_a @ SV16 ) )
= $true )
| ( ( ord_less_eq_set_a @ ( sK5_SY244 @ SV103 @ SV62 @ SV16 ) @ SV62 )
= $false )
| ( ( SV16 @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1171]) ).
thf(1188,plain,
! [SV67: set_a,SV125: set_a] :
( ( ( ord_less_eq_set_a @ SV125 @ SV67 )
= $true )
| ( ( ord_less_eq_set_a @ SV125 @ SV67 )
= $false )
| ( ( ord_less_eq_set_a @ SV67 @ SV125 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1174]) ).
thf(1189,plain,
! [SV125: set_a,SV67: set_a] :
( ( ( ord_less_eq_set_a @ SV67 @ SV125 )
= $true )
| ( ( ord_less_eq_set_a @ SV125 @ SV67 )
= $false )
| ( ( ord_less_eq_set_a @ SV67 @ SV125 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1175]) ).
thf(1190,plain,
! [SV126: set_a,SV68: set_a] :
( ( ( ord_less_eq_set_a @ SV68 @ SV126 )
= $true )
| ( ( ord_less_eq_set_a @ SV68 @ SV126 )
= $false )
| ( ( ord_less_eq_set_a @ SV126 @ SV68 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1176]) ).
thf(1191,plain,
! [SV68: set_a,SV126: set_a] :
( ( ( ord_less_eq_set_a @ SV126 @ SV68 )
= $true )
| ( ( ord_less_eq_set_a @ SV68 @ SV126 )
= $false )
| ( ( ord_less_eq_set_a @ SV126 @ SV68 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1177]) ).
thf(1192,plain,
! [SV132: set_a,SV85: set_a] :
( ( ( ord_less_eq_set_a @ SV85 @ SV132 )
= $true )
| ( ( ord_less_eq_set_a @ SV85 @ SV132 )
= $false )
| ( ( ord_less_eq_set_a @ SV132 @ SV85 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1181]) ).
thf(1193,plain,
! [SV85: set_a,SV132: set_a] :
( ( ( ord_less_eq_set_a @ SV132 @ SV85 )
= $true )
| ( ( ord_less_eq_set_a @ SV85 @ SV132 )
= $false )
| ( ( ord_less_eq_set_a @ SV132 @ SV85 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1182]) ).
thf(1194,plain,
! [SV103: set_a > $o,SV62: set_a,SV145: set_a,SV16: set_a > $o] :
( ( ( SV16 @ SV145 )
= $false )
| ( ( ord_less_eq_set_a @ SV145 @ ( sK17_SY289 @ SV62 @ SV103 @ SV16 ) )
= $true )
| ( ( SV103 @ ( order_Greatest_set_a @ SV16 ) )
= $true )
| ( ( SV16 @ ( sK5_SY244 @ SV103 @ SV62 @ SV16 ) )
= $true )
| ( ( SV16 @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1186]) ).
thf(1195,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[420,1194,1193,1192,1191,1190,1189,1188,1187,1185,1184,1183,1180,1179,1178,1173,1172,1167,1162,1150,1149,1144,1142,1139,1137,1135,1132,1131,1130,1127,1126,1125,1124,1121,1120,1117,1116,1113,1112,1109,1108,1106,1105,1104,1102,1097,1096,1094,1090,1085,1079,1078,1077,1074,1062,1061,1060,1042,1041,1017,1015,1014,1013,1012,1009,1006,996,993,990,982,962,948,930,913,905,897,883,879,878,877,876,875,874,873,872,871,868,867,866,864,860,857,856,852,851,849,839,838,837,825,822,819,815,814,808,801,795,782,774,770,755,753,751,744,732,728,716,712,706,702,698,688,675,669,657,655,653,647,644,637,593,592,591,590,589,587,583,570,553,551,549,540,532,530,529,528,526,470,427,426,425,424,423,421]) ).
thf(1196,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1195]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP154^1 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.18 % Computer : n001.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Oct 6 11:24:53 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.26/1.70 ..
% 8.26/1.70
% 8.26/1.70 No.of.Axioms: 61
% 8.26/1.70
% 8.26/1.70 Length.of.Defs: 0
% 8.26/1.70
% 8.26/1.70 Contains.Choice.Funs: true
% 8.26/1.70 .........................
% 8.26/1.70
% 8.26/1.70 ********************************
% 8.26/1.70 * All subproblems solved! *
% 8.26/1.70 ********************************
% 8.26/1.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:61,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:1195,loop_count:0,foatp_calls:1,translation:fof_full)
% 8.26/1.70
% 8.26/1.70 %**** Beginning of derivation protocol ****
% 8.26/1.70 % SZS output start CNFRefutation
% See solution above
% 1.64/1.71
% 1.64/1.71 %**** End of derivation protocol ****
% 1.64/1.71 %**** no. of clauses in derivation: 903 ****
% 1.64/1.71 %**** clause counter: 1195 ****
% 1.64/1.71
% 1.64/1.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:61,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:1195,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------