%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ITP156^1 : 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 : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:24:24 AM UTC 2026
% Result : Theorem 26.98s 4.80s
% Output : CNFRefutation 4.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 85
% Syntax : Number of formulae : 1052 ( 529 unt; 0 typ; 0 def)
% Number of atoms : 6090 (3363 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 10643 (1565 ~;1439 |; 33 &;7468 @)
% ( 0 <=>; 138 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 33 ( 32 usr)
% Number of type conns : 41 ( 41 >; 0 *; 0 +; 0 <<)
% Number of symbols : 114 ( 111 usr; 23 con; 0-3 aty)
% Number of variables : 3019 ( 41 ^;2972 !; 6 ?;3019 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_produc1016684094_a_a_a,type,
produc1016684094_a_a_a: $tType ).
thf(tp_produc1088645164real_a,type,
produc1088645164real_a: $tType ).
thf(tp_produc1232925073real_a,type,
produc1232925073real_a: $tType ).
thf(tp_produc1286132450l_real,type,
produc1286132450l_real: $tType ).
thf(tp_produc1396156303t_real,type,
produc1396156303t_real: $tType ).
thf(tp_produc1572603623od_a_a,type,
produc1572603623od_a_a: $tType ).
thf(tp_produc1826081171a_real,type,
produc1826081171a_real: $tType ).
thf(tp_produc1921647824od_a_a,type,
produc1921647824od_a_a: $tType ).
thf(tp_produc1923333543_set_a,type,
produc1923333543_set_a: $tType ).
thf(tp_produc2096821232od_a_a,type,
produc2096821232od_a_a: $tType ).
thf(tp_produc348734722a_real,type,
produc348734722a_real: $tType ).
thf(tp_produc391212143l_real,type,
produc391212143l_real: $tType ).
thf(tp_produc443621487t_real,type,
produc443621487t_real: $tType ).
thf(tp_produc578556564l_real,type,
produc578556564l_real: $tType ).
thf(tp_produc826782210l_real,type,
produc826782210l_real: $tType ).
thf(tp_produc957004601l_real,type,
produc957004601l_real: $tType ).
thf(tp_product_prod_a_a,type,
product_prod_a_a: $tType ).
thf(tp_product_prod_a_real,type,
product_prod_a_real: $tType ).
thf(tp_product_prod_a_set_a,type,
product_prod_a_set_a: $tType ).
thf(tp_product_prod_real_a,type,
product_prod_real_a: $tType ).
thf(tp_real,type,
real: $tType ).
thf(tp_set_Pr147102617l_real,type,
set_Pr147102617l_real: $tType ).
thf(tp_set_Pr1741234931a_real,type,
set_Pr1741234931a_real: $tType ).
thf(tp_set_Pr1928503567a_real,type,
set_Pr1928503567a_real: $tType ).
thf(tp_set_Pr1948701895od_a_a,type,
set_Pr1948701895od_a_a: $tType ).
thf(tp_set_Product_prod_a_a,type,
set_Product_prod_a_a: $tType ).
thf(tp_set_a,type,
set_a: $tType ).
thf(tp_set_real,type,
set_real: $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_real,type,
set_set_real: $tType ).
thf(tp_collec1300223524l_real,type,
collec1300223524l_real: ( produc957004601l_real > $o ) > set_Pr147102617l_real ).
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_real,type,
collect_real: ( real > $o ) > set_real ).
thf(tp_member1068169442l_real,type,
member1068169442l_real: produc957004601l_real > set_Pr147102617l_real > $o ).
thf(tp_member1103263856a_real,type,
member1103263856a_real: product_prod_a_real > set_Pr1928503567a_real > $o ).
thf(tp_member1838126896od_a_a,type,
member1838126896od_a_a: set_Product_prod_a_a > set_se1596668135od_a_a > $o ).
thf(tp_member2057358096od_a_a,type,
member2057358096od_a_a: produc1572603623od_a_a > set_Pr1948701895od_a_a > $o ).
thf(tp_member384820540a_real,type,
member384820540a_real: produc1826081171a_real > set_Pr1741234931a_real > $o ).
thf(tp_member449909584od_a_a,type,
member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
thf(tp_member_a,type,
member_a: a > set_a > $o ).
thf(tp_member_real,type,
member_real: real > set_real > $o ).
thf(tp_member_set_a,type,
member_set_a: set_a > set_set_a > $o ).
thf(tp_member_set_real,type,
member_set_real: set_real > set_set_real > $o ).
thf(tp_one_one_real,type,
one_one_real: real ).
thf(tp_ord_le108336051od_a_a,type,
ord_le108336051od_a_a: set_Product_prod_a_a > set_Product_prod_a_a > $o ).
thf(tp_ord_le1342644953l_real,type,
ord_le1342644953l_real: produc957004601l_real > produc957004601l_real > $o ).
thf(tp_ord_le1824328871od_a_a,type,
ord_le1824328871od_a_a: set_Product_prod_a_a > set_Product_prod_a_a > $o ).
thf(tp_ord_less_eq_real,type,
ord_less_eq_real: real > real > $o ).
thf(tp_ord_less_eq_set_real,type,
ord_less_eq_set_real: set_real > set_real > $o ).
thf(tp_ord_less_real,type,
ord_less_real: real > real > $o ).
thf(tp_plus_p1243198544real_a,type,
plus_p1243198544real_a: product_prod_real_a > product_prod_real_a > product_prod_real_a ).
thf(tp_plus_p125342128_set_a,type,
plus_p125342128_set_a: produc1923333543_set_a > produc1923333543_set_a > produc1923333543_set_a ).
thf(tp_plus_p1265825342_set_a,type,
plus_p1265825342_set_a: product_prod_a_set_a > product_prod_a_set_a > product_prod_a_set_a ).
thf(tp_plus_p130512152a_real,type,
plus_p130512152a_real: set_Pr1928503567a_real > set_Pr1928503567a_real > set_Pr1928503567a_real ).
thf(tp_plus_p1505579230od_a_a,type,
plus_p1505579230od_a_a: product_prod_a_a > product_prod_a_a > product_prod_a_a ).
thf(tp_plus_p1582417306real_a,type,
plus_p1582417306real_a: produc1232925073real_a > produc1232925073real_a > produc1232925073real_a ).
thf(tp_plus_p1613276318od_a_a,type,
plus_p1613276318od_a_a: set_se1596668135od_a_a > set_se1596668135od_a_a > set_se1596668135od_a_a ).
thf(tp_plus_p1708760016l_real,type,
plus_p1708760016l_real: set_Pr147102617l_real > set_Pr147102617l_real > set_Pr147102617l_real ).
thf(tp_plus_p1745648536t_real,type,
plus_p1745648536t_real: produc1396156303t_real > produc1396156303t_real > produc1396156303t_real ).
thf(tp_plus_p1952869542l_real,type,
plus_p1952869542l_real: produc391212143l_real > produc391212143l_real > produc391212143l_real ).
thf(tp_plus_p2005278886t_real,type,
plus_p2005278886t_real: produc443621487t_real > produc443621487t_real > produc443621487t_real ).
thf(tp_plus_p541014626a_real,type,
plus_p541014626a_real: product_prod_a_real > product_prod_a_real > product_prod_a_real ).
thf(tp_plus_p634297534od_a_a,type,
plus_p634297534od_a_a: set_Product_prod_a_a > set_Product_prod_a_a > set_Product_prod_a_a ).
thf(tp_plus_p768704801t_real,type,
plus_p768704801t_real: set_set_real > set_set_real > set_set_real ).
thf(tp_plus_p77862768l_real,type,
plus_p77862768l_real: produc957004601l_real > produc957004601l_real > produc957004601l_real ).
thf(tp_plus_plus_a,type,
plus_plus_a: a > a > a ).
thf(tp_plus_plus_real,type,
plus_plus_real: real > real > real ).
thf(tp_plus_plus_set_a,type,
plus_plus_set_a: set_a > set_a > set_a ).
thf(tp_plus_plus_set_real,type,
plus_plus_set_real: set_real > set_real > set_real ).
thf(tp_plus_plus_set_set_a,type,
plus_plus_set_set_a: set_set_a > set_set_a > set_set_a ).
thf(tp_prefer1113819806a_real,type,
prefer1113819806a_real: set_Pr1741234931a_real > $o ).
thf(tp_prefer1247792113f_real,type,
prefer1247792113f_real: set_Pr147102617l_real > $o ).
thf(tp_prefer225425826od_a_a,type,
prefer225425826od_a_a: set_Pr1948701895od_a_a > $o ).
thf(tp_prefer529818233pref_a,type,
prefer529818233pref_a: set_Product_prod_a_a > $o ).
thf(tp_produc1175086478l_real,type,
produc1175086478l_real: produc957004601l_real > real > produc578556564l_real ).
thf(tp_produc1299253312od_a_a,type,
produc1299253312od_a_a: a > product_prod_a_a > produc1921647824od_a_a ).
thf(tp_produc1391501065t_real,type,
produc1391501065t_real: a > set_real > produc1396156303t_real ).
thf(tp_produc1430099868real_a,type,
produc1430099868real_a: produc957004601l_real > a > produc1088645164real_a ).
thf(tp_produc1474507607od_a_a,type,
produc1474507607od_a_a: product_prod_a_a > product_prod_a_a > produc1572603623od_a_a ).
thf(tp_produc1812461223l_real,type,
produc1812461223l_real: set_real > real > produc391212143l_real ).
thf(tp_produc1872317017_set_a,type,
produc1872317017_set_a: real > set_a > produc1923333543_set_a ).
thf(tp_produc1926903988l_real,type,
produc1926903988l_real: real > produc957004601l_real > produc826782210l_real ).
thf(tp_produc2061588782_a_a_a,type,
produc2061588782_a_a_a: product_prod_a_a > a > produc1016684094_a_a_a ).
thf(tp_produc247649703t_real,type,
produc247649703t_real: real > set_real > produc443621487t_real ).
thf(tp_produc454274172a_real,type,
produc454274172a_real: product_prod_a_a > real > produc348734722a_real ).
thf(tp_produc454550562od_a_a,type,
produc454550562od_a_a: real > product_prod_a_a > produc2096821232od_a_a ).
thf(tp_produc617496131real_a,type,
produc617496131real_a: set_real > a > produc1232925073real_a ).
thf(tp_produc64206290l_real,type,
produc64206290l_real: a > produc957004601l_real > produc1286132450l_real ).
thf(tp_produc705216881l_real,type,
produc705216881l_real: real > real > produc957004601l_real ).
thf(tp_produc886678603a_real,type,
produc886678603a_real: product_prod_a_real > product_prod_a_real > produc1826081171a_real ).
thf(tp_product_Pair_a_a,type,
product_Pair_a_a: a > a > product_prod_a_a ).
thf(tp_product_Pair_a_real,type,
product_Pair_a_real: a > real > product_prod_a_real ).
thf(tp_product_Pair_a_set_a,type,
product_Pair_a_set_a: a > set_a > product_prod_a_set_a ).
thf(tp_product_Pair_real_a,type,
product_Pair_real_a: real > a > product_prod_real_a ).
thf(tp_real_V1035702895aleR_a,type,
real_V1035702895aleR_a: real > a > a ).
thf(tp_real_V1139189034l_real,type,
real_V1139189034l_real: real > produc957004601l_real > produc957004601l_real ).
thf(tp_real_V1214981142real_a,type,
real_V1214981142real_a: real > product_prod_real_a > product_prod_real_a ).
thf(tp_real_V1538726831_a_a_a,type,
real_V1538726831_a_a_a: real > produc1016684094_a_a_a > produc1016684094_a_a_a ).
thf(tp_real_V1943155903od_a_a,type,
real_V1943155903od_a_a: real > produc2096821232od_a_a > produc2096821232od_a_a ).
thf(tp_real_V195069393a_real,type,
real_V195069393a_real: real > produc348734722a_real > produc348734722a_real ).
thf(tp_real_V296206913od_a_a,type,
real_V296206913od_a_a: real > produc1921647824od_a_a > produc1921647824od_a_a ).
thf(tp_real_V368978776od_a_a,type,
real_V368978776od_a_a: real > produc1572603623od_a_a > produc1572603623od_a_a ).
thf(tp_real_V453051771R_real,type,
real_V453051771R_real: real > real > real ).
thf(tp_real_V512797224a_real,type,
real_V512797224a_real: real > product_prod_a_real > product_prod_a_real ).
thf(tp_real_V543523736od_a_a,type,
real_V543523736od_a_a: real > product_prod_a_a > product_prod_a_a ).
thf(tp_relation,type,
relation: set_Product_prod_a_a ).
thf(tp_sK10_SY457,type,
sK10_SY457: set_Product_prod_a_a > set_Product_prod_a_a > product_prod_a_a > product_prod_a_a ).
thf(tp_sK11_SY464,type,
sK11_SY464: set_a > set_a > a > a ).
thf(tp_sK12_SY479,type,
sK12_SY479: set_Product_prod_a_a > set_Product_prod_a_a > product_prod_a_a > product_prod_a_a ).
thf(tp_sK13_SY480,type,
sK13_SY480: set_a > set_a > a > a ).
thf(tp_sK14_SY474,type,
sK14_SY474: set_Product_prod_a_a > set_Product_prod_a_a > product_prod_a_a ).
thf(tp_sK15_SY476,type,
sK15_SY476: set_Product_prod_a_a > set_Product_prod_a_a > product_prod_a_a ).
thf(tp_sK1_SY342,type,
sK1_SY342: product_prod_a_a > a ).
thf(tp_sK2_SY347,type,
sK2_SY347: product_prod_a_a > a ).
thf(tp_sK3_SY469,type,
sK3_SY469: product_prod_a_a > a ).
thf(tp_sK4_SY334,type,
sK4_SY334: product_prod_a_a > ( product_prod_a_a > $o ) > a ).
thf(tp_sK5_SY434,type,
sK5_SY434: set_Product_prod_a_a > set_Product_prod_a_a > product_prod_a_a ).
thf(tp_sK6_SY353,type,
sK6_SY353: product_prod_a_a > ( product_prod_a_a > $o ) > a ).
thf(tp_sK7_SY477,type,
sK7_SY477: product_prod_a_a > ( product_prod_a_a > $o ) > a ).
thf(tp_sK8_SY470,type,
sK8_SY470: product_prod_a_a > a ).
thf(tp_sK9_SY478,type,
sK9_SY478: product_prod_a_a > ( product_prod_a_a > $o ) > a ).
thf(tp_u,type,
u: real ).
thf(tp_v,type,
v: real ).
thf(tp_x,type,
x: a ).
thf(tp_y,type,
y: a ).
thf(tp_zero_z1407338960real_a,type,
zero_z1407338960real_a: product_prod_real_a ).
thf(tp_zero_z1937883107real_a,type,
zero_z1937883107real_a: produc1088645164real_a ).
thf(tp_zero_z2135370393l_real,type,
zero_z2135370393l_real: produc1286132450l_real ).
thf(tp_zero_z257140542od_a_a,type,
zero_z257140542od_a_a: set_Product_prod_a_a ).
thf(tp_zero_z342251165l_real,type,
zero_z342251165l_real: produc578556564l_real ).
thf(tp_zero_z396988537od_a_a,type,
zero_z396988537od_a_a: produc2096821232od_a_a ).
thf(tp_zero_z53797895od_a_a,type,
zero_z53797895od_a_a: produc1921647824od_a_a ).
thf(tp_zero_z590476811l_real,type,
zero_z590476811l_real: produc826782210l_real ).
thf(tp_zero_z659284464l_real,type,
zero_z659284464l_real: produc957004601l_real ).
thf(tp_zero_z705155042a_real,type,
zero_z705155042a_real: product_prod_a_real ).
thf(tp_zero_z950819678od_a_a,type,
zero_z950819678od_a_a: product_prod_a_a ).
thf(tp_zero_zero_a,type,
zero_zero_a: a ).
thf(tp_zero_zero_real,type,
zero_zero_real: real ).
thf(tp_zero_zero_set_a,type,
zero_zero_set_a: set_a ).
thf(tp_zero_zero_set_real,type,
zero_zero_set_real: set_real ).
thf(14,axiom,
! [U: real,B: a,V: real,A: a] :
( ( ( plus_plus_a @ ( real_V1035702895aleR_a @ U @ B ) @ ( real_V1035702895aleR_a @ V @ A ) )
= ( plus_plus_a @ ( real_V1035702895aleR_a @ U @ A ) @ ( real_V1035702895aleR_a @ V @ B ) ) )
=> ( ( U != V )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_add__scaleR__degen) ).
thf(22,axiom,
! [A3: set_Product_prod_a_a,B4: set_Product_prod_a_a,C: product_prod_a_a] :
( ( ord_le108336051od_a_a @ A3 @ B4 )
=> ( ( member449909584od_a_a @ C @ A3 )
=> ( member449909584od_a_a @ C @ B4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_psubsetD) ).
thf(31,axiom,
! [A3: set_Product_prod_a_a,B4: set_Product_prod_a_a,X: product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A3 @ B4 )
=> ( ( member449909584od_a_a @ X @ A3 )
=> ( member449909584od_a_a @ X @ B4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_in__mono) ).
thf(32,axiom,
! [A3: set_Product_prod_a_a,B4: set_Product_prod_a_a,C: product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A3 @ B4 )
=> ( ( member449909584od_a_a @ C @ A3 )
=> ( member449909584od_a_a @ C @ B4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_subsetD) ).
thf(33,axiom,
( ord_le1824328871od_a_a
= ( ^ [A6: set_Product_prod_a_a,B6: set_Product_prod_a_a] :
! [X3: product_prod_a_a] :
( ( member449909584od_a_a @ X3 @ A6 )
=> ( member449909584od_a_a @ X3 @ B6 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_subset__eq) ).
thf(34,axiom,
( ord_le1824328871od_a_a
= ( ^ [A6: set_Product_prod_a_a,B6: set_Product_prod_a_a] :
! [T: product_prod_a_a] :
( ( member449909584od_a_a @ T @ A6 )
=> ( member449909584od_a_a @ T @ B6 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_subset__iff) ).
thf(73,axiom,
! [A3: set_Product_prod_a_a,B4: set_Product_prod_a_a] :
( ! [X4: product_prod_a_a] :
( ( member449909584od_a_a @ X4 @ A3 )
=> ( member449909584od_a_a @ X4 @ B4 ) )
=> ( ord_le1824328871od_a_a @ A3 @ B4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_subsetI) ).
thf(91,axiom,
! [A: real,B: real,X: a] :
( ( real_V1035702895aleR_a @ ( plus_plus_real @ A @ B ) @ X )
= ( plus_plus_a @ ( real_V1035702895aleR_a @ A @ X ) @ ( real_V1035702895aleR_a @ B @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_scaleR__add__left) ).
thf(93,axiom,
! [X: real,Y: real,Xa: a] :
( ( real_V1035702895aleR_a @ ( plus_plus_real @ X @ Y ) @ Xa )
= ( plus_plus_a @ ( real_V1035702895aleR_a @ X @ Xa ) @ ( real_V1035702895aleR_a @ Y @ Xa ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_scaleR__left_Oadd) ).
thf(95,axiom,
! [A: real,X: a,Y: a] :
( ( A != zero_zero_real )
=> ( ( ( real_V1035702895aleR_a @ A @ X )
= ( real_V1035702895aleR_a @ A @ Y ) )
=> ( X = Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_scale__left__imp__eq) ).
thf(96,axiom,
! [A: real,X: a,Y: a] :
( ( real_V1035702895aleR_a @ A @ ( plus_plus_a @ X @ Y ) )
= ( plus_plus_a @ ( real_V1035702895aleR_a @ A @ X ) @ ( real_V1035702895aleR_a @ A @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_scaleR__add__right) ).
thf(98,axiom,
! [X: a,A: real,B: real] :
( ( X != zero_zero_a )
=> ( ( ( real_V1035702895aleR_a @ A @ X )
= ( real_V1035702895aleR_a @ B @ X ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_scale__right__imp__eq) ).
thf(100,axiom,
! [A: real,B: real,X: a] :
( ( real_V1035702895aleR_a @ A @ ( real_V1035702895aleR_a @ B @ X ) )
= ( real_V1035702895aleR_a @ B @ ( real_V1035702895aleR_a @ A @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_scale__left__commute) ).
thf(102,axiom,
! [A3: set_Product_prod_a_a,B4: set_Product_prod_a_a] :
( ( member449909584od_a_a @ zero_z950819678od_a_a @ A3 )
=> ( ord_le1824328871od_a_a @ B4 @ ( plus_p634297534od_a_a @ A3 @ B4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_set__zero__plus2) ).
thf(103,axiom,
! [C2: set_Product_prod_a_a,D2: set_Product_prod_a_a,E: set_Product_prod_a_a,F: set_Product_prod_a_a,X: product_prod_a_a] :
( ( ord_le1824328871od_a_a @ C2 @ D2 )
=> ( ( ord_le1824328871od_a_a @ E @ F )
=> ( ( member449909584od_a_a @ X @ ( plus_p634297534od_a_a @ C2 @ E ) )
=> ( member449909584od_a_a @ X @ ( plus_p634297534od_a_a @ D2 @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_set__plus__mono2__b) ).
thf(106,axiom,
! [A: real] :
( ( real_V1035702895aleR_a @ A @ zero_zero_a )
= zero_zero_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_scale__zero__right) ).
thf(108,axiom,
! [A: real,X: a,B: real] :
( ( ( real_V1035702895aleR_a @ A @ X )
= ( real_V1035702895aleR_a @ B @ X ) )
= ( ( A = B )
| ( X = zero_zero_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_scale__cancel__right) ).
thf(111,axiom,
! [A: real,X: a,Y: a] :
( ( ( real_V1035702895aleR_a @ A @ X )
= ( real_V1035702895aleR_a @ A @ Y ) )
= ( ( X = Y )
| ( A = zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_scale__cancel__left) ).
thf(112,axiom,
! [X: a] :
( ( real_V1035702895aleR_a @ one_one_real @ X )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_scaleR__one) ).
thf(113,axiom,
! [A: real,X: a] :
( ( ( real_V1035702895aleR_a @ A @ X )
= zero_zero_a )
= ( ( A = zero_zero_real )
| ( X = zero_zero_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_scale__eq__0__iff) ).
thf(115,axiom,
! [X: a] :
( ( real_V1035702895aleR_a @ zero_zero_real @ X )
= zero_zero_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_scale__zero__left) ).
thf(117,axiom,
! [B: a,U: real,A: a] :
( ( ( plus_plus_a @ B @ ( real_V1035702895aleR_a @ U @ A ) )
= ( plus_plus_a @ A @ ( real_V1035702895aleR_a @ U @ B ) ) )
= ( ( A = B )
| ( U = one_one_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_scaleR__eq__iff) ).
thf(132,axiom,
! [P2: product_prod_a_a] :
? [X4: a,Y3: a] :
( P2
= ( product_Pair_a_a @ X4 @ Y3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_surj__pair) ).
thf(133,axiom,
! [P: product_prod_a_a > $o,P2: product_prod_a_a] :
( ! [A5: a,B5: a] : ( P @ ( product_Pair_a_a @ A5 @ B5 ) )
=> ( P @ P2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_prod__cases) ).
thf(134,axiom,
! [A: a,B: a,A2: a,B2: a] :
( ( ( product_Pair_a_a @ A @ B )
= ( product_Pair_a_a @ A2 @ B2 ) )
=> ~ ( ( A = A2 )
=> ( B != B2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_Pair__inject) ).
thf(135,axiom,
! [Y: product_prod_a_a] :
~ ! [A5: a,B5: a] :
( Y
!= ( product_Pair_a_a @ A5 @ B5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_old_Oprod_Oexhaust) ).
thf(136,axiom,
! [P: product_prod_a_a > $o,Prod: product_prod_a_a] :
( ! [A5: a,B5: a] : ( P @ ( product_Pair_a_a @ A5 @ B5 ) )
=> ( P @ Prod ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_old_Oprod_Oinducts) ).
thf(138,axiom,
! [A: a,B: a,C: a] :
( ( plus_plus_a @ ( plus_plus_a @ A @ B ) @ C )
= ( plus_plus_a @ A @ ( plus_plus_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(141,axiom,
! [A3: a,K: a,A: a,B: a] :
( ( A3
= ( plus_plus_a @ K @ A ) )
=> ( ( plus_plus_a @ A3 @ B )
= ( plus_plus_a @ K @ ( plus_plus_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_group__cancel_Oadd1) ).
thf(143,axiom,
! [B4: a,K: a,B: a,A: a] :
( ( B4
= ( plus_plus_a @ K @ B ) )
=> ( ( plus_plus_a @ A @ B4 )
= ( plus_plus_a @ K @ ( plus_plus_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_group__cancel_Oadd2) ).
thf(145,axiom,
! [X: a,A3: set_a,B4: set_a] :
( ( member_a @ X @ ( plus_plus_set_a @ A3 @ B4 ) )
=> ~ ! [A5: a,B5: a] :
( ( X
= ( plus_plus_a @ A5 @ B5 ) )
=> ( ( member_a @ A5 @ A3 )
=> ~ ( member_a @ B5 @ B4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_set__plus__elim) ).
thf(146,axiom,
! [X: product_prod_a_a,A3: set_Product_prod_a_a,B4: set_Product_prod_a_a] :
( ( member449909584od_a_a @ X @ ( plus_p634297534od_a_a @ A3 @ B4 ) )
=> ~ ! [A5: product_prod_a_a,B5: product_prod_a_a] :
( ( X
= ( plus_p1505579230od_a_a @ A5 @ B5 ) )
=> ( ( member449909584od_a_a @ A5 @ A3 )
=> ~ ( member449909584od_a_a @ B5 @ B4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_set__plus__elim) ).
thf(148,axiom,
! [A: a,B: a,C: a] :
( ( plus_plus_a @ ( plus_plus_a @ A @ B ) @ C )
= ( plus_plus_a @ A @ ( plus_plus_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_add_Oassoc) ).
thf(150,axiom,
! [A: a,B: a,C: a] :
( ( ( plus_plus_a @ A @ B )
= ( plus_plus_a @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_add_Oleft__cancel) ).
thf(152,axiom,
! [B: a,A: a,C: a] :
( ( ( plus_plus_a @ B @ A )
= ( plus_plus_a @ C @ A ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_add_Oright__cancel) ).
thf(154,axiom,
( plus_plus_a
= ( ^ [A4: a,B3: a] : ( plus_plus_a @ B3 @ A4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_add_Ocommute) ).
thf(156,axiom,
! [B: a,A: a,C: a] :
( ( plus_plus_a @ B @ ( plus_plus_a @ A @ C ) )
= ( plus_plus_a @ A @ ( plus_plus_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_add_Oleft__commute) ).
thf(158,axiom,
! [A: a,B: a,C: a] :
( ( ( plus_plus_a @ A @ B )
= ( plus_plus_a @ A @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_add__left__imp__eq) ).
thf(160,axiom,
! [B: a,A: a,C: a] :
( ( ( plus_plus_a @ B @ A )
= ( plus_plus_a @ C @ A ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_add__right__imp__eq) ).
thf(165,axiom,
! [A: a] :
( ( plus_plus_a @ zero_zero_a @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_comm__monoid__add__class_Oadd__0) ).
thf(167,axiom,
! [A: a] :
( ( plus_plus_a @ A @ zero_zero_a )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_add_Ocomm__neutral) ).
thf(172,axiom,
! [A: a] :
( ( plus_plus_a @ zero_zero_a @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_add_Ogroup__left__neutral) ).
thf(207,axiom,
( zero_z950819678od_a_a
= ( product_Pair_a_a @ zero_zero_a @ zero_zero_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_zero__prod__def) ).
thf(223,axiom,
! [A3: set_Product_prod_a_a] :
( ( collec645855634od_a_a
@ ^ [X3: product_prod_a_a] : ( member449909584od_a_a @ X3 @ A3 ) )
= A3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_Collect__mem__eq) ).
thf(227,axiom,
! [A: product_prod_a_a,P: product_prod_a_a > $o] :
( ( member449909584od_a_a @ A @ ( collec645855634od_a_a @ P ) )
= ( P @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_mem__Collect__eq) ).
thf(249,axiom,
! [A: a] :
( ( plus_plus_a @ zero_zero_a @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_add_Oleft__neutral) ).
thf(257,axiom,
! [A: a] :
( ( plus_plus_a @ A @ zero_zero_a )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_add_Oright__neutral) ).
thf(267,axiom,
! [B: a,A: a] :
( ( ( plus_plus_a @ B @ A )
= A )
= ( B = zero_zero_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_add__cancel__left__left) ).
thf(272,axiom,
! [A: a,B: a] :
( ( ( plus_plus_a @ A @ B )
= A )
= ( B = zero_zero_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_add__cancel__left__right) ).
thf(277,axiom,
! [A: a,B: a] :
( ( A
= ( plus_plus_a @ B @ A ) )
= ( B = zero_zero_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_add__cancel__right__left) ).
thf(282,axiom,
! [A: a,B: a] :
( ( A
= ( plus_plus_a @ A @ B ) )
= ( B = zero_zero_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_add__cancel__right__right) ).
thf(292,axiom,
! [B: a,A: a,C: a] :
( ( ( plus_plus_a @ B @ A )
= ( plus_plus_a @ C @ A ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_add__right__cancel) ).
thf(296,axiom,
! [A: a,B: a,C: a] :
( ( ( plus_plus_a @ A @ B )
= ( plus_plus_a @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_add__left__cancel) ).
thf(300,axiom,
! [A: a,C2: set_a,B: a,D2: set_a] :
( ( member_a @ A @ C2 )
=> ( ( member_a @ B @ D2 )
=> ( member_a @ ( plus_plus_a @ A @ B ) @ ( plus_plus_set_a @ C2 @ D2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_set__plus__intro) ).
thf(301,axiom,
! [A: product_prod_a_a,C2: set_Product_prod_a_a,B: product_prod_a_a,D2: set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ C2 )
=> ( ( member449909584od_a_a @ B @ D2 )
=> ( member449909584od_a_a @ ( plus_p1505579230od_a_a @ A @ B ) @ ( plus_p634297534od_a_a @ C2 @ D2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_set__plus__intro) ).
thf(307,axiom,
! [A: a,B: a,A2: a,B2: a] :
( ( ( product_Pair_a_a @ A @ B )
= ( product_Pair_a_a @ A2 @ B2 ) )
= ( ( A = A2 )
& ( B = B2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_old_Oprod_Oinject) ).
thf(311,axiom,
! [X1: a,X2: a,Y1: a,Y2: a] :
( ( ( product_Pair_a_a @ X1 @ X2 )
= ( product_Pair_a_a @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X2 = Y2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_prod_Oinject) ).
thf(316,axiom,
! [A: set_real,B: a,C: set_real,D: a] :
( ( plus_p1582417306real_a @ ( produc617496131real_a @ A @ B ) @ ( produc617496131real_a @ C @ D ) )
= ( produc617496131real_a @ ( plus_plus_set_real @ A @ C ) @ ( plus_plus_a @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_add__Pair) ).
thf(319,axiom,
! [A: a,B: set_a,C: a,D: set_a] :
( ( plus_p1265825342_set_a @ ( product_Pair_a_set_a @ A @ B ) @ ( product_Pair_a_set_a @ C @ D ) )
= ( product_Pair_a_set_a @ ( plus_plus_a @ A @ C ) @ ( plus_plus_set_a @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_add__Pair) ).
thf(320,axiom,
! [A: a,B: set_real,C: a,D: set_real] :
( ( plus_p1745648536t_real @ ( produc1391501065t_real @ A @ B ) @ ( produc1391501065t_real @ C @ D ) )
= ( produc1391501065t_real @ ( plus_plus_a @ A @ C ) @ ( plus_plus_set_real @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_add__Pair) ).
thf(322,axiom,
! [A: real,B: a,C: real,D: a] :
( ( plus_p1243198544real_a @ ( product_Pair_real_a @ A @ B ) @ ( product_Pair_real_a @ C @ D ) )
= ( product_Pair_real_a @ ( plus_plus_real @ A @ C ) @ ( plus_plus_a @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_add__Pair) ).
thf(323,axiom,
! [A: a,B: real,C: a,D: real] :
( ( plus_p541014626a_real @ ( product_Pair_a_real @ A @ B ) @ ( product_Pair_a_real @ C @ D ) )
= ( product_Pair_a_real @ ( plus_plus_a @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_add__Pair) ).
thf(324,axiom,
! [A: a,B: a,C: a,D: a] :
( ( plus_p1505579230od_a_a @ ( product_Pair_a_a @ A @ B ) @ ( product_Pair_a_a @ C @ D ) )
= ( product_Pair_a_a @ ( plus_plus_a @ A @ C ) @ ( plus_plus_a @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_add__Pair) ).
thf(325,axiom,
! [X: real,A: a,B: a] :
( ( real_V543523736od_a_a @ X @ ( product_Pair_a_a @ A @ B ) )
= ( product_Pair_a_a @ ( real_V1035702895aleR_a @ X @ A ) @ ( real_V1035702895aleR_a @ X @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_scale__prod) ).
thf(328,axiom,
! [X: real,A: real,B: a] :
( ( real_V1214981142real_a @ X @ ( product_Pair_real_a @ A @ B ) )
= ( product_Pair_real_a @ ( real_V453051771R_real @ X @ A ) @ ( real_V1035702895aleR_a @ X @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_scale__prod) ).
thf(331,axiom,
! [X: real,A: product_prod_a_a,B: a] :
( ( real_V1538726831_a_a_a @ X @ ( produc2061588782_a_a_a @ A @ B ) )
= ( produc2061588782_a_a_a @ ( real_V543523736od_a_a @ X @ A ) @ ( real_V1035702895aleR_a @ X @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_scale__prod) ).
thf(332,axiom,
! [X: real,A: a,B: real] :
( ( real_V512797224a_real @ X @ ( product_Pair_a_real @ A @ B ) )
= ( product_Pair_a_real @ ( real_V1035702895aleR_a @ X @ A ) @ ( real_V453051771R_real @ X @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_scale__prod) ).
thf(333,axiom,
! [X: real,A: a,B: product_prod_a_a] :
( ( real_V296206913od_a_a @ X @ ( produc1299253312od_a_a @ A @ B ) )
= ( produc1299253312od_a_a @ ( real_V1035702895aleR_a @ X @ A ) @ ( real_V543523736od_a_a @ X @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_scale__prod) ).
thf(334,axiom,
! [R: real,A: a,B: a] :
( ( real_V543523736od_a_a @ R @ ( product_Pair_a_a @ A @ B ) )
= ( product_Pair_a_a @ ( real_V1035702895aleR_a @ R @ A ) @ ( real_V1035702895aleR_a @ R @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_scaleR__Pair) ).
thf(337,axiom,
! [R: real,A: real,B: a] :
( ( real_V1214981142real_a @ R @ ( product_Pair_real_a @ A @ B ) )
= ( product_Pair_real_a @ ( real_V453051771R_real @ R @ A ) @ ( real_V1035702895aleR_a @ R @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_scaleR__Pair) ).
thf(340,axiom,
! [R: real,A: product_prod_a_a,B: a] :
( ( real_V1538726831_a_a_a @ R @ ( produc2061588782_a_a_a @ A @ B ) )
= ( produc2061588782_a_a_a @ ( real_V543523736od_a_a @ R @ A ) @ ( real_V1035702895aleR_a @ R @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_scaleR__Pair) ).
thf(341,axiom,
! [R: real,A: a,B: real] :
( ( real_V512797224a_real @ R @ ( product_Pair_a_real @ A @ B ) )
= ( product_Pair_a_real @ ( real_V1035702895aleR_a @ R @ A ) @ ( real_V453051771R_real @ R @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_scaleR__Pair) ).
thf(342,axiom,
! [R: real,A: a,B: product_prod_a_a] :
( ( real_V296206913od_a_a @ R @ ( produc1299253312od_a_a @ A @ B ) )
= ( produc1299253312od_a_a @ ( real_V1035702895aleR_a @ R @ A ) @ ( real_V543523736od_a_a @ R @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_scaleR__Pair) ).
thf(343,axiom,
ord_less_eq_real @ zero_zero_real @ u,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_assms_I3_J) ).
thf(344,axiom,
( ( plus_plus_real @ u @ v )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_assms_I5_J) ).
thf(345,axiom,
ord_less_eq_real @ zero_zero_real @ v,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_assms_I4_J) ).
thf(346,axiom,
( ( u = zero_zero_real )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_u__0) ).
thf(347,axiom,
( ( ( u != zero_zero_real )
& ( u != one_one_real ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6__092_060open_062u_A_092_060noteq_062_A0_A_092_060and_062_Au_A_092_060noteq_062_A1_A_092_060longrightarrow_062_Au_A_K_092_060_094sub_062R_Ax_A_L_Av_A_K_092_060_094sub_062R_Ay_A_092_060succeq_062_Ay_092_060close_062) ).
thf(348,axiom,
member449909584od_a_a @ ( product_Pair_a_a @ x @ y ) @ relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_assms_I2_J) ).
thf(349,axiom,
! [X: a,Y: a,Z: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ relation ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ Z ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Z @ Y ) @ relation ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Z ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Z @ X ) @ relation ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_strict__trans) ).
thf(350,axiom,
! [X: a,Y: a,Z: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ relation ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ Z ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Z @ Y ) @ relation ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Z ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Z @ X ) @ relation ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_indiff__trans) ).
thf(351,axiom,
! [X: a,Y: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ relation ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_indifferent__imp__weak__pref_I1_J) ).
thf(352,axiom,
! [X: a,Y: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ relation ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_indifferent__imp__weak__pref_I2_J) ).
thf(353,axiom,
prefer529818233pref_a @ relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms_I1_J) ).
thf(354,conjecture,
member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(355,negated_conjecture,
( ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation )
= $false ),
inference(negate_conjecture,[status(cth)],[354]) ).
thf(356,plain,
( ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation )
= $false ),
inference(unfold_def,[status(thm)],[355]) ).
thf(357,plain,
( ( ! [U: real,B: a,V: real,A: a] :
( ( ( plus_plus_a @ ( real_V1035702895aleR_a @ U @ B ) @ ( real_V1035702895aleR_a @ V @ A ) )
= ( plus_plus_a @ ( real_V1035702895aleR_a @ U @ A ) @ ( real_V1035702895aleR_a @ V @ B ) ) )
=> ( ( U != V )
=> ( A = B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(358,plain,
( ( ! [A3: set_Product_prod_a_a,B4: set_Product_prod_a_a,C: product_prod_a_a] :
( ( ord_le108336051od_a_a @ A3 @ B4 )
=> ( ( member449909584od_a_a @ C @ A3 )
=> ( member449909584od_a_a @ C @ B4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(359,plain,
( ( ! [A3: set_Product_prod_a_a,B4: set_Product_prod_a_a,X: product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A3 @ B4 )
=> ( ( member449909584od_a_a @ X @ A3 )
=> ( member449909584od_a_a @ X @ B4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(360,plain,
( ( ! [A3: set_Product_prod_a_a,B4: set_Product_prod_a_a,C: product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A3 @ B4 )
=> ( ( member449909584od_a_a @ C @ A3 )
=> ( member449909584od_a_a @ C @ B4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(361,plain,
( ( ord_le1824328871od_a_a
= ( ^ [A6: set_Product_prod_a_a,B6: set_Product_prod_a_a] :
! [X3: product_prod_a_a] :
( ( member449909584od_a_a @ X3 @ A6 )
=> ( member449909584od_a_a @ X3 @ B6 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(362,plain,
( ( ord_le1824328871od_a_a
= ( ^ [A6: set_Product_prod_a_a,B6: set_Product_prod_a_a] :
! [T: product_prod_a_a] :
( ( member449909584od_a_a @ T @ A6 )
=> ( member449909584od_a_a @ T @ B6 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(363,plain,
( ( ! [A3: set_Product_prod_a_a,B4: set_Product_prod_a_a] :
( ! [X4: product_prod_a_a] :
( ( member449909584od_a_a @ X4 @ A3 )
=> ( member449909584od_a_a @ X4 @ B4 ) )
=> ( ord_le1824328871od_a_a @ A3 @ B4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(364,plain,
( ( ! [A: real,B: real,X: a] :
( ( real_V1035702895aleR_a @ ( plus_plus_real @ A @ B ) @ X )
= ( plus_plus_a @ ( real_V1035702895aleR_a @ A @ X ) @ ( real_V1035702895aleR_a @ B @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(365,plain,
( ( ! [X: real,Y: real,Xa: a] :
( ( real_V1035702895aleR_a @ ( plus_plus_real @ X @ Y ) @ Xa )
= ( plus_plus_a @ ( real_V1035702895aleR_a @ X @ Xa ) @ ( real_V1035702895aleR_a @ Y @ Xa ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(366,plain,
( ( ! [A: real,X: a,Y: a] :
( ( A != zero_zero_real )
=> ( ( ( real_V1035702895aleR_a @ A @ X )
= ( real_V1035702895aleR_a @ A @ Y ) )
=> ( X = Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(367,plain,
( ( ! [A: real,X: a,Y: a] :
( ( real_V1035702895aleR_a @ A @ ( plus_plus_a @ X @ Y ) )
= ( plus_plus_a @ ( real_V1035702895aleR_a @ A @ X ) @ ( real_V1035702895aleR_a @ A @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(368,plain,
( ( ! [X: a,A: real,B: real] :
( ( X != zero_zero_a )
=> ( ( ( real_V1035702895aleR_a @ A @ X )
= ( real_V1035702895aleR_a @ B @ X ) )
=> ( A = B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(369,plain,
( ( ! [A: real,B: real,X: a] :
( ( real_V1035702895aleR_a @ A @ ( real_V1035702895aleR_a @ B @ X ) )
= ( real_V1035702895aleR_a @ B @ ( real_V1035702895aleR_a @ A @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(370,plain,
( ( ! [A3: set_Product_prod_a_a,B4: set_Product_prod_a_a] :
( ( member449909584od_a_a @ zero_z950819678od_a_a @ A3 )
=> ( ord_le1824328871od_a_a @ B4 @ ( plus_p634297534od_a_a @ A3 @ B4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(371,plain,
( ( ! [C2: set_Product_prod_a_a,D2: set_Product_prod_a_a,E: set_Product_prod_a_a,F: set_Product_prod_a_a,X: product_prod_a_a] :
( ( ord_le1824328871od_a_a @ C2 @ D2 )
=> ( ( ord_le1824328871od_a_a @ E @ F )
=> ( ( member449909584od_a_a @ X @ ( plus_p634297534od_a_a @ C2 @ E ) )
=> ( member449909584od_a_a @ X @ ( plus_p634297534od_a_a @ D2 @ F ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(372,plain,
( ( ! [A: real] :
( ( real_V1035702895aleR_a @ A @ zero_zero_a )
= zero_zero_a ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(373,plain,
( ( ! [A: real,X: a,B: real] :
( ( ( real_V1035702895aleR_a @ A @ X )
= ( real_V1035702895aleR_a @ B @ X ) )
= ( ( A = B )
| ( X = zero_zero_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(374,plain,
( ( ! [A: real,X: a,Y: a] :
( ( ( real_V1035702895aleR_a @ A @ X )
= ( real_V1035702895aleR_a @ A @ Y ) )
= ( ( X = Y )
| ( A = zero_zero_real ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(375,plain,
( ( ! [X: a] :
( ( real_V1035702895aleR_a @ one_one_real @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(376,plain,
( ( ! [A: real,X: a] :
( ( ( real_V1035702895aleR_a @ A @ X )
= zero_zero_a )
= ( ( A = zero_zero_real )
| ( X = zero_zero_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(377,plain,
( ( ! [X: a] :
( ( real_V1035702895aleR_a @ zero_zero_real @ X )
= zero_zero_a ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(378,plain,
( ( ! [B: a,U: real,A: a] :
( ( ( plus_plus_a @ B @ ( real_V1035702895aleR_a @ U @ A ) )
= ( plus_plus_a @ A @ ( real_V1035702895aleR_a @ U @ B ) ) )
= ( ( A = B )
| ( U = one_one_real ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(379,plain,
( ( ! [P2: product_prod_a_a] :
? [X4: a,Y3: a] :
( P2
= ( product_Pair_a_a @ X4 @ Y3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(380,plain,
( ( ! [P: product_prod_a_a > $o,P2: product_prod_a_a] :
( ! [A5: a,B5: a] : ( P @ ( product_Pair_a_a @ A5 @ B5 ) )
=> ( P @ P2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(381,plain,
( ( ! [A: a,B: a,A2: a,B2: a] :
( ( ( product_Pair_a_a @ A @ B )
= ( product_Pair_a_a @ A2 @ B2 ) )
=> ~ ( ( A = A2 )
=> ( B != B2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(382,plain,
( ( ! [Y: product_prod_a_a] :
~ ! [A5: a,B5: a] :
( Y
!= ( product_Pair_a_a @ A5 @ B5 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(383,plain,
( ( ! [P: product_prod_a_a > $o,Prod: product_prod_a_a] :
( ! [A5: a,B5: a] : ( P @ ( product_Pair_a_a @ A5 @ B5 ) )
=> ( P @ Prod ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(384,plain,
( ( ! [A: a,B: a,C: a] :
( ( plus_plus_a @ ( plus_plus_a @ A @ B ) @ C )
= ( plus_plus_a @ A @ ( plus_plus_a @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(385,plain,
( ( ! [A3: a,K: a,A: a,B: a] :
( ( A3
= ( plus_plus_a @ K @ A ) )
=> ( ( plus_plus_a @ A3 @ B )
= ( plus_plus_a @ K @ ( plus_plus_a @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(386,plain,
( ( ! [B4: a,K: a,B: a,A: a] :
( ( B4
= ( plus_plus_a @ K @ B ) )
=> ( ( plus_plus_a @ A @ B4 )
= ( plus_plus_a @ K @ ( plus_plus_a @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(387,plain,
( ( ! [X: a,A3: set_a,B4: set_a] :
( ( member_a @ X @ ( plus_plus_set_a @ A3 @ B4 ) )
=> ~ ! [A5: a,B5: a] :
( ( X
= ( plus_plus_a @ A5 @ B5 ) )
=> ( ( member_a @ A5 @ A3 )
=> ~ ( member_a @ B5 @ B4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(388,plain,
( ( ! [X: product_prod_a_a,A3: set_Product_prod_a_a,B4: set_Product_prod_a_a] :
( ( member449909584od_a_a @ X @ ( plus_p634297534od_a_a @ A3 @ B4 ) )
=> ~ ! [A5: product_prod_a_a,B5: product_prod_a_a] :
( ( X
= ( plus_p1505579230od_a_a @ A5 @ B5 ) )
=> ( ( member449909584od_a_a @ A5 @ A3 )
=> ~ ( member449909584od_a_a @ B5 @ B4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(389,plain,
( ( ! [A: a,B: a,C: a] :
( ( plus_plus_a @ ( plus_plus_a @ A @ B ) @ C )
= ( plus_plus_a @ A @ ( plus_plus_a @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(390,plain,
( ( ! [A: a,B: a,C: a] :
( ( ( plus_plus_a @ A @ B )
= ( plus_plus_a @ A @ C ) )
= ( B = C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(391,plain,
( ( ! [B: a,A: a,C: a] :
( ( ( plus_plus_a @ B @ A )
= ( plus_plus_a @ C @ A ) )
= ( B = C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(392,plain,
( ( plus_plus_a
= ( ^ [A4: a,B3: a] : ( plus_plus_a @ B3 @ A4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(393,plain,
( ( ! [B: a,A: a,C: a] :
( ( plus_plus_a @ B @ ( plus_plus_a @ A @ C ) )
= ( plus_plus_a @ A @ ( plus_plus_a @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(394,plain,
( ( ! [A: a,B: a,C: a] :
( ( ( plus_plus_a @ A @ B )
= ( plus_plus_a @ A @ C ) )
=> ( B = C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(395,plain,
( ( ! [B: a,A: a,C: a] :
( ( ( plus_plus_a @ B @ A )
= ( plus_plus_a @ C @ A ) )
=> ( B = C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(396,plain,
( ( ! [A: a] :
( ( plus_plus_a @ zero_zero_a @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(397,plain,
( ( ! [A: a] :
( ( plus_plus_a @ A @ zero_zero_a )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(398,plain,
( ( ! [A: a] :
( ( plus_plus_a @ zero_zero_a @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(399,plain,
( ( zero_z950819678od_a_a
= ( product_Pair_a_a @ zero_zero_a @ zero_zero_a ) )
= $true ),
inference(unfold_def,[status(thm)],[207]) ).
thf(400,plain,
( ( ! [A3: set_Product_prod_a_a] :
( ( collec645855634od_a_a
@ ^ [X3: product_prod_a_a] : ( member449909584od_a_a @ X3 @ A3 ) )
= A3 ) )
= $true ),
inference(unfold_def,[status(thm)],[223]) ).
thf(401,plain,
( ( ! [A: product_prod_a_a,P: product_prod_a_a > $o] :
( ( member449909584od_a_a @ A @ ( collec645855634od_a_a @ P ) )
= ( P @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[227]) ).
thf(402,plain,
( ( ! [A: a] :
( ( plus_plus_a @ zero_zero_a @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(403,plain,
( ( ! [A: a] :
( ( plus_plus_a @ A @ zero_zero_a )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(404,plain,
( ( ! [B: a,A: a] :
( ( ( plus_plus_a @ B @ A )
= A )
= ( B = zero_zero_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[267]) ).
thf(405,plain,
( ( ! [A: a,B: a] :
( ( ( plus_plus_a @ A @ B )
= A )
= ( B = zero_zero_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[272]) ).
thf(406,plain,
( ( ! [A: a,B: a] :
( ( A
= ( plus_plus_a @ B @ A ) )
= ( B = zero_zero_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[277]) ).
thf(407,plain,
( ( ! [A: a,B: a] :
( ( A
= ( plus_plus_a @ A @ B ) )
= ( B = zero_zero_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[282]) ).
thf(408,plain,
( ( ! [B: a,A: a,C: a] :
( ( ( plus_plus_a @ B @ A )
= ( plus_plus_a @ C @ A ) )
= ( B = C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(409,plain,
( ( ! [A: a,B: a,C: a] :
( ( ( plus_plus_a @ A @ B )
= ( plus_plus_a @ A @ C ) )
= ( B = C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(410,plain,
( ( ! [A: a,C2: set_a,B: a,D2: set_a] :
( ( member_a @ A @ C2 )
=> ( ( member_a @ B @ D2 )
=> ( member_a @ ( plus_plus_a @ A @ B ) @ ( plus_plus_set_a @ C2 @ D2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(411,plain,
( ( ! [A: product_prod_a_a,C2: set_Product_prod_a_a,B: product_prod_a_a,D2: set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ C2 )
=> ( ( member449909584od_a_a @ B @ D2 )
=> ( member449909584od_a_a @ ( plus_p1505579230od_a_a @ A @ B ) @ ( plus_p634297534od_a_a @ C2 @ D2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(412,plain,
( ( ! [A: a,B: a,A2: a,B2: a] :
( ( ( product_Pair_a_a @ A @ B )
= ( product_Pair_a_a @ A2 @ B2 ) )
= ( ( A = A2 )
& ( B = B2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(413,plain,
( ( ! [X1: a,X2: a,Y1: a,Y2: a] :
( ( ( product_Pair_a_a @ X1 @ X2 )
= ( product_Pair_a_a @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X2 = Y2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[311]) ).
thf(414,plain,
( ( ! [A: set_real,B: a,C: set_real,D: a] :
( ( plus_p1582417306real_a @ ( produc617496131real_a @ A @ B ) @ ( produc617496131real_a @ C @ D ) )
= ( produc617496131real_a @ ( plus_plus_set_real @ A @ C ) @ ( plus_plus_a @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[316]) ).
thf(415,plain,
( ( ! [A: a,B: set_a,C: a,D: set_a] :
( ( plus_p1265825342_set_a @ ( product_Pair_a_set_a @ A @ B ) @ ( product_Pair_a_set_a @ C @ D ) )
= ( product_Pair_a_set_a @ ( plus_plus_a @ A @ C ) @ ( plus_plus_set_a @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[319]) ).
thf(416,plain,
( ( ! [A: a,B: set_real,C: a,D: set_real] :
( ( plus_p1745648536t_real @ ( produc1391501065t_real @ A @ B ) @ ( produc1391501065t_real @ C @ D ) )
= ( produc1391501065t_real @ ( plus_plus_a @ A @ C ) @ ( plus_plus_set_real @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[320]) ).
thf(417,plain,
( ( ! [A: real,B: a,C: real,D: a] :
( ( plus_p1243198544real_a @ ( product_Pair_real_a @ A @ B ) @ ( product_Pair_real_a @ C @ D ) )
= ( product_Pair_real_a @ ( plus_plus_real @ A @ C ) @ ( plus_plus_a @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[322]) ).
thf(418,plain,
( ( ! [A: a,B: real,C: a,D: real] :
( ( plus_p541014626a_real @ ( product_Pair_a_real @ A @ B ) @ ( product_Pair_a_real @ C @ D ) )
= ( product_Pair_a_real @ ( plus_plus_a @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[323]) ).
thf(419,plain,
( ( ! [A: a,B: a,C: a,D: a] :
( ( plus_p1505579230od_a_a @ ( product_Pair_a_a @ A @ B ) @ ( product_Pair_a_a @ C @ D ) )
= ( product_Pair_a_a @ ( plus_plus_a @ A @ C ) @ ( plus_plus_a @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[324]) ).
thf(420,plain,
( ( ! [X: real,A: a,B: a] :
( ( real_V543523736od_a_a @ X @ ( product_Pair_a_a @ A @ B ) )
= ( product_Pair_a_a @ ( real_V1035702895aleR_a @ X @ A ) @ ( real_V1035702895aleR_a @ X @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[325]) ).
thf(421,plain,
( ( ! [X: real,A: real,B: a] :
( ( real_V1214981142real_a @ X @ ( product_Pair_real_a @ A @ B ) )
= ( product_Pair_real_a @ ( real_V453051771R_real @ X @ A ) @ ( real_V1035702895aleR_a @ X @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[328]) ).
thf(422,plain,
( ( ! [X: real,A: product_prod_a_a,B: a] :
( ( real_V1538726831_a_a_a @ X @ ( produc2061588782_a_a_a @ A @ B ) )
= ( produc2061588782_a_a_a @ ( real_V543523736od_a_a @ X @ A ) @ ( real_V1035702895aleR_a @ X @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[331]) ).
thf(423,plain,
( ( ! [X: real,A: a,B: real] :
( ( real_V512797224a_real @ X @ ( product_Pair_a_real @ A @ B ) )
= ( product_Pair_a_real @ ( real_V1035702895aleR_a @ X @ A ) @ ( real_V453051771R_real @ X @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[332]) ).
thf(424,plain,
( ( ! [X: real,A: a,B: product_prod_a_a] :
( ( real_V296206913od_a_a @ X @ ( produc1299253312od_a_a @ A @ B ) )
= ( produc1299253312od_a_a @ ( real_V1035702895aleR_a @ X @ A ) @ ( real_V543523736od_a_a @ X @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[333]) ).
thf(425,plain,
( ( ! [R: real,A: a,B: a] :
( ( real_V543523736od_a_a @ R @ ( product_Pair_a_a @ A @ B ) )
= ( product_Pair_a_a @ ( real_V1035702895aleR_a @ R @ A ) @ ( real_V1035702895aleR_a @ R @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[334]) ).
thf(426,plain,
( ( ! [R: real,A: real,B: a] :
( ( real_V1214981142real_a @ R @ ( product_Pair_real_a @ A @ B ) )
= ( product_Pair_real_a @ ( real_V453051771R_real @ R @ A ) @ ( real_V1035702895aleR_a @ R @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[337]) ).
thf(427,plain,
( ( ! [R: real,A: product_prod_a_a,B: a] :
( ( real_V1538726831_a_a_a @ R @ ( produc2061588782_a_a_a @ A @ B ) )
= ( produc2061588782_a_a_a @ ( real_V543523736od_a_a @ R @ A ) @ ( real_V1035702895aleR_a @ R @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(428,plain,
( ( ! [R: real,A: a,B: real] :
( ( real_V512797224a_real @ R @ ( product_Pair_a_real @ A @ B ) )
= ( product_Pair_a_real @ ( real_V1035702895aleR_a @ R @ A ) @ ( real_V453051771R_real @ R @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[341]) ).
thf(429,plain,
( ( ! [R: real,A: a,B: product_prod_a_a] :
( ( real_V296206913od_a_a @ R @ ( produc1299253312od_a_a @ A @ B ) )
= ( produc1299253312od_a_a @ ( real_V1035702895aleR_a @ R @ A ) @ ( real_V543523736od_a_a @ R @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(430,plain,
( ( ord_less_eq_real @ zero_zero_real @ u )
= $true ),
inference(unfold_def,[status(thm)],[343]) ).
thf(431,plain,
( ( ( plus_plus_real @ u @ v )
= one_one_real )
= $true ),
inference(unfold_def,[status(thm)],[344]) ).
thf(432,plain,
( ( ord_less_eq_real @ zero_zero_real @ v )
= $true ),
inference(unfold_def,[status(thm)],[345]) ).
thf(433,plain,
( ( ( u = zero_zero_real )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation ) )
= $true ),
inference(unfold_def,[status(thm)],[346]) ).
thf(434,plain,
( ( ( ( u != zero_zero_real )
& ( u != one_one_real ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation ) )
= $true ),
inference(unfold_def,[status(thm)],[347]) ).
thf(435,plain,
( ( member449909584od_a_a @ ( product_Pair_a_a @ x @ y ) @ relation )
= $true ),
inference(unfold_def,[status(thm)],[348]) ).
thf(436,plain,
( ( ! [X: a,Y: a,Z: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ relation ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ Z ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Z @ Y ) @ relation ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Z ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Z @ X ) @ relation ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[349]) ).
thf(437,plain,
( ( ! [X: a,Y: a,Z: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ relation ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ Z ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Z @ Y ) @ relation ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Z ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Z @ X ) @ relation ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[350]) ).
thf(438,plain,
( ( ! [X: a,Y: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ relation ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation ) ) )
= $true ),
inference(unfold_def,[status(thm)],[351]) ).
thf(439,plain,
( ( ! [X: a,Y: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ relation ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ relation ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(440,plain,
( ( prefer529818233pref_a @ relation )
= $true ),
inference(unfold_def,[status(thm)],[353]) ).
thf(441,plain,
( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation ) )
= $true ),
inference(polarity_switch,[status(thm)],[356]) ).
thf(442,plain,
( ( prefer529818233pref_a @ relation )
= $true ),
inference(copy,[status(thm)],[440]) ).
thf(443,plain,
( ( ! [X: a,Y: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ relation ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ relation ) ) )
= $true ),
inference(copy,[status(thm)],[439]) ).
thf(444,plain,
( ( ! [X: a,Y: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ relation ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation ) ) )
= $true ),
inference(copy,[status(thm)],[438]) ).
thf(445,plain,
( ( ! [X: a,Y: a,Z: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ relation ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ Z ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Z @ Y ) @ relation ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Z ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ Z @ X ) @ relation ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[437]) ).
thf(446,plain,
( ( ! [X: a,Y: a,Z: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Y ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ X ) @ relation ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ Y @ Z ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Z @ Y ) @ relation ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X @ Z ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ Z @ X ) @ relation ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[436]) ).
thf(447,plain,
( ( member449909584od_a_a @ ( product_Pair_a_a @ x @ y ) @ relation )
= $true ),
inference(copy,[status(thm)],[435]) ).
thf(448,plain,
( ( ( ( u != zero_zero_real )
& ( u != one_one_real ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation ) )
= $true ),
inference(copy,[status(thm)],[434]) ).
thf(449,plain,
( ( ( u = zero_zero_real )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation ) )
= $true ),
inference(copy,[status(thm)],[433]) ).
thf(450,plain,
( ( ord_less_eq_real @ zero_zero_real @ v )
= $true ),
inference(copy,[status(thm)],[432]) ).
thf(451,plain,
( ( ( plus_plus_real @ u @ v )
= one_one_real )
= $true ),
inference(copy,[status(thm)],[431]) ).
thf(452,plain,
( ( ord_less_eq_real @ zero_zero_real @ u )
= $true ),
inference(copy,[status(thm)],[430]) ).
thf(453,plain,
( ( ! [R: real,A: a,B: product_prod_a_a] :
( ( real_V296206913od_a_a @ R @ ( produc1299253312od_a_a @ A @ B ) )
= ( produc1299253312od_a_a @ ( real_V1035702895aleR_a @ R @ A ) @ ( real_V543523736od_a_a @ R @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[429]) ).
thf(454,plain,
( ( ! [R: real,A: a,B: real] :
( ( real_V512797224a_real @ R @ ( product_Pair_a_real @ A @ B ) )
= ( product_Pair_a_real @ ( real_V1035702895aleR_a @ R @ A ) @ ( real_V453051771R_real @ R @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[428]) ).
thf(455,plain,
( ( ! [R: real,A: product_prod_a_a,B: a] :
( ( real_V1538726831_a_a_a @ R @ ( produc2061588782_a_a_a @ A @ B ) )
= ( produc2061588782_a_a_a @ ( real_V543523736od_a_a @ R @ A ) @ ( real_V1035702895aleR_a @ R @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[427]) ).
thf(456,plain,
( ( ! [R: real,A: real,B: a] :
( ( real_V1214981142real_a @ R @ ( product_Pair_real_a @ A @ B ) )
= ( product_Pair_real_a @ ( real_V453051771R_real @ R @ A ) @ ( real_V1035702895aleR_a @ R @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[426]) ).
thf(457,plain,
( ( ! [R: real,A: a,B: a] :
( ( real_V543523736od_a_a @ R @ ( product_Pair_a_a @ A @ B ) )
= ( product_Pair_a_a @ ( real_V1035702895aleR_a @ R @ A ) @ ( real_V1035702895aleR_a @ R @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[425]) ).
thf(458,plain,
( ( ! [X: real,A: a,B: product_prod_a_a] :
( ( real_V296206913od_a_a @ X @ ( produc1299253312od_a_a @ A @ B ) )
= ( produc1299253312od_a_a @ ( real_V1035702895aleR_a @ X @ A ) @ ( real_V543523736od_a_a @ X @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[424]) ).
thf(459,plain,
( ( ! [X: real,A: a,B: real] :
( ( real_V512797224a_real @ X @ ( product_Pair_a_real @ A @ B ) )
= ( product_Pair_a_real @ ( real_V1035702895aleR_a @ X @ A ) @ ( real_V453051771R_real @ X @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[423]) ).
thf(460,plain,
( ( ! [X: real,A: product_prod_a_a,B: a] :
( ( real_V1538726831_a_a_a @ X @ ( produc2061588782_a_a_a @ A @ B ) )
= ( produc2061588782_a_a_a @ ( real_V543523736od_a_a @ X @ A ) @ ( real_V1035702895aleR_a @ X @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[422]) ).
thf(461,plain,
( ( ! [X: real,A: real,B: a] :
( ( real_V1214981142real_a @ X @ ( product_Pair_real_a @ A @ B ) )
= ( product_Pair_real_a @ ( real_V453051771R_real @ X @ A ) @ ( real_V1035702895aleR_a @ X @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[421]) ).
thf(462,plain,
( ( ! [X: real,A: a,B: a] :
( ( real_V543523736od_a_a @ X @ ( product_Pair_a_a @ A @ B ) )
= ( product_Pair_a_a @ ( real_V1035702895aleR_a @ X @ A ) @ ( real_V1035702895aleR_a @ X @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[420]) ).
thf(463,plain,
( ( ! [A: a,B: a,C: a,D: a] :
( ( plus_p1505579230od_a_a @ ( product_Pair_a_a @ A @ B ) @ ( product_Pair_a_a @ C @ D ) )
= ( product_Pair_a_a @ ( plus_plus_a @ A @ C ) @ ( plus_plus_a @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[419]) ).
thf(464,plain,
( ( ! [A: a,B: real,C: a,D: real] :
( ( plus_p541014626a_real @ ( product_Pair_a_real @ A @ B ) @ ( product_Pair_a_real @ C @ D ) )
= ( product_Pair_a_real @ ( plus_plus_a @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[418]) ).
thf(465,plain,
( ( ! [A: real,B: a,C: real,D: a] :
( ( plus_p1243198544real_a @ ( product_Pair_real_a @ A @ B ) @ ( product_Pair_real_a @ C @ D ) )
= ( product_Pair_real_a @ ( plus_plus_real @ A @ C ) @ ( plus_plus_a @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[417]) ).
thf(466,plain,
( ( ! [A: a,B: set_real,C: a,D: set_real] :
( ( plus_p1745648536t_real @ ( produc1391501065t_real @ A @ B ) @ ( produc1391501065t_real @ C @ D ) )
= ( produc1391501065t_real @ ( plus_plus_a @ A @ C ) @ ( plus_plus_set_real @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[416]) ).
thf(467,plain,
( ( ! [A: a,B: set_a,C: a,D: set_a] :
( ( plus_p1265825342_set_a @ ( product_Pair_a_set_a @ A @ B ) @ ( product_Pair_a_set_a @ C @ D ) )
= ( product_Pair_a_set_a @ ( plus_plus_a @ A @ C ) @ ( plus_plus_set_a @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[415]) ).
thf(468,plain,
( ( ! [A: set_real,B: a,C: set_real,D: a] :
( ( plus_p1582417306real_a @ ( produc617496131real_a @ A @ B ) @ ( produc617496131real_a @ C @ D ) )
= ( produc617496131real_a @ ( plus_plus_set_real @ A @ C ) @ ( plus_plus_a @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[414]) ).
thf(469,plain,
( ( ! [X1: a,X2: a,Y1: a,Y2: a] :
( ( ( product_Pair_a_a @ X1 @ X2 )
= ( product_Pair_a_a @ Y1 @ Y2 ) )
= ( ( X1 = Y1 )
& ( X2 = Y2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[413]) ).
thf(470,plain,
( ( ! [A: a,B: a,A2: a,B2: a] :
( ( ( product_Pair_a_a @ A @ B )
= ( product_Pair_a_a @ A2 @ B2 ) )
= ( ( A = A2 )
& ( B = B2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[412]) ).
thf(471,plain,
( ( ! [A: product_prod_a_a,C2: set_Product_prod_a_a,B: product_prod_a_a,D2: set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ C2 )
=> ( ( member449909584od_a_a @ B @ D2 )
=> ( member449909584od_a_a @ ( plus_p1505579230od_a_a @ A @ B ) @ ( plus_p634297534od_a_a @ C2 @ D2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[411]) ).
thf(472,plain,
( ( ! [A: a,C2: set_a,B: a,D2: set_a] :
( ( member_a @ A @ C2 )
=> ( ( member_a @ B @ D2 )
=> ( member_a @ ( plus_plus_a @ A @ B ) @ ( plus_plus_set_a @ C2 @ D2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[410]) ).
thf(473,plain,
( ( ! [A: a,B: a,C: a] :
( ( ( plus_plus_a @ A @ B )
= ( plus_plus_a @ A @ C ) )
= ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[409]) ).
thf(474,plain,
( ( ! [B: a,A: a,C: a] :
( ( ( plus_plus_a @ B @ A )
= ( plus_plus_a @ C @ A ) )
= ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[408]) ).
thf(475,plain,
( ( ! [A: a,B: a] :
( ( A
= ( plus_plus_a @ A @ B ) )
= ( B = zero_zero_a ) ) )
= $true ),
inference(copy,[status(thm)],[407]) ).
thf(476,plain,
( ( ! [A: a,B: a] :
( ( A
= ( plus_plus_a @ B @ A ) )
= ( B = zero_zero_a ) ) )
= $true ),
inference(copy,[status(thm)],[406]) ).
thf(477,plain,
( ( ! [A: a,B: a] :
( ( ( plus_plus_a @ A @ B )
= A )
= ( B = zero_zero_a ) ) )
= $true ),
inference(copy,[status(thm)],[405]) ).
thf(478,plain,
( ( ! [B: a,A: a] :
( ( ( plus_plus_a @ B @ A )
= A )
= ( B = zero_zero_a ) ) )
= $true ),
inference(copy,[status(thm)],[404]) ).
thf(479,plain,
( ( ! [A: a] :
( ( plus_plus_a @ A @ zero_zero_a )
= A ) )
= $true ),
inference(copy,[status(thm)],[403]) ).
thf(480,plain,
( ( ! [A: a] :
( ( plus_plus_a @ zero_zero_a @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[402]) ).
thf(481,plain,
( ( ! [A: product_prod_a_a,P: product_prod_a_a > $o] :
( ( member449909584od_a_a @ A @ ( collec645855634od_a_a @ P ) )
= ( P @ A ) ) )
= $true ),
inference(copy,[status(thm)],[401]) ).
thf(482,plain,
( ( ! [A3: set_Product_prod_a_a] :
( ( collec645855634od_a_a
@ ^ [X3: product_prod_a_a] : ( member449909584od_a_a @ X3 @ A3 ) )
= A3 ) )
= $true ),
inference(copy,[status(thm)],[400]) ).
thf(483,plain,
( ( zero_z950819678od_a_a
= ( product_Pair_a_a @ zero_zero_a @ zero_zero_a ) )
= $true ),
inference(copy,[status(thm)],[399]) ).
thf(484,plain,
( ( ! [A: a] :
( ( plus_plus_a @ zero_zero_a @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[398]) ).
thf(485,plain,
( ( ! [A: a] :
( ( plus_plus_a @ A @ zero_zero_a )
= A ) )
= $true ),
inference(copy,[status(thm)],[397]) ).
thf(486,plain,
( ( ! [A: a] :
( ( plus_plus_a @ zero_zero_a @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[396]) ).
thf(487,plain,
( ( ! [B: a,A: a,C: a] :
( ( ( plus_plus_a @ B @ A )
= ( plus_plus_a @ C @ A ) )
=> ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[395]) ).
thf(488,plain,
( ( ! [A: a,B: a,C: a] :
( ( ( plus_plus_a @ A @ B )
= ( plus_plus_a @ A @ C ) )
=> ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[394]) ).
thf(489,plain,
( ( ! [B: a,A: a,C: a] :
( ( plus_plus_a @ B @ ( plus_plus_a @ A @ C ) )
= ( plus_plus_a @ A @ ( plus_plus_a @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[393]) ).
thf(490,plain,
( ( plus_plus_a
= ( ^ [A4: a,B3: a] : ( plus_plus_a @ B3 @ A4 ) ) )
= $true ),
inference(copy,[status(thm)],[392]) ).
thf(491,plain,
( ( ! [B: a,A: a,C: a] :
( ( ( plus_plus_a @ B @ A )
= ( plus_plus_a @ C @ A ) )
= ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[391]) ).
thf(492,plain,
( ( ! [A: a,B: a,C: a] :
( ( ( plus_plus_a @ A @ B )
= ( plus_plus_a @ A @ C ) )
= ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[390]) ).
thf(493,plain,
( ( ! [A: a,B: a,C: a] :
( ( plus_plus_a @ ( plus_plus_a @ A @ B ) @ C )
= ( plus_plus_a @ A @ ( plus_plus_a @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[389]) ).
thf(494,plain,
( ( ! [X: product_prod_a_a,A3: set_Product_prod_a_a,B4: set_Product_prod_a_a] :
( ( member449909584od_a_a @ X @ ( plus_p634297534od_a_a @ A3 @ B4 ) )
=> ~ ! [A5: product_prod_a_a,B5: product_prod_a_a] :
( ( X
= ( plus_p1505579230od_a_a @ A5 @ B5 ) )
=> ( ( member449909584od_a_a @ A5 @ A3 )
=> ~ ( member449909584od_a_a @ B5 @ B4 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[388]) ).
thf(495,plain,
( ( ! [X: a,A3: set_a,B4: set_a] :
( ( member_a @ X @ ( plus_plus_set_a @ A3 @ B4 ) )
=> ~ ! [A5: a,B5: a] :
( ( X
= ( plus_plus_a @ A5 @ B5 ) )
=> ( ( member_a @ A5 @ A3 )
=> ~ ( member_a @ B5 @ B4 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[387]) ).
thf(496,plain,
( ( ! [B4: a,K: a,B: a,A: a] :
( ( B4
= ( plus_plus_a @ K @ B ) )
=> ( ( plus_plus_a @ A @ B4 )
= ( plus_plus_a @ K @ ( plus_plus_a @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[386]) ).
thf(497,plain,
( ( ! [A3: a,K: a,A: a,B: a] :
( ( A3
= ( plus_plus_a @ K @ A ) )
=> ( ( plus_plus_a @ A3 @ B )
= ( plus_plus_a @ K @ ( plus_plus_a @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[385]) ).
thf(498,plain,
( ( ! [A: a,B: a,C: a] :
( ( plus_plus_a @ ( plus_plus_a @ A @ B ) @ C )
= ( plus_plus_a @ A @ ( plus_plus_a @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[384]) ).
thf(499,plain,
( ( ! [P: product_prod_a_a > $o,Prod: product_prod_a_a] :
( ! [A5: a,B5: a] : ( P @ ( product_Pair_a_a @ A5 @ B5 ) )
=> ( P @ Prod ) ) )
= $true ),
inference(copy,[status(thm)],[383]) ).
thf(500,plain,
( ( ! [Y: product_prod_a_a] :
~ ! [A5: a,B5: a] :
( Y
!= ( product_Pair_a_a @ A5 @ B5 ) ) )
= $true ),
inference(copy,[status(thm)],[382]) ).
thf(501,plain,
( ( ! [A: a,B: a,A2: a,B2: a] :
( ( ( product_Pair_a_a @ A @ B )
= ( product_Pair_a_a @ A2 @ B2 ) )
=> ~ ( ( A = A2 )
=> ( B != B2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[381]) ).
thf(502,plain,
( ( ! [P: product_prod_a_a > $o,P2: product_prod_a_a] :
( ! [A5: a,B5: a] : ( P @ ( product_Pair_a_a @ A5 @ B5 ) )
=> ( P @ P2 ) ) )
= $true ),
inference(copy,[status(thm)],[380]) ).
thf(503,plain,
( ( ! [P2: product_prod_a_a] :
? [X4: a,Y3: a] :
( P2
= ( product_Pair_a_a @ X4 @ Y3 ) ) )
= $true ),
inference(copy,[status(thm)],[379]) ).
thf(504,plain,
( ( ! [B: a,U: real,A: a] :
( ( ( plus_plus_a @ B @ ( real_V1035702895aleR_a @ U @ A ) )
= ( plus_plus_a @ A @ ( real_V1035702895aleR_a @ U @ B ) ) )
= ( ( A = B )
| ( U = one_one_real ) ) ) )
= $true ),
inference(copy,[status(thm)],[378]) ).
thf(505,plain,
( ( ! [X: a] :
( ( real_V1035702895aleR_a @ zero_zero_real @ X )
= zero_zero_a ) )
= $true ),
inference(copy,[status(thm)],[377]) ).
thf(506,plain,
( ( ! [A: real,X: a] :
( ( ( real_V1035702895aleR_a @ A @ X )
= zero_zero_a )
= ( ( A = zero_zero_real )
| ( X = zero_zero_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[376]) ).
thf(507,plain,
( ( ! [X: a] :
( ( real_V1035702895aleR_a @ one_one_real @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[375]) ).
thf(508,plain,
( ( ! [A: real,X: a,Y: a] :
( ( ( real_V1035702895aleR_a @ A @ X )
= ( real_V1035702895aleR_a @ A @ Y ) )
= ( ( X = Y )
| ( A = zero_zero_real ) ) ) )
= $true ),
inference(copy,[status(thm)],[374]) ).
thf(509,plain,
( ( ! [A: real,X: a,B: real] :
( ( ( real_V1035702895aleR_a @ A @ X )
= ( real_V1035702895aleR_a @ B @ X ) )
= ( ( A = B )
| ( X = zero_zero_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[373]) ).
thf(510,plain,
( ( ! [A: real] :
( ( real_V1035702895aleR_a @ A @ zero_zero_a )
= zero_zero_a ) )
= $true ),
inference(copy,[status(thm)],[372]) ).
thf(511,plain,
( ( ! [C2: set_Product_prod_a_a,D2: set_Product_prod_a_a,E: set_Product_prod_a_a,F: set_Product_prod_a_a,X: product_prod_a_a] :
( ( ord_le1824328871od_a_a @ C2 @ D2 )
=> ( ( ord_le1824328871od_a_a @ E @ F )
=> ( ( member449909584od_a_a @ X @ ( plus_p634297534od_a_a @ C2 @ E ) )
=> ( member449909584od_a_a @ X @ ( plus_p634297534od_a_a @ D2 @ F ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(512,plain,
( ( ! [A3: set_Product_prod_a_a,B4: set_Product_prod_a_a] :
( ( member449909584od_a_a @ zero_z950819678od_a_a @ A3 )
=> ( ord_le1824328871od_a_a @ B4 @ ( plus_p634297534od_a_a @ A3 @ B4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(513,plain,
( ( ! [A: real,B: real,X: a] :
( ( real_V1035702895aleR_a @ A @ ( real_V1035702895aleR_a @ B @ X ) )
= ( real_V1035702895aleR_a @ B @ ( real_V1035702895aleR_a @ A @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[369]) ).
thf(514,plain,
( ( ! [X: a,A: real,B: real] :
( ( X != zero_zero_a )
=> ( ( ( real_V1035702895aleR_a @ A @ X )
= ( real_V1035702895aleR_a @ B @ X ) )
=> ( A = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[368]) ).
thf(515,plain,
( ( ! [A: real,X: a,Y: a] :
( ( real_V1035702895aleR_a @ A @ ( plus_plus_a @ X @ Y ) )
= ( plus_plus_a @ ( real_V1035702895aleR_a @ A @ X ) @ ( real_V1035702895aleR_a @ A @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(516,plain,
( ( ! [A: real,X: a,Y: a] :
( ( A != zero_zero_real )
=> ( ( ( real_V1035702895aleR_a @ A @ X )
= ( real_V1035702895aleR_a @ A @ Y ) )
=> ( X = Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[366]) ).
thf(517,plain,
( ( ! [X: real,Y: real,Xa: a] :
( ( real_V1035702895aleR_a @ ( plus_plus_real @ X @ Y ) @ Xa )
= ( plus_plus_a @ ( real_V1035702895aleR_a @ X @ Xa ) @ ( real_V1035702895aleR_a @ Y @ Xa ) ) ) )
= $true ),
inference(copy,[status(thm)],[365]) ).
thf(518,plain,
( ( ! [A: real,B: real,X: a] :
( ( real_V1035702895aleR_a @ ( plus_plus_real @ A @ B ) @ X )
= ( plus_plus_a @ ( real_V1035702895aleR_a @ A @ X ) @ ( real_V1035702895aleR_a @ B @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[364]) ).
thf(519,plain,
( ( ! [A3: set_Product_prod_a_a,B4: set_Product_prod_a_a] :
( ! [X4: product_prod_a_a] :
( ( member449909584od_a_a @ X4 @ A3 )
=> ( member449909584od_a_a @ X4 @ B4 ) )
=> ( ord_le1824328871od_a_a @ A3 @ B4 ) ) )
= $true ),
inference(copy,[status(thm)],[363]) ).
thf(520,plain,
( ( ord_le1824328871od_a_a
= ( ^ [A6: set_Product_prod_a_a,B6: set_Product_prod_a_a] :
! [T: product_prod_a_a] :
( ( member449909584od_a_a @ T @ A6 )
=> ( member449909584od_a_a @ T @ B6 ) ) ) )
= $true ),
inference(copy,[status(thm)],[362]) ).
thf(521,plain,
( ( ord_le1824328871od_a_a
= ( ^ [A6: set_Product_prod_a_a,B6: set_Product_prod_a_a] :
! [X3: product_prod_a_a] :
( ( member449909584od_a_a @ X3 @ A6 )
=> ( member449909584od_a_a @ X3 @ B6 ) ) ) )
= $true ),
inference(copy,[status(thm)],[361]) ).
thf(522,plain,
( ( ! [A3: set_Product_prod_a_a,B4: set_Product_prod_a_a,C: product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A3 @ B4 )
=> ( ( member449909584od_a_a @ C @ A3 )
=> ( member449909584od_a_a @ C @ B4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[360]) ).
thf(523,plain,
( ( ! [A3: set_Product_prod_a_a,B4: set_Product_prod_a_a,X: product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A3 @ B4 )
=> ( ( member449909584od_a_a @ X @ A3 )
=> ( member449909584od_a_a @ X @ B4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[359]) ).
thf(524,plain,
( ( ! [A3: set_Product_prod_a_a,B4: set_Product_prod_a_a,C: product_prod_a_a] :
( ( ord_le108336051od_a_a @ A3 @ B4 )
=> ( ( member449909584od_a_a @ C @ A3 )
=> ( member449909584od_a_a @ C @ B4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[358]) ).
thf(525,plain,
( ( ! [U: real,B: a,V: real,A: a] :
( ( ( plus_plus_a @ ( real_V1035702895aleR_a @ U @ B ) @ ( real_V1035702895aleR_a @ V @ A ) )
= ( plus_plus_a @ ( real_V1035702895aleR_a @ U @ A ) @ ( real_V1035702895aleR_a @ V @ B ) ) )
=> ( ( U != V )
=> ( A = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[357]) ).
thf(526,plain,
( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation ) )
= $true ),
inference(copy,[status(thm)],[441]) ).
thf(527,plain,
( ( ! [SX0: a,SX1: a,SX2: a,SX3: a] :
( ( ( product_Pair_a_a @ SX0 @ SX1 )
= ( product_Pair_a_a @ SX2 @ SX3 ) )
= ( ~ ( ( SX0 != SX2 )
| ( SX1 != SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[469]) ).
thf(528,plain,
( ( ! [SX0: set_Product_prod_a_a,SX1: set_Product_prod_a_a,SX2: product_prod_a_a] :
( ~ ( ord_le108336051od_a_a @ SX0 @ SX1 )
| ~ ( member449909584od_a_a @ SX2 @ SX0 )
| ( member449909584od_a_a @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[524]) ).
thf(529,plain,
( ( ! [SX0: product_prod_a_a,SX1: set_Product_prod_a_a,SX2: set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ SX0 @ ( plus_p634297534od_a_a @ SX1 @ SX2 ) )
| ~ ! [SX3: product_prod_a_a,SX4: product_prod_a_a] :
( ( SX0
!= ( plus_p1505579230od_a_a @ SX3 @ SX4 ) )
| ~ ( member449909584od_a_a @ SX3 @ SX1 )
| ~ ( member449909584od_a_a @ SX4 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[494]) ).
thf(530,plain,
( ( ! [SX0: product_prod_a_a,SX1: set_Product_prod_a_a,SX2: product_prod_a_a,SX3: set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ SX0 @ SX1 )
| ~ ( member449909584od_a_a @ SX2 @ SX3 )
| ( member449909584od_a_a @ ( plus_p1505579230od_a_a @ SX0 @ SX2 ) @ ( plus_p634297534od_a_a @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[471]) ).
thf(531,plain,
( ( ! [SX0: a,SX1: set_a,SX2: a,SX3: set_a] :
( ~ ( member_a @ SX0 @ SX1 )
| ~ ( member_a @ SX2 @ SX3 )
| ( member_a @ ( plus_plus_a @ SX0 @ SX2 ) @ ( plus_plus_set_a @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[472]) ).
thf(532,plain,
( ( ! [SX0: a,SX1: a,SX2: a,SX3: a] :
( ( ( product_Pair_a_a @ SX0 @ SX1 )
!= ( product_Pair_a_a @ SX2 @ SX3 ) )
| ~ ( ( SX0 != SX2 )
| ( SX1 != SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[501]) ).
thf(533,plain,
( ( ! [SX0: real,SX1: a,SX2: real,SX3: a] :
( ( ( plus_plus_a @ ( real_V1035702895aleR_a @ SX0 @ SX1 ) @ ( real_V1035702895aleR_a @ SX2 @ SX3 ) )
!= ( plus_plus_a @ ( real_V1035702895aleR_a @ SX0 @ SX3 ) @ ( real_V1035702895aleR_a @ SX2 @ SX1 ) ) )
| ~ ( ( SX0 != SX2 ) )
| ( SX3 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[525]) ).
thf(534,plain,
( ( ~ ~ ( ~ ( ( u != zero_zero_real ) )
| ~ ( ( u != one_one_real ) ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation ) )
= $true ),
inference(unfold_def,[status(thm)],[448]) ).
thf(535,plain,
( ( ord_le1824328871od_a_a
= ( ^ [SX0: set_Product_prod_a_a,SX1: set_Product_prod_a_a] :
! [SX2: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SX2 @ SX0 )
| ( member449909584od_a_a @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[520]) ).
thf(536,plain,
( ( ! [SX0: a,SX1: set_a,SX2: set_a] :
( ~ ( member_a @ SX0 @ ( plus_plus_set_a @ SX1 @ SX2 ) )
| ~ ! [SX3: a,SX4: a] :
( ( SX0
!= ( plus_plus_a @ SX3 @ SX4 ) )
| ~ ( member_a @ SX3 @ SX1 )
| ~ ( member_a @ SX4 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[495]) ).
thf(537,plain,
( ( ! [SX0: a,SX1: a,SX2: a,SX3: a] :
( ( ( product_Pair_a_a @ SX0 @ SX1 )
= ( product_Pair_a_a @ SX2 @ SX3 ) )
= ( ~ ( ( SX0 != SX2 )
| ( SX1 != SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[470]) ).
thf(538,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX1 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX1 @ SX0 ) @ relation ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX1 @ SX2 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX1 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX2 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX0 ) @ relation ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[446]) ).
thf(539,plain,
( ( ! [SX0: set_Product_prod_a_a,SX1: set_Product_prod_a_a,SX2: set_Product_prod_a_a,SX3: set_Product_prod_a_a,SX4: product_prod_a_a] :
( ~ ( ord_le1824328871od_a_a @ SX0 @ SX1 )
| ~ ( ord_le1824328871od_a_a @ SX2 @ SX3 )
| ~ ( member449909584od_a_a @ SX4 @ ( plus_p634297534od_a_a @ SX0 @ SX2 ) )
| ( member449909584od_a_a @ SX4 @ ( plus_p634297534od_a_a @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[511]) ).
thf(540,plain,
( ( ! [SX0: product_prod_a_a > $o,SX1: product_prod_a_a] :
( ~ ! [SX2: a,SX3: a] : ( SX0 @ ( product_Pair_a_a @ SX2 @ SX3 ) )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[499]) ).
thf(541,plain,
( ( ! [SX0: set_Product_prod_a_a,SX1: set_Product_prod_a_a] :
( ~ ! [SX2: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SX2 @ SX0 )
| ( member449909584od_a_a @ SX2 @ SX1 ) )
| ( ord_le1824328871od_a_a @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[519]) ).
thf(542,plain,
( ( ( u != zero_zero_real )
| ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation ) )
= $true ),
inference(unfold_def,[status(thm)],[449]) ).
thf(543,plain,
( ( ! [SX0: real,SX1: a,SX2: a] :
( ~ ( ( SX0 != zero_zero_real ) )
| ( ( real_V1035702895aleR_a @ SX0 @ SX1 )
!= ( real_V1035702895aleR_a @ SX0 @ SX2 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[516]) ).
thf(544,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX1 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX1 @ SX0 ) @ relation ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX1 @ SX2 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX1 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX2 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX2 @ SX0 ) @ relation ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[445]) ).
thf(545,plain,
( ( ! [SX0: product_prod_a_a] :
~ ! [SX1: a,SX2: a] :
( SX0
!= ( product_Pair_a_a @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[500]) ).
thf(546,plain,
( ( ! [SX0: a,SX1: a] :
( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX1 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX1 @ SX0 ) @ relation ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SX1 @ SX0 ) @ relation ) ) )
= $true ),
inference(unfold_def,[status(thm)],[443]) ).
thf(547,plain,
( ( ! [SX0: a,SX1: real,SX2: real] :
( ~ ( ( SX0 != zero_zero_a ) )
| ( ( real_V1035702895aleR_a @ SX1 @ SX0 )
!= ( real_V1035702895aleR_a @ SX2 @ SX0 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[514]) ).
thf(548,plain,
( ( ! [SX0: product_prod_a_a] :
~ ! [SX1: a] :
~ ~ ! [SX2: a] :
( SX0
!= ( product_Pair_a_a @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[503]) ).
thf(549,plain,
( ( ! [SX0: a,SX1: a,SX2: a,SX3: a] :
( ( SX0
!= ( plus_plus_a @ SX1 @ SX2 ) )
| ( ( plus_plus_a @ SX0 @ SX3 )
= ( plus_plus_a @ SX1 @ ( plus_plus_a @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[497]) ).
thf(550,plain,
( ( ! [SX0: product_prod_a_a > $o,SX1: product_prod_a_a] :
( ~ ! [SX2: a,SX3: a] : ( SX0 @ ( product_Pair_a_a @ SX2 @ SX3 ) )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[502]) ).
thf(551,plain,
( ( ! [SX0: set_Product_prod_a_a,SX1: set_Product_prod_a_a,SX2: product_prod_a_a] :
( ~ ( ord_le1824328871od_a_a @ SX0 @ SX1 )
| ~ ( member449909584od_a_a @ SX2 @ SX0 )
| ( member449909584od_a_a @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[523]) ).
thf(552,plain,
( ( ! [SX0: a,SX1: a] :
( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX1 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SX1 @ SX0 ) @ relation ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SX0 @ SX1 ) @ relation ) ) )
= $true ),
inference(unfold_def,[status(thm)],[444]) ).
thf(553,plain,
( ( ! [SX0: set_Product_prod_a_a,SX1: set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ zero_z950819678od_a_a @ SX0 )
| ( ord_le1824328871od_a_a @ SX1 @ ( plus_p634297534od_a_a @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[512]) ).
thf(554,plain,
( ( ! [SX0: a,SX1: a,SX2: a,SX3: a] :
( ( SX0
!= ( plus_plus_a @ SX1 @ SX2 ) )
| ( ( plus_plus_a @ SX3 @ SX0 )
= ( plus_plus_a @ SX1 @ ( plus_plus_a @ SX3 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[496]) ).
thf(555,plain,
( ( ! [SX0: set_Product_prod_a_a,SX1: set_Product_prod_a_a,SX2: product_prod_a_a] :
( ~ ( ord_le1824328871od_a_a @ SX0 @ SX1 )
| ~ ( member449909584od_a_a @ SX2 @ SX0 )
| ( member449909584od_a_a @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[522]) ).
thf(556,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ( ( plus_plus_a @ SX0 @ SX1 )
!= ( plus_plus_a @ SX2 @ SX1 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[487]) ).
thf(557,plain,
( ( ord_le1824328871od_a_a
= ( ^ [SX0: set_Product_prod_a_a,SX1: set_Product_prod_a_a] :
! [SX2: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SX2 @ SX0 )
| ( member449909584od_a_a @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[521]) ).
thf(558,plain,
( ( ! [SX0: a,SX1: a,SX2: a] :
( ( ( plus_plus_a @ SX0 @ SX1 )
!= ( plus_plus_a @ SX0 @ SX2 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[488]) ).
thf(559,plain,
! [SV1: real] :
( ( ! [SY223: a,SY224: product_prod_a_a] :
( ( real_V296206913od_a_a @ SV1 @ ( produc1299253312od_a_a @ SY223 @ SY224 ) )
= ( produc1299253312od_a_a @ ( real_V1035702895aleR_a @ SV1 @ SY223 ) @ ( real_V543523736od_a_a @ SV1 @ SY224 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(560,plain,
! [SV2: real] :
( ( ! [SY225: a,SY226: real] :
( ( real_V512797224a_real @ SV2 @ ( product_Pair_a_real @ SY225 @ SY226 ) )
= ( product_Pair_a_real @ ( real_V1035702895aleR_a @ SV2 @ SY225 ) @ ( real_V453051771R_real @ SV2 @ SY226 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(561,plain,
! [SV3: real] :
( ( ! [SY227: product_prod_a_a,SY228: a] :
( ( real_V1538726831_a_a_a @ SV3 @ ( produc2061588782_a_a_a @ SY227 @ SY228 ) )
= ( produc2061588782_a_a_a @ ( real_V543523736od_a_a @ SV3 @ SY227 ) @ ( real_V1035702895aleR_a @ SV3 @ SY228 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(562,plain,
! [SV4: real] :
( ( ! [SY229: real,SY230: a] :
( ( real_V1214981142real_a @ SV4 @ ( product_Pair_real_a @ SY229 @ SY230 ) )
= ( product_Pair_real_a @ ( real_V453051771R_real @ SV4 @ SY229 ) @ ( real_V1035702895aleR_a @ SV4 @ SY230 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(563,plain,
! [SV5: real] :
( ( ! [SY231: a,SY232: a] :
( ( real_V543523736od_a_a @ SV5 @ ( product_Pair_a_a @ SY231 @ SY232 ) )
= ( product_Pair_a_a @ ( real_V1035702895aleR_a @ SV5 @ SY231 ) @ ( real_V1035702895aleR_a @ SV5 @ SY232 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(564,plain,
! [SV6: real] :
( ( ! [SY233: a,SY234: product_prod_a_a] :
( ( real_V296206913od_a_a @ SV6 @ ( produc1299253312od_a_a @ SY233 @ SY234 ) )
= ( produc1299253312od_a_a @ ( real_V1035702895aleR_a @ SV6 @ SY233 ) @ ( real_V543523736od_a_a @ SV6 @ SY234 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(565,plain,
! [SV7: real] :
( ( ! [SY235: a,SY236: real] :
( ( real_V512797224a_real @ SV7 @ ( product_Pair_a_real @ SY235 @ SY236 ) )
= ( product_Pair_a_real @ ( real_V1035702895aleR_a @ SV7 @ SY235 ) @ ( real_V453051771R_real @ SV7 @ SY236 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(566,plain,
! [SV8: real] :
( ( ! [SY237: product_prod_a_a,SY238: a] :
( ( real_V1538726831_a_a_a @ SV8 @ ( produc2061588782_a_a_a @ SY237 @ SY238 ) )
= ( produc2061588782_a_a_a @ ( real_V543523736od_a_a @ SV8 @ SY237 ) @ ( real_V1035702895aleR_a @ SV8 @ SY238 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(567,plain,
! [SV9: real] :
( ( ! [SY239: real,SY240: a] :
( ( real_V1214981142real_a @ SV9 @ ( product_Pair_real_a @ SY239 @ SY240 ) )
= ( product_Pair_real_a @ ( real_V453051771R_real @ SV9 @ SY239 ) @ ( real_V1035702895aleR_a @ SV9 @ SY240 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[461]) ).
thf(568,plain,
! [SV10: real] :
( ( ! [SY241: a,SY242: a] :
( ( real_V543523736od_a_a @ SV10 @ ( product_Pair_a_a @ SY241 @ SY242 ) )
= ( product_Pair_a_a @ ( real_V1035702895aleR_a @ SV10 @ SY241 ) @ ( real_V1035702895aleR_a @ SV10 @ SY242 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(569,plain,
! [SV11: a] :
( ( ! [SY243: a,SY244: a,SY245: a] :
( ( plus_p1505579230od_a_a @ ( product_Pair_a_a @ SV11 @ SY243 ) @ ( product_Pair_a_a @ SY244 @ SY245 ) )
= ( product_Pair_a_a @ ( plus_plus_a @ SV11 @ SY244 ) @ ( plus_plus_a @ SY243 @ SY245 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(570,plain,
! [SV12: a] :
( ( ! [SY246: real,SY247: a,SY248: real] :
( ( plus_p541014626a_real @ ( product_Pair_a_real @ SV12 @ SY246 ) @ ( product_Pair_a_real @ SY247 @ SY248 ) )
= ( product_Pair_a_real @ ( plus_plus_a @ SV12 @ SY247 ) @ ( plus_plus_real @ SY246 @ SY248 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(571,plain,
! [SV13: real] :
( ( ! [SY249: a,SY250: real,SY251: a] :
( ( plus_p1243198544real_a @ ( product_Pair_real_a @ SV13 @ SY249 ) @ ( product_Pair_real_a @ SY250 @ SY251 ) )
= ( product_Pair_real_a @ ( plus_plus_real @ SV13 @ SY250 ) @ ( plus_plus_a @ SY249 @ SY251 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(572,plain,
! [SV14: a] :
( ( ! [SY252: set_real,SY253: a,SY254: set_real] :
( ( plus_p1745648536t_real @ ( produc1391501065t_real @ SV14 @ SY252 ) @ ( produc1391501065t_real @ SY253 @ SY254 ) )
= ( produc1391501065t_real @ ( plus_plus_a @ SV14 @ SY253 ) @ ( plus_plus_set_real @ SY252 @ SY254 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(573,plain,
! [SV15: a] :
( ( ! [SY255: set_a,SY256: a,SY257: set_a] :
( ( plus_p1265825342_set_a @ ( product_Pair_a_set_a @ SV15 @ SY255 ) @ ( product_Pair_a_set_a @ SY256 @ SY257 ) )
= ( product_Pair_a_set_a @ ( plus_plus_a @ SV15 @ SY256 ) @ ( plus_plus_set_a @ SY255 @ SY257 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(574,plain,
! [SV16: set_real] :
( ( ! [SY258: a,SY259: set_real,SY260: a] :
( ( plus_p1582417306real_a @ ( produc617496131real_a @ SV16 @ SY258 ) @ ( produc617496131real_a @ SY259 @ SY260 ) )
= ( produc617496131real_a @ ( plus_plus_set_real @ SV16 @ SY259 ) @ ( plus_plus_a @ SY258 @ SY260 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(575,plain,
! [SV17: a] :
( ( ! [SY261: a,SY262: a] :
( ( ( plus_plus_a @ SV17 @ SY261 )
= ( plus_plus_a @ SV17 @ SY262 ) )
= ( SY261 = SY262 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[473]) ).
thf(576,plain,
! [SV18: a] :
( ( ! [SY263: a,SY264: a] :
( ( ( plus_plus_a @ SV18 @ SY263 )
= ( plus_plus_a @ SY264 @ SY263 ) )
= ( SV18 = SY264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(577,plain,
! [SV19: a] :
( ( ! [SY265: a] :
( ( SV19
= ( plus_plus_a @ SV19 @ SY265 ) )
= ( SY265 = zero_zero_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(578,plain,
! [SV20: a] :
( ( ! [SY266: a] :
( ( SV20
= ( plus_plus_a @ SY266 @ SV20 ) )
= ( SY266 = zero_zero_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[476]) ).
thf(579,plain,
! [SV21: a] :
( ( ! [SY267: a] :
( ( ( plus_plus_a @ SV21 @ SY267 )
= SV21 )
= ( SY267 = zero_zero_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(580,plain,
! [SV22: a] :
( ( ! [SY268: a] :
( ( ( plus_plus_a @ SV22 @ SY268 )
= SY268 )
= ( SV22 = zero_zero_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(581,plain,
! [SV23: a] :
( ( ( plus_plus_a @ SV23 @ zero_zero_a )
= SV23 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(582,plain,
! [SV24: a] :
( ( ( plus_plus_a @ zero_zero_a @ SV24 )
= SV24 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(583,plain,
! [SV25: product_prod_a_a] :
( ( ! [SY269: product_prod_a_a > $o] :
( ( member449909584od_a_a @ SV25 @ ( collec645855634od_a_a @ SY269 ) )
= ( SY269 @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(584,plain,
! [SV26: set_Product_prod_a_a] :
( ( ( collec645855634od_a_a
@ ^ [SY270: product_prod_a_a] : ( member449909584od_a_a @ SY270 @ SV26 ) )
= SV26 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(585,plain,
! [SV27: a] :
( ( ( plus_plus_a @ zero_zero_a @ SV27 )
= SV27 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(586,plain,
! [SV28: a] :
( ( ( plus_plus_a @ SV28 @ zero_zero_a )
= SV28 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(587,plain,
! [SV29: a] :
( ( ( plus_plus_a @ zero_zero_a @ SV29 )
= SV29 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(588,plain,
! [SV30: a] :
( ( ! [SY271: a,SY272: a] :
( ( plus_plus_a @ SV30 @ ( plus_plus_a @ SY271 @ SY272 ) )
= ( plus_plus_a @ SY271 @ ( plus_plus_a @ SV30 @ SY272 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(589,plain,
( ( ! [SV31: a] :
( ( plus_plus_a @ SV31 )
= ( ^ [SY273: a] : ( plus_plus_a @ SY273 @ SV31 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[490]) ).
thf(590,plain,
( ( plus_plus_a
= ( ^ [A4: a,B3: a] : ( plus_plus_a @ B3 @ A4 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[490]) ).
thf(591,plain,
! [SV32: a] :
( ( ! [SY274: a,SY275: a] :
( ( ( plus_plus_a @ SV32 @ SY274 )
= ( plus_plus_a @ SY275 @ SY274 ) )
= ( SV32 = SY275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(592,plain,
! [SV33: a] :
( ( ! [SY276: a,SY277: a] :
( ( ( plus_plus_a @ SV33 @ SY276 )
= ( plus_plus_a @ SV33 @ SY277 ) )
= ( SY276 = SY277 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(593,plain,
! [SV34: a] :
( ( ! [SY278: a,SY279: a] :
( ( plus_plus_a @ ( plus_plus_a @ SV34 @ SY278 ) @ SY279 )
= ( plus_plus_a @ SV34 @ ( plus_plus_a @ SY278 @ SY279 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(594,plain,
! [SV35: a] :
( ( ! [SY280: a,SY281: a] :
( ( plus_plus_a @ ( plus_plus_a @ SV35 @ SY280 ) @ SY281 )
= ( plus_plus_a @ SV35 @ ( plus_plus_a @ SY280 @ SY281 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(595,plain,
! [SV36: a] :
( ( ! [SY282: real,SY283: a] :
( ( ( plus_plus_a @ SV36 @ ( real_V1035702895aleR_a @ SY282 @ SY283 ) )
= ( plus_plus_a @ SY283 @ ( real_V1035702895aleR_a @ SY282 @ SV36 ) ) )
= ( ( SY283 = SV36 )
| ( SY282 = one_one_real ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(596,plain,
! [SV37: a] :
( ( ( real_V1035702895aleR_a @ zero_zero_real @ SV37 )
= zero_zero_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(597,plain,
! [SV38: real] :
( ( ! [SY284: a] :
( ( ( real_V1035702895aleR_a @ SV38 @ SY284 )
= zero_zero_a )
= ( ( SV38 = zero_zero_real )
| ( SY284 = zero_zero_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(598,plain,
! [SV39: a] :
( ( ( real_V1035702895aleR_a @ one_one_real @ SV39 )
= SV39 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(599,plain,
! [SV40: real] :
( ( ! [SY285: a,SY286: a] :
( ( ( real_V1035702895aleR_a @ SV40 @ SY285 )
= ( real_V1035702895aleR_a @ SV40 @ SY286 ) )
= ( ( SY285 = SY286 )
| ( SV40 = zero_zero_real ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(600,plain,
! [SV41: real] :
( ( ! [SY287: a,SY288: real] :
( ( ( real_V1035702895aleR_a @ SV41 @ SY287 )
= ( real_V1035702895aleR_a @ SY288 @ SY287 ) )
= ( ( SV41 = SY288 )
| ( SY287 = zero_zero_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(601,plain,
! [SV42: real] :
( ( ( real_V1035702895aleR_a @ SV42 @ zero_zero_a )
= zero_zero_a )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(602,plain,
! [SV43: real] :
( ( ! [SY289: real,SY290: a] :
( ( real_V1035702895aleR_a @ SV43 @ ( real_V1035702895aleR_a @ SY289 @ SY290 ) )
= ( real_V1035702895aleR_a @ SY289 @ ( real_V1035702895aleR_a @ SV43 @ SY290 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(603,plain,
! [SV44: real] :
( ( ! [SY291: a,SY292: a] :
( ( real_V1035702895aleR_a @ SV44 @ ( plus_plus_a @ SY291 @ SY292 ) )
= ( plus_plus_a @ ( real_V1035702895aleR_a @ SV44 @ SY291 ) @ ( real_V1035702895aleR_a @ SV44 @ SY292 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(604,plain,
! [SV45: real] :
( ( ! [SY293: real,SY294: a] :
( ( real_V1035702895aleR_a @ ( plus_plus_real @ SV45 @ SY293 ) @ SY294 )
= ( plus_plus_a @ ( real_V1035702895aleR_a @ SV45 @ SY294 ) @ ( real_V1035702895aleR_a @ SY293 @ SY294 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(605,plain,
! [SV46: real] :
( ( ! [SY295: real,SY296: a] :
( ( real_V1035702895aleR_a @ ( plus_plus_real @ SV46 @ SY295 ) @ SY296 )
= ( plus_plus_a @ ( real_V1035702895aleR_a @ SV46 @ SY296 ) @ ( real_V1035702895aleR_a @ SY295 @ SY296 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(606,plain,
( ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation )
= $false ),
inference(extcnf_not_pos,[status(thm)],[526]) ).
thf(607,plain,
! [SV47: a] :
( ( ! [SY297: a,SY298: a,SY299: a] :
( ( ( product_Pair_a_a @ SV47 @ SY297 )
= ( product_Pair_a_a @ SY298 @ SY299 ) )
= ( ~ ( ( SV47 != SY298 )
| ( SY297 != SY299 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(608,plain,
! [SV48: set_Product_prod_a_a] :
( ( ! [SY300: set_Product_prod_a_a,SY301: product_prod_a_a] :
( ~ ( ord_le108336051od_a_a @ SV48 @ SY300 )
| ~ ( member449909584od_a_a @ SY301 @ SV48 )
| ( member449909584od_a_a @ SY301 @ SY300 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(609,plain,
! [SV49: product_prod_a_a] :
( ( ! [SY302: set_Product_prod_a_a,SY303: set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ SV49 @ ( plus_p634297534od_a_a @ SY302 @ SY303 ) )
| ~ ! [SY304: product_prod_a_a,SY305: product_prod_a_a] :
( ( SV49
!= ( plus_p1505579230od_a_a @ SY304 @ SY305 ) )
| ~ ( member449909584od_a_a @ SY304 @ SY302 )
| ~ ( member449909584od_a_a @ SY305 @ SY303 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(610,plain,
! [SV50: product_prod_a_a] :
( ( ! [SY306: set_Product_prod_a_a,SY307: product_prod_a_a,SY308: set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ SV50 @ SY306 )
| ~ ( member449909584od_a_a @ SY307 @ SY308 )
| ( member449909584od_a_a @ ( plus_p1505579230od_a_a @ SV50 @ SY307 ) @ ( plus_p634297534od_a_a @ SY306 @ SY308 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(611,plain,
! [SV51: a] :
( ( ! [SY309: set_a,SY310: a,SY311: set_a] :
( ~ ( member_a @ SV51 @ SY309 )
| ~ ( member_a @ SY310 @ SY311 )
| ( member_a @ ( plus_plus_a @ SV51 @ SY310 ) @ ( plus_plus_set_a @ SY309 @ SY311 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(612,plain,
! [SV52: a] :
( ( ! [SY312: a,SY313: a,SY314: a] :
( ( ( product_Pair_a_a @ SV52 @ SY312 )
!= ( product_Pair_a_a @ SY313 @ SY314 ) )
| ~ ( ( SV52 != SY313 )
| ( SY312 != SY314 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(613,plain,
! [SV53: real] :
( ( ! [SY315: a,SY316: real,SY317: a] :
( ( ( plus_plus_a @ ( real_V1035702895aleR_a @ SV53 @ SY315 ) @ ( real_V1035702895aleR_a @ SY316 @ SY317 ) )
!= ( plus_plus_a @ ( real_V1035702895aleR_a @ SV53 @ SY317 ) @ ( real_V1035702895aleR_a @ SY316 @ SY315 ) ) )
| ~ ( ( SV53 != SY316 ) )
| ( SY317 = SY315 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(614,plain,
( ( ( ~ ~ ( ~ ( ( u != zero_zero_real ) )
| ~ ( ( u != one_one_real ) ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[534]) ).
thf(615,plain,
( ( ! [SV54: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ SV54 )
= ( ^ [SY318: set_Product_prod_a_a] :
! [SY319: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY319 @ SV54 )
| ( member449909584od_a_a @ SY319 @ SY318 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[535]) ).
thf(616,plain,
( ( ord_le1824328871od_a_a
= ( ^ [SX0: set_Product_prod_a_a,SX1: set_Product_prod_a_a] :
! [SX2: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SX2 @ SX0 )
| ( member449909584od_a_a @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[535]) ).
thf(617,plain,
! [SV55: a] :
( ( ! [SY320: set_a,SY321: set_a] :
( ~ ( member_a @ SV55 @ ( plus_plus_set_a @ SY320 @ SY321 ) )
| ~ ! [SY322: a,SY323: a] :
( ( SV55
!= ( plus_plus_a @ SY322 @ SY323 ) )
| ~ ( member_a @ SY322 @ SY320 )
| ~ ( member_a @ SY323 @ SY321 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(618,plain,
! [SV56: a] :
( ( ! [SY324: a,SY325: a,SY326: a] :
( ( ( product_Pair_a_a @ SV56 @ SY324 )
= ( product_Pair_a_a @ SY325 @ SY326 ) )
= ( ~ ( ( SV56 != SY325 )
| ( SY324 != SY326 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(619,plain,
! [SV57: a] :
( ( ! [SY327: a,SY328: a] :
( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SY327 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY327 @ SV57 ) @ relation ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY327 @ SY328 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY328 @ SY327 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SY328 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY328 @ SV57 ) @ relation ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(620,plain,
! [SV58: set_Product_prod_a_a] :
( ( ! [SY329: set_Product_prod_a_a,SY330: set_Product_prod_a_a,SY331: set_Product_prod_a_a,SY332: product_prod_a_a] :
( ~ ( ord_le1824328871od_a_a @ SV58 @ SY329 )
| ~ ( ord_le1824328871od_a_a @ SY330 @ SY331 )
| ~ ( member449909584od_a_a @ SY332 @ ( plus_p634297534od_a_a @ SV58 @ SY330 ) )
| ( member449909584od_a_a @ SY332 @ ( plus_p634297534od_a_a @ SY329 @ SY331 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(621,plain,
! [SV59: product_prod_a_a > $o] :
( ( ! [SY333: product_prod_a_a] :
( ~ ! [SY334: a,SY335: a] : ( SV59 @ ( product_Pair_a_a @ SY334 @ SY335 ) )
| ( SV59 @ SY333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(622,plain,
! [SV60: set_Product_prod_a_a] :
( ( ! [SY336: set_Product_prod_a_a] :
( ~ ! [SY337: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY337 @ SV60 )
| ( member449909584od_a_a @ SY337 @ SY336 ) )
| ( ord_le1824328871od_a_a @ SV60 @ SY336 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(623,plain,
( ( ( u != zero_zero_real )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[542]) ).
thf(624,plain,
! [SV61: real] :
( ( ! [SY338: a,SY339: a] :
( ~ ( ( SV61 != zero_zero_real ) )
| ( ( real_V1035702895aleR_a @ SV61 @ SY338 )
!= ( real_V1035702895aleR_a @ SV61 @ SY339 ) )
| ( SY338 = SY339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(625,plain,
! [SV62: a] :
( ( ! [SY340: a,SY341: a] :
( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV62 @ SY340 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY340 @ SV62 ) @ relation ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY340 @ SY341 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY341 @ SY340 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV62 @ SY341 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY341 @ SV62 ) @ relation ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[544]) ).
thf(626,plain,
! [SV63: product_prod_a_a] :
( ( ~ ! [SY342: a,SY343: a] :
( SV63
!= ( product_Pair_a_a @ SY342 @ SY343 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(627,plain,
! [SV64: a] :
( ( ! [SY344: a] :
( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV64 @ SY344 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY344 @ SV64 ) @ relation ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SY344 @ SV64 ) @ relation ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(628,plain,
! [SV65: a] :
( ( ! [SY345: real,SY346: real] :
( ~ ( ( SV65 != zero_zero_a ) )
| ( ( real_V1035702895aleR_a @ SY345 @ SV65 )
!= ( real_V1035702895aleR_a @ SY346 @ SV65 ) )
| ( SY345 = SY346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(629,plain,
! [SV66: product_prod_a_a] :
( ( ~ ! [SY347: a] :
~ ~ ! [SY348: a] :
( SV66
!= ( product_Pair_a_a @ SY347 @ SY348 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[548]) ).
thf(630,plain,
! [SV67: a] :
( ( ! [SY349: a,SY350: a,SY351: a] :
( ( SV67
!= ( plus_plus_a @ SY349 @ SY350 ) )
| ( ( plus_plus_a @ SV67 @ SY351 )
= ( plus_plus_a @ SY349 @ ( plus_plus_a @ SY350 @ SY351 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[549]) ).
thf(631,plain,
! [SV68: product_prod_a_a > $o] :
( ( ! [SY352: product_prod_a_a] :
( ~ ! [SY353: a,SY354: a] : ( SV68 @ ( product_Pair_a_a @ SY353 @ SY354 ) )
| ( SV68 @ SY352 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(632,plain,
! [SV69: set_Product_prod_a_a] :
( ( ! [SY355: set_Product_prod_a_a,SY356: product_prod_a_a] :
( ~ ( ord_le1824328871od_a_a @ SV69 @ SY355 )
| ~ ( member449909584od_a_a @ SY356 @ SV69 )
| ( member449909584od_a_a @ SY356 @ SY355 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(633,plain,
! [SV70: a] :
( ( ! [SY357: a] :
( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV70 @ SY357 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY357 @ SV70 ) @ relation ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV70 @ SY357 ) @ relation ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[552]) ).
thf(634,plain,
! [SV71: set_Product_prod_a_a] :
( ( ! [SY358: set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ zero_z950819678od_a_a @ SV71 )
| ( ord_le1824328871od_a_a @ SY358 @ ( plus_p634297534od_a_a @ SV71 @ SY358 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(635,plain,
! [SV72: a] :
( ( ! [SY359: a,SY360: a,SY361: a] :
( ( SV72
!= ( plus_plus_a @ SY359 @ SY360 ) )
| ( ( plus_plus_a @ SY361 @ SV72 )
= ( plus_plus_a @ SY359 @ ( plus_plus_a @ SY361 @ SY360 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(636,plain,
! [SV73: set_Product_prod_a_a] :
( ( ! [SY362: set_Product_prod_a_a,SY363: product_prod_a_a] :
( ~ ( ord_le1824328871od_a_a @ SV73 @ SY362 )
| ~ ( member449909584od_a_a @ SY363 @ SV73 )
| ( member449909584od_a_a @ SY363 @ SY362 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[555]) ).
thf(637,plain,
! [SV74: a] :
( ( ! [SY364: a,SY365: a] :
( ( ( plus_plus_a @ SV74 @ SY364 )
!= ( plus_plus_a @ SY365 @ SY364 ) )
| ( SV74 = SY365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(638,plain,
( ( ! [SV75: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ SV75 )
= ( ^ [SY366: set_Product_prod_a_a] :
! [SY367: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY367 @ SV75 )
| ( member449909584od_a_a @ SY367 @ SY366 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[557]) ).
thf(639,plain,
( ( ord_le1824328871od_a_a
= ( ^ [SX0: set_Product_prod_a_a,SX1: set_Product_prod_a_a] :
! [SX2: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SX2 @ SX0 )
| ( member449909584od_a_a @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[557]) ).
thf(640,plain,
! [SV76: a] :
( ( ! [SY368: a,SY369: a] :
( ( ( plus_plus_a @ SV76 @ SY368 )
!= ( plus_plus_a @ SV76 @ SY369 ) )
| ( SY368 = SY369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(641,plain,
! [SV77: a,SV1: real] :
( ( ! [SY370: product_prod_a_a] :
( ( real_V296206913od_a_a @ SV1 @ ( produc1299253312od_a_a @ SV77 @ SY370 ) )
= ( produc1299253312od_a_a @ ( real_V1035702895aleR_a @ SV1 @ SV77 ) @ ( real_V543523736od_a_a @ SV1 @ SY370 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(642,plain,
! [SV78: a,SV2: real] :
( ( ! [SY371: real] :
( ( real_V512797224a_real @ SV2 @ ( product_Pair_a_real @ SV78 @ SY371 ) )
= ( product_Pair_a_real @ ( real_V1035702895aleR_a @ SV2 @ SV78 ) @ ( real_V453051771R_real @ SV2 @ SY371 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(643,plain,
! [SV79: product_prod_a_a,SV3: real] :
( ( ! [SY372: a] :
( ( real_V1538726831_a_a_a @ SV3 @ ( produc2061588782_a_a_a @ SV79 @ SY372 ) )
= ( produc2061588782_a_a_a @ ( real_V543523736od_a_a @ SV3 @ SV79 ) @ ( real_V1035702895aleR_a @ SV3 @ SY372 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(644,plain,
! [SV80: real,SV4: real] :
( ( ! [SY373: a] :
( ( real_V1214981142real_a @ SV4 @ ( product_Pair_real_a @ SV80 @ SY373 ) )
= ( product_Pair_real_a @ ( real_V453051771R_real @ SV4 @ SV80 ) @ ( real_V1035702895aleR_a @ SV4 @ SY373 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(645,plain,
! [SV81: a,SV5: real] :
( ( ! [SY374: a] :
( ( real_V543523736od_a_a @ SV5 @ ( product_Pair_a_a @ SV81 @ SY374 ) )
= ( product_Pair_a_a @ ( real_V1035702895aleR_a @ SV5 @ SV81 ) @ ( real_V1035702895aleR_a @ SV5 @ SY374 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(646,plain,
! [SV82: a,SV6: real] :
( ( ! [SY375: product_prod_a_a] :
( ( real_V296206913od_a_a @ SV6 @ ( produc1299253312od_a_a @ SV82 @ SY375 ) )
= ( produc1299253312od_a_a @ ( real_V1035702895aleR_a @ SV6 @ SV82 ) @ ( real_V543523736od_a_a @ SV6 @ SY375 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(647,plain,
! [SV83: a,SV7: real] :
( ( ! [SY376: real] :
( ( real_V512797224a_real @ SV7 @ ( product_Pair_a_real @ SV83 @ SY376 ) )
= ( product_Pair_a_real @ ( real_V1035702895aleR_a @ SV7 @ SV83 ) @ ( real_V453051771R_real @ SV7 @ SY376 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(648,plain,
! [SV84: product_prod_a_a,SV8: real] :
( ( ! [SY377: a] :
( ( real_V1538726831_a_a_a @ SV8 @ ( produc2061588782_a_a_a @ SV84 @ SY377 ) )
= ( produc2061588782_a_a_a @ ( real_V543523736od_a_a @ SV8 @ SV84 ) @ ( real_V1035702895aleR_a @ SV8 @ SY377 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(649,plain,
! [SV85: real,SV9: real] :
( ( ! [SY378: a] :
( ( real_V1214981142real_a @ SV9 @ ( product_Pair_real_a @ SV85 @ SY378 ) )
= ( product_Pair_real_a @ ( real_V453051771R_real @ SV9 @ SV85 ) @ ( real_V1035702895aleR_a @ SV9 @ SY378 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(650,plain,
! [SV86: a,SV10: real] :
( ( ! [SY379: a] :
( ( real_V543523736od_a_a @ SV10 @ ( product_Pair_a_a @ SV86 @ SY379 ) )
= ( product_Pair_a_a @ ( real_V1035702895aleR_a @ SV10 @ SV86 ) @ ( real_V1035702895aleR_a @ SV10 @ SY379 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(651,plain,
! [SV87: a,SV11: a] :
( ( ! [SY380: a,SY381: a] :
( ( plus_p1505579230od_a_a @ ( product_Pair_a_a @ SV11 @ SV87 ) @ ( product_Pair_a_a @ SY380 @ SY381 ) )
= ( product_Pair_a_a @ ( plus_plus_a @ SV11 @ SY380 ) @ ( plus_plus_a @ SV87 @ SY381 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(652,plain,
! [SV88: real,SV12: a] :
( ( ! [SY382: a,SY383: real] :
( ( plus_p541014626a_real @ ( product_Pair_a_real @ SV12 @ SV88 ) @ ( product_Pair_a_real @ SY382 @ SY383 ) )
= ( product_Pair_a_real @ ( plus_plus_a @ SV12 @ SY382 ) @ ( plus_plus_real @ SV88 @ SY383 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(653,plain,
! [SV89: a,SV13: real] :
( ( ! [SY384: real,SY385: a] :
( ( plus_p1243198544real_a @ ( product_Pair_real_a @ SV13 @ SV89 ) @ ( product_Pair_real_a @ SY384 @ SY385 ) )
= ( product_Pair_real_a @ ( plus_plus_real @ SV13 @ SY384 ) @ ( plus_plus_a @ SV89 @ SY385 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(654,plain,
! [SV90: set_real,SV14: a] :
( ( ! [SY386: a,SY387: set_real] :
( ( plus_p1745648536t_real @ ( produc1391501065t_real @ SV14 @ SV90 ) @ ( produc1391501065t_real @ SY386 @ SY387 ) )
= ( produc1391501065t_real @ ( plus_plus_a @ SV14 @ SY386 ) @ ( plus_plus_set_real @ SV90 @ SY387 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(655,plain,
! [SV91: set_a,SV15: a] :
( ( ! [SY388: a,SY389: set_a] :
( ( plus_p1265825342_set_a @ ( product_Pair_a_set_a @ SV15 @ SV91 ) @ ( product_Pair_a_set_a @ SY388 @ SY389 ) )
= ( product_Pair_a_set_a @ ( plus_plus_a @ SV15 @ SY388 ) @ ( plus_plus_set_a @ SV91 @ SY389 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(656,plain,
! [SV92: a,SV16: set_real] :
( ( ! [SY390: set_real,SY391: a] :
( ( plus_p1582417306real_a @ ( produc617496131real_a @ SV16 @ SV92 ) @ ( produc617496131real_a @ SY390 @ SY391 ) )
= ( produc617496131real_a @ ( plus_plus_set_real @ SV16 @ SY390 ) @ ( plus_plus_a @ SV92 @ SY391 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(657,plain,
! [SV93: a,SV17: a] :
( ( ! [SY392: a] :
( ( ( plus_plus_a @ SV17 @ SV93 )
= ( plus_plus_a @ SV17 @ SY392 ) )
= ( SV93 = SY392 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(658,plain,
! [SV94: a,SV18: a] :
( ( ! [SY393: a] :
( ( ( plus_plus_a @ SV18 @ SV94 )
= ( plus_plus_a @ SY393 @ SV94 ) )
= ( SV18 = SY393 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(659,plain,
! [SV95: a,SV19: a] :
( ( ( SV19
= ( plus_plus_a @ SV19 @ SV95 ) )
= ( SV95 = zero_zero_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(660,plain,
! [SV96: a,SV20: a] :
( ( ( SV20
= ( plus_plus_a @ SV96 @ SV20 ) )
= ( SV96 = zero_zero_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(661,plain,
! [SV97: a,SV21: a] :
( ( ( ( plus_plus_a @ SV21 @ SV97 )
= SV21 )
= ( SV97 = zero_zero_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[579]) ).
thf(662,plain,
! [SV98: a,SV22: a] :
( ( ( ( plus_plus_a @ SV22 @ SV98 )
= SV98 )
= ( SV22 = zero_zero_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(663,plain,
! [SV99: product_prod_a_a > $o,SV25: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV25 @ ( collec645855634od_a_a @ SV99 ) )
= ( SV99 @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(664,plain,
! [SV100: a,SV30: a] :
( ( ! [SY394: a] :
( ( plus_plus_a @ SV30 @ ( plus_plus_a @ SV100 @ SY394 ) )
= ( plus_plus_a @ SV100 @ ( plus_plus_a @ SV30 @ SY394 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(665,plain,
! [SV101: a] :
( ( ( plus_plus_a @ SV101 )
= ( ^ [SY395: a] : ( plus_plus_a @ SY395 @ SV101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(666,plain,
! [SV102: a,SV32: a] :
( ( ! [SY396: a] :
( ( ( plus_plus_a @ SV32 @ SV102 )
= ( plus_plus_a @ SY396 @ SV102 ) )
= ( SV32 = SY396 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[591]) ).
thf(667,plain,
! [SV103: a,SV33: a] :
( ( ! [SY397: a] :
( ( ( plus_plus_a @ SV33 @ SV103 )
= ( plus_plus_a @ SV33 @ SY397 ) )
= ( SV103 = SY397 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(668,plain,
! [SV104: a,SV34: a] :
( ( ! [SY398: a] :
( ( plus_plus_a @ ( plus_plus_a @ SV34 @ SV104 ) @ SY398 )
= ( plus_plus_a @ SV34 @ ( plus_plus_a @ SV104 @ SY398 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(669,plain,
! [SV105: a,SV35: a] :
( ( ! [SY399: a] :
( ( plus_plus_a @ ( plus_plus_a @ SV35 @ SV105 ) @ SY399 )
= ( plus_plus_a @ SV35 @ ( plus_plus_a @ SV105 @ SY399 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(670,plain,
! [SV106: real,SV36: a] :
( ( ! [SY400: a] :
( ( ( plus_plus_a @ SV36 @ ( real_V1035702895aleR_a @ SV106 @ SY400 ) )
= ( plus_plus_a @ SY400 @ ( real_V1035702895aleR_a @ SV106 @ SV36 ) ) )
= ( ( SY400 = SV36 )
| ( SV106 = one_one_real ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(671,plain,
! [SV107: a,SV38: real] :
( ( ( ( real_V1035702895aleR_a @ SV38 @ SV107 )
= zero_zero_a )
= ( ( SV38 = zero_zero_real )
| ( SV107 = zero_zero_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(672,plain,
! [SV108: a,SV40: real] :
( ( ! [SY401: a] :
( ( ( real_V1035702895aleR_a @ SV40 @ SV108 )
= ( real_V1035702895aleR_a @ SV40 @ SY401 ) )
= ( ( SV108 = SY401 )
| ( SV40 = zero_zero_real ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(673,plain,
! [SV109: a,SV41: real] :
( ( ! [SY402: real] :
( ( ( real_V1035702895aleR_a @ SV41 @ SV109 )
= ( real_V1035702895aleR_a @ SY402 @ SV109 ) )
= ( ( SV41 = SY402 )
| ( SV109 = zero_zero_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(674,plain,
! [SV110: real,SV43: real] :
( ( ! [SY403: a] :
( ( real_V1035702895aleR_a @ SV43 @ ( real_V1035702895aleR_a @ SV110 @ SY403 ) )
= ( real_V1035702895aleR_a @ SV110 @ ( real_V1035702895aleR_a @ SV43 @ SY403 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(675,plain,
! [SV111: a,SV44: real] :
( ( ! [SY404: a] :
( ( real_V1035702895aleR_a @ SV44 @ ( plus_plus_a @ SV111 @ SY404 ) )
= ( plus_plus_a @ ( real_V1035702895aleR_a @ SV44 @ SV111 ) @ ( real_V1035702895aleR_a @ SV44 @ SY404 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(676,plain,
! [SV112: real,SV45: real] :
( ( ! [SY405: a] :
( ( real_V1035702895aleR_a @ ( plus_plus_real @ SV45 @ SV112 ) @ SY405 )
= ( plus_plus_a @ ( real_V1035702895aleR_a @ SV45 @ SY405 ) @ ( real_V1035702895aleR_a @ SV112 @ SY405 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(677,plain,
! [SV113: real,SV46: real] :
( ( ! [SY406: a] :
( ( real_V1035702895aleR_a @ ( plus_plus_real @ SV46 @ SV113 ) @ SY406 )
= ( plus_plus_a @ ( real_V1035702895aleR_a @ SV46 @ SY406 ) @ ( real_V1035702895aleR_a @ SV113 @ SY406 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[605]) ).
thf(678,plain,
! [SV114: a,SV47: a] :
( ( ! [SY407: a,SY408: a] :
( ( ( product_Pair_a_a @ SV47 @ SV114 )
= ( product_Pair_a_a @ SY407 @ SY408 ) )
= ( ~ ( ( SV47 != SY407 )
| ( SV114 != SY408 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[607]) ).
thf(679,plain,
! [SV115: set_Product_prod_a_a,SV48: set_Product_prod_a_a] :
( ( ! [SY409: product_prod_a_a] :
( ~ ( ord_le108336051od_a_a @ SV48 @ SV115 )
| ~ ( member449909584od_a_a @ SY409 @ SV48 )
| ( member449909584od_a_a @ SY409 @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(680,plain,
! [SV116: set_Product_prod_a_a,SV49: product_prod_a_a] :
( ( ! [SY410: set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ SV49 @ ( plus_p634297534od_a_a @ SV116 @ SY410 ) )
| ~ ! [SY411: product_prod_a_a,SY412: product_prod_a_a] :
( ( SV49
!= ( plus_p1505579230od_a_a @ SY411 @ SY412 ) )
| ~ ( member449909584od_a_a @ SY411 @ SV116 )
| ~ ( member449909584od_a_a @ SY412 @ SY410 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(681,plain,
! [SV117: set_Product_prod_a_a,SV50: product_prod_a_a] :
( ( ! [SY413: product_prod_a_a,SY414: set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ SV50 @ SV117 )
| ~ ( member449909584od_a_a @ SY413 @ SY414 )
| ( member449909584od_a_a @ ( plus_p1505579230od_a_a @ SV50 @ SY413 ) @ ( plus_p634297534od_a_a @ SV117 @ SY414 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(682,plain,
! [SV118: set_a,SV51: a] :
( ( ! [SY415: a,SY416: set_a] :
( ~ ( member_a @ SV51 @ SV118 )
| ~ ( member_a @ SY415 @ SY416 )
| ( member_a @ ( plus_plus_a @ SV51 @ SY415 ) @ ( plus_plus_set_a @ SV118 @ SY416 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(683,plain,
! [SV119: a,SV52: a] :
( ( ! [SY417: a,SY418: a] :
( ( ( product_Pair_a_a @ SV52 @ SV119 )
!= ( product_Pair_a_a @ SY417 @ SY418 ) )
| ~ ( ( SV52 != SY417 )
| ( SV119 != SY418 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(684,plain,
! [SV120: a,SV53: real] :
( ( ! [SY419: real,SY420: a] :
( ( ( plus_plus_a @ ( real_V1035702895aleR_a @ SV53 @ SV120 ) @ ( real_V1035702895aleR_a @ SY419 @ SY420 ) )
!= ( plus_plus_a @ ( real_V1035702895aleR_a @ SV53 @ SY420 ) @ ( real_V1035702895aleR_a @ SY419 @ SV120 ) ) )
| ~ ( ( SV53 != SY419 ) )
| ( SY420 = SV120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(685,plain,
( ( ( ~ ( ~ ( ( u != zero_zero_real ) )
| ~ ( ( u != one_one_real ) ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[614]) ).
thf(686,plain,
! [SV121: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV121 )
= ( ^ [SY421: set_Product_prod_a_a] :
! [SY422: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY422 @ SV121 )
| ( member449909584od_a_a @ SY422 @ SY421 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(687,plain,
! [SV122: set_a,SV55: a] :
( ( ! [SY423: set_a] :
( ~ ( member_a @ SV55 @ ( plus_plus_set_a @ SV122 @ SY423 ) )
| ~ ! [SY424: a,SY425: a] :
( ( SV55
!= ( plus_plus_a @ SY424 @ SY425 ) )
| ~ ( member_a @ SY424 @ SV122 )
| ~ ( member_a @ SY425 @ SY423 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(688,plain,
! [SV123: a,SV56: a] :
( ( ! [SY426: a,SY427: a] :
( ( ( product_Pair_a_a @ SV56 @ SV123 )
= ( product_Pair_a_a @ SY426 @ SY427 ) )
= ( ~ ( ( SV56 != SY426 )
| ( SV123 != SY427 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(689,plain,
! [SV124: a,SV57: a] :
( ( ! [SY428: a] :
( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV124 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV57 ) @ relation ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SY428 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY428 @ SV124 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SY428 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY428 @ SV57 ) @ relation ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(690,plain,
! [SV125: set_Product_prod_a_a,SV58: set_Product_prod_a_a] :
( ( ! [SY429: set_Product_prod_a_a,SY430: set_Product_prod_a_a,SY431: product_prod_a_a] :
( ~ ( ord_le1824328871od_a_a @ SV58 @ SV125 )
| ~ ( ord_le1824328871od_a_a @ SY429 @ SY430 )
| ~ ( member449909584od_a_a @ SY431 @ ( plus_p634297534od_a_a @ SV58 @ SY429 ) )
| ( member449909584od_a_a @ SY431 @ ( plus_p634297534od_a_a @ SV125 @ SY430 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(691,plain,
! [SV126: product_prod_a_a,SV59: product_prod_a_a > $o] :
( ( ~ ! [SY334: a,SY335: a] : ( SV59 @ ( product_Pair_a_a @ SY334 @ SY335 ) )
| ( SV59 @ SV126 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(692,plain,
! [SV127: set_Product_prod_a_a,SV60: set_Product_prod_a_a] :
( ( ~ ! [SY434: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY434 @ SV60 )
| ( member449909584od_a_a @ SY434 @ SV127 ) )
| ( ord_le1824328871od_a_a @ SV60 @ SV127 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(693,plain,
( ( ( u = zero_zero_real )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[623]) ).
thf(694,plain,
! [SV128: a,SV61: real] :
( ( ! [SY435: a] :
( ~ ( ( SV61 != zero_zero_real ) )
| ( ( real_V1035702895aleR_a @ SV61 @ SV128 )
!= ( real_V1035702895aleR_a @ SV61 @ SY435 ) )
| ( SV128 = SY435 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(695,plain,
! [SV129: a,SV62: a] :
( ( ! [SY436: a] :
( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV62 @ SV129 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV129 @ SV62 ) @ relation ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV129 @ SY436 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY436 @ SV129 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV62 @ SY436 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SY436 @ SV62 ) @ relation ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(696,plain,
! [SV63: product_prod_a_a] :
( ( ! [SY342: a,SY343: a] :
( SV63
!= ( product_Pair_a_a @ SY342 @ SY343 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[626]) ).
thf(697,plain,
! [SV130: a,SV64: a] :
( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV64 @ SV130 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV64 ) @ relation ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV64 ) @ relation ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(698,plain,
! [SV131: real,SV65: a] :
( ( ! [SY437: real] :
( ~ ( ( SV65 != zero_zero_a ) )
| ( ( real_V1035702895aleR_a @ SV131 @ SV65 )
!= ( real_V1035702895aleR_a @ SY437 @ SV65 ) )
| ( SV131 = SY437 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(699,plain,
! [SV66: product_prod_a_a] :
( ( ! [SY347: a] :
~ ~ ! [SY348: a] :
( SV66
!= ( product_Pair_a_a @ SY347 @ SY348 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[629]) ).
thf(700,plain,
! [SV132: a,SV67: a] :
( ( ! [SY438: a,SY439: a] :
( ( SV67
!= ( plus_plus_a @ SV132 @ SY438 ) )
| ( ( plus_plus_a @ SV67 @ SY439 )
= ( plus_plus_a @ SV132 @ ( plus_plus_a @ SY438 @ SY439 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(701,plain,
! [SV133: product_prod_a_a,SV68: product_prod_a_a > $o] :
( ( ~ ! [SY353: a,SY354: a] : ( SV68 @ ( product_Pair_a_a @ SY353 @ SY354 ) )
| ( SV68 @ SV133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(702,plain,
! [SV134: set_Product_prod_a_a,SV69: set_Product_prod_a_a] :
( ( ! [SY442: product_prod_a_a] :
( ~ ( ord_le1824328871od_a_a @ SV69 @ SV134 )
| ~ ( member449909584od_a_a @ SY442 @ SV69 )
| ( member449909584od_a_a @ SY442 @ SV134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(703,plain,
! [SV135: a,SV70: a] :
( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV70 @ SV135 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV135 @ SV70 ) @ relation ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ SV70 @ SV135 ) @ relation ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(704,plain,
! [SV136: set_Product_prod_a_a,SV71: set_Product_prod_a_a] :
( ( ~ ( member449909584od_a_a @ zero_z950819678od_a_a @ SV71 )
| ( ord_le1824328871od_a_a @ SV136 @ ( plus_p634297534od_a_a @ SV71 @ SV136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(705,plain,
! [SV137: a,SV72: a] :
( ( ! [SY443: a,SY444: a] :
( ( SV72
!= ( plus_plus_a @ SV137 @ SY443 ) )
| ( ( plus_plus_a @ SY444 @ SV72 )
= ( plus_plus_a @ SV137 @ ( plus_plus_a @ SY444 @ SY443 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(706,plain,
! [SV138: set_Product_prod_a_a,SV73: set_Product_prod_a_a] :
( ( ! [SY445: product_prod_a_a] :
( ~ ( ord_le1824328871od_a_a @ SV73 @ SV138 )
| ~ ( member449909584od_a_a @ SY445 @ SV73 )
| ( member449909584od_a_a @ SY445 @ SV138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(707,plain,
! [SV139: a,SV74: a] :
( ( ! [SY446: a] :
( ( ( plus_plus_a @ SV74 @ SV139 )
!= ( plus_plus_a @ SY446 @ SV139 ) )
| ( SV74 = SY446 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(708,plain,
! [SV140: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV140 )
= ( ^ [SY447: set_Product_prod_a_a] :
! [SY448: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY448 @ SV140 )
| ( member449909584od_a_a @ SY448 @ SY447 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(709,plain,
! [SV141: a,SV76: a] :
( ( ! [SY449: a] :
( ( ( plus_plus_a @ SV76 @ SV141 )
!= ( plus_plus_a @ SV76 @ SY449 ) )
| ( SV141 = SY449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(710,plain,
! [SV142: product_prod_a_a,SV77: a,SV1: real] :
( ( ( real_V296206913od_a_a @ SV1 @ ( produc1299253312od_a_a @ SV77 @ SV142 ) )
= ( produc1299253312od_a_a @ ( real_V1035702895aleR_a @ SV1 @ SV77 ) @ ( real_V543523736od_a_a @ SV1 @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(711,plain,
! [SV143: real,SV78: a,SV2: real] :
( ( ( real_V512797224a_real @ SV2 @ ( product_Pair_a_real @ SV78 @ SV143 ) )
= ( product_Pair_a_real @ ( real_V1035702895aleR_a @ SV2 @ SV78 ) @ ( real_V453051771R_real @ SV2 @ SV143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(712,plain,
! [SV144: a,SV79: product_prod_a_a,SV3: real] :
( ( ( real_V1538726831_a_a_a @ SV3 @ ( produc2061588782_a_a_a @ SV79 @ SV144 ) )
= ( produc2061588782_a_a_a @ ( real_V543523736od_a_a @ SV3 @ SV79 ) @ ( real_V1035702895aleR_a @ SV3 @ SV144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(713,plain,
! [SV145: a,SV80: real,SV4: real] :
( ( ( real_V1214981142real_a @ SV4 @ ( product_Pair_real_a @ SV80 @ SV145 ) )
= ( product_Pair_real_a @ ( real_V453051771R_real @ SV4 @ SV80 ) @ ( real_V1035702895aleR_a @ SV4 @ SV145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(714,plain,
! [SV146: a,SV81: a,SV5: real] :
( ( ( real_V543523736od_a_a @ SV5 @ ( product_Pair_a_a @ SV81 @ SV146 ) )
= ( product_Pair_a_a @ ( real_V1035702895aleR_a @ SV5 @ SV81 ) @ ( real_V1035702895aleR_a @ SV5 @ SV146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(715,plain,
! [SV147: product_prod_a_a,SV82: a,SV6: real] :
( ( ( real_V296206913od_a_a @ SV6 @ ( produc1299253312od_a_a @ SV82 @ SV147 ) )
= ( produc1299253312od_a_a @ ( real_V1035702895aleR_a @ SV6 @ SV82 ) @ ( real_V543523736od_a_a @ SV6 @ SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(716,plain,
! [SV148: real,SV83: a,SV7: real] :
( ( ( real_V512797224a_real @ SV7 @ ( product_Pair_a_real @ SV83 @ SV148 ) )
= ( product_Pair_a_real @ ( real_V1035702895aleR_a @ SV7 @ SV83 ) @ ( real_V453051771R_real @ SV7 @ SV148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(717,plain,
! [SV149: a,SV84: product_prod_a_a,SV8: real] :
( ( ( real_V1538726831_a_a_a @ SV8 @ ( produc2061588782_a_a_a @ SV84 @ SV149 ) )
= ( produc2061588782_a_a_a @ ( real_V543523736od_a_a @ SV8 @ SV84 ) @ ( real_V1035702895aleR_a @ SV8 @ SV149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(718,plain,
! [SV150: a,SV85: real,SV9: real] :
( ( ( real_V1214981142real_a @ SV9 @ ( product_Pair_real_a @ SV85 @ SV150 ) )
= ( product_Pair_real_a @ ( real_V453051771R_real @ SV9 @ SV85 ) @ ( real_V1035702895aleR_a @ SV9 @ SV150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(719,plain,
! [SV151: a,SV86: a,SV10: real] :
( ( ( real_V543523736od_a_a @ SV10 @ ( product_Pair_a_a @ SV86 @ SV151 ) )
= ( product_Pair_a_a @ ( real_V1035702895aleR_a @ SV10 @ SV86 ) @ ( real_V1035702895aleR_a @ SV10 @ SV151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(720,plain,
! [SV152: a,SV87: a,SV11: a] :
( ( ! [SY450: a] :
( ( plus_p1505579230od_a_a @ ( product_Pair_a_a @ SV11 @ SV87 ) @ ( product_Pair_a_a @ SV152 @ SY450 ) )
= ( product_Pair_a_a @ ( plus_plus_a @ SV11 @ SV152 ) @ ( plus_plus_a @ SV87 @ SY450 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(721,plain,
! [SV153: a,SV88: real,SV12: a] :
( ( ! [SY451: real] :
( ( plus_p541014626a_real @ ( product_Pair_a_real @ SV12 @ SV88 ) @ ( product_Pair_a_real @ SV153 @ SY451 ) )
= ( product_Pair_a_real @ ( plus_plus_a @ SV12 @ SV153 ) @ ( plus_plus_real @ SV88 @ SY451 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[652]) ).
thf(722,plain,
! [SV154: real,SV89: a,SV13: real] :
( ( ! [SY452: a] :
( ( plus_p1243198544real_a @ ( product_Pair_real_a @ SV13 @ SV89 ) @ ( product_Pair_real_a @ SV154 @ SY452 ) )
= ( product_Pair_real_a @ ( plus_plus_real @ SV13 @ SV154 ) @ ( plus_plus_a @ SV89 @ SY452 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(723,plain,
! [SV155: a,SV90: set_real,SV14: a] :
( ( ! [SY453: set_real] :
( ( plus_p1745648536t_real @ ( produc1391501065t_real @ SV14 @ SV90 ) @ ( produc1391501065t_real @ SV155 @ SY453 ) )
= ( produc1391501065t_real @ ( plus_plus_a @ SV14 @ SV155 ) @ ( plus_plus_set_real @ SV90 @ SY453 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(724,plain,
! [SV156: a,SV91: set_a,SV15: a] :
( ( ! [SY454: set_a] :
( ( plus_p1265825342_set_a @ ( product_Pair_a_set_a @ SV15 @ SV91 ) @ ( product_Pair_a_set_a @ SV156 @ SY454 ) )
= ( product_Pair_a_set_a @ ( plus_plus_a @ SV15 @ SV156 ) @ ( plus_plus_set_a @ SV91 @ SY454 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(725,plain,
! [SV157: set_real,SV92: a,SV16: set_real] :
( ( ! [SY455: a] :
( ( plus_p1582417306real_a @ ( produc617496131real_a @ SV16 @ SV92 ) @ ( produc617496131real_a @ SV157 @ SY455 ) )
= ( produc617496131real_a @ ( plus_plus_set_real @ SV16 @ SV157 ) @ ( plus_plus_a @ SV92 @ SY455 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(726,plain,
! [SV158: a,SV93: a,SV17: a] :
( ( ( ( plus_plus_a @ SV17 @ SV93 )
= ( plus_plus_a @ SV17 @ SV158 ) )
= ( SV93 = SV158 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(727,plain,
! [SV159: a,SV94: a,SV18: a] :
( ( ( ( plus_plus_a @ SV18 @ SV94 )
= ( plus_plus_a @ SV159 @ SV94 ) )
= ( SV18 = SV159 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(728,plain,
! [SV95: a,SV19: a] :
( ( ~ ( ( SV19
= ( plus_plus_a @ SV19 @ SV95 ) )
| ( SV95 = zero_zero_a ) )
| ~ ( ( SV19
!= ( plus_plus_a @ SV19 @ SV95 ) )
| ( SV95 != zero_zero_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[659]) ).
thf(729,plain,
! [SV95: a,SV19: a] :
( ( ( SV19
= ( plus_plus_a @ SV19 @ SV95 ) )
= ( SV95 = zero_zero_a ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[659]) ).
thf(730,plain,
! [SV96: a,SV20: a] :
( ( ~ ( ( SV20
= ( plus_plus_a @ SV96 @ SV20 ) )
| ( SV96 = zero_zero_a ) )
| ~ ( ( SV20
!= ( plus_plus_a @ SV96 @ SV20 ) )
| ( SV96 != zero_zero_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[660]) ).
thf(731,plain,
! [SV96: a,SV20: a] :
( ( ( SV20
= ( plus_plus_a @ SV96 @ SV20 ) )
= ( SV96 = zero_zero_a ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[660]) ).
thf(732,plain,
! [SV97: a,SV21: a] :
( ( ~ ( ( ( plus_plus_a @ SV21 @ SV97 )
= SV21 )
| ( SV97 = zero_zero_a ) )
| ~ ( ( ( plus_plus_a @ SV21 @ SV97 )
!= SV21 )
| ( SV97 != zero_zero_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[661]) ).
thf(733,plain,
! [SV97: a,SV21: a] :
( ( ( ( plus_plus_a @ SV21 @ SV97 )
= SV21 )
= ( SV97 = zero_zero_a ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[661]) ).
thf(734,plain,
! [SV98: a,SV22: a] :
( ( ~ ( ( ( plus_plus_a @ SV22 @ SV98 )
= SV98 )
| ( SV22 = zero_zero_a ) )
| ~ ( ( ( plus_plus_a @ SV22 @ SV98 )
!= SV98 )
| ( SV22 != zero_zero_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[662]) ).
thf(735,plain,
! [SV98: a,SV22: a] :
( ( ( ( plus_plus_a @ SV22 @ SV98 )
= SV98 )
= ( SV22 = zero_zero_a ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[662]) ).
thf(736,plain,
! [SV99: product_prod_a_a > $o,SV25: product_prod_a_a] :
( ( ~ ( ( member449909584od_a_a @ SV25 @ ( collec645855634od_a_a @ SV99 ) )
| ( SV99 @ SV25 ) )
| ~ ( ~ ( member449909584od_a_a @ SV25 @ ( collec645855634od_a_a @ SV99 ) )
| ~ ( SV99 @ SV25 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[663]) ).
thf(737,plain,
! [SV99: product_prod_a_a > $o,SV25: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV25 @ ( collec645855634od_a_a @ SV99 ) )
= ( SV99 @ SV25 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[663]) ).
thf(738,plain,
! [SV160: a,SV100: a,SV30: a] :
( ( ( plus_plus_a @ SV30 @ ( plus_plus_a @ SV100 @ SV160 ) )
= ( plus_plus_a @ SV100 @ ( plus_plus_a @ SV30 @ SV160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(739,plain,
! [SV101: a] :
( ( ! [SV161: a] :
( ( plus_plus_a @ SV101 @ SV161 )
= ( plus_plus_a @ SV161 @ SV101 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[665]) ).
thf(740,plain,
! [SV101: a] :
( ( ( plus_plus_a @ SV101 )
= ( ^ [SY395: a] : ( plus_plus_a @ SY395 @ SV101 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[665]) ).
thf(741,plain,
! [SV162: a,SV102: a,SV32: a] :
( ( ( ( plus_plus_a @ SV32 @ SV102 )
= ( plus_plus_a @ SV162 @ SV102 ) )
= ( SV32 = SV162 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(742,plain,
! [SV163: a,SV103: a,SV33: a] :
( ( ( ( plus_plus_a @ SV33 @ SV103 )
= ( plus_plus_a @ SV33 @ SV163 ) )
= ( SV103 = SV163 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(743,plain,
! [SV164: a,SV104: a,SV34: a] :
( ( ( plus_plus_a @ ( plus_plus_a @ SV34 @ SV104 ) @ SV164 )
= ( plus_plus_a @ SV34 @ ( plus_plus_a @ SV104 @ SV164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(744,plain,
! [SV165: a,SV105: a,SV35: a] :
( ( ( plus_plus_a @ ( plus_plus_a @ SV35 @ SV105 ) @ SV165 )
= ( plus_plus_a @ SV35 @ ( plus_plus_a @ SV105 @ SV165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(745,plain,
! [SV166: a,SV106: real,SV36: a] :
( ( ( ( plus_plus_a @ SV36 @ ( real_V1035702895aleR_a @ SV106 @ SV166 ) )
= ( plus_plus_a @ SV166 @ ( real_V1035702895aleR_a @ SV106 @ SV36 ) ) )
= ( ( SV166 = SV36 )
| ( SV106 = one_one_real ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(746,plain,
! [SV107: a,SV38: real] :
( ( ~ ( ( ( real_V1035702895aleR_a @ SV38 @ SV107 )
= zero_zero_a )
| ( SV38 = zero_zero_real )
| ( SV107 = zero_zero_a ) )
| ~ ( ( ( real_V1035702895aleR_a @ SV38 @ SV107 )
!= zero_zero_a )
| ~ ( ( SV38 = zero_zero_real )
| ( SV107 = zero_zero_a ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[671]) ).
thf(747,plain,
! [SV107: a,SV38: real] :
( ( ( ( real_V1035702895aleR_a @ SV38 @ SV107 )
= zero_zero_a )
= ( ( SV38 = zero_zero_real )
| ( SV107 = zero_zero_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[671]) ).
thf(748,plain,
! [SV167: a,SV108: a,SV40: real] :
( ( ( ( real_V1035702895aleR_a @ SV40 @ SV108 )
= ( real_V1035702895aleR_a @ SV40 @ SV167 ) )
= ( ( SV108 = SV167 )
| ( SV40 = zero_zero_real ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(749,plain,
! [SV168: real,SV109: a,SV41: real] :
( ( ( ( real_V1035702895aleR_a @ SV41 @ SV109 )
= ( real_V1035702895aleR_a @ SV168 @ SV109 ) )
= ( ( SV41 = SV168 )
| ( SV109 = zero_zero_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(750,plain,
! [SV169: a,SV110: real,SV43: real] :
( ( ( real_V1035702895aleR_a @ SV43 @ ( real_V1035702895aleR_a @ SV110 @ SV169 ) )
= ( real_V1035702895aleR_a @ SV110 @ ( real_V1035702895aleR_a @ SV43 @ SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(751,plain,
! [SV170: a,SV111: a,SV44: real] :
( ( ( real_V1035702895aleR_a @ SV44 @ ( plus_plus_a @ SV111 @ SV170 ) )
= ( plus_plus_a @ ( real_V1035702895aleR_a @ SV44 @ SV111 ) @ ( real_V1035702895aleR_a @ SV44 @ SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(752,plain,
! [SV171: a,SV112: real,SV45: real] :
( ( ( real_V1035702895aleR_a @ ( plus_plus_real @ SV45 @ SV112 ) @ SV171 )
= ( plus_plus_a @ ( real_V1035702895aleR_a @ SV45 @ SV171 ) @ ( real_V1035702895aleR_a @ SV112 @ SV171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(753,plain,
! [SV172: a,SV113: real,SV46: real] :
( ( ( real_V1035702895aleR_a @ ( plus_plus_real @ SV46 @ SV113 ) @ SV172 )
= ( plus_plus_a @ ( real_V1035702895aleR_a @ SV46 @ SV172 ) @ ( real_V1035702895aleR_a @ SV113 @ SV172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(754,plain,
! [SV173: a,SV114: a,SV47: a] :
( ( ! [SY456: a] :
( ( ( product_Pair_a_a @ SV47 @ SV114 )
= ( product_Pair_a_a @ SV173 @ SY456 ) )
= ( ~ ( ( SV47 != SV173 )
| ( SV114 != SY456 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(755,plain,
! [SV174: product_prod_a_a,SV115: set_Product_prod_a_a,SV48: set_Product_prod_a_a] :
( ( ~ ( ord_le108336051od_a_a @ SV48 @ SV115 )
| ~ ( member449909584od_a_a @ SV174 @ SV48 )
| ( member449909584od_a_a @ SV174 @ SV115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(756,plain,
! [SV175: set_Product_prod_a_a,SV116: set_Product_prod_a_a,SV49: product_prod_a_a] :
( ( ~ ( member449909584od_a_a @ SV49 @ ( plus_p634297534od_a_a @ SV116 @ SV175 ) )
| ~ ! [SY457: product_prod_a_a,SY458: product_prod_a_a] :
( ( SV49
!= ( plus_p1505579230od_a_a @ SY457 @ SY458 ) )
| ~ ( member449909584od_a_a @ SY457 @ SV116 )
| ~ ( member449909584od_a_a @ SY458 @ SV175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(757,plain,
! [SV176: product_prod_a_a,SV117: set_Product_prod_a_a,SV50: product_prod_a_a] :
( ( ! [SY459: set_Product_prod_a_a] :
( ~ ( member449909584od_a_a @ SV50 @ SV117 )
| ~ ( member449909584od_a_a @ SV176 @ SY459 )
| ( member449909584od_a_a @ ( plus_p1505579230od_a_a @ SV50 @ SV176 ) @ ( plus_p634297534od_a_a @ SV117 @ SY459 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(758,plain,
! [SV177: a,SV118: set_a,SV51: a] :
( ( ! [SY460: set_a] :
( ~ ( member_a @ SV51 @ SV118 )
| ~ ( member_a @ SV177 @ SY460 )
| ( member_a @ ( plus_plus_a @ SV51 @ SV177 ) @ ( plus_plus_set_a @ SV118 @ SY460 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(759,plain,
! [SV178: a,SV119: a,SV52: a] :
( ( ! [SY461: a] :
( ( ( product_Pair_a_a @ SV52 @ SV119 )
!= ( product_Pair_a_a @ SV178 @ SY461 ) )
| ~ ( ( SV52 != SV178 )
| ( SV119 != SY461 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(760,plain,
! [SV179: real,SV120: a,SV53: real] :
( ( ! [SY462: a] :
( ( ( plus_plus_a @ ( real_V1035702895aleR_a @ SV53 @ SV120 ) @ ( real_V1035702895aleR_a @ SV179 @ SY462 ) )
!= ( plus_plus_a @ ( real_V1035702895aleR_a @ SV53 @ SY462 ) @ ( real_V1035702895aleR_a @ SV179 @ SV120 ) ) )
| ~ ( ( SV53 != SV179 ) )
| ( SY462 = SV120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(761,plain,
( ( ( ~ ( ( u != zero_zero_real ) )
| ~ ( ( u != one_one_real ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[685]) ).
thf(762,plain,
! [SV121: set_Product_prod_a_a] :
( ( ! [SV180: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ SV121 @ SV180 )
= ( ! [SY463: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY463 @ SV121 )
| ( member449909584od_a_a @ SY463 @ SV180 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[686]) ).
thf(763,plain,
! [SV121: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV121 )
= ( ^ [SY421: set_Product_prod_a_a] :
! [SY422: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY422 @ SV121 )
| ( member449909584od_a_a @ SY422 @ SY421 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[686]) ).
thf(764,plain,
! [SV181: set_a,SV122: set_a,SV55: a] :
( ( ~ ( member_a @ SV55 @ ( plus_plus_set_a @ SV122 @ SV181 ) )
| ~ ! [SY464: a,SY465: a] :
( ( SV55
!= ( plus_plus_a @ SY464 @ SY465 ) )
| ~ ( member_a @ SY464 @ SV122 )
| ~ ( member_a @ SY465 @ SV181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(765,plain,
! [SV182: a,SV123: a,SV56: a] :
( ( ! [SY466: a] :
( ( ( product_Pair_a_a @ SV56 @ SV123 )
= ( product_Pair_a_a @ SV182 @ SY466 ) )
= ( ~ ( ( SV56 != SV182 )
| ( SV123 != SY466 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(766,plain,
! [SV183: a,SV124: a,SV57: a] :
( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV124 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV57 ) @ relation ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV183 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV183 @ SV124 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV183 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV183 @ SV57 ) @ relation ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(767,plain,
! [SV184: set_Product_prod_a_a,SV125: set_Product_prod_a_a,SV58: set_Product_prod_a_a] :
( ( ! [SY467: set_Product_prod_a_a,SY468: product_prod_a_a] :
( ~ ( ord_le1824328871od_a_a @ SV58 @ SV125 )
| ~ ( ord_le1824328871od_a_a @ SV184 @ SY467 )
| ~ ( member449909584od_a_a @ SY468 @ ( plus_p634297534od_a_a @ SV58 @ SV184 ) )
| ( member449909584od_a_a @ SY468 @ ( plus_p634297534od_a_a @ SV125 @ SY467 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(768,plain,
! [SV126: product_prod_a_a,SV59: product_prod_a_a > $o] :
( ( ( ~ ! [SY334: a,SY335: a] : ( SV59 @ ( product_Pair_a_a @ SY334 @ SY335 ) ) )
= $true )
| ( ( SV59 @ SV126 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[691]) ).
thf(769,plain,
! [SV127: set_Product_prod_a_a,SV60: set_Product_prod_a_a] :
( ( ( ~ ! [SY434: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY434 @ SV60 )
| ( member449909584od_a_a @ SY434 @ SV127 ) ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV60 @ SV127 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[692]) ).
thf(770,plain,
! [SV185: a,SV128: a,SV61: real] :
( ( ~ ( ( SV61 != zero_zero_real ) )
| ( ( real_V1035702895aleR_a @ SV61 @ SV128 )
!= ( real_V1035702895aleR_a @ SV61 @ SV185 ) )
| ( SV128 = SV185 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(771,plain,
! [SV186: a,SV129: a,SV62: a] :
( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV62 @ SV129 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV129 @ SV62 ) @ relation ) )
| ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV129 @ SV186 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV186 @ SV129 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV62 @ SV186 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV186 @ SV62 ) @ relation ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(772,plain,
! [SV63: product_prod_a_a] :
( ( ! [SY469: a] :
( SV63
!= ( product_Pair_a_a @ ( sK1_SY342 @ SV63 ) @ SY469 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[696]) ).
thf(773,plain,
! [SV130: a,SV64: a] :
( ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV64 @ SV130 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV64 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV64 ) @ relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[697]) ).
thf(774,plain,
! [SV187: real,SV131: real,SV65: a] :
( ( ~ ( ( SV65 != zero_zero_a ) )
| ( ( real_V1035702895aleR_a @ SV131 @ SV65 )
!= ( real_V1035702895aleR_a @ SV187 @ SV65 ) )
| ( SV131 = SV187 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(775,plain,
! [SV66: product_prod_a_a] :
( ( ~ ~ ! [SY470: a] :
( SV66
!= ( product_Pair_a_a @ ( sK2_SY347 @ SV66 ) @ SY470 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[699]) ).
thf(776,plain,
! [SV188: a,SV132: a,SV67: a] :
( ( ! [SY471: a] :
( ( SV67
!= ( plus_plus_a @ SV132 @ SV188 ) )
| ( ( plus_plus_a @ SV67 @ SY471 )
= ( plus_plus_a @ SV132 @ ( plus_plus_a @ SV188 @ SY471 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(777,plain,
! [SV133: product_prod_a_a,SV68: product_prod_a_a > $o] :
( ( ( ~ ! [SY353: a,SY354: a] : ( SV68 @ ( product_Pair_a_a @ SY353 @ SY354 ) ) )
= $true )
| ( ( SV68 @ SV133 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[701]) ).
thf(778,plain,
! [SV189: product_prod_a_a,SV134: set_Product_prod_a_a,SV69: set_Product_prod_a_a] :
( ( ~ ( ord_le1824328871od_a_a @ SV69 @ SV134 )
| ~ ( member449909584od_a_a @ SV189 @ SV69 )
| ( member449909584od_a_a @ SV189 @ SV134 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(779,plain,
! [SV135: a,SV70: a] :
( ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV70 @ SV135 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV135 @ SV70 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV70 @ SV135 ) @ relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[703]) ).
thf(780,plain,
! [SV136: set_Product_prod_a_a,SV71: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ zero_z950819678od_a_a @ SV71 ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV136 @ ( plus_p634297534od_a_a @ SV71 @ SV136 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[704]) ).
thf(781,plain,
! [SV190: a,SV137: a,SV72: a] :
( ( ! [SY472: a] :
( ( SV72
!= ( plus_plus_a @ SV137 @ SV190 ) )
| ( ( plus_plus_a @ SY472 @ SV72 )
= ( plus_plus_a @ SV137 @ ( plus_plus_a @ SY472 @ SV190 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(782,plain,
! [SV191: product_prod_a_a,SV138: set_Product_prod_a_a,SV73: set_Product_prod_a_a] :
( ( ~ ( ord_le1824328871od_a_a @ SV73 @ SV138 )
| ~ ( member449909584od_a_a @ SV191 @ SV73 )
| ( member449909584od_a_a @ SV191 @ SV138 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(783,plain,
! [SV192: a,SV139: a,SV74: a] :
( ( ( ( plus_plus_a @ SV74 @ SV139 )
!= ( plus_plus_a @ SV192 @ SV139 ) )
| ( SV74 = SV192 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(784,plain,
! [SV140: set_Product_prod_a_a] :
( ( ! [SV193: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ SV140 @ SV193 )
= ( ! [SY473: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY473 @ SV140 )
| ( member449909584od_a_a @ SY473 @ SV193 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[708]) ).
thf(785,plain,
! [SV140: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV140 )
= ( ^ [SY447: set_Product_prod_a_a] :
! [SY448: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY448 @ SV140 )
| ( member449909584od_a_a @ SY448 @ SY447 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[708]) ).
thf(786,plain,
! [SV194: a,SV141: a,SV76: a] :
( ( ( ( plus_plus_a @ SV76 @ SV141 )
!= ( plus_plus_a @ SV76 @ SV194 ) )
| ( SV141 = SV194 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(787,plain,
! [SV195: a,SV152: a,SV87: a,SV11: a] :
( ( ( plus_p1505579230od_a_a @ ( product_Pair_a_a @ SV11 @ SV87 ) @ ( product_Pair_a_a @ SV152 @ SV195 ) )
= ( product_Pair_a_a @ ( plus_plus_a @ SV11 @ SV152 ) @ ( plus_plus_a @ SV87 @ SV195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[720]) ).
thf(788,plain,
! [SV196: real,SV153: a,SV88: real,SV12: a] :
( ( ( plus_p541014626a_real @ ( product_Pair_a_real @ SV12 @ SV88 ) @ ( product_Pair_a_real @ SV153 @ SV196 ) )
= ( product_Pair_a_real @ ( plus_plus_a @ SV12 @ SV153 ) @ ( plus_plus_real @ SV88 @ SV196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(789,plain,
! [SV197: a,SV154: real,SV89: a,SV13: real] :
( ( ( plus_p1243198544real_a @ ( product_Pair_real_a @ SV13 @ SV89 ) @ ( product_Pair_real_a @ SV154 @ SV197 ) )
= ( product_Pair_real_a @ ( plus_plus_real @ SV13 @ SV154 ) @ ( plus_plus_a @ SV89 @ SV197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(790,plain,
! [SV198: set_real,SV155: a,SV90: set_real,SV14: a] :
( ( ( plus_p1745648536t_real @ ( produc1391501065t_real @ SV14 @ SV90 ) @ ( produc1391501065t_real @ SV155 @ SV198 ) )
= ( produc1391501065t_real @ ( plus_plus_a @ SV14 @ SV155 ) @ ( plus_plus_set_real @ SV90 @ SV198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(791,plain,
! [SV199: set_a,SV156: a,SV91: set_a,SV15: a] :
( ( ( plus_p1265825342_set_a @ ( product_Pair_a_set_a @ SV15 @ SV91 ) @ ( product_Pair_a_set_a @ SV156 @ SV199 ) )
= ( product_Pair_a_set_a @ ( plus_plus_a @ SV15 @ SV156 ) @ ( plus_plus_set_a @ SV91 @ SV199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(792,plain,
! [SV200: a,SV157: set_real,SV92: a,SV16: set_real] :
( ( ( plus_p1582417306real_a @ ( produc617496131real_a @ SV16 @ SV92 ) @ ( produc617496131real_a @ SV157 @ SV200 ) )
= ( produc617496131real_a @ ( plus_plus_set_real @ SV16 @ SV157 ) @ ( plus_plus_a @ SV92 @ SV200 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(793,plain,
! [SV158: a,SV93: a,SV17: a] :
( ( ~ ( ( ( plus_plus_a @ SV17 @ SV93 )
= ( plus_plus_a @ SV17 @ SV158 ) )
| ( SV93 = SV158 ) )
| ~ ( ( ( plus_plus_a @ SV17 @ SV93 )
!= ( plus_plus_a @ SV17 @ SV158 ) )
| ( SV93 != SV158 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[726]) ).
thf(794,plain,
! [SV158: a,SV93: a,SV17: a] :
( ( ( ( plus_plus_a @ SV17 @ SV93 )
= ( plus_plus_a @ SV17 @ SV158 ) )
= ( SV93 = SV158 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[726]) ).
thf(795,plain,
! [SV159: a,SV94: a,SV18: a] :
( ( ~ ( ( ( plus_plus_a @ SV18 @ SV94 )
= ( plus_plus_a @ SV159 @ SV94 ) )
| ( SV18 = SV159 ) )
| ~ ( ( ( plus_plus_a @ SV18 @ SV94 )
!= ( plus_plus_a @ SV159 @ SV94 ) )
| ( SV18 != SV159 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[727]) ).
thf(796,plain,
! [SV159: a,SV94: a,SV18: a] :
( ( ( ( plus_plus_a @ SV18 @ SV94 )
= ( plus_plus_a @ SV159 @ SV94 ) )
= ( SV18 = SV159 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[727]) ).
thf(797,plain,
! [SV95: a,SV19: a] :
( ( ( ~ ( ( SV19
= ( plus_plus_a @ SV19 @ SV95 ) )
| ( SV95 = zero_zero_a ) ) )
= $true )
| ( ( ~ ( ( SV19
!= ( plus_plus_a @ SV19 @ SV95 ) )
| ( SV95 != zero_zero_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[728]) ).
thf(798,plain,
! [SV96: a,SV20: a] :
( ( ( ~ ( ( SV20
= ( plus_plus_a @ SV96 @ SV20 ) )
| ( SV96 = zero_zero_a ) ) )
= $true )
| ( ( ~ ( ( SV20
!= ( plus_plus_a @ SV96 @ SV20 ) )
| ( SV96 != zero_zero_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[730]) ).
thf(799,plain,
! [SV97: a,SV21: a] :
( ( ( ~ ( ( ( plus_plus_a @ SV21 @ SV97 )
= SV21 )
| ( SV97 = zero_zero_a ) ) )
= $true )
| ( ( ~ ( ( ( plus_plus_a @ SV21 @ SV97 )
!= SV21 )
| ( SV97 != zero_zero_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[732]) ).
thf(800,plain,
! [SV98: a,SV22: a] :
( ( ( ~ ( ( ( plus_plus_a @ SV22 @ SV98 )
= SV98 )
| ( SV22 = zero_zero_a ) ) )
= $true )
| ( ( ~ ( ( ( plus_plus_a @ SV22 @ SV98 )
!= SV98 )
| ( SV22 != zero_zero_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[734]) ).
thf(801,plain,
! [SV99: product_prod_a_a > $o,SV25: product_prod_a_a] :
( ( ( ~ ( ( member449909584od_a_a @ SV25 @ ( collec645855634od_a_a @ SV99 ) )
| ( SV99 @ SV25 ) ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ SV25 @ ( collec645855634od_a_a @ SV99 ) )
| ~ ( SV99 @ SV25 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[736]) ).
thf(802,plain,
! [SV201: a,SV101: a] :
( ( ( plus_plus_a @ SV101 @ SV201 )
= ( plus_plus_a @ SV201 @ SV101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(803,plain,
! [SV162: a,SV102: a,SV32: a] :
( ( ~ ( ( ( plus_plus_a @ SV32 @ SV102 )
= ( plus_plus_a @ SV162 @ SV102 ) )
| ( SV32 = SV162 ) )
| ~ ( ( ( plus_plus_a @ SV32 @ SV102 )
!= ( plus_plus_a @ SV162 @ SV102 ) )
| ( SV32 != SV162 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[741]) ).
thf(804,plain,
! [SV162: a,SV102: a,SV32: a] :
( ( ( ( plus_plus_a @ SV32 @ SV102 )
= ( plus_plus_a @ SV162 @ SV102 ) )
= ( SV32 = SV162 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[741]) ).
thf(805,plain,
! [SV163: a,SV103: a,SV33: a] :
( ( ~ ( ( ( plus_plus_a @ SV33 @ SV103 )
= ( plus_plus_a @ SV33 @ SV163 ) )
| ( SV103 = SV163 ) )
| ~ ( ( ( plus_plus_a @ SV33 @ SV103 )
!= ( plus_plus_a @ SV33 @ SV163 ) )
| ( SV103 != SV163 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[742]) ).
thf(806,plain,
! [SV163: a,SV103: a,SV33: a] :
( ( ( ( plus_plus_a @ SV33 @ SV103 )
= ( plus_plus_a @ SV33 @ SV163 ) )
= ( SV103 = SV163 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[742]) ).
thf(807,plain,
! [SV166: a,SV106: real,SV36: a] :
( ( ~ ( ( ( plus_plus_a @ SV36 @ ( real_V1035702895aleR_a @ SV106 @ SV166 ) )
= ( plus_plus_a @ SV166 @ ( real_V1035702895aleR_a @ SV106 @ SV36 ) ) )
| ( SV166 = SV36 )
| ( SV106 = one_one_real ) )
| ~ ( ( ( plus_plus_a @ SV36 @ ( real_V1035702895aleR_a @ SV106 @ SV166 ) )
!= ( plus_plus_a @ SV166 @ ( real_V1035702895aleR_a @ SV106 @ SV36 ) ) )
| ~ ( ( SV166 = SV36 )
| ( SV106 = one_one_real ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[745]) ).
thf(808,plain,
! [SV166: a,SV106: real,SV36: a] :
( ( ( ( plus_plus_a @ SV36 @ ( real_V1035702895aleR_a @ SV106 @ SV166 ) )
= ( plus_plus_a @ SV166 @ ( real_V1035702895aleR_a @ SV106 @ SV36 ) ) )
= ( ( SV166 = SV36 )
| ( SV106 = one_one_real ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[745]) ).
thf(809,plain,
! [SV107: a,SV38: real] :
( ( ( ~ ( ( ( real_V1035702895aleR_a @ SV38 @ SV107 )
= zero_zero_a )
| ( SV38 = zero_zero_real )
| ( SV107 = zero_zero_a ) ) )
= $true )
| ( ( ~ ( ( ( real_V1035702895aleR_a @ SV38 @ SV107 )
!= zero_zero_a )
| ~ ( ( SV38 = zero_zero_real )
| ( SV107 = zero_zero_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[746]) ).
thf(810,plain,
! [SV167: a,SV108: a,SV40: real] :
( ( ~ ( ( ( real_V1035702895aleR_a @ SV40 @ SV108 )
= ( real_V1035702895aleR_a @ SV40 @ SV167 ) )
| ( SV108 = SV167 )
| ( SV40 = zero_zero_real ) )
| ~ ( ( ( real_V1035702895aleR_a @ SV40 @ SV108 )
!= ( real_V1035702895aleR_a @ SV40 @ SV167 ) )
| ~ ( ( SV108 = SV167 )
| ( SV40 = zero_zero_real ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[748]) ).
thf(811,plain,
! [SV167: a,SV108: a,SV40: real] :
( ( ( ( real_V1035702895aleR_a @ SV40 @ SV108 )
= ( real_V1035702895aleR_a @ SV40 @ SV167 ) )
= ( ( SV108 = SV167 )
| ( SV40 = zero_zero_real ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[748]) ).
thf(812,plain,
! [SV168: real,SV109: a,SV41: real] :
( ( ~ ( ( ( real_V1035702895aleR_a @ SV41 @ SV109 )
= ( real_V1035702895aleR_a @ SV168 @ SV109 ) )
| ( SV41 = SV168 )
| ( SV109 = zero_zero_a ) )
| ~ ( ( ( real_V1035702895aleR_a @ SV41 @ SV109 )
!= ( real_V1035702895aleR_a @ SV168 @ SV109 ) )
| ~ ( ( SV41 = SV168 )
| ( SV109 = zero_zero_a ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[749]) ).
thf(813,plain,
! [SV168: real,SV109: a,SV41: real] :
( ( ( ( real_V1035702895aleR_a @ SV41 @ SV109 )
= ( real_V1035702895aleR_a @ SV168 @ SV109 ) )
= ( ( SV41 = SV168 )
| ( SV109 = zero_zero_a ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[749]) ).
thf(814,plain,
! [SV202: a,SV173: a,SV114: a,SV47: a] :
( ( ( ( product_Pair_a_a @ SV47 @ SV114 )
= ( product_Pair_a_a @ SV173 @ SV202 ) )
= ( ~ ( ( SV47 != SV173 )
| ( SV114 != SV202 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(815,plain,
! [SV174: product_prod_a_a,SV115: set_Product_prod_a_a,SV48: set_Product_prod_a_a] :
( ( ( ~ ( ord_le108336051od_a_a @ SV48 @ SV115 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ SV174 @ SV48 )
| ( member449909584od_a_a @ SV174 @ SV115 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[755]) ).
thf(816,plain,
! [SV175: set_Product_prod_a_a,SV116: set_Product_prod_a_a,SV49: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV49 @ ( plus_p634297534od_a_a @ SV116 @ SV175 ) ) )
= $true )
| ( ( ~ ! [SY457: product_prod_a_a,SY458: product_prod_a_a] :
( ( SV49
!= ( plus_p1505579230od_a_a @ SY457 @ SY458 ) )
| ~ ( member449909584od_a_a @ SY457 @ SV116 )
| ~ ( member449909584od_a_a @ SY458 @ SV175 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[756]) ).
thf(817,plain,
! [SV203: set_Product_prod_a_a,SV176: product_prod_a_a,SV117: set_Product_prod_a_a,SV50: product_prod_a_a] :
( ( ~ ( member449909584od_a_a @ SV50 @ SV117 )
| ~ ( member449909584od_a_a @ SV176 @ SV203 )
| ( member449909584od_a_a @ ( plus_p1505579230od_a_a @ SV50 @ SV176 ) @ ( plus_p634297534od_a_a @ SV117 @ SV203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(818,plain,
! [SV204: set_a,SV177: a,SV118: set_a,SV51: a] :
( ( ~ ( member_a @ SV51 @ SV118 )
| ~ ( member_a @ SV177 @ SV204 )
| ( member_a @ ( plus_plus_a @ SV51 @ SV177 ) @ ( plus_plus_set_a @ SV118 @ SV204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(819,plain,
! [SV205: a,SV178: a,SV119: a,SV52: a] :
( ( ( ( product_Pair_a_a @ SV52 @ SV119 )
!= ( product_Pair_a_a @ SV178 @ SV205 ) )
| ~ ( ( SV52 != SV178 )
| ( SV119 != SV205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(820,plain,
! [SV206: a,SV179: real,SV120: a,SV53: real] :
( ( ( ( plus_plus_a @ ( real_V1035702895aleR_a @ SV53 @ SV120 ) @ ( real_V1035702895aleR_a @ SV179 @ SV206 ) )
!= ( plus_plus_a @ ( real_V1035702895aleR_a @ SV53 @ SV206 ) @ ( real_V1035702895aleR_a @ SV179 @ SV120 ) ) )
| ~ ( ( SV53 != SV179 ) )
| ( SV206 = SV120 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(821,plain,
( ( ( ~ ( ( u != zero_zero_real ) ) )
= $true )
| ( ( ~ ( ( u != one_one_real ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[761]) ).
thf(822,plain,
! [SV207: set_Product_prod_a_a,SV121: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV121 @ SV207 )
= ( ! [SY474: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY474 @ SV121 )
| ( member449909584od_a_a @ SY474 @ SV207 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(823,plain,
! [SV181: set_a,SV122: set_a,SV55: a] :
( ( ( ~ ( member_a @ SV55 @ ( plus_plus_set_a @ SV122 @ SV181 ) ) )
= $true )
| ( ( ~ ! [SY464: a,SY465: a] :
( ( SV55
!= ( plus_plus_a @ SY464 @ SY465 ) )
| ~ ( member_a @ SY464 @ SV122 )
| ~ ( member_a @ SY465 @ SV181 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[764]) ).
thf(824,plain,
! [SV208: a,SV182: a,SV123: a,SV56: a] :
( ( ( ( product_Pair_a_a @ SV56 @ SV123 )
= ( product_Pair_a_a @ SV182 @ SV208 ) )
= ( ~ ( ( SV56 != SV182 )
| ( SV123 != SV208 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(825,plain,
! [SV183: a,SV124: a,SV57: a] :
( ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV124 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV57 ) @ relation ) ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV183 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV183 @ SV124 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV183 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV183 @ SV57 ) @ relation ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[766]) ).
thf(826,plain,
! [SV209: set_Product_prod_a_a,SV184: set_Product_prod_a_a,SV125: set_Product_prod_a_a,SV58: set_Product_prod_a_a] :
( ( ! [SY475: product_prod_a_a] :
( ~ ( ord_le1824328871od_a_a @ SV58 @ SV125 )
| ~ ( ord_le1824328871od_a_a @ SV184 @ SV209 )
| ~ ( member449909584od_a_a @ SY475 @ ( plus_p634297534od_a_a @ SV58 @ SV184 ) )
| ( member449909584od_a_a @ SY475 @ ( plus_p634297534od_a_a @ SV125 @ SV209 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[767]) ).
thf(827,plain,
! [SV126: product_prod_a_a,SV59: product_prod_a_a > $o] :
( ( ( ! [SY334: a,SY335: a] : ( SV59 @ ( product_Pair_a_a @ SY334 @ SY335 ) ) )
= $false )
| ( ( SV59 @ SV126 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[768]) ).
thf(828,plain,
! [SV127: set_Product_prod_a_a,SV60: set_Product_prod_a_a] :
( ( ( ! [SY434: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY434 @ SV60 )
| ( member449909584od_a_a @ SY434 @ SV127 ) ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV60 @ SV127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[769]) ).
thf(829,plain,
! [SV185: a,SV128: a,SV61: real] :
( ( ( ~ ( ( SV61 != zero_zero_real ) ) )
= $true )
| ( ( ( ( real_V1035702895aleR_a @ SV61 @ SV128 )
!= ( real_V1035702895aleR_a @ SV61 @ SV185 ) )
| ( SV128 = SV185 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[770]) ).
thf(830,plain,
! [SV186: a,SV129: a,SV62: a] :
( ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV62 @ SV129 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV129 @ SV62 ) @ relation ) ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV129 @ SV186 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV186 @ SV129 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV62 @ SV186 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV186 @ SV62 ) @ relation ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[771]) ).
thf(831,plain,
! [SV63: product_prod_a_a] :
( ( SV63
!= ( product_Pair_a_a @ ( sK1_SY342 @ SV63 ) @ ( sK3_SY469 @ SV63 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[772]) ).
thf(832,plain,
! [SV130: a,SV64: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV64 @ SV130 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV64 ) @ relation ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV64 ) @ relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[773]) ).
thf(833,plain,
! [SV187: real,SV131: real,SV65: a] :
( ( ( ~ ( ( SV65 != zero_zero_a ) ) )
= $true )
| ( ( ( ( real_V1035702895aleR_a @ SV131 @ SV65 )
!= ( real_V1035702895aleR_a @ SV187 @ SV65 ) )
| ( SV131 = SV187 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[774]) ).
thf(834,plain,
! [SV66: product_prod_a_a] :
( ( ~ ! [SY470: a] :
( SV66
!= ( product_Pair_a_a @ ( sK2_SY347 @ SV66 ) @ SY470 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[775]) ).
thf(835,plain,
! [SV210: a,SV188: a,SV132: a,SV67: a] :
( ( ( SV67
!= ( plus_plus_a @ SV132 @ SV188 ) )
| ( ( plus_plus_a @ SV67 @ SV210 )
= ( plus_plus_a @ SV132 @ ( plus_plus_a @ SV188 @ SV210 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[776]) ).
thf(836,plain,
! [SV133: product_prod_a_a,SV68: product_prod_a_a > $o] :
( ( ( ! [SY353: a,SY354: a] : ( SV68 @ ( product_Pair_a_a @ SY353 @ SY354 ) ) )
= $false )
| ( ( SV68 @ SV133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[777]) ).
thf(837,plain,
! [SV189: product_prod_a_a,SV134: set_Product_prod_a_a,SV69: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV69 @ SV134 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ SV189 @ SV69 )
| ( member449909584od_a_a @ SV189 @ SV134 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[778]) ).
thf(838,plain,
! [SV135: a,SV70: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV70 @ SV135 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV135 @ SV70 ) @ relation ) ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV70 @ SV135 ) @ relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[779]) ).
thf(839,plain,
! [SV136: set_Product_prod_a_a,SV71: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ zero_z950819678od_a_a @ SV71 )
= $false )
| ( ( ord_le1824328871od_a_a @ SV136 @ ( plus_p634297534od_a_a @ SV71 @ SV136 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[780]) ).
thf(840,plain,
! [SV211: a,SV190: a,SV137: a,SV72: a] :
( ( ( SV72
!= ( plus_plus_a @ SV137 @ SV190 ) )
| ( ( plus_plus_a @ SV211 @ SV72 )
= ( plus_plus_a @ SV137 @ ( plus_plus_a @ SV211 @ SV190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[781]) ).
thf(841,plain,
! [SV191: product_prod_a_a,SV138: set_Product_prod_a_a,SV73: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV73 @ SV138 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ SV191 @ SV73 )
| ( member449909584od_a_a @ SV191 @ SV138 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[782]) ).
thf(842,plain,
! [SV192: a,SV139: a,SV74: a] :
( ( ( ( plus_plus_a @ SV74 @ SV139 )
!= ( plus_plus_a @ SV192 @ SV139 ) )
= $true )
| ( ( SV74 = SV192 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[783]) ).
thf(843,plain,
! [SV212: set_Product_prod_a_a,SV140: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV140 @ SV212 )
= ( ! [SY476: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY476 @ SV140 )
| ( member449909584od_a_a @ SY476 @ SV212 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[784]) ).
thf(844,plain,
! [SV194: a,SV141: a,SV76: a] :
( ( ( ( plus_plus_a @ SV76 @ SV141 )
!= ( plus_plus_a @ SV76 @ SV194 ) )
= $true )
| ( ( SV141 = SV194 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[786]) ).
thf(845,plain,
! [SV158: a,SV93: a,SV17: a] :
( ( ( ~ ( ( ( plus_plus_a @ SV17 @ SV93 )
= ( plus_plus_a @ SV17 @ SV158 ) )
| ( SV93 = SV158 ) ) )
= $true )
| ( ( ~ ( ( ( plus_plus_a @ SV17 @ SV93 )
!= ( plus_plus_a @ SV17 @ SV158 ) )
| ( SV93 != SV158 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[793]) ).
thf(846,plain,
! [SV159: a,SV94: a,SV18: a] :
( ( ( ~ ( ( ( plus_plus_a @ SV18 @ SV94 )
= ( plus_plus_a @ SV159 @ SV94 ) )
| ( SV18 = SV159 ) ) )
= $true )
| ( ( ~ ( ( ( plus_plus_a @ SV18 @ SV94 )
!= ( plus_plus_a @ SV159 @ SV94 ) )
| ( SV18 != SV159 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[795]) ).
thf(847,plain,
! [SV95: a,SV19: a] :
( ( ( ( SV19
= ( plus_plus_a @ SV19 @ SV95 ) )
| ( SV95 = zero_zero_a ) )
= $false )
| ( ( ~ ( ( SV19
!= ( plus_plus_a @ SV19 @ SV95 ) )
| ( SV95 != zero_zero_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[797]) ).
thf(848,plain,
! [SV96: a,SV20: a] :
( ( ( ( SV20
= ( plus_plus_a @ SV96 @ SV20 ) )
| ( SV96 = zero_zero_a ) )
= $false )
| ( ( ~ ( ( SV20
!= ( plus_plus_a @ SV96 @ SV20 ) )
| ( SV96 != zero_zero_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[798]) ).
thf(849,plain,
! [SV97: a,SV21: a] :
( ( ( ( ( plus_plus_a @ SV21 @ SV97 )
= SV21 )
| ( SV97 = zero_zero_a ) )
= $false )
| ( ( ~ ( ( ( plus_plus_a @ SV21 @ SV97 )
!= SV21 )
| ( SV97 != zero_zero_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[799]) ).
thf(850,plain,
! [SV98: a,SV22: a] :
( ( ( ( ( plus_plus_a @ SV22 @ SV98 )
= SV98 )
| ( SV22 = zero_zero_a ) )
= $false )
| ( ( ~ ( ( ( plus_plus_a @ SV22 @ SV98 )
!= SV98 )
| ( SV22 != zero_zero_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[800]) ).
thf(851,plain,
! [SV99: product_prod_a_a > $o,SV25: product_prod_a_a] :
( ( ( ( member449909584od_a_a @ SV25 @ ( collec645855634od_a_a @ SV99 ) )
| ( SV99 @ SV25 ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ SV25 @ ( collec645855634od_a_a @ SV99 ) )
| ~ ( SV99 @ SV25 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[801]) ).
thf(852,plain,
! [SV162: a,SV102: a,SV32: a] :
( ( ( ~ ( ( ( plus_plus_a @ SV32 @ SV102 )
= ( plus_plus_a @ SV162 @ SV102 ) )
| ( SV32 = SV162 ) ) )
= $true )
| ( ( ~ ( ( ( plus_plus_a @ SV32 @ SV102 )
!= ( plus_plus_a @ SV162 @ SV102 ) )
| ( SV32 != SV162 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[803]) ).
thf(853,plain,
! [SV163: a,SV103: a,SV33: a] :
( ( ( ~ ( ( ( plus_plus_a @ SV33 @ SV103 )
= ( plus_plus_a @ SV33 @ SV163 ) )
| ( SV103 = SV163 ) ) )
= $true )
| ( ( ~ ( ( ( plus_plus_a @ SV33 @ SV103 )
!= ( plus_plus_a @ SV33 @ SV163 ) )
| ( SV103 != SV163 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[805]) ).
thf(854,plain,
! [SV166: a,SV106: real,SV36: a] :
( ( ( ~ ( ( ( plus_plus_a @ SV36 @ ( real_V1035702895aleR_a @ SV106 @ SV166 ) )
= ( plus_plus_a @ SV166 @ ( real_V1035702895aleR_a @ SV106 @ SV36 ) ) )
| ( SV166 = SV36 )
| ( SV106 = one_one_real ) ) )
= $true )
| ( ( ~ ( ( ( plus_plus_a @ SV36 @ ( real_V1035702895aleR_a @ SV106 @ SV166 ) )
!= ( plus_plus_a @ SV166 @ ( real_V1035702895aleR_a @ SV106 @ SV36 ) ) )
| ~ ( ( SV166 = SV36 )
| ( SV106 = one_one_real ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[807]) ).
thf(855,plain,
! [SV107: a,SV38: real] :
( ( ( ( ( real_V1035702895aleR_a @ SV38 @ SV107 )
= zero_zero_a )
| ( SV38 = zero_zero_real )
| ( SV107 = zero_zero_a ) )
= $false )
| ( ( ~ ( ( ( real_V1035702895aleR_a @ SV38 @ SV107 )
!= zero_zero_a )
| ~ ( ( SV38 = zero_zero_real )
| ( SV107 = zero_zero_a ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[809]) ).
thf(856,plain,
! [SV167: a,SV108: a,SV40: real] :
( ( ( ~ ( ( ( real_V1035702895aleR_a @ SV40 @ SV108 )
= ( real_V1035702895aleR_a @ SV40 @ SV167 ) )
| ( SV108 = SV167 )
| ( SV40 = zero_zero_real ) ) )
= $true )
| ( ( ~ ( ( ( real_V1035702895aleR_a @ SV40 @ SV108 )
!= ( real_V1035702895aleR_a @ SV40 @ SV167 ) )
| ~ ( ( SV108 = SV167 )
| ( SV40 = zero_zero_real ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[810]) ).
thf(857,plain,
! [SV168: real,SV109: a,SV41: real] :
( ( ( ~ ( ( ( real_V1035702895aleR_a @ SV41 @ SV109 )
= ( real_V1035702895aleR_a @ SV168 @ SV109 ) )
| ( SV41 = SV168 )
| ( SV109 = zero_zero_a ) ) )
= $true )
| ( ( ~ ( ( ( real_V1035702895aleR_a @ SV41 @ SV109 )
!= ( real_V1035702895aleR_a @ SV168 @ SV109 ) )
| ~ ( ( SV41 = SV168 )
| ( SV109 = zero_zero_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[812]) ).
thf(858,plain,
! [SV202: a,SV173: a,SV114: a,SV47: a] :
( ( ~ ( ( ( product_Pair_a_a @ SV47 @ SV114 )
= ( product_Pair_a_a @ SV173 @ SV202 ) )
| ~ ( ( SV47 != SV173 )
| ( SV114 != SV202 ) ) )
| ~ ( ( ( product_Pair_a_a @ SV47 @ SV114 )
!= ( product_Pair_a_a @ SV173 @ SV202 ) )
| ~ ~ ( ( SV47 != SV173 )
| ( SV114 != SV202 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[814]) ).
thf(859,plain,
! [SV202: a,SV173: a,SV114: a,SV47: a] :
( ( ( ( product_Pair_a_a @ SV47 @ SV114 )
= ( product_Pair_a_a @ SV173 @ SV202 ) )
= ( ~ ( ( SV47 != SV173 )
| ( SV114 != SV202 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[814]) ).
thf(860,plain,
! [SV174: product_prod_a_a,SV115: set_Product_prod_a_a,SV48: set_Product_prod_a_a] :
( ( ( ord_le108336051od_a_a @ SV48 @ SV115 )
= $false )
| ( ( ~ ( member449909584od_a_a @ SV174 @ SV48 )
| ( member449909584od_a_a @ SV174 @ SV115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[815]) ).
thf(861,plain,
! [SV175: set_Product_prod_a_a,SV116: set_Product_prod_a_a,SV49: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV49 @ ( plus_p634297534od_a_a @ SV116 @ SV175 ) )
= $false )
| ( ( ~ ! [SY457: product_prod_a_a,SY458: product_prod_a_a] :
( ( SV49
!= ( plus_p1505579230od_a_a @ SY457 @ SY458 ) )
| ~ ( member449909584od_a_a @ SY457 @ SV116 )
| ~ ( member449909584od_a_a @ SY458 @ SV175 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[816]) ).
thf(862,plain,
! [SV203: set_Product_prod_a_a,SV176: product_prod_a_a,SV117: set_Product_prod_a_a,SV50: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV50 @ SV117 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ SV176 @ SV203 )
| ( member449909584od_a_a @ ( plus_p1505579230od_a_a @ SV50 @ SV176 ) @ ( plus_p634297534od_a_a @ SV117 @ SV203 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[817]) ).
thf(863,plain,
! [SV204: set_a,SV177: a,SV118: set_a,SV51: a] :
( ( ( ~ ( member_a @ SV51 @ SV118 ) )
= $true )
| ( ( ~ ( member_a @ SV177 @ SV204 )
| ( member_a @ ( plus_plus_a @ SV51 @ SV177 ) @ ( plus_plus_set_a @ SV118 @ SV204 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[818]) ).
thf(864,plain,
! [SV205: a,SV178: a,SV119: a,SV52: a] :
( ( ( ( product_Pair_a_a @ SV52 @ SV119 )
!= ( product_Pair_a_a @ SV178 @ SV205 ) )
= $true )
| ( ( ~ ( ( SV52 != SV178 )
| ( SV119 != SV205 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[819]) ).
thf(865,plain,
! [SV206: a,SV179: real,SV120: a,SV53: real] :
( ( ( ( plus_plus_a @ ( real_V1035702895aleR_a @ SV53 @ SV120 ) @ ( real_V1035702895aleR_a @ SV179 @ SV206 ) )
!= ( plus_plus_a @ ( real_V1035702895aleR_a @ SV53 @ SV206 ) @ ( real_V1035702895aleR_a @ SV179 @ SV120 ) ) )
= $true )
| ( ( ~ ( ( SV53 != SV179 ) )
| ( SV206 = SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[820]) ).
thf(866,plain,
( ( ( u != zero_zero_real )
= $false )
| ( ( ~ ( ( u != one_one_real ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[821]) ).
thf(867,plain,
! [SV207: set_Product_prod_a_a,SV121: set_Product_prod_a_a] :
( ( ~ ( ( ord_le1824328871od_a_a @ SV121 @ SV207 )
| ! [SY474: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY474 @ SV121 )
| ( member449909584od_a_a @ SY474 @ SV207 ) ) )
| ~ ( ~ ( ord_le1824328871od_a_a @ SV121 @ SV207 )
| ~ ! [SY474: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY474 @ SV121 )
| ( member449909584od_a_a @ SY474 @ SV207 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[822]) ).
thf(868,plain,
! [SV207: set_Product_prod_a_a,SV121: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV121 @ SV207 )
= ( ! [SY474: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY474 @ SV121 )
| ( member449909584od_a_a @ SY474 @ SV207 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[822]) ).
thf(869,plain,
! [SV181: set_a,SV122: set_a,SV55: a] :
( ( ( member_a @ SV55 @ ( plus_plus_set_a @ SV122 @ SV181 ) )
= $false )
| ( ( ~ ! [SY464: a,SY465: a] :
( ( SV55
!= ( plus_plus_a @ SY464 @ SY465 ) )
| ~ ( member_a @ SY464 @ SV122 )
| ~ ( member_a @ SY465 @ SV181 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[823]) ).
thf(870,plain,
! [SV208: a,SV182: a,SV123: a,SV56: a] :
( ( ~ ( ( ( product_Pair_a_a @ SV56 @ SV123 )
= ( product_Pair_a_a @ SV182 @ SV208 ) )
| ~ ( ( SV56 != SV182 )
| ( SV123 != SV208 ) ) )
| ~ ( ( ( product_Pair_a_a @ SV56 @ SV123 )
!= ( product_Pair_a_a @ SV182 @ SV208 ) )
| ~ ~ ( ( SV56 != SV182 )
| ( SV123 != SV208 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[824]) ).
thf(871,plain,
! [SV208: a,SV182: a,SV123: a,SV56: a] :
( ( ( ( product_Pair_a_a @ SV56 @ SV123 )
= ( product_Pair_a_a @ SV182 @ SV208 ) )
= ( ~ ( ( SV56 != SV182 )
| ( SV123 != SV208 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[824]) ).
thf(872,plain,
! [SV183: a,SV124: a,SV57: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV124 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV57 ) @ relation ) ) )
= $false )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV183 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV183 @ SV124 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV183 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV183 @ SV57 ) @ relation ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[825]) ).
thf(873,plain,
! [SV213: product_prod_a_a,SV209: set_Product_prod_a_a,SV184: set_Product_prod_a_a,SV125: set_Product_prod_a_a,SV58: set_Product_prod_a_a] :
( ( ~ ( ord_le1824328871od_a_a @ SV58 @ SV125 )
| ~ ( ord_le1824328871od_a_a @ SV184 @ SV209 )
| ~ ( member449909584od_a_a @ SV213 @ ( plus_p634297534od_a_a @ SV58 @ SV184 ) )
| ( member449909584od_a_a @ SV213 @ ( plus_p634297534od_a_a @ SV125 @ SV209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(874,plain,
! [SV126: product_prod_a_a,SV59: product_prod_a_a > $o] :
( ( ( ! [SY477: a] : ( SV59 @ ( product_Pair_a_a @ ( sK4_SY334 @ SV126 @ SV59 ) @ SY477 ) ) )
= $false )
| ( ( SV59 @ SV126 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[827]) ).
thf(875,plain,
! [SV60: set_Product_prod_a_a,SV127: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK5_SY434 @ SV127 @ SV60 ) @ SV60 )
| ( member449909584od_a_a @ ( sK5_SY434 @ SV127 @ SV60 ) @ SV127 ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV60 @ SV127 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[828]) ).
thf(876,plain,
! [SV185: a,SV128: a,SV61: real] :
( ( ( SV61 != zero_zero_real )
= $false )
| ( ( ( ( real_V1035702895aleR_a @ SV61 @ SV128 )
!= ( real_V1035702895aleR_a @ SV61 @ SV185 ) )
| ( SV128 = SV185 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[829]) ).
thf(877,plain,
! [SV186: a,SV129: a,SV62: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV62 @ SV129 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV129 @ SV62 ) @ relation ) ) )
= $false )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV129 @ SV186 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV186 @ SV129 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV62 @ SV186 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV186 @ SV62 ) @ relation ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[830]) ).
thf(878,plain,
! [SV63: product_prod_a_a] :
( ( SV63
= ( product_Pair_a_a @ ( sK1_SY342 @ SV63 ) @ ( sK3_SY469 @ SV63 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[831]) ).
thf(879,plain,
! [SV130: a,SV64: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV64 @ SV130 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV64 ) @ relation ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV64 ) @ relation )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[832]) ).
thf(880,plain,
! [SV187: real,SV131: real,SV65: a] :
( ( ( SV65 != zero_zero_a )
= $false )
| ( ( ( ( real_V1035702895aleR_a @ SV131 @ SV65 )
!= ( real_V1035702895aleR_a @ SV187 @ SV65 ) )
| ( SV131 = SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[833]) ).
thf(881,plain,
! [SV66: product_prod_a_a] :
( ( ! [SY470: a] :
( SV66
!= ( product_Pair_a_a @ ( sK2_SY347 @ SV66 ) @ SY470 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[834]) ).
thf(882,plain,
! [SV210: a,SV188: a,SV132: a,SV67: a] :
( ( ( SV67
!= ( plus_plus_a @ SV132 @ SV188 ) )
= $true )
| ( ( ( plus_plus_a @ SV67 @ SV210 )
= ( plus_plus_a @ SV132 @ ( plus_plus_a @ SV188 @ SV210 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[835]) ).
thf(883,plain,
! [SV133: product_prod_a_a,SV68: product_prod_a_a > $o] :
( ( ( ! [SY478: a] : ( SV68 @ ( product_Pair_a_a @ ( sK6_SY353 @ SV133 @ SV68 ) @ SY478 ) ) )
= $false )
| ( ( SV68 @ SV133 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[836]) ).
thf(884,plain,
! [SV189: product_prod_a_a,SV134: set_Product_prod_a_a,SV69: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV69 @ SV134 )
= $false )
| ( ( ~ ( member449909584od_a_a @ SV189 @ SV69 )
| ( member449909584od_a_a @ SV189 @ SV134 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[837]) ).
thf(885,plain,
! [SV135: a,SV70: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV70 @ SV135 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV135 @ SV70 ) @ relation ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV70 @ SV135 ) @ relation )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[838]) ).
thf(886,plain,
! [SV211: a,SV190: a,SV137: a,SV72: a] :
( ( ( SV72
!= ( plus_plus_a @ SV137 @ SV190 ) )
= $true )
| ( ( ( plus_plus_a @ SV211 @ SV72 )
= ( plus_plus_a @ SV137 @ ( plus_plus_a @ SV211 @ SV190 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[840]) ).
thf(887,plain,
! [SV191: product_prod_a_a,SV138: set_Product_prod_a_a,SV73: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV73 @ SV138 )
= $false )
| ( ( ~ ( member449909584od_a_a @ SV191 @ SV73 )
| ( member449909584od_a_a @ SV191 @ SV138 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[841]) ).
thf(888,plain,
! [SV192: a,SV139: a,SV74: a] :
( ( ( ( plus_plus_a @ SV74 @ SV139 )
= ( plus_plus_a @ SV192 @ SV139 ) )
= $false )
| ( ( SV74 = SV192 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[842]) ).
thf(889,plain,
! [SV212: set_Product_prod_a_a,SV140: set_Product_prod_a_a] :
( ( ~ ( ( ord_le1824328871od_a_a @ SV140 @ SV212 )
| ! [SY476: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY476 @ SV140 )
| ( member449909584od_a_a @ SY476 @ SV212 ) ) )
| ~ ( ~ ( ord_le1824328871od_a_a @ SV140 @ SV212 )
| ~ ! [SY476: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY476 @ SV140 )
| ( member449909584od_a_a @ SY476 @ SV212 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[843]) ).
thf(890,plain,
! [SV212: set_Product_prod_a_a,SV140: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV140 @ SV212 )
= ( ! [SY476: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY476 @ SV140 )
| ( member449909584od_a_a @ SY476 @ SV212 ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[843]) ).
thf(891,plain,
! [SV194: a,SV141: a,SV76: a] :
( ( ( ( plus_plus_a @ SV76 @ SV141 )
= ( plus_plus_a @ SV76 @ SV194 ) )
= $false )
| ( ( SV141 = SV194 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[844]) ).
thf(892,plain,
! [SV158: a,SV93: a,SV17: a] :
( ( ( ( ( plus_plus_a @ SV17 @ SV93 )
= ( plus_plus_a @ SV17 @ SV158 ) )
| ( SV93 = SV158 ) )
= $false )
| ( ( ~ ( ( ( plus_plus_a @ SV17 @ SV93 )
!= ( plus_plus_a @ SV17 @ SV158 ) )
| ( SV93 != SV158 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[845]) ).
thf(893,plain,
! [SV159: a,SV94: a,SV18: a] :
( ( ( ( ( plus_plus_a @ SV18 @ SV94 )
= ( plus_plus_a @ SV159 @ SV94 ) )
| ( SV18 = SV159 ) )
= $false )
| ( ( ~ ( ( ( plus_plus_a @ SV18 @ SV94 )
!= ( plus_plus_a @ SV159 @ SV94 ) )
| ( SV18 != SV159 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[846]) ).
thf(894,plain,
! [SV95: a,SV19: a] :
( ( ( SV19
= ( plus_plus_a @ SV19 @ SV95 ) )
= $false )
| ( ( ~ ( ( SV19
!= ( plus_plus_a @ SV19 @ SV95 ) )
| ( SV95 != zero_zero_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[847]) ).
thf(895,plain,
! [SV19: a,SV95: a] :
( ( ( SV95 = zero_zero_a )
= $false )
| ( ( ~ ( ( SV19
!= ( plus_plus_a @ SV19 @ SV95 ) )
| ( SV95 != zero_zero_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[847]) ).
thf(896,plain,
! [SV96: a,SV20: a] :
( ( ( SV20
= ( plus_plus_a @ SV96 @ SV20 ) )
= $false )
| ( ( ~ ( ( SV20
!= ( plus_plus_a @ SV96 @ SV20 ) )
| ( SV96 != zero_zero_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[848]) ).
thf(897,plain,
! [SV20: a,SV96: a] :
( ( ( SV96 = zero_zero_a )
= $false )
| ( ( ~ ( ( SV20
!= ( plus_plus_a @ SV96 @ SV20 ) )
| ( SV96 != zero_zero_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[848]) ).
thf(898,plain,
! [SV97: a,SV21: a] :
( ( ( ( plus_plus_a @ SV21 @ SV97 )
= SV21 )
= $false )
| ( ( ~ ( ( ( plus_plus_a @ SV21 @ SV97 )
!= SV21 )
| ( SV97 != zero_zero_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[849]) ).
thf(899,plain,
! [SV21: a,SV97: a] :
( ( ( SV97 = zero_zero_a )
= $false )
| ( ( ~ ( ( ( plus_plus_a @ SV21 @ SV97 )
!= SV21 )
| ( SV97 != zero_zero_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[849]) ).
thf(900,plain,
! [SV98: a,SV22: a] :
( ( ( ( plus_plus_a @ SV22 @ SV98 )
= SV98 )
= $false )
| ( ( ~ ( ( ( plus_plus_a @ SV22 @ SV98 )
!= SV98 )
| ( SV22 != zero_zero_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[850]) ).
thf(901,plain,
! [SV98: a,SV22: a] :
( ( ( SV22 = zero_zero_a )
= $false )
| ( ( ~ ( ( ( plus_plus_a @ SV22 @ SV98 )
!= SV98 )
| ( SV22 != zero_zero_a ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[850]) ).
thf(902,plain,
! [SV99: product_prod_a_a > $o,SV25: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV25 @ ( collec645855634od_a_a @ SV99 ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ SV25 @ ( collec645855634od_a_a @ SV99 ) )
| ~ ( SV99 @ SV25 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[851]) ).
thf(903,plain,
! [SV25: product_prod_a_a,SV99: product_prod_a_a > $o] :
( ( ( SV99 @ SV25 )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ SV25 @ ( collec645855634od_a_a @ SV99 ) )
| ~ ( SV99 @ SV25 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[851]) ).
thf(904,plain,
! [SV162: a,SV102: a,SV32: a] :
( ( ( ( ( plus_plus_a @ SV32 @ SV102 )
= ( plus_plus_a @ SV162 @ SV102 ) )
| ( SV32 = SV162 ) )
= $false )
| ( ( ~ ( ( ( plus_plus_a @ SV32 @ SV102 )
!= ( plus_plus_a @ SV162 @ SV102 ) )
| ( SV32 != SV162 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[852]) ).
thf(905,plain,
! [SV163: a,SV103: a,SV33: a] :
( ( ( ( ( plus_plus_a @ SV33 @ SV103 )
= ( plus_plus_a @ SV33 @ SV163 ) )
| ( SV103 = SV163 ) )
= $false )
| ( ( ~ ( ( ( plus_plus_a @ SV33 @ SV103 )
!= ( plus_plus_a @ SV33 @ SV163 ) )
| ( SV103 != SV163 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[853]) ).
thf(906,plain,
! [SV166: a,SV106: real,SV36: a] :
( ( ( ( ( plus_plus_a @ SV36 @ ( real_V1035702895aleR_a @ SV106 @ SV166 ) )
= ( plus_plus_a @ SV166 @ ( real_V1035702895aleR_a @ SV106 @ SV36 ) ) )
| ( SV166 = SV36 )
| ( SV106 = one_one_real ) )
= $false )
| ( ( ~ ( ( ( plus_plus_a @ SV36 @ ( real_V1035702895aleR_a @ SV106 @ SV166 ) )
!= ( plus_plus_a @ SV166 @ ( real_V1035702895aleR_a @ SV106 @ SV36 ) ) )
| ~ ( ( SV166 = SV36 )
| ( SV106 = one_one_real ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[854]) ).
thf(907,plain,
! [SV107: a,SV38: real] :
( ( ( ( real_V1035702895aleR_a @ SV38 @ SV107 )
= zero_zero_a )
= $false )
| ( ( ~ ( ( ( real_V1035702895aleR_a @ SV38 @ SV107 )
!= zero_zero_a )
| ~ ( ( SV38 = zero_zero_real )
| ( SV107 = zero_zero_a ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[855]) ).
thf(908,plain,
! [SV107: a,SV38: real] :
( ( ( ( SV38 = zero_zero_real )
| ( SV107 = zero_zero_a ) )
= $false )
| ( ( ~ ( ( ( real_V1035702895aleR_a @ SV38 @ SV107 )
!= zero_zero_a )
| ~ ( ( SV38 = zero_zero_real )
| ( SV107 = zero_zero_a ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[855]) ).
thf(909,plain,
! [SV167: a,SV108: a,SV40: real] :
( ( ( ( ( real_V1035702895aleR_a @ SV40 @ SV108 )
= ( real_V1035702895aleR_a @ SV40 @ SV167 ) )
| ( SV108 = SV167 )
| ( SV40 = zero_zero_real ) )
= $false )
| ( ( ~ ( ( ( real_V1035702895aleR_a @ SV40 @ SV108 )
!= ( real_V1035702895aleR_a @ SV40 @ SV167 ) )
| ~ ( ( SV108 = SV167 )
| ( SV40 = zero_zero_real ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[856]) ).
thf(910,plain,
! [SV168: real,SV109: a,SV41: real] :
( ( ( ( ( real_V1035702895aleR_a @ SV41 @ SV109 )
= ( real_V1035702895aleR_a @ SV168 @ SV109 ) )
| ( SV41 = SV168 )
| ( SV109 = zero_zero_a ) )
= $false )
| ( ( ~ ( ( ( real_V1035702895aleR_a @ SV41 @ SV109 )
!= ( real_V1035702895aleR_a @ SV168 @ SV109 ) )
| ~ ( ( SV41 = SV168 )
| ( SV109 = zero_zero_a ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[857]) ).
thf(911,plain,
! [SV202: a,SV173: a,SV114: a,SV47: a] :
( ( ( ~ ( ( ( product_Pair_a_a @ SV47 @ SV114 )
= ( product_Pair_a_a @ SV173 @ SV202 ) )
| ~ ( ( SV47 != SV173 )
| ( SV114 != SV202 ) ) ) )
= $true )
| ( ( ~ ( ( ( product_Pair_a_a @ SV47 @ SV114 )
!= ( product_Pair_a_a @ SV173 @ SV202 ) )
| ~ ~ ( ( SV47 != SV173 )
| ( SV114 != SV202 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[858]) ).
thf(912,plain,
! [SV115: set_Product_prod_a_a,SV48: set_Product_prod_a_a,SV174: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV174 @ SV48 ) )
= $true )
| ( ( member449909584od_a_a @ SV174 @ SV115 )
= $true )
| ( ( ord_le108336051od_a_a @ SV48 @ SV115 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[860]) ).
thf(913,plain,
! [SV175: set_Product_prod_a_a,SV116: set_Product_prod_a_a,SV49: product_prod_a_a] :
( ( ( ! [SY457: product_prod_a_a,SY458: product_prod_a_a] :
( ( SV49
!= ( plus_p1505579230od_a_a @ SY457 @ SY458 ) )
| ~ ( member449909584od_a_a @ SY457 @ SV116 )
| ~ ( member449909584od_a_a @ SY458 @ SV175 ) ) )
= $false )
| ( ( member449909584od_a_a @ SV49 @ ( plus_p634297534od_a_a @ SV116 @ SV175 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[861]) ).
thf(914,plain,
! [SV203: set_Product_prod_a_a,SV176: product_prod_a_a,SV117: set_Product_prod_a_a,SV50: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV50 @ SV117 )
= $false )
| ( ( ~ ( member449909584od_a_a @ SV176 @ SV203 )
| ( member449909584od_a_a @ ( plus_p1505579230od_a_a @ SV50 @ SV176 ) @ ( plus_p634297534od_a_a @ SV117 @ SV203 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[862]) ).
thf(915,plain,
! [SV204: set_a,SV177: a,SV118: set_a,SV51: a] :
( ( ( member_a @ SV51 @ SV118 )
= $false )
| ( ( ~ ( member_a @ SV177 @ SV204 )
| ( member_a @ ( plus_plus_a @ SV51 @ SV177 ) @ ( plus_plus_set_a @ SV118 @ SV204 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[863]) ).
thf(916,plain,
! [SV205: a,SV178: a,SV119: a,SV52: a] :
( ( ( ( product_Pair_a_a @ SV52 @ SV119 )
= ( product_Pair_a_a @ SV178 @ SV205 ) )
= $false )
| ( ( ~ ( ( SV52 != SV178 )
| ( SV119 != SV205 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[864]) ).
thf(917,plain,
! [SV206: a,SV179: real,SV120: a,SV53: real] :
( ( ( ( plus_plus_a @ ( real_V1035702895aleR_a @ SV53 @ SV120 ) @ ( real_V1035702895aleR_a @ SV179 @ SV206 ) )
= ( plus_plus_a @ ( real_V1035702895aleR_a @ SV53 @ SV206 ) @ ( real_V1035702895aleR_a @ SV179 @ SV120 ) ) )
= $false )
| ( ( ~ ( ( SV53 != SV179 ) )
| ( SV206 = SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[865]) ).
thf(918,plain,
( ( ( u = zero_zero_real )
= $true )
| ( ( ~ ( ( u != one_one_real ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[866]) ).
thf(919,plain,
! [SV207: set_Product_prod_a_a,SV121: set_Product_prod_a_a] :
( ( ( ~ ( ( ord_le1824328871od_a_a @ SV121 @ SV207 )
| ! [SY474: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY474 @ SV121 )
| ( member449909584od_a_a @ SY474 @ SV207 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV121 @ SV207 )
| ~ ! [SY474: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY474 @ SV121 )
| ( member449909584od_a_a @ SY474 @ SV207 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[867]) ).
thf(920,plain,
! [SV181: set_a,SV122: set_a,SV55: a] :
( ( ( ! [SY464: a,SY465: a] :
( ( SV55
!= ( plus_plus_a @ SY464 @ SY465 ) )
| ~ ( member_a @ SY464 @ SV122 )
| ~ ( member_a @ SY465 @ SV181 ) ) )
= $false )
| ( ( member_a @ SV55 @ ( plus_plus_set_a @ SV122 @ SV181 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[869]) ).
thf(921,plain,
! [SV208: a,SV182: a,SV123: a,SV56: a] :
( ( ( ~ ( ( ( product_Pair_a_a @ SV56 @ SV123 )
= ( product_Pair_a_a @ SV182 @ SV208 ) )
| ~ ( ( SV56 != SV182 )
| ( SV123 != SV208 ) ) ) )
= $true )
| ( ( ~ ( ( ( product_Pair_a_a @ SV56 @ SV123 )
!= ( product_Pair_a_a @ SV182 @ SV208 ) )
| ~ ~ ( ( SV56 != SV182 )
| ( SV123 != SV208 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[870]) ).
thf(922,plain,
! [SV183: a,SV124: a,SV57: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV124 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV57 ) @ relation ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV183 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV183 @ SV124 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV183 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV183 @ SV57 ) @ relation ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[872]) ).
thf(923,plain,
! [SV213: product_prod_a_a,SV209: set_Product_prod_a_a,SV184: set_Product_prod_a_a,SV125: set_Product_prod_a_a,SV58: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV58 @ SV125 ) )
= $true )
| ( ( ~ ( ord_le1824328871od_a_a @ SV184 @ SV209 )
| ~ ( member449909584od_a_a @ SV213 @ ( plus_p634297534od_a_a @ SV58 @ SV184 ) )
| ( member449909584od_a_a @ SV213 @ ( plus_p634297534od_a_a @ SV125 @ SV209 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[873]) ).
thf(924,plain,
! [SV126: product_prod_a_a,SV59: product_prod_a_a > $o] :
( ( ( SV59 @ ( product_Pair_a_a @ ( sK4_SY334 @ SV126 @ SV59 ) @ ( sK7_SY477 @ SV126 @ SV59 ) ) )
= $false )
| ( ( SV59 @ SV126 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[874]) ).
thf(925,plain,
! [SV60: set_Product_prod_a_a,SV127: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK5_SY434 @ SV127 @ SV60 ) @ SV60 ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV60 @ SV127 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[875]) ).
thf(926,plain,
! [SV60: set_Product_prod_a_a,SV127: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( sK5_SY434 @ SV127 @ SV60 ) @ SV127 )
= $false )
| ( ( ord_le1824328871od_a_a @ SV60 @ SV127 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[875]) ).
thf(927,plain,
! [SV185: a,SV128: a,SV61: real] :
( ( ( SV61 = zero_zero_real )
= $true )
| ( ( ( ( real_V1035702895aleR_a @ SV61 @ SV128 )
!= ( real_V1035702895aleR_a @ SV61 @ SV185 ) )
| ( SV128 = SV185 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[876]) ).
thf(928,plain,
! [SV186: a,SV129: a,SV62: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV62 @ SV129 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV129 @ SV62 ) @ relation ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV129 @ SV186 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV186 @ SV129 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV62 @ SV186 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV186 @ SV62 ) @ relation ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[877]) ).
thf(929,plain,
! [SV130: a,SV64: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV64 @ SV130 ) @ relation ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV64 ) @ relation ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV64 ) @ relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[879]) ).
thf(930,plain,
! [SV187: real,SV131: real,SV65: a] :
( ( ( SV65 = zero_zero_a )
= $true )
| ( ( ( ( real_V1035702895aleR_a @ SV131 @ SV65 )
!= ( real_V1035702895aleR_a @ SV187 @ SV65 ) )
| ( SV131 = SV187 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[880]) ).
thf(931,plain,
! [SV66: product_prod_a_a] :
( ( SV66
!= ( product_Pair_a_a @ ( sK2_SY347 @ SV66 ) @ ( sK8_SY470 @ SV66 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[881]) ).
thf(932,plain,
! [SV210: a,SV188: a,SV132: a,SV67: a] :
( ( ( SV67
= ( plus_plus_a @ SV132 @ SV188 ) )
= $false )
| ( ( ( plus_plus_a @ SV67 @ SV210 )
= ( plus_plus_a @ SV132 @ ( plus_plus_a @ SV188 @ SV210 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[882]) ).
thf(933,plain,
! [SV133: product_prod_a_a,SV68: product_prod_a_a > $o] :
( ( ( SV68 @ ( product_Pair_a_a @ ( sK6_SY353 @ SV133 @ SV68 ) @ ( sK9_SY478 @ SV133 @ SV68 ) ) )
= $false )
| ( ( SV68 @ SV133 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[883]) ).
thf(934,plain,
! [SV134: set_Product_prod_a_a,SV69: set_Product_prod_a_a,SV189: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV189 @ SV69 ) )
= $true )
| ( ( member449909584od_a_a @ SV189 @ SV134 )
= $true )
| ( ( ord_le1824328871od_a_a @ SV69 @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[884]) ).
thf(935,plain,
! [SV135: a,SV70: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV70 @ SV135 ) @ relation ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV135 @ SV70 ) @ relation ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV70 @ SV135 ) @ relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[885]) ).
thf(936,plain,
! [SV211: a,SV190: a,SV137: a,SV72: a] :
( ( ( SV72
= ( plus_plus_a @ SV137 @ SV190 ) )
= $false )
| ( ( ( plus_plus_a @ SV211 @ SV72 )
= ( plus_plus_a @ SV137 @ ( plus_plus_a @ SV211 @ SV190 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[886]) ).
thf(937,plain,
! [SV138: set_Product_prod_a_a,SV73: set_Product_prod_a_a,SV191: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV191 @ SV73 ) )
= $true )
| ( ( member449909584od_a_a @ SV191 @ SV138 )
= $true )
| ( ( ord_le1824328871od_a_a @ SV73 @ SV138 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[887]) ).
thf(938,plain,
! [SV212: set_Product_prod_a_a,SV140: set_Product_prod_a_a] :
( ( ( ~ ( ( ord_le1824328871od_a_a @ SV140 @ SV212 )
| ! [SY476: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY476 @ SV140 )
| ( member449909584od_a_a @ SY476 @ SV212 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV140 @ SV212 )
| ~ ! [SY476: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY476 @ SV140 )
| ( member449909584od_a_a @ SY476 @ SV212 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[889]) ).
thf(939,plain,
! [SV158: a,SV93: a,SV17: a] :
( ( ( ( plus_plus_a @ SV17 @ SV93 )
= ( plus_plus_a @ SV17 @ SV158 ) )
= $false )
| ( ( ~ ( ( ( plus_plus_a @ SV17 @ SV93 )
!= ( plus_plus_a @ SV17 @ SV158 ) )
| ( SV93 != SV158 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[892]) ).
thf(940,plain,
! [SV17: a,SV158: a,SV93: a] :
( ( ( SV93 = SV158 )
= $false )
| ( ( ~ ( ( ( plus_plus_a @ SV17 @ SV93 )
!= ( plus_plus_a @ SV17 @ SV158 ) )
| ( SV93 != SV158 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[892]) ).
thf(941,plain,
! [SV159: a,SV94: a,SV18: a] :
( ( ( ( plus_plus_a @ SV18 @ SV94 )
= ( plus_plus_a @ SV159 @ SV94 ) )
= $false )
| ( ( ~ ( ( ( plus_plus_a @ SV18 @ SV94 )
!= ( plus_plus_a @ SV159 @ SV94 ) )
| ( SV18 != SV159 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[893]) ).
thf(942,plain,
! [SV94: a,SV159: a,SV18: a] :
( ( ( SV18 = SV159 )
= $false )
| ( ( ~ ( ( ( plus_plus_a @ SV18 @ SV94 )
!= ( plus_plus_a @ SV159 @ SV94 ) )
| ( SV18 != SV159 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[893]) ).
thf(943,plain,
! [SV95: a,SV19: a] :
( ( ( ( SV19
!= ( plus_plus_a @ SV19 @ SV95 ) )
| ( SV95 != zero_zero_a ) )
= $false )
| ( ( SV19
= ( plus_plus_a @ SV19 @ SV95 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[894]) ).
thf(944,plain,
! [SV95: a,SV19: a] :
( ( ( ( SV19
!= ( plus_plus_a @ SV19 @ SV95 ) )
| ( SV95 != zero_zero_a ) )
= $false )
| ( ( SV95 = zero_zero_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[895]) ).
thf(945,plain,
! [SV96: a,SV20: a] :
( ( ( ( SV20
!= ( plus_plus_a @ SV96 @ SV20 ) )
| ( SV96 != zero_zero_a ) )
= $false )
| ( ( SV20
= ( plus_plus_a @ SV96 @ SV20 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[896]) ).
thf(946,plain,
! [SV96: a,SV20: a] :
( ( ( ( SV20
!= ( plus_plus_a @ SV96 @ SV20 ) )
| ( SV96 != zero_zero_a ) )
= $false )
| ( ( SV96 = zero_zero_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[897]) ).
thf(947,plain,
! [SV97: a,SV21: a] :
( ( ( ( ( plus_plus_a @ SV21 @ SV97 )
!= SV21 )
| ( SV97 != zero_zero_a ) )
= $false )
| ( ( ( plus_plus_a @ SV21 @ SV97 )
= SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[898]) ).
thf(948,plain,
! [SV97: a,SV21: a] :
( ( ( ( ( plus_plus_a @ SV21 @ SV97 )
!= SV21 )
| ( SV97 != zero_zero_a ) )
= $false )
| ( ( SV97 = zero_zero_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[899]) ).
thf(949,plain,
! [SV98: a,SV22: a] :
( ( ( ( ( plus_plus_a @ SV22 @ SV98 )
!= SV98 )
| ( SV22 != zero_zero_a ) )
= $false )
| ( ( ( plus_plus_a @ SV22 @ SV98 )
= SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[900]) ).
thf(950,plain,
! [SV98: a,SV22: a] :
( ( ( ( ( plus_plus_a @ SV22 @ SV98 )
!= SV98 )
| ( SV22 != zero_zero_a ) )
= $false )
| ( ( SV22 = zero_zero_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[901]) ).
thf(951,plain,
! [SV99: product_prod_a_a > $o,SV25: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV25 @ ( collec645855634od_a_a @ SV99 ) )
| ~ ( SV99 @ SV25 ) )
= $false )
| ( ( member449909584od_a_a @ SV25 @ ( collec645855634od_a_a @ SV99 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[902]) ).
thf(952,plain,
! [SV99: product_prod_a_a > $o,SV25: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV25 @ ( collec645855634od_a_a @ SV99 ) )
| ~ ( SV99 @ SV25 ) )
= $false )
| ( ( SV99 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[903]) ).
thf(953,plain,
! [SV162: a,SV102: a,SV32: a] :
( ( ( ( plus_plus_a @ SV32 @ SV102 )
= ( plus_plus_a @ SV162 @ SV102 ) )
= $false )
| ( ( ~ ( ( ( plus_plus_a @ SV32 @ SV102 )
!= ( plus_plus_a @ SV162 @ SV102 ) )
| ( SV32 != SV162 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[904]) ).
thf(954,plain,
! [SV102: a,SV162: a,SV32: a] :
( ( ( SV32 = SV162 )
= $false )
| ( ( ~ ( ( ( plus_plus_a @ SV32 @ SV102 )
!= ( plus_plus_a @ SV162 @ SV102 ) )
| ( SV32 != SV162 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[904]) ).
thf(955,plain,
! [SV163: a,SV103: a,SV33: a] :
( ( ( ( plus_plus_a @ SV33 @ SV103 )
= ( plus_plus_a @ SV33 @ SV163 ) )
= $false )
| ( ( ~ ( ( ( plus_plus_a @ SV33 @ SV103 )
!= ( plus_plus_a @ SV33 @ SV163 ) )
| ( SV103 != SV163 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[905]) ).
thf(956,plain,
! [SV33: a,SV163: a,SV103: a] :
( ( ( SV103 = SV163 )
= $false )
| ( ( ~ ( ( ( plus_plus_a @ SV33 @ SV103 )
!= ( plus_plus_a @ SV33 @ SV163 ) )
| ( SV103 != SV163 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[905]) ).
thf(957,plain,
! [SV166: a,SV106: real,SV36: a] :
( ( ( ( plus_plus_a @ SV36 @ ( real_V1035702895aleR_a @ SV106 @ SV166 ) )
= ( plus_plus_a @ SV166 @ ( real_V1035702895aleR_a @ SV106 @ SV36 ) ) )
= $false )
| ( ( ~ ( ( ( plus_plus_a @ SV36 @ ( real_V1035702895aleR_a @ SV106 @ SV166 ) )
!= ( plus_plus_a @ SV166 @ ( real_V1035702895aleR_a @ SV106 @ SV36 ) ) )
| ~ ( ( SV166 = SV36 )
| ( SV106 = one_one_real ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[906]) ).
thf(958,plain,
! [SV106: real,SV36: a,SV166: a] :
( ( ( ( SV166 = SV36 )
| ( SV106 = one_one_real ) )
= $false )
| ( ( ~ ( ( ( plus_plus_a @ SV36 @ ( real_V1035702895aleR_a @ SV106 @ SV166 ) )
!= ( plus_plus_a @ SV166 @ ( real_V1035702895aleR_a @ SV106 @ SV36 ) ) )
| ~ ( ( SV166 = SV36 )
| ( SV106 = one_one_real ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[906]) ).
thf(959,plain,
! [SV107: a,SV38: real] :
( ( ( ( ( real_V1035702895aleR_a @ SV38 @ SV107 )
!= zero_zero_a )
| ~ ( ( SV38 = zero_zero_real )
| ( SV107 = zero_zero_a ) ) )
= $false )
| ( ( ( real_V1035702895aleR_a @ SV38 @ SV107 )
= zero_zero_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[907]) ).
thf(960,plain,
! [SV107: a,SV38: real] :
( ( ( SV38 = zero_zero_real )
= $false )
| ( ( ~ ( ( ( real_V1035702895aleR_a @ SV38 @ SV107 )
!= zero_zero_a )
| ~ ( ( SV38 = zero_zero_real )
| ( SV107 = zero_zero_a ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[908]) ).
thf(961,plain,
! [SV38: real,SV107: a] :
( ( ( SV107 = zero_zero_a )
= $false )
| ( ( ~ ( ( ( real_V1035702895aleR_a @ SV38 @ SV107 )
!= zero_zero_a )
| ~ ( ( SV38 = zero_zero_real )
| ( SV107 = zero_zero_a ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[908]) ).
thf(962,plain,
! [SV167: a,SV108: a,SV40: real] :
( ( ( ( real_V1035702895aleR_a @ SV40 @ SV108 )
= ( real_V1035702895aleR_a @ SV40 @ SV167 ) )
= $false )
| ( ( ~ ( ( ( real_V1035702895aleR_a @ SV40 @ SV108 )
!= ( real_V1035702895aleR_a @ SV40 @ SV167 ) )
| ~ ( ( SV108 = SV167 )
| ( SV40 = zero_zero_real ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[909]) ).
thf(963,plain,
! [SV40: real,SV167: a,SV108: a] :
( ( ( ( SV108 = SV167 )
| ( SV40 = zero_zero_real ) )
= $false )
| ( ( ~ ( ( ( real_V1035702895aleR_a @ SV40 @ SV108 )
!= ( real_V1035702895aleR_a @ SV40 @ SV167 ) )
| ~ ( ( SV108 = SV167 )
| ( SV40 = zero_zero_real ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[909]) ).
thf(964,plain,
! [SV168: real,SV109: a,SV41: real] :
( ( ( ( real_V1035702895aleR_a @ SV41 @ SV109 )
= ( real_V1035702895aleR_a @ SV168 @ SV109 ) )
= $false )
| ( ( ~ ( ( ( real_V1035702895aleR_a @ SV41 @ SV109 )
!= ( real_V1035702895aleR_a @ SV168 @ SV109 ) )
| ~ ( ( SV41 = SV168 )
| ( SV109 = zero_zero_a ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[910]) ).
thf(965,plain,
! [SV109: a,SV168: real,SV41: real] :
( ( ( ( SV41 = SV168 )
| ( SV109 = zero_zero_a ) )
= $false )
| ( ( ~ ( ( ( real_V1035702895aleR_a @ SV41 @ SV109 )
!= ( real_V1035702895aleR_a @ SV168 @ SV109 ) )
| ~ ( ( SV41 = SV168 )
| ( SV109 = zero_zero_a ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[910]) ).
thf(966,plain,
! [SV202: a,SV173: a,SV114: a,SV47: a] :
( ( ( ( ( product_Pair_a_a @ SV47 @ SV114 )
= ( product_Pair_a_a @ SV173 @ SV202 ) )
| ~ ( ( SV47 != SV173 )
| ( SV114 != SV202 ) ) )
= $false )
| ( ( ~ ( ( ( product_Pair_a_a @ SV47 @ SV114 )
!= ( product_Pair_a_a @ SV173 @ SV202 ) )
| ~ ~ ( ( SV47 != SV173 )
| ( SV114 != SV202 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[911]) ).
thf(967,plain,
! [SV115: set_Product_prod_a_a,SV48: set_Product_prod_a_a,SV174: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV174 @ SV48 )
= $false )
| ( ( member449909584od_a_a @ SV174 @ SV115 )
= $true )
| ( ( ord_le108336051od_a_a @ SV48 @ SV115 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[912]) ).
thf(968,plain,
! [SV116: set_Product_prod_a_a,SV175: set_Product_prod_a_a,SV49: product_prod_a_a] :
( ( ( ! [SY479: product_prod_a_a] :
( ( SV49
!= ( plus_p1505579230od_a_a @ ( sK10_SY457 @ SV175 @ SV116 @ SV49 ) @ SY479 ) )
| ~ ( member449909584od_a_a @ ( sK10_SY457 @ SV175 @ SV116 @ SV49 ) @ SV116 )
| ~ ( member449909584od_a_a @ SY479 @ SV175 ) ) )
= $false )
| ( ( member449909584od_a_a @ SV49 @ ( plus_p634297534od_a_a @ SV116 @ SV175 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[913]) ).
thf(969,plain,
! [SV117: set_Product_prod_a_a,SV50: product_prod_a_a,SV203: set_Product_prod_a_a,SV176: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV176 @ SV203 ) )
= $true )
| ( ( member449909584od_a_a @ ( plus_p1505579230od_a_a @ SV50 @ SV176 ) @ ( plus_p634297534od_a_a @ SV117 @ SV203 ) )
= $true )
| ( ( member449909584od_a_a @ SV50 @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[914]) ).
thf(970,plain,
! [SV118: set_a,SV51: a,SV204: set_a,SV177: a] :
( ( ( ~ ( member_a @ SV177 @ SV204 ) )
= $true )
| ( ( member_a @ ( plus_plus_a @ SV51 @ SV177 ) @ ( plus_plus_set_a @ SV118 @ SV204 ) )
= $true )
| ( ( member_a @ SV51 @ SV118 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[915]) ).
thf(971,plain,
! [SV205: a,SV119: a,SV178: a,SV52: a] :
( ( ( ( SV52 != SV178 )
| ( SV119 != SV205 ) )
= $false )
| ( ( ( product_Pair_a_a @ SV52 @ SV119 )
= ( product_Pair_a_a @ SV178 @ SV205 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[916]) ).
thf(972,plain,
! [SV120: a,SV206: a,SV179: real,SV53: real] :
( ( ( ~ ( ( SV53 != SV179 ) ) )
= $true )
| ( ( SV206 = SV120 )
= $true )
| ( ( ( plus_plus_a @ ( real_V1035702895aleR_a @ SV53 @ SV120 ) @ ( real_V1035702895aleR_a @ SV179 @ SV206 ) )
= ( plus_plus_a @ ( real_V1035702895aleR_a @ SV53 @ SV206 ) @ ( real_V1035702895aleR_a @ SV179 @ SV120 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[917]) ).
thf(973,plain,
( ( ( u != one_one_real )
= $false )
| ( ( u = zero_zero_real )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[918]) ).
thf(974,plain,
! [SV207: set_Product_prod_a_a,SV121: set_Product_prod_a_a] :
( ( ( ( ord_le1824328871od_a_a @ SV121 @ SV207 )
| ! [SY474: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY474 @ SV121 )
| ( member449909584od_a_a @ SY474 @ SV207 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV121 @ SV207 )
| ~ ! [SY474: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY474 @ SV121 )
| ( member449909584od_a_a @ SY474 @ SV207 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[919]) ).
thf(975,plain,
! [SV122: set_a,SV181: set_a,SV55: a] :
( ( ( ! [SY480: a] :
( ( SV55
!= ( plus_plus_a @ ( sK11_SY464 @ SV181 @ SV122 @ SV55 ) @ SY480 ) )
| ~ ( member_a @ ( sK11_SY464 @ SV181 @ SV122 @ SV55 ) @ SV122 )
| ~ ( member_a @ SY480 @ SV181 ) ) )
= $false )
| ( ( member_a @ SV55 @ ( plus_plus_set_a @ SV122 @ SV181 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[920]) ).
thf(976,plain,
! [SV208: a,SV182: a,SV123: a,SV56: a] :
( ( ( ( ( product_Pair_a_a @ SV56 @ SV123 )
= ( product_Pair_a_a @ SV182 @ SV208 ) )
| ~ ( ( SV56 != SV182 )
| ( SV123 != SV208 ) ) )
= $false )
| ( ( ~ ( ( ( product_Pair_a_a @ SV56 @ SV123 )
!= ( product_Pair_a_a @ SV182 @ SV208 ) )
| ~ ~ ( ( SV56 != SV182 )
| ( SV123 != SV208 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[921]) ).
thf(977,plain,
! [SV183: a,SV124: a,SV57: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV124 ) @ relation ) )
= $true )
| ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV57 ) @ relation ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV183 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV183 @ SV124 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV183 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV183 @ SV57 ) @ relation ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[922]) ).
thf(978,plain,
! [SV213: product_prod_a_a,SV209: set_Product_prod_a_a,SV184: set_Product_prod_a_a,SV125: set_Product_prod_a_a,SV58: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV58 @ SV125 )
= $false )
| ( ( ~ ( ord_le1824328871od_a_a @ SV184 @ SV209 )
| ~ ( member449909584od_a_a @ SV213 @ ( plus_p634297534od_a_a @ SV58 @ SV184 ) )
| ( member449909584od_a_a @ SV213 @ ( plus_p634297534od_a_a @ SV125 @ SV209 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[923]) ).
thf(979,plain,
! [SV60: set_Product_prod_a_a,SV127: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( sK5_SY434 @ SV127 @ SV60 ) @ SV60 )
= $true )
| ( ( ord_le1824328871od_a_a @ SV60 @ SV127 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[925]) ).
thf(980,plain,
! [SV185: a,SV128: a,SV61: real] :
( ( ( ( real_V1035702895aleR_a @ SV61 @ SV128 )
!= ( real_V1035702895aleR_a @ SV61 @ SV185 ) )
= $true )
| ( ( SV128 = SV185 )
= $true )
| ( ( SV61 = zero_zero_real )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[927]) ).
thf(981,plain,
! [SV186: a,SV129: a,SV62: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV62 @ SV129 ) @ relation ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV129 @ SV62 ) @ relation ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV129 @ SV186 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV186 @ SV129 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV62 @ SV186 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV186 @ SV62 ) @ relation ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[928]) ).
thf(982,plain,
! [SV130: a,SV64: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV64 @ SV130 ) @ relation )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV64 ) @ relation ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV64 ) @ relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[929]) ).
thf(983,plain,
! [SV187: real,SV65: a,SV131: real] :
( ( ( ( real_V1035702895aleR_a @ SV131 @ SV65 )
!= ( real_V1035702895aleR_a @ SV187 @ SV65 ) )
= $true )
| ( ( SV131 = SV187 )
= $true )
| ( ( SV65 = zero_zero_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[930]) ).
thf(984,plain,
! [SV66: product_prod_a_a] :
( ( SV66
= ( product_Pair_a_a @ ( sK2_SY347 @ SV66 ) @ ( sK8_SY470 @ SV66 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[931]) ).
thf(985,plain,
! [SV134: set_Product_prod_a_a,SV69: set_Product_prod_a_a,SV189: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV189 @ SV69 )
= $false )
| ( ( member449909584od_a_a @ SV189 @ SV134 )
= $true )
| ( ( ord_le1824328871od_a_a @ SV69 @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[934]) ).
thf(986,plain,
! [SV135: a,SV70: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV70 @ SV135 ) @ relation )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV135 @ SV70 ) @ relation ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV70 @ SV135 ) @ relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[935]) ).
thf(987,plain,
! [SV138: set_Product_prod_a_a,SV73: set_Product_prod_a_a,SV191: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV191 @ SV73 )
= $false )
| ( ( member449909584od_a_a @ SV191 @ SV138 )
= $true )
| ( ( ord_le1824328871od_a_a @ SV73 @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[937]) ).
thf(988,plain,
! [SV212: set_Product_prod_a_a,SV140: set_Product_prod_a_a] :
( ( ( ( ord_le1824328871od_a_a @ SV140 @ SV212 )
| ! [SY476: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY476 @ SV140 )
| ( member449909584od_a_a @ SY476 @ SV212 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV140 @ SV212 )
| ~ ! [SY476: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY476 @ SV140 )
| ( member449909584od_a_a @ SY476 @ SV212 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[938]) ).
thf(989,plain,
! [SV158: a,SV93: a,SV17: a] :
( ( ( ( ( plus_plus_a @ SV17 @ SV93 )
!= ( plus_plus_a @ SV17 @ SV158 ) )
| ( SV93 != SV158 ) )
= $false )
| ( ( ( plus_plus_a @ SV17 @ SV93 )
= ( plus_plus_a @ SV17 @ SV158 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[939]) ).
thf(990,plain,
! [SV158: a,SV93: a,SV17: a] :
( ( ( ( ( plus_plus_a @ SV17 @ SV93 )
!= ( plus_plus_a @ SV17 @ SV158 ) )
| ( SV93 != SV158 ) )
= $false )
| ( ( SV93 = SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[940]) ).
thf(991,plain,
! [SV159: a,SV94: a,SV18: a] :
( ( ( ( ( plus_plus_a @ SV18 @ SV94 )
!= ( plus_plus_a @ SV159 @ SV94 ) )
| ( SV18 != SV159 ) )
= $false )
| ( ( ( plus_plus_a @ SV18 @ SV94 )
= ( plus_plus_a @ SV159 @ SV94 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[941]) ).
thf(992,plain,
! [SV159: a,SV94: a,SV18: a] :
( ( ( ( ( plus_plus_a @ SV18 @ SV94 )
!= ( plus_plus_a @ SV159 @ SV94 ) )
| ( SV18 != SV159 ) )
= $false )
| ( ( SV18 = SV159 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[942]) ).
thf(993,plain,
! [SV95: a,SV19: a] :
( ( ( SV19
!= ( plus_plus_a @ SV19 @ SV95 ) )
= $false )
| ( ( SV19
= ( plus_plus_a @ SV19 @ SV95 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[943]) ).
thf(994,plain,
! [SV19: a,SV95: a] :
( ( ( SV95 != zero_zero_a )
= $false )
| ( ( SV19
= ( plus_plus_a @ SV19 @ SV95 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[943]) ).
thf(995,plain,
! [SV95: a,SV19: a] :
( ( ( SV19
!= ( plus_plus_a @ SV19 @ SV95 ) )
= $false )
| ( ( SV95 = zero_zero_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[944]) ).
thf(996,plain,
! [SV95: a] :
( ( ( SV95 != zero_zero_a )
= $false )
| ( ( SV95 = zero_zero_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[944]) ).
thf(997,plain,
! [SV96: a,SV20: a] :
( ( ( SV20
!= ( plus_plus_a @ SV96 @ SV20 ) )
= $false )
| ( ( SV20
= ( plus_plus_a @ SV96 @ SV20 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[945]) ).
thf(998,plain,
! [SV20: a,SV96: a] :
( ( ( SV96 != zero_zero_a )
= $false )
| ( ( SV20
= ( plus_plus_a @ SV96 @ SV20 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[945]) ).
thf(999,plain,
! [SV96: a,SV20: a] :
( ( ( SV20
!= ( plus_plus_a @ SV96 @ SV20 ) )
= $false )
| ( ( SV96 = zero_zero_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[946]) ).
thf(1000,plain,
! [SV96: a] :
( ( ( SV96 != zero_zero_a )
= $false )
| ( ( SV96 = zero_zero_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[946]) ).
thf(1001,plain,
! [SV97: a,SV21: a] :
( ( ( ( plus_plus_a @ SV21 @ SV97 )
!= SV21 )
= $false )
| ( ( ( plus_plus_a @ SV21 @ SV97 )
= SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[947]) ).
thf(1002,plain,
! [SV21: a,SV97: a] :
( ( ( SV97 != zero_zero_a )
= $false )
| ( ( ( plus_plus_a @ SV21 @ SV97 )
= SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[947]) ).
thf(1003,plain,
! [SV97: a,SV21: a] :
( ( ( ( plus_plus_a @ SV21 @ SV97 )
!= SV21 )
= $false )
| ( ( SV97 = zero_zero_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[948]) ).
thf(1004,plain,
! [SV97: a] :
( ( ( SV97 != zero_zero_a )
= $false )
| ( ( SV97 = zero_zero_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[948]) ).
thf(1005,plain,
! [SV98: a,SV22: a] :
( ( ( ( plus_plus_a @ SV22 @ SV98 )
!= SV98 )
= $false )
| ( ( ( plus_plus_a @ SV22 @ SV98 )
= SV98 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[949]) ).
thf(1006,plain,
! [SV98: a,SV22: a] :
( ( ( SV22 != zero_zero_a )
= $false )
| ( ( ( plus_plus_a @ SV22 @ SV98 )
= SV98 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[949]) ).
thf(1007,plain,
! [SV98: a,SV22: a] :
( ( ( ( plus_plus_a @ SV22 @ SV98 )
!= SV98 )
= $false )
| ( ( SV22 = zero_zero_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[950]) ).
thf(1008,plain,
! [SV22: a] :
( ( ( SV22 != zero_zero_a )
= $false )
| ( ( SV22 = zero_zero_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[950]) ).
thf(1009,plain,
! [SV99: product_prod_a_a > $o,SV25: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV25 @ ( collec645855634od_a_a @ SV99 ) ) )
= $false )
| ( ( member449909584od_a_a @ SV25 @ ( collec645855634od_a_a @ SV99 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[951]) ).
thf(1010,plain,
! [SV25: product_prod_a_a,SV99: product_prod_a_a > $o] :
( ( ( ~ ( SV99 @ SV25 ) )
= $false )
| ( ( member449909584od_a_a @ SV25 @ ( collec645855634od_a_a @ SV99 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[951]) ).
thf(1011,plain,
! [SV99: product_prod_a_a > $o,SV25: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV25 @ ( collec645855634od_a_a @ SV99 ) ) )
= $false )
| ( ( SV99 @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[952]) ).
thf(1012,plain,
! [SV25: product_prod_a_a,SV99: product_prod_a_a > $o] :
( ( ( ~ ( SV99 @ SV25 ) )
= $false )
| ( ( SV99 @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[952]) ).
thf(1013,plain,
! [SV162: a,SV102: a,SV32: a] :
( ( ( ( ( plus_plus_a @ SV32 @ SV102 )
!= ( plus_plus_a @ SV162 @ SV102 ) )
| ( SV32 != SV162 ) )
= $false )
| ( ( ( plus_plus_a @ SV32 @ SV102 )
= ( plus_plus_a @ SV162 @ SV102 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[953]) ).
thf(1014,plain,
! [SV162: a,SV102: a,SV32: a] :
( ( ( ( ( plus_plus_a @ SV32 @ SV102 )
!= ( plus_plus_a @ SV162 @ SV102 ) )
| ( SV32 != SV162 ) )
= $false )
| ( ( SV32 = SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[954]) ).
thf(1015,plain,
! [SV163: a,SV103: a,SV33: a] :
( ( ( ( ( plus_plus_a @ SV33 @ SV103 )
!= ( plus_plus_a @ SV33 @ SV163 ) )
| ( SV103 != SV163 ) )
= $false )
| ( ( ( plus_plus_a @ SV33 @ SV103 )
= ( plus_plus_a @ SV33 @ SV163 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[955]) ).
thf(1016,plain,
! [SV163: a,SV103: a,SV33: a] :
( ( ( ( ( plus_plus_a @ SV33 @ SV103 )
!= ( plus_plus_a @ SV33 @ SV163 ) )
| ( SV103 != SV163 ) )
= $false )
| ( ( SV103 = SV163 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[956]) ).
thf(1017,plain,
! [SV166: a,SV106: real,SV36: a] :
( ( ( ( ( plus_plus_a @ SV36 @ ( real_V1035702895aleR_a @ SV106 @ SV166 ) )
!= ( plus_plus_a @ SV166 @ ( real_V1035702895aleR_a @ SV106 @ SV36 ) ) )
| ~ ( ( SV166 = SV36 )
| ( SV106 = one_one_real ) ) )
= $false )
| ( ( ( plus_plus_a @ SV36 @ ( real_V1035702895aleR_a @ SV106 @ SV166 ) )
= ( plus_plus_a @ SV166 @ ( real_V1035702895aleR_a @ SV106 @ SV36 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[957]) ).
thf(1018,plain,
! [SV106: real,SV36: a,SV166: a] :
( ( ( SV166 = SV36 )
= $false )
| ( ( ~ ( ( ( plus_plus_a @ SV36 @ ( real_V1035702895aleR_a @ SV106 @ SV166 ) )
!= ( plus_plus_a @ SV166 @ ( real_V1035702895aleR_a @ SV106 @ SV36 ) ) )
| ~ ( ( SV166 = SV36 )
| ( SV106 = one_one_real ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[958]) ).
thf(1019,plain,
! [SV166: a,SV36: a,SV106: real] :
( ( ( SV106 = one_one_real )
= $false )
| ( ( ~ ( ( ( plus_plus_a @ SV36 @ ( real_V1035702895aleR_a @ SV106 @ SV166 ) )
!= ( plus_plus_a @ SV166 @ ( real_V1035702895aleR_a @ SV106 @ SV36 ) ) )
| ~ ( ( SV166 = SV36 )
| ( SV106 = one_one_real ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[958]) ).
thf(1020,plain,
! [SV107: a,SV38: real] :
( ( ( ( real_V1035702895aleR_a @ SV38 @ SV107 )
!= zero_zero_a )
= $false )
| ( ( ( real_V1035702895aleR_a @ SV38 @ SV107 )
= zero_zero_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[959]) ).
thf(1021,plain,
! [SV107: a,SV38: real] :
( ( ( ~ ( ( SV38 = zero_zero_real )
| ( SV107 = zero_zero_a ) ) )
= $false )
| ( ( ( real_V1035702895aleR_a @ SV38 @ SV107 )
= zero_zero_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[959]) ).
thf(1022,plain,
! [SV107: a,SV38: real] :
( ( ( ( ( real_V1035702895aleR_a @ SV38 @ SV107 )
!= zero_zero_a )
| ~ ( ( SV38 = zero_zero_real )
| ( SV107 = zero_zero_a ) ) )
= $false )
| ( ( SV38 = zero_zero_real )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[960]) ).
thf(1023,plain,
! [SV107: a,SV38: real] :
( ( ( ( ( real_V1035702895aleR_a @ SV38 @ SV107 )
!= zero_zero_a )
| ~ ( ( SV38 = zero_zero_real )
| ( SV107 = zero_zero_a ) ) )
= $false )
| ( ( SV107 = zero_zero_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[961]) ).
thf(1024,plain,
! [SV167: a,SV108: a,SV40: real] :
( ( ( ( ( real_V1035702895aleR_a @ SV40 @ SV108 )
!= ( real_V1035702895aleR_a @ SV40 @ SV167 ) )
| ~ ( ( SV108 = SV167 )
| ( SV40 = zero_zero_real ) ) )
= $false )
| ( ( ( real_V1035702895aleR_a @ SV40 @ SV108 )
= ( real_V1035702895aleR_a @ SV40 @ SV167 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[962]) ).
thf(1025,plain,
! [SV40: real,SV167: a,SV108: a] :
( ( ( SV108 = SV167 )
= $false )
| ( ( ~ ( ( ( real_V1035702895aleR_a @ SV40 @ SV108 )
!= ( real_V1035702895aleR_a @ SV40 @ SV167 ) )
| ~ ( ( SV108 = SV167 )
| ( SV40 = zero_zero_real ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[963]) ).
thf(1026,plain,
! [SV167: a,SV108: a,SV40: real] :
( ( ( SV40 = zero_zero_real )
= $false )
| ( ( ~ ( ( ( real_V1035702895aleR_a @ SV40 @ SV108 )
!= ( real_V1035702895aleR_a @ SV40 @ SV167 ) )
| ~ ( ( SV108 = SV167 )
| ( SV40 = zero_zero_real ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[963]) ).
thf(1027,plain,
! [SV168: real,SV109: a,SV41: real] :
( ( ( ( ( real_V1035702895aleR_a @ SV41 @ SV109 )
!= ( real_V1035702895aleR_a @ SV168 @ SV109 ) )
| ~ ( ( SV41 = SV168 )
| ( SV109 = zero_zero_a ) ) )
= $false )
| ( ( ( real_V1035702895aleR_a @ SV41 @ SV109 )
= ( real_V1035702895aleR_a @ SV168 @ SV109 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[964]) ).
thf(1028,plain,
! [SV109: a,SV168: real,SV41: real] :
( ( ( SV41 = SV168 )
= $false )
| ( ( ~ ( ( ( real_V1035702895aleR_a @ SV41 @ SV109 )
!= ( real_V1035702895aleR_a @ SV168 @ SV109 ) )
| ~ ( ( SV41 = SV168 )
| ( SV109 = zero_zero_a ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[965]) ).
thf(1029,plain,
! [SV168: real,SV41: real,SV109: a] :
( ( ( SV109 = zero_zero_a )
= $false )
| ( ( ~ ( ( ( real_V1035702895aleR_a @ SV41 @ SV109 )
!= ( real_V1035702895aleR_a @ SV168 @ SV109 ) )
| ~ ( ( SV41 = SV168 )
| ( SV109 = zero_zero_a ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[965]) ).
thf(1030,plain,
! [SV202: a,SV173: a,SV114: a,SV47: a] :
( ( ( ( product_Pair_a_a @ SV47 @ SV114 )
= ( product_Pair_a_a @ SV173 @ SV202 ) )
= $false )
| ( ( ~ ( ( ( product_Pair_a_a @ SV47 @ SV114 )
!= ( product_Pair_a_a @ SV173 @ SV202 ) )
| ~ ~ ( ( SV47 != SV173 )
| ( SV114 != SV202 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[966]) ).
thf(1031,plain,
! [SV202: a,SV114: a,SV173: a,SV47: a] :
( ( ( ~ ( ( SV47 != SV173 )
| ( SV114 != SV202 ) ) )
= $false )
| ( ( ~ ( ( ( product_Pair_a_a @ SV47 @ SV114 )
!= ( product_Pair_a_a @ SV173 @ SV202 ) )
| ~ ~ ( ( SV47 != SV173 )
| ( SV114 != SV202 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[966]) ).
thf(1032,plain,
! [SV116: set_Product_prod_a_a,SV175: set_Product_prod_a_a,SV49: product_prod_a_a] :
( ( ( ( SV49
!= ( plus_p1505579230od_a_a @ ( sK10_SY457 @ SV175 @ SV116 @ SV49 ) @ ( sK12_SY479 @ SV116 @ SV175 @ SV49 ) ) )
| ~ ( member449909584od_a_a @ ( sK10_SY457 @ SV175 @ SV116 @ SV49 ) @ SV116 )
| ~ ( member449909584od_a_a @ ( sK12_SY479 @ SV116 @ SV175 @ SV49 ) @ SV175 ) )
= $false )
| ( ( member449909584od_a_a @ SV49 @ ( plus_p634297534od_a_a @ SV116 @ SV175 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[968]) ).
thf(1033,plain,
! [SV117: set_Product_prod_a_a,SV50: product_prod_a_a,SV203: set_Product_prod_a_a,SV176: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV176 @ SV203 )
= $false )
| ( ( member449909584od_a_a @ ( plus_p1505579230od_a_a @ SV50 @ SV176 ) @ ( plus_p634297534od_a_a @ SV117 @ SV203 ) )
= $true )
| ( ( member449909584od_a_a @ SV50 @ SV117 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[969]) ).
thf(1034,plain,
! [SV118: set_a,SV51: a,SV204: set_a,SV177: a] :
( ( ( member_a @ SV177 @ SV204 )
= $false )
| ( ( member_a @ ( plus_plus_a @ SV51 @ SV177 ) @ ( plus_plus_set_a @ SV118 @ SV204 ) )
= $true )
| ( ( member_a @ SV51 @ SV118 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[970]) ).
thf(1035,plain,
! [SV205: a,SV119: a,SV178: a,SV52: a] :
( ( ( SV52 != SV178 )
= $false )
| ( ( ( product_Pair_a_a @ SV52 @ SV119 )
= ( product_Pair_a_a @ SV178 @ SV205 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[971]) ).
thf(1036,plain,
! [SV178: a,SV52: a,SV205: a,SV119: a] :
( ( ( SV119 != SV205 )
= $false )
| ( ( ( product_Pair_a_a @ SV52 @ SV119 )
= ( product_Pair_a_a @ SV178 @ SV205 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[971]) ).
thf(1037,plain,
! [SV120: a,SV206: a,SV179: real,SV53: real] :
( ( ( SV53 != SV179 )
= $false )
| ( ( SV206 = SV120 )
= $true )
| ( ( ( plus_plus_a @ ( real_V1035702895aleR_a @ SV53 @ SV120 ) @ ( real_V1035702895aleR_a @ SV179 @ SV206 ) )
= ( plus_plus_a @ ( real_V1035702895aleR_a @ SV53 @ SV206 ) @ ( real_V1035702895aleR_a @ SV179 @ SV120 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[972]) ).
thf(1038,plain,
( ( ( u = one_one_real )
= $true )
| ( ( u = zero_zero_real )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ ( plus_plus_a @ ( real_V1035702895aleR_a @ u @ x ) @ ( real_V1035702895aleR_a @ v @ y ) ) @ y ) @ relation )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[973]) ).
thf(1039,plain,
! [SV207: set_Product_prod_a_a,SV121: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV121 @ SV207 )
= $false )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV121 @ SV207 )
| ~ ! [SY474: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY474 @ SV121 )
| ( member449909584od_a_a @ SY474 @ SV207 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[974]) ).
thf(1040,plain,
! [SV207: set_Product_prod_a_a,SV121: set_Product_prod_a_a] :
( ( ( ! [SY474: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY474 @ SV121 )
| ( member449909584od_a_a @ SY474 @ SV207 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV121 @ SV207 )
| ~ ! [SY474: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY474 @ SV121 )
| ( member449909584od_a_a @ SY474 @ SV207 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[974]) ).
thf(1041,plain,
! [SV122: set_a,SV181: set_a,SV55: a] :
( ( ( ( SV55
!= ( plus_plus_a @ ( sK11_SY464 @ SV181 @ SV122 @ SV55 ) @ ( sK13_SY480 @ SV122 @ SV181 @ SV55 ) ) )
| ~ ( member_a @ ( sK11_SY464 @ SV181 @ SV122 @ SV55 ) @ SV122 )
| ~ ( member_a @ ( sK13_SY480 @ SV122 @ SV181 @ SV55 ) @ SV181 ) )
= $false )
| ( ( member_a @ SV55 @ ( plus_plus_set_a @ SV122 @ SV181 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[975]) ).
thf(1042,plain,
! [SV208: a,SV182: a,SV123: a,SV56: a] :
( ( ( ( product_Pair_a_a @ SV56 @ SV123 )
= ( product_Pair_a_a @ SV182 @ SV208 ) )
= $false )
| ( ( ~ ( ( ( product_Pair_a_a @ SV56 @ SV123 )
!= ( product_Pair_a_a @ SV182 @ SV208 ) )
| ~ ~ ( ( SV56 != SV182 )
| ( SV123 != SV208 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[976]) ).
thf(1043,plain,
! [SV208: a,SV123: a,SV182: a,SV56: a] :
( ( ( ~ ( ( SV56 != SV182 )
| ( SV123 != SV208 ) ) )
= $false )
| ( ( ~ ( ( ( product_Pair_a_a @ SV56 @ SV123 )
!= ( product_Pair_a_a @ SV182 @ SV208 ) )
| ~ ~ ( ( SV56 != SV182 )
| ( SV123 != SV208 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[976]) ).
thf(1044,plain,
! [SV183: a,SV124: a,SV57: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV124 ) @ relation )
= $false )
| ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV57 ) @ relation ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV183 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV183 @ SV124 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV183 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV183 @ SV57 ) @ relation ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[977]) ).
thf(1045,plain,
! [SV125: set_Product_prod_a_a,SV58: set_Product_prod_a_a,SV213: product_prod_a_a,SV209: set_Product_prod_a_a,SV184: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV184 @ SV209 ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ SV213 @ ( plus_p634297534od_a_a @ SV58 @ SV184 ) )
| ( member449909584od_a_a @ SV213 @ ( plus_p634297534od_a_a @ SV125 @ SV209 ) ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV58 @ SV125 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[978]) ).
thf(1046,plain,
! [SV185: a,SV128: a,SV61: real] :
( ( ( ( real_V1035702895aleR_a @ SV61 @ SV128 )
= ( real_V1035702895aleR_a @ SV61 @ SV185 ) )
= $false )
| ( ( SV128 = SV185 )
= $true )
| ( ( SV61 = zero_zero_real )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[980]) ).
thf(1047,plain,
! [SV186: a,SV129: a,SV62: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV62 @ SV129 ) @ relation )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV129 @ SV62 ) @ relation ) )
= $true )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV129 @ SV186 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV186 @ SV129 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV62 @ SV186 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV186 @ SV62 ) @ relation ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[981]) ).
thf(1048,plain,
! [SV64: a,SV130: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV64 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV64 @ SV130 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV130 @ SV64 ) @ relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[982]) ).
thf(1049,plain,
! [SV187: real,SV65: a,SV131: real] :
( ( ( ( real_V1035702895aleR_a @ SV131 @ SV65 )
= ( real_V1035702895aleR_a @ SV187 @ SV65 ) )
= $false )
| ( ( SV131 = SV187 )
= $true )
| ( ( SV65 = zero_zero_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[983]) ).
thf(1050,plain,
! [SV70: a,SV135: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV135 @ SV70 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV70 @ SV135 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV70 @ SV135 ) @ relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[986]) ).
thf(1051,plain,
! [SV212: set_Product_prod_a_a,SV140: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV140 @ SV212 )
= $false )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV140 @ SV212 )
| ~ ! [SY476: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY476 @ SV140 )
| ( member449909584od_a_a @ SY476 @ SV212 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[988]) ).
thf(1052,plain,
! [SV212: set_Product_prod_a_a,SV140: set_Product_prod_a_a] :
( ( ( ! [SY476: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY476 @ SV140 )
| ( member449909584od_a_a @ SY476 @ SV212 ) ) )
= $false )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV140 @ SV212 )
| ~ ! [SY476: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY476 @ SV140 )
| ( member449909584od_a_a @ SY476 @ SV212 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[988]) ).
thf(1053,plain,
! [SV158: a,SV93: a,SV17: a] :
( ( ( ( plus_plus_a @ SV17 @ SV93 )
!= ( plus_plus_a @ SV17 @ SV158 ) )
= $false )
| ( ( ( plus_plus_a @ SV17 @ SV93 )
= ( plus_plus_a @ SV17 @ SV158 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[989]) ).
thf(1054,plain,
! [SV17: a,SV158: a,SV93: a] :
( ( ( SV93 != SV158 )
= $false )
| ( ( ( plus_plus_a @ SV17 @ SV93 )
= ( plus_plus_a @ SV17 @ SV158 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[989]) ).
thf(1055,plain,
! [SV158: a,SV93: a,SV17: a] :
( ( ( ( plus_plus_a @ SV17 @ SV93 )
!= ( plus_plus_a @ SV17 @ SV158 ) )
= $false )
| ( ( SV93 = SV158 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[990]) ).
thf(1056,plain,
! [SV158: a,SV93: a] :
( ( ( SV93 != SV158 )
= $false )
| ( ( SV93 = SV158 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[990]) ).
thf(1057,plain,
! [SV159: a,SV94: a,SV18: a] :
( ( ( ( plus_plus_a @ SV18 @ SV94 )
!= ( plus_plus_a @ SV159 @ SV94 ) )
= $false )
| ( ( ( plus_plus_a @ SV18 @ SV94 )
= ( plus_plus_a @ SV159 @ SV94 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[991]) ).
thf(1058,plain,
! [SV94: a,SV159: a,SV18: a] :
( ( ( SV18 != SV159 )
= $false )
| ( ( ( plus_plus_a @ SV18 @ SV94 )
= ( plus_plus_a @ SV159 @ SV94 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[991]) ).
thf(1059,plain,
! [SV159: a,SV94: a,SV18: a] :
( ( ( ( plus_plus_a @ SV18 @ SV94 )
!= ( plus_plus_a @ SV159 @ SV94 ) )
= $false )
| ( ( SV18 = SV159 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[992]) ).
thf(1060,plain,
! [SV159: a,SV18: a] :
( ( ( SV18 != SV159 )
= $false )
| ( ( SV18 = SV159 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[992]) ).
thf(1061,plain,
! [SV95: a,SV19: a] :
( ( ( SV19
= ( plus_plus_a @ SV19 @ SV95 ) )
= $true )
| ( ( SV19
= ( plus_plus_a @ SV19 @ SV95 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[993]) ).
thf(1062,plain,
! [SV19: a,SV95: a] :
( ( ( SV95 = zero_zero_a )
= $true )
| ( ( SV19
= ( plus_plus_a @ SV19 @ SV95 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[994]) ).
thf(1063,plain,
! [SV95: a,SV19: a] :
( ( ( SV19
= ( plus_plus_a @ SV19 @ SV95 ) )
= $true )
| ( ( SV95 = zero_zero_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[995]) ).
thf(1064,plain,
! [SV95: a] :
( ( ( SV95 = zero_zero_a )
= $true )
| ( ( SV95 = zero_zero_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[996]) ).
thf(1065,plain,
! [SV96: a,SV20: a] :
( ( ( SV20
= ( plus_plus_a @ SV96 @ SV20 ) )
= $true )
| ( ( SV20
= ( plus_plus_a @ SV96 @ SV20 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[997]) ).
thf(1066,plain,
! [SV20: a,SV96: a] :
( ( ( SV96 = zero_zero_a )
= $true )
| ( ( SV20
= ( plus_plus_a @ SV96 @ SV20 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[998]) ).
thf(1067,plain,
! [SV96: a,SV20: a] :
( ( ( SV20
= ( plus_plus_a @ SV96 @ SV20 ) )
= $true )
| ( ( SV96 = zero_zero_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[999]) ).
thf(1068,plain,
! [SV96: a] :
( ( ( SV96 = zero_zero_a )
= $true )
| ( ( SV96 = zero_zero_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1000]) ).
thf(1069,plain,
! [SV97: a,SV21: a] :
( ( ( ( plus_plus_a @ SV21 @ SV97 )
= SV21 )
= $true )
| ( ( ( plus_plus_a @ SV21 @ SV97 )
= SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1001]) ).
thf(1070,plain,
! [SV21: a,SV97: a] :
( ( ( SV97 = zero_zero_a )
= $true )
| ( ( ( plus_plus_a @ SV21 @ SV97 )
= SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1002]) ).
thf(1071,plain,
! [SV97: a,SV21: a] :
( ( ( ( plus_plus_a @ SV21 @ SV97 )
= SV21 )
= $true )
| ( ( SV97 = zero_zero_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1003]) ).
thf(1072,plain,
! [SV97: a] :
( ( ( SV97 = zero_zero_a )
= $true )
| ( ( SV97 = zero_zero_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1004]) ).
thf(1073,plain,
! [SV98: a,SV22: a] :
( ( ( ( plus_plus_a @ SV22 @ SV98 )
= SV98 )
= $true )
| ( ( ( plus_plus_a @ SV22 @ SV98 )
= SV98 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1005]) ).
thf(1074,plain,
! [SV98: a,SV22: a] :
( ( ( SV22 = zero_zero_a )
= $true )
| ( ( ( plus_plus_a @ SV22 @ SV98 )
= SV98 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1006]) ).
thf(1075,plain,
! [SV98: a,SV22: a] :
( ( ( ( plus_plus_a @ SV22 @ SV98 )
= SV98 )
= $true )
| ( ( SV22 = zero_zero_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1007]) ).
thf(1076,plain,
! [SV22: a] :
( ( ( SV22 = zero_zero_a )
= $true )
| ( ( SV22 = zero_zero_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1008]) ).
thf(1077,plain,
! [SV99: product_prod_a_a > $o,SV25: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV25 @ ( collec645855634od_a_a @ SV99 ) )
= $true )
| ( ( member449909584od_a_a @ SV25 @ ( collec645855634od_a_a @ SV99 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1009]) ).
thf(1078,plain,
! [SV25: product_prod_a_a,SV99: product_prod_a_a > $o] :
( ( ( SV99 @ SV25 )
= $true )
| ( ( member449909584od_a_a @ SV25 @ ( collec645855634od_a_a @ SV99 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1010]) ).
thf(1079,plain,
! [SV99: product_prod_a_a > $o,SV25: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV25 @ ( collec645855634od_a_a @ SV99 ) )
= $true )
| ( ( SV99 @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1011]) ).
thf(1080,plain,
! [SV25: product_prod_a_a,SV99: product_prod_a_a > $o] :
( ( ( SV99 @ SV25 )
= $true )
| ( ( SV99 @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1012]) ).
thf(1081,plain,
! [SV162: a,SV102: a,SV32: a] :
( ( ( ( plus_plus_a @ SV32 @ SV102 )
!= ( plus_plus_a @ SV162 @ SV102 ) )
= $false )
| ( ( ( plus_plus_a @ SV32 @ SV102 )
= ( plus_plus_a @ SV162 @ SV102 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1013]) ).
thf(1082,plain,
! [SV102: a,SV162: a,SV32: a] :
( ( ( SV32 != SV162 )
= $false )
| ( ( ( plus_plus_a @ SV32 @ SV102 )
= ( plus_plus_a @ SV162 @ SV102 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1013]) ).
thf(1083,plain,
! [SV162: a,SV102: a,SV32: a] :
( ( ( ( plus_plus_a @ SV32 @ SV102 )
!= ( plus_plus_a @ SV162 @ SV102 ) )
= $false )
| ( ( SV32 = SV162 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1014]) ).
thf(1084,plain,
! [SV162: a,SV32: a] :
( ( ( SV32 != SV162 )
= $false )
| ( ( SV32 = SV162 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1014]) ).
thf(1085,plain,
! [SV163: a,SV103: a,SV33: a] :
( ( ( ( plus_plus_a @ SV33 @ SV103 )
!= ( plus_plus_a @ SV33 @ SV163 ) )
= $false )
| ( ( ( plus_plus_a @ SV33 @ SV103 )
= ( plus_plus_a @ SV33 @ SV163 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1015]) ).
thf(1086,plain,
! [SV33: a,SV163: a,SV103: a] :
( ( ( SV103 != SV163 )
= $false )
| ( ( ( plus_plus_a @ SV33 @ SV103 )
= ( plus_plus_a @ SV33 @ SV163 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1015]) ).
thf(1087,plain,
! [SV163: a,SV103: a,SV33: a] :
( ( ( ( plus_plus_a @ SV33 @ SV103 )
!= ( plus_plus_a @ SV33 @ SV163 ) )
= $false )
| ( ( SV103 = SV163 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1016]) ).
thf(1088,plain,
! [SV163: a,SV103: a] :
( ( ( SV103 != SV163 )
= $false )
| ( ( SV103 = SV163 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1016]) ).
thf(1089,plain,
! [SV166: a,SV106: real,SV36: a] :
( ( ( ( plus_plus_a @ SV36 @ ( real_V1035702895aleR_a @ SV106 @ SV166 ) )
!= ( plus_plus_a @ SV166 @ ( real_V1035702895aleR_a @ SV106 @ SV36 ) ) )
= $false )
| ( ( ( plus_plus_a @ SV36 @ ( real_V1035702895aleR_a @ SV106 @ SV166 ) )
= ( plus_plus_a @ SV166 @ ( real_V1035702895aleR_a @ SV106 @ SV36 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1017]) ).
thf(1090,plain,
! [SV106: real,SV36: a,SV166: a] :
( ( ( ~ ( ( SV166 = SV36 )
| ( SV106 = one_one_real ) ) )
= $false )
| ( ( ( plus_plus_a @ SV36 @ ( real_V1035702895aleR_a @ SV106 @ SV166 ) )
= ( plus_plus_a @ SV166 @ ( real_V1035702895aleR_a @ SV106 @ SV36 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1017]) ).
thf(1091,plain,
! [SV166: a,SV106: real,SV36: a] :
( ( ( ( ( plus_plus_a @ SV36 @ ( real_V1035702895aleR_a @ SV106 @ SV166 ) )
!= ( plus_plus_a @ SV166 @ ( real_V1035702895aleR_a @ SV106 @ SV36 ) ) )
| ~ ( ( SV166 = SV36 )
| ( SV106 = one_one_real ) ) )
= $false )
| ( ( SV166 = SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1018]) ).
thf(1092,plain,
! [SV166: a,SV106: real,SV36: a] :
( ( ( ( ( plus_plus_a @ SV36 @ ( real_V1035702895aleR_a @ SV106 @ SV166 ) )
!= ( plus_plus_a @ SV166 @ ( real_V1035702895aleR_a @ SV106 @ SV36 ) ) )
| ~ ( ( SV166 = SV36 )
| ( SV106 = one_one_real ) ) )
= $false )
| ( ( SV106 = one_one_real )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1019]) ).
thf(1093,plain,
! [SV107: a,SV38: real] :
( ( ( ( real_V1035702895aleR_a @ SV38 @ SV107 )
= zero_zero_a )
= $true )
| ( ( ( real_V1035702895aleR_a @ SV38 @ SV107 )
= zero_zero_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1020]) ).
thf(1094,plain,
! [SV107: a,SV38: real] :
( ( ( ( SV38 = zero_zero_real )
| ( SV107 = zero_zero_a ) )
= $true )
| ( ( ( real_V1035702895aleR_a @ SV38 @ SV107 )
= zero_zero_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1021]) ).
thf(1095,plain,
! [SV107: a,SV38: real] :
( ( ( ( real_V1035702895aleR_a @ SV38 @ SV107 )
!= zero_zero_a )
= $false )
| ( ( SV38 = zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1022]) ).
thf(1096,plain,
! [SV107: a,SV38: real] :
( ( ( ~ ( ( SV38 = zero_zero_real )
| ( SV107 = zero_zero_a ) ) )
= $false )
| ( ( SV38 = zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1022]) ).
thf(1097,plain,
! [SV107: a,SV38: real] :
( ( ( ( real_V1035702895aleR_a @ SV38 @ SV107 )
!= zero_zero_a )
= $false )
| ( ( SV107 = zero_zero_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1023]) ).
thf(1098,plain,
! [SV107: a,SV38: real] :
( ( ( ~ ( ( SV38 = zero_zero_real )
| ( SV107 = zero_zero_a ) ) )
= $false )
| ( ( SV107 = zero_zero_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1023]) ).
thf(1099,plain,
! [SV167: a,SV108: a,SV40: real] :
( ( ( ( real_V1035702895aleR_a @ SV40 @ SV108 )
!= ( real_V1035702895aleR_a @ SV40 @ SV167 ) )
= $false )
| ( ( ( real_V1035702895aleR_a @ SV40 @ SV108 )
= ( real_V1035702895aleR_a @ SV40 @ SV167 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1024]) ).
thf(1100,plain,
! [SV40: real,SV167: a,SV108: a] :
( ( ( ~ ( ( SV108 = SV167 )
| ( SV40 = zero_zero_real ) ) )
= $false )
| ( ( ( real_V1035702895aleR_a @ SV40 @ SV108 )
= ( real_V1035702895aleR_a @ SV40 @ SV167 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1024]) ).
thf(1101,plain,
! [SV167: a,SV108: a,SV40: real] :
( ( ( ( ( real_V1035702895aleR_a @ SV40 @ SV108 )
!= ( real_V1035702895aleR_a @ SV40 @ SV167 ) )
| ~ ( ( SV108 = SV167 )
| ( SV40 = zero_zero_real ) ) )
= $false )
| ( ( SV108 = SV167 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1025]) ).
thf(1102,plain,
! [SV167: a,SV108: a,SV40: real] :
( ( ( ( ( real_V1035702895aleR_a @ SV40 @ SV108 )
!= ( real_V1035702895aleR_a @ SV40 @ SV167 ) )
| ~ ( ( SV108 = SV167 )
| ( SV40 = zero_zero_real ) ) )
= $false )
| ( ( SV40 = zero_zero_real )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1026]) ).
thf(1103,plain,
! [SV168: real,SV109: a,SV41: real] :
( ( ( ( real_V1035702895aleR_a @ SV41 @ SV109 )
!= ( real_V1035702895aleR_a @ SV168 @ SV109 ) )
= $false )
| ( ( ( real_V1035702895aleR_a @ SV41 @ SV109 )
= ( real_V1035702895aleR_a @ SV168 @ SV109 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1027]) ).
thf(1104,plain,
! [SV109: a,SV168: real,SV41: real] :
( ( ( ~ ( ( SV41 = SV168 )
| ( SV109 = zero_zero_a ) ) )
= $false )
| ( ( ( real_V1035702895aleR_a @ SV41 @ SV109 )
= ( real_V1035702895aleR_a @ SV168 @ SV109 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1027]) ).
thf(1105,plain,
! [SV168: real,SV109: a,SV41: real] :
( ( ( ( ( real_V1035702895aleR_a @ SV41 @ SV109 )
!= ( real_V1035702895aleR_a @ SV168 @ SV109 ) )
| ~ ( ( SV41 = SV168 )
| ( SV109 = zero_zero_a ) ) )
= $false )
| ( ( SV41 = SV168 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1028]) ).
thf(1106,plain,
! [SV168: real,SV109: a,SV41: real] :
( ( ( ( ( real_V1035702895aleR_a @ SV41 @ SV109 )
!= ( real_V1035702895aleR_a @ SV168 @ SV109 ) )
| ~ ( ( SV41 = SV168 )
| ( SV109 = zero_zero_a ) ) )
= $false )
| ( ( SV109 = zero_zero_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1029]) ).
thf(1107,plain,
! [SV202: a,SV173: a,SV114: a,SV47: a] :
( ( ( ( ( product_Pair_a_a @ SV47 @ SV114 )
!= ( product_Pair_a_a @ SV173 @ SV202 ) )
| ~ ~ ( ( SV47 != SV173 )
| ( SV114 != SV202 ) ) )
= $false )
| ( ( ( product_Pair_a_a @ SV47 @ SV114 )
= ( product_Pair_a_a @ SV173 @ SV202 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1030]) ).
thf(1108,plain,
! [SV202: a,SV114: a,SV173: a,SV47: a] :
( ( ( ( SV47 != SV173 )
| ( SV114 != SV202 ) )
= $true )
| ( ( ~ ( ( ( product_Pair_a_a @ SV47 @ SV114 )
!= ( product_Pair_a_a @ SV173 @ SV202 ) )
| ~ ~ ( ( SV47 != SV173 )
| ( SV114 != SV202 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1031]) ).
thf(1109,plain,
! [SV116: set_Product_prod_a_a,SV175: set_Product_prod_a_a,SV49: product_prod_a_a] :
( ( ( SV49
!= ( plus_p1505579230od_a_a @ ( sK10_SY457 @ SV175 @ SV116 @ SV49 ) @ ( sK12_SY479 @ SV116 @ SV175 @ SV49 ) ) )
= $false )
| ( ( member449909584od_a_a @ SV49 @ ( plus_p634297534od_a_a @ SV116 @ SV175 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1032]) ).
thf(1110,plain,
! [SV49: product_prod_a_a,SV116: set_Product_prod_a_a,SV175: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK10_SY457 @ SV175 @ SV116 @ SV49 ) @ SV116 )
| ~ ( member449909584od_a_a @ ( sK12_SY479 @ SV116 @ SV175 @ SV49 ) @ SV175 ) )
= $false )
| ( ( member449909584od_a_a @ SV49 @ ( plus_p634297534od_a_a @ SV116 @ SV175 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1032]) ).
thf(1111,plain,
! [SV205: a,SV119: a,SV178: a,SV52: a] :
( ( ( SV52 = SV178 )
= $true )
| ( ( ( product_Pair_a_a @ SV52 @ SV119 )
= ( product_Pair_a_a @ SV178 @ SV205 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1035]) ).
thf(1112,plain,
! [SV178: a,SV52: a,SV205: a,SV119: a] :
( ( ( SV119 = SV205 )
= $true )
| ( ( ( product_Pair_a_a @ SV52 @ SV119 )
= ( product_Pair_a_a @ SV178 @ SV205 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1036]) ).
thf(1113,plain,
! [SV120: a,SV206: a,SV179: real,SV53: real] :
( ( ( SV53 = SV179 )
= $true )
| ( ( SV206 = SV120 )
= $true )
| ( ( ( plus_plus_a @ ( real_V1035702895aleR_a @ SV53 @ SV120 ) @ ( real_V1035702895aleR_a @ SV179 @ SV206 ) )
= ( plus_plus_a @ ( real_V1035702895aleR_a @ SV53 @ SV206 ) @ ( real_V1035702895aleR_a @ SV179 @ SV120 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1037]) ).
thf(1114,plain,
! [SV207: set_Product_prod_a_a,SV121: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV121 @ SV207 )
| ~ ! [SY474: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY474 @ SV121 )
| ( member449909584od_a_a @ SY474 @ SV207 ) ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV121 @ SV207 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1039]) ).
thf(1115,plain,
! [SV121: set_Product_prod_a_a,SV207: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK14_SY474 @ SV207 @ SV121 ) @ SV121 )
| ( member449909584od_a_a @ ( sK14_SY474 @ SV207 @ SV121 ) @ SV207 ) )
= $false )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV121 @ SV207 )
| ~ ! [SY474: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY474 @ SV121 )
| ( member449909584od_a_a @ SY474 @ SV207 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1040]) ).
thf(1116,plain,
! [SV122: set_a,SV181: set_a,SV55: a] :
( ( ( SV55
!= ( plus_plus_a @ ( sK11_SY464 @ SV181 @ SV122 @ SV55 ) @ ( sK13_SY480 @ SV122 @ SV181 @ SV55 ) ) )
= $false )
| ( ( member_a @ SV55 @ ( plus_plus_set_a @ SV122 @ SV181 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1041]) ).
thf(1117,plain,
! [SV55: a,SV122: set_a,SV181: set_a] :
( ( ( ~ ( member_a @ ( sK11_SY464 @ SV181 @ SV122 @ SV55 ) @ SV122 )
| ~ ( member_a @ ( sK13_SY480 @ SV122 @ SV181 @ SV55 ) @ SV181 ) )
= $false )
| ( ( member_a @ SV55 @ ( plus_plus_set_a @ SV122 @ SV181 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1041]) ).
thf(1118,plain,
! [SV208: a,SV182: a,SV123: a,SV56: a] :
( ( ( ( ( product_Pair_a_a @ SV56 @ SV123 )
!= ( product_Pair_a_a @ SV182 @ SV208 ) )
| ~ ~ ( ( SV56 != SV182 )
| ( SV123 != SV208 ) ) )
= $false )
| ( ( ( product_Pair_a_a @ SV56 @ SV123 )
= ( product_Pair_a_a @ SV182 @ SV208 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1042]) ).
thf(1119,plain,
! [SV208: a,SV123: a,SV182: a,SV56: a] :
( ( ( ( SV56 != SV182 )
| ( SV123 != SV208 ) )
= $true )
| ( ( ~ ( ( ( product_Pair_a_a @ SV56 @ SV123 )
!= ( product_Pair_a_a @ SV182 @ SV208 ) )
| ~ ~ ( ( SV56 != SV182 )
| ( SV123 != SV208 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1043]) ).
thf(1120,plain,
! [SV183: a,SV57: a,SV124: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV57 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV124 ) @ relation )
= $false )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV183 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV183 @ SV124 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV183 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV183 @ SV57 ) @ relation ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1044]) ).
thf(1121,plain,
! [SV125: set_Product_prod_a_a,SV58: set_Product_prod_a_a,SV213: product_prod_a_a,SV209: set_Product_prod_a_a,SV184: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV184 @ SV209 )
= $false )
| ( ( ~ ( member449909584od_a_a @ SV213 @ ( plus_p634297534od_a_a @ SV58 @ SV184 ) )
| ( member449909584od_a_a @ SV213 @ ( plus_p634297534od_a_a @ SV125 @ SV209 ) ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV58 @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1045]) ).
thf(1122,plain,
! [SV186: a,SV62: a,SV129: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV129 @ SV62 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV62 @ SV129 ) @ relation )
= $false )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV129 @ SV186 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV186 @ SV129 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV62 @ SV186 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV186 @ SV62 ) @ relation ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1047]) ).
thf(1123,plain,
! [SV212: set_Product_prod_a_a,SV140: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV140 @ SV212 )
| ~ ! [SY476: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY476 @ SV140 )
| ( member449909584od_a_a @ SY476 @ SV212 ) ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV140 @ SV212 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1051]) ).
thf(1124,plain,
! [SV140: set_Product_prod_a_a,SV212: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK15_SY476 @ SV212 @ SV140 ) @ SV140 )
| ( member449909584od_a_a @ ( sK15_SY476 @ SV212 @ SV140 ) @ SV212 ) )
= $false )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV140 @ SV212 )
| ~ ! [SY476: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY476 @ SV140 )
| ( member449909584od_a_a @ SY476 @ SV212 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1052]) ).
thf(1125,plain,
! [SV158: a,SV93: a,SV17: a] :
( ( ( ( plus_plus_a @ SV17 @ SV93 )
= ( plus_plus_a @ SV17 @ SV158 ) )
= $true )
| ( ( ( plus_plus_a @ SV17 @ SV93 )
= ( plus_plus_a @ SV17 @ SV158 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1053]) ).
thf(1126,plain,
! [SV17: a,SV158: a,SV93: a] :
( ( ( SV93 = SV158 )
= $true )
| ( ( ( plus_plus_a @ SV17 @ SV93 )
= ( plus_plus_a @ SV17 @ SV158 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1054]) ).
thf(1127,plain,
! [SV158: a,SV93: a,SV17: a] :
( ( ( ( plus_plus_a @ SV17 @ SV93 )
= ( plus_plus_a @ SV17 @ SV158 ) )
= $true )
| ( ( SV93 = SV158 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1055]) ).
thf(1128,plain,
! [SV158: a,SV93: a] :
( ( ( SV93 = SV158 )
= $true )
| ( ( SV93 = SV158 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1056]) ).
thf(1129,plain,
! [SV159: a,SV94: a,SV18: a] :
( ( ( ( plus_plus_a @ SV18 @ SV94 )
= ( plus_plus_a @ SV159 @ SV94 ) )
= $true )
| ( ( ( plus_plus_a @ SV18 @ SV94 )
= ( plus_plus_a @ SV159 @ SV94 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1057]) ).
thf(1130,plain,
! [SV94: a,SV159: a,SV18: a] :
( ( ( SV18 = SV159 )
= $true )
| ( ( ( plus_plus_a @ SV18 @ SV94 )
= ( plus_plus_a @ SV159 @ SV94 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1058]) ).
thf(1131,plain,
! [SV159: a,SV94: a,SV18: a] :
( ( ( ( plus_plus_a @ SV18 @ SV94 )
= ( plus_plus_a @ SV159 @ SV94 ) )
= $true )
| ( ( SV18 = SV159 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1059]) ).
thf(1132,plain,
! [SV159: a,SV18: a] :
( ( ( SV18 = SV159 )
= $true )
| ( ( SV18 = SV159 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1060]) ).
thf(1133,plain,
! [SV162: a,SV102: a,SV32: a] :
( ( ( ( plus_plus_a @ SV32 @ SV102 )
= ( plus_plus_a @ SV162 @ SV102 ) )
= $true )
| ( ( ( plus_plus_a @ SV32 @ SV102 )
= ( plus_plus_a @ SV162 @ SV102 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1081]) ).
thf(1134,plain,
! [SV102: a,SV162: a,SV32: a] :
( ( ( SV32 = SV162 )
= $true )
| ( ( ( plus_plus_a @ SV32 @ SV102 )
= ( plus_plus_a @ SV162 @ SV102 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1082]) ).
thf(1135,plain,
! [SV162: a,SV102: a,SV32: a] :
( ( ( ( plus_plus_a @ SV32 @ SV102 )
= ( plus_plus_a @ SV162 @ SV102 ) )
= $true )
| ( ( SV32 = SV162 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1083]) ).
thf(1136,plain,
! [SV162: a,SV32: a] :
( ( ( SV32 = SV162 )
= $true )
| ( ( SV32 = SV162 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1084]) ).
thf(1137,plain,
! [SV163: a,SV103: a,SV33: a] :
( ( ( ( plus_plus_a @ SV33 @ SV103 )
= ( plus_plus_a @ SV33 @ SV163 ) )
= $true )
| ( ( ( plus_plus_a @ SV33 @ SV103 )
= ( plus_plus_a @ SV33 @ SV163 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1085]) ).
thf(1138,plain,
! [SV33: a,SV163: a,SV103: a] :
( ( ( SV103 = SV163 )
= $true )
| ( ( ( plus_plus_a @ SV33 @ SV103 )
= ( plus_plus_a @ SV33 @ SV163 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1086]) ).
thf(1139,plain,
! [SV163: a,SV103: a,SV33: a] :
( ( ( ( plus_plus_a @ SV33 @ SV103 )
= ( plus_plus_a @ SV33 @ SV163 ) )
= $true )
| ( ( SV103 = SV163 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1087]) ).
thf(1140,plain,
! [SV163: a,SV103: a] :
( ( ( SV103 = SV163 )
= $true )
| ( ( SV103 = SV163 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1088]) ).
thf(1141,plain,
! [SV166: a,SV106: real,SV36: a] :
( ( ( ( plus_plus_a @ SV36 @ ( real_V1035702895aleR_a @ SV106 @ SV166 ) )
= ( plus_plus_a @ SV166 @ ( real_V1035702895aleR_a @ SV106 @ SV36 ) ) )
= $true )
| ( ( ( plus_plus_a @ SV36 @ ( real_V1035702895aleR_a @ SV106 @ SV166 ) )
= ( plus_plus_a @ SV166 @ ( real_V1035702895aleR_a @ SV106 @ SV36 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1089]) ).
thf(1142,plain,
! [SV106: real,SV36: a,SV166: a] :
( ( ( ( SV166 = SV36 )
| ( SV106 = one_one_real ) )
= $true )
| ( ( ( plus_plus_a @ SV36 @ ( real_V1035702895aleR_a @ SV106 @ SV166 ) )
= ( plus_plus_a @ SV166 @ ( real_V1035702895aleR_a @ SV106 @ SV36 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1090]) ).
thf(1143,plain,
! [SV166: a,SV106: real,SV36: a] :
( ( ( ( plus_plus_a @ SV36 @ ( real_V1035702895aleR_a @ SV106 @ SV166 ) )
!= ( plus_plus_a @ SV166 @ ( real_V1035702895aleR_a @ SV106 @ SV36 ) ) )
= $false )
| ( ( SV166 = SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1091]) ).
thf(1144,plain,
! [SV106: real,SV36: a,SV166: a] :
( ( ( ~ ( ( SV166 = SV36 )
| ( SV106 = one_one_real ) ) )
= $false )
| ( ( SV166 = SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1091]) ).
thf(1145,plain,
! [SV166: a,SV106: real,SV36: a] :
( ( ( ( plus_plus_a @ SV36 @ ( real_V1035702895aleR_a @ SV106 @ SV166 ) )
!= ( plus_plus_a @ SV166 @ ( real_V1035702895aleR_a @ SV106 @ SV36 ) ) )
= $false )
| ( ( SV106 = one_one_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1092]) ).
thf(1146,plain,
! [SV106: real,SV36: a,SV166: a] :
( ( ( ~ ( ( SV166 = SV36 )
| ( SV106 = one_one_real ) ) )
= $false )
| ( ( SV106 = one_one_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1092]) ).
thf(1147,plain,
! [SV107: a,SV38: real] :
( ( ( SV38 = zero_zero_real )
= $true )
| ( ( SV107 = zero_zero_a )
= $true )
| ( ( ( real_V1035702895aleR_a @ SV38 @ SV107 )
= zero_zero_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1094]) ).
thf(1148,plain,
! [SV107: a,SV38: real] :
( ( ( ( real_V1035702895aleR_a @ SV38 @ SV107 )
= zero_zero_a )
= $true )
| ( ( SV38 = zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1095]) ).
thf(1149,plain,
! [SV107: a,SV38: real] :
( ( ( ( SV38 = zero_zero_real )
| ( SV107 = zero_zero_a ) )
= $true )
| ( ( SV38 = zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1096]) ).
thf(1150,plain,
! [SV107: a,SV38: real] :
( ( ( ( real_V1035702895aleR_a @ SV38 @ SV107 )
= zero_zero_a )
= $true )
| ( ( SV107 = zero_zero_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1097]) ).
thf(1151,plain,
! [SV107: a,SV38: real] :
( ( ( ( SV38 = zero_zero_real )
| ( SV107 = zero_zero_a ) )
= $true )
| ( ( SV107 = zero_zero_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1098]) ).
thf(1152,plain,
! [SV167: a,SV108: a,SV40: real] :
( ( ( ( real_V1035702895aleR_a @ SV40 @ SV108 )
= ( real_V1035702895aleR_a @ SV40 @ SV167 ) )
= $true )
| ( ( ( real_V1035702895aleR_a @ SV40 @ SV108 )
= ( real_V1035702895aleR_a @ SV40 @ SV167 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1099]) ).
thf(1153,plain,
! [SV40: real,SV167: a,SV108: a] :
( ( ( ( SV108 = SV167 )
| ( SV40 = zero_zero_real ) )
= $true )
| ( ( ( real_V1035702895aleR_a @ SV40 @ SV108 )
= ( real_V1035702895aleR_a @ SV40 @ SV167 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1100]) ).
thf(1154,plain,
! [SV167: a,SV108: a,SV40: real] :
( ( ( ( real_V1035702895aleR_a @ SV40 @ SV108 )
!= ( real_V1035702895aleR_a @ SV40 @ SV167 ) )
= $false )
| ( ( SV108 = SV167 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1101]) ).
thf(1155,plain,
! [SV40: real,SV167: a,SV108: a] :
( ( ( ~ ( ( SV108 = SV167 )
| ( SV40 = zero_zero_real ) ) )
= $false )
| ( ( SV108 = SV167 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1101]) ).
thf(1156,plain,
! [SV167: a,SV108: a,SV40: real] :
( ( ( ( real_V1035702895aleR_a @ SV40 @ SV108 )
!= ( real_V1035702895aleR_a @ SV40 @ SV167 ) )
= $false )
| ( ( SV40 = zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1102]) ).
thf(1157,plain,
! [SV40: real,SV167: a,SV108: a] :
( ( ( ~ ( ( SV108 = SV167 )
| ( SV40 = zero_zero_real ) ) )
= $false )
| ( ( SV40 = zero_zero_real )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1102]) ).
thf(1158,plain,
! [SV168: real,SV109: a,SV41: real] :
( ( ( ( real_V1035702895aleR_a @ SV41 @ SV109 )
= ( real_V1035702895aleR_a @ SV168 @ SV109 ) )
= $true )
| ( ( ( real_V1035702895aleR_a @ SV41 @ SV109 )
= ( real_V1035702895aleR_a @ SV168 @ SV109 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1103]) ).
thf(1159,plain,
! [SV109: a,SV168: real,SV41: real] :
( ( ( ( SV41 = SV168 )
| ( SV109 = zero_zero_a ) )
= $true )
| ( ( ( real_V1035702895aleR_a @ SV41 @ SV109 )
= ( real_V1035702895aleR_a @ SV168 @ SV109 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1104]) ).
thf(1160,plain,
! [SV168: real,SV109: a,SV41: real] :
( ( ( ( real_V1035702895aleR_a @ SV41 @ SV109 )
!= ( real_V1035702895aleR_a @ SV168 @ SV109 ) )
= $false )
| ( ( SV41 = SV168 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1105]) ).
thf(1161,plain,
! [SV109: a,SV168: real,SV41: real] :
( ( ( ~ ( ( SV41 = SV168 )
| ( SV109 = zero_zero_a ) ) )
= $false )
| ( ( SV41 = SV168 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1105]) ).
thf(1162,plain,
! [SV168: real,SV109: a,SV41: real] :
( ( ( ( real_V1035702895aleR_a @ SV41 @ SV109 )
!= ( real_V1035702895aleR_a @ SV168 @ SV109 ) )
= $false )
| ( ( SV109 = zero_zero_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1106]) ).
thf(1163,plain,
! [SV109: a,SV168: real,SV41: real] :
( ( ( ~ ( ( SV41 = SV168 )
| ( SV109 = zero_zero_a ) ) )
= $false )
| ( ( SV109 = zero_zero_a )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1106]) ).
thf(1164,plain,
! [SV202: a,SV173: a,SV114: a,SV47: a] :
( ( ( ( product_Pair_a_a @ SV47 @ SV114 )
!= ( product_Pair_a_a @ SV173 @ SV202 ) )
= $false )
| ( ( ( product_Pair_a_a @ SV47 @ SV114 )
= ( product_Pair_a_a @ SV173 @ SV202 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1107]) ).
thf(1165,plain,
! [SV202: a,SV114: a,SV173: a,SV47: a] :
( ( ( ~ ~ ( ( SV47 != SV173 )
| ( SV114 != SV202 ) ) )
= $false )
| ( ( ( product_Pair_a_a @ SV47 @ SV114 )
= ( product_Pair_a_a @ SV173 @ SV202 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1107]) ).
thf(1166,plain,
! [SV202: a,SV114: a,SV173: a,SV47: a] :
( ( ( SV47 != SV173 )
= $true )
| ( ( SV114 != SV202 )
= $true )
| ( ( ~ ( ( ( product_Pair_a_a @ SV47 @ SV114 )
!= ( product_Pair_a_a @ SV173 @ SV202 ) )
| ~ ~ ( ( SV47 != SV173 )
| ( SV114 != SV202 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1108]) ).
thf(1167,plain,
! [SV116: set_Product_prod_a_a,SV175: set_Product_prod_a_a,SV49: product_prod_a_a] :
( ( ( SV49
= ( plus_p1505579230od_a_a @ ( sK10_SY457 @ SV175 @ SV116 @ SV49 ) @ ( sK12_SY479 @ SV116 @ SV175 @ SV49 ) ) )
= $true )
| ( ( member449909584od_a_a @ SV49 @ ( plus_p634297534od_a_a @ SV116 @ SV175 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1109]) ).
thf(1168,plain,
! [SV49: product_prod_a_a,SV116: set_Product_prod_a_a,SV175: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK10_SY457 @ SV175 @ SV116 @ SV49 ) @ SV116 ) )
= $false )
| ( ( member449909584od_a_a @ SV49 @ ( plus_p634297534od_a_a @ SV116 @ SV175 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1110]) ).
thf(1169,plain,
! [SV49: product_prod_a_a,SV175: set_Product_prod_a_a,SV116: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK12_SY479 @ SV116 @ SV175 @ SV49 ) @ SV175 ) )
= $false )
| ( ( member449909584od_a_a @ SV49 @ ( plus_p634297534od_a_a @ SV116 @ SV175 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1110]) ).
thf(1170,plain,
! [SV207: set_Product_prod_a_a,SV121: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV121 @ SV207 ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV121 @ SV207 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1114]) ).
thf(1171,plain,
! [SV207: set_Product_prod_a_a,SV121: set_Product_prod_a_a] :
( ( ( ~ ! [SY474: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY474 @ SV121 )
| ( member449909584od_a_a @ SY474 @ SV207 ) ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV121 @ SV207 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1114]) ).
thf(1172,plain,
! [SV121: set_Product_prod_a_a,SV207: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK14_SY474 @ SV207 @ SV121 ) @ SV121 ) )
= $false )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV121 @ SV207 )
| ~ ! [SY474: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY474 @ SV121 )
| ( member449909584od_a_a @ SY474 @ SV207 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1115]) ).
thf(1173,plain,
! [SV121: set_Product_prod_a_a,SV207: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( sK14_SY474 @ SV207 @ SV121 ) @ SV207 )
= $false )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV121 @ SV207 )
| ~ ! [SY474: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY474 @ SV121 )
| ( member449909584od_a_a @ SY474 @ SV207 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1115]) ).
thf(1174,plain,
! [SV122: set_a,SV181: set_a,SV55: a] :
( ( ( SV55
= ( plus_plus_a @ ( sK11_SY464 @ SV181 @ SV122 @ SV55 ) @ ( sK13_SY480 @ SV122 @ SV181 @ SV55 ) ) )
= $true )
| ( ( member_a @ SV55 @ ( plus_plus_set_a @ SV122 @ SV181 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1116]) ).
thf(1175,plain,
! [SV55: a,SV122: set_a,SV181: set_a] :
( ( ( ~ ( member_a @ ( sK11_SY464 @ SV181 @ SV122 @ SV55 ) @ SV122 ) )
= $false )
| ( ( member_a @ SV55 @ ( plus_plus_set_a @ SV122 @ SV181 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1117]) ).
thf(1176,plain,
! [SV55: a,SV181: set_a,SV122: set_a] :
( ( ( ~ ( member_a @ ( sK13_SY480 @ SV122 @ SV181 @ SV55 ) @ SV181 ) )
= $false )
| ( ( member_a @ SV55 @ ( plus_plus_set_a @ SV122 @ SV181 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1117]) ).
thf(1177,plain,
! [SV208: a,SV182: a,SV123: a,SV56: a] :
( ( ( ( product_Pair_a_a @ SV56 @ SV123 )
!= ( product_Pair_a_a @ SV182 @ SV208 ) )
= $false )
| ( ( ( product_Pair_a_a @ SV56 @ SV123 )
= ( product_Pair_a_a @ SV182 @ SV208 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1118]) ).
thf(1178,plain,
! [SV208: a,SV123: a,SV182: a,SV56: a] :
( ( ( ~ ~ ( ( SV56 != SV182 )
| ( SV123 != SV208 ) ) )
= $false )
| ( ( ( product_Pair_a_a @ SV56 @ SV123 )
= ( product_Pair_a_a @ SV182 @ SV208 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1118]) ).
thf(1179,plain,
! [SV208: a,SV123: a,SV182: a,SV56: a] :
( ( ( SV56 != SV182 )
= $true )
| ( ( SV123 != SV208 )
= $true )
| ( ( ~ ( ( ( product_Pair_a_a @ SV56 @ SV123 )
!= ( product_Pair_a_a @ SV182 @ SV208 ) )
| ~ ~ ( ( SV56 != SV182 )
| ( SV123 != SV208 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1119]) ).
thf(1180,plain,
! [SV183: a,SV57: a,SV124: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV57 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV124 ) @ relation )
= $false )
| ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV183 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV183 @ SV124 ) @ relation ) )
| ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV183 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV183 @ SV57 ) @ relation ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1120]) ).
thf(1181,plain,
! [SV209: set_Product_prod_a_a,SV125: set_Product_prod_a_a,SV184: set_Product_prod_a_a,SV58: set_Product_prod_a_a,SV213: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV213 @ ( plus_p634297534od_a_a @ SV58 @ SV184 ) ) )
= $true )
| ( ( member449909584od_a_a @ SV213 @ ( plus_p634297534od_a_a @ SV125 @ SV209 ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV184 @ SV209 )
= $false )
| ( ( ord_le1824328871od_a_a @ SV58 @ SV125 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1121]) ).
thf(1182,plain,
! [SV62: a,SV186: a,SV129: a] :
( ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV129 @ SV186 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV186 @ SV129 ) @ relation ) ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV62 @ SV186 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV186 @ SV62 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV62 @ SV129 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV129 @ SV62 ) @ relation )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1122]) ).
thf(1183,plain,
! [SV212: set_Product_prod_a_a,SV140: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV140 @ SV212 ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV140 @ SV212 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1123]) ).
thf(1184,plain,
! [SV212: set_Product_prod_a_a,SV140: set_Product_prod_a_a] :
( ( ( ~ ! [SY476: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY476 @ SV140 )
| ( member449909584od_a_a @ SY476 @ SV212 ) ) )
= $false )
| ( ( ord_le1824328871od_a_a @ SV140 @ SV212 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1123]) ).
thf(1185,plain,
! [SV140: set_Product_prod_a_a,SV212: set_Product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ ( sK15_SY476 @ SV212 @ SV140 ) @ SV140 ) )
= $false )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV140 @ SV212 )
| ~ ! [SY476: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY476 @ SV140 )
| ( member449909584od_a_a @ SY476 @ SV212 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1124]) ).
thf(1186,plain,
! [SV140: set_Product_prod_a_a,SV212: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( sK15_SY476 @ SV212 @ SV140 ) @ SV212 )
= $false )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV140 @ SV212 )
| ~ ! [SY476: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY476 @ SV140 )
| ( member449909584od_a_a @ SY476 @ SV212 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1124]) ).
thf(1187,plain,
! [SV106: real,SV36: a,SV166: a] :
( ( ( SV166 = SV36 )
= $true )
| ( ( SV106 = one_one_real )
= $true )
| ( ( ( plus_plus_a @ SV36 @ ( real_V1035702895aleR_a @ SV106 @ SV166 ) )
= ( plus_plus_a @ SV166 @ ( real_V1035702895aleR_a @ SV106 @ SV36 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1142]) ).
thf(1188,plain,
! [SV166: a,SV106: real,SV36: a] :
( ( ( ( plus_plus_a @ SV36 @ ( real_V1035702895aleR_a @ SV106 @ SV166 ) )
= ( plus_plus_a @ SV166 @ ( real_V1035702895aleR_a @ SV106 @ SV36 ) ) )
= $true )
| ( ( SV166 = SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1143]) ).
thf(1189,plain,
! [SV106: real,SV36: a,SV166: a] :
( ( ( ( SV166 = SV36 )
| ( SV106 = one_one_real ) )
= $true )
| ( ( SV166 = SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1144]) ).
thf(1190,plain,
! [SV166: a,SV106: real,SV36: a] :
( ( ( ( plus_plus_a @ SV36 @ ( real_V1035702895aleR_a @ SV106 @ SV166 ) )
= ( plus_plus_a @ SV166 @ ( real_V1035702895aleR_a @ SV106 @ SV36 ) ) )
= $true )
| ( ( SV106 = one_one_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1145]) ).
thf(1191,plain,
! [SV106: real,SV36: a,SV166: a] :
( ( ( ( SV166 = SV36 )
| ( SV106 = one_one_real ) )
= $true )
| ( ( SV106 = one_one_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1146]) ).
thf(1192,plain,
! [SV107: a,SV38: real] :
( ( ( SV38 = zero_zero_real )
= $true )
| ( ( SV107 = zero_zero_a )
= $true )
| ( ( SV38 = zero_zero_real )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1149]) ).
thf(1193,plain,
! [SV107: a,SV38: real] :
( ( ( SV38 = zero_zero_real )
= $true )
| ( ( SV107 = zero_zero_a )
= $true )
| ( ( SV107 = zero_zero_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1151]) ).
thf(1194,plain,
! [SV40: real,SV167: a,SV108: a] :
( ( ( SV108 = SV167 )
= $true )
| ( ( SV40 = zero_zero_real )
= $true )
| ( ( ( real_V1035702895aleR_a @ SV40 @ SV108 )
= ( real_V1035702895aleR_a @ SV40 @ SV167 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1153]) ).
thf(1195,plain,
! [SV167: a,SV108: a,SV40: real] :
( ( ( ( real_V1035702895aleR_a @ SV40 @ SV108 )
= ( real_V1035702895aleR_a @ SV40 @ SV167 ) )
= $true )
| ( ( SV108 = SV167 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1154]) ).
thf(1196,plain,
! [SV40: real,SV167: a,SV108: a] :
( ( ( ( SV108 = SV167 )
| ( SV40 = zero_zero_real ) )
= $true )
| ( ( SV108 = SV167 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1155]) ).
thf(1197,plain,
! [SV167: a,SV108: a,SV40: real] :
( ( ( ( real_V1035702895aleR_a @ SV40 @ SV108 )
= ( real_V1035702895aleR_a @ SV40 @ SV167 ) )
= $true )
| ( ( SV40 = zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1156]) ).
thf(1198,plain,
! [SV40: real,SV167: a,SV108: a] :
( ( ( ( SV108 = SV167 )
| ( SV40 = zero_zero_real ) )
= $true )
| ( ( SV40 = zero_zero_real )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1157]) ).
thf(1199,plain,
! [SV109: a,SV168: real,SV41: real] :
( ( ( SV41 = SV168 )
= $true )
| ( ( SV109 = zero_zero_a )
= $true )
| ( ( ( real_V1035702895aleR_a @ SV41 @ SV109 )
= ( real_V1035702895aleR_a @ SV168 @ SV109 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1159]) ).
thf(1200,plain,
! [SV168: real,SV109: a,SV41: real] :
( ( ( ( real_V1035702895aleR_a @ SV41 @ SV109 )
= ( real_V1035702895aleR_a @ SV168 @ SV109 ) )
= $true )
| ( ( SV41 = SV168 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1160]) ).
thf(1201,plain,
! [SV109: a,SV168: real,SV41: real] :
( ( ( ( SV41 = SV168 )
| ( SV109 = zero_zero_a ) )
= $true )
| ( ( SV41 = SV168 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1161]) ).
thf(1202,plain,
! [SV168: real,SV109: a,SV41: real] :
( ( ( ( real_V1035702895aleR_a @ SV41 @ SV109 )
= ( real_V1035702895aleR_a @ SV168 @ SV109 ) )
= $true )
| ( ( SV109 = zero_zero_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1162]) ).
thf(1203,plain,
! [SV109: a,SV168: real,SV41: real] :
( ( ( ( SV41 = SV168 )
| ( SV109 = zero_zero_a ) )
= $true )
| ( ( SV109 = zero_zero_a )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1163]) ).
thf(1204,plain,
! [SV202: a,SV173: a,SV114: a,SV47: a] :
( ( ( ( product_Pair_a_a @ SV47 @ SV114 )
= ( product_Pair_a_a @ SV173 @ SV202 ) )
= $true )
| ( ( ( product_Pair_a_a @ SV47 @ SV114 )
= ( product_Pair_a_a @ SV173 @ SV202 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1164]) ).
thf(1205,plain,
! [SV202: a,SV114: a,SV173: a,SV47: a] :
( ( ( ~ ( ( SV47 != SV173 )
| ( SV114 != SV202 ) ) )
= $true )
| ( ( ( product_Pair_a_a @ SV47 @ SV114 )
= ( product_Pair_a_a @ SV173 @ SV202 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1165]) ).
thf(1206,plain,
! [SV202: a,SV114: a,SV173: a,SV47: a] :
( ( ( SV47 = SV173 )
= $false )
| ( ( SV114 != SV202 )
= $true )
| ( ( ~ ( ( ( product_Pair_a_a @ SV47 @ SV114 )
!= ( product_Pair_a_a @ SV173 @ SV202 ) )
| ~ ~ ( ( SV47 != SV173 )
| ( SV114 != SV202 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1166]) ).
thf(1207,plain,
! [SV49: product_prod_a_a,SV116: set_Product_prod_a_a,SV175: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( sK10_SY457 @ SV175 @ SV116 @ SV49 ) @ SV116 )
= $true )
| ( ( member449909584od_a_a @ SV49 @ ( plus_p634297534od_a_a @ SV116 @ SV175 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1168]) ).
thf(1208,plain,
! [SV49: product_prod_a_a,SV175: set_Product_prod_a_a,SV116: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( sK12_SY479 @ SV116 @ SV175 @ SV49 ) @ SV175 )
= $true )
| ( ( member449909584od_a_a @ SV49 @ ( plus_p634297534od_a_a @ SV116 @ SV175 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1169]) ).
thf(1209,plain,
! [SV207: set_Product_prod_a_a,SV121: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV121 @ SV207 )
= $true )
| ( ( ord_le1824328871od_a_a @ SV121 @ SV207 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1170]) ).
thf(1210,plain,
! [SV207: set_Product_prod_a_a,SV121: set_Product_prod_a_a] :
( ( ( ! [SY474: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY474 @ SV121 )
| ( member449909584od_a_a @ SY474 @ SV207 ) ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV121 @ SV207 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1171]) ).
thf(1211,plain,
! [SV121: set_Product_prod_a_a,SV207: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( sK14_SY474 @ SV207 @ SV121 ) @ SV121 )
= $true )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV121 @ SV207 )
| ~ ! [SY474: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY474 @ SV121 )
| ( member449909584od_a_a @ SY474 @ SV207 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1172]) ).
thf(1212,plain,
! [SV207: set_Product_prod_a_a,SV121: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV121 @ SV207 )
| ~ ! [SY474: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY474 @ SV121 )
| ( member449909584od_a_a @ SY474 @ SV207 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( sK14_SY474 @ SV207 @ SV121 ) @ SV207 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1173]) ).
thf(1213,plain,
! [SV55: a,SV122: set_a,SV181: set_a] :
( ( ( member_a @ ( sK11_SY464 @ SV181 @ SV122 @ SV55 ) @ SV122 )
= $true )
| ( ( member_a @ SV55 @ ( plus_plus_set_a @ SV122 @ SV181 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1175]) ).
thf(1214,plain,
! [SV55: a,SV181: set_a,SV122: set_a] :
( ( ( member_a @ ( sK13_SY480 @ SV122 @ SV181 @ SV55 ) @ SV181 )
= $true )
| ( ( member_a @ SV55 @ ( plus_plus_set_a @ SV122 @ SV181 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1176]) ).
thf(1215,plain,
! [SV208: a,SV182: a,SV123: a,SV56: a] :
( ( ( ( product_Pair_a_a @ SV56 @ SV123 )
= ( product_Pair_a_a @ SV182 @ SV208 ) )
= $true )
| ( ( ( product_Pair_a_a @ SV56 @ SV123 )
= ( product_Pair_a_a @ SV182 @ SV208 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1177]) ).
thf(1216,plain,
! [SV208: a,SV123: a,SV182: a,SV56: a] :
( ( ( ~ ( ( SV56 != SV182 )
| ( SV123 != SV208 ) ) )
= $true )
| ( ( ( product_Pair_a_a @ SV56 @ SV123 )
= ( product_Pair_a_a @ SV182 @ SV208 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1178]) ).
thf(1217,plain,
! [SV208: a,SV123: a,SV182: a,SV56: a] :
( ( ( SV56 = SV182 )
= $false )
| ( ( SV123 != SV208 )
= $true )
| ( ( ~ ( ( ( product_Pair_a_a @ SV56 @ SV123 )
!= ( product_Pair_a_a @ SV182 @ SV208 ) )
| ~ ~ ( ( SV56 != SV182 )
| ( SV123 != SV208 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1179]) ).
thf(1218,plain,
! [SV57: a,SV183: a,SV124: a] :
( ( ( ~ ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV183 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV183 @ SV124 ) @ relation ) ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV183 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV183 @ SV57 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV124 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV57 ) @ relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1180]) ).
thf(1219,plain,
! [SV209: set_Product_prod_a_a,SV125: set_Product_prod_a_a,SV184: set_Product_prod_a_a,SV58: set_Product_prod_a_a,SV213: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV213 @ ( plus_p634297534od_a_a @ SV58 @ SV184 ) )
= $false )
| ( ( member449909584od_a_a @ SV213 @ ( plus_p634297534od_a_a @ SV125 @ SV209 ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV184 @ SV209 )
= $false )
| ( ( ord_le1824328871od_a_a @ SV58 @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1181]) ).
thf(1220,plain,
! [SV62: a,SV186: a,SV129: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV129 @ SV186 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV186 @ SV129 ) @ relation ) ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV62 @ SV186 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV186 @ SV62 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV62 @ SV129 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV129 @ SV62 ) @ relation )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1182]) ).
thf(1221,plain,
! [SV212: set_Product_prod_a_a,SV140: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV140 @ SV212 )
= $true )
| ( ( ord_le1824328871od_a_a @ SV140 @ SV212 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1183]) ).
thf(1222,plain,
! [SV212: set_Product_prod_a_a,SV140: set_Product_prod_a_a] :
( ( ( ! [SY476: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY476 @ SV140 )
| ( member449909584od_a_a @ SY476 @ SV212 ) ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV140 @ SV212 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1184]) ).
thf(1223,plain,
! [SV140: set_Product_prod_a_a,SV212: set_Product_prod_a_a] :
( ( ( member449909584od_a_a @ ( sK15_SY476 @ SV212 @ SV140 ) @ SV140 )
= $true )
| ( ( ~ ( ~ ( ord_le1824328871od_a_a @ SV140 @ SV212 )
| ~ ! [SY476: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY476 @ SV140 )
| ( member449909584od_a_a @ SY476 @ SV212 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1185]) ).
thf(1224,plain,
! [SV212: set_Product_prod_a_a,SV140: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV140 @ SV212 )
| ~ ! [SY476: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY476 @ SV140 )
| ( member449909584od_a_a @ SY476 @ SV212 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( sK15_SY476 @ SV212 @ SV140 ) @ SV212 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1186]) ).
thf(1225,plain,
! [SV106: real,SV36: a,SV166: a] :
( ( ( SV166 = SV36 )
= $true )
| ( ( SV106 = one_one_real )
= $true )
| ( ( SV166 = SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1189]) ).
thf(1226,plain,
! [SV106: real,SV36: a,SV166: a] :
( ( ( SV166 = SV36 )
= $true )
| ( ( SV106 = one_one_real )
= $true )
| ( ( SV106 = one_one_real )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1191]) ).
thf(1227,plain,
! [SV40: real,SV167: a,SV108: a] :
( ( ( SV108 = SV167 )
= $true )
| ( ( SV40 = zero_zero_real )
= $true )
| ( ( SV108 = SV167 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1196]) ).
thf(1228,plain,
! [SV40: real,SV167: a,SV108: a] :
( ( ( SV108 = SV167 )
= $true )
| ( ( SV40 = zero_zero_real )
= $true )
| ( ( SV40 = zero_zero_real )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1198]) ).
thf(1229,plain,
! [SV109: a,SV168: real,SV41: real] :
( ( ( SV41 = SV168 )
= $true )
| ( ( SV109 = zero_zero_a )
= $true )
| ( ( SV41 = SV168 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1201]) ).
thf(1230,plain,
! [SV109: a,SV168: real,SV41: real] :
( ( ( SV41 = SV168 )
= $true )
| ( ( SV109 = zero_zero_a )
= $true )
| ( ( SV109 = zero_zero_a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1203]) ).
thf(1231,plain,
! [SV202: a,SV114: a,SV173: a,SV47: a] :
( ( ( ( SV47 != SV173 )
| ( SV114 != SV202 ) )
= $false )
| ( ( ( product_Pair_a_a @ SV47 @ SV114 )
= ( product_Pair_a_a @ SV173 @ SV202 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1205]) ).
thf(1232,plain,
! [SV173: a,SV47: a,SV202: a,SV114: a] :
( ( ( SV114 = SV202 )
= $false )
| ( ( SV47 = SV173 )
= $false )
| ( ( ~ ( ( ( product_Pair_a_a @ SV47 @ SV114 )
!= ( product_Pair_a_a @ SV173 @ SV202 ) )
| ~ ~ ( ( SV47 != SV173 )
| ( SV114 != SV202 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1206]) ).
thf(1233,plain,
! [SV207: set_Product_prod_a_a,SV121: set_Product_prod_a_a,SV214: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV214 @ SV121 )
| ( member449909584od_a_a @ SV214 @ SV207 ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV121 @ SV207 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1210]) ).
thf(1234,plain,
! [SV207: set_Product_prod_a_a,SV121: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV121 @ SV207 )
| ~ ! [SY474: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY474 @ SV121 )
| ( member449909584od_a_a @ SY474 @ SV207 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( sK14_SY474 @ SV207 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1211]) ).
thf(1235,plain,
! [SV207: set_Product_prod_a_a,SV121: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV121 @ SV207 ) )
= $false )
| ( ( member449909584od_a_a @ ( sK14_SY474 @ SV207 @ SV121 ) @ SV207 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1212]) ).
thf(1236,plain,
! [SV207: set_Product_prod_a_a,SV121: set_Product_prod_a_a] :
( ( ( ~ ! [SY474: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY474 @ SV121 )
| ( member449909584od_a_a @ SY474 @ SV207 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( sK14_SY474 @ SV207 @ SV121 ) @ SV207 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1212]) ).
thf(1237,plain,
! [SV208: a,SV123: a,SV182: a,SV56: a] :
( ( ( ( SV56 != SV182 )
| ( SV123 != SV208 ) )
= $false )
| ( ( ( product_Pair_a_a @ SV56 @ SV123 )
= ( product_Pair_a_a @ SV182 @ SV208 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1216]) ).
thf(1238,plain,
! [SV182: a,SV56: a,SV208: a,SV123: a] :
( ( ( SV123 = SV208 )
= $false )
| ( ( SV56 = SV182 )
= $false )
| ( ( ~ ( ( ( product_Pair_a_a @ SV56 @ SV123 )
!= ( product_Pair_a_a @ SV182 @ SV208 ) )
| ~ ~ ( ( SV56 != SV182 )
| ( SV123 != SV208 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1217]) ).
thf(1239,plain,
! [SV57: a,SV183: a,SV124: a] :
( ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV183 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV183 @ SV124 ) @ relation ) ) )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV183 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV183 @ SV57 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV124 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV57 ) @ relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1218]) ).
thf(1240,plain,
! [SV62: a,SV186: a,SV129: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV129 @ SV186 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV186 @ SV129 ) @ relation ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV62 @ SV186 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV186 @ SV62 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV62 @ SV129 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV129 @ SV62 ) @ relation )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1220]) ).
thf(1241,plain,
! [SV212: set_Product_prod_a_a,SV140: set_Product_prod_a_a,SV215: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV215 @ SV140 )
| ( member449909584od_a_a @ SV215 @ SV212 ) )
= $true )
| ( ( ord_le1824328871od_a_a @ SV140 @ SV212 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1222]) ).
thf(1242,plain,
! [SV212: set_Product_prod_a_a,SV140: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV140 @ SV212 )
| ~ ! [SY476: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY476 @ SV140 )
| ( member449909584od_a_a @ SY476 @ SV212 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( sK15_SY476 @ SV212 @ SV140 ) @ SV140 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1223]) ).
thf(1243,plain,
! [SV212: set_Product_prod_a_a,SV140: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV140 @ SV212 ) )
= $false )
| ( ( member449909584od_a_a @ ( sK15_SY476 @ SV212 @ SV140 ) @ SV212 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1224]) ).
thf(1244,plain,
! [SV212: set_Product_prod_a_a,SV140: set_Product_prod_a_a] :
( ( ( ~ ! [SY476: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY476 @ SV140 )
| ( member449909584od_a_a @ SY476 @ SV212 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( sK15_SY476 @ SV212 @ SV140 ) @ SV212 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1224]) ).
thf(1245,plain,
! [SV202: a,SV114: a,SV173: a,SV47: a] :
( ( ( SV47 != SV173 )
= $false )
| ( ( ( product_Pair_a_a @ SV47 @ SV114 )
= ( product_Pair_a_a @ SV173 @ SV202 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1231]) ).
thf(1246,plain,
! [SV173: a,SV47: a,SV202: a,SV114: a] :
( ( ( SV114 != SV202 )
= $false )
| ( ( ( product_Pair_a_a @ SV47 @ SV114 )
= ( product_Pair_a_a @ SV173 @ SV202 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1231]) ).
thf(1247,plain,
! [SV202: a,SV173: a,SV114: a,SV47: a] :
( ( ( ( ( product_Pair_a_a @ SV47 @ SV114 )
!= ( product_Pair_a_a @ SV173 @ SV202 ) )
| ~ ~ ( ( SV47 != SV173 )
| ( SV114 != SV202 ) ) )
= $false )
| ( ( SV47 = SV173 )
= $false )
| ( ( SV114 = SV202 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1232]) ).
thf(1248,plain,
! [SV207: set_Product_prod_a_a,SV121: set_Product_prod_a_a,SV214: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV214 @ SV121 ) )
= $true )
| ( ( member449909584od_a_a @ SV214 @ SV207 )
= $true )
| ( ( ord_le1824328871od_a_a @ SV121 @ SV207 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1233]) ).
thf(1249,plain,
! [SV207: set_Product_prod_a_a,SV121: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV121 @ SV207 ) )
= $false )
| ( ( member449909584od_a_a @ ( sK14_SY474 @ SV207 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1234]) ).
thf(1250,plain,
! [SV207: set_Product_prod_a_a,SV121: set_Product_prod_a_a] :
( ( ( ~ ! [SY474: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY474 @ SV121 )
| ( member449909584od_a_a @ SY474 @ SV207 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( sK14_SY474 @ SV207 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1234]) ).
thf(1251,plain,
! [SV207: set_Product_prod_a_a,SV121: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV121 @ SV207 )
= $true )
| ( ( member449909584od_a_a @ ( sK14_SY474 @ SV207 @ SV121 ) @ SV207 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1235]) ).
thf(1252,plain,
! [SV207: set_Product_prod_a_a,SV121: set_Product_prod_a_a] :
( ( ( ! [SY474: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY474 @ SV121 )
| ( member449909584od_a_a @ SY474 @ SV207 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( sK14_SY474 @ SV207 @ SV121 ) @ SV207 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1236]) ).
thf(1253,plain,
! [SV208: a,SV123: a,SV182: a,SV56: a] :
( ( ( SV56 != SV182 )
= $false )
| ( ( ( product_Pair_a_a @ SV56 @ SV123 )
= ( product_Pair_a_a @ SV182 @ SV208 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1237]) ).
thf(1254,plain,
! [SV182: a,SV56: a,SV208: a,SV123: a] :
( ( ( SV123 != SV208 )
= $false )
| ( ( ( product_Pair_a_a @ SV56 @ SV123 )
= ( product_Pair_a_a @ SV182 @ SV208 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1237]) ).
thf(1255,plain,
! [SV208: a,SV182: a,SV123: a,SV56: a] :
( ( ( ( ( product_Pair_a_a @ SV56 @ SV123 )
!= ( product_Pair_a_a @ SV182 @ SV208 ) )
| ~ ~ ( ( SV56 != SV182 )
| ( SV123 != SV208 ) ) )
= $false )
| ( ( SV56 = SV182 )
= $false )
| ( ( SV123 = SV208 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1238]) ).
thf(1256,plain,
! [SV57: a,SV183: a,SV124: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV183 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV183 @ SV124 ) @ relation ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV183 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV183 @ SV57 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV124 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV57 ) @ relation )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1239]) ).
thf(1257,plain,
! [SV62: a,SV186: a,SV129: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV129 @ SV186 ) @ relation ) )
= $true )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV186 @ SV129 ) @ relation ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV62 @ SV186 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV186 @ SV62 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV62 @ SV129 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV129 @ SV62 ) @ relation )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1240]) ).
thf(1258,plain,
! [SV212: set_Product_prod_a_a,SV140: set_Product_prod_a_a,SV215: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV215 @ SV140 ) )
= $true )
| ( ( member449909584od_a_a @ SV215 @ SV212 )
= $true )
| ( ( ord_le1824328871od_a_a @ SV140 @ SV212 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1241]) ).
thf(1259,plain,
! [SV212: set_Product_prod_a_a,SV140: set_Product_prod_a_a] :
( ( ( ~ ( ord_le1824328871od_a_a @ SV140 @ SV212 ) )
= $false )
| ( ( member449909584od_a_a @ ( sK15_SY476 @ SV212 @ SV140 ) @ SV140 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1242]) ).
thf(1260,plain,
! [SV212: set_Product_prod_a_a,SV140: set_Product_prod_a_a] :
( ( ( ~ ! [SY476: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY476 @ SV140 )
| ( member449909584od_a_a @ SY476 @ SV212 ) ) )
= $false )
| ( ( member449909584od_a_a @ ( sK15_SY476 @ SV212 @ SV140 ) @ SV140 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1242]) ).
thf(1261,plain,
! [SV212: set_Product_prod_a_a,SV140: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV140 @ SV212 )
= $true )
| ( ( member449909584od_a_a @ ( sK15_SY476 @ SV212 @ SV140 ) @ SV212 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1243]) ).
thf(1262,plain,
! [SV212: set_Product_prod_a_a,SV140: set_Product_prod_a_a] :
( ( ( ! [SY476: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY476 @ SV140 )
| ( member449909584od_a_a @ SY476 @ SV212 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( sK15_SY476 @ SV212 @ SV140 ) @ SV212 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1244]) ).
thf(1263,plain,
! [SV202: a,SV114: a,SV173: a,SV47: a] :
( ( ( SV47 = SV173 )
= $true )
| ( ( ( product_Pair_a_a @ SV47 @ SV114 )
= ( product_Pair_a_a @ SV173 @ SV202 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1245]) ).
thf(1264,plain,
! [SV173: a,SV47: a,SV202: a,SV114: a] :
( ( ( SV114 = SV202 )
= $true )
| ( ( ( product_Pair_a_a @ SV47 @ SV114 )
= ( product_Pair_a_a @ SV173 @ SV202 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1246]) ).
thf(1265,plain,
! [SV202: a,SV173: a,SV114: a,SV47: a] :
( ( ( ( product_Pair_a_a @ SV47 @ SV114 )
!= ( product_Pair_a_a @ SV173 @ SV202 ) )
= $false )
| ( ( SV47 = SV173 )
= $false )
| ( ( SV114 = SV202 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1247]) ).
thf(1266,plain,
! [SV202: a,SV114: a,SV173: a,SV47: a] :
( ( ( ~ ~ ( ( SV47 != SV173 )
| ( SV114 != SV202 ) ) )
= $false )
| ( ( SV47 = SV173 )
= $false )
| ( ( SV114 = SV202 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1247]) ).
thf(1267,plain,
! [SV207: set_Product_prod_a_a,SV121: set_Product_prod_a_a,SV214: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV214 @ SV121 )
= $false )
| ( ( member449909584od_a_a @ SV214 @ SV207 )
= $true )
| ( ( ord_le1824328871od_a_a @ SV121 @ SV207 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1248]) ).
thf(1268,plain,
! [SV207: set_Product_prod_a_a,SV121: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV121 @ SV207 )
= $true )
| ( ( member449909584od_a_a @ ( sK14_SY474 @ SV207 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1249]) ).
thf(1269,plain,
! [SV207: set_Product_prod_a_a,SV121: set_Product_prod_a_a] :
( ( ( ! [SY474: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY474 @ SV121 )
| ( member449909584od_a_a @ SY474 @ SV207 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( sK14_SY474 @ SV207 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1250]) ).
thf(1270,plain,
! [SV207: set_Product_prod_a_a,SV121: set_Product_prod_a_a,SV216: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV216 @ SV121 )
| ( member449909584od_a_a @ SV216 @ SV207 ) )
= $true )
| ( ( member449909584od_a_a @ ( sK14_SY474 @ SV207 @ SV121 ) @ SV207 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1252]) ).
thf(1271,plain,
! [SV208: a,SV123: a,SV182: a,SV56: a] :
( ( ( SV56 = SV182 )
= $true )
| ( ( ( product_Pair_a_a @ SV56 @ SV123 )
= ( product_Pair_a_a @ SV182 @ SV208 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1253]) ).
thf(1272,plain,
! [SV182: a,SV56: a,SV208: a,SV123: a] :
( ( ( SV123 = SV208 )
= $true )
| ( ( ( product_Pair_a_a @ SV56 @ SV123 )
= ( product_Pair_a_a @ SV182 @ SV208 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1254]) ).
thf(1273,plain,
! [SV208: a,SV182: a,SV123: a,SV56: a] :
( ( ( ( product_Pair_a_a @ SV56 @ SV123 )
!= ( product_Pair_a_a @ SV182 @ SV208 ) )
= $false )
| ( ( SV56 = SV182 )
= $false )
| ( ( SV123 = SV208 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1255]) ).
thf(1274,plain,
! [SV208: a,SV123: a,SV182: a,SV56: a] :
( ( ( ~ ~ ( ( SV56 != SV182 )
| ( SV123 != SV208 ) ) )
= $false )
| ( ( SV56 = SV182 )
= $false )
| ( ( SV123 = SV208 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1255]) ).
thf(1275,plain,
! [SV57: a,SV183: a,SV124: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV183 ) @ relation ) )
= $true )
| ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV183 @ SV124 ) @ relation ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV183 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV183 @ SV57 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV124 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV57 ) @ relation )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1256]) ).
thf(1276,plain,
! [SV62: a,SV186: a,SV129: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV129 @ SV186 ) @ relation )
= $false )
| ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV186 @ SV129 ) @ relation ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV62 @ SV186 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV186 @ SV62 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV62 @ SV129 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV129 @ SV62 ) @ relation )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1257]) ).
thf(1277,plain,
! [SV212: set_Product_prod_a_a,SV140: set_Product_prod_a_a,SV215: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV215 @ SV140 )
= $false )
| ( ( member449909584od_a_a @ SV215 @ SV212 )
= $true )
| ( ( ord_le1824328871od_a_a @ SV140 @ SV212 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1258]) ).
thf(1278,plain,
! [SV212: set_Product_prod_a_a,SV140: set_Product_prod_a_a] :
( ( ( ord_le1824328871od_a_a @ SV140 @ SV212 )
= $true )
| ( ( member449909584od_a_a @ ( sK15_SY476 @ SV212 @ SV140 ) @ SV140 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1259]) ).
thf(1279,plain,
! [SV212: set_Product_prod_a_a,SV140: set_Product_prod_a_a] :
( ( ( ! [SY476: product_prod_a_a] :
( ~ ( member449909584od_a_a @ SY476 @ SV140 )
| ( member449909584od_a_a @ SY476 @ SV212 ) ) )
= $true )
| ( ( member449909584od_a_a @ ( sK15_SY476 @ SV212 @ SV140 ) @ SV140 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1260]) ).
thf(1280,plain,
! [SV212: set_Product_prod_a_a,SV140: set_Product_prod_a_a,SV217: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV217 @ SV140 )
| ( member449909584od_a_a @ SV217 @ SV212 ) )
= $true )
| ( ( member449909584od_a_a @ ( sK15_SY476 @ SV212 @ SV140 ) @ SV212 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1262]) ).
thf(1281,plain,
! [SV202: a,SV173: a,SV114: a,SV47: a] :
( ( ( ( product_Pair_a_a @ SV47 @ SV114 )
= ( product_Pair_a_a @ SV173 @ SV202 ) )
= $true )
| ( ( SV47 = SV173 )
= $false )
| ( ( SV114 = SV202 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1265]) ).
thf(1282,plain,
! [SV202: a,SV114: a,SV173: a,SV47: a] :
( ( ( ~ ( ( SV47 != SV173 )
| ( SV114 != SV202 ) ) )
= $true )
| ( ( SV47 = SV173 )
= $false )
| ( ( SV114 = SV202 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1266]) ).
thf(1283,plain,
! [SV207: set_Product_prod_a_a,SV121: set_Product_prod_a_a,SV218: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV218 @ SV121 )
| ( member449909584od_a_a @ SV218 @ SV207 ) )
= $true )
| ( ( member449909584od_a_a @ ( sK14_SY474 @ SV207 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1269]) ).
thf(1284,plain,
! [SV207: set_Product_prod_a_a,SV121: set_Product_prod_a_a,SV216: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV216 @ SV121 ) )
= $true )
| ( ( member449909584od_a_a @ SV216 @ SV207 )
= $true )
| ( ( member449909584od_a_a @ ( sK14_SY474 @ SV207 @ SV121 ) @ SV207 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1270]) ).
thf(1285,plain,
! [SV208: a,SV182: a,SV123: a,SV56: a] :
( ( ( ( product_Pair_a_a @ SV56 @ SV123 )
= ( product_Pair_a_a @ SV182 @ SV208 ) )
= $true )
| ( ( SV56 = SV182 )
= $false )
| ( ( SV123 = SV208 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1273]) ).
thf(1286,plain,
! [SV208: a,SV123: a,SV182: a,SV56: a] :
( ( ( ~ ( ( SV56 != SV182 )
| ( SV123 != SV208 ) ) )
= $true )
| ( ( SV56 = SV182 )
= $false )
| ( ( SV123 = SV208 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1274]) ).
thf(1287,plain,
! [SV57: a,SV183: a,SV124: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV183 ) @ relation )
= $false )
| ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV183 @ SV124 ) @ relation ) )
= $true )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV183 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV183 @ SV57 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV124 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV57 ) @ relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1275]) ).
thf(1288,plain,
! [SV62: a,SV129: a,SV186: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV186 @ SV129 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV129 @ SV186 ) @ relation )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV62 @ SV186 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV186 @ SV62 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV62 @ SV129 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV129 @ SV62 ) @ relation )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1276]) ).
thf(1289,plain,
! [SV212: set_Product_prod_a_a,SV140: set_Product_prod_a_a,SV219: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV219 @ SV140 )
| ( member449909584od_a_a @ SV219 @ SV212 ) )
= $true )
| ( ( member449909584od_a_a @ ( sK15_SY476 @ SV212 @ SV140 ) @ SV140 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1279]) ).
thf(1290,plain,
! [SV212: set_Product_prod_a_a,SV140: set_Product_prod_a_a,SV217: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV217 @ SV140 ) )
= $true )
| ( ( member449909584od_a_a @ SV217 @ SV212 )
= $true )
| ( ( member449909584od_a_a @ ( sK15_SY476 @ SV212 @ SV140 ) @ SV212 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1280]) ).
thf(1291,plain,
! [SV202: a,SV114: a,SV173: a,SV47: a] :
( ( ( ( SV47 != SV173 )
| ( SV114 != SV202 ) )
= $false )
| ( ( SV47 = SV173 )
= $false )
| ( ( SV114 = SV202 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1282]) ).
thf(1292,plain,
! [SV207: set_Product_prod_a_a,SV121: set_Product_prod_a_a,SV218: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV218 @ SV121 ) )
= $true )
| ( ( member449909584od_a_a @ SV218 @ SV207 )
= $true )
| ( ( member449909584od_a_a @ ( sK14_SY474 @ SV207 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1283]) ).
thf(1293,plain,
! [SV207: set_Product_prod_a_a,SV121: set_Product_prod_a_a,SV216: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV216 @ SV121 )
= $false )
| ( ( member449909584od_a_a @ SV216 @ SV207 )
= $true )
| ( ( member449909584od_a_a @ ( sK14_SY474 @ SV207 @ SV121 ) @ SV207 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1284]) ).
thf(1294,plain,
! [SV208: a,SV123: a,SV182: a,SV56: a] :
( ( ( ( SV56 != SV182 )
| ( SV123 != SV208 ) )
= $false )
| ( ( SV56 = SV182 )
= $false )
| ( ( SV123 = SV208 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1286]) ).
thf(1295,plain,
! [SV57: a,SV124: a,SV183: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV183 @ SV124 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV183 ) @ relation )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV183 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV183 @ SV57 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV124 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV57 ) @ relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1287]) ).
thf(1296,plain,
! [SV129: a,SV186: a,SV62: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV62 @ SV186 ) @ relation )
| ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV186 @ SV62 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV129 @ SV186 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV186 @ SV129 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV62 @ SV129 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV129 @ SV62 ) @ relation )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1288]) ).
thf(1297,plain,
! [SV212: set_Product_prod_a_a,SV140: set_Product_prod_a_a,SV219: product_prod_a_a] :
( ( ( ~ ( member449909584od_a_a @ SV219 @ SV140 ) )
= $true )
| ( ( member449909584od_a_a @ SV219 @ SV212 )
= $true )
| ( ( member449909584od_a_a @ ( sK15_SY476 @ SV212 @ SV140 ) @ SV140 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1289]) ).
thf(1298,plain,
! [SV212: set_Product_prod_a_a,SV140: set_Product_prod_a_a,SV217: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV217 @ SV140 )
= $false )
| ( ( member449909584od_a_a @ SV217 @ SV212 )
= $true )
| ( ( member449909584od_a_a @ ( sK15_SY476 @ SV212 @ SV140 ) @ SV212 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1290]) ).
thf(1299,plain,
! [SV202: a,SV114: a,SV173: a,SV47: a] :
( ( ( SV47 != SV173 )
= $false )
| ( ( SV47 = SV173 )
= $false )
| ( ( SV114 = SV202 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1291]) ).
thf(1300,plain,
! [SV173: a,SV47: a,SV202: a,SV114: a] :
( ( ( SV114 != SV202 )
= $false )
| ( ( SV47 = SV173 )
= $false )
| ( ( SV114 = SV202 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1291]) ).
thf(1301,plain,
! [SV207: set_Product_prod_a_a,SV121: set_Product_prod_a_a,SV218: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV218 @ SV121 )
= $false )
| ( ( member449909584od_a_a @ SV218 @ SV207 )
= $true )
| ( ( member449909584od_a_a @ ( sK14_SY474 @ SV207 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1292]) ).
thf(1302,plain,
! [SV208: a,SV123: a,SV182: a,SV56: a] :
( ( ( SV56 != SV182 )
= $false )
| ( ( SV56 = SV182 )
= $false )
| ( ( SV123 = SV208 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1294]) ).
thf(1303,plain,
! [SV182: a,SV56: a,SV208: a,SV123: a] :
( ( ( SV123 != SV208 )
= $false )
| ( ( SV56 = SV182 )
= $false )
| ( ( SV123 = SV208 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1294]) ).
thf(1304,plain,
! [SV57: a,SV124: a,SV183: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV183 @ SV124 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV183 ) @ relation )
= $false )
| ( ( ~ ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV183 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV183 @ SV57 ) @ relation ) ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV124 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV57 ) @ relation )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1295]) ).
thf(1305,plain,
! [SV129: a,SV186: a,SV62: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV62 @ SV186 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV129 @ SV186 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV186 @ SV129 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV62 @ SV129 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV129 @ SV62 ) @ relation )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1296]) ).
thf(1306,plain,
! [SV129: a,SV62: a,SV186: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV186 @ SV62 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV129 @ SV186 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV186 @ SV129 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV62 @ SV129 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV129 @ SV62 ) @ relation )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1296]) ).
thf(1307,plain,
! [SV212: set_Product_prod_a_a,SV140: set_Product_prod_a_a,SV219: product_prod_a_a] :
( ( ( member449909584od_a_a @ SV219 @ SV140 )
= $false )
| ( ( member449909584od_a_a @ SV219 @ SV212 )
= $true )
| ( ( member449909584od_a_a @ ( sK15_SY476 @ SV212 @ SV140 ) @ SV140 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1297]) ).
thf(1308,plain,
! [SV202: a,SV114: a,SV173: a,SV47: a] :
( ( ( SV47 = SV173 )
= $true )
| ( ( SV47 = SV173 )
= $false )
| ( ( SV114 = SV202 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1299]) ).
thf(1309,plain,
! [SV173: a,SV47: a,SV202: a,SV114: a] :
( ( ( SV114 = SV202 )
= $true )
| ( ( SV47 = SV173 )
= $false )
| ( ( SV114 = SV202 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1300]) ).
thf(1310,plain,
! [SV208: a,SV123: a,SV182: a,SV56: a] :
( ( ( SV56 = SV182 )
= $true )
| ( ( SV56 = SV182 )
= $false )
| ( ( SV123 = SV208 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1302]) ).
thf(1311,plain,
! [SV182: a,SV56: a,SV208: a,SV123: a] :
( ( ( SV123 = SV208 )
= $true )
| ( ( SV56 = SV182 )
= $false )
| ( ( SV123 = SV208 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1303]) ).
thf(1312,plain,
! [SV124: a,SV183: a,SV57: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV183 ) @ relation )
| ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV183 @ SV57 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV183 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV183 @ SV124 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV124 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV57 ) @ relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1304]) ).
thf(1313,plain,
! [SV129: a,SV186: a,SV62: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV62 @ SV186 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV129 @ SV186 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV186 @ SV129 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV62 @ SV129 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV129 @ SV62 ) @ relation )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1305]) ).
thf(1314,plain,
! [SV129: a,SV62: a,SV186: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV186 @ SV62 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV129 @ SV186 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV186 @ SV129 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV62 @ SV129 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV129 @ SV62 ) @ relation )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1306]) ).
thf(1315,plain,
! [SV124: a,SV183: a,SV57: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV183 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV183 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV183 @ SV124 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV124 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV57 ) @ relation )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1312]) ).
thf(1316,plain,
! [SV124: a,SV57: a,SV183: a] :
( ( ( ~ ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV183 @ SV57 ) @ relation ) )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV183 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV183 @ SV124 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV124 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV57 ) @ relation )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1312]) ).
thf(1317,plain,
! [SV124: a,SV183: a,SV57: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV183 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV183 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV183 @ SV124 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV124 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV57 ) @ relation )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1315]) ).
thf(1318,plain,
! [SV124: a,SV57: a,SV183: a] :
( ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ SV183 @ SV57 ) @ relation ) )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV183 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV183 @ SV124 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV124 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV57 ) @ relation )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1316]) ).
thf(1319,plain,
! [SV124: a,SV57: a,SV183: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV183 @ SV57 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV183 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV183 @ SV124 ) @ relation )
= $true )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV57 @ SV124 ) @ relation )
= $false )
| ( ( member449909584od_a_a @ ( product_Pair_a_a @ SV124 @ SV57 ) @ relation )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1318]) ).
thf(1320,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[442,1319,1317,1314,1313,1311,1310,1309,1308,1307,1301,1298,1293,1285,1281,1278,1277,1272,1271,1268,1267,1264,1263,1261,1251,1230,1229,1228,1227,1226,1225,1221,1219,1215,1214,1213,1209,1208,1207,1204,1202,1200,1199,1197,1195,1194,1193,1192,1190,1188,1187,1174,1167,1158,1152,1150,1148,1147,1141,1140,1139,1138,1137,1136,1135,1134,1133,1132,1131,1130,1129,1128,1127,1126,1125,1113,1112,1111,1093,1080,1079,1078,1077,1076,1075,1074,1073,1072,1071,1070,1069,1068,1067,1066,1065,1064,1063,1062,1061,1050,1049,1048,1046,1038,1034,1033,987,985,984,979,967,936,933,932,926,924,891,890,888,878,871,868,859,839,813,811,808,806,804,802,796,794,792,791,790,789,788,787,785,763,753,752,751,750,747,744,743,740,738,737,735,733,731,729,719,718,717,716,715,714,713,712,711,710,693,639,616,606,601,598,596,590,587,586,585,584,582,581,483,452,451,450,447]) ).
thf(1321,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1320]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP156^1 : 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
% 0.08/0.18 % Computer : n009.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 11:18:47 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 26.98/4.80 ..
% 26.98/4.80
% 26.98/4.80 No.of.Axioms: 84
% 26.98/4.80
% 26.98/4.80 Length.of.Defs: 0
% 26.98/4.80
% 26.98/4.80 Contains.Choice.Funs: false
% 26.98/4.80 ..............................
% 26.98/4.80
% 26.98/4.80 ********************************
% 26.98/4.80 * All subproblems solved! *
% 26.98/4.80 ********************************
% 26.98/4.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:84,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:1320,loop_count:0,foatp_calls:1,translation:fof_full)
% 26.98/4.80
% 26.98/4.80 %**** Beginning of derivation protocol ****
% 26.98/4.80 % SZS output start CNFRefutation
% See solution above
% 4.76/4.80
% 4.76/4.80 %**** End of derivation protocol ****
% 4.76/4.80 %**** no. of clauses in derivation: 1052 ****
% 4.76/4.80 %**** clause counter: 1320 ****
% 4.76/4.80
% 4.76/4.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:84,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:1320,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------